Subgroups — #90933

Order 480.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₁₅	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	D₅×C₁₆	—	3	1	no	maximal, Hall
5	C₄×D₁₅	C₄	1	1	yes	characteristic
6	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₃⋊#168	C₄	1	1	yes	characteristic
8	D₃×C₁₆	—	5	1	no	maximal, Hall
9	C₈×D₅	—	3	1	no	—
10	C₅×C₁₆	—	3	1	no	—
11	#672	D₃	1	1	yes	characteristic, complemented
12	C₂×D₁₅	C₈	1	1	yes	characteristic
13	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	Dic₁₅	C₈	1	1	yes	characteristic
15	D₃×C₈	—	5	1	no	—
16	C₃×C₁₆	—	5	1	no	—
17	C₃⋊C₁₆	D₅	1	1	yes	characteristic, complemented
18	C₄×D₅	—	3	1	no	—
19	C₅×C₈	C₂×D₃	1	1	yes	characteristic
20	#168	—	3	1	no	—
21	C₂×C₁₆	—	15	1	no	Sylow
22	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
23	D₁₅	C₁₆	1	2	yes	complemented
24	C₄×D₃	—	5	1	no	—
25	C₃×C₈	C₂×D₅	1	1	yes	characteristic
26	C₃⋊C₈	—	5	1	no	—
27	C₂×D₅	—	3	1	no	—
28	C₄×C₅	C₄×D₃	1	1	yes	characteristic
29	Dic₅	—	3	1	no	—
30	C₂×C₈	—	15	1	no	—
31	C₁₆	—	3	1	no	—
32	C₁₆	—	5	1	no	—
33	C₃×C₅	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃	—	5	1	no	—
35	C₃×C₄	C₄×D₅	1	1	yes	characteristic
36	Dic₃	—	5	1	no	—
37	C₂×C₅	D₃×C₈	1	1	yes	characteristic
38	D₅	—	3	2	no	—
39	C₂×C₄	—	15	1	no	—
40	C₈	—	15	1	no	—
41	C₈	D₃×D₅	1	1	yes	characteristic
42	C₂×C₃	C₈×D₅	1	1	yes	characteristic
43	D₃	—	5	2	no	—
44	C₅	D₃×C₁₆	1	1	yes	characteristic, complemented, Sylow
45	C₂²	—	15	1	no	—
46	C₄	—	15	1	no	—
47	C₄	#1200	1	1	yes	characteristic
48	C₃	D₅×C₁₆	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	15	2	no	—
50	C₂	#6648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₁₆
Fitting, cosocle	C₃×C₅×C₈	C₂²
socle	C₂×C₃×C₅	C₂×C₈
prime radical	C₂×D₁₅	C₈
LCS	G ▷ 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
11. #672	D₃	semidirect
17. C₃⋊C₁₆	D₅	semidirect
23. D₁₅	C₁₆	semidirect
33. C₃×C₅	C₂×C₁₆	semidirect
44. C₅	D₃×C₁₆	semidirect
48. C₃	D₅×C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₈×D₁₅	2
C₃×#672	2
C₅×C₃⋊C₁₆	2
D₅×C₁₆	3
D₃×C₁₆	5