Subgroups — C₂₃×#62550 #19210176

Order 5888.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3318	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3314	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3297	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3295	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3241	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3224	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3179	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
22	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#563	—	2	2	no	—
25	C₂₃×#560	—	2	2	no	—
26	C₂₃×#559	C₂²	1	1	yes	characteristic
27	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#554	C₂²	1	2	yes	complemented
30	C₂₃×#553	C₂²	1	2	yes	complemented
31	C₂₃×#550	C₂²	1	1	yes	characteristic
32	C₂₃×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₂₃	—	2	1	no	—
34	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#548	—	2	1	no	—
36	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#546	—	2	1	no	—
38	C₂₃×#546	C₂²	1	2	yes	—
39	D₄²×C₂₃	—	2	1	no	—
40	D₄²×C₂₃	C₂²	1	1	yes	characteristic
41	D₄²×C₂₃	C₂²	1	2	yes	—
42	C₂₃×#544	C₂²	1	2	yes	complemented
43	C₂₃×#542	C₂²	1	2	yes	complemented
44	C₂₃×#541	—	2	1	no	—
45	C₂₃×#540	—	2	1	no	—
46	C₂₃×#540	C₂²	1	2	yes	—
47	C₂₃×#539	—	2	2	no	—
48	C₂₃×#536	—	2	1	no	—
49	C₂₃×#535	—	2	1	no	—
50	C₂₃×#535	C₂²	1	2	yes	—
51	C₂₃×#534	—	2	2	no	—
52	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
54	C₂₃×#529	C₂²	1	1	yes	characteristic
55	C₂₃×#529	C₂²	1	1	yes	characteristic
56	C₂₃×#529	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#501	C₂²	1	2	yes	complemented
58	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#496	C₂²	1	2	yes	complemented
60	C₂₃×#495	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#490	C₂²	1	2	yes	complemented
62	C₂₃×#490	C₂²	1	2	yes	complemented
63	C₂₃×#489	C₂²	1	2	yes	complemented
64	C₂₃×#489	C₂²	1	2	yes	complemented
65	C₂₃×#488	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#488	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#488	C₂²	1	2	yes	complemented
68	C₂₃×#486	C₂²	1	1	yes	characteristic
69	C₂₃×#486	C₂²	1	1	yes	characteristic
70	C₂₃×#486	C₂²	1	2	yes	complemented
71	C₂₃×#486	C₂²	1	2	yes	complemented
72	C₂₃×#486	C₂²	1	2	yes	complemented
73	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#484	C₂²	1	2	yes	complemented
76	C₂₃×#482	C₂²	1	2	yes	complemented
77	C₂₃×#482	C₂²	1	2	yes	complemented
78	C₂₃×#481	C₂²	1	2	yes	—
79	C₂₃×#481	C₂²	1	2	yes	complemented
80	C₂₃×#480	C₂²	1	2	yes	complemented
81	C₂₃×#478	C₂²	1	2	yes	complemented
82	C₂₃×#478	C₂²	1	2	yes	complemented
83	C₂₃×#476	C₂²	1	2	yes	complemented
84	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
86	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
87	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#474	C₂²	1	2	yes	complemented
89	C₂₃×#469	C₂²	1	2	yes	complemented
90	C₂₃×#468	C₂²	1	2	yes	complemented
91	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#466	C₂²	1	1	yes	characteristic
93	C₂₃×#466	C₂²	1	2	yes	complemented
94	C₂₃×#465	C₂²	1	1	yes	characteristic
95	C₂₃×#465	C₂²	1	1	yes	characteristic, complemented
96	C₂₃×#465	C₂²	1	2	yes	complemented
97	C₂₃×#464	C₂²	1	2	yes	complemented
98	C₂₃×#463	C₂²	1	2	yes	complemented
99	C₂₃×#460	C₂²	1	1	yes	characteristic
100	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#460	C₂²	1	2	yes	complemented
102	C₂₃×#459	C₂²	1	1	yes	characteristic
103	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#459	C₂²	1	2	yes	complemented
105	C₂₃×#452	C₂²	1	2	yes	complemented
106	C₂₃×#450	C₂²	1	2	yes	complemented
107	C₂₃×#450	C₂²	1	2	yes	complemented
108	C₂₃×#449	C₂²	1	2	yes	complemented
109	C₂₃×#447	C₂²	1	2	yes	complemented
110	C₂₃×#447	C₂²	1	2	yes	complemented
111	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#442	C₂²	1	2	yes	complemented
114	C₂₃×#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
121	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
125	C₂₃×#433	C₂²	1	2	yes	complemented
126	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
