Subgroups — C₂₃×#21075 #19168701

Order 5888.

1014 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2896	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#413	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1931	C₂	1	4	yes	maximal, complemented
7	C₂₃×#1930	C₂	1	4	yes	maximal, complemented
8	C₂₃×#1742	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
17	C₂₃×#428	—	2	2	no	—
18	C₂₃×#428	C₂²	1	4	yes	—
19	C₂₃×#427	—	2	2	no	—
20	C₂₃×#419	C₂²	1	2	yes	—
21	C₂₃×#418	C₂²	1	2	yes	—
22	C₂₃×#417	—	2	2	no	—
23	C₂₃×#416	—	2	1	no	—
24	C₂₃×#416	—	2	1	no	—
25	C₂₃×#416	—	2	2	no	—
26	C₂₃×#416	—	2	2	no	—
27	C₂×C₂₃×#103	C₂²	1	2	yes	—
28	C₂×C₂₃×#102	C₂²	1	2	yes	—
29	C₂₃×#413	C₄	1	8	yes	complemented
30	C₂×C₂₃×#101	C₂²	1	2	yes	—
31	C₂×C₂₃×#100	C₂²	1	2	yes	—
32	C₂₃×#405	—	2	2	no	—
33	C₂₃×#405	C₂²	1	4	yes	—
34	C₂×C₂₃×#97	—	2	1	no	—
35	C₂×C₄×C₈×C₂₃	—	2	1	no	—
36	C₂₃×#343	C₂²	1	4	yes	—
37	C₂₃×#341	C₂²	1	4	yes	—
38	C₂×#41×C₂₃	—	2	2	no	—
39	C₂×#41×C₂₃	—	2	1	no	—
40	C₂×#41×C₂₃	—	2	1	no	—
41	C₂×#41×C₂₃	—	2	1	no	—
42	C₂×#41×C₂₃	—	2	1	no	—
43	C₂×#41×C₂₃	—	2	2	no	—
44	C₂×#41×C₂₃	—	2	2	no	—
45	C₂×#41×C₂₃	C₂×C₄	1	4	yes	—
46	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₂₃	—	2	1	no	—
48	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₂₃	—	2	1	no	—
50	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₂₃	—	2	1	no	—
52	C₂×M₁₆×C₂₃	—	2	1	no	—
53	C₂×M₁₆×C₂₃	—	2	2	no	—
54	C₂×M₁₆×C₂₃	—	2	2	no	—
55	C₂×M₁₆×C₂₃	—	2	1	no	—
56	C₂×M₁₆×C₂₃	—	2	2	no	—
57	C₂×M₁₆×C₂₃	—	2	2	no	—
58	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	—
59	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	—
60	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
61	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
62	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₂₃	—	2	1	no	—
64	C₂²×C₈×C₂₃	—	2	1	no	—
65	C₂²×C₈×C₂₃	—	2	2	no	—
66	C₂²×C₈×C₂₃	—	2	2	no	—
67	C₂²×C₈×C₂₃	—	2	1	no	—
68	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₂₃	D₄	1	2	yes	—
71	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
72	C₂₃×#117	—	2	1	no	—
73	C₂₃×#117	—	2	1	no	—
74	C₂₃×#117	—	2	1	no	—
75	C₂₃×#117	—	2	1	no	—
76	C₂₃×#117	—	2	1	no	—
77	C₂₃×#117	—	2	1	no	—
78	C₂₃×#117	D₄	1	2	yes	—
79	C₂₃×#117	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
84	C₂×C₄²×C₂₃	—	2	1	no	—
85	C₂×C₄²×C₂₃	—	2	1	no	—
86	C₂₃×#107	—	2	4	no	—
87	C₂₃×#106	—	2	4	no	—
88	C₂₃×#103	—	2	2	no	—
89	C₂₃×#103	—	2	2	no	—
90	C₂₃×#103	—	2	4	no	—
91	C₂₃×#102	—	2	2	no	—
92	C₂₃×#102	—	2	2	no	—
93	C₂₃×#102	—	2	4	no	—
94	C₂₃×#101	C₂×C₄	1	8	yes	complemented
95	C₂₃×#100	C₂×C₄	1	8	yes	complemented
96	C₂₃×#97	—	2	4	no	—
97	C₄×C₈×C₂₃	—	2	4	no	—
98	C₂⁴×C₂₃	—	2	1	no	—
99	C₂⁴×C₂₃	#41	1	1	yes	characteristic
