Subgroups — C₂₃×#24635 #19172261

Order 5888.

904 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2544	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2014	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1982	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#1958	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#464	—	2	4	no	—
25	C₄×SD₁₆×C₂₃	—	2	4	no	—
26	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
41	C₂₃×#394	—	2	1	no	—
42	C₂₃×#394	—	2	1	no	—
43	C₂₃×#391	C₂²	1	1	yes	characteristic
44	C₂₃×#391	C₂²	1	1	yes	characteristic
45	C₂₃×#391	C₂²	1	1	yes	characteristic
46	C₂₃×#390	C₂²	1	1	yes	characteristic
47	C₂₃×#387	—	2	1	no	—
48	C₂₃×#387	—	2	1	no	—
49	C₂₃×#386	—	2	1	no	—
50	C₂₃×#386	—	2	1	no	—
51	C₂₃×#383	—	2	1	no	—
52	C₂₃×#382	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂₃×#376	—	2	1	no	—
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#336	C₂²	1	1	yes	characteristic
60	C₂₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₃	—	2	1	no	—
64	C₂²×D₄×C₂₃	—	2	1	no	—
65	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₂₃	—	2	1	no	—
68	C₂×Q₁₆×C₂₃	—	2	2	no	—
69	C₂×Q₁₆×C₂₃	—	4	1	no	—
70	C₂×Q₁₆×C₂₃	—	4	1	no	—
71	C₂×SD₁₆×C₂₃	—	2	2	no	—
72	C₂×SD₁₆×C₂₃	—	2	2	no	—
73	C₂×SD₁₆×C₂₃	—	2	2	no	—
74	C₂×SD₁₆×C₂₃	—	2	2	no	—
75	C₂×SD₁₆×C₂₃	—	4	1	no	—
76	C₂×SD₁₆×C₂₃	—	4	1	no	—
77	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂₃×#127	—	2	2	no	—
82	C₂₃×#127	—	4	1	no	—
83	C₂₃×#124	—	2	2	no	—
84	C₂₃×#124	—	2	2	no	—
85	C₂₃×#124	—	2	2	no	—
86	C₂₃×#124	—	4	1	no	—
87	C₄×Q₈×C₂₃	—	2	2	no	—
88	C₄×Q₈×C₂₃	D₄	1	4	yes	complemented
89	C₄×D₄×C₂₃	—	2	2	no	—
90	C₄×D₄×C₂₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₄²×C₂₃	—	2	1	no	—
106	C₂×C₄²×C₂₃	—	2	1	no	—
107	C₂×C₄²×C₂₃	—	2	1	no	—
108	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
111	C₂₃×#106	—	2	2	no	—
112	C₂₃×C₄⋊C₈	—	2	2	no	—
113	C₂₃×C₄⋊C₈	—	4	1	no	—
114	C₂₃×C₄⋊C₈	—	4	1	no	—
115	C₂₃×#103	—	2	2	no	—
116	C₂₃×#103	—	2	2	no	—
117	C₂₃×#103	—	2	2	no	—
118	C₂₃×#103	—	4	1	no	—
119	C₂₃×#102	—	2	2	no	—
120	C₂₃×#102	—	2	2	no	—
121	C₂₃×#102	—	2	2	no	—
122	C₂₃×#102	—	4	1	no	—
123	C₂₃×#102	—	4	1	no	—
124	C₂₃×#102	—	4	1	no	—
125	C₄×C₈×C₂₃	—	2	2	no	—
126	C₂₃×#95	—	2	1	no	—
127	C₂₃×#95	—	2	1	no	—
128	C₂₃×#95	—	2	1	no	—
129	C₂₃×#95	—	2	1	no	—
130	C₂₃×#95	—	2	1	no	—
131	C₂₃×#95	—	2	1	no	—
132	C₂₃×#95	—	2	1	no	—
133	C₂₃×#95	—	2	1	no	—
134	C₂₃×#95	—	2	1	no	—
135	C₂₃×#95	—	2	1	no	—
136	C₂₃×#95	D₄	1	1	yes	characteristic
137	C₂₃×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₂₃	—	2	1	no	—
139	C₂⁴×C₂₃	—	2	1	no	—
140	C₂×Q₈×C₂₃	—	2	1	no	—
141	C₂×Q₈×C₂₃	—	2	1	no	—
142	C₂×Q₈×C₂₃	—	2	1	no	—
143	C₂×Q₈×C₂₃	—	2	1	no	—
144	C₂×Q₈×C₂₃	—	2	1	no	—
