Subgroups — C₂₃×#19736 #19167362

Order 5888.

636 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3231	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3231	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3231	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#3230	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#3229	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#3209	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1723	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1723	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1718	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1718	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1718	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1716	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1710	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1707	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1454	C₂	1	1	yes	maximal, characteristic
16	C₂₃×#533	C₂²	1	1	yes	characteristic
17	C₂₃×#533	C₂²	1	1	yes	characteristic
18	C₂₃×#533	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂₃×#500	C₂²	1	1	yes	characteristic
21	C₂₃×#500	C₂²	1	1	yes	characteristic
22	C₂₃×#500	C₂²	1	1	yes	characteristic
23	C₂₃×#500	C₂²	1	1	yes	characteristic
24	C₂₃×#500	C₂²	1	1	yes	characteristic
25	C₂₃×#498	C₂²	1	1	yes	characteristic
26	C₂₃×#498	C₂²	1	1	yes	characteristic
27	C₂₃×#498	C₂²	1	1	yes	characteristic
28	C₂₃×#498	C₂²	1	1	yes	characteristic
29	C₂₃×#498	C₂²	1	1	yes	characteristic
30	C₂₃×#494	C₂²	1	1	yes	characteristic
31	C₂₃×#494	C₂²	1	1	yes	characteristic
32	C₂₃×#487	C₂²	1	1	yes	characteristic
33	C₂₃×#487	C₂²	1	1	yes	characteristic
34	C₂₃×#487	C₂²	1	1	yes	characteristic
35	C₂₃×#487	C₂²	1	1	yes	characteristic
36	C₂₃×#487	C₂²	1	1	yes	characteristic
37	C₂₃×#487	C₂²	1	1	yes	characteristic
38	C₂₃×#487	C₂²	1	1	yes	characteristic
39	C₂₃×#487	C₂²	1	1	yes	characteristic
40	C₂₃×#487	C₂²	1	1	yes	characteristic
41	C₂₃×#487	C₂²	1	1	yes	characteristic
42	C₂₃×#487	C₂²	1	1	yes	characteristic
43	C₂₃×#487	C₂²	1	1	yes	characteristic
44	C₂₃×#485	—	2	2	no	—
45	C₂₃×#485	—	2	2	no	—
46	C₂₃×#485	—	2	2	no	—
47	C₂₃×#484	—	2	2	no	—
48	C₂₃×#483	—	2	2	no	—
49	C₂₃×#479	—	2	2	no	—
50	C₂₃×#479	—	2	2	no	—
51	C₂₃×#479	—	2	2	no	—
52	C₂₃×#477	—	2	2	no	—
53	C₂₃×#475	—	2	2	no	—
54	C₂₃×#462	—	2	2	no	—
55	C₂₃×#451	—	2	2	no	—
56	C₂₃×#431	C₂²	1	1	yes	characteristic
57	C₂₃×#431	C₂²	1	1	yes	characteristic
58	C₂₃×#431	C₂²	1	1	yes	characteristic
59	C₂₃×#322	C₂²	1	1	yes	characteristic
60	C₂₃×#322	C₂²	1	1	yes	characteristic
61	C₂₃×#322	C₂²	1	1	yes	characteristic
62	C₈²×C₂₃	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₂₃	—	2	1	no	—
64	C₂×Q₁₆×C₂₃	—	2	2	no	—
65	C₂×Q₁₆×C₂₃	—	2	2	no	—
66	C₂₃×C₄⋊Q₈	—	2	1	no	—
67	C₂₃×C₄⋊Q₈	—	2	1	no	—
68	C₂₃×C₄⋊Q₈	—	2	1	no	—
