Subgroups — C₂×C₇×C₃⋊D₃₄₅ #44394682

Order 28980.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₃₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₃₄₅	—	3	4	no	maximal
4	C₃²×C₅×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₃⋊D₆₉	—	5	1	no	maximal, Hall
6	C₇×D₃₄₅	—	3	8	no	—
7	C₂×C₃×C₅×C₇×C₂₃	D₃	1	4	yes	complemented
8	C₂×C₃⋊D₃₄₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₇×D₁₁₅	—	9	1	no	Hall
10	C₇×C₃⋊D₆₉	—	5	2	no	—
11	C₂×C₃²×C₇×C₂₃	D₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₂₃	C₂×D₃	1	4	yes	complemented
13	C₃⋊D₃₄₅	C₂×C₇	1	2	yes	direct product factor
14	C₂×C₃²×C₅×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×C₇×D₆₉	—	15	4	no	—
16	C₂×C₅×C₇×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented
17	C₇×D₁₁₅	—	9	2	no	—
18	C₃²×C₇×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
19	C₂×D₃₄₅	—	3	4	no	—
20	C₂×C₇×C₃⋊D₁₅	—	23	1	no	maximal, Hall
21	C₃²×C₅×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₂₃	D₁₅	1	4	yes	complemented
23	C₇×D₆₉	—	15	8	no	—
24	C₂×C₃⋊D₆₉	—	5	1	no	Hall
25	C₅×C₇×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅×C₂₃	D₃×C₇	1	4	yes	complemented
27	D₃₄₅	—	3	8	no	—
28	C₂×C₇×D₂₃	—	45	1	no	Hall
29	C₂×C₃²×C₅×C₇	D₂₃	1	1	yes	characteristic, complemented
30	C₇×C₃⋊D₁₅	—	23	2	no	—
31	C₃×C₇×C₂₃	C₂×D₁₅	1	4	yes	complemented
32	C₂×D₁₁₅	—	9	1	no	Hall
33	C₂×C₇×D₁₅	—	69	4	no	—
34	C₂×C₃²×C₂₃	C₇×D₅	1	1	yes	characteristic, complemented
35	C₃⋊D₆₉	—	5	2	no	—
36	C₃×C₅×C₂₃	C₂×D₃×C₇	1	4	yes	complemented
37	C₂×C₇×C₂₃	C₃⋊D₁₅	1	1	yes	characteristic, complemented
38	C₇×D₂₃	—	45	2	no	—
39	C₃²×C₅×C₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
40	C₂×D₆₉	—	15	4	no	—
41	C₂×C₇×C₃⋊D₃	—	115	1	no	Hall
42	C₂×C₅×C₂₃	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
43	D₁₁₅	—	9	2	no	—
44	C₂×C₃×C₅×C₇	D₆₉	1	4	yes	complemented
45	C₇×D₁₅	—	69	8	no	—
46	C₃²×C₂₃	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃⋊D₁₅	—	23	1	no	Hall
48	C₇×C₂₃	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇×D₅	—	207	1	no	Hall
50	C₂×C₃×C₂₃	C₇×D₁₅	1	4	yes	complemented
51	D₆₉	—	15	8	no	—
52	C₂×C₃²×C₇	D₁₁₅	1	1	yes	characteristic, complemented
53	C₇×C₃⋊D₃	—	115	2	no	—
54	C₅×C₂₃	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
55	C₃×C₅×C₇	C₂×D₆₉	1	4	yes	complemented
56	C₂×D₂₃	—	45	1	no	Hall
57	C₂×C₃²×C₅	C₇×D₂₃	1	1	yes	characteristic, complemented
58	C₃⋊D₁₅	—	23	2	no	—
59	C₂×D₃×C₇	—	345	4	no	—
60	C₂×C₅×C₇	C₃⋊D₆₉	1	1	yes	characteristic, complemented
61	C₇×D₅	—	207	2	no	—
62	C₃×C₂₃	C₂×C₇×D₁₅	1	4	yes	complemented
63	C₃²×C₇	C₂×D₁₁₅	1	1	yes	characteristic, complemented, Hall
64	C₂×D₁₅	—	69	4	no	—
65	C₂×C₂₃	C₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented
66	D₂₃	—	45	2	no	—
67	C₃²×C₅	C₂×C₇×D₂₃	1	1	yes	characteristic, complemented, Hall
68	C₂×C₃×C₇	D₃₄₅	1	4	yes	complemented
69	D₃×C₇	—	345	8	no	—
70	C₂×C₃⋊D₃	—	115	1	no	Hall
71	C₅×C₇	C₂×C₃⋊D₆₉	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	C₇×D₆₉	1	4	yes	complemented
