Subgroups — C₂₃×#34362 #19181988

Order 5888.

2586 conjugacy classes of subgroups.

The subgroup lattice has 724 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×#2368	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2364	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2354	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2352	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2352	C₂	1	2	yes	maximal, complemented
9	D₄×C₄⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2335	C₂	1	4	yes	maximal, complemented
11	C₂₃×#2321	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2314	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2311	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2280	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	2	yes	—
27	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
28	C₂×C₂₃×#117	C₂²	1	2	yes	—
29	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
31	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
34	C₂₃×#391	C₂²	1	4	yes	complemented
35	C₂₃×#390	C₂²	1	4	yes	—
36	C₂₃×#390	C₂²	1	4	yes	—
37	C₂₃×#389	C₂²	1	4	yes	complemented
38	C₂₃×#388	C₂²	1	4	yes	—
39	C₂₃×#388	C₂²	1	4	yes	—
40	C₂₃×#388	C₂²	1	4	yes	—
41	C₂₃×#388	C₂²	1	4	yes	—
42	C₂₃×#388	C₂²	1	4	yes	complemented
43	C₂₃×#388	C₂²	1	4	yes	complemented
44	C₂₃×#387	C₂²	1	4	yes	complemented
45	C₂₃×#387	C₂²	1	4	yes	complemented
46	C₂₃×#387	C₂²	1	4	yes	complemented
47	C₂₃×#387	C₂²	1	4	yes	complemented
48	C₂₃×#386	C₂²	1	4	yes	—
49	C₂₃×#386	C₂²	1	4	yes	—
50	C₂₃×#386	C₂²	1	4	yes	—
51	C₂₃×#386	C₂²	1	4	yes	complemented
52	C₂₃×#385	C₂²	1	4	yes	—
53	C₂₃×#385	C₂²	1	4	yes	complemented
54	C₂₃×#384	C₂²	1	2	yes	complemented
55	C₂₃×#382	C₂²	1	2	yes	complemented
56	C₂₃×#381	C₂²	1	2	yes	—
57	C₂₃×#380	C₂²	1	2	yes	—
58	C₂₃×#380	C₂²	1	2	yes	—
59	C₂₃×#380	C₂²	1	1	yes	characteristic
60	C₂₃×#380	C₂²	1	1	yes	characteristic
61	C₂₃×#380	C₂²	1	2	yes	—
62	C₂₃×#380	C₂²	1	2	yes	—
63	C₂₃×#380	C₂²	1	1	yes	characteristic
64	C₂₃×#380	C₂²	1	1	yes	characteristic
65	C₂₃×#380	C₂²	1	2	yes	complemented
66	C₂₃×#380	C₂²	1	2	yes	complemented
67	C₂₃×#379	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
69	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
70	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
71	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
75	C₂×C₂₃×#95	C₂²	1	2	yes	—
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	1	yes	characteristic
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×#123	C₂×C₄	1	16	yes	complemented
96	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
97	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
98	C₂₃×#121	C₂×C₄	1	8	yes	—
99	C₂₃×#121	C₂×C₄	1	8	yes	complemented
100	C₂₃×#120	C₂×C₄	1	16	yes	complemented
101	C₄×D₄×C₂₃	—	4	8	no	—
102	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
103	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
104	C₂₃×#117	—	4	4	no	—
105	C₂₃×#117	—	4	4	no	—
106	C₂₃×#117	C₂×C₄	1	8	yes	complemented
107	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
108	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
109	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	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	4	yes	—
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	2	yes	—
121	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
122	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	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	4	yes	—
131	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
138	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
140	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
