Subgroups — C₂₃×#24124 #19171750

Order 5888.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2535	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂₃×#553	—	2	4	no	—
18	C₂₃×#553	—	2	4	no	—
19	C₂×C₂₃×#126	—	2	1	no	—
20	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#123	—	2	1	no	—
22	C₂×C₂₃×#121	—	2	1	no	—
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₂₃	—	2	1	no	—
28	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂₃×#478	—	2	4	no	—
34	C₄×D₈×C₂₃	—	2	4	no	—
35	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
50	C₂₃×#397	—	2	1	no	—
51	C₂₃×#392	—	2	1	no	—
52	C₂₃×#386	—	2	1	no	—
53	C₂₃×#386	—	2	1	no	—
54	C₂₃×#382	C₂²	1	1	yes	characteristic
55	C₂₃×#380	C₂²	1	1	yes	characteristic
56	C₂₃×#380	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#340	C₂²	1	1	yes	characteristic
61	C₂₃×#340	C₂²	1	1	yes	characteristic
62	C₂₃×#340	C₂²	1	1	yes	characteristic
63	C₂²×D₄×C₂₃	—	2	1	no	—
64	C₂²×D₄×C₂₃	—	2	1	no	—
65	C₂²×D₄×C₂₃	—	2	1	no	—
66	C₂²×D₄×C₂₃	—	2	1	no	—
67	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	—	2	1	no	—
71	C₂³×C₄×C₂₃	—	2	1	no	—
72	C₂³×C₄×C₂₃	—	2	1	no	—
73	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×D₈×C₂₃	—	2	2	no	—
76	C₂×D₈×C₂₃	—	2	2	no	—
77	C₂×D₈×C₂₃	—	2	2	no	—
78	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂₃×#126	—	2	8	no	—
83	C₂₃×#125	—	2	2	no	—
84	C₂₃×#125	D₄	1	4	yes	complemented
85	C₂₃×#123	—	2	8	no	—
86	C₂₃×#121	—	2	8	no	—
87	C₂₃×#121	—	2	2	no	—
88	C₂₃×#121	—	2	2	no	—
89	C₂₃×#121	—	2	2	no	—
90	C₂₃×#121	—	2	2	no	—
91	C₂₃×#121	—	2	2	no	—
92	C₂₃×#121	—	2	2	no	—
93	C₂₃×#121	—	4	1	no	—
94	C₂₃×#121	—	4	1	no	—
95	C₄×D₄×C₂₃	—	2	8	no	—
96	C₄×D₄×C₂₃	—	2	2	no	—
97	C₄×D₄×C₂₃	—	2	2	no	—
98	C₄×D₄×C₂₃	—	2	2	no	—
99	C₄×D₄×C₂₃	—	2	2	no	—
100	C₄×D₄×C₂₃	—	2	2	no	—
101	C₄×D₄×C₂₃	D₄	1	4	yes	complemented
102	C₂₃×#117	—	2	2	no	—
103	C₂₃×#117	—	2	2	no	—
104	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
108	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
109	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₂₃	—	2	1	no	—
128	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
129	C₂₃×#107	—	2	2	no	—
130	C₂₃×#107	—	2	2	no	—
131	C₂₃×#106	—	2	2	no	—
132	C₂₃×C₄⋊C₈	—	2	2	no	—
133	C₂₃×#102	—	2	2	no	—
134	C₂₃×#102	—	2	2	no	—
135	C₂₃×#102	—	2	2	no	—
136	C₂₃×#102	—	2	2	no	—
137	C₂₃×#102	—	4	1	no	—
138	C₂₃×#102	—	4	1	no	—
139	C₂₃×C₂²⋊C₈	—	2	2	no	—
140	C₂₃×C₂²⋊C₈	—	2	2	no	—
141	C₂₃×C₂²⋊C₈	—	4	1	no	—
142	C₂₃×C₂²⋊C₈	—	4	1	no	—
143	C₄×C₈×C₂₃	—	2	2	no	—
144	C₂₃×#95	—	2	1	no	—
145	C₂₃×#95	—	2	1	no	—
146	C₂₃×#95	—	2	1	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂⁴×C₂₃	—	2	1	no	—
149	C₂⁴×C₂₃	—	2	1	no	—
150	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₂₃	—	2	4	no	—
