Subgroups — #87773

Order 400.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6045	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₅×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₅	—	2	1	no	—
5	C₄×C₅²	C₂²	1	1	yes	characteristic
6	#1039	—	2	1	no	—
7	#687	—	5	1	no	maximal
8	#677	—	5	1	no	maximal
9	C₂×C₅²	D₄	1	1	yes	characteristic
10	C₅×D₅	—	4	1	no	—
11	C₅×D₄	—	5	1	no	—
12	D₂₀	D₅	1	1	yes	characteristic
13	Dic₁₀	—	5	1	no	—
14	Dic₁₀	—	5	1	no	—
15	Dic₁₀	—	10	2	no	—
16	C₅×C₈	—	5	1	no	—
17	#168	D₅	1	1	yes	characteristic, complemented
18	C₅²	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	—	10	1	no	—
20	C₂×D₅	—	2	1	no	—
21	C₄×C₅	—	2	2	no	—
22	C₄×C₅	C₂×D₅	1	1	yes	characteristic
23	C₄×C₅	C₂×D₅	1	1	yes	characteristic
24	Dic₅	—	10	4	no	—
25	Dic₅	—	10	1	no	—
26	Dic₅	—	10	1	no	—
27	SD₁₆	—	25	1	no	Sylow
28	C₂×C₅	—	2	2	no	—
29	C₂×C₅	—	20	1	no	—
30	C₂×C₅	D₂₀	1	1	yes	characteristic
31	C₂×C₅	C₂²⋊D₅	1	1	yes	characteristic
32	D₅	—	4	1	no	—
33	Q₈	—	25	1	no	—
34	D₄	—	5	1	no	—
35	C₈	—	5	1	no	—
36	C₅	—	2	2	no	—
37	C₅	#677	1	1	yes	characteristic, complemented
38	C₅	#687	1	1	yes	characteristic, complemented
39	C₂²	—	10	1	no	—
40	C₄	—	50	1	no	—
41	C₄	D₅²	1	1	yes	characteristic
42	C₂	—	20	1	no	—
43	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.