Subgroups — C₂₃×#61006 #19208632

Order 5888.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1036 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×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3257	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3198	C₂	1	4	yes	maximal, complemented
13	C₂₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3119	C₂	1	4	yes	maximal, complemented
18	C₂₃×#3118	C₂	1	4	yes	maximal, complemented
19	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#559	—	2	1	no	—
21	C₂₃×#559	—	2	1	no	—
22	C₂₃×#556	—	2	1	no	—
23	C₂₃×#555	—	2	1	no	—
24	C₂₃×#554	—	2	1	no	—
25	C₂₃×#553	—	2	1	no	—
26	C₂₃×#553	—	2	1	no	—
27	C₂₃×#550	—	2	1	no	—
28	C₂₃×#550	—	2	1	no	—
29	C₂₃×#548	—	2	1	no	—
30	C₂₃×#548	—	2	1	no	—
31	C₂₃×#547	—	2	1	no	—
32	C₂₃×#546	—	2	1	no	—
33	C₂₃×#546	—	2	1	no	—
34	C₂₃×#546	—	2	1	no	—
35	C₂₃×#546	—	2	1	no	—
36	C₂₃×#542	C₂²	1	2	yes	—
37	C₂₃×#542	C₂²	1	2	yes	complemented
38	C₂₃×#540	C₂²	1	2	yes	—
39	C₂₃×#540	C₂²	1	2	yes	—
40	C₂₃×#537	C₂²	1	2	yes	—
41	C₂₃×#535	C₂²	1	2	yes	—
42	C₂₃×#533	C₂²	1	1	yes	characteristic
43	C₂₃×#533	C₂²	1	1	yes	characteristic
44	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#532	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, complemented
51	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
54	C₂₃×#520	C₂²	1	2	yes	complemented
55	C₂₃×#518	C₂²	1	2	yes	—
56	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#493	C₂²	1	1	yes	characteristic
62	C₂₃×#493	C₂²	1	1	yes	characteristic
63	C₂₃×#492	C₂²	1	1	yes	characteristic
64	C₂₃×#492	C₂²	1	1	yes	characteristic
65	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#486	C₂²	1	1	yes	characteristic
68	C₂₃×#486	C₂²	1	1	yes	characteristic
69	C₂₃×#486	C₂²	1	1	yes	characteristic
70	C₂₃×#486	C₂²	1	1	yes	characteristic
71	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#485	C₂²	1	4	yes	—
74	C₂₃×#482	C₂²	1	4	yes	—
75	C₂₃×#481	C₂²	1	4	yes	complemented
76	C₂₃×#480	C₂²	1	4	yes	complemented
77	C₂₃×#479	C₂²	1	4	yes	complemented
78	C₂₃×#478	C₂²	1	4	yes	complemented
79	C₂₃×#476	C₂²	1	4	yes	complemented
80	C₂₃×#474	C₂²	1	4	yes	complemented
81	C₂₃×#469	C₂²	1	4	yes	complemented
82	C₂₃×#468	C₂²	1	4	yes	complemented
83	C₂₃×#466	C₂²	1	4	yes	complemented
84	C₂₃×#465	C₂²	1	4	yes	complemented
85	C₂₃×#463	C₂²	1	4	yes	complemented
86	C₂₃×#463	C₂²	1	4	yes	complemented
87	C₂₃×#460	C₂²	1	4	yes	—
88	C₂₃×#459	C₂²	1	4	yes	—
89	C₂₃×#450	C₂²	1	4	yes	—
90	C₂₃×#449	C₂²	1	4	yes	complemented
91	C₂₃×#449	C₂²	1	4	yes	complemented
92	C₂₃×#447	C₂²	1	4	yes	—
93	C₂₃×#442	C₂²	1	4	yes	complemented
94	C₂₃×#440	C₂²	1	4	yes	complemented
95	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
96	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
97	C₂₃×#433	C₂²	1	2	yes	—
98	C₂₃×#433	C₂²	1	2	yes	complemented
99	C₂₃×#431	C₂²	1	1	yes	characteristic
100	C₂₃×#431	C₂²	1	1	yes	characteristic
101	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#424	C₂²	1	2	yes	complemented
104	C₂₃×#408	C₂²	1	2	yes	—
105	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
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	—	2	1	no	—
112	C₂×#41×C₂₃	—	2	1	no	—
113	C₂×#41×C₂₃	C₂³	1	2	yes	—
114	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
115	C₂²×Q₈×C₂₃	—	2	1	no	—
116	C₂²×D₄×C₂₃	—	2	1	no	—
117	C₂²×D₄×C₂₃	—	2	1	no	—
118	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
119	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
121	C₂×D₈×C₂₃	C₂³	1	4	yes	—
122	C₂×D₈×C₂₃	C₂³	1	4	yes	—
123	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
125	C₂₃×C₄⋊Q₈	—	2	1	no	—
126	C₂₃×C₄⋊Q₈	—	2	1	no	—
