Subgroups — C₂×C₃×C₅×#469 #14276086

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#469	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#469	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×D₄	—	2	2	no	—
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×D₈	—	2	4	no	—
12	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
13	C₂×C₃×C₅×M₁₆	—	2	4	no	—
14	C₂×C₃×C₅×M₁₆	C₂²	1	4	yes	complemented
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#121	—	2	4	no	—
18	C₃×C₅×#121	C₂²	1	8	yes	complemented
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
21	C₃×C₅×#106	C₂²	1	4	yes	complemented
22	C₃×C₅×#102	C₂²	1	8	yes	complemented
23	C₂×C₃×#469	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
27	C₅×#469	C₂×C₃	1	8	yes	direct product factor
28	C₂×C₅×#106	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₅×#102	C₂×C₃	1	2	yes	complemented
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
32	C₂×C₃×C₅×D₄	—	2	8	no	—
33	C₂×C₃×C₅×D₄	—	2	4	no	—
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	4	no	—
36	C₂×C₃×C₅×D₄	—	4	8	no	—
37	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
38	C₂²×C₃×C₄×C₅	—	2	2	no	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₃×C₅×D₈	—	2	8	no	—
46	C₃×C₅×M₁₆	—	2	8	no	—
47	C₂×C₃×C₅×C₈	—	2	2	no	—
48	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
49	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
53	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
54	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
57	C₃×#469	C₂×C₅	1	8	yes	direct product factor
58	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×C₃×#102	C₂×C₅	1	2	yes	complemented
60	C₂²×C₅×D₄	—	2	2	no	—
61	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
62	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₅×D₈	—	2	4	no	—
64	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
65	C₂×C₅×M₁₆	—	2	4	no	—
66	C₂×C₅×M₁₆	C₂²×C₃	1	4	yes	complemented
67	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
69	C₅×#121	—	2	4	no	—
70	C₅×#121	C₂²×C₃	1	8	yes	complemented
71	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₅×#106	C₂²×C₃	1	4	yes	complemented
74	C₅×#102	C₂²×C₃	1	8	yes	complemented
75	C₂×#469	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	4	4	no	—
80	C₂³×C₃×C₅	—	4	4	no	—
81	C₂³×C₃×C₅	—	4	4	no	—
82	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
84	C₃×C₅×D₄	—	2	4	no	—
85	C₃×C₅×D₄	—	2	4	no	—
86	C₃×C₅×D₄	—	4	16	no	—
87	C₃×C₅×D₄	—	4	4	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	4	4	no	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	#41	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
99	C₃×C₅×C₈	—	2	2	no	—
100	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
101	C₂²×C₃×D₄	—	2	2	no	—
102	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
103	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
104	C₂×C₃×D₈	—	2	4	no	—
105	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
106	C₂×C₃×M₁₆	—	2	4	no	—
107	C₂×C₃×M₁₆	C₂²×C₅	1	4	yes	complemented
108	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
110	C₃×#121	—	2	4	no	—
111	C₃×#121	C₂²×C₅	1	8	yes	complemented
112	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
114	C₃×#106	C₂²×C₅	1	4	yes	complemented
115	C₃×#102	C₂²×C₅	1	8	yes	complemented
116	C₂⁴×C₅	—	2	2	no	—
117	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	8	no	—
119	C₂×C₅×D₄	—	2	4	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	4	no	—
122	C₂×C₅×D₄	—	4	8	no	—
123	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
129	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₅×D₈	—	2	8	no	—
132	C₅×M₁₆	—	2	8	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
135	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
136	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
139	C₅×C₂²⋊C₄	—	2	8	no	—
140	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
141	C₂²×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
142	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
143	#469	C₂×C₃×C₅	1	8	yes	direct product factor
144	C₂×#106	C₂×C₃×C₅	1	1	yes	characteristic, complemented
145	C₂×#102	C₂×C₃×C₅	1	2	yes	complemented
146	C₂²×C₃×C₅	—	2	2	no	—
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	—	4	4	no	—
150	C₂²×C₃×C₅	—	4	4	no	—
151	C₂²×C₃×C₅	—	4	4	no	—
152	C₂²×C₃×C₅	—	8	8	no	—
