Subgroups — C₂²×C₄×C₂₅ #87751

Order 400.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₂₅	C₄	1	4	yes	direct product factor
4	C₂²×C₂₅	C₂²	1	3	yes	—
5	C₄×C₂₅	C₂²	1	4	yes	direct product factor
6	C₂²×C₄×C₅	C₅	1	1	yes	maximal, characteristic
7	C₂×C₂₅	C₂×C₄	1	6	yes	direct product factor
8	C₂×C₂₅	C₂³	1	1	yes	characteristic
9	C₂³×C₅	C₂×C₅	1	1	yes	characteristic
10	C₂×C₄×C₅	C₂×C₅	1	6	yes	—
11	C₂₅	C₂²×C₄	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₅	C₄×C₅	1	4	yes	—
13	C₂²×C₅	C₂²×C₅	1	3	yes	—
14	C₄×C₅	C₂²×C₅	1	4	yes	—
15	C₂²×C₄	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₅	C₂×C₄×C₅	1	6	yes	—
17	C₂×C₅	C₂³×C₅	1	1	yes	characteristic
18	C₂³	C₂×C₂₅	1	1	yes	characteristic
19	C₂×C₄	C₂×C₂₅	1	6	yes	direct product factor
20	C₅	C₂²×C₄×C₅	1	1	yes	characteristic
21	C₂²	C₄×C₂₅	1	4	yes	direct product factor
22	C₂²	C₂²×C₂₅	1	3	yes	—
23	C₄	C₂²×C₂₅	1	4	yes	direct product factor
24	C₂	C₂×C₄×C₂₅	1	6	yes	direct product factor
25	C₂	C₂³×C₂₅	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.