145	C₂×Q₈×C₂₃	—	2	1	no	—
146	C₂×Q₈×C₂₃	—	2	1	no	—
147	C₂×Q₈×C₂₃	—	2	1	no	—
148	C₂×Q₈×C₂₃	—	2	1	no	—
149	C₂×Q₈×C₂₃	—	2	1	no	—
150	C₂×Q₈×C₂₃	—	2	1	no	—
151	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₂₃	—	2	1	no	—
153	C₂×D₄×C₂₃	—	2	1	no	—
154	C₂×D₄×C₂₃	—	2	1	no	—
155	C₂×D₄×C₂₃	—	2	1	no	—
156	C₂×D₄×C₂₃	—	2	1	no	—
157	C₂×D₄×C₂₃	—	2	1	no	—
158	C₂×D₄×C₂₃	—	2	1	no	—
159	C₂×D₄×C₂₃	—	2	1	no	—
160	C₂×D₄×C₂₃	—	2	1	no	—
161	C₂×D₄×C₂₃	—	2	1	no	—
162	C₂×D₄×C₂₃	—	2	1	no	—
163	C₂×D₄×C₂₃	—	4	2	no	—
164	C₂×D₄×C₂₃	—	4	2	no	—
165	C₂×D₄×C₂₃	—	4	2	no	—
166	C₂×D₄×C₂₃	—	4	2	no	—
167	C₂×D₄×C₂₃	—	8	1	no	—
168	C₂×D₄×C₂₃	—	8	1	no	—
169	C₂×D₄×C₂₃	#41	1	2	yes	—
170	C₂²×C₄×C₂₃	—	2	1	no	—
171	C₂²×C₄×C₂₃	—	2	1	no	—
172	C₂²×C₄×C₂₃	—	2	1	no	—
173	C₂²×C₄×C₂₃	—	2	1	no	—
174	C₂²×C₄×C₂₃	—	2	1	no	—
175	C₂²×C₄×C₂₃	—	2	1	no	—
176	C₂²×C₄×C₂₃	—	4	2	no	—
177	C₂²×C₄×C₂₃	—	8	1	no	—
178	C₂²×C₄×C₂₃	—	8	1	no	—
179	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
186	Q₁₆×C₂₃	—	4	4	no	—
187	SD₁₆×C₂₃	—	2	8	no	—
188	SD₁₆×C₂₃	—	4	4	no	—
189	C₂×C₈×C₂₃	—	2	1	no	—
190	C₂×C₈×C₂₃	—	2	1	no	—
191	C₂×C₈×C₂₃	—	2	1	no	—
192	C₂×C₈×C₂₃	—	2	1	no	—
193	C₂×C₈×C₂₃	—	2	1	no	—
194	C₂×C₈×C₂₃	—	2	1	no	—
195	C₂×C₈×C₂₃	—	2	1	no	—
196	C₂×C₈×C₂₃	—	2	1	no	—
197	C₂×C₈×C₂₃	—	2	1	no	—
198	C₂×C₈×C₂₃	—	2	1	no	—
199	C₂×C₈×C₂₃	—	2	1	no	—
200	C₂×C₈×C₂₃	#41	1	2	yes	—
201	C₄⋊C₄×C₂₃	—	2	4	no	—
202	C₄⋊C₄×C₂₃	—	2	2	no	—
203	C₄⋊C₄×C₂₃	—	2	1	no	—
204	C₄⋊C₄×C₂₃	—	2	1	no	—
205	C₄⋊C₄×C₂₃	—	2	1	no	—
206	C₄⋊C₄×C₂₃	—	2	1	no	—
207	C₄⋊C₄×C₂₃	—	2	1	no	—
208	C₄⋊C₄×C₂₃	—	2	1	no	—
209	C₄⋊C₄×C₂₃	—	2	1	no	—
210	C₄⋊C₄×C₂₃	—	4	1	no	—
211	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
212	C₂²⋊C₄×C₂₃	—	4	2	no	—
213	C₂²⋊C₄×C₂₃	—	4	2	no	—
214	C₂²⋊C₄×C₂₃	—	4	2	no	—
215	C₂²⋊C₄×C₂₃	—	4	2	no	—
216	C₂²⋊C₄×C₂₃	—	4	2	no	—
217	C₂²⋊C₄×C₂₃	—	8	1	no	—
218	C₂²⋊C₄×C₂₃	—	8	1	no	—
219	C₄²×C₂₃	—	2	4	no	—
220	C₄²×C₂₃	—	2	1	no	—
221	C₄²×C₂₃	—	2	1	no	—
222	C₄²×C₂₃	—	2	1	no	—
223	C₄²×C₂₃	—	2	1	no	—
224	C₄²×C₂₃	—	4	2	no	—
225	C₄²×C₂₃	—	4	2	no	—
226	C₄²×C₂₃	C₂×D₄	1	2	yes	—
227	C₄²×C₂₃	#41	1	2	yes	—
228	#24635	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂³×C₂₃	—	2	2	no	—
230	C₂³×C₂₃	—	4	1	no	—
231	C₂³×C₂₃	—	4	1	no	—
232	C₂³×C₂₃	—	4	1	no	—
233	C₂³×C₂₃	—	4	1	no	—
234	C₂³×C₂₃	—	4	1	no	—
235	C₂³×C₂₃	—	4	1	no	—
236	C₂³×C₂₃	—	4	1	no	—
237	C₂³×C₂₃	—	4	1	no	—
238	C₂³×C₂₃	—	4	1	no	—
239	C₂³×C₂₃	—	4	1	no	—
240	C₂³×C₂₃	—	4	1	no	—
241	C₂³×C₂₃	—	4	1	no	—
242	C₂³×C₂₃	—	4	1	no	—
243	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₂₃	—	2	2	no	—
245	Q₈×C₂₃	—	2	2	no	—
246	Q₈×C₂₃	—	4	1	no	—
247	Q₈×C₂₃	—	4	1	no	—
248	Q₈×C₂₃	—	4	1	no	—
249	Q₈×C₂₃	—	4	1	no	—
250	Q₈×C₂₃	—	4	1	no	—
251	Q₈×C₂₃	—	4	1	no	—
252	D₄×C₂₃	—	2	2	no	—
