Subgroups — C₂₃×#61855 #19209481

Order 5888.

1680 conjugacy classes of subgroups.

The subgroup lattice has 1618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3388	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3388	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3376	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3376	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3370	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3370	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3244	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3243	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3242	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3241	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂₃×#3123	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂₃×#3122	C₂	1	1	yes	maximal, characteristic
27	C₂₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂₃×#563	—	2	1	no	—
33	C₂₃×#563	—	2	1	no	—
34	C₂₃×#559	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#559	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#554	—	2	1	no	—
41	C₂₃×#554	—	2	1	no	—
42	C₂₃×#554	—	2	1	no	—
43	C₂₃×#554	C₂²	1	1	yes	characteristic
44	C₂₃×#554	C₂²	1	1	yes	characteristic
45	C₂₃×#554	C₂²	1	1	yes	characteristic
46	C₂₃×#554	C₂²	1	1	yes	characteristic
47	C₂₃×#554	C₂²	1	1	yes	characteristic
48	C₂₃×#554	C₂²	1	1	yes	characteristic
49	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#552	—	2	1	no	—
52	C₂₃×#552	—	2	1	no	—
53	D₄×Q₈×C₂₃	—	2	1	no	—
54	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
55	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
56	C₂₃×#544	C₂²	1	1	yes	characteristic
57	C₂₃×#544	C₂²	1	1	yes	characteristic
58	C₂₃×#543	—	2	1	no	—
59	C₂₃×#543	—	2	1	no	—
60	C₂₃×#542	—	2	1	no	—
61	C₂₃×#542	—	2	1	no	—
62	C₂₃×#542	C₂²	1	1	yes	characteristic
63	C₂₃×#542	C₂²	1	1	yes	characteristic
64	C₂₃×#541	C₂²	1	1	yes	characteristic
65	C₂₃×#540	C₂²	1	1	yes	characteristic
66	C₂₃×#539	—	2	1	no	—
67	C₂₃×#539	—	2	1	no	—
68	C₂₃×#533	C₂²	1	1	yes	characteristic
69	C₂₃×#533	C₂²	1	1	yes	characteristic
70	C₂₃×#529	C₂²	1	1	yes	characteristic
71	C₂₃×#529	C₂²	1	1	yes	characteristic
72	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
73	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
74	C₂₃×#518	C₂²	1	1	yes	characteristic
75	C₂₃×#518	C₂²	1	1	yes	characteristic
76	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
77	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#490	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#488	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#488	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#488	C₂²	1	1	yes	characteristic, complemented
98	C₂₃×#488	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#485	C₂²	1	1	yes	characteristic
102	C₂₃×#485	C₂²	1	1	yes	characteristic
103	C₂₃×#485	C₂²	1	1	yes	characteristic
104	C₂₃×#485	C₂²	1	1	yes	characteristic
105	C₂₃×#484	C₂²	1	1	yes	characteristic
106	C₂₃×#483	C₂²	1	1	yes	characteristic
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×#481	C₂²	1	1	yes	characteristic
112	C₂₃×#480	C₂²	1	1	yes	characteristic
113	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
117	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
118	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×#478	C₂²	1	1	yes	characteristic
120	C₂₃×#478	C₂²	1	1	yes	characteristic
121	C₂₃×#478	C₂²	1	1	yes	characteristic
122	C₂₃×#478	C₂²	1	1	yes	characteristic
123	C₂₃×#478	C₂²	1	1	yes	characteristic
124	C₂₃×#478	C₂²	1	1	yes	characteristic
125	C₂₃×#478	C₂²	1	1	yes	characteristic
126	C₂₃×#478	C₂²	1	1	yes	characteristic
127	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
128	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
130	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
131	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
132	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
133	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
134	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
135	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
136	C₂₃×#476	C₂²	1	1	yes	characteristic
137	C₂₃×#476	C₂²	1	1	yes	characteristic
138	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
139	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
140	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
141	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
142	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
143	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
144	C₂₃×#474	C₂²	1	1	yes	characteristic
145	C₂₃×#474	C₂²	1	1	yes	characteristic
146	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
147	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
148	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
149	C₂₃×#463	C₂²	1	1	yes	characteristic
150	C₂₃×#463	C₂²	1	1	yes	characteristic
151	C₂₃×#463	C₂²	1	1	yes	characteristic
152	C₂₃×#463	C₂²	1	1	yes	characteristic
153	C₂₃×#463	C₂²	1	1	yes	characteristic
154	C₂₃×#463	C₂²	1	1	yes	characteristic
155	C₂₃×#463	C₂²	1	1	yes	characteristic
156	C₂₃×#463	C₂²	1	1	yes	characteristic
157	C₂₃×#461	C₂²	1	1	yes	characteristic
158	C₂₃×#461	C₂²	1	1	yes	characteristic
159	C₂₃×#459	C₂²	1	1	yes	characteristic
160	C₂₃×#459	C₂²	1	1	yes	characteristic
161	C₂₃×#450	C₂²	1	1	yes	characteristic
162	C₂₃×#450	C₂²	1	1	yes	characteristic
163	C₂₃×#447	C₂²	1	1	yes	characteristic
164	C₂₃×#447	C₂²	1	1	yes	characteristic
165	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
166	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
167	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
168	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
169	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
170	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
171	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
172	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
173	C₂₃×#442	C₂²	1	1	yes	characteristic
174	C₂₃×#442	C₂²	1	1	yes	characteristic
175	C₂₃×#442	C₂²	1	1	yes	characteristic
176	C₂₃×#442	C₂²	1	1	yes	characteristic
177	C₂₃×#442	C₂²	1	1	yes	characteristic
178	C₂₃×#442	C₂²	1	1	yes	characteristic
179	C₂₃×#440	C₂²	1	1	yes	characteristic
180	C₂₃×#440	C₂²	1	1	yes	characteristic
181	C₂₃×#440	C₂²	1	1	yes	characteristic
182	C₂₃×#440	C₂²	1	1	yes	characteristic
183	C₂₃×#440	C₂²	1	1	yes	characteristic
184	C₂₃×#440	C₂²	1	1	yes	characteristic
185	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
186	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
187	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
188	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
189	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
190	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
191	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
192	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
193	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
194	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
195	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
196	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
197	C₂₃×#433	C₂²	1	1	yes	characteristic
198	C₂₃×#433	C₂²	1	1	yes	characteristic
199	C₂₃×#433	C₂²	1	1	yes	characteristic
200	C₂₃×#433	C₂²	1	1	yes	characteristic
201	C₂₃×#432	C₂²	1	1	yes	characteristic
202	C₂₃×#431	C₂²	1	1	yes	characteristic
203	C₂²×Q₈×C₂₃	—	2	1	no	—
204	C₂²×Q₈×C₂₃	—	2	1	no	—
205	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₂₃	—	2	1	no	—
207	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
208	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
