Subgroups — C₂₃×#22422 #19170048

Order 5888.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#416	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×#1805	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#550	—	2	4	no	—
21	C₂₃×#550	C₄	1	8	yes	complemented
22	C₂×C₂₃×#127	—	2	1	no	—
23	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	—	2	1	no	—
25	C₂×C₂₃×#121	—	2	1	no	—
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₂₃	—	2	1	no	—
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×#435	—	2	4	no	—
34	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂₃×#417	—	2	4	no	—
36	C₂₃×#416	—	2	4	no	—
37	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#103	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×#102	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
49	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
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
56	C₂₃×#380	C₂²	1	1	yes	characteristic
57	C₂₃×#380	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
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	C₂₃×#340	C₂²	1	1	yes	characteristic
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	—	2	2	no	—
68	C₂×#41×C₂₃	—	2	2	no	—
69	C₂×#41×C₂₃	—	2	2	no	—
70	C₂×#41×C₂₃	—	4	1	no	—
71	C₂×#41×C₂₃	—	4	1	no	—
72	C₂×#41×C₂₃	—	4	1	no	—
73	C₂×#41×C₂₃	—	4	1	no	—
74	C₂×#41×C₂₃	C₂×C₄	1	4	yes	—
75	C₂×#41×C₂₃	C₂×C₄	1	4	yes	complemented
76	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₂₃	—	2	1	no	—
78	C₂²×D₄×C₂₃	—	2	1	no	—
79	C₂²×D₄×C₂₃	—	2	1	no	—
80	C₂²×D₄×C₂₃	—	2	1	no	—
81	C₂²×D₄×C₂₃	—	2	1	no	—
82	C₂²×D₄×C₂₃	—	2	1	no	—
83	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
84	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	—	2	1	no	—
87	C₂³×C₄×C₂₃	—	2	1	no	—
88	C₂³×C₄×C₂₃	—	2	1	no	—
89	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂×M₁₆×C₂₃	—	2	2	no	—
92	C₂×M₁₆×C₂₃	—	2	2	no	—
93	C₂×M₁₆×C₂₃	—	4	1	no	—
94	C₂²×C₈×C₂₃	—	2	2	no	—
95	C₂²×C₈×C₂₃	—	2	2	no	—
96	C₂²×C₈×C₂₃	—	4	1	no	—
97	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂₃×#127	—	2	8	no	—
102	C₂₃×#127	—	2	2	no	—
103	C₂₃×#127	C₂×C₄	1	4	yes	complemented
104	C₂₃×#121	—	2	2	no	—
105	C₂₃×#121	—	2	2	no	—
106	C₂₃×#121	—	2	8	no	—
107	C₂₃×#121	—	2	8	no	—
108	C₂₃×#121	C₂×C₄	1	4	yes	—
109	C₂₃×#121	C₂×C₄	1	4	yes	complemented
110	C₄×Q₈×C₂₃	—	2	2	no	—
111	C₄×Q₈×C₂₃	C₂×C₄	1	4	yes	complemented
112	C₄×D₄×C₂₃	—	2	8	no	—
113	C₄×D₄×C₂₃	C₂×C₄	1	4	yes	—
114	C₄×D₄×C₂₃	D₄	1	4	yes	—
115	C₂₃×#117	—	2	2	no	—
116	C₂₃×#117	—	4	1	no	—
117	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
119	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
120	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
121	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₂₃	C₂³	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×C₂²⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
134	C₂×C₄²×C₂₃	—	2	1	no	—
135	C₂×C₄²×C₂₃	—	2	1	no	—
136	C₂×C₄²×C₂₃	—	2	1	no	—
137	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
138	C₂₃×C₄⋊C₈	—	2	2	no	—
139	C₂₃×#103	—	2	2	no	—
140	C₂₃×#103	—	2	2	no	—
141	C₂₃×#103	—	2	2	no	—
142	C₂₃×#103	D₄	1	4	yes	complemented
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	—	4	1	no	—
148	C₂₃×#102	—	4	1	no	—
149	C₂₃×#102	—	4	1	no	—
150	C₂₃×#102	—	4	1	no	—
151	C₂₃×C₂²⋊C₈	—	2	2	no	—
152	C₂₃×C₂²⋊C₈	—	2	2	no	—