100	#41×C₂₃	—	2	4	no	—
101	#41×C₂₃	—	2	4	no	—
102	#41×C₂₃	—	2	4	no	—
103	#41×C₂₃	—	2	4	no	—
104	#41×C₂₃	—	4	2	no	—
105	#41×C₂₃	—	4	2	no	—
106	#41×C₂₃	—	4	2	no	—
107	#41×C₂₃	—	4	2	no	—
108	C₂×Q₈×C₂₃	—	2	1	no	—
109	C₂×Q₈×C₂₃	—	2	1	no	—
110	C₂×Q₈×C₂₃	—	2	1	no	—
111	C₂×Q₈×C₂₃	—	2	1	no	—
112	C₂×Q₈×C₂₃	—	2	1	no	—
113	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
114	C₂×D₄×C₂₃	—	2	4	no	—
115	C₂×D₄×C₂₃	—	2	1	no	—
116	C₂×D₄×C₂₃	—	2	1	no	—
117	C₂×D₄×C₂₃	—	2	1	no	—
118	C₂×D₄×C₂₃	—	2	1	no	—
119	C₂×D₄×C₂₃	—	2	1	no	—
120	C₂×D₄×C₂₃	—	4	1	no	—
121	C₂×D₄×C₂₃	—	4	1	no	—
122	C₂×D₄×C₂₃	—	4	2	no	—
123	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₂₃	—	2	2	no	—
125	C₂²×C₄×C₂₃	—	2	1	no	—
126	C₂²×C₄×C₂₃	—	2	4	no	—
127	C₂²×C₄×C₂₃	—	2	2	no	—
128	C₂²×C₄×C₂₃	—	4	1	no	—
129	C₂²×C₄×C₂₃	—	4	1	no	—
130	C₂²×C₄×C₂₃	—	4	2	no	—
131	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
137	C₂²×C₄×C₂₃	#41	1	2	yes	—
138	C₂²×C₄×C₂₃	#41	1	2	yes	—
139	C₂²×C₄×C₂₃	#41	1	2	yes	—
140	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
141	M₁₆×C₂₃	—	2	4	no	—
142	M₁₆×C₂₃	—	2	4	no	—
143	M₁₆×C₂₃	—	2	2	no	—
144	M₁₆×C₂₃	—	2	2	no	—
145	M₁₆×C₂₃	—	2	2	no	—
146	M₁₆×C₂₃	—	2	2	no	—
147	M₁₆×C₂₃	—	4	2	no	—
148	M₁₆×C₂₃	C₂²×C₄	1	4	yes	—
149	M₁₆×C₂₃	C₂²×C₄	1	4	yes	—
150	C₂×C₈×C₂₃	—	2	4	no	—
151	C₂×C₈×C₂₃	—	2	4	no	—
152	C₂×C₈×C₂₃	—	2	2	no	—
153	C₂×C₈×C₂₃	—	2	2	no	—
154	C₂×C₈×C₂₃	—	2	4	no	—
155	C₂×C₈×C₂₃	—	2	2	no	—
156	C₂×C₈×C₂₃	—	2	2	no	—
157	C₂×C₈×C₂₃	—	2	2	no	—
158	C₂×C₈×C₂₃	—	2	2	no	—
159	C₂×C₈×C₂₃	—	2	2	no	—
160	C₂×C₈×C₂₃	—	4	2	no	—
161	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₂₃	—	2	2	no	—
164	C₄⋊C₄×C₂₃	—	2	2	no	—
165	C₄⋊C₄×C₂₃	—	2	2	no	—
166	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
167	C₂²⋊C₄×C₂₃	—	2	2	no	—
168	C₂²⋊C₄×C₂₃	—	2	2	no	—
169	C₂²⋊C₄×C₂₃	—	4	1	no	—
170	C₂²⋊C₄×C₂₃	—	4	1	no	—
171	C₄²×C₂₃	—	2	2	no	—
172	C₄²×C₂₃	—	2	2	no	—
173	C₄²×C₂₃	—	4	1	no	—
174	C₄²×C₂₃	—	4	1	no	—
175	#21075	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₂₃	—	2	2	no	—
177	C₂³×C₂₃	—	4	2	no	—
178	C₂³×C₂₃	—	4	1	no	—
179	C₂³×C₂₃	—	4	1	no	—
180	C₂³×C₂₃	—	8	2	no	—
181	C₂³×C₂₃	#117	1	2	yes	—
182	C₂³×C₂₃	#121	1	1	yes	characteristic
183	C₂³×C₂₃	#121	1	1	yes	characteristic
184	C₂³×C₂₃	#126	1	2	yes	—
185	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
186	Q₈×C₂₃	—	2	2	no	—
187	Q₈×C₂₃	—	2	2	no	—
188	Q₈×C₂₃	—	4	1	no	—
189	Q₈×C₂₃	—	4	1	no	—
190	D₄×C₂₃	—	2	2	no	—
191	D₄×C₂₃	—	2	2	no	—
192	D₄×C₂₃	—	4	4	no	—
193	D₄×C₂₃	—	4	4	no	—
194	D₄×C₂₃	—	4	1	no	—
195	D₄×C₂₃	—	4	1	no	—
196	C₂×C₄×C₂₃	—	2	2	no	—
197	C₂×C₄×C₂₃	—	2	4	no	—
198	C₂×C₄×C₂₃	—	4	4	no	—
199	C₂×C₄×C₂₃	—	4	1	no	—
200	C₂×C₄×C₂₃	—	4	1	no	—
201	C₂×C₄×C₂₃	—	4	4	no	—
202	C₂×C₄×C₂₃	—	4	4	no	—
