Subgroups — #13086357

Order 1440.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#634	C₂	1	1	yes	maximal, characteristic
2	#10624111	C₂	1	2	yes	maximal
3	C₂×C₃²×C₄×C₅	C₄	1	1	yes	characteristic
4	C₂×C₅×C₃⋊Dic₃	C₄	1	1	yes	characteristic
5	C₂×C₅×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	C₅×#634	—	2	2	no	—
7	#67126	—	2	2	no	—
8	#63780	—	5	1	no	maximal, Hall
9	C₂×C₅×Dic₆	—	6	2	no	—
10	C₂²×C₃²×C₅	C₂×C₄	1	1	yes	characteristic
11	C₃²×C₄×C₅	—	2	1	no	—
12	C₅×C₃⋊Dic₃	—	2	1	no	—
13	C₅×C₃⋊Dic₃	D₄	1	2	yes	—
14	#3968	—	9	1	no	maximal, Hall
15	C₂×#634	D₅	1	1	yes	characteristic
16	#3792	—	5	2	no	—
17	C₂×C₃×C₄×C₅	—	2	2	no	—
18	C₂×C₅×Dic₃	—	6	2	no	—
19	C₂×C₅×Dic₃	—	6	2	no	—
20	C₅×Dic₆	—	6	8	no	—
21	C₂×C₃²×C₅	—	2	1	no	—
22	C₂×C₃²×C₅	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₅×Q₈	—	9	1	no	—
24	#681	—	9	2	no	—
25	C₂×C₃²×C₄	Dic₅	1	1	yes	characteristic
26	C₂×C₃⋊Dic₃	Dic₅	1	1	yes	characteristic
27	C₂×C₃⋊Dic₃	C₂×D₅	1	1	yes	characteristic
28	#634	—	2	2	no	—
29	#622	—	10	2	no	—
30	C₂²×C₃×C₅	—	2	2	no	—
31	C₃×C₄×C₅	—	2	4	no	—
32	C₅×Dic₃	—	6	4	no	—
33	C₅×Dic₃	—	6	4	no	—
34	C₂×Dic₆	—	6	2	no	—
35	C₃²×C₅	#101	1	1	yes	characteristic, complemented, Hall
36	C₅×Q₈	—	18	2	no	—
37	C₂×C₄×C₅	—	9	1	no	—
38	C₂×C₄×C₅	—	9	1	no	—
39	C₂×C₄×C₅	#157	1	1	yes	characteristic
40	#168	—	18	2	no	—
41	C₂²×C₃²	C₂×Dic₅	1	1	yes	characteristic
42	C₃²×C₄	—	2	1	no	—
43	C₃⋊Dic₃	—	2	1	no	—
44	C₃⋊Dic₃	C₂²⋊D₅	1	2	yes	—
45	#101	—	45	1	no	Sylow
46	C₂×C₃×C₅	—	2	4	no	—
47	C₂×C₃×C₅	—	2	2	no	—
48	C₂×C₃×C₄	—	2	2	no	—
49	C₂×Dic₃	—	6	2	no	—
50	C₂×Dic₃	—	6	2	no	—
51	Dic₆	—	6	8	no	—
52	C₂²×C₅	C₂×#157	1	1	yes	characteristic
53	C₄×C₅	—	2	1	no	—
54	C₄×C₅	—	9	2	no	—
55	C₄×C₅	—	18	1	no	—
56	C₂×C₃²	—	2	1	no	—
57	C₂×C₃²	C₂²⋊Dic₅	1	1	yes	characteristic
58	C₂×Q₈	—	9	1	no	—
59	M₁₆	—	45	2	no	—
60	C₃×C₅	—	2	2	no	—
61	C₂²×C₃	—	2	2	no	—
62	C₃×C₄	—	2	4	no	—
63	Dic₃	—	6	4	no	—
64	Dic₃	—	6	4	no	—
65	C₂×C₅	—	2	1	no	—
66	C₂×C₅	C₂²⋊#157	1	1	yes	characteristic
67	C₃²	#3968	1	1	yes	characteristic, complemented, Sylow
68	Q₈	—	18	2	no	—
69	C₂×C₄	—	9	1	no	—
70	C₂×C₄	—	9	1	no	—
71	C₂×C₄	#4379	1	1	yes	characteristic
72	C₈	—	90	2	no	—
73	C₂×C₃	—	2	4	no	—
74	C₂×C₃	—	2	2	no	—
75	C₅	#63780	1	1	yes	characteristic, complemented, Sylow
76	C₂²	C₂×#4379	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	9	2	no	—
79	C₄	—	18	1	no	—
80	C₃	—	2	2	no	—
81	C₂	—	2	1	no	—
82	C₂	C₂²⋊#4379	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#4379
commutator, prime radical	C₂²×C₃²×C₅	C₂×C₄
Frattini	C₂²	C₂×#4379
Fitting	C₂×C₃²×C₄×C₅	C₄
socle	C₂×C₃²×C₅	C₂²⋊C₄
cosocle	C₂×C₅×C₃⋊Dic₃	C₂²
hypercenter	C₂×C₄	#4379
hypocenter	C₃²×C₅	#101
LCS	G ▷ C₂²×C₃²×C₅ ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
35. C₃²×C₅	#101	semidirect
67. C₃²	#3968	semidirect
75. C₅	#63780	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#634	2
#10624111	2
#63780	5
#3968	9