Subgroups — C₂₃×#61868 #19209494

Order 5888.

1756 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3384	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3381	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3380	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3368	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3366	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3362	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3358	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3241	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3119	C₂	1	4	yes	maximal, complemented
15	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#562	—	2	2	no	—
19	Q₈²×C₂₃	C₂²	1	2	yes	—
20	C₂₃×#557	C₂²	1	2	yes	—
21	C₂₃×#554	—	2	2	no	—
22	C₂₃×#554	C₂²	1	2	yes	—
23	C₂₃×#554	C₂²	1	2	yes	—
24	C₂₃×#554	C₂²	1	2	yes	—
25	C₂₃×#550	C₂²	1	2	yes	—
26	C₂₃×#550	C₂²	1	2	yes	—
27	D₄×Q₈×C₂₃	—	2	2	no	—
28	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
29	C₂₃×#547	—	2	1	no	—
30	C₂₃×#547	—	2	1	no	—
31	C₂₃×#544	—	2	2	no	—
32	C₂₃×#544	C₂²	1	2	yes	—
33	C₂₃×#540	C₂²	1	4	yes	—
34	C₂₃×#537	—	2	2	no	—
35	C₂₃×#537	—	2	2	no	—
36	C₂₃×#533	—	2	1	no	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic
38	C₂₃×#532	C₂²	1	1	yes	characteristic
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂₃×#520	C₂²	1	2	yes	—
43	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#501	C₂²	1	4	yes	—
45	C₂₃×#500	C₂²	1	2	yes	—
46	C₂₃×#499	C₂²	1	4	yes	—
47	C₂₃×#498	C₂²	1	2	yes	—
48	C₂₃×#490	C₂²	1	4	yes	—
49	C₂₃×#486	C₂²	1	2	yes	—
50	C₂₃×#486	C₂²	1	2	yes	—
51	C₂₃×#486	C₂²	1	4	yes	—
52	C₂₃×#482	C₂²	1	2	yes	—
53	C₂₃×#482	C₂²	1	2	yes	—
54	C₂₃×#481	C₂²	1	4	yes	—
55	C₂₃×#480	C₂²	1	4	yes	—
56	C₂₃×#479	C₂²	1	4	yes	—
57	C₂₃×#478	C₂²	1	4	yes	—
58	C₂₃×#478	C₂²	1	4	yes	—
59	C₂₃×#478	C₂²	1	4	yes	—
60	C₂₃×#477	C₂²	1	1	yes	characteristic
61	C₂₃×#477	C₂²	1	1	yes	characteristic
62	C₂₃×#476	C₂²	1	2	yes	—
63	C₂₃×#476	C₂²	1	2	yes	—
64	C₂₃×#476	C₂²	1	4	yes	—
65	C₂₃×#476	C₂²	1	1	yes	characteristic
66	C₂₃×#476	C₂²	1	1	yes	characteristic
67	C₂₃×#474	C₂²	1	2	yes	—
68	C₂₃×#474	C₂²	1	2	yes	—
69	C₂₃×#474	C₂²	1	4	yes	—
70	C₂₃×#460	C₂²	1	1	yes	characteristic
71	C₂₃×#460	C₂²	1	1	yes	characteristic
72	C₂₃×#460	C₂²	1	4	yes	—
73	C₂₃×#459	C₂²	1	1	yes	characteristic
74	C₂₃×#459	C₂²	1	4	yes	—
75	C₂₃×#459	C₂²	1	1	yes	characteristic
76	C₂₃×#449	C₂²	1	2	yes	—
77	C₂₃×#449	C₂²	1	2	yes	—
78	C₂₃×#446	C₂²	1	2	yes	—
79	C₂₃×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
81	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
82	C₂₃×#442	C₂²	1	4	yes	—
83	C₂₃×#440	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
86	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
87	C₄×D₈×C₂₃	C₂²	1	2	yes	—
88	C₄×D₈×C₂₃	C₂²	1	4	yes	—
89	C₄×D₈×C₂₃	C₂²	1	2	yes	—
90	C₂₃×#433	C₂²	1	4	yes	—
91	C₂₃×#431	C₂²	1	1	yes	characteristic
92	C₂₃×#431	C₂²	1	1	yes	characteristic
93	C₂×#41×C₂₃	—	2	2	no	—
94	C₂×#41×C₂₃	—	2	2	no	—
95	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	—	2	1	no	—
97	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₂₃	—	2	2	no	—
