Subgroups — C₂₃×#62585 #19210211

Order 5888.

1736 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3514	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3377	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3371	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3313	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3312	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3311	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3181	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3181	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#559	C₂²	1	1	yes	characteristic
25	C₂₃×#557	—	2	1	no	—
26	C₂₃×#557	C₂²	1	2	yes	complemented
27	C₂₃×#556	—	2	1	no	—
28	C₂₃×#556	C₂²	1	1	yes	characteristic
29	C₂₃×#556	C₂²	1	2	yes	complemented
30	C₂₃×#555	—	2	1	no	—
31	C₂₃×#552	—	2	1	no	—
32	C₂₃×#552	—	2	1	no	—
33	C₂₃×#552	C₂²	1	2	yes	—
34	C₂₃×#552	C₂²	1	2	yes	complemented
35	C₂₃×#551	—	2	1	no	—
36	C₂₃×#551	—	2	1	no	—
37	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂₃×#548	C₂²	1	1	yes	characteristic
39	C₂₃×#548	C₂²	1	1	yes	characteristic
40	C₂₃×#546	—	2	1	no	—
41	C₂₃×#546	C₂²	1	1	yes	characteristic
42	C₂₃×#546	C₂²	1	1	yes	characteristic
43	D₄²×C₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#542	—	2	1	no	—
45	C₂₃×#541	—	2	1	no	—
46	C₂₃×#541	—	2	1	no	—
47	C₂₃×#538	—	2	1	no	—
48	C₂₃×#538	—	2	1	no	—
49	C₂₃×#536	—	2	1	no	—
50	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#532	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#529	C₂²	1	1	yes	characteristic
58	C₂₃×#529	C₂²	1	1	yes	characteristic
59	C₂₃×#529	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
62	C₂₃×#519	—	2	1	no	—
63	C₂₃×#518	—	2	1	no	—
64	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
65	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#501	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#497	C₂²	1	1	yes	characteristic
69	C₂₃×#497	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#497	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#491	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#491	C₂²	1	2	yes	complemented
73	C₂₃×#490	C₂²	1	2	yes	—
74	C₂₃×#489	C₂²	1	1	yes	characteristic
75	C₂₃×#489	C₂²	1	1	yes	characteristic
76	C₂₃×#489	C₂²	1	1	yes	characteristic
77	C₂₃×#489	C₂²	1	2	yes	—
78	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#489	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#489	C₂²	1	2	yes	complemented
85	C₂₃×#488	C₂²	1	2	yes	—
86	C₂₃×#488	C₂²	1	2	yes	complemented
87	C₂₃×#485	C₂²	1	2	yes	complemented
88	C₂₃×#485	C₂²	1	2	yes	complemented
89	C₂₃×#483	C₂²	1	2	yes	complemented
90	C₂₃×#482	C₂²	1	2	yes	—
91	C₂₃×#482	C₂²	1	2	yes	—
92	C₂₃×#480	C₂²	1	2	yes	—
93	C₂₃×#479	C₂²	1	2	yes	complemented
94	C₂₃×#479	C₂²	1	2	yes	complemented
95	C₂₃×#478	C₂²	1	2	yes	—
96	C₂₃×#478	C₂²	1	2	yes	complemented
97	C₂₃×#477	C₂²	1	2	yes	complemented
98	C₂₃×#476	C₂²	1	2	yes	complemented
99	C₂₃×#470	C₂²	1	2	yes	complemented
100	C₂₃×#468	C₂²	1	2	yes	—
101	C₂₃×#467	C₂²	1	2	yes	complemented
102	C₂₃×#467	C₂²	1	2	yes	complemented
103	C₂₃×#465	C₂²	1	2	yes	—
104	C₂₃×#465	C₂²	1	2	yes	—
105	C₂₃×#464	C₂²	1	2	yes	—
106	C₂₃×#464	C₂²	1	2	yes	—
107	C₂₃×#464	C₂²	1	2	yes	complemented
108	C₂₃×#464	C₂²	1	2	yes	complemented
109	C₂₃×#462	C₂²	1	2	yes	complemented
110	C₂₃×#460	C₂²	1	2	yes	—
111	C₂₃×#452	C₂²	1	2	yes	complemented
112	C₂₃×#452	C₂²	1	2	yes	complemented
113	C₂₃×#451	C₂²	1	2	yes	complemented
114	C₂₃×#451	C₂²	1	2	yes	complemented
115	C₂₃×#450	C₂²	1	2	yes	—
116	C₂₃×#450	C₂²	1	2	yes	—
117	C₂₃×#446	C₂²	1	2	yes	complemented
118	C₂₃×#441	C₂²	1	2	yes	complemented
119	C₂₃×#441	C₂²	1	2	yes	complemented
120	C₂₃×#440	C₂²	1	2	yes	—
121	C₂₃×#440	C₂²	1	2	yes	complemented
122	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
123	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	—
125	C₂₃×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
127	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
128	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
130	C₂₃×#419	C₂²	1	2	yes	complemented
131	C₂₃×#418	C₂²	1	2	yes	—
132	C₂₃×#416	C₂²	1	2	yes	complemented
133	C₂₃×#416	C₂²	1	2	yes	complemented
134	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
135	C₂×C₂₃×#102	C₂²	1	2	yes	—
136	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
138	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
139	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
140	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₂₃	—	2	1	no	—
143	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₂₃	—	2	1	no	—
146	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
156	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
157	C₂₃×C₄⋊Q₈	—	2	2	no	—
158	C₂₃×C₄⋊Q₈	—	2	1	no	—
159	C₂₃×C₄⋊Q₈	—	2	1	no	—
160	C₂₃×C₄⋊Q₈	—	2	1	no	—
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₂₃×#127	C₂³	1	1	yes	characteristic
168	C₂₃×#126	—	2	1	no	—
169	C₂₃×#126	—	2	1	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	—	2	2	no	—