153	C₂₃×#97	—	2	2	no	—
154	C₂₃×#95	—	2	1	no	—
155	C₂₃×#95	—	2	1	no	—
156	C₂₃×#95	—	2	1	no	—
157	C₂₃×#95	—	2	1	no	—
158	C₂₃×#95	—	2	1	no	—
159	C₂⁴×C₂₃	—	2	1	no	—
160	C₂⁴×C₂₃	—	2	1	no	—
161	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
163	#41×C₂₃	—	2	8	no	—
164	#41×C₂₃	—	2	8	no	—
165	#41×C₂₃	—	4	4	no	—
166	#41×C₂₃	—	4	4	no	—
167	#41×C₂₃	—	4	4	no	—
168	#41×C₂₃	—	4	4	no	—
169	#41×C₂₃	—	4	4	no	—
170	#41×C₂₃	—	4	4	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	C₂²×C₄	1	2	yes	—
175	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
176	C₂×Q₈×C₂₃	#41	1	2	yes	—
177	C₂×D₄×C₂₃	—	2	4	no	—
178	C₂×D₄×C₂₃	—	2	4	no	—
179	C₂×D₄×C₂₃	—	2	4	no	—
180	C₂×D₄×C₂₃	—	2	4	no	—
181	C₂×D₄×C₂₃	—	2	4	no	—
182	C₂×D₄×C₂₃	—	2	4	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	—	2	1	no	—
189	C₂×D₄×C₂₃	—	2	1	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	—	4	1	no	—
194	C₂×D₄×C₂₃	—	4	1	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	—	8	1	no	—
202	C₂×D₄×C₂₃	—	8	1	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	C₂²⋊C₄	1	4	yes	—
208	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
209	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	2	1	no	—
221	C₂²×C₄×C₂₃	—	2	4	no	—
222	C₂²×C₄×C₂₃	—	2	4	no	—
223	C₂²×C₄×C₂₃	—	2	1	no	—
224	C₂²×C₄×C₂₃	—	2	1	no	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	4	2	no	—
227	C₂²×C₄×C₂₃	—	4	2	no	—
228	C₂²×C₄×C₂₃	—	4	2	no	—
229	C₂²×C₄×C₂₃	—	4	2	no	—
230	C₂²×C₄×C₂₃	—	4	2	no	—
231	C₂²×C₄×C₂₃	—	4	2	no	—
232	C₂²×C₄×C₂₃	—	8	1	no	—
233	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
234	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
235	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
242	M₁₆×C₂₃	—	4	4	no	—
243	C₂×C₈×C₂₃	—	2	1	no	—
244	C₂×C₈×C₂₃	—	2	1	no	—
245	C₂×C₈×C₂₃	—	2	1	no	—
246	C₂×C₈×C₂₃	—	2	1	no	—
247	C₂×C₈×C₂₃	—	2	1	no	—
248	C₂×C₈×C₂₃	—	2	1	no	—
249	C₂×C₈×C₂₃	—	2	1	no	—
250	C₂×C₈×C₂₃	—	2	1	no	—
251	C₂×C₈×C₂₃	—	2	1	no	—
252	C₂×C₈×C₂₃	—	2	1	no	—
253	C₂×C₈×C₂₃	—	2	1	no	—
254	C₂×C₈×C₂₃	—	4	4	no	—
255	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₂₃	—	2	4	no	—
257	C₄⋊C₄×C₂₃	—	2	1	no	—
258	C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₄⋊C₄×C₂₃	—	2	1	no	—
264	C₄⋊C₄×C₂₃	—	2	1	no	—
265	C₄⋊C₄×C₂₃	—	4	2	no	—
266	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
267	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
268	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
269	C₂²⋊C₄×C₂₃	—	2	4	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	—	4	2	no	—
272	C₂²⋊C₄×C₂₃	—	4	2	no	—
273	C₂²⋊C₄×C₂₃	—	8	1	no	—
274	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
275	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
276	C₄²×C₂₃	—	2	4	no	—
277	C₄²×C₂₃	—	4	2	no	—
278	C₄²×C₂₃	—	8	1	no	—
279	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
280	C₄²×C₂₃	C₂×D₄	1	2	yes	—
281	#22422	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	1	no	—
290	C₂³×C₂₃	—	2	1	no	—
291	C₂³×C₂₃	—	2	1	no	—
292	C₂³×C₂₃	—	2	1	no	—
293	C₂³×C₂₃	—	2	1	no	—
294	C₂³×C₂₃	—	2	2	no	—
295	C₂³×C₂₃	—	2	2	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	—	4	1	no	—
303	C₂³×C₂₃	—	4	1	no	—
304	C₂³×C₂₃	—	4	1	no	—
305	C₂³×C₂₃	—	4	1	no	—
306	C₂³×C₂₃	—	4	1	no	—
307	C₂³×C₂₃	—	4	1	no	—
308	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
