Subgroups — C₂₃×#24037 #19171663

Order 5888.

1462 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
19	C₂₃×#546	—	2	4	no	—
20	C₂₃×#546	—	2	4	no	—
21	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#123	—	2	1	no	—
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	—	2	1	no	—
25	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#120	—	2	1	no	—
27	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
31	C₂₃×#482	—	2	4	no	—
32	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#416	—	2	4	no	—
35	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
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×#102	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#102	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×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#397	—	2	1	no	—
51	C₂₃×#394	—	2	1	no	—
52	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#388	—	2	1	no	—
55	C₂₃×#387	—	2	1	no	—
56	C₂₃×#380	C₂²	1	1	yes	characteristic
57	C₂₃×#380	C₂²	1	1	yes	characteristic
58	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
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	C₂×#41×C₂₃	—	2	2	no	—
65	C₂×#41×C₂₃	—	2	2	no	—
66	C₂×#41×C₂₃	—	2	2	no	—
67	C₂×#41×C₂₃	—	4	1	no	—
68	C₂×#41×C₂₃	—	4	1	no	—
69	C₂×#41×C₂₃	D₄	1	4	yes	—
70	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₂₃	—	2	1	no	—
72	C₂²×D₄×C₂₃	—	2	1	no	—
73	C₂²×D₄×C₂₃	—	2	2	no	—
74	C₂²×D₄×C₂₃	—	2	2	no	—
75	C₂²×D₄×C₂₃	—	2	2	no	—
76	C₂²×D₄×C₂₃	—	2	2	no	—
77	C₂²×D₄×C₂₃	—	2	1	no	—
78	C₂²×D₄×C₂₃	—	4	1	no	—
79	C₂²×D₄×C₂₃	—	4	1	no	—
80	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	—	2	1	no	—
84	C₂³×C₄×C₂₃	—	2	1	no	—
85	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₂₃	—	2	2	no	—
88	C₂²×C₈×C₂₃	—	4	1	no	—
89	C₂²×C₈×C₂₃	—	4	1	no	—
90	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂₃×#124	—	2	2	no	—
95	C₂₃×#124	—	2	2	no	—
96	C₂₃×#123	—	2	8	no	—
97	C₂₃×C₂²⋊Q₈	—	2	2	no	—
98	C₂₃×C₂²⋊Q₈	—	2	2	no	—
99	C₂₃×#121	—	2	8	no	—
100	C₂₃×#121	—	2	2	no	—
101	C₂₃×#121	D₄	1	4	yes	—
102	C₂₃×#120	—	2	8	no	—
103	C₄×D₄×C₂₃	—	2	2	no	—
104	C₄×D₄×C₂₃	—	2	2	no	—
105	C₄×D₄×C₂₃	—	2	2	no	—
106	C₄×D₄×C₂₃	—	2	2	no	—
107	C₂₃×#117	—	2	2	no	—
108	C₂₃×#117	—	2	2	no	—
109	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
111	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
112	C₂×C₄⋊C₄×C₂₃	D₄	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×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₂₃	—	2	8	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	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₂₃	—	2	1	no	—
131	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
132	C₂₃×#107	—	2	2	no	—
133	C₂₃×#106	—	2	2	no	—
134	C₂₃×#103	—	2	2	no	—
135	C₂₃×#103	—	2	2	no	—
136	C₂₃×#103	—	4	1	no	—
137	C₂₃×#103	—	4	1	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	—	2	2	no	—