253	D₄×C₂₃	—	2	2	no	—
254	D₄×C₂₃	—	4	1	no	—
255	D₄×C₂₃	—	4	1	no	—
256	D₄×C₂₃	—	4	1	no	—
257	D₄×C₂₃	—	4	1	no	—
258	D₄×C₂₃	—	4	1	no	—
259	D₄×C₂₃	—	4	1	no	—
260	D₄×C₂₃	—	8	4	no	—
261	D₄×C₂₃	—	8	4	no	—
262	C₂×C₄×C₂₃	—	2	1	no	—
263	C₂×C₄×C₂₃	—	2	1	no	—
264	C₂×C₄×C₂₃	—	2	1	no	—
265	C₂×C₄×C₂₃	—	2	1	no	—
266	C₂×C₄×C₂₃	—	2	1	no	—
267	C₂×C₄×C₂₃	—	2	1	no	—
268	C₂×C₄×C₂₃	—	2	2	no	—
269	C₂×C₄×C₂₃	—	2	2	no	—
270	C₂×C₄×C₂₃	—	2	1	no	—
271	C₂×C₄×C₂₃	—	2	1	no	—
272	C₂×C₄×C₂₃	—	2	1	no	—
273	C₂×C₄×C₂₃	—	2	1	no	—
274	C₂×C₄×C₂₃	—	2	1	no	—
275	C₂×C₄×C₂₃	—	2	1	no	—
276	C₂×C₄×C₂₃	—	2	1	no	—
277	C₂×C₄×C₂₃	—	2	1	no	—
278	C₂×C₄×C₂₃	—	2	1	no	—
279	C₂×C₄×C₂₃	—	4	1	no	—
280	C₂×C₄×C₂₃	—	4	1	no	—
281	C₂×C₄×C₂₃	—	4	1	no	—
282	C₂×C₄×C₂₃	—	4	1	no	—
283	C₂×C₄×C₂₃	—	4	1	no	—
284	C₂×C₄×C₂₃	—	4	1	no	—
285	C₂×C₄×C₂₃	—	4	1	no	—
286	C₂×C₄×C₂₃	—	4	1	no	—
287	C₂×C₄×C₂₃	—	4	1	no	—
288	C₂×C₄×C₂₃	—	4	1	no	—
289	C₂×C₄×C₂₃	—	4	1	no	—
290	C₂×C₄×C₂₃	—	4	1	no	—
291	C₂×C₄×C₂₃	—	4	1	no	—
292	C₂×C₄×C₂₃	—	4	1	no	—
293	C₂×C₄×C₂₃	—	4	1	no	—
294	C₂×C₄×C₂₃	—	4	1	no	—
295	C₂×C₄×C₂₃	—	8	4	no	—
296	C₂×C₄×C₂₃	#121	1	2	yes	—
297	C₂×C₄×C₂₃	#121	1	2	yes	—
298	C₂×C₄×C₂₃	#135	1	2	yes	—
299	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
305	C₈×C₂₃	—	2	2	no	—
306	C₈×C₂₃	—	4	1	no	—
307	C₈×C₂₃	—	4	1	no	—
308	C₈×C₂₃	—	4	1	no	—
309	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
310	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
311	#2544	C₂×C₂₃	1	1	yes	characteristic
312	#2356	C₂×C₂₃	1	1	yes	characteristic, complemented
313	#2056	C₂×C₂₃	1	1	yes	characteristic, complemented
314	#2055	C₂×C₂₃	1	1	yes	characteristic, complemented
315	#2015	C₂×C₂₃	1	1	yes	characteristic, complemented
316	#2014	C₂×C₂₃	1	1	yes	characteristic
317	#1983	C₂×C₂₃	1	1	yes	characteristic, complemented
318	#1982	C₂×C₂₃	1	1	yes	characteristic
319	#1958	C₂×C₂₃	1	1	yes	characteristic, complemented
320	#1939	C₂×C₂₃	1	1	yes	characteristic, complemented
321	#1927	C₂×C₂₃	1	1	yes	characteristic, complemented
322	#1926	C₂×C₂₃	1	1	yes	characteristic, complemented
323	#1804	C₂×C₂₃	1	1	yes	characteristic, complemented
324	C₂²×C₂₃	—	4	2	no	—
325	C₂²×C₂₃	—	4	2	no	—
326	C₂²×C₂₃	—	4	2	no	—
327	C₂²×C₂₃	—	8	1	no	—
328	C₂²×C₂₃	—	8	1	no	—
329	C₂²×C₂₃	—	8	1	no	—
330	C₂²×C₂₃	—	8	1	no	—
331	C₂²×C₂₃	—	8	1	no	—
332	C₂²×C₂₃	—	8	1	no	—
333	C₂²×C₂₃	—	8	1	no	—
334	C₂²×C₂₃	—	8	1	no	—
335	C₂²×C₂₃	—	8	1	no	—
336	C₂²×C₂₃	—	8	1	no	—
337	C₂²×C₂₃	—	8	1	no	—
338	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
339	C₂²×C₂₃	#546	1	1	yes	characteristic
340	C₂²×C₂₃	#550	1	1	yes	characteristic
341	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
342	C₂²×C₂₃	#575	1	1	yes	characteristic
343	C₂²×C₂₃	#577	1	1	yes	characteristic
