Subgroups — C₂₃×#61264 #19208890

Order 5888.

1764 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	2	yes	maximal
2	C₂₃×#3349	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3344	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3342	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3338	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3336	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3097	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3095	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic
16	C₂₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#556	C₂²	1	4	yes	—
22	C₂₃×#554	C₂²	1	4	yes	—
23	C₂₃×#552	—	2	4	no	—
24	C₂₃×#552	C₂²	1	4	yes	—
25	C₂₃×#552	C₂²	1	4	yes	—
26	C₂₃×#551	—	2	4	no	—
27	C₂₃×#544	C₂²	1	2	yes	—
28	C₂₃×#542	—	2	2	no	—
29	C₂₃×#541	—	2	2	no	—
30	C₂₃×#536	C₂²	1	2	yes	—
31	C₂₃×#533	—	2	2	no	—
32	C₂₃×#529	—	2	2	no	—
33	C₂₃×#525	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂₃×#520	C₂²	1	2	yes	—
36	C₂₃×#519	C₂²	1	2	yes	—
37	C₂×C₂₃×#117	C₂²	1	2	yes	—
38	C₂₃×#501	C₂²	1	4	yes	complemented
39	C₂₃×#500	C₂²	1	2	yes	complemented
40	C₂₃×#499	C₂²	1	2	yes	complemented
41	C₂₃×#485	C₂²	1	4	yes	—
42	C₂₃×#485	C₂²	1	4	yes	—
43	C₂₃×#485	C₂²	1	4	yes	complemented
44	C₂₃×#485	C₂²	1	4	yes	complemented
45	C₂₃×#484	C₂²	1	4	yes	—
46	C₂₃×#484	C₂²	1	4	yes	complemented
47	C₂₃×#483	C₂²	1	4	yes	—
48	C₂₃×#483	C₂²	1	4	yes	complemented
49	C₂₃×#479	C₂²	1	4	yes	complemented
50	C₂₃×#479	C₂²	1	4	yes	complemented
51	C₂₃×#477	C₂²	1	4	yes	complemented
52	C₂₃×#475	C₂²	1	4	yes	complemented
53	C₂₃×#470	C₂²	1	4	yes	complemented
54	C₂₃×#467	C₂²	1	2	yes	—
55	C₂₃×#467	C₂²	1	2	yes	—
56	C₂₃×#467	C₂²	1	2	yes	—
57	C₂₃×#467	C₂²	1	2	yes	—
58	C₂₃×#467	C₂²	1	2	yes	complemented
59	C₂₃×#467	C₂²	1	2	yes	complemented
60	C₂₃×#441	C₂²	1	4	yes	complemented
61	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
62	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
63	C₂₃×#435	C₂²	1	2	yes	—
64	C₂₃×#435	C₂²	1	2	yes	—
65	C₈×D₄×C₂₃	C₂²	1	2	yes	—
66	C₈×D₄×C₂₃	C₂²	1	2	yes	—
67	C₂₃×#428	C₂²	1	2	yes	—
68	C₂₃×#428	C₂²	1	2	yes	—
69	C₂₃×#428	C₂²	1	4	yes	complemented
70	C₂₃×#427	C₂²	1	1	yes	characteristic
71	C₂₃×#427	C₂²	1	1	yes	characteristic
72	C₂₃×#427	C₂²	1	1	yes	characteristic
73	C₂₃×#427	C₂²	1	2	yes	—
74	C₂₃×#427	C₂²	1	1	yes	characteristic
75	C₂₃×#427	C₂²	1	2	yes	—
76	C₂₃×#427	C₂²	1	2	yes	complemented
77	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
78	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
79	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
80	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
81	C₂×C₂₃×#106	C₂²	1	2	yes	—
82	C₂₃×#424	C₂²	1	1	yes	characteristic
83	C₂₃×#419	C₂²	1	2	yes	—
84	C₂₃×#419	C₂²	1	2	yes	—
85	C₂×C₂₃×#103	C₂²	1	2	yes	—
86	C₂₃×#408	C₂²	1	1	yes	characteristic
87	C₂₃×#407	C₂²	1	1	yes	characteristic
88	C₂₃×#405	C₂²	1	1	yes	characteristic
89	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂×Q₁₆×C₂₃	—	2	4	no	—
93	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
