Subgroups — C₅×#688 #87795

Order 400.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×Q₈	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	—	2	1	no	—
6	C₄×C₅²	C₂²	1	1	yes	characteristic
7	C₅×SD₁₆	—	5	1	no	maximal
8	#688	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅²	D₄	1	1	yes	characteristic
10	C₅×D₅	—	4	1	no	—
11	C₅×Q₈	—	2	2	no	—
12	C₅×Q₈	D₅	1	1	yes	characteristic, complemented
13	C₅×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×D₄	—	5	1	no	—
15	D₂₀	C₂×C₅	1	1	yes	characteristic
16	C₅×C₈	—	5	1	no	—
17	#168	C₂×C₅	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	4	no	—
22	C₄×C₅	—	2	1	no	—
23	C₄×C₅	—	2	1	no	—
24	C₄×C₅	—	2	2	no	—
25	C₄×C₅	C₂×D₅	1	1	yes	characteristic
26	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
27	SD₁₆	—	5	1	no	Sylow
28	C₂×C₅	—	2	2	no	—
29	C₂×C₅	—	20	1	no	—
30	C₂×C₅	C₂²⋊D₅	1	1	yes	characteristic
31	C₂×C₅	C₅×D₄	1	1	yes	characteristic
32	D₅	—	4	1	no	—
33	Q₈	C₅×D₅	1	1	yes	characteristic, complemented
34	D₄	—	5	1	no	—
35	C₈	—	5	1	no	—
36	C₅	—	2	2	no	—
37	C₅	#688	1	1	yes	characteristic, direct product factor
38	C₅	C₅×SD₁₆	1	1	yes	characteristic, complemented
39	C₂²	—	10	1	no	—
40	C₄	—	2	1	no	—
41	C₄	C₂×C₅×D₅	1	1	yes	characteristic
42	C₂	—	20	1	no	—
43	C₂	C₅×C₂²⋊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.