Subgroups — C₂×#11758742 #14522813

Order 2000.

704 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92553	C₂	1	1	yes	maximal, characteristic
2	#11758742	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₅³	C₄	1	1	yes	characteristic
4	#92553	C₄	1	1	yes	characteristic
5	#92553	C₂²	1	1	yes	characteristic
6	C₂×#6033	—	5	31	no	maximal
7	C₂×C₅³	C₈	1	2	yes	complemented
8	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
9	C₂×#1039	—	5	31	no	—
10	#6033	—	5	62	no	—
11	C₅³	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₅²	AGL(1,𝔽₅)	1	31	yes	—
13	#1039	—	5	31	no	—
14	#1039	—	5	31	no	—
15	C₂×#170	—	25	31	no	—
16	C₂×C₅²	#170	1	62	yes	complemented
17	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	31	yes	—
18	C₂×Dic₅	—	25	31	no	—
19	#170	—	25	62	no	—
20	C₅²	C₂×#170	1	31	yes	complemented
21	C₂²×C₅	#1043	1	31	yes	—
22	Dic₅	—	25	31	no	—
23	Dic₅	—	25	31	no	—
24	C₂×C₈	—	125	1	no	Sylow
25	C₂×C₅	#6033	1	62	yes	complemented
26	C₂×C₅	C₂×#1043	1	31	yes	—
27	C₂×C₄	—	125	1	no	—
28	C₈	—	125	2	no	—
29	C₅	C₂×#6033	1	31	yes	complemented
30	C₂²	#92562	1	1	yes	characteristic
31	C₄	—	125	1	no	—
32	C₄	—	125	1	no	—
33	C₂	#11758742	1	2	yes	direct product factor
34	C₂	C₂×#92562	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.