Subgroups — C₂₃×#26304 #19173930

Order 5888.

732 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2562	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2352	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2075	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1824	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×#400	—	2	1	no	—
31	C₂₃×#394	—	2	1	no	—
32	C₂₃×#388	—	2	1	no	—
33	C₂₃×#388	—	2	1	no	—
34	C₂₃×#388	—	2	1	no	—
35	C₂₃×#387	—	2	1	no	—
36	C₂₃×#386	—	2	1	no	—
37	C₂₃×#382	C₂²	1	1	yes	characteristic
38	C₂₃×#380	C₂²	1	1	yes	characteristic
39	C₂₃×#380	C₂²	1	1	yes	characteristic
40	C₂₃×#380	C₂²	1	1	yes	characteristic
41	C₂₃×#380	C₂²	1	1	yes	characteristic
42	C₂₃×#380	C₂²	1	1	yes	characteristic
43	C₂₃×#380	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
47	C₂₃×#340	C₂²	1	1	yes	characteristic
48	C₂₃×#340	C₂²	1	1	yes	characteristic
49	C₂₃×#340	C₂²	1	1	yes	characteristic
50	C₂₃×#340	C₂²	1	1	yes	characteristic
51	C₂₃×#340	C₂²	1	1	yes	characteristic
52	C₂₃×#340	C₂²	1	1	yes	characteristic
53	C₂₃×#340	C₂²	1	1	yes	characteristic
54	C₂₃×#340	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₂₃	—	2	1	no	—
61	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
67	C₂₃×#125	—	2	2	no	—
68	C₂₃×#125	—	2	2	no	—
69	C₄×D₄×C₂₃	—	2	2	no	—
70	C₄×D₄×C₂₃	—	2	2	no	—
71	C₂₃×#117	—	2	2	no	—
72	C₂₃×#117	—	4	1	no	—
73	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
74	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
78	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₂₃	—	2	1	no	—
97	C₂×C₄²×C₂₃	—	2	1	no	—
98	C₂×C₄²×C₂₃	—	2	1	no	—
99	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
100	C₂₃×#107	—	4	1	no	—
101	C₂₃×#106	—	2	2	no	—
102	C₂₃×#106	—	2	2	no	—
103	C₂₃×#106	—	4	1	no	—
104	C₂₃×C₄⋊C₈	—	2	2	no	—
105	C₂₃×C₂²⋊C₈	—	2	2	no	—
106	C₂₃×C₂²⋊C₈	—	2	2	no	—
107	C₂₃×C₂²⋊C₈	—	4	1	no	—
108	C₂₃×C₂²⋊C₈	—	4	1	no	—
109	C₄×C₈×C₂₃	—	2	2	no	—
110	C₂₃×#95	—	2	1	no	—
111	C₂₃×#95	—	2	1	no	—
112	C₂₃×#95	—	2	1	no	—
113	C₂₃×#95	—	2	1	no	—
114	C₂₃×#95	—	2	1	no	—
115	C₂₃×#95	—	2	1	no	—
116	C₂₃×#95	—	2	1	no	—
117	C₂₃×#95	—	2	1	no	—
118	C₂₃×#95	—	2	1	no	—
119	C₂₃×#95	—	2	1	no	—
120	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
122	C₂×D₄×C₂₃	—	2	2	no	—
123	C₂×D₄×C₂₃	—	2	2	no	—
124	C₂×D₄×C₂₃	—	4	1	no	—
125	C₂²×C₄×C₂₃	—	2	1	no	—
126	C₂²×C₄×C₂₃	—	2	1	no	—
127	C₂²×C₄×C₂₃	—	2	1	no	—
128	C₂²×C₄×C₂₃	—	2	1	no	—
129	C₂²×C₄×C₂₃	—	2	1	no	—
130	C₂²×C₄×C₂₃	—	2	1	no	—
131	C₂²×C₄×C₂₃	—	2	1	no	—
132	C₂²×C₄×C₂₃	—	2	1	no	—
133	C₂²×C₄×C₂₃	—	2	1	no	—
134	C₂²×C₄×C₂₃	—	2	1	no	—
135	C₂²×C₄×C₂₃	—	2	1	no	—
136	C₂²×C₄×C₂₃	—	2	1	no	—
137	C₂²×C₄×C₂₃	—	2	1	no	—
138	C₂²×C₄×C₂₃	—	2	1	no	—
139	C₂²×C₄×C₂₃	—	2	1	no	—
140	C₂²×C₄×C₂₃	—	2	1	no	—