127	C₂₃×#418	C₂²	1	2	yes	complemented
128	C₂₃×#417	C₂²	1	2	yes	complemented
129	C₂₃×#416	C₂²	1	2	yes	complemented
130	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
131	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
132	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
133	C₂₃×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₂₃	—	2	1	no	—
139	C₂²×Q₈×C₂₃	—	2	1	no	—
140	C₂²×D₄×C₂₃	—	2	2	no	—
141	C₂²×D₄×C₂₃	—	2	1	no	—
142	C₂²×D₄×C₂₃	—	2	1	no	—
143	C₂²×D₄×C₂₃	—	2	1	no	—
144	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
145	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₂₃	C₂³	1	2	yes	—
153	C₂×D₈×C₂₃	C₂³	1	2	yes	—
154	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
158	C₂₃×C₄⋊Q₈	—	2	1	no	—
159	C₂₃×C₄⋊Q₈	—	2	2	no	—
160	C₂₃×C₄⋊Q₈	—	2	1	no	—
161	C₂₃×C₄⋊Q₈	—	2	1	no	—
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	2	yes	—
166	C₂₃×#127	—	2	1	no	—
167	C₂₃×#127	—	2	1	no	—
168	C₂₃×#127	—	2	1	no	—
169	C₂₃×#127	C₂³	1	1	yes	characteristic
170	C₂₃×#127	C₂³	1	2	yes	—
171	C₂₃×#127	C₂³	1	1	yes	characteristic
172	C₂₃×#127	C₂³	1	2	yes	—
173	C₂₃×#126	—	2	2	no	—
174	C₂₃×#126	—	2	2	no	—
175	C₂₃×#126	—	2	2	no	—
176	C₂₃×#126	—	2	1	no	—
177	C₂₃×#126	—	2	1	no	—
178	C₂₃×#126	D₄	1	2	yes	—
179	C₂₃×#125	—	2	2	no	—
180	C₂₃×#125	—	2	2	no	—
181	C₂₃×#125	—	2	2	no	—
182	C₂₃×#125	D₄	1	1	yes	characteristic
183	C₂₃×#125	C₂³	1	2	yes	—
184	C₂₃×#125	C₂³	1	1	yes	characteristic
185	C₂₃×#125	C₂³	1	1	yes	characteristic
186	C₂₃×#124	—	2	1	no	—
187	C₂₃×#124	—	2	1	no	—
188	C₂₃×#124	—	2	2	no	—
189	C₂₃×#124	D₄	1	1	yes	characteristic
190	C₂₃×#124	C₂³	1	2	yes	—
191	C₂₃×#124	C₂³	1	1	yes	characteristic
192	C₂₃×#124	C₂³	1	1	yes	characteristic
193	C₂₃×#123	—	2	1	no	—
194	C₂₃×#123	—	2	1	no	—
195	C₂₃×#123	—	2	2	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	2	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×#123	D₄	1	2	yes	—
203	C₂₃×C₂²⋊Q₈	—	2	1	no	—
204	C₂₃×C₂²⋊Q₈	—	2	1	no	—
205	C₂₃×C₂²⋊Q₈	—	2	2	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	—	2	2	no	—
209	C₂₃×C₂²⋊Q₈	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	2	no	—
211	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
212	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂₃×#121	—	2	2	no	—
216	C₂₃×#121	—	2	2	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	1	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	—	2	2	no	—
225	C₂₃×#121	—	2	2	no	—
226	C₂₃×#121	D₄	1	1	yes	characteristic
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#121	C₂³	1	1	yes	characteristic
230	C₂₃×#121	C₂³	1	1	yes	characteristic
231	C₂₃×#121	C₂³	1	2	yes	—
232	C₂₃×#120	—	2	2	no	—
233	C₂₃×#120	—	2	2	no	—
234	C₂₃×#120	—	2	2	no	—
235	C₂₃×#120	—	2	2	no	—
236	C₂₃×#120	—	2	2	no	—
237	C₂₃×#120	—	2	2	no	—
238	C₄×Q₈×C₂₃	—	2	1	no	—
239	C₄×Q₈×C₂₃	—	2	1	no	—
240	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₂₃	—	2	2	no	—
245	C₄×D₄×C₂₃	—	2	1	no	—
246	C₄×D₄×C₂₃	—	2	1	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₂₃	C₂³	1	2	yes	—
252	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₂₃	C₂³	1	2	yes	—
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₂₃	C₂³	1	2	yes	—
257	C₂₃×#117	—	2	1	no	—
258	C₂₃×#117	—	2	1	no	—
259	C₂₃×#117	C₂³	1	2	yes	—
260	C₂₃×#117	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
266	C₂₃×#107	C₂³	1	1	yes	characteristic
267	C₂₃×#107	C₂³	1	2	yes	—
268	C₂₃×#107	C₂³	1	1	yes	characteristic
269	C₂₃×#107	C₂³	1	2	yes	—
270	C₂₃×#106	C₂³	1	1	yes	characteristic
271	C₂₃×#106	C₂³	1	1	yes	characteristic
272	C₂₃×#106	C₂³	1	2	yes	—
273	C₂₃×#106	C₂³	1	2	yes	—
274	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₂₃×#103	C₂³	1	1	yes	characteristic
279	C₂₃×#103	C₂³	1	2	yes	—
280	C₂₃×#103	C₂³	1	1	yes	characteristic
281	C₂₃×#103	C₂³	1	2	yes	—
282	C₂₃×#103	C₂³	1	1	yes	characteristic
283	C₂₃×#103	C₂³	1	1	yes	characteristic
284	C₂₃×#102	C₂³	1	1	yes	characteristic
285	C₂₃×#102	C₂³	1	2	yes	—
286	C₂₃×#102	C₂³	1	2	yes	—
287	C₂₃×#102	C₂³	1	2	yes	—
288	C₂₃×#102	C₂³	1	2	yes	—
289	C₂₃×#102	C₂³	1	2	yes	—
290	C₂₃×#102	C₂³	1	2	yes	—
291	C₂₃×#102	C₂³	1	2	yes	—
292	C₂₃×#102	C₂³	1	2	yes	—
293	C₂₃×#102	C₂³	1	2	yes	—
