Subgroups — C₂×C₃×C₅⋊(C₇⋊D₇₇) #44568942

Order 32340.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊(C₇⋊D₇₇)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅⋊(C₇⋊D₇₇)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇⋊D₇₇	—	5	1	no	maximal, Hall
6	C₅⋊(C₇⋊D₇₇)	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅×C₇²×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×D₃₈₅	—	7	8	no	maximal
9	C₃×C₇⋊D₇₇	—	5	2	no	—
10	C₂×C₃×C₇²×C₁₁	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅⋊(C₇⋊D₇)	—	11	1	no	maximal, Hall
12	C₅×C₇²×C₁₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₃₈₅	—	7	16	no	—
14	C₂×C₃×C₅×C₇×C₁₁	D₇	1	8	yes	complemented
15	C₂×C₇⋊D₇₇	—	5	1	no	Hall
16	C₃×C₇²×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×D₃₈₅	—	7	8	no	—
18	C₂×C₃×C₅×C₇²	D₁₁	1	1	yes	characteristic, complemented
19	C₃×C₅⋊(C₇⋊D₇)	—	11	2	no	—
20	C₃×C₅×C₇×C₁₁	C₂×D₇	1	8	yes	complemented
21	C₂×C₇²×C₁₁	C₃×D₅	1	1	yes	characteristic, complemented
22	C₇⋊D₇₇	—	5	2	no	—
23	C₂×C₅⋊(C₇⋊D₇)	—	11	1	no	Hall
24	C₂×C₃×D₇₇	—	35	8	no	—
25	C₂×C₅×C₇×C₁₁	C₃×D₇	1	8	yes	complemented
26	D₃₈₅	—	7	16	no	—
27	C₃×C₅×C₇²	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×D₅₅	—	49	1	no	Hall
29	C₂×C₃×C₇⋊D₇	—	55	1	no	Hall
30	C₇²×C₁₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×C₇²	C₃×D₁₁	1	1	yes	characteristic, complemented
32	C₅⋊(C₇⋊D₇)	—	11	2	no	—
33	C₂×C₃×C₇×C₁₁	D₃₅	1	8	yes	complemented
34	C₃×D₇₇	—	35	16	no	—
35	C₂×C₃×D₃₅	—	77	8	no	—
36	C₅×C₇×C₁₁	C₂×C₃×D₇	1	8	yes	complemented
37	C₂×C₃×C₅×C₁₁	C₇⋊D₇	1	1	yes	characteristic, complemented
38	C₃×D₅₅	—	49	2	no	—
39	C₂×D₇₇	—	35	8	no	—
40	C₂×C₃×C₇²	D₅₅	1	1	yes	characteristic, complemented
41	C₃×C₇⋊D₇	—	55	2	no	—
42	C₅×C₇²	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
43	C₃×C₇×C₁₁	C₂×D₃₅	1	8	yes	complemented
44	C₂×D₅₅	—	49	1	no	Hall
45	C₂×C₃×C₅×C₇	D₇₇	1	8	yes	complemented
46	C₃×D₃₅	—	77	16	no	—
47	C₂×C₇⋊D₇	—	55	1	no	Hall
48	C₃×C₅×C₁₁	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇×C₁₁	C₃×D₃₅	1	8	yes	complemented
50	D₇₇	—	35	16	no	—
51	C₃×C₇²	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
52	C₂×D₃₅	—	77	8	no	—
53	C₂×C₃×D₁₁	—	245	1	no	Hall
54	C₂×C₅×C₁₁	C₃×C₇⋊D₇	1	1	yes	characteristic, complemented
55	D₅₅	—	49	2	no	—
56	C₃×C₅×C₇	C₂×D₇₇	1	8	yes	complemented
57	C₂×C₇²	C₃×D₅₅	1	1	yes	characteristic, complemented
58	C₇⋊D₇	—	55	2	no	—
59	C₂×C₃×D₇	—	385	8	no	—
60	C₇×C₁₁	C₂×C₃×D₃₅	1	8	yes	complemented
61	C₂×C₅×C₇	C₃×D₇₇	1	8	yes	complemented
62	D₃₅	—	77	16	no	—
63	C₂×C₃×C₁₁	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
64	C₃×D₁₁	—	245	2	no	—
65	C₂×C₃×D₅	—	539	1	no	Hall
66	C₅×C₁₁	C₂×C₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
67	C₇²	C₂×C₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
68	C₂×D₁₁	—	245	1	no	Hall
69	C₂×C₃×C₇	D₃₈₅	1	8	yes	complemented
70	C₃×D₇	—	385	16	no	—
71	C₅×C₇	C₂×C₃×D₇₇	1	8	yes	complemented
72	C₃×C₁₁	C₂×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Hall
73	C₂×C₃×C₅	C₇⋊D₇₇	1	1	yes	characteristic, complemented