69	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
75	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₂₃×#125	—	2	1	no	—
78	C₂₃×#125	—	2	1	no	—
79	C₂₃×#125	—	2	1	no	—
80	C₂₃×C₂²⋊Q₈	—	2	1	no	—
81	C₂₃×C₂²⋊Q₈	—	2	1	no	—
82	C₂₃×C₂²⋊Q₈	—	2	1	no	—
83	C₂₃×C₂²⋊Q₈	—	2	1	no	—
84	C₂₃×C₂²⋊Q₈	—	2	1	no	—
85	C₂₃×C₂²⋊Q₈	—	2	1	no	—
86	C₄×Q₈×C₂₃	—	2	1	no	—
87	C₄×Q₈×C₂₃	—	2	1	no	—
88	C₄×Q₈×C₂₃	—	2	1	no	—
89	C₄×Q₈×C₂₃	—	2	1	no	—
90	C₄×Q₈×C₂₃	—	2	1	no	—
91	C₄×Q₈×C₂₃	—	2	1	no	—
92	C₂₃×#117	—	2	1	no	—
93	C₂₃×#117	—	2	1	no	—
94	C₂₃×#117	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
97	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
98	C₂₃×#107	—	2	2	no	—
99	C₂₃×#107	—	2	2	no	—
100	C₂₃×#107	—	2	2	no	—
101	C₂₃×#107	—	2	2	no	—
102	C₂₃×#107	—	2	2	no	—
103	C₂₃×#106	—	2	2	no	—
104	C₂₃×#106	—	2	2	no	—
105	C₂₃×#106	—	2	2	no	—
106	C₂₃×#106	—	2	2	no	—
107	C₂₃×#106	—	2	2	no	—
108	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
109	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
110	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
111	C₂₃×#103	—	2	2	no	—
112	C₂₃×#103	—	2	2	no	—
113	C₂₃×#103	—	2	2	no	—
114	C₂₃×#103	—	2	2	no	—
115	C₂₃×#103	—	2	2	no	—
116	C₂₃×#103	—	2	2	no	—
117	C₂₃×#103	—	2	2	no	—
118	C₂₃×#103	—	2	2	no	—
119	C₂₃×#103	—	2	2	no	—
120	C₂₃×#103	—	2	2	no	—
121	C₂₃×#103	—	2	2	no	—
122	C₂₃×#103	—	2	2	no	—
123	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
124	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
125	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
126	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
129	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
130	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
131	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×Q₈×C₂₃	—	2	1	no	—
133	C₂×Q₈×C₂₃	—	2	1	no	—
134	C₂×Q₈×C₂₃	—	2	1	no	—
135	C₂×Q₈×C₂₃	—	2	1	no	—
136	C₂×Q₈×C₂₃	—	2	1	no	—
137	C₂×Q₈×C₂₃	—	2	1	no	—
138	C₂×Q₈×C₂₃	—	2	1	no	—
139	C₂×Q₈×C₂₃	—	2	1	no	—
140	C₂×Q₈×C₂₃	—	4	1	no	—
141	C₂×Q₈×C₂₃	—	8	2	no	—
142	C₂²×C₄×C₂₃	—	4	1	no	—
143	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₂₃	—	8	2	no	—
147	Q₁₆×C₂₃	—	8	2	no	—
148	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₂₃	—	2	1	no	—
155	C₄⋊C₄×C₂₃	—	2	1	no	—
156	C₄⋊C₄×C₂₃	—	2	1	no	—
157	C₄⋊C₄×C₂₃	—	2	1	no	—
158	C₄⋊C₄×C₂₃	—	2	1	no	—
159	C₄⋊C₄×C₂₃	—	2	1	no	—
160	C₄⋊C₄×C₂₃	—	2	1	no	—
161	C₄⋊C₄×C₂₃	—	2	1	no	—
162	C₄⋊C₄×C₂₃	—	2	1	no	—
163	C₄⋊C₄×C₂₃	—	2	1	no	—
164	C₄⋊C₄×C₂₃	—	2	1	no	—
165	C₄⋊C₄×C₂₃	—	2	1	no	—
166	C₄⋊C₄×C₂₃	—	2	1	no	—
167	C₄⋊C₄×C₂₃	—	2	1	no	—
168	C₄⋊C₄×C₂₃	—	2	1	no	—
169	C₄⋊C₄×C₂₃	—	2	1	no	—
170	C₄⋊C₄×C₂₃	—	4	1	no	—
171	C₄⋊C₄×C₂₃	—	4	1	no	—
172	C₄⋊C₄×C₂₃	—	4	1	no	—
173	C₄⋊C₄×C₂₃	—	4	1	no	—
174	C₄⋊C₄×C₂₃	—	4	1	no	—
175	C₄⋊C₄×C₂₃	—	4	1	no	—
176	C₄⋊C₄×C₂₃	—	4	1	no	—
177	C₄⋊C₄×C₂₃	—	4	1	no	—
