Subgroups — C₂×C₁₁×D₇₃₅ #44568435

Order 32340.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₇₃₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×D₂₄₅	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×D₁₄₇	—	5	1	no	maximal, Hall
6	C₁₁×D₂₄₅	—	3	2	no	—
7	C₂×C₅×C₁₁×C₄₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₁₁×D₁₀₅	—	7	1	no	maximal
9	C₁₁×D₁₄₇	—	5	2	no	—
10	C₂×C₃×C₁₁×C₄₉	D₅	1	1	yes	characteristic, complemented
11	C₂×D₇₃₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×C₁₁×C₄₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	C₁₁×D₁₀₅	—	7	2	no	—
14	C₂×C₃×C₅×C₇×C₁₁	D₇	1	1	yes	characteristic
15	C₂×C₁₁×D₄₉	—	15	1	no	Hall
16	C₃×C₁₁×C₄₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₁×D₃₅	—	21	1	no	—
18	C₂×C₃×C₅×C₄₉	C₂×C₁₁	1	1	yes	characteristic, complemented
19	D₇₃₅	C₂×C₁₁	1	2	yes	direct product factor
20	C₃×C₅×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic
21	C₂×C₁₁×C₄₉	D₁₅	1	1	yes	characteristic, complemented
22	C₁₁×D₄₉	—	15	2	no	—
23	C₂×D₂₄₅	—	3	1	no	Hall
24	C₂×C₁₁×D₂₁	—	35	1	no	—
25	C₂×C₅×C₇×C₁₁	D₂₁	1	1	yes	characteristic
26	C₁₁×D₃₅	—	21	2	no	—
27	C₃×C₅×C₄₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×C₁₁×D₁₅	—	49	1	no	Hall
29	C₂×D₁₄₇	—	5	1	no	Hall
30	C₁₁×C₄₉	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×C₄₉	D₃×C₁₁	1	1	yes	characteristic, complemented
32	D₂₄₅	—	3	2	no	—
33	C₂×C₃×C₇×C₁₁	D₃₅	1	1	yes	characteristic
34	C₁₁×D₂₁	—	35	2	no	—
35	C₂×D₁₀₅	—	7	1	no	—
36	C₅×C₇×C₁₁	C₂×D₂₁	1	1	yes	characteristic
37	C₂×C₃×C₅×C₁₁	D₄₉	1	1	yes	characteristic, complemented
38	C₁₁×D₁₅	—	49	2	no	—
39	C₂×C₁₁×D₇	—	105	1	no	—
40	C₂×C₃×C₄₉	D₅×C₁₁	1	1	yes	characteristic, complemented
41	D₁₄₇	—	5	2	no	—
42	C₅×C₄₉	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
43	C₃×C₇×C₁₁	C₂×D₃₅	1	1	yes	characteristic
44	C₂×D₅×C₁₁	—	147	1	no	Hall
45	C₂×C₃×C₅×C₇	C₁₁×D₇	1	1	yes	characteristic
46	D₁₀₅	—	7	2	no	—
47	C₂×D₄₉	—	15	1	no	Hall
48	C₃×C₅×C₁₁	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇×C₁₁	D₁₀₅	1	1	yes	characteristic
50	C₁₁×D₇	—	105	2	no	—
51	C₃×C₄₉	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
52	C₂×D₃₅	—	21	1	no	—
53	C₂×D₃×C₁₁	—	245	1	no	Hall
54	C₂×C₅×C₁₁	D₁₄₇	1	1	yes	characteristic, complemented
55	D₅×C₁₁	—	147	2	no	—
56	C₃×C₅×C₇	C₂×C₁₁×D₇	1	1	yes	characteristic
57	C₂×C₄₉	C₁₁×D₁₅	1	1	yes	characteristic, complemented
58	D₄₉	—	15	2	no	—
59	C₂×D₂₁	—	35	1	no	—
60	C₇×C₁₁	C₂×D₁₀₅	1	1	yes	characteristic
61	C₂×C₅×C₇	C₁₁×D₂₁	1	1	yes	characteristic
62	D₃₅	—	21	2	no	—
63	C₂×C₃×C₁₁	D₂₄₅	1	1	yes	characteristic, complemented
64	D₃×C₁₁	—	245	2	no	—
65	C₂×D₁₅	—	49	1	no	Hall
