Subgroups — C₄×C₂₃×#481 #19169200

Order 5888.

1060 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1926	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1919	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1874	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1824	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂₃×#106	C₂	1	2	yes	maximal, complemented
10	C₄×C₂₃×#102	C₂	1	2	yes	maximal, complemented
11	C₄×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₂₃	—	2	1	no	—
14	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₂₃	—	2	1	no	—
18	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#481	C₄	1	8	yes	direct product factor
20	C₂×C₂₃×#106	C₂²	1	2	yes	—
21	C₂×C₂₃×#106	C₂²	1	2	yes	—
22	C₂×C₂₃×#102	C₂²	1	2	yes	—
23	C₂×C₂₃×#102	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
27	C₂₃×#390	C₂²	1	1	yes	characteristic
28	C₂₃×#389	C₂²	1	1	yes	characteristic
29	C₂₃×#388	—	2	1	no	—
30	C₂₃×#386	—	2	1	no	—
31	C₂₃×#380	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
33	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
38	C₂×C₂₃×#95	—	2	1	no	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂₃×#340	C₂²	1	2	yes	—
41	C₂₃×#340	C₂²	1	2	yes	—
42	C₂₃×#340	C₂²	1	2	yes	—
43	C₂₃×#336	C₂²	1	2	yes	—
44	C₂²×D₄×C₂₃	—	2	1	no	—
45	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₂₃	—	2	1	no	—
47	C₂³×C₄×C₂₃	—	2	1	no	—
48	C₂³×C₄×C₂₃	—	2	1	no	—
49	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
54	C₂₃×#121	—	2	2	no	—
55	C₂₃×#121	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₂₃	—	2	4	no	—
57	C₄×D₄×C₂₃	—	4	4	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	complemented
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
74	C₂×C₄²×C₂₃	—	2	4	no	—
75	C₂×C₄²×C₂₃	—	2	2	no	—
76	C₂×C₄²×C₂₃	—	2	1	no	—
77	C₂×C₄²×C₂₃	—	2	2	no	—
78	C₂×C₄²×C₂₃	—	4	4	no	—
79	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
83	C₂₃×#106	—	2	4	no	—
84	C₂₃×#106	C₂×C₄	1	8	yes	complemented
85	C₂₃×#102	—	2	4	no	—
86	C₂₃×#102	C₂×C₄	1	8	yes	complemented
87	C₂₃×C₂²⋊C₈	—	2	2	no	—
88	C₂₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
89	C₄×C₈×C₂₃	—	2	4	no	—
90	C₂₃×#95	—	2	2	no	—
91	C₂₃×#95	—	2	2	no	—
92	C₂₃×#95	—	2	1	no	—
93	C₂₃×#95	—	2	1	no	—
94	C₂₃×#95	—	2	1	no	—
95	C₂⁴×C₂₃	—	2	1	no	—
96	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₂₃	—	2	4	no	—
98	C₂×D₄×C₂₃	—	2	2	no	—
99	C₂×D₄×C₂₃	—	2	2	no	—
100	C₂×D₄×C₂₃	—	2	1	no	—
101	C₂×D₄×C₂₃	—	4	2	no	—
102	C₂×D₄×C₂₃	—	4	2	no	—
103	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₂₃	—	2	2	no	—
105	C₂²×C₄×C₂₃	—	2	2	no	—
106	C₂²×C₄×C₂₃	—	2	2	no	—
107	C₂²×C₄×C₂₃	—	2	2	no	—
108	C₂²×C₄×C₂₃	—	2	4	no	—
109	C₂²×C₄×C₂₃	—	2	4	no	—
110	C₂²×C₄×C₂₃	—	2	2	no	—
111	C₂²×C₄×C₂₃	—	2	2	no	—
112	C₂²×C₄×C₂₃	—	2	2	no	—
113	C₂²×C₄×C₂₃	—	2	1	no	—
114	C₂²×C₄×C₂₃	—	2	2	no	—
115	C₂²×C₄×C₂₃	—	2	1	no	—
116	C₂²×C₄×C₂₃	—	2	1	no	—
117	C₂²×C₄×C₂₃	—	4	1	no	—
118	C₂²×C₄×C₂₃	—	4	2	no	—
119	C₂²×C₄×C₂₃	—	4	2	no	—
120	C₂²×C₄×C₂₃	—	4	2	no	—
121	C₂²×C₄×C₂₃	—	4	2	no	—
122	C₂²×C₄×C₂₃	—	4	2	no	—
123	C₂²×C₄×C₂₃	—	4	2	no	—
124	C₂²×C₄×C₂₃	—	4	2	no	—
125	C₂²×C₄×C₂₃	SD₁₆	1	4	yes	—
126	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₃	#41	1	2	yes	—
133	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₂₃	—	2	2	no	—
135	C₂×C₈×C₂₃	—	2	2	no	—
136	C₂×C₈×C₂₃	—	2	2	no	—
137	C₂×C₈×C₂₃	—	2	2	no	—