344	C₂²×C₂₃	#577	1	1	yes	characteristic
345	C₄×C₂₃	—	2	2	no	—
346	C₄×C₂₃	—	2	2	no	—
347	C₄×C₂₃	—	2	2	no	—
348	C₄×C₂₃	—	4	2	no	—
349	C₄×C₂₃	—	4	2	no	—
350	C₄×C₂₃	—	4	1	no	—
351	C₄×C₂₃	—	4	1	no	—
352	C₄×C₂₃	—	4	1	no	—
353	C₄×C₂₃	—	8	1	no	—
354	C₄×C₂₃	—	8	1	no	—
355	C₄×C₂₃	—	8	1	no	—
356	C₄×C₂₃	—	8	1	no	—
357	C₄×C₂₃	#525	1	1	yes	characteristic
358	C₄×C₂₃	#535	1	1	yes	characteristic
359	C₄×C₂₃	#553	1	1	yes	characteristic
360	C₄×C₂₃	#555	1	1	yes	characteristic
361	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
362	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
363	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
364	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
365	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
366	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
367	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
368	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
369	#464	—	2	4	no	—
370	C₄×SD₁₆	—	2	4	no	—
371	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
372	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
373	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
374	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
375	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
376	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
377	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
378	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
379	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
380	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
381	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
383	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
385	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
386	#394	—	2	1	no	—
387	#394	—	2	1	no	—
388	#391	C₂²×C₂₃	1	1	yes	characteristic
389	#391	C₂²×C₂₃	1	1	yes	characteristic
390	#391	C₂²×C₂₃	1	1	yes	characteristic
391	#390	C₂²×C₂₃	1	1	yes	characteristic
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#386	—	2	1	no	—
395	#386	—	2	1	no	—
396	#383	—	2	1	no	—
397	#382	C₂²×C₂₃	1	1	yes	characteristic
398	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
399	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
400	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
401	#376	—	2	1	no	—
402	#340	C₂²×C₂₃	1	1	yes	characteristic
403	#340	C₂²×C₂₃	1	1	yes	characteristic
404	#336	C₂²×C₂₃	1	1	yes	characteristic
405	#336	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×C₂₃	—	8	2	no	—
407	C₂×C₂₃	—	16	1	no	—
408	C₂×C₂₃	#2414	1	1	yes	characteristic
409	C₂×C₂₃	#3035	1	1	yes	characteristic
410	C₂×C₂₃	#3043	1	1	yes	characteristic
411	C₂×C₂₃	#3296	1	1	yes	characteristic