172	C₂₃×#126	—	2	2	no	—
173	C₂₃×#126	—	2	2	no	—
174	C₂₃×#126	—	2	1	no	—
175	C₂₃×#126	—	2	1	no	—
176	C₂₃×#126	—	2	1	no	—
177	C₂₃×#125	—	2	2	no	—
178	C₂₃×#125	—	2	2	no	—
179	C₂₃×#125	—	2	2	no	—
180	C₂₃×#125	—	2	2	no	—
181	C₂₃×#125	—	2	1	no	—
182	C₂₃×#125	—	2	1	no	—
183	C₂₃×#125	—	2	1	no	—
184	C₂₃×#125	C₂³	1	2	yes	—
185	C₂₃×#125	C₂³	1	2	yes	—
186	C₂₃×#125	C₂³	1	1	yes	characteristic
187	C₂₃×#124	—	2	1	no	—
188	C₂₃×#124	—	2	2	no	—
189	C₂₃×#124	—	2	1	no	—
190	C₂₃×#124	—	2	1	no	—
191	C₂₃×#124	—	2	1	no	—
192	C₂₃×#124	—	2	1	no	—
193	C₂₃×#124	—	2	1	no	—
194	C₂₃×#124	—	2	1	no	—
195	C₂₃×#124	C₂³	1	1	yes	characteristic
196	C₂₃×#124	C₂³	1	1	yes	characteristic
197	C₂₃×#124	C₂³	1	1	yes	characteristic
198	C₂₃×#124	C₂³	1	1	yes	characteristic
199	C₂₃×#124	C₂³	1	1	yes	characteristic
200	C₂₃×#124	C₂³	1	1	yes	characteristic
201	C₂₃×#124	C₂³	1	1	yes	characteristic
202	C₂₃×#123	—	2	2	no	—
203	C₂₃×#123	—	2	2	no	—
204	C₂₃×#123	—	2	1	no	—
205	C₂₃×#123	—	2	1	no	—
206	C₂₃×#123	—	2	1	no	—
207	C₂₃×#123	—	2	1	no	—
208	C₂₃×#123	—	2	1	no	—
209	C₂₃×#123	—	2	1	no	—
210	C₂₃×#123	—	2	1	no	—
211	C₂₃×C₂²⋊Q₈	—	2	1	no	—
212	C₂₃×C₂²⋊Q₈	—	2	1	no	—
213	C₂₃×C₂²⋊Q₈	—	2	1	no	—
214	C₂₃×C₂²⋊Q₈	—	2	1	no	—
215	C₂₃×C₂²⋊Q₈	—	2	1	no	—
216	C₂₃×C₂²⋊Q₈	—	2	1	no	—
217	C₂₃×C₂²⋊Q₈	—	2	1	no	—
218	C₂₃×C₂²⋊Q₈	—	2	1	no	—
219	C₂₃×C₂²⋊Q₈	—	2	1	no	—
220	C₂₃×C₂²⋊Q₈	—	2	1	no	—
221	C₂₃×C₂²⋊Q₈	—	2	1	no	—
222	C₂₃×C₂²⋊Q₈	—	2	1	no	—
223	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
228	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
229	C₂₃×#121	—	2	1	no	—
230	C₂₃×#121	—	2	1	no	—
231	C₂₃×#121	—	2	1	no	—
232	C₂₃×#121	—	2	1	no	—
233	C₂₃×#121	—	2	1	no	—
234	C₂₃×#121	—	2	1	no	—
235	C₂₃×#121	—	2	1	no	—
236	C₂₃×#121	C₂³	1	1	yes	characteristic
237	C₂₃×#121	C₂³	1	1	yes	characteristic
238	C₂₃×#121	C₂³	1	1	yes	characteristic
239	C₂₃×#120	—	2	1	no	—
240	C₂₃×#120	—	2	1	no	—
241	C₂₃×#120	—	2	1	no	—
242	C₂₃×#120	—	2	1	no	—
243	C₄×Q₈×C₂₃	—	2	2	no	—
244	C₄×Q₈×C₂₃	—	2	2	no	—
245	C₄×Q₈×C₂₃	—	2	1	no	—
246	C₄×Q₈×C₂₃	—	2	1	no	—
247	C₄×Q₈×C₂₃	—	2	1	no	—
248	C₄×Q₈×C₂₃	—	2	1	no	—
249	C₄×Q₈×C₂₃	—	2	1	no	—
250	C₄×Q₈×C₂₃	—	2	1	no	—
251	C₄×Q₈×C₂₃	—	2	1	no	—
252	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
253	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
254	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
255	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
256	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
257	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
258	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
259	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₂₃	—	2	1	no	—
261	C₄×D₄×C₂₃	—	2	1	no	—
262	C₄×D₄×C₂₃	—	2	1	no	—
263	C₄×D₄×C₂₃	—	2	1	no	—
264	C₄×D₄×C₂₃	—	2	1	no	—
265	C₄×D₄×C₂₃	—	2	1	no	—
266	C₄×D₄×C₂₃	—	2	1	no	—
267	C₄×D₄×C₂₃	—	2	1	no	—
268	C₄×D₄×C₂₃	—	2	1	no	—
269	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
270	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
271	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
272	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
274	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
275	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
277	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
278	C₂₃×#117	—	2	1	no	—
279	C₂₃×#117	—	2	1	no	—
280	C₂₃×#117	—	2	1	no	—
281	C₂₃×#117	—	2	1	no	—
282	C₂₃×#117	—	2	2	no	—
283	C₂₃×#117	—	2	2	no	—
284	C₂₃×#117	—	2	1	no	—
285	C₂₃×#117	—	2	1	no	—
286	C₂₃×#117	—	2	1	no	—
287	C₂₃×#117	D₄	1	1	yes	characteristic
288	C₂₃×#117	D₄	1	1	yes	characteristic
289	C₂₃×#117	D₄	1	1	yes	characteristic
290	C₂₃×#117	C₂³	1	2	yes	—
291	C₂₃×#117	C₂³	1	2	yes	—
292	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
294	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
300	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
303	C₂₃×#107	C₂³	1	2	yes	—
304	C₂₃×#107	C₂³	1	2	yes	—
305	C₂₃×#107	C₂³	1	2	yes	—
306	C₂₃×#106	C₂³	1	2	yes	—
307	C₂₃×#106	C₂³	1	2	yes	—
308	C₂₃×#106	C₂³	1	2	yes	—
309	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
310	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
312	C₂₃×#103	C₂³	1	2	yes	—
313	C₂₃×#103	C₂³	1	2	yes	—
314	C₂₃×#103	C₂³	1	2	yes	—
315	C₂₃×#103	C₂³	1	2	yes	—
316	C₂₃×#103	C₂³	1	2	yes	—
317	C₂₃×#103	C₂³	1	2	yes	—
318	C₂₃×#103	C₂³	1	2	yes	—
319	C₂₃×#103	C₂³	1	2	yes	—
320	C₂₃×#103	C₂³	1	2	yes	—
321	C₂₃×#103	C₂³	1	2	yes	—
322	C₂₃×#103	C₂³	1	2	yes	—
323	C₂₃×#102	C₂³	1	2	yes	—
324	C₂₃×#102	C₂³	1	2	yes	—
325	C₂₃×#102	C₂³	1	2	yes	—
326	C₂₃×#102	C₂³	1	2	yes	—
327	C₂₃×#102	C₂³	1	2	yes	—
328	C₂₃×#102	C₂³	1	2	yes	—
329	C₂₃×#102	C₂³	1	2	yes	—
330	C₂₃×#102	C₂³	1	2	yes	—
331	C₂₃×#102	C₂³	1	2	yes	—
332	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
333	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
334	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₂₃×#97	C₂³	1	1	yes	characteristic
336	C₂₃×#97	C₂³	1	1	yes	characteristic
337	C₂₃×#97	C₂³	1	1	yes	characteristic
