Subgroups — C₂×C₃²×C₅×D₁₁₉ #36339573

Order 21420.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₁₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₁₁₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₁₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×D₁₁₉	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅×C₇×C₁₇	C₂×C₃	1	4	yes	complemented
8	C₂×C₃²×C₅×D₁₇	—	7	1	no	maximal, Hall
9	C₂×C₅×D₁₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×D₁₁₉	C₂×C₅	1	2	yes	direct product factor
11	C₂×C₃²×C₇×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₁₇	C₂²×C₃	1	4	yes	complemented
13	C₂×C₃²×C₅×C₁₇	D₇	1	1	yes	characteristic, complemented
14	C₃²×C₅×D₁₇	—	7	2	no	—
15	C₂×C₃×D₁₁₉	C₃×C₅	1	4	yes	direct product factor
16	C₂×C₃²×C₅×D₇	—	17	1	no	maximal, Hall
17	C₂×C₅×C₇×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₅×D₁₁₉	C₂×C₃²	1	2	yes	direct product factor
19	C₃²×C₇×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅×D₁₇	—	7	4	no	—
21	C₃²×C₅×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₁₇	C₂×C₃×C₅	1	4	yes	complemented
23	C₃×D₁₁₉	C₂×C₃×C₅	1	8	yes	direct product factor
24	C₂×C₃²×C₅×C₇	D₁₇	1	1	yes	characteristic, complemented
25	C₃²×C₅×D₇	—	17	2	no	—
26	C₂×C₃²×D₁₇	—	7	1	no	Hall
27	C₅×C₇×C₁₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₅×C₁₇	C₃×D₇	1	4	yes	complemented
29	C₃×C₅×D₁₇	—	7	8	no	—
30	C₂×D₁₁₉	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃×C₅×D₇	—	17	4	no	—
32	C₃×C₇×C₁₇	C₂²×C₃×C₅	1	4	yes	complemented
33	C₂×C₅×D₁₇	—	7	1	no	Hall
34	C₃²×C₅×C₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃²×C₁₇	C₅×D₇	1	1	yes	characteristic, complemented
36	C₃²×D₁₇	—	7	2	no	—
37	C₃×C₅×C₁₇	C₂×C₃×D₇	1	4	yes	complemented
38	C₂×C₃²×D₇	—	17	1	no	Hall
39	C₂×C₇×C₁₇	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
40	D₁₁₉	C₂×C₃²×C₅	1	2	yes	direct product factor
41	C₂×C₃×C₅×C₇	C₃×D₁₇	1	4	yes	complemented
42	C₃×C₅×D₇	—	17	8	no	—
43	C₂×C₃×D₁₇	—	7	4	no	—
44	C₂²×C₃²×C₅	—	119	1	no	Hall
45	C₂×C₅×C₁₇	C₃²×D₇	1	1	yes	characteristic, complemented
46	C₅×D₁₇	—	7	2	no	—
47	C₃²×C₁₇	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
48	C₂×C₅×D₇	—	17	1	no	Hall
49	C₂×C₃²×C₇	C₅×D₁₇	1	1	yes	characteristic, complemented
50	C₃²×D₇	—	17	2	no	—
51	C₇×C₁₇	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
52	C₃×C₅×C₇	C₂×C₃×D₁₇	1	4	yes	complemented
53	C₂×C₃×C₁₇	C₃×C₅×D₇	1	4	yes	complemented
54	C₃×D₁₇	—	7	8	no	—
55	C₂×C₃²×C₅	—	119	2	no	—
56	C₂×C₃²×C₅	D₁₁₉	1	1	yes	characteristic, direct product factor
57	C₅×C₁₇	C₂×C₃²×D₇	1	1	yes	characteristic, complemented, Hall
58	C₂×C₃×D₇	—	17	4	no	—
59	C₂×C₅×C₇	C₃²×D₁₇	1	1	yes	characteristic, complemented
60	C₅×D₇	—	17	2	no	—
61	C₂×D₁₇	—	7	1	no	Hall
62	C₃²×C₇	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
63	C₂²×C₃×C₅	—	119	4	no	—
64	C₃×C₁₇	C₂×C₃×C₅×D₇	1	4	yes	complemented
65	C₃²×C₅	C₂×D₁₁₉	1	1	yes	characteristic, direct product factor, Hall
66	C₂×C₃×C₇	C₃×C₅×D₁₇	1	4	yes	complemented
67	C₃×D₇	—	17	8	no	—
68	C₂²×C₃²	—	119	1	no	Hall
69	C₅×C₇	C₂×C₃²×D₁₇	1	1	yes	characteristic, complemented, Hall
70	C₂×C₁₇	C₃²×C₅×D₇	1	1	yes	characteristic, complemented
71	D₁₇	—	7	2	no	—
72	C₂×C₃×C₅	—	119	8	no	—
73	C₂×C₃×C₅	C₃×D₁₁₉	1	4	yes	direct product factor
74	C₂×D₇	—	17	1	no	Hall
75	C₃×C₇	C₂×C₃×C₅×D₁₇	1	4	yes	complemented
76	C₂²×C₅	—	119	1	no	Hall