138	C₂×C₈×C₂₃	—	2	2	no	—
139	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
140	C₄⋊C₄×C₂₃	—	2	4	no	—
141	C₄⋊C₄×C₂₃	—	2	4	no	—
142	C₄⋊C₄×C₂₃	—	2	2	no	—
143	C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₄⋊C₄×C₂₃	—	2	1	no	—
145	C₄⋊C₄×C₂₃	—	2	2	no	—
146	C₄⋊C₄×C₂₃	—	2	2	no	—
147	C₄⋊C₄×C₂₃	—	4	2	no	—
148	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
149	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
150	C₄⋊C₄×C₂₃	#41	1	4	yes	—
151	C₂²⋊C₄×C₂₃	—	2	4	no	—
152	C₂²⋊C₄×C₂₃	—	4	2	no	—
153	C₂²⋊C₄×C₂₃	—	4	2	no	—
154	C₂²⋊C₄×C₂₃	—	4	2	no	—
155	C₂²⋊C₄×C₂₃	—	4	2	no	—
156	C₄²×C₂₃	—	2	2	no	—
157	C₄²×C₂₃	—	2	2	no	—
158	C₄²×C₂₃	—	2	2	no	—
159	C₄²×C₂₃	—	4	4	no	—
160	C₄²×C₂₃	—	4	2	no	—
161	C₄²×C₂₃	—	4	4	no	—
162	C₄²×C₂₃	#41	1	4	yes	—
163	C₄×#481	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₂₃	—	2	1	no	—
165	C₂³×C₂₃	—	2	1	no	—
166	C₂³×C₂₃	—	2	1	no	—
167	C₂³×C₂₃	—	2	1	no	—
168	C₂³×C₂₃	—	2	2	no	—
169	C₂³×C₂₃	—	4	1	no	—
170	C₂³×C₂₃	—	4	1	no	—
171	C₂³×C₂₃	—	4	1	no	—
172	C₂³×C₂₃	—	4	1	no	—
173	C₂³×C₂₃	—	4	1	no	—
174	C₂³×C₂₃	—	4	1	no	—
175	C₂³×C₂₃	C₄×D₄	1	2	yes	—
176	C₂³×C₂₃	C₂×SD₁₆	1	2	yes	—
177	C₂³×C₂₃	#135	1	2	yes	—
178	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
179	D₄×C₂₃	—	2	4	no	—
180	D₄×C₂₃	—	4	8	no	—
181	D₄×C₂₃	—	4	2	no	—
182	C₂×C₄×C₂₃	—	2	1	no	—
183	C₂×C₄×C₂₃	—	2	1	no	—
184	C₂×C₄×C₂₃	—	2	1	no	—
185	C₂×C₄×C₂₃	—	2	1	no	—
186	C₂×C₄×C₂₃	—	2	1	no	—
187	C₂×C₄×C₂₃	—	2	1	no	—
188	C₂×C₄×C₂₃	—	2	4	no	—
189	C₂×C₄×C₂₃	—	2	4	no	—
190	C₂×C₄×C₂₃	—	2	8	no	—
191	C₂×C₄×C₂₃	—	2	2	no	—
192	C₂×C₄×C₂₃	—	2	4	no	—
193	C₂×C₄×C₂₃	—	2	1	no	—
194	C₂×C₄×C₂₃	—	2	4	no	—
195	C₂×C₄×C₂₃	—	2	1	no	—
196	C₂×C₄×C₂₃	—	2	1	no	—
197	C₂×C₄×C₂₃	—	4	4	no	—
198	C₂×C₄×C₂₃	—	4	8	no	—
199	C₂×C₄×C₂₃	—	4	8	no	—
200	C₂×C₄×C₂₃	—	4	1	no	—
201	C₂×C₄×C₂₃	—	4	2	no	—
202	C₂×C₄×C₂₃	—	4	1	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	1	no	—
207	C₂×C₄×C₂₃	—	4	1	no	—
208	C₂×C₄×C₂₃	—	4	1	no	—
209	C₂×C₄×C₂₃	—	4	1	no	—
210	C₂×C₄×C₂₃	—	4	1	no	—
211	C₂×C₄×C₂₃	—	4	1	no	—
212	C₂×C₄×C₂₃	—	8	4	no	—
213	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₂₃	#123	1	2	yes	—
215	C₂×C₄×C₂₃	#123	1	2	yes	—
216	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
217	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
218	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
221	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
222	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
223	C₈×C₂₃	—	2	4	no	—
224	C₈×C₂₃	—	4	2	no	—
225	C₂×#481	C₂×C₂₃	1	1	yes	characteristic
226	C₄×#121	C₂×C₂₃	1	1	yes	characteristic
227	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
228	#1926	C₂×C₂₃	1	2	yes	complemented
229	#1919	C₂×C₂₃	1	2	yes	complemented
230	#1874	C₂×C₂₃	1	1	yes	characteristic
231	#1853	C₂×C₂₃	1	1	yes	characteristic, complemented
232	#1824	C₂×C₂₃	1	1	yes	characteristic, complemented
233	C₄×#106	C₂×C₂₃	1	2	yes	complemented
234	C₄×#102	C₂×C₂₃	1	2	yes	complemented
235	C₄×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
236	C₂²×C₂₃	—	2	2	no	—
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	—	4	2	no	—
243	C₂²×C₂₃	—	4	2	no	—
244	C₂²×C₂₃	—	4	2	no	—
245	C₂²×C₂₃	—	8	1	no	—
246	C₂²×C₂₃	—	8	1	no	—
247	C₂²×C₂₃	—	8	1	no	—
248	C₂²×C₂₃	—	8	1	no	—
249	C₂²×C₂₃	C₄×SD₁₆	1	4	yes	—
250	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₂₃	C₂×#123	1	1	yes	characteristic