144	C₂₃×#102	—	4	1	no	—
145	C₂₃×#102	—	4	1	no	—
146	C₂₃×C₂²⋊C₈	—	2	2	no	—
147	C₂₃×C₂²⋊C₈	—	4	1	no	—
148	C₂₃×C₂²⋊C₈	—	4	1	no	—
149	C₂₃×#95	—	2	1	no	—
150	C₂₃×#95	—	2	1	no	—
151	C₂₃×#95	—	2	1	no	—
152	C₂₃×#95	—	2	1	no	—
153	C₂₃×#95	—	2	1	no	—
154	C₂⁴×C₂₃	—	2	1	no	—
155	C₂⁴×C₂₃	—	2	4	no	—
156	C₂⁴×C₂₃	—	2	1	no	—
157	C₂⁴×C₂₃	—	4	2	no	—
158	C₂⁴×C₂₃	—	4	2	no	—
159	C₂⁴×C₂₃	—	4	2	no	—
160	C₂⁴×C₂₃	—	4	2	no	—
161	C₂⁴×C₂₃	—	8	1	no	—
162	C₂⁴×C₂₃	—	8	1	no	—
163	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
164	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
165	#41×C₂₃	—	2	8	no	—
166	#41×C₂₃	—	4	4	no	—
167	#41×C₂₃	—	4	4	no	—
168	#41×C₂₃	—	4	4	no	—
169	C₂×Q₈×C₂₃	—	2	1	no	—
170	C₂×Q₈×C₂₃	—	2	1	no	—
171	C₂×Q₈×C₂₃	—	2	1	no	—
172	C₂×Q₈×C₂₃	—	2	1	no	—
173	C₂×Q₈×C₂₃	—	2	1	no	—
174	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₂₃	—	2	4	no	—
176	C₂×D₄×C₂₃	—	2	2	no	—
177	C₂×D₄×C₂₃	—	2	4	no	—
178	C₂×D₄×C₂₃	—	2	2	no	—
179	C₂×D₄×C₂₃	—	2	4	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	—	2	1	no	—
187	C₂×D₄×C₂₃	—	2	1	no	—
188	C₂×D₄×C₂₃	—	4	1	no	—
189	C₂×D₄×C₂₃	—	4	2	no	—
190	C₂×D₄×C₂₃	—	4	2	no	—
191	C₂×D₄×C₂₃	—	4	4	no	—
192	C₂×D₄×C₂₃	—	4	4	no	—
193	C₂×D₄×C₂₃	—	4	4	no	—
194	C₂×D₄×C₂₃	—	4	2	no	—
195	C₂×D₄×C₂₃	—	4	2	no	—
196	C₂×D₄×C₂₃	—	4	4	no	—
197	C₂×D₄×C₂₃	—	8	1	no	—
198	C₂×D₄×C₂₃	—	8	1	no	—
199	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
200	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
201	C₂×D₄×C₂₃	#41	1	2	yes	—
202	C₂×D₄×C₂₃	#41	1	2	yes	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	2	1	no	—
205	C₂²×C₄×C₂₃	—	2	1	no	—
206	C₂²×C₄×C₂₃	—	2	1	no	—
207	C₂²×C₄×C₂₃	—	2	1	no	—
208	C₂²×C₄×C₂₃	—	2	1	no	—
209	C₂²×C₄×C₂₃	—	2	4	no	—
210	C₂²×C₄×C₂₃	—	2	4	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	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	2	1	no	—
221	C₂²×C₄×C₂₃	—	4	2	no	—
222	C₂²×C₄×C₂₃	—	4	2	no	—
223	C₂²×C₄×C₂₃	—	8	1	no	—
224	C₂²×C₄×C₂₃	—	8	1	no	—
225	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
242	C₂×C₈×C₂₃	—	2	1	no	—
243	C₂×C₈×C₂₃	—	2	1	no	—
244	C₂×C₈×C₂₃	—	4	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	2	no	—
247	C₄⋊C₄×C₂₃	—	2	1	no	—
248	C₄⋊C₄×C₂₃	—	2	1	no	—
249	C₄⋊C₄×C₂₃	—	2	1	no	—
250	C₄⋊C₄×C₂₃	—	2	1	no	—
251	C₄⋊C₄×C₂₃	—	2	1	no	—
252	C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₄⋊C₄×C₂₃	—	2	1	no	—
254	C₄⋊C₄×C₂₃	—	2	1	no	—
255	C₄⋊C₄×C₂₃	—	2	1	no	—
256	C₄⋊C₄×C₂₃	—	4	2	no	—
257	C₄⋊C₄×C₂₃	—	8	1	no	—
258	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	—	2	4	no	—
262	C₂²⋊C₄×C₂₃	—	2	4	no	—
263	C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	4	2	no	—
267	C₂²⋊C₄×C₂₃	—	4	2	no	—
268	C₂²⋊C₄×C₂₃	—	8	1	no	—
269	C₂²⋊C₄×C₂₃	—	8	1	no	—
270	C₄²×C₂₃	—	2	1	no	—
271	C₄²×C₂₃	—	2	1	no	—
272	C₄²×C₂₃	—	4	2	no	—