209	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
213	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
215	C₂₃×C₄⋊Q₈	—	2	1	no	—
216	C₂₃×C₄⋊Q₈	—	2	1	no	—
217	C₂₃×C₄⋊Q₈	—	2	1	no	—
218	C₂₃×C₄⋊Q₈	—	2	1	no	—
219	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
220	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
221	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
229	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
230	C₂₃×#127	C₂³	1	1	yes	characteristic
231	C₂₃×#126	—	2	1	no	—
232	C₂₃×#126	—	2	1	no	—
233	C₂₃×#126	—	2	1	no	—
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×#125	—	2	1	no	—
242	C₂₃×#125	—	2	1	no	—
243	C₂₃×#125	—	2	1	no	—
244	C₂₃×#125	—	2	1	no	—
245	C₂₃×#125	—	2	1	no	—
246	C₂₃×#125	—	2	1	no	—
247	C₂₃×#125	—	2	1	no	—
248	C₂₃×#125	—	2	1	no	—
249	C₂₃×#125	D₄	1	1	yes	characteristic
250	C₂₃×#125	D₄	1	1	yes	characteristic
251	C₂₃×#125	C₂³	1	1	yes	characteristic
252	C₂₃×#125	C₂³	1	1	yes	characteristic
253	C₂₃×#125	C₂³	1	1	yes	characteristic
254	C₂₃×#125	C₂³	1	1	yes	characteristic
255	C₂₃×#125	C₂³	1	1	yes	characteristic
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×#125	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
266	C₂₃×#124	C₂³	1	1	yes	characteristic
267	C₂₃×#124	C₂³	1	1	yes	characteristic
268	C₂₃×#124	C₂³	1	1	yes	characteristic
269	C₂₃×#123	—	2	1	no	—
270	C₂₃×#123	—	2	1	no	—
271	C₂₃×#123	—	2	1	no	—
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×C₂²⋊Q₈	—	2	1	no	—
280	C₂₃×C₂²⋊Q₈	—	2	1	no	—
281	C₂₃×C₂²⋊Q₈	—	2	1	no	—
282	C₂₃×C₂²⋊Q₈	—	2	1	no	—
283	C₂₃×C₂²⋊Q₈	—	2	1	no	—
284	C₂₃×C₂²⋊Q₈	—	2	1	no	—
285	C₂₃×C₂²⋊Q₈	—	2	1	no	—
286	C₂₃×C₂²⋊Q₈	—	2	1	no	—
287	C₂₃×C₂²⋊Q₈	—	2	1	no	—
288	C₂₃×C₂²⋊Q₈	—	2	1	no	—
289	C₂₃×C₂²⋊Q₈	—	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	—	2	1	no	—
301	C₂₃×C₂²⋊Q₈	—	2	1	no	—
302	C₂₃×C₂²⋊Q₈	—	2	1	no	—
303	C₂₃×C₂²⋊Q₈	—	2	1	no	—
304	C₂₃×C₂²⋊Q₈	—	2	1	no	—
305	C₂₃×C₂²⋊Q₈	—	2	1	no	—
306	C₂₃×C₂²⋊Q₈	—	2	1	no	—
307	C₂₃×C₂²⋊Q₈	—	2	1	no	—
308	C₂₃×C₂²⋊Q₈	—	2	1	no	—
309	C₂₃×C₂²⋊Q₈	—	2	1	no	—
310	C₂₃×C₂²⋊Q₈	—	2	1	no	—
311	C₂₃×C₂²⋊Q₈	—	2	1	no	—
312	C₂₃×C₂²⋊Q₈	—	2	1	no	—
313	C₂₃×C₂²⋊Q₈	—	2	1	no	—
314	C₂₃×C₂²⋊Q₈	—	2	1	no	—
315	C₂₃×C₂²⋊Q₈	—	2	1	no	—
316	C₂₃×C₂²⋊Q₈	—	2	1	no	—
317	C₂₃×C₂²⋊Q₈	—	2	1	no	—
318	C₂₃×C₂²⋊Q₈	—	2	1	no	—
319	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
320	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
321	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
322	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
323	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
325	C₂₃×#121	—	2	1	no	—
326	C₂₃×#121	—	2	1	no	—
327	C₂₃×#121	C₂³	1	1	yes	characteristic
328	C₂₃×#121	C₂³	1	1	yes	characteristic
329	C₄×Q₈×C₂₃	—	2	1	no	—
330	C₄×Q₈×C₂₃	—	2	1	no	—
331	C₄×Q₈×C₂₃	—	2	1	no	—
332	C₄×Q₈×C₂₃	—	2	1	no	—
333	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
334	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
335	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
336	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
337	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
338	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
339	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
340	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
341	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
342	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
343	C₄×D₄×C₂₃	—	2	1	no	—
344	C₄×D₄×C₂₃	—	2	1	no	—
345	C₄×D₄×C₂₃	—	2	1	no	—
346	C₄×D₄×C₂₃	—	2	1	no	—
347	C₄×D₄×C₂₃	—	2	1	no	—
348	C₄×D₄×C₂₃	—	2	1	no	—
349	C₄×D₄×C₂₃	—	2	1	no	—
350	C₄×D₄×C₂₃	—	2	1	no	—
351	C₄×D₄×C₂₃	—	2	1	no	—
352	C₄×D₄×C₂₃	—	2	1	no	—
353	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
354	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
355	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
356	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
357	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
358	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
359	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
360	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
361	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
362	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
363	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
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	C₂₃×#117	—	2	1	no	—
372	C₂₃×#117	—	2	1	no	—
373	C₂₃×#117	—	2	1	no	—
374	C₂₃×#117	—	2	1	no	—
375	C₂₃×#117	C₂³	1	1	yes	characteristic
376	C₂₃×#117	C₂³	1	1	yes	characteristic
377	C₂₃×#117	C₂³	1	1	yes	characteristic
378	C₂₃×#117	C₂³	1	1	yes	characteristic
379	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
380	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
382	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
383	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
387	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
388	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
389	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
390	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
391	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
392	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
393	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
394	C₂₃×#107	C₂³	1	1	yes	characteristic
395	C₂₃×#107	C₂³	1	1	yes	characteristic
396	C₂₃×#107	C₂³	1	1	yes	characteristic
397	C₂₃×#107	C₂³	1	1	yes	characteristic
398	C₂₃×#107	C₂³	1	1	yes	characteristic
399	C₂₃×#107	C₂³	1	1	yes	characteristic
400	C₂₃×#107	C₂³	1	1	yes	characteristic
401	C₂₃×#107	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×#106	C₂³	1	1	yes	characteristic
407	C₂₃×#106	C₂³	1	1	yes	characteristic
408	C₂₃×#106	C₂³	1	1	yes	characteristic
409	C₂₃×#106	C₂³	1	1	yes	characteristic
410	C₂₃×#106	C₂³	1	1	yes	characteristic
411	C₂₃×#106	C₂³	1	1	yes	characteristic
412	C₂₃×#106	C₂³	1	1	yes	characteristic
413	C₂₃×#106	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
419	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
420	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
421	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
422	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
423	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
424	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
425	C₂₃×C₄⋊C₈	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×#102	C₂³	1	1	yes	characteristic
443	C₂₃×#102	C₂³	1	1	yes	characteristic
444	C₂₃×#102	C₂³	1	1	yes	characteristic
445	C₂₃×#102	C₂³	1	1	yes	characteristic
446	C₂₃×#102	C₂³	1	1	yes	characteristic
447	C₂₃×#102	C₂³	1	1	yes	characteristic
448	C₂₃×#102	C₂³	1	1	yes	characteristic
449	C₂₃×#102	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×#97	C₂³	1	1	yes	characteristic
467	C₂₃×#97	C₂³	1	1	yes	characteristic
468	C₂₃×#97	C₂³	1	1	yes	characteristic
469	C₂₃×#97	C₂³	1	1	yes	characteristic
470	C₂₃×#97	C₂³	1	1	yes	characteristic
471	C₂₃×#97	C₂³	1	1	yes	characteristic
472	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
473	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
474	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
475	C₄×C₈×C₂₃	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	C₂×Q₈×C₂₃	—	2	1	no	—
480	C₂×Q₈×C₂₃	—	2	1	no	—
481	C₂×Q₈×C₂₃	—	2	1	no	—
482	C₂×Q₈×C₂₃	—	2	1	no	—
483	C₂×Q₈×C₂₃	—	2	1	no	—
484	C₂×Q₈×C₂₃	—	2	1	no	—
485	C₂×Q₈×C₂₃	—	2	1	no	—
486	C₂×Q₈×C₂₃	—	2	1	no	—
487	C₂×Q₈×C₂₃	—	8	2	no	—
488	C₂×Q₈×C₂₃	—	8	2	no	—
489	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
490	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
491	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
492	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
