Subgroups — C₅×C₂²⋊D₅ #6044

Order 200.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²	—	2	1	no	—
5	C₂×C₅²	C₂²	1	1	yes	characteristic
6	C₅×D₅	—	2	1	no	—
7	C₅×D₄	—	5	1	no	maximal
8	C₂²⋊D₅	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₅²	D₄	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₅	—	2	2	no	—
11	C₂²×C₅	—	5	1	no	—
12	C₂²×C₅	D₅	1	1	yes	characteristic, complemented
13	C₂²×C₅	C₂×C₅	1	1	yes	characteristic, complemented
14	C₂×D₅	C₂×C₅	1	1	yes	characteristic, complemented
15	C₄×C₅	—	5	1	no	—
16	Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
17	C₂×C₅	—	2	4	no	—
18	C₂×C₅	—	2	1	no	—
19	C₂×C₅	—	2	1	no	—
20	C₂×C₅	—	2	2	no	—
21	C₂×C₅	—	10	1	no	—
22	C₂×C₅	C₂×D₅	1	1	yes	characteristic
23	C₂×C₅	C₂²×C₅	1	1	yes	characteristic
24	D₅	—	2	1	no	—
25	D₄	—	5	1	no	Sylow
26	C₅	—	2	2	no	—
27	C₅	C₂²⋊D₅	1	1	yes	characteristic, direct product factor
28	C₅	C₅×D₄	1	1	yes	characteristic, complemented
29	C₂²	—	5	1	no	—
30	C₂²	C₅×D₅	1	1	yes	characteristic, complemented
31	C₄	—	5	1	no	—
32	C₂	—	2	1	no	—
33	C₂	—	10	1	no	—
34	C₂	C₂×C₅×D₅	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.