Subgroups — C₂₃×#19649 #19167275

Order 5888.

720 conjugacy classes of subgroups.

The subgroup lattice has 526 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, complemented
2	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1718	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1717	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1714	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1714	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1711	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1710	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1708	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1706	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#533	C₂²	1	1	yes	characteristic
17	C₂₃×#533	C₂²	1	1	yes	characteristic
18	C₂₃×#532	C₂²	1	1	yes	characteristic
19	C₂₃×#532	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×#498	C₂²	1	1	yes	characteristic
24	C₂₃×#498	C₂²	1	1	yes	characteristic
25	C₂₃×#493	C₂²	1	1	yes	characteristic
26	C₂₃×#492	C₂²	1	1	yes	characteristic
27	C₂₃×#492	C₂²	1	1	yes	characteristic
28	C₂₃×#492	C₂²	1	1	yes	characteristic
29	C₂₃×#492	C₂²	1	1	yes	characteristic
30	C₂₃×#488	—	2	2	no	—
31	C₂₃×#487	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×#486	C₂²	1	1	yes	characteristic
40	C₂₃×#486	C₂²	1	1	yes	characteristic
41	C₂₃×#486	C₂²	1	1	yes	characteristic
42	C₂₃×#486	C₂²	1	1	yes	characteristic
43	C₂₃×#486	C₂²	1	1	yes	characteristic
44	C₂₃×#486	C₂²	1	1	yes	characteristic
45	C₂₃×#485	—	2	2	no	—
46	C₂₃×#479	—	2	2	no	—
47	C₂₃×#468	—	2	2	no	—
48	C₂₃×#468	—	2	2	no	—
49	C₂₃×#465	—	2	2	no	—
50	C₂₃×#463	—	2	2	no	—
51	C₂₃×#449	—	2	2	no	—
52	C₂₃×#440	—	2	2	no	—
53	C₂₃×#440	—	2	2	no	—
54	C₄×SD₁₆×C₂₃	—	2	2	no	—
55	C₂₃×#431	C₂²	1	1	yes	characteristic
56	C₂₃×#416	—	2	2	no	—
57	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#322	C₂²	1	1	yes	characteristic
60	C₂₃×#322	C₂²	1	1	yes	characteristic
61	C₈²×C₂₃	C₂²	1	1	yes	characteristic
62	C₈²×C₂₃	C₂²	1	1	yes	characteristic
63	C₂×#41×C₂₃	—	2	1	no	—
64	C₂×#41×C₂₃	—	2	1	no	—
65	C₂×SD₁₆×C₂₃	—	2	2	no	—
66	C₂×SD₁₆×C₂₃	—	2	2	no	—
67	C₂×SD₁₆×C₂₃	—	2	2	no	—
68	C₂×SD₁₆×C₂₃	—	2	2	no	—
69	C₂×D₈×C₂₃	—	2	2	no	—
70	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
71	C₂²×C₈×C₂₃	D₄	1	2	yes	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₂₃×#127	C₂³	1	1	yes	characteristic
79	C₂₃×#127	C₂³	1	1	yes	characteristic
80	C₂₃×#125	—	2	1	no	—
81	C₂₃×#125	—	2	1	no	—
82	C₂₃×#124	—	2	1	no	—
83	C₂₃×#124	—	2	1	no	—
84	C₂₃×C₂²⋊Q₈	—	2	1	no	—
85	C₂₃×C₂²⋊Q₈	—	2	1	no	—
86	C₂₃×C₂²⋊Q₈	—	2	1	no	—
87	C₂₃×C₂²⋊Q₈	—	2	1	no	—
88	C₂₃×#121	—	2	1	no	—
89	C₂₃×#121	—	2	1	no	—
90	C₂₃×#121	—	2	1	no	—
91	C₂₃×#121	—	2	1	no	—
92	C₄×Q₈×C₂₃	—	2	1	no	—
93	C₄×Q₈×C₂₃	—	2	1	no	—
94	C₄×Q₈×C₂₃	—	2	1	no	—
95	C₄×Q₈×C₂₃	—	2	1	no	—
96	C₄×D₄×C₂₃	—	2	1	no	—
97	C₄×D₄×C₂₃	—	2	1	no	—
98	C₄×D₄×C₂₃	—	2	1	no	—
