Subgroups — #17987529

Order 4617.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095333	C₃	1	3	yes	maximal, complemented
2	C₃×#10587022	C₃	1	1	yes	maximal, characteristic, complemented
3	#13095322	C₃	1	1	yes	maximal, characteristic, complemented
4	#13095320	C₃	1	1	yes	maximal, characteristic, complemented
5	#13095318	C₃	1	3	yes	maximal, complemented
6	#13095315	C₃	1	3	yes	maximal, complemented
7	C₁₉×#733	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
9	C₁₉×3₋¹⁺²	C₃²	1	3	yes	—
10	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
11	C₃²⋊(C₁₉⋊C₃)	C₃²	1	3	yes	—
12	#10587025	C₃²	1	3	yes	—
13	C₃×#4294	C₃²	1	1	yes	characteristic
14	C₃×#4294	C₃²	1	1	yes	characteristic
15	#10587023	—	3	3	no	—
16	#10587022	—	3	3	no	—
17	#10587022	—	3	3	no	—
18	C₉×C₁₉⋊C₃	—	3	3	no	—
19	#6913	—	19	1	no	maximal, Sylow
20	C₃²×C₁₉	C₃³	1	1	yes	characteristic
21	C₃×C₁₉⋊C₃	—	3	3	no	—
22	C₃×C₁₉⋊C₃	—	3	1	no	—
23	C₃×C₁₉⋊C₃	—	9	1	no	—
24	C₉×C₁₉	—	3	3	no	—
25	C₉×C₁₉	—	3	1	no	—
26	#4294	—	3	3	no	—
27	#4294	—	3	1	no	—
28	#4294	H(3,𝔽₃)	1	3	yes	—
29	#737	—	19	3	no	—
30	C₃×3₋¹⁺²	—	19	1	no	—
31	#733	—	19	1	no	—
32	#733	C₁₉⋊C₃	1	1	yes	characteristic, complemented
33	#732	—	19	1	no	—
34	#731	—	19	3	no	—
35	AΣL(1,𝔽₂₇)	—	19	3	no	—
36	C₃×C₁₉	—	3	1	no	—
37	C₃×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₁₉⋊C₃	—	9	3	no	—
39	C₁₉⋊C₃	—	9	1	no	—
40	C₃³	—	19	1	no	—
41	3₋¹⁺²	—	19	3	no	—
42	3₋¹⁺²	—	57	3	no	—
43	3₋¹⁺²	—	57	3	no	—
44	3₋¹⁺²	—	57	3	no	—
45	3₋¹⁺²	C₃×C₁₉⋊C₃	1	3	yes	—
46	H(3,𝔽₃)	—	19	3	no	—
47	C₃×C₉	—	19	1	no	—
48	C₃×C₉	—	19	1	no	—
49	C₃×C₉	—	57	3	no	—
50	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
51	C₁₉	#6913	1	1	yes	characteristic, complemented, Sylow
52	C₃²	—	57	3	no	—
53	C₃²	—	57	1	no	—
54	C₃²	—	171	1	no	—
55	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
56	C₉	—	3	3	no	—
57	C₉	—	3	1	no	—
58	C₉	—	19	3	no	—
59	C₉	—	57	1	no	—
60	C₉	—	57	3	no	—
61	C₃	—	3	1	no	—
62	C₃	—	171	1	no	—
63	C₃	—	171	3	no	—
64	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×#733	C₃
socle	C₃×C₁₉	C₃×H(3,𝔽₃)
hypercenter	#733	C₁₉⋊C₃
hypocenter	C₁₉	#6913
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #733

Complements

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

N	H ≅ G/N	type
1. #13095333	C₃	semidirect
2. C₃×#10587022	C₃	semidirect
3. #13095322	C₃	semidirect
4. #13095320	C₃	semidirect
5. #13095318	C₃	semidirect
6. #13095315	C₃	semidirect
7. C₁₉×#733	C₃	semidirect
32. #733	C₁₉⋊C₃	semidirect
51. C₁₉	#6913	semidirect

Maximal subgroups

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

subgroup	index
#13095333	3
C₃×#10587022	3
#13095322	3
#13095320	3
#13095318	3
#13095315	3
C₁₉×#733	3
#6913	19