99	C₂²×Q₈×C₂₃	—	2	1	no	—
100	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
102	C₂×D₈×C₂₃	C₂³	1	2	yes	—
103	C₂×D₈×C₂₃	C₂³	1	2	yes	—
104	C₂₃×C₄⋊Q₈	—	2	2	no	—
105	C₂₃×C₄⋊Q₈	—	2	4	no	—
106	C₂₃×C₄⋊Q₈	—	2	2	no	—
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	—	2	1	no	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×#127	C₂³	1	1	yes	characteristic
118	C₂₃×#127	C₂³	1	1	yes	characteristic
119	C₂₃×#127	C₂³	1	4	yes	—
120	C₂₃×#125	—	2	4	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	D₄	1	2	yes	—
123	C₂₃×#125	C₂³	1	4	yes	—
124	C₂₃×#125	C₂³	1	4	yes	—
125	C₂₃×#124	—	2	1	no	—
126	C₂₃×#124	—	2	1	no	—
127	C₂₃×#123	—	2	4	no	—
128	C₂₃×#123	—	2	4	no	—
129	C₂₃×C₂²⋊Q₈	—	2	2	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	4	no	—
134	C₂₃×C₂²⋊Q₈	—	2	4	no	—
135	C₂₃×C₂²⋊Q₈	—	2	4	no	—
136	C₂₃×C₂²⋊Q₈	—	2	4	no	—
137	C₂₃×C₂²⋊Q₈	—	2	4	no	—
138	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
139	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
140	C₂₃×#121	—	2	1	no	—
141	C₂₃×#121	—	2	1	no	—
142	C₂₃×#121	—	2	2	no	—
143	C₂₃×#121	—	2	2	no	—
144	C₂₃×#121	—	2	4	no	—
145	C₂₃×#121	—	2	4	no	—
146	C₂₃×#121	—	2	4	no	—
147	C₂₃×#121	—	2	4	no	—
148	C₂₃×#121	C₂³	1	2	yes	—
149	C₂₃×#121	C₂³	1	2	yes	—
150	C₄×Q₈×C₂₃	—	2	2	no	—
151	C₄×Q₈×C₂₃	—	2	2	no	—
152	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
157	C₄×D₄×C₂₃	—	2	1	no	—
158	C₄×D₄×C₂₃	—	2	1	no	—
159	C₄×D₄×C₂₃	—	2	4	no	—
160	C₄×D₄×C₂₃	—	2	1	no	—
161	C₄×D₄×C₂₃	—	2	1	no	—
162	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
163	C₄×D₄×C₂₃	C₂³	1	4	yes	—
164	C₄×D₄×C₂₃	C₂³	1	2	yes	—
165	C₄×D₄×C₂₃	C₂³	1	2	yes	—
166	C₄×D₄×C₂₃	C₂³	1	4	yes	—
167	C₄×D₄×C₂₃	C₂³	1	4	yes	—
168	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
169	C₂₃×#117	—	2	2	no	—
170	C₂₃×#117	—	2	1	no	—
171	C₂₃×#117	C₂³	1	1	yes	characteristic
172	C₂₃×#117	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
174	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
175	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
176	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
177	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₂₃	—	2	1	no	—
180	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
181	C₂₃×#107	C₂³	1	2	yes	—
182	C₂₃×#107	C₂³	1	4	yes	—
183	C₂₃×#107	C₂³	1	2	yes	—
184	C₂₃×#107	C₂³	1	4	yes	—
185	C₂₃×#106	C₂³	1	2	yes	—
186	C₂₃×#106	C₂³	1	4	yes	—
187	C₂₃×#106	C₂³	1	2	yes	—
188	C₂₃×#106	C₂³	1	4	yes	—
189	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
190	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
191	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
194	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₂₃×#103	C₂³	1	2	yes	—
196	C₂₃×#103	C₂³	1	2	yes	—
197	C₂₃×#102	C₂³	1	2	yes	—
198	C₂₃×#102	C₂³	1	2	yes	—
199	C₂₃×#102	C₂³	1	2	yes	—
200	C₂₃×#102	C₂³	1	4	yes	—
201	C₂₃×#102	C₂³	1	2	yes	—
202	C₂₃×#102	C₂³	1	2	yes	—
203	C₂₃×#102	C₂³	1	4	yes	—
204	C₂₃×#102	C₂³	1	2	yes	—
205	C₂₃×#102	C₂³	1	4	yes	—
206	C₂₃×#102	C₂³	1	4	yes	—
207	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₂₃×#97	C₂³	1	4	yes	—
210	C₄×C₈×C₂₃	C₂³	1	2	yes	—
