Subgroups — C₅×#687 #87794

Order 400.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₄	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅²	—	2	1	no	—
5	C₄×C₅²	C₂²	1	1	yes	characteristic
6	C₅×Dic₅	—	2	1	no	—
7	C₅×SD₁₆	—	5	1	no	maximal
8	#687	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₅²	—	4	1	no	—
10	C₂×C₅²	D₄	1	1	yes	characteristic
11	C₅×Q₈	—	5	1	no	—
12	C₅×D₄	—	2	2	no	—
13	C₅×D₄	D₅	1	1	yes	characteristic
14	C₅×D₄	C₂×C₅	1	1	yes	characteristic
15	Dic₁₀	C₂×C₅	1	1	yes	characteristic, complemented
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	—	2	4	no	—
20	C₂²×C₅	—	2	1	no	—
21	C₂²×C₅	—	2	1	no	—
22	C₄×C₅	—	2	2	no	—
23	C₄×C₅	—	10	1	no	—
24	C₄×C₅	C₂×D₅	1	1	yes	characteristic
25	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
26	Dic₅	—	2	1	no	—
27	SD₁₆	—	5	1	no	Sylow
28	C₂×C₅	—	2	2	no	—
29	C₂×C₅	—	4	4	no	—
30	C₂×C₅	—	4	1	no	—
31	C₂×C₅	—	4	1	no	—
32	C₂×C₅	C₂²⋊D₅	1	1	yes	characteristic
33	C₂×C₅	C₅×D₄	1	1	yes	characteristic
34	Q₈	—	5	1	no	—
35	D₄	C₅×D₅	1	1	yes	characteristic
36	C₈	—	5	1	no	—
37	C₅	—	2	2	no	—
38	C₅	#687	1	1	yes	characteristic, direct product factor
39	C₅	C₅×SD₁₆	1	1	yes	characteristic, complemented
40	C₂²	—	2	1	no	—
41	C₄	—	10	1	no	—
42	C₄	C₂×C₅×D₅	1	1	yes	characteristic
43	C₂	—	4	1	no	—
44	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.