141	C₂²×C₄×C₂₃	—	2	1	no	—
142	C₂²×C₄×C₂₃	—	2	1	no	—
143	C₂²×C₄×C₂₃	—	2	1	no	—
144	C₂²×C₄×C₂₃	—	2	1	no	—
145	C₂²×C₄×C₂₃	—	4	2	no	—
146	C₂²×C₄×C₂₃	—	4	2	no	—
147	C₂²×C₄×C₂₃	—	8	1	no	—
148	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
153	C₂×C₈×C₂₃	—	2	1	no	—
154	C₂×C₈×C₂₃	—	2	1	no	—
155	C₂×C₈×C₂₃	—	2	1	no	—
156	C₂×C₈×C₂₃	—	2	1	no	—
157	C₂×C₈×C₂₃	—	2	1	no	—
158	C₂×C₈×C₂₃	—	2	1	no	—
159	C₂×C₈×C₂₃	—	2	1	no	—
160	C₂×C₈×C₂₃	—	2	1	no	—
161	C₂×C₈×C₂₃	—	2	1	no	—
162	C₂×C₈×C₂₃	—	2	1	no	—
163	C₂×C₈×C₂₃	—	2	1	no	—
164	C₂×C₈×C₂₃	#41	1	2	yes	—
165	C₄⋊C₄×C₂₃	—	2	2	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	—	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	—	2	1	no	—
179	C₄⋊C₄×C₂₃	—	2	1	no	—
180	C₄⋊C₄×C₂₃	—	2	1	no	—
181	C₄⋊C₄×C₂₃	—	4	2	no	—
182	C₄⋊C₄×C₂₃	—	4	2	no	—
183	C₄⋊C₄×C₂₃	—	4	2	no	—
184	C₄⋊C₄×C₂₃	#41	1	2	yes	—
185	C₂²⋊C₄×C₂₃	—	2	2	no	—
186	C₂²⋊C₄×C₂₃	—	2	2	no	—
187	C₂²⋊C₄×C₂₃	—	4	2	no	—
188	C₂²⋊C₄×C₂₃	—	4	2	no	—
189	C₂²⋊C₄×C₂₃	—	4	2	no	—
190	C₂²⋊C₄×C₂₃	—	4	2	no	—
191	C₂²⋊C₄×C₂₃	—	8	1	no	—
192	C₂²⋊C₄×C₂₃	—	8	1	no	—
193	C₂²⋊C₄×C₂₃	—	8	1	no	—
194	C₄²×C₂₃	—	4	2	no	—
195	C₄²×C₂₃	—	8	1	no	—
196	C₄²×C₂₃	—	8	1	no	—
197	C₄²×C₂₃	#41	1	2	yes	—
198	C₄²×C₂₃	#41	1	2	yes	—
199	#26304	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂³×C₂₃	—	2	1	no	—
201	C₂³×C₂₃	—	2	1	no	—
202	C₂³×C₂₃	—	2	1	no	—
203	C₂³×C₂₃	—	2	1	no	—
204	C₂³×C₂₃	—	2	1	no	—
205	C₂³×C₂₃	—	2	1	no	—
206	C₂³×C₂₃	—	2	1	no	—
207	C₂³×C₂₃	—	2	1	no	—
208	C₂³×C₂₃	—	2	1	no	—
209	C₂³×C₂₃	—	2	1	no	—
210	C₂³×C₂₃	—	2	1	no	—
211	C₂³×C₂₃	—	2	1	no	—
212	C₂³×C₂₃	—	2	1	no	—
213	C₂³×C₂₃	#135	1	2	yes	—
214	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
215	D₄×C₂₃	—	4	4	no	—
216	C₂×C₄×C₂₃	—	2	1	no	—
217	C₂×C₄×C₂₃	—	2	1	no	—
218	C₂×C₄×C₂₃	—	2	1	no	—
219	C₂×C₄×C₂₃	—	2	1	no	—
220	C₂×C₄×C₂₃	—	2	1	no	—
221	C₂×C₄×C₂₃	—	2	1	no	—
222	C₂×C₄×C₂₃	—	2	1	no	—
223	C₂×C₄×C₂₃	—	2	2	no	—
224	C₂×C₄×C₂₃	—	2	1	no	—
225	C₂×C₄×C₂₃	—	2	1	no	—
226	C₂×C₄×C₂₃	—	2	1	no	—
227	C₂×C₄×C₂₃	—	4	1	no	—
228	C₂×C₄×C₂₃	—	4	1	no	—
229	C₂×C₄×C₂₃	—	4	1	no	—
230	C₂×C₄×C₂₃	—	4	1	no	—
231	C₂×C₄×C₂₃	—	4	1	no	—
232	C₂×C₄×C₂₃	—	4	1	no	—
233	C₂×C₄×C₂₃	—	4	1	no	—
234	C₂×C₄×C₂₃	—	4	1	no	—
235	C₂×C₄×C₂₃	—	4	1	no	—
236	C₂×C₄×C₂₃	—	4	1	no	—
237	C₂×C₄×C₂₃	—	4	1	no	—
238	C₂×C₄×C₂₃	—	4	1	no	—
239	C₂×C₄×C₂₃	—	4	1	no	—
240	C₂×C₄×C₂₃	—	4	1	no	—
241	C₂×C₄×C₂₃	—	4	1	no	—
242	C₂×C₄×C₂₃	—	4	1	no	—
243	C₂×C₄×C₂₃	—	4	1	no	—
244	C₂×C₄×C₂₃	—	4	1	no	—
245	C₂×C₄×C₂₃	—	4	1	no	—
246	C₂×C₄×C₂₃	—	4	1	no	—
247	C₂×C₄×C₂₃	—	4	1	no	—
248	C₂×C₄×C₂₃	—	4	1	no	—
249	C₂×C₄×C₂₃	—	4	1	no	—
250	C₂×C₄×C₂₃	—	4	1	no	—
251	C₂×C₄×C₂₃	—	4	1	no	—
252	C₂×C₄×C₂₃	—	4	1	no	—
253	C₂×C₄×C₂₃	—	4	1	no	—
254	C₂×C₄×C₂₃	—	4	1	no	—
255	C₂×C₄×C₂₃	—	4	1	no	—