94	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
95	C₂₃×#131	—	2	4	no	—
96	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
98	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₂₃	—	2	4	no	—
100	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
106	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	—	2	2	no	—
109	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₂₃×#126	—	2	4	no	—
111	C₂₃×#126	—	2	4	no	—
112	C₂₃×#126	—	2	4	no	—
113	C₂₃×#126	—	2	4	no	—
114	C₂₃×#125	—	2	4	no	—
115	C₂₃×#125	—	2	4	no	—
116	C₂₃×#125	—	2	4	no	—
117	C₂₃×#125	—	2	2	no	—
118	C₂₃×#125	C₂³	1	4	yes	—
119	C₂₃×#124	—	2	4	no	—
120	C₂₃×#124	—	2	2	no	—
121	C₂₃×#123	—	2	4	no	—
122	C₂₃×#123	—	2	4	no	—
123	C₂₃×#123	—	2	4	no	—
124	C₂₃×#123	D₄	1	2	yes	—
125	C₂₃×C₂²⋊Q₈	—	2	2	no	—
126	C₂₃×C₂²⋊Q₈	—	2	2	no	—
127	C₂₃×C₂²⋊Q₈	—	2	4	no	—
128	C₂₃×C₂²⋊Q₈	—	2	4	no	—
129	C₂₃×C₂²⋊Q₈	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
131	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
132	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₂₃×#121	D₄	1	1	yes	characteristic
137	C₂₃×#121	D₄	1	1	yes	characteristic
138	C₂₃×#120	D₄	1	2	yes	—
139	C₄×Q₈×C₂₃	—	2	2	no	—
140	C₄×Q₈×C₂₃	—	2	4	no	—
141	C₄×Q₈×C₂₃	—	2	2	no	—
142	C₄×Q₈×C₂₃	—	2	2	no	—
143	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
144	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
145	C₄×D₄×C₂₃	—	2	4	no	—
146	C₄×D₄×C₂₃	—	2	4	no	—
147	C₄×D₄×C₂₃	—	2	2	no	—
148	C₄×D₄×C₂₃	C₂³	1	2	yes	—
149	C₄×D₄×C₂₃	C₂³	1	2	yes	—
150	C₂₃×#117	—	2	2	no	—
151	C₂₃×#117	—	2	2	no	—
152	C₂₃×#117	—	2	4	no	—
153	C₂₃×#117	—	2	4	no	—
154	C₂₃×#117	—	2	4	no	—
155	C₂₃×#117	C₂³	1	2	yes	—
156	C₂₃×#117	C₂³	1	4	yes	—
157	C₂₃×#117	C₂³	1	2	yes	—
158	C₂₃×#117	C₂³	1	2	yes	—
159	C₂₃×#117	C₂³	1	2	yes	—
160	C₂₃×#117	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
167	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
168	C₂×C₄²×C₂₃	—	2	2	no	—
169	C₂₃×#107	C₂³	1	1	yes	characteristic
170	C₂₃×#107	C₂³	1	2	yes	—
171	C₂₃×#107	C₂³	1	1	yes	characteristic
172	C₂₃×#107	C₂³	1	1	yes	characteristic
173	C₂₃×#107	C₂³	1	1	yes	characteristic
174	C₂₃×#107	C₂³	1	2	yes	—
175	C₂₃×#107	C₂³	1	2	yes	—
176	C₂₃×#107	C₂³	1	2	yes	—
177	C₂₃×#107	C₂³	1	4	yes	—
178	C₂₃×#107	C₂³	1	4	yes	—
179	C₂₃×#106	C₂³	1	2	yes	—
180	C₂₃×#106	C₂³	1	2	yes	—
181	C₂₃×#106	C₂³	1	2	yes	—
182	C₂₃×#106	C₂³	1	2	yes	—
183	C₂₃×#106	C₂³	1	4	yes	—
184	C₂₃×#106	C₂³	1	4	yes	—
185	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
186	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
187	C₂₃×#103	C₂³	1	4	yes	—
188	C₂₃×#103	C₂³	1	4	yes	—
189	C₂₃×#103	C₂³	1	4	yes	—
190	C₂₃×#103	C₂³	1	4	yes	—
191	C₂₃×#103	C₂³	1	4	yes	—
192	C₂₃×#103	C₂³	1	4	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₂₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₂₃	C₂³	1	2	yes	—
199	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
200	#41×C₂₃	—	2	2	no	—
201	#41×C₂₃	—	2	2	no	—
202	C₂×Q₈×C₂₃	—	2	2	no	—
203	C₂×Q₈×C₂₃	—	2	4	no	—
204	C₂×Q₈×C₂₃	—	2	4	no	—
205	C₂×Q₈×C₂₃	—	2	4	no	—
