Subgroups — C₂₃×#36705 #19184331

Order 5888.

2406 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#538	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2849	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2689	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2687	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2674	C₂	1	4	yes	maximal, complemented
7	C₂₃×#2672	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2622	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2591	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2583	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2579	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2487	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2436	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#538	—	2	8	no	—
19	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₂×C₂₃×#126	C₂²	1	2	yes	—
21	C₂×C₂₃×#124	C₂²	1	2	yes	—
22	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
23	C₂×C₂₃×#123	C₂²	1	2	yes	—
24	C₂×C₂₃×#123	C₂²	1	4	yes	—
25	C₂×C₂₃×C₂²⋊Q₈	—	2	8	no	—
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#121	C₂²	1	2	yes	—
30	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#120	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂₃×#400	C₂²	1	4	yes	complemented
39	C₂₃×#400	C₂²	1	2	yes	complemented
40	C₂₃×#399	C₂²	1	4	yes	complemented
41	C₂₃×#398	C₂²	1	2	yes	complemented
42	C₂₃×#398	C₂²	1	4	yes	complemented
43	C₂₃×#397	C₂²	1	4	yes	—
44	C₂₃×#397	C₂²	1	4	yes	—
45	C₂₃×#396	C₂²	1	4	yes	complemented
46	C₂₃×#395	C₂²	1	4	yes	complemented
47	C₂₃×#395	C₂²	1	2	yes	complemented
48	C₂₃×#394	C₂²	1	4	yes	—
49	C₂₃×#394	C₂²	1	4	yes	—
50	C₂₃×#394	C₂²	1	2	yes	complemented
51	C₂₃×#393	C₂²	1	4	yes	complemented
52	C₂₃×#391	C₂²	1	2	yes	complemented
53	C₂₃×#391	C₂²	1	2	yes	complemented
54	C₂₃×#389	C₂²	1	4	yes	complemented
55	C₂₃×#389	C₂²	1	4	yes	complemented
56	C₂₃×#388	C₂²	1	4	yes	—
57	C₂₃×#388	C₂²	1	4	yes	—
58	C₂₃×#388	C₂²	1	4	yes	complemented
59	C₂₃×#387	C₂²	1	4	yes	complemented
60	C₂₃×#386	C₂²	1	4	yes	—
61	C₂₃×#386	C₂²	1	2	yes	—
62	C₂₃×#386	C₂²	1	2	yes	—
63	C₂₃×#386	C₂²	1	2	yes	—
64	C₂₃×#386	C₂²	1	2	yes	—
65	C₂₃×#385	C₂²	1	4	yes	—
66	C₂₃×#385	C₂²	1	2	yes	—
67	C₂₃×#385	C₂²	1	2	yes	—
68	C₂₃×#385	C₂²	1	2	yes	—
69	C₂₃×#385	C₂²	1	2	yes	—
70	C₂₃×#385	C₂²	1	4	yes	complemented
71	C₂₃×#381	C₂²	1	4	yes	—
72	C₂₃×#380	C₂²	1	2	yes	—
73	C₂₃×#380	C₂²	1	4	yes	complemented
74	C₂₃×#379	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
77	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₂₃	—	2	4	no	—
79	C₂²×Q₈×C₂₃	—	4	4	no	—
80	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
81	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
82	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	—	2	4	no	—