178	C₂²⋊C₄×C₂₃	—	4	1	no	—
179	C₂²⋊C₄×C₂₃	—	4	1	no	—
180	C₂²⋊C₄×C₂₃	—	4	1	no	—
181	C₄²×C₂₃	—	4	1	no	—
182	C₄²×C₂₃	—	4	1	no	—
183	C₄²×C₂₃	—	4	1	no	—
184	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
188	#19736	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₂₃	#127	1	1	yes	characteristic
190	Q₈×C₂₃	—	4	2	no	—
191	Q₈×C₂₃	—	4	2	no	—
192	Q₈×C₂₃	—	4	2	no	—
193	Q₈×C₂₃	—	4	2	no	—
194	Q₈×C₂₃	—	4	2	no	—
195	Q₈×C₂₃	—	4	2	no	—
196	Q₈×C₂₃	—	4	2	no	—
197	Q₈×C₂₃	—	4	2	no	—
198	Q₈×C₂₃	—	8	2	no	—
199	C₂×C₄×C₂₃	—	2	2	no	—
200	C₂×C₄×C₂₃	—	2	2	no	—
201	C₂×C₄×C₂₃	—	2	2	no	—
202	C₂×C₄×C₂₃	—	4	1	no	—
203	C₂×C₄×C₂₃	—	4	1	no	—
204	C₂×C₄×C₂₃	—	4	1	no	—
205	C₂×C₄×C₂₃	—	4	1	no	—
206	C₂×C₄×C₂₃	—	4	1	no	—
207	C₂×C₄×C₂₃	—	4	1	no	—
208	C₂×C₄×C₂₃	—	4	1	no	—
209	C₂×C₄×C₂₃	—	4	1	no	—
210	C₂×C₄×C₂₃	—	8	2	no	—
211	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
212	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
213	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
214	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
217	C₈×C₂₃	—	2	2	no	—
218	C₈×C₂₃	—	2	2	no	—
219	C₈×C₂₃	—	2	2	no	—
220	C₈×C₂₃	—	2	2	no	—
221	C₈×C₂₃	—	2	2	no	—
222	C₈×C₂₃	—	2	2	no	—
223	#3231	C₂×C₂₃	1	1	yes	characteristic
224	#3231	C₂×C₂₃	1	1	yes	characteristic
225	#3231	C₂×C₂₃	1	1	yes	characteristic
226	#3230	C₂×C₂₃	1	1	yes	characteristic
227	#3229	C₂×C₂₃	1	1	yes	characteristic
228	#3209	C₂×C₂₃	1	1	yes	characteristic
229	#1723	C₂×C₂₃	1	1	yes	characteristic, complemented
230	#1723	C₂×C₂₃	1	1	yes	characteristic, complemented
231	#1718	C₂×C₂₃	1	1	yes	characteristic, complemented
232	#1718	C₂×C₂₃	1	1	yes	characteristic, complemented
233	#1718	C₂×C₂₃	1	1	yes	characteristic, complemented
234	#1716	C₂×C₂₃	1	1	yes	characteristic, complemented
235	#1710	C₂×C₂₃	1	1	yes	characteristic, complemented
236	#1707	C₂×C₂₃	1	1	yes	characteristic, complemented
237	#1454	C₂×C₂₃	1	1	yes	characteristic
238	C₂²×C₂₃	—	2	1	no	—
239	C₂²×C₂₃	—	2	1	no	—
240	C₂²×C₂₃	—	2	1	no	—
241	C₂²×C₂₃	C₂×#127	1	1	yes	characteristic
242	C₄×C₂₃	—	2	1	no	—
243	C₄×C₂₃	—	2	1	no	—
244	C₄×C₂₃	—	2	1	no	—
245	C₄×C₂₃	—	8	1	no	—
246	C₄×C₂₃	—	8	1	no	—
247	C₄×C₂₃	—	8	1	no	—
248	C₄×C₂₃	—	8	1	no	—
249	C₄×C₂₃	—	8	1	no	—
250	C₄×C₂₃	—	8	1	no	—
251	C₄×C₂₃	—	8	1	no	—
252	C₄×C₂₃	—	8	1	no	—
253	C₄×C₂₃	#577	1	2	yes	—
254	C₄×C₂₃	#578	1	2	yes	—
255	C₄×C₂₃	#578	1	2	yes	—
256	#533	C₂²×C₂₃	1	1	yes	characteristic
257	#533	C₂²×C₂₃	1	1	yes	characteristic
258	#533	C₂²×C₂₃	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
260	#500	C₂²×C₂₃	1	1	yes	characteristic
261	#500	C₂²×C₂₃	1	1	yes	characteristic
262	#500	C₂²×C₂₃	1	1	yes	characteristic
263	#500	C₂²×C₂₃	1	1	yes	characteristic
264	#500	C₂²×C₂₃	1	1	yes	characteristic
265	#498	C₂²×C₂₃	1	1	yes	characteristic
266	#498	C₂²×C₂₃	1	1	yes	characteristic
267	#498	C₂²×C₂₃	1	1	yes	characteristic
