Subgroups — C₂×C₃²×D₆₆₅ #37561635

Order 23940.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₆₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₆₆₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₁₃₃	—	5	1	no	maximal, Hall
6	C₃×D₆₆₅	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	1	4	yes	complemented
8	C₂×C₃²×D₉₅	—	7	1	no	maximal, Hall
9	C₂×D₆₆₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×D₁₃₃	—	5	2	no	—
11	C₂×C₃²×C₇×C₁₉	D₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₁₉	C₂²×C₃	1	4	yes	complemented
13	C₂×C₃²×C₅×C₁₉	D₇	1	1	yes	characteristic, complemented
14	C₃²×D₉₅	—	7	2	no	—
15	C₂×C₃×D₁₃₃	—	5	4	no	—
16	C₂×C₅×C₇×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
17	D₆₆₅	C₂×C₃²	1	2	yes	direct product factor
18	C₂×C₃²×D₃₅	—	19	1	no	maximal, Hall
19	C₃²×C₇×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×D₉₅	—	7	4	no	—
21	C₃²×C₅×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₁₉	C₃×D₅	1	4	yes	complemented
23	C₃×D₁₃₃	—	5	8	no	—
24	C₂×C₃²×D₁₉	—	35	1	no	Hall
25	C₅×C₇×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃²×C₅×C₇	D₁₉	1	1	yes	characteristic, complemented
27	C₃²×D₃₅	—	19	2	no	—
28	C₂×C₃×C₅×C₁₉	C₃×D₇	1	4	yes	complemented
29	C₃×D₉₅	—	7	8	no	—
30	C₂×D₁₃₃	—	5	1	no	Hall
31	C₂×C₃×D₃₅	—	19	4	no	—
32	C₃×C₇×C₁₉	C₂×C₃×D₅	1	4	yes	complemented
33	C₂×D₉₅	—	7	1	no	Hall
34	C₂×C₃²×C₁₉	D₃₅	1	1	yes	characteristic, complemented
35	C₃²×D₁₉	—	35	2	no	—
36	C₃²×C₅×C₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×C₁₉	C₂×C₃×D₇	1	4	yes	complemented
38	C₂×C₇×C₁₉	C₃²×D₅	1	1	yes	characteristic, complemented
39	D₁₃₃	—	5	2	no	—
40	C₂×C₃²×D₇	—	95	1	no	Hall
41	C₂×C₃×D₁₉	—	35	4	no	—
42	C₂×C₃×C₅×C₇	C₃×D₁₉	1	4	yes	complemented
43	C₃×D₃₅	—	19	8	no	—
44	C₂×C₅×C₁₉	C₃²×D₇	1	1	yes	characteristic, complemented
45	D₉₅	—	7	2	no	—
46	C₂×C₃²×D₅	—	133	1	no	Hall
47	C₃²×C₁₉	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
48	C₂×D₃₅	—	19	1	no	Hall
49	C₇×C₁₉	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃²×C₇	D₉₅	1	1	yes	characteristic, complemented
51	C₃²×D₇	—	95	2	no	—
52	C₂×C₃×C₁₉	C₃×D₃₅	1	4	yes	complemented
53	C₃×D₁₉	—	35	8	no	—
54	C₃×C₅×C₇	C₂×C₃×D₁₉	1	4	yes	complemented
55	C₅×C₁₉	C₂×C₃²×D₇	1	1	yes	characteristic, complemented, Hall
56	C₂×C₃²×C₅	D₁₃₃	1	1	yes	characteristic, complemented
57	C₃²×D₅	—	133	2	no	—
58	C₂×C₃×D₇	—	95	4	no	—
59	C₂×D₁₉	—	35	1	no	Hall
60	C₂×C₅×C₇	C₃²×D₁₉	1	1	yes	characteristic, complemented
61	D₃₅	—	19	2	no	—
62	C₃²×C₇	C₂×D₉₅	1	1	yes	characteristic, complemented, Hall
63	C₂×C₃×D₅	—	133	4	no	—
64	C₃×C₁₉	C₂×C₃×D₃₅	1	4	yes	complemented
65	C₃²×C₅	C₂×D₁₃₃	1	1	yes	characteristic, complemented, Hall
66	C₂×C₃×C₇	C₃×D₉₅	1	4	yes	complemented
67	C₃×D₇	—	95	8	no	—
68	C₂×C₁₉	C₃²×D₃₅	1	1	yes	characteristic, complemented
69	D₁₉	—	35	2	no	—
70	C₂²×C₃²	—	665	1	no	Hall
71	C₅×C₇	C₂×C₃²×D₁₉	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	C₃×D₁₃₃	1	4	yes	complemented