203	C₂×C₄×C₂₃	—	4	2	no	—
204	C₂×C₄×C₂₃	—	8	2	no	—
205	C₂×C₄×C₂₃	#117	1	2	yes	—
206	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
211	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
212	C₂×C₄×C₂₃	#123	1	2	yes	—
213	C₂×C₄×C₂₃	#123	1	2	yes	—
214	C₂×C₄×C₂₃	#124	1	2	yes	—
215	C₂×C₄×C₂₃	#124	1	2	yes	—
216	C₂×C₄×C₂₃	#126	1	2	yes	—
217	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
223	C₈×C₂₃	—	2	4	no	—
224	C₈×C₂₃	—	2	4	no	—
225	C₈×C₂₃	—	2	2	no	—
226	C₈×C₂₃	—	2	2	no	—
227	C₈×C₂₃	—	4	2	no	—
228	#2911	C₂×C₂₃	1	1	yes	characteristic, complemented
229	#2896	C₂×C₂₃	1	1	yes	characteristic
230	C₂×#416	C₂×C₂₃	1	1	yes	characteristic
231	C₂×#413	C₂×C₂₃	1	1	yes	characteristic
232	C₂×#405	C₂×C₂₃	1	1	yes	characteristic, complemented
233	#1931	C₂×C₂₃	1	4	yes	complemented
234	#1930	C₂×C₂₃	1	4	yes	complemented
235	#1742	C₂×C₂₃	1	1	yes	characteristic, complemented
236	C₂×#341	C₂×C₂₃	1	1	yes	characteristic, complemented
237	C₂²×C₂₃	—	2	2	no	—
238	C₂²×C₂₃	—	2	2	no	—
239	C₂²×C₂₃	—	2	2	no	—
240	C₂²×C₂₃	—	4	2	no	—
241	C₂²×C₂₃	—	4	2	no	—
242	C₂²×C₂₃	—	4	2	no	—
243	C₂²×C₂₃	—	8	2	no	—
244	C₂²×C₂₃	—	8	2	no	—
245	C₂²×C₂₃	—	8	2	no	—
246	C₂²×C₂₃	#388	1	2	yes	—
247	C₂²×C₂₃	#388	1	2	yes	—
248	C₂²×C₂₃	C₂×#117	1	1	yes	characteristic
249	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
250	C₂²×C₂₃	C₂×#126	1	1	yes	characteristic
251	C₄×C₂₃	—	4	2	no	—
252	C₄×C₂₃	—	4	4	no	—
253	C₄×C₂₃	—	8	2	no	—
254	C₄×C₂₃	#388	1	2	yes	—
255	C₄×C₂₃	#388	1	2	yes	—
256	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
258	C₄×C₂₃	C₂×#123	1	1	yes	characteristic
259	C₄×C₂₃	C₂×#124	1	1	yes	characteristic
260	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
262	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
263	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
264	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
265	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
266	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
267	#428	—	2	2	no	—
268	#428	C₂²×C₂₃	1	4	yes	—
269	#427	—	2	2	no	—
270	#419	C₂²×C₂₃	1	2	yes	—
271	#418	C₂²×C₂₃	1	2	yes	—
272	#417	—	2	2	no	—
273	#416	—	2	1	no	—
274	#416	—	2	1	no	—
275	#416	—	2	2	no	—
276	#416	—	2	2	no	—
277	C₂×#103	C₂²×C₂₃	1	2	yes	—
278	C₂×#102	C₂²×C₂₃	1	2	yes	—
279	#413	C₄×C₂₃	1	8	yes	complemented
280	C₂×#101	C₂²×C₂₃	1	2	yes	—
281	C₂×#100	C₂²×C₂₃	1	2	yes	—
282	#405	—	2	2	no	—
283	#405	C₂²×C₂₃	1	4	yes	—
284	C₂×#97	—	2	1	no	—
285	C₂×C₄×C₈	—	2	1	no	—
286	#343	C₂²×C₂₃	1	4	yes	—
287	#341	C₂²×C₂₃	1	4	yes	—
288	C₂×C₂₃	—	2	1	no	—
289	C₂×C₂₃	—	2	1	no	—
290	C₂×C₂₃	—	2	2	no	—
291	C₂×C₂₃	—	2	2	no	—
292	C₂×C₂₃	—	8	2	no	—
293	C₂×C₂₃	C₂×#388	1	1	yes	characteristic
294	C₂×C₂₃	#3067	1	2	yes	—
