Subgroups — C₂₃×#22423 #19170049

Order 5888.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₂₃	—	2	1	no	—
17	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	D₄²×C₂₃	—	2	4	no	—
22	D₄²×C₂₃	C₄	1	8	yes	complemented
23	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	—	2	1	no	—
25	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#120	—	2	1	no	—
28	C₂×C₂₃×#120	—	2	1	no	—
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, complemented
32	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#435	—	2	4	no	—
34	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#418	—	2	4	no	—
36	C₂×C₂₃×#102	—	2	4	no	—
37	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#102	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, complemented
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#388	—	2	1	no	—
53	C₂₃×#387	—	2	1	no	—
54	C₂₃×#386	—	2	1	no	—
55	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
60	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
64	C₂⁵×C₂₃	—	2	1	no	—
65	C₂⁵×C₂₃	—	2	1	no	—
66	C₂²×D₄×C₂₃	—	2	2	no	—
67	C₂²×D₄×C₂₃	—	2	2	no	—
68	C₂²×D₄×C₂₃	—	2	2	no	—
69	C₂²×D₄×C₂₃	—	2	2	no	—
70	C₂²×D₄×C₂₃	—	2	1	no	—
71	C₂²×D₄×C₂₃	—	2	1	no	—
72	C₂²×D₄×C₂₃	—	2	8	no	—
73	C₂²×D₄×C₂₃	—	2	1	no	—
74	C₂²×D₄×C₂₃	—	2	1	no	—
75	C₂²×D₄×C₂₃	—	2	1	no	—
76	C₂²×D₄×C₂₃	—	2	2	no	—
77	C₂²×D₄×C₂₃	—	2	2	no	—
78	C₂²×D₄×C₂₃	—	2	1	no	—
79	C₂²×D₄×C₂₃	—	4	1	no	—
80	C₂²×D₄×C₂₃	—	4	1	no	—
81	C₂²×D₄×C₂₃	—	4	1	no	—
82	C₂²×D₄×C₂₃	—	4	1	no	—
83	C₂²×D₄×C₂₃	—	4	4	no	—
84	C₂²×D₄×C₂₃	—	4	4	no	—
85	C₂²×D₄×C₂₃	C₂×C₄	1	4	yes	—
86	C₂²×D₄×C₂₃	C₂×C₄	1	4	yes	complemented
87	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
88	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₂₃	—	2	1	no	—
92	C₂³×C₄×C₂₃	—	2	1	no	—
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₂₃	—	2	2	no	—
96	C₂×M₁₆×C₂₃	—	2	2	no	—
97	C₂×M₁₆×C₂₃	—	4	1	no	—
98	C₂²×C₈×C₂₃	—	2	2	no	—
99	C₂²×C₈×C₂₃	—	2	2	no	—
100	C₂²×C₈×C₂₃	—	4	1	no	—
101	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
105	C₂₃×#127	—	2	2	no	—
106	C₂₃×#127	C₂×C₄	1	4	yes	complemented
107	C₂₃×#121	—	2	2	no	—
108	C₂₃×#121	—	2	2	no	—
109	C₂₃×#121	—	2	8	no	—
110	C₂₃×#121	C₂×C₄	1	4	yes	—
111	C₂₃×#121	C₂×C₄	1	4	yes	complemented
112	C₂₃×#120	—	2	8	no	—
113	C₂₃×#120	—	2	8	no	—
114	C₄×D₄×C₂₃	—	2	2	no	—
115	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
116	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	complemented
117	C₄×D₄×C₂₃	D₄	1	4	yes	—
118	C₂₃×#117	—	2	2	no	—
119	C₂₃×#117	—	4	1	no	—
120	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
122	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
123	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
137	C₂×C₄²×C₂₃	—	2	1	no	—
138	C₂×C₄²×C₂₃	—	2	1	no	—
139	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
140	C₂₃×C₄⋊C₈	—	2	2	no	—
141	C₂₃×#102	—	2	2	no	—
142	C₂₃×#102	—	2	2	no	—
143	C₂₃×#102	—	2	2	no	—
144	C₂₃×#102	—	2	2	no	—
145	C₂₃×#102	—	2	2	no	—
146	C₂₃×#102	—	2	2	no	—
147	C₂₃×#102	—	2	2	no	—
148	C₂₃×#102	—	4	1	no	—
149	C₂₃×#102	—	4	1	no	—
150	C₂₃×#102	—	4	1	no	—
151	C₂₃×#102	—	4	1	no	—
152	C₂₃×#102	D₄	1	4	yes	complemented
153	C₂₃×C₂²⋊C₈	—	2	2	no	—
154	C₂₃×C₂²⋊C₈	—	2	2	no	—
155	C₂₃×#97	—	2	2	no	—
156	C₂₃×#95	—	2	1	no	—
