Subgroups — C₂×C₃⋊D₂₈₀₅ #46778216

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₂₈₀₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₈₀₅	—	3	4	no	maximal
4	C₃²×C₅×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₅₆₁	—	5	1	no	maximal, Hall
6	D₂₈₀₅	—	3	8	no	—
7	C₂×C₃×C₅×C₁₁×C₁₇	D₃	1	4	yes	complemented
8	C₂×D₉₃₅	—	9	1	no	Hall
9	C₃⋊D₅₆₁	—	5	2	no	—
10	C₂×C₃²×C₁₁×C₁₇	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃⋊D₂₅₅	—	11	1	no	maximal, Hall
12	C₃×C₅×C₁₁×C₁₇	C₂×D₃	1	4	yes	complemented
13	C₂×D₅₆₁	—	15	4	no	—
14	C₂×C₃⋊D₁₆₅	—	17	1	no	maximal, Hall
15	C₂×C₅×C₁₁×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented
16	D₉₃₅	—	9	2	no	—
17	C₃²×C₁₁×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₅×C₁₇	D₁₁	1	1	yes	characteristic, complemented
19	C₃⋊D₂₅₅	—	11	2	no	—
20	C₂×C₃×C₁₁×C₁₇	D₁₅	1	4	yes	complemented
21	D₅₆₁	—	15	8	no	—
22	C₂×D₂₅₅	—	33	4	no	—
23	C₂×C₃²×C₅×C₁₁	D₁₇	1	1	yes	characteristic, complemented
24	C₃⋊D₁₆₅	—	17	2	no	—
25	C₅×C₁₁×C₁₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₅×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×D₁₈₇	—	45	1	no	Hall
28	C₂×D₁₆₅	—	51	4	no	—
29	C₂×C₃⋊D₅₁	—	55	1	no	Hall
30	C₃×C₁₁×C₁₇	C₂×D₁₅	1	4	yes	complemented
31	C₂×C₃×C₅×C₁₇	D₃₃	1	4	yes	complemented
32	D₂₅₅	—	33	8	no	—
33	C₃²×C₅×C₁₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃⋊D₃₃	—	85	1	no	Hall
35	C₂×C₁₁×C₁₇	C₃⋊D₁₅	1	1	yes	characteristic, complemented
36	D₁₈₇	—	45	2	no	—
37	C₂×D₈₅	—	99	1	no	Hall
38	C₂×C₃×C₅×C₁₁	D₅₁	1	4	yes	complemented
39	D₁₆₅	—	51	8	no	—
40	C₂×C₃²×C₁₇	D₅₅	1	1	yes	characteristic, complemented
41	C₃⋊D₅₁	—	55	2	no	—
42	C₃×C₅×C₁₇	C₂×D₃₃	1	4	yes	complemented
43	C₂×D₅₅	—	153	1	no	Hall
44	C₂×D₅₁	—	165	4	no	—
45	C₂×C₃²×C₁₁	D₈₅	1	1	yes	characteristic, complemented
46	C₃⋊D₃₃	—	85	2	no	—
47	C₁₁×C₁₇	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃⋊D₁₅	—	187	1	no	Hall
49	C₂×C₅×C₁₇	C₃⋊D₃₃	1	1	yes	characteristic, complemented
50	D₈₅	—	99	2	no	—
51	C₃×C₅×C₁₁	C₂×D₅₁	1	4	yes	complemented
52	C₃²×C₁₇	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
53	C₂×D₃₃	—	255	4	no	—
54	C₂×C₅×C₁₁	C₃⋊D₅₁	1	1	yes	characteristic, complemented
55	D₅₅	—	153	2	no	—
56	C₂×C₃×C₁₇	D₁₆₅	1	4	yes	complemented
57	D₅₁	—	165	8	no	—
58	C₃²×C₁₁	C₂×D₈₅	1	1	yes	characteristic, complemented, Hall
59	C₂×C₃²×C₅	D₁₈₇	1	1	yes	characteristic, complemented
60	C₃⋊D₁₅	—	187	2	no	—
61	C₅×C₁₇	C₂×C₃⋊D₃₃	1	1	yes	characteristic, complemented, Hall
62	C₂×D₁₇	—	495	1	no	Hall
63	C₂×C₃×C₁₁	D₂₅₅	1	4	yes	complemented
64	D₃₃	—	255	8	no	—
65	C₂×D₁₅	—	561	4	no	—
66	C₅×C₁₁	C₂×C₃⋊D₅₁	1	1	yes	characteristic, complemented, Hall
67	C₃×C₁₇	C₂×D₁₆₅	1	4	yes	complemented
68	C₃²×C₅	C₂×D₁₈₇	1	1	yes	characteristic, complemented, Hall
69	C₂×D₁₁	—	765	1	no	Hall
70	C₂×C₃⋊D₃	—	935	1	no	Hall
71	C₂×C₁₇	C₃⋊D₁₆₅	1	1	yes	characteristic, complemented
72	D₁₇	—	495	2	no	—
