Subgroups — #87746

Order 400.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₂₅	C₂	1	2	yes	maximal, complemented
3	C₂×Dic₂₅	C₂	1	2	yes	maximal, complemented
4	C₄×D₂₅	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₅₀	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₅	C₂²	1	2	yes	—
7	C₂×D₂₅	C₂²	1	1	yes	characteristic
8	C₄×C₂₅	C₂²	1	1	yes	characteristic
9	Dic₂₅	C₂²	1	2	yes	—
10	Dic₂₅	C₂²	1	1	yes	characteristic
11	#711	—	5	1	no	maximal
12	C₂×C₂₅	—	2	2	no	—
13	C₂×C₂₅	C₂³	1	1	yes	characteristic
14	D₂₅	—	2	1	no	—
15	C₅×D₄	D₅	1	1	yes	characteristic
16	C₂²⋊D₅	—	5	2	no	—
17	C₂×Dic₅	—	5	2	no	—
18	C₄×D₅	—	5	1	no	—
19	Dic₁₀	—	5	1	no	—
20	C₂₅	#41	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₅	C₂×D₅	1	2	yes	—
22	C₂×D₅	—	5	1	no	—
23	C₄×C₅	C₂×D₅	1	1	yes	characteristic
24	Dic₅	—	5	2	no	—
25	Dic₅	—	5	1	no	—
26	#41	—	25	1	no	Sylow
27	C₂×C₅	—	2	2	no	—
28	C₂×C₅	C₂²×D₅	1	1	yes	characteristic
29	D₅	—	10	1	no	—
30	Q₈	—	25	1	no	—
31	D₄	—	25	2	no	—
32	D₄	D₂₅	1	1	yes	characteristic, complemented
33	C₂×C₄	—	25	2	no	—
34	C₂×C₄	—	25	1	no	—
35	C₅	#711	1	1	yes	characteristic
36	C₂²	—	25	1	no	—
37	C₂²	C₂×D₂₅	1	2	yes	—
38	C₄	—	25	1	no	—
39	C₄	—	25	2	no	—
40	C₄	C₂×D₂₅	1	1	yes	characteristic
41	C₂	—	2	2	no	—
42	C₂	—	50	1	no	—
43	C₂	C₂²×D₂₅	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.