88	C₂³×C₄×C₂₃	—	4	4	no	—
89	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
94	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂₃×C₄⋊Q₈	—	4	4	no	—
98	C₂₃×#126	—	2	8	no	—
99	C₂₃×#124	—	2	8	no	—
100	C₂₃×#124	—	4	4	no	—
101	C₂₃×#123	—	2	8	no	—
102	C₂₃×#123	—	4	8	no	—
103	C₂₃×C₂²⋊Q₈	—	2	4	no	—
104	C₂₃×C₂²⋊Q₈	—	2	16	no	—
105	C₂₃×C₂²⋊Q₈	—	2	16	no	—
106	C₂₃×#121	—	2	4	no	—
107	C₂₃×#121	—	2	8	no	—
108	C₂₃×#120	—	2	8	no	—
109	C₄×D₄×C₂₃	—	2	8	no	—
110	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
111	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
112	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
127	C₂×C₂²⋊C₄×C₂₃	D₄	1	8	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
147	C₂₃×#95	C₂³	1	2	yes	—
148	C₂₃×#95	C₂³	1	2	yes	—
149	C₂₃×#95	C₂³	1	4	yes	—
150	C₂₃×#95	C₂³	1	4	yes	—
151	C₂₃×#95	C₂³	1	4	yes	—
152	C₂₃×#95	C₂³	1	4	yes	—
153	C₂₃×#95	C₂³	1	4	yes	—
154	C₂₃×#95	C₂³	1	4	yes	—
155	C₂₃×#95	C₂³	1	4	yes	—
156	C₂₃×#95	C₂³	1	4	yes	—
157	C₂₃×#95	C₂³	1	4	yes	—
158	C₂⁴×C₂₃	—	2	4	no	—
159	C₂⁴×C₂₃	—	4	2	no	—
160	C₂⁴×C₂₃	—	4	2	no	—
161	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
162	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
163	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
164	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
165	C₂×Q₈×C₂₃	—	2	4	no	—
166	C₂×Q₈×C₂₃	—	2	4	no	—
167	C₂×Q₈×C₂₃	—	2	2	no	—
168	C₂×Q₈×C₂₃	—	2	4	no	—
169	C₂×Q₈×C₂₃	—	2	4	no	—
170	C₂×Q₈×C₂₃	—	4	2	no	—
171	C₂×Q₈×C₂₃	—	4	2	no	—
172	C₂×Q₈×C₂₃	—	4	2	no	—
173	C₂×Q₈×C₂₃	—	4	16	no	—
174	C₂×D₄×C₂₃	—	2	4	no	—
175	C₂×D₄×C₂₃	—	2	8	no	—
176	C₂×D₄×C₂₃	—	2	4	no	—
177	C₂×D₄×C₂₃	—	2	4	no	—
178	C₂×D₄×C₂₃	—	2	2	no	—
179	C₂×D₄×C₂₃	—	4	4	no	—
180	C₂×D₄×C₂₃	—	4	2	no	—
181	C₂×D₄×C₂₃	—	4	4	no	—
182	C₂²×C₄×C₂₃	—	2	2	no	—
183	C₂²×C₄×C₂₃	—	2	4	no	—
184	C₂²×C₄×C₂₃	—	2	2	no	—
185	C₂²×C₄×C₂₃	—	2	2	no	—
186	C₂²×C₄×C₂₃	—	2	2	no	—
187	C₂²×C₄×C₂₃	—	2	8	no	—
188	C₂²×C₄×C₂₃	—	2	8	no	—
189	C₂²×C₄×C₂₃	—	2	4	no	—
190	C₂²×C₄×C₂₃	—	4	4	no	—
191	C₂²×C₄×C₂₃	—	4	2	no	—
192	C₂²×C₄×C₂₃	—	4	2	no	—
193	C₂²×C₄×C₂₃	—	4	2	no	—
194	C₂²×C₄×C₂₃	—	4	2	no	—
195	C₂²×C₄×C₂₃	—	4	2	no	—
196	C₂²×C₄×C₂₃	—	4	4	no	—
197	C₂²×C₄×C₂₃	—	4	16	no	—
198	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
212	C₄⋊C₄×C₂₃	—	2	8	no	—
213	C₄⋊C₄×C₂₃	—	2	4	no	—
214	C₄⋊C₄×C₂₃	—	2	4	no	—
215	C₄⋊C₄×C₂₃	—	2	8	no	—
216	C₄⋊C₄×C₂₃	—	2	4	no	—
217	C₄⋊C₄×C₂₃	—	2	4	no	—
218	C₄⋊C₄×C₂₃	—	2	2	no	—
219	C₄⋊C₄×C₂₃	—	2	2	no	—
220	C₄⋊C₄×C₂₃	—	2	8	no	—
221	C₄⋊C₄×C₂₃	—	4	4	no	—
222	C₄⋊C₄×C₂₃	—	4	4	no	—
223	C₄⋊C₄×C₂₃	—	4	4	no	—
224	C₄⋊C₄×C₂₃	—	4	4	no	—
225	C₂²⋊C₄×C₂₃	—	2	8	no	—
226	C₂²⋊C₄×C₂₃	—	2	4	no	—
227	C₂²⋊C₄×C₂₃	—	2	4	no	—
228	C₂²⋊C₄×C₂₃	—	2	4	no	—
229	C₂²⋊C₄×C₂₃	—	2	4	no	—
230	C₂²⋊C₄×C₂₃	—	2	4	no	—
