Subgroups — C₅×C₇×C₁₉⋊#157 #37561498

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	C₇×C₁₉⋊#157	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×D₃×C₇×C₁₉	—	6	2	no	—
5	C₅×C₁₉⋊#157	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇×Dic₁₉	—	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	C₂×C₇	1	1	yes	characteristic
10	C₂×C₅×C₇×C₁₉	—	9	1	no	—
11	C₅×C₇×#157	—	19	1	no	maximal, Hall
12	C₃²×C₇×C₁₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₃²×C₅×C₁₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	D₃×C₇×C₁₉	—	6	2	no	—
15	C₁₉⋊#157	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₅×C₇×C₁₉	#157	1	1	yes	characteristic, complemented, Hall
17	C₅×C₇×C₃⋊D₃	D₁₉	1	1	yes	characteristic
18	C₅×D₃×C₁₉	—	6	2	no	—
19	C₇×Dic₁₉	—	9	1	no	Hall
20	C₃×C₇×C₁₉	—	2	2	no	—
21	C₅×Dic₁₉	—	9	1	no	Hall
22	C₃⋊D₃×C₁₉	C₂×C₅×C₇	1	1	yes	characteristic
23	C₃²×C₅×C₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₉	—	2	2	no	—
25	C₂×C₇×C₁₉	—	9	1	no	—
26	C₇×#157	—	19	1	no	Hall
27	C₅×D₃×C₇	—	6	2	no	—
28	C₂×C₅×C₁₉	—	9	1	no	—
29	C₅×#157	—	19	1	no	Hall
30	C₃²×C₁₉	C₄×C₅×C₇	1	1	yes	characteristic, complemented, Hall
31	C₄×C₅×C₇	—	171	1	no	Hall
32	C₇×C₁₉	C₅×#157	1	1	yes	characteristic, complemented, Hall
33	C₇×C₃⋊D₃	C₅×D₁₉	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, complemented, Hall
37	C₅×C₃⋊D₃	C₇×D₁₉	1	1	yes	characteristic
38	Dic₁₉	—	9	1	no	Hall
39	C₂×C₅×C₇	—	9	1	no	—
40	C₃²×C₇	C₅×Dic₁₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₉	—	2	2	no	—
42	C₃²×C₅	C₇×Dic₁₉	1	1	yes	characteristic, complemented, Hall
43	D₃×C₇	—	6	2	no	—
44	C₂×C₁₉	—	9	1	no	—
45	#157	—	19	1	no	Hall
46	C₅×C₇	C₁₉⋊#157	1	1	yes	characteristic, direct product factor, Hall
47	C₅×D₃	—	6	2	no	—
48	C₄×C₇	—	171	1	no	Hall
49	C₃×C₇	—	2	2	no	—
50	C₄×C₅	—	171	1	no	Hall
51	C₁₉	C₅×C₇×#157	1	1	yes	characteristic, complemented, Sylow
52	C₃⋊D₃	C₅×C₇×D₁₉	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×C₇×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
57	C₇	C₅×C₁₉⋊#157	1	1	yes	characteristic, direct product factor, Sylow
58	D₃	—	6	2	no	—
59	C₅	C₇×C₁₉⋊#157	1	1	yes	characteristic, direct product factor, Sylow
60	C₄	—	171	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	9	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₇×C₁₉	C₄	semidirect
3. C₇×C₁₉⋊#157	C₅	direct (N × H)
5. C₅×C₁₉⋊#157	C₇	direct (N × H)
12. C₃²×C₇×C₁₉	C₄×C₅	semidirect
13. C₃²×C₅×C₁₉	C₄×C₇	semidirect
15. C₁₉⋊#157	C₅×C₇	direct (N × H)
16. C₅×C₇×C₁₉	#157	semidirect
23. C₃²×C₅×C₇	Dic₁₉	semidirect
30. C₃²×C₁₉	C₄×C₅×C₇	semidirect
32. C₇×C₁₉	C₅×#157	semidirect
36. C₅×C₁₉	C₇×#157	semidirect
40. C₃²×C₇	C₅×Dic₁₉	semidirect
42. C₃²×C₅	C₇×Dic₁₉	semidirect
46. C₅×C₇	C₁₉⋊#157	direct (N × H)
51. C₁₉	C₅×C₇×#157	semidirect
56. C₃²	C₅×C₇×Dic₁₉	semidirect
57. C₇	C₅×C₁₉⋊#157	direct (N × H)
59. C₅	C₇×C₁₉⋊#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
C₇×C₁₉⋊#157	5
C₅×C₁₉⋊#157	7
C₅×C₇×Dic₁₉	9
C₅×C₇×#157	19

Subgroups — C5×C7×C19⋊#157 #37561498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₁₉⋊#157 #37561498