268	#498	C₂²×C₂₃	1	1	yes	characteristic
269	#498	C₂²×C₂₃	1	1	yes	characteristic
270	#494	C₂²×C₂₃	1	1	yes	characteristic
271	#494	C₂²×C₂₃	1	1	yes	characteristic
272	#487	C₂²×C₂₃	1	1	yes	characteristic
273	#487	C₂²×C₂₃	1	1	yes	characteristic
274	#487	C₂²×C₂₃	1	1	yes	characteristic
275	#487	C₂²×C₂₃	1	1	yes	characteristic
276	#487	C₂²×C₂₃	1	1	yes	characteristic
277	#487	C₂²×C₂₃	1	1	yes	characteristic
278	#487	C₂²×C₂₃	1	1	yes	characteristic
279	#487	C₂²×C₂₃	1	1	yes	characteristic
280	#487	C₂²×C₂₃	1	1	yes	characteristic
281	#487	C₂²×C₂₃	1	1	yes	characteristic
282	#487	C₂²×C₂₃	1	1	yes	characteristic
283	#487	C₂²×C₂₃	1	1	yes	characteristic
284	#485	—	2	2	no	—
285	#485	—	2	2	no	—
286	#485	—	2	2	no	—
287	#484	—	2	2	no	—
288	#483	—	2	2	no	—
289	#479	—	2	2	no	—
290	#479	—	2	2	no	—
291	#479	—	2	2	no	—
292	#477	—	2	2	no	—
293	#475	—	2	2	no	—
294	#462	—	2	2	no	—
295	#451	—	2	2	no	—
296	#431	C₂²×C₂₃	1	1	yes	characteristic
297	#431	C₂²×C₂₃	1	1	yes	characteristic
298	#431	C₂²×C₂₃	1	1	yes	characteristic
299	#322	C₂²×C₂₃	1	1	yes	characteristic
300	#322	C₂²×C₂₃	1	1	yes	characteristic
301	#322	C₂²×C₂₃	1	1	yes	characteristic
302	C₈²	C₂²×C₂₃	1	1	yes	characteristic
303	C₂×C₂₃	—	4	1	no	—
304	C₂×C₂₃	#3154	1	1	yes	characteristic
305	C₂×C₂₃	#3156	1	1	yes	characteristic
306	C₂×C₂₃	#3156	1	1	yes	characteristic
307	C₂²×Q₈	—	2	1	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂×Q₁₆	—	2	2	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
314	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
315	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
316	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
317	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
318	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
319	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
321	#125	—	2	1	no	—
322	#125	—	2	1	no	—
323	#125	—	2	1	no	—
324	C₂²⋊Q₈	—	2	1	no	—
325	C₂²⋊Q₈	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	—	2	1	no	—
333	C₄×Q₈	—	2	1	no	—
334	C₄×Q₈	—	2	1	no	—
335	C₄×Q₈	—	2	1	no	—
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
342	#107	—	2	2	no	—
343	#107	—	2	2	no	—
344	#107	—	2	2	no	—
345	#107	—	2	2	no	—
346	#107	—	2	2	no	—
347	#106	—	2	2	no	—
348	#106	—	2	2	no	—
349	#106	—	2	2	no	—
350	#106	—	2	2	no	—
351	#106	—	2	2	no	—
352	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
353	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
354	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
355	#103	—	2	2	no	—
356	#103	—	2	2	no	—
357	#103	—	2	2	no	—
358	#103	—	2	2	no	—
359	#103	—	2	2	no	—
360	#103	—	2	2	no	—
361	#103	—	2	2	no	—
362	#103	—	2	2	no	—
363	#103	—	2	2	no	—
364	#103	—	2	2	no	—
365	#103	—	2	2	no	—
366	#103	—	2	2	no	—
367	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