157	C₂₃×#95	—	2	1	no	—
158	C₂₃×#95	—	2	1	no	—
159	C₂₃×#95	—	2	1	no	—
160	C₂₃×#95	—	2	1	no	—
161	C₂⁴×C₂₃	—	2	1	no	—
162	C₂⁴×C₂₃	—	2	1	no	—
163	C₂⁴×C₂₃	—	2	1	no	—
164	C₂⁴×C₂₃	—	2	4	no	—
165	C₂⁴×C₂₃	—	2	4	no	—
166	C₂⁴×C₂₃	—	4	2	no	—
167	C₂⁴×C₂₃	—	4	2	no	—
168	C₂⁴×C₂₃	—	4	2	no	—
169	C₂⁴×C₂₃	—	4	2	no	—
170	C₂⁴×C₂₃	—	4	2	no	—
171	C₂⁴×C₂₃	—	4	2	no	—
172	C₂⁴×C₂₃	—	4	2	no	—
173	C₂⁴×C₂₃	—	4	2	no	—
174	C₂⁴×C₂₃	—	8	1	no	—
175	C₂⁴×C₂₃	—	8	1	no	—
176	C₂⁴×C₂₃	—	8	1	no	—
177	C₂⁴×C₂₃	—	8	1	no	—
178	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
179	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
180	C₂×D₄×C₂₃	—	2	2	no	—
181	C₂×D₄×C₂₃	—	2	2	no	—
182	C₂×D₄×C₂₃	—	2	8	no	—
183	C₂×D₄×C₂₃	—	2	8	no	—
184	C₂×D₄×C₂₃	—	2	4	no	—
185	C₂×D₄×C₂₃	—	2	4	no	—
186	C₂×D₄×C₂₃	—	2	4	no	—
187	C₂×D₄×C₂₃	—	2	4	no	—
188	C₂×D₄×C₂₃	—	2	4	no	—
189	C₂×D₄×C₂₃	—	2	4	no	—
190	C₂×D₄×C₂₃	—	2	1	no	—
191	C₂×D₄×C₂₃	—	2	1	no	—
192	C₂×D₄×C₂₃	—	2	1	no	—
193	C₂×D₄×C₂₃	—	2	1	no	—
194	C₂×D₄×C₂₃	—	2	1	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	2	1	no	—
198	C₂×D₄×C₂₃	—	2	1	no	—
199	C₂×D₄×C₂₃	—	2	1	no	—
200	C₂×D₄×C₂₃	—	2	1	no	—
201	C₂×D₄×C₂₃	—	2	1	no	—
202	C₂×D₄×C₂₃	—	2	1	no	—
203	C₂×D₄×C₂₃	—	4	4	no	—
204	C₂×D₄×C₂₃	—	4	4	no	—
205	C₂×D₄×C₂₃	—	4	4	no	—
206	C₂×D₄×C₂₃	—	4	4	no	—
207	C₂×D₄×C₂₃	—	4	4	no	—
208	C₂×D₄×C₂₃	—	4	4	no	—
209	C₂×D₄×C₂₃	—	4	2	no	—
210	C₂×D₄×C₂₃	—	4	2	no	—
211	C₂×D₄×C₂₃	—	4	2	no	—
212	C₂×D₄×C₂₃	—	4	2	no	—
213	C₂×D₄×C₂₃	—	4	2	no	—
214	C₂×D₄×C₂₃	—	4	2	no	—
215	C₂×D₄×C₂₃	—	4	32	no	—
216	C₂×D₄×C₂₃	—	4	2	no	—
217	C₂×D₄×C₂₃	—	4	2	no	—
218	C₂×D₄×C₂₃	—	4	2	no	—
219	C₂×D₄×C₂₃	—	4	2	no	—
220	C₂×D₄×C₂₃	—	8	1	no	—
221	C₂×D₄×C₂₃	—	8	1	no	—
222	C₂×D₄×C₂₃	C₂²⋊C₄	1	4	yes	—
223	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
224	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
225	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
226	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₂₃	#41	1	2	yes	—
228	C₂²×C₄×C₂₃	—	2	1	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	1	no	—
231	C₂²×C₄×C₂₃	—	2	1	no	—
232	C₂²×C₄×C₂₃	—	2	1	no	—
233	C₂²×C₄×C₂₃	—	2	1	no	—
234	C₂²×C₄×C₂₃	—	2	1	no	—
235	C₂²×C₄×C₂₃	—	2	1	no	—
236	C₂²×C₄×C₂₃	—	2	1	no	—
237	C₂²×C₄×C₂₃	—	2	1	no	—
238	C₂²×C₄×C₂₃	—	2	4	no	—
239	C₂²×C₄×C₂₃	—	2	1	no	—
240	C₂²×C₄×C₂₃	—	2	1	no	—
241	C₂²×C₄×C₂₃	—	2	1	no	—
242	C₂²×C₄×C₂₃	—	4	2	no	—
243	C₂²×C₄×C₂₃	—	4	2	no	—
244	C₂²×C₄×C₂₃	—	4	2	no	—
245	C₂²×C₄×C₂₃	—	4	2	no	—
246	C₂²×C₄×C₂₃	—	8	1	no	—
247	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
248	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
249	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
255	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	M₁₆×C₂₃	—	4	4	no	—
257	C₂×C₈×C₂₃	—	2	1	no	—
258	C₂×C₈×C₂₃	—	2	1	no	—
259	C₂×C₈×C₂₃	—	2	1	no	—
260	C₂×C₈×C₂₃	—	2	1	no	—
261	C₂×C₈×C₂₃	—	2	1	no	—
262	C₂×C₈×C₂₃	—	2	1	no	—
263	C₂×C₈×C₂₃	—	2	1	no	—
264	C₂×C₈×C₂₃	—	2	1	no	—
265	C₂×C₈×C₂₃	—	2	1	no	—
266	C₂×C₈×C₂₃	—	2	1	no	—
267	C₂×C₈×C₂₃	—	2	1	no	—
268	C₂×C₈×C₂₃	—	4	4	no	—
269	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	complemented
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	1	no	—
272	C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	4	2	no	—
