Subgroups — C₂×Dic₅₀ #87741

Order 400.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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