127	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#127	—	2	2	no	—
134	C₂₃×#127	—	2	1	no	—
135	C₂₃×#127	—	2	1	no	—
136	C₂₃×#127	C₂³	1	2	yes	—
137	C₂₃×#127	C₂³	1	1	yes	characteristic
138	C₂₃×#127	C₂³	1	1	yes	characteristic
139	C₂₃×#127	C₂³	1	1	yes	characteristic
140	C₂₃×#126	—	2	2	no	—
141	C₂₃×#126	—	2	2	no	—
142	C₂₃×#125	—	2	1	no	—
143	C₂₃×#125	—	2	1	no	—
144	C₂₃×#125	C₂³	1	2	yes	—
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	—	2	1	no	—
153	C₂₃×#124	—	2	1	no	—
154	C₂₃×#124	C₂³	1	2	yes	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×#123	—	2	2	no	—
157	C₂₃×#123	—	2	2	no	—
158	C₂₃×#123	—	2	2	no	—
159	C₂₃×#123	—	2	2	no	—
160	C₂₃×#123	—	2	2	no	—
161	C₂₃×C₂²⋊Q₈	—	2	2	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	C₂³	1	2	yes	—
169	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₂₃×#121	—	2	2	no	—
171	C₂₃×#121	—	2	2	no	—
172	C₂₃×#121	—	2	2	no	—
173	C₂₃×#121	—	2	1	no	—
174	C₂₃×#121	—	2	1	no	—
175	C₂₃×#121	—	2	1	no	—
176	C₂₃×#121	—	2	1	no	—
177	C₂₃×#121	—	2	1	no	—
178	C₂₃×#121	—	2	1	no	—
179	C₂₃×#121	—	2	1	no	—
180	C₂₃×#121	—	2	1	no	—
181	C₂₃×#121	—	2	2	no	—
182	C₂₃×#121	—	2	2	no	—
183	C₂₃×#121	—	2	2	no	—
184	C₂₃×#121	—	2	2	no	—
185	C₂₃×#121	C₂³	1	2	yes	—
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	C₂₃×#121	C₂³	1	2	yes	—
191	C₂₃×#120	—	2	2	no	—
192	C₂₃×#120	—	2	2	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	—	2	1	no	—
197	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
198	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
199	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
200	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
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	2	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	—	2	1	no	—
213	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
214	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
215	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
216	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
217	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
218	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
219	C₄×D₄×C₂₃	C₂³	1	2	yes	—
220	C₄×D₄×C₂₃	C₂³	1	2	yes	—
221	C₄×D₄×C₂₃	C₂³	1	2	yes	—
222	C₄×D₄×C₂₃	C₂³	1	2	yes	—
223	C₄×D₄×C₂₃	C₂³	1	2	yes	—
224	C₄×D₄×C₂₃	C₂³	1	2	yes	—
225	C₂₃×#117	—	2	1	no	—
226	C₂₃×#117	—	2	1	no	—
227	C₂₃×#117	—	2	2	no	—
228	C₂₃×#117	C₂³	1	2	yes	—
229	C₂₃×#117	C₂³	1	1	yes	characteristic
230	C₂₃×#117	C₂³	1	1	yes	characteristic
231	C₂₃×#117	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
234	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
235	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
236	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
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×#107	C₂³	1	4	yes	—
242	C₂₃×#106	C₂³	1	4	yes	—
243	C₂₃×#106	C₂³	1	4	yes	—
244	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
245	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
246	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
247	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₂₃×#103	C₂³	1	4	yes	—
249	C₂₃×#103	C₂³	1	4	yes	—
250	C₂₃×#102	C₂³	1	4	yes	—
251	C₂₃×#102	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×C₂²⋊C₈	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	C₂⁴×C₂₃	—	2	2	no	—
267	#41×C₂₃	—	4	2	no	—
268	#41×C₂₃	—	4	4	no	—
269	#41×C₂₃	—	8	2	no	—
270	#41×C₂₃	—	8	2	no	—
271	#41×C₂₃	—	8	2	no	—
272	#41×C₂₃	—	8	2	no	—
273	#41×C₂₃	—	8	2	no	—
274	#41×C₂₃	—	8	2	no	—
275	C₂×Q₈×C₂₃	—	2	1	no	—
276	C₂×Q₈×C₂₃	—	2	1	no	—
277	C₂×Q₈×C₂₃	—	2	1	no	—
278	C₂×Q₈×C₂₃	—	2	1	no	—
