Subgroups — C₂₃×#25549 #19173175

Order 5888.

1390 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1879	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×#1870	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	—	2	1	no	—
17	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#547	—	2	4	no	—
20	C₂₃×#547	—	2	4	no	—
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#123	—	2	1	no	—
23	C₂×C₂₃×#123	—	2	1	no	—
24	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#481	—	2	4	no	—
35	C₂₃×#469	—	2	4	no	—
36	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂₃×#394	—	2	1	no	—
49	C₂₃×#392	—	2	1	no	—
50	C₂₃×#390	—	2	1	no	—
51	C₂₃×#390	C₂²	1	1	yes	characteristic
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#388	—	2	1	no	—
54	C₂₃×#380	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#340	C₂²	1	1	yes	characteristic
61	C₂₃×#336	C₂²	1	1	yes	characteristic
62	C₂₃×#336	C₂²	1	1	yes	characteristic
63	C₂×#41×C₂₃	—	2	8	no	—
64	C₂×#41×C₂₃	—	4	4	no	—
65	C₂×#41×C₂₃	—	4	4	no	—
66	C₂²×Q₈×C₂₃	—	2	1	no	—
67	C₂²×D₄×C₂₃	—	2	1	no	—
68	C₂²×D₄×C₂₃	—	2	1	no	—
69	C₂²×D₄×C₂₃	—	2	1	no	—
70	C₂²×D₄×C₂₃	—	2	1	no	—
71	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
72	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₂₃	—	2	1	no	—
75	C₂³×C₄×C₂₃	—	2	1	no	—
76	C₂³×C₄×C₂₃	—	2	1	no	—
77	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂×D₈×C₂₃	—	2	2	no	—
80	C₂×D₈×C₂₃	—	2	2	no	—
81	C₂×D₈×C₂₃	—	4	1	no	—
82	C₂×M₁₆×C₂₃	—	2	2	no	—
83	C₂×M₁₆×C₂₃	—	2	2	no	—
84	C₂×M₁₆×C₂₃	—	4	1	no	—
85	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
89	C₂₃×C₄⋊Q₈	—	2	2	no	—
90	C₂₃×C₄⋊Q₈	—	2	2	no	—
91	C₂₃×#123	—	2	8	no	—
92	C₂₃×#123	—	2	8	no	—
93	C₂₃×C₂²⋊Q₈	—	2	8	no	—
94	C₂₃×#121	—	2	2	no	—
95	C₂₃×#121	—	2	2	no	—
96	C₂₃×#121	—	2	2	no	—
97	C₂₃×#121	—	2	2	no	—
98	C₂₃×#121	—	2	2	no	—
99	C₂₃×#121	—	2	2	no	—
100	C₂₃×#121	—	4	1	no	—
101	C₂₃×#121	D₄	1	4	yes	complemented
102	C₄×D₄×C₂₃	—	2	2	no	—
103	C₄×D₄×C₂₃	—	2	2	no	—
104	C₄×D₄×C₂₃	—	2	2	no	—
105	C₄×D₄×C₂₃	—	2	2	no	—
106	C₂₃×#117	—	2	2	no	—
107	C₂₃×#117	—	4	1	no	—
108	C₂×C₄⋊C₄×C₂₃	—	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	—	2	2	no	—
113	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
114	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
115	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₃	D₄	1	4	yes	complemented
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	—	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	C₂³	1	1	yes	characteristic
136	C₂₃×#106	—	2	2	no	—
137	C₂₃×#106	—	2	2	no	—
138	C₂₃×#106	—	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×C₂²⋊C₈	—	2	2	no	—
146	C₂₃×C₂²⋊C₈	—	2	2	no	—
147	C₂₃×C₂²⋊C₈	—	4	1	no	—
148	C₂₃×#95	—	2	1	no	—
149	C₂₃×#95	—	2	1	no	—
150	C₂⁴×C₂₃	—	2	1	no	—
151	C₂⁴×C₂₃	—	2	1	no	—
152	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
154	#41×C₂₃	—	4	32	no	—
155	C₂×Q₈×C₂₃	—	2	4	no	—
