Subgroups — C₂×C₅×#14558780 #37560969

Order 23940.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14558780	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#11924776	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₇×D₁₉	C₃	1	1	yes	maximal, characteristic
4	C₅×#11924776	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#14558780	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₇×D₁₉	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅×#4294⋊C₂	—	7	1	no	maximal, Hall
9	C₂×C₅×C₇×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×#11924776	C₂×C₅	1	1	yes	characteristic, complemented
11	#14558780	C₂×C₅	1	2	yes	direct product factor
12	C₃×C₅×C₇×C₁₉	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₅×#4294	—	7	1	no	—
14	C₅×#4294⋊C₂	—	7	2	no	—
15	C₂×C₃×C₇×D₁₉	C₃×C₅	1	1	yes	characteristic
16	C₂×C₅×C₇×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
17	C₅×C₇×D₁₉	C₂×C₉	1	2	yes	complemented
18	C₂²×C₅×C₇⋊C₉	—	19	1	no	maximal, Hall
19	#11924776	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅×D₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
21	C₅×#4294	—	7	1	no	Hall
22	C₂×C₃×C₇×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
23	C₃×C₇×D₁₉	C₂×C₃×C₅	1	2	yes	—
24	C₂×#4294⋊C₂	—	7	1	no	Hall
25	C₅×C₇×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅×C₇⋊C₉	—	19	2	no	—
27	C₂×C₅×C₇⋊C₉	—	19	1	no	—
28	C₂×C₃×C₅×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₃×C₅×D₁₉	C₂×ΓL(1,𝔽₈)	1	2	yes	—
30	C₂×C₇×D₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₃×C₅×C₇	—	57	1	no	—
32	C₃×C₇×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic
33	C₂×C₅×D₁₉	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
34	C₂×#4294	—	7	1	no	—
35	#4294⋊C₂	—	7	2	no	—
36	C₅×C₇⋊C₉	—	19	1	no	Hall
37	C₃×C₅×C₁₉	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
38	C₂×C₇×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented
39	C₇×D₁₉	C₂×C₅×C₉	1	2	yes	complemented
40	C₂²×C₇⋊C₉	—	19	1	no	Hall
41	C₂×C₃×D₁₉	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
42	C₂×C₃×C₅×C₇	—	57	2	no	—
43	C₂×C₃×C₅×C₇	D₁₉⋊C₃	1	1	yes	characteristic
44	C₂×C₅×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
45	C₅×D₁₉	C₂×C₇⋊C₉	1	2	yes	complemented
46	C₂²×C₅×C₉	—	133	1	no	Hall
47	#4294	—	7	1	no	Hall
48	C₂²×C₅×C₇	—	57	1	no	Hall
49	C₇×C₁₉	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇⋊C₉	—	19	2	no	—
51	C₂×C₇⋊C₉	—	19	1	no	—
52	C₂×C₃×C₁₉	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
53	C₃×D₁₉	C₂×C₅×ΓL(1,𝔽₈)	1	2	yes	—
54	C₃×C₅×C₇	C₂×D₁₉⋊C₃	1	1	yes	characteristic
55	C₅×C₁₉	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
56	C₂×C₅×C₉	—	133	2	no	—
57	C₂×C₅×C₉	—	133	1	no	—
58	C₂²×C₃×C₇	—	57	1	no	—
59	C₂×D₁₉	C₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
60	C₂×C₅×C₇	—	57	2	no	—
