Subgroups — C₄×C₂₃×#466 #19169147

Order 5888.

1222 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₃×#121	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1934	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1893	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#102	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₂₃	—	2	2	no	—
17	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#466	C₄	1	8	yes	direct product factor
20	C₄×D₈×C₂₃	—	2	4	no	—
21	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#102	C₂²	1	2	yes	—
25	C₂×C₂₃×#102	C₂²	1	2	yes	—
26	C₂×C₂₃×#102	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₂₃	—	2	4	no	—
28	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×#390	C₂²	1	2	yes	—
33	C₂₃×#389	C₂²	1	2	yes	—
34	C₂₃×#388	—	2	2	no	—
35	C₂₃×#386	—	2	2	no	—
36	C₂₃×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂₃×#340	C₂²	1	2	yes	—
41	C₂₃×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₂₃	—	2	2	no	—
43	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₂₃	—	2	2	no	—
45	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₂₃	—	2	2	no	—
49	C₂×D₈×C₂₃	—	2	2	no	—
50	C₂×D₈×C₂₃	C₂×C₄	1	4	yes	complemented
51	C₂²×C₈×C₂₃	—	2	2	no	—
52	C₂²×C₈×C₂₃	—	2	2	no	—
53	C₂²×C₈×C₂₃	—	2	2	no	—
54	C₂²×C₈×C₂₃	—	2	2	no	—
55	C₂²×C₈×C₂₃	—	2	2	no	—
56	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	complemented
57	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
61	C₂₃×#121	—	2	4	no	—
62	C₂₃×#121	C₂×C₄	1	8	yes	complemented
63	C₄×D₄×C₂₃	—	2	4	no	—
64	C₄×D₄×C₂₃	—	2	4	no	—
65	C₄×D₄×C₂₃	—	4	8	no	—
66	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
75	C₂×C₄²×C₂₃	—	2	2	no	—
76	C₂×C₄²×C₂₃	—	2	2	no	—
77	C₂×C₄²×C₂₃	—	2	2	no	—
78	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
82	C₂₃×#107	—	2	2	no	—
83	C₂₃×#107	—	2	2	no	—
84	C₂₃×#107	C₂×C₄	1	4	yes	complemented
85	C₂₃×#102	—	2	4	no	—
86	C₂₃×#102	—	2	4	no	—
87	C₂₃×#102	C₂×C₄	1	8	yes	complemented
88	C₄×C₈×C₂₃	—	2	2	no	—
89	C₄×C₈×C₂₃	—	2	2	no	—
90	C₄×C₈×C₂₃	—	2	2	no	—
91	C₄×C₈×C₂₃	D₄	1	4	yes	complemented
92	C₂₃×#95	—	2	2	no	—
93	C₂₃×#95	—	2	2	no	—
94	C₂₃×#95	—	2	2	no	—
95	C₂⁴×C₂₃	—	2	2	no	—
96	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₂₃	—	2	8	no	—
98	C₂×D₄×C₂₃	—	2	2	no	—
99	C₂×D₄×C₂₃	—	2	2	no	—
100	C₂×D₄×C₂₃	—	2	2	no	—
101	C₂×D₄×C₂₃	—	2	2	no	—
102	C₂×D₄×C₂₃	—	2	2	no	—
103	C₂×D₄×C₂₃	—	4	4	no	—
104	C₂×D₄×C₂₃	—	4	4	no	—
105	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₂₃	—	2	2	no	—
107	C₂²×C₄×C₂₃	—	2	2	no	—
108	C₂²×C₄×C₂₃	—	2	2	no	—
109	C₂²×C₄×C₂₃	—	2	2	no	—
110	C₂²×C₄×C₂₃	—	2	2	no	—
111	C₂²×C₄×C₂₃	—	2	1	no	—
112	C₂²×C₄×C₂₃	—	2	1	no	—
113	C₂²×C₄×C₂₃	—	2	1	no	—
114	C₂²×C₄×C₂₃	—	2	1	no	—
115	C₂²×C₄×C₂₃	—	2	2	no	—
116	C₂²×C₄×C₂₃	—	2	2	no	—
117	C₂²×C₄×C₂₃	—	2	2	no	—
118	C₂²×C₄×C₂₃	—	4	4	no	—
119	C₂²×C₄×C₂₃	—	4	4	no	—
120	C₂²×C₄×C₂₃	—	4	4	no	—
121	C₂²×C₄×C₂₃	D₈	1	4	yes	complemented
