Subgroups — C₂₃×#18660 #19166286

Order 5888.

908 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1644	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1643	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1626	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1625	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1622	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1622	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1554	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#557	C₂²	1	1	yes	characteristic
17	C₂₃×#554	C₂²	1	1	yes	characteristic
18	C₂₃×#554	C₂²	1	1	yes	characteristic
19	C₂₃×#553	—	2	1	no	—
20	C₂₃×#552	—	2	1	no	—
21	C₂₃×#552	—	2	2	no	—
22	C₂₃×#552	—	2	1	no	—
23	C₂₃×#547	—	2	1	no	—
24	C₂₃×#547	C₂²	1	1	yes	characteristic
25	C₂₃×#541	—	2	1	no	—
26	C₂₃×#539	—	2	2	no	—
27	C₂₃×#533	C₂²	1	1	yes	characteristic
28	C₂₃×#532	C₂²	1	1	yes	characteristic
29	C₂₃×#529	—	2	1	no	—
30	C₂₃×#529	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#125	—	2	1	no	—
32	C₂₃×#520	—	2	1	no	—
33	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#498	C₂²	1	1	yes	characteristic
35	C₂₃×#495	—	2	1	no	—
36	C₂₃×#492	C₂²	1	1	yes	characteristic
37	C₂₃×#488	—	2	1	no	—
38	C₂₃×#487	C₂²	1	1	yes	characteristic
39	C₂₃×#486	C₂²	1	1	yes	characteristic
40	C₂₃×#482	—	2	1	no	—
41	C₂₃×#475	C₂²	1	1	yes	characteristic
42	C₂₃×#474	C₂²	1	1	yes	characteristic
43	C₂₃×#465	—	2	2	no	—
44	C₂₃×#462	C₂²	1	1	yes	characteristic
45	C₂₃×#461	C₂²	1	1	yes	characteristic
46	C₂₃×#460	C₂²	1	1	yes	characteristic
47	C₂₃×#460	C₂²	1	1	yes	characteristic
48	C₂₃×#459	C₂²	1	1	yes	characteristic
49	C₂₃×#459	C₂²	1	1	yes	characteristic
50	C₂₃×#452	—	2	1	no	—
51	C₂₃×#449	—	2	1	no	—
52	C₂₃×#449	—	2	1	no	—
53	C₂₃×#442	—	2	1	no	—
54	C₂₃×#440	—	2	1	no	—
55	C₄×SD₁₆×C₂₃	—	2	2	no	—
56	C₂₃×#432	C₂²	1	1	yes	characteristic
57	C₂₃×#431	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#333	C₂²	1	1	yes	characteristic
60	C₂₃×#333	C₂²	1	1	yes	characteristic
61	C₂₃×#332	C₂²	1	1	yes	characteristic
62	C₂₃×#332	C₂²	1	1	yes	characteristic
63	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×#41×C₂₃	—	2	1	no	—
72	C₂×#41×C₂₃	—	2	1	no	—
73	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
74	C₂×Q₁₆×C₂₃	—	2	1	no	—
75	C₂×SD₁₆×C₂₃	—	2	2	no	—
76	C₂×SD₁₆×C₂₃	—	2	1	no	—
77	C₂×SD₁₆×C₂₃	—	2	1	no	—
78	C₂×SD₁₆×C₂₃	—	2	1	no	—
79	C₂×D₈×C₂₃	—	2	1	no	—
80	C₂×D₈×C₂₃	—	2	1	no	—
81	C₂²×C₈×C₂₃	—	2	1	no	—
82	C₂₃×C₄⋊Q₈	—	2	1	no	—
83	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₂₃×#127	C₂³	1	1	yes	characteristic
87	C₂₃×#126	—	2	2	no	—
88	C₂₃×#126	—	2	2	no	—
89	C₂₃×#126	—	2	2	no	—
90	C₂₃×#126	—	2	1	no	—
91	C₂₃×#125	—	2	2	no	—
92	C₂₃×#125	—	2	2	no	—
93	C₂₃×#125	—	2	2	no	—
94	C₂₃×#125	—	2	1	no	—
95	C₂₃×#125	—	2	1	no	—
96	C₂₃×#125	—	2	2	no	—
97	C₂₃×#125	—	2	1	no	—
98	C₂₃×#125	—	2	1	no	—
99	C₂₃×#125	D₄	1	1	yes	characteristic
100	C₂₃×#124	—	2	1	no	—
101	C₂₃×#124	D₄	1	1	yes	characteristic
102	C₂₃×#123	—	2	2	no	—
103	C₂₃×#123	—	2	2	no	—
104	C₂₃×#123	—	2	2	no	—
105	C₂₃×#123	—	2	1	no	—
106	C₂₃×#123	—	2	2	no	—
107	C₂₃×C₂²⋊Q₈	—	2	1	no	—
108	C₂₃×C₂²⋊Q₈	—	2	1	no	—
109	C₂₃×C₂²⋊Q₈	—	2	2	no	—
110	C₂₃×C₂²⋊Q₈	—	2	2	no	—
