Subgroups — #17987481

Order 4617.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095332	C₃	1	1	yes	maximal, characteristic
2	#13095312	C₃	1	1	yes	maximal, characteristic, complemented
3	#13095311	C₃	1	3	yes	maximal, complemented
4	#13095310	C₃	1	3	yes	maximal, complemented
5	C₃×#10587018	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂₇×C₁₉⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₁₉×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
9	C₃²⋊(C₁₉⋊C₃)	C₉	1	1	yes	characteristic
10	#10587025	C₉	1	2	yes	—
11	#10587023	C₉	1	3	yes	—
12	#10587022	C₉	1	3	yes	—
13	C₉×C₁₉⋊C₃	C₃²	1	3	yes	—
14	C₁₉×C₂₇	C₃²	1	3	yes	—
15	#10587018	C₃²	1	1	yes	characteristic
16	#10587018	C₃²	1	3	yes	—
17	#10587018	C₃²	1	1	yes	characteristic
18	#10587018	C₃²	1	1	yes	characteristic
19	#6903	—	19	1	no	maximal, Sylow
20	C₃²×C₁₉	C₃×C₉	1	1	yes	characteristic
21	C₃×C₁₉⋊C₃	C₃×C₉	1	3	yes	—
22	C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
23	C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
24	C₉×C₁₉	C₃³	1	1	yes	characteristic
25	#4294	C₃×C₉	1	6	yes	—
26	#737	—	19	1	no	—
27	C₂₇⋊C₃	—	19	1	no	—
28	C₂₇⋊C₃	—	19	3	no	—
29	C₂₇⋊C₃	—	19	3	no	—
30	C₂₇⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented
31	C₃×C₂₇	—	19	1	no	—
32	C₃×C₂₇	—	19	3	no	—
33	C₃×C₁₉	—	3	1	no	—
34	C₃×C₁₉	C₃²×C₉	1	1	yes	characteristic
35	C₁₉⋊C₃	—	3	3	no	—
36	3₋¹⁺²	—	19	2	no	—
37	3₋¹⁺²	—	19	3	no	—
38	3₋¹⁺²	—	19	3	no	—
39	H(3,𝔽₃)	—	19	1	no	—
40	C₃×C₉	—	19	3	no	—
41	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
42	C₂₇	—	19	1	no	—
43	C₂₇	—	19	3	no	—
44	C₂₇	—	19	1	no	—
45	C₂₇	—	19	1	no	—
46	C₂₇	C₃×C₁₉⋊C₃	1	3	yes	—
47	C₁₉	#6903	1	1	yes	characteristic, complemented, Sylow
48	C₃²	—	19	3	no	—
49	C₃²	C₉×C₁₉⋊C₃	1	1	yes	characteristic
50	C₉	—	19	6	no	—
51	C₉	C₉×C₁₉⋊C₃	1	1	yes	characteristic
52	C₉	C₉×C₁₉⋊C₃	1	1	yes	characteristic
53	C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
54	C₃	—	3	1	no	—
55	C₃	—	57	3	no	—
56	C₃	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₉	C₃²×C₁₉⋊C₃
commutator, socle	C₃×C₁₉	C₃²×C₉
Fitting	C₁₉×C₂₇⋊C₃	C₃
prime radical	C₃²⋊(C₁₉⋊C₃)	C₉
cosocle	C₉×C₁₉	C₃³
hypercenter	C₂₇⋊C₃	C₁₉⋊C₃
hypocenter	C₁₉	#6903
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #13095312	C₃	semidirect
3. #13095311	C₃	semidirect
4. #13095310	C₃	semidirect
5. C₃×#10587018	C₃	semidirect
6. C₂₇×C₁₉⋊C₃	C₃	semidirect
7. C₁₉×C₂₇⋊C₃	C₃	semidirect
30. C₂₇⋊C₃	C₁₉⋊C₃	semidirect
47. C₁₉	#6903	semidirect

Maximal subgroups

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

subgroup	index
#13095332	3
#13095312	3
#13095311	3
#13095310	3
C₃×#10587018	3
C₂₇×C₁₉⋊C₃	3
C₁₉×C₂₇⋊C₃	3
#6903	19