Subgroups — C₂×#11758769 #14522919

Order 2000.

1216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅³	C₂	1	1	yes	maximal, characteristic
2	C₂×#92553	C₂	1	2	yes	maximal
3	#11758769	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₅³	C₂²	1	1	yes	characteristic
5	C₄×C₅³	C₂²	1	2	yes	—
6	#92553	C₂²	1	4	yes	—
7	C₂×#6045	—	5	31	no	maximal
8	C₂×C₅³	Q₈	1	2	yes	complemented
9	C₂×C₅³	C₂³	1	1	yes	characteristic
10	C₂×C₄×C₅²	D₅	1	31	yes	—
11	C₂×#1039	—	5	62	no	—
12	#6045	—	5	124	no	—
13	C₅³	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
14	C₂²×C₅²	C₂×D₅	1	31	yes	—
15	C₄×C₅²	C₂×D₅	1	62	yes	—
16	#1039	—	5	124	no	—
17	C₂×Dic₁₀	—	25	31	no	—
18	C₂×C₅²	Dic₁₀	1	62	yes	complemented
19	C₂×C₅²	C₂²×D₅	1	31	yes	—
20	C₂×C₄×C₅	C₅⋊D₅	1	31	yes	—
21	C₂×Dic₅	—	25	62	no	—
22	Dic₁₀	—	25	124	no	—
23	C₅²	C₂×Dic₁₀	1	31	yes	complemented
24	C₂²×C₅	C₂×C₅⋊D₅	1	31	yes	—
25	C₄×C₅	C₂×C₅⋊D₅	1	62	yes	—
26	Dic₅	—	25	124	no	—
27	C₂×Q₈	—	125	1	no	Sylow
28	C₂×C₅	#6045	1	62	yes	complemented
29	C₂×C₅	C₂²×C₅⋊D₅	1	31	yes	—
30	Q₈	—	125	4	no	—
31	C₂×C₄	—	125	2	no	—
32	C₂×C₄	C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
33	C₅	C₂×#6045	1	31	yes	complemented
34	C₂²	C₂×C₅⋊(C₅⋊D₅)	1	1	yes	characteristic
35	C₄	—	125	4	no	—
36	C₄	C₂×C₅⋊(C₅⋊D₅)	1	2	yes	—
37	C₂	#11758769	1	2	yes	direct product factor
38	C₂	C₂²×C₅⋊(C₅⋊D₅)	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.