Subgroups — C₄×C₅×D₈ #65600

Order 320.

134 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×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#102	C₂	1	2	yes	maximal, complemented
5	C₄×C₅×C₈	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	direct product factor
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	C₄×D₈	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	1	yes	characteristic
21	C₂×C₄×C₅	D₄	1	1	yes	characteristic
22	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₅×C₈	—	2	1	no	—
24	C₅×C₈	C₂×C₄	1	2	yes	complemented
25	C₂×D₈	C₂×C₅	1	1	yes	characteristic
26	C₄×D₄	C₂×C₅	1	2	yes	complemented
27	#107	C₂×C₅	1	1	yes	characteristic, complemented
28	#102	C₂×C₅	1	2	yes	complemented
29	C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
30	C₂²×C₅	—	2	4	no	—
31	C₂²×C₅	—	4	2	no	—
32	C₂²×C₅	—	4	2	no	—
33	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
34	C₄×C₅	—	2	1	no	—
35	C₄×C₅	—	4	2	no	—
36	C₄×C₅	D₈	1	2	yes	direct product factor
37	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
38	C₄×C₅	#41	1	1	yes	characteristic
39	C₂×D₄	C₂²×C₅	1	2	yes	—
40	C₂²×C₄	—	2	2	no	—
41	D₈	C₄×C₅	1	4	yes	direct product factor
42	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
43	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
44	C₄⋊C₄	C₂²×C₅	1	2	yes	—
45	C₂²⋊C₄	—	2	2	no	—
46	C₄²	C₂²×C₅	1	1	yes	characteristic
47	C₂×C₅	—	4	4	no	—
48	C₂×C₅	C₄×D₄	1	1	yes	characteristic
49	C₂×C₅	C₂×D₈	1	1	yes	characteristic
50	C₂×C₅	#135	1	1	yes	characteristic
51	C₂³	—	2	2	no	—
52	D₄	—	2	2	no	—
53	D₄	C₂×C₄×C₅	1	4	yes	complemented
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	4	4	no	—
56	C₂×C₄	C₅×D₄	1	1	yes	characteristic
57	C₂×C₄	C₅×D₄	1	1	yes	characteristic
58	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
59	C₈	—	2	1	no	—
60	C₈	C₂×C₄×C₅	1	2	yes	complemented
61	C₅	C₄×D₈	1	1	yes	characteristic, direct product factor, Sylow
62	C₂²	—	2	4	no	—
63	C₂²	—	4	2	no	—
64	C₂²	—	4	2	no	—
65	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	4	2	no	—
68	C₄	C₅×D₈	1	2	yes	direct product factor
69	C₄	C₂²×C₄×C₅	1	1	yes	characteristic
70	C₄	C₅×#41	1	1	yes	characteristic
71	C₂	—	4	4	no	—
72	C₂	C₄×C₅×D₄	1	1	yes	characteristic
73	C₂	C₂×C₅×D₈	1	1	yes	characteristic
74	C₂	C₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₄
commutator	C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂³×C₅
socle	C₂²×C₅	C₂×D₄
prime radical	C₂×C₅×D₈	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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×#107	C₂	semidirect
4. C₅×#102	C₂	semidirect
5. C₄×C₅×C₈	C₂	semidirect
8. C₅×D₈	C₄	direct (N × H)
14. C₄×D₈	C₅	direct (N × H)
17. C₅×D₄	C₂×C₄	semidirect
24. C₅×C₈	C₂×C₄	semidirect
26. C₄×D₄	C₂×C₅	semidirect
27. #107	C₂×C₅	semidirect
28. #102	C₂×C₅	semidirect
29. C₄×C₈	C₂×C₅	semidirect
36. C₄×C₅	D₈	direct (N × H)
41. D₈	C₄×C₅	direct (N × H)
53. D₄	C₂×C₄×C₅	semidirect
60. C₈	C₂×C₄×C₅	semidirect
61. C₅	C₄×D₈	direct (N × H)
68. C₄	C₅×D₈	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×#107	2
C₅×#102	2
C₄×C₅×C₈	2
C₄×D₈	5

Subgroups — C4×C5×D8 #65600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×D₈ #65600