493	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
494	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
495	C₂×D₄×C₂₃	—	2	2	no	—
496	C₂×D₄×C₂₃	—	2	2	no	—
497	C₂×D₄×C₂₃	—	2	1	no	—
498	C₂×D₄×C₂₃	—	2	1	no	—
499	C₂×D₄×C₂₃	—	2	1	no	—
500	C₂×D₄×C₂₃	—	2	1	no	—
501	C₂×D₄×C₂₃	—	2	1	no	—
502	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
503	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
504	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
505	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₂₃	—	2	1	no	—
507	C₂²×C₄×C₂₃	—	2	1	no	—
508	C₂²×C₄×C₂₃	—	2	1	no	—
509	C₂²×C₄×C₂₃	—	2	1	no	—
510	C₂²×C₄×C₂₃	—	2	1	no	—
511	C₂²×C₄×C₂₃	—	2	1	no	—
512	C₂²×C₄×C₂₃	—	2	1	no	—
513	C₂²×C₄×C₂₃	—	2	1	no	—
514	C₂²×C₄×C₂₃	—	2	1	no	—
515	C₂²×C₄×C₂₃	—	2	1	no	—
516	C₂²×C₄×C₂₃	—	2	1	no	—
517	C₂²×C₄×C₂₃	—	2	1	no	—
518	C₂²×C₄×C₂₃	—	2	1	no	—
519	C₂²×C₄×C₂₃	—	2	1	no	—
520	C₂²×C₄×C₂₃	—	2	1	no	—
521	C₂²×C₄×C₂₃	—	2	1	no	—
522	C₂²×C₄×C₂₃	—	2	1	no	—
523	C₂²×C₄×C₂₃	—	2	1	no	—
524	C₂²×C₄×C₂₃	—	2	1	no	—
525	C₂²×C₄×C₂₃	—	8	2	no	—
526	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
527	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
528	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
529	SD₁₆×C₂₃	—	2	2	no	—
530	SD₁₆×C₂₃	—	2	2	no	—
531	SD₁₆×C₂₃	—	2	2	no	—
532	SD₁₆×C₂₃	—	2	2	no	—
533	D₈×C₂₃	—	2	2	no	—
534	D₈×C₂₃	—	2	2	no	—
535	D₈×C₂₃	—	2	2	no	—
536	D₈×C₂₃	—	2	2	no	—
537	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
538	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
539	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
540	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
541	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
542	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
543	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
544	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
545	C₄⋊C₄×C₂₃	—	2	1	no	—
546	C₄⋊C₄×C₂₃	—	2	1	no	—
547	C₄⋊C₄×C₂₃	—	2	1	no	—
548	C₄⋊C₄×C₂₃	—	2	1	no	—
549	C₄⋊C₄×C₂₃	—	2	1	no	—
550	C₄⋊C₄×C₂₃	—	2	1	no	—
551	C₄⋊C₄×C₂₃	—	2	1	no	—
552	C₄⋊C₄×C₂₃	—	2	1	no	—
553	C₄⋊C₄×C₂₃	—	2	1	no	—
554	C₄⋊C₄×C₂₃	—	2	1	no	—
555	C₄⋊C₄×C₂₃	—	2	1	no	—
556	C₄⋊C₄×C₂₃	—	2	1	no	—
557	C₄⋊C₄×C₂₃	—	2	1	no	—
558	C₄⋊C₄×C₂₃	—	2	1	no	—
559	C₄⋊C₄×C₂₃	—	2	1	no	—
560	C₄⋊C₄×C₂₃	—	2	1	no	—
561	C₄⋊C₄×C₂₃	—	2	1	no	—
562	C₄⋊C₄×C₂₃	—	2	1	no	—
563	C₄⋊C₄×C₂₃	—	2	1	no	—
564	C₄⋊C₄×C₂₃	—	2	1	no	—
565	C₄⋊C₄×C₂₃	—	2	1	no	—
566	C₄⋊C₄×C₂₃	—	2	1	no	—
567	C₄⋊C₄×C₂₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
585	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
586	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
587	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
588	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
589	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
590	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
591	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
592	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
593	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
594	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
595	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
596	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
601	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
602	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
603	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
604	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
606	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
607	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
608	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
609	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
610	C₂²⋊C₄×C₂₃	—	2	1	no	—
611	C₂²⋊C₄×C₂₃	—	2	1	no	—
612	C₂²⋊C₄×C₂₃	—	2	1	no	—
613	C₂²⋊C₄×C₂₃	—	2	1	no	—
614	C₂²⋊C₄×C₂₃	—	2	1	no	—
615	C₂²⋊C₄×C₂₃	—	2	1	no	—
616	C₂²⋊C₄×C₂₃	—	2	1	no	—
617	C₂²⋊C₄×C₂₃	—	2	1	no	—
618	C₂²⋊C₄×C₂₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
643	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
644	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
645	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
646	C₄²×C₂₃	—	2	1	no	—
647	C₄²×C₂₃	—	2	1	no	—
648	C₄²×C₂₃	—	2	1	no	—
649	C₄²×C₂₃	—	2	1	no	—
650	C₄²×C₂₃	—	2	1	no	—
651	C₄²×C₂₃	—	2	1	no	—
652	C₄²×C₂₃	—	2	1	no	—
653	C₄²×C₂₃	—	2	1	no	—
654	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
655	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
656	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
657	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
658	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
659	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
660	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
661	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
662	#61855	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
663	C₂³×C₂₃	—	2	4	no	—
664	C₂³×C₂₃	—	2	1	no	—
665	C₂³×C₂₃	—	2	1	no	—
666	C₂³×C₂₃	—	2	1	no	—
667	C₂³×C₂₃	—	2	1	no	—
668	C₂³×C₂₃	—	8	1	no	—
669	C₂³×C₂₃	—	8	1	no	—
670	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
671	Q₈×C₂₃	—	2	1	no	—
672	Q₈×C₂₃	—	2	1	no	—
673	Q₈×C₂₃	—	2	1	no	—
674	Q₈×C₂₃	—	2	1	no	—
675	Q₈×C₂₃	—	4	1	no	—
676	Q₈×C₂₃	—	4	1	no	—
677	Q₈×C₂₃	—	4	1	no	—
678	Q₈×C₂₃	—	4	1	no	—
679	Q₈×C₂₃	—	4	2	no	—
680	Q₈×C₂₃	—	8	1	no	—
681	Q₈×C₂₃	—	8	1	no	—
682	Q₈×C₂₃	—	8	1	no	—
683	Q₈×C₂₃	—	8	1	no	—
684	Q₈×C₂₃	—	8	1	no	—
685	Q₈×C₂₃	—	8	1	no	—
686	Q₈×C₂₃	—	8	1	no	—
687	D₄×C₂₃	—	2	4	no	—
688	D₄×C₂₃	—	2	1	no	—
689	D₄×C₂₃	—	2	1	no	—
690	D₄×C₂₃	—	2	1	no	—
691	D₄×C₂₃	—	2	1	no	—
692	D₄×C₂₃	—	2	1	no	—
693	D₄×C₂₃	—	2	1	no	—
694	D₄×C₂₃	—	8	1	no	—
695	D₄×C₂₃	—	8	1	no	—
696	D₄×C₂₃	—	8	1	no	—
697	D₄×C₂₃	—	8	1	no	—
698	D₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
699	D₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
700	C₂×C₄×C₂₃	—	2	1	no	—
701	C₂×C₄×C₂₃	—	2	1	no	—
702	C₂×C₄×C₂₃	—	2	1	no	—
703	C₂×C₄×C₂₃	—	2	1	no	—
704	C₂×C₄×C₂₃	—	2	1	no	—
705	C₂×C₄×C₂₃	—	2	1	no	—
706	C₂×C₄×C₂₃	—	2	1	no	—
707	C₂×C₄×C₂₃	—	2	1	no	—
708	C₂×C₄×C₂₃	—	2	1	no	—
709	C₂×C₄×C₂₃	—	2	1	no	—
710	C₂×C₄×C₂₃	—	2	1	no	—
711	C₂×C₄×C₂₃	—	2	1	no	—
712	C₂×C₄×C₂₃	—	2	1	no	—
713	C₂×C₄×C₂₃	—	2	1	no	—
714	C₂×C₄×C₂₃	—	4	1	no	—
715	C₂×C₄×C₂₃	—	4	1	no	—
716	C₂×C₄×C₂₃	—	4	2	no	—
717	C₂×C₄×C₂₃	—	4	2	no	—
718	C₂×C₄×C₂₃	—	8	1	no	—
719	C₂×C₄×C₂₃	—	8	1	no	—
720	C₂×C₄×C₂₃	—	8	1	no	—
721	C₂×C₄×C₂₃	—	8	1	no	—
722	C₂×C₄×C₂₃	—	8	1	no	—
723	C₂×C₄×C₂₃	—	8	1	no	—
724	C₂×C₄×C₂₃	—	8	1	no	—
725	C₂×C₄×C₂₃	—	8	1	no	—
726	C₂×C₄×C₂₃	—	8	1	no	—
727	C₂×C₄×C₂₃	—	8	1	no	—
728	C₂×C₄×C₂₃	—	8	1	no	—
729	C₂×C₄×C₂₃	—	8	1	no	—
730	C₂×C₄×C₂₃	—	8	1	no	—
731	C₂×C₄×C₂₃	—	8	1	no	—
732	C₂×C₄×C₂₃	—	8	1	no	—
733	C₂×C₄×C₂₃	—	8	1	no	—
734	C₂×C₄×C₂₃	—	8	1	no	—
735	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
736	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
737	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
738	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
739	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
740	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
741	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
742	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
743	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
745	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
746	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
747	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
748	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
749	C₈×C₂₃	—	2	1	no	—
750	C₈×C₂₃	—	2	1	no	—
751	C₈×C₂₃	—	2	1	no	—
752	C₈×C₂₃	—	2	1	no	—
753	C₈×C₂₃	—	2	1	no	—