99	C₄×D₄×C₂₃	—	2	1	no	—
100	C₂₃×#117	—	2	1	no	—
101	C₂₃×#117	—	2	1	no	—
102	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
103	C₂₃×#107	—	2	2	no	—
104	C₂₃×#107	—	2	2	no	—
105	C₂₃×#107	—	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×#103	—	2	2	no	—
110	C₂₃×#103	—	2	2	no	—
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×#102	—	2	2	no	—
118	C₂₃×#102	—	2	2	no	—
119	C₂₃×#102	—	2	2	no	—
120	C₂₃×#102	—	2	2	no	—
121	C₂₃×#102	—	2	2	no	—
122	C₂₃×#102	—	2	2	no	—
123	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
124	C₂₃×#97	D₄	1	2	yes	—
125	C₄×C₈×C₂₃	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	#41×C₂₃	—	4	4	no	—
133	#41×C₂₃	—	8	2	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×D₄×C₂₃	—	2	1	no	—
141	C₂×D₄×C₂₃	—	2	1	no	—
142	C₂×D₄×C₂₃	—	2	1	no	—
143	C₂×D₄×C₂₃	—	2	1	no	—
144	C₂×D₄×C₂₃	—	2	1	no	—
145	C₂×D₄×C₂₃	—	2	1	no	—
146	C₂×D₄×C₂₃	—	4	1	no	—
147	C₂×D₄×C₂₃	—	4	1	no	—
148	C₂²×C₄×C₂₃	—	4	1	no	—
149	C₂²×C₄×C₂₃	—	4	1	no	—
150	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
153	SD₁₆×C₂₃	—	4	4	no	—
154	SD₁₆×C₂₃	—	4	4	no	—
155	SD₁₆×C₂₃	—	4	4	no	—
156	SD₁₆×C₂₃	—	8	2	no	—
157	D₈×C₂₃	—	8	2	no	—
158	M₁₆×C₂₃	—	2	4	no	—
159	C₂×C₈×C₂₃	—	4	2	no	—
160	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
171	C₄⋊C₄×C₂₃	—	2	1	no	—
172	C₄⋊C₄×C₂₃	—	2	1	no	—
173	C₄⋊C₄×C₂₃	—	2	1	no	—
174	C₄⋊C₄×C₂₃	—	2	1	no	—
175	C₄⋊C₄×C₂₃	—	2	1	no	—
176	C₄⋊C₄×C₂₃	—	2	1	no	—
177	C₄⋊C₄×C₂₃	—	2	1	no	—
178	C₄⋊C₄×C₂₃	—	4	1	no	—
179	C₄⋊C₄×C₂₃	—	4	1	no	—
180	C₄⋊C₄×C₂₃	—	4	1	no	—
181	C₄⋊C₄×C₂₃	—	4	1	no	—
182	C₂²⋊C₄×C₂₃	—	4	1	no	—
183	C₂²⋊C₄×C₂₃	—	4	1	no	—
184	C₂²⋊C₄×C₂₃	—	4	1	no	—
185	C₂²⋊C₄×C₂₃	—	4	1	no	—
186	C₂²⋊C₄×C₂₃	—	4	1	no	—
187	C₂²⋊C₄×C₂₃	—	4	1	no	—
188	C₄²×C₂₃	—	4	1	no	—
189	C₄²×C₂₃	—	4	1	no	—
190	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
194	#19649	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₂₃	—	4	1	no	—
196	C₂³×C₂₃	—	4	1	no	—
197	C₂³×C₂₃	#127	1	1	yes	characteristic
198	Q₈×C₂₃	—	4	2	no	—
199	Q₈×C₂₃	—	4	2	no	—
200	Q₈×C₂₃	—	4	2	no	—
201	Q₈×C₂₃	—	4	2	no	—
202	Q₈×C₂₃	—	4	2	no	—
203	Q₈×C₂₃	—	4	2	no	—
204	D₄×C₂₃	—	4	2	no	—
205	D₄×C₂₃	—	4	2	no	—
206	D₄×C₂₃	—	4	2	no	—
207	D₄×C₂₃	—	4	2	no	—
208	D₄×C₂₃	—	4	2	no	—
209	D₄×C₂₃	—	4	2	no	—
210	D₄×C₂₃	—	8	2	no	—
211	D₄×C₂₃	—	8	2	no	—
212	C₂×C₄×C₂₃	—	2	2	no	—
213	C₂×C₄×C₂₃	—	2	2	no	—
214	C₂×C₄×C₂₃	—	2	2	no	—
215	C₂×C₄×C₂₃	—	4	1	no	—
216	C₂×C₄×C₂₃	—	4	1	no	—
217	C₂×C₄×C₂₃	—	4	1	no	—
218	C₂×C₄×C₂₃	—	4	1	no	—
219	C₂×C₄×C₂₃	—	4	1	no	—
220	C₂×C₄×C₂₃	—	4	1	no	—
221	C₂×C₄×C₂₃	—	8	2	no	—
222	C₂×C₄×C₂₃	—	8	2	no	—
223	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
224	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
225	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
226	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
229	C₈×C₂₃	—	2	2	no	—
230	C₈×C₂₃	—	2	2	no	—