412	C₂×C₂₃	#3323	1	1	yes	characteristic
413	C₂×C₂₃	#3394	1	1	yes	characteristic
414	C₂×C₂₃	#3401	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
416	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	—	2	1	no	—
419	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
421	C₂³×C₄	—	2	1	no	—
422	C₂×Q₁₆	—	2	2	no	—
423	C₂×Q₁₆	—	4	1	no	—
424	C₂×Q₁₆	—	4	1	no	—
425	C₂×SD₁₆	—	2	2	no	—
426	C₂×SD₁₆	—	2	2	no	—
427	C₂×SD₁₆	—	2	2	no	—
428	C₂×SD₁₆	—	2	2	no	—
429	C₂×SD₁₆	—	4	1	no	—
430	C₂×SD₁₆	—	4	1	no	—
431	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
435	#127	—	2	2	no	—
436	#127	—	4	1	no	—
437	#124	—	2	2	no	—
438	#124	—	2	2	no	—
439	#124	—	2	2	no	—
440	#124	—	4	1	no	—
441	C₄×Q₈	—	2	2	no	—
442	C₄×Q₈	D₄×C₂₃	1	4	yes	complemented
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	2	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
465	#106	—	2	2	no	—
466	C₄⋊C₈	—	2	2	no	—
467	C₄⋊C₈	—	4	1	no	—
468	C₄⋊C₈	—	4	1	no	—
469	#103	—	2	2	no	—
470	#103	—	2	2	no	—
471	#103	—	2	2	no	—
472	#103	—	4	1	no	—
473	#102	—	2	2	no	—
474	#102	—	2	2	no	—
475	#102	—	2	2	no	—
476	#102	—	4	1	no	—
477	#102	—	4	1	no	—
478	#102	—	4	1	no	—
479	C₄×C₈	—	2	2	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	D₄×C₂₃	1	1	yes	characteristic
491	#95	D₄×C₂₃	1	1	yes	characteristic
492	C₂₃	#24635	1	1	yes	characteristic, direct product factor, Sylow
493	C₂⁴	—	2	1	no	—
494	C₂⁴	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	4	2	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	8	1	no	—
523	C₂×D₄	—	8	1	no	—
524	C₂×D₄	#41×C₂₃	1	2	yes	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	8	1	no	—
533	C₂²×C₄	—	8	1	no	—
534	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
541	Q₁₆	—	4	4	no	—
542	SD₁₆	—	2	8	no	—
543	SD₁₆	—	4	4	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	#41×C₂₃	1	2	yes	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	4	1	no	—
566	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	8	1	no	—
573	C₂²⋊C₄	—	8	1	no	—
574	C₄²	—	2	4	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	4	2	no	—
580	C₄²	—	4	2	no	—
581	C₄²	C₂×D₄×C₂₃	1	2	yes	—
582	C₄²	#41×C₂₃	1	2	yes	—
583	C₂³	—	2	2	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	4	1	no	—
601	Q₈	—	4	1	no	—
602	Q₈	—	4	1	no	—
603	Q₈	—	4	1	no	—
604	Q₈	—	4	1	no	—
605	Q₈	—	4	1	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	2	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	1	no	—
610	D₄	—	4	1	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	1	no	—
614	D₄	—	8	4	no	—
615	D₄	—	8	4	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	8	4	no	—
650	C₂×C₄	C₂₃×#121	1	2	yes	—
651	C₂×C₄	C₂₃×#121	1	2	yes	—
