Subgroups — C₂×C₄⋊AGL(1,𝔽₅) #4129

Order 160.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
3. C₄⋊AGL(1,𝔽₅)	C₂	direct (N × H)
7. C₂×C₄×C₅	C₄	semidirect
8. C₂×Dic₅	C₄	semidirect
9. C₄×D₅	C₄	semidirect
18. C₄×C₅	C₂×C₄	semidirect
19. Dic₅	C₂×C₄	semidirect
23. C₂×C₅	C₄⋊C₄	semidirect
25. D₅	C₄⋊C₄	semidirect
34. C₂×C₄	AGL(1,𝔽₅)	semidirect
35. C₅	C₂×C₄⋊C₄	semidirect
43. C₄	C₂×AGL(1,𝔽₅)	semidirect
47. C₂	C₄⋊AGL(1,𝔽₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,𝔽₅)	2
C₂×C₄×D₅	2
C₄⋊AGL(1,𝔽₅)	2
C₂×C₄⋊C₄	5

Subgroups — C2×C4⋊AGL(1,𝔽5) #4129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊AGL(1,𝔽₅) #4129