231	C₂²⋊C₄×C₂₃	—	2	4	no	—
232	C₂²⋊C₄×C₂₃	—	2	4	no	—
233	C₂²⋊C₄×C₂₃	—	2	8	no	—
234	C₂²⋊C₄×C₂₃	—	4	4	no	—
235	C₂²⋊C₄×C₂₃	—	4	4	no	—
236	C₂²⋊C₄×C₂₃	—	4	4	no	—
237	C₂²⋊C₄×C₂₃	—	4	4	no	—
238	C₂²⋊C₄×C₂₃	—	4	4	no	—
239	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
240	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
241	C₄²×C₂₃	—	2	4	no	—
242	C₄²×C₂₃	—	4	2	no	—
243	C₄²×C₂₃	—	4	2	no	—
244	#36705	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂³×C₂₃	—	2	2	no	—
246	C₂³×C₂₃	—	2	2	no	—
247	C₂³×C₂₃	—	2	8	no	—
248	C₂³×C₂₃	—	2	4	no	—
249	C₂³×C₂₃	—	2	4	no	—
250	C₂³×C₂₃	—	2	4	no	—
251	C₂³×C₂₃	—	2	2	no	—
252	C₂³×C₂₃	—	2	4	no	—
253	C₂³×C₂₃	—	2	4	no	—
254	C₂³×C₂₃	—	2	4	no	—
255	C₂³×C₂₃	—	4	4	no	—
256	C₂³×C₂₃	—	4	4	no	—
257	C₂³×C₂₃	—	4	16	no	—
258	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
259	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
260	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	—
261	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
262	Q₈×C₂₃	—	4	8	no	—
263	Q₈×C₂₃	—	4	8	no	—
264	Q₈×C₂₃	—	8	2	no	—
265	D₄×C₂₃	—	4	8	no	—
266	D₄×C₂₃	—	8	2	no	—
267	D₄×C₂₃	—	8	4	no	—
268	D₄×C₂₃	—	8	4	no	—
269	C₂×C₄×C₂₃	—	2	8	no	—
270	C₂×C₄×C₂₃	—	2	2	no	—
271	C₂×C₄×C₂₃	—	2	2	no	—
272	C₂×C₄×C₂₃	—	2	2	no	—
273	C₂×C₄×C₂₃	—	2	2	no	—
274	C₂×C₄×C₂₃	—	2	4	no	—
275	C₂×C₄×C₂₃	—	2	2	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	2	no	—
278	C₂×C₄×C₂₃	—	2	2	no	—
279	C₂×C₄×C₂₃	—	2	2	no	—
280	C₂×C₄×C₂₃	—	2	2	no	—
281	C₂×C₄×C₂₃	—	2	4	no	—
282	C₂×C₄×C₂₃	—	2	4	no	—
283	C₂×C₄×C₂₃	—	2	2	no	—
284	C₂×C₄×C₂₃	—	2	4	no	—
285	C₂×C₄×C₂₃	—	2	4	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	4	no	—
288	C₂×C₄×C₂₃	—	2	4	no	—
289	C₂×C₄×C₂₃	—	2	4	no	—
290	C₂×C₄×C₂₃	—	2	4	no	—
291	C₂×C₄×C₂₃	—	2	2	no	—
292	C₂×C₄×C₂₃	—	2	4	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	4	no	—
295	C₂×C₄×C₂₃	—	4	4	no	—
296	C₂×C₄×C₂₃	—	4	4	no	—
297	C₂×C₄×C₂₃	—	4	16	no	—
298	C₂×C₄×C₂₃	—	4	4	no	—
299	C₂×C₄×C₂₃	—	4	4	no	—
300	C₂×C₄×C₂₃	—	4	4	no	—
301	C₂×C₄×C₂₃	—	8	4	no	—
302	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
303	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
306	C₂×#538	C₂×C₂₃	1	1	yes	characteristic
307	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
308	#2849	C₂×C₂₃	1	2	yes	complemented
309	#2689	C₂×C₂₃	1	4	yes	complemented
310	#2687	C₂×C₂₃	1	4	yes	complemented
311	#2674	C₂×C₂₃	1	4	yes	complemented
312	#2672	C₂×C₂₃	1	4	yes	complemented
313	#2622	C₂×C₂₃	1	2	yes	complemented
314	#2591	C₂×C₂₃	1	1	yes	characteristic, complemented
315	#2583	C₂×C₂₃	1	1	yes	characteristic, complemented
316	#2579	C₂×C₂₃	1	2	yes	complemented
317	#2487	C₂×C₂₃	1	2	yes	complemented
318	#2436	C₂×C₂₃	1	1	yes	characteristic, complemented