252	C₂²×C₂₃	#525	1	1	yes	characteristic
253	C₂²×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
254	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
255	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂²×C₂₃	#575	1	1	yes	characteristic
257	C₄×C₂₃	—	2	2	no	—
258	C₄×C₂₃	—	2	2	no	—
259	C₄×C₂₃	—	2	2	no	—
260	C₄×C₂₃	—	4	1	no	—
261	C₄×C₂₃	—	4	4	no	—
262	C₄×C₂₃	—	4	2	no	—
263	C₄×C₂₃	—	4	4	no	—
264	C₄×C₂₃	—	8	1	no	—
265	C₄×C₂₃	—	8	1	no	—
266	C₄×C₂₃	#481	1	4	yes	direct product factor
267	C₄×C₂₃	C₄×#41	1	2	yes	—
268	C₄×C₂₃	#529	1	2	yes	—
269	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
270	C₂×C₄×D₄	—	2	1	no	—
271	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
274	C₂²×C₄²	—	2	1	no	—
275	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
276	#481	C₄×C₂₃	1	8	yes	direct product factor
277	C₂×#106	C₂²×C₂₃	1	2	yes	—
278	C₂×#106	C₂²×C₂₃	1	2	yes	—
279	C₂×#102	C₂²×C₂₃	1	2	yes	—
280	C₂×#102	C₂²×C₂₃	1	2	yes	—
281	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
284	#390	C₂²×C₂₃	1	1	yes	characteristic
285	#389	C₂²×C₂₃	1	1	yes	characteristic
286	#388	—	2	1	no	—
287	#386	—	2	1	no	—
288	#380	C₂²×C₂₃	1	1	yes	characteristic
289	C₄×C₄⋊C₄	—	2	1	no	—
290	C₄×C₄⋊C₄	—	2	1	no	—
291	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
292	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
293	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
294	C₄×C₂²⋊C₄	—	2	1	no	—
295	C₂×#95	—	2	1	no	—
296	#340	C₂²×C₂₃	1	2	yes	—
297	#340	C₂²×C₂₃	1	2	yes	—
298	#340	C₂²×C₂₃	1	2	yes	—
299	#340	C₂²×C₂₃	1	2	yes	—
300	#336	C₂²×C₂₃	1	2	yes	—
301	C₂×C₂₃	—	2	4	no	—
302	C₂×C₂₃	—	8	2	no	—
303	C₂×C₂₃	C₄×#123	1	1	yes	characteristic
304	C₂×C₂₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
305	C₂×C₂₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₂×C₂₃	C₂×#481	1	1	yes	characteristic
307	C₂×C₂₃	#3091	1	1	yes	characteristic
308	C₂×C₂₃	#3103	1	1	yes	characteristic
309	C₂×C₂₃	#3105	1	1	yes	characteristic
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
316	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
319	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
320	#121	—	2	2	no	—
321	#121	C₂×C₄×C₂₃	1	4	yes	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	4	4	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	complemented
330	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	—	2	4	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	4	4	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	#106	—	2	4	no	—
350	#106	C₂×C₄×C₂₃	1	8	yes	complemented
351	#102	—	2	4	no	—
352	#102	C₂×C₄×C₂₃	1	8	yes	complemented
353	C₂²⋊C₈	—	2	2	no	—
354	C₂²⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
355	C₄×C₈	—	2	4	no	—
356	#95	—	2	2	no	—
357	#95	—	2	2	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	#95	—	2	1	no	—
361	C₂₃	C₄×#481	1	1	yes	characteristic, direct product factor, Sylow
362	C₂⁴	—	2	1	no	—
363	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	SD₁₆×C₂₃	1	4	yes	—
393	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
399	C₂²×C₄	#41×C₂₃	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
416	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
417	C₄⋊C₄	#41×C₂₃	1	4	yes	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	4	4	no	—
