Subgroups — C₂×C₂²⋊(C₅⋊D₅) #87906

Order 400.

216 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, complemented
2	C₂²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊(C₅⋊D₅)	C₂	1	4	yes	maximal, direct product factor
4	C₂×#1039	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅²	—	2	2	no	—
6	C₂²×C₅²	C₂²	1	1	yes	characteristic
7	C₂²×C₅²	C₂²	1	2	yes	complemented
8	C₂×C₅⋊D₅	—	2	2	no	—
9	C₂×C₅⋊D₅	C₂²	1	2	yes	complemented
10	#1039	C₂²	1	2	yes	complemented
11	C₂×C₂²⋊D₅	—	5	6	no	maximal
12	C₂×C₅²	—	2	2	no	—
13	C₂×C₅²	D₄	1	2	yes	complemented
14	C₂×C₅²	C₂³	1	1	yes	characteristic
15	C₅⋊D₅	—	2	2	no	—
16	C₂³×C₅	D₅	1	6	yes	complemented
17	C₂²×D₅	—	5	6	no	—
18	C₂²⋊D₅	—	5	24	no	—
19	C₂×Dic₅	—	5	6	no	—
20	C₅²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₅	—	2	12	no	—
22	C₂²×C₅	C₂×D₅	1	6	yes	—
23	C₂²×C₅	C₂×D₅	1	12	yes	complemented
24	C₂×D₅	—	5	12	no	—
25	C₂×D₅	—	10	12	no	—
26	Dic₅	—	5	12	no	—
27	C₂×D₄	—	25	1	no	Sylow
28	C₂×C₅	—	2	12	no	—
29	C₂×C₅	C₂²⋊D₅	1	12	yes	complemented
30	C₂×C₅	C₂²×D₅	1	6	yes	—
31	D₅	—	10	12	no	—
32	C₂³	—	25	1	no	—
33	C₂³	C₅⋊D₅	1	1	yes	characteristic, complemented
34	D₄	—	25	4	no	—
35	C₂×C₄	—	25	1	no	—
36	C₅	C₂×C₂²⋊D₅	1	6	yes	complemented
37	C₂²	—	2	2	no	—
38	C₂²	—	25	2	no	—
39	C₂²	—	50	2	no	—
40	C₂²	C₂×C₅⋊D₅	1	1	yes	characteristic
41	C₂²	C₂×C₅⋊D₅	1	2	yes	complemented
42	C₄	—	25	2	no	—
43	C₂	—	2	2	no	—
44	C₂	—	50	2	no	—
45	C₂	C₂²⋊(C₅⋊D₅)	1	2	yes	direct product factor
46	C₂	C₂²×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₅⋊D₅
commutator, cosocle	C₂×C₅²	C₂³
Frattini	C₂	C₂²×C₅⋊D₅
Fitting	C₂³×C₅²	C₂
socle	C₂²×C₅²	C₂²
hypercenter	C₂³	C₅⋊D₅
hypocenter	C₅²	C₂×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅²	C₂	semidirect
2. C₂²×C₅⋊D₅	C₂	semidirect
3. C₂²⋊(C₅⋊D₅)	C₂	direct (N × H)
4. C₂×#1039	C₂	semidirect
7. C₂²×C₅²	C₂²	semidirect
9. C₂×C₅⋊D₅	C₂²	semidirect
10. #1039	C₂²	semidirect
13. C₂×C₅²	D₄	semidirect
16. C₂³×C₅	D₅	semidirect
20. C₅²	C₂×D₄	semidirect
23. C₂²×C₅	C₂×D₅	semidirect
29. C₂×C₅	C₂²⋊D₅	semidirect
33. C₂³	C₅⋊D₅	semidirect
36. C₅	C₂×C₂²⋊D₅	semidirect
41. C₂²	C₂×C₅⋊D₅	semidirect
45. C₂	C₂²⋊(C₅⋊D₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅²	2
C₂²×C₅⋊D₅	2
C₂²⋊(C₅⋊D₅)	2
C₂×#1039	2
C₂×C₂²⋊D₅	5

Subgroups — C2×C22⋊(C5⋊D5) #87906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊(C₅⋊D₅) #87906