111	C₂₃×C₂²⋊Q₈	—	2	1	no	—
112	C₂₃×C₂²⋊Q₈	—	2	1	no	—
113	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
114	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
115	C₂₃×#121	—	2	2	no	—
116	C₂₃×#121	—	2	1	no	—
117	C₂₃×#121	—	2	1	no	—
118	C₂₃×#121	—	2	1	no	—
119	C₂₃×#121	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₂₃	—	2	1	no	—
121	C₄×Q₈×C₂₃	—	2	1	no	—
122	C₄×Q₈×C₂₃	—	2	1	no	—
123	C₄×Q₈×C₂₃	D₄	1	2	yes	—
124	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
125	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
126	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
127	C₄×D₄×C₂₃	—	2	2	no	—
128	C₄×D₄×C₂₃	—	2	2	no	—
129	C₄×D₄×C₂₃	—	2	1	no	—
130	C₄×D₄×C₂₃	—	2	1	no	—
131	C₄×D₄×C₂₃	—	2	1	no	—
132	C₄×D₄×C₂₃	—	2	1	no	—
133	C₄×D₄×C₂₃	—	2	1	no	—
134	C₄×D₄×C₂₃	—	2	1	no	—
135	C₄×D₄×C₂₃	—	2	1	no	—
136	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
137	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂₃×#117	—	2	2	no	—
140	C₂₃×#117	—	2	2	no	—
141	C₂₃×#117	—	2	1	no	—
142	C₂₃×#117	—	2	1	no	—
143	C₂₃×#117	—	2	1	no	—
144	C₂₃×#117	D₄	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
146	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
147	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₄²×C₂₃	—	2	1	no	—
151	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
152	C₂₃×#107	—	2	1	no	—
153	C₂₃×#106	—	2	2	no	—
154	C₂₃×#106	—	2	1	no	—
155	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₃×#103	—	2	2	no	—
160	C₂₃×#103	—	2	1	no	—
161	C₂₃×#103	—	2	1	no	—
162	C₂₃×#103	—	2	1	no	—
163	C₂₃×#102	—	2	1	no	—
164	C₂₃×#102	—	2	2	no	—
165	C₂₃×#102	—	2	1	no	—
166	C₂₃×#102	—	2	1	no	—
167	C₂₃×#102	—	2	1	no	—
168	C₂₃×#102	—	2	1	no	—
169	C₂₃×C₂²⋊C₈	—	2	1	no	—
170	C₂₃×C₂²⋊C₈	—	2	1	no	—
171	C₂₃×#97	—	2	1	no	—
172	C₄×C₈×C₂₃	—	2	1	no	—
173	C₄×C₈×C₂₃	—	2	1	no	—
174	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
176	#41×C₂₃	—	2	2	no	—
177	#41×C₂₃	—	4	1	no	—
178	#41×C₂₃	—	4	2	no	—
179	#41×C₂₃	—	4	2	no	—
180	#41×C₂₃	—	8	1	no	—
181	#41×C₂₃	—	8	1	no	—
182	C₂×Q₈×C₂₃	—	2	1	no	—
183	C₂×Q₈×C₂₃	—	2	1	no	—
184	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
186	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
187	C₂×D₄×C₂₃	—	2	2	no	—
188	C₂×D₄×C₂₃	—	2	1	no	—
189	C₂×D₄×C₂₃	—	2	1	no	—
190	C₂×D₄×C₂₃	—	2	1	no	—
191	C₂×D₄×C₂₃	—	2	1	no	—
192	C₂×D₄×C₂₃	—	2	1	no	—
193	C₂×D₄×C₂₃	—	4	1	no	—
194	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	—	2	2	no	—
197	C₂²×C₄×C₂₃	—	2	2	no	—
198	C₂²×C₄×C₂₃	—	2	2	no	—
199	C₂²×C₄×C₂₃	—	2	1	no	—
200	C₂²×C₄×C₂₃	—	2	1	no	—
201	C₂²×C₄×C₂₃	—	2	1	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	4	1	no	—
204	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
207	Q₁₆×C₂₃	—	8	1	no	—
208	SD₁₆×C₂₃	—	4	4	no	—
209	SD₁₆×C₂₃	—	4	2	no	—
210	SD₁₆×C₂₃	—	8	1	no	—
211	SD₁₆×C₂₃	—	8	1	no	—
212	D₈×C₂₃	—	4	2	no	—
213	D₈×C₂₃	—	8	1	no	—
214	C₂×C₈×C₂₃	—	2	1	no	—
215	C₂×C₈×C₂₃	—	2	1	no	—
216	C₂×C₈×C₂₃	—	2	1	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	—	2	1	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	4	2	no	—
221	C₄⋊C₄×C₂₃	—	2	2	no	—
222	C₄⋊C₄×C₂₃	—	2	2	no	—
223	C₄⋊C₄×C₂₃	—	2	2	no	—
224	C₄⋊C₄×C₂₃	—	2	2	no	—
