Subgroups — C₅×C₁₁×2₋¹⁺⁴ #13183460

Order 1760.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×#41	C₂	1	10	yes	maximal, complemented
2	C₂×C₅×Q₈×C₁₁	C₂	1	5	yes	maximal, complemented
3	C₅×Q₈×C₁₁	C₂²	1	10	yes	—
4	C₅×D₄×C₁₁	C₂²	1	10	yes	—
5	C₂×C₄×C₅×C₁₁	C₂²	1	15	yes	—
6	C₁₁×2₋¹⁺⁴	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₅×C₁₁	C₂³	1	5	yes	—
8	C₄×C₅×C₁₁	C₂³	1	10	yes	—
9	C₁₁×#41	C₂×C₅	1	10	yes	complemented
10	C₂×Q₈×C₁₁	C₂×C₅	1	5	yes	complemented
11	C₅×2₋¹⁺⁴	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×C₁₁	—	2	5	no	—
13	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
14	Q₈×C₁₁	C₂²×C₅	1	10	yes	—
15	D₄×C₁₁	C₂²×C₅	1	10	yes	—
16	C₂×C₄×C₁₁	C₂²×C₅	1	15	yes	—
17	C₅×#41	C₂×C₁₁	1	10	yes	complemented
18	C₂×C₅×Q₈	C₂×C₁₁	1	5	yes	complemented
19	C₅×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₁₁	C₂³×C₅	1	5	yes	—
21	C₄×C₁₁	C₂³×C₅	1	10	yes	—
22	C₅×Q₈	C₂²×C₁₁	1	10	yes	—
23	C₅×D₄	C₂²×C₁₁	1	10	yes	—
24	C₂×C₄×C₅	C₂²×C₁₁	1	15	yes	—
25	2₋¹⁺⁴	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₁₁	—	2	5	no	—
27	C₂×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
28	C₂²×C₅	C₂³×C₁₁	1	5	yes	—
29	C₄×C₅	C₂³×C₁₁	1	10	yes	—
30	#41	C₂×C₅×C₁₁	1	10	yes	complemented
31	C₂×Q₈	C₂×C₅×C₁₁	1	5	yes	complemented
32	C₁₁	C₅×2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₅	—	2	5	no	—
34	C₂×C₅	C₂⁴×C₁₁	1	1	yes	characteristic
35	Q₈	C₂²×C₅×C₁₁	1	10	yes	—
36	D₄	C₂²×C₅×C₁₁	1	10	yes	—
37	C₂×C₄	C₂²×C₅×C₁₁	1	15	yes	—
38	C₅	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²	C₂³×C₅×C₁₁	1	5	yes	—
40	C₄	C₂³×C₅×C₁₁	1	10	yes	—
41	C₂	—	2	5	no	—
42	C₂	C₂⁴×C₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁴×C₅×C₁₁
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×#41	C₂	semidirect
2. C₂×C₅×Q₈×C₁₁	C₂	semidirect
6. C₁₁×2₋¹⁺⁴	C₅	direct (N × H)
9. C₁₁×#41	C₂×C₅	semidirect
10. C₂×Q₈×C₁₁	C₂×C₅	semidirect
11. C₅×2₋¹⁺⁴	C₁₁	direct (N × H)
17. C₅×#41	C₂×C₁₁	semidirect
18. C₂×C₅×Q₈	C₂×C₁₁	semidirect
19. C₅×C₁₁	2₋¹⁺⁴	direct (N × H)
25. 2₋¹⁺⁴	C₅×C₁₁	direct (N × H)
30. #41	C₂×C₅×C₁₁	semidirect
31. C₂×Q₈	C₂×C₅×C₁₁	semidirect
32. C₁₁	C₅×2₋¹⁺⁴	direct (N × H)
38. C₅	C₁₁×2₋¹⁺⁴	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁×#41	2
C₂×C₅×Q₈×C₁₁	2
C₁₁×2₋¹⁺⁴	5
C₅×2₋¹⁺⁴	11

Subgroups — C5×C11×2−1+4 #13183460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×2₋¹⁺⁴ #13183460