Subgroups — #37560927

Order 23940.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#11924776	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×C₇⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic
3	C₅×#11924776	C₄	1	1	yes	characteristic, complemented, Hall
4	#18012094	—	5	1	no	maximal, Hall
5	C₃×C₇×D₅×C₁₉	C₂×C₃	1	1	yes	characteristic
6	AGL(1,𝔽₅)×#4294	—	7	1	no	maximal, Hall
7	C₁₉×C₇⋊AGL(1,𝔽₅)	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×#11924776	—	5	1	no	—
9	C₃×C₅×C₇×C₁₉	C₃×C₄	1	1	yes	characteristic
10	D₅×#4294	—	7	1	no	—
11	C₃×C₁₉×Dic₇	—	5	1	no	—
12	C₇×D₅×C₁₉	C₂×C₉	1	1	yes	characteristic
13	(C₇⋊C₉)⋊AGL(1,𝔽₅)	—	19	1	no	maximal, Hall
14	#11924776	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₉×AGL(1,𝔽₅)	—	21	1	no	—
16	C₅×#4294	—	7	1	no	Hall
17	C₂×C₃×C₇×C₁₉	—	5	1	no	—
18	C₄×#4294	—	35	1	no	Hall
19	C₅×C₇×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
20	D₅×C₇⋊C₉	—	19	1	no	—
21	C₃×D₅×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic
22	C₁₉×Dic₇	—	5	1	no	Hall
23	C₃×C₇⋊AGL(1,𝔽₅)	C₁₉⋊C₃	1	1	yes	characteristic
24	C₃×C₇×C₁₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₁₉×AGL(1,𝔽₅)	—	21	1	no	Hall
26	C₂×#4294	—	35	1	no	—
27	C₅×C₇⋊C₉	—	19	1	no	Hall
28	C₃×C₅×C₁₉	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
29	C₂×C₇×C₁₉	—	5	1	no	—
30	Dic₇⋊C₉	—	95	1	no	Hall
31	C₃×C₄×C₁₉	—	105	1	no	—
32	C₃×C₇×D₅	C₂×C₁₉⋊C₃	1	1	yes	characteristic
33	D₅×C₁₉	D₇⋊C₉	1	1	yes	characteristic
34	C₉×AGL(1,𝔽₅)	—	133	1	no	Hall
35	#4294	—	7	1	no	Hall
36	C₇⋊AGL(1,𝔽₅)	#4294	1	1	yes	characteristic, complemented, Hall
37	C₇×C₁₉	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇⋊C₉	—	95	1	no	—
39	C₂×C₃×C₁₉	—	5	1	no	—
40	C₃×C₅×C₇	C₄×C₁₉⋊C₃	1	1	yes	characteristic
41	C₅×C₁₉	Dic₇⋊C₉	1	1	yes	characteristic, complemented, Hall
42	C₉×D₅	—	133	1	no	—
43	C₃×Dic₇	—	5	1	no	—
44	C₄×C₁₉	—	105	1	no	Hall
45	C₇×D₅	C₂×#4294	1	1	yes	characteristic
46	C₇⋊C₉	—	19	1	no	Hall
47	C₃×AGL(1,𝔽₅)	—	21	1	no	—
48	C₃×C₁₉	ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
49	C₅×C₉	—	133	1	no	Hall
50	C₂×C₃×C₇	—	5	1	no	—
51	C₂×C₁₉	—	5	1	no	—
52	C₄×C₉	—	665	1	no	Hall
53	C₅×C₇	C₄×#4294	1	1	yes	characteristic, complemented, Hall
54	C₃×D₅	#11716325	1	1	yes	characteristic
55	Dic₇	—	5	1	no	Hall
56	C₃×C₇	AGL(1,𝔽₅)×C₁₉⋊C₃	1	1	yes	characteristic
57	AGL(1,𝔽₅)	—	21	1	no	Hall
58	C₁₉	(C₇⋊C₉)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₉	—	665	1	no	—
60	C₃×C₅	#13097586	1	1	yes	characteristic
61	C₂×C₇	—	5	1	no	—
62	C₃×C₄	—	105	1	no	—
63	D₅	#14558784	1	1	yes	characteristic
64	C₉	—	133	1	no	Sylow
65	C₇	AGL(1,𝔽₅)×#4294	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	5	1	no	—
67	C₅	#18012094	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	105	1	no	Sylow
69	C₃	#22547634	1	1	yes	characteristic
70	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#22547634
commutator, hypocenter	C₅×C₇×C₁₉	C₄×C₉
Fitting, socle	C₃×C₅×C₇×C₁₉	C₃×C₄
prime radical, cosocle	C₃×C₇×D₅×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₅×#11924776	C₄	semidirect
7. C₁₉×C₇⋊AGL(1,𝔽₅)	C₉	semidirect
14. #11924776	AGL(1,𝔽₅)	semidirect
19. C₅×C₇×C₁₉	C₄×C₉	semidirect
36. C₇⋊AGL(1,𝔽₅)	#4294	semidirect
37. C₇×C₁₉	C₉×AGL(1,𝔽₅)	semidirect
41. C₅×C₁₉	Dic₇⋊C₉	semidirect
53. C₅×C₇	C₄×#4294	semidirect
58. C₁₉	(C₇⋊C₉)⋊AGL(1,𝔽₅)	semidirect
65. C₇	AGL(1,𝔽₅)×#4294	semidirect
67. C₅	#18012094	semidirect

Maximal subgroups

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

subgroup	index
D₅×#11924776	2
C₃×C₁₉×C₇⋊AGL(1,𝔽₅)	3
#18012094	5
AGL(1,𝔽₅)×#4294	7
(C₇⋊C₉)⋊AGL(1,𝔽₅)	19