Subgroups — D₅⋊(C₄⋊C₈) #65679

Order 320.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅⋊C₈	C₂	1	2	yes	maximal
2	C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	#4004	C₂	1	2	yes	maximal, complemented
4	C₄⋊#170	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₅	C₄	1	1	yes	characteristic
6	C₂×C₄×D₅	C₄	1	1	yes	characteristic
7	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂×#170	C₂²	1	4	yes	—
9	D₅⋊C₈	—	2	4	no	—
10	C₄²×C₅	C₄	1	1	yes	characteristic
11	C₄×Dic₅	C₄	1	1	yes	characteristic
12	C₄×Dic₅	C₂²	1	1	yes	characteristic
13	C₄×Dic₅	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈	—	5	1	no	maximal, Sylow
15	C₂²×D₅	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₅	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₅	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₅	C₂³	1	1	yes	characteristic
22	C₄×D₅	—	2	2	no	—
23	C₄×D₅	C₈	1	4	yes	complemented
24	C₄×D₅	D₄	1	2	yes	—
25	C₄×D₅	Q₈	1	2	yes	—
26	#170	—	2	4	no	—
27	C₂²×C₈	—	5	2	no	—
28	C₂×C₄²	—	5	1	no	—
29	C₄⋊C₈	—	5	2	no	—
30	C₄⋊C₈	—	5	2	no	—
31	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₂×D₅	C₄⋊C₄	1	2	yes	—
33	C₂×D₅	C₂×C₈	1	2	yes	—
34	C₂×D₅	M₁₆	1	2	yes	—
35	C₄×C₅	—	2	1	no	—
36	C₄×C₅	C₄⋊C₄	1	2	yes	—
37	C₄×C₅	C₂×C₈	1	2	yes	complemented
38	Dic₅	—	2	1	no	—
39	Dic₅	C₂×C₈	1	2	yes	complemented
40	Dic₅	C₂×D₄	1	1	yes	characteristic
41	Dic₅	C₂×Q₈	1	1	yes	characteristic
42	C₂²×C₄	—	5	1	no	—
43	C₂²×C₄	—	5	1	no	—
44	C₂²×C₄	—	5	1	no	—
45	C₂×C₈	—	5	4	no	—
46	C₂×C₈	—	10	4	no	—
47	C₄²	—	5	1	no	—
48	C₄²	—	5	1	no	—
49	C₄²	—	5	1	no	—
50	C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic
51	C₂×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₅	C₂²×C₈	1	1	yes	characteristic
53	C₂×C₅	C₂×M₁₆	1	1	yes	characteristic
54	D₅	C₄⋊C₈	1	4	yes	complemented
55	C₂³	—	5	1	no	—
56	C₂×C₄	—	5	1	no	—
57	C₂×C₄	—	5	1	no	—
58	C₂×C₄	—	5	4	no	—
59	C₂×C₄	—	5	2	no	—
60	C₂×C₄	—	5	2	no	—
61	C₂×C₄	—	5	1	no	—
62	C₂×C₄	—	10	2	no	—
63	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
64	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
65	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
66	C₈	—	10	4	no	—
67	C₅	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
68	C₂²	—	5	2	no	—
69	C₂²	—	5	2	no	—
70	C₂²	—	5	2	no	—
71	C₂²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	—	5	2	no	—
74	C₄	—	5	1	no	—
75	C₄	—	5	1	no	—
76	C₄	—	10	1	no	—
77	C₄	D₅⋊C₈	1	2	yes	complemented
78	C₄	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
79	C₂	—	5	4	no	—
80	C₂	C₂×D₅⋊C₈	1	1	yes	characteristic
81	C₂	D₅⋊M₁₆	1	1	yes	characteristic
82	C₂	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₈
Frattini	C₂²	C₂²×AGL(1,𝔽₅)
Fitting	C₄²×C₅	C₄
socle	C₂²×C₅	C₂²×C₄
prime radical	C₂²×D₅	C₂×C₄
cosocle	C₂×Dic₅	C₂³
hypercenter	C₄²	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
3. #4004	C₂	semidirect
4. C₄⋊#170	C₂	semidirect
23. C₄×D₅	C₈	semidirect
37. C₄×C₅	C₂×C₈	semidirect
39. Dic₅	C₂×C₈	semidirect
54. D₅	C₄⋊C₈	semidirect
67. C₅	C₂×C₄⋊C₈	semidirect
77. C₄	D₅⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅⋊C₈	2
C₄²×D₅	2
#4004	2
C₄⋊#170	2
C₂×C₄⋊C₈	5

Subgroups — D5⋊(C4⋊C8) #65679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊(C₄⋊C₈) #65679