652	C₂×C₄	C₂₃×#135	1	2	yes	—
653	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
654	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
655	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
656	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
657	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
658	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
659	C₈	—	2	2	no	—
660	C₈	—	4	1	no	—
661	C₈	—	4	1	no	—
662	C₈	—	4	1	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	8	1	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	—	8	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
678	C₂²	C₂₃×#546	1	1	yes	characteristic
679	C₂²	C₂₃×#550	1	1	yes	characteristic
680	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
681	C₂²	C₂₃×#575	1	1	yes	characteristic
682	C₂²	C₂₃×#577	1	1	yes	characteristic
683	C₂²	C₂₃×#577	1	1	yes	characteristic
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	C₂₃×#525	1	1	yes	characteristic
697	C₄	C₂₃×#535	1	1	yes	characteristic
698	C₄	C₂₃×#553	1	1	yes	characteristic
699	C₄	C₂₃×#555	1	1	yes	characteristic
700	C₂	—	8	2	no	—
701	C₂	—	16	1	no	—
702	C₂	C₂₃×#2414	1	1	yes	characteristic
703	C₂	C₂₃×#3035	1	1	yes	characteristic
704	C₂	C₂₃×#3043	1	1	yes	characteristic
705	C₂	C₂₃×#3296	1	1	yes	characteristic
706	C₂	C₂₃×#3323	1	1	yes	characteristic
707	C₂	C₂₃×#3394	1	1	yes	characteristic
708	C₂	C₂₃×#3401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄×C₄⋊C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#464	C₂	semidirect
2. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
4. C₂₃×#2356	C₂	semidirect
5. C₂₃×#2056	C₂	semidirect
6. C₂₃×#2055	C₂	semidirect
7. C₂₃×#2015	C₂	semidirect
9. C₂₃×#1983	C₂	semidirect
11. C₂₃×#1958	C₂	semidirect
12. C₂₃×#1939	C₂	semidirect
13. C₂₃×#1927	C₂	semidirect
14. C₂₃×#1926	C₂	semidirect
15. C₂₃×#1804	C₂	semidirect
88. C₄×Q₈×C₂₃	D₄	semidirect
228. #24635	C₂₃	direct (N × H)
309. C₂×#464	C₂×C₂₃	semidirect
310. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
312. #2356	C₂×C₂₃	semidirect
313. #2056	C₂×C₂₃	semidirect
314. #2055	C₂×C₂₃	semidirect
315. #2015	C₂×C₂₃	semidirect
317. #1983	C₂×C₂₃	semidirect
319. #1958	C₂×C₂₃	semidirect
320. #1939	C₂×C₂₃	semidirect
321. #1927	C₂×C₂₃	semidirect
322. #1926	C₂×C₂₃	semidirect
323. #1804	C₂×C₂₃	semidirect
442. C₄×Q₈	D₄×C₂₃	semidirect
492. C₂₃	#24635	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#464	2
C₂×C₄×SD₁₆×C₂₃	2
C₂₃×#2544	2
C₂₃×#2356	2
C₂₃×#2056	2
C₂₃×#2055	2
C₂₃×#2015	2
C₂₃×#2014	2
C₂₃×#1983	2
C₂₃×#1982	2
C₂₃×#1958	2
C₂₃×#1939	2
C₂₃×#1927	2
C₂₃×#1926	2
C₂₃×#1804	2
#24635	23

Subgroups — C23×#24635 #19172261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24635 #19172261