279	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
280	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
281	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	complemented
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	—	2	4	no	—
285	C₂²⋊C₄×C₂₃	—	4	2	no	—
286	C₂²⋊C₄×C₂₃	—	4	2	no	—
287	C₂²⋊C₄×C₂₃	—	8	1	no	—
288	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
289	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
290	C₄²×C₂₃	—	4	2	no	—
291	C₄²×C₂₃	—	8	1	no	—
292	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
293	C₄²×C₂₃	C₂×D₄	1	2	yes	—
294	#22423	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂³×C₂₃	—	2	1	no	—
296	C₂³×C₂₃	—	2	1	no	—
297	C₂³×C₂₃	—	2	1	no	—
298	C₂³×C₂₃	—	2	1	no	—
299	C₂³×C₂₃	—	2	2	no	—
300	C₂³×C₂₃	—	2	1	no	—
301	C₂³×C₂₃	—	2	2	no	—
302	C₂³×C₂₃	—	2	1	no	—
303	C₂³×C₂₃	—	2	2	no	—
304	C₂³×C₂₃	—	2	1	no	—
305	C₂³×C₂₃	—	2	1	no	—
306	C₂³×C₂₃	—	2	1	no	—
307	C₂³×C₂₃	—	2	1	no	—
308	C₂³×C₂₃	—	2	2	no	—
309	C₂³×C₂₃	—	2	2	no	—
310	C₂³×C₂₃	—	4	8	no	—
311	C₂³×C₂₃	—	4	8	no	—
312	C₂³×C₂₃	—	4	8	no	—
313	C₂³×C₂₃	—	4	1	no	—
314	C₂³×C₂₃	—	4	1	no	—
315	C₂³×C₂₃	—	4	1	no	—
316	C₂³×C₂₃	—	4	1	no	—
317	C₂³×C₂₃	—	4	1	no	—
318	C₂³×C₂₃	—	4	1	no	—
319	C₂³×C₂₃	—	4	1	no	—
320	C₂³×C₂₃	—	4	1	no	—
321	C₂³×C₂₃	—	4	1	no	—
322	C₂³×C₂₃	—	4	1	no	—
323	C₂³×C₂₃	—	4	1	no	—
324	C₂³×C₂₃	—	4	1	no	—
325	C₂³×C₂₃	—	4	1	no	—
326	C₂³×C₂₃	—	4	1	no	—
327	C₂³×C₂₃	—	4	1	no	—
328	C₂³×C₂₃	—	4	1	no	—
329	C₂³×C₂₃	—	4	8	no	—
330	C₂³×C₂₃	—	8	4	no	—
331	C₂³×C₂₃	—	8	4	no	—
332	C₂³×C₂₃	—	8	4	no	—
333	C₂³×C₂₃	—	8	4	no	—
334	C₂³×C₂₃	—	8	4	no	—
335	C₂³×C₂₃	—	8	4	no	—
336	C₂³×C₂₃	—	8	4	no	—
337	C₂³×C₂₃	—	8	4	no	—
338	C₂³×C₂₃	—	8	4	no	—
339	C₂³×C₂₃	—	8	4	no	—
340	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
341	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
342	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
343	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
344	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
345	D₄×C₂₃	—	2	8	no	—
346	D₄×C₂₃	—	2	2	no	—
347	D₄×C₂₃	—	2	2	no	—
348	D₄×C₂₃	—	2	2	no	—
349	D₄×C₂₃	—	2	2	no	—
350	D₄×C₂₃	—	2	2	no	—
351	D₄×C₂₃	—	2	2	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	4	8	no	—
354	D₄×C₂₃	—	4	8	no	—
355	D₄×C₂₃	—	4	8	no	—
356	D₄×C₂₃	—	4	8	no	—
357	D₄×C₂₃	—	4	8	no	—
358	D₄×C₂₃	—	4	1	no	—
359	D₄×C₂₃	—	4	1	no	—
360	D₄×C₂₃	—	4	1	no	—
361	D₄×C₂₃	—	4	1	no	—
362	D₄×C₂₃	—	8	4	no	—
363	D₄×C₂₃	C₄×D₄	1	4	yes	—
364	C₂×C₄×C₂₃	—	2	1	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	1	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	4	8	no	—
383	C₂×C₄×C₂₃	—	4	1	no	—
384	C₂×C₄×C₂₃	—	4	1	no	—
385	C₂×C₄×C₂₃	—	4	1	no	—
386	C₂×C₄×C₂₃	—	4	1	no	—
387	C₂×C₄×C₂₃	—	4	1	no	—
388	C₂×C₄×C₂₃	—	4	1	no	—
389	C₂×C₄×C₂₃	—	4	1	no	—
390	C₂×C₄×C₂₃	—	4	1	no	—
391	C₂×C₄×C₂₃	—	4	1	no	—
392	C₂×C₄×C₂₃	—	4	1	no	—
393	C₂×C₄×C₂₃	—	4	1	no	—
394	C₂×C₄×C₂₃	—	4	1	no	—
395	C₂×C₄×C₂₃	—	4	1	no	—
396	C₂×C₄×C₂₃	—	8	4	no	—
397	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
398	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
399	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
400	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
401	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