206	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
208	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
209	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
210	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₂₃	—	2	2	no	—
213	C₂²×C₄×C₂₃	—	2	2	no	—
214	C₂²×C₄×C₂₃	—	2	2	no	—
215	C₂²×C₄×C₂₃	—	2	2	no	—
216	C₂²×C₄×C₂₃	—	2	2	no	—
217	C₂²×C₄×C₂₃	—	2	2	no	—
218	C₂²×C₄×C₂₃	—	2	4	no	—
219	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
226	Q₁₆×C₂₃	—	2	4	no	—
227	Q₁₆×C₂₃	—	2	4	no	—
228	M₁₆×C₂₃	—	2	2	no	—
229	M₁₆×C₂₃	—	2	2	no	—
230	M₁₆×C₂₃	—	2	4	no	—
231	C₂×C₈×C₂₃	—	2	2	no	—
232	C₂×C₈×C₂₃	—	2	2	no	—
233	C₂×C₈×C₂₃	—	2	2	no	—
234	C₂×C₈×C₂₃	—	2	2	no	—
235	C₂×C₈×C₂₃	—	2	2	no	—
236	C₂×C₈×C₂₃	—	2	4	no	—
237	C₂×C₈×C₂₃	#41	1	4	yes	—
238	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
242	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	2	no	—
247	C₄⋊C₄×C₂₃	—	2	2	no	—
248	C₄⋊C₄×C₂₃	—	2	2	no	—
249	C₄⋊C₄×C₂₃	—	2	4	no	—
250	C₄⋊C₄×C₂₃	—	2	4	no	—
251	C₄⋊C₄×C₂₃	—	2	4	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	—	2	4	no	—
256	C₄⋊C₄×C₂₃	—	2	4	no	—
257	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
266	C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂²⋊C₄×C₂₃	—	2	2	no	—
268	C₂²⋊C₄×C₂₃	—	2	2	no	—
269	C₂²⋊C₄×C₂₃	—	2	2	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	—	2	4	no	—
272	C₂²⋊C₄×C₂₃	—	2	4	no	—
273	C₂²⋊C₄×C₂₃	—	2	4	no	—
274	C₂²⋊C₄×C₂₃	—	2	4	no	—
275	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
278	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
280	C₄²×C₂₃	—	2	2	no	—
281	C₄²×C₂₃	—	2	2	no	—
282	C₄²×C₂₃	—	2	2	no	—
283	C₄²×C₂₃	—	2	2	no	—
284	C₄²×C₂₃	—	2	4	no	—
285	C₄²×C₂₃	—	2	4	no	—
286	C₄²×C₂₃	—	2	4	no	—
287	C₄²×C₂₃	C₂⁴	1	2	yes	—
288	#61264	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂³×C₂₃	—	2	2	no	—
290	C₂³×C₂₃	—	2	2	no	—
291	C₂³×C₂₃	—	4	1	no	—
292	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
293	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
294	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
295	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₂₃	—	2	2	no	—
297	Q₈×C₂₃	—	2	4	no	—
298	Q₈×C₂₃	—	2	4	no	—
299	Q₈×C₂₃	—	4	4	no	—
300	Q₈×C₂₃	—	8	4	no	—
301	D₄×C₂₃	—	2	4	no	—
302	D₄×C₂₃	—	2	4	no	—
303	D₄×C₂₃	—	2	2	no	—
304	D₄×C₂₃	—	4	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	2	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	1	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	4	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	4	no	—
320	C₂×C₄×C₂₃	—	4	4	no	—
321	C₂×C₄×C₂₃	—	4	4	no	—
322	C₂×C₄×C₂₃	—	8	4	no	—
323	C₂×C₄×C₂₃	—	8	2	no	—
324	C₂×C₄×C₂₃	—	8	2	no	—
325	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
332	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
333	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
334	C₈×C₂₃	—	2	1	no	—
335	C₈×C₂₃	—	2	1	no	—
336	C₈×C₂₃	—	2	2	no	—
337	C₈×C₂₃	—	2	2	no	—
338	C₈×C₂₃	C₂×#41	1	2	yes	—
339	C₈×C₂₃	C₂×#41	1	2	yes	—
340	#3495	C₂×C₂₃	1	2	yes	—
341	#3349	C₂×C₂₃	1	4	yes	complemented
