Subgroups — C₂×C₃×D₅₅₅ #20269178

Order 6660.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₁₈₅	—	3	1	no	maximal
5	C₃²×C₅×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₁₁₁	—	5	1	no	maximal, Hall
7	C₂×C₃×C₅×C₃₇	—	2	1	no	—
8	C₂×C₃×C₅×C₃₇	D₃	1	1	yes	characteristic, complemented
9	C₂×C₃×C₅×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
10	D₅₅₅	C₂×C₃	1	2	yes	direct product factor
11	C₃×D₁₈₅	—	3	2	no	—
12	C₂×D₁₈₅	—	3	1	no	Hall
13	C₂×C₃²×C₃₇	D₅	1	1	yes	characteristic, complemented
14	C₃×D₁₁₁	—	5	2	no	—
15	C₃×C₅×C₃₇	—	2	1	no	—
16	C₃×C₅×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₅×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×D₁₁₁	—	5	1	no	—
19	C₂×C₃×D₃₇	—	15	1	no	—
20	C₂×C₅×C₃₇	C₃×D₃	1	1	yes	characteristic, complemented
21	D₁₈₅	—	3	2	no	—
22	C₃²×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₃₇	—	2	1	no	—
24	C₂×C₃×C₃₇	C₃×D₅	1	1	yes	characteristic, complemented
25	C₂×C₃×C₃₇	D₁₅	1	1	yes	characteristic, complemented
26	D₁₁₁	—	5	2	no	—
27	C₃×D₃₇	—	15	2	no	—
28	C₅×C₃₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×D₁₅	—	37	1	no	maximal, Hall
30	C₂×D₃₇	—	15	1	no	Hall
31	C₃×C₃₇	—	2	1	no	—
32	C₃×C₃₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented
33	C₃×C₃₇	C₂×D₁₅	1	1	yes	characteristic, complemented
34	C₂×C₃²×C₅	D₃₇	1	1	yes	characteristic, complemented
35	C₃×D₁₅	—	37	2	no	—
36	C₂×C₃₇	C₃×D₁₅	1	1	yes	characteristic, complemented
37	D₃₇	—	15	2	no	—
38	C₂×D₁₅	—	37	1	no	—
39	C₂×C₃×D₅	—	111	1	no	—
40	C₃²×C₅	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
41	C₃₇	C₂×C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃×D₃	—	185	1	no	Hall
43	C₂×C₃×C₅	—	2	1	no	—
44	C₂×C₃×C₅	C₃×D₃₇	1	1	yes	characteristic, complemented
45	C₂×C₃×C₅	D₁₁₁	1	1	yes	characteristic, complemented
46	D₁₅	—	37	2	no	—
47	C₃×D₅	—	111	2	no	—
48	C₂×D₅	—	111	1	no	Hall
49	C₂×C₃²	D₁₈₅	1	1	yes	characteristic, complemented
50	C₃×D₃	—	185	2	no	—
51	C₃×C₅	—	2	1	no	—
52	C₃×C₅	C₂×C₃×D₃₇	1	1	yes	characteristic, complemented
53	C₃×C₅	C₂×D₁₁₁	1	1	yes	characteristic, complemented
54	C₂²×C₃	—	555	1	no	—
55	C₂×D₃	—	185	1	no	—
56	C₂×C₅	C₃×D₁₁₁	1	1	yes	characteristic, complemented
57	D₅	—	111	2	no	—
58	C₃²	C₂×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	—	555	2	no	—
61	C₂×C₃	C₃×D₁₈₅	1	1	yes	characteristic, complemented
62	C₂×C₃	D₅₅₅	1	1	yes	characteristic, direct product factor
63	D₃	—	185	2	no	—
64	C₅	C₂×C₃×D₁₁₁	1	1	yes	characteristic, complemented, Sylow
65	C₂²	—	555	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×D₁₈₅	1	1	yes	characteristic, complemented
68	C₃	C₂×D₅₅₅	1	1	yes	characteristic, direct product factor
69	C₂	—	555	2	no	—
70	C₂	C₃×D₅₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₅₅₅
commutator, hypocenter	C₃×C₅×C₃₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₃₇	C₂
LCS	G ▷ C₃×C₅×C₃₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₅₅₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₃₇	C₂	semidirect
3. C₂×D₅₅₅	C₃	direct (N × H)
5. C₃²×C₅×C₃₇	C₂²	semidirect
8. C₂×C₃×C₅×C₃₇	D₃	semidirect
9. C₂×C₃×C₅×C₃₇	C₂×C₃	semidirect
10. D₅₅₅	C₂×C₃	direct (N × H)
13. C₂×C₃²×C₃₇	D₅	semidirect
16. C₃×C₅×C₃₇	C₂×D₃	semidirect
17. C₃×C₅×C₃₇	C₂²×C₃	semidirect
20. C₂×C₅×C₃₇	C₃×D₃	semidirect
22. C₃²×C₃₇	C₂×D₅	semidirect
24. C₂×C₃×C₃₇	C₃×D₅	semidirect
25. C₂×C₃×C₃₇	D₁₅	semidirect
28. C₅×C₃₇	C₂×C₃×D₃	semidirect
32. C₃×C₃₇	C₂×C₃×D₅	semidirect
33. C₃×C₃₇	C₂×D₁₅	semidirect
34. C₂×C₃²×C₅	D₃₇	semidirect
36. C₂×C₃₇	C₃×D₁₅	semidirect
40. C₃²×C₅	C₂×D₃₇	semidirect
41. C₃₇	C₂×C₃×D₁₅	semidirect
44. C₂×C₃×C₅	C₃×D₃₇	semidirect
45. C₂×C₃×C₅	D₁₁₁	semidirect
49. C₂×C₃²	D₁₈₅	semidirect
52. C₃×C₅	C₂×C₃×D₃₇	semidirect
53. C₃×C₅	C₂×D₁₁₁	semidirect
56. C₂×C₅	C₃×D₁₁₁	semidirect
58. C₃²	C₂×D₁₈₅	semidirect
61. C₂×C₃	C₃×D₁₈₅	semidirect
62. C₂×C₃	D₅₅₅	direct (N × H)
64. C₅	C₂×C₃×D₁₁₁	semidirect
67. C₃	C₂×C₃×D₁₈₅	semidirect
68. C₃	C₂×D₅₅₅	direct (N × H)
70. C₂	C₃×D₅₅₅	direct (N × H)

Subgroups — C2×C3×D555 #20269178

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₅₅₅ #20269178