402	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
405	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
406	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
407	C₈×C₂₃	—	2	2	no	—
408	C₈×C₂₃	—	4	1	no	—
409	C₈×C₂₃	—	4	1	no	—
410	C₈×C₂₃	—	4	1	no	—
411	C₂×D₄²	C₂×C₂₃	1	1	yes	characteristic
412	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
413	C₂×#418	C₂×C₂₃	1	1	yes	characteristic, complemented
414	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#2352	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#1982	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#1961	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#1895	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#1893	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#1875	C₂×C₂₃	1	1	yes	characteristic, complemented
421	#1874	C₂×C₂₃	1	1	yes	characteristic, complemented
422	#1804	C₂×C₂₃	1	1	yes	characteristic, complemented
423	#1786	C₂×C₂₃	1	1	yes	characteristic, complemented
424	#1786	C₂×C₂₃	1	1	yes	characteristic, complemented
425	#1762	C₂×C₂₃	1	1	yes	characteristic, complemented
426	C₂²×C₂₃	—	2	2	no	—
427	C₂²×C₂₃	—	2	2	no	—
428	C₂²×C₂₃	—	2	2	no	—
429	C₂²×C₂₃	—	2	2	no	—
430	C₂²×C₂₃	—	2	2	no	—
431	C₂²×C₂₃	—	2	2	no	—
432	C₂²×C₂₃	—	2	2	no	—
433	C₂²×C₂₃	—	2	4	no	—
434	C₂²×C₂₃	—	2	2	no	—
435	C₂²×C₂₃	—	2	2	no	—
436	C₂²×C₂₃	—	4	2	no	—
437	C₂²×C₂₃	—	4	2	no	—
438	C₂²×C₂₃	—	4	1	no	—
439	C₂²×C₂₃	—	4	2	no	—
440	C₂²×C₂₃	—	4	1	no	—
441	C₂²×C₂₃	—	4	2	no	—
442	C₂²×C₂₃	—	4	1	no	—
443	C₂²×C₂₃	—	4	2	no	—
444	C₂²×C₂₃	—	4	1	no	—
445	C₂²×C₂₃	—	4	2	no	—
446	C₂²×C₂₃	—	4	2	no	—
447	C₂²×C₂₃	—	4	2	no	—
448	C₂²×C₂₃	—	4	2	no	—
449	C₂²×C₂₃	—	4	2	no	—
450	C₂²×C₂₃	—	4	2	no	—
451	C₂²×C₂₃	—	4	2	no	—
452	C₂²×C₂₃	—	8	16	no	—
453	C₂²×C₂₃	—	8	16	no	—
454	C₂²×C₂₃	—	8	1	no	—
455	C₂²×C₂₃	—	8	1	no	—
456	C₂²×C₂₃	—	8	1	no	—
457	C₂²×C₂₃	—	8	1	no	—
458	C₂²×C₂₃	—	8	1	no	—
459	C₂²×C₂₃	—	8	1	no	—
460	C₂²×C₂₃	—	8	1	no	—
461	C₂²×C₂₃	—	8	1	no	—
462	C₂²×C₂₃	#418	1	4	yes	complemented
463	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×C₂₃	D₄²	1	1	yes	characteristic
465	C₂²×C₂₃	#546	1	1	yes	characteristic
466	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
467	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
468	C₂²×C₂₃	#576	1	1	yes	characteristic
469	C₂²×C₂₃	#577	1	1	yes	characteristic
470	C₄×C₂₃	—	2	2	no	—
471	C₄×C₂₃	—	2	2	no	—
472	C₄×C₂₃	—	2	2	no	—
473	C₄×C₂₃	—	2	2	no	—
474	C₄×C₂₃	—	4	2	no	—
475	C₄×C₂₃	—	4	2	no	—
476	C₄×C₂₃	—	8	1	no	—
477	C₄×C₂₃	—	8	1	no	—
478	C₄×C₂₃	—	8	1	no	—
479	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
480	C₄×C₂₃	#518	1	1	yes	characteristic
481	C₄×C₂₃	D₄²	1	1	yes	characteristic
482	C₄×C₂₃	#546	1	1	yes	characteristic
483	C₂³×D₄	—	2	1	no	—
484	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
485	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
486	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	D₄²	—	2	4	no	—
489	D₄²	C₄×C₂₃	1	8	yes	complemented
490	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
491	C₂×#121	—	2	1	no	—
492	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
493	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×#120	—	2	1	no	—
495	C₂×#120	—	2	1	no	—
496	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
