Subgroups — D₃×D₅₅₅ #20269155

Order 6660.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₅₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅₅₅	—	3	1	no	maximal
5	D₃×D₁₈₅	—	3	1	no	maximal
6	C₃²×C₅×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×D₁₁₁	—	5	1	no	maximal, Hall
8	C₂×C₃×C₅×C₃₇	—	3	1	no	—
9	D₅₅₅	—	3	1	no	—
10	D₅₅₅	—	3	1	no	—
11	D₅₅₅	—	6	1	no	—
12	D₅₅₅	D₃	1	1	yes	characteristic, direct product factor
13	C₅×D₃×C₃₇	D₃	1	1	yes	characteristic, complemented
14	C₃×D₁₈₅	—	3	1	no	—
15	C₂×D₁₈₅	—	9	1	no	Hall
16	C₃⋊D₁₁₁	—	5	1	no	—
17	C₃×D₁₁₁	—	5	1	no	—
18	C₃×D₃×C₃₇	D₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₃₇	—	2	1	no	—
20	C₃×C₅×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented
22	C₂×D₁₁₁	—	15	1	no	—
23	D₃×D₃₇	—	15	1	no	—
24	C₂×C₅×C₃₇	—	3	1	no	—
25	D₁₈₅	—	3	1	no	—
26	D₁₈₅	—	9	1	no	—
27	C₃²×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₃₇	—	3	1	no	—
29	D₁₁₁	—	5	1	no	—
30	D₁₁₁	—	15	1	no	—
31	D₁₁₁	—	15	1	no	—
32	D₁₁₁	—	30	1	no	—
33	C₃×D₃₇	—	15	1	no	—
34	D₃×C₃₇	D₁₅	1	1	yes	characteristic, complemented
35	C₅×C₃₇	D₃²	1	1	yes	characteristic, complemented, Hall
36	D₃×D₁₅	—	37	1	no	maximal, Hall
37	C₂×D₃₇	—	45	1	no	Hall
38	C₃×C₃₇	—	2	1	no	—
39	C₃×C₃₇	D₃×D₅	1	1	yes	characteristic, complemented
40	C₃×C₃₇	C₂×D₁₅	1	1	yes	characteristic, complemented
41	C₃⋊D₁₅	—	37	1	no	—
42	C₃×D₁₅	—	37	1	no	—
43	C₃×C₅×D₃	D₃₇	1	1	yes	characteristic, complemented
44	C₂×C₃₇	—	3	1	no	—
45	D₃₇	—	15	1	no	—
46	D₃₇	—	45	1	no	—
47	C₂×D₁₅	—	111	1	no	—
48	D₃×D₅	—	111	1	no	—
49	C₃²×C₅	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
50	C₃₇	D₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
51	D₃²	—	185	1	no	Hall
52	C₂×C₃×C₅	—	3	1	no	—
53	D₁₅	—	37	1	no	—
54	D₁₅	—	111	1	no	—
55	D₁₅	—	111	1	no	—
56	D₁₅	—	222	1	no	—
57	C₃×D₅	—	111	1	no	—
58	C₅×D₃	D₁₁₁	1	1	yes	characteristic, complemented
59	C₂×D₅	—	333	1	no	Hall
60	C₃⋊D₃	—	185	1	no	—
61	C₃×D₃	—	185	1	no	—
62	C₃×D₃	D₁₈₅	1	1	yes	characteristic, complemented
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	D₃×D₃₇	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×D₁₁₁	1	1	yes	characteristic, complemented
66	C₂×D₃	—	555	1	no	—
67	C₂×D₃	—	555	1	no	—
68	C₂×C₅	—	3	1	no	—
69	D₅	—	333	1	no	—
70	D₅	—	111	1	no	—
71	C₃²	C₂×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	3	1	no	—
73	C₂×C₃	—	555	1	no	—
74	D₃	—	555	1	no	—
75	D₃	—	555	1	no	—
76	D₃	—	1110	1	no	—
77	D₃	—	185	1	no	—
78	D₃	D₅₅₅	1	1	yes	characteristic, direct product factor
79	C₅	D₃×D₁₁₁	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	1665	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₁₈₅	1	1	yes	characteristic, complemented
83	C₃	C₂×D₅₅₅	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	555	1	no	—
86	C₂	—	1665	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₅₅₅	C₂	semidirect
2. C₃×D₅₅₅	C₂	semidirect
3. C₃×C₅×D₃×C₃₇	C₂	semidirect
6. C₃²×C₅×C₃₇	C₂²	semidirect
12. D₅₅₅	D₃	direct (N × H)
13. C₅×D₃×C₃₇	D₃	semidirect
18. C₃×D₃×C₃₇	D₅	semidirect
20. C₃×C₅×C₃₇	C₂×D₃	semidirect
21. C₃×C₅×C₃₇	C₂×D₃	semidirect
27. C₃²×C₃₇	C₂×D₅	semidirect
34. D₃×C₃₇	D₁₅	semidirect
35. C₅×C₃₇	D₃²	semidirect
39. C₃×C₃₇	D₃×D₅	semidirect
40. C₃×C₃₇	C₂×D₁₅	semidirect
43. C₃×C₅×D₃	D₃₇	semidirect
49. C₃²×C₅	C₂×D₃₇	semidirect
50. C₃₇	D₃×D₁₅	semidirect
58. C₅×D₃	D₁₁₁	semidirect
62. C₃×D₃	D₁₈₅	semidirect
64. C₃×C₅	D₃×D₃₇	semidirect
65. C₃×C₅	C₂×D₁₁₁	semidirect
71. C₃²	C₂×D₁₈₅	semidirect
78. D₃	D₅₅₅	direct (N × H)
79. C₅	D₃×D₁₁₁	semidirect
82. C₃	D₃×D₁₈₅	semidirect
83. C₃	C₂×D₅₅₅	semidirect

Subgroups — D3×D555 #20269155

Conjugacy classes of subgroups

Complements

Subgroups — D₃×D₅₅₅ #20269155