Subgroups — C₂²×#1044 #87923

Order 400.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×#1044	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₅²	C₄	1	1	yes	characteristic, complemented
4	C₂×C₅⋊D₅	C₄	1	3	yes	complemented
5	C₂×C₅⋊D₅	C₂²	1	3	yes	—
6	#1044	C₂²	1	4	yes	direct product factor
7	C₂²×AGL(1,𝔽₅)	—	5	2	no	maximal
8	C₂×C₅²	C₂×C₄	1	3	yes	complemented
9	C₅⋊D₅	C₂×C₄	1	3	yes	complemented
10	C₅⋊D₅	C₂³	1	1	yes	characteristic
11	C₂²×D₅	—	5	2	no	—
12	C₂²×D₅	—	10	2	no	—
13	C₂×AGL(1,𝔽₅)	—	5	12	no	—
14	C₅²	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂²×C₅	—	2	2	no	—
16	C₂²×C₅	AGL(1,𝔽₅)	1	2	yes	complemented
17	C₂×D₅	—	5	6	no	—
18	C₂×D₅	—	5	6	no	—
19	C₂×D₅	—	10	6	no	—
20	C₂×D₅	—	10	6	no	—
21	AGL(1,𝔽₅)	—	5	8	no	—
22	C₂²×C₄	—	25	1	no	Sylow
23	C₂×C₅	—	2	6	no	—
24	C₂×C₅	C₂×AGL(1,𝔽₅)	1	6	yes	complemented
25	D₅	—	5	6	no	—
26	D₅	—	5	2	no	—
27	D₅	—	10	6	no	—
28	D₅	—	10	2	no	—
29	C₂³	—	25	1	no	—
30	C₂×C₄	—	25	6	no	—
31	C₅	—	2	2	no	—
32	C₅	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
33	C₂²	—	25	3	no	—
34	C₂²	—	25	3	no	—
35	C₂²	#1044	1	1	yes	characteristic, direct product factor
36	C₄	—	25	4	no	—
37	C₂	—	25	1	no	—
38	C₂	—	25	3	no	—
39	C₂	C₂×#1044	1	3	yes	direct product factor

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.