Subgroups — #64906

Order 320.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×D₈	C₂	1	1	yes	maximal, characteristic
2	#3995	C₂	1	1	yes	maximal, characteristic, complemented
3	#3990	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×D₅	—	2	1	no	—
5	#700	—	2	1	no	—
6	C₅×D₈	C₄	1	1	yes	characteristic
7	#686	—	2	1	no	—
8	D₄₀	C₄	1	1	yes	characteristic
9	C₈×D₅	C₂²	1	1	yes	characteristic
10	#674	—	2	1	no	—
11	#361	—	5	1	no	maximal, Sylow
12	C₂²×D₅	—	4	1	no	—
13	C₅×D₄	—	2	1	no	—
14	C₂²⋊D₅	—	4	1	no	—
15	D₂₀	—	2	1	no	—
16	C₄×D₅	D₄	1	1	yes	characteristic
17	#170	—	4	1	no	—
18	C₅×C₈	C₂×C₄	1	1	yes	characteristic
19	#168	D₄	1	1	yes	characteristic
20	C₂×D₈	—	5	1	no	—
21	M₃₂	—	5	1	no	—
22	#108	—	5	1	no	—
23	C₂²×C₅	—	4	1	no	—
24	C₂×D₅	—	4	1	no	—
25	C₂×D₅	—	8	2	no	—
26	C₂×D₅	SD₁₆	1	1	yes	characteristic
27	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
28	Dic₅	D₈	1	1	yes	characteristic
29	C₂×D₄	—	10	1	no	—
30	D₈	—	5	1	no	—
31	D₈	—	10	1	no	—
32	D₈	AGL(1,𝔽₅)	1	1	yes	characteristic
33	M₁₆	—	10	1	no	—
34	C₂×C₈	—	5	1	no	—
35	C₁₆	—	10	1	no	—
36	C₂×C₅	—	8	1	no	—
37	C₂×C₅	#102	1	1	yes	characteristic
38	D₅	—	2	1	no	—
39	D₅	—	8	1	no	—
40	C₂³	—	20	1	no	—
41	D₄	—	2	1	no	—
42	D₄	—	10	1	no	—
43	D₄	—	20	1	no	—
44	C₂×C₄	—	5	1	no	—
45	C₈	—	5	1	no	—
46	C₈	—	20	1	no	—
47	C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
48	C₅	#361	1	1	yes	characteristic, complemented, Sylow
49	C₂²	—	4	1	no	—
50	C₂²	—	5	1	no	—
51	C₂²	—	20	1	no	—
52	C₂²	—	40	2	no	—
53	C₄	—	5	1	no	—
54	C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	10	1	no	—
57	C₂	—	40	1	no	—
58	C₂	#4007	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#4007
commutator	C₅×C₈	C₂×C₄
Frattini	C₈	C₂×AGL(1,𝔽₅)
Fitting	C₅×D₈	C₄
socle	C₂×C₅	#102
prime radical	D₅×D₈	C₂
cosocle	C₈×D₅	C₂²
hypercenter	D₈	AGL(1,𝔽₅)
hypocenter	C₅	#361
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
2. #3995	C₂	semidirect
3. #3990	C₂	semidirect
48. C₅	#361	semidirect

Maximal subgroups

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

subgroup	index
D₅×D₈	2
#3995	2
#3990	2
#361	5