309	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₂₃	—	2	2	no	—
312	Q₈×C₂₃	—	2	2	no	—
313	Q₈×C₂₃	—	2	2	no	—
314	Q₈×C₂₃	C₄×D₄	1	4	yes	—
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	8	no	—
323	D₄×C₂₃	—	4	1	no	—
324	D₄×C₂₃	—	4	1	no	—
325	D₄×C₂₃	—	4	1	no	—
326	D₄×C₂₃	—	4	1	no	—
327	D₄×C₂₃	—	8	4	no	—
328	D₄×C₂₃	—	8	4	no	—
329	D₄×C₂₃	—	8	4	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	1	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	1	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	2	2	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	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	4	8	no	—
352	C₂×C₄×C₂₃	—	4	8	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	—	4	1	no	—
365	C₂×C₄×C₂₃	—	4	1	no	—
366	C₂×C₄×C₂₃	—	8	4	no	—
367	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
368	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
369	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
370	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
371	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
372	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
375	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
376	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
377	C₈×C₂₃	—	2	2	no	—
378	C₈×C₂₃	—	4	1	no	—
379	C₈×C₂₃	—	4	1	no	—
380	C₈×C₂₃	—	4	1	no	—
381	C₂×#550	C₂×C₂₃	1	1	yes	characteristic
382	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
383	C₂×#417	C₂×C₂₃	1	1	yes	characteristic, complemented
384	C₂×#416	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#2352	C₂×C₂₃	1	1	yes	characteristic, complemented
386	#1982	C₂×C₂₃	1	1	yes	characteristic, complemented
387	#1961	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#1895	C₂×C₂₃	1	1	yes	characteristic, complemented
389	#1893	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#1875	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#1874	C₂×C₂₃	1	1	yes	characteristic, complemented
392	#1805	C₂×C₂₃	1	1	yes	characteristic, complemented
393	#1788	C₂×C₂₃	1	1	yes	characteristic, complemented
394	#1788	C₂×C₂₃	1	1	yes	characteristic, complemented
395	#1763	C₂×C₂₃	1	1	yes	characteristic, complemented
396	C₂²×C₂₃	—	2	2	no	—
397	C₂²×C₂₃	—	2	2	no	—
398	C₂²×C₂₃	—	2	2	no	—
399	C₂²×C₂₃	—	2	2	no	—
400	C₂²×C₂₃	—	2	2	no	—
401	C₂²×C₂₃	—	2	2	no	—
402	C₂²×C₂₃	—	4	1	no	—
403	C₂²×C₂₃	—	4	1	no	—
404	C₂²×C₂₃	—	4	1	no	—
405	C₂²×C₂₃	—	4	1	no	—
406	C₂²×C₂₃	—	4	1	no	—
407	C₂²×C₂₃	—	4	1	no	—
408	C₂²×C₂₃	—	4	1	no	—
409	C₂²×C₂₃	—	4	1	no	—
410	C₂²×C₂₃	—	4	2	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	—	4	2	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	—	8	1	no	—
421	C₂²×C₂₃	—	8	1	no	—
422	C₂²×C₂₃	—	8	1	no	—
423	C₂²×C₂₃	—	8	1	no	—
424	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
425	C₂²×C₂₃	D₄²	1	1	yes	characteristic
426	C₂²×C₂₃	#546	1	1	yes	characteristic
427	C₂²×C₂₃	#575	1	1	yes	characteristic
428	C₂²×C₂₃	#575	1	1	yes	characteristic
429	C₂²×C₂₃	#576	1	1	yes	characteristic
430	C₂²×C₂₃	#577	1	1	yes	characteristic
431	C₄×C₂₃	—	2	2	no	—
432	C₄×C₂₃	—	2	2	no	—
433	C₄×C₂₃	—	2	4	no	—
434	C₄×C₂₃	—	2	2	no	—
435	C₄×C₂₃	—	2	2	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	2	no	—
438	C₄×C₂₃	—	8	1	no	—
439	C₄×C₂₃	—	8	1	no	—
440	C₄×C₂₃	—	8	1	no	—
441	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