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	1	no	—
297	C₂×#41	—	2	1	no	—
298	C₂×#41	—	2	1	no	—
299	C₂×#41	—	2	1	no	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	C₂×C₄×C₂₃	1	4	yes	—
303	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	2	no	—
315	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	—
316	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	—
317	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
318	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
319	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
320	C₂²×C₈	—	2	1	no	—
321	C₂²×C₈	—	2	1	no	—
322	C₂²×C₈	—	2	2	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
326	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
327	C₂²×C₈	D₄×C₂₃	1	2	yes	—
328	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
329	#117	—	2	1	no	—
330	#117	—	2	1	no	—
331	#117	—	2	1	no	—
332	#117	—	2	1	no	—
333	#117	—	2	1	no	—
334	#117	—	2	1	no	—
335	#117	D₄×C₂₃	1	2	yes	—
336	#117	C₂³×C₂₃	1	2	yes	—
337	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	#107	—	2	4	no	—
344	#106	—	2	4	no	—
345	#103	—	2	2	no	—
346	#103	—	2	2	no	—
347	#103	—	2	4	no	—
348	#102	—	2	2	no	—
349	#102	—	2	2	no	—
350	#102	—	2	4	no	—
351	#101	C₂×C₄×C₂₃	1	8	yes	complemented
352	#100	C₂×C₄×C₂₃	1	8	yes	complemented
353	#97	—	2	4	no	—
354	C₄×C₈	—	2	4	no	—
355	C₂₃	#21075	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	—	2	1	no	—
357	C₂⁴	#41×C₂₃	1	1	yes	characteristic
358	#41	—	2	4	no	—
359	#41	—	2	4	no	—
360	#41	—	2	4	no	—
361	#41	—	2	4	no	—
362	#41	—	4	2	no	—
363	#41	—	4	2	no	—
364	#41	—	4	2	no	—
365	#41	—	4	2	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
394	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
395	C₂²×C₄	#41×C₂₃	1	2	yes	—
396	C₂²×C₄	#41×C₂₃	1	2	yes	—
397	C₂²×C₄	#41×C₂₃	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
399	M₁₆	—	2	4	no	—
400	M₁₆	—	2	4	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	4	2	no	—
406	M₁₆	C₂²×C₄×C₂₃	1	4	yes	—
407	M₁₆	C₂²×C₄×C₂₃	1	4	yes	—
408	C₂×C₈	—	2	4	no	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	4	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	4	2	no	—
419	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
420	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	4	1	no	—
432	C₄²	—	4	1	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	8	2	no	—
438	C₂³	C₂₃×#117	1	2	yes	—
439	C₂³	C₂₃×#121	1	1	yes	characteristic
440	C₂³	C₂₃×#121	1	1	yes	characteristic
441	C₂³	C₂₃×#126	1	2	yes	—
442	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
443	Q₈	—	2	2	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	4	1	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	1	no	—