211	C₄×C₈×C₂₃	C₂³	1	2	yes	—
212	C₄×C₈×C₂₃	C₂³	1	4	yes	—
213	#41×C₂₃	—	2	2	no	—
214	#41×C₂₃	—	2	2	no	—
215	#41×C₂₃	—	8	2	no	—
216	#41×C₂₃	—	8	2	no	—
217	#41×C₂₃	—	8	4	no	—
218	#41×C₂₃	—	8	4	no	—
219	C₂×Q₈×C₂₃	—	2	2	no	—
220	C₂×Q₈×C₂₃	—	2	1	no	—
221	C₂×Q₈×C₂₃	—	2	1	no	—
222	C₂×Q₈×C₂₃	—	2	4	no	—
223	C₂×Q₈×C₂₃	—	2	2	no	—
224	C₂×Q₈×C₂₃	—	8	2	no	—
225	C₂×Q₈×C₂₃	—	8	4	no	—
226	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	2	2	no	—
231	C₂×D₄×C₂₃	—	2	2	no	—
232	C₂×D₄×C₂₃	—	2	1	no	—
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	—	2	4	no	—
235	C₂×D₄×C₂₃	—	2	4	no	—
236	C₂×D₄×C₂₃	—	2	1	no	—
237	C₂×D₄×C₂₃	—	2	1	no	—
238	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₂₃	—	2	1	no	—
242	C₂²×C₄×C₂₃	—	2	2	no	—
243	C₂²×C₄×C₂₃	—	2	1	no	—
244	C₂²×C₄×C₂₃	—	2	1	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	4	no	—
248	C₂²×C₄×C₂₃	—	2	4	no	—
249	C₂²×C₄×C₂₃	—	2	4	no	—
250	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	SD₁₆×C₂₃	—	2	4	no	—
254	SD₁₆×C₂₃	—	2	4	no	—
255	D₈×C₂₃	—	2	4	no	—
256	D₈×C₂₃	—	2	4	no	—
257	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
258	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
259	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
260	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₄⋊C₄×C₂₃	—	2	2	no	—
264	C₄⋊C₄×C₂₃	—	2	2	no	—
265	C₄⋊C₄×C₂₃	—	2	4	no	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	2	4	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	4	no	—
274	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
280	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
281	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₂²⋊C₄×C₂₃	—	2	1	no	—
286	C₂²⋊C₄×C₂₃	—	2	1	no	—
287	C₂²⋊C₄×C₂₃	—	2	1	no	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
289	C₂²⋊C₄×C₂₃	—	2	2	no	—
290	C₂²⋊C₄×C₂₃	—	2	2	no	—
291	C₂²⋊C₄×C₂₃	—	2	4	no	—
292	C₂²⋊C₄×C₂₃	—	2	4	no	—
293	C₂²⋊C₄×C₂₃	—	2	2	no	—
294	C₂²⋊C₄×C₂₃	—	2	2	no	—
295	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
296	C₄²×C₂₃	—	2	1	no	—
297	C₄²×C₂₃	—	2	1	no	—
298	C₄²×C₂₃	—	2	1	no	—
299	C₄²×C₂₃	—	2	4	no	—
300	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₄²×C₂₃	C₂⁴	1	4	yes	—
305	#61868	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
306	C₂³×C₂₃	—	2	1	no	—
307	C₂³×C₂₃	—	2	2	no	—
308	C₂³×C₂₃	—	2	2	no	—
309	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₂₃	—	2	4	no	—
311	Q₈×C₂₃	—	2	4	no	—
312	Q₈×C₂₃	—	2	1	no	—
313	Q₈×C₂₃	—	4	4	no	—
314	Q₈×C₂₃	—	8	2	no	—
315	Q₈×C₂₃	—	8	4	no	—
316	Q₈×C₂₃	—	8	1	no	—
317	Q₈×C₂₃	—	8	1	no	—
318	Q₈×C₂₃	2₋¹⁺⁴	1	2	yes	—
319	D₄×C₂₃	—	2	4	no	—
320	D₄×C₂₃	—	2	1	no	—
321	D₄×C₂₃	—	2	2	no	—
322	D₄×C₂₃	—	2	2	no	—
323	D₄×C₂₃	—	2	2	no	—
324	D₄×C₂₃	—	2	2	no	—
325	D₄×C₂₃	—	4	2	no	—
326	D₄×C₂₃	—	4	2	no	—
327	D₄×C₂₃	—	8	1	no	—
328	D₄×C₂₃	—	8	4	no	—
329	D₄×C₂₃	—	8	1	no	—
330	D₄×C₂₃	—	8	4	no	—
331	D₄×C₂₃	—	8	2	no	—
332	D₄×C₂₃	—	8	2	no	—
333	D₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
334	C₂×C₄×C₂₃	—	2	4	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	1	no	—
339	C₂×C₄×C₂₃	—	2	1	no	—
340	C₂×C₄×C₂₃	—	2	1	no	—
341	C₂×C₄×C₂₃	—	2	1	no	—