497	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
498	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
499	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
500	#435	—	2	4	no	—
501	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
502	#418	—	2	4	no	—
503	C₂×#102	—	2	4	no	—
504	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
505	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
506	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
507	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
508	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
509	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
512	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
513	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
514	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
515	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
516	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
517	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
518	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
519	#388	—	2	1	no	—
520	#387	—	2	1	no	—
521	#386	—	2	1	no	—
522	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
523	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
524	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
526	C₄×C₂²⋊C₄	—	2	1	no	—
527	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
529	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
530	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
531	C₂×C₂₃	—	2	4	no	—
532	C₂×C₂₃	—	4	2	no	—
533	C₂×C₂₃	—	4	4	no	—
534	C₂×C₂₃	—	8	2	no	—
535	C₂×C₂₃	—	8	2	no	—
536	C₂×C₂₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
537	C₂×C₂₃	C₂×#418	1	1	yes	characteristic
538	C₂×C₂₃	#2897	1	1	yes	characteristic
539	C₂×C₂₃	#3264	1	1	yes	characteristic
540	C₂×C₂₃	#3265	1	1	yes	characteristic
541	C₂×C₂₃	#3310	1	1	yes	characteristic
542	C₂×C₂₃	#3318	1	1	yes	characteristic
543	C₂⁵	—	2	1	no	—
544	C₂⁵	—	2	1	no	—
545	C₂²×D₄	—	2	2	no	—
546	C₂²×D₄	—	2	2	no	—
547	C₂²×D₄	—	2	2	no	—
548	C₂²×D₄	—	2	2	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	8	no	—
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	2	no	—
556	C₂²×D₄	—	2	2	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	4	1	no	—
559	C₂²×D₄	—	4	1	no	—
560	C₂²×D₄	—	4	1	no	—
561	C₂²×D₄	—	4	1	no	—
562	C₂²×D₄	—	4	4	no	—
563	C₂²×D₄	—	4	4	no	—
564	C₂²×D₄	C₂×C₄×C₂₃	1	4	yes	—
565	C₂²×D₄	C₂×C₄×C₂₃	1	4	yes	complemented
566	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	—	2	1	no	—
572	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
574	C₂×M₁₆	—	2	2	no	—
575	C₂×M₁₆	—	2	2	no	—
576	C₂×M₁₆	—	4	1	no	—
577	C₂²×C₈	—	2	2	no	—
578	C₂²×C₈	—	2	2	no	—
579	C₂²×C₈	—	4	1	no	—
580	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
581	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
582	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
583	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
584	#127	—	2	2	no	—
585	#127	C₂×C₄×C₂₃	1	4	yes	complemented
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	8	no	—
589	#121	C₂×C₄×C₂₃	1	4	yes	—
590	#121	C₂×C₄×C₂₃	1	4	yes	complemented
591	#120	—	2	8	no	—
592	#120	—	2	8	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
