Subgroups — C₂×D₃₅×#4296 #37561249

Order 23940.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×#4296	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₅×#4296	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₉⋊C₃×D₃₅	C₃	1	1	yes	maximal, characteristic
4	C₅×C₇×#4296	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₇×#4296	—	5	1	no	maximal, Hall
6	C₁₉⋊C₃×D₃₅	C₂×C₃	1	2	yes	—
7	C₂×C₅×C₇×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
8	C₂×D₅×#4296	—	7	1	no	maximal, Hall
9	C₂×C₁₉×D₃₅	C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×#4296	D₅	1	1	yes	characteristic, complemented
11	D₇×#4296	—	5	2	no	—
12	C₅×C₇×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₅×#4296	D₇	1	1	yes	characteristic, complemented
14	D₅×#4296	—	7	2	no	—
15	C₂×D₇×C₁₉⋊C₃	—	5	1	no	—
16	C₂×C₅×C₇×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
17	C₁₉×D₃₅	C₂×C₉	1	2	yes	complemented
18	C₂×C₉×D₃₅	—	19	1	no	maximal, Hall
19	C₇×#4296	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅×C₁₉⋊C₃	—	7	1	no	—
21	C₅×#4296	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₁₉⋊C₃	C₃×D₅	1	1	yes	characteristic
23	D₇×C₁₉⋊C₃	—	5	2	no	—
24	C₂²×#4296	—	35	1	no	Hall
25	C₅×C₇×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×C₇×C₉	—	19	1	no	—
27	C₉×D₃₅	—	19	2	no	—
28	C₂×C₅×C₁₉⋊C₃	C₃×D₇	1	1	yes	characteristic
29	D₅×C₁₉⋊C₃	—	7	2	no	—
30	C₂×D₇×C₁₉	—	5	1	no	Hall
31	C₂×C₃×D₃₅	—	19	1	no	—
32	C₇×C₁₉⋊C₃	C₂×C₃×D₅	1	1	yes	characteristic
33	C₂×D₅×C₁₉	—	7	1	no	Hall
34	C₂×#4296	—	35	2	no	—
35	C₂×#4296	D₃₅	1	1	yes	characteristic, direct product factor
36	C₅×C₇×C₉	—	19	1	no	Hall
37	C₅×C₁₉⋊C₃	C₂×C₃×D₇	1	1	yes	characteristic
38	C₂×C₇×C₁₉	C₉×D₅	1	1	yes	characteristic, complemented
39	D₇×C₁₉	—	5	2	no	—
40	C₂×C₉×D₇	—	95	1	no	Hall
41	C₂²×C₁₉⋊C₃	—	35	1	no	—
42	C₂×C₃×C₅×C₇	—	19	1	no	—
43	C₃×D₃₅	—	19	2	no	—
44	C₂×C₅×C₁₉	C₉×D₇	1	1	yes	characteristic, complemented
45	D₅×C₁₉	—	7	2	no	—
46	C₂×C₉×D₅	—	133	1	no	Hall
47	#4296	C₂×D₃₅	1	1	yes	characteristic, direct product factor, Hall
48	C₂×D₃₅	#4296	1	1	yes	characteristic, direct product factor, Hall
49	C₇×C₁₉	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇×C₉	—	19	1	no	—
51	C₉×D₇	—	95	2	no	—
52	C₂×C₁₉⋊C₃	—	35	2	no	—
53	C₂×C₁₉⋊C₃	C₃×D₃₅	1	1	yes	characteristic
54	C₃×C₅×C₇	—	19	1	no	—
55	C₅×C₁₉	C₂×C₉×D₇	1	1	yes	characteristic, complemented, Hall
56	C₂×C₅×C₉	—	19	1	no	—
57	C₉×D₅	—	133	2	no	—
58	C₂×C₃×D₇	—	95	1	no	—
59	C₂²×C₁₉	—	35	1	no	Hall