156	C₂×Q₈×C₂₃	—	4	2	no	—
157	C₂×Q₈×C₂₃	—	4	2	no	—
158	C₂×D₄×C₂₃	—	2	2	no	—
159	C₂×D₄×C₂₃	—	2	2	no	—
160	C₂×D₄×C₂₃	—	2	4	no	—
161	C₂×D₄×C₂₃	—	2	4	no	—
162	C₂×D₄×C₂₃	—	2	2	no	—
163	C₂×D₄×C₂₃	—	2	1	no	—
164	C₂×D₄×C₂₃	—	2	1	no	—
165	C₂×D₄×C₂₃	—	2	1	no	—
166	C₂×D₄×C₂₃	—	2	1	no	—
167	C₂×D₄×C₂₃	—	2	1	no	—
168	C₂×D₄×C₂₃	—	2	1	no	—
169	C₂×D₄×C₂₃	—	2	1	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	—	4	2	no	—
175	C₂×D₄×C₂₃	—	4	2	no	—
176	C₂×D₄×C₂₃	—	4	2	no	—
177	C₂×D₄×C₂₃	—	4	2	no	—
178	C₂×D₄×C₂₃	—	4	2	no	—
179	C₂×D₄×C₂₃	—	4	2	no	—
180	C₂×D₄×C₂₃	—	4	2	no	—
181	C₂×D₄×C₂₃	—	8	1	no	—
182	C₂×D₄×C₂₃	—	8	1	no	—
183	C₂×D₄×C₂₃	—	8	1	no	—
184	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	2	1	no	—
187	C₂²×C₄×C₂₃	—	2	1	no	—
188	C₂²×C₄×C₂₃	—	2	1	no	—
189	C₂²×C₄×C₂₃	—	2	4	no	—
190	C₂²×C₄×C₂₃	—	2	4	no	—
191	C₂²×C₄×C₂₃	—	2	4	no	—
192	C₂²×C₄×C₂₃	—	2	1	no	—
193	C₂²×C₄×C₂₃	—	2	1	no	—
194	C₂²×C₄×C₂₃	—	2	1	no	—
195	C₂²×C₄×C₂₃	—	2	1	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	2	1	no	—
200	C₂²×C₄×C₂₃	—	2	1	no	—
201	C₂²×C₄×C₂₃	—	2	1	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	4	2	no	—
205	C₂²×C₄×C₂₃	—	4	2	no	—
206	C₂²×C₄×C₂₃	—	4	2	no	—
207	C₂²×C₄×C₂₃	—	4	2	no	—
208	C₂²×C₄×C₂₃	—	4	2	no	—
209	C₂²×C₄×C₂₃	—	4	2	no	—
210	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
217	D₈×C₂₃	—	4	4	no	—
218	M₁₆×C₂₃	—	4	4	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	2	1	no	—
221	C₂×C₈×C₂₃	—	2	1	no	—
222	C₂×C₈×C₂₃	—	2	1	no	—
223	C₂×C₈×C₂₃	—	2	1	no	—
224	C₂×C₈×C₂₃	—	2	1	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	—	2	1	no	—
227	C₂×C₈×C₂₃	—	2	1	no	—
228	C₂×C₈×C₂₃	—	2	1	no	—
229	C₂×C₈×C₂₃	—	2	1	no	—
230	C₂×C₈×C₂₃	#41	1	2	yes	complemented
231	C₄⋊C₄×C₂₃	—	2	4	no	—
232	C₄⋊C₄×C₂₃	—	2	4	no	—
233	C₄⋊C₄×C₂₃	—	2	4	no	—
234	C₄⋊C₄×C₂₃	—	2	2	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	1	no	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	1	no	—
241	C₄⋊C₄×C₂₃	—	2	1	no	—
242	C₄⋊C₄×C₂₃	—	2	1	no	—
243	C₄⋊C₄×C₂₃	—	8	1	no	—
244	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
246	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
247	C₄⋊C₄×C₂₃	#41	1	2	yes	complemented
248	C₂²⋊C₄×C₂₃	—	2	4	no	—
249	C₂²⋊C₄×C₂₃	—	2	4	no	—
250	C₂²⋊C₄×C₂₃	—	2	2	no	—
251	C₂²⋊C₄×C₂₃	—	2	4	no	—
252	C₂²⋊C₄×C₂₃	—	2	2	no	—
253	C₂²⋊C₄×C₂₃	—	4	2	no	—
254	C₂²⋊C₄×C₂₃	—	4	2	no	—
255	C₂²⋊C₄×C₂₃	—	4	2	no	—
256	C₂²⋊C₄×C₂₃	—	4	2	no	—
257	C₂²⋊C₄×C₂₃	—	8	1	no	—
258	C₂²⋊C₄×C₂₃	—	8	1	no	—
259	C₄²×C₂₃	—	2	1	no	—
260	C₄²×C₂₃	—	2	1	no	—
261	C₄²×C₂₃	—	4	2	no	—
262	#25549	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	1	no	—
265	C₂³×C₂₃	—	2	1	no	—
266	C₂³×C₂₃	—	2	1	no	—
267	C₂³×C₂₃	—	2	1	no	—
268	C₂³×C₂₃	—	2	1	no	—
269	C₂³×C₂₃	—	2	1	no	—
270	C₂³×C₂₃	—	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	2	no	—
276	C₂³×C₂₃	—	4	1	no	—
277	C₂³×C₂₃	—	4	1	no	—
278	C₂³×C₂₃	—	4	1	no	—