595	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	complemented
596	C₄×D₄	D₄×C₂₃	1	4	yes	—
597	#117	—	2	2	no	—
598	#117	—	4	1	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	4	1	no	—
602	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
616	C₂×C₄²	—	2	1	no	—
617	C₂×C₄²	—	2	1	no	—
618	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
619	C₄⋊C₈	—	2	2	no	—
620	#102	—	2	2	no	—
621	#102	—	2	2	no	—
622	#102	—	2	2	no	—
623	#102	—	2	2	no	—
624	#102	—	2	2	no	—
625	#102	—	2	2	no	—
626	#102	—	2	2	no	—
627	#102	—	4	1	no	—
628	#102	—	4	1	no	—
629	#102	—	4	1	no	—
630	#102	—	4	1	no	—
631	#102	D₄×C₂₃	1	4	yes	complemented
632	C₂²⋊C₈	—	2	2	no	—
633	C₂²⋊C₈	—	2	2	no	—
634	#97	—	2	2	no	—
635	#95	—	2	1	no	—
636	#95	—	2	1	no	—
637	#95	—	2	1	no	—
638	#95	—	2	1	no	—
639	#95	—	2	1	no	—
640	C₂₃	#22423	1	1	yes	characteristic, direct product factor, Sylow
641	C₂⁴	—	2	1	no	—
642	C₂⁴	—	2	1	no	—
643	C₂⁴	—	2	1	no	—
644	C₂⁴	—	2	4	no	—
645	C₂⁴	—	2	4	no	—
646	C₂⁴	—	4	2	no	—
647	C₂⁴	—	4	2	no	—
648	C₂⁴	—	4	2	no	—
649	C₂⁴	—	4	2	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	—	4	2	no	—
652	C₂⁴	—	4	2	no	—
653	C₂⁴	—	4	2	no	—
654	C₂⁴	—	8	1	no	—
655	C₂⁴	—	8	1	no	—
656	C₂⁴	—	8	1	no	—
657	C₂⁴	—	8	1	no	—
658	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
659	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	8	no	—
663	C₂×D₄	—	2	8	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	—	4	4	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	2	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	32	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	8	1	no	—
701	C₂×D₄	—	8	1	no	—
702	C₂×D₄	C₂²⋊C₄×C₂₃	1	4	yes	—
703	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
704	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
705	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
707	C₂×D₄	#41×C₂₃	1	2	yes	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	8	1	no	—
727	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
728	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
729	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
734	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
736	M₁₆	—	4	4	no	—
737	C₂×C₈	—	2	1	no	—
738	C₂×C₈	—	2	1	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	2	1	no	—
742	C₂×C₈	—	2	1	no	—
743	C₂×C₈	—	2	1	no	—
744	C₂×C₈	—	2	1	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	4	4	no	—
749	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	complemented
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
760	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
761	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	complemented
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	8	1	no	—
768	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
769	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
770	C₄²	—	4	2	no	—
771	C₄²	—	8	1	no	—
772	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
773	C₄²	C₂×D₄×C₂₃	1	2	yes	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	4	8	no	—
790	C₂³	—	4	8	no	—
791	C₂³	—	4	8	no	—
792	C₂³	—	4	1	no	—
793	C₂³	—	4	1	no	—
794	C₂³	—	4	1	no	—
795	C₂³	—	4	1	no	—
796	C₂³	—	4	1	no	—
797	C₂³	—	4	1	no	—
