Subgroups — C₂×C₄⋊(C₅⋊D₅) #87899

Order 400.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅⋊D₅	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₅⋊D₅)	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅²	C₂²	1	1	yes	characteristic
5	C₂×C₅⋊D₅	—	2	4	no	—
6	C₂×C₅⋊D₅	C₂²	1	4	yes	complemented
7	C₄×C₅²	C₂²	1	2	yes	complemented
8	C₂×D₂₀	—	5	6	no	maximal
9	C₂×C₅²	D₄	1	2	yes	complemented
10	C₂×C₅²	C₂³	1	1	yes	characteristic
11	C₅⋊D₅	—	2	4	no	—
12	C₂²×D₅	—	5	12	no	—
13	C₂×C₄×C₅	D₅	1	6	yes	complemented
14	D₂₀	—	5	24	no	—
15	C₅²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅	C₂×D₅	1	6	yes	—
17	C₂×D₅	—	5	24	no	—
18	C₂×D₅	—	10	24	no	—
19	C₄×C₅	C₂×D₅	1	12	yes	complemented
20	C₂×D₄	—	25	1	no	Sylow
21	C₂×C₅	D₂₀	1	12	yes	complemented
22	C₂×C₅	C₂²×D₅	1	6	yes	—
23	D₅	—	10	24	no	—
24	C₂³	—	25	2	no	—
25	D₄	—	25	4	no	—
26	C₂×C₄	C₅⋊D₅	1	1	yes	characteristic, complemented
27	C₅	C₂×D₂₀	1	6	yes	complemented
28	C₂²	—	25	4	no	—
29	C₂²	—	50	4	no	—
30	C₂²	C₂×C₅⋊D₅	1	1	yes	characteristic
31	C₄	C₂×C₅⋊D₅	1	2	yes	complemented
32	C₂	—	50	4	no	—
33	C₂	C₄⋊(C₅⋊D₅)	1	2	yes	direct product factor
34	C₂	C₂²×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.