Subgroups — #11746332

Order 960.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₅	C₂	1	1	yes	maximal, characteristic
3	#91096	C₂	1	1	yes	maximal, characteristic
4	#64731	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₄×Dic₁₅	C₄	1	1	yes	characteristic
7	C₂×C₃⋊#168	C₄	1	1	yes	characteristic
8	C₃×C₅×C₁₆	—	2	1	no	—
9	C₃⋊#672	—	2	1	no	—
10	#4511	—	5	1	no	maximal, Hall
11	C₅×M₃₂	D₃	1	1	yes	characteristic
12	C₈×Dic₅	—	3	1	no	—
13	#3944	—	3	1	no	—
14	C₂×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₁₅	—	2	1	no	—
16	C₃×C₅×C₈	D₄	1	1	yes	characteristic
17	C₃×C₅×C₈	Q₈	1	1	yes	characteristic
18	C₃⋊#168	C₈	1	2	yes	—
19	C₃×M₃₂	D₅	1	1	yes	characteristic
20	C₈×Dic₃	—	5	1	no	—
21	#812	—	5	1	no	—
22	C₂×C₅×C₈	C₂×D₃	1	1	yes	characteristic
23	C₄×Dic₅	—	3	1	no	—
24	C₂×#168	—	3	1	no	—
25	C₅×C₁₆	—	2	1	no	—
26	#672	—	6	1	no	—
27	#364	—	15	1	no	Sylow
28	C₂²×C₃×C₅	M₁₆	1	1	yes	characteristic
29	C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
30	C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
31	Dic₁₅	—	2	2	no	—
32	C₂×C₃×C₈	C₂×D₅	1	1	yes	characteristic
33	C₄×Dic₃	—	5	1	no	—
34	C₂×C₃⋊C₈	—	5	1	no	—
35	C₃×C₁₆	—	2	1	no	—
36	C₃⋊C₁₆	—	10	1	no	—
37	C₂×C₄×C₅	C₄×D₃	1	1	yes	characteristic
38	C₂×Dic₅	—	6	1	no	—
39	C₅×C₈	Dic₆	1	1	yes	characteristic
40	C₅×C₈	#67	1	1	yes	characteristic
41	#168	—	3	2	no	—
42	M₃₂	—	15	1	no	—
43	M₃₂	D₁₅	1	1	yes	characteristic
44	C₄×C₈	—	15	1	no	—
45	C₂×C₃×C₅	—	2	1	no	—
46	C₂×C₃×C₅	C₄⋊C₈	1	1	yes	characteristic
47	C₂×C₃×C₄	C₄×D₅	1	1	yes	characteristic
48	C₂×Dic₃	—	10	1	no	—
49	C₃×C₈	Dic₁₀	1	1	yes	characteristic
50	C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
51	C₃⋊C₈	—	5	2	no	—
52	C₂²×C₅	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
53	C₄×C₅	D₃×C₈	1	1	yes	characteristic
54	C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
55	Dic₅	—	6	2	no	—
56	C₂×C₈	—	15	1	no	—
57	C₂×C₈	C₂×D₁₅	1	1	yes	characteristic
58	C₄²	—	15	1	no	—
59	C₁₆	—	2	1	no	—
60	C₁₆	—	30	1	no	—
61	C₃×C₅	#364	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₃	#676	1	1	yes	characteristic
63	C₃×C₄	C₈×D₅	1	1	yes	characteristic
64	C₃×C₄	#683	1	1	yes	characteristic
65	Dic₃	—	10	2	no	—
66	C₂×C₅	—	2	1	no	—
67	C₂×C₅	Dic₃⋊C₈	1	1	yes	characteristic
68	C₂×C₄	—	30	1	no	—
69	C₂×C₄	C₄×D₁₅	1	1	yes	characteristic
70	C₈	—	15	2	no	—
71	C₈	Dic₃₀	1	1	yes	characteristic
72	C₈	#1220	1	1	yes	characteristic
73	C₂×C₃	—	2	1	no	—
74	C₂×C₃	#3946	1	1	yes	characteristic
75	C₅	#4511	1	1	yes	characteristic, complemented, Sylow
76	C₂²	#6705	1	1	yes	characteristic
77	C₄	—	30	2	no	—
78	C₄	C₈×D₁₅	1	1	yes	characteristic
79	C₄	#6712	1	1	yes	characteristic
80	C₃	#64731	1	1	yes	characteristic, complemented, Sylow
81	C₂	—	2	1	no	—
82	C₂	#91098	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#1220
commutator	C₃×C₄×C₅	C₂×C₈
Frattini	C₂×C₈	C₂×D₁₅
Fitting	C₃×C₅×M₃₂	C₂
socle	C₂×C₃×C₅	C₄⋊C₈
prime radical	C₂²×C₃×C₅	M₁₆
cosocle	C₂×C₃×C₅×C₈	C₂²
hypercenter	M₃₂	D₁₅
hypocenter	C₃×C₅	#364
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
61. C₃×C₅	#364	semidirect
75. C₅	#4511	semidirect
80. C₃	#64731	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×M₃₂	2
C₈×Dic₁₅	2
#91096	2
#64731	3
#4511	5