319	#2434	C₂×C₂₃	1	1	yes	characteristic, complemented
320	#2312	C₂×C₂₃	1	1	yes	characteristic, complemented
321	C₂²×C₂₃	—	2	2	no	—
322	C₂²×C₂₃	—	2	2	no	—
323	C₂²×C₂₃	—	2	8	no	—
324	C₂²×C₂₃	—	2	4	no	—
325	C₂²×C₂₃	—	2	4	no	—
326	C₂²×C₂₃	—	2	4	no	—
327	C₂²×C₂₃	—	4	16	no	—
328	C₂²×C₂₃	—	4	8	no	—
329	C₂²×C₂₃	—	4	2	no	—
330	C₂²×C₂₃	—	4	2	no	—
331	C₂²×C₂₃	—	4	2	no	—
332	C₂²×C₂₃	—	4	8	no	—
333	C₂²×C₂₃	#536	1	4	yes	—
334	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
335	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
336	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
337	C₂²×C₂₃	#585	1	2	yes	—
338	C₄×C₂₃	—	2	4	no	—
339	C₄×C₂₃	—	2	2	no	—
340	C₄×C₂₃	—	2	2	no	—
341	C₄×C₂₃	—	2	4	no	—
342	C₄×C₂₃	—	4	2	no	—
343	C₄×C₂₃	—	4	2	no	—
344	C₄×C₂₃	—	4	2	no	—
345	C₄×C₂₃	—	4	2	no	—
346	C₄×C₂₃	—	4	2	no	—
347	C₄×C₂₃	—	4	2	no	—
348	C₄×C₂₃	—	4	4	no	—
349	C₄×C₂₃	—	4	4	no	—
350	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
351	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
352	#538	—	2	8	no	—
353	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
354	C₂×#126	C₂²×C₂₃	1	2	yes	—
355	C₂×#124	C₂²×C₂₃	1	2	yes	—
356	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
357	C₂×#123	C₂²×C₂₃	1	2	yes	—
358	C₂×#123	C₂²×C₂₃	1	4	yes	—
359	C₂×C₂²⋊Q₈	—	2	8	no	—
360	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
361	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
362	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
363	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
364	C₂×#121	C₂²×C₂₃	1	2	yes	—
365	C₂×#120	C₂²×C₂₃	1	2	yes	—
366	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
367	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
368	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
369	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
370	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
371	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
372	#400	C₂²×C₂₃	1	2	yes	complemented
373	#400	C₂²×C₂₃	1	4	yes	complemented
374	#399	C₂²×C₂₃	1	4	yes	complemented
375	#398	C₂²×C₂₃	1	4	yes	complemented
376	#398	C₂²×C₂₃	1	2	yes	complemented
377	#397	C₂²×C₂₃	1	4	yes	—
378	#397	C₂²×C₂₃	1	4	yes	—
379	#396	C₂²×C₂₃	1	4	yes	complemented
380	#395	C₂²×C₂₃	1	2	yes	complemented
381	#395	C₂²×C₂₃	1	4	yes	complemented
382	#394	C₂²×C₂₃	1	4	yes	—
383	#394	C₂²×C₂₃	1	4	yes	—
384	#394	C₂²×C₂₃	1	2	yes	complemented
385	#393	C₂²×C₂₃	1	4	yes	complemented
386	#391	C₂²×C₂₃	1	2	yes	complemented
387	#391	C₂²×C₂₃	1	2	yes	complemented
388	#389	C₂²×C₂₃	1	4	yes	complemented
389	#389	C₂²×C₂₃	1	4	yes	complemented
390	#388	C₂²×C₂₃	1	4	yes	—
391	#388	C₂²×C₂₃	1	4	yes	—
392	#388	C₂²×C₂₃	1	4	yes	complemented
393	#387	C₂²×C₂₃	1	4	yes	complemented
394	#386	C₂²×C₂₃	1	2	yes	—
