Subgroups — C₂₃×#34386 #19182012

Order 5888.

2614 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2377	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2358	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2353	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2349	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2343	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2339	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2329	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2325	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2322	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2319	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2318	C₂	1	2	yes	maximal, complemented
14	C₂×C₂₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#525	C₄	1	16	yes	complemented
19	C₂×C₂₃×#123	C₂²	1	2	yes	—
20	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#120	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
29	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
33	C₂₃×#391	C₂²	1	4	yes	complemented
34	C₂₃×#390	C₂²	1	4	yes	—
35	C₂₃×#389	C₂²	1	4	yes	complemented
36	C₂₃×#389	C₂²	1	4	yes	complemented
37	C₂₃×#388	C₂²	1	4	yes	—
38	C₂₃×#388	C₂²	1	4	yes	—
39	C₂₃×#388	C₂²	1	4	yes	complemented
40	C₂₃×#388	C₂²	1	4	yes	complemented
41	C₂₃×#387	C₂²	1	4	yes	complemented
42	C₂₃×#387	C₂²	1	4	yes	complemented
43	C₂₃×#387	C₂²	1	4	yes	complemented
44	C₂₃×#387	C₂²	1	4	yes	complemented
45	C₂₃×#386	C₂²	1	4	yes	—
46	C₂₃×#386	C₂²	1	4	yes	—
47	C₂₃×#386	C₂²	1	4	yes	—
48	C₂₃×#386	C₂²	1	4	yes	complemented
49	C₂₃×#385	C₂²	1	4	yes	—
50	C₂₃×#385	C₂²	1	4	yes	—
51	C₂₃×#385	C₂²	1	4	yes	complemented
52	C₂₃×#385	C₂²	1	4	yes	complemented
53	C₂₃×#383	C₂²	1	2	yes	complemented
54	C₂₃×#382	C₂²	1	2	yes	complemented
55	C₂₃×#381	C₂²	1	2	yes	—
56	C₂₃×#381	C₂²	1	2	yes	—
57	C₂₃×#381	C₂²	1	2	yes	—
58	C₂₃×#381	C₂²	1	2	yes	—
59	C₂₃×#381	C₂²	1	2	yes	complemented
60	C₂₃×#380	C₂²	1	1	yes	characteristic
61	C₂₃×#380	C₂²	1	1	yes	characteristic
62	C₂₃×#380	C₂²	1	2	yes	—
63	C₂₃×#380	C₂²	1	2	yes	—
64	C₂₃×#380	C₂²	1	2	yes	—
65	C₂₃×#380	C₂²	1	2	yes	complemented
66	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
68	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
69	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
70	C₂₃×#376	C₂²	1	2	yes	complemented
71	C₂×C₂₃×#95	C₂²	1	2	yes	—
72	C₂×C₂₃×#95	C₂²	1	2	yes	—
73	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
76	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×#41×C₂₃	—	4	4	no	—
78	C₂×#41×C₂₃	C₂×C₄	1	8	yes	complemented
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₂₃	—	4	4	no	—
85	C₂³×C₄×C₂₃	C₂×C₄	1	8	yes	complemented
86	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
92	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
97	C₂₃×#123	C₂×C₄	1	16	yes	complemented
98	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
99	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
100	C₂₃×#121	C₂×C₄	1	8	yes	complemented
101	C₂₃×#121	C₂×C₄	1	8	yes	complemented
102	C₂₃×#120	C₂×C₄	1	16	yes	complemented
103	C₄×D₄×C₂₃	—	4	8	no	—
104	C₄×D₄×C₂₃	—	4	8	no	—
105	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
106	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
107	C₂₃×#117	C₂×C₄	1	8	yes	complemented
108	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
109	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
120	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
121	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	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	2	yes	—
134	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
138	C₂₃×#95	C₂³	1	2	yes	—
139	C₂₃×#95	C₂³	1	2	yes	—
140	C₂₃×#95	C₂³	1	2	yes	—
141	C₂₃×#95	C₂³	1	2	yes	—
