Subgroups — C₅×#63764 #13086316

Order 1440.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₅×#3708	C₂	1	2	yes	maximal, complemented
3	C₄×C₅×C₃⋊D₃	C₄	1	1	yes	characteristic
4	C₃²×C₅×C₈	C₄	1	1	yes	characteristic
5	C₅×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
6	#63764	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₃×C₈	—	6	2	no	—
8	C₂×C₅×C₃⋊D₃	C₈	1	1	yes	characteristic
9	C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
10	C₅×C₃⋊Dic₃	C₈	1	1	yes	characteristic
11	C₂×C₅×C₁₆	—	9	1	no	maximal, Hall
12	C₈×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
13	#3708	C₂×C₅	1	2	yes	complemented
14	C₄×C₅×D₃	—	6	2	no	—
15	C₃×C₅×C₈	—	2	2	no	—
16	C₅×C₃⋊C₈	—	6	2	no	—
17	C₂×C₃²×C₅	C₂×C₈	1	1	yes	characteristic
18	C₅×C₃⋊D₃	C₁₆	1	2	yes	complemented
19	C₂×C₅×C₈	—	9	1	no	—
20	C₅×C₁₆	—	9	2	no	—
21	C₄×C₃⋊D₃	C₄×C₅	1	1	yes	characteristic
22	C₃²×C₈	C₄×C₅	1	1	yes	characteristic
23	C₃⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
24	C₂×C₅×D₃	—	6	2	no	—
25	C₃×C₄×C₅	—	2	2	no	—
26	C₅×Dic₃	—	6	2	no	—
27	D₃×C₈	—	6	2	no	—
28	C₃²×C₅	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
29	C₂×C₄×C₅	—	9	1	no	—
30	C₅×C₈	—	9	1	no	—
31	C₅×C₈	#157	1	1	yes	characteristic
32	C₂×C₃⋊D₃	C₅×C₈	1	1	yes	characteristic
33	C₃²×C₄	C₂×C₄×C₅	1	1	yes	characteristic
34	C₃⋊Dic₃	C₅×C₈	1	1	yes	characteristic
35	C₂×C₁₆	—	9	1	no	Sylow
36	C₂×C₃×C₅	—	2	2	no	—
37	C₅×D₃	—	6	4	no	—
38	C₄×D₃	—	6	2	no	—
39	C₃×C₈	—	2	2	no	—
40	C₃⋊C₈	—	6	2	no	—
41	C₂²×C₅	—	9	1	no	—
42	C₄×C₅	—	9	1	no	—
43	C₄×C₅	C₂×#157	1	1	yes	characteristic
44	C₂×C₃²	C₂×C₅×C₈	1	1	yes	characteristic
45	C₃⋊D₃	C₅×C₁₆	1	2	yes	complemented
46	C₂×C₈	—	9	1	no	—
47	C₁₆	—	9	2	no	—
48	C₃×C₅	—	2	2	no	—
49	C₂×D₃	—	6	2	no	—
50	C₃×C₄	—	2	2	no	—
51	Dic₃	—	6	2	no	—
52	C₂×C₅	—	9	2	no	—
53	C₂×C₅	#3787	1	1	yes	characteristic
54	C₃²	C₂×C₅×C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₄	—	9	1	no	—
56	C₈	—	9	1	no	—
57	C₈	C₅×#157	1	1	yes	characteristic
58	C₂×C₃	—	2	2	no	—
59	D₃	—	6	4	no	—
60	C₅	#63764	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²	—	9	1	no	—
62	C₄	—	9	1	no	—
63	C₄	C₂×C₅×#157	1	1	yes	characteristic
64	C₃	—	2	2	no	—
65	C₂	—	9	2	no	—
66	C₂	C₅×#3787	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₅×C₈	#157
commutator, hypocenter	C₃²	C₂×C₅×C₁₆
Frattini	C₄	C₂×C₅×#157
Fitting	C₃²×C₅×C₈	C₄
socle	C₂×C₃²×C₅	C₂×C₈
prime radical	C₂×C₅×C₃⋊D₃	C₈
cosocle	C₃⋊(C₃⋊C₈)	C₂²×C₅
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₅×#3708	C₂	semidirect
6. #63764	C₅	direct (N × H)
13. #3708	C₂×C₅	semidirect
18. C₅×C₃⋊D₃	C₁₆	semidirect
28. C₃²×C₅	C₂×C₁₆	semidirect
45. C₃⋊D₃	C₅×C₁₆	semidirect
54. C₃²	C₂×C₅×C₁₆	semidirect
60. C₅	#63764	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₈×C₃⋊D₃	2
C₅×#3708	2
#63764	5
C₂×C₅×C₁₆	9

Subgroups — C5×#63764 #13086316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#63764 #13086316