Subgroups — C₅×#876 #91679

Order 480.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×(C₂×D₃)⋊C₄	C₂	1	3	yes	maximal
3	C₅×Dic₃⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₅×#126	—	3	1	no	maximal, Hall
5	C₂²×C₅×D₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
7	C₂×C₅×Dic₃	C₂²	1	3	yes	—
8	#876	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₄⋊C₄	—	3	3	no	—
10	C₅×C₂²⋊C₄	—	3	3	no	—
11	C₄²×C₅	D₃	1	1	yes	characteristic, complemented
12	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
13	C₂×C₅×D₃	—	2	3	no	—
14	C₃×C₄×C₅	—	2	3	no	—
15	C₅×Dic₃	—	2	3	no	—
16	C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
17	(C₂×D₃)⋊C₄	C₂×C₅	1	3	yes	—
18	Dic₃⋊C₄	C₂×C₅	1	3	yes	complemented
19	C₂³×C₅	—	3	1	no	—
20	C₂×C₄×C₅	—	3	3	no	—
21	C₂×C₄×C₅	C₂×D₃	1	3	yes	—
22	#126	—	3	1	no	Sylow
23	C₂×C₃×C₅	#41	1	3	yes	—
24	C₅×D₃	—	4	1	no	—
25	C₂²×D₃	C₂²×C₅	1	1	yes	characteristic
26	C₂×C₃×C₄	C₂²×C₅	1	3	yes	—
27	C₂×Dic₃	C₂²×C₅	1	3	yes	—
28	C₂²×C₅	—	6	3	no	—
29	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
30	C₄×C₅	—	2	3	no	—
31	C₄×C₅	—	6	3	no	—
32	C₄⋊C₄	—	3	3	no	—
33	C₂²⋊C₄	—	3	3	no	—
34	C₄²	C₅×D₃	1	1	yes	characteristic, complemented
35	C₃×C₅	#126	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
37	C₂×D₃	—	2	3	no	—
38	C₃×C₄	—	2	3	no	—
39	Dic₃	—	2	3	no	—
40	C₂×C₅	—	12	1	no	—
41	C₂×C₅	#235	1	3	yes	—
42	C₂³	—	3	1	no	—
43	C₂×C₄	—	3	3	no	—
44	C₂×C₄	C₂×C₅×D₃	1	3	yes	—
45	C₂×C₃	C₅×#41	1	3	yes	—
46	D₃	—	4	1	no	—
47	C₅	#876	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²	—	6	3	no	—
49	C₂²	C₂²×C₅×D₃	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	—	6	3	no	—
52	C₃	C₅×#126	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	12	1	no	—
54	C₂	C₅×#235	1	3	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₃
Fitting	C₃×C₄²×C₅	C₂
socle	C₂²×C₃×C₅	C₂³
prime radical	C₂²×C₅×D₃	C₂²
hypercenter	C₄²×C₅	D₃
hypocenter	C₃	C₅×#126
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₄²×C₅	C₂	semidirect
3. C₅×Dic₃⋊C₄	C₂	semidirect
8. #876	C₅	direct (N × H)
11. C₄²×C₅	D₃	semidirect
16. C₃×C₄²	C₂×C₅	semidirect
18. Dic₃⋊C₄	C₂×C₅	semidirect
34. C₄²	C₅×D₃	semidirect
35. C₃×C₅	#126	semidirect
47. C₅	#876	direct (N × H)
52. C₃	C₅×#126	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₅	2
C₅×(C₂×D₃)⋊C₄	2
C₅×Dic₃⋊C₄	2
C₅×#126	3
#876	5

Subgroups — C5×#876 #91679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#876 #91679