Subgroups — #87900

Order 400.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊(C₅⋊D₅)	C₂	1	2	yes	maximal, complemented
3	C₄⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅⋊D₅	C₂	1	2	yes	maximal, complemented
5	#6045	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅²	C₂²	1	1	yes	characteristic
7	C₂×C₅⋊D₅	C₂²	1	2	yes	—
8	C₄×C₅²	C₂²	1	1	yes	characteristic
9	C₄×C₅²	C₂²	1	1	yes	characteristic
10	#1039	C₂²	1	2	yes	—
11	#709	—	5	6	no	maximal
12	C₂×C₅²	—	2	1	no	—
13	C₂×C₅²	C₂³	1	1	yes	characteristic
14	C₅⋊D₅	—	2	2	no	—
15	C₂×C₄×C₅	D₅	1	6	yes	complemented
16	C₂²⋊D₅	—	5	12	no	—
17	D₂₀	—	5	6	no	—
18	C₄×D₅	—	5	12	no	—
19	Dic₁₀	—	5	6	no	—
20	C₅²	#41	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₅	C₂×D₅	1	6	yes	—
22	C₂×D₅	—	5	12	no	—
23	C₄×C₅	C₂×D₅	1	6	yes	—
24	C₄×C₅	C₂×D₅	1	6	yes	—
25	Dic₅	—	5	12	no	—
26	#41	—	25	1	no	Sylow
27	C₂×C₅	—	2	6	no	—
28	C₂×C₅	C₂²×D₅	1	6	yes	—
29	D₅	—	10	12	no	—
30	Q₈	—	25	1	no	—
31	D₄	—	25	2	no	—
32	D₄	—	25	1	no	—
33	C₂×C₄	—	25	2	no	—
34	C₂×C₄	C₅⋊D₅	1	1	yes	characteristic, complemented
35	C₅	#709	1	6	yes	complemented
36	C₂²	—	25	2	no	—
37	C₂²	C₂×C₅⋊D₅	1	1	yes	characteristic
38	C₄	—	25	2	no	—
39	C₄	C₂×C₅⋊D₅	1	1	yes	characteristic
40	C₄	C₂×C₅⋊D₅	1	1	yes	characteristic
41	C₂	—	2	1	no	—
42	C₂	—	50	2	no	—
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.