142	C₂₃×#95	C₂³	1	4	yes	—
143	C₂₃×#95	C₂³	1	2	yes	—
144	C₂₃×#95	C₂³	1	4	yes	—
145	C₂₃×#95	C₂³	1	4	yes	—
146	C₂₃×#95	C₂³	1	2	yes	—
147	C₂₃×#95	C₂³	1	4	yes	—
148	C₂₃×#95	C₂³	1	4	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	C₂⁴×C₂₃	—	2	2	no	—
154	C₂⁴×C₂₃	—	2	4	no	—
155	C₂⁴×C₂₃	—	2	2	no	—
156	C₂⁴×C₂₃	—	4	2	no	—
157	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
158	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
159	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
160	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
161	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
162	#41×C₂₃	—	4	16	no	—
163	C₂×Q₈×C₂₃	—	4	2	no	—
164	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
165	C₂×D₄×C₂₃	—	2	4	no	—
166	C₂×D₄×C₂₃	—	2	8	no	—
167	C₂×D₄×C₂₃	—	2	4	no	—
168	C₂×D₄×C₂₃	—	4	4	no	—
169	C₂×D₄×C₂₃	—	4	2	no	—
170	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
173	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₂₃	—	2	4	no	—
175	C₂²×C₄×C₂₃	—	2	4	no	—
176	C₂²×C₄×C₂₃	—	2	8	no	—
177	C₂²×C₄×C₂₃	—	2	4	no	—
178	C₂²×C₄×C₂₃	—	2	4	no	—
179	C₂²×C₄×C₂₃	—	4	16	no	—
180	C₂²×C₄×C₂₃	—	4	2	no	—
181	C₂²×C₄×C₂₃	—	4	2	no	—
182	C₂²×C₄×C₂₃	—	4	2	no	—
183	C₂²×C₄×C₂₃	—	4	2	no	—
184	C₂²×C₄×C₂₃	—	4	4	no	—
185	C₂²×C₄×C₂₃	—	4	2	no	—
186	C₂²×C₄×C₂₃	—	4	4	no	—
187	C₂²×C₄×C₂₃	—	4	2	no	—
188	C₂²×C₄×C₂₃	—	4	4	no	—
189	C₂²×C₄×C₂₃	—	4	4	no	—
190	C₂²×C₄×C₂₃	—	4	2	no	—
191	C₂²×C₄×C₂₃	—	4	4	no	—
192	C₂²×C₄×C₂₃	—	4	4	no	—
193	C₂²×C₄×C₂₃	—	4	2	no	—
194	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
199	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
200	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₂₃	C₂⁴	1	4	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	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
212	C₄⋊C₄×C₂₃	—	4	2	no	—
213	C₄⋊C₄×C₂₃	—	4	4	no	—
214	C₄⋊C₄×C₂₃	—	4	2	no	—
215	C₄⋊C₄×C₂₃	—	4	4	no	—
216	C₄⋊C₄×C₂₃	—	4	4	no	—
217	C₄⋊C₄×C₂₃	—	4	4	no	—
218	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
219	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
221	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₂₃	—	2	8	no	—
223	C₂²⋊C₄×C₂₃	—	2	8	no	—
224	C₂²⋊C₄×C₂₃	—	4	2	no	—
225	C₂²⋊C₄×C₂₃	—	4	4	no	—
226	C₂²⋊C₄×C₂₃	—	4	2	no	—
227	C₂²⋊C₄×C₂₃	—	4	4	no	—
228	C₂²⋊C₄×C₂₃	—	4	4	no	—
229	C₂²⋊C₄×C₂₃	—	4	4	no	—
230	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
231	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
232	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
233	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
234	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
235	C₄²×C₂₃	—	4	4	no	—
236	C₄²×C₂₃	—	4	4	no	—
237	C₄²×C₂₃	—	4	4	no	—
238	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
239	#34386	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₂₃	—	2	2	no	—
241	C₂³×C₂₃	—	2	1	no	—
242	C₂³×C₂₃	—	2	1	no	—
243	C₂³×C₂₃	—	2	2	no	—
244	C₂³×C₂₃	—	2	2	no	—
245	C₂³×C₂₃	—	2	8	no	—
246	C₂³×C₂₃	—	2	8	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	2	no	—
249	C₂³×C₂₃	—	2	2	no	—
250	C₂³×C₂₃	—	2	4	no	—
251	C₂³×C₂₃	—	2	2	no	—
252	C₂³×C₂₃	—	2	1	no	—
253	C₂³×C₂₃	—	2	4	no	—
254	C₂³×C₂₃	—	2	2	no	—
255	C₂³×C₂₃	—	4	4	no	—
256	C₂³×C₂₃	—	4	8	no	—
257	C₂³×C₂₃	—	4	8	no	—
258	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
259	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
260	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
261	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
262	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
263	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
264	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
265	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
266	Q₈×C₂₃	—	4	4	no	—