754	C₈×C₂₃	—	2	1	no	—
755	C₈×C₂₃	—	2	1	no	—
756	C₈×C₂₃	—	2	1	no	—
757	#3557	C₂×C₂₃	1	1	yes	characteristic, complemented
758	#3501	C₂×C₂₃	1	1	yes	characteristic, complemented
759	#3389	C₂×C₂₃	1	1	yes	characteristic, complemented
760	#3389	C₂×C₂₃	1	1	yes	characteristic, complemented
761	#3388	C₂×C₂₃	1	1	yes	characteristic, complemented
762	#3388	C₂×C₂₃	1	1	yes	characteristic, complemented
763	#3386	C₂×C₂₃	1	1	yes	characteristic, complemented
764	#3384	C₂×C₂₃	1	1	yes	characteristic, complemented
765	#3381	C₂×C₂₃	1	1	yes	characteristic, complemented
766	#3380	C₂×C₂₃	1	1	yes	characteristic, complemented
767	#3376	C₂×C₂₃	1	1	yes	characteristic, complemented
768	#3376	C₂×C₂₃	1	1	yes	characteristic, complemented
769	#3373	C₂×C₂₃	1	1	yes	characteristic, complemented
770	#3370	C₂×C₂₃	1	1	yes	characteristic, complemented
771	#3370	C₂×C₂₃	1	1	yes	characteristic, complemented
772	#3367	C₂×C₂₃	1	1	yes	characteristic, complemented
773	#3361	C₂×C₂₃	1	1	yes	characteristic, complemented
774	#3360	C₂×C₂₃	1	1	yes	characteristic, complemented
775	#3244	C₂×C₂₃	1	1	yes	characteristic, complemented
776	#3243	C₂×C₂₃	1	1	yes	characteristic, complemented
777	#3242	C₂×C₂₃	1	1	yes	characteristic, complemented
778	#3241	C₂×C₂₃	1	1	yes	characteristic, complemented
779	#3240	C₂×C₂₃	1	1	yes	characteristic, complemented
780	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
781	#3123	C₂×C₂₃	1	1	yes	characteristic, complemented
782	#3122	C₂×C₂₃	1	1	yes	characteristic
783	#3118	C₂×C₂₃	1	1	yes	characteristic, complemented
784	#3118	C₂×C₂₃	1	1	yes	characteristic, complemented
785	#3114	C₂×C₂₃	1	1	yes	characteristic, complemented
786	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
787	#2985	C₂×C₂₃	1	1	yes	characteristic, complemented
788	C₂²×C₂₃	—	2	1	no	—
789	C₂²×C₂₃	—	2	1	no	—
790	C₂²×C₂₃	—	2	1	no	—
791	C₂²×C₂₃	—	2	2	no	—
792	C₂²×C₂₃	—	2	2	no	—
793	C₂²×C₂₃	—	4	1	no	—
794	C₂²×C₂₃	—	4	1	no	—
795	C₂²×C₂₃	—	4	1	no	—
796	C₂²×C₂₃	—	4	1	no	—
797	C₂²×C₂₃	—	4	1	no	—
798	C₂²×C₂₃	—	4	1	no	—
799	C₂²×C₂₃	—	4	1	no	—
800	C₂²×C₂₃	—	4	1	no	—
801	C₂²×C₂₃	—	4	1	no	—
802	C₂²×C₂₃	—	4	1	no	—
803	C₂²×C₂₃	—	8	4	no	—
804	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
805	C₄×C₂₃	—	2	1	no	—
806	C₄×C₂₃	—	2	1	no	—
807	C₄×C₂₃	—	2	1	no	—
808	C₄×C₂₃	—	2	1	no	—
809	C₄×C₂₃	—	2	1	no	—
810	C₄×C₂₃	—	2	1	no	—
811	C₄×C₂₃	—	2	1	no	—
812	C₄×C₂₃	—	2	1	no	—
813	C₄×C₂₃	—	2	1	no	—
814	C₄×C₂₃	—	2	1	no	—
815	C₄×C₂₃	—	2	1	no	—
816	C₄×C₂₃	—	2	1	no	—
817	C₄×C₂₃	—	2	1	no	—
818	C₄×C₂₃	—	4	1	no	—
819	C₄×C₂₃	—	4	1	no	—
820	C₄×C₂₃	—	4	1	no	—
821	C₄×C₂₃	—	4	1	no	—
822	C₄×C₂₃	—	4	1	no	—
823	C₄×C₂₃	—	4	1	no	—
824	C₄×C₂₃	—	4	1	no	—
825	C₄×C₂₃	—	4	1	no	—
826	C₄×C₂₃	—	4	1	no	—
827	C₄×C₂₃	—	4	1	no	—
828	C₄×C₂₃	—	4	1	no	—
829	C₄×C₂₃	—	4	1	no	—
830	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
831	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
832	#563	—	2	1	no	—
833	#563	—	2	1	no	—
834	#559	C₂²×C₂₃	1	1	yes	characteristic, complemented
835	#559	C₂²×C₂₃	1	1	yes	characteristic, complemented
836	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
837	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
838	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
839	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
840	#554	—	2	1	no	—
841	#554	—	2	1	no	—
842	#554	—	2	1	no	—
843	#554	C₂²×C₂₃	1	1	yes	characteristic
844	#554	C₂²×C₂₃	1	1	yes	characteristic
845	#554	C₂²×C₂₃	1	1	yes	characteristic
846	#554	C₂²×C₂₃	1	1	yes	characteristic
847	#554	C₂²×C₂₃	1	1	yes	characteristic
848	#554	C₂²×C₂₃	1	1	yes	characteristic
849	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
850	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
851	#552	—	2	1	no	—
852	#552	—	2	1	no	—
853	D₄×Q₈	—	2	1	no	—
854	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
855	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
856	#544	C₂²×C₂₃	1	1	yes	characteristic
857	#544	C₂²×C₂₃	1	1	yes	characteristic
858	#543	—	2	1	no	—
859	#543	—	2	1	no	—
860	#542	—	2	1	no	—
861	#542	—	2	1	no	—
862	#542	C₂²×C₂₃	1	1	yes	characteristic
863	#542	C₂²×C₂₃	1	1	yes	characteristic
864	#541	C₂²×C₂₃	1	1	yes	characteristic
865	#540	C₂²×C₂₃	1	1	yes	characteristic
866	#539	—	2	1	no	—
867	#539	—	2	1	no	—
868	#533	C₂²×C₂₃	1	1	yes	characteristic
869	#533	C₂²×C₂₃	1	1	yes	characteristic
870	#529	C₂²×C₂₃	1	1	yes	characteristic
871	#529	C₂²×C₂₃	1	1	yes	characteristic
872	C₂×C₂²⋊Q₈	—	2	1	no	—
873	C₂×C₂²⋊Q₈	—	2	1	no	—
874	#518	C₂²×C₂₃	1	1	yes	characteristic
875	#518	C₂²×C₂₃	1	1	yes	characteristic
876	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
877	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
878	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
879	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
880	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
881	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
882	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
883	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
884	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
885	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
886	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
887	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
888	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
889	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
890	#490	C₂²×C₂₃	1	1	yes	characteristic, complemented
891	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
892	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
893	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
894	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
895	#488	C₂²×C₂₃	1	1	yes	characteristic, complemented
896	#488	C₂²×C₂₃	1	1	yes	characteristic, complemented
897	#488	C₂²×C₂₃	1	1	yes	characteristic, complemented
898	#488	C₂²×C₂₃	1	1	yes	characteristic, complemented
899	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
900	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
901	#485	C₂²×C₂₃	1	1	yes	characteristic
902	#485	C₂²×C₂₃	1	1	yes	characteristic
903	#485	C₂²×C₂₃	1	1	yes	characteristic
904	#485	C₂²×C₂₃	1	1	yes	characteristic
905	#484	C₂²×C₂₃	1	1	yes	characteristic
906	#483	C₂²×C₂₃	1	1	yes	characteristic
907	#482	C₂²×C₂₃	1	1	yes	characteristic
908	#482	C₂²×C₂₃	1	1	yes	characteristic
909	#482	C₂²×C₂₃	1	1	yes	characteristic
910	#482	C₂²×C₂₃	1	1	yes	characteristic
911	#481	C₂²×C₂₃	1	1	yes	characteristic
912	#480	C₂²×C₂₃	1	1	yes	characteristic
913	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
914	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
915	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
916	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
917	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
918	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
919	#478	C₂²×C₂₃	1	1	yes	characteristic
920	#478	C₂²×C₂₃	1	1	yes	characteristic
921	#478	C₂²×C₂₃	1	1	yes	characteristic
922	#478	C₂²×C₂₃	1	1	yes	characteristic
923	#478	C₂²×C₂₃	1	1	yes	characteristic
924	#478	C₂²×C₂₃	1	1	yes	characteristic
925	#478	C₂²×C₂₃	1	1	yes	characteristic
926	#478	C₂²×C₂₃	1	1	yes	characteristic
927	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
928	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
929	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
930	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
931	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
932	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
933	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
934	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