153	C₂²×C₃×C₅	#121	1	2	yes	—
154	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
155	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
156	C₃×C₄×C₅	—	2	2	no	—
157	C₃×C₄×C₅	—	4	4	no	—
158	C₃×C₄×C₅	#121	1	2	yes	—
159	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
160	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
161	C₂⁴×C₃	—	2	2	no	—
162	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
163	C₂×C₃×D₄	—	2	8	no	—
164	C₂×C₃×D₄	—	2	4	no	—
165	C₂×C₃×D₄	—	2	2	no	—
166	C₂×C₃×D₄	—	2	4	no	—
167	C₂×C₃×D₄	—	4	8	no	—
168	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
169	C₂²×C₃×C₄	—	2	2	no	—
170	C₂²×C₃×C₄	—	2	2	no	—
171	C₂²×C₃×C₄	—	2	2	no	—
172	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
174	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
175	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
176	C₃×D₈	—	2	8	no	—
177	C₃×M₁₆	—	2	8	no	—
178	C₂×C₃×C₈	—	2	2	no	—
179	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
180	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
181	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
182	C₃×C₄⋊C₄	—	2	2	no	—
183	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
184	C₃×C₂²⋊C₄	—	2	8	no	—
185	C₂³×C₅	—	2	2	no	—
186	C₂³×C₅	—	2	4	no	—
187	C₂³×C₅	—	2	4	no	—
188	C₂³×C₅	—	4	4	no	—
189	C₂³×C₅	—	4	4	no	—
190	C₂³×C₅	—	4	4	no	—
191	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
192	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	4	16	no	—
196	C₅×D₄	—	4	4	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	4	no	—
202	C₂×C₄×C₅	—	4	4	no	—
203	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
204	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
206	C₂×C₄×C₅	C₃×#41	1	2	yes	—
207	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
208	C₅×C₈	—	2	2	no	—
209	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
210	C₂²×D₄	—	2	2	no	—
211	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
212	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
213	C₂×D₈	—	2	4	no	—
214	C₂×D₈	C₂²×C₃×C₅	1	4	yes	complemented
215	C₂×M₁₆	—	2	4	no	—
216	C₂×M₁₆	C₂²×C₃×C₅	1	4	yes	complemented
217	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
219	#121	—	2	4	no	—
220	#121	C₂²×C₃×C₅	1	8	yes	complemented
221	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
222	C₂×C₂²⋊C₄	—	2	2	no	—
223	#106	C₂²×C₃×C₅	1	4	yes	complemented
224	#102	C₂²×C₃×C₅	1	8	yes	complemented
225	C₂×C₃×C₅	—	4	2	no	—
226	C₂×C₃×C₅	—	8	4	no	—
227	C₂×C₃×C₅	#469	1	4	yes	direct product factor
228	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
229	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	2	4	no	—
232	C₂³×C₃	—	2	4	no	—
233	C₂³×C₃	—	4	4	no	—
234	C₂³×C₃	—	4	4	no	—
235	C₂³×C₃	—	4	4	no	—
236	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
237	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
238	C₃×D₄	—	2	4	no	—
239	C₃×D₄	—	2	4	no	—
240	C₃×D₄	—	4	16	no	—
241	C₃×D₄	—	4	4	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	4	4	no	—
248	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
249	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
251	C₂×C₃×C₄	C₅×#41	1	2	yes	—
252	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
253	C₃×C₈	—	2	2	no	—
254	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
255	C₂²×C₅	—	2	4	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	—	4	4	no	—
259	C₂²×C₅	—	4	4	no	—
260	C₂²×C₅	—	4	4	no	—
261	C₂²×C₅	—	8	8	no	—
262	C₂²×C₅	C₃×#121	1	2	yes	—
263	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
264	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
265	C₄×C₅	—	2	2	no	—
266	C₄×C₅	—	4	4	no	—
267	C₄×C₅	C₃×#121	1	2	yes	—
268	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
269	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
270	C₂⁴	—	2	2	no	—
271	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	4	8	no	—
277	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
283	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
284	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
285	D₈	—	2	8	no	—
286	M₁₆	—	2	8	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
289	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
290	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
293	C₂²⋊C₄	—	2	8	no	—
294	C₃×C₅	C₂×#469	1	1	yes	characteristic, direct product factor, Hall