142	C₂₃×#95	C₂³	1	2	yes	—
143	C₂₃×#95	C₂³	1	2	yes	—
144	C₂₃×#95	C₂³	1	4	yes	—
145	C₂₃×#95	C₂³	1	2	yes	—
146	C₂₃×#95	C₂³	1	4	yes	—
147	C₂₃×#95	C₂³	1	2	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	C₂₃×#95	C₂³	1	4	yes	—
154	C₂⁴×C₂₃	—	2	2	no	—
155	C₂⁴×C₂₃	—	2	2	no	—
156	C₂⁴×C₂₃	—	4	2	no	—
157	C₂⁴×C₂₃	—	4	2	no	—
158	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
159	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
161	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
162	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
163	#41×C₂₃	—	4	16	no	—
164	C₂×Q₈×C₂₃	—	4	2	no	—
165	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
166	C₂×D₄×C₂₃	—	2	4	no	—
167	C₂×D₄×C₂₃	—	2	4	no	—
168	C₂×D₄×C₂₃	—	4	2	no	—
169	C₂×D₄×C₂₃	—	4	2	no	—
170	C₂×D₄×C₂₃	—	4	2	no	—
171	C₂×D₄×C₂₃	—	4	2	no	—
172	C₂×D₄×C₂₃	—	4	2	no	—
173	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
174	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
175	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
176	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₂₃	—	2	4	no	—
178	C₂²×C₄×C₂₃	—	2	4	no	—
179	C₂²×C₄×C₂₃	—	2	4	no	—
180	C₂²×C₄×C₂₃	—	2	4	no	—
181	C₂²×C₄×C₂₃	—	2	4	no	—
182	C₂²×C₄×C₂₃	—	2	8	no	—
183	C₂²×C₄×C₂₃	—	4	16	no	—
184	C₂²×C₄×C₂₃	—	4	2	no	—
185	C₂²×C₄×C₂₃	—	4	2	no	—
186	C₂²×C₄×C₂₃	—	4	2	no	—
187	C₂²×C₄×C₂₃	—	4	4	no	—
188	C₂²×C₄×C₂₃	—	4	4	no	—
189	C₂²×C₄×C₂₃	—	4	4	no	—
190	C₂²×C₄×C₂₃	—	4	4	no	—
191	C₂²×C₄×C₂₃	—	4	4	no	—
192	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₂₃	C₂²×C₄	1	8	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	4	yes	—
199	C₂²×C₄×C₂₃	C₂⁴	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	4	yes	—
203	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
210	C₄⋊C₄×C₂₃	—	2	4	no	—
211	C₄⋊C₄×C₂₃	—	2	4	no	—
212	C₄⋊C₄×C₂₃	—	2	4	no	—
213	C₄⋊C₄×C₂₃	—	2	4	no	—
214	C₄⋊C₄×C₂₃	—	4	4	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	4	no	—
223	C₂²⋊C₄×C₂₃	—	2	4	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	—	4	4	no	—
231	C₂²⋊C₄×C₂₃	—	4	4	no	—
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	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
236	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
237	C₄²×C₂₃	—	4	4	no	—
238	C₄²×C₂₃	—	4	4	no	—
239	C₄²×C₂₃	—	4	4	no	—
240	C₄²×C₂₃	—	4	4	no	—
241	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
242	#34362	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₂₃	—	2	2	no	—
244	C₂³×C₂₃	—	2	2	no	—
245	C₂³×C₂₃	—	2	8	no	—
246	C₂³×C₂₃	—	2	1	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	2	no	—
249	C₂³×C₂₃	—	2	2	no	—
250	C₂³×C₂₃	—	2	2	no	—
251	C₂³×C₂₃	—	2	2	no	—
252	C₂³×C₂₃	—	2	2	no	—
253	C₂³×C₂₃	—	2	2	no	—
254	C₂³×C₂₃	—	2	1	no	—
255	C₂³×C₂₃	—	2	1	no	—
256	C₂³×C₂₃	—	2	2	no	—
257	C₂³×C₂₃	—	2	2	no	—
258	C₂³×C₂₃	—	2	2	no	—
259	C₂³×C₂₃	—	2	2	no	—
260	C₂³×C₂₃	—	4	4	no	—
261	C₂³×C₂₃	—	4	4	no	—
262	C₂³×C₂₃	—	4	8	no	—
263	C₂³×C₂₃	—	4	8	no	—
264	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
265	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
266	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
267	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
268	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
269	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
270	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
271	Q₈×C₂₃	—	4	4	no	—
272	D₄×C₂₃	—	2	16	no	—
273	D₄×C₂₃	—	4	8	no	—
274	D₄×C₂₃	—	4	4	no	—
275	D₄×C₂₃	—	4	8	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	2	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	2	no	—
284	C₂×C₄×C₂₃	—	2	2	no	—
285	C₂×C₄×C₂₃	—	2	8	no	—
286	C₂×C₄×C₂₃	—	2	8	no	—