395	#386	C₂²×C₂₃	1	2	yes	—
396	#386	C₂²×C₂₃	1	2	yes	—
397	#386	C₂²×C₂₃	1	4	yes	—
398	#386	C₂²×C₂₃	1	2	yes	—
399	#385	C₂²×C₂₃	1	2	yes	—
400	#385	C₂²×C₂₃	1	2	yes	—
401	#385	C₂²×C₂₃	1	2	yes	—
402	#385	C₂²×C₂₃	1	4	yes	—
403	#385	C₂²×C₂₃	1	2	yes	—
404	#385	C₂²×C₂₃	1	4	yes	complemented
405	#381	C₂²×C₂₃	1	4	yes	—
406	#380	C₂²×C₂₃	1	2	yes	—
407	#380	C₂²×C₂₃	1	4	yes	complemented
408	#379	C₂²×C₂₃	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×C₂₃	—	2	4	no	—
412	C₂×C₂₃	—	4	4	no	—
413	C₂×C₂₃	—	8	2	no	—
414	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
415	C₂×C₂₃	#3484	1	1	yes	characteristic
416	C₂×C₂₃	#3485	1	1	yes	characteristic
417	C₂×C₂₃	#3541	1	4	yes	—
418	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
419	C₂²×Q₈	—	2	4	no	—
420	C₂²×Q₈	—	4	4	no	—
421	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
422	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
423	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
424	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
425	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
426	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
427	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
428	C₂³×C₄	—	2	4	no	—
429	C₂³×C₄	—	4	4	no	—
430	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
432	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
436	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
438	C₄⋊Q₈	—	4	4	no	—
439	#126	—	2	8	no	—
440	#124	—	2	8	no	—
441	#124	—	4	4	no	—
442	#123	—	2	8	no	—
443	#123	—	4	8	no	—
444	C₂²⋊Q₈	—	2	4	no	—
445	C₂²⋊Q₈	—	2	16	no	—
446	C₂²⋊Q₈	—	2	16	no	—
447	#121	—	2	4	no	—
448	#121	—	2	8	no	—
449	#120	—	2	8	no	—
450	C₄×D₄	—	2	8	no	—
451	C₂×C₄⋊C₄	—	2	4	no	—
452	C₂×C₄⋊C₄	—	2	4	no	—
453	C₂×C₄⋊C₄	—	2	4	no	—
454	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
467	C₂×C₂²⋊C₄	—	2	4	no	—
468	C₂×C₂²⋊C₄	D₄×C₂₃	1	8	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
485	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
486	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
487	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
488	#95	C₂³×C₂₃	1	2	yes	—
489	#95	C₂³×C₂₃	1	2	yes	—
490	#95	C₂³×C₂₃	1	4	yes	—
491	#95	C₂³×C₂₃	1	4	yes	—
492	#95	C₂³×C₂₃	1	4	yes	—
493	#95	C₂³×C₂₃	1	4	yes	—
494	#95	C₂³×C₂₃	1	4	yes	—
495	#95	C₂³×C₂₃	1	4	yes	—
496	#95	C₂³×C₂₃	1	4	yes	—
497	#95	C₂³×C₂₃	1	4	yes	—
498	#95	C₂³×C₂₃	1	4	yes	—
499	C₂₃	#36705	1	1	yes	characteristic, direct product factor, Sylow
500	C₂⁴	—	2	4	no	—
501	C₂⁴	—	4	2	no	—
502	C₂⁴	—	4	2	no	—
503	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
504	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
505	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
