Subgroups — D₃₃×D₅₅ #20300115

Order 7260.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊(C₁₁⋊D₁₁))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₁×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₅₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₁×D₃₃	—	5	1	no	maximal, Hall
7	C₅⋊(C₁₁⋊D₁₁)	—	3	1	no	—
8	C₁₁×D₅₅	D₃	1	1	yes	characteristic, complemented
9	C₅×C₁₁×D₁₁	—	3	1	no	—
10	C₃⋊(C₁₁⋊D₁₁)	—	5	1	no	—
11	C₁₁×D₃₃	D₅	1	1	yes	characteristic, complemented
12	C₃×C₁₁×D₁₁	—	5	1	no	—
13	D₃×D₅₅	—	11	1	no	maximal
14	D₅×D₃₃	—	11	1	no	maximal
15	C₅×C₁₁²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
16	D₁₁²	—	15	1	no	Hall
17	C₃×C₁₁²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	D₁₆₅	—	11	1	no	—
19	D₁₆₅	—	11	1	no	—
20	D₁₆₅	—	22	5	no	—
21	C₅×D₃₃	D₁₁	1	1	yes	characteristic, complemented
22	C₅×D₃×C₁₁	—	11	1	no	—
23	C₃×D₅₅	D₁₁	1	1	yes	characteristic, complemented
24	C₃×D₅×C₁₁	—	11	1	no	—
25	C₁₁⋊D₁₁	—	15	1	no	—
26	C₁₁×D₁₁	—	3	1	no	—
27	C₁₁×D₁₁	—	5	1	no	—
28	C₂×D₅₅	—	33	1	no	—
29	D₅×D₁₁	—	33	1	no	—
30	C₃×C₅×C₁₁	—	2	5	no	—
31	C₃×C₅×C₁₁	C₂×D₁₁	1	1	yes	characteristic, complemented
32	C₃×C₅×C₁₁	C₂×D₁₁	1	1	yes	characteristic, complemented
33	C₂×D₃₃	—	55	1	no	—
34	D₃×D₁₁	—	55	1	no	—
35	C₁₁²	D₃×D₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₅×C₁₁	—	33	1	no	—
37	D₅₅	—	33	1	no	—
38	D₅₅	—	33	1	no	—
39	D₅₅	—	66	5	no	—
40	D₅₅	D₃₃	1	1	yes	characteristic, direct product factor
41	C₅×D₁₁	—	3	1	no	—
42	D₅×C₁₁	—	11	1	no	—
43	C₂×C₃×C₁₁	—	55	1	no	—
44	D₃₃	—	55	1	no	—
45	D₃₃	—	55	1	no	—
46	D₃₃	—	110	5	no	—
47	D₃₃	D₅₅	1	1	yes	characteristic, direct product factor
48	C₃×D₁₁	—	5	1	no	—
49	D₃×C₁₁	—	11	1	no	—
50	D₃×D₅	—	121	1	no	Hall
51	C₅×C₁₁	—	2	5	no	—
52	C₅×C₁₁	D₃×D₁₁	1	1	yes	characteristic, complemented
53	C₅×C₁₁	C₂×D₃₃	1	1	yes	characteristic, complemented
54	C₂×D₁₁	—	165	1	no	—
55	C₂×D₁₁	—	165	1	no	—
56	C₃×C₁₁	—	2	5	no	—
57	C₃×C₁₁	D₅×D₁₁	1	1	yes	characteristic, complemented
58	C₃×C₁₁	C₂×D₅₅	1	1	yes	characteristic, complemented
59	D₁₅	—	121	1	no	—
60	C₃×D₅	—	11	1	no	—
61	C₅×D₃	—	11	1	no	—
62	C₂×C₁₁	—	33	1	no	—
63	C₂×C₁₁	—	55	1	no	—
64	D₁₁	—	3	1	no	—
65	D₁₁	—	5	1	no	—
66	D₁₁	—	330	5	no	—
67	D₁₁	—	165	1	no	—
68	D₁₁	—	165	1	no	—
69	C₂×D₅	—	363	1	no	Hall
70	C₃×C₅	D₁₁²	1	1	yes	characteristic, complemented, Hall
71	C₂×D₃	—	605	1	no	Hall
72	C₁₁	—	2	5	no	—
73	C₁₁	D₅×D₃₃	1	1	yes	characteristic, complemented
74	C₁₁	D₃×D₅₅	1	1	yes	characteristic, complemented
75	C₂×C₅	—	33	1	no	—
76	D₅	—	11	1	no	—
77	D₅	—	363	1	no	—
78	C₂×C₃	—	55	1	no	—
79	D₃	—	11	1	no	—
80	D₃	—	605	1	no	—
81	C₅	D₁₁×D₃₃	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	1815	1	no	Sylow
83	C₃	D₁₁×D₅₅	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	1815	1	no	—
85	C₂	—	33	1	no	—
86	C₂	—	55	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₁₁²	C₂²
LCS	G ▷ C₃×C₅×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊(C₁₁⋊D₁₁))	C₂	semidirect
2. C₅×C₁₁×D₃₃	C₂	semidirect
3. C₃×C₁₁×D₅₅	C₂	semidirect
5. C₃×C₅×C₁₁²	C₂²	semidirect
8. C₁₁×D₅₅	D₃	semidirect
11. C₁₁×D₃₃	D₅	semidirect
15. C₅×C₁₁²	C₂×D₃	semidirect
17. C₃×C₁₁²	C₂×D₅	semidirect
21. C₅×D₃₃	D₁₁	semidirect
23. C₃×D₅₅	D₁₁	semidirect
31. C₃×C₅×C₁₁	C₂×D₁₁	semidirect
32. C₃×C₅×C₁₁	C₂×D₁₁	semidirect
35. C₁₁²	D₃×D₅	semidirect
40. D₅₅	D₃₃	direct (N × H)
47. D₃₃	D₅₅	direct (N × H)
52. C₅×C₁₁	D₃×D₁₁	semidirect
53. C₅×C₁₁	C₂×D₃₃	semidirect
57. C₃×C₁₁	D₅×D₁₁	semidirect
58. C₃×C₁₁	C₂×D₅₅	semidirect
70. C₃×C₅	D₁₁²	semidirect
73. C₁₁	D₅×D₃₃	semidirect
74. C₁₁	D₃×D₅₅	semidirect
81. C₅	D₁₁×D₃₃	semidirect
83. C₃	D₁₁×D₅₅	semidirect

Subgroups — D33×D55 #20300115

Conjugacy classes of subgroups

Complements

Subgroups — D₃₃×D₅₅ #20300115