279	C₂×Q₈×C₂₃	—	2	2	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×D₄×C₂₃	—	2	2	no	—
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	2	no	—
292	C₂×D₄×C₂₃	—	2	1	no	—
293	C₂×D₄×C₂₃	—	2	1	no	—
294	C₂×D₄×C₂₃	—	2	1	no	—
295	C₂×D₄×C₂₃	—	2	1	no	—
296	C₂×D₄×C₂₃	—	2	1	no	—
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	2	no	—
299	C₂×D₄×C₂₃	—	4	4	no	—
300	C₂×D₄×C₂₃	—	8	2	no	—
301	C₂×D₄×C₂₃	—	8	2	no	—
302	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
306	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
307	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₂₃	—	2	2	no	—
309	C₂²×C₄×C₂₃	—	2	2	no	—
310	C₂²×C₄×C₂₃	—	2	2	no	—
311	C₂²×C₄×C₂₃	—	2	2	no	—
312	C₂²×C₄×C₂₃	—	2	2	no	—
313	C₂²×C₄×C₂₃	—	2	2	no	—
314	C₂²×C₄×C₂₃	—	2	2	no	—
315	C₂²×C₄×C₂₃	—	2	2	no	—
316	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
325	SD₁₆×C₂₃	—	4	4	no	—
326	SD₁₆×C₂₃	—	4	4	no	—
327	D₈×C₂₃	—	4	4	no	—
328	D₈×C₂₃	—	4	4	no	—
329	M₁₆×C₂₃	—	4	2	no	—
330	C₂×C₈×C₂₃	—	4	2	no	—
331	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
332	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
334	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	1	no	—
337	C₄⋊C₄×C₂₃	—	2	1	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	—	2	2	no	—
341	C₄⋊C₄×C₂₃	—	2	1	no	—
342	C₄⋊C₄×C₂₃	—	2	1	no	—
343	C₄⋊C₄×C₂₃	—	2	1	no	—
344	C₄⋊C₄×C₂₃	—	2	1	no	—
345	C₄⋊C₄×C₂₃	—	2	2	no	—
346	C₄⋊C₄×C₂₃	—	2	2	no	—
347	C₄⋊C₄×C₂₃	—	2	2	no	—
348	C₄⋊C₄×C₂₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
373	C₂²⋊C₄×C₂₃	—	2	2	no	—
374	C₂²⋊C₄×C₂₃	—	2	2	no	—
375	C₂²⋊C₄×C₂₃	—	2	2	no	—
376	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
377	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
378	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
379	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
380	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
381	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₂₃	—	2	2	no	—
383	C₄²×C₂₃	—	2	2	no	—
384	C₄²×C₂₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
392	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
393	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
394	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
395	#61006	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂³×C₂₃	—	2	2	no	—
397	C₂³×C₂₃	—	2	2	no	—
398	C₂³×C₂₃	—	2	2	no	—
399	C₂³×C₂₃	—	4	4	no	—
400	C₂³×C₂₃	—	8	2	no	—
401	C₂³×C₂₃	—	8	2	no	—
402	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
403	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
404	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
405	Q₈×C₂₃	—	2	4	no	—
406	Q₈×C₂₃	—	4	1	no	—
407	Q₈×C₂₃	—	4	2	no	—
408	Q₈×C₂₃	—	4	2	no	—
409	Q₈×C₂₃	—	4	2	no	—
410	Q₈×C₂₃	—	4	2	no	—
411	Q₈×C₂₃	—	8	2	no	—
412	D₄×C₂₃	—	2	4	no	—
413	D₄×C₂₃	—	2	4	no	—
414	D₄×C₂₃	—	2	4	no	—
415	D₄×C₂₃	—	4	1	no	—
416	D₄×C₂₃	—	4	1	no	—
417	D₄×C₂₃	—	4	1	no	—
418	D₄×C₂₃	—	4	4	no	—
419	D₄×C₂₃	—	4	4	no	—
420	D₄×C₂₃	—	4	2	no	—
421	D₄×C₂₃	—	4	2	no	—
422	D₄×C₂₃	—	4	2	no	—
423	D₄×C₂₃	—	4	2	no	—
424	D₄×C₂₃	—	4	2	no	—
425	D₄×C₂₃	—	4	2	no	—
426	D₄×C₂₃	—	8	2	no	—
427	D₄×C₂₃	—	8	2	no	—
428	D₄×C₂₃	—	8	2	no	—
429	D₄×C₂₃	—	8	2	no	—
430	D₄×C₂₃	—	8	2	no	—
431	D₄×C₂₃	—	8	2	no	—
432	D₄×C₂₃	—	8	2	no	—
433	D₄×C₂₃	—	8	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	—	2	2	no	—
438	C₂×C₄×C₂₃	—	2	2	no	—
439	C₂×C₄×C₂₃	—	2	2	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	2	2	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	2	no	—
446	C₂×C₄×C₂₃	—	2	2	no	—
447	C₂×C₄×C₂₃	—	2	2	no	—
448	C₂×C₄×C₂₃	—	4	4	no	—
449	C₂×C₄×C₂₃	—	8	2	no	—
450	C₂×C₄×C₂₃	—	8	2	no	—
