Subgroups — C₂₃×#61801 #19209427

Order 5888.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3551	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3352	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3351	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3350	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3349	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3346	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3344	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3337	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3336	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3327	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3323	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3316	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3314	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3313	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3300	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3202	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3201	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#3201	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#3200	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂₃×#563	—	2	1	no	—
33	C₂₃×#560	—	2	1	no	—
34	C₂₃×#559	—	2	1	no	—
35	C₂₃×#557	—	2	1	no	—
36	C₂₃×#556	—	2	1	no	—
37	C₂₃×#556	—	2	1	no	—
38	C₂₃×#556	C₂²	1	1	yes	characteristic
39	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#555	—	2	1	no	—
41	C₂₃×#554	C₂²	1	1	yes	characteristic
42	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#553	C₂²	1	1	yes	characteristic
44	C₂₃×#553	C₂²	1	1	yes	characteristic
45	C₂₃×#552	C₂²	1	1	yes	characteristic
46	C₂₃×#552	C₂²	1	1	yes	characteristic
47	C₂₃×#552	C₂²	1	1	yes	characteristic
48	C₂₃×#552	C₂²	1	1	yes	characteristic
49	C₂₃×#552	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#552	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#551	—	2	1	no	—
52	C₂₃×#548	C₂²	1	1	yes	characteristic
53	C₂₃×#548	C₂²	1	1	yes	characteristic
54	C₂₃×#546	C₂²	1	1	yes	characteristic
55	C₂₃×#546	C₂²	1	1	yes	characteristic
56	C₂₃×#540	—	2	1	no	—
57	C₂₃×#540	—	2	1	no	—
58	C₂₃×#539	—	2	1	no	—
59	C₂₃×#539	—	2	1	no	—
60	C₂₃×#538	—	2	1	no	—
61	C₂₃×#538	—	2	1	no	—
62	C₂₃×#537	C₂²	1	1	yes	characteristic
63	C₂₃×#537	C₂²	1	1	yes	characteristic
64	C₂₃×#536	C₂²	1	1	yes	characteristic
65	C₂₃×#536	C₂²	1	1	yes	characteristic
66	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#535	C₂²	1	1	yes	characteristic
68	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#532	C₂²	1	1	yes	characteristic
70	C₂₃×#529	—	2	1	no	—
71	C₂₃×#529	—	2	1	no	—
72	C₂₃×#529	C₂²	1	1	yes	characteristic
73	C₂₃×#529	C₂²	1	1	yes	characteristic
74	C₂₃×#520	C₂²	1	1	yes	characteristic
75	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#489	C₂²	1	1	yes	characteristic
82	C₂₃×#489	C₂²	1	1	yes	characteristic
83	C₂₃×#488	C₂²	1	1	yes	characteristic
84	C₂₃×#488	C₂²	1	1	yes	characteristic
85	C₂₃×#485	C₂²	1	1	yes	characteristic
86	C₂₃×#485	C₂²	1	1	yes	characteristic
87	C₂₃×#485	C₂²	1	1	yes	characteristic
88	C₂₃×#485	C₂²	1	1	yes	characteristic
89	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#485	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#484	C₂²	1	1	yes	characteristic
98	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#483	C₂²	1	1	yes	characteristic
103	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#483	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#482	C₂²	1	1	yes	characteristic
108	C₂₃×#482	C₂²	1	1	yes	characteristic
109	C₂₃×#482	C₂²	1	1	yes	characteristic
110	C₂₃×#482	C₂²	1	1	yes	characteristic
111	C₂₃×#482	C₂²	1	1	yes	characteristic
112	C₂₃×#482	C₂²	1	1	yes	characteristic
113	C₂₃×#482	C₂²	1	1	yes	characteristic
114	C₂₃×#482	C₂²	1	1	yes	characteristic
115	C₂₃×#481	C₂²	1	1	yes	characteristic
116	C₂₃×#481	C₂²	1	1	yes	characteristic
117	C₂₃×#481	C₂²	1	1	yes	characteristic
118	C₂₃×#480	C₂²	1	1	yes	characteristic
119	C₂₃×#480	C₂²	1	1	yes	characteristic
120	C₂₃×#480	C₂²	1	1	yes	characteristic
121	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
124	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
125	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
126	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#478	C₂²	1	1	yes	characteristic
128	C₂₃×#478	C₂²	1	1	yes	characteristic
129	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
130	C₂₃×#476	C₂²	1	1	yes	characteristic
131	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
132	C₂₃×#474	C₂²	1	1	yes	characteristic
133	C₂₃×#470	C₂²	1	1	yes	characteristic
134	C₂₃×#470	C₂²	1	1	yes	characteristic
135	C₂₃×#470	C₂²	1	1	yes	characteristic, complemented
136	C₂₃×#470	C₂²	1	1	yes	characteristic, complemented
137	C₂₃×#468	C₂²	1	1	yes	characteristic
138	C₂₃×#468	C₂²	1	1	yes	characteristic
139	C₂₃×#468	C₂²	1	1	yes	characteristic
140	C₂₃×#468	C₂²	1	1	yes	characteristic
141	C₂₃×#467	C₂²	1	1	yes	characteristic
142	C₂₃×#467	C₂²	1	1	yes	characteristic
143	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
144	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
145	C₂₃×#465	C₂²	1	1	yes	characteristic
146	C₂₃×#465	C₂²	1	1	yes	characteristic
147	C₂₃×#465	C₂²	1	1	yes	characteristic
148	C₂₃×#465	C₂²	1	1	yes	characteristic
149	C₂₃×#464	C₂²	1	1	yes	characteristic
150	C₂₃×#464	C₂²	1	1	yes	characteristic
151	C₂₃×#464	C₂²	1	1	yes	characteristic
152	C₂₃×#464	C₂²	1	1	yes	characteristic
153	C₂₃×#452	C₂²	1	1	yes	characteristic
154	C₂₃×#452	C₂²	1	1	yes	characteristic
155	C₂₃×#452	C₂²	1	1	yes	characteristic
156	C₂₃×#452	C₂²	1	1	yes	characteristic
157	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
158	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
159	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
160	C₂₃×#451	C₂²	1	1	yes	characteristic, complemented
161	C₂₃×#450	C₂²	1	1	yes	characteristic
162	C₂₃×#450	C₂²	1	1	yes	characteristic
163	C₂₃×#448	C₂²	1	1	yes	characteristic
164	C₂₃×#448	C₂²	1	1	yes	characteristic
165	C₂₃×#441	C₂²	1	1	yes	characteristic, complemented
166	C₂₃×#441	C₂²	1	1	yes	characteristic, complemented
167	C₂₃×#440	C₂²	1	1	yes	characteristic
168	C₂₃×#440	C₂²	1	1	yes	characteristic
169	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
170	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
172	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
173	C₂₃×#436	C₂²	1	1	yes	characteristic
174	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
175	C₂₃×#435	C₂²	1	1	yes	characteristic
176	C₂₃×#435	C₂²	1	1	yes	characteristic
177	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
178	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
179	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
180	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
181	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
182	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
183	C₂₃×#428	C₂²	1	1	yes	characteristic
184	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
185	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
186	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
187	C₂₃×#427	C₂²	1	1	yes	characteristic
188	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
189	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
190	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
191	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
192	C₂₃×#418	C₂²	1	1	yes	characteristic
193	C₂₃×#417	C₂²	1	1	yes	characteristic
194	C₂₃×#417	C₂²	1	1	yes	characteristic
195	C₂₃×#416	C₂²	1	1	yes	characteristic
196	C₂₃×#416	C₂²	1	1	yes	characteristic
197	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
198	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
199	C₂₃×#408	C₂²	1	1	yes	characteristic
200	C₂₃×#408	C₂²	1	1	yes	characteristic
201	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
202	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
205	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
207	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
209	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
213	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
218	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
219	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