225	C₄⋊C₄×C₂₃	—	2	2	no	—
226	C₄⋊C₄×C₂₃	—	2	2	no	—
227	C₄⋊C₄×C₂₃	—	2	2	no	—
228	C₄⋊C₄×C₂₃	—	2	2	no	—
229	C₄⋊C₄×C₂₃	—	2	1	no	—
230	C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₄⋊C₄×C₂₃	—	2	2	no	—
232	C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	1	no	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	1	no	—
241	C₄⋊C₄×C₂₃	—	2	1	no	—
242	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
246	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₂²⋊C₄×C₂₃	—	2	2	no	—
248	C₂²⋊C₄×C₂₃	—	2	2	no	—
249	C₂²⋊C₄×C₂₃	—	2	2	no	—
250	C₂²⋊C₄×C₂₃	—	2	2	no	—
251	C₂²⋊C₄×C₂₃	—	2	1	no	—
252	C₂²⋊C₄×C₂₃	—	2	1	no	—
253	C₂²⋊C₄×C₂₃	—	2	1	no	—
254	C₂²⋊C₄×C₂₃	—	2	1	no	—
255	C₂²⋊C₄×C₂₃	—	2	1	no	—
256	C₂²⋊C₄×C₂₃	—	2	1	no	—
257	C₂²⋊C₄×C₂₃	—	2	1	no	—
258	C₂²⋊C₄×C₂₃	—	2	1	no	—
259	C₂²⋊C₄×C₂₃	—	4	1	no	—
260	C₂²⋊C₄×C₂₃	—	4	1	no	—
261	C₄²×C₂₃	—	2	2	no	—
262	C₄²×C₂₃	—	2	1	no	—
263	C₄²×C₂₃	—	2	1	no	—
264	C₄²×C₂₃	—	2	2	no	—
265	C₄²×C₂₃	—	2	1	no	—
266	C₄²×C₂₃	—	2	1	no	—
267	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
271	#18660	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	1	no	—
274	C₂³×C₂₃	—	4	1	no	—
275	C₂³×C₂₃	#120	1	1	yes	characteristic
276	Q₈×C₂₃	—	2	1	no	—
277	Q₈×C₂₃	—	2	1	no	—
278	Q₈×C₂₃	—	2	1	no	—
279	Q₈×C₂₃	—	2	1	no	—
280	Q₈×C₂₃	—	4	2	no	—
281	Q₈×C₂₃	—	4	1	no	—
282	Q₈×C₂₃	—	4	1	no	—
283	Q₈×C₂₃	—	4	1	no	—
284	Q₈×C₂₃	—	4	1	no	—
285	D₄×C₂₃	—	2	1	no	—
286	D₄×C₂₃	—	2	1	no	—
287	D₄×C₂₃	—	2	1	no	—
288	D₄×C₂₃	—	4	2	no	—
289	D₄×C₂₃	—	4	2	no	—
290	D₄×C₂₃	—	4	4	no	—
291	D₄×C₂₃	—	4	1	no	—
292	D₄×C₂₃	—	4	1	no	—
293	D₄×C₂₃	—	4	1	no	—
294	D₄×C₂₃	—	4	1	no	—
295	D₄×C₂₃	—	8	1	no	—
296	D₄×C₂₃	—	8	2	no	—
297	D₄×C₂₃	#135	1	2	yes	—
298	C₂×C₄×C₂₃	—	2	1	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	1	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	2	1	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	—	4	1	no	—
311	C₂×C₄×C₂₃	—	4	2	no	—
312	C₂×C₄×C₂₃	—	4	4	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	8	1	no	—
319	C₂×C₄×C₂₃	—	8	2	no	—
320	C₂×C₄×C₂₃	—	8	2	no	—
321	C₂×C₄×C₂₃	—	8	2	no	—
322	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
323	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
324	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
325	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
328	C₈×C₂₃	—	2	2	no	—
329	C₈×C₂₃	—	4	1	no	—
330	C₈×C₂₃	—	4	1	no	—
331	C₈×C₂₃	—	4	1	no	—
332	C₈×C₂₃	—	4	1	no	—
333	C₈×C₂₃	—	4	1	no	—
334	#3515	C₂×C₂₃	1	1	yes	characteristic, complemented
335	#3212	C₂×C₂₃	1	1	yes	characteristic, complemented
336	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#3115	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#1654	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#1653	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#1644	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#1643	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#1626	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#1625	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#1622	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#1622	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#1554	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1494	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1476	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂²×C₂₃	—	2	1	no	—