267	D₄×C₂₃	—	2	16	no	—
268	D₄×C₂₃	—	2	16	no	—
269	D₄×C₂₃	—	4	8	no	—
270	D₄×C₂₃	—	4	4	no	—
271	C₂×C₄×C₂₃	—	2	8	no	—
272	C₂×C₄×C₂₃	—	2	8	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	4	no	—
281	C₂×C₄×C₂₃	—	2	4	no	—
282	C₂×C₄×C₂₃	—	2	4	no	—
283	C₂×C₄×C₂₃	—	2	4	no	—
284	C₂×C₄×C₂₃	—	2	4	no	—
285	C₂×C₄×C₂₃	—	2	4	no	—
286	C₂×C₄×C₂₃	—	2	4	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	4	no	—
292	C₂×C₄×C₂₃	—	2	4	no	—
293	C₂×C₄×C₂₃	—	4	4	no	—
294	C₂×C₄×C₂₃	—	4	4	no	—
295	C₂×C₄×C₂₃	—	4	4	no	—
296	C₂×C₄×C₂₃	—	4	4	no	—
297	C₂×C₄×C₂₃	—	4	8	no	—
298	C₂×C₄×C₂₃	—	8	8	no	—
299	C₂×C₄×C₂₃	—	8	4	no	—
300	C₂×C₄×C₂₃	—	8	4	no	—
301	C₂×C₄×C₂₃	—	8	8	no	—
302	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
303	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
305	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
307	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
309	C₂×#525	C₂×C₂₃	1	1	yes	characteristic
310	#2378	C₂×C₂₃	1	2	yes	complemented
311	#2377	C₂×C₂₃	1	2	yes	complemented
312	#2358	C₂×C₂₃	1	4	yes	complemented
313	#2353	C₂×C₂₃	1	2	yes	complemented
314	#2349	C₂×C₂₃	1	2	yes	complemented
315	#2343	C₂×C₂₃	1	2	yes	complemented
316	#2339	C₂×C₂₃	1	2	yes	complemented
317	#2329	C₂×C₂₃	1	2	yes	complemented
318	#2325	C₂×C₂₃	1	2	yes	complemented
319	#2322	C₂×C₂₃	1	4	yes	complemented
320	#2319	C₂×C₂₃	1	2	yes	complemented
321	#2318	C₂×C₂₃	1	2	yes	complemented
322	C₂×#381	C₂×C₂₃	1	1	yes	characteristic, complemented
323	C₂×#380	C₂×C₂₃	1	1	yes	characteristic, complemented
324	C₂²×C₂₃	—	2	2	no	—
325	C₂²×C₂₃	—	2	2	no	—
326	C₂²×C₂₃	—	2	2	no	—
327	C₂²×C₂₃	—	2	2	no	—
328	C₂²×C₂₃	—	2	4	no	—
329	C₂²×C₂₃	—	2	4	no	—
330	C₂²×C₂₃	—	2	4	no	—
331	C₂²×C₂₃	—	2	4	no	—
332	C₂²×C₂₃	—	2	2	no	—
333	C₂²×C₂₃	—	2	4	no	—
334	C₂²×C₂₃	—	2	4	no	—
335	C₂²×C₂₃	—	2	2	no	—
336	C₂²×C₂₃	—	2	2	no	—
337	C₂²×C₂₃	—	2	4	no	—
338	C₂²×C₂₃	—	4	16	no	—
339	C₂²×C₂₃	—	4	4	no	—
340	C₂²×C₂₃	—	4	2	no	—
341	C₂²×C₂₃	—	4	4	no	—
342	C₂²×C₂₃	—	4	2	no	—
343	C₂²×C₂₃	#518	1	4	yes	—
344	C₂²×C₂₃	#520	1	4	yes	—
345	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
346	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
347	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
349	C₂²×C₂₃	#585	1	2	yes	—
350	C₄×C₂₃	—	2	2	no	—
351	C₄×C₂₃	—	2	2	no	—
352	C₄×C₂₃	—	2	2	no	—
353	C₄×C₂₃	—	2	2	no	—
354	C₄×C₂₃	—	2	4	no	—
355	C₄×C₂₃	—	2	4	no	—
356	C₄×C₂₃	—	2	4	no	—
357	C₄×C₂₃	—	4	4	no	—
358	C₄×C₂₃	—	4	4	no	—
359	C₄×C₂₃	—	4	4	no	—
360	C₄×C₂₃	—	4	4	no	—
361	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
362	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
363	#525	C₄×C₂₃	1	16	yes	complemented
364	C₂×#123	C₂²×C₂₃	1	2	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
366	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
367	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
368	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
369	C₂×#120	C₂²×C₂₃	1	2	yes	—
370	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
371	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
372	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
374	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
375	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
376	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
377	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
378	#391	C₂²×C₂₃	1	4	yes	complemented
379	#390	C₂²×C₂₃	1	4	yes	—
380	#389	C₂²×C₂₃	1	4	yes	complemented
381	#389	C₂²×C₂₃	1	4	yes	complemented
382	#388	C₂²×C₂₃	1	4	yes	—
383	#388	C₂²×C₂₃	1	4	yes	—
384	#388	C₂²×C₂₃	1	4	yes	complemented
385	#388	C₂²×C₂₃	1	4	yes	complemented
386	#387	C₂²×C₂₃	1	4	yes	complemented
387	#387	C₂²×C₂₃	1	4	yes	complemented
388	#387	C₂²×C₂₃	1	4	yes	complemented
389	#387	C₂²×C₂₃	1	4	yes	complemented
