Subgroups — #17987523

Order 4617.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095332	C₃	1	2	yes	maximal, complemented
2	C₃×#10587023	C₃	1	1	yes	maximal, characteristic, complemented
3	#13095321	C₃	1	2	yes	maximal, complemented
4	#13095319	C₃	1	1	yes	maximal, characteristic, complemented
5	#13095318	C₃	1	2	yes	maximal, complemented
6	#13095316	C₃	1	1	yes	maximal, characteristic, complemented
7	#13095315	C₃	1	2	yes	maximal, complemented
8	#13095313	C₃	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#737	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
11	C₁₉×3₋¹⁺²	—	3	2	no	—
12	C₁₉×3₋¹⁺²	C₃²	1	2	yes	—
13	C₁₉×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
14	C₃×C₉×C₁₉	—	3	1	no	—
15	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
16	C₃²⋊(C₁₉⋊C₃)	C₃²	1	2	yes	—
17	#10587025	C₃²	1	2	yes	—
18	#10587025	C₃²	1	2	yes	—
19	C₃×#4294	C₃²	1	1	yes	characteristic
20	C₃×#4294	C₃²	1	1	yes	characteristic
21	#10587023	—	3	2	no	—
22	#10587023	—	3	1	no	—
23	#10587023	—	3	2	no	—
24	#10587022	—	3	2	no	—
25	C₉×C₁₉⋊C₃	—	3	2	no	—
26	#6913	—	19	1	no	maximal, Sylow
27	C₃²×C₁₉	—	3	1	no	—
28	C₃²×C₁₉	C₃³	1	1	yes	characteristic
29	C₃×C₁₉⋊C₃	—	3	2	no	—
30	C₃×C₁₉⋊C₃	—	3	1	no	—
31	C₃×C₁₉⋊C₃	—	9	1	no	—
32	C₉×C₁₉	—	3	2	no	—
33	C₉×C₁₉	H(3,𝔽₃)	1	2	yes	—
34	C₉×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
35	#4294	—	3	2	no	—
36	#4294	—	3	2	no	—
37	#4294	—	3	1	no	—
38	#4294	—	3	1	no	—
39	#737	—	19	2	no	—
40	#737	C₁₉⋊C₃	1	1	yes	characteristic, complemented
41	C₃×3₋¹⁺²	—	19	1	no	—
42	#733	—	19	2	no	—
43	#732	—	19	1	no	—
44	#731	—	19	2	no	—
45	#731	—	19	1	no	—
46	AΣL(1,𝔽₂₇)	—	19	2	no	—
47	AΣL(1,𝔽₂₇)	—	19	1	no	—
48	C₃×C₁₉	—	3	1	no	—
49	C₃×C₁₉	—	9	1	no	—
50	C₃×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
51	C₁₉⋊C₃	—	9	2	no	—
52	C₁₉⋊C₃	—	9	1	no	—
53	C₃³	—	19	1	no	—
54	3₋¹⁺²	—	3	2	no	—
55	3₋¹⁺²	—	19	2	no	—
56	3₋¹⁺²	—	19	2	no	—
57	3₋¹⁺²	—	57	2	no	—
58	3₋¹⁺²	—	57	1	no	—
59	3₋¹⁺²	—	57	2	no	—
60	3₋¹⁺²	—	57	2	no	—
61	3₋¹⁺²	C₃×C₁₉⋊C₃	1	2	yes	—
62	H(3,𝔽₃)	—	19	2	no	—
63	H(3,𝔽₃)	C₃×C₁₉⋊C₃	1	1	yes	characteristic
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	19	1	no	—
66	C₃×C₉	—	19	1	no	—
67	C₃×C₉	—	57	2	no	—
68	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
69	C₁₉	#6913	1	1	yes	characteristic, complemented, Sylow
70	C₃²	—	3	1	no	—
71	C₃²	—	57	2	no	—
72	C₃²	—	57	1	no	—
73	C₃²	—	171	1	no	—
74	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
75	C₉	—	3	2	no	—
76	C₉	—	57	1	no	—
77	C₉	—	57	1	no	—
78	C₉	—	57	2	no	—
79	C₉	—	57	2	no	—
80	C₉	C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
81	C₉	C₃²⋊(C₁₉⋊C₃)	1	2	yes	—
82	C₃	—	3	1	no	—
83	C₃	—	9	1	no	—
84	C₃	—	171	1	no	—
85	C₃	—	171	2	no	—
86	C₃	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊(C₁₉⋊C₃)
commutator, cosocle	C₃²×C₁₉	C₃³
Frattini	C₃²	C₃²×C₁₉⋊C₃
Fitting	C₁₉×#737	C₃
socle	C₃×C₁₉	C₃×H(3,𝔽₃)
hypercenter	#737	C₁₉⋊C₃
hypocenter	C₁₉	#6913
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ #737

Complements

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

N	H ≅ G/N	type
1. #13095332	C₃	semidirect
2. C₃×#10587023	C₃	semidirect
3. #13095321	C₃	semidirect
4. #13095319	C₃	semidirect
5. #13095318	C₃	semidirect
6. #13095316	C₃	semidirect
7. #13095315	C₃	semidirect
8. #13095313	C₃	semidirect
9. C₁₉×#737	C₃	semidirect
40. #737	C₁₉⋊C₃	semidirect
69. C₁₉	#6913	semidirect

Maximal subgroups

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

subgroup	index
#13095332	3
C₃×#10587023	3
#13095321	3
#13095319	3
#13095318	3
#13095316	3
#13095315	3
#13095313	3
C₁₉×#737	3
#6913	19