220	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
221	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
223	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
225	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
226	C₂₃×C₄⋊Q₈	—	2	1	no	—
227	C₂₃×C₄⋊Q₈	—	2	1	no	—
228	C₂₃×C₄⋊Q₈	—	2	1	no	—
229	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
230	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
232	C₂₃×#127	—	2	1	no	—
233	C₂₃×#127	D₄	1	1	yes	characteristic
234	C₂₃×#126	—	2	1	no	—
235	C₂₃×#126	—	2	1	no	—
236	C₂₃×#126	—	2	1	no	—
237	C₂₃×#126	—	2	1	no	—
238	C₂₃×#126	—	2	1	no	—
239	C₂₃×#126	—	2	1	no	—
240	C₂₃×#126	—	2	1	no	—
241	C₂₃×#126	—	2	1	no	—
242	C₂₃×#126	—	2	1	no	—
243	C₂₃×#126	—	2	1	no	—
244	C₂₃×#126	—	2	1	no	—
245	C₂₃×#126	—	2	1	no	—
246	C₂₃×#126	—	2	1	no	—
247	C₂₃×#126	—	2	1	no	—
248	C₂₃×#125	—	2	1	no	—
249	C₂₃×#125	—	2	1	no	—
250	C₂₃×#125	—	2	1	no	—
251	C₂₃×#125	—	2	1	no	—
252	C₂₃×#125	—	2	1	no	—
253	C₂₃×#125	—	2	1	no	—
254	C₂₃×#125	—	2	1	no	—
255	C₂₃×#125	—	2	1	no	—
256	C₂₃×#125	C₂³	1	1	yes	characteristic
257	C₂₃×#125	C₂³	1	1	yes	characteristic
258	C₂₃×#125	C₂³	1	1	yes	characteristic
259	C₂₃×#125	C₂³	1	1	yes	characteristic
260	C₂₃×#124	—	2	1	no	—
261	C₂₃×#124	—	2	1	no	—
262	C₂₃×#124	—	2	1	no	—
263	C₂₃×#124	—	2	1	no	—
264	C₂₃×#124	—	2	1	no	—
265	C₂₃×#124	—	2	1	no	—
266	C₂₃×#124	—	2	1	no	—
267	C₂₃×#124	—	2	1	no	—
268	C₂₃×#124	D₄	1	1	yes	characteristic
269	C₂₃×#124	D₄	1	1	yes	characteristic
270	C₂₃×#124	C₂³	1	1	yes	characteristic
271	C₂₃×#124	C₂³	1	1	yes	characteristic
272	C₂₃×#123	—	2	1	no	—
273	C₂₃×#123	—	2	1	no	—
274	C₂₃×#123	—	2	1	no	—
275	C₂₃×#123	—	2	1	no	—
276	C₂₃×#123	—	2	1	no	—
277	C₂₃×#123	—	2	1	no	—
278	C₂₃×#123	—	2	1	no	—
279	C₂₃×#123	—	2	1	no	—
280	C₂₃×#123	—	2	1	no	—
281	C₂₃×#123	—	2	1	no	—
282	C₂₃×#123	—	2	1	no	—
283	C₂₃×#123	—	2	1	no	—
284	C₂₃×#123	—	2	1	no	—
285	C₂₃×#123	—	2	1	no	—
286	C₂₃×#123	—	2	1	no	—
287	C₂₃×#123	—	2	1	no	—
288	C₂₃×#123	—	2	1	no	—
289	C₂₃×#123	—	2	1	no	—
290	C₂₃×C₂²⋊Q₈	—	2	1	no	—
291	C₂₃×C₂²⋊Q₈	—	2	1	no	—
292	C₂₃×C₂²⋊Q₈	—	2	1	no	—
293	C₂₃×C₂²⋊Q₈	—	2	1	no	—
294	C₂₃×C₂²⋊Q₈	—	2	1	no	—
295	C₂₃×C₂²⋊Q₈	—	2	1	no	—
296	C₂₃×C₂²⋊Q₈	—	2	1	no	—
297	C₂₃×C₂²⋊Q₈	—	2	1	no	—
298	C₂₃×C₂²⋊Q₈	—	2	1	no	—
299	C₂₃×C₂²⋊Q₈	—	2	1	no	—
300	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
301	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
302	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
303	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
304	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
305	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
306	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
307	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
308	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
309	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
310	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
311	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
312	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
313	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
314	C₂₃×#121	—	2	1	no	—
315	C₂₃×#121	—	2	1	no	—
316	C₂₃×#121	—	2	1	no	—
317	C₂₃×#121	—	2	1	no	—
318	C₂₃×#121	—	2	1	no	—
319	C₂₃×#121	—	2	1	no	—
320	C₂₃×#121	—	2	1	no	—
321	C₂₃×#121	—	2	1	no	—
322	C₂₃×#121	—	2	1	no	—
323	C₂₃×#121	—	2	1	no	—
324	C₂₃×#121	—	2	1	no	—
325	C₂₃×#121	—	2	1	no	—
326	C₂₃×#121	D₄	1	1	yes	characteristic
327	C₂₃×#121	D₄	1	1	yes	characteristic
328	C₂₃×#121	D₄	1	1	yes	characteristic
329	C₂₃×#121	D₄	1	1	yes	characteristic
330	C₂₃×#121	C₂³	1	1	yes	characteristic
331	C₂₃×#121	C₂³	1	1	yes	characteristic
332	C₂₃×#121	C₂³	1	1	yes	characteristic
333	C₂₃×#121	C₂³	1	1	yes	characteristic
334	C₂₃×#121	C₂³	1	1	yes	characteristic
335	C₂₃×#121	C₂³	1	1	yes	characteristic
336	C₂₃×#120	—	2	1	no	—
337	C₂₃×#120	—	2	1	no	—
338	C₂₃×#120	—	2	1	no	—
339	C₂₃×#120	—	2	1	no	—
340	C₄×Q₈×C₂₃	—	2	1	no	—
341	C₄×Q₈×C₂₃	—	2	1	no	—
342	C₄×Q₈×C₂₃	—	2	1	no	—
343	C₄×Q₈×C₂₃	—	2	1	no	—
344	C₄×Q₈×C₂₃	—	2	1	no	—
345	C₄×Q₈×C₂₃	—	2	1	no	—
346	C₄×Q₈×C₂₃	—	2	1	no	—
347	C₄×Q₈×C₂₃	—	2	1	no	—
348	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
352	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
354	C₄×D₄×C₂₃	—	2	1	no	—
355	C₄×D₄×C₂₃	—	2	1	no	—
356	C₄×D₄×C₂₃	—	2	1	no	—
357	C₄×D₄×C₂₃	—	2	1	no	—
358	C₄×D₄×C₂₃	—	2	1	no	—
359	C₄×D₄×C₂₃	—	2	1	no	—
360	C₄×D₄×C₂₃	—	2	1	no	—
361	C₄×D₄×C₂₃	—	2	1	no	—
362	C₄×D₄×C₂₃	—	2	1	no	—
363	C₄×D₄×C₂₃	—	2	1	no	—
364	C₄×D₄×C₂₃	—	2	1	no	—
365	C₄×D₄×C₂₃	—	2	1	no	—
366	C₄×D₄×C₂₃	—	2	1	no	—
367	C₄×D₄×C₂₃	—	2	1	no	—
368	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
371	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
372	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
373	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
374	C₂₃×#117	—	2	1	no	—
375	C₂₃×#117	—	2	1	no	—
376	C₂₃×#117	—	2	1	no	—
377	C₂₃×#117	—	2	1	no	—
378	C₂₃×#117	—	2	1	no	—
379	C₂₃×#117	—	2	1	no	—
380	C₂₃×#117	—	2	1	no	—
381	C₂₃×#117	—	2	1	no	—
382	C₂₃×#117	C₂³	1	1	yes	characteristic
383	C₂₃×#117	C₂³	1	1	yes	characteristic
384	C₂₃×#117	C₂³	1	1	yes	characteristic
385	C₂₃×#117	C₂³	1	1	yes	characteristic
386	C₂₃×#117	C₂³	1	1	yes	characteristic
387	C₂₃×#117	C₂³	1	1	yes	characteristic
388	C₂₃×#117	C₂³	1	1	yes	characteristic
389	C₂₃×#117	C₂³	1	1	yes	characteristic
390	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
391	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
392	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
394	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
395	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
396	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
397	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
398	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
399	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
400	C₂×C₄²×C₂₃	—	2	1	no	—
401	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
402	C₂₃×#107	C₂³	1	1	yes	characteristic
403	C₂₃×#107	C₂³	1	1	yes	characteristic
404	C₂₃×#107	C₂³	1	1	yes	characteristic
405	C₂₃×#107	C₂³	1	1	yes	characteristic
406	C₂₃×#107	C₂³	1	1	yes	characteristic
407	C₂₃×#107	C₂³	1	1	yes	characteristic
408	C₂₃×#107	C₂³	1	1	yes	characteristic
409	C₂₃×#107	C₂³	1	1	yes	characteristic
410	C₂₃×#107	C₂³	1	1	yes	characteristic
411	C₂₃×#107	C₂³	1	1	yes	characteristic
412	C₂₃×#107	C₂³	1	1	yes	characteristic
413	C₂₃×#107	C₂³	1	1	yes	characteristic
414	C₂₃×#106	C₂³	1	1	yes	characteristic
415	C₂₃×#106	C₂³	1	1	yes	characteristic
416	C₂₃×#106	C₂³	1	1	yes	characteristic
417	C₂₃×#106	C₂³	1	1	yes	characteristic
418	C₂₃×#106	C₂³	1	1	yes	characteristic
419	C₂₃×#106	C₂³	1	1	yes	characteristic
420	C₂₃×#106	C₂³	1	1	yes	characteristic
421	C₂₃×#106	C₂³	1	1	yes	characteristic
422	C₂₃×#106	C₂³	1	1	yes	characteristic
423	C₂₃×#106	C₂³	1	1	yes	characteristic
424	C₂₃×#106	C₂³	1	1	yes	characteristic
425	C₂₃×#106	C₂³	1	1	yes	characteristic
426	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
427	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
428	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
429	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
430	C₂₃×#103	C₂³	1	1	yes	characteristic
431	C₂₃×#103	C₂³	1	1	yes	characteristic
432	C₂₃×#103	C₂³	1	1	yes	characteristic
433	C₂₃×#103	C₂³	1	1	yes	characteristic
434	C₂₃×#103	C₂³	1	1	yes	characteristic
435	C₂₃×#103	C₂³	1	1	yes	characteristic
436	C₂₃×#103	C₂³	1	1	yes	characteristic
437	C₂₃×#103	C₂³	1	1	yes	characteristic
438	C₂₃×#103	C₂³	1	1	yes	characteristic
439	C₂₃×#103	C₂³	1	1	yes	characteristic
440	C₂₃×#103	C₂³	1	1	yes	characteristic
441	C₂₃×#103	C₂³	1	1	yes	characteristic
442	C₂₃×#103	C₂³	1	1	yes	characteristic
443	C₂₃×#103	C₂³	1	1	yes	characteristic
444	C₂₃×#103	C₂³	1	1	yes	characteristic
445	C₂₃×#103	C₂³	1	1	yes	characteristic
446	C₂₃×#103	C₂³	1	1	yes	characteristic
447	C₂₃×#103	C₂³	1	1	yes	characteristic
448	C₂₃×#103	C₂³	1	1	yes	characteristic
449	C₂₃×#103	C₂³	1	1	yes	characteristic
450	C₂₃×#102	C₂³	1	1	yes	characteristic
451	C₂₃×#102	C₂³	1	1	yes	characteristic
452	C₂₃×#102	C₂³	1	1	yes	characteristic
453	C₂₃×#102	C₂³	1	1	yes	characteristic
454	C₂₃×#102	C₂³	1	1	yes	characteristic
455	C₂₃×#102	C₂³	1	1	yes	characteristic