338	C₂₃×#97	C₂³	1	2	yes	—
339	C₂₃×#97	C₂³	1	2	yes	—
340	C₂₃×#97	C₂³	1	1	yes	characteristic
341	C₄×C₈×C₂₃	C₂³	1	2	yes	—
342	C₂⁴×C₂₃	—	2	1	no	—
343	C₂⁴×C₂₃	—	2	1	no	—
344	#41×C₂₃	—	4	2	no	—
345	#41×C₂₃	—	4	2	no	—
346	#41×C₂₃	—	4	2	no	—
347	C₂×Q₈×C₂₃	—	2	1	no	—
348	C₂×Q₈×C₂₃	—	2	1	no	—
349	C₂×Q₈×C₂₃	—	2	1	no	—
350	C₂×Q₈×C₂₃	—	2	2	no	—
351	C₂×Q₈×C₂₃	—	2	1	no	—
352	C₂×Q₈×C₂₃	—	2	1	no	—
353	C₂×Q₈×C₂₃	—	4	4	no	—
354	C₂×Q₈×C₂₃	—	4	2	no	—
355	C₂×Q₈×C₂₃	—	4	2	no	—
356	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
357	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
358	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
360	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
361	C₂×D₄×C₂₃	—	2	1	no	—
362	C₂×D₄×C₂₃	—	2	1	no	—
363	C₂×D₄×C₂₃	—	2	1	no	—
364	C₂×D₄×C₂₃	—	2	1	no	—
365	C₂×D₄×C₂₃	—	2	1	no	—
366	C₂×D₄×C₂₃	—	2	1	no	—
367	C₂×D₄×C₂₃	—	2	1	no	—
368	C₂×D₄×C₂₃	—	2	1	no	—
369	C₂×D₄×C₂₃	—	2	1	no	—
370	C₂×D₄×C₂₃	—	4	2	no	—
371	C₂×D₄×C₂₃	—	4	2	no	—
372	C₂×D₄×C₂₃	—	4	4	no	—
373	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
377	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₂₃	—	2	2	no	—
380	C₂²×C₄×C₂₃	—	2	1	no	—
381	C₂²×C₄×C₂₃	—	2	1	no	—
382	C₂²×C₄×C₂₃	—	2	1	no	—
383	C₂²×C₄×C₂₃	—	2	1	no	—
384	C₂²×C₄×C₂₃	—	2	1	no	—
385	C₂²×C₄×C₂₃	—	2	1	no	—
386	C₂²×C₄×C₂₃	—	2	1	no	—
387	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
396	Q₁₆×C₂₃	—	4	2	no	—
397	Q₁₆×C₂₃	—	4	2	no	—
398	Q₁₆×C₂₃	—	4	2	no	—
399	SD₁₆×C₂₃	—	4	2	no	—
400	SD₁₆×C₂₃	—	4	2	no	—
401	SD₁₆×C₂₃	—	4	2	no	—
402	M₁₆×C₂₃	—	4	2	no	—
403	C₂×C₈×C₂₃	—	4	2	no	—
404	C₂×C₈×C₂₃	—	4	2	no	—
405	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
406	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
407	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
408	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₂₃	—	2	1	no	—
410	C₄⋊C₄×C₂₃	—	2	1	no	—
411	C₄⋊C₄×C₂₃	—	2	2	no	—
412	C₄⋊C₄×C₂₃	—	2	2	no	—
413	C₄⋊C₄×C₂₃	—	2	1	no	—
414	C₄⋊C₄×C₂₃	—	2	1	no	—
415	C₄⋊C₄×C₂₃	—	2	1	no	—
416	C₄⋊C₄×C₂₃	—	2	1	no	—
417	C₄⋊C₄×C₂₃	—	2	1	no	—
418	C₄⋊C₄×C₂₃	—	2	1	no	—
419	C₄⋊C₄×C₂₃	—	2	1	no	—
420	C₄⋊C₄×C₂₃	—	2	2	no	—
421	C₄⋊C₄×C₂₃	—	2	2	no	—
422	C₄⋊C₄×C₂₃	—	2	2	no	—
423	C₄⋊C₄×C₂₃	—	2	2	no	—
424	C₄⋊C₄×C₂₃	—	2	1	no	—
425	C₄⋊C₄×C₂₃	—	2	1	no	—
426	C₄⋊C₄×C₂₃	—	2	1	no	—
427	C₄⋊C₄×C₂₃	—	2	2	no	—
428	C₄⋊C₄×C₂₃	—	2	2	no	—
429	C₄⋊C₄×C₂₃	—	2	2	no	—
430	C₄⋊C₄×C₂₃	—	2	1	no	—
431	C₄⋊C₄×C₂₃	—	2	1	no	—
432	C₄⋊C₄×C₂₃	—	2	1	no	—
433	C₄⋊C₄×C₂₃	—	2	2	no	—
434	C₄⋊C₄×C₂₃	—	2	2	no	—
435	C₄⋊C₄×C₂₃	—	2	2	no	—
436	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
443	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
444	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
447	C₂²⋊C₄×C₂₃	—	2	1	no	—
448	C₂²⋊C₄×C₂₃	—	2	1	no	—
449	C₂²⋊C₄×C₂₃	—	2	2	no	—
450	C₂²⋊C₄×C₂₃	—	2	2	no	—
451	C₂²⋊C₄×C₂₃	—	2	2	no	—
452	C₂²⋊C₄×C₂₃	—	2	2	no	—
453	C₂²⋊C₄×C₂₃	—	2	2	no	—
454	C₂²⋊C₄×C₂₃	—	2	1	no	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	1	no	—
457	C₂²⋊C₄×C₂₃	—	2	1	no	—
458	C₂²⋊C₄×C₂₃	—	2	1	no	—
459	C₂²⋊C₄×C₂₃	—	2	1	no	—
460	C₂²⋊C₄×C₂₃	—	2	1	no	—
461	C₂²⋊C₄×C₂₃	—	2	1	no	—
462	C₂²⋊C₄×C₂₃	—	2	1	no	—
463	C₂²⋊C₄×C₂₃	—	2	1	no	—
464	C₂²⋊C₄×C₂₃	—	2	1	no	—
465	C₂²⋊C₄×C₂₃	—	2	1	no	—
466	C₂²⋊C₄×C₂₃	—	2	1	no	—
467	C₂²⋊C₄×C₂₃	—	2	1	no	—
468	C₂²⋊C₄×C₂₃	—	2	1	no	—
469	C₂²⋊C₄×C₂₃	—	2	1	no	—
470	C₂²⋊C₄×C₂₃	—	2	1	no	—
471	C₂²⋊C₄×C₂₃	—	2	1	no	—
472	C₂²⋊C₄×C₂₃	—	2	1	no	—
473	C₂²⋊C₄×C₂₃	—	2	1	no	—
474	C₂²⋊C₄×C₂₃	—	2	1	no	—
475	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
481	C₄²×C₂₃	—	2	1	no	—
482	C₄²×C₂₃	—	2	1	no	—
483	C₄²×C₂₃	—	2	2	no	—
484	C₄²×C₂₃	—	2	2	no	—
485	C₄²×C₂₃	—	2	2	no	—
486	C₄²×C₂₃	—	2	2	no	—
487	C₄²×C₂₃	—	2	1	no	—
488	C₄²×C₂₃	—	2	2	no	—
489	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
490	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
496	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
497	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
498	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
499	#62585	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
500	C₂³×C₂₃	—	2	1	no	—
501	C₂³×C₂₃	—	2	1	no	—
502	C₂³×C₂₃	—	2	1	no	—
503	C₂³×C₂₃	—	4	2	no	—
504	C₂³×C₂₃	—	4	2	no	—
505	C₂³×C₂₃	—	8	1	no	—
506	C₂³×C₂₃	—	8	1	no	—
507	C₂³×C₂₃	—	8	1	no	—
508	C₂³×C₂₃	—	8	1	no	—
509	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
511	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
512	Q₈×C₂₃	—	2	2	no	—
513	Q₈×C₂₃	—	2	2	no	—
514	Q₈×C₂₃	—	2	2	no	—
515	Q₈×C₂₃	—	2	2	no	—
516	Q₈×C₂₃	—	2	2	no	—
517	Q₈×C₂₃	—	4	1	no	—
518	Q₈×C₂₃	—	4	2	no	—
519	Q₈×C₂₃	—	4	2	no	—
520	Q₈×C₂₃	—	4	2	no	—
521	Q₈×C₂₃	—	4	4	no	—
522	Q₈×C₂₃	—	8	1	no	—
523	Q₈×C₂₃	—	8	1	no	—
524	D₄×C₂₃	—	2	2	no	—
525	D₄×C₂₃	—	2	2	no	—
526	D₄×C₂₃	—	2	2	no	—
527	D₄×C₂₃	—	2	2	no	—
528	D₄×C₂₃	—	2	2	no	—
529	D₄×C₂₃	—	4	1	no	—
530	D₄×C₂₃	—	4	2	no	—
531	D₄×C₂₃	—	4	2	no	—
532	D₄×C₂₃	—	4	2	no	—
533	D₄×C₂₃	—	8	1	no	—
534	D₄×C₂₃	—	8	1	no	—
535	D₄×C₂₃	—	8	1	no	—
