Subgroups — #14522243

Order 2000.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×H(3,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#6953	C₂	1	1	yes	maximal, characteristic
3	#11758635	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#6953	—	2	1	no	—
5	C₄×H(3,𝔽₅)	—	2	1	no	—
6	C₄×H(3,𝔽₅)	C₂²	1	1	yes	characteristic
7	C₅×#688	—	5	6	no	maximal
8	C₂×H(3,𝔽₅)	D₄	1	1	yes	characteristic
9	#6953	—	4	1	no	—
10	C₅²×Q₈	D₅	1	6	yes	complemented
11	C₅×D₂₀	—	5	6	no	—
12	C₅×#168	—	5	6	no	—
13	H(3,𝔽₅)	SD₁₆	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₅×D₅	—	10	6	no	—
15	C₄×C₅²	—	2	6	no	—
16	C₄×C₅²	C₂×D₅	1	6	yes	—
17	C₅×SD₁₆	—	25	1	no	—
18	#688	—	5	6	no	—
19	C₂×C₅²	C₂²⋊D₅	1	6	yes	—
20	C₅×D₅	—	20	6	no	—
21	C₅×Q₈	—	5	6	no	—
22	C₅×Q₈	C₅⋊D₅	1	1	yes	characteristic
23	C₅×D₄	—	25	1	no	—
24	D₂₀	—	5	6	no	—
25	C₅×C₈	—	25	1	no	—
26	#168	—	5	6	no	—
27	C₅²	#688	1	6	yes	complemented
28	C₂²×C₅	—	50	1	no	—
29	C₂×D₅	—	10	6	no	—
30	C₄×C₅	—	2	1	no	—
31	C₄×C₅	—	5	6	no	—
32	C₄×C₅	—	10	6	no	—
33	C₄×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
34	SD₁₆	—	25	1	no	Sylow
35	C₂×C₅	—	5	6	no	—
36	C₂×C₅	—	100	1	no	—
37	C₂×C₅	C₂²⋊(C₅⋊D₅)	1	1	yes	characteristic
38	D₅	—	20	6	no	—
39	Q₈	#6953	1	1	yes	characteristic, complemented
40	D₄	—	25	1	no	—
41	C₈	—	25	1	no	—
42	C₅	—	5	6	no	—
43	C₅	#87811	1	1	yes	characteristic
44	C₂²	—	50	1	no	—
45	C₄	—	2	1	no	—
46	C₄	C₂×#6953	1	1	yes	characteristic
47	C₂	—	100	1	no	—
48	C₂	C₂²⋊#6953	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.