Subgroups — C₂₃×#25093 #19172719

Order 5888.

1322 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2433	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1925	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#120	—	2	1	no	—
26	C₂×C₂₃×#120	—	2	1	no	—
27	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
29	C₂₃×#468	—	2	4	no	—
30	C₂₃×#460	—	2	4	no	—
31	C₂₃×#450	—	2	4	no	—
32	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#418	—	2	4	no	—
36	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
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
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂₃×#392	—	2	1	no	—
48	C₂₃×#392	—	2	1	no	—
49	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#390	C₂²	1	1	yes	characteristic
51	C₂₃×#390	C₂²	1	1	yes	characteristic
52	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#388	—	2	1	no	—
54	C₂₃×#388	—	2	1	no	—
55	C₂₃×#387	—	2	1	no	—
56	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
57	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₂₃	—	2	1	no	—
64	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₂₃	—	2	2	no	—
66	C₂²×D₄×C₂₃	—	2	2	no	—
67	C₂²×D₄×C₂₃	—	2	1	no	—
68	C₂²×D₄×C₂₃	—	2	2	no	—
69	C₂²×D₄×C₂₃	—	2	1	no	—
70	C₂²×D₄×C₂₃	—	2	1	no	—
71	C₂²×D₄×C₂₃	—	2	1	no	—
72	C₂²×D₄×C₂₃	—	2	1	no	—
73	C₂²×D₄×C₂₃	—	2	1	no	—
74	C₂²×D₄×C₂₃	—	2	2	no	—
75	C₂²×D₄×C₂₃	—	4	1	no	—
76	C₂²×D₄×C₂₃	—	4	1	no	—
77	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×SD₁₆×C₂₃	—	2	2	no	—
82	C₂×SD₁₆×C₂₃	—	2	2	no	—
83	C₂×SD₁₆×C₂₃	—	2	2	no	—
84	C₂×SD₁₆×C₂₃	—	2	2	no	—
85	C₂×SD₁₆×C₂₃	—	2	2	no	—
86	C₂×SD₁₆×C₂₃	—	2	2	no	—
87	C₂×SD₁₆×C₂₃	—	4	1	no	—
88	C₂×SD₁₆×C₂₃	—	4	1	no	—
89	C₂×SD₁₆×C₂₃	—	4	1	no	—
90	C₂×M₁₆×C₂₃	—	2	2	no	—
91	C₂×M₁₆×C₂₃	—	2	2	no	—
92	C₂×M₁₆×C₂₃	—	4	1	no	—
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂₃×#127	—	2	2	no	—
98	C₂₃×#127	—	2	2	no	—
99	C₂₃×#127	—	4	1	no	—
100	C₂₃×#127	—	4	1	no	—
101	C₂₃×C₂²⋊Q₈	—	2	2	no	—
102	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	complemented
103	C₂₃×#121	—	2	2	no	—
104	C₂₃×#121	—	2	2	no	—
105	C₂₃×#120	—	4	4	no	—
106	C₂₃×#120	—	4	4	no	—
107	C₄×Q₈×C₂₃	—	2	2	no	—
108	C₄×Q₈×C₂₃	—	4	1	no	—
109	C₂₃×#117	—	2	2	no	—
110	C₂₃×#117	—	4	1	no	—
111	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
112	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
129	C₂×C₄²×C₂₃	—	2	1	no	—
130	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
132	C₂₃×#107	—	2	2	no	—
133	C₂₃×C₄⋊C₈	—	2	2	no	—
134	C₂₃×C₄⋊C₈	—	4	1	no	—
135	C₂₃×#103	—	2	2	no	—
136	C₂₃×#102	—	2	2	no	—
137	C₂₃×#102	—	2	2	no	—
138	C₂₃×#102	—	2	2	no	—
139	C₂₃×#102	—	2	2	no	—
140	C₂₃×#102	—	2	2	no	—
141	C₂₃×#102	—	2	2	no	—
142	C₂₃×#102	—	2	2	no	—
143	C₂₃×#102	—	4	1	no	—
144	C₂₃×#102	D₄	1	4	yes	complemented
145	C₂₃×C₂²⋊C₈	—	2	2	no	—
146	C₂₃×#95	—	2	1	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂₃×#95	—	2	1	no	—
149	C₂₃×#95	—	2	1	no	—
150	C₂₃×#95	D₄	1	1	yes	characteristic
151	C₂₃×#95	D₄	1	1	yes	characteristic
152	C₂⁴×C₂₃	—	2	1	no	—
153	C₂⁴×C₂₃	—	2	1	no	—
154	C₂⁴×C₂₃	—	2	1	no	—
155	C₂⁴×C₂₃	—	4	2	no	—
156	C₂⁴×C₂₃	—	4	2	no	—
157	C₂⁴×C₂₃	—	4	2	no	—
158	C₂⁴×C₂₃	—	4	2	no	—
159	C₂⁴×C₂₃	—	4	2	no	—
160	C₂⁴×C₂₃	—	8	1	no	—
161	C₂⁴×C₂₃	—	8	1	no	—
162	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
163	C₂×Q₈×C₂₃	—	2	1	no	—
164	C₂×Q₈×C₂₃	—	2	1	no	—
165	C₂×Q₈×C₂₃	—	2	1	no	—
166	C₂×Q₈×C₂₃	—	2	1	no	—
167	C₂×Q₈×C₂₃	—	2	1	no	—
168	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
169	C₂×D₄×C₂₃	—	2	8	no	—
170	C₂×D₄×C₂₃	—	2	1	no	—
171	C₂×D₄×C₂₃	—	2	1	no	—
172	C₂×D₄×C₂₃	—	2	1	no	—
173	C₂×D₄×C₂₃	—	2	1	no	—
174	C₂×D₄×C₂₃	—	2	1	no	—
175	C₂×D₄×C₂₃	—	2	1	no	—
176	C₂×D₄×C₂₃	—	2	1	no	—
177	C₂×D₄×C₂₃	—	2	1	no	—
178	C₂×D₄×C₂₃	—	2	1	no	—
179	C₂×D₄×C₂₃	—	2	1	no	—
180	C₂×D₄×C₂₃	—	2	1	no	—
181	C₂×D₄×C₂₃	—	2	1	no	—
182	C₂×D₄×C₂₃	—	2	1	no	—
183	C₂×D₄×C₂₃	—	2	1	no	—
184	C₂×D₄×C₂₃	—	2	1	no	—
185	C₂×D₄×C₂₃	—	2	1	no	—
186	C₂×D₄×C₂₃	—	4	4	no	—
187	C₂×D₄×C₂₃	—	4	4	no	—
188	C₂×D₄×C₂₃	—	4	2	no	—
189	C₂×D₄×C₂₃	—	4	2	no	—
190	C₂×D₄×C₂₃	—	4	4	no	—
191	C₂×D₄×C₂₃	—	4	2	no	—
192	C₂×D₄×C₂₃	—	4	2	no	—
193	C₂×D₄×C₂₃	—	4	2	no	—
194	C₂×D₄×C₂₃	—	4	2	no	—
195	C₂×D₄×C₂₃	—	4	2	no	—
196	C₂×D₄×C₂₃	—	4	2	no	—
197	C₂×D₄×C₂₃	—	4	2	no	—
198	C₂×D₄×C₂₃	—	4	2	no	—
199	C₂×D₄×C₂₃	—	4	2	no	—
200	C₂×D₄×C₂₃	—	4	2	no	—
201	C₂×D₄×C₂₃	—	4	2	no	—
202	C₂×D₄×C₂₃	—	4	2	no	—
203	C₂×D₄×C₂₃	—	8	1	no	—
204	C₂×D₄×C₂₃	—	8	1	no	—
205	C₂×D₄×C₂₃	—	8	1	no	—
206	C₂×D₄×C₂₃	—	8	1	no	—
207	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₂₃	#41	1	2	yes	—
209	C₂²×C₄×C₂₃	—	2	1	no	—
210	C₂²×C₄×C₂₃	—	2	1	no	—
211	C₂²×C₄×C₂₃	—	2	1	no	—
212	C₂²×C₄×C₂₃	—	2	1	no	—
213	C₂²×C₄×C₂₃	—	2	1	no	—
214	C₂²×C₄×C₂₃	—	2	1	no	—
215	C₂²×C₄×C₂₃	—	2	1	no	—
216	C₂²×C₄×C₂₃	—	2	1	no	—
217	C₂²×C₄×C₂₃	—	2	1	no	—
218	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	#41	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
226	SD₁₆×C₂₃	—	4	4	no	—
227	SD₁₆×C₂₃	—	4	4	no	—
228	SD₁₆×C₂₃	—	4	4	no	—
229	M₁₆×C₂₃	—	4	4	no	—
230	C₂×C₈×C₂₃	—	2	1	no	—
231	C₂×C₈×C₂₃	—	2	1	no	—
232	C₂×C₈×C₂₃	—	2	1	no	—
233	C₂×C₈×C₂₃	—	2	1	no	—
234	C₂×C₈×C₂₃	—	2	1	no	—
235	C₂×C₈×C₂₃	—	2	1	no	—
236	C₂×C₈×C₂₃	—	2	1	no	—
237	C₂×C₈×C₂₃	—	2	1	no	—
238	C₂×C₈×C₂₃	—	2	1	no	—
239	C₂×C₈×C₂₃	—	2	1	no	—
240	C₂×C₈×C₂₃	—	2	1	no	—
241	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	1	no	—
244	C₄⋊C₄×C₂₃	—	2	1	no	—
245	C₄⋊C₄×C₂₃	—	2	1	no	—
246	C₄⋊C₄×C₂₃	—	2	1	no	—
247	C₄⋊C₄×C₂₃	—	2	1	no	—
248	C₄⋊C₄×C₂₃	—	2	1	no	—
249	C₄⋊C₄×C₂₃	—	4	2	no	—
250	C₄⋊C₄×C₂₃	—	4	2	no	—
251	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
252	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
253	C₂²⋊C₄×C₂₃	—	2	4	no	—
254	C₂²⋊C₄×C₂₃	—	2	2	no	—
255	C₂²⋊C₄×C₂₃	—	2	2	no	—
256	C₂²⋊C₄×C₂₃	—	4	2	no	—
257	C₂²⋊C₄×C₂₃	—	4	2	no	—
258	C₂²⋊C₄×C₂₃	—	4	2	no	—
259	C₂²⋊C₄×C₂₃	—	4	2	no	—
260	C₂²⋊C₄×C₂₃	—	4	2	no	—
261	C₂²⋊C₄×C₂₃	—	4	2	no	—
262	C₄²×C₂₃	—	2	1	no	—
263	C₄²×C₂₃	—	2	1	no	—
264	C₄²×C₂₃	—	2	1	no	—
