Subgroups — #170⋊C₈ #64880

Order 320.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#170	C₂	1	1	yes	maximal, characteristic
2	C₄×#170	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×#170	C₄	1	2	yes	—
5	C₂×#170	C₄	1	2	yes	—
6	C₂×C₅×C₈	C₄	1	1	yes	characteristic
7	C₄×Dic₅	C₂²	1	1	yes	characteristic
8	C₂×#168	C₄	1	1	yes	characteristic
9	#322	—	5	1	no	maximal, Sylow
10	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
11	C₂×Dic₅	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₅	C₂×C₄	1	1	yes	characteristic
13	#170	—	2	2	no	—
14	#170	C₈	1	4	yes	complemented
15	C₅×C₈	—	2	1	no	—
16	#168	—	2	1	no	—
17	C₄×C₈	—	5	1	no	—
18	C₄×C₈	—	5	1	no	—
19	C₄×C₈	—	5	1	no	—
20	C₂²×C₅	C₄²	1	1	yes	characteristic
21	C₄×C₅	M₁₆	1	1	yes	characteristic
22	C₄×C₅	M₁₆	1	1	yes	characteristic
23	Dic₅	C₂×C₈	1	2	yes	—
24	Dic₅	M₁₆	1	2	yes	—
25	C₂×C₈	—	5	2	no	—
26	C₂×C₈	—	5	2	no	—
27	C₂×C₈	—	5	1	no	—
28	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₄²	—	5	1	no	—
30	C₂×C₅	C₄×C₈	1	1	yes	characteristic
31	C₂×C₅	#97	1	1	yes	characteristic
32	C₂×C₅	#97	1	1	yes	characteristic
33	C₂×C₄	—	5	1	no	—
34	C₂×C₄	—	5	1	no	—
35	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
36	C₈	—	2	1	no	—
37	C₈	—	5	4	no	—
38	C₈	—	10	2	no	—
39	C₈	—	10	1	no	—
40	C₅	#322	1	1	yes	characteristic, complemented, Sylow
41	C₂²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
42	C₄	—	5	2	no	—
43	C₄	—	5	2	no	—
44	C₄	#700	1	1	yes	characteristic
45	C₄	#704	1	1	yes	characteristic
46	C₂	C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
47	C₂	#3992	1	1	yes	characteristic
48	C₂	#4002	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₄×C₈
Fitting	C₂×C₅×C₈	C₄
socle, prime radical	C₂²×C₅	C₄²
cosocle	C₄×Dic₅	C₂²
hypercenter	C₂×C₈	AGL(1,𝔽₅)
hypocenter	C₅	#322
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
14. #170	C₈	semidirect
40. C₅	#322	semidirect

Maximal subgroups

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

subgroup	index
C₄×#170	2
C₈×Dic₅	2
#322	5

Subgroups — #170⋊C8 #64880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #170⋊C₈ #64880