Subgroups — #87808

Order 400.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#1039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅²	C₂²	1	1	yes	characteristic
5	C₂×C₅⋊D₅	—	2	1	no	—
6	C₂×C₅⋊D₅	—	2	1	no	—
7	C₂×C₅⋊D₅	C₄	1	2	yes	complemented
8	C₄×C₅²	—	2	1	no	—
9	#1039	—	2	1	no	—
10	#685	—	5	6	no	maximal
11	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
12	C₂×C₅²	D₄	1	1	yes	characteristic
13	C₂×C₅²	D₄	1	1	yes	characteristic
14	C₅⋊D₅	—	2	2	no	—
15	C₂²×D₅	—	5	6	no	—
16	C₂×C₄×C₅	D₅	1	6	yes	complemented
17	C₂×Dic₅	—	5	6	no	—
18	C₅²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	C₂×D₅	1	6	yes	—
20	C₂×D₅	—	5	12	no	—
21	C₂×D₅	—	10	6	no	—
22	C₂×D₅	—	10	6	no	—
23	C₄×C₅	—	2	6	no	—
24	Dic₅	—	10	6	no	—
25	C₂²⋊C₄	—	25	1	no	Sylow
26	C₂×C₅	C₄×D₅	1	6	yes	—
27	C₂×C₅	D₂₀	1	6	yes	—
28	C₂×C₅	C₂²⋊D₅	1	6	yes	—
29	D₅	—	10	12	no	—
30	C₂³	—	25	1	no	—
31	C₂×C₄	—	25	1	no	—
32	C₂×C₄	C₅⋊D₅	1	1	yes	characteristic, complemented
33	C₅	#685	1	6	yes	complemented
34	C₂²	—	25	2	no	—
35	C₂²	—	50	1	no	—
36	C₂²	—	50	1	no	—
37	C₂²	C₂×C₅⋊D₅	1	1	yes	characteristic
38	C₄	—	2	1	no	—
39	C₄	—	50	1	no	—
40	C₂	—	50	2	no	—
41	C₂	C₄×C₅⋊D₅	1	1	yes	characteristic
42	C₂	C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
43	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.