Subgroups — #11717196

Order 800.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	#87808	C₂	1	3	yes	maximal
3	#87806	C₂	1	3	yes	maximal, complemented
4	C₂²×C₅⋊D₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅²	C₂²	1	3	yes	—
6	C₂×#1039	C₂²	1	3	yes	—
7	#4022	—	5	6	no	maximal
8	C₂²×C₅²	C₂³	1	1	yes	characteristic
9	C₂×C₅⋊D₅	—	2	3	no	—
10	C₄×C₅²	—	2	3	no	—
11	#1039	—	2	3	no	—
12	C₄²×C₅	D₅	1	6	yes	complemented
13	#685	—	5	18	no	—
14	#683	—	5	18	no	—
15	C₂×C₅²	#41	1	3	yes	—
16	C₅⋊D₅	—	4	1	no	—
17	C₂²×D₅	—	5	6	no	—
18	C₂×C₄×C₅	C₂×D₅	1	18	yes	—
19	C₂×Dic₅	—	5	18	no	—
20	#126	—	25	1	no	Sylow
21	C₅²	#126	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₅	C₂²×D₅	1	6	yes	—
23	C₂×D₅	—	10	18	no	—
24	C₄×C₅	—	2	18	no	—
25	Dic₅	—	10	18	no	—
26	C₄⋊C₄	—	25	3	no	—
27	C₂²⋊C₄	—	25	3	no	—
28	C₄²	C₅⋊D₅	1	1	yes	characteristic, complemented
29	C₂×C₅	#709	1	18	yes	—
30	D₅	—	20	6	no	—
31	C₂³	—	25	1	no	—
32	C₂×C₄	—	25	3	no	—
33	C₂×C₄	C₂×C₅⋊D₅	1	3	yes	—
34	C₅	#4022	1	6	yes	complemented
35	C₂²	—	50	3	no	—
36	C₂²	C₂²×C₅⋊D₅	1	1	yes	characteristic
37	C₄	—	2	3	no	—
38	C₄	—	50	3	no	—
39	C₂	—	100	1	no	—
40	C₂	#87900	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.