279	C₂³×C₂₃	—	4	1	no	—
280	C₂³×C₂₃	—	4	1	no	—
281	C₂³×C₂₃	—	4	1	no	—
282	C₂³×C₂₃	—	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	#120	1	2	yes	—
290	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
291	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₂₃	—	4	8	no	—
293	D₄×C₂₃	—	2	8	no	—
294	D₄×C₂₃	—	2	2	no	—
295	D₄×C₂₃	—	2	2	no	—
296	D₄×C₂₃	—	4	8	no	—
297	D₄×C₂₃	—	4	8	no	—
298	D₄×C₂₃	—	4	1	no	—
299	D₄×C₂₃	—	4	1	no	—
300	D₄×C₂₃	—	4	1	no	—
301	D₄×C₂₃	—	4	1	no	—
302	D₄×C₂₃	—	4	1	no	—
303	D₄×C₂₃	—	4	1	no	—
304	D₄×C₂₃	—	8	4	no	—
305	D₄×C₂₃	—	8	4	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	1	no	—
308	C₂×C₄×C₂₃	—	2	1	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	1	no	—
321	C₂×C₄×C₂₃	—	2	1	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	1	no	—
324	C₂×C₄×C₂₃	—	4	8	no	—
325	C₂×C₄×C₂₃	—	4	8	no	—
326	C₂×C₄×C₂₃	—	4	8	no	—
327	C₂×C₄×C₂₃	—	4	1	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	1	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	4	1	no	—
332	C₂×C₄×C₂₃	—	4	1	no	—
333	C₂×C₄×C₂₃	—	4	1	no	—
334	C₂×C₄×C₂₃	—	4	1	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	1	no	—
339	C₂×C₄×C₂₃	—	4	1	no	—
340	C₂×C₄×C₂₃	—	4	1	no	—
341	C₂×C₄×C₂₃	—	4	1	no	—
342	C₂×C₄×C₂₃	—	4	1	no	—
343	C₂×C₄×C₂₃	—	4	1	no	—
344	C₂×C₄×C₂₃	—	4	1	no	—
345	C₂×C₄×C₂₃	#120	1	2	yes	—
346	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
347	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
353	C₈×C₂₃	—	2	2	no	—
354	C₈×C₂₃	—	4	1	no	—
355	C₈×C₂₃	—	4	1	no	—
356	C₈×C₂₃	—	4	1	no	—
357	C₂×#547	C₂×C₂₃	1	1	yes	characteristic, complemented
358	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
359	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#2414	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#2058	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#2034	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#2023	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#1999	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#1875	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#1874	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#1853	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#1736	C₂×C₂₃	1	1	yes	characteristic, complemented
372	C₂²×C₂₃	—	2	2	no	—
373	C₂²×C₂₃	—	2	2	no	—
374	C₂²×C₂₃	—	2	2	no	—
375	C₂²×C₂₃	—	2	2	no	—
376	C₂²×C₂₃	—	2	2	no	—
377	C₂²×C₂₃	—	2	2	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	4	1	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	1	no	—
382	C₂²×C₂₃	—	4	1	no	—
383	C₂²×C₂₃	—	4	1	no	—
384	C₂²×C₂₃	—	4	1	no	—
385	C₂²×C₂₃	—	4	1	no	—
386	C₂²×C₂₃	—	4	2	no	—
387	C₂²×C₂₃	—	4	2	no	—
388	C₂²×C₂₃	—	4	2	no	—
389	C₂²×C₂₃	—	8	1	no	—
390	C₂²×C₂₃	—	8	1	no	—
391	C₂²×C₂₃	—	8	1	no	—
392	C₂²×C₂₃	—	8	1	no	—
393	C₂²×C₂₃	—	8	1	no	—
394	C₂²×C₂₃	—	8	1	no	—
395	C₂²×C₂₃	—	8	1	no	—
396	C₂²×C₂₃	—	8	1	no	—
397	C₂²×C₂₃	—	8	1	no	—