287	C₂×C₄×C₂₃	—	2	8	no	—
288	C₂×C₄×C₂₃	—	2	16	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	—	2	4	no	—
294	C₂×C₄×C₂₃	—	2	4	no	—
295	C₂×C₄×C₂₃	—	2	4	no	—
296	C₂×C₄×C₂₃	—	2	4	no	—
297	C₂×C₄×C₂₃	—	2	4	no	—
298	C₂×C₄×C₂₃	—	2	4	no	—
299	C₂×C₄×C₂₃	—	2	4	no	—
300	C₂×C₄×C₂₃	—	2	4	no	—
301	C₂×C₄×C₂₃	—	4	4	no	—
302	C₂×C₄×C₂₃	—	4	4	no	—
303	C₂×C₄×C₂₃	—	4	4	no	—
304	C₂×C₄×C₂₃	—	8	8	no	—
305	C₂×C₄×C₂₃	—	8	8	no	—
306	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
307	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
309	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
310	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
313	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
314	C₂×#525	C₂×C₂₃	1	1	yes	characteristic
315	#2378	C₂×C₂₃	1	2	yes	complemented
316	#2377	C₂×C₂₃	1	2	yes	complemented
317	#2368	C₂×C₂₃	1	2	yes	complemented
318	#2364	C₂×C₂₃	1	2	yes	complemented
319	#2354	C₂×C₂₃	1	2	yes	complemented
320	#2352	C₂×C₂₃	1	2	yes	complemented
321	#2352	C₂×C₂₃	1	2	yes	complemented
322	D₄×C₄⋊C₄	C₂×C₂₃	1	2	yes	complemented
323	#2335	C₂×C₂₃	1	4	yes	complemented
324	#2321	C₂×C₂₃	1	4	yes	complemented
325	#2314	C₂×C₂₃	1	2	yes	complemented
326	#2311	C₂×C₂₃	1	2	yes	complemented
327	#2280	C₂×C₂₃	1	1	yes	characteristic, complemented
328	C₂×#380	C₂×C₂₃	1	1	yes	characteristic, complemented
329	C₂²×C₂₃	—	2	2	no	—
330	C₂²×C₂₃	—	2	2	no	—
331	C₂²×C₂₃	—	2	4	no	—
332	C₂²×C₂₃	—	2	4	no	—
333	C₂²×C₂₃	—	2	2	no	—
334	C₂²×C₂₃	—	2	2	no	—
335	C₂²×C₂₃	—	2	4	no	—
336	C₂²×C₂₃	—	2	4	no	—
337	C₂²×C₂₃	—	2	2	no	—
338	C₂²×C₂₃	—	2	2	no	—
339	C₂²×C₂₃	—	2	2	no	—
340	C₂²×C₂₃	—	2	4	no	—
341	C₂²×C₂₃	—	2	2	no	—
342	C₂²×C₂₃	—	4	16	no	—
343	C₂²×C₂₃	—	4	2	no	—
344	C₂²×C₂₃	—	4	2	no	—
345	C₂²×C₂₃	—	4	2	no	—
346	C₂²×C₂₃	—	4	2	no	—
347	C₂²×C₂₃	—	4	2	no	—
348	C₂²×C₂₃	—	4	2	no	—
349	C₂²×C₂₃	—	4	2	no	—
350	C₂²×C₂₃	—	4	2	no	—
351	C₂²×C₂₃	#520	1	4	yes	—
352	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
353	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
354	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
356	C₂²×C₂₃	#585	1	2	yes	—
357	C₄×C₂₃	—	2	2	no	—
358	C₄×C₂₃	—	2	2	no	—
359	C₄×C₂₃	—	2	2	no	—
360	C₄×C₂₃	—	2	4	no	—
361	C₄×C₂₃	—	2	4	no	—
362	C₄×C₂₃	—	2	4	no	—
363	C₄×C₂₃	—	4	4	no	—
364	C₄×C₂₃	—	4	4	no	—
365	C₄×C₂₃	—	4	4	no	—
366	C₄×C₂₃	—	4	4	no	—
367	C₄×C₂₃	#518	1	4	yes	—
368	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
369	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
370	#525	C₄×C₂₃	1	16	yes	complemented
371	C₂×#123	C₂²×C₂₃	1	2	yes	—
372	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
374	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
375	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
376	C₂×#120	C₂²×C₂₃	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
378	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
379	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
380	C₂×#117	C₂²×C₂₃	1	2	yes	—
381	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
383	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
384	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
385	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
386	#391	C₂²×C₂₃	1	4	yes	complemented
387	#390	C₂²×C₂₃	1	4	yes	—
388	#390	C₂²×C₂₃	1	4	yes	—
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	—
393	#388	C₂²×C₂₃	1	4	yes	—
394	#388	C₂²×C₂₃	1	4	yes	complemented
395	#388	C₂²×C₂₃	1	4	yes	complemented
396	#387	C₂²×C₂₃	1	4	yes	complemented
397	#387	C₂²×C₂₃	1	4	yes	complemented
398	#387	C₂²×C₂₃	1	4	yes	complemented
399	#387	C₂²×C₂₃	1	4	yes	complemented
400	#386	C₂²×C₂₃	1	4	yes	—
401	#386	C₂²×C₂₃	1	4	yes	—