451	C₂×C₄×C₂₃	—	8	2	no	—
452	C₂×C₄×C₂₃	—	8	2	no	—
453	C₂×C₄×C₂₃	—	8	2	no	—
454	C₂×C₄×C₂₃	—	8	2	no	—
455	C₂×C₄×C₂₃	—	8	2	no	—
456	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
468	C₈×C₂₃	—	2	2	no	—
469	C₈×C₂₃	—	2	2	no	—
470	C₈×C₂₃	—	2	2	no	—
471	C₈×C₂₃	—	2	2	no	—
472	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
473	#3508	C₂×C₂₃	1	1	yes	characteristic, complemented
474	#3257	C₂×C₂₃	1	4	yes	complemented
475	#3231	C₂×C₂₃	1	1	yes	characteristic, complemented
476	#3228	C₂×C₂₃	1	1	yes	characteristic, complemented
477	#3227	C₂×C₂₃	1	1	yes	characteristic, complemented
478	#3226	C₂×C₂₃	1	1	yes	characteristic, complemented
479	#3208	C₂×C₂₃	1	1	yes	characteristic, complemented
480	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
481	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
482	#3205	C₂×C₂₃	1	1	yes	characteristic, complemented
483	#3198	C₂×C₂₃	1	4	yes	complemented
484	#3184	C₂×C₂₃	1	1	yes	characteristic, complemented
485	#3182	C₂×C₂₃	1	1	yes	characteristic, complemented
486	#3169	C₂×C₂₃	1	1	yes	characteristic, complemented
487	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
488	#3119	C₂×C₂₃	1	4	yes	complemented
489	#3118	C₂×C₂₃	1	4	yes	complemented
490	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
491	C₂²×C₂₃	—	2	1	no	—
492	C₂²×C₂₃	—	2	1	no	—
493	C₂²×C₂₃	—	2	1	no	—
494	C₂²×C₂₃	—	2	1	no	—
495	C₂²×C₂₃	—	2	1	no	—
496	C₂²×C₂₃	—	2	1	no	—
497	C₂²×C₂₃	—	2	1	no	—
498	C₂²×C₂₃	—	2	1	no	—
499	C₂²×C₂₃	—	2	1	no	—
500	C₂²×C₂₃	—	4	2	no	—
501	C₂²×C₂₃	—	4	2	no	—
502	C₂²×C₂₃	—	4	2	no	—
503	C₂²×C₂₃	—	4	2	no	—
504	C₂²×C₂₃	—	4	2	no	—
505	C₂²×C₂₃	—	4	2	no	—
506	C₂²×C₂₃	—	4	2	no	—
507	C₂²×C₂₃	—	4	2	no	—
508	C₂²×C₂₃	—	4	2	no	—
509	C₂²×C₂₃	—	16	4	no	—
510	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
511	C₄×C₂₃	—	2	1	no	—
512	C₄×C₂₃	—	2	1	no	—
513	C₄×C₂₃	—	2	1	no	—
514	C₄×C₂₃	—	2	1	no	—
515	C₄×C₂₃	—	2	1	no	—
516	C₄×C₂₃	—	2	1	no	—
517	C₄×C₂₃	—	2	1	no	—
518	C₄×C₂₃	—	2	1	no	—
519	C₄×C₂₃	—	2	1	no	—
520	C₄×C₂₃	—	4	2	no	—
521	C₄×C₂₃	—	4	2	no	—
522	C₄×C₂₃	—	4	2	no	—
523	C₄×C₂₃	—	4	2	no	—
524	C₄×C₂₃	—	4	2	no	—
525	C₄×C₂₃	#576	1	2	yes	—
526	C₄×C₂₃	#577	1	2	yes	—
527	C₄×C₂₃	#585	1	2	yes	—
528	#559	—	2	1	no	—
529	#559	—	2	1	no	—
530	#556	—	2	1	no	—
531	#555	—	2	1	no	—
532	#554	—	2	1	no	—
533	#553	—	2	1	no	—
534	#553	—	2	1	no	—
535	#550	—	2	1	no	—
536	#550	—	2	1	no	—
537	#548	—	2	1	no	—
538	#548	—	2	1	no	—
539	#547	—	2	1	no	—
540	#546	—	2	1	no	—
541	#546	—	2	1	no	—
542	#546	—	2	1	no	—
543	#546	—	2	1	no	—
544	#542	C₂²×C₂₃	1	2	yes	—
545	#542	C₂²×C₂₃	1	2	yes	complemented
546	#540	C₂²×C₂₃	1	2	yes	—
547	#540	C₂²×C₂₃	1	2	yes	—
548	#537	C₂²×C₂₃	1	2	yes	—
549	#535	C₂²×C₂₃	1	2	yes	—
550	#533	C₂²×C₂₃	1	1	yes	characteristic
551	#533	C₂²×C₂₃	1	1	yes	characteristic
552	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
553	#532	C₂²×C₂₃	1	1	yes	characteristic
554	#532	C₂²×C₂₃	1	1	yes	characteristic
555	#532	C₂²×C₂₃	1	1	yes	characteristic
556	#532	C₂²×C₂₃	1	1	yes	characteristic
557	#532	C₂²×C₂₃	1	1	yes	characteristic
558	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
559	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
560	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
561	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
562	#520	C₂²×C₂₃	1	2	yes	complemented
563	#518	C₂²×C₂₃	1	2	yes	—
564	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
565	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
566	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
567	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
568	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