442	C₄×C₂₃	#518	1	1	yes	characteristic
443	C₄×C₂₃	D₄²	1	1	yes	characteristic
444	C₄×C₂₃	#546	1	1	yes	characteristic
445	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
446	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
447	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
448	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
449	#550	—	2	4	no	—
450	#550	C₄×C₂₃	1	8	yes	complemented
451	C₂×#127	—	2	1	no	—
452	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#121	—	2	1	no	—
454	C₂×#121	—	2	1	no	—
455	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×C₄×D₄	—	2	1	no	—
459	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
460	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
461	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
462	#435	—	2	4	no	—
463	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
464	#417	—	2	4	no	—
465	#416	—	2	4	no	—
466	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
467	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
469	C₂×#103	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×#102	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
475	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
476	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
477	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
478	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
481	#388	—	2	1	no	—
482	#387	—	2	1	no	—
483	#386	—	2	1	no	—
484	#382	C₂²×C₂₃	1	1	yes	characteristic
485	#380	C₂²×C₂₃	1	1	yes	characteristic
486	#380	C₂²×C₂₃	1	1	yes	characteristic
487	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	—	2	1	no	—
489	#340	C₂²×C₂₃	1	1	yes	characteristic
490	#340	C₂²×C₂₃	1	1	yes	characteristic
491	#340	C₂²×C₂₃	1	1	yes	characteristic
492	#340	C₂²×C₂₃	1	1	yes	characteristic
493	C₂×C₂₃	—	4	2	no	—
494	C₂×C₂₃	—	4	2	no	—
495	C₂×C₂₃	—	8	2	no	—
496	C₂×C₂₃	—	8	2	no	—
497	C₂×C₂₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
498	C₂×C₂₃	#2896	1	1	yes	characteristic
499	C₂×C₂₃	#2897	1	1	yes	characteristic
500	C₂×C₂₃	#3268	1	1	yes	characteristic
501	C₂×C₂₃	#3271	1	1	yes	characteristic
502	C₂×C₂₃	#3309	1	1	yes	characteristic
503	C₂×C₂₃	#3317	1	1	yes	characteristic
504	C₂×#41	—	2	2	no	—
505	C₂×#41	—	2	2	no	—
506	C₂×#41	—	2	2	no	—
507	C₂×#41	—	2	2	no	—
508	C₂×#41	—	2	2	no	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	4	1	no	—
511	C₂×#41	—	4	1	no	—
512	C₂×#41	—	4	1	no	—
513	C₂×#41	—	4	1	no	—
514	C₂×#41	C₂×C₄×C₂₃	1	4	yes	—
515	C₂×#41	C₂×C₄×C₂₃	1	4	yes	complemented
516	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
524	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
526	C₂³×C₄	—	2	1	no	—
527	C₂³×C₄	—	2	1	no	—
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
531	C₂×M₁₆	—	2	2	no	—
532	C₂×M₁₆	—	2	2	no	—
533	C₂×M₁₆	—	4	1	no	—
534	C₂²×C₈	—	2	2	no	—
535	C₂²×C₈	—	2	2	no	—
536	C₂²×C₈	—	4	1	no	—
537	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
539	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
540	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
541	#127	—	2	8	no	—
542	#127	—	2	2	no	—
543	#127	C₂×C₄×C₂₃	1	4	yes	complemented
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	2	8	no	—
547	#121	—	2	8	no	—
548	#121	C₂×C₄×C₂₃	1	4	yes	—
549	#121	C₂×C₄×C₂₃	1	4	yes	complemented
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	C₂×C₄×C₂₃	1	4	yes	complemented
