Subgroups — #17987599

Order 4617.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095344	C₃	1	3	yes	maximal, complemented
2	#13095343	C₃	1	3	yes	maximal, complemented
3	#13095342	C₃	1	2	yes	maximal, complemented
4	(C₁₉⋊C₃)⋊C₂₇	C₃	1	3	yes	maximal, complemented
5	C₃×#10587020	C₃	1	1	yes	maximal, characteristic, complemented
6	#13095333	C₃	1	1	yes	maximal, characteristic
7	C₁₉×3₋¹⁺²	C₉	1	1	yes	characteristic
8	C₃²⋊(C₁₉⋊C₃)	C₉	1	1	yes	characteristic
9	#10587025	C₉	1	1	yes	characteristic
10	C₃×#4294	C₃²	1	1	yes	characteristic
11	#10587023	C₉	1	3	yes	—
12	#10587022	C₉	1	3	yes	—
13	C₉×C₁₉⋊C₃	C₃²	1	3	yes	—
14	#10587020	C₃²	1	1	yes	characteristic
15	#10587020	C₃²	1	1	yes	characteristic
16	#10587020	C₃²	1	1	yes	characteristic
17	#10587020	C₃²	1	6	yes	—
18	#6903	—	19	1	no	maximal, Sylow
19	C₃²×C₁₉	C₃×C₉	1	1	yes	characteristic
20	C₃×C₁₉⋊C₃	C₃×C₉	1	3	yes	—
21	C₉×C₁₉	C₃×C₉	1	3	yes	—
22	#4294	C₃×C₉	1	3	yes	—
23	#4294	C₃×C₉	1	1	yes	characteristic
24	#4294	C₃×C₉	1	1	yes	characteristic
25	#4294	C₃³	1	1	yes	characteristic
26	#737	—	19	1	no	—
27	C₂₇⋊C₃	—	19	2	no	—
28	C₂₇⋊C₃	—	19	3	no	—
29	C₂₇⋊C₃	—	19	3	no	—
30	C₃×C₂₇	—	19	1	no	—
31	C₃×C₂₇	—	19	3	no	—
32	C₃×C₁₉	—	3	1	no	—
33	C₃×C₁₉	C₃²×C₉	1	1	yes	characteristic
34	C₁₉⋊C₃	—	3	3	no	—
35	3₋¹⁺²	—	19	1	no	—
36	3₋¹⁺²	—	19	3	no	—
37	3₋¹⁺²	—	19	3	no	—
38	3₋¹⁺²	#4296	1	1	yes	characteristic
39	H(3,𝔽₃)	—	19	1	no	—
40	C₃×C₉	—	19	1	no	—
41	C₃×C₉	—	19	3	no	—
42	C₂₇	—	19	1	no	—
43	C₂₇	—	19	1	no	—
44	C₂₇	—	19	1	no	—
45	C₂₇	—	19	6	no	—
46	C₁₉	#6903	1	1	yes	characteristic, complemented, Sylow
47	C₃²	—	19	3	no	—
48	C₃²	C₃×#4296	1	1	yes	characteristic
49	C₉	—	19	1	no	—
50	C₉	—	19	1	no	—
51	C₉	—	19	1	no	—
52	C₉	—	19	3	no	—
53	C₉	C₃×#4296	1	3	yes	—
54	C₃	—	3	1	no	—
55	C₃	—	57	3	no	—
56	C₃	C₃²×#4296	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃	C₃²×#4296
commutator, socle	C₃×C₁₉	C₃²×C₉
Fitting	C₁₉×3₋¹⁺²	C₉
prime radical	C₃²⋊(C₁₉⋊C₃)	C₉
cosocle	#4294	C₃³
hypercenter	3₋¹⁺²	#4296
hypocenter	C₁₉	#6903
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ 3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #13095344	C₃	semidirect
2. #13095343	C₃	semidirect
3. #13095342	C₃	semidirect
4. (C₁₉⋊C₃)⋊C₂₇	C₃	semidirect
5. C₃×#10587020	C₃	semidirect
46. C₁₉	#6903	semidirect

Maximal subgroups

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

subgroup	index
#13095344	3
#13095343	3
#13095342	3
(C₁₉⋊C₃)⋊C₂₇	3
C₃×#10587020	3
#13095333	3
#6903	19