Subgroups — C₂₅×#127 #11716529

Order 800.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₂₅	C₂	1	6	yes	maximal, complemented
2	C₄²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₂₅	C₂²	1	4	yes	—
4	D₄×C₂₅	—	2	12	no	—
5	C₂×C₄×C₂₅	C₂²	1	3	yes	—
6	C₅×#127	C₅	1	1	yes	maximal, characteristic
7	C₂²×C₂₅	—	2	12	no	—
8	C₂²×C₂₅	C₂³	1	1	yes	characteristic
9	C₄×C₂₅	D₄	1	6	yes	complemented
10	C₂×C₅×D₄	C₂×C₅	1	6	yes	—
11	C₄²×C₅	C₂×C₅	1	1	yes	characteristic
12	C₂×C₂₅	—	4	4	no	—
13	C₂×C₂₅	C₂×D₄	1	3	yes	—
14	C₂³×C₅	C₂²×C₅	1	4	yes	—
15	C₅×D₄	—	2	12	no	—
16	C₂×C₄×C₅	C₂²×C₅	1	3	yes	—
17	#127	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₂₅	#127	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²×C₅	—	2	12	no	—
20	C₂²×C₅	C₂³×C₅	1	1	yes	characteristic
21	C₄×C₅	C₅×D₄	1	6	yes	—
22	C₂×D₄	C₂×C₂₅	1	6	yes	complemented
23	C₄²	C₂×C₂₅	1	1	yes	characteristic, complemented
24	C₂×C₅	—	4	4	no	—
25	C₂×C₅	C₂×C₅×D₄	1	3	yes	—
26	C₂³	C₂²×C₂₅	1	4	yes	—
27	D₄	—	2	12	no	—
28	C₂×C₄	C₂²×C₂₅	1	3	yes	—
29	C₅	C₅×#127	1	1	yes	characteristic
30	C₂²	—	2	12	no	—
31	C₂²	C₂³×C₂₅	1	1	yes	characteristic
32	C₄	D₄×C₂₅	1	6	yes	complemented
33	C₂	—	4	4	no	—
34	C₂	C₂×D₄×C₂₅	1	3	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.