506	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
507	C₂×Q₈	—	2	4	no	—
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	4	no	—
511	C₂×Q₈	—	2	4	no	—
512	C₂×Q₈	—	4	2	no	—
513	C₂×Q₈	—	4	2	no	—
514	C₂×Q₈	—	4	2	no	—
515	C₂×Q₈	—	4	16	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	8	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	4	4	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	4	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	8	no	—
530	C₂²×C₄	—	2	8	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	4	4	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	4	no	—
539	C₂²×C₄	—	4	16	no	—
540	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
541	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	8	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	4	4	no	—
564	C₄⋊C₄	—	4	4	no	—
565	C₄⋊C₄	—	4	4	no	—
566	C₄⋊C₄	—	4	4	no	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	8	no	—
576	C₂²⋊C₄	—	4	4	no	—
577	C₂²⋊C₄	—	4	4	no	—
578	C₂²⋊C₄	—	4	4	no	—
579	C₂²⋊C₄	—	4	4	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
582	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
583	C₄²	—	2	4	no	—
584	C₄²	—	4	2	no	—
585	C₄²	—	4	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	4	no	—
589	C₂³	—	2	4	no	—
590	C₂³	—	2	4	no	—
591	C₂³	—	2	8	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	4	no	—
594	C₂³	—	2	4	no	—
595	C₂³	—	2	4	no	—
596	C₂³	—	4	4	no	—
597	C₂³	—	4	4	no	—
598	C₂³	—	4	16	no	—
599	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
600	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
601	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	—
602	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
603	Q₈	—	4	8	no	—
604	Q₈	—	4	8	no	—
605	Q₈	—	8	2	no	—
606	D₄	—	4	8	no	—
607	D₄	—	8	2	no	—
608	D₄	—	8	4	no	—
609	D₄	—	8	4	no	—
610	C₂×C₄	—	2	8	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	16	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	8	4	no	—
643	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
644	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
645	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
646	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	8	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	4	no	—
653	C₂²	—	4	16	no	—
654	C₂²	—	4	8	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	8	no	—
659	C₂²	C₂₃×#536	1	4	yes	—
660	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
661	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
662	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
663	C₂²	C₂₃×#585	1	2	yes	—
664	C₄	—	2	4	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	4	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	4	no	—
675	C₄	—	4	4	no	—