427	C₄²	—	4	2	no	—
428	C₄²	—	4	4	no	—
429	C₄²	#41×C₂₃	1	4	yes	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	C₄×D₄×C₂₃	1	2	yes	—
442	C₂³	C₂×SD₁₆×C₂₃	1	2	yes	—
443	C₂³	C₂₃×#135	1	2	yes	—
444	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
445	D₄	—	2	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
480	C₂×C₄	C₂₃×#123	1	2	yes	—
481	C₂×C₄	C₂₃×#123	1	2	yes	—
482	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
483	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
484	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
485	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
486	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
487	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
488	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
489	C₈	—	2	4	no	—
490	C₈	—	4	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	C₄×SD₁₆×C₂₃	1	4	yes	—
505	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
506	C₂²	C₂×C₂₃×#123	1	1	yes	characteristic
507	C₂²	C₂₃×#525	1	1	yes	characteristic
508	C₂²	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
509	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
510	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
511	C₂²	C₂₃×#575	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	4	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	4	no	—
519	C₄	—	8	1	no	—
520	C₄	—	8	1	no	—
521	C₄	C₂₃×#481	1	4	yes	direct product factor
522	C₄	C₄×#41×C₂₃	1	2	yes	—
523	C₄	C₂₃×#529	1	2	yes	—
524	C₂	—	2	4	no	—
525	C₂	—	8	2	no	—
526	C₂	C₄×C₂₃×#123	1	1	yes	characteristic
527	C₂	C₂×C₄×SD₁₆×C₂₃	1	1	yes	characteristic
528	C₂	C₄×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
529	C₂	C₂×C₂₃×#481	1	1	yes	characteristic
530	C₂	C₂₃×#3091	1	1	yes	characteristic
531	C₂	C₂₃×#3103	1	1	yes	characteristic
532	C₂	C₂₃×#3105	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×#121	C₂²
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
3. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
4. C₂₃×#1926	C₂	semidirect
5. C₂₃×#1919	C₂	semidirect
7. C₂₃×#1853	C₂	semidirect
8. C₂₃×#1824	C₂	semidirect
9. C₄×C₂₃×#106	C₂	semidirect
10. C₄×C₂₃×#102	C₂	semidirect
11. C₄×C₂₃×C₂²⋊C₈	C₂	semidirect
19. C₂₃×#481	C₄	direct (N × H)
63. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
84. C₂₃×#106	C₂×C₄	semidirect
86. C₂₃×#102	C₂×C₄	semidirect
88. C₂₃×C₂²⋊C₈	C₂×C₄	semidirect
163. C₄×#481	C₂₃	direct (N × H)
227. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
228. #1926	C₂×C₂₃	semidirect
229. #1919	C₂×C₂₃	semidirect
231. #1853	C₂×C₂₃	semidirect
232. #1824	C₂×C₂₃	semidirect
233. C₄×#106	C₂×C₂₃	semidirect
234. C₄×#102	C₂×C₂₃	semidirect
235. C₄×C₂²⋊C₈	C₂×C₂₃	semidirect
266. C₄×C₂₃	#481	direct (N × H)
276. #481	C₄×C₂₃	direct (N × H)
329. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
350. #106	C₂×C₄×C₂₃	semidirect
352. #102	C₂×C₄×C₂₃	semidirect
354. C₂²⋊C₈	C₂×C₄×C₂₃	semidirect
361. C₂₃	C₄×#481	direct (N × H)
521. C₄	C₂₃×#481	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×#481	2
C₄×C₂₃×#121	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂₃×#1926	2
C₂₃×#1919	2
C₂₃×#1874	2
C₂₃×#1853	2
C₂₃×#1824	2
C₄×C₂₃×#106	2
C₄×C₂₃×#102	2
C₄×C₂₃×C₂²⋊C₈	2
C₄×#481	23

Subgroups — C4×C23×#481 #19169200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#481 #19169200