Subgroups — C₄×C₅×Dic₅ #87789

Order 400.

76 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	C₄	1	4	yes	direct product factor
6	C₄²×C₅	—	5	1	no	maximal
7	C₄×Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₅²	C₂×C₄	1	2	yes	—
9	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₅	—	2	2	no	—
11	C₂×C₄×C₅	—	5	2	no	—
12	C₂×C₄×C₅	D₅	1	1	yes	characteristic
13	C₂×C₄×C₅	C₂×C₅	1	1	yes	characteristic
14	C₂×Dic₅	C₂×C₅	1	2	yes	—
15	C₅²	C₄²	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅	—	2	2	no	—
17	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
18	C₂²×C₅	C₂²×C₅	1	1	yes	characteristic
19	C₄×C₅	—	2	4	no	—
20	C₄×C₅	—	5	4	no	—
21	C₄×C₅	Dic₅	1	2	yes	direct product factor
22	C₄×C₅	C₄×C₅	1	2	yes	complemented
23	Dic₅	C₄×C₅	1	4	yes	direct product factor
24	C₄²	—	5	1	no	Sylow
25	C₂×C₅	—	2	4	no	—
26	C₂×C₅	—	2	2	no	—
27	C₂×C₅	C₄×D₅	1	2	yes	—
28	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
29	C₂×C₅	C₂×C₄×C₅	1	2	yes	—
30	C₂×C₅	C₂×C₄×C₅	1	1	yes	characteristic
31	C₂×C₄	—	5	2	no	—
32	C₂×C₄	C₅×D₅	1	1	yes	characteristic
33	C₅	—	2	2	no	—
34	C₅	C₄×Dic₅	1	1	yes	characteristic, direct product factor
35	C₅	C₄²×C₅	1	1	yes	characteristic, complemented
36	C₂²	C₂×C₅×D₅	1	1	yes	characteristic
37	C₄	—	5	4	no	—
38	C₄	C₅×Dic₅	1	2	yes	direct product factor
39	C₂	C₄×C₅×D₅	1	2	yes	—
40	C₂	C₂×C₅×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₅	D₅
commutator, hypocenter	C₅	C₄²×C₅
Frattini	C₂²	C₂×C₅×D₅
Fitting	C₂×C₄×C₅²	C₂
socle, prime radical	C₂²×C₅²	C₂²
cosocle	C₂²×C₅	C₂²×C₅
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
4. C₄×C₅²	C₄	semidirect
5. C₅×Dic₅	C₄	direct (N × H)
7. C₄×Dic₅	C₅	direct (N × H)
15. C₅²	C₄²	semidirect
21. C₄×C₅	Dic₅	direct (N × H)
22. C₄×C₅	C₄×C₅	semidirect
23. Dic₅	C₄×C₅	direct (N × H)
34. C₅	C₄×Dic₅	direct (N × H)
35. C₅	C₄²×C₅	semidirect
38. C₄	C₅×Dic₅	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×C₅²	2
C₂×C₅×Dic₅	2
C₄²×C₅	5
C₄×Dic₅	5

Subgroups — C4×C5×Dic5 #87789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×Dic₅ #87789