265	C₄²×C₂₃	—	2	1	no	—
266	C₄²×C₂₃	—	4	2	no	—
267	C₄²×C₂₃	—	4	2	no	—
268	C₄²×C₂₃	—	4	2	no	—
269	#25093	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂³×C₂₃	—	2	1	no	—
271	C₂³×C₂₃	—	2	1	no	—
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	1	no	—
274	C₂³×C₂₃	—	2	1	no	—
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	2	no	—
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	4	8	no	—
279	C₂³×C₂₃	—	4	1	no	—
280	C₂³×C₂₃	—	4	1	no	—
281	C₂³×C₂₃	—	4	1	no	—
282	C₂³×C₂₃	—	4	1	no	—
283	C₂³×C₂₃	—	4	1	no	—
284	C₂³×C₂₃	—	4	1	no	—
285	C₂³×C₂₃	—	4	1	no	—
286	C₂³×C₂₃	—	4	1	no	—
287	C₂³×C₂₃	—	4	1	no	—
288	C₂³×C₂₃	—	4	1	no	—
289	C₂³×C₂₃	—	4	1	no	—
290	C₂³×C₂₃	—	4	1	no	—
291	C₂³×C₂₃	—	4	1	no	—
292	C₂³×C₂₃	—	4	1	no	—
293	C₂³×C₂₃	—	4	1	no	—
294	C₂³×C₂₃	—	4	1	no	—
295	C₂³×C₂₃	—	4	1	no	—
296	C₂³×C₂₃	—	4	1	no	—
297	C₂³×C₂₃	—	4	1	no	—
298	C₂³×C₂₃	—	8	4	no	—
299	C₂³×C₂₃	—	8	4	no	—
300	C₂³×C₂₃	—	8	4	no	—
301	C₂³×C₂₃	—	8	4	no	—
302	C₂³×C₂₃	—	8	4	no	—
303	C₂³×C₂₃	—	8	4	no	—
304	C₂³×C₂₃	#121	1	2	yes	—
305	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₂₃	—	2	2	no	—
307	Q₈×C₂₃	—	2	2	no	—
308	Q₈×C₂₃	—	4	1	no	—
309	Q₈×C₂₃	—	4	1	no	—
310	D₄×C₂₃	—	2	2	no	—
311	D₄×C₂₃	—	2	2	no	—
312	D₄×C₂₃	—	2	2	no	—
313	D₄×C₂₃	—	2	2	no	—
314	D₄×C₂₃	—	4	8	no	—
315	D₄×C₂₃	—	4	1	no	—
316	D₄×C₂₃	—	4	1	no	—
317	D₄×C₂₃	—	4	1	no	—
318	D₄×C₂₃	—	4	1	no	—
319	D₄×C₂₃	—	4	1	no	—
320	D₄×C₂₃	—	4	1	no	—
321	D₄×C₂₃	—	4	1	no	—
322	D₄×C₂₃	—	4	1	no	—
323	D₄×C₂₃	—	8	4	no	—
324	D₄×C₂₃	—	8	4	no	—
325	D₄×C₂₃	—	8	4	no	—
326	D₄×C₂₃	—	8	4	no	—
327	D₄×C₂₃	—	8	4	no	—
328	C₂×C₄×C₂₃	—	2	1	no	—
329	C₂×C₄×C₂₃	—	2	1	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	1	no	—
333	C₂×C₄×C₂₃	—	2	1	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	1	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	1	no	—
343	C₂×C₄×C₂₃	—	2	1	no	—
344	C₂×C₄×C₂₃	—	2	1	no	—
345	C₂×C₄×C₂₃	—	2	1	no	—
346	C₂×C₄×C₂₃	—	2	1	no	—
347	C₂×C₄×C₂₃	—	4	1	no	—
348	C₂×C₄×C₂₃	—	4	1	no	—
349	C₂×C₄×C₂₃	—	4	1	no	—
350	C₂×C₄×C₂₃	—	4	1	no	—
351	C₂×C₄×C₂₃	—	4	1	no	—
352	C₂×C₄×C₂₃	—	4	1	no	—
353	C₂×C₄×C₂₃	—	4	1	no	—
354	C₂×C₄×C₂₃	—	4	1	no	—
355	C₂×C₄×C₂₃	—	4	1	no	—
356	C₂×C₄×C₂₃	—	4	1	no	—
357	C₂×C₄×C₂₃	—	4	1	no	—
358	C₂×C₄×C₂₃	—	4	1	no	—
359	C₂×C₄×C₂₃	#121	1	2	yes	—
360	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
361	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
362	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
365	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
366	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
368	C₈×C₂₃	—	2	2	no	—
369	C₈×C₂₃	—	4	1	no	—
370	C₈×C₂₃	—	4	1	no	—
371	C₈×C₂₃	—	4	1	no	—
372	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
373	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
374	C₂×#450	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₂×#418	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#2433	C₂×C₂₃	1	1	yes	characteristic
377	#2362	C₂×C₂₃	1	1	yes	characteristic, complemented