294	C₂₃×#102	C₂³	1	2	yes	—
295	C₂₃×#102	C₂³	1	2	yes	—
296	C₂₃×#102	C₂³	1	2	yes	—
297	C₂₃×#102	C₂³	1	1	yes	characteristic
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×#97	C₂³	1	2	yes	—
306	C₂₃×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	C₂⁴×C₂₃	—	2	2	no	—
313	C₂⁴×C₂₃	—	2	2	no	—
314	#41×C₂₃	—	4	2	no	—
315	#41×C₂₃	—	4	2	no	—
316	#41×C₂₃	—	8	2	no	—
317	#41×C₂₃	—	8	2	no	—
318	C₂×Q₈×C₂₃	—	2	1	no	—
319	C₂×Q₈×C₂₃	—	2	1	no	—
320	C₂×Q₈×C₂₃	—	2	2	no	—
321	C₂×Q₈×C₂₃	—	2	2	no	—
322	C₂×Q₈×C₂₃	—	8	2	no	—
323	C₂×Q₈×C₂₃	—	8	2	no	—
324	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₂₃	—	2	1	no	—
328	C₂×D₄×C₂₃	—	2	1	no	—
329	C₂×D₄×C₂₃	—	2	2	no	—
330	C₂×D₄×C₂₃	—	2	2	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	1	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	1	no	—
338	C₂×D₄×C₂₃	—	2	2	no	—
339	C₂×D₄×C₂₃	—	2	2	no	—
340	C₂×D₄×C₂₃	—	2	2	no	—
341	C₂×D₄×C₂₃	—	2	2	no	—
342	C₂×D₄×C₂₃	—	2	1	no	—
343	C₂×D₄×C₂₃	—	4	2	no	—
344	C₂×D₄×C₂₃	—	4	2	no	—
345	C₂×D₄×C₂₃	—	4	2	no	—
346	C₂×D₄×C₂₃	—	4	2	no	—
347	C₂×D₄×C₂₃	—	8	2	no	—
348	C₂×D₄×C₂₃	—	8	2	no	—
349	C₂×D₄×C₂₃	—	8	2	no	—
350	C₂×D₄×C₂₃	—	8	4	no	—
351	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
355	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
356	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	—	2	2	no	—
358	C₂²×C₄×C₂₃	—	2	2	no	—
359	C₂²×C₄×C₂₃	—	2	1	no	—
360	C₂²×C₄×C₂₃	—	2	1	no	—
361	C₂²×C₄×C₂₃	—	2	2	no	—
362	C₂²×C₄×C₂₃	—	2	2	no	—
363	C₂²×C₄×C₂₃	—	2	2	no	—
364	C₂²×C₄×C₂₃	—	2	2	no	—
365	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
369	Q₁₆×C₂₃	—	4	1	no	—
370	SD₁₆×C₂₃	—	4	2	no	—
371	SD₁₆×C₂₃	—	4	1	no	—
372	SD₁₆×C₂₃	—	4	1	no	—
373	SD₁₆×C₂₃	—	4	2	no	—
374	D₈×C₂₃	—	4	2	no	—
375	D₈×C₂₃	—	4	1	no	—
376	D₈×C₂₃	—	4	2	no	—
377	M₁₆×C₂₃	—	4	2	no	—
378	C₂×C₈×C₂₃	—	4	2	no	—
379	C₂×C₈×C₂₃	—	4	1	no	—
380	C₂×C₈×C₂₃	—	4	1	no	—
381	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
386	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
387	C₄⋊C₄×C₂₃	—	2	1	no	—
388	C₄⋊C₄×C₂₃	—	2	2	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	1	no	—
393	C₄⋊C₄×C₂₃	—	2	1	no	—
394	C₄⋊C₄×C₂₃	—	2	1	no	—
395	C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	—	2	1	no	—
399	C₄⋊C₄×C₂₃	—	2	2	no	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	1	no	—
403	C₄⋊C₄×C₂₃	—	2	2	no	—
404	C₄⋊C₄×C₂₃	—	2	1	no	—
405	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₂₃	—	2	1	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	1	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	2	no	—
423	C₂²⋊C₄×C₂₃	—	2	1	no	—
424	C₂²⋊C₄×C₂₃	—	2	1	no	—
425	C₂²⋊C₄×C₂₃	—	2	1	no	—
426	C₂²⋊C₄×C₂₃	—	2	1	no	—
427	C₂²⋊C₄×C₂₃	—	2	1	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	2	no	—
431	C₂²⋊C₄×C₂₃	—	2	1	no	—
432	C₂²⋊C₄×C₂₃	—	2	1	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	2	no	—
435	C₂²⋊C₄×C₂₃	—	2	2	no	—
436	C₂²⋊C₄×C₂₃	—	2	1	no	—
437	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
442	C₄²×C₂₃	—	2	1	no	—
443	C₄²×C₂₃	—	2	1	no	—
444	C₄²×C₂₃	—	2	2	no	—
445	C₄²×C₂₃	—	2	2	no	—
446	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₄²×C₂₃	C₂⁴	1	2	yes	—
450	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
451	#62550	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂³×C₂₃	—	2	1	no	—
453	C₂³×C₂₃	—	2	1	no	—
454	C₂³×C₂₃	—	2	2	no	—
455	C₂³×C₂₃	—	2	2	no	—
456	C₂³×C₂₃	—	4	4	no	—
457	C₂³×C₂₃	—	8	2	no	—
458	C₂³×C₂₃	—	8	2	no	—
459	C₂³×C₂₃	—	8	2	no	—
460	C₂³×C₂₃	—	8	2	no	—
461	C₂³×C₂₃	—	8	2	no	—
462	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
463	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
464	Q₈×C₂₃	—	2	2	no	—
465	Q₈×C₂₃	—	2	1	no	—
466	Q₈×C₂₃	—	2	1	no	—
467	Q₈×C₂₃	—	2	1	no	—
468	Q₈×C₂₃	—	2	1	no	—
469	Q₈×C₂₃	—	4	2	no	—
470	Q₈×C₂₃	—	4	2	no	—
471	Q₈×C₂₃	—	8	2	no	—
472	Q₈×C₂₃	—	8	2	no	—
473	D₄×C₂₃	—	2	4	no	—
474	D₄×C₂₃	—	2	2	no	—
475	D₄×C₂₃	—	2	1	no	—
476	D₄×C₂₃	—	2	1	no	—
477	D₄×C₂₃	—	2	2	no	—
478	D₄×C₂₃	—	2	1	no	—
479	D₄×C₂₃	—	2	2	no	—
480	D₄×C₂₃	—	2	1	no	—
481	D₄×C₂₃	—	2	2	no	—
482	D₄×C₂₃	—	2	2	no	—
483	D₄×C₂₃	—	4	2	no	—
484	D₄×C₂₃	—	4	2	no	—
485	D₄×C₂₃	—	4	2	no	—
486	D₄×C₂₃	—	4	2	no	—
