Subgroups — C₂×Q₈×C₂₅ #87753

Order 400.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₂₅	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₄×C₂₅	C₂	1	3	yes	maximal
3	C₂²×C₂₅	C₂²	1	1	yes	characteristic
4	C₄×C₂₅	C₂²	1	6	yes	—
5	C₂×C₅×Q₈	C₅	1	1	yes	maximal, characteristic
6	C₂×C₂₅	Q₈	1	2	yes	direct product factor
7	C₂×C₂₅	C₂³	1	1	yes	characteristic
8	C₅×Q₈	C₂×C₅	1	4	yes	—
9	C₂×C₄×C₅	C₂×C₅	1	3	yes	—
10	C₂₅	C₂×Q₈	1	1	yes	characteristic, direct product factor, Sylow
11	C₂²×C₅	C₂²×C₅	1	1	yes	characteristic
12	C₄×C₅	C₂²×C₅	1	6	yes	—
13	C₂×Q₈	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₅	C₅×Q₈	1	2	yes	—
15	C₂×C₅	C₂³×C₅	1	1	yes	characteristic
16	Q₈	C₂×C₂₅	1	4	yes	direct product factor
17	C₂×C₄	C₂×C₂₅	1	3	yes	—
18	C₅	C₂×C₅×Q₈	1	1	yes	characteristic
19	C₂²	C₂²×C₂₅	1	1	yes	characteristic
20	C₄	C₂²×C₂₅	1	6	yes	—
21	C₂	Q₈×C₂₅	1	2	yes	direct product factor
22	C₂	C₂³×C₂₅	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.