569	#493	C₂²×C₂₃	1	1	yes	characteristic
570	#493	C₂²×C₂₃	1	1	yes	characteristic
571	#492	C₂²×C₂₃	1	1	yes	characteristic
572	#492	C₂²×C₂₃	1	1	yes	characteristic
573	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
574	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
575	#486	C₂²×C₂₃	1	1	yes	characteristic
576	#486	C₂²×C₂₃	1	1	yes	characteristic
577	#486	C₂²×C₂₃	1	1	yes	characteristic
578	#486	C₂²×C₂₃	1	1	yes	characteristic
579	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
580	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
581	#485	C₂²×C₂₃	1	4	yes	—
582	#482	C₂²×C₂₃	1	4	yes	—
583	#481	C₂²×C₂₃	1	4	yes	complemented
584	#480	C₂²×C₂₃	1	4	yes	complemented
585	#479	C₂²×C₂₃	1	4	yes	complemented
586	#478	C₂²×C₂₃	1	4	yes	complemented
587	#476	C₂²×C₂₃	1	4	yes	complemented
588	#474	C₂²×C₂₃	1	4	yes	complemented
589	#469	C₂²×C₂₃	1	4	yes	complemented
590	#468	C₂²×C₂₃	1	4	yes	complemented
591	#466	C₂²×C₂₃	1	4	yes	complemented
592	#465	C₂²×C₂₃	1	4	yes	complemented
593	#463	C₂²×C₂₃	1	4	yes	complemented
594	#463	C₂²×C₂₃	1	4	yes	complemented
595	#460	C₂²×C₂₃	1	4	yes	—
596	#459	C₂²×C₂₃	1	4	yes	—
597	#450	C₂²×C₂₃	1	4	yes	—
598	#449	C₂²×C₂₃	1	4	yes	complemented
599	#449	C₂²×C₂₃	1	4	yes	complemented
600	#447	C₂²×C₂₃	1	4	yes	—
601	#442	C₂²×C₂₃	1	4	yes	complemented
602	#440	C₂²×C₂₃	1	4	yes	complemented
603	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
604	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
605	#433	C₂²×C₂₃	1	2	yes	—
606	#433	C₂²×C₂₃	1	2	yes	complemented
607	#431	C₂²×C₂₃	1	1	yes	characteristic
608	#431	C₂²×C₂₃	1	1	yes	characteristic
609	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
610	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
611	#424	C₂²×C₂₃	1	2	yes	complemented
612	#408	C₂²×C₂₃	1	2	yes	—
613	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
614	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	C₂×C₂₃	—	4	1	no	—
616	C₂×C₂₃	—	4	1	no	—
617	C₂×C₂₃	—	4	1	no	—
618	C₂×C₂₃	—	8	2	no	—
619	C₂×C₂₃	—	8	2	no	—
620	C₂×C₂₃	—	8	2	no	—
621	C₂×C₂₃	#3449	1	1	yes	characteristic
622	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
623	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
624	C₂×#41	—	2	1	no	—
625	C₂×#41	—	2	1	no	—
626	C₂×#41	—	2	1	no	—
627	C₂×#41	—	2	1	no	—
628	C₂×#41	—	2	1	no	—
629	C₂×#41	—	2	1	no	—
630	C₂×#41	C₂³×C₂₃	1	2	yes	—
631	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
632	C₂²×Q₈	—	2	1	no	—
633	C₂²×D₄	—	2	1	no	—
634	C₂²×D₄	—	2	1	no	—
635	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
637	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
638	C₂×D₈	C₂³×C₂₃	1	4	yes	—
639	C₂×D₈	C₂³×C₂₃	1	4	yes	—
640	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
641	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
642	C₄⋊Q₈	—	2	1	no	—
643	C₄⋊Q₈	—	2	1	no	—
644	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
647	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
648	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
650	#127	—	2	2	no	—
651	#127	—	2	1	no	—
652	#127	—	2	1	no	—
653	#127	C₂³×C₂₃	1	1	yes	characteristic
654	#127	C₂³×C₂₃	1	1	yes	characteristic
655	#127	C₂³×C₂₃	1	2	yes	—
656	#127	C₂³×C₂₃	1	1	yes	characteristic
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#125	—	2	1	no	—
660	#125	—	2	1	no	—
661	#125	C₂³×C₂₃	1	2	yes	—
662	#124	—	2	2	no	—
663	#124	—	2	2	no	—
664	#124	—	2	2	no	—
665	#124	—	2	1	no	—
666	#124	—	2	1	no	—
667	#124	—	2	1	no	—
668	#124	—	2	1	no	—
669	#124	—	2	1	no	—
670	#124	—	2	1	no	—
671	#124	C₂³×C₂₃	1	2	yes	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	1	no	—