935	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
936	#476	C₂²×C₂₃	1	1	yes	characteristic
937	#476	C₂²×C₂₃	1	1	yes	characteristic
938	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
939	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
940	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
941	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
942	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
943	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
944	#474	C₂²×C₂₃	1	1	yes	characteristic
945	#474	C₂²×C₂₃	1	1	yes	characteristic
946	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
947	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
948	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
949	#463	C₂²×C₂₃	1	1	yes	characteristic
950	#463	C₂²×C₂₃	1	1	yes	characteristic
951	#463	C₂²×C₂₃	1	1	yes	characteristic
952	#463	C₂²×C₂₃	1	1	yes	characteristic
953	#463	C₂²×C₂₃	1	1	yes	characteristic
954	#463	C₂²×C₂₃	1	1	yes	characteristic
955	#463	C₂²×C₂₃	1	1	yes	characteristic
956	#463	C₂²×C₂₃	1	1	yes	characteristic
957	#461	C₂²×C₂₃	1	1	yes	characteristic
958	#461	C₂²×C₂₃	1	1	yes	characteristic
959	#459	C₂²×C₂₃	1	1	yes	characteristic
960	#459	C₂²×C₂₃	1	1	yes	characteristic
961	#450	C₂²×C₂₃	1	1	yes	characteristic
962	#450	C₂²×C₂₃	1	1	yes	characteristic
963	#447	C₂²×C₂₃	1	1	yes	characteristic
964	#447	C₂²×C₂₃	1	1	yes	characteristic
965	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
966	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
967	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
968	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
969	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
970	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
971	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
972	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
973	#442	C₂²×C₂₃	1	1	yes	characteristic
974	#442	C₂²×C₂₃	1	1	yes	characteristic
975	#442	C₂²×C₂₃	1	1	yes	characteristic
976	#442	C₂²×C₂₃	1	1	yes	characteristic
977	#442	C₂²×C₂₃	1	1	yes	characteristic
978	#442	C₂²×C₂₃	1	1	yes	characteristic
979	#440	C₂²×C₂₃	1	1	yes	characteristic
980	#440	C₂²×C₂₃	1	1	yes	characteristic
981	#440	C₂²×C₂₃	1	1	yes	characteristic
982	#440	C₂²×C₂₃	1	1	yes	characteristic
983	#440	C₂²×C₂₃	1	1	yes	characteristic
984	#440	C₂²×C₂₃	1	1	yes	characteristic
985	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
986	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
987	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
988	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
989	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
990	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
991	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
992	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
993	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
994	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
995	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
996	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
997	#433	C₂²×C₂₃	1	1	yes	characteristic
998	#433	C₂²×C₂₃	1	1	yes	characteristic
999	#433	C₂²×C₂₃	1	1	yes	characteristic
1000	#433	C₂²×C₂₃	1	1	yes	characteristic
1001	#432	C₂²×C₂₃	1	1	yes	characteristic
1002	#431	C₂²×C₂₃	1	1	yes	characteristic
1003	C₂×C₂₃	—	4	1	no	—
1004	C₂×C₂₃	—	4	2	no	—
1005	C₂×C₂₃	—	4	2	no	—
1006	C₂×C₂₃	—	8	1	no	—
1007	C₂×C₂₃	—	8	1	no	—
1008	C₂×C₂₃	#3486	1	1	yes	characteristic
1009	C₂×C₂₃	#3584	1	1	yes	characteristic
1010	C₂×C₂₃	#3585	1	1	yes	characteristic
1011	C₂²×Q₈	—	2	1	no	—
1012	C₂²×Q₈	—	2	1	no	—
1013	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
1014	C₂³×C₄	—	2	1	no	—
1015	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1016	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1017	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1018	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
1019	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1020	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1021	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1022	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
1023	C₄⋊Q₈	—	2	1	no	—
1024	C₄⋊Q₈	—	2	1	no	—
1025	C₄⋊Q₈	—	2	1	no	—
1026	C₄⋊Q₈	—	2	1	no	—
1027	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
1028	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
1029	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1030	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1031	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1032	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1033	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1034	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1035	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1036	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1037	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1038	#127	C₂³×C₂₃	1	1	yes	characteristic
1039	#126	—	2	1	no	—
1040	#126	—	2	1	no	—
1041	#126	—	2	1	no	—
1042	#126	—	2	1	no	—
1043	#126	—	2	1	no	—
1044	#126	—	2	1	no	—
1045	#126	—	2	1	no	—
1046	#126	—	2	1	no	—
1047	#126	—	2	1	no	—
1048	#126	—	2	1	no	—
1049	#125	—	2	1	no	—
1050	#125	—	2	1	no	—
1051	#125	—	2	1	no	—
1052	#125	—	2	1	no	—
1053	#125	—	2	1	no	—
1054	#125	—	2	1	no	—
1055	#125	—	2	1	no	—
1056	#125	—	2	1	no	—
1057	#125	D₄×C₂₃	1	1	yes	characteristic
1058	#125	D₄×C₂₃	1	1	yes	characteristic
1059	#125	C₂³×C₂₃	1	1	yes	characteristic
1060	#125	C₂³×C₂₃	1	1	yes	characteristic
1061	#125	C₂³×C₂₃	1	1	yes	characteristic
1062	#125	C₂³×C₂₃	1	1	yes	characteristic
1063	#125	C₂³×C₂₃	1	1	yes	characteristic
1064	#125	C₂³×C₂₃	1	1	yes	characteristic
1065	#125	C₂³×C₂₃	1	1	yes	characteristic
1066	#125	C₂³×C₂₃	1	1	yes	characteristic
1067	#125	C₂³×C₂₃	1	1	yes	characteristic
1068	#125	C₂³×C₂₃	1	1	yes	characteristic
1069	#124	—	2	1	no	—
1070	#124	—	2	1	no	—
1071	#124	—	2	1	no	—
1072	#124	—	2	1	no	—
1073	#124	C₂³×C₂₃	1	1	yes	characteristic
1074	#124	C₂³×C₂₃	1	1	yes	characteristic
1075	#124	C₂³×C₂₃	1	1	yes	characteristic
1076	#124	C₂³×C₂₃	1	1	yes	characteristic
1077	#123	—	2	1	no	—
1078	#123	—	2	1	no	—
1079	#123	—	2	1	no	—
1080	#123	—	2	1	no	—
1081	#123	—	2	1	no	—
1082	#123	—	2	1	no	—
1083	#123	—	2	1	no	—
1084	#123	—	2	1	no	—
1085	#123	—	2	1	no	—
1086	#123	—	2	1	no	—
1087	C₂²⋊Q₈	—	2	1	no	—
1088	C₂²⋊Q₈	—	2	1	no	—
1089	C₂²⋊Q₈	—	2	1	no	—
1090	C₂²⋊Q₈	—	2	1	no	—
1091	C₂²⋊Q₈	—	2	1	no	—
1092	C₂²⋊Q₈	—	2	1	no	—
1093	C₂²⋊Q₈	—	2	1	no	—
1094	C₂²⋊Q₈	—	2	1	no	—
1095	C₂²⋊Q₈	—	2	1	no	—
1096	C₂²⋊Q₈	—	2	1	no	—
1097	C₂²⋊Q₈	—	2	1	no	—
1098	C₂²⋊Q₈	—	2	1	no	—
1099	C₂²⋊Q₈	—	2	1	no	—
1100	C₂²⋊Q₈	—	2	1	no	—
1101	C₂²⋊Q₈	—	2	1	no	—
1102	C₂²⋊Q₈	—	2	1	no	—
1103	C₂²⋊Q₈	—	2	1	no	—
1104	C₂²⋊Q₈	—	2	1	no	—
1105	C₂²⋊Q₈	—	2	1	no	—
1106	C₂²⋊Q₈	—	2	1	no	—
1107	C₂²⋊Q₈	—	2	1	no	—
1108	C₂²⋊Q₈	—	2	1	no	—
1109	C₂²⋊Q₈	—	2	1	no	—
1110	C₂²⋊Q₈	—	2	1	no	—
1111	C₂²⋊Q₈	—	2	1	no	—
1112	C₂²⋊Q₈	—	2	1	no	—
1113	C₂²⋊Q₈	—	2	1	no	—
1114	C₂²⋊Q₈	—	2	1	no	—
1115	C₂²⋊Q₈	—	2	1	no	—
1116	C₂²⋊Q₈	—	2	1	no	—
1117	C₂²⋊Q₈	—	2	1	no	—
1118	C₂²⋊Q₈	—	2	1	no	—
1119	C₂²⋊Q₈	—	2	1	no	—
1120	C₂²⋊Q₈	—	2	1	no	—
1121	C₂²⋊Q₈	—	2	1	no	—
1122	C₂²⋊Q₈	—	2	1	no	—
1123	C₂²⋊Q₈	—	2	1	no	—
1124	C₂²⋊Q₈	—	2	1	no	—
1125	C₂²⋊Q₈	—	2	1	no	—
1126	C₂²⋊Q₈	—	2	1	no	—
1127	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
1128	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
1129	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
1130	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
1131	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1132	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
1133	#121	—	2	1	no	—
1134	#121	—	2	1	no	—
