Subgroups — C₅×#874 #91677

Order 480.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₁₂	C₂	1	6	yes	maximal, complemented
2	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#127	—	3	1	no	maximal, Hall
4	C₂²×C₅×D₃	C₂²	1	4	yes	—
5	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
6	C₅×D₁₂	—	2	12	no	—
7	#874	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×D₄	—	3	6	no	—
9	C₄²×C₅	D₃	1	1	yes	characteristic, complemented
10	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
11	C₂×C₅×D₃	—	2	12	no	—
12	C₃×C₄×C₅	D₄	1	6	yes	complemented
13	C₂×D₁₂	C₂×C₅	1	6	yes	complemented
14	C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
15	C₂³×C₅	—	3	4	no	—
16	C₅×D₄	—	6	12	no	—
17	C₂×C₄×C₅	C₂×D₃	1	3	yes	—
18	#127	—	3	1	no	Sylow
19	C₂×C₃×C₅	C₂×D₄	1	3	yes	—
20	C₅×D₃	—	4	4	no	—
21	C₂²×D₃	C₂²×C₅	1	4	yes	—
22	C₂×C₃×C₄	C₂²×C₅	1	3	yes	—
23	D₁₂	—	2	12	no	—
24	C₂²×C₅	—	6	12	no	—
25	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
26	C₄×C₅	D₁₂	1	6	yes	complemented
27	C₂×D₄	—	3	6	no	—
28	C₄²	C₅×D₃	1	1	yes	characteristic, complemented
29	C₃×C₅	#127	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
31	C₂×D₃	—	2	12	no	—
32	C₃×C₄	C₅×D₄	1	6	yes	complemented
33	C₂×C₅	—	12	4	no	—
34	C₂×C₅	C₂×D₁₂	1	3	yes	—
35	C₂³	—	3	4	no	—
36	D₄	—	6	12	no	—
37	C₂×C₄	C₂×C₅×D₃	1	3	yes	—
38	C₂×C₃	C₂×C₅×D₄	1	3	yes	—
39	D₃	—	4	4	no	—
40	C₅	#874	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²	—	6	12	no	—
42	C₂²	C₂²×C₅×D₃	1	1	yes	characteristic
43	C₄	C₅×D₁₂	1	6	yes	complemented
44	C₃	C₅×#127	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	12	4	no	—
46	C₂	C₂×C₅×D₁₂	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
hypercenter	C₄²×C₅	D₃
hypocenter	C₃	C₅×#127
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. C₂×C₅×D₁₂	C₂	semidirect
2. C₃×C₄²×C₅	C₂	semidirect
7. #874	C₅	direct (N × H)
9. C₄²×C₅	D₃	semidirect
12. C₃×C₄×C₅	D₄	semidirect
13. C₂×D₁₂	C₂×C₅	semidirect
14. C₃×C₄²	C₂×C₅	semidirect
26. C₄×C₅	D₁₂	semidirect
28. C₄²	C₅×D₃	semidirect
29. C₃×C₅	#127	semidirect
32. C₃×C₄	C₅×D₄	semidirect
40. C₅	#874	direct (N × H)
43. C₄	C₅×D₁₂	semidirect
44. C₃	C₅×#127	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₁₂	2
C₃×C₄²×C₅	2
C₅×#127	3
#874	5

Subgroups — C5×#874 #91677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#874 #91677