122	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₂₃	#41	1	2	yes	—
129	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
130	D₈×C₂₃	—	2	8	no	—
131	C₂×C₈×C₂₃	—	2	8	no	—
132	C₂×C₈×C₂₃	—	2	1	no	—
133	C₂×C₈×C₂₃	—	2	1	no	—
134	C₂×C₈×C₂₃	—	2	1	no	—
135	C₂×C₈×C₂₃	—	2	1	no	—
136	C₂×C₈×C₂₃	—	2	1	no	—
137	C₂×C₈×C₂₃	—	2	1	no	—
138	C₂×C₈×C₂₃	—	2	8	no	—
139	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₂₃	#41	1	2	yes	—
144	C₂×C₈×C₂₃	#41	1	2	yes	—
145	C₄⋊C₄×C₂₃	—	2	2	no	—
146	C₄⋊C₄×C₂₃	—	2	2	no	—
147	C₄⋊C₄×C₂₃	—	2	2	no	—
148	C₄⋊C₄×C₂₃	—	2	2	no	—
149	C₄⋊C₄×C₂₃	—	2	2	no	—
150	C₄⋊C₄×C₂₃	—	4	4	no	—
151	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
152	C₂²⋊C₄×C₂₃	—	2	8	no	—
153	C₂²⋊C₄×C₂₃	—	4	4	no	—
154	C₂²⋊C₄×C₂₃	—	4	4	no	—
155	C₂²⋊C₄×C₂₃	—	4	4	no	—
156	C₂²⋊C₄×C₂₃	—	4	4	no	—
157	C₄²×C₂₃	—	2	2	no	—
158	C₄²×C₂₃	—	2	2	no	—
159	C₄²×C₂₃	—	2	1	no	—
160	C₄²×C₂₃	—	2	1	no	—
161	C₄²×C₂₃	—	4	4	no	—
162	C₄²×C₂₃	C₂×D₄	1	2	yes	—
163	C₄²×C₂₃	#41	1	2	yes	—
164	C₄×#466	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₂₃	—	2	1	no	—
166	C₂³×C₂₃	—	2	1	no	—
167	C₂³×C₂₃	—	2	1	no	—
168	C₂³×C₂₃	—	2	1	no	—
169	C₂³×C₂₃	—	2	4	no	—
170	C₂³×C₂₃	—	4	2	no	—
171	C₂³×C₂₃	—	4	2	no	—
172	C₂³×C₂₃	—	4	2	no	—
173	C₂³×C₂₃	—	4	2	no	—
174	C₂³×C₂₃	—	4	2	no	—
175	C₂³×C₂₃	—	4	2	no	—
176	C₂³×C₂₃	C₄×D₄	1	2	yes	—
177	C₂³×C₂₃	C₂×D₈	1	2	yes	—
178	C₂³×C₂₃	#135	1	2	yes	—
179	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
180	D₄×C₂₃	—	2	4	no	—
181	D₄×C₂₃	—	2	4	no	—
182	D₄×C₂₃	—	4	16	no	—
183	D₄×C₂₃	—	4	2	no	—
184	D₄×C₂₃	—	4	2	no	—
185	C₂×C₄×C₂₃	—	2	8	no	—
186	C₂×C₄×C₂₃	—	2	1	no	—
187	C₂×C₄×C₂₃	—	2	1	no	—
188	C₂×C₄×C₂₃	—	2	1	no	—
189	C₂×C₄×C₂₃	—	2	1	no	—
190	C₂×C₄×C₂₃	—	2	1	no	—
191	C₂×C₄×C₂₃	—	2	1	no	—
192	C₂×C₄×C₂₃	—	2	1	no	—
193	C₂×C₄×C₂₃	—	2	1	no	—
194	C₂×C₄×C₂₃	—	2	2	no	—
195	C₂×C₄×C₂₃	—	2	2	no	—
196	C₂×C₄×C₂₃	—	2	2	no	—
197	C₂×C₄×C₂₃	—	2	2	no	—
198	C₂×C₄×C₂₃	—	2	8	no	—
199	C₂×C₄×C₂₃	—	2	4	no	—
200	C₂×C₄×C₂₃	—	4	2	no	—
201	C₂×C₄×C₂₃	—	4	2	no	—
202	C₂×C₄×C₂₃	—	4	2	no	—
203	C₂×C₄×C₂₃	—	4	2	no	—
204	C₂×C₄×C₂₃	—	4	2	no	—
205	C₂×C₄×C₂₃	—	4	2	no	—
206	C₂×C₄×C₂₃	—	4	2	no	—
207	C₂×C₄×C₂₃	—	4	2	no	—
208	C₂×C₄×C₂₃	—	8	8	no	—
209	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₂₃	#121	1	2	yes	—
211	C₂×C₄×C₂₃	#121	1	2	yes	—
212	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
213	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
214	C₂×C₄×C₂₃	#135	1	2	yes	—
215	C₂×C₄×C₂₃	#135	1	2	yes	—
216	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₂₃	C₂×#41	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	C₈×C₂₃	—	2	2	no	—
223	C₈×C₂₃	—	2	2	no	—
224	C₈×C₂₃	—	2	2	no	—
225	C₈×C₂₃	C₄×D₄	1	4	yes	complemented
226	C₂×#466	C₂×C₂₃	1	1	yes	characteristic
227	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
228	C₂²×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
229	C₄×#121	C₂×C₂₃	1	2	yes	complemented
230	#1970	C₂×C₂₃	1	1	yes	characteristic, complemented
