Subgroups — C₂²×#1035 #87759

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×#1035	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₂₅	C₄	1	1	yes	characteristic, complemented
4	C₂×D₂₅	C₄	1	3	yes	complemented
5	C₂×D₂₅	C₂²	1	3	yes	—
6	#1035	C₂²	1	4	yes	direct product factor
7	C₂²×AGL(1,𝔽₅)	—	5	1	no	maximal
8	C₂×C₂₅	C₂×C₄	1	3	yes	complemented
9	D₂₅	C₂×C₄	1	3	yes	complemented
10	D₂₅	C₂³	1	1	yes	characteristic
11	C₂²×D₅	—	5	1	no	—
12	C₂×AGL(1,𝔽₅)	—	5	6	no	—
13	C₂₅	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
15	C₂×D₅	—	5	3	no	—
16	C₂×D₅	—	5	3	no	—
17	AGL(1,𝔽₅)	—	5	4	no	—
18	C₂²×C₄	—	25	1	no	Sylow
19	C₂×C₅	C₂×AGL(1,𝔽₅)	1	3	yes	—
20	D₅	—	5	1	no	—
21	D₅	—	5	3	no	—
22	C₂³	—	25	1	no	—
23	C₂×C₄	—	25	6	no	—
24	C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₂²	—	25	3	no	—
26	C₂²	—	25	3	no	—
27	C₂²	#1035	1	1	yes	characteristic, direct product factor
28	C₄	—	25	4	no	—
29	C₂	—	25	1	no	—
30	C₂	—	25	3	no	—
31	C₂	C₂×#1035	1	3	yes	direct product factor

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.