536	D₄×C₂₃	—	8	1	no	—
537	D₄×C₂₃	—	8	1	no	—
538	D₄×C₂₃	—	8	1	no	—
539	C₂×C₄×C₂₃	—	2	2	no	—
540	C₂×C₄×C₂₃	—	2	2	no	—
541	C₂×C₄×C₂₃	—	2	2	no	—
542	C₂×C₄×C₂₃	—	2	2	no	—
543	C₂×C₄×C₂₃	—	2	2	no	—
544	C₂×C₄×C₂₃	—	2	2	no	—
545	C₂×C₄×C₂₃	—	2	1	no	—
546	C₂×C₄×C₂₃	—	2	2	no	—
547	C₂×C₄×C₂₃	—	2	2	no	—
548	C₂×C₄×C₂₃	—	2	1	no	—
549	C₂×C₄×C₂₃	—	2	1	no	—
550	C₂×C₄×C₂₃	—	2	1	no	—
551	C₂×C₄×C₂₃	—	2	1	no	—
552	C₂×C₄×C₂₃	—	4	1	no	—
553	C₂×C₄×C₂₃	—	4	1	no	—
554	C₂×C₄×C₂₃	—	4	1	no	—
555	C₂×C₄×C₂₃	—	4	1	no	—
556	C₂×C₄×C₂₃	—	4	1	no	—
557	C₂×C₄×C₂₃	—	4	2	no	—
558	C₂×C₄×C₂₃	—	4	4	no	—
559	C₂×C₄×C₂₃	—	8	1	no	—
560	C₂×C₄×C₂₃	—	8	1	no	—
561	C₂×C₄×C₂₃	—	8	1	no	—
562	C₂×C₄×C₂₃	—	8	1	no	—
563	C₂×C₄×C₂₃	—	8	1	no	—
564	C₂×C₄×C₂₃	—	8	1	no	—
565	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
577	C₈×C₂₃	—	2	2	no	—
578	C₈×C₂₃	—	2	2	no	—
579	C₈×C₂₃	—	2	2	no	—
580	C₈×C₂₃	—	2	2	no	—
581	#3514	C₂×C₂₃	1	1	yes	characteristic
582	#3509	C₂×C₂₃	1	1	yes	characteristic, complemented
583	#3377	C₂×C₂₃	1	2	yes	complemented
584	#3371	C₂×C₂₃	1	2	yes	complemented
585	#3313	C₂×C₂₃	1	2	yes	complemented
586	#3312	C₂×C₂₃	1	2	yes	complemented
587	#3311	C₂×C₂₃	1	2	yes	complemented
588	#3310	C₂×C₂₃	1	2	yes	complemented
589	#3300	C₂×C₂₃	1	2	yes	complemented
590	#3296	C₂×C₂₃	1	2	yes	complemented
591	#3240	C₂×C₂₃	1	1	yes	characteristic, complemented
592	#3240	C₂×C₂₃	1	1	yes	characteristic, complemented
593	#3238	C₂×C₂₃	1	1	yes	characteristic, complemented
594	#3216	C₂×C₂₃	1	1	yes	characteristic, complemented
595	#3215	C₂×C₂₃	1	1	yes	characteristic, complemented
596	#3215	C₂×C₂₃	1	1	yes	characteristic, complemented
597	#3181	C₂×C₂₃	1	1	yes	characteristic, complemented
598	#3181	C₂×C₂₃	1	1	yes	characteristic, complemented
599	#3172	C₂×C₂₃	1	1	yes	characteristic, complemented
600	#3140	C₂×C₂₃	1	1	yes	characteristic, complemented
601	#3135	C₂×C₂₃	1	1	yes	characteristic, complemented
602	C₂×#489	C₂×C₂₃	1	1	yes	characteristic, complemented
603	#2970	C₂×C₂₃	1	1	yes	characteristic, complemented
604	C₂²×C₂₃	—	2	1	no	—
605	C₂²×C₂₃	—	2	1	no	—
606	C₂²×C₂₃	—	2	1	no	—
607	C₂²×C₂₃	—	2	1	no	—
608	C₂²×C₂₃	—	2	1	no	—
609	C₂²×C₂₃	—	2	1	no	—
610	C₂²×C₂₃	—	2	1	no	—
611	C₂²×C₂₃	—	2	1	no	—
612	C₂²×C₂₃	—	4	1	no	—
613	C₂²×C₂₃	—	4	1	no	—
614	C₂²×C₂₃	—	4	1	no	—
615	C₂²×C₂₃	—	4	1	no	—
616	C₂²×C₂₃	—	4	1	no	—
617	C₂²×C₂₃	—	4	1	no	—
618	C₂²×C₂₃	—	4	1	no	—
619	C₂²×C₂₃	—	4	1	no	—
620	C₂²×C₂₃	—	4	1	no	—
621	C₂²×C₂₃	—	16	2	no	—
622	C₂²×C₂₃	—	16	2	no	—
623	C₂²×C₂₃	#575	1	2	yes	—
624	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
625	C₄×C₂₃	—	2	1	no	—
626	C₄×C₂₃	—	2	1	no	—
627	C₄×C₂₃	—	2	1	no	—
628	C₄×C₂₃	—	2	1	no	—
629	C₄×C₂₃	—	2	1	no	—
630	C₄×C₂₃	—	2	1	no	—
631	C₄×C₂₃	—	2	1	no	—
632	C₄×C₂₃	—	2	1	no	—
633	C₄×C₂₃	—	2	1	no	—
634	C₄×C₂₃	—	2	1	no	—
635	C₄×C₂₃	—	2	1	no	—
636	C₄×C₂₃	—	4	1	no	—
637	C₄×C₂₃	—	4	2	no	—
638	C₄×C₂₃	—	4	1	no	—
639	C₄×C₂₃	—	4	1	no	—
640	C₄×C₂₃	—	4	1	no	—
641	C₄×C₂₃	—	4	2	no	—
642	C₄×C₂₃	—	4	1	no	—
643	C₄×C₂₃	—	4	2	no	—
644	C₄×C₂₃	—	4	2	no	—
645	C₄×C₂₃	#585	1	2	yes	—
646	#559	C₂²×C₂₃	1	1	yes	characteristic
647	#557	—	2	1	no	—
648	#557	C₂²×C₂₃	1	2	yes	complemented
649	#556	—	2	1	no	—
650	#556	C₂²×C₂₃	1	1	yes	characteristic
651	#556	C₂²×C₂₃	1	2	yes	complemented
652	#555	—	2	1	no	—
653	#552	—	2	1	no	—
654	#552	—	2	1	no	—
655	#552	C₂²×C₂₃	1	2	yes	—
656	#552	C₂²×C₂₃	1	2	yes	complemented
657	#551	—	2	1	no	—
658	#551	—	2	1	no	—
659	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
660	#548	C₂²×C₂₃	1	1	yes	characteristic
661	#548	C₂²×C₂₃	1	1	yes	characteristic
662	#546	—	2	1	no	—
663	#546	C₂²×C₂₃	1	1	yes	characteristic
664	#546	C₂²×C₂₃	1	1	yes	characteristic
665	D₄²	C₂²×C₂₃	1	1	yes	characteristic
666	#542	—	2	1	no	—
667	#541	—	2	1	no	—
668	#541	—	2	1	no	—
669	#538	—	2	1	no	—
670	#538	—	2	1	no	—
671	#536	—	2	1	no	—
672	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
675	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#532	C₂²×C₂₃	1	1	yes	characteristic
678	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
679	#529	C₂²×C₂₃	1	1	yes	characteristic
680	#529	C₂²×C₂₃	1	1	yes	characteristic
681	#529	C₂²×C₂₃	1	1	yes	characteristic
682	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
683	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
684	#519	—	2	1	no	—
685	#518	—	2	1	no	—
686	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
687	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
688	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
689	#501	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#497	C₂²×C₂₃	1	1	yes	characteristic
691	#497	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	#497	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	#491	C₂²×C₂₃	1	2	yes	complemented
694	#491	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	#490	C₂²×C₂₃	1	2	yes	—
696	#489	C₂²×C₂₃	1	2	yes	—
697	#489	C₂²×C₂₃	1	1	yes	characteristic
698	#489	C₂²×C₂₃	1	1	yes	characteristic
699	#489	C₂²×C₂₃	1	1	yes	characteristic
