Subgroups — C₂₅×C₄⋊Q₈ #11716530

Order 800.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₂₅	C₂	1	2	yes	maximal
2	C₄⋊C₄×C₂₅	C₂	1	4	yes	maximal
3	C₄²×C₂₅	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₂₅	—	2	4	no	—
5	C₂×C₄×C₂₅	C₂²	1	4	yes	—
6	C₂×C₄×C₂₅	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₂₅	C₂²	1	2	yes	—
8	C₅×C₄⋊Q₈	C₅	1	1	yes	maximal, characteristic
9	C₂²×C₂₅	C₂³	1	1	yes	characteristic
10	C₄×C₂₅	—	2	4	no	—
11	C₄×C₂₅	D₄	1	2	yes	—
12	C₄×C₂₅	Q₈	1	4	yes	complemented
13	C₂×C₅×Q₈	C₂×C₅	1	2	yes	—
14	C₅×C₄⋊C₄	C₂×C₅	1	4	yes	—
15	C₄²×C₅	C₂×C₅	1	1	yes	characteristic
16	C₂×C₂₅	C₂×D₄	1	1	yes	characteristic
17	C₂×C₂₅	C₂×Q₈	1	2	yes	—
18	C₅×Q₈	—	2	4	no	—
19	C₂×C₄×C₅	C₂²×C₅	1	4	yes	—
20	C₂×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
21	C₂×C₄×C₅	C₂²×C₅	1	2	yes	—
22	C₄⋊Q₈	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₂₅	C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₅	C₂³×C₅	1	1	yes	characteristic
25	C₄×C₅	—	2	4	no	—
26	C₄×C₅	C₅×D₄	1	2	yes	—
27	C₄×C₅	C₅×Q₈	1	4	yes	—
28	C₂×Q₈	C₂×C₂₅	1	2	yes	—
29	C₄⋊C₄	C₂×C₂₅	1	4	yes	—
30	C₄²	C₂×C₂₅	1	1	yes	characteristic
31	C₂×C₅	C₂×C₅×D₄	1	1	yes	characteristic
32	C₂×C₅	C₂×C₅×Q₈	1	2	yes	—
33	Q₈	—	2	4	no	—
34	C₂×C₄	C₂²×C₂₅	1	4	yes	—
35	C₂×C₄	C₂²×C₂₅	1	1	yes	characteristic
36	C₂×C₄	C₂²×C₂₅	1	2	yes	—
37	C₅	C₅×C₄⋊Q₈	1	1	yes	characteristic
38	C₂²	C₂³×C₂₅	1	1	yes	characteristic
39	C₄	—	2	4	no	—
40	C₄	D₄×C₂₅	1	2	yes	—
41	C₄	Q₈×C₂₅	1	4	yes	complemented
42	C₂	C₂×D₄×C₂₅	1	1	yes	characteristic
43	C₂	C₂×Q₈×C₂₅	1	2	yes	—

	subgroup	G/H
center	C₂²×C₂₅	C₂³
commutator	C₂²	C₂³×C₂₅
Frattini, socle, prime radical, cosocle	C₂²×C₅	C₂³×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₄×C₂₅	Q₈	semidirect
22. C₄⋊Q₈	C₂₅	direct (N × H)
23. C₂₅	C₄⋊Q₈	direct (N × H)
41. C₄	Q₈×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₂₅	2
C₄⋊C₄×C₂₅	2
C₄²×C₂₅	2
C₅×C₄⋊Q₈	5

Subgroups — C25×C4⋊Q8 #11716530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×C₄⋊Q₈ #11716530