273	#24037	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
274	C₂³×C₂₃	—	2	1	no	—
275	C₂³×C₂₃	—	2	2	no	—
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	2	1	no	—
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	—	2	1	no	—
280	C₂³×C₂₃	—	2	2	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	—	2	1	no	—
283	C₂³×C₂₃	—	2	1	no	—
284	C₂³×C₂₃	—	2	1	no	—
285	C₂³×C₂₃	—	2	1	no	—
286	C₂³×C₂₃	—	2	1	no	—
287	C₂³×C₂₃	—	2	1	no	—
288	C₂³×C₂₃	—	2	1	no	—
289	C₂³×C₂₃	—	2	2	no	—
290	C₂³×C₂₃	—	4	8	no	—
291	C₂³×C₂₃	—	4	8	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	—	4	1	no	—
299	C₂³×C₂₃	—	4	1	no	—
300	C₂³×C₂₃	—	4	1	no	—
301	C₂³×C₂₃	—	4	1	no	—
302	C₂³×C₂₃	—	8	4	no	—
303	C₂³×C₂₃	—	8	4	no	—
304	C₂³×C₂₃	—	8	4	no	—
305	C₂³×C₂₃	—	8	4	no	—
306	C₂³×C₂₃	—	8	4	no	—
307	C₂³×C₂₃	#120	1	2	yes	—
308	C₂³×C₂₃	#135	1	2	yes	—
309	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₂₃	—	2	2	no	—
311	Q₈×C₂₃	—	2	2	no	—
312	Q₈×C₂₃	—	4	1	no	—
313	Q₈×C₂₃	—	4	1	no	—
314	D₄×C₂₃	—	2	2	no	—
315	D₄×C₂₃	—	2	2	no	—
316	D₄×C₂₃	—	2	2	no	—
317	D₄×C₂₃	—	2	2	no	—
318	D₄×C₂₃	—	2	2	no	—
319	D₄×C₂₃	—	4	4	no	—
320	D₄×C₂₃	—	4	8	no	—
321	D₄×C₂₃	—	4	8	no	—
322	D₄×C₂₃	—	4	1	no	—
323	D₄×C₂₃	—	4	1	no	—
324	D₄×C₂₃	—	8	4	no	—
325	D₄×C₂₃	#123	1	4	yes	—
326	C₂×C₄×C₂₃	—	2	1	no	—
327	C₂×C₄×C₂₃	—	2	1	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	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	1	no	—
337	C₂×C₄×C₂₃	—	2	1	no	—
338	C₂×C₄×C₂₃	—	2	1	no	—
339	C₂×C₄×C₂₃	—	2	1	no	—
340	C₂×C₄×C₂₃	—	2	1	no	—
341	C₂×C₄×C₂₃	—	2	1	no	—
342	C₂×C₄×C₂₃	—	2	1	no	—
343	C₂×C₄×C₂₃	—	4	8	no	—
344	C₂×C₄×C₂₃	—	4	1	no	—
345	C₂×C₄×C₂₃	—	4	1	no	—
346	C₂×C₄×C₂₃	—	4	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	—	4	1	no	—
360	C₂×C₄×C₂₃	—	4	1	no	—
361	C₂×C₄×C₂₃	—	4	1	no	—
362	C₂×C₄×C₂₃	—	4	1	no	—
363	C₂×C₄×C₂₃	—	4	1	no	—
364	C₂×C₄×C₂₃	—	8	4	no	—
365	C₂×C₄×C₂₃	#120	1	2	yes	—
366	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
369	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
370	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
372	C₈×C₂₃	—	4	1	no	—
373	C₈×C₂₃	—	4	1	no	—
374	C₈×C₂₃	—	4	1	no	—
375	C₈×C₂₃	—	4	1	no	—
376	C₂×#546	C₂×C₂₃	1	1	yes	characteristic
377	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
378	C₂×#416	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#2485	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#2042	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#2042	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#2036	C₂×C₂₃	1	1	yes	characteristic, complemented
383	#2035	C₂×C₂₃	1	1	yes	characteristic, complemented
384	#1893	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#1869	C₂×C₂₃	1	1	yes	characteristic, complemented
386	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