73	C₃×C₁₁	C₂×D₂₅₅	1	4	yes	complemented
74	C₂×C₃×C₅	D₅₆₁	1	4	yes	complemented
75	D₁₅	—	561	8	no	—
76	C₂×C₁₁	C₃⋊D₂₅₅	1	1	yes	characteristic, complemented
77	D₁₁	—	765	2	no	—
78	C₂×D₅	—	1683	1	no	Hall
79	C₂×C₃²	D₉₃₅	1	1	yes	characteristic, complemented
80	C₃⋊D₃	—	935	2	no	—
81	C₁₇	C₂×C₃⋊D₁₆₅	1	1	yes	characteristic, complemented, Sylow
82	C₃×C₅	C₂×D₅₆₁	1	4	yes	complemented
83	C₂×D₃	—	2805	4	no	—
84	C₁₁	C₂×C₃⋊D₂₅₅	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	C₃⋊D₅₆₁	1	1	yes	characteristic, complemented
86	D₅	—	1683	2	no	—
87	C₃²	C₂×D₉₃₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	D₂₈₀₅	1	4	yes	complemented
89	D₃	—	2805	8	no	—
90	C₅	C₂×C₃⋊D₅₆₁	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	8415	1	no	Sylow
92	C₃	C₂×D₂₈₀₅	1	4	yes	complemented
93	C₂	—	8415	2	no	—
94	C₂	C₃⋊D₂₈₀₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₂₈₀₅
commutator, cosocle, hypocenter	C₃²×C₅×C₁₁×C₁₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁×C₁₇	C₂
LCS	G ▷ C₃²×C₅×C₁₁×C₁₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₂₈₀₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₁×C₁₇	C₂	semidirect
4. C₃²×C₅×C₁₁×C₁₇	C₂²	semidirect
7. C₂×C₃×C₅×C₁₁×C₁₇	D₃	semidirect
10. C₂×C₃²×C₁₁×C₁₇	D₅	semidirect
12. C₃×C₅×C₁₁×C₁₇	C₂×D₃	semidirect
15. C₂×C₅×C₁₁×C₁₇	C₃⋊D₃	semidirect
17. C₃²×C₁₁×C₁₇	C₂×D₅	semidirect
18. C₂×C₃²×C₅×C₁₇	D₁₁	semidirect
20. C₂×C₃×C₁₁×C₁₇	D₁₅	semidirect
23. C₂×C₃²×C₅×C₁₁	D₁₇	semidirect
25. C₅×C₁₁×C₁₇	C₂×C₃⋊D₃	semidirect
26. C₃²×C₅×C₁₇	C₂×D₁₁	semidirect
30. C₃×C₁₁×C₁₇	C₂×D₁₅	semidirect
31. C₂×C₃×C₅×C₁₇	D₃₃	semidirect
33. C₃²×C₅×C₁₁	C₂×D₁₇	semidirect
35. C₂×C₁₁×C₁₇	C₃⋊D₁₅	semidirect
38. C₂×C₃×C₅×C₁₁	D₅₁	semidirect
40. C₂×C₃²×C₁₇	D₅₅	semidirect
42. C₃×C₅×C₁₇	C₂×D₃₃	semidirect
45. C₂×C₃²×C₁₁	D₈₅	semidirect
47. C₁₁×C₁₇	C₂×C₃⋊D₁₅	semidirect
49. C₂×C₅×C₁₇	C₃⋊D₃₃	semidirect
51. C₃×C₅×C₁₁	C₂×D₅₁	semidirect
52. C₃²×C₁₇	C₂×D₅₅	semidirect
54. C₂×C₅×C₁₁	C₃⋊D₅₁	semidirect
56. C₂×C₃×C₁₇	D₁₆₅	semidirect
58. C₃²×C₁₁	C₂×D₈₅	semidirect
59. C₂×C₃²×C₅	D₁₈₇	semidirect
61. C₅×C₁₇	C₂×C₃⋊D₃₃	semidirect
63. C₂×C₃×C₁₁	D₂₅₅	semidirect
66. C₅×C₁₁	C₂×C₃⋊D₅₁	semidirect
67. C₃×C₁₇	C₂×D₁₆₅	semidirect
68. C₃²×C₅	C₂×D₁₈₇	semidirect
71. C₂×C₁₇	C₃⋊D₁₆₅	semidirect
73. C₃×C₁₁	C₂×D₂₅₅	semidirect
74. C₂×C₃×C₅	D₅₆₁	semidirect
76. C₂×C₁₁	C₃⋊D₂₅₅	semidirect
79. C₂×C₃²	D₉₃₅	semidirect
81. C₁₇	C₂×C₃⋊D₁₆₅	semidirect
82. C₃×C₅	C₂×D₅₆₁	semidirect
84. C₁₁	C₂×C₃⋊D₂₅₅	semidirect
85. C₂×C₅	C₃⋊D₅₆₁	semidirect
87. C₃²	C₂×D₉₃₅	semidirect
88. C₂×C₃	D₂₈₀₅	semidirect
90. C₅	C₂×C₃⋊D₅₆₁	semidirect
92. C₃	C₂×D₂₈₀₅	semidirect
94. C₂	C₃⋊D₂₈₀₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⋊D₂₈₀₅	2
C₂×C₃²×C₅×C₁₁×C₁₇	2
C₂×D₂₈₀₅	3
C₂×C₃⋊D₅₆₁	5
C₂×C₃⋊D₂₅₅	11
C₂×C₃⋊D₁₆₅	17

Subgroups — C2×C3⋊D2805 #46778216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₂₈₀₅ #46778216