Subgroups — C₂₃×#61220 #19208846

Order 5888.

2082 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3321	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3320	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3309	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3308	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3098	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3062	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3010	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2898	C₂	1	2	yes	maximal, complemented
16	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#131	C₂²	1	2	yes	—
20	C₂₃×#559	—	2	2	no	—
21	C₂₃×#556	—	2	1	no	—
22	C₂₃×#555	C₂²	1	2	yes	—
23	C₂₃×#553	C₂²	1	4	yes	—
24	C₂₃×#550	—	2	1	no	—
25	C₂₃×#550	—	2	1	no	—
26	C₂₃×#550	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₂₃	—	2	1	no	—
28	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
29	C₂₃×#548	—	2	2	no	—
30	C₂₃×#548	C₂²	1	4	yes	complemented
31	C₂₃×#547	C₂²	1	2	yes	—
32	C₂₃×#538	—	2	2	no	—
33	C₂₃×#537	—	2	2	no	—
34	C₂₃×#537	C₂²	1	2	yes	—
35	C₂₃×#535	C₂²	1	2	yes	—
36	C₂₃×#533	C₂²	1	1	yes	characteristic
37	C₂₃×#532	—	2	2	no	—
38	C₂₃×#532	C₂²	1	1	yes	characteristic
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂₃×#525	—	2	2	no	—
41	C₂₃×#520	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#491	C₂²	1	2	yes	complemented
45	C₂₃×#490	C₂²	1	2	yes	complemented
46	C₂₃×#489	C₂²	1	2	yes	complemented
47	C₂₃×#489	C₂²	1	2	yes	complemented
48	C₂₃×#485	C₂²	1	4	yes	complemented
49	C₂₃×#484	C₂²	1	4	yes	complemented
50	C₂₃×#482	C₂²	1	4	yes	complemented
51	C₂₃×#480	C₂²	1	4	yes	complemented
52	C₂₃×#479	C₂²	1	4	yes	complemented
53	C₂₃×#477	C₂²	1	2	yes	complemented
54	C₂₃×#475	C₂²	1	2	yes	complemented
55	C₂₃×#469	C₂²	1	4	yes	—
56	C₂₃×#468	C₂²	1	4	yes	—
57	C₂₃×#466	C₂²	1	4	yes	—
58	C₂₃×#465	C₂²	1	4	yes	—
59	C₂₃×#463	C₂²	1	4	yes	—
60	C₂₃×#461	C₂²	1	2	yes	—
61	C₂₃×#459	C₂²	1	2	yes	—
62	C₂₃×#449	C₂²	1	4	yes	—
63	C₂₃×#449	C₂²	1	4	yes	—
64	C₂₃×#448	C₂²	1	4	yes	—
65	C₂₃×#448	C₂²	1	4	yes	—
66	C₂₃×#440	C₂²	1	4	yes	—
67	C₂₃×#440	C₂²	1	4	yes	—
68	C₂₃×#435	C₂²	1	4	yes	complemented
69	C₂₃×#435	C₂²	1	4	yes	complemented
70	C₂₃×#428	C₂²	1	2	yes	—
71	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
72	C₂₃×#423	C₂²	1	1	yes	characteristic
73	C₂₃×#419	C₂²	1	2	yes	—
74	C₂₃×#419	C₂²	1	4	yes	complemented
75	C₂₃×#417	C₂²	1	2	yes	—
76	C₂₃×#417	C₂²	1	4	yes	complemented
77	C₂₃×#416	C₂²	1	2	yes	—
78	C₂₃×#416	C₂²	1	2	yes	—
79	C₂₃×#416	C₂²	1	4	yes	complemented
80	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
81	C₂×C₂₃×#103	C₂²	1	4	yes	complemented
82	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
83	C₂₃×#408	C₂²	1	2	yes	—
84	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
85	C₂₃×2₋¹⁺⁴	—	2	8	no	—