398	C₂²×C₂₃	—	8	1	no	—
399	C₂²×C₂₃	—	8	1	no	—
400	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
401	C₂²×C₂₃	#546	1	1	yes	characteristic
402	C₂²×C₂₃	#547	1	1	yes	characteristic
403	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
405	C₂²×C₂₃	#577	1	1	yes	characteristic
406	C₂²×C₂₃	#577	1	1	yes	characteristic
407	C₄×C₂₃	—	2	2	no	—
408	C₄×C₂₃	—	2	2	no	—
409	C₄×C₂₃	—	4	1	no	—
410	C₄×C₂₃	—	4	2	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	—	4	2	no	—
413	C₄×C₂₃	—	4	1	no	—
414	C₄×C₂₃	—	4	2	no	—
415	C₄×C₂₃	—	8	1	no	—
416	C₄×C₂₃	—	8	1	no	—
417	C₄×C₂₃	#532	1	1	yes	characteristic
418	C₄×C₂₃	#537	1	1	yes	characteristic
419	C₄×C₂₃	#546	1	1	yes	characteristic
420	C₄×C₂₃	#547	1	1	yes	characteristic
421	C₂²×#41	—	2	1	no	—
422	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
423	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
424	#547	—	2	4	no	—
425	#547	—	2	4	no	—
426	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#123	—	2	1	no	—
428	C₂×#123	—	2	1	no	—
429	C₂×C₂²⋊Q₈	—	2	1	no	—
430	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
437	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
439	#481	—	2	4	no	—
440	#469	—	2	4	no	—
441	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
453	#394	—	2	1	no	—
454	#392	—	2	1	no	—
455	#390	—	2	1	no	—
456	#390	C₂²×C₂₃	1	1	yes	characteristic
457	#389	C₂²×C₂₃	1	1	yes	characteristic
458	#388	—	2	1	no	—
459	#380	C₂²×C₂₃	1	1	yes	characteristic
460	#340	C₂²×C₂₃	1	1	yes	characteristic
461	#340	C₂²×C₂₃	1	1	yes	characteristic
462	#340	C₂²×C₂₃	1	1	yes	characteristic
463	#340	C₂²×C₂₃	1	1	yes	characteristic
464	#340	C₂²×C₂₃	1	1	yes	characteristic
465	#340	C₂²×C₂₃	1	1	yes	characteristic
466	#336	C₂²×C₂₃	1	1	yes	characteristic
467	#336	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×C₂₃	—	4	2	no	—
469	C₂×C₂₃	—	4	2	no	—
470	C₂×C₂₃	—	8	2	no	—
471	C₂×C₂₃	—	16	1	no	—
472	C₂×C₂₃	#2430	1	1	yes	characteristic
473	C₂×C₂₃	#3003	1	1	yes	characteristic
474	C₂×C₂₃	#3010	1	1	yes	characteristic
475	C₂×C₂₃	#3306	1	1	yes	characteristic
476	C₂×C₂₃	#3332	1	1	yes	characteristic
477	C₂×C₂₃	#3345	1	1	yes	characteristic
478	C₂×C₂₃	#3354	1	1	yes	characteristic
479	C₂×#41	—	2	8	no	—
480	C₂×#41	—	4	4	no	—
481	C₂×#41	—	4	4	no	—
482	C₂²×Q₈	—	2	1	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
488	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	—	2	1	no	—
493	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×D₈	—	2	2	no	—
496	C₂×D₈	—	2	2	no	—
497	C₂×D₈	—	4	1	no	—
498	C₂×M₁₆	—	2	2	no	—
499	C₂×M₁₆	—	2	2	no	—
500	C₂×M₁₆	—	4	1	no	—
501	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	—	2	2	no	—
507	#123	—	2	8	no	—
508	#123	—	2	8	no	—
509	C₂²⋊Q₈	—	2	8	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	2	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	4	1	no	—
517	#121	D₄×C₂₃	1	4	yes	complemented