456	C₂₃×#102	C₂³	1	1	yes	characteristic
457	C₂₃×#102	C₂³	1	1	yes	characteristic
458	C₂₃×#102	C₂³	1	1	yes	characteristic
459	C₂₃×#102	C₂³	1	1	yes	characteristic
460	C₂₃×#102	C₂³	1	1	yes	characteristic
461	C₂₃×#102	C₂³	1	1	yes	characteristic
462	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
463	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
464	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
465	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
466	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
467	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
468	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
469	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
470	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
471	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
472	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
474	C₂₃×#97	C₂³	1	1	yes	characteristic
475	C₂₃×#97	C₂³	1	1	yes	characteristic
476	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
478	C₂⁴×C₂₃	—	2	1	no	—
479	#41×C₂₃	—	4	1	no	—
480	#41×C₂₃	—	4	1	no	—
481	#41×C₂₃	—	4	1	no	—
482	#41×C₂₃	—	4	1	no	—
483	#41×C₂₃	—	4	1	no	—
484	#41×C₂₃	—	4	1	no	—
485	#41×C₂₃	—	4	1	no	—
486	#41×C₂₃	—	4	1	no	—
487	C₂×Q₈×C₂₃	—	2	1	no	—
488	C₂×Q₈×C₂₃	—	2	1	no	—
489	C₂×Q₈×C₂₃	—	2	1	no	—
490	C₂×Q₈×C₂₃	—	2	1	no	—
491	C₂×Q₈×C₂₃	—	4	1	no	—
492	C₂×Q₈×C₂₃	—	4	1	no	—
493	C₂×Q₈×C₂₃	—	4	1	no	—
494	C₂×Q₈×C₂₃	—	4	1	no	—
495	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
496	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
497	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
498	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
499	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
500	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
501	C₂×D₄×C₂₃	—	2	1	no	—
502	C₂×D₄×C₂₃	—	2	1	no	—
503	C₂×D₄×C₂₃	—	2	1	no	—
504	C₂×D₄×C₂₃	—	2	1	no	—
505	C₂×D₄×C₂₃	—	2	1	no	—
506	C₂×D₄×C₂₃	—	2	1	no	—
507	C₂×D₄×C₂₃	—	2	1	no	—
508	C₂×D₄×C₂₃	—	2	1	no	—
509	C₂×D₄×C₂₃	—	2	1	no	—
510	C₂×D₄×C₂₃	—	4	1	no	—
511	C₂×D₄×C₂₃	—	4	1	no	—
512	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
513	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
514	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
515	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
516	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
517	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
518	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
519	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
520	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
521	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
522	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
523	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
524	C₂²×C₄×C₂₃	—	2	1	no	—
525	C₂²×C₄×C₂₃	—	2	1	no	—
526	C₂²×C₄×C₂₃	—	2	1	no	—
527	C₂²×C₄×C₂₃	—	2	1	no	—
528	C₂²×C₄×C₂₃	—	2	1	no	—
529	C₂²×C₄×C₂₃	—	2	1	no	—
530	C₂²×C₄×C₂₃	—	2	1	no	—
531	C₂²×C₄×C₂₃	—	2	1	no	—
532	C₂²×C₄×C₂₃	—	2	1	no	—
533	C₂²×C₄×C₂₃	—	2	1	no	—
534	C₂²×C₄×C₂₃	—	2	1	no	—
535	C₂²×C₄×C₂₃	—	2	1	no	—
536	C₂²×C₄×C₂₃	—	2	1	no	—
537	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
538	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
539	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
540	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
541	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
542	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
543	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
544	Q₁₆×C₂₃	—	4	1	no	—
545	Q₁₆×C₂₃	—	4	1	no	—
546	Q₁₆×C₂₃	—	4	1	no	—
547	Q₁₆×C₂₃	—	4	1	no	—
548	SD₁₆×C₂₃	—	4	1	no	—
549	SD₁₆×C₂₃	—	4	1	no	—
550	SD₁₆×C₂₃	—	4	1	no	—
551	SD₁₆×C₂₃	—	4	1	no	—
552	M₁₆×C₂₃	—	4	1	no	—
553	M₁₆×C₂₃	—	4	1	no	—
554	M₁₆×C₂₃	—	4	1	no	—
555	M₁₆×C₂₃	—	4	1	no	—
556	C₂×C₈×C₂₃	—	4	1	no	—
557	C₂×C₈×C₂₃	—	4	1	no	—
558	C₂×C₈×C₂₃	—	4	1	no	—
559	C₂×C₈×C₂₃	—	4	1	no	—
560	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
561	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
562	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
563	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
564	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
565	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
566	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
567	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
568	C₄⋊C₄×C₂₃	—	2	1	no	—
569	C₄⋊C₄×C₂₃	—	2	1	no	—
570	C₄⋊C₄×C₂₃	—	2	1	no	—
571	C₄⋊C₄×C₂₃	—	2	1	no	—
572	C₄⋊C₄×C₂₃	—	2	1	no	—
573	C₄⋊C₄×C₂₃	—	2	1	no	—
574	C₄⋊C₄×C₂₃	—	2	1	no	—
575	C₄⋊C₄×C₂₃	—	2	1	no	—
576	C₄⋊C₄×C₂₃	—	2	1	no	—
577	C₄⋊C₄×C₂₃	—	2	1	no	—
578	C₄⋊C₄×C₂₃	—	2	1	no	—
579	C₄⋊C₄×C₂₃	—	2	1	no	—
580	C₄⋊C₄×C₂₃	—	2	1	no	—
581	C₄⋊C₄×C₂₃	—	2	1	no	—
582	C₄⋊C₄×C₂₃	—	2	1	no	—
583	C₄⋊C₄×C₂₃	—	2	1	no	—
584	C₄⋊C₄×C₂₃	—	2	1	no	—
585	C₄⋊C₄×C₂₃	—	2	1	no	—
586	C₄⋊C₄×C₂₃	—	2	1	no	—
587	C₄⋊C₄×C₂₃	—	2	1	no	—
588	C₄⋊C₄×C₂₃	—	2	1	no	—
589	C₄⋊C₄×C₂₃	—	2	1	no	—
590	C₄⋊C₄×C₂₃	—	2	1	no	—
591	C₄⋊C₄×C₂₃	—	2	1	no	—
592	C₄⋊C₄×C₂₃	—	2	1	no	—
593	C₄⋊C₄×C₂₃	—	2	1	no	—
594	C₄⋊C₄×C₂₃	—	2	1	no	—
595	C₄⋊C₄×C₂₃	—	2	1	no	—
596	C₄⋊C₄×C₂₃	—	2	1	no	—
597	C₄⋊C₄×C₂₃	—	2	1	no	—
598	C₄⋊C₄×C₂₃	—	2	1	no	—
599	C₄⋊C₄×C₂₃	—	2	1	no	—
600	C₄⋊C₄×C₂₃	—	2	1	no	—
601	C₄⋊C₄×C₂₃	—	2	1	no	—
602	C₄⋊C₄×C₂₃	—	2	1	no	—
603	C₄⋊C₄×C₂₃	—	2	1	no	—
604	C₄⋊C₄×C₂₃	—	2	1	no	—
605	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
610	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
611	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
612	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
615	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
617	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
618	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
619	C₂²⋊C₄×C₂₃	—	2	1	no	—
620	C₂²⋊C₄×C₂₃	—	2	1	no	—
621	C₂²⋊C₄×C₂₃	—	2	1	no	—
622	C₂²⋊C₄×C₂₃	—	2	1	no	—
623	C₂²⋊C₄×C₂₃	—	2	1	no	—
624	C₂²⋊C₄×C₂₃	—	2	1	no	—
625	C₂²⋊C₄×C₂₃	—	2	1	no	—
626	C₂²⋊C₄×C₂₃	—	2	1	no	—
627	C₂²⋊C₄×C₂₃	—	2	1	no	—
628	C₂²⋊C₄×C₂₃	—	2	1	no	—
629	C₂²⋊C₄×C₂₃	—	2	1	no	—
630	C₂²⋊C₄×C₂₃	—	2	1	no	—
631	C₂²⋊C₄×C₂₃	—	2	1	no	—
632	C₂²⋊C₄×C₂₃	—	2	1	no	—
633	C₂²⋊C₄×C₂₃	—	2	1	no	—
634	C₂²⋊C₄×C₂₃	—	2	1	no	—
635	C₂²⋊C₄×C₂₃	—	2	1	no	—
636	C₂²⋊C₄×C₂₃	—	2	1	no	—
637	C₂²⋊C₄×C₂₃	—	2	1	no	—
638	C₂²⋊C₄×C₂₃	—	2	1	no	—
639	C₂²⋊C₄×C₂₃	—	2	1	no	—
640	C₂²⋊C₄×C₂₃	—	2	1	no	—
641	C₂²⋊C₄×C₂₃	—	2	1	no	—
642	C₂²⋊C₄×C₂₃	—	2	1	no	—
643	C₂²⋊C₄×C₂₃	—	2	1	no	—
644	C₂²⋊C₄×C₂₃	—	2	1	no	—
645	C₂²⋊C₄×C₂₃	—	2	1	no	—
646	C₂²⋊C₄×C₂₃	—	2	1	no	—
647	C₂²⋊C₄×C₂₃	—	2	1	no	—
648	C₂²⋊C₄×C₂₃	—	2	1	no	—
649	C₂²⋊C₄×C₂₃	—	2	1	no	—
650	C₂²⋊C₄×C₂₃	—	2	1	no	—
651	C₂²⋊C₄×C₂₃	—	2	1	no	—
652	C₂²⋊C₄×C₂₃	—	2	1	no	—
653	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
655	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
656	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
657	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
658	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
659	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
660	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
661	C₄²×C₂₃	—	2	1	no	—
662	C₄²×C₂₃	—	2	1	no	—
663	C₄²×C₂₃	—	2	1	no	—
664	C₄²×C₂₃	—	2	1	no	—
665	C₄²×C₂₃	—	2	1	no	—
666	C₄²×C₂₃	—	2	1	no	—
667	C₄²×C₂₃	—	2	1	no	—
668	C₄²×C₂₃	—	2	1	no	—
669	C₄²×C₂₃	—	2	1	no	—
670	C₄²×C₂₃	—	2	1	no	—
671	C₄²×C₂₃	—	2	1	no	—
672	C₄²×C₂₃	—	2	1	no	—
673	C₄²×C₂₃	—	2	1	no	—
674	C₄²×C₂₃	—	2	1	no	—
675	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
676	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
677	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
678	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
679	#61801	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
680	C₂³×C₂₃	—	2	1	no	—
681	C₂³×C₂₃	—	2	1	no	—
682	C₂³×C₂₃	—	8	1	no	—
683	C₂³×C₂₃	—	8	1	no	—
684	C₂³×C₂₃	—	8	1	no	—
685	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
686	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
687	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
688	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
689	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
690	Q₈×C₂₃	—	2	1	no	—
691	Q₈×C₂₃	—	2	1	no	—
692	Q₈×C₂₃	—	2	1	no	—
693	Q₈×C₂₃	—	2	1	no	—
694	Q₈×C₂₃	—	2	1	no	—
