Subgroups — C₂₃×#62543 #19210169

Order 5888.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3326	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3321	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3307	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#556	—	2	1	no	—
21	C₂₃×#556	C₂²	1	2	yes	—
22	C₂₃×#555	—	2	1	no	—
23	C₂₃×#555	C₂²	1	2	yes	—
24	C₂₃×#554	—	2	1	no	—
25	C₂₃×#554	C₂²	1	2	yes	—
26	C₂₃×#553	—	2	1	no	—
27	C₂₃×#553	—	2	1	no	—
28	C₂₃×#553	C₂²	1	2	yes	—
29	C₂₃×#553	C₂²	1	2	yes	—
30	C₂₃×#548	—	2	1	no	—
31	C₂₃×#548	—	2	1	no	—
32	C₂₃×#548	C₂²	1	2	yes	—
33	C₂₃×#548	C₂²	1	2	yes	—
34	C₂₃×#547	—	2	1	no	—
35	C₂₃×#547	C₂²	1	2	yes	—
36	C₂₃×#542	—	2	1	no	—
37	C₂₃×#542	—	2	1	no	—
38	C₂₃×#542	—	2	1	no	—
39	C₂₃×#542	—	2	1	no	—
40	C₂₃×#537	—	2	1	no	—
41	C₂₃×#537	—	2	1	no	—
42	C₂₃×#533	C₂²	1	1	yes	characteristic
43	C₂₃×#533	C₂²	1	1	yes	characteristic
44	C₂₃×#533	C₂²	1	1	yes	characteristic
45	C₂₃×#533	C₂²	1	1	yes	characteristic
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#532	C₂²	1	1	yes	characteristic
48	C₂₃×#532	C₂²	1	1	yes	characteristic
49	C₂₃×#532	C₂²	1	1	yes	characteristic
50	C₂₃×#532	C₂²	1	1	yes	characteristic
51	C₂₃×#532	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₂₃×#520	—	2	1	no	—
55	C₂₃×#520	—	2	1	no	—
56	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#500	C₂²	1	1	yes	characteristic
58	C₂₃×#498	C₂²	1	1	yes	characteristic
59	C₂₃×#498	C₂²	1	1	yes	characteristic
60	C₂₃×#493	C₂²	1	1	yes	characteristic
61	C₂₃×#492	C₂²	1	1	yes	characteristic
62	C₂₃×#492	C₂²	1	1	yes	characteristic
63	C₂₃×#491	C₂²	1	4	yes	—
64	C₂₃×#489	C₂²	1	4	yes	—
65	C₂₃×#488	C₂²	1	4	yes	—
66	C₂₃×#487	C₂²	1	1	yes	characteristic
67	C₂₃×#487	C₂²	1	1	yes	characteristic
68	C₂₃×#487	C₂²	1	1	yes	characteristic
69	C₂₃×#487	C₂²	1	1	yes	characteristic
70	C₂₃×#487	C₂²	1	1	yes	characteristic
71	C₂₃×#487	C₂²	1	1	yes	characteristic
72	C₂₃×#486	C₂²	1	1	yes	characteristic
73	C₂₃×#486	C₂²	1	1	yes	characteristic
74	C₂₃×#486	C₂²	1	1	yes	characteristic
75	C₂₃×#486	C₂²	1	1	yes	characteristic
76	C₂₃×#485	C₂²	1	4	yes	—
77	C₂₃×#483	C₂²	1	4	yes	—
78	C₂₃×#482	C₂²	1	4	yes	—
79	C₂₃×#479	C₂²	1	4	yes	—
80	C₂₃×#478	C₂²	1	4	yes	—
81	C₂₃×#475	C₂²	1	4	yes	—
82	C₂₃×#469	C₂²	1	4	yes	—
83	C₂₃×#468	C₂²	1	4	yes	—
84	C₂₃×#465	C₂²	1	4	yes	—
85	C₂₃×#463	C₂²	1	4	yes	—
86	C₂₃×#463	C₂²	1	4	yes	—
87	C₂₃×#461	C₂²	1	4	yes	—
88	C₂₃×#449	C₂²	1	4	yes	—
89	C₂₃×#449	C₂²	1	4	yes	—
90	C₂₃×#448	C₂²	1	4	yes	—
91	C₂₃×#446	C₂²	1	2	yes	—
92	C₂₃×#442	C₂²	1	4	yes	—
93	C₂₃×#440	C₂²	1	4	yes	—
94	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
95	C₂₃×#436	C₂²	1	2	yes	—
96	C₂₃×#435	C₂²	1	2	yes	—
97	C₂₃×#435	C₂²	1	2	yes	—
98	C₂₃×#431	C₂²	1	1	yes	characteristic
99	C₂₃×#431	C₂²	1	1	yes	characteristic
100	C₂₃×#431	C₂²	1	1	yes	characteristic
101	C₂₃×#419	C₂²	1	4	yes	—
102	C₂₃×#417	C₂²	1	4	yes	—
103	C₂₃×#416	C₂²	1	4	yes	—
104	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
105	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
106	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
107	C₂×#41×C₂₃	—	2	1	no	—
108	C₂×#41×C₂₃	—	2	1	no	—
109	C₂×#41×C₂₃	—	2	1	no	—
110	C₂×#41×C₂₃	—	2	1	no	—
111	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
112	C₂×#41×C₂₃	C₂³	1	2	yes	—
113	C₂×#41×C₂₃	C₂³	1	2	yes	—
114	C₂²×Q₈×C₂₃	—	2	1	no	—
115	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
118	C₂×D₈×C₂₃	C₂³	1	4	yes	—
119	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
120	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
121	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
