Subgroups — C₂×C₁₇×C₃⋊D₁₀₅ #36339592

Order 21420.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊D₁₀₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₁₀₅	—	3	4	no	maximal
4	C₃²×C₅×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×C₃⋊D₂₁	—	5	1	no	maximal, Hall
6	C₁₇×D₁₀₅	—	3	8	no	—
7	C₂×C₃×C₅×C₇×C₁₇	D₃	1	4	yes	complemented
8	C₂×C₁₇×C₃⋊D₁₅	—	7	1	no	maximal, Hall
9	C₂×C₁₇×D₃₅	—	9	1	no	Hall
10	C₁₇×C₃⋊D₂₁	—	5	2	no	—
11	C₂×C₃²×C₇×C₁₇	D₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₁₇	C₂×D₃	1	4	yes	complemented
13	C₂×C₃²×C₅×C₁₇	D₇	1	1	yes	characteristic, complemented
14	C₁₇×C₃⋊D₁₅	—	7	2	no	—
15	C₂×C₁₇×D₂₁	—	15	4	no	—
16	C₂×C₃⋊D₁₀₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×C₇×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₁₇×D₃₅	—	9	2	no	—
19	C₃²×C₇×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₇×D₁₅	—	21	4	no	—
21	C₃²×C₅×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₁₇	D₁₅	1	4	yes	complemented
23	C₁₇×D₂₁	—	15	8	no	—
24	C₂×C₃²×C₅×C₇	C₂×C₁₇	1	1	yes	characteristic, complemented
25	C₃⋊D₁₀₅	C₂×C₁₇	1	2	yes	direct product factor
26	C₂×C₁₇×C₃⋊D₃	—	35	1	no	Hall
27	C₅×C₇×C₁₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₅×C₁₇	D₂₁	1	4	yes	complemented
29	C₁₇×D₁₅	—	21	8	no	—
30	C₂×D₇×C₁₇	—	45	1	no	Hall
31	C₂×D₁₀₅	—	3	4	no	—
32	C₃×C₇×C₁₇	C₂×D₁₅	1	4	yes	complemented
33	C₂×D₅×C₁₇	—	63	1	no	Hall
34	C₃²×C₅×C₇	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃²×C₁₇	D₃₅	1	1	yes	characteristic, complemented
36	C₁₇×C₃⋊D₃	—	35	2	no	—
37	C₃×C₅×C₁₇	C₂×D₂₁	1	4	yes	complemented
38	C₂×C₃⋊D₂₁	—	5	1	no	Hall
39	C₂×C₇×C₁₇	C₃⋊D₁₅	1	1	yes	characteristic, complemented
40	D₇×C₁₇	—	45	2	no	—
41	C₂×C₃×C₅×C₇	D₃×C₁₇	1	4	yes	complemented
42	D₁₀₅	—	3	8	no	—
43	C₂×D₃×C₁₇	—	105	4	no	—
44	C₂×C₃⋊D₁₅	—	7	1	no	Hall
45	C₂×C₅×C₁₇	C₃⋊D₂₁	1	1	yes	characteristic, complemented
46	D₅×C₁₇	—	63	2	no	—
47	C₃²×C₁₇	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
48	C₂×D₃₅	—	9	1	no	Hall
49	C₂×C₃²×C₇	D₅×C₁₇	1	1	yes	characteristic, complemented
50	C₃⋊D₂₁	—	5	2	no	—
51	C₇×C₁₇	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
52	C₃×C₅×C₇	C₂×D₃×C₁₇	1	4	yes	complemented
53	C₂×C₃×C₁₇	D₁₀₅	1	4	yes	complemented
54	D₃×C₁₇	—	105	8	no	—
55	C₂×C₃²×C₅	D₇×C₁₇	1	1	yes	characteristic, complemented
56	C₃⋊D₁₅	—	7	2	no	—
57	C₅×C₁₇	C₂×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
58	C₂×D₂₁	—	15	4	no	—
59	C₂×C₅×C₇	C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented
60	D₃₅	—	9	2	no	—
61	C₂²×C₁₇	—	315	1	no	Hall
62	C₃²×C₇	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
63	C₂×D₁₅	—	21	4	no	—
64	C₃×C₁₇	C₂×D₁₀₅	1	4	yes	complemented
65	C₃²×C₅	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
66	C₂×C₃×C₇	C₁₇×D₁₅	1	4	yes	complemented
67	D₂₁	—	15	8	no	—
68	C₂×C₃⋊D₃	—	35	1	no	Hall
69	C₅×C₇	C₂×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
70	C₂×C₁₇	—	315	2	no	—
71	C₂×C₁₇	C₃⋊D₁₀₅	1	1	yes	characteristic, direct product factor
72	C₂×C₃×C₅	C₁₇×D₂₁	1	4	yes	complemented