402	#386	C₂²×C₂₃	1	4	yes	—
403	#386	C₂²×C₂₃	1	4	yes	complemented
404	#385	C₂²×C₂₃	1	4	yes	—
405	#385	C₂²×C₂₃	1	4	yes	complemented
406	#384	C₂²×C₂₃	1	2	yes	complemented
407	#382	C₂²×C₂₃	1	2	yes	complemented
408	#381	C₂²×C₂₃	1	2	yes	—
409	#380	C₂²×C₂₃	1	2	yes	—
410	#380	C₂²×C₂₃	1	2	yes	—
411	#380	C₂²×C₂₃	1	2	yes	—
412	#380	C₂²×C₂₃	1	1	yes	characteristic
413	#380	C₂²×C₂₃	1	1	yes	characteristic
414	#380	C₂²×C₂₃	1	1	yes	characteristic
415	#380	C₂²×C₂₃	1	1	yes	characteristic
416	#380	C₂²×C₂₃	1	2	yes	—
417	#380	C₂²×C₂₃	1	2	yes	complemented
418	#380	C₂²×C₂₃	1	2	yes	complemented
419	#379	C₂²×C₂₃	1	2	yes	—
420	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
421	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
422	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
423	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
425	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
426	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
427	C₂×#95	C₂²×C₂₃	1	2	yes	—
428	C₂×C₂₃	—	2	4	no	—
429	C₂×C₂₃	—	4	4	no	—
430	C₂×C₂₃	—	4	2	no	—
431	C₂×C₂₃	—	4	2	no	—
432	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
433	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
434	C₂×C₂₃	#3428	1	1	yes	characteristic
435	C₂×C₂₃	#3541	1	2	yes	—
436	C₂×C₂₃	#3542	1	2	yes	—
437	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
438	C₂×#41	—	4	4	no	—
439	C₂×#41	C₂×C₄×C₂₃	1	8	yes	complemented
440	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
442	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
443	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
444	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
445	C₂³×C₄	—	4	4	no	—
446	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	complemented
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	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
452	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
453	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
456	#123	C₂×C₄×C₂₃	1	16	yes	complemented
457	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
458	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
459	#121	C₂×C₄×C₂₃	1	8	yes	—
460	#121	C₂×C₄×C₂₃	1	8	yes	complemented
461	#120	C₂×C₄×C₂₃	1	16	yes	complemented
462	C₄×D₄	—	4	8	no	—
463	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
464	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
465	#117	—	4	4	no	—
466	#117	—	4	4	no	—
467	#117	C₂×C₄×C₂₃	1	8	yes	complemented
468	C₂×C₄⋊C₄	—	4	4	no	—
469	C₂×C₄⋊C₄	—	4	4	no	—
470	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
477	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
482	C₂×C₂²⋊C₄	—	4	4	no	—
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	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
498	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
499	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
500	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
501	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
502	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
503	#95	C₂³×C₂₃	1	2	yes	—
504	#95	C₂³×C₂₃	1	2	yes	—
505	#95	C₂³×C₂₃	1	4	yes	—
506	#95	C₂³×C₂₃	1	2	yes	—
507	#95	C₂³×C₂₃	1	4	yes	—
508	#95	C₂³×C₂₃	1	2	yes	—
509	#95	C₂³×C₂₃	1	4	yes	—
510	#95	C₂³×C₂₃	1	4	yes	—
511	#95	C₂³×C₂₃	1	4	yes	—
512	#95	C₂³×C₂₃	1	4	yes	—
513	#95	C₂³×C₂₃	1	4	yes	—
514	#95	C₂³×C₂₃	1	4	yes	—
515	C₂₃	#34362	1	1	yes	characteristic, direct product factor, Sylow
516	C₂⁴	—	2	2	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	—	4	2	no	—
519	C₂⁴	—	4	2	no	—
520	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