122	C₂₃×C₄⋊Q₈	—	2	1	no	—
123	C₂₃×C₄⋊Q₈	—	2	1	no	—
124	C₂₃×C₄⋊Q₈	—	2	1	no	—
125	C₂₃×C₄⋊Q₈	—	2	1	no	—
126	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
134	C₂₃×#127	C₂³	1	1	yes	characteristic
135	C₂₃×#127	C₂³	1	1	yes	characteristic
136	C₂₃×#126	—	2	2	no	—
137	C₂₃×#126	—	2	2	no	—
138	C₂₃×#126	—	2	2	no	—
139	C₂₃×#126	—	2	2	no	—
140	C₂₃×#125	—	2	1	no	—
141	C₂₃×#125	—	2	1	no	—
142	C₂₃×#125	C₂³	1	2	yes	—
143	C₂₃×#125	C₂³	1	2	yes	—
144	C₂₃×#124	—	2	2	no	—
145	C₂₃×#124	—	2	2	no	—
146	C₂₃×#124	—	2	2	no	—
147	C₂₃×#124	—	2	2	no	—
148	C₂₃×#124	—	2	1	no	—
149	C₂₃×#124	—	2	1	no	—
150	C₂₃×#124	—	2	1	no	—
151	C₂₃×#124	—	2	1	no	—
152	C₂₃×#124	C₂³	1	2	yes	—
153	C₂₃×#124	C₂³	1	2	yes	—
154	C₂₃×#123	—	2	2	no	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×#123	—	2	2	no	—
157	C₂₃×#123	—	2	2	no	—
158	C₂₃×C₂²⋊Q₈	—	2	2	no	—
159	C₂₃×C₂²⋊Q₈	—	2	2	no	—
160	C₂₃×C₂²⋊Q₈	—	2	1	no	—
161	C₂₃×C₂²⋊Q₈	—	2	1	no	—
162	C₂₃×C₂²⋊Q₈	—	2	1	no	—
163	C₂₃×C₂²⋊Q₈	—	2	1	no	—
164	C₂₃×C₂²⋊Q₈	—	2	1	no	—
165	C₂₃×C₂²⋊Q₈	—	2	1	no	—
166	C₂₃×C₂²⋊Q₈	—	2	2	no	—
167	C₂₃×C₂²⋊Q₈	—	2	2	no	—
168	C₂₃×C₂²⋊Q₈	—	2	2	no	—
169	C₂₃×C₂²⋊Q₈	—	2	2	no	—
170	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
171	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₂₃×#121	—	2	2	no	—
173	C₂₃×#121	—	2	2	no	—
174	C₂₃×#121	—	2	2	no	—
175	C₂₃×#121	—	2	2	no	—
176	C₂₃×#121	—	2	2	no	—
177	C₂₃×#121	—	2	2	no	—
178	C₂₃×#121	—	2	1	no	—
179	C₂₃×#121	—	2	1	no	—
180	C₂₃×#121	—	2	1	no	—
181	C₂₃×#121	—	2	1	no	—
182	C₂₃×#121	—	2	1	no	—
183	C₂₃×#121	—	2	1	no	—
184	C₂₃×#121	—	2	1	no	—
185	C₂₃×#121	—	2	1	no	—
186	C₂₃×#121	C₂³	1	2	yes	—
187	C₂₃×#121	C₂³	1	2	yes	—
188	C₂₃×#121	C₂³	1	2	yes	—
189	C₂₃×#121	C₂³	1	2	yes	—
190	C₄×Q₈×C₂₃	—	2	1	no	—
191	C₄×Q₈×C₂₃	—	2	1	no	—
192	C₄×Q₈×C₂₃	—	2	1	no	—
193	C₄×Q₈×C₂₃	—	2	1	no	—
194	C₄×Q₈×C₂₃	—	2	1	no	—
195	C₄×Q₈×C₂₃	—	2	1	no	—
196	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
197	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
198	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
199	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₂₃	—	2	2	no	—
201	C₄×D₄×C₂₃	—	2	2	no	—
202	C₄×D₄×C₂₃	—	2	2	no	—
203	C₄×D₄×C₂₃	—	2	2	no	—
204	C₄×D₄×C₂₃	—	2	1	no	—
205	C₄×D₄×C₂₃	—	2	1	no	—
206	C₄×D₄×C₂₃	—	2	1	no	—
207	C₄×D₄×C₂₃	—	2	1	no	—
208	C₄×D₄×C₂₃	—	2	1	no	—
209	C₄×D₄×C₂₃	—	2	1	no	—
210	C₄×D₄×C₂₃	—	2	1	no	—
211	C₄×D₄×C₂₃	—	2	1	no	—
212	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
213	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
214	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
215	C₄×D₄×C₂₃	C₂³	1	2	yes	—
216	C₄×D₄×C₂₃	C₂³	1	2	yes	—
217	C₄×D₄×C₂₃	C₂³	1	2	yes	—
218	C₄×D₄×C₂₃	C₂³	1	2	yes	—
219	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
222	C₂₃×#117	—	2	1	no	—
223	C₂₃×#117	—	2	1	no	—
224	C₂₃×#117	—	2	2	no	—
225	C₂₃×#117	—	2	2	no	—
226	C₂₃×#117	D₄	1	1	yes	characteristic
227	C₂₃×#117	D₄	1	1	yes	characteristic
228	C₂₃×#117	D₄	1	1	yes	characteristic
229	C₂₃×#117	C₂³	1	2	yes	—
230	C₂₃×#117	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
235	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
236	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
237	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
240	C₂₃×#107	C₂³	1	4	yes	—
241	C₂₃×#106	C₂³	1	4	yes	—
242	C₂₃×#106	C₂³	1	4	yes	—
243	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
244	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
245	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
246	C₂₃×#103	C₂³	1	4	yes	—
247	C₂₃×#103	C₂³	1	4	yes	—
