Subgroups — C₂₅×C₄⋊C₈ #11716396

Order 800.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₂₅	C₂	1	2	yes	maximal
2	C₄²×C₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂₅	C₄	1	1	yes	characteristic
4	C₂×C₄×C₂₅	C₄	1	1	yes	characteristic
5	C₂×C₄×C₂₅	C₂²	1	1	yes	characteristic
6	C₈×C₂₅	—	2	2	no	—
7	C₅×C₄⋊C₈	C₅	1	1	yes	maximal, characteristic
8	C₂²×C₂₅	C₂×C₄	1	1	yes	characteristic
9	C₄×C₂₅	—	2	1	no	—
10	C₄×C₂₅	C₈	1	2	yes	complemented
11	C₄×C₂₅	D₄	1	1	yes	characteristic
12	C₄×C₂₅	Q₈	1	1	yes	characteristic
13	C₂×C₅×C₈	C₂×C₅	1	2	yes	—
14	C₄²×C₅	C₂×C₅	1	1	yes	characteristic
15	C₂×C₂₅	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₂₅	C₂×C₈	1	1	yes	characteristic
17	C₂×C₂₅	M₁₆	1	1	yes	characteristic
18	C₂×C₄×C₅	C₄×C₅	1	1	yes	characteristic
19	C₂×C₄×C₅	C₄×C₅	1	1	yes	characteristic
20	C₂×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
21	C₅×C₈	—	2	2	no	—
22	C₄⋊C₈	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₂₅	C₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₅	C₂×C₄×C₅	1	1	yes	characteristic
25	C₄×C₅	—	2	1	no	—
26	C₄×C₅	C₅×C₈	1	2	yes	—
27	C₄×C₅	C₅×D₄	1	1	yes	characteristic
28	C₄×C₅	C₅×Q₈	1	1	yes	characteristic
29	C₂×C₈	C₂×C₂₅	1	2	yes	—
30	C₄²	C₂×C₂₅	1	1	yes	characteristic
31	C₂×C₅	C₅×C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₅	C₂×C₅×C₈	1	1	yes	characteristic
33	C₂×C₅	C₅×M₁₆	1	1	yes	characteristic
34	C₂×C₄	C₄×C₂₅	1	1	yes	characteristic
35	C₂×C₄	C₄×C₂₅	1	1	yes	characteristic
36	C₂×C₄	C₂²×C₂₅	1	1	yes	characteristic
37	C₈	—	2	2	no	—
38	C₅	C₅×C₄⋊C₈	1	1	yes	characteristic
39	C₂²	C₂×C₄×C₂₅	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	C₈×C₂₅	1	2	yes	complemented
42	C₄	D₄×C₂₅	1	1	yes	characteristic
43	C₄	Q₈×C₂₅	1	1	yes	characteristic
44	C₂	C₄⋊C₄×C₂₅	1	1	yes	characteristic
45	C₂	C₂×C₈×C₂₅	1	1	yes	characteristic
46	C₂	M₁₆×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₅	C₂²
commutator	C₂	C₂×C₈×C₂₅
Frattini, cosocle	C₂×C₄×C₅	C₂²×C₅
socle, prime radical	C₂²×C₅	C₂×C₄×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₄×C₂₅	C₈	semidirect
22. C₄⋊C₈	C₂₅	direct (N × H)
23. C₂₅	C₄⋊C₈	direct (N × H)
41. C₄	C₈×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₂₅	2
C₄²×C₂₅	2
C₅×C₄⋊C₈	5

Subgroups — C25×C4⋊C8 #11716396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×C₄⋊C₈ #11716396