342	#3344	C₂×C₂₃	1	4	yes	complemented
343	#3342	C₂×C₂₃	1	2	yes	complemented
344	#3338	C₂×C₂₃	1	2	yes	complemented
345	#3336	C₂×C₂₃	1	2	yes	complemented
346	#3336	C₂×C₂₃	1	2	yes	complemented
347	#3164	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#3097	C₂×C₂₃	1	2	yes	complemented
349	#3095	C₂×C₂₃	1	2	yes	complemented
350	#3082	C₂×C₂₃	1	2	yes	complemented
351	#3059	C₂×C₂₃	1	1	yes	characteristic, complemented
352	C₂×#467	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#2950	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#2929	C₂×C₂₃	1	1	yes	characteristic
355	#2913	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₂×#427	C₂×C₂₃	1	1	yes	characteristic, complemented
357	C₂²×C₂₃	—	2	1	no	—
358	C₂²×C₂₃	—	2	1	no	—
359	C₂²×C₂₃	—	2	1	no	—
360	C₂²×C₂₃	—	2	1	no	—
361	C₂²×C₂₃	—	2	2	no	—
362	C₂²×C₂₃	—	2	1	no	—
363	C₂²×C₂₃	—	2	1	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	2	2	no	—
366	C₂²×C₂₃	—	2	1	no	—
367	C₂²×C₂₃	—	4	4	no	—
368	C₂²×C₂₃	#547	1	2	yes	—
369	C₂²×C₂₃	#578	1	2	yes	—
370	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₂₃	—	2	2	no	—
372	C₄×C₂₃	—	2	1	no	—
373	C₄×C₂₃	—	2	1	no	—
374	C₄×C₂₃	—	2	2	no	—
375	C₄×C₂₃	—	2	2	no	—
376	C₄×C₂₃	—	4	2	no	—
377	C₄×C₂₃	—	4	4	no	—
378	C₄×C₂₃	—	4	2	no	—
379	C₄×C₂₃	—	4	4	no	—
380	C₄×C₂₃	—	4	2	no	—
381	C₄×C₂₃	—	4	2	no	—
382	C₄×C₂₃	#547	1	2	yes	—
383	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
384	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
385	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
386	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
387	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
388	#556	C₂²×C₂₃	1	4	yes	—
389	#554	C₂²×C₂₃	1	4	yes	—
390	#552	—	2	4	no	—
391	#552	C₂²×C₂₃	1	4	yes	—
392	#552	C₂²×C₂₃	1	4	yes	—
393	#551	—	2	4	no	—
394	#544	C₂²×C₂₃	1	2	yes	—
395	#542	—	2	2	no	—
396	#541	—	2	2	no	—
397	#536	C₂²×C₂₃	1	2	yes	—
398	#533	—	2	2	no	—
399	#529	—	2	2	no	—
400	#525	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
402	#520	C₂²×C₂₃	1	2	yes	—
403	#519	C₂²×C₂₃	1	2	yes	—
404	C₂×#117	C₂²×C₂₃	1	2	yes	—
405	#501	C₂²×C₂₃	1	4	yes	complemented
406	#500	C₂²×C₂₃	1	2	yes	complemented
407	#499	C₂²×C₂₃	1	2	yes	complemented
408	#485	C₂²×C₂₃	1	4	yes	—
409	#485	C₂²×C₂₃	1	4	yes	—
410	#485	C₂²×C₂₃	1	4	yes	complemented
411	#485	C₂²×C₂₃	1	4	yes	complemented
412	#484	C₂²×C₂₃	1	4	yes	—
413	#484	C₂²×C₂₃	1	4	yes	complemented
414	#483	C₂²×C₂₃	1	4	yes	—
415	#483	C₂²×C₂₃	1	4	yes	complemented
416	#479	C₂²×C₂₃	1	4	yes	complemented
417	#479	C₂²×C₂₃	1	4	yes	complemented
418	#477	C₂²×C₂₃	1	4	yes	complemented
419	#475	C₂²×C₂₃	1	4	yes	complemented
420	#470	C₂²×C₂₃	1	4	yes	complemented
421	#467	C₂²×C₂₃	1	2	yes	—
422	#467	C₂²×C₂₃	1	2	yes	—
423	#467	C₂²×C₂₃	1	2	yes	—
424	#467	C₂²×C₂₃	1	2	yes	—
425	#467	C₂²×C₂₃	1	2	yes	complemented
426	#467	C₂²×C₂₃	1	2	yes	complemented
427	#441	C₂²×C₂₃	1	4	yes	complemented
428	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
429	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
430	#435	C₂²×C₂₃	1	2	yes	—