1135	#121	C₂³×C₂₃	1	1	yes	characteristic
1136	#121	C₂³×C₂₃	1	1	yes	characteristic
1137	C₄×Q₈	—	2	1	no	—
1138	C₄×Q₈	—	2	1	no	—
1139	C₄×Q₈	—	2	1	no	—
1140	C₄×Q₈	—	2	1	no	—
1141	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1142	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1143	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1144	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1145	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1146	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1147	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1148	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1149	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1150	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
1151	C₄×D₄	—	2	1	no	—
1152	C₄×D₄	—	2	1	no	—
1153	C₄×D₄	—	2	1	no	—
1154	C₄×D₄	—	2	1	no	—
1155	C₄×D₄	—	2	1	no	—
1156	C₄×D₄	—	2	1	no	—
1157	C₄×D₄	—	2	1	no	—
1158	C₄×D₄	—	2	1	no	—
1159	C₄×D₄	—	2	1	no	—
1160	C₄×D₄	—	2	1	no	—
1161	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1162	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1163	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1164	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1165	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1166	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1167	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1168	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1169	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1170	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1171	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1172	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1173	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1174	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1175	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1176	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1177	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1178	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
1179	#117	—	2	1	no	—
1180	#117	—	2	1	no	—
1181	#117	—	2	1	no	—
1182	#117	—	2	1	no	—
1183	#117	C₂³×C₂₃	1	1	yes	characteristic
1184	#117	C₂³×C₂₃	1	1	yes	characteristic
1185	#117	C₂³×C₂₃	1	1	yes	characteristic
1186	#117	C₂³×C₂₃	1	1	yes	characteristic
1187	C₂×C₄⋊C₄	—	2	1	no	—
1188	C₂×C₄⋊C₄	—	2	1	no	—
1189	C₂×C₄⋊C₄	—	2	1	no	—
1190	C₂×C₄⋊C₄	—	2	1	no	—
1191	C₂×C₄⋊C₄	—	2	1	no	—
1192	C₂×C₄⋊C₄	—	2	1	no	—
1193	C₂×C₄⋊C₄	—	2	1	no	—
1194	C₂×C₄⋊C₄	—	2	1	no	—
1195	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
1196	C₂×C₂²⋊C₄	—	2	1	no	—
1197	C₂×C₂²⋊C₄	—	2	1	no	—
1198	C₂×C₂²⋊C₄	—	2	1	no	—
1199	C₂×C₂²⋊C₄	—	2	1	no	—
1200	C₂×C₂²⋊C₄	—	2	1	no	—
1201	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
1202	#107	C₂³×C₂₃	1	1	yes	characteristic
1203	#107	C₂³×C₂₃	1	1	yes	characteristic
1204	#107	C₂³×C₂₃	1	1	yes	characteristic
1205	#107	C₂³×C₂₃	1	1	yes	characteristic
1206	#107	C₂³×C₂₃	1	1	yes	characteristic
1207	#107	C₂³×C₂₃	1	1	yes	characteristic
1208	#107	C₂³×C₂₃	1	1	yes	characteristic
1209	#107	C₂³×C₂₃	1	1	yes	characteristic
1210	#107	C₂³×C₂₃	1	1	yes	characteristic
1211	#107	C₂³×C₂₃	1	1	yes	characteristic
1212	#107	C₂³×C₂₃	1	1	yes	characteristic
1213	#107	C₂³×C₂₃	1	1	yes	characteristic
1214	#106	C₂³×C₂₃	1	1	yes	characteristic
1215	#106	C₂³×C₂₃	1	1	yes	characteristic
1216	#106	C₂³×C₂₃	1	1	yes	characteristic
1217	#106	C₂³×C₂₃	1	1	yes	characteristic
1218	#106	C₂³×C₂₃	1	1	yes	characteristic
1219	#106	C₂³×C₂₃	1	1	yes	characteristic
1220	#106	C₂³×C₂₃	1	1	yes	characteristic
1221	#106	C₂³×C₂₃	1	1	yes	characteristic
1222	#106	C₂³×C₂₃	1	1	yes	characteristic
1223	#106	C₂³×C₂₃	1	1	yes	characteristic
1224	#106	C₂³×C₂₃	1	1	yes	characteristic
1225	#106	C₂³×C₂₃	1	1	yes	characteristic
1226	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1227	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1228	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1229	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1230	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1231	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1232	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1233	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1234	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1235	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1236	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1237	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1238	#103	C₂³×C₂₃	1	1	yes	characteristic
1239	#103	C₂³×C₂₃	1	1	yes	characteristic
1240	#103	C₂³×C₂₃	1	1	yes	characteristic
1241	#103	C₂³×C₂₃	1	1	yes	characteristic
1242	#103	C₂³×C₂₃	1	1	yes	characteristic
1243	#103	C₂³×C₂₃	1	1	yes	characteristic
1244	#103	C₂³×C₂₃	1	1	yes	characteristic
1245	#103	C₂³×C₂₃	1	1	yes	characteristic
1246	#103	C₂³×C₂₃	1	1	yes	characteristic
1247	#103	C₂³×C₂₃	1	1	yes	characteristic
1248	#103	C₂³×C₂₃	1	1	yes	characteristic
1249	#103	C₂³×C₂₃	1	1	yes	characteristic
1250	#102	C₂³×C₂₃	1	1	yes	characteristic
1251	#102	C₂³×C₂₃	1	1	yes	characteristic
1252	#102	C₂³×C₂₃	1	1	yes	characteristic
1253	#102	C₂³×C₂₃	1	1	yes	characteristic
1254	#102	C₂³×C₂₃	1	1	yes	characteristic
1255	#102	C₂³×C₂₃	1	1	yes	characteristic
1256	#102	C₂³×C₂₃	1	1	yes	characteristic
1257	#102	C₂³×C₂₃	1	1	yes	characteristic
1258	#102	C₂³×C₂₃	1	1	yes	characteristic
1259	#102	C₂³×C₂₃	1	1	yes	characteristic
1260	#102	C₂³×C₂₃	1	1	yes	characteristic
1261	#102	C₂³×C₂₃	1	1	yes	characteristic
1262	#102	C₂³×C₂₃	1	1	yes	characteristic
1263	#102	C₂³×C₂₃	1	1	yes	characteristic
1264	#102	C₂³×C₂₃	1	1	yes	characteristic
1265	#102	C₂³×C₂₃	1	1	yes	characteristic
1266	#102	C₂³×C₂₃	1	1	yes	characteristic
1267	#102	C₂³×C₂₃	1	1	yes	characteristic
1268	#102	C₂³×C₂₃	1	1	yes	characteristic
1269	#102	C₂³×C₂₃	1	1	yes	characteristic
1270	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1271	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1272	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1273	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
1274	#97	C₂³×C₂₃	1	1	yes	characteristic
1275	#97	C₂³×C₂₃	1	1	yes	characteristic
1276	#97	C₂³×C₂₃	1	1	yes	characteristic
1277	#97	C₂³×C₂₃	1	1	yes	characteristic
1278	#97	C₂³×C₂₃	1	1	yes	characteristic
1279	#97	C₂³×C₂₃	1	1	yes	characteristic
1280	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1281	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1282	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1283	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1284	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1285	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
1286	C₂₃	#61855	1	1	yes	characteristic, direct product factor, Sylow
1287	C₂⁴	—	2	1	no	—
1288	C₂×Q₈	—	2	1	no	—
1289	C₂×Q₈	—	2	1	no	—
1290	C₂×Q₈	—	2	1	no	—
1291	C₂×Q₈	—	2	1	no	—
1292	C₂×Q₈	—	2	1	no	—
1293	C₂×Q₈	—	2	1	no	—
1294	C₂×Q₈	—	2	1	no	—
1295	C₂×Q₈	—	2	1	no	—
1296	C₂×Q₈	—	8	2	no	—
1297	C₂×Q₈	—	8	2	no	—
1298	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1299	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1300	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1301	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
1302	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1303	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
1304	C₂×D₄	—	2	2	no	—
1305	C₂×D₄	—	2	2	no	—
1306	C₂×D₄	—	2	1	no	—
1307	C₂×D₄	—	2	1	no	—
1308	C₂×D₄	—	2	1	no	—
1309	C₂×D₄	—	2	1	no	—
1310	C₂×D₄	—	2	1	no	—
1311	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1312	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1313	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1314	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1315	C₂²×C₄	—	2	1	no	—