521	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
522	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
523	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
524	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
525	#41	—	4	16	no	—
526	C₂×Q₈	—	4	2	no	—
527	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	—	4	2	no	—
534	C₂×D₄	—	4	2	no	—
535	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
536	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
537	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
538	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	8	no	—
545	C₂²×C₄	—	4	16	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	—	4	4	no	—
552	C₂²×C₄	—	4	4	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
555	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
556	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
557	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
558	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
559	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
560	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
563	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
564	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
565	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	4	4	no	—
577	C₄⋊C₄	—	4	4	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	—	4	4	no	—
580	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
581	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
582	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
583	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	4	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	4	4	no	—
590	C₂²⋊C₄	—	4	4	no	—
591	C₂²⋊C₄	—	4	4	no	—
592	C₂²⋊C₄	—	4	4	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
595	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
598	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
599	C₄²	—	4	4	no	—
600	C₄²	—	4	4	no	—
601	C₄²	—	4	4	no	—
602	C₄²	—	4	4	no	—
603	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	8	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	4	4	no	—
623	C₂³	—	4	8	no	—
624	C₂³	—	4	8	no	—
625	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
626	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
627	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
628	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
629	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
630	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
631	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
632	Q₈	—	4	4	no	—
633	D₄	—	2	16	no	—
634	D₄	—	4	4	no	—
635	D₄	—	4	8	no	—
636	D₄	—	4	8	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	16	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	8	8	no	—
666	C₂×C₄	—	8	8	no	—
667	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
668	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
670	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
671	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
672	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
673	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
674	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	4	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	4	16	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	C₂₃×#520	1	4	yes	—
698	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
699	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
700	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
702	C₂²	C₂₃×#585	1	2	yes	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	4	no	—
712	C₄	—	4	4	no	—
