Subgroups — C₂⁴×D₅×C₁₁ #13183474

Order 1760.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₅×C₁₁	C₂	1	30	yes	maximal, direct product factor
3	C₂³×C₅×C₁₁	C₂²	1	15	yes	complemented
4	C₂²×D₅×C₁₁	C₂²	1	140	yes	direct product factor
5	C₂⁵×C₁₁	—	5	1	no	maximal, Hall
6	C₂²×C₅×C₁₁	C₂³	1	35	yes	complemented
7	C₂×D₅×C₁₁	C₂³	1	120	yes	direct product factor
8	C₂⁴×C₁₁	—	5	30	no	—
9	C₂⁴×C₁₁	D₅	1	1	yes	characteristic, direct product factor
10	C₂⁴×D₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₅×C₁₁	C₂⁴	1	15	yes	complemented
12	D₅×C₁₁	C₂⁴	1	16	yes	direct product factor
13	C₂³×C₁₁	—	5	140	no	—
14	C₂³×C₁₁	C₂×D₅	1	15	yes	direct product factor
15	C₂⁴×C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₂³×D₅	C₂×C₁₁	1	30	yes	direct product factor
17	C₅×C₁₁	C₂⁵	1	1	yes	characteristic, complemented, Hall
18	C₂²×C₁₁	—	5	120	no	—
19	C₂²×C₁₁	C₂²×D₅	1	35	yes	direct product factor
20	C₂³×C₅	C₂²×C₁₁	1	15	yes	complemented
21	C₂²×D₅	C₂²×C₁₁	1	140	yes	direct product factor
22	C₂⁵	—	5	1	no	Sylow
23	C₂×C₁₁	—	5	16	no	—
24	C₂×C₁₁	C₂³×D₅	1	15	yes	direct product factor
25	C₂²×C₅	C₂³×C₁₁	1	35	yes	complemented
26	C₂×D₅	C₂³×C₁₁	1	120	yes	direct product factor
27	C₂⁴	—	5	30	no	—
28	C₂⁴	D₅×C₁₁	1	1	yes	characteristic, direct product factor
29	C₁₁	C₂⁴×D₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₅	C₂⁴×C₁₁	1	15	yes	complemented
31	D₅	C₂⁴×C₁₁	1	16	yes	direct product factor
32	C₂³	—	5	140	no	—
33	C₂³	C₂×D₅×C₁₁	1	15	yes	direct product factor
34	C₅	C₂⁵×C₁₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	5	120	no	—
36	C₂²	C₂²×D₅×C₁₁	1	35	yes	direct product factor
37	C₂	—	5	16	no	—
38	C₂	C₂³×D₅×C₁₁	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴×C₁₁	D₅
commutator, cosocle, hypocenter	C₅	C₂⁵×C₁₁
Frattini	C₁	G
Fitting, socle	C₂⁴×C₅×C₁₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂⁴×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×C₁₁	C₂	semidirect
2. C₂³×D₅×C₁₁	C₂	direct (N × H)
3. C₂³×C₅×C₁₁	C₂²	semidirect
4. C₂²×D₅×C₁₁	C₂²	direct (N × H)
6. C₂²×C₅×C₁₁	C₂³	semidirect
7. C₂×D₅×C₁₁	C₂³	direct (N × H)
9. C₂⁴×C₁₁	D₅	direct (N × H)
10. C₂⁴×D₅	C₁₁	direct (N × H)
11. C₂×C₅×C₁₁	C₂⁴	semidirect
12. D₅×C₁₁	C₂⁴	direct (N × H)
14. C₂³×C₁₁	C₂×D₅	direct (N × H)
15. C₂⁴×C₅	C₂×C₁₁	semidirect
16. C₂³×D₅	C₂×C₁₁	direct (N × H)
17. C₅×C₁₁	C₂⁵	semidirect
19. C₂²×C₁₁	C₂²×D₅	direct (N × H)
20. C₂³×C₅	C₂²×C₁₁	semidirect
21. C₂²×D₅	C₂²×C₁₁	direct (N × H)
24. C₂×C₁₁	C₂³×D₅	direct (N × H)
25. C₂²×C₅	C₂³×C₁₁	semidirect
26. C₂×D₅	C₂³×C₁₁	direct (N × H)
28. C₂⁴	D₅×C₁₁	direct (N × H)
29. C₁₁	C₂⁴×D₅	direct (N × H)
30. C₂×C₅	C₂⁴×C₁₁	semidirect
31. D₅	C₂⁴×C₁₁	direct (N × H)
33. C₂³	C₂×D₅×C₁₁	direct (N × H)
34. C₅	C₂⁵×C₁₁	semidirect
36. C₂²	C₂²×D₅×C₁₁	direct (N × H)
38. C₂	C₂³×D₅×C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×C₁₁	2
C₂³×D₅×C₁₁	2
C₂⁵×C₁₁	5
C₂⁴×D₅	11

Subgroups — C24×D5×C11 #13183474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×D₅×C₁₁ #13183474