695	Q₈×C₂₃	—	2	1	no	—
696	Q₈×C₂₃	—	2	1	no	—
697	Q₈×C₂₃	—	2	1	no	—
698	Q₈×C₂₃	—	4	1	no	—
699	Q₈×C₂₃	—	4	1	no	—
700	Q₈×C₂₃	—	4	2	no	—
701	Q₈×C₂₃	—	4	2	no	—
702	Q₈×C₂₃	—	8	1	no	—
703	Q₈×C₂₃	—	8	1	no	—
704	D₄×C₂₃	—	2	1	no	—
705	D₄×C₂₃	—	2	1	no	—
706	D₄×C₂₃	—	2	1	no	—
707	D₄×C₂₃	—	2	1	no	—
708	D₄×C₂₃	—	4	1	no	—
709	D₄×C₂₃	—	4	1	no	—
710	D₄×C₂₃	—	4	1	no	—
711	D₄×C₂₃	—	4	1	no	—
712	D₄×C₂₃	—	4	1	no	—
713	D₄×C₂₃	—	4	1	no	—
714	D₄×C₂₃	—	4	1	no	—
715	D₄×C₂₃	—	4	1	no	—
716	D₄×C₂₃	—	4	1	no	—
717	D₄×C₂₃	—	4	1	no	—
718	D₄×C₂₃	—	8	1	no	—
719	D₄×C₂₃	—	8	1	no	—
720	D₄×C₂₃	—	8	1	no	—
721	D₄×C₂₃	—	8	1	no	—
722	D₄×C₂₃	—	8	1	no	—
723	D₄×C₂₃	—	8	1	no	—
724	D₄×C₂₃	—	8	1	no	—
725	D₄×C₂₃	—	8	1	no	—
726	D₄×C₂₃	—	8	1	no	—
727	C₂×C₄×C₂₃	—	2	1	no	—
728	C₂×C₄×C₂₃	—	2	1	no	—
729	C₂×C₄×C₂₃	—	2	1	no	—
730	C₂×C₄×C₂₃	—	2	1	no	—
731	C₂×C₄×C₂₃	—	2	1	no	—
732	C₂×C₄×C₂₃	—	2	1	no	—
733	C₂×C₄×C₂₃	—	2	1	no	—
734	C₂×C₄×C₂₃	—	2	1	no	—
735	C₂×C₄×C₂₃	—	2	1	no	—
736	C₂×C₄×C₂₃	—	2	1	no	—
737	C₂×C₄×C₂₃	—	2	1	no	—
738	C₂×C₄×C₂₃	—	2	1	no	—
739	C₂×C₄×C₂₃	—	2	1	no	—
740	C₂×C₄×C₂₃	—	2	1	no	—
741	C₂×C₄×C₂₃	—	2	1	no	—
742	C₂×C₄×C₂₃	—	2	1	no	—
743	C₂×C₄×C₂₃	—	2	1	no	—
744	C₂×C₄×C₂₃	—	2	1	no	—
745	C₂×C₄×C₂₃	—	2	1	no	—
746	C₂×C₄×C₂₃	—	2	1	no	—
747	C₂×C₄×C₂₃	—	2	1	no	—
748	C₂×C₄×C₂₃	—	2	1	no	—
749	C₂×C₄×C₂₃	—	2	1	no	—
750	C₂×C₄×C₂₃	—	2	1	no	—
751	C₂×C₄×C₂₃	—	4	1	no	—
752	C₂×C₄×C₂₃	—	4	1	no	—
753	C₂×C₄×C₂₃	—	4	2	no	—
754	C₂×C₄×C₂₃	—	8	1	no	—
755	C₂×C₄×C₂₃	—	8	1	no	—
756	C₂×C₄×C₂₃	—	8	1	no	—
757	C₂×C₄×C₂₃	—	8	1	no	—
758	C₂×C₄×C₂₃	—	8	1	no	—
759	C₂×C₄×C₂₃	—	8	1	no	—
760	C₂×C₄×C₂₃	—	8	1	no	—
761	C₂×C₄×C₂₃	—	8	1	no	—
762	C₂×C₄×C₂₃	—	8	1	no	—
763	C₂×C₄×C₂₃	—	8	1	no	—
764	C₂×C₄×C₂₃	—	8	1	no	—
765	C₂×C₄×C₂₃	—	8	1	no	—
766	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
767	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
768	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
769	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
770	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
771	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
772	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
773	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
774	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
775	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
776	C₈×C₂₃	—	2	1	no	—
777	C₈×C₂₃	—	2	1	no	—
778	C₈×C₂₃	—	2	1	no	—
779	C₈×C₂₃	—	2	1	no	—
780	C₈×C₂₃	—	2	1	no	—
781	C₈×C₂₃	—	2	1	no	—
782	C₈×C₂₃	—	2	1	no	—
783	C₈×C₂₃	—	2	1	no	—
784	#3551	C₂×C₂₃	1	1	yes	characteristic
785	#3507	C₂×C₂₃	1	1	yes	characteristic, complemented
786	#3352	C₂×C₂₃	1	1	yes	characteristic, complemented
787	#3351	C₂×C₂₃	1	1	yes	characteristic, complemented
788	#3350	C₂×C₂₃	1	1	yes	characteristic, complemented
789	#3349	C₂×C₂₃	1	1	yes	characteristic, complemented
790	#3346	C₂×C₂₃	1	1	yes	characteristic, complemented
791	#3344	C₂×C₂₃	1	1	yes	characteristic, complemented
792	#3337	C₂×C₂₃	1	1	yes	characteristic, complemented
793	#3336	C₂×C₂₃	1	1	yes	characteristic, complemented
794	#3327	C₂×C₂₃	1	1	yes	characteristic, complemented
795	#3323	C₂×C₂₃	1	1	yes	characteristic, complemented
796	#3316	C₂×C₂₃	1	1	yes	characteristic, complemented
797	#3314	C₂×C₂₃	1	1	yes	characteristic, complemented
798	#3313	C₂×C₂₃	1	1	yes	characteristic, complemented
799	#3311	C₂×C₂₃	1	1	yes	characteristic, complemented
800	#3300	C₂×C₂₃	1	1	yes	characteristic, complemented
801	#3296	C₂×C₂₃	1	1	yes	characteristic, complemented
802	#3240	C₂×C₂₃	1	1	yes	characteristic, complemented
803	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
804	#3202	C₂×C₂₃	1	1	yes	characteristic, complemented
805	#3201	C₂×C₂₃	1	1	yes	characteristic, complemented
806	#3201	C₂×C₂₃	1	1	yes	characteristic, complemented
807	#3200	C₂×C₂₃	1	1	yes	characteristic, complemented
808	#3117	C₂×C₂₃	1	1	yes	characteristic, complemented
809	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
810	#3099	C₂×C₂₃	1	1	yes	characteristic, complemented
811	#3098	C₂×C₂₃	1	1	yes	characteristic, complemented
812	#3097	C₂×C₂₃	1	1	yes	characteristic, complemented
813	#3096	C₂×C₂₃	1	1	yes	characteristic, complemented
814	#2981	C₂×C₂₃	1	1	yes	characteristic, complemented
815	C₂²×C₂₃	—	2	1	no	—
816	C₂²×C₂₃	—	2	1	no	—
817	C₂²×C₂₃	—	2	1	no	—
818	C₂²×C₂₃	—	2	1	no	—
819	C₂²×C₂₃	—	2	1	no	—
820	C₂²×C₂₃	—	2	1	no	—
821	C₂²×C₂₃	—	2	1	no	—
822	C₂²×C₂₃	—	2	1	no	—
823	C₂²×C₂₃	—	2	1	no	—
824	C₂²×C₂₃	—	2	1	no	—
825	C₂²×C₂₃	—	2	1	no	—
826	C₂²×C₂₃	—	2	1	no	—
827	C₂²×C₂₃	—	2	1	no	—
828	C₂²×C₂₃	—	2	1	no	—
829	C₂²×C₂₃	—	2	1	no	—
830	C₂²×C₂₃	—	4	1	no	—
831	C₂²×C₂₃	—	4	1	no	—
832	C₂²×C₂₃	—	4	1	no	—
833	C₂²×C₂₃	—	4	1	no	—
834	C₂²×C₂₃	—	4	1	no	—
835	C₂²×C₂₃	—	4	1	no	—
836	C₂²×C₂₃	—	16	2	no	—
837	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
838	C₄×C₂₃	—	2	1	no	—
839	C₄×C₂₃	—	2	1	no	—
840	C₄×C₂₃	—	2	1	no	—
841	C₄×C₂₃	—	2	1	no	—
842	C₄×C₂₃	—	2	1	no	—
843	C₄×C₂₃	—	2	1	no	—
844	C₄×C₂₃	—	2	1	no	—
845	C₄×C₂₃	—	2	1	no	—
846	C₄×C₂₃	—	2	1	no	—
847	C₄×C₂₃	—	4	1	no	—
848	C₄×C₂₃	—	4	1	no	—
849	C₄×C₂₃	—	4	1	no	—
850	C₄×C₂₃	—	4	1	no	—
851	C₄×C₂₃	—	4	1	no	—
852	C₄×C₂₃	—	4	1	no	—
853	C₄×C₂₃	—	4	1	no	—
854	C₄×C₂₃	—	4	1	no	—
855	C₄×C₂₃	—	4	1	no	—
856	C₄×C₂₃	—	4	1	no	—
857	C₄×C₂₃	—	4	1	no	—
858	C₄×C₂₃	—	4	1	no	—
859	C₄×C₂₃	—	4	1	no	—
860	C₄×C₂₃	—	4	1	no	—
861	C₄×C₂₃	#585	1	1	yes	characteristic
862	C₄×C₂₃	#585	1	1	yes	characteristic
863	#563	—	2	1	no	—
864	#560	—	2	1	no	—
865	#559	—	2	1	no	—
866	#557	—	2	1	no	—
867	#556	—	2	1	no	—
868	#556	—	2	1	no	—
869	#556	C₂²×C₂₃	1	1	yes	characteristic
870	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
871	#555	—	2	1	no	—
872	#554	C₂²×C₂₃	1	1	yes	characteristic
873	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
874	#553	C₂²×C₂₃	1	1	yes	characteristic
875	#553	C₂²×C₂₃	1	1	yes	characteristic
876	#552	C₂²×C₂₃	1	1	yes	characteristic
877	#552	C₂²×C₂₃	1	1	yes	characteristic
878	#552	C₂²×C₂₃	1	1	yes	characteristic
879	#552	C₂²×C₂₃	1	1	yes	characteristic
880	#552	C₂²×C₂₃	1	1	yes	characteristic, complemented
881	#552	C₂²×C₂₃	1	1	yes	characteristic, complemented
882	#551	—	2	1	no	—
883	#548	C₂²×C₂₃	1	1	yes	characteristic
884	#548	C₂²×C₂₃	1	1	yes	characteristic
885	#546	C₂²×C₂₃	1	1	yes	characteristic
886	#546	C₂²×C₂₃	1	1	yes	characteristic
887	#540	—	2	1	no	—
888	#540	—	2	1	no	—
889	#539	—	2	1	no	—
890	#539	—	2	1	no	—
891	#538	—	2	1	no	—
892	#538	—	2	1	no	—
893	#537	C₂²×C₂₃	1	1	yes	characteristic
894	#537	C₂²×C₂₃	1	1	yes	characteristic
895	#536	C₂²×C₂₃	1	1	yes	characteristic
896	#536	C₂²×C₂₃	1	1	yes	characteristic
897	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
898	#535	C₂²×C₂₃	1	1	yes	characteristic
899	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
900	#532	C₂²×C₂₃	1	1	yes	characteristic
901	#529	—	2	1	no	—
902	#529	—	2	1	no	—
903	#529	C₂²×C₂₃	1	1	yes	characteristic
904	#529	C₂²×C₂₃	1	1	yes	characteristic
905	#520	C₂²×C₂₃	1	1	yes	characteristic
906	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
907	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
908	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
909	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
910	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
911	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
912	#489	C₂²×C₂₃	1	1	yes	characteristic
913	#489	C₂²×C₂₃	1	1	yes	characteristic
914	#488	C₂²×C₂₃	1	1	yes	characteristic
915	#488	C₂²×C₂₃	1	1	yes	characteristic
916	#485	C₂²×C₂₃	1	1	yes	characteristic
917	#485	C₂²×C₂₃	1	1	yes	characteristic
918	#485	C₂²×C₂₃	1	1	yes	characteristic
919	#485	C₂²×C₂₃	1	1	yes	characteristic
920	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
921	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
922	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
923	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
924	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
925	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
926	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
927	#485	C₂²×C₂₃	1	1	yes	characteristic, complemented
928	#484	C₂²×C₂₃	1	1	yes	characteristic
929	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
930	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
931	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