66	C₅×C₁₁	C₂×D₁₄₇	1	1	yes	characteristic, complemented, Hall
67	C₄₉	C₂×C₁₁×D₁₅	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₁₁	—	735	1	no	Hall
69	C₂×C₃×C₇	C₁₁×D₃₅	1	1	yes	characteristic
70	D₂₁	—	35	2	no	—
71	C₅×C₇	C₂×C₁₁×D₂₁	1	1	yes	characteristic
72	C₃×C₁₁	C₂×D₂₄₅	1	1	yes	characteristic, complemented, Hall
73	C₂×C₃×C₅	C₁₁×D₄₉	1	1	yes	characteristic, complemented
74	D₁₅	—	49	2	no	—
75	C₂×D₇	—	105	1	no	—
76	C₂×C₁₁	—	735	2	no	—
77	C₂×C₁₁	D₇₃₅	1	1	yes	characteristic, direct product factor
78	C₃×C₇	C₂×C₁₁×D₃₅	1	1	yes	characteristic
79	C₂×D₅	—	147	1	no	Hall
80	C₃×C₅	C₂×C₁₁×D₄₉	1	1	yes	characteristic, complemented, Hall
81	C₂×C₇	C₁₁×D₁₀₅	1	1	yes	characteristic
82	D₇	—	105	2	no	—
83	C₂×D₃	—	245	1	no	Hall
84	C₁₁	C₂×D₇₃₅	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₅	C₁₁×D₁₄₇	1	1	yes	characteristic, complemented
86	D₅	—	147	2	no	—
87	C₇	C₂×C₁₁×D₁₀₅	1	1	yes	characteristic
88	C₂×C₃	C₁₁×D₂₄₅	1	1	yes	characteristic, complemented
89	D₃	—	245	2	no	—
90	C₅	C₂×C₁₁×D₁₄₇	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	735	1	no	Sylow
92	C₃	C₂×C₁₁×D₂₄₅	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	735	2	no	—
94	C₂	C₁₁×D₇₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₇₃₅
commutator, cosocle, hypocenter	C₃×C₅×C₄₉	C₂²×C₁₁
Frattini	C₇	C₂×C₁₁×D₁₀₅
Fitting	C₂×C₃×C₅×C₁₁×C₄₉	C₂
socle	C₂×C₃×C₅×C₇×C₁₁	D₇
LCS	G ▷ C₃×C₅×C₄₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₇₃₅	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
11. C₂×D₇₃₅	C₁₁	direct (N × H)
12. C₅×C₁₁×C₄₉	C₂×D₃	semidirect
16. C₃×C₁₁×C₄₉	C₂×D₅	semidirect
18. C₂×C₃×C₅×C₄₉	C₂×C₁₁	semidirect
19. D₇₃₅	C₂×C₁₁	direct (N × H)
21. C₂×C₁₁×C₄₉	D₁₅	semidirect
27. C₃×C₅×C₄₉	C₂²×C₁₁	semidirect
30. C₁₁×C₄₉	C₂×D₁₅	semidirect
31. C₂×C₅×C₄₉	D₃×C₁₁	semidirect
37. C₂×C₃×C₅×C₁₁	D₄₉	semidirect
40. C₂×C₃×C₄₉	D₅×C₁₁	semidirect
42. C₅×C₄₉	C₂×D₃×C₁₁	semidirect
48. C₃×C₅×C₁₁	C₂×D₄₉	semidirect
51. C₃×C₄₉	C₂×D₅×C₁₁	semidirect
54. C₂×C₅×C₁₁	D₁₄₇	semidirect
57. C₂×C₄₉	C₁₁×D₁₅	semidirect
63. C₂×C₃×C₁₁	D₂₄₅	semidirect
66. C₅×C₁₁	C₂×D₁₄₇	semidirect
67. C₄₉	C₂×C₁₁×D₁₅	semidirect
72. C₃×C₁₁	C₂×D₂₄₅	semidirect
73. C₂×C₃×C₅	C₁₁×D₄₉	semidirect
77. C₂×C₁₁	D₇₃₅	direct (N × H)
80. C₃×C₅	C₂×C₁₁×D₄₉	semidirect
84. C₁₁	C₂×D₇₃₅	direct (N × H)
85. C₂×C₅	C₁₁×D₁₄₇	semidirect
88. C₂×C₃	C₁₁×D₂₄₅	semidirect
90. C₅	C₂×C₁₁×D₁₄₇	semidirect
92. C₃	C₂×C₁₁×D₂₄₅	semidirect
94. C₂	C₁₁×D₇₃₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₇₃₅	2
C₂×C₃×C₅×C₁₁×C₄₉	2
C₂×C₁₁×D₂₄₅	3
C₂×C₁₁×D₁₄₇	5
C₂×C₁₁×D₁₀₅	7
C₂×D₇₃₅	11

Subgroups — C2×C11×D735 #44568435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₇₃₅ #44568435