700	#489	C₂²×C₂₃	1	2	yes	complemented
701	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
702	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
703	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
704	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
705	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
706	#489	C₂²×C₂₃	1	1	yes	characteristic, complemented
707	#488	C₂²×C₂₃	1	2	yes	—
708	#488	C₂²×C₂₃	1	2	yes	complemented
709	#485	C₂²×C₂₃	1	2	yes	complemented
710	#485	C₂²×C₂₃	1	2	yes	complemented
711	#483	C₂²×C₂₃	1	2	yes	complemented
712	#482	C₂²×C₂₃	1	2	yes	—
713	#482	C₂²×C₂₃	1	2	yes	—
714	#480	C₂²×C₂₃	1	2	yes	—
715	#479	C₂²×C₂₃	1	2	yes	complemented
716	#479	C₂²×C₂₃	1	2	yes	complemented
717	#478	C₂²×C₂₃	1	2	yes	—
718	#478	C₂²×C₂₃	1	2	yes	complemented
719	#477	C₂²×C₂₃	1	2	yes	complemented
720	#476	C₂²×C₂₃	1	2	yes	complemented
721	#470	C₂²×C₂₃	1	2	yes	complemented
722	#468	C₂²×C₂₃	1	2	yes	—
723	#467	C₂²×C₂₃	1	2	yes	complemented
724	#467	C₂²×C₂₃	1	2	yes	complemented
725	#465	C₂²×C₂₃	1	2	yes	—
726	#465	C₂²×C₂₃	1	2	yes	—
727	#464	C₂²×C₂₃	1	2	yes	—
728	#464	C₂²×C₂₃	1	2	yes	—
729	#464	C₂²×C₂₃	1	2	yes	complemented
730	#464	C₂²×C₂₃	1	2	yes	complemented
731	#462	C₂²×C₂₃	1	2	yes	complemented
732	#460	C₂²×C₂₃	1	2	yes	—
733	#452	C₂²×C₂₃	1	2	yes	complemented
734	#452	C₂²×C₂₃	1	2	yes	complemented
735	#451	C₂²×C₂₃	1	2	yes	complemented
736	#451	C₂²×C₂₃	1	2	yes	complemented
737	#450	C₂²×C₂₃	1	2	yes	—
738	#450	C₂²×C₂₃	1	2	yes	—
739	#446	C₂²×C₂₃	1	2	yes	complemented
740	#441	C₂²×C₂₃	1	2	yes	complemented
741	#441	C₂²×C₂₃	1	2	yes	complemented
742	#440	C₂²×C₂₃	1	2	yes	—
743	#440	C₂²×C₂₃	1	2	yes	complemented
744	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
745	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
746	#435	C₂²×C₂₃	1	2	yes	—
747	#435	C₂²×C₂₃	1	2	yes	complemented
748	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
749	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
750	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
751	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
752	#419	C₂²×C₂₃	1	2	yes	complemented
753	#418	C₂²×C₂₃	1	2	yes	—
754	#416	C₂²×C₂₃	1	2	yes	complemented
755	#416	C₂²×C₂₃	1	2	yes	complemented
756	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
757	C₂×#102	C₂²×C₂₃	1	2	yes	—
758	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
759	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
760	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
761	C₂×C₂₃	—	2	2	no	—
762	C₂×C₂₃	—	4	1	no	—
763	C₂×C₂₃	—	4	1	no	—
764	C₂×C₂₃	—	8	1	no	—
765	C₂×C₂₃	—	8	1	no	—
766	C₂×C₂₃	—	8	1	no	—
767	C₂×C₂₃	#3500	1	1	yes	characteristic
768	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
769	C₂×C₂₃	#3586	1	1	yes	characteristic
770	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
771	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
772	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
773	C₂²×Q₈	—	2	1	no	—
774	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
775	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
776	C₂²×D₄	—	2	1	no	—
777	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
778	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
779	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
780	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
781	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
782	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
783	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
784	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
785	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
786	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
787	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
788	C₄⋊Q₈	—	2	2	no	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	—	2	1	no	—
792	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
793	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
795	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
797	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
798	#127	C₂³×C₂₃	1	1	yes	characteristic
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	2	no	—
802	#126	—	2	2	no	—
803	#126	—	2	2	no	—
804	#126	—	2	2	no	—
805	#126	—	2	1	no	—
806	#126	—	2	1	no	—
807	#126	—	2	1	no	—
808	#125	—	2	2	no	—
809	#125	—	2	2	no	—
810	#125	—	2	2	no	—
811	#125	—	2	2	no	—
812	#125	—	2	1	no	—
813	#125	—	2	1	no	—
814	#125	—	2	1	no	—
815	#125	C₂³×C₂₃	1	1	yes	characteristic
816	#125	C₂³×C₂₃	1	2	yes	—
817	#125	C₂³×C₂₃	1	2	yes	—
818	#124	—	2	1	no	—
819	#124	—	2	2	no	—
820	#124	—	2	1	no	—
821	#124	—	2	1	no	—
822	#124	—	2	1	no	—
823	#124	—	2	1	no	—
824	#124	—	2	1	no	—
825	#124	—	2	1	no	—
826	#124	C₂³×C₂₃	1	1	yes	characteristic
827	#124	C₂³×C₂₃	1	1	yes	characteristic
828	#124	C₂³×C₂₃	1	1	yes	characteristic
829	#124	C₂³×C₂₃	1	1	yes	characteristic
830	#124	C₂³×C₂₃	1	1	yes	characteristic
831	#124	C₂³×C₂₃	1	1	yes	characteristic
