Subgroups — C₄×#92537 #14522366

Order 2000.

225 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92537	C₂	1	2	yes	maximal
2	C₄×#6953	C₂	1	1	yes	maximal, characteristic
3	C₂×#6953	C₂²	1	1	yes	characteristic
4	#92537	C₄	1	4	yes	direct product factor
5	C₄×H(3,𝔽₅)	C₄	1	1	yes	characteristic, complemented
6	#92525	C₄	1	1	yes	characteristic, complemented
7	C₄×#1042	—	5	6	no	maximal
8	C₂×H(3,𝔽₅)	C₂×C₄	1	1	yes	characteristic
9	#6953	C₂×C₄	1	2	yes	—
10	C₂×#1042	—	5	12	no	—
11	C₄×C₅×D₅	—	5	6	no	—
12	H(3,𝔽₅)	C₄²	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₅×D₅	—	5	6	no	—
14	#1042	—	5	24	no	—
15	C₄×C₅²	AGL(1,𝔽₅)	1	6	yes	complemented
16	C₅×Dic₅	—	5	6	no	—
17	C₄×AGL(1,𝔽₅)	—	25	6	no	—
18	C₄×Dic₅	—	25	1	no	—
19	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	6	yes	—
20	C₅×D₅	—	5	12	no	—
21	C₂×AGL(1,𝔽₅)	—	25	12	no	—
22	C₂×C₄×C₅	—	25	1	no	—
23	C₂×Dic₅	—	25	2	no	—
24	C₄×D₅	—	5	6	no	—
25	C₅²	C₄×AGL(1,𝔽₅)	1	6	yes	complemented
26	C₂²×C₅	—	25	1	no	—
27	C₂×D₅	—	5	6	no	—
28	AGL(1,𝔽₅)	—	25	24	no	—
29	C₄×C₅	—	5	6	no	—
30	C₄×C₅	—	25	1	no	—
31	C₄×C₅	#1043	1	1	yes	characteristic
32	Dic₅	—	5	6	no	—
33	Dic₅	—	25	4	no	—
34	C₄²	—	125	1	no	Sylow
35	C₂×C₅	—	5	6	no	—
36	C₂×C₅	—	25	2	no	—
37	C₂×C₅	C₂×#1043	1	1	yes	characteristic
38	D₅	—	5	12	no	—
39	C₂×C₄	—	25	1	no	—
40	C₂×C₄	—	125	2	no	—
41	C₅	—	5	6	no	—
42	C₅	C₄×#1043	1	1	yes	characteristic
43	C₂²	—	25	1	no	—
44	C₄	—	25	1	no	—
45	C₄	—	125	4	no	—
46	C₄	#92537	1	1	yes	characteristic, direct product factor
47	C₂	—	25	2	no	—
48	C₂	C₂×#92537	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.