248	C₂₃×#103	C₂³	1	4	yes	—
249	C₂₃×#103	C₂³	1	4	yes	—
250	C₂₃×#103	C₂³	1	4	yes	—
251	C₂₃×#103	C₂³	1	4	yes	—
252	C₂₃×#102	C₂³	1	4	yes	—
253	C₂₃×#102	C₂³	1	4	yes	—
254	C₂₃×#102	C₂³	1	4	yes	—
255	C₂₃×#102	C₂³	1	4	yes	—
256	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₂₃×#97	C₂³	1	2	yes	—
260	C₂₃×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₂₃	C₂³	1	2	yes	—
264	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
266	#41×C₂₃	—	4	2	no	—
267	#41×C₂₃	—	4	4	no	—
268	#41×C₂₃	—	4	4	no	—
269	#41×C₂₃	—	4	4	no	—
270	#41×C₂₃	—	4	4	no	—
271	#41×C₂₃	—	8	2	no	—
272	#41×C₂₃	—	8	2	no	—
273	C₂×Q₈×C₂₃	—	2	1	no	—
274	C₂×Q₈×C₂₃	—	2	1	no	—
275	C₂×Q₈×C₂₃	—	2	1	no	—
276	C₂×Q₈×C₂₃	—	2	1	no	—
277	C₂×Q₈×C₂₃	—	2	2	no	—
278	C₂×Q₈×C₂₃	—	2	2	no	—
279	C₂×Q₈×C₂₃	—	4	4	no	—
280	C₂×Q₈×C₂₃	—	8	2	no	—
281	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
282	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
283	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
284	C₂×D₄×C₂₃	—	2	2	no	—
285	C₂×D₄×C₂₃	—	2	2	no	—
286	C₂×D₄×C₂₃	—	2	2	no	—
287	C₂×D₄×C₂₃	—	2	2	no	—
288	C₂×D₄×C₂₃	—	2	2	no	—
289	C₂×D₄×C₂₃	—	2	2	no	—
290	C₂×D₄×C₂₃	—	2	1	no	—
291	C₂×D₄×C₂₃	—	2	1	no	—
292	C₂×D₄×C₂₃	—	2	1	no	—
293	C₂×D₄×C₂₃	—	2	1	no	—
294	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
296	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
298	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₂₃	—	2	2	no	—
300	C₂²×C₄×C₂₃	—	2	2	no	—
301	C₂²×C₄×C₂₃	—	2	2	no	—
302	C₂²×C₄×C₂₃	—	2	2	no	—
303	C₂²×C₄×C₂₃	—	2	2	no	—
304	C₂²×C₄×C₂₃	—	2	2	no	—
305	C₂²×C₄×C₂₃	—	2	2	no	—
306	C₂²×C₄×C₂₃	—	2	2	no	—
307	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
316	SD₁₆×C₂₃	—	4	4	no	—
317	SD₁₆×C₂₃	—	4	4	no	—
318	D₈×C₂₃	—	4	4	no	—
319	M₁₆×C₂₃	—	4	2	no	—
320	M₁₆×C₂₃	—	4	2	no	—
321	C₂×C₈×C₂₃	—	4	2	no	—
322	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
323	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
324	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
325	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
326	C₄⋊C₄×C₂₃	—	2	2	no	—
327	C₄⋊C₄×C₂₃	—	2	2	no	—
328	C₄⋊C₄×C₂₃	—	2	1	no	—
329	C₄⋊C₄×C₂₃	—	2	1	no	—
330	C₄⋊C₄×C₂₃	—	2	1	no	—
331	C₄⋊C₄×C₂₃	—	2	1	no	—
332	C₄⋊C₄×C₂₃	—	2	1	no	—
333	C₄⋊C₄×C₂₃	—	2	1	no	—
334	C₄⋊C₄×C₂₃	—	2	2	no	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	2	no	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	—	2	1	no	—
341	C₄⋊C₄×C₂₃	—	2	1	no	—
342	C₄⋊C₄×C₂₃	—	2	2	no	—
343	C₄⋊C₄×C₂₃	—	2	2	no	—
344	C₄⋊C₄×C₂₃	—	2	2	no	—
345	C₄⋊C₄×C₂₃	—	2	2	no	—
346	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
347	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
348	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
353	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
355	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
356	C₂²⋊C₄×C₂₃	—	2	2	no	—
357	C₂²⋊C₄×C₂₃	—	2	2	no	—
358	C₂²⋊C₄×C₂₃	—	2	2	no	—
359	C₂²⋊C₄×C₂₃	—	2	2	no	—
360	C₂²⋊C₄×C₂₃	—	2	2	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	—	2	2	no	—
366	C₂²⋊C₄×C₂₃	—	2	2	no	—
367	C₂²⋊C₄×C₂₃	—	2	2	no	—
368	C₂²⋊C₄×C₂₃	—	2	2	no	—
369	C₂²⋊C₄×C₂₃	—	2	2	no	—
370	C₂²⋊C₄×C₂₃	—	2	2	no	—
371	C₂²⋊C₄×C₂₃	—	2	2	no	—
372	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
373	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
374	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
375	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
376	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
377	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₂₃	—	2	2	no	—