932	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
933	#483	C₂²×C₂₃	1	1	yes	characteristic
934	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
935	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
936	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
937	#483	C₂²×C₂₃	1	1	yes	characteristic, complemented
938	#482	C₂²×C₂₃	1	1	yes	characteristic
939	#482	C₂²×C₂₃	1	1	yes	characteristic
940	#482	C₂²×C₂₃	1	1	yes	characteristic
941	#482	C₂²×C₂₃	1	1	yes	characteristic
942	#482	C₂²×C₂₃	1	1	yes	characteristic
943	#482	C₂²×C₂₃	1	1	yes	characteristic
944	#482	C₂²×C₂₃	1	1	yes	characteristic
945	#482	C₂²×C₂₃	1	1	yes	characteristic
946	#481	C₂²×C₂₃	1	1	yes	characteristic
947	#481	C₂²×C₂₃	1	1	yes	characteristic
948	#481	C₂²×C₂₃	1	1	yes	characteristic
949	#480	C₂²×C₂₃	1	1	yes	characteristic
950	#480	C₂²×C₂₃	1	1	yes	characteristic
951	#480	C₂²×C₂₃	1	1	yes	characteristic
952	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
953	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
954	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
955	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
956	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
957	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
958	#478	C₂²×C₂₃	1	1	yes	characteristic
959	#478	C₂²×C₂₃	1	1	yes	characteristic
960	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
961	#476	C₂²×C₂₃	1	1	yes	characteristic
962	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
963	#474	C₂²×C₂₃	1	1	yes	characteristic
964	#470	C₂²×C₂₃	1	1	yes	characteristic
965	#470	C₂²×C₂₃	1	1	yes	characteristic
966	#470	C₂²×C₂₃	1	1	yes	characteristic, complemented
967	#470	C₂²×C₂₃	1	1	yes	characteristic, complemented
968	#468	C₂²×C₂₃	1	1	yes	characteristic
969	#468	C₂²×C₂₃	1	1	yes	characteristic
970	#468	C₂²×C₂₃	1	1	yes	characteristic
971	#468	C₂²×C₂₃	1	1	yes	characteristic
972	#467	C₂²×C₂₃	1	1	yes	characteristic
973	#467	C₂²×C₂₃	1	1	yes	characteristic
974	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
975	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
976	#465	C₂²×C₂₃	1	1	yes	characteristic
977	#465	C₂²×C₂₃	1	1	yes	characteristic
978	#465	C₂²×C₂₃	1	1	yes	characteristic
979	#465	C₂²×C₂₃	1	1	yes	characteristic
980	#464	C₂²×C₂₃	1	1	yes	characteristic
981	#464	C₂²×C₂₃	1	1	yes	characteristic
982	#464	C₂²×C₂₃	1	1	yes	characteristic
983	#464	C₂²×C₂₃	1	1	yes	characteristic
984	#452	C₂²×C₂₃	1	1	yes	characteristic
985	#452	C₂²×C₂₃	1	1	yes	characteristic
986	#452	C₂²×C₂₃	1	1	yes	characteristic
987	#452	C₂²×C₂₃	1	1	yes	characteristic
988	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
989	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
990	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
991	#451	C₂²×C₂₃	1	1	yes	characteristic, complemented
992	#450	C₂²×C₂₃	1	1	yes	characteristic
993	#450	C₂²×C₂₃	1	1	yes	characteristic
994	#448	C₂²×C₂₃	1	1	yes	characteristic
995	#448	C₂²×C₂₃	1	1	yes	characteristic
996	#441	C₂²×C₂₃	1	1	yes	characteristic, complemented
997	#441	C₂²×C₂₃	1	1	yes	characteristic, complemented
998	#440	C₂²×C₂₃	1	1	yes	characteristic
999	#440	C₂²×C₂₃	1	1	yes	characteristic
1000	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
1001	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
1002	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
1003	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
1004	#436	C₂²×C₂₃	1	1	yes	characteristic
1005	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
1006	#435	C₂²×C₂₃	1	1	yes	characteristic
1007	#435	C₂²×C₂₃	1	1	yes	characteristic
1008	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
1009	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
1010	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
1011	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
1012	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
1013	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
1014	#428	C₂²×C₂₃	1	1	yes	characteristic
1015	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
1016	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
1017	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
1018	#427	C₂²×C₂₃	1	1	yes	characteristic
1019	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
1020	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
1021	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
1022	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
1023	#418	C₂²×C₂₃	1	1	yes	characteristic
1024	#417	C₂²×C₂₃	1	1	yes	characteristic
1025	#417	C₂²×C₂₃	1	1	yes	characteristic
1026	#416	C₂²×C₂₃	1	1	yes	characteristic
1027	#416	C₂²×C₂₃	1	1	yes	characteristic
1028	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
1029	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
1030	#408	C₂²×C₂₃	1	1	yes	characteristic
1031	#408	C₂²×C₂₃	1	1	yes	characteristic
1032	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
1033	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
1034	C₂×C₂₃	—	4	1	no	—
1035	C₂×C₂₃	—	4	1	no	—
1036	C₂×C₂₃	—	4	1	no	—
1037	C₂×C₂₃	—	4	1	no	—
1038	C₂×C₂₃	—	4	1	no	—
1039	C₂×C₂₃	—	8	1	no	—
1040	C₂×C₂₃	—	8	1	no	—
1041	C₂×C₂₃	#3485	1	1	yes	characteristic
1042	C₂×C₂₃	#3584	1	1	yes	characteristic
1043	C₂×C₂₃	#3586	1	1	yes	characteristic
1044	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
1045	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
1046	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
1047	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
1048	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1049	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1050	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1051	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
1052	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
1053	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
1054	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
1055	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1056	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1057	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1058	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1059	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
1060	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
1061	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
1062	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
1063	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
1064	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
1065	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
1066	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
1067	C₄⋊Q₈	—	2	1	no	—
1068	C₄⋊Q₈	—	2	1	no	—
1069	C₄⋊Q₈	—	2	1	no	—
1070	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
1071	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1072	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1073	#127	—	2	1	no	—
1074	#127	D₄×C₂₃	1	1	yes	characteristic
1075	#126	—	2	1	no	—
1076	#126	—	2	1	no	—
1077	#126	—	2	1	no	—
1078	#126	—	2	1	no	—
1079	#126	—	2	1	no	—
1080	#126	—	2	1	no	—
1081	#126	—	2	1	no	—
1082	#126	—	2	1	no	—
1083	#126	—	2	1	no	—
1084	#126	—	2	1	no	—
1085	#126	—	2	1	no	—
1086	#126	—	2	1	no	—
1087	#126	—	2	1	no	—
1088	#126	—	2	1	no	—
1089	#125	—	2	1	no	—
1090	#125	—	2	1	no	—
1091	#125	—	2	1	no	—
1092	#125	—	2	1	no	—
1093	#125	—	2	1	no	—
1094	#125	—	2	1	no	—
1095	#125	—	2	1	no	—
1096	#125	—	2	1	no	—
1097	#125	C₂³×C₂₃	1	1	yes	characteristic
1098	#125	C₂³×C₂₃	1	1	yes	characteristic
1099	#125	C₂³×C₂₃	1	1	yes	characteristic
1100	#125	C₂³×C₂₃	1	1	yes	characteristic
1101	#124	—	2	1	no	—
1102	#124	—	2	1	no	—
1103	#124	—	2	1	no	—
1104	#124	—	2	1	no	—
1105	#124	—	2	1	no	—
1106	#124	—	2	1	no	—
1107	#124	—	2	1	no	—
1108	#124	—	2	1	no	—
1109	#124	D₄×C₂₃	1	1	yes	characteristic
1110	#124	D₄×C₂₃	1	1	yes	characteristic
1111	#124	C₂³×C₂₃	1	1	yes	characteristic
1112	#124	C₂³×C₂₃	1	1	yes	characteristic
1113	#123	—	2	1	no	—
1114	#123	—	2	1	no	—
1115	#123	—	2	1	no	—
1116	#123	—	2	1	no	—
1117	#123	—	2	1	no	—
1118	#123	—	2	1	no	—
1119	#123	—	2	1	no	—
1120	#123	—	2	1	no	—
1121	#123	—	2	1	no	—
1122	#123	—	2	1	no	—
1123	#123	—	2	1	no	—
1124	#123	—	2	1	no	—
1125	#123	—	2	1	no	—
