Subgroups — C₅×#442 #65605

Order 320.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×D₄	C₂	1	2	yes	maximal, complemented
3	C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#102	C₂	1	2	yes	maximal, complemented
5	C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×D₄	C₂²	1	2	yes	—
7	C₂²×C₄×C₅	—	2	2	no	—
8	C₅×D₈	C₄	1	4	yes	complemented
9	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₅×C₂²⋊C₄	—	2	2	no	—
13	C₄²×C₅	C₂²	1	1	yes	characteristic
14	#442	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂³×C₅	—	2	2	no	—
16	C₅×D₄	—	2	2	no	—
17	C₅×D₄	C₂×C₄	1	4	yes	complemented
18	C₂×C₄×C₅	—	2	2	no	—
19	C₂×C₄×C₅	—	4	4	no	—
20	C₂×C₄×C₅	D₄	1	2	yes	—
21	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₅×C₈	—	2	1	no	—
23	C₅×C₈	C₂×C₄	1	2	yes	complemented
24	C₂×D₈	C₂×C₅	1	1	yes	characteristic
25	C₄×D₄	C₂×C₅	1	2	yes	complemented
26	#106	C₂×C₅	1	1	yes	characteristic, complemented
27	#102	C₂×C₅	1	2	yes	complemented
28	#97	C₂×C₅	1	1	yes	characteristic, complemented
29	C₂²×C₅	—	2	4	no	—
30	C₂²×C₅	—	4	2	no	—
31	C₂²×C₅	—	4	2	no	—
32	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
33	C₄×C₅	—	2	2	no	—
34	C₄×C₅	—	4	2	no	—
35	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₅	#41	1	1	yes	characteristic
37	C₂×D₄	C₂²×C₅	1	2	yes	—
38	C₂²×C₄	—	2	2	no	—
39	D₈	C₄×C₅	1	4	yes	complemented
40	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
41	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
42	C₄⋊C₄	C₂²×C₅	1	2	yes	—
43	C₂²⋊C₄	—	2	2	no	—
44	C₄²	C₂²×C₅	1	1	yes	characteristic
45	C₂×C₅	—	4	4	no	—
46	C₂×C₅	C₄×D₄	1	1	yes	characteristic
47	C₂×C₅	AGL(1,ℤ/8)	1	2	yes	—
48	C₂³	—	2	2	no	—
49	D₄	—	2	2	no	—
50	D₄	C₂×C₄×C₅	1	4	yes	complemented
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	4	4	no	—
53	C₂×C₄	C₅×D₄	1	2	yes	—
54	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	C₂×C₄×C₅	1	2	yes	complemented
57	C₅	#442	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²	—	2	4	no	—
59	C₂²	—	4	2	no	—
60	C₂²	—	4	2	no	—
61	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
62	C₄	—	2	2	no	—
63	C₄	—	4	2	no	—
64	C₄	C₂²×C₄×C₅	1	1	yes	characteristic
65	C₄	C₅×#41	1	1	yes	characteristic
66	C₂	—	4	4	no	—
67	C₂	C₄×C₅×D₄	1	1	yes	characteristic
68	C₂	C₅×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂×D₄
commutator	C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂³×C₅
prime radical	C₂×C₅×D₈	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×D₄	C₂	semidirect
3. C₅×#106	C₂	semidirect
4. C₅×#102	C₂	semidirect
5. C₅×#97	C₂	semidirect
8. C₅×D₈	C₄	semidirect
14. #442	C₅	direct (N × H)
17. C₅×D₄	C₂×C₄	semidirect
23. C₅×C₈	C₂×C₄	semidirect
25. C₄×D₄	C₂×C₅	semidirect
26. #106	C₂×C₅	semidirect
27. #102	C₂×C₅	semidirect
28. #97	C₂×C₅	semidirect
39. D₈	C₄×C₅	semidirect
50. D₄	C₂×C₄×C₅	semidirect
56. C₈	C₂×C₄×C₅	semidirect
57. C₅	#442	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×D₈	2
C₄×C₅×D₄	2
C₅×#106	2
C₅×#102	2
C₅×#97	2
#442	5

Subgroups — C5×#442 #65605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#442 #65605