231	C₈×C₂₃	—	2	2	no	—
232	C₈×C₂₃	—	2	2	no	—
233	C₈×C₂₃	—	2	2	no	—
234	C₈×C₂₃	#135	1	4	yes	—
235	#3231	C₂×C₂₃	1	1	yes	characteristic, complemented
236	#3207	C₂×C₂₃	1	1	yes	characteristic
237	#3182	C₂×C₂₃	1	1	yes	characteristic, complemented
238	#3182	C₂×C₂₃	1	1	yes	characteristic, complemented
239	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
240	#3131	C₂×C₂₃	1	1	yes	characteristic, complemented
241	#1718	C₂×C₂₃	1	1	yes	characteristic, complemented
242	#1717	C₂×C₂₃	1	1	yes	characteristic, complemented
243	#1714	C₂×C₂₃	1	1	yes	characteristic, complemented
244	#1714	C₂×C₂₃	1	1	yes	characteristic, complemented
245	#1711	C₂×C₂₃	1	1	yes	characteristic, complemented
246	#1710	C₂×C₂₃	1	1	yes	characteristic, complemented
247	#1708	C₂×C₂₃	1	1	yes	characteristic, complemented
248	#1706	C₂×C₂₃	1	1	yes	characteristic, complemented
249	C₈×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
250	C₂²×C₂₃	—	2	1	no	—
251	C₂²×C₂₃	—	2	1	no	—
252	C₂²×C₂₃	—	2	1	no	—
253	C₂²×C₂₃	—	8	1	no	—
254	C₂²×C₂₃	—	8	1	no	—
255	C₂²×C₂₃	—	8	1	no	—
256	C₂²×C₂₃	—	8	1	no	—
257	C₂²×C₂₃	—	8	1	no	—
258	C₂²×C₂₃	—	8	1	no	—
259	C₂²×C₂₃	C₂×#127	1	1	yes	characteristic
260	C₄×C₂₃	—	2	1	no	—
261	C₄×C₂₃	—	2	1	no	—
262	C₄×C₂₃	—	2	1	no	—
263	C₄×C₂₃	—	8	1	no	—
264	C₄×C₂₃	—	8	1	no	—
265	C₄×C₂₃	—	8	1	no	—
266	C₄×C₂₃	—	8	1	no	—
267	C₄×C₂₃	—	8	1	no	—
268	C₄×C₂₃	—	8	1	no	—
269	C₄×C₂₃	C₂×#135	1	2	yes	—
270	C₄×C₂₃	#575	1	2	yes	—
271	C₄×C₂₃	#577	1	2	yes	—
272	#533	C₂²×C₂₃	1	1	yes	characteristic
273	#533	C₂²×C₂₃	1	1	yes	characteristic
274	#532	C₂²×C₂₃	1	1	yes	characteristic
275	#532	C₂²×C₂₃	1	1	yes	characteristic
276	#500	C₂²×C₂₃	1	1	yes	characteristic
277	#500	C₂²×C₂₃	1	1	yes	characteristic
278	#500	C₂²×C₂₃	1	1	yes	characteristic
279	#498	C₂²×C₂₃	1	1	yes	characteristic
280	#498	C₂²×C₂₃	1	1	yes	characteristic
281	#493	C₂²×C₂₃	1	1	yes	characteristic
282	#492	C₂²×C₂₃	1	1	yes	characteristic
283	#492	C₂²×C₂₃	1	1	yes	characteristic
284	#492	C₂²×C₂₃	1	1	yes	characteristic
285	#492	C₂²×C₂₃	1	1	yes	characteristic
286	#488	—	2	2	no	—
287	#487	C₂²×C₂₃	1	1	yes	characteristic
288	#487	C₂²×C₂₃	1	1	yes	characteristic
289	#487	C₂²×C₂₃	1	1	yes	characteristic
290	#487	C₂²×C₂₃	1	1	yes	characteristic
291	#487	C₂²×C₂₃	1	1	yes	characteristic
292	#487	C₂²×C₂₃	1	1	yes	characteristic
293	#487	C₂²×C₂₃	1	1	yes	characteristic
294	#487	C₂²×C₂₃	1	1	yes	characteristic
295	#486	C₂²×C₂₃	1	1	yes	characteristic
296	#486	C₂²×C₂₃	1	1	yes	characteristic
297	#486	C₂²×C₂₃	1	1	yes	characteristic
298	#486	C₂²×C₂₃	1	1	yes	characteristic
299	#486	C₂²×C₂₃	1	1	yes	characteristic
300	#486	C₂²×C₂₃	1	1	yes	characteristic
301	#485	—	2	2	no	—
302	#479	—	2	2	no	—
303	#468	—	2	2	no	—
304	#468	—	2	2	no	—
305	#465	—	2	2	no	—
306	#463	—	2	2	no	—
307	#449	—	2	2	no	—
308	#440	—	2	2	no	—
309	#440	—	2	2	no	—
310	C₄×SD₁₆	—	2	2	no	—