676	C₂	—	2	4	no	—
677	C₂	—	4	4	no	—
678	C₂	—	8	2	no	—
679	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
680	C₂	C₂₃×#3484	1	1	yes	characteristic
681	C₂	C₂₃×#3485	1	1	yes	characteristic
682	C₂	C₂₃×#3541	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#538	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂₃×C₂²⋊Q₈	C₂	semidirect
3. C₂₃×#2849	C₂	semidirect
4. C₂₃×#2689	C₂	semidirect
5. C₂₃×#2687	C₂	semidirect
6. C₂₃×#2674	C₂	semidirect
7. C₂₃×#2672	C₂	semidirect
8. C₂₃×#2622	C₂	semidirect
9. C₂₃×#2591	C₂	semidirect
10. C₂₃×#2583	C₂	semidirect
11. C₂₃×#2579	C₂	semidirect
12. C₂₃×#2487	C₂	semidirect
13. C₂₃×#2436	C₂	semidirect
14. C₂₃×#2434	C₂	semidirect
15. C₂₃×#2312	C₂	semidirect
19. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₂₃×#124	C₂²	semidirect
38. C₂₃×#400	C₂²	semidirect
39. C₂₃×#400	C₂²	semidirect
40. C₂₃×#399	C₂²	semidirect
41. C₂₃×#398	C₂²	semidirect
42. C₂₃×#398	C₂²	semidirect
45. C₂₃×#396	C₂²	semidirect
46. C₂₃×#395	C₂²	semidirect
47. C₂₃×#395	C₂²	semidirect
50. C₂₃×#394	C₂²	semidirect
51. C₂₃×#393	C₂²	semidirect
52. C₂₃×#391	C₂²	semidirect
53. C₂₃×#391	C₂²	semidirect
54. C₂₃×#389	C₂²	semidirect
55. C₂₃×#389	C₂²	semidirect
58. C₂₃×#388	C₂²	semidirect
59. C₂₃×#387	C₂²	semidirect
70. C₂₃×#385	C₂²	semidirect
73. C₂₃×#380	C₂²	semidirect
244. #36705	C₂₃	direct (N × H)
307. C₂²×C₂²⋊Q₈	C₂×C₂₃	semidirect
308. #2849	C₂×C₂₃	semidirect
309. #2689	C₂×C₂₃	semidirect
310. #2687	C₂×C₂₃	semidirect
311. #2674	C₂×C₂₃	semidirect
312. #2672	C₂×C₂₃	semidirect
313. #2622	C₂×C₂₃	semidirect
314. #2591	C₂×C₂₃	semidirect
315. #2583	C₂×C₂₃	semidirect
316. #2579	C₂×C₂₃	semidirect
317. #2487	C₂×C₂₃	semidirect
318. #2436	C₂×C₂₃	semidirect
319. #2434	C₂×C₂₃	semidirect
320. #2312	C₂×C₂₃	semidirect
353. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
356. C₂×#124	C₂²×C₂₃	semidirect
372. #400	C₂²×C₂₃	semidirect
373. #400	C₂²×C₂₃	semidirect
374. #399	C₂²×C₂₃	semidirect
375. #398	C₂²×C₂₃	semidirect
376. #398	C₂²×C₂₃	semidirect
379. #396	C₂²×C₂₃	semidirect
380. #395	C₂²×C₂₃	semidirect
381. #395	C₂²×C₂₃	semidirect
384. #394	C₂²×C₂₃	semidirect
385. #393	C₂²×C₂₃	semidirect
386. #391	C₂²×C₂₃	semidirect
387. #391	C₂²×C₂₃	semidirect
388. #389	C₂²×C₂₃	semidirect
389. #389	C₂²×C₂₃	semidirect
392. #388	C₂²×C₂₃	semidirect
393. #387	C₂²×C₂₃	semidirect
404. #385	C₂²×C₂₃	semidirect
407. #380	C₂²×C₂₃	semidirect
499. C₂₃	#36705	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×#538	2
C₂²×C₂₃×C₂²⋊Q₈	2
C₂₃×#2849	2
C₂₃×#2689	2
C₂₃×#2687	2
C₂₃×#2674	2
C₂₃×#2672	2
C₂₃×#2622	2
C₂₃×#2591	2
C₂₃×#2583	2
C₂₃×#2579	2
C₂₃×#2487	2
C₂₃×#2436	2
C₂₃×#2434	2
C₂₃×#2312	2
#36705	23

Subgroups — C23×#36705 #19184331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36705 #19184331