Subgroups — #91102

Order 480.

72 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	C₄⋊Dic₁₅	C₂	1	2	yes	maximal
3	#3950	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₂×Dic₁₅	—	2	2	no	—
6	C₃×C₅×C₈	C₄	1	2	yes	complemented
7	#818	—	5	1	no	maximal, Hall
8	C₂×C₅×C₈	D₃	1	1	yes	characteristic
9	C₄⋊Dic₅	—	3	2	no	—
10	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
11	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×C₅	Q₈	1	1	yes	characteristic
13	Dic₁₅	—	4	2	no	—
14	C₂×C₃×C₈	D₅	1	1	yes	characteristic
15	C₄⋊Dic₃	—	5	2	no	—
16	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
17	C₂×Dic₅	—	6	2	no	—
18	C₅×C₈	Dic₃	1	2	yes	complemented
19	#107	—	15	1	no	Sylow
20	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₃×C₅	D₈	1	1	yes	characteristic
22	C₂×C₃×C₅	Q₁₆	1	1	yes	characteristic
23	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
24	C₂×Dic₃	—	10	2	no	—
25	C₃×C₈	Dic₅	1	2	yes	complemented
26	C₂²×C₅	D₁₂	1	1	yes	characteristic
27	C₄×C₅	Dic₆	1	1	yes	characteristic
28	C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
29	Dic₅	—	12	2	no	—
30	C₂×C₈	D₁₅	1	1	yes	characteristic
31	C₄⋊C₄	—	15	2	no	—
32	C₃×C₅	#107	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₃	D₂₀	1	1	yes	characteristic
34	C₃×C₄	Dic₁₀	1	1	yes	characteristic
35	C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
36	Dic₃	—	20	2	no	—
37	C₂×C₅	D₂₄	1	1	yes	characteristic
38	C₂×C₅	Dic₁₂	1	1	yes	characteristic
39	C₂×C₅	C₄⋊Dic₃	1	1	yes	characteristic
40	C₂×C₄	—	30	2	no	—
41	C₂×C₄	C₂×D₁₅	1	1	yes	characteristic
42	C₈	Dic₁₅	1	2	yes	complemented
43	C₂×C₃	D₄₀	1	1	yes	characteristic
44	C₂×C₃	Dic₂₀	1	1	yes	characteristic
45	C₂×C₃	C₄⋊Dic₅	1	1	yes	characteristic
46	C₅	#818	1	1	yes	characteristic, complemented, Sylow
47	C₂²	D₆₀	1	1	yes	characteristic
48	C₄	—	60	2	no	—
49	C₄	Dic₃₀	1	1	yes	characteristic
50	C₄	C₂×Dic₁₅	1	1	yes	characteristic
51	C₃	#3950	1	1	yes	characteristic, complemented, Sylow
52	C₂	D₁₂₀	1	1	yes	characteristic
53	C₂	Dic₆₀	1	1	yes	characteristic
54	C₂	C₄⋊Dic₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₆₀
commutator	C₃×C₄×C₅	C₂×C₄
Frattini	C₂×C₄	C₂×D₁₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	D₄
cosocle	C₂×C₃×C₄×C₅	C₂²
hypercenter	C₂×C₈	D₁₅
hypocenter	C₃×C₅	#107
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. C₃×C₅×C₈	C₄	semidirect
18. C₅×C₈	Dic₃	semidirect
25. C₃×C₈	Dic₅	semidirect
32. C₃×C₅	#107	semidirect
42. C₈	Dic₁₅	semidirect
46. C₅	#818	semidirect
51. C₃	#3950	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
C₄⋊Dic₁₅	2
#3950	3
#818	5