390	#386	C₂²×C₂₃	1	4	yes	—
391	#386	C₂²×C₂₃	1	4	yes	—
392	#386	C₂²×C₂₃	1	4	yes	—
393	#386	C₂²×C₂₃	1	4	yes	complemented
394	#385	C₂²×C₂₃	1	4	yes	—
395	#385	C₂²×C₂₃	1	4	yes	—
396	#385	C₂²×C₂₃	1	4	yes	complemented
397	#385	C₂²×C₂₃	1	4	yes	complemented
398	#383	C₂²×C₂₃	1	2	yes	complemented
399	#382	C₂²×C₂₃	1	2	yes	complemented
400	#381	C₂²×C₂₃	1	2	yes	—
401	#381	C₂²×C₂₃	1	2	yes	—
402	#381	C₂²×C₂₃	1	2	yes	—
403	#381	C₂²×C₂₃	1	2	yes	—
404	#381	C₂²×C₂₃	1	2	yes	complemented
405	#380	C₂²×C₂₃	1	1	yes	characteristic
406	#380	C₂²×C₂₃	1	1	yes	characteristic
407	#380	C₂²×C₂₃	1	2	yes	—
408	#380	C₂²×C₂₃	1	2	yes	—
409	#380	C₂²×C₂₃	1	2	yes	—
410	#380	C₂²×C₂₃	1	2	yes	complemented
411	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
412	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
415	#376	C₂²×C₂₃	1	2	yes	complemented
416	C₂×#95	C₂²×C₂₃	1	2	yes	—
417	C₂×#95	C₂²×C₂₃	1	2	yes	—
418	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
421	C₂×C₂₃	—	2	4	no	—
422	C₂×C₂₃	—	2	4	no	—
423	C₂×C₂₃	—	4	4	no	—
424	C₂×C₂₃	—	4	2	no	—
425	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
426	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
427	C₂×C₂₃	#3428	1	1	yes	characteristic
428	C₂×C₂₃	#3534	1	2	yes	—
429	C₂×C₂₃	#3535	1	2	yes	—
430	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
431	C₂×#41	—	4	4	no	—
432	C₂×#41	C₂×C₄×C₂₃	1	8	yes	complemented
433	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
434	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
435	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
436	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
437	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
438	C₂³×C₄	—	4	4	no	—
439	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	complemented
440	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
443	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
444	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
445	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
446	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
449	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
451	#123	C₂×C₄×C₂₃	1	16	yes	complemented
452	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
453	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
454	#121	C₂×C₄×C₂₃	1	8	yes	complemented
455	#121	C₂×C₄×C₂₃	1	8	yes	complemented
456	#120	C₂×C₄×C₂₃	1	16	yes	complemented
457	C₄×D₄	—	4	8	no	—
458	C₄×D₄	—	4	8	no	—
459	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
460	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
461	#117	C₂×C₄×C₂₃	1	8	yes	complemented
462	C₂×C₄⋊C₄	—	4	4	no	—
463	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
473	C₂×C₂²⋊C₄	—	4	4	no	—
474	C₂×C₂²⋊C₄	—	4	4	no	—
475	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	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×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
488	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
489	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
490	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
491	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
492	#95	C₂³×C₂₃	1	2	yes	—
493	#95	C₂³×C₂₃	1	2	yes	—
494	#95	C₂³×C₂₃	1	2	yes	—
495	#95	C₂³×C₂₃	1	2	yes	—
496	#95	C₂³×C₂₃	1	4	yes	—
497	#95	C₂³×C₂₃	1	2	yes	—
498	#95	C₂³×C₂₃	1	4	yes	—
499	#95	C₂³×C₂₃	1	4	yes	—
500	#95	C₂³×C₂₃	1	2	yes	—
501	#95	C₂³×C₂₃	1	4	yes	—
502	#95	C₂³×C₂₃	1	4	yes	—
503	#95	C₂³×C₂₃	1	4	yes	—
504	#95	C₂³×C₂₃	1	4	yes	—
505	#95	C₂³×C₂₃	1	4	yes	—
506	#95	C₂³×C₂₃	1	4	yes	—
507	C₂₃	#34386	1	1	yes	characteristic, direct product factor, Sylow
508	C₂⁴	—	2	2	no	—
509	C₂⁴	—	2	4	no	—
510	C₂⁴	—	2	2	no	—
511	C₂⁴	—	4	2	no	—