431	#435	C₂²×C₂₃	1	2	yes	—
432	C₈×D₄	C₂²×C₂₃	1	2	yes	—
433	C₈×D₄	C₂²×C₂₃	1	2	yes	—
434	#428	C₂²×C₂₃	1	2	yes	—
435	#428	C₂²×C₂₃	1	2	yes	—
436	#428	C₂²×C₂₃	1	4	yes	complemented
437	#427	C₂²×C₂₃	1	1	yes	characteristic
438	#427	C₂²×C₂₃	1	2	yes	—
439	#427	C₂²×C₂₃	1	1	yes	characteristic
440	#427	C₂²×C₂₃	1	2	yes	—
441	#427	C₂²×C₂₃	1	1	yes	characteristic
442	#427	C₂²×C₂₃	1	1	yes	characteristic
443	#427	C₂²×C₂₃	1	2	yes	complemented
444	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
448	C₂×#106	C₂²×C₂₃	1	2	yes	—
449	#424	C₂²×C₂₃	1	1	yes	characteristic
450	#419	C₂²×C₂₃	1	2	yes	—
451	#419	C₂²×C₂₃	1	2	yes	—
452	C₂×#103	C₂²×C₂₃	1	2	yes	—
453	#408	C₂²×C₂₃	1	1	yes	characteristic
454	#407	C₂²×C₂₃	1	1	yes	characteristic
455	#405	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×C₂₃	—	2	2	no	—
457	C₂×C₂₃	—	2	2	no	—
458	C₂×C₂₃	—	4	2	no	—
459	C₂×C₂₃	—	4	1	no	—
460	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
461	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
462	C₂×C₂₃	#3584	1	1	yes	characteristic
463	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
464	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
465	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
466	C₂×Q₁₆	—	2	4	no	—
467	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
468	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
469	#131	—	2	4	no	—
470	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
471	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
472	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×C₈	—	2	4	no	—
474	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
480	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	—	2	2	no	—
483	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
484	#126	—	2	4	no	—
485	#126	—	2	4	no	—
486	#126	—	2	4	no	—
487	#126	—	2	4	no	—
488	#125	—	2	2	no	—
489	#125	—	2	4	no	—
490	#125	—	2	4	no	—
491	#125	—	2	4	no	—
492	#125	C₂³×C₂₃	1	4	yes	—
493	#124	—	2	2	no	—
494	#124	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	—	2	4	no	—
497	#123	—	2	4	no	—
498	#123	D₄×C₂₃	1	2	yes	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
505	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
506	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
507	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
508	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
509	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
510	#121	D₄×C₂₃	1	1	yes	characteristic
511	#121	D₄×C₂₃	1	1	yes	characteristic
512	#120	D₄×C₂₃	1	2	yes	—
513	C₄×Q₈	—	2	2	no	—
514	C₄×Q₈	—	2	2	no	—
515	C₄×Q₈	—	2	2	no	—
516	C₄×Q₈	—	2	4	no	—
517	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
518	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	C₂³×C₂₃	1	2	yes	—
523	C₄×D₄	C₂³×C₂₃	1	2	yes	—
524	#117	—	2	2	no	—
525	#117	—	2	2	no	—
526	#117	—	2	4	no	—
527	#117	—	2	4	no	—
528	#117	—	2	4	no	—
529	#117	C₂³×C₂₃	1	2	yes	—
530	#117	C₂³×C₂₃	1	2	yes	—
531	#117	C₂³×C₂₃	1	2	yes	—
532	#117	C₂³×C₂₃	1	2	yes	—
533	#117	C₂³×C₂₃	1	4	yes	—