1126	#123	—	2	1	no	—
1127	#123	—	2	1	no	—
1128	#123	—	2	1	no	—
1129	#123	—	2	1	no	—
1130	#123	—	2	1	no	—
1131	C₂²⋊Q₈	—	2	1	no	—
1132	C₂²⋊Q₈	—	2	1	no	—
1133	C₂²⋊Q₈	—	2	1	no	—
1134	C₂²⋊Q₈	—	2	1	no	—
1135	C₂²⋊Q₈	—	2	1	no	—
1136	C₂²⋊Q₈	—	2	1	no	—
1137	C₂²⋊Q₈	—	2	1	no	—
1138	C₂²⋊Q₈	—	2	1	no	—
1139	C₂²⋊Q₈	—	2	1	no	—
1140	C₂²⋊Q₈	—	2	1	no	—
1141	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1142	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1143	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1144	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1145	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1146	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1147	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1148	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1149	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1150	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1151	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1152	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1153	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1154	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1155	#121	—	2	1	no	—
1156	#121	—	2	1	no	—
1157	#121	—	2	1	no	—
1158	#121	—	2	1	no	—
1159	#121	—	2	1	no	—
1160	#121	—	2	1	no	—
1161	#121	—	2	1	no	—
1162	#121	—	2	1	no	—
1163	#121	—	2	1	no	—
1164	#121	—	2	1	no	—
1165	#121	—	2	1	no	—
1166	#121	—	2	1	no	—
1167	#121	D₄×C₂₃	1	1	yes	characteristic
1168	#121	D₄×C₂₃	1	1	yes	characteristic
1169	#121	D₄×C₂₃	1	1	yes	characteristic
1170	#121	D₄×C₂₃	1	1	yes	characteristic
1171	#121	C₂³×C₂₃	1	1	yes	characteristic
1172	#121	C₂³×C₂₃	1	1	yes	characteristic
1173	#121	C₂³×C₂₃	1	1	yes	characteristic
1174	#121	C₂³×C₂₃	1	1	yes	characteristic
1175	#121	C₂³×C₂₃	1	1	yes	characteristic
1176	#121	C₂³×C₂₃	1	1	yes	characteristic
1177	#120	—	2	1	no	—
1178	#120	—	2	1	no	—
1179	#120	—	2	1	no	—
1180	#120	—	2	1	no	—
1181	C₄×Q₈	—	2	1	no	—
1182	C₄×Q₈	—	2	1	no	—
1183	C₄×Q₈	—	2	1	no	—
1184	C₄×Q₈	—	2	1	no	—
1185	C₄×Q₈	—	2	1	no	—
1186	C₄×Q₈	—	2	1	no	—
1187	C₄×Q₈	—	2	1	no	—
1188	C₄×Q₈	—	2	1	no	—
1189	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1190	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1191	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1192	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1193	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1194	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1195	C₄×D₄	—	2	1	no	—
1196	C₄×D₄	—	2	1	no	—
1197	C₄×D₄	—	2	1	no	—
1198	C₄×D₄	—	2	1	no	—
1199	C₄×D₄	—	2	1	no	—
1200	C₄×D₄	—	2	1	no	—
1201	C₄×D₄	—	2	1	no	—
1202	C₄×D₄	—	2	1	no	—
1203	C₄×D₄	—	2	1	no	—
1204	C₄×D₄	—	2	1	no	—
1205	C₄×D₄	—	2	1	no	—
1206	C₄×D₄	—	2	1	no	—
1207	C₄×D₄	—	2	1	no	—
1208	C₄×D₄	—	2	1	no	—
1209	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1210	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1211	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1212	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1213	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1214	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1215	#117	—	2	1	no	—
1216	#117	—	2	1	no	—
1217	#117	—	2	1	no	—
1218	#117	—	2	1	no	—
1219	#117	—	2	1	no	—
1220	#117	—	2	1	no	—
1221	#117	—	2	1	no	—
1222	#117	—	2	1	no	—
1223	#117	C₂³×C₂₃	1	1	yes	characteristic
1224	#117	C₂³×C₂₃	1	1	yes	characteristic
1225	#117	C₂³×C₂₃	1	1	yes	characteristic
1226	#117	C₂³×C₂₃	1	1	yes	characteristic
1227	#117	C₂³×C₂₃	1	1	yes	characteristic
1228	#117	C₂³×C₂₃	1	1	yes	characteristic
1229	#117	C₂³×C₂₃	1	1	yes	characteristic
1230	#117	C₂³×C₂₃	1	1	yes	characteristic
1231	C₂×C₄⋊C₄	—	2	1	no	—
1232	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1233	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1234	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1235	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1236	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1237	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1238	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1239	C₂×C₂²⋊C₄	—	2	1	no	—
1240	C₂×C₂²⋊C₄	—	2	1	no	—
1241	C₂×C₄²	—	2	1	no	—
1242	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1243	#107	C₂³×C₂₃	1	1	yes	characteristic
1244	#107	C₂³×C₂₃	1	1	yes	characteristic
1245	#107	C₂³×C₂₃	1	1	yes	characteristic
1246	#107	C₂³×C₂₃	1	1	yes	characteristic
1247	#107	C₂³×C₂₃	1	1	yes	characteristic
1248	#107	C₂³×C₂₃	1	1	yes	characteristic
1249	#107	C₂³×C₂₃	1	1	yes	characteristic
1250	#107	C₂³×C₂₃	1	1	yes	characteristic
1251	#107	C₂³×C₂₃	1	1	yes	characteristic
1252	#107	C₂³×C₂₃	1	1	yes	characteristic
1253	#107	C₂³×C₂₃	1	1	yes	characteristic
1254	#107	C₂³×C₂₃	1	1	yes	characteristic
1255	#106	C₂³×C₂₃	1	1	yes	characteristic
1256	#106	C₂³×C₂₃	1	1	yes	characteristic
1257	#106	C₂³×C₂₃	1	1	yes	characteristic
1258	#106	C₂³×C₂₃	1	1	yes	characteristic
1259	#106	C₂³×C₂₃	1	1	yes	characteristic
1260	#106	C₂³×C₂₃	1	1	yes	characteristic
1261	#106	C₂³×C₂₃	1	1	yes	characteristic
1262	#106	C₂³×C₂₃	1	1	yes	characteristic
1263	#106	C₂³×C₂₃	1	1	yes	characteristic
1264	#106	C₂³×C₂₃	1	1	yes	characteristic
1265	#106	C₂³×C₂₃	1	1	yes	characteristic
1266	#106	C₂³×C₂₃	1	1	yes	characteristic
1267	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1268	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1269	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1270	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1271	#103	C₂³×C₂₃	1	1	yes	characteristic
1272	#103	C₂³×C₂₃	1	1	yes	characteristic
1273	#103	C₂³×C₂₃	1	1	yes	characteristic
1274	#103	C₂³×C₂₃	1	1	yes	characteristic
1275	#103	C₂³×C₂₃	1	1	yes	characteristic
1276	#103	C₂³×C₂₃	1	1	yes	characteristic
1277	#103	C₂³×C₂₃	1	1	yes	characteristic
1278	#103	C₂³×C₂₃	1	1	yes	characteristic
1279	#103	C₂³×C₂₃	1	1	yes	characteristic
1280	#103	C₂³×C₂₃	1	1	yes	characteristic
1281	#103	C₂³×C₂₃	1	1	yes	characteristic
1282	#103	C₂³×C₂₃	1	1	yes	characteristic
1283	#103	C₂³×C₂₃	1	1	yes	characteristic
1284	#103	C₂³×C₂₃	1	1	yes	characteristic
1285	#103	C₂³×C₂₃	1	1	yes	characteristic
1286	#103	C₂³×C₂₃	1	1	yes	characteristic
1287	#103	C₂³×C₂₃	1	1	yes	characteristic
1288	#103	C₂³×C₂₃	1	1	yes	characteristic
1289	#103	C₂³×C₂₃	1	1	yes	characteristic
1290	#103	C₂³×C₂₃	1	1	yes	characteristic
1291	#102	C₂³×C₂₃	1	1	yes	characteristic
1292	#102	C₂³×C₂₃	1	1	yes	characteristic
1293	#102	C₂³×C₂₃	1	1	yes	characteristic
1294	#102	C₂³×C₂₃	1	1	yes	characteristic
1295	#102	C₂³×C₂₃	1	1	yes	characteristic
1296	#102	C₂³×C₂₃	1	1	yes	characteristic
1297	#102	C₂³×C₂₃	1	1	yes	characteristic
1298	#102	C₂³×C₂₃	1	1	yes	characteristic
1299	#102	C₂³×C₂₃	1	1	yes	characteristic
1300	#102	C₂³×C₂₃	1	1	yes	characteristic
1301	#102	C₂³×C₂₃	1	1	yes	characteristic
1302	#102	C₂³×C₂₃	1	1	yes	characteristic
1303	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1304	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1305	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1306	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1307	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1308	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1309	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1310	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1311	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1312	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1313	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1314	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1315	#97	C₂³×C₂₃	1	1	yes	characteristic
1316	#97	C₂³×C₂₃	1	1	yes	characteristic
1317	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1318	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1319	C₂₃	#61801	1	1	yes	characteristic, direct product factor, Sylow
1320	C₂⁴	—	2	1	no	—
1321	#41	—	4	1	no	—
1322	#41	—	4	1	no	—
1323	#41	—	4	1	no	—
1324	#41	—	4	1	no	—
1325	#41	—	4	1	no	—
1326	#41	—	4	1	no	—
1327	#41	—	4	1	no	—
1328	#41	—	4	1	no	—
1329	C₂×Q₈	—	2	1	no	—
1330	C₂×Q₈	—	2	1	no	—
1331	C₂×Q₈	—	2	1	no	—
1332	C₂×Q₈	—	2	1	no	—
1333	C₂×Q₈	—	4	1	no	—
1334	C₂×Q₈	—	4	1	no	—
1335	C₂×Q₈	—	4	1	no	—
1336	C₂×Q₈	—	4	1	no	—