311	#431	C₂²×C₂₃	1	1	yes	characteristic
312	#416	—	2	2	no	—
313	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
314	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
315	#322	C₂²×C₂₃	1	1	yes	characteristic
316	#322	C₂²×C₂₃	1	1	yes	characteristic
317	C₈²	C₂²×C₂₃	1	1	yes	characteristic
318	C₈²	C₂²×C₂₃	1	1	yes	characteristic
319	C₂×C₂₃	—	4	1	no	—
320	C₂×C₂₃	—	16	1	no	—
321	C₂×C₂₃	—	16	1	no	—
322	C₂×C₂₃	#3147	1	1	yes	characteristic
323	C₂×C₂₃	#3153	1	1	yes	characteristic
324	C₂×C₂₃	#3154	1	1	yes	characteristic
325	C₂×#41	—	2	1	no	—
326	C₂×#41	—	2	1	no	—
327	C₂×SD₁₆	—	2	2	no	—
328	C₂×SD₁₆	—	2	2	no	—
329	C₂×SD₁₆	—	2	2	no	—
330	C₂×SD₁₆	—	2	2	no	—
331	C₂×D₈	—	2	2	no	—
332	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
333	C₂²×C₈	D₄×C₂₃	1	2	yes	—
334	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
335	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
336	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
337	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
338	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
339	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
340	#127	C₂³×C₂₃	1	1	yes	characteristic
341	#127	C₂³×C₂₃	1	1	yes	characteristic
342	#125	—	2	1	no	—
343	#125	—	2	1	no	—
344	#124	—	2	1	no	—
345	#124	—	2	1	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	2	1	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	#121	—	2	1	no	—
351	#121	—	2	1	no	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
365	#107	—	2	2	no	—
366	#107	—	2	2	no	—
367	#107	—	2	2	no	—
368	#106	—	2	2	no	—
369	#106	—	2	2	no	—
370	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
371	#103	—	2	2	no	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#103	—	2	2	no	—
375	#103	—	2	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#103	—	2	2	no	—
379	#102	—	2	2	no	—
380	#102	—	2	2	no	—
381	#102	—	2	2	no	—
382	#102	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	2	no	—
385	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
386	#97	D₄×C₂₃	1	2	yes	—
387	C₄×C₈	D₄×C₂₃	1	2	yes	—
388	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
389	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
390	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
391	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
392	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
393	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
394	C₂₃	#19649	1	1	yes	characteristic, direct product factor, Sylow
395	#41	—	4	4	no	—
396	#41	—	8	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	—	4	1	no	—
413	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
416	SD₁₆	—	4	4	no	—
417	SD₁₆	—	4	4	no	—
418	SD₁₆	—	4	4	no	—
419	SD₁₆	—	8	2	no	—
420	D₈	—	8	2	no	—
421	M₁₆	—	2	4	no	—
422	C₂×C₈	—	4	2	no	—
423	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