73	D₁₅	—	21	8	no	—
74	C₂×D₇	—	45	1	no	Hall
75	C₃×C₇	C₂×C₁₇×D₁₅	1	4	yes	complemented
76	C₂×D₅	—	63	1	no	Hall
77	C₂×C₃²	C₁₇×D₃₅	1	1	yes	characteristic, complemented
78	C₃⋊D₃	—	35	2	no	—
79	C₁₇	C₂×C₃⋊D₁₀₅	1	1	yes	characteristic, direct product factor, Sylow
80	C₃×C₅	C₂×C₁₇×D₂₁	1	4	yes	complemented
81	C₂×C₇	C₁₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented
82	D₇	—	45	2	no	—
83	C₂×D₃	—	105	4	no	—
84	C₂×C₅	C₁₇×C₃⋊D₂₁	1	1	yes	characteristic, complemented
85	D₅	—	63	2	no	—
86	C₃²	C₂×C₁₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
87	C₇	C₂×C₁₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₁₇×D₁₀₅	1	4	yes	complemented
89	D₃	—	105	8	no	—
90	C₅	C₂×C₁₇×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	315	1	no	Sylow
92	C₃	C₂×C₁₇×D₁₀₅	1	4	yes	complemented
93	C₂	—	315	2	no	—
94	C₂	C₁₇×C₃⋊D₁₀₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₃⋊D₁₀₅
commutator, cosocle, hypocenter	C₃²×C₅×C₇	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₃²×C₅×C₇
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊D₁₀₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₁₇	C₂	semidirect
4. C₃²×C₅×C₇×C₁₇	C₂²	semidirect
7. C₂×C₃×C₅×C₇×C₁₇	D₃	semidirect
11. C₂×C₃²×C₇×C₁₇	D₅	semidirect
12. C₃×C₅×C₇×C₁₇	C₂×D₃	semidirect
13. C₂×C₃²×C₅×C₁₇	D₇	semidirect
16. C₂×C₃⋊D₁₀₅	C₁₇	direct (N × H)
17. C₂×C₅×C₇×C₁₇	C₃⋊D₃	semidirect
19. C₃²×C₇×C₁₇	C₂×D₅	semidirect
21. C₃²×C₅×C₁₇	C₂×D₇	semidirect
22. C₂×C₃×C₇×C₁₇	D₁₅	semidirect
24. C₂×C₃²×C₅×C₇	C₂×C₁₇	semidirect
25. C₃⋊D₁₀₅	C₂×C₁₇	direct (N × H)
27. C₅×C₇×C₁₇	C₂×C₃⋊D₃	semidirect
28. C₂×C₃×C₅×C₁₇	D₂₁	semidirect
32. C₃×C₇×C₁₇	C₂×D₁₅	semidirect
34. C₃²×C₅×C₇	C₂²×C₁₇	semidirect
35. C₂×C₃²×C₁₇	D₃₅	semidirect
37. C₃×C₅×C₁₇	C₂×D₂₁	semidirect
39. C₂×C₇×C₁₇	C₃⋊D₁₅	semidirect
41. C₂×C₃×C₅×C₇	D₃×C₁₇	semidirect
45. C₂×C₅×C₁₇	C₃⋊D₂₁	semidirect
47. C₃²×C₁₇	C₂×D₃₅	semidirect
49. C₂×C₃²×C₇	D₅×C₁₇	semidirect
51. C₇×C₁₇	C₂×C₃⋊D₁₅	semidirect
52. C₃×C₅×C₇	C₂×D₃×C₁₇	semidirect
53. C₂×C₃×C₁₇	D₁₀₅	semidirect
55. C₂×C₃²×C₅	D₇×C₁₇	semidirect
57. C₅×C₁₇	C₂×C₃⋊D₂₁	semidirect
59. C₂×C₅×C₇	C₁₇×C₃⋊D₃	semidirect
62. C₃²×C₇	C₂×D₅×C₁₇	semidirect
64. C₃×C₁₇	C₂×D₁₀₅	semidirect
65. C₃²×C₅	C₂×D₇×C₁₇	semidirect
66. C₂×C₃×C₇	C₁₇×D₁₅	semidirect
69. C₅×C₇	C₂×C₁₇×C₃⋊D₃	semidirect
71. C₂×C₁₇	C₃⋊D₁₀₅	direct (N × H)
72. C₂×C₃×C₅	C₁₇×D₂₁	semidirect
75. C₃×C₇	C₂×C₁₇×D₁₅	semidirect
77. C₂×C₃²	C₁₇×D₃₅	semidirect
79. C₁₇	C₂×C₃⋊D₁₀₅	direct (N × H)
80. C₃×C₅	C₂×C₁₇×D₂₁	semidirect
81. C₂×C₇	C₁₇×C₃⋊D₁₅	semidirect
84. C₂×C₅	C₁₇×C₃⋊D₂₁	semidirect
86. C₃²	C₂×C₁₇×D₃₅	semidirect
87. C₇	C₂×C₁₇×C₃⋊D₁₅	semidirect
88. C₂×C₃	C₁₇×D₁₀₅	semidirect
90. C₅	C₂×C₁₇×C₃⋊D₂₁	semidirect
92. C₃	C₂×C₁₇×D₁₀₅	semidirect
94. C₂	C₁₇×C₃⋊D₁₀₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₃⋊D₁₀₅	2
C₂×C₃²×C₅×C₇×C₁₇	2
C₂×C₁₇×D₁₀₅	3
C₂×C₁₇×C₃⋊D₂₁	5
C₂×C₁₇×C₃⋊D₁₅	7
C₂×C₃⋊D₁₀₅	17

Subgroups — C2×C17×C3⋊D105 #36339592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₃⋊D₁₀₅ #36339592