Subgroups — C₅×C₄⋊Dic₅ #87791

Order 400.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₅	C₂	1	2	yes	maximal
3	C₂²×C₅²	C₂²	1	1	yes	characteristic
4	C₄×C₅²	C₄	1	2	yes	complemented
5	C₅×Dic₅	—	2	2	no	—
6	C₅×C₄⋊C₄	—	5	1	no	maximal
7	C₄⋊Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
9	C₂×C₅²	D₄	1	1	yes	characteristic
10	C₂×C₅²	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₅	—	2	2	no	—
12	C₂×C₄×C₅	—	5	2	no	—
13	C₂×C₄×C₅	D₅	1	1	yes	characteristic
14	C₂×C₄×C₅	C₂×C₅	1	1	yes	characteristic
15	C₂×Dic₅	C₂×C₅	1	2	yes	—
16	C₅²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₅	—	2	2	no	—
18	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
19	C₂²×C₅	C₂²×C₅	1	1	yes	characteristic
20	C₄×C₅	—	2	4	no	—
21	C₄×C₅	—	10	2	no	—
22	C₄×C₅	Dic₅	1	2	yes	complemented
23	C₄×C₅	C₄×C₅	1	2	yes	complemented
24	Dic₅	—	2	2	no	—
25	C₄⋊C₄	—	5	1	no	Sylow
26	C₂×C₅	—	2	2	no	—
27	C₂×C₅	—	2	2	no	—
28	C₂×C₅	—	2	2	no	—
29	C₂×C₅	Dic₁₀	1	1	yes	characteristic
30	C₂×C₅	D₂₀	1	1	yes	characteristic
31	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
32	C₂×C₅	C₂×C₄×C₅	1	1	yes	characteristic
33	C₂×C₅	C₅×D₄	1	1	yes	characteristic
34	C₂×C₅	C₅×Q₈	1	1	yes	characteristic
35	C₂×C₄	—	5	2	no	—
36	C₂×C₄	C₅×D₅	1	1	yes	characteristic
37	C₅	—	2	2	no	—
38	C₅	C₄⋊Dic₅	1	1	yes	characteristic, direct product factor
39	C₅	C₅×C₄⋊C₄	1	1	yes	characteristic, complemented
40	C₂²	C₂×C₅×D₅	1	1	yes	characteristic
41	C₄	—	10	2	no	—
42	C₄	C₅×Dic₅	1	2	yes	complemented
43	C₂	C₅×Dic₁₀	1	1	yes	characteristic
44	C₂	C₅×D₂₀	1	1	yes	characteristic
45	C₂	C₂×C₅×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₅
commutator	C₂×C₅	C₂×C₄×C₅
Frattini	C₂²	C₂×C₅×D₅
Fitting	C₂×C₄×C₅²	C₂
socle, prime radical	C₂²×C₅²	C₂²
cosocle	C₂²×C₅	C₂²×C₅
hypercenter	C₂×C₄×C₅	D₅
hypocenter	C₅	C₅×C₄⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
4. C₄×C₅²	C₄	semidirect
7. C₄⋊Dic₅	C₅	direct (N × H)
16. C₅²	C₄⋊C₄	semidirect
22. C₄×C₅	Dic₅	semidirect
23. C₄×C₅	C₄×C₅	semidirect
38. C₅	C₄⋊Dic₅	direct (N × H)
39. C₅	C₅×C₄⋊C₄	semidirect
42. C₄	C₅×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅²	2
C₂×C₅×Dic₅	2
C₅×C₄⋊C₄	5
C₄⋊Dic₅	5

Subgroups — C5×C4⋊Dic5 #87791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄⋊Dic₅ #87791