487	D₄×C₂₃	—	8	2	no	—
488	D₄×C₂₃	—	8	2	no	—
489	D₄×C₂₃	—	8	2	no	—
490	D₄×C₂₃	—	8	1	no	—
491	D₄×C₂₃	—	8	2	no	—
492	D₄×C₂₃	—	8	1	no	—
493	D₄×C₂₃	—	8	2	no	—
494	D₄×C₂₃	—	8	2	no	—
495	D₄×C₂₃	—	8	2	no	—
496	D₄×C₂₃	—	8	2	no	—
497	D₄×C₂₃	—	8	2	no	—
498	D₄×C₂₃	—	8	2	no	—
499	C₂×C₄×C₂₃	—	2	2	no	—
500	C₂×C₄×C₂₃	—	2	2	no	—
501	C₂×C₄×C₂₃	—	2	1	no	—
502	C₂×C₄×C₂₃	—	2	1	no	—
503	C₂×C₄×C₂₃	—	2	2	no	—
504	C₂×C₄×C₂₃	—	2	2	no	—
505	C₂×C₄×C₂₃	—	2	1	no	—
506	C₂×C₄×C₂₃	—	2	1	no	—
507	C₂×C₄×C₂₃	—	2	1	no	—
508	C₂×C₄×C₂₃	—	2	1	no	—
509	C₂×C₄×C₂₃	—	2	2	no	—
510	C₂×C₄×C₂₃	—	2	2	no	—
511	C₂×C₄×C₂₃	—	2	1	no	—
512	C₂×C₄×C₂₃	—	2	1	no	—
513	C₂×C₄×C₂₃	—	4	2	no	—
514	C₂×C₄×C₂₃	—	4	2	no	—
515	C₂×C₄×C₂₃	—	8	2	no	—
516	C₂×C₄×C₂₃	—	8	2	no	—
517	C₂×C₄×C₂₃	—	8	2	no	—
518	C₂×C₄×C₂₃	—	8	2	no	—
519	C₂×C₄×C₂₃	—	8	2	no	—
520	C₂×C₄×C₂₃	—	8	2	no	—
521	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
530	C₈×C₂₃	—	2	1	no	—
531	C₈×C₂₃	—	2	1	no	—
532	C₈×C₂₃	—	2	2	no	—
533	C₈×C₂₃	—	2	1	no	—
534	C₈×C₂₃	—	2	1	no	—
535	C₈×C₂₃	—	2	2	no	—
536	#3552	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3543	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3373	C₂×C₂₃	1	1	yes	characteristic, complemented
539	#3368	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3365	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3358	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3332	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#3324	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3318	C₂×C₂₃	1	2	yes	complemented
545	#3314	C₂×C₂₃	1	2	yes	complemented
546	#3304	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#3297	C₂×C₂₃	1	2	yes	complemented
548	#3295	C₂×C₂₃	1	2	yes	complemented
549	#3294	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#3241	C₂×C₂₃	1	2	yes	complemented
551	#3239	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#3224	C₂×C₂₃	1	2	yes	complemented
553	#3217	C₂×C₂₃	1	1	yes	characteristic, complemented
554	#3179	C₂×C₂₃	1	2	yes	complemented
555	#3168	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#3136	C₂×C₂₃	1	2	yes	complemented
557	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
558	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
559	C₂²×C₂₃	—	2	1	no	—
560	C₂²×C₂₃	—	2	1	no	—
561	C₂²×C₂₃	—	2	2	no	—
562	C₂²×C₂₃	—	2	2	no	—
563	C₂²×C₂₃	—	2	2	no	—
564	C₂²×C₂₃	—	4	2	no	—
565	C₂²×C₂₃	—	4	1	no	—
566	C₂²×C₂₃	—	4	2	no	—
567	C₂²×C₂₃	—	4	1	no	—
568	C₂²×C₂₃	—	4	1	no	—
569	C₂²×C₂₃	—	4	1	no	—
570	C₂²×C₂₃	—	4	2	no	—
571	C₂²×C₂₃	—	4	2	no	—
572	C₂²×C₂₃	—	4	2	no	—
573	C₂²×C₂₃	—	4	1	no	—
574	C₂²×C₂₃	—	4	1	no	—
575	C₂²×C₂₃	—	4	2	no	—
576	C₂²×C₂₃	—	16	4	no	—
577	C₂²×C₂₃	—	16	4	no	—
578	C₂²×C₂₃	#577	1	2	yes	—
579	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
580	C₄×C₂₃	—	2	2	no	—
581	C₄×C₂₃	—	2	1	no	—
582	C₄×C₂₃	—	2	1	no	—
583	C₄×C₂₃	—	2	2	no	—
584	C₄×C₂₃	—	2	1	no	—
585	C₄×C₂₃	—	2	1	no	—
586	C₄×C₂₃	—	2	2	no	—
587	C₄×C₂₃	—	4	1	no	—
588	C₄×C₂₃	—	4	1	no	—
589	C₄×C₂₃	—	4	1	no	—
590	C₄×C₂₃	—	4	1	no	—
591	C₄×C₂₃	—	4	2	no	—
592	C₄×C₂₃	—	4	2	no	—
593	C₄×C₂₃	—	4	1	no	—
594	C₄×C₂₃	—	4	1	no	—
595	C₄×C₂₃	#576	1	2	yes	—
596	C₄×C₂₃	#585	1	1	yes	characteristic
597	C₄×C₂₃	#585	1	1	yes	characteristic
598	#563	—	2	2	no	—
599	#560	—	2	2	no	—
600	#559	C₂²×C₂₃	1	1	yes	characteristic
601	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
602	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
603	#554	C₂²×C₂₃	1	2	yes	complemented
604	#553	C₂²×C₂₃	1	2	yes	complemented
605	#550	C₂²×C₂₃	1	1	yes	characteristic
606	#550	C₂²×C₂₃	1	1	yes	characteristic
607	D₄×Q₈	—	2	1	no	—
608	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
609	#548	—	2	1	no	—
610	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
611	#546	—	2	1	no	—
612	#546	C₂²×C₂₃	1	2	yes	—
613	D₄²	—	2	1	no	—
614	D₄²	C₂²×C₂₃	1	1	yes	characteristic
615	D₄²	C₂²×C₂₃	1	2	yes	—
616	#544	C₂²×C₂₃	1	2	yes	complemented
617	#542	C₂²×C₂₃	1	2	yes	complemented
618	#541	—	2	1	no	—
619	#540	—	2	1	no	—
620	#540	C₂²×C₂₃	1	2	yes	—
621	#539	—	2	2	no	—
622	#536	—	2	1	no	—
623	#535	—	2	1	no	—
624	#535	C₂²×C₂₃	1	2	yes	—
625	#534	—	2	2	no	—