713	C₄	C₂₃×#518	1	4	yes	—
714	C₂	—	2	4	no	—
715	C₂	—	4	2	no	—
716	C₂	—	4	2	no	—
717	C₂	—	4	4	no	—
718	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
719	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
720	C₂	C₂₃×#3428	1	1	yes	characteristic
721	C₂	C₂₃×#3541	1	2	yes	—
722	C₂	C₂₃×#3542	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×#2368	C₂	semidirect
5. C₂₃×#2364	C₂	semidirect
6. C₂₃×#2354	C₂	semidirect
7. C₂₃×#2352	C₂	semidirect
8. C₂₃×#2352	C₂	semidirect
9. D₄×C₄⋊C₄×C₂₃	C₂	semidirect
10. C₂₃×#2335	C₂	semidirect
11. C₂₃×#2321	C₂	semidirect
12. C₂₃×#2314	C₂	semidirect
13. C₂₃×#2311	C₂	semidirect
14. C₂₃×#2280	C₂	semidirect
15. C₂×C₂₃×#380	C₂	semidirect
18. C₂₃×#525	C₄	semidirect
30. C₂×C₂₃×#117	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
34. C₂₃×#391	C₂²	semidirect
37. C₂₃×#389	C₂²	semidirect
42. C₂₃×#388	C₂²	semidirect
43. C₂₃×#388	C₂²	semidirect
44. C₂₃×#387	C₂²	semidirect
45. C₂₃×#387	C₂²	semidirect
46. C₂₃×#387	C₂²	semidirect
47. C₂₃×#387	C₂²	semidirect
51. C₂₃×#386	C₂²	semidirect
53. C₂₃×#385	C₂²	semidirect
54. C₂₃×#384	C₂²	semidirect
55. C₂₃×#382	C₂²	semidirect
65. C₂₃×#380	C₂²	semidirect
66. C₂₃×#380	C₂²	semidirect
68. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
69. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
70. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
78. C₂×#41×C₂₃	C₂×C₄	semidirect
85. C₂³×C₄×C₂₃	C₂×C₄	semidirect
95. C₂₃×#123	C₂×C₄	semidirect
96. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
97. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₂₃×#121	C₂×C₄	semidirect
100. C₂₃×#120	C₂×C₄	semidirect
102. C₄×D₄×C₂₃	C₂×C₄	semidirect
103. C₄×D₄×C₂₃	C₂×C₄	semidirect
106. C₂₃×#117	C₂×C₄	semidirect
242. #34362	C₂₃	direct (N × H)
315. #2378	C₂×C₂₃	semidirect
316. #2377	C₂×C₂₃	semidirect
317. #2368	C₂×C₂₃	semidirect
318. #2364	C₂×C₂₃	semidirect
319. #2354	C₂×C₂₃	semidirect
320. #2352	C₂×C₂₃	semidirect
321. #2352	C₂×C₂₃	semidirect
322. D₄×C₄⋊C₄	C₂×C₂₃	semidirect
323. #2335	C₂×C₂₃	semidirect
324. #2321	C₂×C₂₃	semidirect
325. #2314	C₂×C₂₃	semidirect
326. #2311	C₂×C₂₃	semidirect
327. #2280	C₂×C₂₃	semidirect
328. C₂×#380	C₂×C₂₃	semidirect
370. #525	C₄×C₂₃	semidirect
382. C₂×#117	C₂²×C₂₃	semidirect
384. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
386. #391	C₂²×C₂₃	semidirect
389. #389	C₂²×C₂₃	semidirect
394. #388	C₂²×C₂₃	semidirect
395. #388	C₂²×C₂₃	semidirect
396. #387	C₂²×C₂₃	semidirect
397. #387	C₂²×C₂₃	semidirect
398. #387	C₂²×C₂₃	semidirect
399. #387	C₂²×C₂₃	semidirect
403. #386	C₂²×C₂₃	semidirect
405. #385	C₂²×C₂₃	semidirect
406. #384	C₂²×C₂₃	semidirect
407. #382	C₂²×C₂₃	semidirect
417. #380	C₂²×C₂₃	semidirect
418. #380	C₂²×C₂₃	semidirect
420. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
421. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
422. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
426. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
439. C₂×#41	C₂×C₄×C₂₃	semidirect
446. C₂³×C₄	C₂×C₄×C₂₃	semidirect
456. #123	C₂×C₄×C₂₃	semidirect
457. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
458. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
460. #121	C₂×C₄×C₂₃	semidirect
461. #120	C₂×C₄×C₂₃	semidirect
463. C₄×D₄	C₂×C₄×C₂₃	semidirect
464. C₄×D₄	C₂×C₄×C₂₃	semidirect
467. #117	C₂×C₄×C₂₃	semidirect
515. C₂₃	#34362	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×#2368	2
C₂₃×#2364	2
C₂₃×#2354	2
C₂₃×#2352	2
D₄×C₄⋊C₄×C₂₃	2
C₂₃×#2335	2
C₂₃×#2321	2
C₂₃×#2314	2
C₂₃×#2311	2
C₂₃×#2280	2
C₂×C₂₃×#380	2
#34362	23

Subgroups — C23×#34362 #19181988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34362 #19181988