Subgroups — C₂²⋊#1035 #87740

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×#1035	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₅	C₄	1	1	yes	characteristic, complemented
4	C₂×D₂₅	—	2	2	no	—
5	C₂×D₂₅	C₄	1	1	yes	characteristic, complemented
6	C₂×D₂₅	C₂²	1	1	yes	characteristic
7	#1035	—	2	2	no	—
8	C₂²⋊AGL(1,𝔽₅)	—	5	1	no	maximal
9	C₂×C₂₅	—	2	1	no	—
10	C₂×C₂₅	C₂×C₄	1	1	yes	characteristic
11	D₂₅	—	2	1	no	—
12	D₂₅	D₄	1	2	yes	—
13	C₂²×D₅	—	5	1	no	—
14	C₂×AGL(1,𝔽₅)	—	5	2	no	—
15	C₂₅	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
17	C₂×D₅	—	5	1	no	—
18	C₂×D₅	—	5	1	no	—
19	C₂×D₅	—	10	2	no	—
20	AGL(1,𝔽₅)	—	10	2	no	—
21	C₂²⋊C₄	—	25	1	no	Sylow
22	C₂×C₅	—	2	1	no	—
23	C₂×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
24	D₅	—	5	2	no	—
25	D₅	—	10	1	no	—
26	C₂³	—	25	1	no	—
27	C₂×C₄	—	25	2	no	—
28	C₅	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₂²	—	25	1	no	—
30	C₂²	—	25	1	no	—
31	C₂²	—	50	2	no	—
32	C₂²	#1035	1	1	yes	characteristic, complemented
33	C₄	—	50	2	no	—
34	C₂	—	2	1	no	—
35	C₂	—	25	2	no	—
36	C₂	—	50	1	no	—
37	C₂	C₂×#1035	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.