798	C₂³	—	4	1	no	—
799	C₂³	—	4	1	no	—
800	C₂³	—	4	1	no	—
801	C₂³	—	4	1	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	8	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	8	4	no	—
810	C₂³	—	8	4	no	—
811	C₂³	—	8	4	no	—
812	C₂³	—	8	4	no	—
813	C₂³	—	8	4	no	—
814	C₂³	—	8	4	no	—
815	C₂³	—	8	4	no	—
816	C₂³	—	8	4	no	—
817	C₂³	—	8	4	no	—
818	C₂³	—	8	4	no	—
819	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
820	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
821	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
822	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
823	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
824	D₄	—	2	8	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	2	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	8	no	—
834	D₄	—	4	8	no	—
835	D₄	—	4	8	no	—
836	D₄	—	4	8	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	4	1	no	—
841	D₄	—	8	4	no	—
842	D₄	C₄×D₄×C₂₃	1	4	yes	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
877	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
878	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
879	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
880	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
881	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
883	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
884	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
885	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
886	C₈	—	2	2	no	—
887	C₈	—	4	1	no	—
888	C₈	—	4	1	no	—
889	C₈	—	4	1	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	8	16	no	—
917	C₂²	—	8	16	no	—
918	C₂²	—	8	1	no	—
919	C₂²	—	8	1	no	—
920	C₂²	—	8	1	no	—
921	C₂²	—	8	1	no	—
922	C₂²	—	8	1	no	—
923	C₂²	—	8	1	no	—
924	C₂²	—	8	1	no	—
925	C₂²	—	8	1	no	—
926	C₂²	C₂₃×#418	1	4	yes	complemented
927	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
928	C₂²	D₄²×C₂₃	1	1	yes	characteristic
929	C₂²	C₂₃×#546	1	1	yes	characteristic
930	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
931	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
932	C₂²	C₂₃×#576	1	1	yes	characteristic
933	C₂²	C₂₃×#577	1	1	yes	characteristic
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	8	1	no	—
941	C₄	—	8	1	no	—
942	C₄	—	8	1	no	—
943	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
944	C₄	C₂₃×#518	1	1	yes	characteristic
945	C₄	D₄²×C₂₃	1	1	yes	characteristic
946	C₄	C₂₃×#546	1	1	yes	characteristic
947	C₂	—	2	4	no	—
948	C₂	—	4	2	no	—
949	C₂	—	4	4	no	—
950	C₂	—	8	2	no	—
951	C₂	—	8	2	no	—
952	C₂	D₄×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
953	C₂	C₂×C₂₃×#418	1	1	yes	characteristic
954	C₂	C₂₃×#2897	1	1	yes	characteristic
955	C₂	C₂₃×#3264	1	1	yes	characteristic
956	C₂	C₂₃×#3265	1	1	yes	characteristic
957	C₂	C₂₃×#3310	1	1	yes	characteristic
958	C₂	C₂₃×#3318	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×D₄²×C₂₃	C₂
LCS	G ▷ C₂×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
2. C₂×C₂₃×#435	C₂	semidirect
3. C₂×C₂₃×#418	C₂	semidirect
4. C₂²×C₂₃×#102	C₂	semidirect
5. C₂₃×#2352	C₂	semidirect
6. C₂₃×#1982	C₂	semidirect
7. C₂₃×#1961	C₂	semidirect
8. C₂₃×#1895	C₂	semidirect
9. C₂₃×#1893	C₂	semidirect
10. C₂₃×#1875	C₂	semidirect
11. C₂₃×#1874	C₂	semidirect