153	C₂×D₄×C₂₃	—	2	2	no	—
154	C₂×D₄×C₂₃	—	2	4	no	—
155	C₂×D₄×C₂₃	—	2	2	no	—
156	C₂×D₄×C₂₃	—	2	1	no	—
157	C₂×D₄×C₂₃	—	2	1	no	—
158	C₂×D₄×C₂₃	—	2	1	no	—
159	C₂×D₄×C₂₃	—	2	1	no	—
160	C₂×D₄×C₂₃	—	2	1	no	—
161	C₂×D₄×C₂₃	—	2	1	no	—
162	C₂×D₄×C₂₃	—	2	1	no	—
163	C₂×D₄×C₂₃	—	2	1	no	—
164	C₂×D₄×C₂₃	—	2	1	no	—
165	C₂×D₄×C₂₃	—	2	1	no	—
166	C₂×D₄×C₂₃	—	4	1	no	—
167	C₂×D₄×C₂₃	—	4	2	no	—
168	C₂×D₄×C₂₃	—	4	2	no	—
169	C₂×D₄×C₂₃	—	4	2	no	—
170	C₂×D₄×C₂₃	—	4	2	no	—
171	C₂×D₄×C₂₃	—	4	2	no	—
172	C₂×D₄×C₂₃	—	4	2	no	—
173	C₂×D₄×C₂₃	—	8	1	no	—
174	C₂×D₄×C₂₃	—	8	1	no	—
175	C₂×D₄×C₂₃	—	8	1	no	—
176	C₂×D₄×C₂₃	—	8	1	no	—
177	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
178	C₂×D₄×C₂₃	#41	1	2	yes	—
179	C₂²×C₄×C₂₃	—	2	1	no	—
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	4	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	1	no	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	2	1	no	—
187	C₂²×C₄×C₂₃	—	2	1	no	—
188	C₂²×C₄×C₂₃	—	2	1	no	—
189	C₂²×C₄×C₂₃	—	2	1	no	—
190	C₂²×C₄×C₂₃	—	2	1	no	—
191	C₂²×C₄×C₂₃	—	2	1	no	—
192	C₂²×C₄×C₂₃	—	2	1	no	—
193	C₂²×C₄×C₂₃	—	2	1	no	—
194	C₂²×C₄×C₂₃	—	2	1	no	—
195	C₂²×C₄×C₂₃	—	2	4	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	4	2	no	—
200	C₂²×C₄×C₂₃	—	8	1	no	—
201	C₂²×C₄×C₂₃	—	8	1	no	—
202	C₂²×C₄×C₂₃	—	8	1	no	—
203	C₂²×C₄×C₂₃	—	8	1	no	—
204	C₂²×C₄×C₂₃	—	8	1	no	—
205	C₂²×C₄×C₂₃	—	8	1	no	—
206	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
211	D₈×C₂₃	—	2	8	no	—
212	C₂×C₈×C₂₃	—	2	1	no	—
213	C₂×C₈×C₂₃	—	2	1	no	—
214	C₂×C₈×C₂₃	—	2	1	no	—
215	C₂×C₈×C₂₃	—	2	1	no	—
216	C₂×C₈×C₂₃	—	2	1	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	—	2	1	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	2	1	no	—
221	C₂×C₈×C₂₃	—	2	1	no	—
222	C₂×C₈×C₂₃	—	2	1	no	—
223	C₂×C₈×C₂₃	#41	1	2	yes	—
224	C₄⋊C₄×C₂₃	—	2	4	no	—
225	C₄⋊C₄×C₂₃	—	2	4	no	—
226	C₄⋊C₄×C₂₃	—	2	4	no	—
227	C₄⋊C₄×C₂₃	—	2	2	no	—
228	C₄⋊C₄×C₂₃	—	2	1	no	—
229	C₄⋊C₄×C₂₃	—	2	1	no	—
230	C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
239	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
240	C₂²⋊C₄×C₂₃	—	2	4	no	—
241	C₂²⋊C₄×C₂₃	—	2	4	no	—
242	C₂²⋊C₄×C₂₃	—	2	4	no	—
243	C₂²⋊C₄×C₂₃	—	2	4	no	—
244	C₂²⋊C₄×C₂₃	—	2	2	no	—
245	C₂²⋊C₄×C₂₃	—	2	2	no	—
246	C₂²⋊C₄×C₂₃	—	4	2	no	—
247	C₂²⋊C₄×C₂₃	—	4	2	no	—
248	C₂²⋊C₄×C₂₃	—	4	2	no	—
249	C₂²⋊C₄×C₂₃	—	8	1	no	—
250	C₂²⋊C₄×C₂₃	—	8	1	no	—
251	C₄²×C₂₃	—	2	4	no	—
252	C₄²×C₂₃	C₂×D₄	1	2	yes	—
253	C₄²×C₂₃	C₂×D₄	1	2	yes	—
254	#24124	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂³×C₂₃	—	2	1	no	—
256	C₂³×C₂₃	—	2	1	no	—
257	C₂³×C₂₃	—	2	1	no	—
258	C₂³×C₂₃	—	2	1	no	—
259	C₂³×C₂₃	—	2	1	no	—
260	C₂³×C₂₃	—	2	1	no	—
261	C₂³×C₂₃	—	2	1	no	—