86	C₂₃×2₋¹⁺⁴	—	4	4	no	—
87	C₂×#41×C₂₃	—	2	2	no	—
88	C₂×#41×C₂₃	—	2	4	no	—
89	C₂×#41×C₂₃	—	2	2	no	—
90	C₂×#41×C₂₃	C₂³	1	2	yes	—
91	C₂×#41×C₂₃	C₂³	1	4	yes	—
92	C₂×#41×C₂₃	C₂³	1	2	yes	—
93	C₂²×Q₈×C₂₃	—	2	2	no	—
94	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
95	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₂₃	—	2	1	no	—
98	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
99	C₂×SD₁₆×C₂₃	—	2	4	no	—
100	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
102	C₂×D₈×C₂₃	C₂³	1	4	yes	—
103	C₂₃×#131	—	4	4	no	—
104	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×#127	—	2	2	no	—
115	C₂₃×#127	—	2	2	no	—
116	C₂₃×#127	D₄	1	1	yes	characteristic
117	C₂₃×#127	C₂³	1	1	yes	characteristic
118	C₂₃×#126	—	2	4	no	—
119	C₂₃×#125	C₂³	1	2	yes	—
120	C₂₃×#124	—	2	2	no	—
121	C₂₃×#124	—	2	4	no	—
122	C₂₃×#124	—	2	4	no	—
123	C₂₃×#124	D₄	1	2	yes	—
124	C₂₃×#124	C₂³	1	2	yes	—
125	C₂₃×#123	—	2	4	no	—
126	C₂₃×#123	—	2	4	no	—
127	C₂₃×C₂²⋊Q₈	—	2	2	no	—
128	C₂₃×C₂²⋊Q₈	—	2	1	no	—
129	C₂₃×C₂²⋊Q₈	—	2	1	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	—	2	4	no	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×#121	—	2	2	no	—
135	C₂₃×#121	—	2	4	no	—
136	C₂₃×#121	—	2	4	no	—
137	C₂₃×#121	—	2	2	no	—
138	C₂₃×#121	—	2	4	no	—
139	C₂₃×#121	—	2	1	no	—
140	C₂₃×#121	—	2	1	no	—
141	C₂₃×#121	—	2	4	no	—
142	C₂₃×#121	D₄	1	2	yes	—
143	C₂₃×#121	D₄	1	2	yes	—
144	C₂₃×#121	C₂³	1	4	yes	—
145	C₂₃×#121	C₂³	1	4	yes	—
146	C₂₃×#121	C₂³	1	4	yes	—
147	C₂₃×#120	—	2	4	no	—
148	C₄×Q₈×C₂₃	—	2	2	no	—
149	C₄×Q₈×C₂₃	—	2	1	no	—
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×Q₈×C₂₃	—	2	1	no	—
152	C₄×Q₈×C₂₃	—	2	1	no	—
153	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
155	C₄×D₄×C₂₃	—	2	2	no	—
156	C₄×D₄×C₂₃	—	2	2	no	—
157	C₄×D₄×C₂₃	—	2	4	no	—
158	C₄×D₄×C₂₃	—	2	2	no	—
159	C₄×D₄×C₂₃	—	2	4	no	—
160	C₄×D₄×C₂₃	—	2	4	no	—
161	C₄×D₄×C₂₃	—	2	1	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	C₂³	1	2	yes	—
166	C₄×D₄×C₂₃	C₂³	1	2	yes	—
167	C₄×D₄×C₂₃	C₂³	1	2	yes	—
168	C₄×D₄×C₂₃	C₂³	1	2	yes	—
169	C₂₃×#117	—	2	2	no	—
170	C₂₃×#117	C₂³	1	4	yes	—
171	C₂₃×#117	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
177	C₂×C₄²×C₂₃	—	2	1	no	—
178	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
179	C₂₃×#107	C₂³	1	4	yes	—
180	C₂₃×#107	C₂³	1	4	yes	—
181	C₂₃×#106	C₂³	1	4	yes	—
182	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
184	C₂₃×#103	C₂³	1	4	yes	—
185	C₂₃×#103	C₂³	1	2	yes	—
186	C₂₃×#103	C₂³	1	4	yes	—
187	C₂₃×#103	C₂³	1	4	yes	—
188	C₂₃×#103	C₂³	1	2	yes	—
189	C₂₃×#103	C₂³	1	2	yes	—
190	C₂₃×#103	C₂³	1	2	yes	—
191	C₂₃×#103	C₂³	1	4	yes	—
192	C₂₃×#102	C₂³	1	4	yes	—
193	C₂₃×#102	C₂³	1	2	yes	—
194	C₂₃×#102	C₂³	1	2	yes	—
195	C₂₃×#102	C₂³	1	2	yes	—
196	C₂₃×#102	C₂³	1	2	yes	—
197	C₂₃×#102	C₂³	1	4	yes	—
