Subgroups — C₅×C₂²⋊Dic₅ #87797

Order 400.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₅	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅²	—	2	2	no	—
4	C₂²×C₅²	C₄	1	2	yes	complemented
5	C₂²×C₅²	C₂²	1	1	yes	characteristic
6	C₅×Dic₅	—	2	2	no	—
7	C₅×C₂²⋊C₄	—	5	1	no	maximal
8	C₂²⋊Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅²	—	2	2	no	—
10	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
11	C₂×C₅²	D₄	1	2	yes	—
12	C₂³×C₅	—	2	2	no	—
13	C₂³×C₅	D₅	1	1	yes	characteristic
14	C₂³×C₅	C₂×C₅	1	1	yes	characteristic
15	C₂×C₄×C₅	—	5	2	no	—
16	C₂×Dic₅	C₂×C₅	1	2	yes	complemented
17	C₅²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₅	—	2	8	no	—
19	C₂²×C₅	—	2	2	no	—
20	C₂²×C₅	—	2	2	no	—
21	C₂²×C₅	—	2	4	no	—
22	C₂²×C₅	—	2	2	no	—
23	C₂²×C₅	Dic₅	1	2	yes	complemented
24	C₂²×C₅	C₄×C₅	1	2	yes	complemented
25	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
26	C₂²×C₅	C₂²×C₅	1	1	yes	characteristic
27	C₄×C₅	—	10	2	no	—
28	Dic₅	—	2	2	no	—
29	C₂²⋊C₄	—	5	1	no	Sylow
30	C₂×C₅	—	2	8	no	—
31	C₂×C₅	—	2	2	no	—
32	C₂×C₅	—	2	2	no	—
33	C₂×C₅	—	2	2	no	—
34	C₂×C₅	—	2	4	no	—
35	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
36	C₂×C₅	C₂²⋊D₅	1	2	yes	—
37	C₂×C₅	C₂×C₄×C₅	1	1	yes	characteristic
38	C₂×C₅	C₅×D₄	1	2	yes	—
39	C₂³	C₅×D₅	1	1	yes	characteristic
40	C₂×C₄	—	5	2	no	—
41	C₅	—	2	2	no	—
42	C₅	C₂²⋊Dic₅	1	1	yes	characteristic, direct product factor
43	C₅	C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented
44	C₂²	—	2	2	no	—
45	C₂²	C₅×Dic₅	1	2	yes	complemented
46	C₂²	C₂×C₅×D₅	1	1	yes	characteristic
47	C₄	—	10	2	no	—
48	C₂	—	2	2	no	—
49	C₂	C₂×C₅×Dic₅	1	1	yes	characteristic
50	C₂	C₅×C₂²⋊D₅	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₅
commutator	C₂×C₅	C₂×C₄×C₅
Frattini	C₂²	C₂×C₅×D₅
Fitting, prime radical	C₂³×C₅²	C₂
socle	C₂²×C₅²	C₂²
cosocle	C₂²×C₅	C₂²×C₅
hypercenter	C₂³×C₅	D₅
hypocenter	C₅	C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Dic₅	C₂	semidirect
4. C₂²×C₅²	C₄	semidirect
8. C₂²⋊Dic₅	C₅	direct (N × H)
16. C₂×Dic₅	C₂×C₅	semidirect
17. C₅²	C₂²⋊C₄	semidirect
23. C₂²×C₅	Dic₅	semidirect
24. C₂²×C₅	C₄×C₅	semidirect
42. C₅	C₂²⋊Dic₅	direct (N × H)
43. C₅	C₅×C₂²⋊C₄	semidirect
45. C₂²	C₅×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅²	2
C₂×C₅×Dic₅	2
C₅×C₂²⋊C₄	5
C₂²⋊Dic₅	5

Subgroups — C5×C22⋊Dic5 #87797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊Dic₅ #87797