Subgroups — #41×C₂₅ #87754

Order 400.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₂₅	C₂	1	3	yes	maximal, complemented
3	C₂×C₄×C₂₅	C₂	1	3	yes	maximal, complemented
4	C₂²×C₂₅	C₂²	1	3	yes	—
5	C₄×C₂₅	C₂²	1	3	yes	—
6	C₄×C₂₅	C₂²	1	1	yes	characteristic
7	C₅×#41	C₅	1	1	yes	maximal, characteristic
8	C₂×C₂₅	—	2	3	no	—
9	C₂×C₂₅	C₂³	1	1	yes	characteristic
10	C₅×Q₈	C₂×C₅	1	1	yes	characteristic
11	C₅×D₄	C₂×C₅	1	3	yes	—
12	C₂×C₄×C₅	C₂×C₅	1	3	yes	—
13	C₂₅	#41	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₅	C₂²×C₅	1	3	yes	—
15	C₄×C₅	C₂²×C₅	1	3	yes	—
16	C₄×C₅	C₂²×C₅	1	1	yes	characteristic
17	#41	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₅	—	2	3	no	—
19	C₂×C₅	C₂³×C₅	1	1	yes	characteristic
20	Q₈	C₂×C₂₅	1	1	yes	characteristic, complemented
21	D₄	C₂×C₂₅	1	3	yes	complemented
22	C₂×C₄	C₂×C₂₅	1	3	yes	complemented
23	C₅	C₅×#41	1	1	yes	characteristic
24	C₂²	C₂²×C₂₅	1	3	yes	—
25	C₄	C₂²×C₂₅	1	1	yes	characteristic
26	C₄	C₂²×C₂₅	1	3	yes	—
27	C₂	—	2	3	no	—
28	C₂	C₂³×C₂₅	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.