198	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
200	C₂₃×#97	C₂³	1	2	yes	—
201	C₂₃×#97	C₂³	1	2	yes	—
202	C₂⁴×C₂₃	—	2	1	no	—
203	#41×C₂₃	—	2	4	no	—
204	#41×C₂₃	—	2	4	no	—
205	#41×C₂₃	—	2	8	no	—
206	#41×C₂₃	—	2	4	no	—
207	#41×C₂₃	—	2	4	no	—
208	#41×C₂₃	—	4	4	no	—
209	#41×C₂₃	—	4	16	no	—
210	#41×C₂₃	—	4	8	no	—
211	#41×C₂₃	—	8	4	no	—
212	C₂×Q₈×C₂₃	—	2	1	no	—
213	C₂×Q₈×C₂₃	—	2	1	no	—
214	C₂×Q₈×C₂₃	—	2	4	no	—
215	C₂×Q₈×C₂₃	—	2	1	no	—
216	C₂×Q₈×C₂₃	—	2	2	no	—
217	C₂×Q₈×C₂₃	—	2	8	no	—
218	C₂×Q₈×C₂₃	—	4	4	no	—
219	C₂×Q₈×C₂₃	—	4	8	no	—
220	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
221	C₂×Q₈×C₂₃	#41	1	4	yes	complemented
222	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
224	C₂×D₄×C₂₃	—	2	2	no	—
225	C₂×D₄×C₂₃	—	2	4	no	—
226	C₂×D₄×C₂₃	—	2	4	no	—
227	C₂×D₄×C₂₃	—	2	4	no	—
228	C₂×D₄×C₂₃	—	2	4	no	—
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	2	1	no	—
231	C₂×D₄×C₂₃	—	2	1	no	—
232	C₂×D₄×C₂₃	—	2	2	no	—
233	C₂×D₄×C₂₃	—	2	2	no	—
234	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
235	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₂₃	—	2	1	no	—
241	C₂²×C₄×C₂₃	—	2	4	no	—
242	C₂²×C₄×C₂₃	—	2	1	no	—
243	C₂²×C₄×C₂₃	—	2	1	no	—
244	C₂²×C₄×C₂₃	—	2	4	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	4	no	—
247	C₂²×C₄×C₂₃	—	2	2	no	—
248	C₂²×C₄×C₂₃	—	2	2	no	—
249	C₂²×C₄×C₂₃	—	8	2	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	4	yes	—
253	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₂₃	—	2	8	no	—
255	SD₁₆×C₂₃	—	4	4	no	—
256	D₈×C₂₃	—	4	4	no	—
257	M₁₆×C₂₃	—	2	4	no	—
258	M₁₆×C₂₃	—	4	4	no	—
259	C₂×C₈×C₂₃	—	2	2	no	—
260	C₂×C₈×C₂₃	—	2	2	no	—
261	C₂×C₈×C₂₃	—	4	4	no	—
262	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
263	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
264	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₂₃	—	2	2	no	—
266	C₄⋊C₄×C₂₃	—	2	2	no	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	4	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₂₃	—	2	2	no	—
284	C₂²⋊C₄×C₂₃	—	2	4	no	—
285	C₂²⋊C₄×C₂₃	—	2	4	no	—
286	C₂²⋊C₄×C₂₃	—	2	2	no	—
287	C₂²⋊C₄×C₂₃	—	2	2	no	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
289	C₂²⋊C₄×C₂₃	—	2	2	no	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	2	2	no	—
292	C₂²⋊C₄×C₂₃	—	2	4	no	—
293	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
294	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
295	C₄²×C₂₃	—	2	2	no	—
296	C₄²×C₂₃	—	2	2	no	—
297	C₄²×C₂₃	—	2	4	no	—
298	C₄²×C₂₃	—	2	2	no	—
299	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
302	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
303	#61220	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂³×C₂₃	—	2	2	no	—
305	C₂³×C₂₃	—	2	2	no	—
306	C₂³×C₂₃	—	4	2	no	—
307	C₂³×C₂₃	—	8	1	no	—
308	C₂³×C₂₃	—	8	1	no	—
309	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