256	C₂×C₄×C₂₃	—	4	1	no	—
257	C₂×C₄×C₂₃	—	4	1	no	—
258	C₂×C₄×C₂₃	—	8	4	no	—
259	C₂×C₄×C₂₃	#123	1	2	yes	—
260	C₂×C₄×C₂₃	#123	1	2	yes	—
261	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
267	C₈×C₂₃	—	2	2	no	—
268	C₈×C₂₃	—	4	1	no	—
269	C₈×C₂₃	—	4	1	no	—
270	C₈×C₂₃	—	4	1	no	—
271	#2562	C₂×C₂₃	1	1	yes	characteristic
272	#2352	C₂×C₂₃	1	1	yes	characteristic
273	#2077	C₂×C₂₃	1	1	yes	characteristic, complemented
274	#2077	C₂×C₂₃	1	1	yes	characteristic, complemented
275	#2077	C₂×C₂₃	1	1	yes	characteristic, complemented
276	#2075	C₂×C₂₃	1	1	yes	characteristic, complemented
277	#1991	C₂×C₂₃	1	1	yes	characteristic, complemented
278	#1989	C₂×C₂₃	1	1	yes	characteristic, complemented
279	#1954	C₂×C₂₃	1	1	yes	characteristic
280	#1949	C₂×C₂₃	1	1	yes	characteristic, complemented
281	#1854	C₂×C₂₃	1	1	yes	characteristic, complemented
282	#1853	C₂×C₂₃	1	1	yes	characteristic, complemented
283	#1825	C₂×C₂₃	1	1	yes	characteristic, complemented
284	#1824	C₂×C₂₃	1	1	yes	characteristic, complemented
285	C₄×#106	C₂×C₂₃	1	1	yes	characteristic, complemented
286	C₂²×C₂₃	—	2	2	no	—
287	C₂²×C₂₃	—	2	2	no	—
288	C₂²×C₂₃	—	2	2	no	—
289	C₂²×C₂₃	—	4	1	no	—
290	C₂²×C₂₃	—	4	1	no	—
291	C₂²×C₂₃	—	4	1	no	—
292	C₂²×C₂₃	—	4	1	no	—
293	C₂²×C₂₃	—	4	1	no	—
294	C₂²×C₂₃	—	4	1	no	—
295	C₂²×C₂₃	—	4	1	no	—
296	C₂²×C₂₃	—	4	1	no	—
297	C₂²×C₂₃	—	4	1	no	—
298	C₂²×C₂₃	—	4	1	no	—
299	C₂²×C₂₃	—	4	1	no	—
300	C₂²×C₂₃	C₂×#123	1	1	yes	characteristic
301	C₂²×C₂₃	#546	1	1	yes	characteristic
302	C₂²×C₂₃	#547	1	1	yes	characteristic
303	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
304	C₂²×C₂₃	#575	1	1	yes	characteristic
305	C₂²×C₂₃	#577	1	1	yes	characteristic
306	C₂²×C₂₃	#577	1	1	yes	characteristic
307	C₄×C₂₃	—	2	2	no	—
308	C₄×C₂₃	—	2	2	no	—
309	C₄×C₂₃	—	4	1	no	—
310	C₄×C₂₃	—	4	1	no	—
311	C₄×C₂₃	—	4	2	no	—
312	C₄×C₂₃	—	8	1	no	—
313	C₄×C₂₃	—	8	1	no	—
314	C₄×C₂₃	—	8	1	no	—
315	C₄×C₂₃	—	8	1	no	—
316	C₄×C₂₃	—	8	1	no	—
317	C₄×C₂₃	—	8	1	no	—
318	C₄×C₂₃	—	8	1	no	—
319	C₄×C₂₃	#529	1	1	yes	characteristic
320	C₄×C₂₃	#542	1	1	yes	characteristic
321	C₄×C₂₃	#556	1	1	yes	characteristic
322	C₄×C₂₃	#559	1	1	yes	characteristic
323	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
325	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
326	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
327	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
328	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
329	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
330	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
331	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
332	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
333	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