378	#2067	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#2055	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#2041	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#2014	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#1982	C₂×C₂₃	1	1	yes	characteristic, complemented
383	#1925	C₂×C₂₃	1	1	yes	characteristic, complemented
384	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#1875	C₂×C₂₃	1	1	yes	characteristic, complemented
386	#1851	C₂×C₂₃	1	1	yes	characteristic, complemented
387	C₂²×C₂₃	—	2	2	no	—
388	C₂²×C₂₃	—	2	2	no	—
389	C₂²×C₂₃	—	2	2	no	—
390	C₂²×C₂₃	—	4	1	no	—
391	C₂²×C₂₃	—	4	1	no	—
392	C₂²×C₂₃	—	4	1	no	—
393	C₂²×C₂₃	—	4	1	no	—
394	C₂²×C₂₃	—	4	2	no	—
395	C₂²×C₂₃	—	4	2	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	—	4	2	no	—
398	C₂²×C₂₃	—	4	2	no	—
399	C₂²×C₂₃	—	4	2	no	—
400	C₂²×C₂₃	—	8	16	no	—
401	C₂²×C₂₃	—	8	1	no	—
402	C₂²×C₂₃	—	8	1	no	—
403	C₂²×C₂₃	—	8	1	no	—
404	C₂²×C₂₃	—	8	1	no	—
405	C₂²×C₂₃	—	8	1	no	—
406	C₂²×C₂₃	—	8	1	no	—
407	C₂²×C₂₃	—	8	1	no	—
408	C₂²×C₂₃	—	8	1	no	—
409	C₂²×C₂₃	—	8	1	no	—
410	C₂²×C₂₃	—	8	1	no	—
411	C₂²×C₂₃	—	8	1	no	—
412	C₂²×C₂₃	—	8	1	no	—
413	C₂²×C₂₃	—	8	1	no	—
414	C₂²×C₂₃	—	8	1	no	—
415	C₂²×C₂₃	—	8	1	no	—
416	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
417	C₂²×C₂₃	D₄²	1	1	yes	characteristic
418	C₂²×C₂₃	#546	1	1	yes	characteristic
419	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂²×C₂₃	#577	1	1	yes	characteristic
422	C₂²×C₂₃	#577	1	1	yes	characteristic
423	C₄×C₂₃	—	2	2	no	—
424	C₄×C₂₃	—	2	2	no	—
425	C₄×C₂₃	—	2	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	—	4	1	no	—
428	C₄×C₂₃	—	4	2	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	—	4	1	no	—
431	C₄×C₂₃	—	8	1	no	—
432	C₄×C₂₃	—	8	1	no	—
433	C₄×C₂₃	#525	1	1	yes	characteristic
434	C₄×C₂₃	#538	1	1	yes	characteristic
435	C₄×C₂₃	D₄²	1	1	yes	characteristic
436	C₄×C₂₃	#546	1	1	yes	characteristic
437	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
438	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
439	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
440	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#120	—	2	1	no	—
447	C₂×#120	—	2	1	no	—
448	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
449	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
450	#468	—	2	4	no	—
451	#460	—	2	4	no	—
452	#450	—	2	4	no	—
453	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#418	—	2	4	no	—
457	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
460	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
463	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
465	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
468	#392	—	2	1	no	—
469	#392	—	2	1	no	—
470	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
471	#390	C₂²×C₂₃	1	1	yes	characteristic
472	#390	C₂²×C₂₃	1	1	yes	characteristic
473	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
474	#388	—	2	1	no	—
