Subgroups — (((C₅⋊D₅)⋊C₅)⋊C₂)⋊C₂ #11758707

Order 1000.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	((C₅⋊D₅)⋊C₅)⋊C₂	C₂	1	2	yes	maximal, complemented
2	#92539	C₂	1	1	yes	maximal, characteristic, complemented
3	#6953	C₂²	1	1	yes	characteristic
4	(C₅⋊D₅)⋊C₅	—	2	2	no	—
5	H(3,𝔽₅)	D₄	1	1	yes	characteristic, complemented, Sylow
6	D₅²	—	10	2	no	—
7	C₅×AGL(1,𝔽₅)	—	10	1	no	—
8	C₅⋊D₅	—	2	2	no	—
9	C₅×D₅	—	10	1	no	—
10	C₅×D₅	—	10	2	no	—
11	C₅×D₅	—	10	2	no	—
12	D₂₀	—	25	1	no	maximal
13	C₅²	—	2	2	no	—
14	C₅²	—	2	1	no	—
15	C₂×D₅	—	25	2	no	—
16	C₂×D₅	—	50	2	no	—
17	AGL(1,𝔽₅)	—	10	1	no	—
18	C₄×C₅	—	25	1	no	—
19	C₂×C₅	—	25	1	no	—
20	C₂×C₅	—	50	2	no	—
21	D₅	—	10	1	no	—
22	D₅	—	10	2	no	—
23	D₅	—	10	2	no	—
24	D₅	—	50	2	no	—
25	D₄	—	125	1	no	Sylow
26	C₅	—	10	2	no	—
27	C₅	—	10	1	no	—
28	C₅	D₅²⋊C₂	1	1	yes	characteristic
29	C₂²	—	125	2	no	—
30	C₄	—	25	1	no	—
31	C₂	—	25	1	no	—
32	C₂	—	50	2	no	—

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.