Subgroups — #64897

Order 320.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×#676	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
4	#704	—	2	2	no	—
5	#700	—	2	2	no	—
6	D₅⋊C₈	C₄	1	4	yes	—
7	C₂×C₅×C₈	C₄	1	1	yes	characteristic
8	C₂×#168	C₄	1	1	yes	characteristic
9	#676	—	2	2	no	—
10	#338	—	5	1	no	maximal, Sylow
11	C₂²×D₅	Q₈	1	1	yes	characteristic
12	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₅	D₄	1	1	yes	characteristic
14	C₄×D₅	C₂×C₄	1	2	yes	—
15	C₄×D₅	D₄	1	2	yes	—
16	#170	—	2	4	no	—
17	C₅×C₈	—	2	1	no	—
18	#168	—	2	1	no	—
19	C₂×M₁₆	—	5	2	no	—
20	C₂×M₁₆	—	5	1	no	—
21	C₂²×C₅	C₄⋊C₄	1	1	yes	characteristic
22	C₂×D₅	—	4	1	no	—
23	C₂×D₅	C₄⋊C₄	1	2	yes	—
24	C₄×C₅	C₄²	1	1	yes	characteristic
25	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
26	Dic₅	C₂²⋊C₄	1	2	yes	—
27	C₂²×C₄	—	5	1	no	—
28	M₁₆	—	10	2	no	—
29	M₁₆	—	10	2	no	—
30	M₁₆	—	10	2	no	—
31	C₂×C₈	—	5	4	no	—
32	C₂×C₈	—	5	1	no	—
33	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
34	C₂×C₅	—	2	1	no	—
35	C₂×C₅	#95	1	1	yes	characteristic
36	D₅	—	2	2	no	—
37	C₂³	—	5	1	no	—
38	C₂×C₄	—	5	1	no	—
39	C₂×C₄	—	5	2	no	—
40	C₂×C₄	—	5	2	no	—
41	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
42	C₈	—	2	1	no	—
43	C₈	—	10	4	no	—
44	C₈	—	10	1	no	—
45	C₅	#338	1	1	yes	characteristic, complemented, Sylow
46	C₂²	—	5	2	no	—
47	C₂²	—	20	1	no	—
48	C₂²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
49	C₄	—	5	2	no	—
50	C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
51	C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	10	2	no	—
54	C₂	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₄²
Frattini	C₂×C₄	C₂×AGL(1,𝔽₅)
Fitting	C₂×C₅×C₈	C₄
socle	C₂×C₅	#95
prime radical	C₂²×D₅	Q₈
cosocle	C₂×C₄×D₅	C₂²
hypercenter	C₂×C₈	AGL(1,𝔽₅)
hypocenter	C₅	#338
LCS	G ▷ C₄×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
45. C₅	#338	semidirect

Maximal subgroups

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

subgroup	index
D₅⋊M₁₆	2
C₂×#676	2
#338	5