Subgroups — C₂×C₄₉×D₁₆₅ #44568434

Order 32340.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×D₁₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₉×D₅₅	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₉×D₃₃	—	5	1	no	maximal, Hall
6	C₄₉×D₅₅	—	3	2	no	—
7	C₂×C₅×C₁₁×C₄₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₇×D₁₆₅	C₇	1	1	yes	maximal, characteristic
9	C₄₉×D₃₃	—	5	2	no	—
10	C₂×C₃×C₁₁×C₄₉	D₅	1	1	yes	characteristic, complemented
11	C₂×D₁₅×C₄₉	—	11	1	no	maximal, Hall
12	C₅×C₁₁×C₄₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	C₇×D₁₆₅	C₂×C₇	1	2	yes	—
14	C₂×C₃×C₅×C₇×C₁₁	C₂×C₇	1	1	yes	characteristic
15	C₂×D₁₁×C₄₉	—	15	1	no	Hall
16	C₃×C₁₁×C₄₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₇×D₅₅	—	3	1	no	—
18	C₂×C₃×C₅×C₄₉	D₁₁	1	1	yes	characteristic, complemented
19	D₁₅×C₄₉	—	11	2	no	—
20	C₃×C₅×C₇×C₁₁	C₂²×C₇	1	1	yes	characteristic
21	C₂×C₁₁×C₄₉	D₁₅	1	1	yes	characteristic, complemented
22	D₁₁×C₄₉	—	15	2	no	—
23	C₂×D₅×C₄₉	—	33	1	no	Hall
24	C₂×C₇×D₃₃	—	5	1	no	—
25	C₂×C₅×C₇×C₁₁	D₃×C₇	1	1	yes	characteristic
26	C₇×D₅₅	—	3	2	no	—
27	C₃×C₅×C₄₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×D₁₆₅	C₄₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×D₃×C₄₉	—	55	1	no	Hall
30	C₁₁×C₄₉	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×C₄₉	D₃₃	1	1	yes	characteristic, complemented
32	D₅×C₄₉	—	33	2	no	—
33	C₂×C₃×C₇×C₁₁	C₇×D₅	1	1	yes	characteristic
34	C₇×D₃₃	—	5	2	no	—
35	C₂×C₇×D₁₅	—	11	1	no	—
36	C₅×C₇×C₁₁	C₂×D₃×C₇	1	1	yes	characteristic
37	C₂×C₃×C₅×C₁₁	C₂×C₄₉	1	1	yes	characteristic, complemented
38	D₁₆₅	C₂×C₄₉	1	2	yes	direct product factor
39	C₂×C₇×D₁₁	—	15	1	no	—
40	C₂×C₃×C₄₉	D₅₅	1	1	yes	characteristic, complemented
41	D₃×C₄₉	—	55	2	no	—
42	C₅×C₄₉	C₂×D₃₃	1	1	yes	characteristic, complemented, Hall
43	C₃×C₇×C₁₁	C₂×C₇×D₅	1	1	yes	characteristic
44	C₂×D₅₅	—	3	1	no	Hall
45	C₂×C₃×C₅×C₇	C₇×D₁₁	1	1	yes	characteristic
46	C₇×D₁₅	—	11	2	no	—
47	C₂²×C₄₉	—	165	1	no	Hall
48	C₃×C₅×C₁₁	C₂²×C₄₉	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇×C₁₁	C₇×D₁₅	1	1	yes	characteristic
50	C₇×D₁₁	—	15	2	no	—
51	C₃×C₄₉	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
52	C₂×C₇×D₅	—	33	1	no	—
53	C₂×D₃₃	—	5	1	no	Hall
54	C₂×C₅×C₁₁	D₃×C₄₉	1	1	yes	characteristic, complemented
55	D₅₅	—	3	2	no	—
56	C₃×C₅×C₇	C₂×C₇×D₁₁	1	1	yes	characteristic
57	C₂×C₄₉	—	165	2	no	—
58	C₂×C₄₉	D₁₆₅	1	1	yes	characteristic, direct product factor
59	C₂×D₃×C₇	—	55	1	no	—
60	C₇×C₁₁	C₂×C₇×D₁₅	1	1	yes	characteristic
61	C₂×C₅×C₇	C₇×D₃₃	1	1	yes	characteristic
62	C₇×D₅	—	33	2	no	—
63	C₂×C₃×C₁₁	D₅×C₄₉	1	1	yes	characteristic, complemented
64	D₃₃	—	5	2	no	—
65	C₂×D₁₅	—	11	1	no	Hall
66	C₅×C₁₁	C₂×D₃×C₄₉	1	1	yes	characteristic, complemented, Hall