73	D₁₅	—	69	8	no	—
74	C₂²×C₇	—	1035	1	no	Hall
75	C₂₃	C₂×C₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
76	C₃×C₇	C₂×D₃₄₅	1	4	yes	complemented
77	C₂×D₅	—	207	1	no	Hall
78	C₂×C₃²	C₇×D₁₁₅	1	1	yes	characteristic, complemented
79	C₃⋊D₃	—	115	2	no	—
80	C₃×C₅	C₂×C₇×D₆₉	1	4	yes	complemented
81	C₂×C₇	—	1035	2	no	—
82	C₂×C₇	C₃⋊D₃₄₅	1	1	yes	characteristic, direct product factor
83	C₂×D₃	—	345	4	no	—
84	C₂×C₅	C₇×C₃⋊D₆₉	1	1	yes	characteristic, complemented
85	D₅	—	207	2	no	—
86	C₃²	C₂×C₇×D₁₁₅	1	1	yes	characteristic, complemented, Sylow
87	C₇	C₂×C₃⋊D₃₄₅	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	C₇×D₃₄₅	1	4	yes	complemented
89	D₃	—	345	8	no	—
90	C₅	C₂×C₇×C₃⋊D₆₉	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	1035	1	no	Sylow
92	C₃	C₂×C₇×D₃₄₅	1	4	yes	complemented
93	C₂	—	1035	2	no	—
94	C₂	C₇×C₃⋊D₃₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	C₃⋊D₃₄₅
commutator, cosocle, hypocenter	C₃²×C₅×C₂₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₂₃	C₂
LCS	G ▷ C₃²×C₅×C₂₃
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃⋊D₃₄₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₂₃	C₂	semidirect
4. C₃²×C₅×C₇×C₂₃	C₂²	semidirect
7. C₂×C₃×C₅×C₇×C₂₃	D₃	semidirect
8. C₂×C₃⋊D₃₄₅	C₇	direct (N × H)
11. C₂×C₃²×C₇×C₂₃	D₅	semidirect
12. C₃×C₅×C₇×C₂₃	C₂×D₃	semidirect
13. C₃⋊D₃₄₅	C₂×C₇	direct (N × H)
14. C₂×C₃²×C₅×C₂₃	C₂×C₇	semidirect
16. C₂×C₅×C₇×C₂₃	C₃⋊D₃	semidirect
18. C₃²×C₇×C₂₃	C₂×D₅	semidirect
21. C₃²×C₅×C₂₃	C₂²×C₇	semidirect
22. C₂×C₃×C₇×C₂₃	D₁₅	semidirect
25. C₅×C₇×C₂₃	C₂×C₃⋊D₃	semidirect
26. C₂×C₃×C₅×C₂₃	D₃×C₇	semidirect
29. C₂×C₃²×C₅×C₇	D₂₃	semidirect
31. C₃×C₇×C₂₃	C₂×D₁₅	semidirect
34. C₂×C₃²×C₂₃	C₇×D₅	semidirect
36. C₃×C₅×C₂₃	C₂×D₃×C₇	semidirect
37. C₂×C₇×C₂₃	C₃⋊D₁₅	semidirect
39. C₃²×C₅×C₇	C₂×D₂₃	semidirect
42. C₂×C₅×C₂₃	C₇×C₃⋊D₃	semidirect
44. C₂×C₃×C₅×C₇	D₆₉	semidirect
46. C₃²×C₂₃	C₂×C₇×D₅	semidirect
48. C₇×C₂₃	C₂×C₃⋊D₁₅	semidirect
50. C₂×C₃×C₂₃	C₇×D₁₅	semidirect
52. C₂×C₃²×C₇	D₁₁₅	semidirect
54. C₅×C₂₃	C₂×C₇×C₃⋊D₃	semidirect
55. C₃×C₅×C₇	C₂×D₆₉	semidirect
57. C₂×C₃²×C₅	C₇×D₂₃	semidirect
60. C₂×C₅×C₇	C₃⋊D₆₉	semidirect
62. C₃×C₂₃	C₂×C₇×D₁₅	semidirect
63. C₃²×C₇	C₂×D₁₁₅	semidirect
65. C₂×C₂₃	C₇×C₃⋊D₁₅	semidirect
67. C₃²×C₅	C₂×C₇×D₂₃	semidirect
68. C₂×C₃×C₇	D₃₄₅	semidirect
71. C₅×C₇	C₂×C₃⋊D₆₉	semidirect
72. C₂×C₃×C₅	C₇×D₆₉	semidirect
75. C₂₃	C₂×C₇×C₃⋊D₁₅	semidirect
76. C₃×C₇	C₂×D₃₄₅	semidirect
78. C₂×C₃²	C₇×D₁₁₅	semidirect
80. C₃×C₅	C₂×C₇×D₆₉	semidirect
82. C₂×C₇	C₃⋊D₃₄₅	direct (N × H)
84. C₂×C₅	C₇×C₃⋊D₆₉	semidirect
86. C₃²	C₂×C₇×D₁₁₅	semidirect
87. C₇	C₂×C₃⋊D₃₄₅	direct (N × H)
88. C₂×C₃	C₇×D₃₄₅	semidirect
90. C₅	C₂×C₇×C₃⋊D₆₉	semidirect
92. C₃	C₂×C₇×D₃₄₅	semidirect
94. C₂	C₇×C₃⋊D₃₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₃⋊D₃₄₅	2
C₂×C₃²×C₅×C₇×C₂₃	2
C₂×C₇×D₃₄₅	3
C₂×C₇×C₃⋊D₆₉	5
C₂×C₃⋊D₃₄₅	7
C₂×C₇×C₃⋊D₁₅	23

Subgroups — C2×C7×C3⋊D345 #44394682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₃⋊D₃₄₅ #44394682