626	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
628	#529	C₂²×C₂₃	1	1	yes	characteristic
629	#529	C₂²×C₂₃	1	1	yes	characteristic
630	#529	C₂²×C₂₃	1	1	yes	characteristic, complemented
631	#501	C₂²×C₂₃	1	2	yes	complemented
632	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
633	#496	C₂²×C₂₃	1	2	yes	complemented
634	#495	C₂²×C₂₃	1	1	yes	characteristic, complemented
635	#490	C₂²×C₂₃	1	2	yes	complemented
636	#490	C₂²×C₂₃	1	2	yes	complemented
637	#489	C₂²×C₂₃	1	2	yes	complemented
638	#489	C₂²×C₂₃	1	2	yes	complemented
639	#488	C₂²×C₂₃	1	2	yes	complemented
640	#488	C₂²×C₂₃	1	1	yes	characteristic, complemented
641	#488	C₂²×C₂₃	1	1	yes	characteristic, complemented
642	#486	C₂²×C₂₃	1	1	yes	characteristic
643	#486	C₂²×C₂₃	1	1	yes	characteristic
644	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#486	C₂²×C₂₃	1	2	yes	complemented
647	#486	C₂²×C₂₃	1	2	yes	complemented
648	#486	C₂²×C₂₃	1	2	yes	complemented
649	#484	C₂²×C₂₃	1	2	yes	complemented
650	#482	C₂²×C₂₃	1	2	yes	complemented
651	#482	C₂²×C₂₃	1	2	yes	complemented
652	#481	C₂²×C₂₃	1	2	yes	—
653	#481	C₂²×C₂₃	1	2	yes	complemented
654	#480	C₂²×C₂₃	1	2	yes	complemented
655	#478	C₂²×C₂₃	1	2	yes	complemented
656	#478	C₂²×C₂₃	1	2	yes	complemented
657	#476	C₂²×C₂₃	1	2	yes	complemented
658	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
660	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
661	#474	C₂²×C₂₃	1	2	yes	complemented
662	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	#469	C₂²×C₂₃	1	2	yes	complemented
664	#468	C₂²×C₂₃	1	2	yes	complemented
665	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	#466	C₂²×C₂₃	1	1	yes	characteristic
667	#466	C₂²×C₂₃	1	2	yes	complemented
668	#465	C₂²×C₂₃	1	1	yes	characteristic
669	#465	C₂²×C₂₃	1	1	yes	characteristic, complemented
670	#465	C₂²×C₂₃	1	2	yes	complemented
671	#464	C₂²×C₂₃	1	2	yes	complemented
672	#463	C₂²×C₂₃	1	2	yes	complemented
673	#460	C₂²×C₂₃	1	1	yes	characteristic
674	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
675	#460	C₂²×C₂₃	1	2	yes	complemented
676	#459	C₂²×C₂₃	1	1	yes	characteristic
677	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	#459	C₂²×C₂₃	1	2	yes	complemented
679	#452	C₂²×C₂₃	1	2	yes	complemented
680	#450	C₂²×C₂₃	1	2	yes	complemented
681	#450	C₂²×C₂₃	1	2	yes	complemented
682	#449	C₂²×C₂₃	1	2	yes	complemented
683	#447	C₂²×C₂₃	1	2	yes	complemented
684	#447	C₂²×C₂₃	1	2	yes	complemented
685	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	#442	C₂²×C₂₃	1	2	yes	complemented
688	#440	C₂²×C₂₃	1	2	yes	complemented
689	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
695	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
696	#435	C₂²×C₂₃	1	2	yes	complemented
697	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
699	#433	C₂²×C₂₃	1	2	yes	complemented
700	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
701	#418	C₂²×C₂₃	1	2	yes	complemented
702	#417	C₂²×C₂₃	1	2	yes	complemented
703	#416	C₂²×C₂₃	1	2	yes	complemented
704	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
705	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
706	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
707	#405	C₂²×C₂₃	1	2	yes	complemented
708	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
709	C₂×C₂₃	—	2	2	no	—
710	C₂×C₂₃	—	4	2	no	—
711	C₂×C₂₃	—	8	1	no	—
712	C₂×C₂₃	—	8	2	no	—
713	C₂×C₂₃	—	8	1	no	—
714	C₂×C₂₃	—	8	2	no	—
715	C₂×C₂₃	#3500	1	1	yes	characteristic
716	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
717	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
718	C₂×#41	—	2	1	no	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	C₂³×C₂₃	1	2	yes	—
721	C₂²×Q₈	—	2	1	no	—
722	C₂²×Q₈	—	2	1	no	—
723	C₂²×D₄	—	2	2	no	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	—	2	1	no	—
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
728	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
734	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₂×D₈	C₂³×C₂₃	1	2	yes	—
736	C₂×D₈	C₂³×C₂₃	1	2	yes	—
737	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
738	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
