Subgroups — D₅⋊M₃₂ #65715

Order 320.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	#3998	C₂	1	2	yes	maximal, complemented
3	#3990	C₂	1	2	yes	maximal, complemented
4	D₅⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₅	C₄	1	1	yes	characteristic
6	C₂×C₅×C₈	C₄	1	1	yes	characteristic
7	C₂×#168	C₂²	1	1	yes	characteristic
8	C₈×D₅	C₄	1	1	yes	characteristic
9	C₈×D₅	C₄	1	1	yes	characteristic
10	C₈×D₅	C₂²	1	1	yes	characteristic
11	C₈×D₅	C₂²	1	1	yes	characteristic
12	#674	C₂²	1	4	yes	complemented
13	C₂×M₃₂	—	5	1	no	maximal, Sylow
14	C₂²×D₅	C₈	1	1	yes	characteristic
15	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₅	C₈	1	1	yes	characteristic
17	C₄×D₅	C₈	1	1	yes	characteristic
18	C₄×D₅	C₈	1	1	yes	characteristic
19	C₄×D₅	C₂×C₄	1	1	yes	characteristic
20	C₄×D₅	C₂×C₄	1	1	yes	characteristic
21	C₅×C₈	C₂×C₄	1	1	yes	characteristic
22	C₅×C₈	C₂×C₄	1	1	yes	characteristic
23	#168	C₂×C₄	1	1	yes	characteristic
24	#168	C₂³	1	1	yes	characteristic
25	C₂²×C₈	—	5	1	no	—
26	M₃₂	—	5	2	no	—
27	M₃₂	—	5	2	no	—
28	C₂×C₁₆	—	5	2	no	—
29	C₂²×C₅	C₂×C₈	1	1	yes	characteristic
30	C₂×D₅	—	2	2	no	—
31	C₂×D₅	C₂×C₈	1	1	yes	characteristic
32	C₂×D₅	C₂×C₈	1	1	yes	characteristic
33	C₄×C₅	C₂×C₈	1	1	yes	characteristic
34	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
35	Dic₅	C₂×C₈	1	1	yes	characteristic
36	Dic₅	C₂×C₈	1	1	yes	characteristic
37	C₂²×C₄	—	5	1	no	—
38	C₂×C₈	—	5	1	no	—
39	C₂×C₈	—	5	1	no	—
40	C₂×C₈	—	5	1	no	—
41	C₂×C₈	—	5	1	no	—
42	C₂×C₈	—	5	1	no	—
43	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
44	C₁₆	—	5	4	no	—
45	C₂×C₅	—	2	1	no	—
46	C₂×C₅	C₂²×C₈	1	1	yes	characteristic
47	D₅	—	2	1	no	—
48	D₅	M₃₂	1	2	yes	complemented
49	C₂³	—	5	1	no	—
50	C₂×C₄	—	5	1	no	—
51	C₂×C₄	—	5	1	no	—
52	C₂×C₄	—	5	1	no	—
53	C₂×C₄	—	5	1	no	—
54	C₂×C₄	—	5	1	no	—
55	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
56	C₈	—	5	1	no	—
57	C₈	—	5	1	no	—
58	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
59	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
60	C₅	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
61	C₂²	—	5	1	no	—
62	C₂²	—	5	1	no	—
63	C₂²	—	10	2	no	—
64	C₂²	D₅⋊C₈	1	1	yes	characteristic
65	C₄	—	5	1	no	—
66	C₄	—	5	1	no	—
67	C₄	D₅⋊C₈	1	1	yes	characteristic
68	C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	5	2	no	—
71	C₂	—	10	1	no	—
72	C₂	C₂×D₅⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×AGL(1,𝔽₅)
commutator, socle	C₂×C₅	C₂²×C₈
Frattini	C₄	C₂²×AGL(1,𝔽₅)
Fitting	C₂×C₅×C₈	C₄
prime radical	C₂²×D₅	C₈
cosocle	#168	C₂³
hypercenter	C₂×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×M₃₂
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #3998	C₂	semidirect
3. #3990	C₂	semidirect
4. D₅⋊C₁₆	C₂	semidirect
12. #674	C₂²	semidirect
48. D₅	M₃₂	semidirect
60. C₅	C₂×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₅	2
#3998	2
#3990	2
D₅⋊C₁₆	2
C₂×M₃₂	5

Subgroups — D5⋊M32 #65715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊M₃₂ #65715