552	C₄×D₄	—	2	8	no	—
553	C₄×D₄	C₂×C₄×C₂₃	1	4	yes	—
554	C₄×D₄	D₄×C₂₃	1	4	yes	—
555	#117	—	2	2	no	—
556	#117	—	4	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	2	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	4	1	no	—
561	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
574	C₂×C₄²	—	2	1	no	—
575	C₂×C₄²	—	2	1	no	—
576	C₂×C₄²	—	2	1	no	—
577	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
578	C₄⋊C₈	—	2	2	no	—
579	#103	—	2	2	no	—
580	#103	—	2	2	no	—
581	#103	—	2	2	no	—
582	#103	D₄×C₂₃	1	4	yes	complemented
583	#102	—	2	2	no	—
584	#102	—	2	2	no	—
585	#102	—	2	2	no	—
586	#102	—	2	2	no	—
587	#102	—	4	1	no	—
588	#102	—	4	1	no	—
589	#102	—	4	1	no	—
590	#102	—	4	1	no	—
591	C₂²⋊C₈	—	2	2	no	—
592	C₂²⋊C₈	—	2	2	no	—
593	#97	—	2	2	no	—
594	#95	—	2	1	no	—
595	#95	—	2	1	no	—
596	#95	—	2	1	no	—
597	#95	—	2	1	no	—
598	#95	—	2	1	no	—
599	C₂₃	#22422	1	1	yes	characteristic, direct product factor, Sylow
600	C₂⁴	—	2	1	no	—
601	C₂⁴	—	2	1	no	—
602	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
603	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
604	#41	—	2	8	no	—
605	#41	—	2	8	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	4	no	—
609	#41	—	4	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
616	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
617	C₂×Q₈	#41×C₂₃	1	2	yes	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	2	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	8	1	no	—
643	C₂×D₄	—	8	1	no	—
644	C₂×D₄	—	8	1	no	—
645	C₂×D₄	—	8	1	no	—
646	C₂×D₄	—	8	1	no	—
647	C₂×D₄	—	8	1	no	—
648	C₂×D₄	C₂²⋊C₄×C₂₃	1	4	yes	—
649	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
650	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
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	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	8	1	no	—
674	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
675	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
676	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
681	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
683	M₁₆	—	4	4	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	4	4	no	—
696	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
708	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
709	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	8	1	no	—
715	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
716	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
717	C₄²	—	2	4	no	—
718	C₄²	—	4	2	no	—
719	C₄²	—	8	1	no	—
720	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
721	C₄²	C₂×D₄×C₂₃	1	2	yes	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	4	1	no	—
737	C₂³	—	4	1	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
749	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
750	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	C₄×D₄×C₂₃	1	4	yes	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	4	4	no	—
760	D₄	—	4	8	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	8	no	—
763	D₄	—	4	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	8	4	no	—
768	D₄	—	8	4	no	—
769	D₄	—	8	4	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	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	4	8	no	—