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	2	no	—
522	#117	—	2	2	no	—
523	#117	—	4	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	2	no	—
529	C₂×C₄⋊C₄	—	2	2	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
532	C₂×C₄⋊C₄	D₄×C₂₃	1	4	yes	complemented
533	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
550	C₂×C₄²	—	2	1	no	—
551	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
552	#106	—	2	2	no	—
553	#106	—	2	2	no	—
554	#106	—	2	2	no	—
555	#102	—	2	2	no	—
556	#102	—	2	2	no	—
557	#102	—	2	2	no	—
558	#102	—	2	2	no	—
559	#102	—	2	2	no	—
560	#102	—	4	1	no	—
561	C₂²⋊C₈	—	2	2	no	—
562	C₂²⋊C₈	—	2	2	no	—
563	C₂²⋊C₈	—	4	1	no	—
564	#95	—	2	1	no	—
565	#95	—	2	1	no	—
566	C₂₃	#25549	1	1	yes	characteristic, direct product factor, Sylow
567	C₂⁴	—	2	1	no	—
568	C₂⁴	—	2	1	no	—
569	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
570	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
571	#41	—	4	32	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	—	4	2	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	4	2	no	—
592	C₂×D₄	—	4	2	no	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	8	1	no	—
599	C₂×D₄	—	8	1	no	—
600	C₂×D₄	—	8	1	no	—
601	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
628	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
631	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
632	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
634	D₈	—	4	4	no	—
635	M₁₆	—	4	4	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	#41×C₂₃	1	2	yes	complemented
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	8	1	no	—
661	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
663	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
664	C₄⋊C₄	#41×C₂₃	1	2	yes	complemented
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	8	1	no	—
675	C₂²⋊C₄	—	8	1	no	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	4	2	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	4	1	no	—
697	C₂³	—	4	1	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	—	4	1	no	—
703	C₂³	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	C₂₃×#120	1	2	yes	—
706	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
707	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
708	Q₈	—	4	8	no	—
709	D₄	—	2	8	no	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	1	no	—
715	D₄	—	4	1	no	—
716	D₄	—	4	1	no	—
717	D₄	—	4	1	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	1	no	—
720	D₄	—	8	4	no	—
721	D₄	—	8	4	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	8	no	—
742	C₂×C₄	—	4	8	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	C₂₃×#120	1	2	yes	—
762	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
763	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
765	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
766	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
