Subgroups — C₂×#11758755 #14522885

Order 2000.

496 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	C₂×C₅×#1039	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅²×Dic₅	C₂	1	1	yes	maximal, characteristic
4	#11758755	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅³	C₂²	1	1	yes	characteristic
6	#92553	C₂²	1	2	yes	—
7	C₅×#1039	C₂²	1	2	yes	—
8	C₅²×Dic₅	C₂²	1	2	yes	—
9	C₂×#6045	—	5	1	no	maximal
10	C₂×#6039	—	5	6	no	maximal
11	C₂×C₅³	Q₈	1	2	yes	complemented
12	C₂×C₅³	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₅²	—	5	1	no	—
14	C₂×#1039	—	5	1	no	—
15	C₂×#1039	—	5	6	no	—
16	C₂×#1039	—	10	12	no	—
17	C₂×#1039	D₅	1	1	yes	characteristic
18	#6045	—	5	4	no	—
19	C₂×C₅×Dic₅	—	5	6	no	—
20	C₂×C₅×Dic₅	D₅	1	6	yes	—
21	#6039	—	5	24	no	—
22	C₅³	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
23	C₂²×C₅²	—	2	12	no	—
24	C₂²×C₅²	C₂×D₅	1	6	yes	—
25	C₂²×C₅²	C₂×D₅	1	1	yes	characteristic
26	C₄×C₅²	—	5	2	no	—
27	#1039	—	5	2	no	—
28	#1039	—	5	12	no	—
29	#1039	—	10	24	no	—
30	#1039	C₂×D₅	1	2	yes	—
31	C₅×Dic₅	—	5	12	no	—
32	C₅×Dic₅	C₂×D₅	1	12	yes	—
33	C₂×Dic₁₀	—	25	6	no	—
34	C₂×Dic₁₀	—	25	1	no	—
35	C₂×C₅²	—	2	24	no	—
36	C₂×C₅²	—	2	12	no	—
37	C₂×C₅²	Dic₁₀	1	12	yes	complemented
38	C₂×C₅²	Dic₁₀	1	2	yes	complemented
39	C₂×C₅²	C₂²×D₅	1	6	yes	—
40	C₂×C₅²	C₂²×D₅	1	1	yes	characteristic
41	C₂×C₄×C₅	—	5	6	no	—
42	C₂×C₄×C₅	—	25	1	no	—
43	C₂×Dic₅	—	5	6	no	—
44	C₂×Dic₅	—	25	6	no	—
45	C₂×Dic₅	—	25	1	no	—
46	C₂×Dic₅	—	50	12	no	—
47	C₂×Dic₅	C₅⋊D₅	1	1	yes	characteristic
48	Dic₁₀	—	25	24	no	—
49	Dic₁₀	—	25	4	no	—
50	C₅²	—	2	12	no	—
51	C₅²	C₂×Dic₁₀	1	6	yes	complemented
52	C₅²	C₂×Dic₁₀	1	1	yes	characteristic, complemented
53	C₂²×C₅	—	2	12	no	—
54	C₂²×C₅	D₅²	1	6	yes	—
55	C₂²×C₅	C₂×C₅⋊D₅	1	1	yes	characteristic
56	C₄×C₅	—	5	12	no	—
57	C₄×C₅	—	25	2	no	—
58	Dic₅	—	5	12	no	—
59	Dic₅	—	25	12	no	—
60	Dic₅	—	25	2	no	—
61	Dic₅	—	50	24	no	—
62	Dic₅	C₂×C₅⋊D₅	1	2	yes	—
63	C₂×Q₈	—	125	1	no	Sylow
64	C₂×C₅	—	2	24	no	—
65	C₂×C₅	—	2	12	no	—
66	C₂×C₅	#6039	1	12	yes	complemented
67	C₂×C₅	#6045	1	2	yes	complemented
68	C₂×C₅	C₂×D₅²	1	6	yes	—
69	C₂×C₅	C₂²×C₅⋊D₅	1	1	yes	characteristic
70	Q₈	—	125	4	no	—
71	C₂×C₄	—	5	1	no	—
72	C₂×C₄	—	25	1	no	—
73	C₂×C₄	—	125	1	no	—
74	C₅	—	2	12	no	—
75	C₅	C₂×#6039	1	6	yes	complemented
76	C₅	C₂×#6045	1	1	yes	characteristic, complemented
77	C₂²	D₅×C₅⋊D₅	1	1	yes	characteristic
78	C₄	—	5	2	no	—
79	C₄	—	25	2	no	—
80	C₄	—	125	2	no	—
81	C₂	#11758755	1	2	yes	direct product factor
82	C₂	C₂×D₅×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₅×C₅⋊D₅
commutator, cosocle	C₂×C₅³	C₂³
Frattini	C₂	C₂×D₅×C₅⋊D₅
Fitting, socle, prime radical	C₂²×C₅³	C₂²
hypocenter	C₅³	C₂×Q₈
LCS	G ▷ C₂×C₅³ ▷ C₅³
UCS	C₁ ◁ C₂²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #11758755	C₂	direct (N × H)
11. C₂×C₅³	Q₈	semidirect
22. C₅³	C₂×Q₈	semidirect
37. C₂×C₅²	Dic₁₀	semidirect
38. C₂×C₅²	Dic₁₀	semidirect
51. C₅²	C₂×Dic₁₀	semidirect
52. C₅²	C₂×Dic₁₀	semidirect
66. C₂×C₅	#6039	semidirect
67. C₂×C₅	#6045	semidirect
75. C₅	C₂×#6039	semidirect
76. C₅	C₂×#6045	semidirect
81. C₂	#11758755	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#92553	2
C₂×C₅×#1039	2
C₂×C₅²×Dic₅	2
#11758755	2
C₂×#6045	5
C₂×#6039	5

Subgroups — C2×#11758755 #14522885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758755 #14522885