379	C₄²×C₂₃	—	2	2	no	—
380	C₄²×C₂₃	—	2	2	no	—
381	C₄²×C₂₃	—	2	2	no	—
382	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
386	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
387	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
389	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
390	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
391	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
392	#62543	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
393	C₂³×C₂₃	—	2	2	no	—
394	C₂³×C₂₃	—	2	2	no	—
395	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
396	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
397	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
398	Q₈×C₂₃	—	2	4	no	—
399	Q₈×C₂₃	—	2	4	no	—
400	Q₈×C₂₃	—	4	1	no	—
401	Q₈×C₂₃	—	4	2	no	—
402	Q₈×C₂₃	—	4	2	no	—
403	Q₈×C₂₃	—	4	2	no	—
404	Q₈×C₂₃	—	4	2	no	—
405	Q₈×C₂₃	—	8	2	no	—
406	Q₈×C₂₃	—	8	2	no	—
407	D₄×C₂₃	—	2	4	no	—
408	D₄×C₂₃	—	2	4	no	—
409	D₄×C₂₃	—	4	1	no	—
410	D₄×C₂₃	—	4	1	no	—
411	D₄×C₂₃	—	4	1	no	—
412	D₄×C₂₃	—	4	4	no	—
413	D₄×C₂₃	—	4	4	no	—
414	D₄×C₂₃	—	4	2	no	—
415	D₄×C₂₃	—	4	2	no	—
416	D₄×C₂₃	—	4	2	no	—
417	D₄×C₂₃	—	4	2	no	—
418	D₄×C₂₃	—	8	2	no	—
419	D₄×C₂₃	—	8	2	no	—
420	D₄×C₂₃	—	8	2	no	—
421	D₄×C₂₃	—	8	2	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	2	no	—
424	C₂×C₄×C₂₃	—	2	2	no	—
425	C₂×C₄×C₂₃	—	2	2	no	—
426	C₂×C₄×C₂₃	—	2	2	no	—
427	C₂×C₄×C₂₃	—	2	2	no	—
428	C₂×C₄×C₂₃	—	2	2	no	—
429	C₂×C₄×C₂₃	—	2	2	no	—
430	C₂×C₄×C₂₃	—	2	2	no	—
431	C₂×C₄×C₂₃	—	2	2	no	—
432	C₂×C₄×C₂₃	—	2	2	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	2	no	—
435	C₂×C₄×C₂₃	—	2	2	no	—
436	C₂×C₄×C₂₃	—	2	2	no	—
437	C₂×C₄×C₂₃	—	4	4	no	—
438	C₂×C₄×C₂₃	—	4	4	no	—
439	C₂×C₄×C₂₃	—	8	2	no	—
440	C₂×C₄×C₂₃	—	8	2	no	—
441	C₂×C₄×C₂₃	—	8	2	no	—
442	C₂×C₄×C₂₃	—	8	2	no	—
443	C₂×C₄×C₂₃	—	8	2	no	—
444	C₂×C₄×C₂₃	—	8	2	no	—
445	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
457	C₈×C₂₃	—	2	2	no	—
458	C₈×C₂₃	—	2	2	no	—
459	C₈×C₂₃	—	2	2	no	—
460	C₈×C₂₃	—	2	2	no	—
461	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
462	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
463	#3376	C₂×C₂₃	1	4	yes	complemented
464	#3326	C₂×C₂₃	1	4	yes	complemented
465	#3321	C₂×C₂₃	1	4	yes	complemented
466	#3307	C₂×C₂₃	1	4	yes	complemented
467	#3231	C₂×C₂₃	1	1	yes	characteristic, complemented
468	#3229	C₂×C₂₃	1	1	yes	characteristic, complemented
469	#3228	C₂×C₂₃	1	1	yes	characteristic, complemented
470	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
471	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
472	#3206	C₂×C₂₃	1	1	yes	characteristic, complemented
473	#3184	C₂×C₂₃	1	1	yes	characteristic, complemented
474	#3182	C₂×C₂₃	1	1	yes	characteristic, complemented
475	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
476	#3141	C₂×C₂₃	1	1	yes	characteristic, complemented
477	#3139	C₂×C₂₃	1	1	yes	characteristic, complemented
478	#3131	C₂×C₂₃	1	1	yes	characteristic, complemented
479	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
480	C₂²×C₂₃	—	2	1	no	—
481	C₂²×C₂₃	—	2	1	no	—
482	C₂²×C₂₃	—	2	1	no	—
483	C₂²×C₂₃	—	2	1	no	—
484	C₂²×C₂₃	—	2	1	no	—
485	C₂²×C₂₃	—	2	1	no	—
486	C₂²×C₂₃	—	2	1	no	—
487	C₂²×C₂₃	—	2	1	no	—
488	C₂²×C₂₃	—	2	1	no	—
489	C₂²×C₂₃	—	4	2	no	—
490	C₂²×C₂₃	—	4	2	no	—
491	C₂²×C₂₃	—	4	2	no	—
492	C₂²×C₂₃	—	4	2	no	—
493	C₂²×C₂₃	—	4	2	no	—
494	C₂²×C₂₃	—	4	2	no	—
495	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
496	C₄×C₂₃	—	2	1	no	—
497	C₄×C₂₃	—	2	1	no	—
498	C₄×C₂₃	—	2	1	no	—
499	C₄×C₂₃	—	2	1	no	—
500	C₄×C₂₃	—	2	1	no	—
501	C₄×C₂₃	—	2	1	no	—