368	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
369	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
370	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
371	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
372	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
373	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
374	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
375	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
376	C₂₃	#19736	1	1	yes	characteristic, direct product factor, Sylow
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	4	1	no	—
386	C₂×Q₈	—	8	2	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
391	Q₁₆	—	8	2	no	—
392	Q₁₆	—	8	2	no	—
393	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
395	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
396	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
397	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	4	1	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₂²⋊C₄	—	4	1	no	—
424	C₂²⋊C₄	—	4	1	no	—
425	C₂²⋊C₄	—	4	1	no	—
426	C₄²	—	4	1	no	—
427	C₄²	—	4	1	no	—
428	C₄²	—	4	1	no	—
429	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
431	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
432	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
433	C₂³	C₂₃×#127	1	1	yes	characteristic
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	Q₈	—	8	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
456	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
457	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	C₂×C₂₃×#127	1	1	yes	characteristic
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	1	no	—
481	C₄	—	8	1	no	—
482	C₄	C₂₃×#577	1	2	yes	—
483	C₄	C₂₃×#578	1	2	yes	—
484	C₄	C₂₃×#578	1	2	yes	—
485	C₂	—	4	1	no	—
486	C₂	C₂₃×#3154	1	1	yes	characteristic
487	C₂	C₂₃×#3156	1	1	yes	characteristic
488	C₂	C₂₃×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂³×C₂₃	#127
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
7. C₂₃×#1723	C₂	semidirect
8. C₂₃×#1723	C₂	semidirect
9. C₂₃×#1718	C₂	semidirect
10. C₂₃×#1718	C₂	semidirect
11. C₂₃×#1718	C₂	semidirect
12. C₂₃×#1716	C₂	semidirect
13. C₂₃×#1710	C₂	semidirect
14. C₂₃×#1707	C₂	semidirect
188. #19736	C₂₃	direct (N × H)
229. #1723	C₂×C₂₃	semidirect
230. #1723	C₂×C₂₃	semidirect
231. #1718	C₂×C₂₃	semidirect
232. #1718	C₂×C₂₃	semidirect
233. #1718	C₂×C₂₃	semidirect
234. #1716	C₂×C₂₃	semidirect
235. #1710	C₂×C₂₃	semidirect
236. #1707	C₂×C₂₃	semidirect
376. C₂₃	#19736	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×#3231	2
C₂₃×#3230	2
C₂₃×#3229	2
C₂₃×#3209	2
C₂₃×#1723	2
C₂₃×#1718	2
C₂₃×#1716	2
C₂₃×#1710	2
C₂₃×#1707	2
C₂₃×#1454	2
#19736	23

Subgroups — C23×#19736 #19167362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19736 #19167362