739	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
740	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
741	C₄⋊Q₈	—	2	1	no	—
742	C₄⋊Q₈	—	2	2	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
746	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
749	#127	—	2	1	no	—
750	#127	—	2	1	no	—
751	#127	—	2	1	no	—
752	#127	C₂³×C₂₃	1	2	yes	—
753	#127	C₂³×C₂₃	1	1	yes	characteristic
754	#127	C₂³×C₂₃	1	1	yes	characteristic
755	#127	C₂³×C₂₃	1	2	yes	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	1	no	—
760	#126	—	2	1	no	—
761	#126	D₄×C₂₃	1	2	yes	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	2	no	—
765	#125	D₄×C₂₃	1	1	yes	characteristic
766	#125	C₂³×C₂₃	1	1	yes	characteristic
767	#125	C₂³×C₂₃	1	1	yes	characteristic
768	#125	C₂³×C₂₃	1	2	yes	—
769	#124	—	2	1	no	—
770	#124	—	2	1	no	—
771	#124	—	2	2	no	—
772	#124	D₄×C₂₃	1	1	yes	characteristic
773	#124	C₂³×C₂₃	1	1	yes	characteristic
774	#124	C₂³×C₂₃	1	1	yes	characteristic
775	#124	C₂³×C₂₃	1	2	yes	—
776	#123	—	2	1	no	—
777	#123	—	2	1	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	D₄×C₂₃	1	2	yes	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
795	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
797	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	D₄×C₂₃	1	1	yes	characteristic
810	#121	C₂³×C₂₃	1	1	yes	characteristic
811	#121	C₂³×C₂₃	1	1	yes	characteristic
812	#121	C₂³×C₂₃	1	2	yes	—
813	#121	C₂³×C₂₃	1	2	yes	—
814	#121	C₂³×C₂₃	1	2	yes	—
815	#120	—	2	2	no	—
816	#120	—	2	2	no	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
824	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
826	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₂₃	1	2	yes	—
836	C₄×D₄	C₂³×C₂₃	1	2	yes	—
837	C₄×D₄	C₂³×C₂₃	1	2	yes	—
838	C₄×D₄	C₂³×C₂₃	1	2	yes	—
839	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	C₂³×C₂₃	1	2	yes	—
843	#117	C₂³×C₂₃	1	2	yes	—
844	C₂×C₄⋊C₄	—	2	1	no	—
845	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
846	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
849	#107	C₂³×C₂₃	1	1	yes	characteristic
850	#107	C₂³×C₂₃	1	2	yes	—
851	#107	C₂³×C₂₃	1	1	yes	characteristic
852	#107	C₂³×C₂₃	1	2	yes	—
853	#106	C₂³×C₂₃	1	1	yes	characteristic
854	#106	C₂³×C₂₃	1	1	yes	characteristic
855	#106	C₂³×C₂₃	1	2	yes	—
856	#106	C₂³×C₂₃	1	2	yes	—
857	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
860	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
861	#103	C₂³×C₂₃	1	1	yes	characteristic
862	#103	C₂³×C₂₃	1	2	yes	—
863	#103	C₂³×C₂₃	1	1	yes	characteristic
864	#103	C₂³×C₂₃	1	2	yes	—
865	#103	C₂³×C₂₃	1	1	yes	characteristic
866	#103	C₂³×C₂₃	1	1	yes	characteristic
867	#102	C₂³×C₂₃	1	1	yes	characteristic
868	#102	C₂³×C₂₃	1	2	yes	—
869	#102	C₂³×C₂₃	1	2	yes	—
870	#102	C₂³×C₂₃	1	2	yes	—
871	#102	C₂³×C₂₃	1	2	yes	—
872	#102	C₂³×C₂₃	1	2	yes	—
873	#102	C₂³×C₂₃	1	2	yes	—
874	#102	C₂³×C₂₃	1	2	yes	—
875	#102	C₂³×C₂₃	1	2	yes	—
876	#102	C₂³×C₂₃	1	2	yes	—
877	#102	C₂³×C₂₃	1	2	yes	—
878	#102	C₂³×C₂₃	1	2	yes	—
879	#102	C₂³×C₂₃	1	2	yes	—
880	#102	C₂³×C₂₃	1	1	yes	characteristic
881	#102	C₂³×C₂₃	1	2	yes	—
882	#102	C₂³×C₂₃	1	2	yes	—
883	#102	C₂³×C₂₃	1	1	yes	characteristic
884	#102	C₂³×C₂₃	1	1	yes	characteristic
885	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
888	#97	C₂³×C₂₃	1	2	yes	—
889	#97	C₂³×C₂₃	1	2	yes	—
890	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₂₃	1	2	yes	—
895	C₂₃	#62550	1	1	yes	characteristic, direct product factor, Sylow
896	C₂⁴	—	2	2	no	—
897	C₂⁴	—	2	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	8	2	no	—
907	C₂×Q₈	—	8	2	no	—
908	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	8	2	no	—
932	C₂×D₄	—	8	2	no	—
933	C₂×D₄	—	8	2	no	—
934	C₂×D₄	—	8	4	no	—
935	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
936	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
939	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
940	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
950	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
953	Q₁₆	—	4	1	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	1	no	—
956	SD₁₆	—	4	1	no	—
957	SD₁₆	—	4	2	no	—
958	D₈	—	4	2	no	—