1316	C₂²×C₄	—	2	1	no	—
1317	C₂²×C₄	—	2	1	no	—
1318	C₂²×C₄	—	2	1	no	—
1319	C₂²×C₄	—	2	1	no	—
1320	C₂²×C₄	—	2	1	no	—
1321	C₂²×C₄	—	2	1	no	—
1322	C₂²×C₄	—	2	1	no	—
1323	C₂²×C₄	—	2	1	no	—
1324	C₂²×C₄	—	2	1	no	—
1325	C₂²×C₄	—	2	1	no	—
1326	C₂²×C₄	—	2	1	no	—
1327	C₂²×C₄	—	2	1	no	—
1328	C₂²×C₄	—	2	1	no	—
1329	C₂²×C₄	—	2	1	no	—
1330	C₂²×C₄	—	2	1	no	—
1331	C₂²×C₄	—	2	1	no	—
1332	C₂²×C₄	—	2	1	no	—
1333	C₂²×C₄	—	2	1	no	—
1334	C₂²×C₄	—	8	2	no	—
1335	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1336	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1337	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1338	SD₁₆	—	2	2	no	—
1339	SD₁₆	—	2	2	no	—
1340	SD₁₆	—	2	2	no	—
1341	SD₁₆	—	2	2	no	—
1342	D₈	—	2	2	no	—
1343	D₈	—	2	2	no	—
1344	D₈	—	2	2	no	—
1345	D₈	—	2	2	no	—
1346	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1347	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1348	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1349	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1350	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1351	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1352	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1353	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1354	C₄⋊C₄	—	2	1	no	—
1355	C₄⋊C₄	—	2	1	no	—
1356	C₄⋊C₄	—	2	1	no	—
1357	C₄⋊C₄	—	2	1	no	—
1358	C₄⋊C₄	—	2	1	no	—
1359	C₄⋊C₄	—	2	1	no	—
1360	C₄⋊C₄	—	2	1	no	—
1361	C₄⋊C₄	—	2	1	no	—
1362	C₄⋊C₄	—	2	1	no	—
1363	C₄⋊C₄	—	2	1	no	—
1364	C₄⋊C₄	—	2	1	no	—
1365	C₄⋊C₄	—	2	1	no	—
1366	C₄⋊C₄	—	2	1	no	—
1367	C₄⋊C₄	—	2	1	no	—
1368	C₄⋊C₄	—	2	1	no	—
1369	C₄⋊C₄	—	2	1	no	—
1370	C₄⋊C₄	—	2	1	no	—
1371	C₄⋊C₄	—	2	1	no	—
1372	C₄⋊C₄	—	2	1	no	—
1373	C₄⋊C₄	—	2	1	no	—
1374	C₄⋊C₄	—	2	1	no	—
1375	C₄⋊C₄	—	2	1	no	—
1376	C₄⋊C₄	—	2	1	no	—
1377	C₄⋊C₄	—	2	1	no	—
1378	C₄⋊C₄	—	2	1	no	—
1379	C₄⋊C₄	—	2	1	no	—
1380	C₄⋊C₄	—	2	1	no	—
1381	C₄⋊C₄	—	2	1	no	—
1382	C₄⋊C₄	—	2	1	no	—
1383	C₄⋊C₄	—	2	1	no	—
1384	C₄⋊C₄	—	2	1	no	—
1385	C₄⋊C₄	—	2	1	no	—
1386	C₄⋊C₄	—	2	1	no	—
1387	C₄⋊C₄	—	2	1	no	—
1388	C₄⋊C₄	—	2	1	no	—
1389	C₄⋊C₄	—	2	1	no	—
1390	C₄⋊C₄	—	2	1	no	—
1391	C₄⋊C₄	—	2	1	no	—
1392	C₄⋊C₄	—	2	1	no	—
1393	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1394	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1395	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1396	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1397	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1398	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1399	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1400	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1401	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1402	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1403	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1404	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1405	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1406	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1407	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1408	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1409	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1410	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1411	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1412	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1413	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1414	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1415	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1416	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1417	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1418	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1419	C₂²⋊C₄	—	2	1	no	—
1420	C₂²⋊C₄	—	2	1	no	—
1421	C₂²⋊C₄	—	2	1	no	—
1422	C₂²⋊C₄	—	2	1	no	—
1423	C₂²⋊C₄	—	2	1	no	—
1424	C₂²⋊C₄	—	2	1	no	—
1425	C₂²⋊C₄	—	2	1	no	—
1426	C₂²⋊C₄	—	2	1	no	—
1427	C₂²⋊C₄	—	2	1	no	—
1428	C₂²⋊C₄	—	2	1	no	—
1429	C₂²⋊C₄	—	2	1	no	—
1430	C₂²⋊C₄	—	2	1	no	—
1431	C₂²⋊C₄	—	2	1	no	—
1432	C₂²⋊C₄	—	2	1	no	—
1433	C₂²⋊C₄	—	2	1	no	—
1434	C₂²⋊C₄	—	2	1	no	—
1435	C₂²⋊C₄	—	2	1	no	—
1436	C₂²⋊C₄	—	2	1	no	—
1437	C₂²⋊C₄	—	2	1	no	—
1438	C₂²⋊C₄	—	2	1	no	—
1439	C₂²⋊C₄	—	2	1	no	—
1440	C₂²⋊C₄	—	2	1	no	—
1441	C₂²⋊C₄	—	2	1	no	—
1442	C₂²⋊C₄	—	2	1	no	—
1443	C₂²⋊C₄	—	2	1	no	—
1444	C₂²⋊C₄	—	2	1	no	—
1445	C₂²⋊C₄	—	2	1	no	—
1446	C₂²⋊C₄	—	2	1	no	—
1447	C₂²⋊C₄	—	2	1	no	—
1448	C₂²⋊C₄	—	2	1	no	—
1449	C₂²⋊C₄	—	2	1	no	—
1450	C₂²⋊C₄	—	2	1	no	—
1451	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1452	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1453	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1454	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1455	C₄²	—	2	1	no	—
1456	C₄²	—	2	1	no	—
1457	C₄²	—	2	1	no	—
1458	C₄²	—	2	1	no	—
1459	C₄²	—	2	1	no	—
1460	C₄²	—	2	1	no	—
1461	C₄²	—	2	1	no	—
1462	C₄²	—	2	1	no	—
1463	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1464	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1465	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1466	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1467	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1468	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1469	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1470	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1471	C₂³	—	2	4	no	—
1472	C₂³	—	2	1	no	—
1473	C₂³	—	2	1	no	—
1474	C₂³	—	2	1	no	—
1475	C₂³	—	2	1	no	—
1476	C₂³	—	8	1	no	—
1477	C₂³	—	8	1	no	—
1478	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1479	Q₈	—	2	1	no	—
1480	Q₈	—	2	1	no	—
1481	Q₈	—	2	1	no	—
1482	Q₈	—	2	1	no	—
1483	Q₈	—	4	1	no	—
1484	Q₈	—	4	1	no	—
1485	Q₈	—	4	1	no	—
1486	Q₈	—	4	1	no	—
1487	Q₈	—	4	2	no	—
1488	Q₈	—	8	1	no	—
1489	Q₈	—	8	1	no	—
1490	Q₈	—	8	1	no	—
1491	Q₈	—	8	1	no	—
1492	Q₈	—	8	1	no	—
1493	Q₈	—	8	1	no	—
1494	Q₈	—	8	1	no	—
1495	D₄	—	2	4	no	—
1496	D₄	—	2	1	no	—
1497	D₄	—	2	1	no	—
1498	D₄	—	2	1	no	—
1499	D₄	—	2	1	no	—
1500	D₄	—	2	1	no	—
1501	D₄	—	2	1	no	—
1502	D₄	—	8	1	no	—
1503	D₄	—	8	1	no	—
1504	D₄	—	8	1	no	—
1505	D₄	—	8	1	no	—
1506	D₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1507	D₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1508	C₂×C₄	—	2	1	no	—
1509	C₂×C₄	—	2	1	no	—
1510	C₂×C₄	—	2	1	no	—
1511	C₂×C₄	—	2	1	no	—
1512	C₂×C₄	—	2	1	no	—
1513	C₂×C₄	—	2	1	no	—
1514	C₂×C₄	—	2	1	no	—
1515	C₂×C₄	—	2	1	no	—
1516	C₂×C₄	—	2	1	no	—
1517	C₂×C₄	—	2	1	no	—
1518	C₂×C₄	—	2	1	no	—
1519	C₂×C₄	—	2	1	no	—
1520	C₂×C₄	—	2	1	no	—
1521	C₂×C₄	—	2	1	no	—
1522	C₂×C₄	—	4	1	no	—
1523	C₂×C₄	—	4	1	no	—
1524	C₂×C₄	—	4	2	no	—
1525	C₂×C₄	—	4	2	no	—
1526	C₂×C₄	—	8	1	no	—
1527	C₂×C₄	—	8	1	no	—
1528	C₂×C₄	—	8	1	no	—
1529	C₂×C₄	—	8	1	no	—
1530	C₂×C₄	—	8	1	no	—
1531	C₂×C₄	—	8	1	no	—
1532	C₂×C₄	—	8	1	no	—
1533	C₂×C₄	—	8	1	no	—
1534	C₂×C₄	—	8	1	no	—
1535	C₂×C₄	—	8	1	no	—
1536	C₂×C₄	—	8	1	no	—
1537	C₂×C₄	—	8	1	no	—
1538	C₂×C₄	—	8	1	no	—
1539	C₂×C₄	—	8	1	no	—
1540	C₂×C₄	—	8	1	no	—
1541	C₂×C₄	—	8	1	no	—
1542	C₂×C₄	—	8	1	no	—
1543	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1544	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1545	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1546	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1547	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1548	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1549	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1550	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1551	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1552	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1553	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1554	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1555	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1556	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1557	C₈	—	2	1	no	—
