Subgroups — C₄×#1035 #87736

Order 400.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1035	C₂	1	2	yes	maximal
2	C₄×D₂₅	C₂	1	1	yes	maximal, characteristic
3	C₂×D₂₅	C₂²	1	1	yes	characteristic
4	#1035	C₄	1	4	yes	direct product factor
5	C₄×C₂₅	C₄	1	1	yes	characteristic, complemented
6	Dic₂₅	C₄	1	1	yes	characteristic, complemented
7	C₄×AGL(1,𝔽₅)	—	5	1	no	maximal
8	C₂×C₂₅	C₂×C₄	1	1	yes	characteristic
9	D₂₅	C₂×C₄	1	2	yes	—
10	C₂×AGL(1,𝔽₅)	—	5	2	no	—
11	C₄×D₅	—	5	1	no	—
12	C₂₅	C₄²	1	1	yes	characteristic, complemented, Sylow
13	C₂×D₅	—	5	1	no	—
14	AGL(1,𝔽₅)	—	5	4	no	—
15	C₄×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
16	Dic₅	—	5	1	no	—
17	C₄²	—	25	1	no	Sylow
18	C₂×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
19	D₅	—	5	2	no	—
20	C₂×C₄	—	25	2	no	—
21	C₂×C₄	—	25	1	no	—
22	C₅	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
23	C₂²	—	25	1	no	—
24	C₄	—	25	4	no	—
25	C₄	—	25	1	no	—
26	C₄	#1035	1	1	yes	characteristic, direct product factor
27	C₂	—	25	2	no	—
28	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.