959	D₈	—	4	1	no	—
960	D₈	—	4	2	no	—
961	M₁₆	—	4	2	no	—
962	C₂×C₈	—	4	2	no	—
963	C₂×C₈	—	4	1	no	—
964	C₂×C₈	—	4	1	no	—
965	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
970	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
990	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1031	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₂₃	1	2	yes	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	4	4	no	—
1040	C₂³	—	8	2	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	—	8	2	no	—
1045	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1046	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	4	2	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	8	2	no	—
1055	Q₈	—	8	2	no	—
1056	D₄	—	2	4	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1112	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	2	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	2	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	16	4	no	—
1137	C₂²	—	16	4	no	—
1138	C₂²	C₂₃×#577	1	2	yes	—
1139	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	1	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	C₂₃×#576	1	2	yes	—
1156	C₄	C₂₃×#585	1	1	yes	characteristic
1157	C₄	C₂₃×#585	1	1	yes	characteristic
1158	C₂	—	2	2	no	—
1159	C₂	—	4	2	no	—
1160	C₂	—	8	1	no	—
1161	C₂	—	8	2	no	—
1162	C₂	—	8	2	no	—
1163	C₂	—	8	1	no	—
1164	C₂	C₂₃×#3500	1	1	yes	characteristic
1165	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
1166	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3552	C₂	semidirect
2. C₂₃×#3543	C₂	semidirect
3. C₂₃×#3373	C₂	semidirect
4. C₂₃×#3368	C₂	semidirect
5. C₂₃×#3365	C₂	semidirect
6. C₂₃×#3358	C₂	semidirect
7. C₂₃×#3332	C₂	semidirect
8. C₂₃×#3324	C₂	semidirect
9. C₂₃×#3318	C₂	semidirect
10. C₂₃×#3314	C₂	semidirect
11. C₂₃×#3304	C₂	semidirect
12. C₂₃×#3297	C₂	semidirect
13. C₂₃×#3295	C₂	semidirect
14. C₂₃×#3294	C₂	semidirect
15. C₂₃×#3241	C₂	semidirect
16. C₂₃×#3239	C₂	semidirect
17. C₂₃×#3224	C₂	semidirect
18. C₂₃×#3217	C₂	semidirect
19. C₂₃×#3179	C₂	semidirect
20. C₂₃×#3168	C₂	semidirect
21. C₂₃×#3136	C₂	semidirect
22. C₂×C₂₃×#486	C₂	semidirect
23. C₂₃×#2966	C₂	semidirect
27. C₂₃×#557	C₂²	semidirect
28. C₂₃×#556	C₂²	semidirect
29. C₂₃×#554	C₂²	semidirect
30. C₂₃×#553	C₂²	semidirect
34. D₄×Q₈×C₂₃	C₂²	semidirect
36. C₂₃×#547	C₂²	semidirect
42. C₂₃×#544	C₂²	semidirect
43. C₂₃×#542	C₂²	semidirect
52. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
56. C₂₃×#529	C₂²	semidirect
57. C₂₃×#501	C₂²	semidirect
58. C₂₃×#499	C₂²	semidirect
59. C₂₃×#496	C₂²	semidirect
60. C₂₃×#495	C₂²	semidirect
61. C₂₃×#490	C₂²	semidirect
62. C₂₃×#490	C₂²	semidirect
63. C₂₃×#489	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
65. C₂₃×#488	C₂²	semidirect
66. C₂₃×#488	C₂²	semidirect
67. C₂₃×#488	C₂²	semidirect
70. C₂₃×#486	C₂²	semidirect
71. C₂₃×#486	C₂²	semidirect
72. C₂₃×#486	C₂²	semidirect
73. C₂₃×#486	C₂²	semidirect
74. C₂₃×#486	C₂²	semidirect
75. C₂₃×#484	C₂²	semidirect
76. C₂₃×#482	C₂²	semidirect
77. C₂₃×#482	C₂²	semidirect
79. C₂₃×#481	C₂²	semidirect
80. C₂₃×#480	C₂²	semidirect
81. C₂₃×#478	C₂²	semidirect
82. C₂₃×#478	C₂²	semidirect
83. C₂₃×#476	C₂²	semidirect
84. C₂₃×#475	C₂²	semidirect
85. C₂₃×#475	C₂²	semidirect
86. C₂₃×#474	C₂²	semidirect
87. C₂₃×#474	C₂²	semidirect
88. C₂₃×#474	C₂²	semidirect
89. C₂₃×#469	C₂²	semidirect
90. C₂₃×#468	C₂²	semidirect
91. C₂₃×#467	C₂²	semidirect
93. C₂₃×#466	C₂²	semidirect
95. C₂₃×#465	C₂²	semidirect
96. C₂₃×#465	C₂²	semidirect
97. C₂₃×#464	C₂²	semidirect
98. C₂₃×#463	C₂²	semidirect
100. C₂₃×#460	C₂²	semidirect
101. C₂₃×#460	C₂²	semidirect
103. C₂₃×#459	C₂²	semidirect
104. C₂₃×#459	C₂²	semidirect
105. C₂₃×#452	C₂²	semidirect
106. C₂₃×#450	C₂²	semidirect
107. C₂₃×#450	C₂²	semidirect
108. C₂₃×#449	C₂²	semidirect
109. C₂₃×#447	C₂²	semidirect
110. C₂₃×#447	C₂²	semidirect
111. C₂₃×#446	C₂²	semidirect
112. C₈×Q₈×C₂₃	C₂²	semidirect
113. C₂₃×#442	C₂²	semidirect
114. C₂₃×#440	C₂²	semidirect
115. C₄×Q₁₆×C₂₃	C₂²	semidirect
116. C₄×SD₁₆×C₂₃	C₂²	semidirect
117. C₄×SD₁₆×C₂₃	C₂²	semidirect
118. C₄×SD₁₆×C₂₃	C₂²	semidirect
