Subgroups — Q₈×D₂₅ #87747

Order 400.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₂₅	C₂	1	3	yes	maximal
3	Dic₅₀	C₂	1	3	yes	maximal, complemented
4	C₂×D₂₅	C₂²	1	1	yes	characteristic
5	C₄×C₂₅	C₂²	1	3	yes	—
6	Dic₂₅	C₂²	1	3	yes	—
7	Q₈×D₅	—	5	1	no	maximal
8	C₂×C₂₅	C₂³	1	1	yes	characteristic
9	D₂₅	Q₈	1	2	yes	direct product factor
10	C₅×Q₈	D₅	1	1	yes	characteristic
11	C₄×D₅	—	5	3	no	—
12	Dic₁₀	—	5	3	no	—
13	C₂₅	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
14	C₂×D₅	—	5	1	no	—
15	C₄×C₅	C₂×D₅	1	3	yes	—
16	Dic₅	—	5	3	no	—
17	C₂×Q₈	—	25	1	no	Sylow
18	C₂×C₅	C₂²×D₅	1	1	yes	characteristic
19	D₅	—	5	2	no	—
20	Q₈	—	25	3	no	—
21	Q₈	D₂₅	1	1	yes	characteristic, direct product factor
22	C₂×C₄	—	25	3	no	—
23	C₅	Q₈×D₅	1	1	yes	characteristic
24	C₂²	—	25	1	no	—
25	C₄	—	25	3	no	—
26	C₄	C₂×D₂₅	1	3	yes	—
27	C₂	—	25	2	no	—
28	C₂	C₂²×D₂₅	1	1	yes	characteristic

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

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