Subgroups — #87720

Order 400.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂₅	C₂²	1	1	yes	characteristic
5	C₂×D₂₅	—	2	1	no	—
6	C₂×D₂₅	—	2	1	no	—
7	C₂×D₂₅	C₄	1	2	yes	complemented
8	C₄×C₂₅	—	2	1	no	—
9	Dic₂₅	—	2	1	no	—
10	#685	—	5	1	no	maximal
11	C₂×C₂₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₂₅	D₄	1	1	yes	characteristic
13	C₂×C₂₅	D₄	1	1	yes	characteristic
14	D₂₅	—	2	2	no	—
15	C₂²×D₅	—	5	1	no	—
16	C₂×C₄×C₅	D₅	1	1	yes	characteristic
17	C₂×Dic₅	—	5	1	no	—
18	C₂₅	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
20	C₂×D₅	—	5	2	no	—
21	C₂×D₅	—	10	1	no	—
22	C₂×D₅	—	10	1	no	—
23	C₄×C₅	—	2	1	no	—
24	Dic₅	—	10	1	no	—
25	C₂²⋊C₄	—	25	1	no	Sylow
26	C₂×C₅	C₄×D₅	1	1	yes	characteristic
27	C₂×C₅	D₂₀	1	1	yes	characteristic
28	C₂×C₅	C₂²⋊D₅	1	1	yes	characteristic
29	D₅	—	10	2	no	—
30	C₂³	—	25	1	no	—
31	C₂×C₄	—	25	1	no	—
32	C₂×C₄	D₂₅	1	1	yes	characteristic, complemented
33	C₅	#685	1	1	yes	characteristic
34	C₂²	—	25	2	no	—
35	C₂²	—	50	1	no	—
36	C₂²	—	50	1	no	—
37	C₂²	C₂×D₂₅	1	1	yes	characteristic
38	C₄	—	2	1	no	—
39	C₄	—	50	1	no	—
40	C₂	—	50	2	no	—
41	C₂	C₄×D₂₅	1	1	yes	characteristic
42	C₂	D₁₀₀	1	1	yes	characteristic
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.