Subgroups — C₂×C₃⋊D₁₃₆₅ #30655779

Order 16380.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₃₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃₆₅	—	3	4	no	maximal
4	C₃²×C₅×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₂₇₃	—	5	1	no	maximal, Hall
6	D₁₃₆₅	—	3	8	no	—
7	C₂×C₃×C₅×C₇×C₁₃	D₃	1	4	yes	complemented
8	C₂×C₃⋊D₁₉₅	—	7	1	no	maximal, Hall
9	C₂×D₄₅₅	—	9	1	no	Hall
10	C₂×C₃²×C₇×C₁₃	D₅	1	1	yes	characteristic, complemented
11	C₃⋊D₂₇₃	—	5	2	no	—
12	C₃×C₅×C₇×C₁₃	C₂×D₃	1	4	yes	complemented
13	C₂×C₃⋊D₁₀₅	—	13	1	no	maximal, Hall
14	C₂×C₃²×C₅×C₁₃	D₇	1	1	yes	characteristic, complemented
15	C₃⋊D₁₉₅	—	7	2	no	—
16	C₂×D₂₇₃	—	15	4	no	—
17	C₂×C₅×C₇×C₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented
18	D₄₅₅	—	9	2	no	—
19	C₃²×C₇×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₉₅	—	21	4	no	—
21	C₂×C₃²×C₅×C₇	D₁₃	1	1	yes	characteristic, complemented
22	C₃⋊D₁₀₅	—	13	2	no	—
23	C₃²×C₅×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₇×C₁₃	D₁₅	1	4	yes	complemented
25	D₂₇₃	—	15	8	no	—
26	C₂×C₃⋊D₃₉	—	35	1	no	Hall
27	C₅×C₇×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
28	C₂×D₁₀₅	—	39	4	no	—
29	C₂×C₃×C₅×C₁₃	D₂₁	1	4	yes	complemented
30	D₁₉₅	—	21	8	no	—
31	C₂×D₉₁	—	45	1	no	Hall
32	C₃²×C₅×C₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₇×C₁₃	C₂×D₁₅	1	4	yes	complemented
34	C₂×D₆₅	—	63	1	no	Hall
35	C₂×C₃⋊D₂₁	—	65	1	no	Hall
36	C₂×C₃²×C₁₃	D₃₅	1	1	yes	characteristic, complemented
37	C₃⋊D₃₉	—	35	2	no	—
38	C₂×C₃×C₅×C₇	D₃₉	1	4	yes	complemented
39	D₁₀₅	—	39	8	no	—
40	C₃×C₅×C₁₃	C₂×D₂₁	1	4	yes	complemented
41	C₂×C₇×C₁₃	C₃⋊D₁₅	1	1	yes	characteristic, complemented
42	D₉₁	—	45	2	no	—
43	C₂×C₃⋊D₁₅	—	91	1	no	Hall
44	C₂×D₃₉	—	105	4	no	—
45	C₂×D₃₅	—	117	1	no	Hall
46	C₂×C₅×C₁₃	C₃⋊D₂₁	1	1	yes	characteristic, complemented
47	D₆₅	—	63	2	no	—
48	C₂×C₃²×C₇	D₆₅	1	1	yes	characteristic, complemented
49	C₃⋊D₂₁	—	65	2	no	—
50	C₃²×C₁₃	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
51	C₃×C₅×C₇	C₂×D₃₉	1	4	yes	complemented
52	C₇×C₁₃	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃²×C₅	D₉₁	1	1	yes	characteristic, complemented
54	C₃⋊D₁₅	—	91	2	no	—
55	C₂×D₂₁	—	195	4	no	—
56	C₂×C₃×C₁₃	D₁₀₅	1	4	yes	complemented
57	D₃₉	—	105	8	no	—
58	C₂×C₅×C₇	C₃⋊D₃₉	1	1	yes	characteristic, complemented
59	D₃₅	—	117	2	no	—
60	C₅×C₁₃	C₂×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
61	C₃²×C₇	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
62	C₂×D₁₅	—	273	4	no	—
63	C₂×D₁₃	—	315	1	no	Hall
64	C₃²×C₅	C₂×D₉₁	1	1	yes	characteristic, complemented, Hall
65	C₂×C₃×C₇	D₁₉₅	1	4	yes	complemented
66	D₂₁	—	195	8	no	—
67	C₃×C₁₃	C₂×D₁₀₅	1	4	yes	complemented
68	C₂×C₃⋊D₃	—	455	1	no	Hall
69	C₅×C₇	C₂×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Hall
70	C₂×C₃×C₅	D₂₇₃	1	4	yes	complemented
71	D₁₅	—	273	8	no	—
72	C₂×D₇	—	585	1	no	Hall