832	#124	C₂³×C₂₃	1	1	yes	characteristic
833	#123	—	2	2	no	—
834	#123	—	2	2	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	1	no	—
839	#123	—	2	1	no	—
840	#123	—	2	1	no	—
841	#123	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
855	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
856	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
858	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
859	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	1	no	—
864	#121	—	2	1	no	—
865	#121	—	2	1	no	—
866	#121	—	2	1	no	—
867	#121	C₂³×C₂₃	1	1	yes	characteristic
868	#121	C₂³×C₂₃	1	1	yes	characteristic
869	#121	C₂³×C₂₃	1	1	yes	characteristic
870	#120	—	2	1	no	—
871	#120	—	2	1	no	—
872	#120	—	2	1	no	—
873	#120	—	2	1	no	—
874	C₄×Q₈	—	2	2	no	—
875	C₄×Q₈	—	2	2	no	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	—	2	1	no	—
878	C₄×Q₈	—	2	1	no	—
879	C₄×Q₈	—	2	1	no	—
880	C₄×Q₈	—	2	1	no	—
881	C₄×Q₈	—	2	1	no	—
882	C₄×Q₈	—	2	1	no	—
883	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
884	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
885	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
886	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
887	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
888	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
889	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
890	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
901	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
902	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
903	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
904	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
905	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
908	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
909	#117	—	2	1	no	—
910	#117	—	2	1	no	—
911	#117	—	2	1	no	—
912	#117	—	2	1	no	—
913	#117	—	2	2	no	—
914	#117	—	2	2	no	—
915	#117	—	2	1	no	—
916	#117	—	2	1	no	—
917	#117	—	2	1	no	—
918	#117	D₄×C₂₃	1	1	yes	characteristic
919	#117	D₄×C₂₃	1	1	yes	characteristic
920	#117	D₄×C₂₃	1	1	yes	characteristic
921	#117	C₂³×C₂₃	1	2	yes	—
922	#117	C₂³×C₂₃	1	2	yes	—
923	C₂×C₄⋊C₄	—	2	1	no	—
924	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
925	C₂×C₂²⋊C₄	—	2	1	no	—
926	C₂×C₂²⋊C₄	—	2	1	no	—
927	C₂×C₂²⋊C₄	—	2	1	no	—
928	C₂×C₂²⋊C₄	—	2	1	no	—
929	C₂×C₂²⋊C₄	—	2	1	no	—
930	C₂×C₂²⋊C₄	—	2	1	no	—
931	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
932	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
933	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
934	#107	C₂³×C₂₃	1	2	yes	—
935	#107	C₂³×C₂₃	1	2	yes	—
936	#107	C₂³×C₂₃	1	2	yes	—
937	#106	C₂³×C₂₃	1	2	yes	—
938	#106	C₂³×C₂₃	1	2	yes	—
939	#106	C₂³×C₂₃	1	2	yes	—
940	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
941	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
942	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
943	#103	C₂³×C₂₃	1	2	yes	—
944	#103	C₂³×C₂₃	1	2	yes	—
945	#103	C₂³×C₂₃	1	2	yes	—
946	#103	C₂³×C₂₃	1	2	yes	—
947	#103	C₂³×C₂₃	1	2	yes	—
948	#103	C₂³×C₂₃	1	2	yes	—
949	#103	C₂³×C₂₃	1	2	yes	—
950	#103	C₂³×C₂₃	1	2	yes	—
951	#103	C₂³×C₂₃	1	2	yes	—
952	#103	C₂³×C₂₃	1	2	yes	—
953	#103	C₂³×C₂₃	1	2	yes	—
954	#102	C₂³×C₂₃	1	2	yes	—
955	#102	C₂³×C₂₃	1	2	yes	—
956	#102	C₂³×C₂₃	1	2	yes	—
957	#102	C₂³×C₂₃	1	2	yes	—
958	#102	C₂³×C₂₃	1	2	yes	—
959	#102	C₂³×C₂₃	1	2	yes	—
960	#102	C₂³×C₂₃	1	2	yes	—
961	#102	C₂³×C₂₃	1	2	yes	—
962	#102	C₂³×C₂₃	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
966	#97	C₂³×C₂₃	1	1	yes	characteristic
967	#97	C₂³×C₂₃	1	1	yes	characteristic
968	#97	C₂³×C₂₃	1	1	yes	characteristic
969	#97	C₂³×C₂₃	1	2	yes	—
970	#97	C₂³×C₂₃	1	2	yes	—
971	#97	C₂³×C₂₃	1	1	yes	characteristic
972	C₄×C₈	C₂³×C₂₃	1	2	yes	—
973	C₂₃	#62585	1	1	yes	characteristic, direct product factor, Sylow
974	C₂⁴	—	2	1	no	—
975	C₂⁴	—	2	1	no	—
976	#41	—	4	2	no	—
977	#41	—	4	2	no	—
978	#41	—	4	2	no	—
979	C₂×Q₈	—	2	1	no	—
980	C₂×Q₈	—	2	1	no	—
981	C₂×Q₈	—	2	1	no	—
982	C₂×Q₈	—	2	2	no	—
983	C₂×Q₈	—	2	1	no	—
984	C₂×Q₈	—	2	1	no	—
985	C₂×Q₈	—	4	4	no	—
986	C₂×Q₈	—	4	2	no	—
987	C₂×Q₈	—	4	2	no	—
988	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
989	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
990	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
991	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
992	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	4	2	no	—
1003	C₂×D₄	—	4	2	no	—
1004	C₂×D₄	—	4	4	no	—
1005	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1006	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1007	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1008	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1009	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1010	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	2	1	no	—
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1022	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1024	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1027	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1028	Q₁₆	—	4	2	no	—
