Subgroups — C₂×D₄×C₂₅ #87752

Order 400.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₅	C₂	1	2	yes	maximal, complemented
2	D₄×C₂₅	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂₅	—	2	4	no	—
5	C₂²×C₂₅	C₂²	1	1	yes	characteristic
6	C₂²×C₂₅	C₂²	1	4	yes	complemented
7	C₄×C₂₅	C₂²	1	2	yes	complemented
8	C₂×C₅×D₄	C₅	1	1	yes	maximal, characteristic
9	C₂×C₂₅	—	2	4	no	—
10	C₂×C₂₅	D₄	1	2	yes	direct product factor
11	C₂×C₂₅	C₂³	1	1	yes	characteristic
12	C₂³×C₅	C₂×C₅	1	2	yes	—
13	C₅×D₄	C₂×C₅	1	4	yes	—
14	C₂×C₄×C₅	C₂×C₅	1	1	yes	characteristic
15	C₂₅	C₂×D₄	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₅	—	2	4	no	—
17	C₂²×C₅	C₂²×C₅	1	1	yes	characteristic
18	C₂²×C₅	C₂²×C₅	1	4	yes	—
19	C₄×C₅	C₂²×C₅	1	2	yes	—
20	C₂×D₄	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₅	—	2	4	no	—
22	C₂×C₅	C₅×D₄	1	2	yes	—
23	C₂×C₅	C₂³×C₅	1	1	yes	characteristic
24	C₂³	C₂×C₂₅	1	2	yes	complemented
25	D₄	C₂×C₂₅	1	4	yes	direct product factor
26	C₂×C₄	C₂×C₂₅	1	1	yes	characteristic, complemented
27	C₅	C₂×C₅×D₄	1	1	yes	characteristic
28	C₂²	—	2	4	no	—
29	C₂²	C₂²×C₂₅	1	1	yes	characteristic
30	C₂²	C₂²×C₂₅	1	4	yes	complemented
31	C₄	C₂²×C₂₅	1	2	yes	complemented
32	C₂	—	2	4	no	—
33	C₂	D₄×C₂₅	1	2	yes	direct product factor
34	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.