231	#1942	C₂×C₂₃	1	1	yes	characteristic, complemented
232	#1934	C₂×C₂₃	1	2	yes	complemented
233	#1893	C₂×C₂₃	1	2	yes	complemented
234	#1808	C₂×C₂₃	1	1	yes	characteristic, complemented
235	C₄×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
236	C₄×#102	C₂×C₂₃	1	2	yes	complemented
237	C₂²×C₂₃	—	2	2	no	—
238	C₂²×C₂₃	—	2	2	no	—
239	C₂²×C₂₃	—	2	2	no	—
240	C₂²×C₂₃	—	2	2	no	—
241	C₂²×C₂₃	—	2	2	no	—
242	C₂²×C₂₃	—	2	2	no	—
243	C₂²×C₂₃	—	4	4	no	—
244	C₂²×C₂₃	—	4	4	no	—
245	C₂²×C₂₃	—	4	4	no	—
246	C₂²×C₂₃	—	8	2	no	—
247	C₂²×C₂₃	—	8	2	no	—
248	C₂²×C₂₃	—	8	2	no	—
249	C₂²×C₂₃	—	8	2	no	—
250	C₂²×C₂₃	C₄×D₈	1	4	yes	complemented
251	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
253	C₂²×C₂₃	#532	1	1	yes	characteristic
254	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
255	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
256	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
257	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
258	C₄×C₂₃	—	2	2	no	—
259	C₄×C₂₃	—	2	2	no	—
260	C₄×C₂₃	—	2	2	no	—
261	C₄×C₂₃	—	2	2	no	—
262	C₄×C₂₃	—	4	4	no	—
263	C₄×C₂₃	—	8	2	no	—
264	C₄×C₂₃	—	8	2	no	—
265	C₄×C₂₃	#466	1	4	yes	direct product factor
266	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
268	C₄×C₂₃	#525	1	1	yes	characteristic
269	C₄×C₂₃	#529	1	1	yes	characteristic
270	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
271	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
272	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
273	C₂×#121	C₂²×C₂₃	1	2	yes	—
274	C₂×C₄×D₄	—	2	2	no	—
275	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
276	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
277	#466	C₄×C₂₃	1	8	yes	direct product factor
278	C₄×D₈	—	2	4	no	—
279	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
280	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
281	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
282	C₂×#102	C₂²×C₂₃	1	2	yes	—
283	C₂×#102	C₂²×C₂₃	1	2	yes	—
284	C₂×#102	C₂²×C₂₃	1	2	yes	—
285	C₂×C₄×C₈	—	2	4	no	—
286	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
290	#390	C₂²×C₂₃	1	2	yes	—
291	#389	C₂²×C₂₃	1	2	yes	—
292	#388	—	2	2	no	—
293	#386	—	2	2	no	—
294	#380	C₂²×C₂₃	1	2	yes	—
295	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
296	C₄×C₂²⋊C₄	—	2	2	no	—
297	#340	C₂²×C₂₃	1	2	yes	—
298	#340	C₂²×C₂₃	1	2	yes	—
299	#340	C₂²×C₂₃	1	2	yes	—
300	C₂×C₂₃	—	2	4	no	—
301	C₂×C₂₃	—	8	4	no	—
302	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
303	C₂×C₂₃	C₂×C₄×D₈	1	1	yes	characteristic
304	C₂×C₂₃	C₄×#135	1	1	yes	characteristic
305	C₂×C₂₃	C₂×#466	1	1	yes	characteristic
306	C₂×C₂₃	#3050	1	1	yes	characteristic
307	C₂×C₂₃	#3168	1	1	yes	characteristic
308	C₂×C₂₃	#3169	1	1	yes	characteristic
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
311	C₂³×C₄	—	2	2	no	—
312	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
313	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