334	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
335	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
336	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
337	#400	—	2	1	no	—
338	#394	—	2	1	no	—
339	#388	—	2	1	no	—
340	#388	—	2	1	no	—
341	#388	—	2	1	no	—
342	#387	—	2	1	no	—
343	#386	—	2	1	no	—
344	#382	C₂²×C₂₃	1	1	yes	characteristic
345	#380	C₂²×C₂₃	1	1	yes	characteristic
346	#380	C₂²×C₂₃	1	1	yes	characteristic
347	#380	C₂²×C₂₃	1	1	yes	characteristic
348	#380	C₂²×C₂₃	1	1	yes	characteristic
349	#380	C₂²×C₂₃	1	1	yes	characteristic
350	#380	C₂²×C₂₃	1	1	yes	characteristic
351	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
353	C₄×C₂²⋊C₄	—	2	1	no	—
354	#340	C₂²×C₂₃	1	1	yes	characteristic
355	#340	C₂²×C₂₃	1	1	yes	characteristic
356	#340	C₂²×C₂₃	1	1	yes	characteristic
357	#340	C₂²×C₂₃	1	1	yes	characteristic
358	#340	C₂²×C₂₃	1	1	yes	characteristic
359	#340	C₂²×C₂₃	1	1	yes	characteristic
360	#340	C₂²×C₂₃	1	1	yes	characteristic
361	#340	C₂²×C₂₃	1	1	yes	characteristic
362	#340	C₂²×C₂₃	1	1	yes	characteristic
363	#340	C₂²×C₂₃	1	1	yes	characteristic
364	#340	C₂²×C₂₃	1	1	yes	characteristic
365	#340	C₂²×C₂₃	1	1	yes	characteristic
366	C₂×C₂₃	—	4	2	no	—
367	C₂×C₂₃	—	8	1	no	—
368	C₂×C₂₃	#2447	1	1	yes	characteristic
369	C₂×C₂₃	#3091	1	1	yes	characteristic
370	C₂×C₂₃	#3099	1	1	yes	characteristic
371	C₂×C₂₃	#3301	1	1	yes	characteristic
372	C₂×C₂₃	#3323	1	1	yes	characteristic
373	C₂×C₂₃	#3337	1	1	yes	characteristic
374	C₂×C₂₃	#3351	1	1	yes	characteristic
375	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
383	#125	—	2	2	no	—
384	#125	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	#117	—	2	2	no	—
388	#117	—	4	1	no	—
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	4	1	no	—
394	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
416	#107	—	4	1	no	—
417	#106	—	2	2	no	—
418	#106	—	2	2	no	—
419	#106	—	4	1	no	—
420	C₄⋊C₈	—	2	2	no	—
421	C₂²⋊C₈	—	2	2	no	—
422	C₂²⋊C₈	—	2	2	no	—
423	C₂²⋊C₈	—	4	1	no	—
424	C₂²⋊C₈	—	4	1	no	—
425	C₄×C₈	—	2	2	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	C₂₃	#26304	1	1	yes	characteristic, direct product factor, Sylow
437	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
438	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	8	1	no	—
465	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	#41×C₂₃	1	2	yes	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	#41×C₂₃	1	2	yes	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	4	2	no	—
505	C₂²⋊C₄	—	4	2	no	—
506	C₂²⋊C₄	—	4	2	no	—
507	C₂²⋊C₄	—	4	2	no	—
508	C₂²⋊C₄	—	8	1	no	—
509	C₂²⋊C₄	—	8	1	no	—
510	C₂²⋊C₄	—	8	1	no	—
511	C₄²	—	4	2	no	—
512	C₄²	—	8	1	no	—
513	C₄²	—	8	1	no	—
514	C₄²	#41×C₂₃	1	2	yes	—