310	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₂₃	—	2	4	no	—
312	Q₈×C₂₃	—	2	4	no	—
313	Q₈×C₂₃	—	2	2	no	—
314	Q₈×C₂₃	—	2	2	no	—
315	Q₈×C₂₃	—	2	2	no	—
316	Q₈×C₂₃	—	4	8	no	—
317	Q₈×C₂₃	—	4	2	no	—
318	Q₈×C₂₃	—	8	1	no	—
319	Q₈×C₂₃	C₂×#41	1	4	yes	—
320	D₄×C₂₃	—	2	8	no	—
321	D₄×C₂₃	—	2	4	no	—
322	D₄×C₂₃	—	2	2	no	—
323	D₄×C₂₃	—	2	2	no	—
324	D₄×C₂₃	—	2	2	no	—
325	D₄×C₂₃	—	2	2	no	—
326	D₄×C₂₃	—	4	2	no	—
327	D₄×C₂₃	—	4	2	no	—
328	D₄×C₂₃	—	4	8	no	—
329	D₄×C₂₃	—	4	2	no	—
330	D₄×C₂₃	—	4	4	no	—
331	D₄×C₂₃	—	4	2	no	—
332	D₄×C₂₃	—	8	1	no	—
333	D₄×C₂₃	—	8	4	no	—
334	D₄×C₂₃	—	8	4	no	—
335	D₄×C₂₃	—	8	4	no	—
336	C₂×C₄×C₂₃	—	2	4	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	4	no	—
339	C₂×C₄×C₂₃	—	2	4	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	4	1	no	—
346	C₂×C₄×C₂₃	—	4	1	no	—
347	C₂×C₄×C₂₃	—	4	8	no	—
348	C₂×C₄×C₂₃	—	4	8	no	—
349	C₂×C₄×C₂₃	—	4	4	no	—
350	C₂×C₄×C₂₃	—	4	4	no	—
351	C₂×C₄×C₂₃	—	8	2	no	—
352	C₂×C₄×C₂₃	—	8	1	no	—
353	C₂×C₄×C₂₃	—	8	1	no	—
354	C₂×C₄×C₂₃	—	8	4	no	—
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	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
362	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
363	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
364	C₈×C₂₃	—	2	2	no	—
365	C₈×C₂₃	—	2	2	no	—
366	C₈×C₂₃	—	2	4	no	—
367	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#3497	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#3321	C₂×C₂₃	1	4	yes	complemented
370	#3320	C₂×C₂₃	1	4	yes	complemented
371	#3309	C₂×C₂₃	1	4	yes	complemented
372	#3308	C₂×C₂₃	1	4	yes	complemented
373	#3135	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#3098	C₂×C₂₃	1	2	yes	complemented
375	#3078	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#3062	C₂×C₂₃	1	2	yes	complemented
377	#3036	C₂×C₂₃	1	1	yes	characteristic, complemented
378	#3010	C₂×C₂₃	1	2	yes	complemented
379	C₂×#440	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#2932	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#2898	C₂×C₂₃	1	2	yes	complemented
382	C₂²×C₂₃	—	2	1	no	—
383	C₂²×C₂₃	—	2	1	no	—
384	C₂²×C₂₃	—	2	4	no	—
385	C₂²×C₂₃	—	2	4	no	—
386	C₂²×C₂₃	—	2	4	no	—
387	C₂²×C₂₃	—	4	2	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	—	8	4	no	—
394	C₂²×C₂₃	#546	1	2	yes	—
395	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
396	C₄×C₂₃	—	2	1	no	—
397	C₄×C₂₃	—	2	1	no	—
398	C₄×C₂₃	—	2	1	no	—
399	C₄×C₂₃	—	2	1	no	—
400	C₄×C₂₃	—	2	4	no	—
401	C₄×C₂₃	—	2	4	no	—
402	C₄×C₂₃	—	4	2	no	—
403	C₄×C₂₃	—	4	2	no	—
404	C₄×C₂₃	—	4	2	no	—
405	C₄×C₂₃	—	4	2	no	—
406	C₄×C₂₃	—	4	2	no	—
407	C₄×C₂₃	#546	1	2	yes	—
408	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
409	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
410	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	—
