Subgroups — #90934

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#672	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#3930	—	3	1	no	maximal, Hall
5	C₃×C₄×D₅	C₄	1	1	yes	characteristic
6	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₃×#168	C₄	1	1	yes	characteristic
8	#812	—	5	1	no	maximal, Hall
9	C₈×D₅	D₃	1	1	yes	characteristic
10	C₅×C₁₆	—	3	1	no	—
11	#672	—	3	1	no	—
12	C₂×C₃×D₅	C₈	1	1	yes	characteristic
13	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₃×Dic₅	C₈	1	1	yes	characteristic
15	C₂×C₃×C₈	—	5	1	no	—
16	C₃⋊C₁₆	—	5	1	no	—
17	C₃⋊C₁₆	D₅	1	1	yes	characteristic, complemented
18	C₄×D₅	Dic₃	1	1	yes	characteristic
19	C₅×C₈	C₂×D₃	1	1	yes	characteristic
20	#168	Dic₃	1	1	yes	characteristic
21	M₃₂	—	15	1	no	Sylow
22	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
23	C₃×D₅	—	2	1	no	—
24	C₂×C₃×C₄	—	5	1	no	—
25	C₃×C₈	—	5	1	no	—
26	C₃×C₈	C₂×D₅	1	1	yes	characteristic
27	C₂×D₅	C₃⋊C₈	1	1	yes	characteristic
28	C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
29	Dic₅	C₃⋊C₈	1	1	yes	characteristic
30	C₂×C₈	—	5	1	no	—
31	C₁₆	—	3	1	no	—
32	C₁₆	—	15	1	no	—
33	C₃×C₅	M₃₂	1	1	yes	characteristic, complemented, Hall
34	C₂²×C₃	—	5	1	no	—
35	C₃×C₄	—	5	1	no	—
36	C₃×C₄	C₄×D₅	1	1	yes	characteristic
37	C₂×C₅	C₂×C₃⋊C₈	1	1	yes	characteristic
38	D₅	—	2	1	no	—
39	C₂×C₄	—	5	1	no	—
40	C₈	—	5	1	no	—
41	C₈	D₃×D₅	1	1	yes	characteristic
42	C₂×C₃	—	10	1	no	—
43	C₂×C₃	C₈×D₅	1	1	yes	characteristic
44	C₅	#812	1	1	yes	characteristic, complemented, Sylow
45	C₂²	—	5	1	no	—
46	C₄	—	5	1	no	—
47	C₄	D₅×Dic₃	1	1	yes	characteristic
48	C₃	#3930	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	10	1	no	—
50	C₂	D₅×C₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₃×D₅
commutator, socle	C₂×C₃×C₅	C₂×C₈
Fitting, cosocle	C₃×C₅×C₈	C₂²
prime radical	C₂×C₃×D₅	C₈
hypocenter	C₃×C₅	M₃₂
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈

Complements

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

N	H ≅ G/N	type
2. C₃⋊#672	C₂	semidirect
3. C₅×C₃⋊C₁₆	C₂	semidirect
17. C₃⋊C₁₆	D₅	semidirect
33. C₃×C₅	M₃₂	semidirect
44. C₅	#812	semidirect
48. C₃	#3930	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₈×D₅	2
C₃⋊#672	2
C₅×C₃⋊C₁₆	2
#3930	3
#812	5