Subgroups — C₂×C₃²×D₅₅ #14520486

Order 1980.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×D₅₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₅₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₁₁	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅×C₁₁	C₂×C₃	1	4	yes	complemented
7	C₃×D₅₅	C₂×C₃	1	8	yes	direct product factor
8	C₂×D₅₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₁₁	D₅	1	1	yes	characteristic, complemented
10	C₃²×D₁₁	—	5	2	no	—
11	C₂×C₃²×D₅	—	11	1	no	maximal, Hall
12	C₃×C₅×C₁₁	C₂²×C₃	1	4	yes	complemented
13	C₂×C₃×D₁₁	—	5	4	no	—
14	C₂×C₅×C₁₁	C₂×C₃²	1	1	yes	characteristic, complemented
15	D₅₅	C₂×C₃²	1	2	yes	direct product factor
16	C₃²×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃²×C₅	D₁₁	1	1	yes	characteristic, complemented
18	C₃²×D₅	—	11	2	no	—
19	C₂×C₃×C₁₁	C₃×D₅	1	4	yes	complemented
20	C₃×D₁₁	—	5	8	no	—
21	C₂×C₃×D₅	—	11	4	no	—
22	C₅×C₁₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₃²×C₅	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₁	—	5	1	no	Hall
25	C₂²×C₃²	—	55	1	no	Hall
26	C₃×C₁₁	C₂×C₃×D₅	1	4	yes	complemented
27	C₂×C₃×C₅	C₃×D₁₁	1	4	yes	complemented
28	C₃×D₅	—	11	8	no	—
29	C₂×C₁₁	C₃²×D₅	1	1	yes	characteristic, complemented
30	D₁₁	—	5	2	no	—
31	C₂×D₅	—	11	1	no	Hall
32	C₂×C₃²	—	55	2	no	—
33	C₂×C₃²	D₅₅	1	1	yes	characteristic, direct product factor
34	C₃×C₅	C₂×C₃×D₁₁	1	4	yes	complemented
35	C₂²×C₃	—	55	4	no	—
36	C₁₁	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₅	C₃²×D₁₁	1	1	yes	characteristic, complemented
38	D₅	—	11	2	no	—
39	C₃²	C₂×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	55	8	no	—
41	C₂×C₃	C₃×D₅₅	1	4	yes	direct product factor
42	C₅	C₂×C₃²×D₁₁	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	55	1	no	Sylow
44	C₃	C₂×C₃×D₅₅	1	4	yes	direct product factor
45	C₂	—	55	2	no	—
46	C₂	C₃²×D₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₅×C₁₁	C₂	semidirect
2. C₃²×D₅₅	C₂	direct (N × H)
3. C₂×C₃×D₅₅	C₃	direct (N × H)
4. C₃²×C₅×C₁₁	C₂²	semidirect
6. C₂×C₃×C₅×C₁₁	C₂×C₃	semidirect
7. C₃×D₅₅	C₂×C₃	direct (N × H)
8. C₂×D₅₅	C₃²	direct (N × H)
9. C₂×C₃²×C₁₁	D₅	semidirect
12. C₃×C₅×C₁₁	C₂²×C₃	semidirect
14. C₂×C₅×C₁₁	C₂×C₃²	semidirect
15. D₅₅	C₂×C₃²	direct (N × H)
16. C₃²×C₁₁	C₂×D₅	semidirect
17. C₂×C₃²×C₅	D₁₁	semidirect
19. C₂×C₃×C₁₁	C₃×D₅	semidirect
22. C₅×C₁₁	C₂²×C₃²	semidirect
23. C₃²×C₅	C₂×D₁₁	semidirect
26. C₃×C₁₁	C₂×C₃×D₅	semidirect
27. C₂×C₃×C₅	C₃×D₁₁	semidirect
29. C₂×C₁₁	C₃²×D₅	semidirect
33. C₂×C₃²	D₅₅	direct (N × H)
34. C₃×C₅	C₂×C₃×D₁₁	semidirect
36. C₁₁	C₂×C₃²×D₅	semidirect
37. C₂×C₅	C₃²×D₁₁	semidirect
39. C₃²	C₂×D₅₅	direct (N × H)
41. C₂×C₃	C₃×D₅₅	direct (N × H)
42. C₅	C₂×C₃²×D₁₁	semidirect
44. C₃	C₂×C₃×D₅₅	direct (N × H)
46. C₂	C₃²×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
C₂×C₃²×C₅×C₁₁	2
C₃²×D₅₅	2
C₂×C₃×D₅₅	3
C₂×C₃²×D₁₁	5
C₂×C₃²×D₅	11

Subgroups — C2×C32×D55 #14520486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₅₅ #14520486