387	#1862	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#1788	C₂×C₂₃	1	1	yes	characteristic, complemented
389	#1786	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#1786	C₂×C₂₃	1	1	yes	characteristic, complemented
391	C₂²×C₂₃	—	2	2	no	—
392	C₂²×C₂₃	—	2	4	no	—
393	C₂²×C₂₃	—	2	2	no	—
394	C₂²×C₂₃	—	2	2	no	—
395	C₂²×C₂₃	—	2	2	no	—
396	C₂²×C₂₃	—	2	2	no	—
397	C₂²×C₂₃	—	2	2	no	—
398	C₂²×C₂₃	—	4	1	no	—
399	C₂²×C₂₃	—	4	2	no	—
400	C₂²×C₂₃	—	4	2	no	—
401	C₂²×C₂₃	—	4	1	no	—
402	C₂²×C₂₃	—	4	1	no	—
403	C₂²×C₂₃	—	4	2	no	—
404	C₂²×C₂₃	—	4	1	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	1	no	—
407	C₂²×C₂₃	—	4	1	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	—	4	1	no	—
410	C₂²×C₂₃	—	4	1	no	—
411	C₂²×C₂₃	—	4	2	no	—
412	C₂²×C₂₃	—	4	2	no	—
413	C₂²×C₂₃	—	4	2	no	—
414	C₂²×C₂₃	—	4	2	no	—
415	C₂²×C₂₃	—	8	16	no	—
416	C₂²×C₂₃	—	8	1	no	—
417	C₂²×C₂₃	—	8	1	no	—
418	C₂²×C₂₃	—	8	1	no	—
419	C₂²×C₂₃	—	8	1	no	—
420	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
421	C₂²×C₂₃	#546	1	1	yes	characteristic
422	C₂²×C₂₃	#546	1	1	yes	characteristic
423	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
424	C₂²×C₂₃	#575	1	1	yes	characteristic
425	C₂²×C₂₃	#576	1	1	yes	characteristic
426	C₂²×C₂₃	#577	1	1	yes	characteristic
427	C₄×C₂₃	—	2	2	no	—
428	C₄×C₂₃	—	4	1	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	—	4	1	no	—
431	C₄×C₂₃	—	4	1	no	—
432	C₄×C₂₃	—	4	2	no	—
433	C₄×C₂₃	—	8	1	no	—
434	C₄×C₂₃	—	8	1	no	—
435	C₄×C₂₃	—	8	1	no	—
436	C₄×C₂₃	—	8	1	no	—
437	C₄×C₂₃	C₂×#123	1	1	yes	characteristic
438	C₄×C₂₃	#534	1	1	yes	characteristic
439	C₄×C₂₃	#546	1	1	yes	characteristic
440	C₄×C₂₃	#546	1	1	yes	characteristic
441	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
442	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
443	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	#546	—	2	4	no	—
445	#546	—	2	4	no	—
446	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#123	—	2	1	no	—
448	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×#121	—	2	1	no	—
450	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×#120	—	2	1	no	—
452	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	C₂²×C₂²⋊C₄	—	2	1	no	—
456	#482	—	2	4	no	—
457	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	#416	—	2	4	no	—
460	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
464	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
467	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
469	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
471	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	#397	—	2	1	no	—
476	#394	—	2	1	no	—
477	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
478	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
479	#388	—	2	1	no	—
480	#387	—	2	1	no	—
481	#380	C₂²×C₂₃	1	1	yes	characteristic
482	#380	C₂²×C₂₃	1	1	yes	characteristic