411	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
412	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#131	C₂²×C₂₃	1	2	yes	—
414	#559	—	2	2	no	—
415	#556	—	2	1	no	—
416	#555	C₂²×C₂₃	1	2	yes	—
417	#553	C₂²×C₂₃	1	4	yes	—
418	#550	—	2	1	no	—
419	#550	—	2	1	no	—
420	#550	C₂²×C₂₃	1	2	yes	complemented
421	D₄×Q₈	—	2	1	no	—
422	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
423	#548	—	2	2	no	—
424	#548	C₂²×C₂₃	1	4	yes	complemented
425	#547	C₂²×C₂₃	1	2	yes	—
426	#538	—	2	2	no	—
427	#537	—	2	2	no	—
428	#537	C₂²×C₂₃	1	2	yes	—
429	#535	C₂²×C₂₃	1	2	yes	—
430	#533	C₂²×C₂₃	1	1	yes	characteristic
431	#532	—	2	2	no	—
432	#532	C₂²×C₂₃	1	1	yes	characteristic
433	#532	C₂²×C₂₃	1	1	yes	characteristic
434	#525	—	2	2	no	—
435	#520	C₂²×C₂₃	1	2	yes	—
436	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
438	#491	C₂²×C₂₃	1	2	yes	complemented
439	#490	C₂²×C₂₃	1	2	yes	complemented
440	#489	C₂²×C₂₃	1	2	yes	complemented
441	#489	C₂²×C₂₃	1	2	yes	complemented
442	#485	C₂²×C₂₃	1	4	yes	complemented
443	#484	C₂²×C₂₃	1	4	yes	complemented
444	#482	C₂²×C₂₃	1	4	yes	complemented
445	#480	C₂²×C₂₃	1	4	yes	complemented
446	#479	C₂²×C₂₃	1	4	yes	complemented
447	#477	C₂²×C₂₃	1	2	yes	complemented
448	#475	C₂²×C₂₃	1	2	yes	complemented
449	#469	C₂²×C₂₃	1	4	yes	—
450	#468	C₂²×C₂₃	1	4	yes	—
451	#466	C₂²×C₂₃	1	4	yes	—
452	#465	C₂²×C₂₃	1	4	yes	—
453	#463	C₂²×C₂₃	1	4	yes	—
454	#461	C₂²×C₂₃	1	2	yes	—
455	#459	C₂²×C₂₃	1	2	yes	—
456	#449	C₂²×C₂₃	1	4	yes	—
457	#449	C₂²×C₂₃	1	4	yes	—
458	#448	C₂²×C₂₃	1	4	yes	—
459	#448	C₂²×C₂₃	1	4	yes	—
460	#440	C₂²×C₂₃	1	4	yes	—
461	#440	C₂²×C₂₃	1	4	yes	—
462	#435	C₂²×C₂₃	1	4	yes	complemented
463	#435	C₂²×C₂₃	1	4	yes	complemented
464	#428	C₂²×C₂₃	1	2	yes	—
465	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
466	#423	C₂²×C₂₃	1	1	yes	characteristic
467	#419	C₂²×C₂₃	1	2	yes	—
468	#419	C₂²×C₂₃	1	4	yes	complemented
469	#417	C₂²×C₂₃	1	2	yes	—
470	#417	C₂²×C₂₃	1	4	yes	complemented
471	#416	C₂²×C₂₃	1	2	yes	—
472	#416	C₂²×C₂₃	1	2	yes	—
473	#416	C₂²×C₂₃	1	4	yes	complemented
474	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
475	C₂×#103	C₂²×C₂₃	1	4	yes	complemented
476	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
477	#408	C₂²×C₂₃	1	2	yes	—
478	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×C₂₃	—	2	2	no	—
480	C₂×C₂₃	—	4	4	no	—
481	C₂×C₂₃	—	8	2	no	—
482	C₂×C₂₃	—	8	2	no	—
483	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
484	C₂×C₂₃	#3585	1	1	yes	characteristic
485	C₂×C₂₃	#3586	1	1	yes	characteristic
486	2₋¹⁺⁴	—	2	8	no	—
487	2₋¹⁺⁴	—	4	4	no	—
488	C₂×#41	—	2	4	no	—
489	C₂×#41	—	2	2	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	C₂³×C₂₃	1	2	yes	—
492	C₂×#41	C₂³×C₂₃	1	4	yes	—
493	C₂×#41	C₂³×C₂₃	1	2	yes	—
494	C₂²×Q₈	—	2	2	no	—