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	4	no	—
297	C₂²×C₃	—	4	4	no	—
298	C₂²×C₃	—	4	4	no	—
299	C₂²×C₃	—	4	4	no	—
300	C₂²×C₃	—	4	4	no	—
301	C₂²×C₃	—	8	8	no	—
302	C₂²×C₃	C₅×#121	1	2	yes	—
303	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	4	yes	—
304	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	4	4	no	—
307	C₃×C₄	C₅×#121	1	2	yes	—
308	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
309	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
310	C₂×C₅	—	4	2	no	—
311	C₂×C₅	—	8	4	no	—
312	C₂×C₅	C₃×#469	1	4	yes	direct product factor
313	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
314	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	4	4	no	—
321	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
322	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
323	D₄	—	2	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	4	16	no	—
326	D₄	—	4	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
334	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
335	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
336	C₂×C₄	C₃×C₅×#41	1	2	yes	—
337	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
338	C₈	—	2	2	no	—
339	C₈	C₂×C₃×C₅×D₄	1	4	yes	complemented
340	C₂×C₃	—	4	2	no	—
341	C₂×C₃	—	8	4	no	—
342	C₂×C₃	C₅×#469	1	4	yes	direct product factor
343	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
344	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
345	C₅	C₂×C₃×#469	1	1	yes	characteristic, direct product factor, Sylow
346	C₂²	—	2	2	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	8	8	no	—
353	C₂²	C₃×C₅×#121	1	2	yes	—
354	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	4	yes	—
355	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	4	4	no	—
358	C₄	C₃×C₅×#121	1	2	yes	—
359	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
360	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
361	C₃	C₂×C₅×#469	1	1	yes	characteristic, direct product factor, Sylow
362	C₂	—	4	2	no	—
363	C₂	—	8	4	no	—
364	C₂	C₃×C₅×#469	1	4	yes	direct product factor
365	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
366	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₃×C₅×#469	C₂	direct (N × H)
5. C₂×C₃×C₅×#106	C₂	semidirect
6. C₂×C₃×C₅×#102	C₂	semidirect
7. C₂×C₅×#469	C₃	direct (N × H)
12. C₂×C₃×C₅×D₈	C₂²	semidirect
14. C₂×C₃×C₅×M₁₆	C₂²	semidirect
18. C₃×C₅×#121	C₂²	semidirect
21. C₃×C₅×#106	C₂²	semidirect
22. C₃×C₅×#102	C₂²	semidirect
23. C₂×C₃×#469	C₅	direct (N × H)
24. C₂²×C₅×D₈	C₂×C₃	semidirect
25. C₂²×C₅×M₁₆	C₂×C₃	semidirect
26. C₂×C₅×#121	C₂×C₃	semidirect
27. C₅×#469	C₂×C₃	direct (N × H)
28. C₂×C₅×#106	C₂×C₃	semidirect
29. C₂×C₅×#102	C₂×C₃	semidirect
48. C₂×C₃×C₅×C₈	D₄	semidirect
54. C₂²×C₃×D₈	C₂×C₅	semidirect
55. C₂²×C₃×M₁₆	C₂×C₅	semidirect
56. C₂×C₃×#121	C₂×C₅	semidirect
57. C₃×#469	C₂×C₅	direct (N × H)
58. C₂×C₃×#106	C₂×C₅	semidirect
59. C₂×C₃×#102	C₂×C₅	semidirect
64. C₂×C₅×D₈	C₂²×C₃	semidirect
66. C₂×C₅×M₁₆	C₂²×C₃	semidirect
70. C₅×#121	C₂²×C₃	semidirect
73. C₅×#106	C₂²×C₃	semidirect
74. C₅×#102	C₂²×C₃	semidirect
75. C₂×#469	C₃×C₅	direct (N × H)
100. C₃×C₅×C₈	C₂×D₄	semidirect
105. C₂×C₃×D₈	C₂²×C₅	semidirect
107. C₂×C₃×M₁₆	C₂²×C₅	semidirect
111. C₃×#121	C₂²×C₅	semidirect
114. C₃×#106	C₂²×C₅	semidirect
115. C₃×#102	C₂²×C₅	semidirect
134. C₂×C₅×C₈	C₃×D₄	semidirect
140. C₂²×D₈	C₂×C₃×C₅	semidirect
141. C₂²×M₁₆	C₂×C₃×C₅	semidirect
142. C₂×#121	C₂×C₃×C₅	semidirect
143. #469	C₂×C₃×C₅	direct (N × H)
144. C₂×#106	C₂×C₃×C₅	semidirect
145. C₂×#102	C₂×C₃×C₅	semidirect
179. C₂×C₃×C₈	C₅×D₄	semidirect
209. C₅×C₈	C₂×C₃×D₄	semidirect
214. C₂×D₈	C₂²×C₃×C₅	semidirect
216. C₂×M₁₆	C₂²×C₃×C₅	semidirect
220. #121	C₂²×C₃×C₅	semidirect
223. #106	C₂²×C₃×C₅	semidirect
224. #102	C₂²×C₃×C₅	semidirect
227. C₂×C₃×C₅	#469	direct (N × H)
254. C₃×C₈	C₂×C₅×D₄	semidirect
288. C₂×C₈	C₃×C₅×D₄	semidirect
294. C₃×C₅	C₂×#469	direct (N × H)
312. C₂×C₅	C₃×#469	direct (N × H)
339. C₈	C₂×C₃×C₅×D₄	semidirect
342. C₂×C₃	C₅×#469	direct (N × H)
345. C₅	C₂×C₃×#469	direct (N × H)
361. C₃	C₂×C₅×#469	direct (N × H)
364. C₂	C₃×C₅×#469	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×D₈	2
C₂²×C₃×C₅×M₁₆	2
C₂×C₃×C₅×#121	2
C₃×C₅×#469	2
C₂×C₃×C₅×#106	2
C₂×C₃×C₅×#102	2
C₂×C₅×#469	3
C₂×C₃×#469	5

Subgroups — C2×C3×C5×#469 #14276086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#469 #14276086