77	C₂×C₃²	—	119	2	no	—
78	C₂×C₃²	C₅×D₁₁₉	1	1	yes	characteristic, direct product factor
79	C₁₇	C₂×C₃²×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
80	C₃×C₅	C₂×C₃×D₁₁₉	1	4	yes	direct product factor
81	C₂×C₇	C₃²×C₅×D₁₇	1	1	yes	characteristic, complemented
82	D₇	—	17	2	no	—
83	C₂²×C₃	—	119	4	no	—
84	C₂×C₅	—	119	2	no	—
85	C₂×C₅	C₃²×D₁₁₉	1	1	yes	characteristic, direct product factor
86	C₃²	C₂×C₅×D₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
87	C₇	C₂×C₃²×C₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	119	8	no	—
89	C₂×C₃	C₃×C₅×D₁₁₉	1	4	yes	direct product factor
90	C₅	C₂×C₃²×D₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	119	1	no	Sylow
92	C₃	C₂×C₃×C₅×D₁₁₉	1	4	yes	direct product factor
93	C₂	—	119	2	no	—
94	C₂	C₃²×C₅×D₁₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅	D₁₁₉
commutator, cosocle, hypocenter	C₇×C₁₇	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₇	C₂
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₂×C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×D₁₁₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₁₇	C₂	semidirect
3. C₂×C₃×C₅×D₁₁₉	C₃	direct (N × H)
4. C₃²×C₅×C₇×C₁₇	C₂²	semidirect
5. C₂×C₃²×D₁₁₉	C₅	direct (N × H)
6. C₃×C₅×D₁₁₉	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₇×C₁₇	C₂×C₃	semidirect
9. C₂×C₅×D₁₁₉	C₃²	direct (N × H)
10. C₃²×D₁₁₉	C₂×C₅	direct (N × H)
11. C₂×C₃²×C₇×C₁₇	C₂×C₅	semidirect
12. C₃×C₅×C₇×C₁₇	C₂²×C₃	semidirect
13. C₂×C₃²×C₅×C₁₇	D₇	semidirect
15. C₂×C₃×D₁₁₉	C₃×C₅	direct (N × H)
17. C₂×C₅×C₇×C₁₇	C₂×C₃²	semidirect
18. C₅×D₁₁₉	C₂×C₃²	direct (N × H)
19. C₃²×C₇×C₁₇	C₂²×C₅	semidirect
21. C₃²×C₅×C₁₇	C₂×D₇	semidirect
22. C₂×C₃×C₇×C₁₇	C₂×C₃×C₅	semidirect
23. C₃×D₁₁₉	C₂×C₃×C₅	direct (N × H)
24. C₂×C₃²×C₅×C₇	D₁₇	semidirect
27. C₅×C₇×C₁₇	C₂²×C₃²	semidirect
28. C₂×C₃×C₅×C₁₇	C₃×D₇	semidirect
30. C₂×D₁₁₉	C₃²×C₅	direct (N × H)
32. C₃×C₇×C₁₇	C₂²×C₃×C₅	semidirect
34. C₃²×C₅×C₇	C₂×D₁₇	semidirect
35. C₂×C₃²×C₁₇	C₅×D₇	semidirect
37. C₃×C₅×C₁₇	C₂×C₃×D₇	semidirect
39. C₂×C₇×C₁₇	C₂×C₃²×C₅	semidirect
40. D₁₁₉	C₂×C₃²×C₅	direct (N × H)
41. C₂×C₃×C₅×C₇	C₃×D₁₇	semidirect
45. C₂×C₅×C₁₇	C₃²×D₇	semidirect
47. C₃²×C₁₇	C₂×C₅×D₇	semidirect
49. C₂×C₃²×C₇	C₅×D₁₇	semidirect
51. C₇×C₁₇	C₂²×C₃²×C₅	semidirect
52. C₃×C₅×C₇	C₂×C₃×D₁₇	semidirect
53. C₂×C₃×C₁₇	C₃×C₅×D₇	semidirect
56. C₂×C₃²×C₅	D₁₁₉	direct (N × H)
57. C₅×C₁₇	C₂×C₃²×D₇	semidirect
59. C₂×C₅×C₇	C₃²×D₁₇	semidirect
62. C₃²×C₇	C₂×C₅×D₁₇	semidirect
64. C₃×C₁₇	C₂×C₃×C₅×D₇	semidirect
65. C₃²×C₅	C₂×D₁₁₉	direct (N × H)
66. C₂×C₃×C₇	C₃×C₅×D₁₇	semidirect
69. C₅×C₇	C₂×C₃²×D₁₇	semidirect
70. C₂×C₁₇	C₃²×C₅×D₇	semidirect
73. C₂×C₃×C₅	C₃×D₁₁₉	direct (N × H)
75. C₃×C₇	C₂×C₃×C₅×D₁₇	semidirect
78. C₂×C₃²	C₅×D₁₁₉	direct (N × H)
79. C₁₇	C₂×C₃²×C₅×D₇	semidirect
80. C₃×C₅	C₂×C₃×D₁₁₉	direct (N × H)
81. C₂×C₇	C₃²×C₅×D₁₇	semidirect
85. C₂×C₅	C₃²×D₁₁₉	direct (N × H)
86. C₃²	C₂×C₅×D₁₁₉	direct (N × H)
87. C₇	C₂×C₃²×C₅×D₁₇	semidirect
89. C₂×C₃	C₃×C₅×D₁₁₉	direct (N × H)
90. C₅	C₂×C₃²×D₁₁₉	direct (N × H)
92. C₃	C₂×C₃×C₅×D₁₁₉	direct (N × H)
94. C₂	C₃²×C₅×D₁₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×D₁₁₉	2
C₂×C₃²×C₅×C₇×C₁₇	2
C₂×C₃×C₅×D₁₁₉	3
C₂×C₃²×D₁₁₉	5
C₂×C₃²×C₅×D₁₇	7
C₂×C₃²×C₅×D₇	17

Subgroups — C2×C32×C5×D119 #36339573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×D₁₁₉ #36339573