Subgroups — D₄×D₂₅ #87745

Order 400.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₅	C₂	1	2	yes	maximal, complemented
2	D₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊D₂₅	C₂	1	2	yes	maximal, complemented
4	D₁₀₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₅	C₂²	1	2	yes	complemented
7	C₂×D₂₅	—	2	4	no	—
8	C₂×D₂₅	C₂²	1	1	yes	characteristic
9	C₂×D₂₅	C₂²	1	2	yes	complemented
10	C₄×C₂₅	C₂²	1	1	yes	characteristic, complemented
11	Dic₂₅	C₂²	1	1	yes	characteristic, complemented
12	D₄×D₅	—	5	1	no	maximal
13	C₂×C₂₅	—	2	2	no	—
14	C₂×C₂₅	C₂³	1	1	yes	characteristic
15	D₂₅	—	2	2	no	—
16	D₂₅	D₄	1	2	yes	direct product factor
17	C₂²×D₅	—	5	2	no	—
18	C₅×D₄	D₅	1	1	yes	characteristic
19	C₂²⋊D₅	—	5	2	no	—
20	D₂₀	—	5	1	no	—
21	C₄×D₅	—	5	1	no	—
22	C₂₅	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
23	C₂²×C₅	C₂×D₅	1	2	yes	—
24	C₂×D₅	—	5	1	no	—
25	C₂×D₅	—	5	2	no	—
26	C₂×D₅	—	10	4	no	—
27	C₄×C₅	C₂×D₅	1	1	yes	characteristic
28	Dic₅	—	5	1	no	—
29	C₂×D₄	—	25	1	no	Sylow
30	C₂×C₅	—	2	2	no	—
31	C₂×C₅	C₂²×D₅	1	1	yes	characteristic
32	D₅	—	5	2	no	—
33	D₅	—	10	2	no	—
34	C₂³	—	25	2	no	—
35	D₄	—	25	2	no	—
36	D₄	—	25	1	no	—
37	D₄	D₂₅	1	1	yes	characteristic, direct product factor
38	C₂×C₄	—	25	1	no	—
39	C₅	D₄×D₅	1	1	yes	characteristic
40	C₂²	—	25	1	no	—
41	C₂²	—	25	2	no	—
42	C₂²	—	50	4	no	—
43	C₂²	C₂×D₂₅	1	2	yes	complemented
44	C₄	—	25	1	no	—
45	C₄	C₂×D₂₅	1	1	yes	characteristic, complemented
46	C₂	—	2	2	no	—
47	C₂	—	25	2	no	—
48	C₂	—	50	2	no	—
49	C₂	C₂²×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₂₅
commutator, cosocle	C₂×C₂₅	C₂³
Frattini, socle	C₂×C₅	C₂²×D₅
Fitting	D₄×C₂₅	C₂
hypercenter	D₄	D₂₅
hypocenter	C₂₅	C₂×D₄
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₂₅	C₂	semidirect
2. D₄×C₂₅	C₂	semidirect
3. C₂²⋊D₂₅	C₂	semidirect
4. D₁₀₀	C₂	semidirect
5. C₄×D₂₅	C₂	semidirect
6. C₂²×C₂₅	C₂²	semidirect
9. C₂×D₂₅	C₂²	semidirect
10. C₄×C₂₅	C₂²	semidirect
11. Dic₂₅	C₂²	semidirect
16. D₂₅	D₄	direct (N × H)
22. C₂₅	C₂×D₄	semidirect
37. D₄	D₂₅	direct (N × H)
43. C₂²	C₂×D₂₅	semidirect
45. C₄	C₂×D₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₂₅	2
D₄×C₂₅	2
C₂²⋊D₂₅	2
D₁₀₀	2
C₄×D₂₅	2
D₄×D₅	5

Subgroups — D4×D25 #87745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×D₂₅ #87745