Subgroups — #17987418

Order 4617.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃×#10587025	C₃	1	2	yes	maximal, complemented
3	#13095303	C₃	1	9	yes	maximal, complemented
4	C₃×C₁₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₁₉	C₃²	1	1	yes	characteristic
6	C₃²×C₁₉⋊C₃	—	3	3	no	—
7	C₃²×C₁₉⋊C₃	—	3	9	no	—
8	C₃²×C₁₉⋊C₃	C₃²	1	3	yes	—
9	C₁₉×3₋¹⁺²	—	3	3	no	—
10	C₃×C₉×C₁₉	C₃²	1	3	yes	complemented
11	#10587025	—	3	6	no	—
12	C₃×#4294	C₃²	1	6	yes	complemented
13	#6891	—	19	1	no	maximal, Sylow
14	C₃²×C₁₉	—	3	3	no	—
15	C₃²×C₁₉	H(3,𝔽₃)	1	3	yes	—
16	C₃²×C₁₉	C₃³	1	1	yes	characteristic
17	C₃×C₁₉⋊C₃	—	3	27	no	—
18	C₃×C₁₉⋊C₃	—	3	3	no	—
19	C₃×C₁₉⋊C₃	—	3	6	no	—
20	C₃×C₁₉⋊C₃	3₋¹⁺²	1	9	yes	complemented
21	C₉×C₁₉	—	3	3	no	—
22	#4294	—	3	6	no	—
23	C₃⁴	—	19	1	no	—
24	C₃×3₋¹⁺²	—	19	2	no	—
25	C₃×3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic, complemented
26	C₃²⋊C₉	—	19	9	no	—
27	C₃×C₁₉	—	3	3	no	—
28	C₃×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
29	C₃×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
30	C₁₉⋊C₃	—	3	9	no	—
31	C₃³	—	19	3	no	—
32	C₃³	—	57	9	no	—
33	C₃³	—	57	3	no	—
34	C₃³	C₃×C₁₉⋊C₃	1	1	yes	characteristic
35	3₋¹⁺²	—	3	3	no	—
36	3₋¹⁺²	—	57	6	no	—
37	C₃×C₉	—	19	6	no	—
38	C₃×C₉	C₃×C₁₉⋊C₃	1	3	yes	complemented
39	C₁₉	#6891	1	1	yes	characteristic, complemented, Sylow
40	C₃²	—	3	3	no	—
41	C₃²	—	19	9	no	—
42	C₃²	—	57	27	no	—
43	C₃²	—	57	3	no	—
44	C₃²	—	57	6	no	—
45	C₃²	C₃²⋊(C₁₉⋊C₃)	1	3	yes	—
46	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
47	C₉	—	3	3	no	—
48	C₉	—	57	6	no	—
49	C₃	—	3	3	no	—
50	C₃	—	57	9	no	—
51	C₃	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
52	C₃	3₋¹⁺²×C₁₉⋊C₃	1	3	yes	—

	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⋊C₃	C₃
hypercenter	C₃×3₋¹⁺²	C₁₉⋊C₃
hypocenter	C₁₉	#6891
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. C₃×#10587025	C₃	semidirect
3. #13095303	C₃	semidirect
4. C₃×C₁₉×3₋¹⁺²	C₃	semidirect
10. C₃×C₉×C₁₉	C₃²	semidirect
12. C₃×#4294	C₃²	semidirect
20. C₃×C₁₉⋊C₃	3₋¹⁺²	semidirect
25. C₃×3₋¹⁺²	C₁₉⋊C₃	semidirect
38. C₃×C₉	C₃×C₁₉⋊C₃	semidirect
39. C₁₉	#6891	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₁₉⋊C₃	3
C₃×#10587025	3
#13095303	3
C₃×C₁₉×3₋¹⁺²	3
#6891	19