Subgroups — C₂×C₅×Dic₅ #6043

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
2	C₅×Dic₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²	C₄	1	2	yes	complemented
4	C₂×C₅²	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅	—	5	1	no	maximal
6	C₂×Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
8	C₂²×C₅	—	2	2	no	—
9	C₂²×C₅	D₅	1	1	yes	characteristic
10	C₂²×C₅	C₂×C₅	1	1	yes	characteristic
11	C₄×C₅	—	5	2	no	—
12	Dic₅	C₂×C₅	1	2	yes	direct product factor
13	C₂×C₅	—	2	4	no	—
14	C₂×C₅	—	2	2	no	—
15	C₂×C₅	Dic₅	1	2	yes	direct product factor
16	C₂×C₅	C₄×C₅	1	2	yes	complemented
17	C₂×C₅	C₂×D₅	1	1	yes	characteristic
18	C₂×C₅	C₂²×C₅	1	1	yes	characteristic
19	C₂×C₄	—	5	1	no	Sylow
20	C₅	—	2	2	no	—
21	C₅	C₂×Dic₅	1	1	yes	characteristic, direct product factor
22	C₅	C₂×C₄×C₅	1	1	yes	characteristic, complemented
23	C₂²	C₅×D₅	1	1	yes	characteristic
24	C₄	—	5	2	no	—
25	C₂	C₅×Dic₅	1	2	yes	direct product factor
26	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.