342	C₂×C₄×C₂₃	—	2	4	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	4	2	no	—
346	C₂×C₄×C₂₃	—	4	4	no	—
347	C₂×C₄×C₂₃	—	4	2	no	—
348	C₂×C₄×C₂₃	—	4	4	no	—
349	C₂×C₄×C₂₃	—	8	4	no	—
350	C₂×C₄×C₂₃	—	8	4	no	—
351	C₂×C₄×C₂₃	—	8	4	no	—
352	C₂×C₄×C₂₃	—	8	2	no	—
353	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
355	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
361	C₈×C₂₃	—	2	2	no	—
362	C₈×C₂₃	—	2	2	no	—
363	C₈×C₂₃	—	2	2	no	—
364	C₈×C₂₃	—	2	2	no	—
365	#3548	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#3503	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#3385	C₂×C₂₃	1	2	yes	complemented
368	#3384	C₂×C₂₃	1	2	yes	complemented
369	#3381	C₂×C₂₃	1	2	yes	complemented
370	#3380	C₂×C₂₃	1	2	yes	complemented
371	#3368	C₂×C₂₃	1	2	yes	complemented
372	#3366	C₂×C₂₃	1	2	yes	complemented
373	#3362	C₂×C₂₃	1	2	yes	complemented
374	#3358	C₂×C₂₃	1	2	yes	complemented
375	#3241	C₂×C₂₃	1	4	yes	complemented
376	#3227	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#3226	C₂×C₂₃	1	1	yes	characteristic, complemented
378	#3119	C₂×C₂₃	1	4	yes	complemented
379	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#2986	C₂×C₂₃	1	1	yes	characteristic, complemented
382	C₂²×C₂₃	—	2	1	no	—
383	C₂²×C₂₃	—	2	2	no	—
384	C₂²×C₂₃	—	2	1	no	—
385	C₂²×C₂₃	—	2	1	no	—
386	C₂²×C₂₃	—	4	1	no	—
387	C₂²×C₂₃	—	4	1	no	—
388	C₂²×C₂₃	—	4	2	no	—
389	C₂²×C₂₃	—	4	2	no	—
390	C₂²×C₂₃	—	4	2	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	2	no	—
393	C₂²×C₂₃	—	4	2	no	—
394	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
395	C₄×C₂₃	—	2	1	no	—
396	C₄×C₂₃	—	2	2	no	—
397	C₄×C₂₃	—	2	1	no	—
398	C₄×C₂₃	—	2	4	no	—
399	C₄×C₂₃	—	2	1	no	—
400	C₄×C₂₃	—	2	4	no	—
401	C₄×C₂₃	—	4	2	no	—
402	C₄×C₂₃	—	4	1	no	—
403	C₄×C₂₃	—	4	4	no	—
404	C₄×C₂₃	—	4	1	no	—
405	C₄×C₂₃	—	4	2	no	—
406	C₄×C₂₃	#576	1	2	yes	—
407	C₄×C₂₃	#577	1	2	yes	—
408	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
409	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
410	#562	—	2	2	no	—
411	Q₈²	C₂²×C₂₃	1	2	yes	—
412	#557	C₂²×C₂₃	1	2	yes	—
413	#554	—	2	2	no	—
414	#554	C₂²×C₂₃	1	2	yes	—
415	#554	C₂²×C₂₃	1	2	yes	—
416	#554	C₂²×C₂₃	1	2	yes	—
417	#550	C₂²×C₂₃	1	2	yes	—
418	#550	C₂²×C₂₃	1	2	yes	—
419	D₄×Q₈	—	2	2	no	—
420	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
421	#547	—	2	1	no	—
422	#547	—	2	1	no	—
423	#544	—	2	2	no	—
424	#544	C₂²×C₂₃	1	2	yes	—
425	#540	C₂²×C₂₃	1	4	yes	—
426	#537	—	2	2	no	—
427	#537	—	2	2	no	—
428	#533	—	2	1	no	—
429	#533	C₂²×C₂₃	1	1	yes	characteristic
430	#532	C₂²×C₂₃	1	1	yes	characteristic
431	#532	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	—	2	1	no	—
433	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
434	#520	C₂²×C₂₃	1	2	yes	—
435	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
436	#501	C₂²×C₂₃	1	4	yes	—
437	#500	C₂²×C₂₃	1	2	yes	—
438	#499	C₂²×C₂₃	1	4	yes	—
439	#498	C₂²×C₂₃	1	2	yes	—
440	#490	C₂²×C₂₃	1	4	yes	—
441	#486	C₂²×C₂₃	1	4	yes	—
442	#486	C₂²×C₂₃	1	2	yes	—
443	#486	C₂²×C₂₃	1	2	yes	—
444	#482	C₂²×C₂₃	1	2	yes	—
445	#482	C₂²×C₂₃	1	2	yes	—
446	#481	C₂²×C₂₃	1	4	yes	—
