Subgroups — #91103

Order 480.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	#6710	C₂	1	2	yes	maximal
3	#3951	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₃×C₅×C₈	C₄	1	2	yes	—
6	C₃⋊#168	—	2	2	no	—
7	#819	—	5	1	no	maximal, Hall
8	C₂×C₅×C₈	D₃	1	1	yes	characteristic
9	#681	—	3	2	no	—
10	C₂²×C₃×C₅	Q₈	1	1	yes	characteristic
11	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×C₅	D₄	1	1	yes	characteristic
13	C₂×C₃×C₈	D₅	1	1	yes	characteristic
14	#208	—	5	2	no	—
15	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
16	C₅×C₈	Dic₃	1	2	yes	—
17	#168	—	6	2	no	—
18	#108	—	15	1	no	Sylow
19	C₂×C₃×C₅	—	2	1	no	—
20	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
22	C₃×C₈	Dic₅	1	2	yes	—
23	C₃⋊C₈	—	10	2	no	—
24	C₂²×C₅	Dic₆	1	1	yes	characteristic
25	C₄×C₅	D₁₂	1	1	yes	characteristic
26	C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
27	M₁₆	—	15	2	no	—
28	C₂×C₈	D₁₅	1	1	yes	characteristic
29	C₃×C₅	#108	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	Dic₁₀	1	1	yes	characteristic
31	C₃×C₄	D₂₀	1	1	yes	characteristic
32	C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
33	C₂×C₅	—	2	1	no	—
34	C₂×C₅	C₄⋊Dic₃	1	1	yes	characteristic
35	C₂×C₄	C₂×D₁₅	1	1	yes	characteristic
36	C₈	—	30	2	no	—
37	C₈	Dic₁₅	1	2	yes	—
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	C₄⋊Dic₅	1	1	yes	characteristic
40	C₅	#819	1	1	yes	characteristic, complemented, Sylow
41	C₂²	Dic₃₀	1	1	yes	characteristic
42	C₄	D₆₀	1	1	yes	characteristic
43	C₄	C₂×Dic₁₅	1	1	yes	characteristic
44	C₃	#3951	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	2	1	no	—
46	C₂	C₄⋊Dic₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₆₀
commutator	C₃×C₄×C₅	C₂×C₄
Frattini	C₂×C₄	C₂×D₁₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle	C₂×C₃×C₅	C₄⋊C₄
prime radical	C₂²×C₃×C₅	Q₈
cosocle	C₂×C₃×C₄×C₅	C₂²
hypercenter	C₂×C₈	D₁₅
hypocenter	C₃×C₅	#108
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
29. C₃×C₅	#108	semidirect
40. C₅	#819	semidirect
44. C₃	#3951	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₈	2
#6710	2
#3951	3
#819	5