502	C₄×C₂₃	—	2	1	no	—
503	C₄×C₂₃	—	2	1	no	—
504	C₄×C₂₃	—	2	1	no	—
505	C₄×C₂₃	—	4	2	no	—
506	C₄×C₂₃	—	4	2	no	—
507	C₄×C₂₃	—	4	2	no	—
508	C₄×C₂₃	—	4	2	no	—
509	C₄×C₂₃	—	4	2	no	—
510	C₄×C₂₃	—	4	2	no	—
511	C₄×C₂₃	#575	1	2	yes	—
512	C₄×C₂₃	#577	1	2	yes	—
513	C₄×C₂₃	#585	1	2	yes	—
514	#556	—	2	1	no	—
515	#556	C₂²×C₂₃	1	2	yes	—
516	#555	—	2	1	no	—
517	#555	C₂²×C₂₃	1	2	yes	—
518	#554	—	2	1	no	—
519	#554	C₂²×C₂₃	1	2	yes	—
520	#553	—	2	1	no	—
521	#553	—	2	1	no	—
522	#553	C₂²×C₂₃	1	2	yes	—
523	#553	C₂²×C₂₃	1	2	yes	—
524	#548	—	2	1	no	—
525	#548	—	2	1	no	—
526	#548	C₂²×C₂₃	1	2	yes	—
527	#548	C₂²×C₂₃	1	2	yes	—
528	#547	—	2	1	no	—
529	#547	C₂²×C₂₃	1	2	yes	—
530	#542	—	2	1	no	—
531	#542	—	2	1	no	—
532	#542	—	2	1	no	—
533	#542	—	2	1	no	—
534	#537	—	2	1	no	—
535	#537	—	2	1	no	—
536	#533	C₂²×C₂₃	1	1	yes	characteristic
537	#533	C₂²×C₂₃	1	1	yes	characteristic
538	#533	C₂²×C₂₃	1	1	yes	characteristic
539	#533	C₂²×C₂₃	1	1	yes	characteristic
540	#532	C₂²×C₂₃	1	1	yes	characteristic
541	#532	C₂²×C₂₃	1	1	yes	characteristic
542	#532	C₂²×C₂₃	1	1	yes	characteristic
543	#532	C₂²×C₂₃	1	1	yes	characteristic
544	#532	C₂²×C₂₃	1	1	yes	characteristic
545	#532	C₂²×C₂₃	1	1	yes	characteristic
546	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
547	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
548	#520	—	2	1	no	—
549	#520	—	2	1	no	—
550	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
551	#500	C₂²×C₂₃	1	1	yes	characteristic
552	#498	C₂²×C₂₃	1	1	yes	characteristic
553	#498	C₂²×C₂₃	1	1	yes	characteristic
554	#493	C₂²×C₂₃	1	1	yes	characteristic
555	#492	C₂²×C₂₃	1	1	yes	characteristic
556	#492	C₂²×C₂₃	1	1	yes	characteristic
557	#491	C₂²×C₂₃	1	4	yes	—
558	#489	C₂²×C₂₃	1	4	yes	—
559	#488	C₂²×C₂₃	1	4	yes	—
560	#487	C₂²×C₂₃	1	1	yes	characteristic
561	#487	C₂²×C₂₃	1	1	yes	characteristic
562	#487	C₂²×C₂₃	1	1	yes	characteristic
563	#487	C₂²×C₂₃	1	1	yes	characteristic
564	#487	C₂²×C₂₃	1	1	yes	characteristic
565	#487	C₂²×C₂₃	1	1	yes	characteristic
566	#486	C₂²×C₂₃	1	1	yes	characteristic
567	#486	C₂²×C₂₃	1	1	yes	characteristic
568	#486	C₂²×C₂₃	1	1	yes	characteristic
569	#486	C₂²×C₂₃	1	1	yes	characteristic
570	#485	C₂²×C₂₃	1	4	yes	—
571	#483	C₂²×C₂₃	1	4	yes	—
572	#482	C₂²×C₂₃	1	4	yes	—
573	#479	C₂²×C₂₃	1	4	yes	—
574	#478	C₂²×C₂₃	1	4	yes	—
575	#475	C₂²×C₂₃	1	4	yes	—
576	#469	C₂²×C₂₃	1	4	yes	—
577	#468	C₂²×C₂₃	1	4	yes	—
578	#465	C₂²×C₂₃	1	4	yes	—
579	#463	C₂²×C₂₃	1	4	yes	—
580	#463	C₂²×C₂₃	1	4	yes	—
581	#461	C₂²×C₂₃	1	4	yes	—
582	#449	C₂²×C₂₃	1	4	yes	—
583	#449	C₂²×C₂₃	1	4	yes	—
584	#448	C₂²×C₂₃	1	4	yes	—
585	#446	C₂²×C₂₃	1	2	yes	—
586	#442	C₂²×C₂₃	1	4	yes	—
587	#440	C₂²×C₂₃	1	4	yes	—
588	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
589	#436	C₂²×C₂₃	1	2	yes	—
590	#435	C₂²×C₂₃	1	2	yes	—
591	#435	C₂²×C₂₃	1	2	yes	—
592	#431	C₂²×C₂₃	1	1	yes	characteristic
593	#431	C₂²×C₂₃	1	1	yes	characteristic
594	#431	C₂²×C₂₃	1	1	yes	characteristic
595	#419	C₂²×C₂₃	1	4	yes	—
596	#417	C₂²×C₂₃	1	4	yes	—
597	#416	C₂²×C₂₃	1	4	yes	—
598	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
599	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
600	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
601	C₂×C₂₃	—	4	1	no	—
602	C₂×C₂₃	—	4	1	no	—
603	C₂×C₂₃	—	4	1	no	—
604	C₂×C₂₃	—	8	2	no	—
605	C₂×C₂₃	—	8	2	no	—
606	C₂×C₂₃	#3500	1	1	yes	characteristic
607	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
608	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
609	C₂×#41	—	2	1	no	—
610	C₂×#41	—	2	1	no	—
611	C₂×#41	—	2	1	no	—
612	C₂×#41	—	2	1	no	—