447	#480	C₂²×C₂₃	1	4	yes	—
448	#479	C₂²×C₂₃	1	4	yes	—
449	#478	C₂²×C₂₃	1	4	yes	—
450	#478	C₂²×C₂₃	1	4	yes	—
451	#478	C₂²×C₂₃	1	4	yes	—
452	#477	C₂²×C₂₃	1	1	yes	characteristic
453	#477	C₂²×C₂₃	1	1	yes	characteristic
454	#476	C₂²×C₂₃	1	1	yes	characteristic
455	#476	C₂²×C₂₃	1	1	yes	characteristic
456	#476	C₂²×C₂₃	1	2	yes	—
457	#476	C₂²×C₂₃	1	4	yes	—
458	#476	C₂²×C₂₃	1	2	yes	—
459	#474	C₂²×C₂₃	1	2	yes	—
460	#474	C₂²×C₂₃	1	4	yes	—
461	#474	C₂²×C₂₃	1	2	yes	—
462	#460	C₂²×C₂₃	1	1	yes	characteristic
463	#460	C₂²×C₂₃	1	1	yes	characteristic
464	#460	C₂²×C₂₃	1	4	yes	—
465	#459	C₂²×C₂₃	1	1	yes	characteristic
466	#459	C₂²×C₂₃	1	4	yes	—
467	#459	C₂²×C₂₃	1	1	yes	characteristic
468	#449	C₂²×C₂₃	1	2	yes	—
469	#449	C₂²×C₂₃	1	2	yes	—
470	#446	C₂²×C₂₃	1	2	yes	—
471	#446	C₂²×C₂₃	1	2	yes	—
472	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
473	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
474	#442	C₂²×C₂₃	1	4	yes	—
475	#440	C₂²×C₂₃	1	4	yes	—
476	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
477	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
478	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
479	C₄×D₈	C₂²×C₂₃	1	2	yes	—
480	C₄×D₈	C₂²×C₂₃	1	4	yes	—
481	C₄×D₈	C₂²×C₂₃	1	2	yes	—
482	#433	C₂²×C₂₃	1	4	yes	—
483	#431	C₂²×C₂₃	1	1	yes	characteristic
484	#431	C₂²×C₂₃	1	1	yes	characteristic
485	C₂×C₂₃	—	4	1	no	—
486	C₂×C₂₃	—	4	2	no	—
487	C₂×C₂₃	—	8	2	no	—
488	C₂×C₂₃	—	8	2	no	—
489	C₂×C₂₃	#3486	1	1	yes	characteristic
490	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
491	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	1	no	—
495	C₂×#41	—	2	1	no	—
496	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
497	C₂²×Q₈	—	2	2	no	—
498	C₂²×Q₈	—	2	1	no	—
499	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
500	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
501	C₂×D₈	C₂³×C₂₃	1	2	yes	—
502	C₂×D₈	C₂³×C₂₃	1	2	yes	—
503	C₄⋊Q₈	—	2	2	no	—
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	—	2	4	no	—
507	C₄⋊Q₈	—	2	1	no	—
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
510	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
512	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
513	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
516	#127	C₂³×C₂₃	1	1	yes	characteristic
517	#127	C₂³×C₂₃	1	1	yes	characteristic
518	#127	C₂³×C₂₃	1	4	yes	—
519	#125	—	2	2	no	—
520	#125	—	2	4	no	—
521	#125	D₄×C₂₃	1	2	yes	—
522	#125	C₂³×C₂₃	1	4	yes	—
523	#125	C₂³×C₂₃	1	4	yes	—
524	#124	—	2	1	no	—
525	#124	—	2	1	no	—
526	#123	—	2	4	no	—
527	#123	—	2	4	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
538	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	#121	—	2	2	no	—
542	#121	—	2	2	no	—
543	#121	—	2	4	no	—
544	#121	—	2	4	no	—
545	#121	—	2	4	no	—
546	#121	—	2	4	no	—
547	#121	C₂³×C₂₃	1	2	yes	—
548	#121	C₂³×C₂₃	1	2	yes	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
552	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
553	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
554	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
