Subgroups — C₂×#3994 #65720

Order 320.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₂×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	#3994	C₂	1	4	yes	maximal, direct product factor
4	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
5	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
6	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
7	C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
8	C₂×C₅×C₈	C₄	1	1	yes	characteristic, complemented
9	C₂×#168	C₄	1	1	yes	characteristic, complemented
10	C₈×D₅	C₄	1	2	yes	complemented
11	C₈×D₅	C₂²	1	2	yes	—
12	C₂×#107	—	5	1	no	maximal, Sylow
13	C₂²×D₅	D₄	1	1	yes	characteristic
14	C₂×AGL(1,𝔽₅)	—	2	4	no	—
15	C₂×AGL(1,𝔽₅)	—	4	4	no	—
16	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₅	Q₈	1	1	yes	characteristic
18	C₄×D₅	C₂×C₄	1	1	yes	characteristic
19	C₄×D₅	D₄	1	1	yes	characteristic
20	C₄×D₅	Q₈	1	1	yes	characteristic
21	C₄×D₅	C₂³	1	1	yes	characteristic
22	C₅×C₈	C₂×C₄	1	2	yes	complemented
23	#168	C₂×C₄	1	2	yes	complemented
24	C₂²×C₈	—	5	1	no	—
25	C₂×C₄⋊C₄	—	5	2	no	—
26	#107	—	5	4	no	—
27	C₂²×C₅	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₅	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₅	D₈	1	2	yes	—
30	C₂×D₅	Q₁₆	1	2	yes	—
31	C₂×D₅	C₂×D₄	1	1	yes	characteristic
32	AGL(1,𝔽₅)	—	4	4	no	—
33	C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
34	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
35	Dic₅	C₄⋊C₄	1	1	yes	characteristic
36	Dic₅	C₂×Q₈	1	1	yes	characteristic
37	C₂²×C₄	—	5	1	no	—
38	C₂²×C₄	—	10	2	no	—
39	C₂×C₈	—	5	1	no	—
40	C₂×C₈	—	5	2	no	—
41	C₂×C₈	—	5	2	no	—
42	C₂×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
43	C₄⋊C₄	—	5	4	no	—
44	C₄⋊C₄	—	10	2	no	—
45	C₂×C₅	#107	1	2	yes	complemented
46	C₂×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
47	D₅	#107	1	2	yes	complemented
48	D₅	C₂×D₈	1	1	yes	characteristic
49	D₅	C₂×Q₁₆	1	1	yes	characteristic
50	C₂³	—	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	—	5	1	no	—
56	C₂×C₄	—	10	4	no	—
57	C₂×C₄	—	20	4	no	—
58	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
59	C₈	—	5	2	no	—
60	C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
61	C₅	C₂×#107	1	1	yes	characteristic, complemented, Sylow
62	C₂²	—	5	1	no	—
63	C₂²	—	5	1	no	—
64	C₂²	—	5	2	no	—
65	C₂²	—	5	2	no	—
66	C₂²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
67	C₄	—	5	1	no	—
68	C₄	—	5	1	no	—
69	C₄	—	20	4	no	—
70	C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
71	C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
72	C₂	—	5	1	no	—
73	C₂	—	5	2	no	—
74	C₂	—	5	1	no	—
75	C₂	#3994	1	2	yes	direct product factor
76	C₂	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₄
Frattini	C₄	C₂²×AGL(1,𝔽₅)
Fitting	C₂×C₅×C₈	C₄
socle	C₂²×C₅	C₄⋊C₄
prime radical	C₂²×D₅	D₄
cosocle	C₄×D₅	C₂³
hypercenter	C₂×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×#107
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #3994	C₂	direct (N × H)
8. C₂×C₅×C₈	C₄	semidirect
9. C₂×#168	C₄	semidirect
10. C₈×D₅	C₄	semidirect
22. C₅×C₈	C₂×C₄	semidirect
23. #168	C₂×C₄	semidirect
42. C₂×C₈	AGL(1,𝔽₅)	semidirect
45. C₂×C₅	#107	semidirect
47. D₅	#107	semidirect
60. C₈	C₂×AGL(1,𝔽₅)	semidirect
61. C₅	C₂×#107	semidirect
75. C₂	#3994	direct (N × H)

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×C₈×D₅	2
#3994	2
C₂×#107	5

Subgroups — C2×#3994 #65720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3994 #65720