Subgroups — C₂²⋊#1039 #87813

Order 400.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂×#1039	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅²	—	2	2	no	—
4	C₂²×C₅²	C₄	1	2	yes	complemented
5	C₂²×C₅²	C₂²	1	1	yes	characteristic
6	#1039	—	2	2	no	—
7	C₂²⋊Dic₅	—	5	6	no	maximal
8	C₂×C₅²	—	2	2	no	—
9	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
10	C₂×C₅²	D₄	1	2	yes	—
11	C₂³×C₅	D₅	1	6	yes	—
12	C₂×Dic₅	—	5	12	no	—
13	C₅²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₅	—	2	12	no	—
15	C₂²×C₅	Dic₅	1	12	yes	complemented
16	C₂²×C₅	C₂×D₅	1	6	yes	—
17	Dic₅	—	10	12	no	—
18	C₂²⋊C₄	—	25	1	no	Sylow
19	C₂×C₅	—	2	12	no	—
20	C₂×C₅	C₂×Dic₅	1	6	yes	—
21	C₂×C₅	C₂²⋊D₅	1	12	yes	—
22	C₂³	C₅⋊D₅	1	1	yes	characteristic
23	C₂×C₄	—	25	2	no	—
24	C₅	C₂²⋊Dic₅	1	6	yes	complemented
25	C₂²	—	2	2	no	—
26	C₂²	#1039	1	2	yes	complemented
27	C₂²	C₂×C₅⋊D₅	1	1	yes	characteristic
28	C₄	—	50	2	no	—
29	C₂	—	2	2	no	—
30	C₂	C₂×#1039	1	1	yes	characteristic
31	C₂	C₂²⋊(C₅⋊D₅)	1	2	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.