Subgroups — D₄×C₅⋊D₅ #87901

Order 400.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅⋊D₅	C₂	1	2	yes	maximal, complemented
2	C₅²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊(C₅⋊D₅)	C₂	1	2	yes	maximal, complemented
4	C₄⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅²	C₂²	1	2	yes	complemented
7	C₂×C₅⋊D₅	—	2	4	no	—
8	C₂×C₅⋊D₅	C₂²	1	1	yes	characteristic
9	C₂×C₅⋊D₅	C₂²	1	2	yes	complemented
10	C₄×C₅²	C₂²	1	1	yes	characteristic, complemented
11	#1039	C₂²	1	1	yes	characteristic, complemented
12	D₄×D₅	—	5	6	no	maximal
13	C₂×C₅²	—	2	2	no	—
14	C₂×C₅²	C₂³	1	1	yes	characteristic
15	C₅⋊D₅	—	2	2	no	—
16	C₅⋊D₅	D₄	1	2	yes	direct product factor
17	C₂²×D₅	—	5	12	no	—
18	C₅×D₄	D₅	1	6	yes	complemented
19	C₂²⋊D₅	—	5	12	no	—
20	D₂₀	—	5	6	no	—
21	C₄×D₅	—	5	6	no	—
22	C₅²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
23	C₂²×C₅	C₂×D₅	1	12	yes	complemented
24	C₂×D₅	—	5	6	no	—
25	C₂×D₅	—	5	12	no	—
26	C₂×D₅	—	10	24	no	—
27	C₄×C₅	C₂×D₅	1	6	yes	complemented
28	Dic₅	—	5	6	no	—
29	C₂×D₄	—	25	1	no	Sylow
30	C₂×C₅	—	2	12	no	—
31	C₂×C₅	C₂²×D₅	1	6	yes	—
32	D₅	—	5	12	no	—
33	D₅	—	10	12	no	—
34	C₂³	—	25	2	no	—
35	D₄	—	25	2	no	—
36	D₄	—	25	1	no	—
37	D₄	C₅⋊D₅	1	1	yes	characteristic, direct product factor
38	C₂×C₄	—	25	1	no	—
39	C₅	D₄×D₅	1	6	yes	complemented
40	C₂²	—	25	1	no	—
41	C₂²	—	25	2	no	—
42	C₂²	—	50	4	no	—
43	C₂²	C₂×C₅⋊D₅	1	2	yes	complemented
44	C₄	—	25	1	no	—
45	C₄	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented
46	C₂	—	2	2	no	—
47	C₂	—	25	2	no	—
48	C₂	—	50	2	no	—
49	C₂	C₂²×C₅⋊D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅⋊D₅	C₂	semidirect
2. C₅²×D₄	C₂	semidirect
3. C₂²⋊(C₅⋊D₅)	C₂	semidirect
4. C₄⋊(C₅⋊D₅)	C₂	semidirect
5. C₄×C₅⋊D₅	C₂	semidirect
6. C₂²×C₅²	C₂²	semidirect
9. C₂×C₅⋊D₅	C₂²	semidirect
10. C₄×C₅²	C₂²	semidirect
11. #1039	C₂²	semidirect
16. C₅⋊D₅	D₄	direct (N × H)
18. C₅×D₄	D₅	semidirect
22. C₅²	C₂×D₄	semidirect
23. C₂²×C₅	C₂×D₅	semidirect
27. C₄×C₅	C₂×D₅	semidirect
37. D₄	C₅⋊D₅	direct (N × H)
39. C₅	D₄×D₅	semidirect
43. C₂²	C₂×C₅⋊D₅	semidirect
45. C₄	C₂×C₅⋊D₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅⋊D₅	2
C₅²×D₄	2
C₂²⋊(C₅⋊D₅)	2
C₄⋊(C₅⋊D₅)	2
C₄×C₅⋊D₅	2
D₄×D₅	5

Subgroups — D4×C5⋊D5 #87901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₅⋊D₅ #87901