483	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
485	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
486	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	C₂×C₂₃	—	4	2	no	—
489	C₂×C₂₃	—	4	2	no	—
490	C₂×C₂₃	—	4	4	no	—
491	C₂×C₂₃	—	8	2	no	—
492	C₂×C₂₃	#2405	1	1	yes	characteristic
493	C₂×C₂₃	#3002	1	1	yes	characteristic
494	C₂×C₂₃	#3012	1	1	yes	characteristic
495	C₂×C₂₃	#3296	1	1	yes	characteristic
496	C₂×C₂₃	#3297	1	1	yes	characteristic
497	C₂×C₂₃	#3311	1	1	yes	characteristic
498	C₂×C₂₃	#3319	1	1	yes	characteristic
499	C₂⁵	—	2	1	no	—
500	C₂×#41	—	2	2	no	—
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	4	1	no	—
504	C₂×#41	—	4	1	no	—
505	C₂×#41	D₄×C₂₃	1	4	yes	—
506	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	2	no	—
510	C₂²×D₄	—	2	2	no	—
511	C₂²×D₄	—	2	2	no	—
512	C₂²×D₄	—	2	2	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	4	1	no	—
515	C₂²×D₄	—	4	1	no	—
516	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
517	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
523	C₂²×C₈	—	2	2	no	—
524	C₂²×C₈	—	4	1	no	—
525	C₂²×C₈	—	4	1	no	—
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	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
530	#124	—	2	2	no	—
531	#124	—	2	2	no	—
532	#123	—	2	8	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	#121	—	2	8	no	—
536	#121	—	2	2	no	—
537	#121	D₄×C₂₃	1	4	yes	—
538	#120	—	2	8	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	#117	—	2	2	no	—
544	#117	—	2	2	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	—	2	8	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
566	C₂×C₄²	—	2	1	no	—
567	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
568	#107	—	2	2	no	—
569	#106	—	2	2	no	—
570	#103	—	2	2	no	—
571	#103	—	2	2	no	—
572	#103	—	4	1	no	—
573	#103	—	4	1	no	—
574	#102	—	2	2	no	—
575	#102	—	2	2	no	—
576	#102	—	2	2	no	—
577	#102	—	2	2	no	—
578	#102	—	2	2	no	—
579	#102	—	2	2	no	—
580	#102	—	4	1	no	—
581	#102	—	4	1	no	—
582	C₂²⋊C₈	—	2	2	no	—
583	C₂²⋊C₈	—	4	1	no	—
584	C₂²⋊C₈	—	4	1	no	—
585	#95	—	2	1	no	—
586	#95	—	2	1	no	—
587	#95	—	2	1	no	—
588	#95	—	2	1	no	—
589	#95	—	2	1	no	—
590	C₂₃	#24037	1	1	yes	characteristic, direct product factor, Sylow
591	C₂⁴	—	2	1	no	—
592	C₂⁴	—	2	4	no	—
593	C₂⁴	—	2	1	no	—
594	C₂⁴	—	4	2	no	—
595	C₂⁴	—	4	2	no	—
596	C₂⁴	—	4	2	no	—
597	C₂⁴	—	4	2	no	—
598	C₂⁴	—	8	1	no	—
599	C₂⁴	—	8	1	no	—
600	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
601	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
602	#41	—	2	8	no	—
603	#41	—	4	4	no	—
604	#41	—	4	4	no	—
605	#41	—	4	4	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	4	1	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	8	1	no	—
635	C₂×D₄	—	8	1	no	—
636	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
637	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