315	C₂×D₈	—	2	2	no	—
316	C₂×D₈	—	2	2	no	—
317	C₂×D₈	C₂×C₄×C₂₃	1	4	yes	complemented
318	C₂²×C₈	—	2	2	no	—
319	C₂²×C₈	—	2	2	no	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	—	2	2	no	—
322	C₂²×C₈	—	2	2	no	—
323	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	complemented
324	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
328	#121	—	2	4	no	—
329	#121	C₂×C₄×C₂₃	1	8	yes	complemented
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	4	8	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
346	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
349	#107	—	2	2	no	—
350	#107	—	2	2	no	—
351	#107	C₂×C₄×C₂₃	1	4	yes	complemented
352	#102	—	2	4	no	—
353	#102	—	2	4	no	—
354	#102	C₂×C₄×C₂₃	1	8	yes	complemented
355	C₄×C₈	—	2	2	no	—
356	C₄×C₈	—	2	2	no	—
357	C₄×C₈	—	2	2	no	—
358	C₄×C₈	D₄×C₂₃	1	4	yes	complemented
359	#95	—	2	2	no	—
360	#95	—	2	2	no	—
361	#95	—	2	2	no	—
362	C₂₃	C₄×#466	1	1	yes	characteristic, direct product factor, Sylow
363	C₂⁴	—	2	2	no	—
364	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	—	4	4	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	D₈×C₂₃	1	4	yes	complemented
390	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
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	C₂×D₄×C₂₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
396	C₂²×C₄	#41×C₂₃	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
398	D₈	—	2	8	no	—
399	C₂×C₈	—	2	8	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	8	no	—
407	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
408	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
409	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
410	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
411	C₂×C₈	#41×C₂₃	1	2	yes	—
412	C₂×C₈	#41×C₂₃	1	2	yes	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	4	4	no	—
419	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	4	4	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	4	4	no	—
430	C₄²	C₂×D₄×C₂₃	1	2	yes	—
431	C₄²	#41×C₂₃	1	2	yes	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	C₄×D₄×C₂₃	1	2	yes	—
444	C₂³	C₂×D₈×C₂₃	1	2	yes	—
445	C₂³	C₂₃×#135	1	2	yes	—
446	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
447	D₄	—	2	4	no	—
448	D₄	—	2	4	no	—
449	D₄	—	4	16	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	8	8	no	—
476	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
477	C₂×C₄	C₂₃×#121	1	2	yes	—
478	C₂×C₄	C₂₃×#121	1	2	yes	—
479	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
480	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
481	C₂×C₄	C₂₃×#135	1	2	yes	—
482	C₂×C₄	C₂₃×#135	1	2	yes	—
483	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
485	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
486	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
487	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