680	C₂²⋊Q₈	—	2	1	no	—
681	C₂²⋊Q₈	—	2	1	no	—
682	C₂²⋊Q₈	—	2	1	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
687	#121	—	2	2	no	—
688	#121	—	2	2	no	—
689	#121	—	2	2	no	—
690	#121	—	2	1	no	—
691	#121	—	2	1	no	—
692	#121	—	2	1	no	—
693	#121	—	2	1	no	—
694	#121	—	2	1	no	—
695	#121	—	2	1	no	—
696	#121	—	2	1	no	—
697	#121	—	2	1	no	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	C₂³×C₂₃	1	2	yes	—
703	#121	C₂³×C₂₃	1	2	yes	—
704	#121	C₂³×C₂₃	1	2	yes	—
705	#121	C₂³×C₂₃	1	2	yes	—
706	#121	C₂³×C₂₃	1	2	yes	—
707	#121	C₂³×C₂₃	1	2	yes	—
708	#120	—	2	2	no	—
709	#120	—	2	2	no	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	—	2	1	no	—
713	C₄×Q₈	—	2	1	no	—
714	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
715	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
716	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
717	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	1	no	—
723	C₄×D₄	—	2	1	no	—
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
731	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
732	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
733	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
734	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
735	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
736	C₄×D₄	C₂³×C₂₃	1	2	yes	—
737	C₄×D₄	C₂³×C₂₃	1	2	yes	—
738	C₄×D₄	C₂³×C₂₃	1	2	yes	—
739	C₄×D₄	C₂³×C₂₃	1	2	yes	—
740	C₄×D₄	C₂³×C₂₃	1	2	yes	—
741	C₄×D₄	C₂³×C₂₃	1	2	yes	—
742	#117	—	2	1	no	—
743	#117	—	2	1	no	—
744	#117	—	2	2	no	—
745	#117	C₂³×C₂₃	1	2	yes	—
746	#117	C₂³×C₂₃	1	1	yes	characteristic
747	#117	C₂³×C₂₃	1	1	yes	characteristic
748	#117	C₂³×C₂₃	1	1	yes	characteristic
749	C₂×C₄⋊C₄	—	2	1	no	—
750	C₂×C₄⋊C₄	—	2	2	no	—
751	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
752	C₂×C₂²⋊C₄	—	2	2	no	—
753	C₂×C₂²⋊C₄	—	2	2	no	—
754	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
756	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
757	#107	C₂³×C₂₃	1	4	yes	—
758	#107	C₂³×C₂₃	1	4	yes	—
759	#106	C₂³×C₂₃	1	4	yes	—
760	#106	C₂³×C₂₃	1	4	yes	—
761	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
762	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
763	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
764	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
765	#103	C₂³×C₂₃	1	4	yes	—
766	#103	C₂³×C₂₃	1	4	yes	—
767	#102	C₂³×C₂₃	1	4	yes	—
768	#102	C₂³×C₂₃	1	4	yes	—
769	#102	C₂³×C₂₃	1	4	yes	—
770	#102	C₂³×C₂₃	1	4	yes	—
771	#102	C₂³×C₂₃	1	4	yes	—
772	#102	C₂³×C₂₃	1	4	yes	—
773	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
777	#97	C₂³×C₂₃	1	2	yes	—
778	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
779	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
780	C₄×C₈	C₂³×C₂₃	1	2	yes	—
781	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
782	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
783	C₂₃	#61006	1	1	yes	characteristic, direct product factor, Sylow
784	C₂⁴	—	2	2	no	—
785	#41	—	4	2	no	—
786	#41	—	4	4	no	—
787	#41	—	8	2	no	—
788	#41	—	8	2	no	—
789	#41	—	8	2	no	—
790	#41	—	8	2	no	—
791	#41	—	8	2	no	—
792	#41	—	8	2	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	8	2	no	—
799	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
800	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	4	4	no	—
818	C₂×D₄	—	8	2	no	—
819	C₂×D₄	—	8	2	no	—
820	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
821	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
822	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
823	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
