Subgroups — C₄⋊#1039 #87807

Order 400.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂×#1039	C₂	1	2	yes	maximal
3	C₂²×C₅²	C₂²	1	1	yes	characteristic
4	C₄×C₅²	C₄	1	2	yes	complemented
5	#1039	—	2	2	no	—
6	C₄⋊Dic₅	—	5	6	no	maximal
7	C₂×C₅²	C₂×C₄	1	1	yes	characteristic
8	C₂×C₅²	D₄	1	1	yes	characteristic
9	C₂×C₅²	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₅	D₅	1	6	yes	—
11	C₂×Dic₅	—	5	12	no	—
12	C₅²	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₅	C₂×D₅	1	6	yes	—
14	C₄×C₅	Dic₅	1	12	yes	complemented
15	Dic₅	—	10	12	no	—
16	C₄⋊C₄	—	25	1	no	Sylow
17	C₂×C₅	Dic₁₀	1	6	yes	—
18	C₂×C₅	D₂₀	1	6	yes	—
19	C₂×C₅	C₂×Dic₅	1	6	yes	—
20	C₂×C₄	—	25	2	no	—
21	C₂×C₄	C₅⋊D₅	1	1	yes	characteristic
22	C₅	C₄⋊Dic₅	1	6	yes	complemented
23	C₂²	C₂×C₅⋊D₅	1	1	yes	characteristic
24	C₄	—	50	2	no	—
25	C₄	#1039	1	2	yes	complemented
26	C₂	#6045	1	1	yes	characteristic
27	C₂	C₄⋊(C₅⋊D₅)	1	1	yes	characteristic
28	C₂	C₂×#1039	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.