Subgroups — #90944

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#672	C₂	1	1	yes	maximal, characteristic, complemented
4	#3959	—	3	1	no	maximal, Hall
5	Dic₃₀	—	2	1	no	—
6	C₅×D₁₂	—	2	1	no	—
7	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	#800	—	5	1	no	maximal, Hall
9	C₅×D₈	—	3	1	no	—
10	Dic₂₀	—	3	1	no	—
11	#672	D₃	1	1	yes	characteristic, complemented
12	C₂×C₅×D₃	—	4	1	no	—
13	C₃×C₄×C₅	D₄	1	1	yes	characteristic
14	Dic₁₅	—	4	1	no	—
15	Dic₁₂	—	5	1	no	—
16	D₂₄	D₅	1	1	yes	characteristic
17	C₃×C₁₆	—	5	1	no	—
18	C₅×D₄	—	6	1	no	—
19	Dic₁₀	—	6	1	no	—
20	C₅×C₈	C₂×D₃	1	1	yes	characteristic
21	SD₃₂	—	15	1	no	Sylow
22	C₂×C₃×C₅	D₈	1	1	yes	characteristic
23	C₅×D₃	—	8	1	no	—
24	D₁₂	—	2	1	no	—
25	Dic₆	—	10	1	no	—
26	C₃×C₈	C₂×D₅	1	1	yes	characteristic
27	C₂²×C₅	—	12	1	no	—
28	C₄×C₅	D₁₂	1	1	yes	characteristic
29	Dic₅	—	12	1	no	—
30	Q₁₆	—	15	1	no	—
31	D₈	—	3	1	no	—
32	C₁₆	—	5	1	no	—
33	C₃×C₅	SD₃₂	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃	—	4	1	no	—
35	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
36	Dic₃	—	20	1	no	—
37	C₂×C₅	—	24	1	no	—
38	C₂×C₅	D₂₄	1	1	yes	characteristic
39	Q₈	—	30	1	no	—
40	D₄	—	6	1	no	—
41	C₈	D₃×D₅	1	1	yes	characteristic
42	C₂×C₃	#686	1	1	yes	characteristic
43	D₃	—	8	1	no	—
44	C₅	#800	1	1	yes	characteristic, complemented, Sylow
45	C₂²	—	12	1	no	—
46	C₄	—	60	1	no	—
47	C₄	#1203	1	1	yes	characteristic
48	C₃	#3959	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	24	1	no	—
50	C₂	#6654	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#6654
commutator, Fitting, cosocle	C₃×C₅×C₈	C₂²
Frattini, hypercenter	C₈	D₃×D₅
socle	C₂×C₃×C₅	D₈
prime radical	C₅×D₂₄	C₂
hypocenter	C₃×C₅	SD₃₂
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. Dic₆₀	C₂	semidirect
3. C₃×#672	C₂	semidirect
11. #672	D₃	semidirect
33. C₃×C₅	SD₃₂	semidirect
44. C₅	#800	semidirect
48. C₃	#3959	semidirect

Maximal subgroups

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

subgroup	index
Dic₆₀	2
C₅×D₂₄	2
C₃×#672	2
#3959	3
#800	5