824	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
825	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
835	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
836	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
837	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
839	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
843	SD₁₆	—	4	4	no	—
844	SD₁₆	—	4	4	no	—
845	D₈	—	4	4	no	—
846	D₈	—	4	4	no	—
847	M₁₆	—	4	2	no	—
848	C₂×C₈	—	4	2	no	—
849	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
850	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
851	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
852	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	1	no	—
855	C₄⋊C₄	—	2	1	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
868	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
869	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
870	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
872	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
873	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
876	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
895	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
896	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
897	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
898	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
899	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
904	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
905	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
906	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
907	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
908	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
909	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
910	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
911	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
912	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	4	4	no	—
917	C₂³	—	8	2	no	—
918	C₂³	—	8	2	no	—
919	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
920	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
921	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
922	Q₈	—	2	4	no	—
923	Q₈	—	4	1	no	—
924	Q₈	—	4	2	no	—
925	Q₈	—	4	2	no	—
926	Q₈	—	4	2	no	—
927	Q₈	—	4	2	no	—
928	Q₈	—	8	2	no	—
929	D₄	—	2	4	no	—
930	D₄	—	2	4	no	—
931	D₄	—	2	4	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	4	no	—
936	D₄	—	4	4	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	2	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	2	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	2	no	—
949	D₄	—	8	2	no	—
950	D₄	—	8	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
976	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
977	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
979	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
984	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	1	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	16	4	no	—
1008	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₄	C₂₃×#576	1	2	yes	—
1024	C₄	C₂₃×#577	1	2	yes	—
1025	C₄	C₂₃×#585	1	2	yes	—
1026	C₂	—	4	1	no	—
1027	C₂	—	4	1	no	—
1028	C₂	—	4	1	no	—
1029	C₂	—	8	2	no	—
1030	C₂	—	8	2	no	—
1031	C₂	—	8	2	no	—
1032	C₂	C₂₃×#3449	1	1	yes	characteristic
1033	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
1034	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×#3508	C₂	semidirect
3. C₂₃×#3257	C₂	semidirect
4. C₂₃×#3231	C₂	semidirect
5. C₂₃×#3228	C₂	semidirect
6. C₂₃×#3227	C₂	semidirect
7. C₂₃×#3226	C₂	semidirect