424	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
425	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
426	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
427	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	4	1	no	—
442	C₄⋊C₄	—	4	1	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₂²⋊C₄	—	4	1	no	—
446	C₂²⋊C₄	—	4	1	no	—
447	C₂²⋊C₄	—	4	1	no	—
448	C₂²⋊C₄	—	4	1	no	—
449	C₂²⋊C₄	—	4	1	no	—
450	C₂²⋊C₄	—	4	1	no	—
451	C₄²	—	4	1	no	—
452	C₄²	—	4	1	no	—
453	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
454	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
455	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
456	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	C₂₃×#127	1	1	yes	characteristic
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	8	2	no	—
473	D₄	—	8	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
486	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
487	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	—	2	2	no	—
494	C₈	—	2	2	no	—
495	C₈	—	2	2	no	—
496	C₈	C₂₃×#135	1	4	yes	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	1	no	—
506	C₂²	C₂×C₂₃×#127	1	1	yes	characteristic
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	1	no	—
512	C₄	—	8	1	no	—
513	C₄	—	8	1	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	C₂×C₂₃×#135	1	2	yes	—
517	C₄	C₂₃×#575	1	2	yes	—
518	C₄	C₂₃×#577	1	2	yes	—
519	C₂	—	4	1	no	—
520	C₂	—	16	1	no	—
521	C₂	—	16	1	no	—
522	C₂	C₂₃×#3147	1	1	yes	characteristic
523	C₂	C₂₃×#3153	1	1	yes	characteristic
524	C₂	C₂₃×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂₃×#3207	C₂
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×#3231	C₂	semidirect
3. C₂₃×#3182	C₂	semidirect
4. C₂₃×#3182	C₂	semidirect
5. C₂₃×#3167	C₂	semidirect
6. C₂₃×#3131	C₂	semidirect
7. C₂₃×#1718	C₂	semidirect
8. C₂₃×#1717	C₂	semidirect
9. C₂₃×#1714	C₂	semidirect
10. C₂₃×#1714	C₂	semidirect
11. C₂₃×#1711	C₂	semidirect
12. C₂₃×#1710	C₂	semidirect
13. C₂₃×#1708	C₂	semidirect
14. C₂₃×#1706	C₂	semidirect
15. C₈×M₁₆×C₂₃	C₂	semidirect
194. #19649	C₂₃	direct (N × H)
235. #3231	C₂×C₂₃	semidirect
237. #3182	C₂×C₂₃	semidirect
238. #3182	C₂×C₂₃	semidirect
239. #3167	C₂×C₂₃	semidirect
240. #3131	C₂×C₂₃	semidirect
241. #1718	C₂×C₂₃	semidirect
242. #1717	C₂×C₂₃	semidirect
243. #1714	C₂×C₂₃	semidirect
244. #1714	C₂×C₂₃	semidirect
245. #1711	C₂×C₂₃	semidirect
246. #1710	C₂×C₂₃	semidirect
247. #1708	C₂×C₂₃	semidirect
248. #1706	C₂×C₂₃	semidirect
249. C₈×M₁₆	C₂×C₂₃	semidirect
394. C₂₃	#19649	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×#3207	2
C₂₃×#3182	2
C₂₃×#3167	2
C₂₃×#3131	2
C₂₃×#1718	2
C₂₃×#1717	2
C₂₃×#1714	2
C₂₃×#1711	2
C₂₃×#1710	2
C₂₃×#1708	2
C₂₃×#1706	2
C₈×M₁₆×C₂₃	2
#19649	23

Subgroups — C23×#19649 #19167275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19649 #19167275