512	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
513	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
514	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
515	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
516	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
517	#41	—	4	16	no	—
518	C₂×Q₈	—	4	2	no	—
519	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	8	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
526	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
527	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
528	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	8	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	4	16	no	—
535	C₂²×C₄	—	4	2	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	4	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
550	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
551	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
552	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
553	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
554	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
555	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
556	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
558	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
559	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
565	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	4	4	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	4	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
575	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
576	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	4	4	no	—
584	C₂²⋊C₄	—	4	4	no	—
585	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
589	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
590	C₄²	—	4	4	no	—
591	C₄²	—	4	4	no	—
592	C₄²	—	4	4	no	—
593	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	8	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	4	4	no	—
610	C₂³	—	4	8	no	—
611	C₂³	—	4	8	no	—
612	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
613	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
614	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
615	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
616	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
617	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
618	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
619	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
620	Q₈	—	4	4	no	—
621	D₄	—	2	16	no	—
622	D₄	—	2	16	no	—
623	D₄	—	4	4	no	—
624	D₄	—	4	8	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	8	no	—
634	C₂×C₄	—	2	8	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	4	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	8	no	—
652	C₂×C₄	—	8	4	no	—
653	C₂×C₄	—	8	8	no	—
654	C₂×C₄	—	8	4	no	—
655	C₂×C₄	—	8	8	no	—
656	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
657	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
658	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
659	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
660	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
661	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
662	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	4	16	no	—
678	C₂²	—	4	4	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	4	no	—
682	C₂²	C₂₃×#518	1	4	yes	—
683	C₂²	C₂₃×#520	1	4	yes	—
684	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
685	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
686	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
688	C₂²	C₂₃×#585	1	2	yes	—
689	C₄	—	2	2	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	2	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	4	no	—