534	#117	C₂³×C₂₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	—	2	2	no	—
536	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	C₂×C₂²⋊C₄	—	2	2	no	—
542	C₂×C₄²	—	2	2	no	—
543	#107	C₂³×C₂₃	1	1	yes	characteristic
544	#107	C₂³×C₂₃	1	2	yes	—
545	#107	C₂³×C₂₃	1	1	yes	characteristic
546	#107	C₂³×C₂₃	1	1	yes	characteristic
547	#107	C₂³×C₂₃	1	1	yes	characteristic
548	#107	C₂³×C₂₃	1	2	yes	—
549	#107	C₂³×C₂₃	1	2	yes	—
550	#107	C₂³×C₂₃	1	2	yes	—
551	#107	C₂³×C₂₃	1	4	yes	—
552	#107	C₂³×C₂₃	1	4	yes	—
553	#106	C₂³×C₂₃	1	2	yes	—
554	#106	C₂³×C₂₃	1	2	yes	—
555	#106	C₂³×C₂₃	1	2	yes	—
556	#106	C₂³×C₂₃	1	2	yes	—
557	#106	C₂³×C₂₃	1	4	yes	—
558	#106	C₂³×C₂₃	1	4	yes	—
559	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
560	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
561	#103	C₂³×C₂₃	1	4	yes	—
562	#103	C₂³×C₂₃	1	4	yes	—
563	#103	C₂³×C₂₃	1	4	yes	—
564	#103	C₂³×C₂₃	1	4	yes	—
565	#103	C₂³×C₂₃	1	4	yes	—
566	#103	C₂³×C₂₃	1	4	yes	—
567	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
568	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
570	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
571	#97	C₂³×C₂₃	1	2	yes	—
572	C₄×C₈	C₂³×C₂₃	1	2	yes	—
573	C₂₃	#61264	1	1	yes	characteristic, direct product factor, Sylow
574	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
582	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
583	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
584	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
585	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
601	Q₁₆	—	2	4	no	—
602	Q₁₆	—	2	4	no	—
603	M₁₆	—	2	2	no	—
604	M₁₆	—	2	2	no	—
605	M₁₆	—	2	4	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	2	no	—
611	C₂×C₈	—	2	4	no	—
612	C₂×C₈	#41×C₂₃	1	4	yes	—
613	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
614	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
615	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
633	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
640	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
651	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
652	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
654	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	4	no	—
662	C₄²	C₂⁴×C₂₃	1	2	yes	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	4	1	no	—
666	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
667	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
668	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
669	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
670	Q₈	—	2	2	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	2	4	no	—
673	Q₈	—	4	4	no	—
674	Q₈	—	8	4	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
705	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
706	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
707	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
708	C₈	—	2	1	no	—
709	C₈	—	2	1	no	—
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	C₂×#41×C₂₃	1	2	yes	—