613	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
614	C₂×#41	C₂³×C₂₃	1	2	yes	—
615	C₂×#41	C₂³×C₂₃	1	2	yes	—
616	C₂²×Q₈	—	2	1	no	—
617	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
618	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
619	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
620	C₂×D₈	C₂³×C₂₃	1	4	yes	—
621	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
622	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
623	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
624	C₄⋊Q₈	—	2	1	no	—
625	C₄⋊Q₈	—	2	1	no	—
626	C₄⋊Q₈	—	2	1	no	—
627	C₄⋊Q₈	—	2	1	no	—
628	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
629	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
630	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
631	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
633	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
634	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
635	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
636	#127	C₂³×C₂₃	1	1	yes	characteristic
637	#127	C₂³×C₂₃	1	1	yes	characteristic
638	#126	—	2	2	no	—
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#125	—	2	1	no	—
643	#125	—	2	1	no	—
644	#125	C₂³×C₂₃	1	2	yes	—
645	#125	C₂³×C₂₃	1	2	yes	—
646	#124	—	2	2	no	—
647	#124	—	2	2	no	—
648	#124	—	2	2	no	—
649	#124	—	2	2	no	—
650	#124	—	2	1	no	—
651	#124	—	2	1	no	—
652	#124	—	2	1	no	—
653	#124	—	2	1	no	—
654	#124	C₂³×C₂₃	1	2	yes	—
655	#124	C₂³×C₂₃	1	2	yes	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	1	no	—
663	C₂²⋊Q₈	—	2	1	no	—
664	C₂²⋊Q₈	—	2	1	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	—	2	1	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
673	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
674	#121	—	2	2	no	—
675	#121	—	2	2	no	—
676	#121	—	2	2	no	—
677	#121	—	2	2	no	—
678	#121	—	2	2	no	—
679	#121	—	2	2	no	—
680	#121	—	2	1	no	—
681	#121	—	2	1	no	—
682	#121	—	2	1	no	—
683	#121	—	2	1	no	—
684	#121	—	2	1	no	—
685	#121	—	2	1	no	—
686	#121	—	2	1	no	—
687	#121	—	2	1	no	—
688	#121	C₂³×C₂₃	1	2	yes	—
689	#121	C₂³×C₂₃	1	2	yes	—
690	#121	C₂³×C₂₃	1	2	yes	—
691	#121	C₂³×C₂₃	1	2	yes	—
692	C₄×Q₈	—	2	1	no	—
693	C₄×Q₈	—	2	1	no	—
694	C₄×Q₈	—	2	1	no	—
695	C₄×Q₈	—	2	1	no	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	—	2	1	no	—
698	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
699	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
700	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
701	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
702	C₄×D₄	—	2	2	no	—
703	C₄×D₄	—	2	2	no	—
704	C₄×D₄	—	2	2	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	1	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	—	2	1	no	—
712	C₄×D₄	—	2	1	no	—
713	C₄×D₄	—	2	1	no	—
714	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
715	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
716	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
717	C₄×D₄	C₂³×C₂₃	1	2	yes	—
718	C₄×D₄	C₂³×C₂₃	1	2	yes	—
719	C₄×D₄	C₂³×C₂₃	1	2	yes	—
720	C₄×D₄	C₂³×C₂₃	1	2	yes	—
721	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
722	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
723	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
724	#117	—	2	1	no	—
725	#117	—	2	1	no	—
726	#117	—	2	2	no	—
727	#117	—	2	2	no	—
728	#117	D₄×C₂₃	1	1	yes	characteristic
729	#117	D₄×C₂₃	1	1	yes	characteristic
730	#117	D₄×C₂₃	1	1	yes	characteristic
731	#117	C₂³×C₂₃	1	2	yes	—
732	#117	C₂³×C₂₃	1	2	yes	—
733	C₂×C₄⋊C₄	—	2	1	no	—
734	C₂×C₄⋊C₄	—	2	1	no	—
735	C₂×C₄⋊C₄	—	2	1	no	—
