Subgroups — #91099

Order 480.

80 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	1	yes	maximal, characteristic
3	C₂×C₃⋊#168	C₂	1	1	yes	maximal, characteristic
4	#3947	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂×Dic₁₅	C₄	1	2	yes	—
7	C₃×C₅×C₈	C₄	1	2	yes	complemented
8	C₃⋊#168	C₄	1	2	yes	complemented
9	#815	—	5	1	no	maximal, Hall
10	C₂×C₅×C₈	D₃	1	1	yes	characteristic
11	C₄×Dic₅	—	3	1	no	—
12	C₂×#168	—	3	1	no	—
13	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
16	Dic₁₅	—	2	2	no	—
17	C₂×C₃×C₈	D₅	1	1	yes	characteristic
18	C₄×Dic₃	—	5	1	no	—
19	C₂×C₃⋊C₈	—	5	1	no	—
20	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
21	C₂×Dic₅	—	3	2	no	—
22	C₅×C₈	Dic₃	1	2	yes	complemented
23	#168	—	3	2	no	—
24	#97	—	15	1	no	Sylow
25	C₂×C₃×C₅	C₄²	1	1	yes	characteristic
26	C₂×C₃×C₅	M₁₆	1	2	yes	—
27	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
28	C₂×Dic₃	—	5	2	no	—
29	C₃×C₈	Dic₅	1	2	yes	complemented
30	C₃⋊C₈	—	5	2	no	—
31	C₂²×C₅	C₄×D₃	1	1	yes	characteristic
32	C₄×C₅	C₄×D₃	1	1	yes	characteristic
33	C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
34	Dic₅	—	6	2	no	—
35	C₂×C₈	—	15	1	no	—
36	C₂×C₈	D₁₅	1	1	yes	characteristic
37	C₄²	—	15	1	no	—
38	C₃×C₅	#97	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₃	C₄×D₅	1	1	yes	characteristic
40	C₃×C₄	C₄×D₅	1	1	yes	characteristic
41	C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
42	Dic₃	—	10	2	no	—
43	C₂×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
44	C₂×C₅	C₄×Dic₃	1	1	yes	characteristic
45	C₂×C₄	—	15	2	no	—
46	C₂×C₄	C₂×D₁₅	1	1	yes	characteristic
47	C₈	—	15	2	no	—
48	C₈	Dic₁₅	1	2	yes	complemented
49	C₂×C₃	#676	1	2	yes	—
50	C₂×C₃	C₄×Dic₅	1	1	yes	characteristic
51	C₅	#815	1	1	yes	characteristic, complemented, Sylow
52	C₂²	C₄×D₁₅	1	1	yes	characteristic
53	C₄	—	30	2	no	—
54	C₄	C₄×D₁₅	1	1	yes	characteristic
55	C₄	C₂×Dic₁₅	1	1	yes	characteristic
56	C₃	#3947	1	1	yes	characteristic, complemented, Sylow
57	C₂	#6705	1	2	yes	—
58	C₂	C₄×Dic₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₁₅
commutator	C₂×C₃×C₅	C₄²
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂²
hypercenter	C₂×C₈	D₁₅
hypocenter	C₃×C₅	#97
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
7. C₃×C₅×C₈	C₄	semidirect
8. C₃⋊#168	C₄	semidirect
22. C₅×C₈	Dic₃	semidirect
29. C₃×C₈	Dic₅	semidirect
38. C₃×C₅	#97	semidirect
48. C₈	Dic₁₅	semidirect
51. C₅	#815	semidirect
56. C₃	#3947	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
C₂×C₃⋊#168	2
#3947	3
#815	5