61	C₂×C₅×C₇	#4294⋊C₂	1	1	yes	characteristic, complemented
62	C₇⋊C₉	—	19	1	no	Hall
63	C₂²×C₃×C₅	—	57	1	no	—
64	C₃×C₁₉	C₂²×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
65	C₅×C₉	—	133	1	no	Hall
66	C₂×C₃×C₇	—	57	2	no	—
67	C₂×C₃×C₇	C₅×D₁₉⋊C₃	1	1	yes	characteristic
68	C₂×C₁₉	C₂×C₅×C₇⋊C₉	1	1	yes	characteristic, complemented
69	D₁₉	C₂×C₅×C₇⋊C₉	1	2	yes	complemented
70	C₂²×C₉	—	133	1	no	Hall
71	C₅×C₇	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	—	57	2	no	—
73	C₂×C₃×C₅	#11716321	1	1	yes	characteristic
74	C₂²×C₇	—	57	1	no	Hall
75	C₃×C₇	C₂×C₅×D₁₉⋊C₃	1	1	yes	characteristic
76	C₂²×C₅	—	57	1	no	Hall
77	C₁₉	C₂²×C₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₉	—	133	2	no	—
79	C₂×C₉	—	133	1	no	—
80	C₃×C₅	C₂×#11716321	1	1	yes	characteristic
81	C₂×C₇	—	57	2	no	—
82	C₂×C₇	C₅×#4294⋊C₂	1	1	yes	characteristic, complemented
83	C₂²×C₃	—	57	1	no	—
84	C₂×C₅	—	57	2	no	—
85	C₂×C₅	#14558780	1	1	yes	characteristic, direct product factor
86	C₉	—	133	1	no	Sylow
87	C₇	C₂×C₅×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	57	2	no	—
89	C₂×C₃	C₅×#11716321	1	1	yes	characteristic
90	C₅	C₂×#14558780	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	57	1	no	Sylow
92	C₃	C₂×C₅×#11716321	1	1	yes	characteristic
93	C₂	—	57	2	no	—
94	C₂	C₅×#14558780	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	#11716321
commutator, hypocenter	C₇×C₁₉	C₂²×C₅×C₉
Frattini	C₃	C₂×C₅×#11716321
Fitting, socle	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₅×C₇×D₁₉	C₃
cosocle	C₃×C₇×C₁₉	C₂²×C₃×C₅
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#14558780	C₂	direct (N × H)
2. C₂×C₅×#11924776	C₂	semidirect
4. C₅×#11924776	C₂²	semidirect
5. C₂×#14558780	C₅	direct (N × H)
9. C₂×C₅×C₇×D₁₉	C₉	semidirect
10. C₂×#11924776	C₂×C₅	semidirect
11. #14558780	C₂×C₅	direct (N × H)
16. C₂×C₅×C₇×C₁₉	C₂×C₉	semidirect
17. C₅×C₇×D₁₉	C₂×C₉	semidirect
19. #11924776	C₂²×C₅	semidirect
25. C₅×C₇×C₁₉	C₂²×C₉	semidirect
30. C₂×C₇×D₁₉	C₅×C₉	semidirect
33. C₂×C₅×D₁₉	C₇⋊C₉	semidirect
38. C₂×C₇×C₁₉	C₂×C₅×C₉	semidirect
39. C₇×D₁₉	C₂×C₅×C₉	semidirect
44. C₂×C₅×C₁₉	C₂×C₇⋊C₉	semidirect
45. C₅×D₁₉	C₂×C₇⋊C₉	semidirect
49. C₇×C₁₉	C₂²×C₅×C₉	semidirect
55. C₅×C₁₉	C₂²×C₇⋊C₉	semidirect
59. C₂×D₁₉	C₅×C₇⋊C₉	semidirect
61. C₂×C₅×C₇	#4294⋊C₂	semidirect
68. C₂×C₁₉	C₂×C₅×C₇⋊C₉	semidirect
69. D₁₉	C₂×C₅×C₇⋊C₉	semidirect
71. C₅×C₇	C₂×#4294⋊C₂	semidirect
77. C₁₉	C₂²×C₅×C₇⋊C₉	semidirect
82. C₂×C₇	C₅×#4294⋊C₂	semidirect
85. C₂×C₅	#14558780	direct (N × H)
87. C₇	C₂×C₅×#4294⋊C₂	semidirect
90. C₅	C₂×#14558780	direct (N × H)
94. C₂	C₅×#14558780	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#14558780	2
C₂×C₅×#11924776	2
C₂×C₃×C₅×C₇×D₁₉	3
C₂×#14558780	5
C₂×C₅×#4294⋊C₂	7
C₂²×C₅×C₇⋊C₉	19

Subgroups — C2×C5×#14558780 #37560969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#14558780 #37560969