792	C₂×C₄	—	4	8	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	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	8	4	no	—
807	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
808	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
809	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
810	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
811	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
814	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
815	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
816	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
817	C₈	—	2	2	no	—
818	C₈	—	4	1	no	—
819	C₈	—	4	1	no	—
820	C₈	—	4	1	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	8	1	no	—
842	C₂²	—	8	1	no	—
843	C₂²	—	8	1	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	8	1	no	—
847	C₂²	—	8	1	no	—
848	C₂²	—	8	1	no	—
849	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
850	C₂²	D₄²×C₂₃	1	1	yes	characteristic
851	C₂²	C₂₃×#546	1	1	yes	characteristic
852	C₂²	C₂₃×#575	1	1	yes	characteristic
853	C₂²	C₂₃×#575	1	1	yes	characteristic
854	C₂²	C₂₃×#576	1	1	yes	characteristic
855	C₂²	C₂₃×#577	1	1	yes	characteristic
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	4	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	8	1	no	—
864	C₄	—	8	1	no	—
865	C₄	—	8	1	no	—
866	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
867	C₄	C₂₃×#518	1	1	yes	characteristic
868	C₄	D₄²×C₂₃	1	1	yes	characteristic
869	C₄	C₂₃×#546	1	1	yes	characteristic
870	C₂	—	4	2	no	—
871	C₂	—	4	2	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	2	no	—
874	C₂	D₄×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
875	C₂	C₂₃×#2896	1	1	yes	characteristic
876	C₂	C₂₃×#2897	1	1	yes	characteristic
877	C₂	C₂₃×#3268	1	1	yes	characteristic
878	C₂	C₂₃×#3271	1	1	yes	characteristic
879	C₂	C₂₃×#3309	1	1	yes	characteristic
880	C₂	C₂₃×#3317	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×C₂₃×#550	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×#417	C₂	semidirect
4. C₂×C₂₃×#416	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×#1805	C₂	semidirect
13. C₂₃×#1788	C₂	semidirect
14. C₂₃×#1788	C₂	semidirect
15. C₂₃×#1763	C₂	semidirect
21. C₂₃×#550	C₄	semidirect
75. C₂×#41×C₂₃	C₂×C₄	semidirect
103. C₂₃×#127	C₂×C₄	semidirect
109. C₂₃×#121	C₂×C₄	semidirect
111. C₄×Q₈×C₂₃	C₂×C₄	semidirect
142. C₂₃×#103	D₄	semidirect
281. #22422	C₂₃	direct (N × H)
382. C₂×#435	C₂×C₂₃	semidirect
383. C₂×#417	C₂×C₂₃	semidirect
384. C₂×#416	C₂×C₂₃	semidirect
385. #2352	C₂×C₂₃	semidirect
386. #1982	C₂×C₂₃	semidirect
387. #1961	C₂×C₂₃	semidirect
388. #1895	C₂×C₂₃	semidirect
389. #1893	C₂×C₂₃	semidirect
390. #1875	C₂×C₂₃	semidirect
391. #1874	C₂×C₂₃	semidirect
392. #1805	C₂×C₂₃	semidirect
393. #1788	C₂×C₂₃	semidirect
394. #1788	C₂×C₂₃	semidirect
395. #1763	C₂×C₂₃	semidirect
450. #550	C₄×C₂₃	semidirect
515. C₂×#41	C₂×C₄×C₂₃	semidirect
543. #127	C₂×C₄×C₂₃	semidirect
549. #121	C₂×C₄×C₂₃	semidirect
551. C₄×Q₈	C₂×C₄×C₂₃	semidirect
582. #103	D₄×C₂₃	semidirect
599. C₂₃	#22422	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×#550	2
C₂×C₂₃×#435	2
C₂×C₂₃×#417	2
C₂×C₂₃×#416	2
C₂₃×#2352	2
C₂₃×#1982	2
C₂₃×#1961	2
C₂₃×#1895	2
C₂₃×#1893	2
C₂₃×#1875	2
C₂₃×#1874	2
C₂₃×#1805	2
C₂₃×#1788	2
C₂₃×#1763	2
#22422	23

Subgroups — C23×#22422 #19170048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22422 #19170048