736	C₂×C₄⋊C₄	—	2	2	no	—
737	C₂×C₄⋊C₄	—	2	2	no	—
738	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
739	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
742	#107	C₂³×C₂₃	1	4	yes	—
743	#106	C₂³×C₂₃	1	4	yes	—
744	#106	C₂³×C₂₃	1	4	yes	—
745	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
746	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
747	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
748	#103	C₂³×C₂₃	1	4	yes	—
749	#103	C₂³×C₂₃	1	4	yes	—
750	#103	C₂³×C₂₃	1	4	yes	—
751	#103	C₂³×C₂₃	1	4	yes	—
752	#103	C₂³×C₂₃	1	4	yes	—
753	#103	C₂³×C₂₃	1	4	yes	—
754	#102	C₂³×C₂₃	1	4	yes	—
755	#102	C₂³×C₂₃	1	4	yes	—
756	#102	C₂³×C₂₃	1	4	yes	—
757	#102	C₂³×C₂₃	1	4	yes	—
758	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
759	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
760	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
761	#97	C₂³×C₂₃	1	2	yes	—
762	#97	C₂³×C₂₃	1	2	yes	—
763	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
764	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
765	C₄×C₈	C₂³×C₂₃	1	2	yes	—
766	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
767	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
768	C₂₃	#62543	1	1	yes	characteristic, direct product factor, Sylow
769	#41	—	4	2	no	—
770	#41	—	4	4	no	—
771	#41	—	4	4	no	—
772	#41	—	4	4	no	—
773	#41	—	4	4	no	—
774	#41	—	8	2	no	—
775	#41	—	8	2	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	2	1	no	—
778	C₂×Q₈	—	2	1	no	—
779	C₂×Q₈	—	2	1	no	—
780	C₂×Q₈	—	2	2	no	—
781	C₂×Q₈	—	2	2	no	—
782	C₂×Q₈	—	4	4	no	—
783	C₂×Q₈	—	8	2	no	—
784	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
785	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
786	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
798	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
799	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
800	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
801	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
811	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
812	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
813	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
814	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
815	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
819	SD₁₆	—	4	4	no	—
820	SD₁₆	—	4	4	no	—
821	D₈	—	4	4	no	—
822	M₁₆	—	4	2	no	—
823	M₁₆	—	4	2	no	—
824	C₂×C₈	—	4	2	no	—
825	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
826	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
827	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
828	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
850	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
851	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
852	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
853	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
854	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
855	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
856	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
857	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
858	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
876	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
877	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
878	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
879	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
880	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
886	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
