Subgroups — C₅×#870 #91673

Order 480.

112 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
2	C₅×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	C₅×Dic₃⋊C₄	C₂	1	4	yes	maximal
4	C₅×#125	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
6	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₅×Dic₃	C₂²	1	4	yes	—
8	#870	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₄⋊C₄	—	3	4	no	—
10	C₅×C₄⋊C₄	—	3	2	no	—
11	C₄²×C₅	D₃	1	1	yes	characteristic
12	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
13	C₃×C₄×C₅	—	2	2	no	—
14	C₃×C₄×C₅	Q₈	1	2	yes	—
15	C₅×Dic₃	—	2	4	no	—
16	C₃×C₄²	C₂×C₅	1	1	yes	characteristic
17	C₄⋊Dic₃	C₂×C₅	1	2	yes	—
18	Dic₃⋊C₄	C₂×C₅	1	4	yes	—
19	C₂×C₄×C₅	—	3	4	no	—
20	C₂×C₄×C₅	C₂×D₃	1	2	yes	—
21	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
22	#125	—	3	1	no	Sylow
23	C₂×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₃×C₅	#41	1	2	yes	—
25	C₂×C₃×C₄	C₂²×C₅	1	2	yes	—
26	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
27	C₂×Dic₃	C₂²×C₅	1	4	yes	—
28	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
29	C₄×C₅	—	2	2	no	—
30	C₄×C₅	—	6	4	no	—
31	C₄×C₅	Dic₆	1	2	yes	—
32	C₄⋊C₄	—	3	4	no	—
33	C₄⋊C₄	—	3	2	no	—
34	C₄²	C₅×D₃	1	1	yes	characteristic
35	C₃×C₅	#125	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
37	C₃×C₄	—	2	2	no	—
38	C₃×C₄	C₅×Q₈	1	2	yes	—
39	Dic₃	—	2	4	no	—
40	C₂×C₅	C₂×Dic₆	1	1	yes	characteristic
41	C₂×C₅	#235	1	2	yes	—
42	C₂×C₄	—	3	4	no	—
43	C₂×C₄	C₂×C₅×D₃	1	2	yes	—
44	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
45	C₂×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
46	C₂×C₃	C₅×#41	1	2	yes	—
47	C₅	#870	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²	C₂²×C₅×D₃	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	6	4	no	—
51	C₄	C₅×Dic₆	1	2	yes	—
52	C₃	C₅×#125	1	1	yes	characteristic, complemented, Sylow
53	C₂	C₂×C₅×Dic₆	1	1	yes	characteristic
54	C₂	C₅×#235	1	2	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, prime radical	C₂²×C₃×C₅	C₂³
hypercenter	C₄²×C₅	D₃
hypocenter	C₃	C₅×#125
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
8. #870	C₅	direct (N × H)
35. C₃×C₅	#125	semidirect
47. C₅	#870	direct (N × H)
52. C₃	C₅×#125	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×C₄⋊Dic₃	2
C₅×Dic₃⋊C₄	2
C₅×#125	3
#870	5

Subgroups — C5×#870 #91673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#870 #91673