60	C₂×C₅×C₇	C₂×#4296	1	1	yes	characteristic, complemented
61	D₃₅	C₂×#4296	1	2	yes	direct product factor
62	C₇×C₉	—	19	1	no	Hall
63	C₂×C₃×D₅	—	133	1	no	—
64	C₁₉⋊C₃	C₂×C₃×D₃₅	1	1	yes	characteristic
65	C₅×C₉	—	19	1	no	Hall
66	C₂×C₃×C₇	—	19	1	no	—
67	C₃×D₇	—	95	2	no	—
68	C₂×C₁₉	—	35	2	no	—
69	C₂×C₁₉	C₉×D₃₅	1	1	yes	characteristic, complemented
70	C₂²×C₉	—	665	1	no	Hall
71	C₅×C₇	C₂²×#4296	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	—	19	1	no	—
73	C₃×D₅	—	133	2	no	—
74	C₂×D₇	—	5	1	no	Hall
75	C₃×C₇	—	19	1	no	—
76	C₂×D₅	—	7	1	no	Hall
77	C₁₉	C₂×C₉×D₃₅	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₉	—	19	1	no	—
79	C₂×C₉	—	665	2	no	—
80	C₃×C₅	—	19	1	no	—
81	C₂×C₇	D₅×#4296	1	1	yes	characteristic, complemented
82	D₇	—	5	2	no	—
83	C₂²×C₃	—	665	1	no	—
84	C₂×C₅	D₇×#4296	1	1	yes	characteristic, complemented
85	D₅	—	7	2	no	—
86	C₉	—	19	1	no	Sylow
87	C₇	C₂×D₅×#4296	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	19	1	no	—
89	C₂×C₃	—	665	2	no	—
90	C₅	C₂×D₇×#4296	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	35	1	no	Sylow
92	C₃	—	19	1	no	—
93	C₂	—	35	2	no	—
94	C₂	D₃₅×#4296	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃₅×#4296
commutator, hypocenter	C₅×C₇×C₁₉	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₉	C₂×C₉
prime radical	C₂×C₁₉⋊C₃×D₃₅	C₃
cosocle	C₅×C₇×C₁₉⋊C₃	C₂²×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₇×#4296	C₂	semidirect
2. D₃₅×#4296	C₂	direct (N × H)
4. C₅×C₇×#4296	C₂²	semidirect
9. C₂×C₁₉×D₃₅	C₉	semidirect
10. C₂×C₇×#4296	D₅	semidirect
13. C₂×C₅×#4296	D₇	semidirect
16. C₂×C₅×C₇×C₁₉	C₂×C₉	semidirect
17. C₁₉×D₃₅	C₂×C₉	semidirect
19. C₇×#4296	C₂×D₅	semidirect
21. C₅×#4296	C₂×D₇	semidirect
25. C₅×C₇×C₁₉	C₂²×C₉	semidirect
35. C₂×#4296	D₃₅	direct (N × H)
38. C₂×C₇×C₁₉	C₉×D₅	semidirect
44. C₂×C₅×C₁₉	C₉×D₇	semidirect
47. #4296	C₂×D₃₅	direct (N × H)
48. C₂×D₃₅	#4296	direct (N × H)
49. C₇×C₁₉	C₂×C₉×D₅	semidirect
55. C₅×C₁₉	C₂×C₉×D₇	semidirect
60. C₂×C₅×C₇	C₂×#4296	semidirect
61. D₃₅	C₂×#4296	direct (N × H)
69. C₂×C₁₉	C₉×D₃₅	semidirect
71. C₅×C₇	C₂²×#4296	semidirect
77. C₁₉	C₂×C₉×D₃₅	semidirect
81. C₂×C₇	D₅×#4296	semidirect
84. C₂×C₅	D₇×#4296	semidirect
87. C₇	C₂×D₅×#4296	semidirect
90. C₅	C₂×D₇×#4296	semidirect
94. C₂	D₃₅×#4296	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇×#4296	2
D₃₅×#4296	2
C₂×C₁₉⋊C₃×D₃₅	3
C₂×D₇×#4296	5
C₂×D₅×#4296	7
C₂×C₉×D₃₅	19

Subgroups — C2×D35×#4296 #37561249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₅×#4296 #37561249