555	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	4	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
562	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
563	C₄×D₄	C₂³×C₂₃	1	4	yes	—
564	C₄×D₄	C₂³×C₂₃	1	2	yes	—
565	C₄×D₄	C₂³×C₂₃	1	2	yes	—
566	C₄×D₄	C₂³×C₂₃	1	4	yes	—
567	C₄×D₄	C₂³×C₂₃	1	4	yes	—
568	#117	—	2	2	no	—
569	#117	—	2	1	no	—
570	#117	C₂³×C₂₃	1	1	yes	characteristic
571	#117	C₂³×C₂₃	1	2	yes	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	2	no	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	—	2	2	no	—
576	C₂×C₄⋊C₄	—	2	2	no	—
577	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
578	C₂×C₄²	—	2	1	no	—
579	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
580	#107	C₂³×C₂₃	1	2	yes	—
581	#107	C₂³×C₂₃	1	4	yes	—
582	#107	C₂³×C₂₃	1	2	yes	—
583	#107	C₂³×C₂₃	1	4	yes	—
584	#106	C₂³×C₂₃	1	2	yes	—
585	#106	C₂³×C₂₃	1	4	yes	—
586	#106	C₂³×C₂₃	1	2	yes	—
587	#106	C₂³×C₂₃	1	4	yes	—
588	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
589	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
590	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
591	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
592	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
593	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
594	#103	C₂³×C₂₃	1	2	yes	—
595	#103	C₂³×C₂₃	1	2	yes	—
596	#102	C₂³×C₂₃	1	2	yes	—
597	#102	C₂³×C₂₃	1	2	yes	—
598	#102	C₂³×C₂₃	1	2	yes	—
599	#102	C₂³×C₂₃	1	4	yes	—
600	#102	C₂³×C₂₃	1	2	yes	—
601	#102	C₂³×C₂₃	1	2	yes	—
602	#102	C₂³×C₂₃	1	4	yes	—
603	#102	C₂³×C₂₃	1	2	yes	—
604	#102	C₂³×C₂₃	1	4	yes	—
605	#102	C₂³×C₂₃	1	4	yes	—
606	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
607	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
608	#97	C₂³×C₂₃	1	4	yes	—
609	C₄×C₈	C₂³×C₂₃	1	2	yes	—
610	C₄×C₈	C₂³×C₂₃	1	2	yes	—
611	C₄×C₈	C₂³×C₂₃	1	4	yes	—
612	C₂₃	#61868	1	1	yes	characteristic, direct product factor, Sylow
613	#41	—	2	2	no	—
614	#41	—	2	2	no	—
615	#41	—	8	2	no	—
616	#41	—	8	2	no	—
617	#41	—	8	4	no	—
618	#41	—	8	4	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	4	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	8	2	no	—
625	C₂×Q₈	—	8	4	no	—
626	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
627	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
628	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
639	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
640	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
653	SD₁₆	—	2	4	no	—
654	SD₁₆	—	2	4	no	—
655	D₈	—	2	4	no	—
656	D₈	—	2	4	no	—
657	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
658	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
659	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
660	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
679	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
680	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
682	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
683	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	4	no	—
700	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
701	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