12. C₂₃×#1804	C₂	semidirect
13. C₂₃×#1786	C₂	semidirect
14. C₂₃×#1786	C₂	semidirect
15. C₂₃×#1762	C₂	semidirect
19. C₂²×M₁₆×C₂₃	C₂²	semidirect
20. C₂³×C₈×C₂₃	C₂²	semidirect
22. D₄²×C₂₃	C₄	semidirect
31. C₂×C₂₃×#117	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
34. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
41. C₂×C₂₃×#102	C₂²	semidirect
42. C₂×C₂₃×#102	C₂²	semidirect
43. C₂×C₂₃×#102	C₂²	semidirect
44. C₂×C₂₃×#102	C₂²	semidirect
45. C₂×C₂₃×#102	C₂²	semidirect
46. C₂×C₂₃×#102	C₂²	semidirect
47. C₂×C₂₃×#102	C₂²	semidirect
48. C₂×C₂₃×#102	C₂²	semidirect
49. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
50. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
51. C₂×C₂₃×#97	C₂²	semidirect
55. C₂₃×#382	C₂²	semidirect
56. C₂₃×#380	C₂²	semidirect
57. C₂₃×#380	C₂²	semidirect
58. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
60. C₂₃×#340	C₂²	semidirect
61. C₂₃×#340	C₂²	semidirect
62. C₂₃×#340	C₂²	semidirect
63. C₂₃×#340	C₂²	semidirect
86. C₂²×D₄×C₂₃	C₂×C₄	semidirect
106. C₂₃×#127	C₂×C₄	semidirect
111. C₂₃×#121	C₂×C₄	semidirect
116. C₄×D₄×C₂₃	C₂×C₄	semidirect
152. C₂₃×#102	D₄	semidirect
269. C₂×C₈×C₂₃	C₂×D₄	semidirect
281. C₄⋊C₄×C₂₃	C₂×D₄	semidirect
294. #22423	C₂₃	direct (N × H)
412. C₂×#435	C₂×C₂₃	semidirect
413. C₂×#418	C₂×C₂₃	semidirect
414. C₂²×#102	C₂×C₂₃	semidirect
415. #2352	C₂×C₂₃	semidirect
416. #1982	C₂×C₂₃	semidirect
417. #1961	C₂×C₂₃	semidirect
418. #1895	C₂×C₂₃	semidirect
419. #1893	C₂×C₂₃	semidirect
420. #1875	C₂×C₂₃	semidirect
421. #1874	C₂×C₂₃	semidirect
422. #1804	C₂×C₂₃	semidirect
423. #1786	C₂×C₂₃	semidirect
424. #1786	C₂×C₂₃	semidirect
425. #1762	C₂×C₂₃	semidirect
462. C₂²×C₂₃	#418	semidirect
486. C₂²×M₁₆	C₂²×C₂₃	semidirect
487. C₂³×C₈	C₂²×C₂₃	semidirect
489. D₄²	C₄×C₂₃	semidirect
498. C₂×#117	C₂²×C₂₃	semidirect
499. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
501. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
508. C₂×#102	C₂²×C₂₃	semidirect
509. C₂×#102	C₂²×C₂₃	semidirect
510. C₂×#102	C₂²×C₂₃	semidirect
511. C₂×#102	C₂²×C₂₃	semidirect
512. C₂×#102	C₂²×C₂₃	semidirect
513. C₂×#102	C₂²×C₂₃	semidirect
514. C₂×#102	C₂²×C₂₃	semidirect
515. C₂×#102	C₂²×C₂₃	semidirect
516. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
517. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
518. C₂×#97	C₂²×C₂₃	semidirect
522. #382	C₂²×C₂₃	semidirect
523. #380	C₂²×C₂₃	semidirect
524. #380	C₂²×C₂₃	semidirect
525. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
527. #340	C₂²×C₂₃	semidirect
528. #340	C₂²×C₂₃	semidirect
529. #340	C₂²×C₂₃	semidirect
530. #340	C₂²×C₂₃	semidirect
565. C₂²×D₄	C₂×C₄×C₂₃	semidirect
585. #127	C₂×C₄×C₂₃	semidirect
590. #121	C₂×C₄×C₂₃	semidirect
595. C₄×D₄	C₂×C₄×C₂₃	semidirect
631. #102	D₄×C₂₃	semidirect
640. C₂₃	#22423	direct (N × H)
749. C₂×C₈	C₂×D₄×C₂₃	semidirect
761. C₄⋊C₄	C₂×D₄×C₂₃	semidirect
926. C₂²	C₂₃×#418	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₂₃	2
C₂×C₂₃×#435	2
C₂×C₂₃×#418	2
C₂²×C₂₃×#102	2
C₂₃×#2352	2
C₂₃×#1982	2
C₂₃×#1961	2
C₂₃×#1895	2
C₂₃×#1893	2
C₂₃×#1875	2
C₂₃×#1874	2
C₂₃×#1804	2
C₂₃×#1786	2
C₂₃×#1762	2
#22423	23

Subgroups — C23×#22423 #19170049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22423 #19170049