1029	Q₁₆	—	4	2	no	—
1030	Q₁₆	—	4	2	no	—
1031	SD₁₆	—	4	2	no	—
1032	SD₁₆	—	4	2	no	—
1033	SD₁₆	—	4	2	no	—
1034	M₁₆	—	4	2	no	—
1035	C₂×C₈	—	4	2	no	—
1036	C₂×C₈	—	4	2	no	—
1037	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1038	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1039	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1040	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1069	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1070	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1071	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1072	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1073	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1074	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1075	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1076	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1077	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1078	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1108	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1109	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1110	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1111	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1112	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	2	no	—
1116	C₄²	—	2	2	no	—
1117	C₄²	—	2	2	no	—
1118	C₄²	—	2	2	no	—
1119	C₄²	—	2	1	no	—
1120	C₄²	—	2	2	no	—
1121	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1122	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1123	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1124	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1125	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1126	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1127	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1128	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1129	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1130	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1131	C₂³	—	2	1	no	—
1132	C₂³	—	2	1	no	—
1133	C₂³	—	2	1	no	—
1134	C₂³	—	4	2	no	—
1135	C₂³	—	4	2	no	—
1136	C₂³	—	8	1	no	—
1137	C₂³	—	8	1	no	—
1138	C₂³	—	8	1	no	—
1139	C₂³	—	8	1	no	—
1140	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1141	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1142	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1143	Q₈	—	2	2	no	—
1144	Q₈	—	2	2	no	—
1145	Q₈	—	2	2	no	—
1146	Q₈	—	2	2	no	—
1147	Q₈	—	2	2	no	—
1148	Q₈	—	4	1	no	—
1149	Q₈	—	4	2	no	—
1150	Q₈	—	4	2	no	—
1151	Q₈	—	4	4	no	—
1152	Q₈	—	4	2	no	—
1153	Q₈	—	8	1	no	—
1154	Q₈	—	8	1	no	—
1155	D₄	—	2	2	no	—
1156	D₄	—	2	2	no	—
1157	D₄	—	2	2	no	—
1158	D₄	—	2	2	no	—
1159	D₄	—	2	2	no	—
1160	D₄	—	4	1	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	4	2	no	—
1164	D₄	—	8	1	no	—
1165	D₄	—	8	1	no	—
1166	D₄	—	8	1	no	—
1167	D₄	—	8	1	no	—
1168	D₄	—	8	1	no	—
1169	D₄	—	8	1	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	4	no	—
1190	C₂×C₄	—	8	1	no	—
1191	C₂×C₄	—	8	1	no	—
1192	C₂×C₄	—	8	1	no	—
1193	C₂×C₄	—	8	1	no	—
1194	C₂×C₄	—	8	1	no	—
1195	C₂×C₄	—	8	1	no	—
1196	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1197	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1198	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1199	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1200	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1201	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1202	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1203	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1204	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1207	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1208	C₈	—	2	2	no	—
1209	C₈	—	2	2	no	—
1210	C₈	—	2	2	no	—
1211	C₈	—	2	2	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	16	2	no	—
1230	C₂²	—	16	2	no	—
1231	C₂²	C₂₃×#575	1	2	yes	—
1232	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	2	1	no	—
1243	C₄	—	2	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	2	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	2	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	C₂₃×#585	1	2	yes	—
1254	C₂	—	2	2	no	—
1255	C₂	—	4	1	no	—
1256	C₂	—	4	1	no	—
1257	C₂	—	8	1	no	—
1258	C₂	—	8	1	no	—
1259	C₂	—	8	1	no	—
1260	C₂	C₂₃×#3500	1	1	yes	characteristic
1261	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1262	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×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3509	C₂	semidirect
3. C₂₃×#3377	C₂	semidirect
4. C₂₃×#3371	C₂	semidirect
5. C₂₃×#3313	C₂	semidirect
6. C₂₃×#3312	C₂	semidirect
7. C₂₃×#3311	C₂	semidirect
8. C₂₃×#3310	C₂	semidirect
9. C₂₃×#3300	C₂	semidirect
10. C₂₃×#3296	C₂	semidirect
11. C₂₃×#3240	C₂	semidirect
12. C₂₃×#3240	C₂	semidirect
13. C₂₃×#3238	C₂	semidirect
14. C₂₃×#3216	C₂	semidirect
15. C₂₃×#3215	C₂	semidirect