694	C₄	—	2	4	no	—
695	C₄	—	2	4	no	—
696	C₄	—	4	4	no	—
697	C₄	—	4	4	no	—
698	C₄	—	4	4	no	—
699	C₄	—	4	4	no	—
700	C₂	—	2	4	no	—
701	C₂	—	2	4	no	—
702	C₂	—	4	2	no	—
703	C₂	—	4	4	no	—
704	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
705	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
706	C₂	C₂₃×#3428	1	1	yes	characteristic
707	C₂	C₂₃×#3534	1	2	yes	—
708	C₂	C₂₃×#3535	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2378	C₂	semidirect
3. C₂₃×#2377	C₂	semidirect
4. C₂₃×#2358	C₂	semidirect
5. C₂₃×#2353	C₂	semidirect
6. C₂₃×#2349	C₂	semidirect
7. C₂₃×#2343	C₂	semidirect
8. C₂₃×#2339	C₂	semidirect
9. C₂₃×#2329	C₂	semidirect
10. C₂₃×#2325	C₂	semidirect
11. C₂₃×#2322	C₂	semidirect
12. C₂₃×#2319	C₂	semidirect
13. C₂₃×#2318	C₂	semidirect
14. C₂×C₂₃×#381	C₂	semidirect
15. C₂×C₂₃×#380	C₂	semidirect
18. C₂₃×#525	C₄	semidirect
33. C₂₃×#391	C₂²	semidirect
35. C₂₃×#389	C₂²	semidirect
36. C₂₃×#389	C₂²	semidirect
39. C₂₃×#388	C₂²	semidirect
40. C₂₃×#388	C₂²	semidirect
41. C₂₃×#387	C₂²	semidirect
42. C₂₃×#387	C₂²	semidirect
43. C₂₃×#387	C₂²	semidirect
44. C₂₃×#387	C₂²	semidirect
48. C₂₃×#386	C₂²	semidirect
51. C₂₃×#385	C₂²	semidirect
52. C₂₃×#385	C₂²	semidirect
53. C₂₃×#383	C₂²	semidirect
54. C₂₃×#382	C₂²	semidirect
59. C₂₃×#381	C₂²	semidirect
65. C₂₃×#380	C₂²	semidirect
66. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
69. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
70. C₂₃×#376	C₂²	semidirect
75. C₂×C₂₃×#95	C₂²	semidirect
78. C₂×#41×C₂₃	C₂×C₄	semidirect
85. C₂³×C₄×C₂₃	C₂×C₄	semidirect
97. C₂₃×#123	C₂×C₄	semidirect
98. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
100. C₂₃×#121	C₂×C₄	semidirect
101. C₂₃×#121	C₂×C₄	semidirect
102. C₂₃×#120	C₂×C₄	semidirect
105. C₄×D₄×C₂₃	C₂×C₄	semidirect
106. C₄×D₄×C₂₃	C₂×C₄	semidirect
107. C₂₃×#117	C₂×C₄	semidirect
239. #34386	C₂₃	direct (N × H)
310. #2378	C₂×C₂₃	semidirect
311. #2377	C₂×C₂₃	semidirect
312. #2358	C₂×C₂₃	semidirect
313. #2353	C₂×C₂₃	semidirect
314. #2349	C₂×C₂₃	semidirect
315. #2343	C₂×C₂₃	semidirect
316. #2339	C₂×C₂₃	semidirect
317. #2329	C₂×C₂₃	semidirect
318. #2325	C₂×C₂₃	semidirect
319. #2322	C₂×C₂₃	semidirect
320. #2319	C₂×C₂₃	semidirect
321. #2318	C₂×C₂₃	semidirect
322. C₂×#381	C₂×C₂₃	semidirect
323. C₂×#380	C₂×C₂₃	semidirect
363. #525	C₄×C₂₃	semidirect
378. #391	C₂²×C₂₃	semidirect
380. #389	C₂²×C₂₃	semidirect
381. #389	C₂²×C₂₃	semidirect
384. #388	C₂²×C₂₃	semidirect
385. #388	C₂²×C₂₃	semidirect
386. #387	C₂²×C₂₃	semidirect
387. #387	C₂²×C₂₃	semidirect
388. #387	C₂²×C₂₃	semidirect
389. #387	C₂²×C₂₃	semidirect
393. #386	C₂²×C₂₃	semidirect
396. #385	C₂²×C₂₃	semidirect
397. #385	C₂²×C₂₃	semidirect
398. #383	C₂²×C₂₃	semidirect
399. #382	C₂²×C₂₃	semidirect
404. #381	C₂²×C₂₃	semidirect
410. #380	C₂²×C₂₃	semidirect
411. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
414. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
415. #376	C₂²×C₂₃	semidirect
420. C₂×#95	C₂²×C₂₃	semidirect
432. C₂×#41	C₂×C₄×C₂₃	semidirect
439. C₂³×C₄	C₂×C₄×C₂₃	semidirect
451. #123	C₂×C₄×C₂₃	semidirect
452. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
453. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
454. #121	C₂×C₄×C₂₃	semidirect
455. #121	C₂×C₄×C₂₃	semidirect
456. #120	C₂×C₄×C₂₃	semidirect
459. C₄×D₄	C₂×C₄×C₂₃	semidirect
460. C₄×D₄	C₂×C₄×C₂₃	semidirect
461. #117	C₂×C₄×C₂₃	semidirect
507. C₂₃	#34386	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×#525	2
C₂₃×#2378	2
C₂₃×#2377	2
C₂₃×#2358	2
C₂₃×#2353	2
C₂₃×#2349	2
C₂₃×#2343	2
C₂₃×#2339	2
C₂₃×#2329	2
C₂₃×#2325	2
C₂₃×#2322	2
C₂₃×#2319	2
C₂₃×#2318	2
C₂×C₂₃×#381	2
C₂×C₂₃×#380	2
#34386	23

Subgroups — C23×#34386 #19182012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34386 #19182012