Subgroups — #11745821

Order 960.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₂₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₈₀	C₂	1	1	yes	maximal, characteristic
3	C₃⋊#3926	C₂	1	1	yes	maximal, characteristic, complemented
4	#64741	—	3	1	no	maximal, Hall
5	C₅×Dic₁₂	—	2	1	no	—
6	C₃×D₄₀	—	2	1	no	—
7	C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic
8	#4520	—	5	1	no	maximal, Hall
9	C₅×Q₃₂	—	3	1	no	—
10	D₈₀	D₃	1	1	yes	characteristic
11	#3926	—	3	1	no	—
12	C₅×Dic₆	—	4	1	no	—
13	C₃×D₂₀	—	4	1	no	—
14	C₃×C₅×C₈	D₄	1	1	yes	characteristic
15	C₃×D₁₆	—	5	1	no	—
16	Dic₂₄	D₅	1	1	yes	characteristic, complemented
17	C₃⋊C₃₂	—	5	1	no	—
18	C₅×Q₁₆	—	6	1	no	—
19	D₄₀	—	2	1	no	—
20	C₅×C₁₆	C₂×D₃	1	1	yes	characteristic
21	SD₆₄	—	15	1	no	Sylow
22	C₂×C₃×D₅	—	8	1	no	—
23	C₃×C₄×C₅	D₈	1	1	yes	characteristic
24	C₅×Dic₃	—	8	1	no	—
25	C₃×D₈	—	10	1	no	—
26	Dic₁₂	—	2	1	no	—
27	C₃×C₁₆	C₂×D₅	1	1	yes	characteristic
28	C₅×Q₈	—	12	1	no	—
29	D₂₀	—	4	1	no	—
30	C₅×C₈	#67	1	1	yes	characteristic
31	Q₃₂	—	3	1	no	—
32	D₁₆	—	5	1	no	—
33	C₃₂	—	15	1	no	—
34	C₂×C₃×C₅	D₁₆	1	1	yes	characteristic
35	C₃×D₅	—	16	1	no	—
36	C₃×D₄	—	20	1	no	—
37	Dic₆	—	4	1	no	—
38	C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
39	C₂×D₅	—	8	1	no	—
40	C₄×C₅	—	24	1	no	—
41	C₄×C₅	#213	1	1	yes	characteristic
42	Q₁₆	—	6	1	no	—
43	D₈	—	10	1	no	—
44	C₁₆	D₃×D₅	1	1	yes	characteristic
45	C₃×C₅	SD₆₄	1	1	yes	characteristic, complemented, Hall
46	C₂²×C₃	—	40	1	no	—
47	C₃×C₄	#686	1	1	yes	characteristic
48	Dic₃	—	8	1	no	—
49	C₂×C₅	#826	1	1	yes	characteristic
50	D₅	—	16	1	no	—
51	Q₈	—	12	1	no	—
52	D₄	—	20	1	no	—
53	C₈	#1201	1	1	yes	characteristic
54	C₂×C₃	—	80	1	no	—
55	C₂×C₃	#3958	1	1	yes	characteristic
56	C₅	#4520	1	1	yes	characteristic, complemented, Sylow
57	C₂²	—	40	1	no	—
58	C₄	—	24	1	no	—
59	C₄	#6652	1	1	yes	characteristic
60	C₃	#64741	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	80	1	no	—
62	C₂	#90937	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#90937
commutator, Fitting, cosocle	C₃×C₅×C₁₆	C₂²
Frattini, hypercenter	C₁₆	D₃×D₅
socle	C₂×C₃×C₅	D₁₆
prime radical	C₃×D₈₀	C₂
hypocenter	C₃×C₅	SD₆₄
LCS	G ▷ C₃×C₅×C₁₆ ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
1. C₅×Dic₂₄	C₂	semidirect
3. C₃⋊#3926	C₂	semidirect
16. Dic₂₄	D₅	semidirect
45. C₃×C₅	SD₆₄	semidirect
56. C₅	#4520	semidirect
60. C₃	#64741	semidirect

Maximal subgroups

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

subgroup	index
C₅×Dic₂₄	2
C₃×D₈₀	2
C₃⋊#3926	2
#64741	3
#4520	5