350	C₂²×C₂₃	—	2	2	no	—
351	C₂²×C₂₃	—	2	1	no	—
352	C₂²×C₂₃	—	2	1	no	—
353	C₂²×C₂₃	—	4	1	no	—
354	C₂²×C₂₃	—	4	1	no	—
355	C₂²×C₂₃	—	4	1	no	—
356	C₂²×C₂₃	—	4	1	no	—
357	C₂²×C₂₃	—	4	1	no	—
358	C₂²×C₂₃	—	8	1	no	—
359	C₂²×C₂₃	—	8	1	no	—
360	C₂²×C₂₃	—	8	1	no	—
361	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
362	C₄×C₂₃	—	2	1	no	—
363	C₄×C₂₃	—	2	1	no	—
364	C₄×C₂₃	—	2	1	no	—
365	C₄×C₂₃	—	2	1	no	—
366	C₄×C₂₃	—	4	1	no	—
367	C₄×C₂₃	—	4	1	no	—
368	C₄×C₂₃	—	4	2	no	—
369	C₄×C₂₃	—	4	1	no	—
370	C₄×C₂₃	—	4	1	no	—
371	C₄×C₂₃	—	4	1	no	—
372	C₄×C₂₃	—	4	1	no	—
373	C₄×C₂₃	—	4	2	no	—
374	C₄×C₂₃	—	8	1	no	—
375	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
376	C₄×C₂₃	#575	1	1	yes	characteristic
377	C₄×C₂₃	#577	1	1	yes	characteristic
378	C₄×C₂₃	#577	1	1	yes	characteristic
379	#557	C₂²×C₂₃	1	1	yes	characteristic
380	#554	C₂²×C₂₃	1	1	yes	characteristic
381	#554	C₂²×C₂₃	1	1	yes	characteristic
382	#553	—	2	1	no	—
383	#552	—	2	1	no	—
384	#552	—	2	2	no	—
385	#552	—	2	1	no	—
386	#547	—	2	1	no	—
387	#547	C₂²×C₂₃	1	1	yes	characteristic
388	#541	—	2	1	no	—
389	#539	—	2	2	no	—
390	#533	C₂²×C₂₃	1	1	yes	characteristic
391	#532	C₂²×C₂₃	1	1	yes	characteristic
392	#529	—	2	1	no	—
393	#529	C₂²×C₂₃	1	1	yes	characteristic
394	C₂×#125	—	2	1	no	—
395	#520	—	2	1	no	—
396	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
397	#498	C₂²×C₂₃	1	1	yes	characteristic
398	#495	—	2	1	no	—
399	#492	C₂²×C₂₃	1	1	yes	characteristic
400	#488	—	2	1	no	—
401	#487	C₂²×C₂₃	1	1	yes	characteristic
402	#486	C₂²×C₂₃	1	1	yes	characteristic
403	#482	—	2	1	no	—
404	#475	C₂²×C₂₃	1	1	yes	characteristic
405	#474	C₂²×C₂₃	1	1	yes	characteristic
406	#465	—	2	2	no	—
407	#462	C₂²×C₂₃	1	1	yes	characteristic
408	#461	C₂²×C₂₃	1	1	yes	characteristic
409	#460	C₂²×C₂₃	1	1	yes	characteristic
410	#460	C₂²×C₂₃	1	1	yes	characteristic
411	#459	C₂²×C₂₃	1	1	yes	characteristic
412	#459	C₂²×C₂₃	1	1	yes	characteristic
413	#452	—	2	1	no	—
414	#449	—	2	1	no	—
415	#449	—	2	1	no	—
416	#442	—	2	1	no	—
417	#440	—	2	1	no	—
418	C₄×SD₁₆	—	2	2	no	—
419	#432	C₂²×C₂₃	1	1	yes	characteristic
420	#431	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
422	#333	C₂²×C₂₃	1	1	yes	characteristic
423	#333	C₂²×C₂₃	1	1	yes	characteristic
424	#332	C₂²×C₂₃	1	1	yes	characteristic
425	#332	C₂²×C₂₃	1	1	yes	characteristic
426	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
427	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
428	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
429	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
430	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
431	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
432	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
433	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₂₃	—	4	1	no	—
435	C₂×C₂₃	—	4	2	no	—
436	C₂×C₂₃	—	8	1	no	—
437	C₂×C₂₃	—	16	1	no	—
438	C₂×C₂₃	#3002	1	1	yes	characteristic
439	C₂×C₂₃	#3010	1	1	yes	characteristic
440	C₂×C₂₃	#3018	1	1	yes	characteristic