262	C₂³×C₂₃	—	2	2	no	—
263	C₂³×C₂₃	—	2	2	no	—
264	C₂³×C₂₃	—	2	1	no	—
265	C₂³×C₂₃	—	2	1	no	—
266	C₂³×C₂₃	—	2	1	no	—
267	C₂³×C₂₃	—	2	1	no	—
268	C₂³×C₂₃	—	2	1	no	—
269	C₂³×C₂₃	—	2	1	no	—
270	C₂³×C₂₃	—	4	1	no	—
271	C₂³×C₂₃	—	4	1	no	—
272	C₂³×C₂₃	—	4	1	no	—
273	C₂³×C₂₃	—	4	1	no	—
274	C₂³×C₂₃	—	4	1	no	—
275	C₂³×C₂₃	—	4	1	no	—
276	C₂³×C₂₃	—	4	1	no	—
277	C₂³×C₂₃	—	4	1	no	—
278	C₂³×C₂₃	—	4	1	no	—
279	C₂³×C₂₃	—	4	1	no	—
280	C₂³×C₂₃	—	4	1	no	—
281	C₂³×C₂₃	—	4	1	no	—
282	C₂³×C₂₃	#135	1	2	yes	—
283	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
284	D₄×C₂₃	—	2	2	no	—
285	D₄×C₂₃	—	2	2	no	—
286	D₄×C₂₃	—	2	2	no	—
287	D₄×C₂₃	—	2	2	no	—
288	D₄×C₂₃	—	4	4	no	—
289	D₄×C₂₃	—	4	8	no	—
290	D₄×C₂₃	—	4	1	no	—
291	D₄×C₂₃	—	4	1	no	—
292	D₄×C₂₃	—	4	1	no	—
293	D₄×C₂₃	—	4	1	no	—
294	D₄×C₂₃	—	8	4	no	—
295	D₄×C₂₃	—	8	4	no	—
296	D₄×C₂₃	—	8	4	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	1	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	1	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	1	no	—
308	C₂×C₄×C₂₃	—	2	1	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	4	1	no	—
311	C₂×C₄×C₂₃	—	4	1	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	1	no	—
319	C₂×C₄×C₂₃	—	4	1	no	—
320	C₂×C₄×C₂₃	—	4	1	no	—
321	C₂×C₄×C₂₃	—	4	1	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	4	1	no	—
324	C₂×C₄×C₂₃	—	4	1	no	—
325	C₂×C₄×C₂₃	—	4	1	no	—
326	C₂×C₄×C₂₃	—	4	1	no	—
327	C₂×C₄×C₂₃	—	4	1	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	1	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	4	1	no	—
332	C₂×C₄×C₂₃	—	4	1	no	—
333	C₂×C₄×C₂₃	—	8	4	no	—
334	C₂×C₄×C₂₃	—	8	4	no	—
335	C₂×C₄×C₂₃	—	8	4	no	—
336	C₂×C₄×C₂₃	#120	1	2	yes	—
337	C₂×C₄×C₂₃	#120	1	2	yes	—
338	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
342	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
344	C₈×C₂₃	—	2	2	no	—
345	C₈×C₂₃	—	4	1	no	—
346	C₈×C₂₃	—	4	1	no	—
347	C₈×C₂₃	—	4	1	no	—
348	C₂×#553	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#2535	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#2034	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#2033	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1999	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1999	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#1991	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1954	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1875	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1874	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1854	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1852	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#1804	C₂×C₂₃	1	1	yes	characteristic, complemented