702	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
703	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
704	C₄²	C₂⁴×C₂₃	1	4	yes	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
709	Q₈	—	2	4	no	—
710	Q₈	—	2	4	no	—
711	Q₈	—	2	1	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	8	2	no	—
714	Q₈	—	8	4	no	—
715	Q₈	—	8	1	no	—
716	Q₈	—	8	1	no	—
717	Q₈	C₂₃×2₋¹⁺⁴	1	2	yes	—
718	D₄	—	2	4	no	—
719	D₄	—	2	1	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	4	2	no	—
725	D₄	—	4	2	no	—
726	D₄	—	8	1	no	—
727	D₄	—	8	4	no	—
728	D₄	—	8	1	no	—
729	D₄	—	8	4	no	—
730	D₄	—	8	2	no	—
731	D₄	—	8	2	no	—
732	D₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	4	4	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	—	8	4	no	—
751	C₂×C₄	—	8	2	no	—
752	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
757	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
759	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
760	C₈	—	2	2	no	—
761	C₈	—	2	2	no	—
762	C₈	—	2	2	no	—
763	C₈	—	2	2	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
777	C₄	—	2	1	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	4	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	4	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	1	no	—
788	C₄	C₂₃×#576	1	2	yes	—
789	C₄	C₂₃×#577	1	2	yes	—
790	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
791	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
792	C₂	—	4	1	no	—
793	C₂	—	4	2	no	—
794	C₂	—	8	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₂₃×#3486	1	1	yes	characteristic
797	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
798	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3548	C₂	semidirect
2. C₂₃×#3503	C₂	semidirect
3. C₂₃×#3385	C₂	semidirect
4. C₂₃×#3384	C₂	semidirect
5. C₂₃×#3381	C₂	semidirect
6. C₂₃×#3380	C₂	semidirect
7. C₂₃×#3368	C₂	semidirect
8. C₂₃×#3366	C₂	semidirect
9. C₂₃×#3362	C₂	semidirect
10. C₂₃×#3358	C₂	semidirect
11. C₂₃×#3241	C₂	semidirect
12. C₂₃×#3227	C₂	semidirect
13. C₂₃×#3226	C₂	semidirect
14. C₂₃×#3119	C₂	semidirect
15. C₂₃×#3106	C₂	semidirect
16. C₂₃×#3106	C₂	semidirect
17. C₂₃×#2986	C₂	semidirect
305. #61868	C₂₃	direct (N × H)
365. #3548	C₂×C₂₃	semidirect
366. #3503	C₂×C₂₃	semidirect
367. #3385	C₂×C₂₃	semidirect
368. #3384	C₂×C₂₃	semidirect
369. #3381	C₂×C₂₃	semidirect
370. #3380	C₂×C₂₃	semidirect
371. #3368	C₂×C₂₃	semidirect
372. #3366	C₂×C₂₃	semidirect
373. #3362	C₂×C₂₃	semidirect
374. #3358	C₂×C₂₃	semidirect
375. #3241	C₂×C₂₃	semidirect
376. #3227	C₂×C₂₃	semidirect
377. #3226	C₂×C₂₃	semidirect
378. #3119	C₂×C₂₃	semidirect
379. #3106	C₂×C₂₃	semidirect
380. #3106	C₂×C₂₃	semidirect
381. #2986	C₂×C₂₃	semidirect
612. C₂₃	#61868	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×#3548	2
C₂₃×#3503	2
C₂₃×#3385	2
C₂₃×#3384	2
C₂₃×#3381	2
C₂₃×#3380	2
C₂₃×#3368	2
C₂₃×#3366	2
C₂₃×#3362	2
C₂₃×#3358	2
C₂₃×#3241	2
C₂₃×#3227	2
C₂₃×#3226	2
C₂₃×#3119	2
C₂₃×#3106	2
C₂₃×#2986	2
#61868	23

Subgroups — C23×#61868 #19209494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61868 #19209494