638	C₂×D₄	#41×C₂₃	1	2	yes	—
639	C₂×D₄	#41×C₂₃	1	2	yes	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
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	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	8	1	no	—
661	C₂²×C₄	—	8	1	no	—
662	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
667	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
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	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	4	4	no	—
682	C₄⋊C₄	—	2	4	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	8	1	no	—
695	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	8	1	no	—
706	C₂²⋊C₄	—	8	1	no	—
707	C₄²	—	2	1	no	—
708	C₄²	—	2	1	no	—
709	C₄²	—	4	2	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	4	8	no	—
727	C₂³	—	4	8	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	4	1	no	—
736	C₂³	—	4	1	no	—
737	C₂³	—	4	1	no	—
738	C₂³	—	8	4	no	—
739	C₂³	—	8	4	no	—
740	C₂³	—	8	4	no	—
741	C₂³	—	8	4	no	—
742	C₂³	—	8	4	no	—
743	C₂³	C₂₃×#120	1	2	yes	—
744	C₂³	C₂₃×#135	1	2	yes	—
745	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
746	Q₈	—	2	2	no	—
747	Q₈	—	2	2	no	—
748	Q₈	—	4	1	no	—
749	Q₈	—	4	1	no	—
750	D₄	—	2	2	no	—
751	D₄	—	2	2	no	—
752	D₄	—	2	2	no	—
753	D₄	—	2	2	no	—
754	D₄	—	2	2	no	—
755	D₄	—	4	4	no	—
756	D₄	—	4	8	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	1	no	—
759	D₄	—	4	1	no	—
760	D₄	—	8	4	no	—
761	D₄	C₂₃×#123	1	4	yes	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	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	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	4	8	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	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	8	4	no	—
801	C₂×C₄	C₂₃×#120	1	2	yes	—
802	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
804	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
805	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
806	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
807	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
808	C₈	—	4	1	no	—
809	C₈	—	4	1	no	—
810	C₈	—	4	1	no	—
811	C₈	—	4	1	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	4	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	8	16	no	—
837	C₂²	—	8	1	no	—
838	C₂²	—	8	1	no	—
839	C₂²	—	8	1	no	—
840	C₂²	—	8	1	no	—
841	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
842	C₂²	C₂₃×#546	1	1	yes	characteristic
843	C₂²	C₂₃×#546	1	1	yes	characteristic
844	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
845	C₂²	C₂₃×#575	1	1	yes	characteristic
846	C₂²	C₂₃×#576	1	1	yes	characteristic
847	C₂²	C₂₃×#577	1	1	yes	characteristic
848	C₄	—	2	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	2	no	—
854	C₄	—	8	1	no	—
855	C₄	—	8	1	no	—
856	C₄	—	8	1	no	—
857	C₄	—	8	1	no	—
858	C₄	C₂×C₂₃×#123	1	1	yes	characteristic
859	C₄	C₂₃×#534	1	1	yes	characteristic
860	C₄	C₂₃×#546	1	1	yes	characteristic
861	C₄	C₂₃×#546	1	1	yes	characteristic
862	C₂	—	4	2	no	—
863	C₂	—	4	2	no	—
864	C₂	—	4	4	no	—
865	C₂	—	8	2	no	—
866	C₂	C₂₃×#2405	1	1	yes	characteristic
867	C₂	C₂₃×#3002	1	1	yes	characteristic
868	C₂	C₂₃×#3012	1	1	yes	characteristic
869	C₂	C₂₃×#3296	1	1	yes	characteristic
870	C₂	C₂₃×#3297	1	1	yes	characteristic
871	C₂	C₂₃×#3311	1	1	yes	characteristic
872	C₂	C₂₃×#3319	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#546	C₂
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
2. C₂×C₂₃×#482	C₂	semidirect
3. C₂×C₂₃×#416	C₂	semidirect
4. C₂₃×#2485	C₂	semidirect
5. C₂₃×#2042	C₂	semidirect
6. C₂₃×#2042	C₂	semidirect
7. C₂₃×#2036	C₂	semidirect
8. C₂₃×#2035	C₂	semidirect
9. C₂₃×#1893	C₂	semidirect
10. C₂₃×#1869	C₂	semidirect
11. C₂₃×#1864	C₂	semidirect
12. C₂₃×#1862	C₂	semidirect
13. C₂₃×#1788	C₂	semidirect
14. C₂₃×#1786	C₂	semidirect
15. C₂₃×#1786	C₂	semidirect
18. C₂³×C₈×C₂₃	C₂²	semidirect
29. C₂×C₂₃×#117	C₂²	semidirect
32. C₂×C₂₃×#107	C₂²	semidirect
33. C₂×C₂₃×#106	C₂²	semidirect
35. C₂×C₂₃×#103	C₂²	semidirect
36. C₂×C₂₃×#103	C₂²	semidirect
37. C₂×C₂₃×#103	C₂²	semidirect
38. C₂×C₂₃×#103	C₂²	semidirect
49. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
52. C₂₃×#389	C₂²	semidirect
53. C₂₃×#389	C₂²	semidirect
58. C₂₃×#380	C₂²	semidirect
59. C₂₃×#340	C₂²	semidirect
60. C₂₃×#340	C₂²	semidirect
61. C₂₃×#336	C₂²	semidirect
62. C₂₃×#336	C₂²	semidirect
273. #24037	C₂₃	direct (N × H)
377. C₂×#482	C₂×C₂₃	semidirect
378. C₂×#416	C₂×C₂₃	semidirect
379. #2485	C₂×C₂₃	semidirect
380. #2042	C₂×C₂₃	semidirect
381. #2042	C₂×C₂₃	semidirect
382. #2036	C₂×C₂₃	semidirect
383. #2035	C₂×C₂₃	semidirect
384. #1893	C₂×C₂₃	semidirect
385. #1869	C₂×C₂₃	semidirect
386. #1864	C₂×C₂₃	semidirect
387. #1862	C₂×C₂₃	semidirect
388. #1788	C₂×C₂₃	semidirect
389. #1786	C₂×C₂₃	semidirect
390. #1786	C₂×C₂₃	semidirect
443. C₂³×C₈	C₂²×C₂₃	semidirect
454. C₂×#117	C₂²×C₂₃	semidirect
457. C₂×#107	C₂²×C₂₃	semidirect
458. C₂×#106	C₂²×C₂₃	semidirect
460. C₂×#103	C₂²×C₂₃	semidirect
461. C₂×#103	C₂²×C₂₃	semidirect
462. C₂×#103	C₂²×C₂₃	semidirect
463. C₂×#103	C₂²×C₂₃	semidirect
474. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
477. #389	C₂²×C₂₃	semidirect
478. #389	C₂²×C₂₃	semidirect
483. #380	C₂²×C₂₃	semidirect
484. #340	C₂²×C₂₃	semidirect
485. #340	C₂²×C₂₃	semidirect
486. #336	C₂²×C₂₃	semidirect
487. #336	C₂²×C₂₃	semidirect
590. C₂₃	#24037	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×#546	2
C₂×C₂₃×#482	2
C₂×C₂₃×#416	2
C₂₃×#2485	2
C₂₃×#2042	2
C₂₃×#2036	2
C₂₃×#2035	2
C₂₃×#1893	2
C₂₃×#1869	2
C₂₃×#1864	2
C₂₃×#1862	2
C₂₃×#1788	2
C₂₃×#1786	2
#24037	23

Subgroups — C23×#24037 #19171663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24037 #19171663