Subgroups — C₂×C₃⋊D₂₁₄₅ #38788323

Order 25740.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₂₁₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₁₄₅	—	3	4	no	maximal
4	C₃²×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₄₂₉	—	5	1	no	maximal, Hall
6	D₂₁₄₅	—	3	8	no	—
7	C₂×C₃×C₅×C₁₁×C₁₃	D₃	1	4	yes	complemented
8	C₂×D₇₁₅	—	9	1	no	Hall
9	C₃⋊D₄₂₉	—	5	2	no	—
10	C₂×C₃²×C₁₁×C₁₃	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃⋊D₁₉₅	—	11	1	no	maximal, Hall
12	C₃×C₅×C₁₁×C₁₃	C₂×D₃	1	4	yes	complemented
13	C₂×C₃⋊D₁₆₅	—	13	1	no	maximal, Hall
14	C₂×D₄₂₉	—	15	4	no	—
15	C₂×C₅×C₁₁×C₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented
16	D₇₁₅	—	9	2	no	—
17	C₃²×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₅×C₁₃	D₁₁	1	1	yes	characteristic, complemented
19	C₃⋊D₁₉₅	—	11	2	no	—
20	C₂×C₃²×C₅×C₁₁	D₁₃	1	1	yes	characteristic, complemented
21	C₃⋊D₁₆₅	—	13	2	no	—
22	C₂×C₃×C₁₁×C₁₃	D₁₅	1	4	yes	complemented
23	D₄₂₉	—	15	8	no	—
24	C₂×D₁₉₅	—	33	4	no	—
25	C₅×C₁₁×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×D₁₆₅	—	39	4	no	—
27	C₃²×C₅×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×D₁₄₃	—	45	1	no	Hall
29	C₃²×C₅×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃⋊D₃₉	—	55	1	no	Hall
31	C₃×C₁₁×C₁₃	C₂×D₁₅	1	4	yes	complemented
32	C₂×C₃⋊D₃₃	—	65	1	no	Hall
33	C₂×C₃×C₅×C₁₃	D₃₃	1	4	yes	complemented
34	D₁₉₅	—	33	8	no	—
35	C₂×C₃×C₅×C₁₁	D₃₉	1	4	yes	complemented
36	D₁₆₅	—	39	8	no	—
37	C₂×C₁₁×C₁₃	C₃⋊D₁₅	1	1	yes	characteristic, complemented
38	D₁₄₃	—	45	2	no	—
39	C₂×D₆₅	—	99	1	no	Hall
40	C₂×C₃²×C₁₃	D₅₅	1	1	yes	characteristic, complemented
41	C₃⋊D₃₉	—	55	2	no	—
42	C₂×D₅₅	—	117	1	no	Hall
43	C₂×C₃²×C₁₁	D₆₅	1	1	yes	characteristic, complemented
44	C₃⋊D₃₃	—	65	2	no	—
45	C₃×C₅×C₁₃	C₂×D₃₃	1	4	yes	complemented
46	C₂×C₃⋊D₁₅	—	143	1	no	Hall
47	C₃×C₅×C₁₁	C₂×D₃₉	1	4	yes	complemented
48	C₂×D₃₉	—	165	4	no	—
49	C₁₁×C₁₃	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
50	C₂×D₃₃	—	195	4	no	—
51	C₂×C₅×C₁₃	C₃⋊D₃₃	1	1	yes	characteristic, complemented
52	D₆₅	—	99	2	no	—
53	C₃²×C₁₃	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
54	C₂×C₅×C₁₁	C₃⋊D₃₉	1	1	yes	characteristic, complemented
55	D₅₅	—	117	2	no	—
56	C₃²×C₁₁	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃²×C₅	D₁₄₃	1	1	yes	characteristic, complemented
58	C₃⋊D₁₅	—	143	2	no	—
59	C₂×C₃×C₁₃	D₁₆₅	1	4	yes	complemented
60	D₃₉	—	165	8	no	—
61	C₂×C₃×C₁₁	D₁₉₅	1	4	yes	complemented
62	D₃₃	—	195	8	no	—
63	C₅×C₁₃	C₂×C₃⋊D₃₃	1	1	yes	characteristic, complemented, Hall
64	C₂×D₁₅	—	429	4	no	—
65	C₅×C₁₁	C₂×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Hall
66	C₂×D₁₃	—	495	1	no	Hall
67	C₃²×C₅	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
68	C₂×D₁₁	—	585	1	no	Hall
69	C₃×C₁₃	C₂×D₁₆₅	1	4	yes	complemented
70	C₂×C₃⋊D₃	—	715	1	no	Hall
71	C₃×C₁₁	C₂×D₁₉₅	1	4	yes	complemented