452	D₄	—	4	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	8	2	no	—
462	C₂×C₄	C₂₃×#117	1	2	yes	—
463	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
464	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
465	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
466	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
467	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
468	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
469	C₂×C₄	C₂₃×#123	1	2	yes	—
470	C₂×C₄	C₂₃×#123	1	2	yes	—
471	C₂×C₄	C₂₃×#124	1	2	yes	—
472	C₂×C₄	C₂₃×#124	1	2	yes	—
473	C₂×C₄	C₂₃×#126	1	2	yes	—
474	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
477	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
478	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
479	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
480	C₈	—	2	4	no	—
481	C₈	—	2	4	no	—
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	—	4	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	C₂₃×#388	1	2	yes	—
495	C₂²	C₂₃×#388	1	2	yes	—
496	C₂²	C₂×C₂₃×#117	1	1	yes	characteristic
497	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
498	C₂²	C₂×C₂₃×#126	1	1	yes	characteristic
499	C₄	—	4	2	no	—
500	C₄	—	4	4	no	—
501	C₄	—	8	2	no	—
502	C₄	C₂₃×#388	1	2	yes	—
503	C₄	C₂₃×#388	1	2	yes	—
504	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
505	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
506	C₄	C₂×C₂₃×#123	1	1	yes	characteristic
507	C₄	C₂×C₂₃×#124	1	1	yes	characteristic
508	C₂	—	2	1	no	—
509	C₂	—	2	1	no	—
510	C₂	—	2	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	8	2	no	—
513	C₂	C₂×C₂₃×#388	1	1	yes	characteristic
514	C₂	C₂₃×#3067	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	#121
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×#121
prime radical	C₂²×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2911	C₂	semidirect
5. C₂×C₂₃×#405	C₂	semidirect
6. C₂₃×#1931	C₂	semidirect
7. C₂₃×#1930	C₂	semidirect
8. C₂₃×#1742	C₂	semidirect
9. C₂×C₂₃×#341	C₂	semidirect
29. C₂₃×#413	C₄	semidirect
94. C₂₃×#101	C₂×C₄	semidirect
95. C₂₃×#100	C₂×C₄	semidirect
175. #21075	C₂₃	direct (N × H)
228. #2911	C₂×C₂₃	semidirect
232. C₂×#405	C₂×C₂₃	semidirect
233. #1931	C₂×C₂₃	semidirect
234. #1930	C₂×C₂₃	semidirect
235. #1742	C₂×C₂₃	semidirect
236. C₂×#341	C₂×C₂₃	semidirect
279. #413	C₄×C₂₃	semidirect
351. #101	C₂×C₄×C₂₃	semidirect
352. #100	C₂×C₄×C₂₃	semidirect
355. C₂₃	#21075	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×#2911	2
C₂₃×#2896	2
C₂×C₂₃×#416	2
C₂×C₂₃×#413	2
C₂×C₂₃×#405	2
C₂₃×#1931	2
C₂₃×#1930	2
C₂₃×#1742	2
C₂×C₂₃×#341	2
#21075	23

Subgroups — C23×#21075 #19168701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21075 #19168701