Subgroups — C₂×#6037 #87882

Order 400.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₅	C₂	1	2	yes	maximal, complemented
2	C₂×#1039	C₂	1	1	yes	maximal, characteristic, complemented
3	#6037	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅²	C₂²	1	1	yes	characteristic
5	C₂×C₅×D₅	—	2	4	no	—
6	C₂×C₅×D₅	C₂²	1	4	yes	complemented
7	#1039	C₂²	1	2	yes	complemented
8	C₂×C₂²⋊D₅	—	5	2	no	maximal
9	C₂×C₅²	D₄	1	2	yes	complemented
10	C₂×C₅²	C₂³	1	1	yes	characteristic
11	C₅×D₅	—	2	4	no	—
12	C₂³×C₅	—	5	2	no	—
13	C₂²×D₅	D₅	1	2	yes	complemented
14	C₂²⋊D₅	—	5	8	no	—
15	C₂×Dic₅	—	5	2	no	—
16	C₂×Dic₅	—	10	2	no	—
17	C₅²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₅	—	2	2	no	—
19	C₂²×C₅	—	5	4	no	—
20	C₂²×C₅	—	10	4	no	—
21	C₂²×C₅	C₂×D₅	1	2	yes	—
22	C₂×D₅	—	2	4	no	—
23	C₂×D₅	C₂×D₅	1	4	yes	complemented
24	Dic₅	—	5	4	no	—
25	Dic₅	—	10	4	no	—
26	C₂×D₄	—	25	1	no	Sylow
27	C₂×C₅	—	2	4	no	—
28	C₂×C₅	—	2	2	no	—
29	C₂×C₅	—	10	4	no	—
30	C₂×C₅	C₂²⋊D₅	1	4	yes	complemented
31	C₂×C₅	C₂²×D₅	1	2	yes	—
32	D₅	—	2	4	no	—
33	C₂³	—	5	2	no	—
34	D₄	—	25	4	no	—
35	C₂×C₄	—	25	1	no	—
36	C₅	—	2	2	no	—
37	C₅	C₂×C₂²⋊D₅	1	2	yes	complemented
38	C₂²	—	5	4	no	—
39	C₂²	—	10	4	no	—
40	C₂²	D₅²	1	1	yes	characteristic
41	C₄	—	25	2	no	—
42	C₂	—	10	4	no	—
43	C₂	#6037	1	2	yes	direct product factor
44	C₂	C₂×D₅²	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.