Subgroups — C₇×C₁₉×#4380 #37561501

Order 23940.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₇×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×C₁₉×#157	—	5	1	no	maximal, Hall
4	C₇×C₁₉×D₁₅	—	6	2	no	—
5	C₁₉×#4380	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₉×AGL(1,𝔽₅)	—	9	1	no	maximal, Hall
7	C₇×C₃⋊D₃×C₁₉	—	5	1	no	—
8	C₃×C₅×C₇×C₁₉	—	2	2	no	—
9	C₁₉×C₃⋊D₁₅	C₂×C₇	1	1	yes	characteristic
10	C₇×D₅×C₁₉	—	9	1	no	—
11	C₇×#4380	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃²×C₇×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₅×C₁₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	D₃×C₇×C₁₉	—	30	2	no	—
15	C₁₉×#157	—	5	1	no	Hall
16	C₅×C₇×C₁₉	#157	1	1	yes	characteristic, complemented, Hall
17	C₇×C₃⋊D₁₅	C₂×C₁₉	1	1	yes	characteristic
18	C₁₉×D₁₅	—	6	2	no	—
19	C₄×C₇×C₁₉	—	45	1	no	Hall
20	C₃×C₇×C₁₉	—	2	2	no	—
21	C₁₉×AGL(1,𝔽₅)	—	9	1	no	Hall
22	C₃⋊D₃×C₁₉	—	5	1	no	—
23	C₃²×C₅×C₇	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₉	—	2	2	no	—
25	C₂×C₇×C₁₉	—	45	1	no	—
26	C₇×#157	—	5	1	no	Hall
27	C₇×D₁₅	—	6	2	no	—
28	D₅×C₁₉	—	9	1	no	—
29	#4380	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
30	C₃²×C₁₉	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
31	C₇×AGL(1,𝔽₅)	—	9	1	no	Hall
32	C₇×C₁₉	#4380	1	1	yes	characteristic, direct product factor, Hall
33	C₇×C₃⋊D₃	—	5	1	no	—
34	D₃×C₁₉	—	30	2	no	—
35	C₃×C₅×C₇	—	2	2	no	—
36	C₅×C₁₉	C₇×#157	1	1	yes	characteristic, complemented, Hall
37	C₃⋊D₁₅	C₂×C₇×C₁₉	1	1	yes	characteristic
38	C₄×C₁₉	—	45	1	no	Hall
39	C₇×D₅	—	9	1	no	—
40	C₃²×C₇	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₉	—	2	2	no	—
42	C₃²×C₅	C₄×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
43	D₃×C₇	—	30	2	no	—
44	C₂×C₁₉	—	45	1	no	—
45	#157	—	5	1	no	Hall
46	C₅×C₇	C₁₉×#157	1	1	yes	characteristic, complemented, Hall
47	D₁₅	—	6	2	no	—
48	C₄×C₇	—	45	1	no	Hall
49	C₃×C₇	—	2	2	no	—
50	AGL(1,𝔽₅)	—	9	1	no	Hall
51	C₁₉	C₇×#4380	1	1	yes	characteristic, direct product factor, Sylow
52	C₃⋊D₃	—	5	1	no	—
53	C₃×C₅	—	2	2	no	—
54	C₂×C₇	—	45	1	no	—
55	D₅	—	9	1	no	—
56	C₃²	C₇×C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
57	C₇	C₁₉×#4380	1	1	yes	characteristic, direct product factor, Sylow
58	D₃	—	30	2	no	—
59	C₅	C₇×C₁₉×#157	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	45	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₉	#4380
commutator, hypocenter	C₃²×C₅	C₄×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₄
prime radical	C₇×C₁₉×C₃⋊D₁₅	C₂
cosocle	C₃⋊D₁₅	C₂×C₇×C₁₉
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₇×C₁₉	C₄	semidirect
5. C₁₉×#4380	C₇	direct (N × H)
11. C₇×#4380	C₁₉	direct (N × H)
12. C₃²×C₇×C₁₉	AGL(1,𝔽₅)	semidirect
13. C₃²×C₅×C₁₉	C₄×C₇	semidirect
16. C₅×C₇×C₁₉	#157	semidirect
23. C₃²×C₅×C₇	C₄×C₁₉	semidirect
29. #4380	C₇×C₁₉	direct (N × H)
30. C₃²×C₁₉	C₇×AGL(1,𝔽₅)	semidirect
32. C₇×C₁₉	#4380	direct (N × H)
36. C₅×C₁₉	C₇×#157	semidirect
40. C₃²×C₇	C₁₉×AGL(1,𝔽₅)	semidirect
42. C₃²×C₅	C₄×C₇×C₁₉	semidirect
46. C₅×C₇	C₁₉×#157	semidirect
51. C₁₉	C₇×#4380	direct (N × H)
56. C₃²	C₇×C₁₉×AGL(1,𝔽₅)	semidirect
57. C₇	C₁₉×#4380	direct (N × H)
59. C₅	C₇×C₁₉×#157	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₉×C₃⋊D₁₅	2
C₇×C₁₉×#157	5
C₁₉×#4380	7
C₇×C₁₉×AGL(1,𝔽₅)	9
C₇×#4380	19

Subgroups — C7×C19×#4380 #37561501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₉×#4380 #37561501