475	#388	—	2	1	no	—
476	#387	—	2	1	no	—
477	C₄×C₄⋊C₄	—	2	1	no	—
478	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
479	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
480	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
482	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
483	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	C₂×C₂₃	—	4	2	no	—
485	C₂×C₂₃	—	8	2	no	—
486	C₂×C₂₃	—	8	2	no	—
487	C₂×C₂₃	—	16	1	no	—
488	C₂×C₂₃	#2424	1	1	yes	characteristic
489	C₂×C₂₃	#3038	1	1	yes	characteristic
490	C₂×C₂₃	#3043	1	1	yes	characteristic
491	C₂×C₂₃	#3265	1	1	yes	characteristic
492	C₂×C₂₃	#3272	1	1	yes	characteristic
493	C₂×C₂₃	#3310	1	1	yes	characteristic
494	C₂×C₂₃	#3324	1	1	yes	characteristic
495	C₂⁵	—	2	1	no	—
496	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	2	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	2	no	—
507	C₂²×D₄	—	4	1	no	—
508	C₂²×D₄	—	4	1	no	—
509	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₂×SD₁₆	—	2	2	no	—
514	C₂×SD₁₆	—	2	2	no	—
515	C₂×SD₁₆	—	2	2	no	—
516	C₂×SD₁₆	—	2	2	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	4	1	no	—
520	C₂×SD₁₆	—	4	1	no	—
521	C₂×SD₁₆	—	4	1	no	—
522	C₂×M₁₆	—	2	2	no	—
523	C₂×M₁₆	—	2	2	no	—
524	C₂×M₁₆	—	4	1	no	—
525	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
526	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
529	#127	—	2	2	no	—
530	#127	—	2	2	no	—
531	#127	—	4	1	no	—
532	#127	—	4	1	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	complemented
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	#120	—	4	4	no	—
538	#120	—	4	4	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	4	1	no	—
541	#117	—	2	2	no	—
542	#117	—	4	1	no	—
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
559	C₂×C₄²	—	2	1	no	—
560	C₂×C₄²	—	2	1	no	—
561	C₂×C₄²	—	2	1	no	—
562	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
564	#107	—	2	2	no	—
565	C₄⋊C₈	—	2	2	no	—
566	C₄⋊C₈	—	4	1	no	—
567	#103	—	2	2	no	—
568	#102	—	2	2	no	—
569	#102	—	2	2	no	—
570	#102	—	2	2	no	—
571	#102	—	2	2	no	—
572	#102	—	2	2	no	—
573	#102	—	2	2	no	—
574	#102	—	2	2	no	—
575	#102	—	4	1	no	—
576	#102	D₄×C₂₃	1	4	yes	complemented
577	C₂²⋊C₈	—	2	2	no	—
578	#95	—	2	1	no	—
579	#95	—	2	1	no	—
580	#95	—	2	1	no	—
581	#95	—	2	1	no	—
582	#95	D₄×C₂₃	1	1	yes	characteristic
583	#95	D₄×C₂₃	1	1	yes	characteristic
584	C₂₃	#25093	1	1	yes	characteristic, direct product factor, Sylow
585	C₂⁴	—	2	1	no	—
586	C₂⁴	—	2	1	no	—
587	C₂⁴	—	2	1	no	—
588	C₂⁴	—	4	2	no	—
589	C₂⁴	—	4	2	no	—
590	C₂⁴	—	4	2	no	—
591	C₂⁴	—	4	2	no	—
592	C₂⁴	—	4	2	no	—
593	C₂⁴	—	8	1	no	—
594	C₂⁴	—	8	1	no	—
595	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
602	C₂×D₄	—	2	8	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	4	4	no	—
620	C₂×D₄	—	4	4	no	—
621	C₂×D₄	—	4	2	no	—
622	C₂×D₄	—	4	2	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	2	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	2	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂×D₄	—	8	1	no	—