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	2	2	no	—
366	C₂²×C₂₃	—	4	1	no	—
367	C₂²×C₂₃	—	4	1	no	—
368	C₂²×C₂₃	—	4	1	no	—
369	C₂²×C₂₃	—	4	1	no	—
370	C₂²×C₂₃	—	4	1	no	—
371	C₂²×C₂₃	—	4	1	no	—
372	C₂²×C₂₃	—	4	1	no	—
373	C₂²×C₂₃	—	4	2	no	—
374	C₂²×C₂₃	—	4	2	no	—
375	C₂²×C₂₃	—	4	1	no	—
376	C₂²×C₂₃	—	4	2	no	—
377	C₂²×C₂₃	—	4	2	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	4	2	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	1	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	8	1	no	—
384	C₂²×C₂₃	—	8	1	no	—
385	C₂²×C₂₃	—	8	1	no	—
386	C₂²×C₂₃	—	8	1	no	—
387	C₂²×C₂₃	—	8	1	no	—
388	C₂²×C₂₃	—	8	1	no	—
389	C₂²×C₂₃	—	8	1	no	—
390	C₂²×C₂₃	—	8	1	no	—
391	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
392	C₂²×C₂₃	#546	1	1	yes	characteristic
393	C₂²×C₂₃	#547	1	1	yes	characteristic
394	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
395	C₂²×C₂₃	#575	1	1	yes	characteristic
396	C₂²×C₂₃	#576	1	1	yes	characteristic
397	C₂²×C₂₃	#576	1	1	yes	characteristic
398	C₄×C₂₃	—	2	2	no	—
399	C₄×C₂₃	—	2	2	no	—
400	C₄×C₂₃	—	4	1	no	—
401	C₄×C₂₃	—	4	1	no	—
402	C₄×C₂₃	—	4	2	no	—
403	C₄×C₂₃	—	4	2	no	—
404	C₄×C₂₃	—	4	2	no	—
405	C₄×C₂₃	—	8	1	no	—
406	C₄×C₂₃	—	8	1	no	—
407	C₄×C₂₃	—	8	1	no	—
408	C₄×C₂₃	#525	1	1	yes	characteristic
409	C₄×C₂₃	#537	1	1	yes	characteristic
410	C₄×C₂₃	#548	1	1	yes	characteristic
411	C₄×C₂₃	#550	1	1	yes	characteristic
412	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
413	#553	—	2	4	no	—
414	#553	—	2	4	no	—
415	C₂×#126	—	2	1	no	—
416	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#123	—	2	1	no	—
418	C₂×#121	—	2	1	no	—
419	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×C₄×D₄	—	2	1	no	—
424	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
428	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
429	#478	—	2	4	no	—
430	C₄×D₈	—	2	4	no	—
431	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
446	#397	—	2	1	no	—
447	#392	—	2	1	no	—
448	#386	—	2	1	no	—
449	#386	—	2	1	no	—
450	#382	C₂²×C₂₃	1	1	yes	characteristic
451	#380	C₂²×C₂₃	1	1	yes	characteristic
452	#380	C₂²×C₂₃	1	1	yes	characteristic
453	#340	C₂²×C₂₃	1	1	yes	characteristic
454	#340	C₂²×C₂₃	1	1	yes	characteristic
455	#340	C₂²×C₂₃	1	1	yes	characteristic
456	#340	C₂²×C₂₃	1	1	yes	characteristic
457	#340	C₂²×C₂₃	1	1	yes	characteristic
458	#340	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×C₂₃	—	4	2	no	—
460	C₂×C₂₃	—	8	1	no	—
461	C₂×C₂₃	—	8	2	no	—
462	C₂×C₂₃	—	8	2	no	—
463	C₂×C₂₃	#2407	1	1	yes	characteristic
464	C₂×C₂₃	#3002	1	1	yes	characteristic
465	C₂×C₂₃	#3008	1	1	yes	characteristic
466	C₂×C₂₃	#3297	1	1	yes	characteristic
467	C₂×C₂₃	#3322	1	1	yes	characteristic
468	C₂×C₂₃	#3339	1	1	yes	characteristic
