Subgroups — #91096

Order 480.

52 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	C₃⋊#672	C₂	1	2	yes	maximal, complemented
3	#3944	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₅	C₄	1	1	yes	characteristic
5	C₃×C₅×C₈	C₄	1	1	yes	characteristic
6	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	#812	—	5	1	no	maximal, Hall
8	C₂×C₅×C₈	D₃	1	1	yes	characteristic
9	#672	—	3	2	no	—
10	C₂²×C₃×C₅	C₈	1	1	yes	characteristic
11	C₃×C₄×C₅	C₈	1	1	yes	characteristic
12	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃×C₈	D₅	1	1	yes	characteristic
14	C₃⋊C₁₆	—	5	2	no	—
15	C₂×C₄×C₅	Dic₃	1	1	yes	characteristic
16	C₅×C₈	Dic₃	1	1	yes	characteristic
17	C₅×C₈	C₂×D₃	1	1	yes	characteristic
18	M₃₂	—	15	1	no	Sylow
19	C₂×C₃×C₅	—	2	1	no	—
20	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
21	C₂×C₃×C₄	Dic₅	1	1	yes	characteristic
22	C₃×C₈	Dic₅	1	1	yes	characteristic
23	C₃×C₈	C₂×D₅	1	1	yes	characteristic
24	C₂²×C₅	C₃⋊C₈	1	1	yes	characteristic
25	C₄×C₅	C₃⋊C₈	1	1	yes	characteristic
26	C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
27	C₂×C₈	D₁₅	1	1	yes	characteristic
28	C₁₆	—	15	2	no	—
29	C₃×C₅	M₃₂	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	#168	1	1	yes	characteristic
31	C₃×C₄	#168	1	1	yes	characteristic
32	C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
33	C₂×C₅	—	2	1	no	—
34	C₂×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
35	C₂×C₄	Dic₁₅	1	1	yes	characteristic
36	C₈	Dic₁₅	1	1	yes	characteristic
37	C₈	C₂×D₁₅	1	1	yes	characteristic
38	C₂×C₃	—	2	1	no	—
39	C₂×C₃	C₂×#168	1	1	yes	characteristic
40	C₅	#812	1	1	yes	characteristic, complemented, Sylow
41	C₂²	C₃⋊#168	1	1	yes	characteristic
42	C₄	C₃⋊#168	1	1	yes	characteristic
43	C₄	C₂×Dic₁₅	1	1	yes	characteristic
44	C₃	#3944	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	2	1	no	—
46	C₂	C₂×C₃⋊#168	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂×D₁₅
commutator, socle	C₂×C₃×C₅	C₂×C₈
Fitting	C₂×C₃×C₅×C₈	C₂
prime radical	C₂²×C₃×C₅	C₈
cosocle	C₃×C₅×C₈	C₂²
hypercenter	C₂×C₈	D₁₅
hypocenter	C₃×C₅	M₃₂
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₃⋊#672	C₂	semidirect
29. C₃×C₅	M₃₂	semidirect
40. C₅	#812	semidirect
44. C₃	#3944	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
C₃⋊#672	2
#3944	3
#812	5