Subgroups — #87771

Order 400.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊D₅	—	2	1	no	—
5	C₂×C₅×D₅	—	2	1	no	—
6	C₄×C₅²	C₂²	1	1	yes	characteristic
7	#686	—	5	1	no	maximal
8	D₄₀	—	5	1	no	maximal
9	C₂×C₅²	D₄	1	1	yes	characteristic
10	C₅⋊D₅	—	4	1	no	—
11	C₅×D₅	—	4	1	no	—
12	C₅×D₄	—	5	1	no	—
13	D₂₀	—	5	1	no	—
14	D₂₀	—	5	1	no	—
15	D₂₀	—	10	2	no	—
16	D₂₀	D₅	1	1	yes	characteristic, complemented
17	C₅×C₈	—	5	1	no	—
18	#168	D₅	1	1	yes	characteristic, complemented
19	C₅²	D₈	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₅	—	10	1	no	—
21	C₂×D₅	—	2	1	no	—
22	C₂×D₅	—	10	4	no	—
23	C₂×D₅	—	10	1	no	—
24	C₂×D₅	—	10	1	no	—
25	C₄×C₅	—	2	2	no	—
26	C₄×C₅	C₂×D₅	1	1	yes	characteristic
27	C₄×C₅	C₂×D₅	1	1	yes	characteristic
28	D₈	—	25	1	no	Sylow
29	C₂×C₅	—	2	2	no	—
30	C₂×C₅	—	20	1	no	—
31	C₂×C₅	D₂₀	1	1	yes	characteristic
32	C₂×C₅	C₂²⋊D₅	1	1	yes	characteristic
33	D₅	—	4	1	no	—
34	D₅	—	20	4	no	—
35	D₅	—	20	1	no	—
36	D₅	—	20	1	no	—
37	D₄	—	5	1	no	—
38	D₄	—	25	1	no	—
39	C₈	—	5	1	no	—
40	C₅	—	2	2	no	—
41	C₅	D₄₀	1	1	yes	characteristic, complemented
42	C₅	#686	1	1	yes	characteristic, complemented
43	C₂²	—	10	1	no	—
44	C₂²	—	50	1	no	—
45	C₄	D₅²	1	1	yes	characteristic
46	C₂	—	20	1	no	—
47	C₂	—	100	1	no	—
48	C₂	#6038	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.