1337	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1338	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1339	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1340	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1341	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1342	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1343	C₂×D₄	—	2	1	no	—
1344	C₂×D₄	—	2	1	no	—
1345	C₂×D₄	—	2	1	no	—
1346	C₂×D₄	—	2	1	no	—
1347	C₂×D₄	—	2	1	no	—
1348	C₂×D₄	—	2	1	no	—
1349	C₂×D₄	—	2	1	no	—
1350	C₂×D₄	—	2	1	no	—
1351	C₂×D₄	—	2	1	no	—
1352	C₂×D₄	—	4	1	no	—
1353	C₂×D₄	—	4	1	no	—
1354	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1355	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1356	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1357	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1358	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1359	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1360	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1361	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1362	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1363	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1364	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1365	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1366	C₂²×C₄	—	2	1	no	—
1367	C₂²×C₄	—	2	1	no	—
1368	C₂²×C₄	—	2	1	no	—
1369	C₂²×C₄	—	2	1	no	—
1370	C₂²×C₄	—	2	1	no	—
1371	C₂²×C₄	—	2	1	no	—
1372	C₂²×C₄	—	2	1	no	—
1373	C₂²×C₄	—	2	1	no	—
1374	C₂²×C₄	—	2	1	no	—
1375	C₂²×C₄	—	2	1	no	—
1376	C₂²×C₄	—	2	1	no	—
1377	C₂²×C₄	—	2	1	no	—
1378	C₂²×C₄	—	2	1	no	—
1379	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1380	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1381	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1382	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1383	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1384	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1385	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1386	Q₁₆	—	4	1	no	—
1387	Q₁₆	—	4	1	no	—
1388	Q₁₆	—	4	1	no	—
1389	Q₁₆	—	4	1	no	—
1390	SD₁₆	—	4	1	no	—
1391	SD₁₆	—	4	1	no	—
1392	SD₁₆	—	4	1	no	—
1393	SD₁₆	—	4	1	no	—
1394	M₁₆	—	4	1	no	—
1395	M₁₆	—	4	1	no	—
1396	M₁₆	—	4	1	no	—
1397	M₁₆	—	4	1	no	—
1398	C₂×C₈	—	4	1	no	—
1399	C₂×C₈	—	4	1	no	—
1400	C₂×C₈	—	4	1	no	—
1401	C₂×C₈	—	4	1	no	—
1402	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1403	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1404	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1405	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1406	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1407	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1408	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1409	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1410	C₄⋊C₄	—	2	1	no	—
1411	C₄⋊C₄	—	2	1	no	—
1412	C₄⋊C₄	—	2	1	no	—
1413	C₄⋊C₄	—	2	1	no	—
1414	C₄⋊C₄	—	2	1	no	—
1415	C₄⋊C₄	—	2	1	no	—
1416	C₄⋊C₄	—	2	1	no	—
1417	C₄⋊C₄	—	2	1	no	—
1418	C₄⋊C₄	—	2	1	no	—
1419	C₄⋊C₄	—	2	1	no	—
1420	C₄⋊C₄	—	2	1	no	—
1421	C₄⋊C₄	—	2	1	no	—
1422	C₄⋊C₄	—	2	1	no	—
1423	C₄⋊C₄	—	2	1	no	—
1424	C₄⋊C₄	—	2	1	no	—
1425	C₄⋊C₄	—	2	1	no	—
1426	C₄⋊C₄	—	2	1	no	—
1427	C₄⋊C₄	—	2	1	no	—
1428	C₄⋊C₄	—	2	1	no	—
1429	C₄⋊C₄	—	2	1	no	—
1430	C₄⋊C₄	—	2	1	no	—
1431	C₄⋊C₄	—	2	1	no	—
1432	C₄⋊C₄	—	2	1	no	—
1433	C₄⋊C₄	—	2	1	no	—
1434	C₄⋊C₄	—	2	1	no	—
1435	C₄⋊C₄	—	2	1	no	—
1436	C₄⋊C₄	—	2	1	no	—
1437	C₄⋊C₄	—	2	1	no	—
1438	C₄⋊C₄	—	2	1	no	—
1439	C₄⋊C₄	—	2	1	no	—
1440	C₄⋊C₄	—	2	1	no	—
1441	C₄⋊C₄	—	2	1	no	—
1442	C₄⋊C₄	—	2	1	no	—
1443	C₄⋊C₄	—	2	1	no	—
1444	C₄⋊C₄	—	2	1	no	—
1445	C₄⋊C₄	—	2	1	no	—
1446	C₄⋊C₄	—	2	1	no	—
1447	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1448	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1449	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1450	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1451	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1452	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1453	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1454	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1455	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1456	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1457	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1458	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1459	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1460	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1461	C₂²⋊C₄	—	2	1	no	—
1462	C₂²⋊C₄	—	2	1	no	—
1463	C₂²⋊C₄	—	2	1	no	—
1464	C₂²⋊C₄	—	2	1	no	—
1465	C₂²⋊C₄	—	2	1	no	—
1466	C₂²⋊C₄	—	2	1	no	—
1467	C₂²⋊C₄	—	2	1	no	—
1468	C₂²⋊C₄	—	2	1	no	—
1469	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	—	2	1	no	—
1471	C₂²⋊C₄	—	2	1	no	—
1472	C₂²⋊C₄	—	2	1	no	—
1473	C₂²⋊C₄	—	2	1	no	—
1474	C₂²⋊C₄	—	2	1	no	—
1475	C₂²⋊C₄	—	2	1	no	—
1476	C₂²⋊C₄	—	2	1	no	—
1477	C₂²⋊C₄	—	2	1	no	—
1478	C₂²⋊C₄	—	2	1	no	—
1479	C₂²⋊C₄	—	2	1	no	—
1480	C₂²⋊C₄	—	2	1	no	—
1481	C₂²⋊C₄	—	2	1	no	—
1482	C₂²⋊C₄	—	2	1	no	—
1483	C₂²⋊C₄	—	2	1	no	—
1484	C₂²⋊C₄	—	2	1	no	—
1485	C₂²⋊C₄	—	2	1	no	—
1486	C₂²⋊C₄	—	2	1	no	—
1487	C₂²⋊C₄	—	2	1	no	—
1488	C₂²⋊C₄	—	2	1	no	—
1489	C₂²⋊C₄	—	2	1	no	—
1490	C₂²⋊C₄	—	2	1	no	—
1491	C₂²⋊C₄	—	2	1	no	—
1492	C₂²⋊C₄	—	2	1	no	—
1493	C₂²⋊C₄	—	2	1	no	—
1494	C₂²⋊C₄	—	2	1	no	—
1495	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1496	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1497	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1498	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1499	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1500	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1501	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1502	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1503	C₄²	—	2	1	no	—
1504	C₄²	—	2	1	no	—
1505	C₄²	—	2	1	no	—
1506	C₄²	—	2	1	no	—
1507	C₄²	—	2	1	no	—
1508	C₄²	—	2	1	no	—
1509	C₄²	—	2	1	no	—
1510	C₄²	—	2	1	no	—
1511	C₄²	—	2	1	no	—
1512	C₄²	—	2	1	no	—
1513	C₄²	—	2	1	no	—
1514	C₄²	—	2	1	no	—
1515	C₄²	—	2	1	no	—
1516	C₄²	—	2	1	no	—
1517	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1518	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1519	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1520	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1521	C₂³	—	2	1	no	—
1522	C₂³	—	2	1	no	—
1523	C₂³	—	8	1	no	—
1524	C₂³	—	8	1	no	—
1525	C₂³	—	8	1	no	—
1526	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1527	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1528	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1529	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1530	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1531	Q₈	—	2	1	no	—
1532	Q₈	—	2	1	no	—
1533	Q₈	—	2	1	no	—
1534	Q₈	—	2	1	no	—
1535	Q₈	—	2	1	no	—
1536	Q₈	—	2	1	no	—
1537	Q₈	—	2	1	no	—
1538	Q₈	—	2	1	no	—
1539	Q₈	—	4	1	no	—
1540	Q₈	—	4	1	no	—
1541	Q₈	—	4	2	no	—
1542	Q₈	—	4	2	no	—
1543	Q₈	—	8	1	no	—
1544	Q₈	—	8	1	no	—
1545	D₄	—	2	1	no	—
1546	D₄	—	2	1	no	—
1547	D₄	—	2	1	no	—
1548	D₄	—	2	1	no	—
1549	D₄	—	4	1	no	—
1550	D₄	—	4	1	no	—
1551	D₄	—	4	1	no	—
1552	D₄	—	4	1	no	—
1553	D₄	—	4	1	no	—
1554	D₄	—	4	1	no	—
1555	D₄	—	4	1	no	—
1556	D₄	—	4	1	no	—
1557	D₄	—	4	1	no	—
1558	D₄	—	4	1	no	—
1559	D₄	—	8	1	no	—
1560	D₄	—	8	1	no	—
1561	D₄	—	8	1	no	—
1562	D₄	—	8	1	no	—
1563	D₄	—	8	1	no	—
1564	D₄	—	8	1	no	—
1565	D₄	—	8	1	no	—
1566	D₄	—	8	1	no	—
1567	D₄	—	8	1	no	—
1568	C₂×C₄	—	2	1	no	—
1569	C₂×C₄	—	2	1	no	—
1570	C₂×C₄	—	2	1	no	—
1571	C₂×C₄	—	2	1	no	—
1572	C₂×C₄	—	2	1	no	—
1573	C₂×C₄	—	2	1	no	—
1574	C₂×C₄	—	2	1	no	—
1575	C₂×C₄	—	2	1	no	—
1576	C₂×C₄	—	2	1	no	—
1577	C₂×C₄	—	2	1	no	—
1578	C₂×C₄	—	2	1	no	—
1579	C₂×C₄	—	2	1	no	—
1580	C₂×C₄	—	2	1	no	—
1581	C₂×C₄	—	2	1	no	—
1582	C₂×C₄	—	2	1	no	—
1583	C₂×C₄	—	2	1	no	—
1584	C₂×C₄	—	2	1	no	—
1585	C₂×C₄	—	2	1	no	—
1586	C₂×C₄	—	2	1	no	—
1587	C₂×C₄	—	2	1	no	—
1588	C₂×C₄	—	2	1	no	—
1589	C₂×C₄	—	2	1	no	—
1590	C₂×C₄	—	2	1	no	—
1591	C₂×C₄	—	2	1	no	—
1592	C₂×C₄	—	4	1	no	—
1593	C₂×C₄	—	4	1	no	—
1594	C₂×C₄	—	4	2	no	—
1595	C₂×C₄	—	8	1	no	—
1596	C₂×C₄	—	8	1	no	—
1597	C₂×C₄	—	8	1	no	—
1598	C₂×C₄	—	8	1	no	—
1599	C₂×C₄	—	8	1	no	—
1600	C₂×C₄	—	8	1	no	—
1601	C₂×C₄	—	8	1	no	—
1602	C₂×C₄	—	8	1	no	—
1603	C₂×C₄	—	8	1	no	—
1604	C₂×C₄	—	8	1	no	—
1605	C₂×C₄	—	8	1	no	—
1606	C₂×C₄	—	8	1	no	—