469	C₂×C₂₃	#3355	1	1	yes	characteristic
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
482	C₂×D₈	—	2	2	no	—
483	C₂×D₈	—	2	2	no	—
484	C₂×D₈	—	2	2	no	—
485	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
486	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
489	#126	—	2	8	no	—
490	#125	—	2	2	no	—
491	#125	D₄×C₂₃	1	4	yes	complemented
492	#123	—	2	8	no	—
493	#121	—	2	8	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	4	1	no	—
501	#121	—	4	1	no	—
502	C₄×D₄	—	2	8	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	D₄×C₂₃	1	4	yes	complemented
509	#117	—	2	2	no	—
510	#117	—	2	2	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	2	no	—
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
534	C₂×C₄²	—	2	1	no	—
535	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
536	#107	—	2	2	no	—
537	#107	—	2	2	no	—
538	#106	—	2	2	no	—
539	C₄⋊C₈	—	2	2	no	—
540	#102	—	2	2	no	—
541	#102	—	2	2	no	—
542	#102	—	2	2	no	—
543	#102	—	2	2	no	—
544	#102	—	4	1	no	—
545	#102	—	4	1	no	—
546	C₂²⋊C₈	—	2	2	no	—
547	C₂²⋊C₈	—	2	2	no	—
548	C₂²⋊C₈	—	4	1	no	—
549	C₂²⋊C₈	—	4	1	no	—
550	C₄×C₈	—	2	2	no	—
551	#95	—	2	1	no	—
552	#95	—	2	1	no	—
553	#95	—	2	1	no	—
554	#95	—	2	1	no	—
555	C₂₃	#24124	1	1	yes	characteristic, direct product factor, Sylow
556	C₂⁴	—	2	1	no	—
557	C₂⁴	—	2	1	no	—
558	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
559	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	8	1	no	—
582	C₂×D₄	—	8	1	no	—
583	C₂×D₄	—	8	1	no	—
584	C₂×D₄	—	8	1	no	—
585	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
586	C₂×D₄	#41×C₂₃	1	2	yes	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	8	1	no	—
609	C₂²×C₄	—	8	1	no	—
610	C₂²×C₄	—	8	1	no	—
611	C₂²×C₄	—	8	1	no	—
612	C₂²×C₄	—	8	1	no	—
613	C₂²×C₄	—	8	1	no	—
614	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
619	D₈	—	2	8	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	#41×C₂₃	1	2	yes	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
646	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
647	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	8	1	no	—
658	C₂²⋊C₄	—	8	1	no	—
659	C₄²	—	2	4	no	—
660	C₄²	C₂×D₄×C₂₃	1	2	yes	—
661	C₄²	C₂×D₄×C₂₃	1	2	yes	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	4	1	no	—
689	C₂³	C₂₃×#135	1	2	yes	—
690	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	4	4	no	—
696	D₄	—	4	8	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	1	no	—
700	D₄	—	4	1	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	—	8	4	no	—
743	C₂×C₄	C₂₃×#120	1	2	yes	—
744	C₂×C₄	C₂₃×#120	1	2	yes	—
745	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
747	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