713	C₈	C₂×#41×C₂₃	1	2	yes	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	4	4	no	—
725	C₂²	C₂₃×#547	1	2	yes	—
726	C₂²	C₂₃×#578	1	2	yes	—
727	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	4	4	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	4	no	—
738	C₄	—	4	2	no	—
739	C₄	C₂₃×#547	1	2	yes	—
740	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
741	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
742	C₂	—	2	2	no	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
747	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
748	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3349	C₂	semidirect
3. C₂₃×#3344	C₂	semidirect
4. C₂₃×#3342	C₂	semidirect
5. C₂₃×#3338	C₂	semidirect
6. C₂₃×#3336	C₂	semidirect
7. C₂₃×#3336	C₂	semidirect
8. C₂₃×#3164	C₂	semidirect
9. C₂₃×#3097	C₂	semidirect
10. C₂₃×#3095	C₂	semidirect
11. C₂₃×#3082	C₂	semidirect
12. C₂₃×#3059	C₂	semidirect
13. C₂×C₂₃×#467	C₂	semidirect
14. C₂₃×#2950	C₂	semidirect
16. C₂₃×#2913	C₂	semidirect
17. C₂×C₂₃×#427	C₂	semidirect
38. C₂₃×#501	C₂²	semidirect
39. C₂₃×#500	C₂²	semidirect
40. C₂₃×#499	C₂²	semidirect
43. C₂₃×#485	C₂²	semidirect
44. C₂₃×#485	C₂²	semidirect
46. C₂₃×#484	C₂²	semidirect
48. C₂₃×#483	C₂²	semidirect
49. C₂₃×#479	C₂²	semidirect
50. C₂₃×#479	C₂²	semidirect
51. C₂₃×#477	C₂²	semidirect
52. C₂₃×#475	C₂²	semidirect
53. C₂₃×#470	C₂²	semidirect
58. C₂₃×#467	C₂²	semidirect
59. C₂₃×#467	C₂²	semidirect
60. C₂₃×#441	C₂²	semidirect
61. C₄×Q₁₆×C₂₃	C₂²	semidirect
62. C₄×Q₁₆×C₂₃	C₂²	semidirect
69. C₂₃×#428	C₂²	semidirect
76. C₂₃×#427	C₂²	semidirect
80. C₂×C₂₃×#107	C₂²	semidirect
288. #61264	C₂₃	direct (N × H)
341. #3349	C₂×C₂₃	semidirect
342. #3344	C₂×C₂₃	semidirect
343. #3342	C₂×C₂₃	semidirect
344. #3338	C₂×C₂₃	semidirect
345. #3336	C₂×C₂₃	semidirect
346. #3336	C₂×C₂₃	semidirect
347. #3164	C₂×C₂₃	semidirect
348. #3097	C₂×C₂₃	semidirect
349. #3095	C₂×C₂₃	semidirect
350. #3082	C₂×C₂₃	semidirect
351. #3059	C₂×C₂₃	semidirect
352. C₂×#467	C₂×C₂₃	semidirect
353. #2950	C₂×C₂₃	semidirect
355. #2913	C₂×C₂₃	semidirect
356. C₂×#427	C₂×C₂₃	semidirect
405. #501	C₂²×C₂₃	semidirect
406. #500	C₂²×C₂₃	semidirect
407. #499	C₂²×C₂₃	semidirect
410. #485	C₂²×C₂₃	semidirect
411. #485	C₂²×C₂₃	semidirect
413. #484	C₂²×C₂₃	semidirect
415. #483	C₂²×C₂₃	semidirect
416. #479	C₂²×C₂₃	semidirect
417. #479	C₂²×C₂₃	semidirect
418. #477	C₂²×C₂₃	semidirect
419. #475	C₂²×C₂₃	semidirect
420. #470	C₂²×C₂₃	semidirect
425. #467	C₂²×C₂₃	semidirect
426. #467	C₂²×C₂₃	semidirect
427. #441	C₂²×C₂₃	semidirect
428. C₄×Q₁₆	C₂²×C₂₃	semidirect
429. C₄×Q₁₆	C₂²×C₂₃	semidirect
436. #428	C₂²×C₂₃	semidirect
443. #427	C₂²×C₂₃	semidirect
447. C₂×#107	C₂²×C₂₃	semidirect
573. C₂₃	#61264	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3495	2
C₂₃×#3349	2
C₂₃×#3344	2
C₂₃×#3342	2
C₂₃×#3338	2
C₂₃×#3336	2
C₂₃×#3164	2
C₂₃×#3097	2
C₂₃×#3095	2
C₂₃×#3082	2
C₂₃×#3059	2
C₂×C₂₃×#467	2
C₂₃×#2950	2
C₂₃×#2929	2
C₂₃×#2913	2
C₂×C₂₃×#427	2
#61264	23

Subgroups — C23×#61264 #19208890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61264 #19208890