Subgroups — C₃×#19150288 #30660764

Order 16758.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇⋊D₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#19150288	C₃	1	3	yes	maximal, direct product factor
4	C₁₉×#3861	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×ΓL(1,𝔽₈)⋊D₁₉	—	7	3	no	maximal
7	C₃×ΓL(1,𝔽₈)⋊D₁₉	—	7	1	no	maximal
8	C₃×ΓL(1,𝔽₈)⋊D₁₉	—	7	4	no	maximal
9	C₇⋊D₁₃₃	C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	3	no	—
11	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	1	no	—
12	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	4	no	—
13	C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×#64424	—	19	1	no	maximal, Hall
15	C₃×D₁₃₃	—	7	3	no	—
16	C₃×D₁₃₃	—	21	1	no	—
17	C₃×D₁₃₃	—	21	4	no	—
18	ΓL(1,𝔽₈)⋊D₁₉	—	7	9	no	—
19	ΓL(1,𝔽₈)⋊D₁₉	—	7	3	no	—
20	ΓL(1,𝔽₈)⋊D₁₉	—	7	12	no	—
21	C₃×#3861	D₁₉	1	1	yes	characteristic, complemented, Hall
22	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	3	yes	complemented
23	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
24	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	4	yes	complemented
25	C₁₉×ΓL(1,𝔽₈)	—	7	9	no	—
26	C₁₉×ΓL(1,𝔽₈)	—	7	3	no	—
27	C₁₉×ΓL(1,𝔽₈)	—	7	12	no	—
28	C₃²×D₁₉	—	49	1	no	Hall
29	C₃×C₇⋊D₇	—	19	1	no	—
30	#64424	—	19	3	no	—
31	D₁₃₃	—	7	3	no	—
32	D₁₃₃	—	21	1	no	—
33	D₁₃₃	—	21	4	no	—
34	C₃²×C₁₉	—	49	1	no	Hall
35	C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic, complemented
36	#3861	C₃×D₁₉	1	3	yes	complemented
37	C₇×C₁₉	C₃×AGL(1,𝔽₇)	1	3	yes	complemented
38	C₇×C₁₉	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
39	C₇×C₁₉	C₃×AGL(1,𝔽₇)	1	4	yes	complemented
40	C₃×AGL(1,𝔽₇)	—	133	1	no	—
41	C₃×AGL(1,𝔽₇)	—	133	3	no	—
42	C₃×AGL(1,𝔽₇)	—	133	4	no	—
43	C₃×D₁₉	—	49	3	no	—
44	C₃×D₁₉	—	147	1	no	—
45	C₇⋊D₇	—	19	1	no	Hall
46	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
47	C₃×ΓL(1,𝔽₈)	—	7	3	no	—
48	C₃×ΓL(1,𝔽₈)	—	7	4	no	—
49	C₃×C₁₉	—	49	3	no	—
50	C₃×C₁₉	#64424	1	1	yes	characteristic, complemented
51	C₇²	C₃²×D₁₉	1	1	yes	characteristic, complemented, Sylow
52	C₃×D₇	—	133	1	no	—
53	C₃×D₇	—	399	3	no	—
54	C₃×D₇	—	399	4	no	—
55	AGL(1,𝔽₇)	—	133	3	no	—
56	AGL(1,𝔽₇)	—	133	9	no	—
57	AGL(1,𝔽₇)	—	133	12	no	—
58	D₁₉	—	147	1	no	Hall
59	C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented
60	C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	1	3	yes	complemented
61	C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	1	4	yes	complemented
62	ΓL(1,𝔽₈)	—	7	3	no	—
63	ΓL(1,𝔽₈)	—	7	9	no	—
64	ΓL(1,𝔽₈)	—	7	12	no	—
65	C₁₉	C₃×#64424	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃²	—	931	1	no	Hall
67	D₇	—	133	1	no	—
68	D₇	—	399	3	no	—
69	D₇	—	399	4	no	—
70	C₃²	—	49	1	no	Sylow
71	C₇	C₃×ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented
72	C₇	C₃×ΓL(1,𝔽₈)⋊D₁₉	1	3	yes	complemented
73	C₇	C₃×ΓL(1,𝔽₈)⋊D₁₉	1	4	yes	complemented
74	C₂×C₃	—	931	3	no	—
75	C₂×C₃	—	2793	1	no	—
76	C₃	—	49	3	no	—
77	C₃	#19150288	1	1	yes	characteristic, direct product factor
78	C₂	—	2793	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#19150288
commutator, cosocle, hypocenter	C₇²×C₁₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#3861	C₂	semidirect
2. C₃×C₇⋊D₁₃₃	C₃	semidirect
3. #19150288	C₃	direct (N × H)
4. C₁₉×#3861	C₂×C₃	semidirect
5. C₃×C₇²×C₁₉	C₂×C₃	semidirect
9. C₇⋊D₁₃₃	C₃²	semidirect
13. C₇²×C₁₉	C₂×C₃²	semidirect
21. C₃×#3861	D₁₉	semidirect
22. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
23. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
24. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
35. C₃×C₇²	C₃×D₁₉	semidirect
36. #3861	C₃×D₁₉	semidirect
37. C₇×C₁₉	C₃×AGL(1,𝔽₇)	semidirect
38. C₇×C₁₉	C₃×AGL(1,𝔽₇)	semidirect
39. C₇×C₁₉	C₃×AGL(1,𝔽₇)	semidirect
50. C₃×C₁₉	#64424	semidirect
51. C₇²	C₃²×D₁₉	semidirect
59. C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	semidirect
60. C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	semidirect
61. C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	semidirect
65. C₁₉	C₃×#64424	semidirect
71. C₇	C₃×ΓL(1,𝔽₈)⋊D₁₉	semidirect
72. C₇	C₃×ΓL(1,𝔽₈)⋊D₁₉	semidirect
73. C₇	C₃×ΓL(1,𝔽₈)⋊D₁₉	semidirect
77. C₃	#19150288	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₉×#3861	2
C₃×C₇⋊D₁₃₃	3
#19150288	3
C₃×ΓL(1,𝔽₈)⋊D₁₉	7
C₃×#64424	19

Subgroups — C3×#19150288 #30660764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#19150288 #30660764