488	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	C₄×D₄×C₂₃	1	4	yes	complemented
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	C₄×D₈×C₂₃	1	4	yes	complemented
507	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
508	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
509	C₂²	C₂₃×#532	1	1	yes	characteristic
510	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
511	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
512	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
513	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	8	2	no	—
520	C₄	—	8	2	no	—
521	C₄	C₂₃×#466	1	4	yes	direct product factor
522	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
523	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
524	C₄	C₂₃×#525	1	1	yes	characteristic
525	C₄	C₂₃×#529	1	1	yes	characteristic
526	C₂	—	2	4	no	—
527	C₂	—	8	4	no	—
528	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
529	C₂	C₂×C₄×D₈×C₂₃	1	1	yes	characteristic
530	C₂	C₄×C₂₃×#135	1	1	yes	characteristic
531	C₂	C₂×C₂₃×#466	1	1	yes	characteristic
532	C₂	C₂₃×#3050	1	1	yes	characteristic
533	C₂	C₂₃×#3168	1	1	yes	characteristic
534	C₂	C₂₃×#3169	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂²×D₄
prime radical	C₂×C₂₃×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₂₃	C₂	semidirect
3. C₂²×C₄×C₈×C₂₃	C₂	semidirect
4. C₄×C₂₃×#121	C₂	semidirect
5. C₂₃×#1970	C₂	semidirect
6. C₂₃×#1942	C₂	semidirect
7. C₂₃×#1934	C₂	semidirect
8. C₂₃×#1893	C₂	semidirect
9. C₂₃×#1808	C₂	semidirect
10. C₄×C₂₃×#107	C₂	semidirect
11. C₄×C₂₃×#102	C₂	semidirect
19. C₂₃×#466	C₄	direct (N × H)
50. C₂×D₈×C₂₃	C₂×C₄	semidirect
56. C₂²×C₈×C₂₃	C₂×C₄	semidirect
62. C₂₃×#121	C₂×C₄	semidirect
84. C₂₃×#107	C₂×C₄	semidirect
87. C₂₃×#102	C₂×C₄	semidirect
91. C₄×C₈×C₂₃	D₄	semidirect
121. C₂²×C₄×C₂₃	D₈	semidirect
164. C₄×#466	C₂₃	direct (N × H)
225. C₈×C₂₃	C₄×D₄	semidirect
227. C₂×C₄×D₈	C₂×C₂₃	semidirect
228. C₂²×C₄×C₈	C₂×C₂₃	semidirect
229. C₄×#121	C₂×C₂₃	semidirect
230. #1970	C₂×C₂₃	semidirect
231. #1942	C₂×C₂₃	semidirect
232. #1934	C₂×C₂₃	semidirect
233. #1893	C₂×C₂₃	semidirect
234. #1808	C₂×C₂₃	semidirect
235. C₄×#107	C₂×C₂₃	semidirect
236. C₄×#102	C₂×C₂₃	semidirect
250. C₂²×C₂₃	C₄×D₈	semidirect
265. C₄×C₂₃	#466	direct (N × H)
277. #466	C₄×C₂₃	direct (N × H)
317. C₂×D₈	C₂×C₄×C₂₃	semidirect
323. C₂²×C₈	C₂×C₄×C₂₃	semidirect
329. #121	C₂×C₄×C₂₃	semidirect
351. #107	C₂×C₄×C₂₃	semidirect
354. #102	C₂×C₄×C₂₃	semidirect
358. C₄×C₈	D₄×C₂₃	semidirect
362. C₂₃	C₄×#466	direct (N × H)
389. C₂²×C₄	D₈×C₂₃	semidirect
492. C₈	C₄×D₄×C₂₃	semidirect
506. C₂²	C₄×D₈×C₂₃	semidirect
521. C₄	C₂₃×#466	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×#466	2
C₂×C₄×D₈×C₂₃	2
C₂²×C₄×C₈×C₂₃	2
C₄×C₂₃×#121	2
C₂₃×#1970	2
C₂₃×#1942	2
C₂₃×#1934	2
C₂₃×#1893	2
C₂₃×#1808	2
C₄×C₂₃×#107	2
C₄×C₂₃×#102	2
C₄×#466	23

Subgroups — C4×C23×#466 #19169147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#466 #19169147