Subgroups — C₅×#815 #91058

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

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₃
commutator	C₂×C₃	C₄²×C₅
Frattini	C₂×C₄	C₂×C₅×D₃
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₅
hypercenter	C₂×C₅×C₈	D₃
hypocenter	C₃	C₅×#97
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈

Complements

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

N	H ≅ G/N	type
7. C₃×C₅×C₈	C₄	semidirect
8. C₅×C₃⋊C₈	C₄	semidirect
9. #815	C₅	direct (N × H)
23. C₅×C₈	Dic₃	semidirect
29. C₃×C₈	C₄×C₅	semidirect
30. C₃⋊C₈	C₄×C₅	semidirect
38. C₃×C₅	#97	semidirect
48. C₈	C₅×Dic₃	semidirect
51. C₅	#815	direct (N × H)
56. C₃	C₅×#97	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×C₅×Dic₃	2
C₂×C₅×C₃⋊C₈	2
C₅×#97	3
#815	5

Subgroups — C5×#815 #91058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#815 #91058