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	2	1	no	—
443	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
444	C₂×Q₁₆	—	2	1	no	—
445	C₂×SD₁₆	—	2	2	no	—
446	C₂×SD₁₆	—	2	1	no	—
447	C₂×SD₁₆	—	2	1	no	—
448	C₂×SD₁₆	—	2	1	no	—
449	C₂×D₈	—	2	1	no	—
450	C₂×D₈	—	2	1	no	—
451	C₂²×C₈	—	2	1	no	—
452	C₄⋊Q₈	—	2	1	no	—
453	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
454	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
456	#127	C₂³×C₂₃	1	1	yes	characteristic
457	#126	—	2	2	no	—
458	#126	—	2	2	no	—
459	#126	—	2	2	no	—
460	#126	—	2	1	no	—
461	#125	—	2	2	no	—
462	#125	—	2	2	no	—
463	#125	—	2	2	no	—
464	#125	—	2	1	no	—
465	#125	—	2	1	no	—
466	#125	—	2	2	no	—
467	#125	—	2	1	no	—
468	#125	—	2	1	no	—
469	#125	D₄×C₂₃	1	1	yes	characteristic
470	#124	—	2	1	no	—
471	#124	D₄×C₂₃	1	1	yes	characteristic
472	#123	—	2	2	no	—
473	#123	—	2	2	no	—
474	#123	—	2	2	no	—
475	#123	—	2	1	no	—
476	#123	—	2	2	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	1	no	—
481	C₂²⋊Q₈	—	2	1	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
484	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
485	#121	—	2	2	no	—
486	#121	—	2	1	no	—
487	#121	—	2	1	no	—
488	#121	—	2	1	no	—
489	#121	D₄×C₂₃	1	1	yes	characteristic
490	C₄×Q₈	—	2	1	no	—
491	C₄×Q₈	—	2	1	no	—
492	C₄×Q₈	—	2	1	no	—
493	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
494	C₄×Q₈	D₄×C₂₃	1	2	yes	—
495	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
496	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	1	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	1	no	—
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
507	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
508	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
509	#117	—	2	2	no	—
510	#117	—	2	2	no	—
511	#117	—	2	1	no	—
512	#117	—	2	1	no	—
513	#117	—	2	1	no	—
514	#117	D₄×C₂₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	—	2	2	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄²	—	2	1	no	—
521	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
522	#107	—	2	1	no	—
523	#106	—	2	2	no	—
524	#106	—	2	1	no	—
525	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
526	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
527	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
528	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
529	#103	—	2	2	no	—
530	#103	—	2	1	no	—
531	#103	—	2	1	no	—
532	#103	—	2	1	no	—
533	#102	—	2	1	no	—
534	#102	—	2	2	no	—
535	#102	—	2	1	no	—
536	#102	—	2	1	no	—
537	#102	—	2	1	no	—
538	#102	—	2	1	no	—
539	C₂²⋊C₈	—	2	1	no	—
540	C₂²⋊C₈	—	2	1	no	—
541	#97	—	2	1	no	—
542	C₄×C₈	—	2	1	no	—
543	C₄×C₈	—	2	1	no	—
544	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
545	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
546	C₂₃	#18660	1	1	yes	characteristic, direct product factor, Sylow
547	#41	—	2	2	no	—
548	#41	—	4	1	no	—
549	#41	—	4	2	no	—
550	#41	—	4	2	no	—
551	#41	—	8	1	no	—
552	#41	—	8	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
556	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
557	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
566	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	4	1	no	—
