Subgroups — C₅×C₁₉×C₇⋊#157 #37561499

Order 23940.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₇×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×C₇⋊#157	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×D₃×C₇×C₁₉	—	6	2	no	—
5	C₅×C₁₉×#157	—	7	1	no	maximal, Hall
6	C₅×C₁₉×Dic₇	—	9	1	no	maximal, Hall
7	C₇×C₃⋊D₃×C₁₉	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₇×C₁₉	—	2	2	no	—
9	C₅×C₃⋊D₃×C₁₉	D₇	1	1	yes	characteristic
10	C₂×C₅×C₇×C₁₉	—	9	1	no	—
11	C₅×C₇⋊#157	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃²×C₇×C₁₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₅×C₁₉	Dic₇	1	1	yes	characteristic, complemented, Hall
14	D₃×C₇×C₁₉	—	6	2	no	—
15	C₁₉×#157	—	7	1	no	Hall
16	C₅×C₇×C₁₉	#157	1	1	yes	characteristic, complemented, Hall
17	C₅×C₇×C₃⋊D₃	C₂×C₁₉	1	1	yes	characteristic
18	C₅×D₃×C₁₉	—	6	2	no	—
19	C₁₉×Dic₇	—	9	1	no	Hall
20	C₃×C₇×C₁₉	—	2	2	no	—
21	C₄×C₅×C₁₉	—	63	1	no	Hall
22	C₃⋊D₃×C₁₉	C₅×D₇	1	1	yes	characteristic
23	C₃²×C₅×C₇	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₉	—	2	2	no	—
25	C₂×C₇×C₁₉	—	9	1	no	—
26	C₇⋊#157	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
27	C₅×D₃×C₇	—	6	2	no	—
28	C₂×C₅×C₁₉	—	9	1	no	—
29	C₅×#157	—	7	1	no	Hall
30	C₃²×C₁₉	C₅×Dic₇	1	1	yes	characteristic, complemented, Hall
31	C₅×Dic₇	—	9	1	no	Hall
32	C₇×C₁₉	C₅×#157	1	1	yes	characteristic, complemented, Hall
33	C₇×C₃⋊D₃	C₂×C₅×C₁₉	1	1	yes	characteristic
34	D₃×C₁₉	—	6	2	no	—
35	C₃×C₅×C₇	—	2	2	no	—
36	C₅×C₁₉	C₇⋊#157	1	1	yes	characteristic, direct product factor, Hall
37	C₅×C₃⋊D₃	D₇×C₁₉	1	1	yes	characteristic
38	C₄×C₁₉	—	63	1	no	Hall
39	C₂×C₅×C₇	—	9	1	no	—
40	C₃²×C₇	C₄×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₉	—	2	2	no	—
42	C₃²×C₅	C₁₉×Dic₇	1	1	yes	characteristic, complemented, Hall
43	D₃×C₇	—	6	2	no	—
44	C₂×C₁₉	—	9	1	no	—
45	#157	—	7	1	no	Hall
46	C₅×C₇	C₁₉×#157	1	1	yes	characteristic, complemented, Hall
47	C₅×D₃	—	6	2	no	—
48	Dic₇	—	9	1	no	Hall
49	C₃×C₇	—	2	2	no	—
50	C₄×C₅	—	63	1	no	Hall
51	C₁₉	C₅×C₇⋊#157	1	1	yes	characteristic, direct product factor, Sylow
52	C₃⋊D₃	C₅×D₇×C₁₉	1	1	yes	characteristic
53	C₃×C₅	—	2	2	no	—
54	C₂×C₇	—	9	1	no	—
55	C₂×C₅	—	9	1	no	—
56	C₃²	C₅×C₁₉×Dic₇	1	1	yes	characteristic, complemented, Sylow
57	C₇	C₅×C₁₉×#157	1	1	yes	characteristic, complemented, Sylow
58	D₃	—	6	2	no	—
59	C₅	C₁₉×C₇⋊#157	1	1	yes	characteristic, direct product factor, Sylow
60	C₄	—	63	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₇⋊#157
commutator, hypocenter	C₃²×C₇	C₄×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₄
prime radical	C₅×C₇×C₃⋊D₃×C₁₉	C₂
cosocle	C₇×C₃⋊D₃	C₂×C₅×C₁₉
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₅×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₇×C₁₉	C₄	semidirect
3. C₁₉×C₇⋊#157	C₅	direct (N × H)
11. C₅×C₇⋊#157	C₁₉	direct (N × H)
12. C₃²×C₇×C₁₉	C₄×C₅	semidirect
13. C₃²×C₅×C₁₉	Dic₇	semidirect
16. C₅×C₇×C₁₉	#157	semidirect
23. C₃²×C₅×C₇	C₄×C₁₉	semidirect
26. C₇⋊#157	C₅×C₁₉	direct (N × H)
30. C₃²×C₁₉	C₅×Dic₇	semidirect
32. C₇×C₁₉	C₅×#157	semidirect
36. C₅×C₁₉	C₇⋊#157	direct (N × H)
40. C₃²×C₇	C₄×C₅×C₁₉	semidirect
42. C₃²×C₅	C₁₉×Dic₇	semidirect
46. C₅×C₇	C₁₉×#157	semidirect
51. C₁₉	C₅×C₇⋊#157	direct (N × H)
56. C₃²	C₅×C₁₉×Dic₇	semidirect
57. C₇	C₅×C₁₉×#157	semidirect
59. C₅	C₁₉×C₇⋊#157	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×C₇×C₃⋊D₃×C₁₉	2
C₁₉×C₇⋊#157	5
C₅×C₁₉×#157	7
C₅×C₁₉×Dic₇	9
C₅×C₇⋊#157	19

Subgroups — C5×C19×C7⋊#157 #37561499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉×C₇⋊#157 #37561499