74	C₃×D₅	—	539	2	no	—
75	C₂×D₇	—	385	8	no	—
76	C₂×C₁₁	C₃×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
77	D₁₁	—	245	2	no	—
78	C₃×C₇	C₂×D₃₈₅	1	8	yes	complemented
79	C₂×D₅	—	539	1	no	Hall
80	C₃×C₅	C₂×C₇⋊D₇₇	1	1	yes	characteristic, complemented, Hall
81	C₂×C₇	C₃×D₃₈₅	1	8	yes	complemented
82	D₇	—	385	16	no	—
83	C₂²×C₃	—	2695	1	no	Hall
84	C₁₁	C₂×C₃×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	C₃×C₇⋊D₇₇	1	1	yes	characteristic, complemented
86	D₅	—	539	2	no	—
87	C₇	C₂×C₃×D₃₈₅	1	8	yes	complemented
88	C₂×C₃	—	2695	2	no	—
89	C₂×C₃	C₅⋊(C₇⋊D₇₇)	1	1	yes	characteristic, direct product factor
90	C₅	C₂×C₃×C₇⋊D₇₇	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	2695	1	no	Sylow
92	C₃	C₂×C₅⋊(C₇⋊D₇₇)	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	—	2695	2	no	—
94	C₂	C₃×C₅⋊(C₇⋊D₇₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊(C₇⋊D₇₇)
commutator, cosocle, hypocenter	C₅×C₇²×C₁₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₅×C₇²×C₁₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅⋊(C₇⋊D₇₇)	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇²×C₁₁	C₂	semidirect
3. C₂×C₅⋊(C₇⋊D₇₇)	C₃	direct (N × H)
4. C₃×C₅×C₇²×C₁₁	C₂²	semidirect
6. C₅⋊(C₇⋊D₇₇)	C₂×C₃	direct (N × H)
7. C₂×C₅×C₇²×C₁₁	C₂×C₃	semidirect
10. C₂×C₃×C₇²×C₁₁	D₅	semidirect
12. C₅×C₇²×C₁₁	C₂²×C₃	semidirect
14. C₂×C₃×C₅×C₇×C₁₁	D₇	semidirect
16. C₃×C₇²×C₁₁	C₂×D₅	semidirect
18. C₂×C₃×C₅×C₇²	D₁₁	semidirect
20. C₃×C₅×C₇×C₁₁	C₂×D₇	semidirect
21. C₂×C₇²×C₁₁	C₃×D₅	semidirect
25. C₂×C₅×C₇×C₁₁	C₃×D₇	semidirect
27. C₃×C₅×C₇²	C₂×D₁₁	semidirect
30. C₇²×C₁₁	C₂×C₃×D₅	semidirect
31. C₂×C₅×C₇²	C₃×D₁₁	semidirect
33. C₂×C₃×C₇×C₁₁	D₃₅	semidirect
36. C₅×C₇×C₁₁	C₂×C₃×D₇	semidirect
37. C₂×C₃×C₅×C₁₁	C₇⋊D₇	semidirect
40. C₂×C₃×C₇²	D₅₅	semidirect
42. C₅×C₇²	C₂×C₃×D₁₁	semidirect
43. C₃×C₇×C₁₁	C₂×D₃₅	semidirect
45. C₂×C₃×C₅×C₇	D₇₇	semidirect
48. C₃×C₅×C₁₁	C₂×C₇⋊D₇	semidirect
49. C₂×C₇×C₁₁	C₃×D₃₅	semidirect
51. C₃×C₇²	C₂×D₅₅	semidirect
54. C₂×C₅×C₁₁	C₃×C₇⋊D₇	semidirect
56. C₃×C₅×C₇	C₂×D₇₇	semidirect
57. C₂×C₇²	C₃×D₅₅	semidirect
60. C₇×C₁₁	C₂×C₃×D₃₅	semidirect
61. C₂×C₅×C₇	C₃×D₇₇	semidirect
63. C₂×C₃×C₁₁	C₅⋊(C₇⋊D₇)	semidirect
66. C₅×C₁₁	C₂×C₃×C₇⋊D₇	semidirect
67. C₇²	C₂×C₃×D₅₅	semidirect
69. C₂×C₃×C₇	D₃₈₅	semidirect
71. C₅×C₇	C₂×C₃×D₇₇	semidirect
72. C₃×C₁₁	C₂×C₅⋊(C₇⋊D₇)	semidirect
73. C₂×C₃×C₅	C₇⋊D₇₇	semidirect
76. C₂×C₁₁	C₃×C₅⋊(C₇⋊D₇)	semidirect
78. C₃×C₇	C₂×D₃₈₅	semidirect
80. C₃×C₅	C₂×C₇⋊D₇₇	semidirect
81. C₂×C₇	C₃×D₃₈₅	semidirect
84. C₁₁	C₂×C₃×C₅⋊(C₇⋊D₇)	semidirect
85. C₂×C₅	C₃×C₇⋊D₇₇	semidirect
87. C₇	C₂×C₃×D₃₈₅	semidirect
89. C₂×C₃	C₅⋊(C₇⋊D₇₇)	direct (N × H)
90. C₅	C₂×C₃×C₇⋊D₇₇	semidirect
92. C₃	C₂×C₅⋊(C₇⋊D₇₇)	direct (N × H)
94. C₂	C₃×C₅⋊(C₇⋊D₇₇)	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×C₅⋊(C₇⋊D₇₇)	2
C₂×C₃×C₅×C₇²×C₁₁	2
C₂×C₅⋊(C₇⋊D₇₇)	3
C₂×C₃×C₇⋊D₇₇	5
C₂×C₃×D₃₈₅	7
C₂×C₃×C₅⋊(C₇⋊D₇)	11

Subgroups — C2×C3×C5⋊(C7⋊D77) #44568942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅⋊(C₇⋊D₇₇) #44568942