Subgroups — C₂⁴×D₅₅ #13183475

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×D₅₅	C₂	1	30	yes	maximal, direct product factor
3	C₂³×C₅×C₁₁	C₂²	1	15	yes	complemented
4	C₂²×D₅₅	C₂²	1	140	yes	direct product factor
5	C₂⁴×D₁₁	—	5	1	no	maximal, Hall
6	C₂²×C₅×C₁₁	C₂³	1	35	yes	complemented
7	C₂×D₅₅	C₂³	1	120	yes	direct product factor
8	C₂⁴×C₁₁	D₅	1	1	yes	characteristic, complemented
9	C₂³×D₁₁	—	5	30	no	—
10	C₂⁴×D₅	—	11	1	no	maximal, Hall
11	C₂×C₅×C₁₁	C₂⁴	1	15	yes	complemented
12	D₅₅	C₂⁴	1	16	yes	direct product factor
13	C₂³×C₁₁	C₂×D₅	1	15	yes	complemented
14	C₂²×D₁₁	—	5	140	no	—
15	C₂⁴×C₅	D₁₁	1	1	yes	characteristic, complemented
16	C₂³×D₅	—	11	30	no	—
17	C₅×C₁₁	C₂⁵	1	1	yes	characteristic, complemented, Hall
18	C₂²×C₁₁	C₂²×D₅	1	35	yes	complemented
19	C₂×D₁₁	—	5	120	no	—
20	C₂³×C₅	C₂×D₁₁	1	15	yes	complemented
21	C₂²×D₅	—	11	140	no	—
22	C₂⁵	—	55	1	no	Sylow
23	C₂×C₁₁	C₂³×D₅	1	15	yes	complemented
24	D₁₁	—	5	16	no	—
25	C₂²×C₅	C₂²×D₁₁	1	35	yes	complemented
26	C₂×D₅	—	11	120	no	—
27	C₂⁴	—	55	30	no	—
28	C₂⁴	D₅₅	1	1	yes	characteristic, direct product factor
29	C₁₁	C₂⁴×D₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₅	C₂³×D₁₁	1	15	yes	complemented
31	D₅	—	11	16	no	—
32	C₂³	—	55	140	no	—
33	C₂³	C₂×D₅₅	1	15	yes	direct product factor
34	C₅	C₂⁴×D₁₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	55	120	no	—
36	C₂²	C₂²×D₅₅	1	35	yes	direct product factor
37	C₂	—	55	16	no	—
38	C₂	C₂³×D₅₅	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₅×C₁₁	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×C₁₁	C₂	semidirect
2. C₂³×D₅₅	C₂	direct (N × H)
3. C₂³×C₅×C₁₁	C₂²	semidirect
4. C₂²×D₅₅	C₂²	direct (N × H)
6. C₂²×C₅×C₁₁	C₂³	semidirect
7. C₂×D₅₅	C₂³	direct (N × H)
8. C₂⁴×C₁₁	D₅	semidirect
11. C₂×C₅×C₁₁	C₂⁴	semidirect
12. D₅₅	C₂⁴	direct (N × H)
13. C₂³×C₁₁	C₂×D₅	semidirect
15. C₂⁴×C₅	D₁₁	semidirect
17. C₅×C₁₁	C₂⁵	semidirect
18. C₂²×C₁₁	C₂²×D₅	semidirect
20. C₂³×C₅	C₂×D₁₁	semidirect
23. C₂×C₁₁	C₂³×D₅	semidirect
25. C₂²×C₅	C₂²×D₁₁	semidirect
28. C₂⁴	D₅₅	direct (N × H)
29. C₁₁	C₂⁴×D₅	semidirect
30. C₂×C₅	C₂³×D₁₁	semidirect
33. C₂³	C₂×D₅₅	direct (N × H)
34. C₅	C₂⁴×D₁₁	semidirect
36. C₂²	C₂²×D₅₅	direct (N × H)
38. C₂	C₂³×D₅₅	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×D₅₅	2
C₂⁴×D₁₁	5
C₂⁴×D₅	11

Subgroups — C24×D55 #13183475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×D₅₅ #13183475