Subgroups — C₅×#360 #64827

Order 320.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#41	—	2	1	no	—
5	C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
6	C₅×SD₁₆	—	2	1	no	—
7	C₅×D₈	C₄	1	1	yes	characteristic, complemented
8	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₅×C₄⋊C₄	—	2	1	no	—
10	C₅×C₁₆	—	2	1	no	—
11	#360	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₅×Q₈	—	2	1	no	—
13	C₅×D₄	—	2	1	no	—
14	C₅×D₄	—	4	1	no	—
15	C₂×C₄×C₅	—	4	1	no	—
16	C₂×C₄×C₅	—	4	1	no	—
17	C₂×C₄×C₅	D₄	1	1	yes	characteristic
18	C₅×C₈	C₂×C₄	1	1	yes	characteristic
19	C₅×C₈	D₄	1	1	yes	characteristic
20	#135	C₂×C₅	1	1	yes	characteristic
21	M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
22	#106	C₂×C₅	1	1	yes	characteristic, complemented
23	C₂²×C₅	—	4	1	no	—
24	C₂²×C₅	D₈	1	1	yes	characteristic
25	C₄×C₅	—	4	1	no	—
26	C₄×C₅	—	8	1	no	—
27	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
28	C₄×C₅	SD₁₆	1	1	yes	characteristic
29	#41	—	2	1	no	—
30	Q₁₆	C₄×C₅	1	1	yes	characteristic, complemented
31	SD₁₆	—	2	1	no	—
32	D₈	C₄×C₅	1	1	yes	characteristic, complemented
33	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
34	C₄⋊C₄	—	2	1	no	—
35	C₁₆	—	2	1	no	—
36	C₂×C₅	—	2	1	no	—
37	C₂×C₅	—	8	1	no	—
38	C₂×C₅	#102	1	1	yes	characteristic
39	Q₈	—	2	1	no	—
40	D₄	—	2	1	no	—
41	D₄	—	4	1	no	—
42	C₂×C₄	—	4	1	no	—
43	C₂×C₄	—	4	1	no	—
44	C₂×C₄	C₅×D₄	1	1	yes	characteristic
45	C₈	C₂×C₄×C₅	1	1	yes	characteristic
46	C₈	C₅×D₄	1	1	yes	characteristic
47	C₅	#360	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²	—	4	1	no	—
49	C₂²	C₅×D₈	1	1	yes	characteristic
50	C₄	—	4	1	no	—
51	C₄	—	8	1	no	—
52	C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
53	C₄	C₅×SD₁₆	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	8	1	no	—
56	C₂	C₅×#102	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#102
commutator	C₈	C₂×C₄×C₅
Frattini, cosocle	C₂×C₈	C₂²×C₅
prime radical	C₅×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×M₃₂	C₂	semidirect
3. C₅×#106	C₂	semidirect
5. C₅×Q₁₆	C₄	semidirect
7. C₅×D₈	C₄	semidirect
11. #360	C₅	direct (N × H)
21. M₃₂	C₂×C₅	semidirect
22. #106	C₂×C₅	semidirect
30. Q₁₆	C₄×C₅	semidirect
32. D₈	C₄×C₅	semidirect
47. C₅	#360	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×#135	2
C₅×M₃₂	2
C₅×#106	2
#360	5

Subgroups — C5×#360 #64827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#360 #64827