72	C₂×C₃×C₅	D₄₂₉	1	4	yes	complemented
73	D₁₅	—	429	8	no	—
74	C₂×C₁₃	C₃⋊D₁₆₅	1	1	yes	characteristic, complemented
75	D₁₃	—	495	2	no	—
76	C₂×C₁₁	C₃⋊D₁₉₅	1	1	yes	characteristic, complemented
77	D₁₁	—	585	2	no	—
78	C₂×D₅	—	1287	1	no	Hall
79	C₂×C₃²	D₇₁₅	1	1	yes	characteristic, complemented
80	C₃⋊D₃	—	715	2	no	—
81	C₃×C₅	C₂×D₄₂₉	1	4	yes	complemented
82	C₁₃	C₂×C₃⋊D₁₆₅	1	1	yes	characteristic, complemented, Sylow
83	C₂×D₃	—	2145	4	no	—
84	C₁₁	C₂×C₃⋊D₁₉₅	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	C₃⋊D₄₂₉	1	1	yes	characteristic, complemented
86	D₅	—	1287	2	no	—
87	C₃²	C₂×D₇₁₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	D₂₁₄₅	1	4	yes	complemented
89	D₃	—	2145	8	no	—
90	C₅	C₂×C₃⋊D₄₂₉	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	6435	1	no	Sylow
92	C₃	C₂×D₂₁₄₅	1	4	yes	complemented
93	C₂	—	6435	2	no	—
94	C₂	C₃⋊D₂₁₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₂₁₄₅
commutator, cosocle, hypocenter	C₃²×C₅×C₁₁×C₁₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₃²×C₅×C₁₁×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₂₁₄₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₁×C₁₃	C₂	semidirect
4. C₃²×C₅×C₁₁×C₁₃	C₂²	semidirect
7. C₂×C₃×C₅×C₁₁×C₁₃	D₃	semidirect
10. C₂×C₃²×C₁₁×C₁₃	D₅	semidirect
12. C₃×C₅×C₁₁×C₁₃	C₂×D₃	semidirect
15. C₂×C₅×C₁₁×C₁₃	C₃⋊D₃	semidirect
17. C₃²×C₁₁×C₁₃	C₂×D₅	semidirect
18. C₂×C₃²×C₅×C₁₃	D₁₁	semidirect
20. C₂×C₃²×C₅×C₁₁	D₁₃	semidirect
22. C₂×C₃×C₁₁×C₁₃	D₁₅	semidirect
25. C₅×C₁₁×C₁₃	C₂×C₃⋊D₃	semidirect
27. C₃²×C₅×C₁₃	C₂×D₁₁	semidirect
29. C₃²×C₅×C₁₁	C₂×D₁₃	semidirect
31. C₃×C₁₁×C₁₃	C₂×D₁₅	semidirect
33. C₂×C₃×C₅×C₁₃	D₃₃	semidirect
35. C₂×C₃×C₅×C₁₁	D₃₉	semidirect
37. C₂×C₁₁×C₁₃	C₃⋊D₁₅	semidirect
40. C₂×C₃²×C₁₃	D₅₅	semidirect
43. C₂×C₃²×C₁₁	D₆₅	semidirect
45. C₃×C₅×C₁₃	C₂×D₃₃	semidirect
47. C₃×C₅×C₁₁	C₂×D₃₉	semidirect
49. C₁₁×C₁₃	C₂×C₃⋊D₁₅	semidirect
51. C₂×C₅×C₁₃	C₃⋊D₃₃	semidirect
53. C₃²×C₁₃	C₂×D₅₅	semidirect
54. C₂×C₅×C₁₁	C₃⋊D₃₉	semidirect
56. C₃²×C₁₁	C₂×D₆₅	semidirect
57. C₂×C₃²×C₅	D₁₄₃	semidirect
59. C₂×C₃×C₁₃	D₁₆₅	semidirect
61. C₂×C₃×C₁₁	D₁₉₅	semidirect
63. C₅×C₁₃	C₂×C₃⋊D₃₃	semidirect
65. C₅×C₁₁	C₂×C₃⋊D₃₉	semidirect
67. C₃²×C₅	C₂×D₁₄₃	semidirect
69. C₃×C₁₃	C₂×D₁₆₅	semidirect
71. C₃×C₁₁	C₂×D₁₉₅	semidirect
72. C₂×C₃×C₅	D₄₂₉	semidirect
74. C₂×C₁₃	C₃⋊D₁₆₅	semidirect
76. C₂×C₁₁	C₃⋊D₁₉₅	semidirect
79. C₂×C₃²	D₇₁₅	semidirect
81. C₃×C₅	C₂×D₄₂₉	semidirect
82. C₁₃	C₂×C₃⋊D₁₆₅	semidirect
84. C₁₁	C₂×C₃⋊D₁₉₅	semidirect
85. C₂×C₅	C₃⋊D₄₂₉	semidirect
87. C₃²	C₂×D₇₁₅	semidirect
88. C₂×C₃	D₂₁₄₅	semidirect
90. C₅	C₂×C₃⋊D₄₂₉	semidirect
92. C₃	C₂×D₂₁₄₅	semidirect
94. C₂	C₃⋊D₂₁₄₅	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⋊D₂₁₄₅	2
C₂×C₃²×C₅×C₁₁×C₁₃	2
C₂×D₂₁₄₅	3
C₂×C₃⋊D₄₂₉	5
C₂×C₃⋊D₁₉₅	11
C₂×C₃⋊D₁₆₅	13

Subgroups — C2×C3⋊D2145 #38788323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₂₁₄₅ #38788323