575	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
578	Q₁₆	—	8	1	no	—
579	SD₁₆	—	4	4	no	—
580	SD₁₆	—	4	2	no	—
581	SD₁₆	—	8	1	no	—
582	SD₁₆	—	8	1	no	—
583	D₈	—	4	2	no	—
584	D₈	—	8	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	4	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
614	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
615	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	4	1	no	—
631	C₂²⋊C₄	—	4	1	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	C₂₃×#120	1	1	yes	characteristic
646	Q₈	—	2	1	no	—
647	Q₈	—	2	1	no	—
648	Q₈	—	2	1	no	—
649	Q₈	—	2	1	no	—
650	Q₈	—	4	2	no	—
651	Q₈	—	4	1	no	—
652	Q₈	—	4	1	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	D₄	—	2	1	no	—
656	D₄	—	2	1	no	—
657	D₄	—	2	1	no	—
658	D₄	—	4	2	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	4	no	—
661	D₄	—	4	1	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	D₄	—	4	1	no	—
665	D₄	—	8	1	no	—
666	D₄	—	8	2	no	—
667	D₄	C₂₃×#135	1	2	yes	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	8	1	no	—
689	C₂×C₄	—	8	2	no	—
690	C₂×C₄	—	8	2	no	—
691	C₂×C₄	—	8	2	no	—
692	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
693	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
694	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
695	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
698	C₈	—	2	2	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	—	8	1	no	—
716	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	2	no	—
729	C₄	—	8	1	no	—
730	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
731	C₄	C₂₃×#575	1	1	yes	characteristic
732	C₄	C₂₃×#577	1	1	yes	characteristic
733	C₄	C₂₃×#577	1	1	yes	characteristic
734	C₂	—	4	1	no	—
735	C₂	—	4	2	no	—
736	C₂	—	8	1	no	—
737	C₂	—	16	1	no	—
738	C₂	C₂₃×#3002	1	1	yes	characteristic
739	C₂	C₂₃×#3010	1	1	yes	characteristic
740	C₂	C₂₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3515	C₂	semidirect
2. C₂₃×#3212	C₂	semidirect
3. C₂₃×#3167	C₂	semidirect
4. C₂₃×#3115	C₂	semidirect
5. C₂₃×#1654	C₂	semidirect
6. C₂₃×#1653	C₂	semidirect
7. C₂₃×#1644	C₂	semidirect
8. C₂₃×#1643	C₂	semidirect
9. C₂₃×#1626	C₂	semidirect
10. C₂₃×#1625	C₂	semidirect
11. C₂₃×#1622	C₂	semidirect
12. C₂₃×#1622	C₂	semidirect
13. C₂₃×#1554	C₂	semidirect
14. C₂₃×#1494	C₂	semidirect
15. C₂₃×#1476	C₂	semidirect
271. #18660	C₂₃	direct (N × H)
334. #3515	C₂×C₂₃	semidirect
335. #3212	C₂×C₂₃	semidirect
336. #3167	C₂×C₂₃	semidirect
337. #3115	C₂×C₂₃	semidirect
338. #1654	C₂×C₂₃	semidirect
339. #1653	C₂×C₂₃	semidirect
340. #1644	C₂×C₂₃	semidirect
341. #1643	C₂×C₂₃	semidirect
342. #1626	C₂×C₂₃	semidirect
343. #1625	C₂×C₂₃	semidirect
344. #1622	C₂×C₂₃	semidirect
345. #1622	C₂×C₂₃	semidirect
346. #1554	C₂×C₂₃	semidirect
347. #1494	C₂×C₂₃	semidirect
348. #1476	C₂×C₂₃	semidirect
546. C₂₃	#18660	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×#3515	2
C₂₃×#3212	2
C₂₃×#3167	2
C₂₃×#3115	2
C₂₃×#1654	2
C₂₃×#1653	2
C₂₃×#1644	2
C₂₃×#1643	2
C₂₃×#1626	2
C₂₃×#1625	2
C₂₃×#1622	2
C₂₃×#1554	2
C₂₃×#1494	2
C₂₃×#1476	2
#18660	23

Subgroups — C23×#18660 #19166286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18660 #19166286