767	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
768	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
769	C₈	—	2	2	no	—
770	C₈	—	4	1	no	—
771	C₈	—	4	1	no	—
772	C₈	—	4	1	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	8	1	no	—
791	C₂²	—	8	1	no	—
792	C₂²	—	8	1	no	—
793	C₂²	—	8	1	no	—
794	C₂²	—	8	1	no	—
795	C₂²	—	8	1	no	—
796	C₂²	—	8	1	no	—
797	C₂²	—	8	1	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
802	C₂²	C₂₃×#546	1	1	yes	characteristic
803	C₂²	C₂₃×#547	1	1	yes	characteristic
804	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
805	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
806	C₂²	C₂₃×#577	1	1	yes	characteristic
807	C₂²	C₂₃×#577	1	1	yes	characteristic
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	2	no	—
816	C₄	—	8	1	no	—
817	C₄	—	8	1	no	—
818	C₄	C₂₃×#532	1	1	yes	characteristic
819	C₄	C₂₃×#537	1	1	yes	characteristic
820	C₄	C₂₃×#546	1	1	yes	characteristic
821	C₄	C₂₃×#547	1	1	yes	characteristic
822	C₂	—	4	2	no	—
823	C₂	—	4	2	no	—
824	C₂	—	8	2	no	—
825	C₂	—	16	1	no	—
826	C₂	C₂₃×#2430	1	1	yes	characteristic
827	C₂	C₂₃×#3003	1	1	yes	characteristic
828	C₂	C₂₃×#3010	1	1	yes	characteristic
829	C₂	C₂₃×#3306	1	1	yes	characteristic
830	C₂	C₂₃×#3332	1	1	yes	characteristic
831	C₂	C₂₃×#3345	1	1	yes	characteristic
832	C₂	C₂₃×#3354	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#547	C₂	semidirect
2. C₂×C₂₃×#481	C₂	semidirect
3. C₂×C₂₃×#469	C₂	semidirect
4. C₂₃×#2414	C₂	semidirect
5. C₂₃×#2058	C₂	semidirect
6. C₂₃×#2034	C₂	semidirect
7. C₂₃×#2023	C₂	semidirect
8. C₂₃×#1999	C₂	semidirect
9. C₂₃×#1879	C₂	semidirect
10. C₂₃×#1875	C₂	semidirect
11. C₂₃×#1874	C₂	semidirect
12. C₂₃×#1870	C₂	semidirect
13. C₂₃×#1864	C₂	semidirect
14. C₂₃×#1853	C₂	semidirect
15. C₂₃×#1736	C₂	semidirect
101. C₂₃×#121	D₄	semidirect
116. C₂×C₄⋊C₄×C₂₃	D₄	semidirect
230. C₂×C₈×C₂₃	#41	semidirect
247. C₄⋊C₄×C₂₃	#41	semidirect
262. #25549	C₂₃	direct (N × H)
357. C₂×#547	C₂×C₂₃	semidirect
358. C₂×#481	C₂×C₂₃	semidirect
359. C₂×#469	C₂×C₂₃	semidirect
360. #2414	C₂×C₂₃	semidirect
361. #2058	C₂×C₂₃	semidirect
362. #2034	C₂×C₂₃	semidirect
363. #2023	C₂×C₂₃	semidirect
364. #1999	C₂×C₂₃	semidirect
365. #1879	C₂×C₂₃	semidirect
366. #1875	C₂×C₂₃	semidirect
367. #1874	C₂×C₂₃	semidirect
368. #1870	C₂×C₂₃	semidirect
369. #1864	C₂×C₂₃	semidirect
370. #1853	C₂×C₂₃	semidirect
371. #1736	C₂×C₂₃	semidirect
517. #121	D₄×C₂₃	semidirect
532. C₂×C₄⋊C₄	D₄×C₂₃	semidirect
566. C₂₃	#25549	direct (N × H)
647. C₂×C₈	#41×C₂₃	semidirect
664. C₄⋊C₄	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#547	2
C₂×C₂₃×#481	2
C₂×C₂₃×#469	2
C₂₃×#2414	2
C₂₃×#2058	2
C₂₃×#2034	2
C₂₃×#2023	2
C₂₃×#1999	2
C₂₃×#1879	2
C₂₃×#1875	2
C₂₃×#1874	2
C₂₃×#1870	2
C₂₃×#1864	2
C₂₃×#1853	2
C₂₃×#1736	2
#25549	23

Subgroups — C23×#25549 #19173175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25549 #19173175