637	C₂×D₄	—	8	1	no	—
638	C₂×D₄	—	8	1	no	—
639	C₂×D₄	—	8	1	no	—
640	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
641	C₂×D₄	#41×C₂₃	1	2	yes	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
655	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
657	C₂²×C₄	#41×C₂₃	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
659	SD₁₆	—	4	4	no	—
660	SD₁₆	—	4	4	no	—
661	SD₁₆	—	4	4	no	—
662	M₁₆	—	4	4	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
685	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	4	2	no	—
690	C₂²⋊C₄	—	4	2	no	—
691	C₂²⋊C₄	—	4	2	no	—
692	C₂²⋊C₄	—	4	2	no	—
693	C₂²⋊C₄	—	4	2	no	—
694	C₂²⋊C₄	—	4	2	no	—
695	C₄²	—	2	1	no	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	4	8	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	4	1	no	—
726	C₂³	—	4	1	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	8	4	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	—	8	4	no	—
734	C₂³	—	8	4	no	—
735	C₂³	—	8	4	no	—
736	C₂³	C₂₃×#121	1	2	yes	—
737	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
738	Q₈	—	2	2	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	4	1	no	—
741	Q₈	—	4	1	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	2	no	—
746	D₄	—	4	8	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	1	no	—
753	D₄	—	4	1	no	—
754	D₄	—	4	1	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	4	no	—
758	D₄	—	8	4	no	—
759	D₄	—	8	4	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	C₂₃×#121	1	2	yes	—
792	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
793	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
796	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
797	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
798	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
799	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
800	C₈	—	2	2	no	—
801	C₈	—	4	1	no	—
802	C₈	—	4	1	no	—
803	C₈	—	4	1	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	8	16	no	—
818	C₂²	—	8	1	no	—
819	C₂²	—	8	1	no	—
820	C₂²	—	8	1	no	—
821	C₂²	—	8	1	no	—
822	C₂²	—	8	1	no	—
823	C₂²	—	8	1	no	—
824	C₂²	—	8	1	no	—
825	C₂²	—	8	1	no	—
826	C₂²	—	8	1	no	—
827	C₂²	—	8	1	no	—
828	C₂²	—	8	1	no	—
829	C₂²	—	8	1	no	—
830	C₂²	—	8	1	no	—
831	C₂²	—	8	1	no	—
832	C₂²	—	8	1	no	—
833	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
834	C₂²	D₄²×C₂₃	1	1	yes	characteristic
835	C₂²	C₂₃×#546	1	1	yes	characteristic
836	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
837	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
838	C₂²	C₂₃×#577	1	1	yes	characteristic
839	C₂²	C₂₃×#577	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	1	no	—
848	C₄	—	8	1	no	—
849	C₄	—	8	1	no	—
850	C₄	C₂₃×#525	1	1	yes	characteristic
851	C₄	C₂₃×#538	1	1	yes	characteristic
852	C₄	D₄²×C₂₃	1	1	yes	characteristic
853	C₄	C₂₃×#546	1	1	yes	characteristic
854	C₂	—	4	2	no	—
855	C₂	—	8	2	no	—
856	C₂	—	8	2	no	—
857	C₂	—	16	1	no	—
