Subgroups — C₂×C₄×D₂₅ #87742

Order 400.

81 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	C₄×D₂₅	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×D₂₅	C₄	1	4	yes	direct product factor
7	C₂×D₂₅	C₂²	1	2	yes	—
8	C₄×C₂₅	C₂²	1	2	yes	complemented
9	Dic₂₅	C₂²	1	2	yes	complemented
10	C₂×C₄×D₅	—	5	1	no	maximal
11	C₂×C₂₅	C₂×C₄	1	2	yes	complemented
12	C₂×C₂₅	C₂³	1	1	yes	characteristic
13	D₂₅	C₂×C₄	1	4	yes	direct product factor
14	C₂²×D₅	—	5	1	no	—
15	C₂×C₄×C₅	D₅	1	1	yes	characteristic
16	C₂×Dic₅	—	5	1	no	—
17	C₄×D₅	—	5	4	no	—
18	C₂₅	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
20	C₂×D₅	—	5	4	no	—
21	C₂×D₅	—	5	2	no	—
22	C₄×C₅	C₂×D₅	1	2	yes	—
23	Dic₅	—	5	2	no	—
24	C₂²×C₄	—	25	1	no	Sylow
25	C₂×C₅	C₄×D₅	1	2	yes	—
26	C₂×C₅	C₂²×D₅	1	1	yes	characteristic
27	D₅	—	5	4	no	—
28	C₂³	—	25	1	no	—
29	C₂×C₄	—	25	1	no	—
30	C₂×C₄	—	25	4	no	—
31	C₂×C₄	D₂₅	1	1	yes	characteristic, direct product factor
32	C₅	C₂×C₄×D₅	1	1	yes	characteristic
33	C₂²	—	25	4	no	—
34	C₂²	—	25	2	no	—
35	C₂²	C₂×D₂₅	1	1	yes	characteristic
36	C₄	—	25	2	no	—
37	C₄	C₂×D₂₅	1	2	yes	direct product factor
38	C₂	—	25	4	no	—
39	C₂	C₄×D₂₅	1	2	yes	direct product factor
40	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.