495	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
496	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
498	C₂³×C₄	—	2	1	no	—
499	AGL(1,ℤ/8)	—	4	4	no	—
500	C₂×SD₁₆	—	2	4	no	—
501	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
502	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
503	C₂×D₈	C₂³×C₂₃	1	4	yes	—
504	#131	—	4	4	no	—
505	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
506	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
507	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
510	C₄⋊Q₈	—	2	2	no	—
511	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
512	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
515	#127	—	2	2	no	—
516	#127	—	2	2	no	—
517	#127	D₄×C₂₃	1	1	yes	characteristic
518	#127	C₂³×C₂₃	1	1	yes	characteristic
519	#126	—	2	4	no	—
520	#125	C₂³×C₂₃	1	2	yes	—
521	#124	—	2	2	no	—
522	#124	—	2	4	no	—
523	#124	—	2	4	no	—
524	#124	D₄×C₂₃	1	2	yes	—
525	#124	C₂³×C₂₃	1	2	yes	—
526	#123	—	2	4	no	—
527	#123	—	2	4	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
535	#121	—	2	2	no	—
536	#121	—	2	4	no	—
537	#121	—	2	4	no	—
538	#121	—	2	2	no	—
539	#121	—	2	4	no	—
540	#121	—	2	1	no	—
541	#121	—	2	1	no	—
542	#121	—	2	4	no	—
543	#121	D₄×C₂₃	1	2	yes	—
544	#121	D₄×C₂₃	1	2	yes	—
545	#121	C₂³×C₂₃	1	4	yes	—
546	#121	C₂³×C₂₃	1	4	yes	—
547	#121	C₂³×C₂₃	1	4	yes	—
548	#120	—	2	4	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
555	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
556	C₄×D₄	—	2	4	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	C₂³×C₂₃	1	2	yes	—
567	C₄×D₄	C₂³×C₂₃	1	2	yes	—
568	C₄×D₄	C₂³×C₂₃	1	2	yes	—
569	C₄×D₄	C₂³×C₂₃	1	2	yes	—
570	#117	—	2	2	no	—
571	#117	C₂³×C₂₃	1	2	yes	—
572	#117	C₂³×C₂₃	1	4	yes	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₄²	—	2	1	no	—
579	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
580	#107	C₂³×C₂₃	1	4	yes	—
581	#107	C₂³×C₂₃	1	4	yes	—
582	#106	C₂³×C₂₃	1	4	yes	—
583	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
584	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
585	#103	C₂³×C₂₃	1	4	yes	—
586	#103	C₂³×C₂₃	1	2	yes	—
587	#103	C₂³×C₂₃	1	4	yes	—
588	#103	C₂³×C₂₃	1	4	yes	—
589	#103	C₂³×C₂₃	1	2	yes	—
590	#103	C₂³×C₂₃	1	2	yes	—
591	#103	C₂³×C₂₃	1	2	yes	—
592	#103	C₂³×C₂₃	1	4	yes	—
593	#102	C₂³×C₂₃	1	4	yes	—
594	#102	C₂³×C₂₃	1	2	yes	—
595	#102	C₂³×C₂₃	1	2	yes	—
596	#102	C₂³×C₂₃	1	2	yes	—
597	#102	C₂³×C₂₃	1	2	yes	—
598	#102	C₂³×C₂₃	1	4	yes	—
599	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
601	#97	C₂³×C₂₃	1	2	yes	—
602	#97	C₂³×C₂₃	1	2	yes	—
603	C₂₃	#61220	1	1	yes	characteristic, direct product factor, Sylow
604	C₂⁴	—	2	1	no	—
605	#41	—	2	4	no	—
606	#41	—	2	4	no	—
607	#41	—	2	8	no	—
608	#41	—	2	4	no	—
609	#41	—	2	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	16	no	—
612	#41	—	4	8	no	—