1607	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1608	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1609	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1610	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1611	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1612	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1613	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1614	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1615	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1616	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1617	C₈	—	2	1	no	—
1618	C₈	—	2	1	no	—
1619	C₈	—	2	1	no	—
1620	C₈	—	2	1	no	—
1621	C₈	—	2	1	no	—
1622	C₈	—	2	1	no	—
1623	C₈	—	2	1	no	—
1624	C₈	—	2	1	no	—
1625	C₂²	—	2	1	no	—
1626	C₂²	—	2	1	no	—
1627	C₂²	—	2	1	no	—
1628	C₂²	—	2	1	no	—
1629	C₂²	—	2	1	no	—
1630	C₂²	—	2	1	no	—
1631	C₂²	—	2	1	no	—
1632	C₂²	—	2	1	no	—
1633	C₂²	—	2	1	no	—
1634	C₂²	—	2	1	no	—
1635	C₂²	—	2	1	no	—
1636	C₂²	—	2	1	no	—
1637	C₂²	—	2	1	no	—
1638	C₂²	—	2	1	no	—
1639	C₂²	—	2	1	no	—
1640	C₂²	—	4	1	no	—
1641	C₂²	—	4	1	no	—
1642	C₂²	—	4	1	no	—
1643	C₂²	—	4	1	no	—
1644	C₂²	—	4	1	no	—
1645	C₂²	—	4	1	no	—
1646	C₂²	—	16	2	no	—
1647	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1648	C₄	—	2	1	no	—
1649	C₄	—	2	1	no	—
1650	C₄	—	2	1	no	—
1651	C₄	—	2	1	no	—
1652	C₄	—	2	1	no	—
1653	C₄	—	2	1	no	—
1654	C₄	—	2	1	no	—
1655	C₄	—	2	1	no	—
1656	C₄	—	2	1	no	—
1657	C₄	—	4	1	no	—
1658	C₄	—	4	1	no	—
1659	C₄	—	4	1	no	—
1660	C₄	—	4	1	no	—
1661	C₄	—	4	1	no	—
1662	C₄	—	4	1	no	—
1663	C₄	—	4	1	no	—
1664	C₄	—	4	1	no	—
1665	C₄	—	4	1	no	—
1666	C₄	—	4	1	no	—
1667	C₄	—	4	1	no	—
1668	C₄	—	4	1	no	—
1669	C₄	—	4	1	no	—
1670	C₄	—	4	1	no	—
1671	C₄	C₂₃×#585	1	1	yes	characteristic
1672	C₄	C₂₃×#585	1	1	yes	characteristic
1673	C₂	—	4	1	no	—
1674	C₂	—	4	1	no	—
1675	C₂	—	4	1	no	—
1676	C₂	—	4	1	no	—
1677	C₂	—	4	1	no	—
1678	C₂	—	8	1	no	—
1679	C₂	—	8	1	no	—
1680	C₂	C₂₃×#3485	1	1	yes	characteristic
1681	C₂	C₂₃×#3584	1	1	yes	characteristic
1682	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3551	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂₃×#3507	C₂	semidirect
3. C₂₃×#3352	C₂	semidirect
4. C₂₃×#3351	C₂	semidirect
5. C₂₃×#3350	C₂	semidirect
6. C₂₃×#3349	C₂	semidirect
7. C₂₃×#3346	C₂	semidirect
8. C₂₃×#3344	C₂	semidirect
9. C₂₃×#3337	C₂	semidirect
10. C₂₃×#3336	C₂	semidirect
11. C₂₃×#3327	C₂	semidirect
12. C₂₃×#3323	C₂	semidirect
13. C₂₃×#3316	C₂	semidirect
14. C₂₃×#3314	C₂	semidirect
15. C₂₃×#3313	C₂	semidirect
16. C₂₃×#3311	C₂	semidirect
17. C₂₃×#3300	C₂	semidirect
18. C₂₃×#3296	C₂	semidirect
19. C₂₃×#3240	C₂	semidirect
20. C₂₃×#3233	C₂	semidirect
21. C₂₃×#3202	C₂	semidirect
22. C₂₃×#3201	C₂	semidirect
23. C₂₃×#3201	C₂	semidirect
24. C₂₃×#3200	C₂	semidirect
25. C₂₃×#3117	C₂	semidirect
26. C₂₃×#3108	C₂	semidirect
27. C₂₃×#3099	C₂	semidirect
28. C₂₃×#3098	C₂	semidirect
29. C₂₃×#3097	C₂	semidirect
30. C₂₃×#3096	C₂	semidirect
31. C₂₃×#2981	C₂	semidirect
39. C₂₃×#556	C₂²	semidirect
42. C₂₃×#554	C₂²	semidirect
49. C₂₃×#552	C₂²	semidirect
50. C₂₃×#552	C₂²	semidirect
66. C₂₃×#536	C₂²	semidirect
68. C₂₃×#533	C₂²	semidirect
75. C₂₃×#520	C₂²	semidirect
76. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
77. C₂₃×#501	C₂²	semidirect
78. C₂₃×#501	C₂²	semidirect
79. C₂₃×#499	C₂²	semidirect
80. C₂₃×#499	C₂²	semidirect
89. C₂₃×#485	C₂²	semidirect
90. C₂₃×#485	C₂²	semidirect
91. C₂₃×#485	C₂²	semidirect
92. C₂₃×#485	C₂²	semidirect
93. C₂₃×#485	C₂²	semidirect
94. C₂₃×#485	C₂²	semidirect
95. C₂₃×#485	C₂²	semidirect
96. C₂₃×#485	C₂²	semidirect
98. C₂₃×#484	C₂²	semidirect
99. C₂₃×#484	C₂²	semidirect
100. C₂₃×#484	C₂²	semidirect
101. C₂₃×#484	C₂²	semidirect
103. C₂₃×#483	C₂²	semidirect
104. C₂₃×#483	C₂²	semidirect
105. C₂₃×#483	C₂²	semidirect
106. C₂₃×#483	C₂²	semidirect
121. C₂₃×#479	C₂²	semidirect
122. C₂₃×#479	C₂²	semidirect
123. C₂₃×#479	C₂²	semidirect
124. C₂₃×#479	C₂²	semidirect
125. C₂₃×#479	C₂²	semidirect
126. C₂₃×#479	C₂²	semidirect
129. C₂₃×#477	C₂²	semidirect
131. C₂₃×#475	C₂²	semidirect
135. C₂₃×#470	C₂²	semidirect
136. C₂₃×#470	C₂²	semidirect
143. C₂₃×#467	C₂²	semidirect
144. C₂₃×#467	C₂²	semidirect
157. C₂₃×#451	C₂²	semidirect
158. C₂₃×#451	C₂²	semidirect
159. C₂₃×#451	C₂²	semidirect
160. C₂₃×#451	C₂²	semidirect
165. C₂₃×#441	C₂²	semidirect
166. C₂₃×#441	C₂²	semidirect
169. C₄×Q₁₆×C₂₃	C₂²	semidirect
170. C₄×Q₁₆×C₂₃	C₂²	semidirect
174. C₂₃×#436	C₂²	semidirect
177. C₂₃×#435	C₂²	semidirect
178. C₂₃×#435	C₂²	semidirect
180. C₈×D₄×C₂₃	C₂²	semidirect
181. C₂₃×#432	C₂²	semidirect
182. C₂₃×#431	C₂²	semidirect
184. C₂₃×#428	C₂²	semidirect
185. C₂₃×#428	C₂²	semidirect
186. C₂₃×#428	C₂²	semidirect
188. C₂₃×#427	C₂²	semidirect
189. C₂×C₂₃×#107	C₂²	semidirect
190. C₂×C₂₃×#106	C₂²	semidirect
191. C₂₃×#419	C₂²	semidirect
197. C₂×C₂₃×#103	C₂²	semidirect
201. C₂₃×#408	C₂²	semidirect
202. C₂₃×#408	C₂²	semidirect
679. #61801	C₂₃	direct (N × H)
785. #3507	C₂×C₂₃	semidirect
786. #3352	C₂×C₂₃	semidirect
787. #3351	C₂×C₂₃	semidirect
788. #3350	C₂×C₂₃	semidirect
789. #3349	C₂×C₂₃	semidirect
790. #3346	C₂×C₂₃	semidirect
791. #3344	C₂×C₂₃	semidirect
792. #3337	C₂×C₂₃	semidirect
793. #3336	C₂×C₂₃	semidirect
794. #3327	C₂×C₂₃	semidirect
795. #3323	C₂×C₂₃	semidirect
796. #3316	C₂×C₂₃	semidirect
797. #3314	C₂×C₂₃	semidirect
798. #3313	C₂×C₂₃	semidirect
799. #3311	C₂×C₂₃	semidirect
800. #3300	C₂×C₂₃	semidirect
801. #3296	C₂×C₂₃	semidirect
802. #3240	C₂×C₂₃	semidirect
803. #3233	C₂×C₂₃	semidirect
804. #3202	C₂×C₂₃	semidirect
805. #3201	C₂×C₂₃	semidirect
806. #3201	C₂×C₂₃	semidirect
807. #3200	C₂×C₂₃	semidirect
808. #3117	C₂×C₂₃	semidirect
809. #3108	C₂×C₂₃	semidirect
810. #3099	C₂×C₂₃	semidirect
811. #3098	C₂×C₂₃	semidirect
812. #3097	C₂×C₂₃	semidirect
813. #3096	C₂×C₂₃	semidirect
814. #2981	C₂×C₂₃	semidirect
870. #556	C₂²×C₂₃	semidirect
873. #554	C₂²×C₂₃	semidirect
880. #552	C₂²×C₂₃	semidirect
881. #552	C₂²×C₂₃	semidirect
897. #536	C₂²×C₂₃	semidirect
899. #533	C₂²×C₂₃	semidirect
906. #520	C₂²×C₂₃	semidirect
907. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
908. #501	C₂²×C₂₃	semidirect
909. #501	C₂²×C₂₃	semidirect
910. #499	C₂²×C₂₃	semidirect
911. #499	C₂²×C₂₃	semidirect
920. #485	C₂²×C₂₃	semidirect
921. #485	C₂²×C₂₃	semidirect
922. #485	C₂²×C₂₃	semidirect
923. #485	C₂²×C₂₃	semidirect
924. #485	C₂²×C₂₃	semidirect
925. #485	C₂²×C₂₃	semidirect
926. #485	C₂²×C₂₃	semidirect
927. #485	C₂²×C₂₃	semidirect
929. #484	C₂²×C₂₃	semidirect
930. #484	C₂²×C₂₃	semidirect
931. #484	C₂²×C₂₃	semidirect
932. #484	C₂²×C₂₃	semidirect
934. #483	C₂²×C₂₃	semidirect
935. #483	C₂²×C₂₃	semidirect
936. #483	C₂²×C₂₃	semidirect
937. #483	C₂²×C₂₃	semidirect
952. #479	C₂²×C₂₃	semidirect
953. #479	C₂²×C₂₃	semidirect
954. #479	C₂²×C₂₃	semidirect
955. #479	C₂²×C₂₃	semidirect
956. #479	C₂²×C₂₃	semidirect
957. #479	C₂²×C₂₃	semidirect
960. #477	C₂²×C₂₃	semidirect
962. #475	C₂²×C₂₃	semidirect
966. #470	C₂²×C₂₃	semidirect
967. #470	C₂²×C₂₃	semidirect
974. #467	C₂²×C₂₃	semidirect
975. #467	C₂²×C₂₃	semidirect
988. #451	C₂²×C₂₃	semidirect
989. #451	C₂²×C₂₃	semidirect
990. #451	C₂²×C₂₃	semidirect
991. #451	C₂²×C₂₃	semidirect
996. #441	C₂²×C₂₃	semidirect
997. #441	C₂²×C₂₃	semidirect
1000. C₄×Q₁₆	C₂²×C₂₃	semidirect
1001. C₄×Q₁₆	C₂²×C₂₃	semidirect
1005. #436	C₂²×C₂₃	semidirect
1008. #435	C₂²×C₂₃	semidirect
1009. #435	C₂²×C₂₃	semidirect
1011. C₈×D₄	C₂²×C₂₃	semidirect
1012. #432	C₂²×C₂₃	semidirect
1013. #431	C₂²×C₂₃	semidirect
1015. #428	C₂²×C₂₃	semidirect
1016. #428	C₂²×C₂₃	semidirect
1017. #428	C₂²×C₂₃	semidirect
1019. #427	C₂²×C₂₃	semidirect
1020. C₂×#107	C₂²×C₂₃	semidirect
1021. C₂×#106	C₂²×C₂₃	semidirect
1022. #419	C₂²×C₂₃	semidirect
1028. C₂×#103	C₂²×C₂₃	semidirect
1032. #408	C₂²×C₂₃	semidirect
1033. #408	C₂²×C₂₃	semidirect
1319. C₂₃	#61801	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3551	2
C₂₃×#3507	2
C₂₃×#3352	2
C₂₃×#3351	2
C₂₃×#3350	2
C₂₃×#3349	2
C₂₃×#3346	2
C₂₃×#3344	2
C₂₃×#3337	2
C₂₃×#3336	2
C₂₃×#3327	2
C₂₃×#3323	2
C₂₃×#3316	2
C₂₃×#3314	2
C₂₃×#3313	2
C₂₃×#3311	2
C₂₃×#3300	2
C₂₃×#3296	2
C₂₃×#3240	2
C₂₃×#3233	2
C₂₃×#3202	2
C₂₃×#3201	2
C₂₃×#3200	2
C₂₃×#3117	2
C₂₃×#3108	2
C₂₃×#3099	2
C₂₃×#3098	2
C₂₃×#3097	2
C₂₃×#3096	2
C₂₃×#2981	2
#61801	23

Subgroups — C23×#61801 #19209427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61801 #19209427