748	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
749	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
750	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
751	C₈	—	2	2	no	—
752	C₈	—	4	1	no	—
753	C₈	—	4	1	no	—
754	C₈	—	4	1	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	—	8	1	no	—
780	C₂²	—	8	1	no	—
781	C₂²	—	8	1	no	—
782	C₂²	—	8	1	no	—
783	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
784	C₂²	C₂₃×#546	1	1	yes	characteristic
785	C₂²	C₂₃×#547	1	1	yes	characteristic
786	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
787	C₂²	C₂₃×#575	1	1	yes	characteristic
788	C₂²	C₂₃×#576	1	1	yes	characteristic
789	C₂²	C₂₃×#576	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	8	1	no	—
798	C₄	—	8	1	no	—
799	C₄	—	8	1	no	—
800	C₄	C₂₃×#525	1	1	yes	characteristic
801	C₄	C₂₃×#537	1	1	yes	characteristic
802	C₄	C₂₃×#548	1	1	yes	characteristic
803	C₄	C₂₃×#550	1	1	yes	characteristic
804	C₂	—	4	2	no	—
805	C₂	—	8	1	no	—
806	C₂	—	8	2	no	—
807	C₂	—	8	2	no	—
808	C₂	C₂₃×#2407	1	1	yes	characteristic
809	C₂	C₂₃×#3002	1	1	yes	characteristic
810	C₂	C₂₃×#3008	1	1	yes	characteristic
811	C₂	C₂₃×#3297	1	1	yes	characteristic
812	C₂	C₂₃×#3322	1	1	yes	characteristic
813	C₂	C₂₃×#3339	1	1	yes	characteristic
814	C₂	C₂₃×#3355	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#553	C₂	semidirect
2. C₂×C₂₃×#478	C₂	semidirect
3. C₂×C₄×D₈×C₂₃	C₂	semidirect
4. C₂₃×#2535	C₂	semidirect
5. C₂₃×#2034	C₂	semidirect
6. C₂₃×#2033	C₂	semidirect
7. C₂₃×#1999	C₂	semidirect
8. C₂₃×#1999	C₂	semidirect
9. C₂₃×#1991	C₂	semidirect
10. C₂₃×#1954	C₂	semidirect
11. C₂₃×#1875	C₂	semidirect
12. C₂₃×#1874	C₂	semidirect
13. C₂₃×#1854	C₂	semidirect
14. C₂₃×#1852	C₂	semidirect
15. C₂₃×#1804	C₂	semidirect
84. C₂₃×#125	D₄	semidirect
101. C₄×D₄×C₂₃	D₄	semidirect
254. #24124	C₂₃	direct (N × H)
348. C₂×#553	C₂×C₂₃	semidirect
349. C₂×#478	C₂×C₂₃	semidirect
350. C₂×C₄×D₈	C₂×C₂₃	semidirect
351. #2535	C₂×C₂₃	semidirect
352. #2034	C₂×C₂₃	semidirect
353. #2033	C₂×C₂₃	semidirect
354. #1999	C₂×C₂₃	semidirect
355. #1999	C₂×C₂₃	semidirect
356. #1991	C₂×C₂₃	semidirect
357. #1954	C₂×C₂₃	semidirect
358. #1875	C₂×C₂₃	semidirect
359. #1874	C₂×C₂₃	semidirect
360. #1854	C₂×C₂₃	semidirect
361. #1852	C₂×C₂₃	semidirect
362. #1804	C₂×C₂₃	semidirect
491. #125	D₄×C₂₃	semidirect
508. C₄×D₄	D₄×C₂₃	semidirect
555. C₂₃	#24124	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#553	2
C₂×C₂₃×#478	2
C₂×C₄×D₈×C₂₃	2
C₂₃×#2535	2
C₂₃×#2034	2
C₂₃×#2033	2
C₂₃×#1999	2
C₂₃×#1991	2
C₂₃×#1954	2
C₂₃×#1875	2
C₂₃×#1874	2
C₂₃×#1854	2
C₂₃×#1852	2
C₂₃×#1804	2
#24124	23

Subgroups — C23×#24124 #19171750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24124 #19171750