613	#41	—	8	4	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	8	no	—
620	C₂×Q₈	—	4	4	no	—
621	C₂×Q₈	—	4	8	no	—
622	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
623	C₂×Q₈	#41×C₂₃	1	4	yes	complemented
624	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
637	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
638	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
639	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
640	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
641	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	8	2	no	—
652	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
655	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
656	SD₁₆	—	2	8	no	—
657	SD₁₆	—	4	4	no	—
658	D₈	—	4	4	no	—
659	M₁₆	—	2	4	no	—
660	M₁₆	—	4	4	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	2	2	no	—
663	C₂×C₈	—	4	4	no	—
664	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
665	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
666	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
680	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
696	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	2	no	—
701	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
702	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
703	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
704	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	8	1	no	—
709	C₂³	—	8	1	no	—
710	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
711	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
712	Q₈	—	2	2	no	—
713	Q₈	—	2	4	no	—
714	Q₈	—	2	4	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	4	8	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	8	1	no	—
720	Q₈	C₂×#41×C₂₃	1	4	yes	—
721	D₄	—	2	8	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	4	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	—	8	4	no	—
735	D₄	—	8	4	no	—
736	D₄	—	8	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	8	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	—	8	1	no	—
754	C₂×C₄	—	8	4	no	—
755	C₂×C₄	—	8	1	no	—
756	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
759	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
762	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
763	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
764	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
765	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₈	—	2	4	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	8	4	no	—
780	C₂²	C₂₃×#546	1	2	yes	—
781	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
782	C₄	—	2	4	no	—
783	C₄	—	2	4	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	C₂₃×#546	1	2	yes	—
794	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
