Subgroups — C₂²⋊Dic₂₅ #87725

Order 400.

51 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×Dic₂₅	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₅	—	2	2	no	—
4	C₂²×C₂₅	C₄	1	2	yes	complemented
5	C₂²×C₂₅	C₂²	1	1	yes	characteristic
6	Dic₂₅	—	2	2	no	—
7	C₂²⋊Dic₅	—	5	1	no	maximal
8	C₂×C₂₅	—	2	2	no	—
9	C₂×C₂₅	C₂×C₄	1	1	yes	characteristic
10	C₂×C₂₅	D₄	1	2	yes	—
11	C₂³×C₅	D₅	1	1	yes	characteristic
12	C₂×Dic₅	—	5	2	no	—
13	C₂₅	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₅	—	2	2	no	—
15	C₂²×C₅	Dic₅	1	2	yes	—
16	C₂²×C₅	C₂×D₅	1	1	yes	characteristic
17	Dic₅	—	10	2	no	—
18	C₂²⋊C₄	—	25	1	no	Sylow
19	C₂×C₅	—	2	2	no	—
20	C₂×C₅	C₂×Dic₅	1	1	yes	characteristic
21	C₂×C₅	C₂²⋊D₅	1	2	yes	—
22	C₂³	D₂₅	1	1	yes	characteristic
23	C₂×C₄	—	25	2	no	—
24	C₅	C₂²⋊Dic₅	1	1	yes	characteristic
25	C₂²	—	2	2	no	—
26	C₂²	Dic₂₅	1	2	yes	complemented
27	C₂²	C₂×D₂₅	1	1	yes	characteristic
28	C₄	—	50	2	no	—
29	C₂	—	2	2	no	—
30	C₂	C₂×Dic₂₅	1	1	yes	characteristic
31	C₂	C₂²⋊D₂₅	1	2	yes	—

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.