16. C₂₃×#3215	C₂	semidirect
17. C₂₃×#3181	C₂	semidirect
18. C₂₃×#3181	C₂	semidirect
19. C₂₃×#3172	C₂	semidirect
20. C₂₃×#3140	C₂	semidirect
21. C₂₃×#3135	C₂	semidirect
22. C₂×C₂₃×#489	C₂	semidirect
23. C₂₃×#2970	C₂	semidirect
26. C₂₃×#557	C₂²	semidirect
29. C₂₃×#556	C₂²	semidirect
34. C₂₃×#552	C₂²	semidirect
50. C₂₃×#533	C₂²	semidirect
51. C₂₃×#533	C₂²	semidirect
52. C₂₃×#533	C₂²	semidirect
53. C₂₃×#533	C₂²	semidirect
54. C₂₃×#533	C₂²	semidirect
56. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
65. C₂₃×#501	C₂²	semidirect
66. C₂₃×#501	C₂²	semidirect
67. C₂₃×#501	C₂²	semidirect
69. C₂₃×#497	C₂²	semidirect
70. C₂₃×#497	C₂²	semidirect
71. C₂₃×#491	C₂²	semidirect
72. C₂₃×#491	C₂²	semidirect
78. C₂₃×#489	C₂²	semidirect
79. C₂₃×#489	C₂²	semidirect
80. C₂₃×#489	C₂²	semidirect
81. C₂₃×#489	C₂²	semidirect
82. C₂₃×#489	C₂²	semidirect
83. C₂₃×#489	C₂²	semidirect
84. C₂₃×#489	C₂²	semidirect
86. C₂₃×#488	C₂²	semidirect
87. C₂₃×#485	C₂²	semidirect
88. C₂₃×#485	C₂²	semidirect
89. C₂₃×#483	C₂²	semidirect
93. C₂₃×#479	C₂²	semidirect
94. C₂₃×#479	C₂²	semidirect
96. C₂₃×#478	C₂²	semidirect
97. C₂₃×#477	C₂²	semidirect
98. C₂₃×#476	C₂²	semidirect
99. C₂₃×#470	C₂²	semidirect
101. C₂₃×#467	C₂²	semidirect
102. C₂₃×#467	C₂²	semidirect
107. C₂₃×#464	C₂²	semidirect
108. C₂₃×#464	C₂²	semidirect
109. C₂₃×#462	C₂²	semidirect
111. C₂₃×#452	C₂²	semidirect
112. C₂₃×#452	C₂²	semidirect
113. C₂₃×#451	C₂²	semidirect
114. C₂₃×#451	C₂²	semidirect
117. C₂₃×#446	C₂²	semidirect
118. C₂₃×#441	C₂²	semidirect
119. C₂₃×#441	C₂²	semidirect
121. C₂₃×#440	C₂²	semidirect
122. C₄×Q₁₆×C₂₃	C₂²	semidirect
123. C₄×SD₁₆×C₂₃	C₂²	semidirect
125. C₂₃×#435	C₂²	semidirect
126. C₈×D₄×C₂₃	C₂²	semidirect
127. C₂₃×#432	C₂²	semidirect
128. C₂₃×#432	C₂²	semidirect
129. C₂₃×#432	C₂²	semidirect
130. C₂₃×#419	C₂²	semidirect
132. C₂₃×#416	C₂²	semidirect
133. C₂₃×#416	C₂²	semidirect
134. C₂×C₂₃×#103	C₂²	semidirect
136. C₄×M₁₆×C₂₃	C₂²	semidirect
137. C₂×C₂₃×#97	C₂²	semidirect
138. C₂×C₂₃×#97	C₂²	semidirect
499. #62585	C₂₃	direct (N × H)
582. #3509	C₂×C₂₃	semidirect
583. #3377	C₂×C₂₃	semidirect
584. #3371	C₂×C₂₃	semidirect
585. #3313	C₂×C₂₃	semidirect
586. #3312	C₂×C₂₃	semidirect
587. #3311	C₂×C₂₃	semidirect
588. #3310	C₂×C₂₃	semidirect
589. #3300	C₂×C₂₃	semidirect
590. #3296	C₂×C₂₃	semidirect
591. #3240	C₂×C₂₃	semidirect
592. #3240	C₂×C₂₃	semidirect
593. #3238	C₂×C₂₃	semidirect
594. #3216	C₂×C₂₃	semidirect
595. #3215	C₂×C₂₃	semidirect
596. #3215	C₂×C₂₃	semidirect
597. #3181	C₂×C₂₃	semidirect
598. #3181	C₂×C₂₃	semidirect
599. #3172	C₂×C₂₃	semidirect
600. #3140	C₂×C₂₃	semidirect
601. #3135	C₂×C₂₃	semidirect
602. C₂×#489	C₂×C₂₃	semidirect
603. #2970	C₂×C₂₃	semidirect
648. #557	C₂²×C₂₃	semidirect
651. #556	C₂²×C₂₃	semidirect
656. #552	C₂²×C₂₃	semidirect
672. #533	C₂²×C₂₃	semidirect
673. #533	C₂²×C₂₃	semidirect
674. #533	C₂²×C₂₃	semidirect
675. #533	C₂²×C₂₃	semidirect
676. #533	C₂²×C₂₃	semidirect
678. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
687. #501	C₂²×C₂₃	semidirect
688. #501	C₂²×C₂₃	semidirect
689. #501	C₂²×C₂₃	semidirect
691. #497	C₂²×C₂₃	semidirect
692. #497	C₂²×C₂₃	semidirect
693. #491	C₂²×C₂₃	semidirect
694. #491	C₂²×C₂₃	semidirect
700. #489	C₂²×C₂₃	semidirect
701. #489	C₂²×C₂₃	semidirect
702. #489	C₂²×C₂₃	semidirect
703. #489	C₂²×C₂₃	semidirect
704. #489	C₂²×C₂₃	semidirect
705. #489	C₂²×C₂₃	semidirect
706. #489	C₂²×C₂₃	semidirect
708. #488	C₂²×C₂₃	semidirect
709. #485	C₂²×C₂₃	semidirect
710. #485	C₂²×C₂₃	semidirect
711. #483	C₂²×C₂₃	semidirect
715. #479	C₂²×C₂₃	semidirect
716. #479	C₂²×C₂₃	semidirect
718. #478	C₂²×C₂₃	semidirect
719. #477	C₂²×C₂₃	semidirect
720. #476	C₂²×C₂₃	semidirect
721. #470	C₂²×C₂₃	semidirect
723. #467	C₂²×C₂₃	semidirect
724. #467	C₂²×C₂₃	semidirect
729. #464	C₂²×C₂₃	semidirect
730. #464	C₂²×C₂₃	semidirect
731. #462	C₂²×C₂₃	semidirect
733. #452	C₂²×C₂₃	semidirect
734. #452	C₂²×C₂₃	semidirect
735. #451	C₂²×C₂₃	semidirect
736. #451	C₂²×C₂₃	semidirect
739. #446	C₂²×C₂₃	semidirect
740. #441	C₂²×C₂₃	semidirect
741. #441	C₂²×C₂₃	semidirect
743. #440	C₂²×C₂₃	semidirect
744. C₄×Q₁₆	C₂²×C₂₃	semidirect
745. C₄×SD₁₆	C₂²×C₂₃	semidirect
747. #435	C₂²×C₂₃	semidirect
748. C₈×D₄	C₂²×C₂₃	semidirect
749. #432	C₂²×C₂₃	semidirect
750. #432	C₂²×C₂₃	semidirect
751. #432	C₂²×C₂₃	semidirect
752. #419	C₂²×C₂₃	semidirect
754. #416	C₂²×C₂₃	semidirect
755. #416	C₂²×C₂₃	semidirect
756. C₂×#103	C₂²×C₂₃	semidirect
758. C₄×M₁₆	C₂²×C₂₃	semidirect
759. C₂×#97	C₂²×C₂₃	semidirect
760. C₂×#97	C₂²×C₂₃	semidirect
973. C₂₃	#62585	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×#3514	2
C₂₃×#3509	2
C₂₃×#3377	2
C₂₃×#3371	2
C₂₃×#3313	2
C₂₃×#3312	2
C₂₃×#3311	2
C₂₃×#3310	2
C₂₃×#3300	2
C₂₃×#3296	2
C₂₃×#3240	2
C₂₃×#3238	2
C₂₃×#3216	2
C₂₃×#3215	2
C₂₃×#3181	2
C₂₃×#3172	2
C₂₃×#3140	2
C₂₃×#3135	2
C₂×C₂₃×#489	2
C₂₃×#2970	2
#62585	23

Subgroups — C23×#62585 #19210211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62585 #19210211