Subgroups — C₂²⋊(C₅⋊D₅) #6049

Order 200.

64 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	#1039	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	C₂²⋊D₅	—	5	6	no	maximal
8	C₅²	D₄	1	1	yes	characteristic, complemented, Sylow
9	C₂²×C₅	D₅	1	6	yes	complemented
10	C₂×D₅	—	5	6	no	—
11	Dic₅	—	5	6	no	—
12	C₂×C₅	—	2	6	no	—
13	C₂×C₅	C₂×D₅	1	6	yes	—
14	D₅	—	10	6	no	—
15	D₄	—	25	1	no	Sylow
16	C₅	C₂²⋊D₅	1	6	yes	complemented
17	C₂²	—	25	1	no	—
18	C₂²	C₅⋊D₅	1	1	yes	characteristic, complemented
19	C₄	—	25	1	no	—
20	C₂	—	2	1	no	—
21	C₂	—	50	1	no	—
22	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.