73	C₂×C₁₃	C₃⋊D₁₀₅	1	1	yes	characteristic, complemented
74	D₁₃	—	315	2	no	—
75	C₃×C₇	C₂×D₁₉₅	1	4	yes	complemented
76	C₂×D₅	—	819	1	no	Hall
77	C₂×C₃²	D₄₅₅	1	1	yes	characteristic, complemented
78	C₃⋊D₃	—	455	2	no	—
79	C₃×C₅	C₂×D₂₇₃	1	4	yes	complemented
80	C₂×C₇	C₃⋊D₁₉₅	1	1	yes	characteristic, complemented
81	D₇	—	585	2	no	—
82	C₁₃	C₂×C₃⋊D₁₀₅	1	1	yes	characteristic, complemented, Sylow
83	C₂×D₃	—	1365	4	no	—
84	C₂×C₅	C₃⋊D₂₇₃	1	1	yes	characteristic, complemented
85	D₅	—	819	2	no	—
86	C₃²	C₂×D₄₅₅	1	1	yes	characteristic, complemented, Sylow
87	C₇	C₂×C₃⋊D₁₉₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	D₁₃₆₅	1	4	yes	complemented
89	D₃	—	1365	8	no	—
90	C₅	C₂×C₃⋊D₂₇₃	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	4095	1	no	Sylow
92	C₃	C₂×D₁₃₆₅	1	4	yes	complemented
93	C₂	—	4095	2	no	—
94	C₂	C₃⋊D₁₃₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₁₃₆₅
commutator, cosocle, hypocenter	C₃²×C₅×C₇×C₁₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₃	C₂
LCS	G ▷ C₃²×C₅×C₇×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₃₆₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₁₃	C₂	semidirect
4. C₃²×C₅×C₇×C₁₃	C₂²	semidirect
7. C₂×C₃×C₅×C₇×C₁₃	D₃	semidirect
10. C₂×C₃²×C₇×C₁₃	D₅	semidirect
12. C₃×C₅×C₇×C₁₃	C₂×D₃	semidirect
14. C₂×C₃²×C₅×C₁₃	D₇	semidirect
17. C₂×C₅×C₇×C₁₃	C₃⋊D₃	semidirect
19. C₃²×C₇×C₁₃	C₂×D₅	semidirect
21. C₂×C₃²×C₅×C₇	D₁₃	semidirect
23. C₃²×C₅×C₁₃	C₂×D₇	semidirect
24. C₂×C₃×C₇×C₁₃	D₁₅	semidirect
27. C₅×C₇×C₁₃	C₂×C₃⋊D₃	semidirect
29. C₂×C₃×C₅×C₁₃	D₂₁	semidirect
32. C₃²×C₅×C₇	C₂×D₁₃	semidirect
33. C₃×C₇×C₁₃	C₂×D₁₅	semidirect
36. C₂×C₃²×C₁₃	D₃₅	semidirect
38. C₂×C₃×C₅×C₇	D₃₉	semidirect
40. C₃×C₅×C₁₃	C₂×D₂₁	semidirect
41. C₂×C₇×C₁₃	C₃⋊D₁₅	semidirect
46. C₂×C₅×C₁₃	C₃⋊D₂₁	semidirect
48. C₂×C₃²×C₇	D₆₅	semidirect
50. C₃²×C₁₃	C₂×D₃₅	semidirect
51. C₃×C₅×C₇	C₂×D₃₉	semidirect
52. C₇×C₁₃	C₂×C₃⋊D₁₅	semidirect
53. C₂×C₃²×C₅	D₉₁	semidirect
56. C₂×C₃×C₁₃	D₁₀₅	semidirect
58. C₂×C₅×C₇	C₃⋊D₃₉	semidirect
60. C₅×C₁₃	C₂×C₃⋊D₂₁	semidirect
61. C₃²×C₇	C₂×D₆₅	semidirect
64. C₃²×C₅	C₂×D₉₁	semidirect
65. C₂×C₃×C₇	D₁₉₅	semidirect
67. C₃×C₁₃	C₂×D₁₀₅	semidirect
69. C₅×C₇	C₂×C₃⋊D₃₉	semidirect
70. C₂×C₃×C₅	D₂₇₃	semidirect
73. C₂×C₁₃	C₃⋊D₁₀₅	semidirect
75. C₃×C₇	C₂×D₁₉₅	semidirect
77. C₂×C₃²	D₄₅₅	semidirect
79. C₃×C₅	C₂×D₂₇₃	semidirect
80. C₂×C₇	C₃⋊D₁₉₅	semidirect
82. C₁₃	C₂×C₃⋊D₁₀₅	semidirect
84. C₂×C₅	C₃⋊D₂₇₃	semidirect
86. C₃²	C₂×D₄₅₅	semidirect
87. C₇	C₂×C₃⋊D₁₉₅	semidirect
88. C₂×C₃	D₁₃₆₅	semidirect
90. C₅	C₂×C₃⋊D₂₇₃	semidirect
92. C₃	C₂×D₁₃₆₅	semidirect
94. C₂	C₃⋊D₁₃₆₅	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⋊D₁₃₆₅	2
C₂×C₃²×C₅×C₇×C₁₃	2
C₂×D₁₃₆₅	3
C₂×C₃⋊D₂₇₃	5
C₂×C₃⋊D₁₉₅	7
C₂×C₃⋊D₁₀₅	13

Subgroups — C2×C3⋊D1365 #30655779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₁₃₆₅ #30655779