Subgroups — #91101

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	#3949	—	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	#817	—	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	#106	—	15	1	no	Sylow
20	C₂×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₃×C₅	SD₁₆	1	2	yes	—
22	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
23	C₂×Dic₃	—	10	2	no	—
24	C₃×C₈	Dic₅	1	2	yes	complemented
25	C₂²×C₅	D₁₂	1	1	yes	characteristic
26	C₄×C₅	Dic₆	1	1	yes	characteristic
27	C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
28	Dic₅	—	12	2	no	—
29	C₂×C₈	D₁₅	1	1	yes	characteristic
30	C₄⋊C₄	—	15	2	no	—
31	C₃×C₅	#106	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₃	D₂₀	1	1	yes	characteristic
33	C₃×C₄	Dic₁₀	1	1	yes	characteristic
34	C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
35	Dic₃	—	20	2	no	—
36	C₂×C₅	#204	1	2	yes	—
37	C₂×C₅	C₄⋊Dic₃	1	1	yes	characteristic
38	C₂×C₄	—	30	2	no	—
39	C₂×C₄	C₂×D₁₅	1	1	yes	characteristic
40	C₈	Dic₁₅	1	2	yes	complemented
41	C₂×C₃	#677	1	2	yes	—
42	C₂×C₃	C₄⋊Dic₅	1	1	yes	characteristic
43	C₅	#817	1	1	yes	characteristic, complemented, Sylow
44	C₂²	D₆₀	1	1	yes	characteristic
45	C₄	—	60	2	no	—
46	C₄	Dic₃₀	1	1	yes	characteristic
47	C₄	C₂×Dic₁₅	1	1	yes	characteristic
48	C₃	#3949	1	1	yes	characteristic, complemented, Sylow
49	C₂	#6706	1	2	yes	—
50	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	#106
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
24. C₃×C₈	Dic₅	semidirect
31. C₃×C₅	#106	semidirect
40. C₈	Dic₁₅	semidirect
43. C₅	#817	semidirect
48. C₃	#3949	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
#3949	3
#817	5