1558	C₈	—	2	1	no	—
1559	C₈	—	2	1	no	—
1560	C₈	—	2	1	no	—
1561	C₈	—	2	1	no	—
1562	C₈	—	2	1	no	—
1563	C₈	—	2	1	no	—
1564	C₈	—	2	1	no	—
1565	C₂²	—	2	1	no	—
1566	C₂²	—	2	2	no	—
1567	C₂²	—	2	2	no	—
1568	C₂²	—	2	1	no	—
1569	C₂²	—	2	1	no	—
1570	C₂²	—	4	1	no	—
1571	C₂²	—	4	1	no	—
1572	C₂²	—	4	1	no	—
1573	C₂²	—	4	1	no	—
1574	C₂²	—	4	1	no	—
1575	C₂²	—	4	1	no	—
1576	C₂²	—	4	1	no	—
1577	C₂²	—	4	1	no	—
1578	C₂²	—	4	1	no	—
1579	C₂²	—	4	1	no	—
1580	C₂²	—	8	4	no	—
1581	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1582	C₄	—	2	1	no	—
1583	C₄	—	2	1	no	—
1584	C₄	—	2	1	no	—
1585	C₄	—	2	1	no	—
1586	C₄	—	2	1	no	—
1587	C₄	—	2	1	no	—
1588	C₄	—	2	1	no	—
1589	C₄	—	2	1	no	—
1590	C₄	—	2	1	no	—
1591	C₄	—	2	1	no	—
1592	C₄	—	2	1	no	—
1593	C₄	—	2	1	no	—
1594	C₄	—	2	1	no	—
1595	C₄	—	4	1	no	—
1596	C₄	—	4	1	no	—
1597	C₄	—	4	1	no	—
1598	C₄	—	4	1	no	—
1599	C₄	—	4	1	no	—
1600	C₄	—	4	1	no	—
1601	C₄	—	4	1	no	—
1602	C₄	—	4	1	no	—
1603	C₄	—	4	1	no	—
1604	C₄	—	4	1	no	—
1605	C₄	—	4	1	no	—
1606	C₄	—	4	1	no	—
1607	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1608	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1609	C₂	—	4	1	no	—
1610	C₂	—	4	2	no	—
1611	C₂	—	4	2	no	—
1612	C₂	—	8	1	no	—
1613	C₂	—	8	1	no	—
1614	C₂	C₂₃×#3486	1	1	yes	characteristic
1615	C₂	C₂₃×#3584	1	1	yes	characteristic
1616	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3122	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3557	C₂	semidirect
2. C₂₃×#3501	C₂	semidirect
3. C₂₃×#3389	C₂	semidirect
4. C₂₃×#3389	C₂	semidirect
5. C₂₃×#3388	C₂	semidirect
6. C₂₃×#3388	C₂	semidirect
7. C₂₃×#3386	C₂	semidirect
8. C₂₃×#3384	C₂	semidirect
9. C₂₃×#3381	C₂	semidirect
10. C₂₃×#3380	C₂	semidirect
11. C₂₃×#3376	C₂	semidirect
12. C₂₃×#3376	C₂	semidirect
13. C₂₃×#3373	C₂	semidirect
14. C₂₃×#3370	C₂	semidirect
15. C₂₃×#3370	C₂	semidirect
16. C₂₃×#3367	C₂	semidirect
17. C₂₃×#3361	C₂	semidirect
18. C₂₃×#3360	C₂	semidirect
19. C₂₃×#3244	C₂	semidirect
20. C₂₃×#3243	C₂	semidirect
21. C₂₃×#3242	C₂	semidirect
22. C₂₃×#3241	C₂	semidirect
23. C₂₃×#3240	C₂	semidirect
24. C₂₃×#3233	C₂	semidirect
25. C₂₃×#3123	C₂	semidirect
27. C₂₃×#3118	C₂	semidirect
28. C₂₃×#3118	C₂	semidirect
29. C₂₃×#3114	C₂	semidirect
30. C₂₃×#3105	C₂	semidirect
31. C₂₃×#2985	C₂	semidirect
34. C₂₃×#559	C₂²	semidirect
35. C₂₃×#559	C₂²	semidirect
36. C₂₃×#557	C₂²	semidirect
37. C₂₃×#557	C₂²	semidirect
38. C₂₃×#556	C₂²	semidirect
39. C₂₃×#556	C₂²	semidirect
49. C₂₃×#554	C₂²	semidirect
50. C₂₃×#554	C₂²	semidirect
77. C₂₃×#501	C₂²	semidirect
78. C₂₃×#501	C₂²	semidirect
79. C₂₃×#501	C₂²	semidirect
80. C₂₃×#501	C₂²	semidirect
81. C₂₃×#501	C₂²	semidirect
82. C₂₃×#501	C₂²	semidirect
83. C₂₃×#500	C₂²	semidirect
84. C₂₃×#499	C₂²	semidirect
85. C₂₃×#499	C₂²	semidirect
86. C₂₃×#499	C₂²	semidirect
87. C₂₃×#499	C₂²	semidirect
88. C₂₃×#498	C₂²	semidirect
89. C₂₃×#491	C₂²	semidirect
90. C₂₃×#490	C₂²	semidirect
91. C₂₃×#489	C₂²	semidirect
92. C₂₃×#489	C₂²	semidirect
93. C₂₃×#489	C₂²	semidirect
94. C₂₃×#489	C₂²	semidirect
95. C₂₃×#488	C₂²	semidirect
96. C₂₃×#488	C₂²	semidirect
97. C₂₃×#488	C₂²	semidirect
98. C₂₃×#488	C₂²	semidirect
99. C₂₃×#487	C₂²	semidirect
100. C₂₃×#486	C₂²	semidirect
113. C₂₃×#479	C₂²	semidirect
114. C₂₃×#479	C₂²	semidirect
115. C₂₃×#479	C₂²	semidirect
116. C₂₃×#479	C₂²	semidirect
117. C₂₃×#479	C₂²	semidirect
118. C₂₃×#479	C₂²	semidirect
127. C₂₃×#478	C₂²	semidirect
128. C₂₃×#478	C₂²	semidirect
129. C₂₃×#478	C₂²	semidirect
130. C₂₃×#478	C₂²	semidirect
131. C₂₃×#478	C₂²	semidirect
132. C₂₃×#478	C₂²	semidirect
133. C₂₃×#477	C₂²	semidirect
134. C₂₃×#477	C₂²	semidirect
135. C₂₃×#477	C₂²	semidirect
138. C₂₃×#476	C₂²	semidirect
139. C₂₃×#476	C₂²	semidirect
140. C₂₃×#476	C₂²	semidirect
141. C₂₃×#475	C₂²	semidirect
142. C₂₃×#475	C₂²	semidirect
143. C₂₃×#475	C₂²	semidirect
146. C₂₃×#474	C₂²	semidirect
147. C₂₃×#474	C₂²	semidirect
148. C₂₃×#474	C₂²	semidirect
165. C₂₃×#446	C₂²	semidirect
166. C₂₃×#446	C₂²	semidirect
167. C₂₃×#446	C₂²	semidirect
168. C₂₃×#446	C₂²	semidirect
169. C₂₃×#446	C₂²	semidirect
170. C₂₃×#446	C₂²	semidirect
171. C₈×Q₈×C₂₃	C₂²	semidirect
172. C₈×Q₈×C₂₃	C₂²	semidirect
662. #61855	C₂₃	direct (N × H)
757. #3557	C₂×C₂₃	semidirect
758. #3501	C₂×C₂₃	semidirect
759. #3389	C₂×C₂₃	semidirect
760. #3389	C₂×C₂₃	semidirect
761. #3388	C₂×C₂₃	semidirect
762. #3388	C₂×C₂₃	semidirect
763. #3386	C₂×C₂₃	semidirect
764. #3384	C₂×C₂₃	semidirect
765. #3381	C₂×C₂₃	semidirect
766. #3380	C₂×C₂₃	semidirect
767. #3376	C₂×C₂₃	semidirect
768. #3376	C₂×C₂₃	semidirect
769. #3373	C₂×C₂₃	semidirect
770. #3370	C₂×C₂₃	semidirect
771. #3370	C₂×C₂₃	semidirect
772. #3367	C₂×C₂₃	semidirect
773. #3361	C₂×C₂₃	semidirect
774. #3360	C₂×C₂₃	semidirect
775. #3244	C₂×C₂₃	semidirect
776. #3243	C₂×C₂₃	semidirect
777. #3242	C₂×C₂₃	semidirect
778. #3241	C₂×C₂₃	semidirect
779. #3240	C₂×C₂₃	semidirect
780. #3233	C₂×C₂₃	semidirect
781. #3123	C₂×C₂₃	semidirect
783. #3118	C₂×C₂₃	semidirect
784. #3118	C₂×C₂₃	semidirect
785. #3114	C₂×C₂₃	semidirect
786. #3105	C₂×C₂₃	semidirect
787. #2985	C₂×C₂₃	semidirect
834. #559	C₂²×C₂₃	semidirect
835. #559	C₂²×C₂₃	semidirect
836. #557	C₂²×C₂₃	semidirect
837. #557	C₂²×C₂₃	semidirect
838. #556	C₂²×C₂₃	semidirect
839. #556	C₂²×C₂₃	semidirect
849. #554	C₂²×C₂₃	semidirect
850. #554	C₂²×C₂₃	semidirect
877. #501	C₂²×C₂₃	semidirect
878. #501	C₂²×C₂₃	semidirect
879. #501	C₂²×C₂₃	semidirect
880. #501	C₂²×C₂₃	semidirect
881. #501	C₂²×C₂₃	semidirect
882. #501	C₂²×C₂₃	semidirect
883. #500	C₂²×C₂₃	semidirect
884. #499	C₂²×C₂₃	semidirect
885. #499	C₂²×C₂₃	semidirect
886. #499	C₂²×C₂₃	semidirect
887. #499	C₂²×C₂₃	semidirect
888. #498	C₂²×C₂₃	semidirect
889. #491	C₂²×C₂₃	semidirect
890. #490	C₂²×C₂₃	semidirect
891. #489	C₂²×C₂₃	semidirect
892. #489	C₂²×C₂₃	semidirect
893. #489	C₂²×C₂₃	semidirect
894. #489	C₂²×C₂₃	semidirect
895. #488	C₂²×C₂₃	semidirect
896. #488	C₂²×C₂₃	semidirect
897. #488	C₂²×C₂₃	semidirect
898. #488	C₂²×C₂₃	semidirect
899. #487	C₂²×C₂₃	semidirect
900. #486	C₂²×C₂₃	semidirect
913. #479	C₂²×C₂₃	semidirect
914. #479	C₂²×C₂₃	semidirect
915. #479	C₂²×C₂₃	semidirect
916. #479	C₂²×C₂₃	semidirect
917. #479	C₂²×C₂₃	semidirect
918. #479	C₂²×C₂₃	semidirect
927. #478	C₂²×C₂₃	semidirect
928. #478	C₂²×C₂₃	semidirect
929. #478	C₂²×C₂₃	semidirect
930. #478	C₂²×C₂₃	semidirect
931. #478	C₂²×C₂₃	semidirect
932. #478	C₂²×C₂₃	semidirect
933. #477	C₂²×C₂₃	semidirect
934. #477	C₂²×C₂₃	semidirect
935. #477	C₂²×C₂₃	semidirect
938. #476	C₂²×C₂₃	semidirect
939. #476	C₂²×C₂₃	semidirect
940. #476	C₂²×C₂₃	semidirect
941. #475	C₂²×C₂₃	semidirect
942. #475	C₂²×C₂₃	semidirect
943. #475	C₂²×C₂₃	semidirect
946. #474	C₂²×C₂₃	semidirect
947. #474	C₂²×C₂₃	semidirect
948. #474	C₂²×C₂₃	semidirect
965. #446	C₂²×C₂₃	semidirect
966. #446	C₂²×C₂₃	semidirect
967. #446	C₂²×C₂₃	semidirect
968. #446	C₂²×C₂₃	semidirect
969. #446	C₂²×C₂₃	semidirect
970. #446	C₂²×C₂₃	semidirect
971. C₈×Q₈	C₂²×C₂₃	semidirect
972. C₈×Q₈	C₂²×C₂₃	semidirect
1286. C₂₃	#61855	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×#3557	2
C₂₃×#3501	2
C₂₃×#3389	2
C₂₃×#3388	2
C₂₃×#3386	2
C₂₃×#3384	2
C₂₃×#3381	2
C₂₃×#3380	2
C₂₃×#3376	2
C₂₃×#3373	2
C₂₃×#3370	2
C₂₃×#3367	2
C₂₃×#3361	2
C₂₃×#3360	2
C₂₃×#3244	2
C₂₃×#3243	2
C₂₃×#3242	2
C₂₃×#3241	2
C₂₃×#3240	2
C₂₃×#3233	2
C₂₃×#3123	2
C₂₃×#3122	2
C₂₃×#3118	2
C₂₃×#3114	2
C₂₃×#3105	2
C₂₃×#2985	2
#61855	23

Subgroups — C23×#61855 #19209481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61855 #19209481