67	C₄₉	C₂×D₁₆₅	1	1	yes	characteristic, direct product factor, Sylow
68	C₂×D₁₁	—	15	1	no	Hall
69	C₂×C₃×C₇	C₇×D₅₅	1	1	yes	characteristic
70	D₃×C₇	—	55	2	no	—
71	C₅×C₇	C₂×C₇×D₃₃	1	1	yes	characteristic
72	C₃×C₁₁	C₂×D₅×C₄₉	1	1	yes	characteristic, complemented, Hall
73	C₂×C₃×C₅	D₁₁×C₄₉	1	1	yes	characteristic, complemented
74	D₁₅	—	11	2	no	—
75	C₂²×C₇	—	165	1	no	—
76	C₂×C₁₁	D₁₅×C₄₉	1	1	yes	characteristic, complemented
77	D₁₁	—	15	2	no	—
78	C₃×C₇	C₂×C₇×D₅₅	1	1	yes	characteristic
79	C₂×D₅	—	33	1	no	Hall
80	C₃×C₅	C₂×D₁₁×C₄₉	1	1	yes	characteristic, complemented, Hall
81	C₂×C₇	—	165	2	no	—
82	C₂×C₇	C₇×D₁₆₅	1	1	yes	characteristic
83	C₂×D₃	—	55	1	no	Hall
84	C₁₁	C₂×D₁₅×C₄₉	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	C₄₉×D₃₃	1	1	yes	characteristic, complemented
86	D₅	—	33	2	no	—
87	C₇	C₂×C₇×D₁₆₅	1	1	yes	characteristic
88	C₂×C₃	C₄₉×D₅₅	1	1	yes	characteristic, complemented
89	D₃	—	55	2	no	—
90	C₅	C₂×C₄₉×D₃₃	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	165	1	no	Sylow
92	C₃	C₂×C₄₉×D₅₅	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	165	2	no	—
94	C₂	C₄₉×D₁₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₉	D₁₆₅
commutator, hypocenter	C₃×C₅×C₁₁	C₂²×C₄₉
Frattini	C₇	C₂×C₇×D₁₆₅
Fitting	C₂×C₃×C₅×C₁₁×C₄₉	C₂
socle	C₂×C₃×C₅×C₇×C₁₁	C₂×C₇
prime radical	C₂×C₇×D₁₆₅	C₇
cosocle	C₃×C₅×C₇×C₁₁	C₂²×C₇
LCS	G ▷ C₃×C₅×C₁₁
UCS	C₁ ◁ C₂×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₄₉×D₁₆₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₄₉	C₂	semidirect
4. C₃×C₅×C₁₁×C₄₉	C₂²	semidirect
7. C₂×C₅×C₁₁×C₄₉	D₃	semidirect
10. C₂×C₃×C₁₁×C₄₉	D₅	semidirect
12. C₅×C₁₁×C₄₉	C₂×D₃	semidirect
16. C₃×C₁₁×C₄₉	C₂×D₅	semidirect
18. C₂×C₃×C₅×C₄₉	D₁₁	semidirect
21. C₂×C₁₁×C₄₉	D₁₅	semidirect
27. C₃×C₅×C₄₉	C₂×D₁₁	semidirect
28. C₂×D₁₆₅	C₄₉	direct (N × H)
30. C₁₁×C₄₉	C₂×D₁₅	semidirect
31. C₂×C₅×C₄₉	D₃₃	semidirect
37. C₂×C₃×C₅×C₁₁	C₂×C₄₉	semidirect
38. D₁₆₅	C₂×C₄₉	direct (N × H)
40. C₂×C₃×C₄₉	D₅₅	semidirect
42. C₅×C₄₉	C₂×D₃₃	semidirect
48. C₃×C₅×C₁₁	C₂²×C₄₉	semidirect
51. C₃×C₄₉	C₂×D₅₅	semidirect
54. C₂×C₅×C₁₁	D₃×C₄₉	semidirect
58. C₂×C₄₉	D₁₆₅	direct (N × H)
63. C₂×C₃×C₁₁	D₅×C₄₉	semidirect
66. C₅×C₁₁	C₂×D₃×C₄₉	semidirect
67. C₄₉	C₂×D₁₆₅	direct (N × H)
72. C₃×C₁₁	C₂×D₅×C₄₉	semidirect
73. C₂×C₃×C₅	D₁₁×C₄₉	semidirect
76. C₂×C₁₁	D₁₅×C₄₉	semidirect
80. C₃×C₅	C₂×D₁₁×C₄₉	semidirect
84. C₁₁	C₂×D₁₅×C₄₉	semidirect
85. C₂×C₅	C₄₉×D₃₃	semidirect
88. C₂×C₃	C₄₉×D₅₅	semidirect
90. C₅	C₂×C₄₉×D₃₃	semidirect
92. C₃	C₂×C₄₉×D₅₅	semidirect
94. C₂	C₄₉×D₁₆₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₉×D₁₆₅	2
C₂×C₃×C₅×C₁₁×C₄₉	2
C₂×C₄₉×D₅₅	3
C₂×C₄₉×D₃₃	5
C₂×C₇×D₁₆₅	7
C₂×D₁₅×C₄₉	11

Subgroups — C2×C49×D165 #44568434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₉×D₁₆₅ #44568434