795	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
796	C₂	—	2	2	no	—
797	C₂	—	4	4	no	—
798	C₂	—	8	2	no	—
799	C₂	—	8	2	no	—
800	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
801	C₂	C₂₃×#3585	1	1	yes	characteristic
802	C₂	C₂₃×#3586	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3506	C₂	semidirect
2. C₂₃×#3497	C₂	semidirect
3. C₂₃×#3321	C₂	semidirect
4. C₂₃×#3320	C₂	semidirect
5. C₂₃×#3309	C₂	semidirect
6. C₂₃×#3308	C₂	semidirect
7. C₂₃×#3135	C₂	semidirect
8. C₂₃×#3098	C₂	semidirect
9. C₂₃×#3078	C₂	semidirect
10. C₂₃×#3062	C₂	semidirect
11. C₂₃×#3036	C₂	semidirect
12. C₂₃×#3010	C₂	semidirect
13. C₂×C₂₃×#440	C₂	semidirect
14. C₂₃×#2932	C₂	semidirect
15. C₂₃×#2898	C₂	semidirect
26. C₂₃×#550	C₂²	semidirect
28. D₄×Q₈×C₂₃	C₂²	semidirect
30. C₂₃×#548	C₂²	semidirect
44. C₂₃×#491	C₂²	semidirect
45. C₂₃×#490	C₂²	semidirect
46. C₂₃×#489	C₂²	semidirect
47. C₂₃×#489	C₂²	semidirect
48. C₂₃×#485	C₂²	semidirect
49. C₂₃×#484	C₂²	semidirect
50. C₂₃×#482	C₂²	semidirect
51. C₂₃×#480	C₂²	semidirect
52. C₂₃×#479	C₂²	semidirect
53. C₂₃×#477	C₂²	semidirect
54. C₂₃×#475	C₂²	semidirect
68. C₂₃×#435	C₂²	semidirect
69. C₂₃×#435	C₂²	semidirect
74. C₂₃×#419	C₂²	semidirect
76. C₂₃×#417	C₂²	semidirect
79. C₂₃×#416	C₂²	semidirect
81. C₂×C₂₃×#103	C₂²	semidirect
221. C₂×Q₈×C₂₃	#41	semidirect
303. #61220	C₂₃	direct (N × H)
367. #3506	C₂×C₂₃	semidirect
368. #3497	C₂×C₂₃	semidirect
369. #3321	C₂×C₂₃	semidirect
370. #3320	C₂×C₂₃	semidirect
371. #3309	C₂×C₂₃	semidirect
372. #3308	C₂×C₂₃	semidirect
373. #3135	C₂×C₂₃	semidirect
374. #3098	C₂×C₂₃	semidirect
375. #3078	C₂×C₂₃	semidirect
376. #3062	C₂×C₂₃	semidirect
377. #3036	C₂×C₂₃	semidirect
378. #3010	C₂×C₂₃	semidirect
379. C₂×#440	C₂×C₂₃	semidirect
380. #2932	C₂×C₂₃	semidirect
381. #2898	C₂×C₂₃	semidirect
420. #550	C₂²×C₂₃	semidirect
422. D₄×Q₈	C₂²×C₂₃	semidirect
424. #548	C₂²×C₂₃	semidirect
438. #491	C₂²×C₂₃	semidirect
439. #490	C₂²×C₂₃	semidirect
440. #489	C₂²×C₂₃	semidirect
441. #489	C₂²×C₂₃	semidirect
442. #485	C₂²×C₂₃	semidirect
443. #484	C₂²×C₂₃	semidirect
444. #482	C₂²×C₂₃	semidirect
445. #480	C₂²×C₂₃	semidirect
446. #479	C₂²×C₂₃	semidirect
447. #477	C₂²×C₂₃	semidirect
448. #475	C₂²×C₂₃	semidirect
462. #435	C₂²×C₂₃	semidirect
463. #435	C₂²×C₂₃	semidirect
468. #419	C₂²×C₂₃	semidirect
470. #417	C₂²×C₂₃	semidirect
473. #416	C₂²×C₂₃	semidirect
475. C₂×#103	C₂²×C₂₃	semidirect
603. C₂₃	#61220	direct (N × H)
623. C₂×Q₈	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3506	2
C₂₃×#3497	2
C₂₃×#3321	2
C₂₃×#3320	2
C₂₃×#3309	2
C₂₃×#3308	2
C₂₃×#3135	2
C₂₃×#3098	2
C₂₃×#3078	2
C₂₃×#3062	2
C₂₃×#3036	2
C₂₃×#3010	2
C₂×C₂₃×#440	2
C₂₃×#2932	2
C₂₃×#2898	2
#61220	23

Subgroups — C23×#61220 #19208846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61220 #19208846