73	C₃×D₅	—	133	8	no	—
74	C₂×D₇	—	95	1	no	Hall
75	C₃×C₇	C₂×C₃×D₉₅	1	4	yes	complemented
76	C₂×D₅	—	133	1	no	Hall
77	C₁₉	C₂×C₃²×D₃₅	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₃²	—	665	2	no	—
79	C₂×C₃²	D₆₆₅	1	1	yes	characteristic, direct product factor
80	C₃×C₅	C₂×C₃×D₁₃₃	1	4	yes	complemented
81	C₂×C₇	C₃²×D₉₅	1	1	yes	characteristic, complemented
82	D₇	—	95	2	no	—
83	C₂²×C₃	—	665	4	no	—
84	C₂×C₅	C₃²×D₁₃₃	1	1	yes	characteristic, complemented
85	D₅	—	133	2	no	—
86	C₃²	C₂×D₆₆₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₇	C₂×C₃²×D₉₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	665	8	no	—
89	C₂×C₃	C₃×D₆₆₅	1	4	yes	direct product factor
90	C₅	C₂×C₃²×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	665	1	no	Sylow
92	C₃	C₂×C₃×D₆₆₅	1	4	yes	direct product factor
93	C₂	—	665	2	no	—
94	C₂	C₃²×D₆₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₆₆₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₉	C₂
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×D₆₆₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₁₉	C₂	semidirect
3. C₂×C₃×D₆₆₅	C₃	direct (N × H)
4. C₃²×C₅×C₇×C₁₉	C₂²	semidirect
6. C₃×D₆₆₅	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	semidirect
9. C₂×D₆₆₅	C₃²	direct (N × H)
11. C₂×C₃²×C₇×C₁₉	D₅	semidirect
12. C₃×C₅×C₇×C₁₉	C₂²×C₃	semidirect
13. C₂×C₃²×C₅×C₁₉	D₇	semidirect
16. C₂×C₅×C₇×C₁₉	C₂×C₃²	semidirect
17. D₆₆₅	C₂×C₃²	direct (N × H)
19. C₃²×C₇×C₁₉	C₂×D₅	semidirect
21. C₃²×C₅×C₁₉	C₂×D₇	semidirect
22. C₂×C₃×C₇×C₁₉	C₃×D₅	semidirect
25. C₅×C₇×C₁₉	C₂²×C₃²	semidirect
26. C₂×C₃²×C₅×C₇	D₁₉	semidirect
28. C₂×C₃×C₅×C₁₉	C₃×D₇	semidirect
32. C₃×C₇×C₁₉	C₂×C₃×D₅	semidirect
34. C₂×C₃²×C₁₉	D₃₅	semidirect
36. C₃²×C₅×C₇	C₂×D₁₉	semidirect
37. C₃×C₅×C₁₉	C₂×C₃×D₇	semidirect
38. C₂×C₇×C₁₉	C₃²×D₅	semidirect
42. C₂×C₃×C₅×C₇	C₃×D₁₉	semidirect
44. C₂×C₅×C₁₉	C₃²×D₇	semidirect
47. C₃²×C₁₉	C₂×D₃₅	semidirect
49. C₇×C₁₉	C₂×C₃²×D₅	semidirect
50. C₂×C₃²×C₇	D₉₅	semidirect
52. C₂×C₃×C₁₉	C₃×D₃₅	semidirect
54. C₃×C₅×C₇	C₂×C₃×D₁₉	semidirect
55. C₅×C₁₉	C₂×C₃²×D₇	semidirect
56. C₂×C₃²×C₅	D₁₃₃	semidirect
60. C₂×C₅×C₇	C₃²×D₁₉	semidirect
62. C₃²×C₇	C₂×D₉₅	semidirect
64. C₃×C₁₉	C₂×C₃×D₃₅	semidirect
65. C₃²×C₅	C₂×D₁₃₃	semidirect
66. C₂×C₃×C₇	C₃×D₉₅	semidirect
68. C₂×C₁₉	C₃²×D₃₅	semidirect
71. C₅×C₇	C₂×C₃²×D₁₉	semidirect
72. C₂×C₃×C₅	C₃×D₁₃₃	semidirect
75. C₃×C₇	C₂×C₃×D₉₅	semidirect
77. C₁₉	C₂×C₃²×D₃₅	semidirect
79. C₂×C₃²	D₆₆₅	direct (N × H)
80. C₃×C₅	C₂×C₃×D₁₃₃	semidirect
81. C₂×C₇	C₃²×D₉₅	semidirect
84. C₂×C₅	C₃²×D₁₃₃	semidirect
86. C₃²	C₂×D₆₆₅	direct (N × H)
87. C₇	C₂×C₃²×D₉₅	semidirect
89. C₂×C₃	C₃×D₆₆₅	direct (N × H)
90. C₅	C₂×C₃²×D₁₃₃	semidirect
92. C₃	C₂×C₃×D₆₆₅	direct (N × H)
94. C₂	C₃²×D₆₆₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₆₆₅	2
C₂×C₃²×C₅×C₇×C₁₉	2
C₂×C₃×D₆₆₅	3
C₂×C₃²×D₁₃₃	5
C₂×C₃²×D₉₅	7
C₂×C₃²×D₃₅	19

Subgroups — C2×C32×D665 #37561635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₆₆₅ #37561635