Subgroups — D₃₃⋊D₁₅ #14520479

Order 1980.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅⋊D₁₁	—	3	1	no	maximal
5	D₁₁×D₁₅	—	3	1	no	maximal
6	C₃²×C₅×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
7	(C₃⋊D₃)⋊D₁₁	—	5	1	no	maximal, Hall
8	D₁₆₅	D₃	1	1	yes	characteristic, complemented
9	C₁₁×D₁₅	—	3	1	no	—
10	C₁₁×D₁₅	—	3	1	no	—
11	C₁₁×D₁₅	—	6	1	no	—
12	C₅×D₃₃	D₃	1	1	yes	characteristic, complemented
13	C₃×D₅₅	—	3	1	no	—
14	C₃×C₅×D₁₁	—	3	1	no	—
15	D₅×D₁₁	—	9	1	no	Hall
16	C₁₁×C₃⋊D₃	—	5	1	no	—
17	C₃×D₃₃	—	5	1	no	—
18	C₃×D₃₃	D₅	1	1	yes	characteristic, complemented
19	D₃×D₁₅	—	11	1	no	maximal, Hall
20	C₃×C₅×C₁₁	—	2	1	no	—
21	C₃×C₅×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented
22	C₃×C₅×C₁₁	C₂×D₃	1	1	yes	characteristic, complemented
23	D₃×D₁₁	—	15	1	no	—
24	D₃×D₁₁	—	15	1	no	—
25	D₅₅	—	3	1	no	—
26	C₅×D₁₁	—	3	1	no	—
27	D₅×C₁₁	—	9	1	no	—
28	C₃²×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
29	C₃⋊D₁₅	D₁₁	1	1	yes	characteristic, complemented
30	C₃×D₁₅	—	11	1	no	—
31	C₃×C₅×D₃	—	11	1	no	—
32	D₃₃	—	5	1	no	—
33	D₃₃	D₁₅	1	1	yes	characteristic, complemented
34	C₃×D₁₁	—	3	1	no	—
35	C₃×D₁₁	—	15	1	no	—
36	D₃×C₁₁	—	15	1	no	—
37	D₃×C₁₁	—	15	1	no	—
38	D₃×C₁₁	—	30	1	no	—
39	C₂×D₁₅	—	33	1	no	—
40	D₃×D₅	—	33	1	no	—
41	C₅×C₁₁	D₃²	1	1	yes	characteristic, complemented, Hall
42	C₃²×C₅	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
43	C₂×D₁₁	—	45	1	no	Hall
44	D₃²	—	55	1	no	Hall
45	C₃×C₁₁	—	2	1	no	—
46	C₃×C₁₁	D₃×D₅	1	1	yes	characteristic, complemented
47	C₃×C₁₁	C₂×D₁₅	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅	—	33	1	no	—
49	D₁₅	—	3	1	no	—
50	D₁₅	—	3	1	no	—
51	D₁₅	—	6	1	no	—
52	D₁₅	—	11	1	no	—
53	C₃×D₅	—	33	1	no	—
54	C₅×D₃	—	11	1	no	—
55	C₂×C₁₁	—	45	1	no	—
56	D₁₁	—	3	1	no	—
57	D₁₁	—	15	1	no	—
58	C₂×D₅	—	99	1	no	Hall
59	C₃⋊D₃	—	5	1	no	—
60	C₃×D₃	—	11	1	no	—
61	C₃×D₃	—	55	1	no	—
62	C₃×C₅	—	2	1	no	—
63	C₃×C₅	D₃×D₁₁	1	1	yes	characteristic, complemented
64	C₃×C₅	D₃×D₁₁	1	1	yes	characteristic, complemented
65	C₂×D₃	—	165	1	no	—
66	C₂×D₃	—	165	1	no	—
67	C₁₁	D₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₅	—	33	1	no	—
69	D₅	—	9	1	no	—
70	D₅	—	33	1	no	—
71	C₃²	D₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	33	1	no	—
73	C₂×C₃	—	165	1	no	—
74	D₃	—	11	1	no	—
75	D₃	—	15	1	no	—
76	D₃	—	15	1	no	—
77	D₃	—	30	1	no	—
78	D₃	—	55	1	no	—
79	C₅	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	495	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₁×D₁₅	1	1	yes	characteristic, complemented
83	C₃	D₁₅⋊D₁₁	1	1	yes	characteristic, complemented
84	C₂	—	33	1	no	—
85	C₂	—	45	1	no	—
86	C₂	—	165	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₃⋊D₁₅	C₂	semidirect
2. C₃×D₁₆₅	C₂	semidirect
3. C₃×C₅×D₃₃	C₂	semidirect
6. C₃²×C₅×C₁₁	C₂²	semidirect
8. D₁₆₅	D₃	semidirect
12. C₅×D₃₃	D₃	semidirect
18. C₃×D₃₃	D₅	semidirect
21. C₃×C₅×C₁₁	C₂×D₃	semidirect
22. C₃×C₅×C₁₁	C₂×D₃	semidirect
28. C₃²×C₁₁	C₂×D₅	semidirect
29. C₃⋊D₁₅	D₁₁	semidirect
33. D₃₃	D₁₅	semidirect
41. C₅×C₁₁	D₃²	semidirect
42. C₃²×C₅	C₂×D₁₁	semidirect
46. C₃×C₁₁	D₃×D₅	semidirect
47. C₃×C₁₁	C₂×D₁₅	semidirect
63. C₃×C₅	D₃×D₁₁	semidirect
64. C₃×C₅	D₃×D₁₁	semidirect
67. C₁₁	D₃×D₁₅	semidirect
71. C₃²	D₅×D₁₁	semidirect
79. C₅	(C₃⋊D₃)⋊D₁₁	semidirect
82. C₃	D₁₁×D₁₅	semidirect
83. C₃	D₁₅⋊D₁₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×C₃⋊D₁₅	2
C₃×D₁₆₅	2
C₃×C₅×D₃₃	2
D₁₅⋊D₁₁	3
D₁₁×D₁₅	3
(C₃⋊D₃)⋊D₁₁	5
D₃×D₁₅	11

Subgroups — D33⋊D15 #14520479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₃⋊D₁₅ #14520479