858	C₂	C₂₃×#2424	1	1	yes	characteristic
859	C₂	C₂₃×#3038	1	1	yes	characteristic
860	C₂	C₂₃×#3043	1	1	yes	characteristic
861	C₂	C₂₃×#3265	1	1	yes	characteristic
862	C₂	C₂₃×#3272	1	1	yes	characteristic
863	C₂	C₂₃×#3310	1	1	yes	characteristic
864	C₂	C₂₃×#3324	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#2433	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄×C₂²⋊C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#468	C₂	semidirect
2. C₂×C₂₃×#460	C₂	semidirect
3. C₂×C₂₃×#450	C₂	semidirect
4. C₂×C₂₃×#418	C₂	semidirect
6. C₂₃×#2362	C₂	semidirect
7. C₂₃×#2067	C₂	semidirect
8. C₂₃×#2055	C₂	semidirect
9. C₂₃×#2041	C₂	semidirect
10. C₂₃×#2014	C₂	semidirect
11. C₂₃×#1982	C₂	semidirect
12. C₂₃×#1925	C₂	semidirect
13. C₂₃×#1880	C₂	semidirect
14. C₂₃×#1875	C₂	semidirect
15. C₂₃×#1851	C₂	semidirect
19. C₂²×SD₁₆×C₂₃	C₂²	semidirect
27. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
32. C₂×C₂₃×#107	C₂²	semidirect
33. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
34. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
36. C₂×C₂₃×#103	C₂²	semidirect
43. C₂×C₂₃×#102	C₂²	semidirect
44. C₂×C₂₃×#102	C₂²	semidirect
45. C₂×C₂₃×#102	C₂²	semidirect
49. C₂₃×#391	C₂²	semidirect
52. C₂₃×#389	C₂²	semidirect
57. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
59. C₂₃×#340	C₂²	semidirect
60. C₂₃×#340	C₂²	semidirect
61. C₂₃×#336	C₂²	semidirect
62. C₂₃×#336	C₂²	semidirect
102. C₂₃×C₂²⋊Q₈	D₄	semidirect
144. C₂₃×#102	D₄	semidirect
269. #25093	C₂₃	direct (N × H)
372. C₂×#468	C₂×C₂₃	semidirect
373. C₂×#460	C₂×C₂₃	semidirect
374. C₂×#450	C₂×C₂₃	semidirect
375. C₂×#418	C₂×C₂₃	semidirect
377. #2362	C₂×C₂₃	semidirect
378. #2067	C₂×C₂₃	semidirect
379. #2055	C₂×C₂₃	semidirect
380. #2041	C₂×C₂₃	semidirect
381. #2014	C₂×C₂₃	semidirect
382. #1982	C₂×C₂₃	semidirect
383. #1925	C₂×C₂₃	semidirect
384. #1880	C₂×C₂₃	semidirect
385. #1875	C₂×C₂₃	semidirect
386. #1851	C₂×C₂₃	semidirect
440. C₂²×SD₁₆	C₂²×C₂₃	semidirect
448. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
453. C₂×#107	C₂²×C₂₃	semidirect
454. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
455. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
457. C₂×#103	C₂²×C₂₃	semidirect
464. C₂×#102	C₂²×C₂₃	semidirect
465. C₂×#102	C₂²×C₂₃	semidirect
466. C₂×#102	C₂²×C₂₃	semidirect
470. #391	C₂²×C₂₃	semidirect
473. #389	C₂²×C₂₃	semidirect
478. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
480. #340	C₂²×C₂₃	semidirect
481. #340	C₂²×C₂₃	semidirect
482. #336	C₂²×C₂₃	semidirect
483. #336	C₂²×C₂₃	semidirect
534. C₂²⋊Q₈	D₄×C₂₃	semidirect
576. #102	D₄×C₂₃	semidirect
584. C₂₃	#25093	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×#468	2
C₂×C₂₃×#460	2
C₂×C₂₃×#450	2
C₂×C₂₃×#418	2
C₂₃×#2433	2
C₂₃×#2362	2
C₂₃×#2067	2
C₂₃×#2055	2
C₂₃×#2041	2
C₂₃×#2014	2
C₂₃×#1982	2
C₂₃×#1925	2
C₂₃×#1880	2
C₂₃×#1875	2
C₂₃×#1851	2
#25093	23

Subgroups — C23×#25093 #19172719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25093 #19172719