Subgroups — #17987439

Order 4617.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587025	C₃	1	1	yes	maximal, characteristic
2	#13095307	C₃	1	3	yes	maximal, complemented
3	#13095305	C₃	1	6	yes	maximal, complemented
4	C₃²⋊#4294	C₃	1	2	yes	maximal
5	C₃²×C₉×C₁₉	C₃	1	1	yes	maximal, characteristic
6	C₃³×C₁₉	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₁₉	—	3	3	no	—
8	C₃×C₉×C₁₉	C₃²	1	2	yes	—
9	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
10	#10587025	—	3	3	no	—
11	C₃×#4294	C₃²	1	6	yes	—
12	C₃×#4294	C₃²	1	3	yes	—
13	#6894	—	19	1	no	maximal, Sylow
14	C₃²×C₁₉	—	3	1	no	—
15	C₃²×C₁₉	—	3	2	no	—
16	C₃²×C₁₉	3₋¹⁺²	1	3	yes	—
17	C₃²×C₁₉	C₃³	1	1	yes	characteristic
18	C₉×C₁₉	—	3	2	no	—
19	C₉×C₁₉	3₋¹⁺²	1	3	yes	complemented
20	#4294	—	3	3	no	—
21	#4294	—	3	6	no	—
22	C₃×3₋¹⁺²	—	19	1	no	—
23	C₃²×C₉	C₁₉⋊C₃	1	1	yes	characteristic
24	C₉⋊C₉	—	19	6	no	—
25	C₉⋊C₉	—	19	3	no	—
26	C₃²⋊C₉	—	19	2	no	—
27	C₃×C₁₉	—	3	3	no	—
28	C₃×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
30	C₃×C₁₉	#737	1	2	yes	—
31	C₃³	C₃×C₁₉⋊C₃	1	1	yes	characteristic
32	3₋¹⁺²	—	57	3	no	—
33	C₃×C₉	—	3	3	no	—
34	C₃×C₉	—	19	6	no	—
35	C₃×C₉	—	19	3	no	—
36	C₃×C₉	C₃×C₁₉⋊C₃	1	2	yes	—
37	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
38	C₁₉	#6894	1	1	yes	characteristic, complemented, Sylow
39	C₃²	—	3	1	no	—
40	C₃²	—	3	2	no	—
41	C₃²	#10587023	1	3	yes	—
42	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
43	C₉	—	3	2	no	—
44	C₉	—	57	3	no	—
45	C₉	—	57	6	no	—
46	C₉	#10587025	1	3	yes	complemented
47	C₃	—	3	3	no	—
48	C₃	C₃×#10587023	1	1	yes	characteristic
49	C₃	C₃×#10587025	1	1	yes	characteristic
50	C₃	#13095332	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₉	C₃³
Fitting	C₃²×C₉×C₁₉	C₃
prime radical	C₃³×C₁₉	C₃²
hypercenter	C₃²×C₉	C₁₉⋊C₃
hypocenter	C₁₉	#6894
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. #13095307	C₃	semidirect
3. #13095305	C₃	semidirect
19. C₉×C₁₉	3₋¹⁺²	semidirect
38. C₁₉	#6894	semidirect
46. 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
#13095305	3
C₃²⋊#4294	3
C₃²×C₉×C₁₉	3
#6894	19