Subgroups — #17987468

Order 4617.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587025	C₃	1	3	yes	maximal
2	#13095307	C₃	1	1	yes	maximal, characteristic, complemented
3	#13095306	C₃	1	1	yes	maximal, characteristic, complemented
4	#13095305	C₃	1	6	yes	maximal, complemented
5	C₉×#4294	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×C₁₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
7	C₃³×C₁₉	C₃²	1	1	yes	characteristic
8	C₁₉×3₋¹⁺²	—	3	3	no	—
9	C₃×C₉×C₁₉	C₃²	1	2	yes	—
10	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
11	#10587025	—	3	9	no	—
12	C₃×#4294	C₃²	1	3	yes	—
13	C₃×#4294	C₃²	1	3	yes	—
14	C₃×#4294	C₃²	1	3	yes	—
15	#6900	—	19	1	no	maximal, Sylow
16	C₃²×C₁₉	—	3	3	no	—
17	C₃²×C₁₉	—	3	1	no	—
18	C₃²×C₁₉	C₃³	1	1	yes	characteristic
19	C₉×C₁₉	—	3	2	no	—
20	C₉×C₁₉	3₋¹⁺²	1	3	yes	complemented
21	#4294	—	3	3	no	—
22	#4294	—	3	3	no	—
23	#4294	3₋¹⁺²	1	9	yes	complemented
24	C₃×3₋¹⁺²	—	19	3	no	—
25	C₃×3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic
26	C₉⋊C₉	—	19	6	no	—
27	C₉⋊C₉	—	19	1	no	—
28	C₉⋊C₉	—	19	1	no	—
29	C₉²	—	19	1	no	—
30	C₃×C₁₉	—	9	1	no	—
31	C₃×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
32	C₃×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
33	C₃³	C₃×C₁₉⋊C₃	1	1	yes	characteristic
34	3₋¹⁺²	—	3	3	no	—
35	3₋¹⁺²	—	57	9	no	—
36	C₃×C₉	—	19	3	no	—
37	C₃×C₉	—	19	3	no	—
38	C₃×C₉	—	19	3	no	—
39	C₃×C₉	C₃×C₁₉⋊C₃	1	2	yes	—
40	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
41	C₁₉	#6900	1	1	yes	characteristic, complemented, Sylow
42	C₃²	—	3	3	no	—
43	C₃²	—	3	1	no	—
44	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
45	C₉	—	3	2	no	—
46	C₉	—	19	9	no	—
47	C₉	—	57	3	no	—
48	C₉	—	57	3	no	—
49	C₉	#10587025	1	3	yes	complemented
50	C₃	—	9	1	no	—
51	C₃	3₋¹⁺²×C₁₉⋊C₃	1	3	yes	—
52	C₃	C₃×#10587025	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₉	C₃³
Fitting	C₃×C₁₉×3₋¹⁺²	C₃
prime radical	C₃³×C₁₉	C₃²
hypercenter	C₃×3₋¹⁺²	C₁₉⋊C₃
hypocenter	C₁₉	#6900
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #13095307	C₃	semidirect
3. #13095306	C₃	semidirect
4. #13095305	C₃	semidirect
5. C₉×#4294	C₃	semidirect
20. C₉×C₁₉	3₋¹⁺²	semidirect
23. #4294	3₋¹⁺²	semidirect
41. C₁₉	#6900	semidirect
49. C₉	#10587025	semidirect

Maximal subgroups

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

subgroup	index
C₃×#10587025	3
#13095307	3
#13095306	3
#13095305	3
C₉×#4294	3
C₃×C₁₉×3₋¹⁺²	3
#6900	19