887	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
888	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
889	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
890	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
891	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
892	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
893	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
894	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
898	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
899	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
900	Q₈	—	2	4	no	—
901	Q₈	—	2	4	no	—
902	Q₈	—	4	1	no	—
903	Q₈	—	4	2	no	—
904	Q₈	—	4	2	no	—
905	Q₈	—	4	2	no	—
906	Q₈	—	4	2	no	—
907	Q₈	—	8	2	no	—
908	Q₈	—	8	2	no	—
909	D₄	—	2	4	no	—
910	D₄	—	2	4	no	—
911	D₄	—	4	1	no	—
912	D₄	—	4	1	no	—
913	D₄	—	4	1	no	—
914	D₄	—	4	4	no	—
915	D₄	—	4	4	no	—
916	D₄	—	4	2	no	—
917	D₄	—	4	2	no	—
918	D₄	—	4	2	no	—
919	D₄	—	4	2	no	—
920	D₄	—	8	2	no	—
921	D₄	—	8	2	no	—
922	D₄	—	8	2	no	—
923	D₄	—	8	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	2	no	—
945	C₂×C₄	—	8	2	no	—
946	C₂×C₄	—	8	2	no	—
947	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
951	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
952	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
953	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
955	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
956	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
957	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
958	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
959	C₈	—	2	2	no	—
960	C₈	—	2	2	no	—
961	C₈	—	2	2	no	—
962	C₈	—	2	2	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	C₂₃×#575	1	2	yes	—
995	C₄	C₂₃×#577	1	2	yes	—
996	C₄	C₂₃×#585	1	2	yes	—
997	C₂	—	4	1	no	—
998	C₂	—	4	1	no	—
999	C₂	—	4	1	no	—
1000	C₂	—	8	2	no	—
1001	C₂	—	8	2	no	—
1002	C₂	C₂₃×#3500	1	1	yes	characteristic
1003	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1004	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3511	C₂	semidirect
2. C₂₃×#3511	C₂	semidirect
3. C₂₃×#3376	C₂	semidirect
4. C₂₃×#3326	C₂	semidirect
5. C₂₃×#3321	C₂	semidirect
6. C₂₃×#3307	C₂	semidirect
7. C₂₃×#3231	C₂	semidirect
8. C₂₃×#3229	C₂	semidirect
9. C₂₃×#3228	C₂	semidirect
10. C₂₃×#3207	C₂	semidirect
11. C₂₃×#3207	C₂	semidirect
12. C₂₃×#3206	C₂	semidirect
13. C₂₃×#3184	C₂	semidirect
14. C₂₃×#3182	C₂	semidirect
15. C₂₃×#3167	C₂	semidirect
16. C₂₃×#3141	C₂	semidirect
17. C₂₃×#3139	C₂	semidirect
18. C₂₃×#3131	C₂	semidirect
19. C₂₃×#2965	C₂	semidirect
392. #62543	C₂₃	direct (N × H)
461. #3511	C₂×C₂₃	semidirect
462. #3511	C₂×C₂₃	semidirect
463. #3376	C₂×C₂₃	semidirect
464. #3326	C₂×C₂₃	semidirect
465. #3321	C₂×C₂₃	semidirect
466. #3307	C₂×C₂₃	semidirect
467. #3231	C₂×C₂₃	semidirect
468. #3229	C₂×C₂₃	semidirect
469. #3228	C₂×C₂₃	semidirect
470. #3207	C₂×C₂₃	semidirect
471. #3207	C₂×C₂₃	semidirect
472. #3206	C₂×C₂₃	semidirect
473. #3184	C₂×C₂₃	semidirect
474. #3182	C₂×C₂₃	semidirect
475. #3167	C₂×C₂₃	semidirect
476. #3141	C₂×C₂₃	semidirect
477. #3139	C₂×C₂₃	semidirect
478. #3131	C₂×C₂₃	semidirect
479. #2965	C₂×C₂₃	semidirect
768. C₂₃	#62543	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×#3511	2
C₂₃×#3376	2
C₂₃×#3326	2
C₂₃×#3321	2
C₂₃×#3307	2
C₂₃×#3231	2
C₂₃×#3229	2
C₂₃×#3228	2
C₂₃×#3207	2
C₂₃×#3206	2
C₂₃×#3184	2
C₂₃×#3182	2
C₂₃×#3167	2
C₂₃×#3141	2
C₂₃×#3139	2
C₂₃×#3131	2
C₂₃×#2965	2
#62543	23

Subgroups — C23×#62543 #19210169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62543 #19210169