515	C₄²	#41×C₂₃	1	2	yes	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	C₂₃×#135	1	2	yes	—
530	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
531	D₄	—	4	4	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	8	4	no	—
575	C₂×C₄	C₂₃×#123	1	2	yes	—
576	C₂×C₄	C₂₃×#123	1	2	yes	—
577	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
578	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
579	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
580	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
581	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
583	C₈	—	2	2	no	—
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	C₂×C₂₃×#123	1	1	yes	characteristic
602	C₂²	C₂₃×#546	1	1	yes	characteristic
603	C₂²	C₂₃×#547	1	1	yes	characteristic
604	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
605	C₂²	C₂₃×#575	1	1	yes	characteristic
606	C₂²	C₂₃×#577	1	1	yes	characteristic
607	C₂²	C₂₃×#577	1	1	yes	characteristic
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	2	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	—	8	1	no	—
616	C₄	—	8	1	no	—
617	C₄	—	8	1	no	—
618	C₄	—	8	1	no	—
619	C₄	—	8	1	no	—
620	C₄	C₂₃×#529	1	1	yes	characteristic
621	C₄	C₂₃×#542	1	1	yes	characteristic
622	C₄	C₂₃×#556	1	1	yes	characteristic
623	C₄	C₂₃×#559	1	1	yes	characteristic
624	C₂	—	4	2	no	—
625	C₂	—	8	1	no	—
626	C₂	C₂₃×#2447	1	1	yes	characteristic
627	C₂	C₂₃×#3091	1	1	yes	characteristic
628	C₂	C₂₃×#3099	1	1	yes	characteristic
629	C₂	C₂₃×#3301	1	1	yes	characteristic
630	C₂	C₂₃×#3323	1	1	yes	characteristic
631	C₂	C₂₃×#3337	1	1	yes	characteristic
632	C₂	C₂₃×#3351	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₃×#2077	C₂	semidirect
4. C₂₃×#2077	C₂	semidirect
5. C₂₃×#2077	C₂	semidirect
6. C₂₃×#2075	C₂	semidirect
7. C₂₃×#1991	C₂	semidirect
8. C₂₃×#1989	C₂	semidirect
10. C₂₃×#1949	C₂	semidirect
11. C₂₃×#1854	C₂	semidirect
12. C₂₃×#1853	C₂	semidirect
13. C₂₃×#1825	C₂	semidirect
14. C₂₃×#1824	C₂	semidirect
15. C₄×C₂₃×#106	C₂	semidirect
199. #26304	C₂₃	direct (N × H)
273. #2077	C₂×C₂₃	semidirect
274. #2077	C₂×C₂₃	semidirect
275. #2077	C₂×C₂₃	semidirect
276. #2075	C₂×C₂₃	semidirect
277. #1991	C₂×C₂₃	semidirect
278. #1989	C₂×C₂₃	semidirect
280. #1949	C₂×C₂₃	semidirect
281. #1854	C₂×C₂₃	semidirect
282. #1853	C₂×C₂₃	semidirect
283. #1825	C₂×C₂₃	semidirect
284. #1824	C₂×C₂₃	semidirect
285. C₄×#106	C₂×C₂₃	semidirect
436. C₂₃	#26304	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×#2562	2
C₂₃×#2352	2
C₂₃×#2077	2
C₂₃×#2075	2
C₂₃×#1991	2
C₂₃×#1989	2
C₂₃×#1954	2
C₂₃×#1949	2
C₂₃×#1854	2
C₂₃×#1853	2
C₂₃×#1825	2
C₂₃×#1824	2
C₄×C₂₃×#106	2
#26304	23

Subgroups — C23×#26304 #19173930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#26304 #19173930