Subgroups — (C₂×AGL(1,𝔽₅))⋊C₈ #64892

Order 320.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₅	C₂	1	1	yes	maximal, characteristic
4	C₂²×AGL(1,𝔽₅)	C₄	1	2	yes	—
5	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
6	C₂×#170	C₄	1	2	yes	complemented
7	C₄×AGL(1,𝔽₅)	—	2	1	no	—
8	C₄×AGL(1,𝔽₅)	—	2	1	no	—
9	D₅⋊C₈	—	2	1	no	—
10	D₅⋊C₈	—	2	1	no	—
11	C₂×C₅×C₈	C₄	1	1	yes	characteristic, complemented
12	C₂×#168	C₄	1	1	yes	characteristic, complemented
13	C₈×D₅	—	2	1	no	—
14	C₈×D₅	—	2	1	no	—
15	#336	—	5	1	no	maximal, Sylow
16	C₂²×D₅	C₂×C₄	1	1	yes	characteristic
17	C₂×AGL(1,𝔽₅)	—	2	2	no	—
18	C₂×AGL(1,𝔽₅)	—	2	2	no	—
19	C₂×AGL(1,𝔽₅)	C₈	1	4	yes	complemented
20	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₅	C₂×C₄	1	1	yes	characteristic
22	C₄×D₅	D₄	1	1	yes	characteristic
23	C₄×D₅	D₄	1	1	yes	characteristic
24	C₄×D₅	D₄	1	1	yes	characteristic
25	C₄×D₅	Q₈	1	1	yes	characteristic
26	#170	—	2	2	no	—
27	C₅×C₈	—	2	1	no	—
28	#168	—	2	1	no	—
29	C₂²×C₈	—	5	1	no	—
30	C₂²×C₈	—	5	1	no	—
31	C₂×C₄²	—	5	1	no	—
32	C₂²×C₅	C₄²	1	1	yes	characteristic
33	C₂×D₅	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×D₅	C₄⋊C₄	1	1	yes	characteristic
35	C₂×D₅	C₂×C₈	1	2	yes	—
36	C₂×D₅	M₁₆	1	2	yes	—
37	AGL(1,𝔽₅)	—	2	4	no	—
38	C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
40	Dic₅	C₂²⋊C₄	1	1	yes	characteristic
41	Dic₅	C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₄	—	5	1	no	—
43	C₂²×C₄	—	5	2	no	—
44	C₂×C₈	—	5	2	no	—
45	C₂×C₈	—	5	1	no	—
46	C₂×C₈	—	10	1	no	—
47	C₂×C₈	—	10	1	no	—
48	C₂×C₈	—	10	1	no	—
49	C₂×C₈	—	10	1	no	—
50	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
51	C₄²	—	10	1	no	—
52	C₄²	—	10	1	no	—
53	C₂×C₅	#95	1	1	yes	characteristic
54	C₂×C₅	C₄×C₈	1	1	yes	characteristic
55	C₂×C₅	#97	1	1	yes	characteristic
56	D₅	C₂²⋊C₈	1	2	yes	—
57	D₅	C₄⋊C₈	1	2	yes	—
58	C₂³	—	5	1	no	—
59	C₂×C₄	—	5	1	no	—
60	C₂×C₄	—	5	1	no	—
61	C₂×C₄	—	5	1	no	—
62	C₂×C₄	—	5	1	no	—
63	C₂×C₄	—	5	1	no	—
64	C₂×C₄	—	5	4	no	—
65	C₂×C₄	—	10	2	no	—
66	C₂×C₄	—	10	2	no	—
67	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
68	C₈	—	2	1	no	—
69	C₈	—	10	2	no	—
70	C₈	—	10	1	no	—
71	C₅	#336	1	1	yes	characteristic, complemented, Sylow
72	C₂²	—	5	2	no	—
73	C₂²	—	5	2	no	—
74	C₂²	—	5	1	no	—
75	C₂²	—	5	1	no	—
76	C₂²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
77	C₄	—	5	1	no	—
78	C₄	—	5	1	no	—
79	C₄	—	10	4	no	—
80	C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
81	C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
82	C₂	—	5	2	no	—
83	C₂	—	5	2	no	—
84	C₂	C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
85	C₂	#3992	1	1	yes	characteristic
86	C₂	(C₂×AGL(1,𝔽₅))⋊C₄	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	C₂²×C₅	C₄²
prime radical	C₂²×D₅	C₂×C₄
cosocle	C₂×C₄×D₅	C₂²
hypercenter	C₂×C₈	AGL(1,𝔽₅)
hypocenter	C₅	#336
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
6. C₂×#170	C₄	semidirect
11. C₂×C₅×C₈	C₄	semidirect
12. C₂×#168	C₄	semidirect
19. C₂×AGL(1,𝔽₅)	C₈	semidirect
50. C₂×C₈	AGL(1,𝔽₅)	semidirect
71. C₅	#336	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×AGL(1,𝔽₅)	2
C₂×D₅⋊C₈	2
C₂×C₈×D₅	2
#336	5

Subgroups — (C2×AGL(1,𝔽5))⋊C8 #64892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×AGL(1,𝔽₅))⋊C₈ #64892