Subgroups — #17987524

Order 4617.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095331	C₃	1	3	yes	maximal, complemented
2	C₃×#10587022	C₃	1	1	yes	maximal, characteristic, complemented
3	#13095322	C₃	1	2	yes	maximal, complemented
4	#13095316	C₃	1	3	yes	maximal, complemented
5	#13095313	C₃	1	3	yes	maximal, complemented
6	C₁₉×#732	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
8	C₁₉×H(3,𝔽₃)	C₃²	1	3	yes	—
9	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
10	#10587025	—	3	6	no	—
11	#10587025	C₃²	1	6	yes	—
12	C₃×#4294	—	3	3	no	—
13	C₃×#4294	C₃²	1	1	yes	characteristic
14	C₃×#4294	C₃²	1	1	yes	characteristic
15	#10587022	—	3	3	no	—
16	#6913	—	19	1	no	maximal, Sylow
17	C₃²×C₁₉	—	3	3	no	—
18	C₃²×C₁₉	C₃³	1	1	yes	characteristic
19	C₃×C₁₉⋊C₃	—	3	1	no	—
20	C₃×C₁₉⋊C₃	—	9	1	no	—
21	C₉×C₁₉	—	3	1	no	—
22	#4294	—	3	1	no	—
23	#4294	—	3	6	no	—
24	#4294	H(3,𝔽₃)	1	3	yes	—
25	#737	—	19	3	no	—
26	C₃×3₋¹⁺²	—	19	1	no	—
27	#733	—	19	2	no	—
28	#732	C₁₉⋊C₃	1	1	yes	characteristic, complemented
29	#731	—	19	3	no	—
30	AΣL(1,𝔽₂₇)	—	19	3	no	—
31	C₃×C₁₉	—	3	1	no	—
32	C₃×C₁₉	—	9	3	no	—
33	C₃×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₁₉⋊C₃	—	9	1	no	—
35	C₃³	—	19	1	no	—
36	3₋¹⁺²	—	19	6	no	—
37	3₋¹⁺²	—	57	3	no	—
38	3₋¹⁺²	—	57	6	no	—
39	H(3,𝔽₃)	C₃×C₁₉⋊C₃	1	3	yes	—
40	C₃×C₉	—	19	1	no	—
41	C₃×C₉	—	19	1	no	—
42	C₃×C₉	—	57	3	no	—
43	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
44	C₁₉	#6913	1	1	yes	characteristic, complemented, Sylow
45	C₃²	—	3	3	no	—
46	C₃²	—	57	1	no	—
47	C₃²	—	171	1	no	—
48	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
49	C₉	—	3	1	no	—
50	C₉	—	19	3	no	—
51	C₉	—	57	1	no	—
52	C₉	—	57	6	no	—
53	C₃	—	3	1	no	—
54	C₃	—	9	3	no	—
55	C₃	—	171	1	no	—
56	C₃	H(3,𝔽₃)×C₁₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₁₉⋊C₃
commutator, cosocle	C₃²×C₁₉	C₃³
Frattini	C₃²	C₃²×C₁₉⋊C₃
Fitting	C₁₉×#732	C₃
socle	C₃×C₁₉	C₃×H(3,𝔽₃)
hypercenter	#732	C₁₉⋊C₃
hypocenter	C₁₉	#6913
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #732

Complements

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

N	H ≅ G/N	type
1. #13095331	C₃	semidirect
2. C₃×#10587022	C₃	semidirect
3. #13095322	C₃	semidirect
4. #13095316	C₃	semidirect
5. #13095313	C₃	semidirect
6. C₁₉×#732	C₃	semidirect
28. #732	C₁₉⋊C₃	semidirect
44. C₁₉	#6913	semidirect

Maximal subgroups

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

subgroup	index
#13095331	3
C₃×#10587022	3
#13095322	3
#13095316	3
#13095313	3
C₁₉×#732	3
#6913	19