119. C₄×D₈×C₂₃	C₂²	semidirect
120. C₄×D₈×C₂₃	C₂²	semidirect
121. C₂₃×#436	C₂²	semidirect
122. C₂₃×#435	C₂²	semidirect
123. C₈×D₄×C₂₃	C₂²	semidirect
124. C₈×D₄×C₂₃	C₂²	semidirect
125. C₂₃×#433	C₂²	semidirect
126. C₂₃×#432	C₂²	semidirect
127. C₂₃×#418	C₂²	semidirect
128. C₂₃×#417	C₂²	semidirect
129. C₂₃×#416	C₂²	semidirect
130. C₂×C₂₃×#102	C₂²	semidirect
131. C₂×C₂₃×#102	C₂²	semidirect
132. C₂×C₂₃×#102	C₂²	semidirect
133. C₂₃×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
451. #62550	C₂₃	direct (N × H)
536. #3552	C₂×C₂₃	semidirect
537. #3543	C₂×C₂₃	semidirect
538. #3373	C₂×C₂₃	semidirect
539. #3368	C₂×C₂₃	semidirect
540. #3365	C₂×C₂₃	semidirect
541. #3358	C₂×C₂₃	semidirect
542. #3332	C₂×C₂₃	semidirect
543. #3324	C₂×C₂₃	semidirect
544. #3318	C₂×C₂₃	semidirect
545. #3314	C₂×C₂₃	semidirect
546. #3304	C₂×C₂₃	semidirect
547. #3297	C₂×C₂₃	semidirect
548. #3295	C₂×C₂₃	semidirect
549. #3294	C₂×C₂₃	semidirect
550. #3241	C₂×C₂₃	semidirect
551. #3239	C₂×C₂₃	semidirect
552. #3224	C₂×C₂₃	semidirect
553. #3217	C₂×C₂₃	semidirect
554. #3179	C₂×C₂₃	semidirect
555. #3168	C₂×C₂₃	semidirect
556. #3136	C₂×C₂₃	semidirect
557. C₂×#486	C₂×C₂₃	semidirect
558. #2966	C₂×C₂₃	semidirect
601. #557	C₂²×C₂₃	semidirect
602. #556	C₂²×C₂₃	semidirect
603. #554	C₂²×C₂₃	semidirect
604. #553	C₂²×C₂₃	semidirect
608. D₄×Q₈	C₂²×C₂₃	semidirect
610. #547	C₂²×C₂₃	semidirect
616. #544	C₂²×C₂₃	semidirect
617. #542	C₂²×C₂₃	semidirect
626. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
630. #529	C₂²×C₂₃	semidirect
631. #501	C₂²×C₂₃	semidirect
632. #499	C₂²×C₂₃	semidirect
633. #496	C₂²×C₂₃	semidirect
634. #495	C₂²×C₂₃	semidirect
635. #490	C₂²×C₂₃	semidirect
636. #490	C₂²×C₂₃	semidirect
637. #489	C₂²×C₂₃	semidirect
638. #489	C₂²×C₂₃	semidirect
639. #488	C₂²×C₂₃	semidirect
640. #488	C₂²×C₂₃	semidirect
641. #488	C₂²×C₂₃	semidirect
644. #486	C₂²×C₂₃	semidirect
645. #486	C₂²×C₂₃	semidirect
646. #486	C₂²×C₂₃	semidirect
647. #486	C₂²×C₂₃	semidirect
648. #486	C₂²×C₂₃	semidirect
649. #484	C₂²×C₂₃	semidirect
650. #482	C₂²×C₂₃	semidirect
651. #482	C₂²×C₂₃	semidirect
653. #481	C₂²×C₂₃	semidirect
654. #480	C₂²×C₂₃	semidirect
655. #478	C₂²×C₂₃	semidirect
656. #478	C₂²×C₂₃	semidirect
657. #476	C₂²×C₂₃	semidirect
658. #475	C₂²×C₂₃	semidirect
659. #475	C₂²×C₂₃	semidirect
660. #474	C₂²×C₂₃	semidirect
661. #474	C₂²×C₂₃	semidirect
662. #474	C₂²×C₂₃	semidirect
663. #469	C₂²×C₂₃	semidirect
664. #468	C₂²×C₂₃	semidirect
665. #467	C₂²×C₂₃	semidirect
667. #466	C₂²×C₂₃	semidirect
669. #465	C₂²×C₂₃	semidirect
670. #465	C₂²×C₂₃	semidirect
671. #464	C₂²×C₂₃	semidirect
672. #463	C₂²×C₂₃	semidirect
674. #460	C₂²×C₂₃	semidirect
675. #460	C₂²×C₂₃	semidirect
677. #459	C₂²×C₂₃	semidirect
678. #459	C₂²×C₂₃	semidirect
679. #452	C₂²×C₂₃	semidirect
680. #450	C₂²×C₂₃	semidirect
681. #450	C₂²×C₂₃	semidirect
682. #449	C₂²×C₂₃	semidirect
683. #447	C₂²×C₂₃	semidirect
684. #447	C₂²×C₂₃	semidirect
685. #446	C₂²×C₂₃	semidirect
686. C₈×Q₈	C₂²×C₂₃	semidirect
687. #442	C₂²×C₂₃	semidirect
688. #440	C₂²×C₂₃	semidirect
689. C₄×Q₁₆	C₂²×C₂₃	semidirect
690. C₄×SD₁₆	C₂²×C₂₃	semidirect
691. C₄×SD₁₆	C₂²×C₂₃	semidirect
692. C₄×SD₁₆	C₂²×C₂₃	semidirect
693. C₄×D₈	C₂²×C₂₃	semidirect
694. C₄×D₈	C₂²×C₂₃	semidirect
695. #436	C₂²×C₂₃	semidirect
696. #435	C₂²×C₂₃	semidirect
697. C₈×D₄	C₂²×C₂₃	semidirect
698. C₈×D₄	C₂²×C₂₃	semidirect
699. #433	C₂²×C₂₃	semidirect
700. #432	C₂²×C₂₃	semidirect
701. #418	C₂²×C₂₃	semidirect
702. #417	C₂²×C₂₃	semidirect
703. #416	C₂²×C₂₃	semidirect
704. C₂×#102	C₂²×C₂₃	semidirect
705. C₂×#102	C₂²×C₂₃	semidirect
706. C₂×#102	C₂²×C₂₃	semidirect
707. #405	C₂²×C₂₃	semidirect
708. C₂×C₄×C₈	C₂²×C₂₃	semidirect
895. C₂₃	#62550	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×#3552	2
C₂₃×#3543	2
C₂₃×#3373	2
C₂₃×#3368	2
C₂₃×#3365	2
C₂₃×#3358	2
C₂₃×#3332	2
C₂₃×#3324	2
C₂₃×#3318	2
C₂₃×#3314	2
C₂₃×#3304	2
C₂₃×#3297	2
C₂₃×#3295	2
C₂₃×#3294	2
C₂₃×#3241	2
C₂₃×#3239	2
C₂₃×#3224	2
C₂₃×#3217	2
C₂₃×#3179	2
C₂₃×#3168	2
C₂₃×#3136	2
C₂×C₂₃×#486	2
C₂₃×#2966	2
#62550	23

Subgroups — C23×#62550 #19210176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62550 #19210176