Subgroups — C₅×#869 #91672

Order 480.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₆	C₂	1	2	yes	maximal
2	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
3	C₅×C₄⋊Dic₃	C₂	1	4	yes	maximal
4	C₅×C₄⋊Q₈	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
7	C₂×C₅×Dic₃	C₂²	1	4	yes	—
8	C₅×Dic₆	—	2	4	no	—
9	#869	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×Q₈	—	3	2	no	—
11	C₅×C₄⋊C₄	—	3	4	no	—
12	C₄²×C₅	D₃	1	1	yes	characteristic
13	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
14	C₃×C₄×C₅	D₄	1	2	yes	—
15	C₃×C₄×C₅	Q₈	1	4	yes	complemented
16	C₅×Dic₃	—	2	4	no	—
17	C₂×Dic₆	C₂×C₅	1	2	yes	—
18	C₃×C₄²	C₂×C₅	1	1	yes	characteristic
19	C₄⋊Dic₃	C₂×C₅	1	4	yes	—
20	C₅×Q₈	—	6	4	no	—
21	C₂×C₄×C₅	—	3	4	no	—
22	C₂×C₄×C₅	C₂×D₃	1	2	yes	—
23	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
24	C₄⋊Q₈	—	3	1	no	Sylow
25	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
26	C₂×C₃×C₅	C₂×Q₈	1	2	yes	—
27	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
28	C₂×C₃×C₄	C₂²×C₅	1	2	yes	—
29	C₂×Dic₃	C₂²×C₅	1	4	yes	—
30	Dic₆	—	2	4	no	—
31	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
32	C₄×C₅	—	6	4	no	—
33	C₄×C₅	Dic₆	1	4	yes	complemented
34	C₄×C₅	D₁₂	1	2	yes	—
35	C₂×Q₈	—	3	2	no	—
36	C₄⋊C₄	—	3	4	no	—
37	C₄²	C₅×D₃	1	1	yes	characteristic
38	C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
40	C₃×C₄	C₅×D₄	1	2	yes	—
41	C₃×C₄	C₅×Q₈	1	4	yes	complemented
42	Dic₃	—	2	4	no	—
43	C₂×C₅	C₂×Dic₆	1	2	yes	—
44	C₂×C₅	C₂×D₁₂	1	1	yes	characteristic
45	Q₈	—	6	4	no	—
46	C₂×C₄	—	3	4	no	—
47	C₂×C₄	C₂×C₅×D₃	1	2	yes	—
48	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
49	C₂×C₃	C₂×C₅×D₄	1	1	yes	characteristic
50	C₂×C₃	C₂×C₅×Q₈	1	2	yes	—
51	C₅	#869	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²	C₂²×C₅×D₃	1	1	yes	characteristic
53	C₄	—	6	4	no	—
54	C₄	C₅×Dic₆	1	4	yes	complemented
55	C₄	C₅×D₁₂	1	2	yes	—
56	C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
57	C₂	C₂×C₅×Dic₆	1	2	yes	—
58	C₂	C₂×C₅×D₁₂	1	1	yes	characteristic

	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, prime radical	C₂²×C₃×C₅	C₂³
hypercenter	C₄²×C₅	D₃
hypocenter	C₃	C₅×C₄⋊Q₈
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
9. #869	C₅	direct (N × H)
15. C₃×C₄×C₅	Q₈	semidirect
33. C₄×C₅	Dic₆	semidirect
38. C₃×C₅	C₄⋊Q₈	semidirect
41. C₃×C₄	C₅×Q₈	semidirect
51. C₅	#869	direct (N × H)
54. C₄	C₅×Dic₆	semidirect
56. C₃	C₅×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Dic₆	2
C₃×C₄²×C₅	2
C₅×C₄⋊Dic₃	2
C₅×C₄⋊Q₈	3
#869	5

Subgroups — C5×#869 #91672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#869 #91672