8. C₂₃×#3208	C₂	semidirect
9. C₂₃×#3207	C₂	semidirect
10. C₂₃×#3207	C₂	semidirect
11. C₂₃×#3205	C₂	semidirect
12. C₂₃×#3198	C₂	semidirect
13. C₂₃×#3184	C₂	semidirect
14. C₂₃×#3182	C₂	semidirect
15. C₂₃×#3169	C₂	semidirect
16. C₂₃×#3167	C₂	semidirect
17. C₂₃×#3119	C₂	semidirect
18. C₂₃×#3118	C₂	semidirect
19. C₂₃×#2922	C₂	semidirect
37. C₂₃×#542	C₂²	semidirect
44. C₂₃×#533	C₂²	semidirect
50. C₂₃×#532	C₂²	semidirect
51. C₂₃×#532	C₂²	semidirect
52. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
54. C₂₃×#520	C₂²	semidirect
57. C₂₃×#500	C₂²	semidirect
58. C₂₃×#500	C₂²	semidirect
59. C₂₃×#498	C₂²	semidirect
60. C₂₃×#498	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#487	C₂²	semidirect
71. C₂₃×#486	C₂²	semidirect
72. C₂₃×#486	C₂²	semidirect
75. C₂₃×#481	C₂²	semidirect
76. C₂₃×#480	C₂²	semidirect
77. C₂₃×#479	C₂²	semidirect
78. C₂₃×#478	C₂²	semidirect
79. C₂₃×#476	C₂²	semidirect
80. C₂₃×#474	C₂²	semidirect
81. C₂₃×#469	C₂²	semidirect
82. C₂₃×#468	C₂²	semidirect
83. C₂₃×#466	C₂²	semidirect
84. C₂₃×#465	C₂²	semidirect
85. C₂₃×#463	C₂²	semidirect
86. C₂₃×#463	C₂²	semidirect
90. C₂₃×#449	C₂²	semidirect
91. C₂₃×#449	C₂²	semidirect
93. C₂₃×#442	C₂²	semidirect
94. C₂₃×#440	C₂²	semidirect
95. C₄×SD₁₆×C₂₃	C₂²	semidirect
96. C₄×D₈×C₂₃	C₂²	semidirect
98. C₂₃×#433	C₂²	semidirect
101. C₂₃×#431	C₂²	semidirect
102. C₂₃×#431	C₂²	semidirect
103. C₂₃×#424	C₂²	semidirect
105. C₄×M₁₆×C₂₃	C₂²	semidirect
106. C₂×C₄×C₈×C₂₃	C₂²	semidirect
395. #61006	C₂₃	direct (N × H)
472. #3511	C₂×C₂₃	semidirect
473. #3508	C₂×C₂₃	semidirect
474. #3257	C₂×C₂₃	semidirect
475. #3231	C₂×C₂₃	semidirect
476. #3228	C₂×C₂₃	semidirect
477. #3227	C₂×C₂₃	semidirect
478. #3226	C₂×C₂₃	semidirect
479. #3208	C₂×C₂₃	semidirect
480. #3207	C₂×C₂₃	semidirect
481. #3207	C₂×C₂₃	semidirect
482. #3205	C₂×C₂₃	semidirect
483. #3198	C₂×C₂₃	semidirect
484. #3184	C₂×C₂₃	semidirect
485. #3182	C₂×C₂₃	semidirect
486. #3169	C₂×C₂₃	semidirect
487. #3167	C₂×C₂₃	semidirect
488. #3119	C₂×C₂₃	semidirect
489. #3118	C₂×C₂₃	semidirect
490. #2922	C₂×C₂₃	semidirect
545. #542	C₂²×C₂₃	semidirect
552. #533	C₂²×C₂₃	semidirect
558. #532	C₂²×C₂₃	semidirect
559. #532	C₂²×C₂₃	semidirect
560. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
562. #520	C₂²×C₂₃	semidirect
565. #500	C₂²×C₂₃	semidirect
566. #500	C₂²×C₂₃	semidirect
567. #498	C₂²×C₂₃	semidirect
568. #498	C₂²×C₂₃	semidirect
573. #487	C₂²×C₂₃	semidirect
574. #487	C₂²×C₂₃	semidirect
579. #486	C₂²×C₂₃	semidirect
580. #486	C₂²×C₂₃	semidirect
583. #481	C₂²×C₂₃	semidirect
584. #480	C₂²×C₂₃	semidirect
585. #479	C₂²×C₂₃	semidirect
586. #478	C₂²×C₂₃	semidirect
587. #476	C₂²×C₂₃	semidirect
588. #474	C₂²×C₂₃	semidirect
589. #469	C₂²×C₂₃	semidirect
590. #468	C₂²×C₂₃	semidirect
591. #466	C₂²×C₂₃	semidirect
592. #465	C₂²×C₂₃	semidirect
593. #463	C₂²×C₂₃	semidirect
594. #463	C₂²×C₂₃	semidirect
598. #449	C₂²×C₂₃	semidirect
599. #449	C₂²×C₂₃	semidirect
601. #442	C₂²×C₂₃	semidirect
602. #440	C₂²×C₂₃	semidirect
603. C₄×SD₁₆	C₂²×C₂₃	semidirect
604. C₄×D₈	C₂²×C₂₃	semidirect
606. #433	C₂²×C₂₃	semidirect
609. #431	C₂²×C₂₃	semidirect
610. #431	C₂²×C₂₃	semidirect
611. #424	C₂²×C₂₃	semidirect
613. C₄×M₁₆	C₂²×C₂₃	semidirect
614. C₂×C₄×C₈	C₂²×C₂₃	semidirect
783. C₂₃	#61006	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×#3508	2
C₂₃×#3257	2
C₂₃×#3231	2
C₂₃×#3228	2
C₂₃×#3227	2
C₂₃×#3226	2
C₂₃×#3208	2
C₂₃×#3207	2
C₂₃×#3205	2
C₂₃×#3198	2
C₂₃×#3184	2
C₂₃×#3182	2
C₂₃×#3169	2
C₂₃×#3167	2
C₂₃×#3119	2
C₂₃×#3118	2
C₂₃×#2922	2
#61006	23

Subgroups — C23×#61006 #19208632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61006 #19208632