Subgroups — #17987451

Order 4617.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10587022	C₃	1	1	yes	maximal, characteristic
2	C₃×#10587023	C₃	1	1	yes	maximal, characteristic
3	#13095307	C₃	1	2	yes	maximal, complemented
4	#13095307	C₃	1	1	yes	maximal, characteristic, complemented
5	#13095305	C₃	1	2	yes	maximal, complemented
6	#13095305	C₃	1	2	yes	maximal, complemented
7	#13095303	C₃	1	2	yes	maximal
8	C₉×#4294	C₃	1	1	yes	maximal, characteristic, complemented
9	C₁₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
11	C₃×C₉×C₁₉	C₃²	1	2	yes	—
12	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
14	C₃×#4294	C₃²	1	2	yes	—
15	C₃×#4294	C₃²	1	2	yes	—
16	C₃×#4294	C₃²	1	2	yes	—
17	C₃×#4294	C₃²	1	1	yes	characteristic
18	C₃×#4294	C₃²	1	1	yes	characteristic
19	#10587023	—	3	3	no	—
20	#10587022	—	3	3	no	—
21	#6896	—	19	1	no	maximal, Sylow
22	C₃²×C₁₉	C₃³	1	1	yes	characteristic
23	C₃×C₁₉⋊C₃	—	3	1	no	—
24	C₃×C₁₉⋊C₃	—	3	1	no	—
25	C₃×C₁₉⋊C₃	—	3	2	no	—
26	C₉×C₁₉	—	3	1	no	—
27	C₉×C₁₉	—	3	2	no	—
28	C₉×C₁₉	3₋¹⁺²	1	3	yes	complemented
29	#4294	—	3	2	no	—
30	#4294	—	3	1	no	—
31	#4294	—	3	2	no	—
32	#4294	—	3	2	no	—
33	#4294	3₋¹⁺²	1	3	yes	complemented
34	C₃×3₋¹⁺²	—	19	1	no	—
35	C₃×3₋¹⁺²	—	19	1	no	—
36	C₉⋊C₉	—	19	2	no	—
37	C₉⋊C₉	—	19	2	no	—
38	C₉⋊C₉	—	19	2	no	—
39	C₉⋊C₉	—	19	1	no	—
40	C₉⋊C₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented
41	C₃²⋊C₉	—	19	2	no	—
42	C₉²	—	19	1	no	—
43	C₃×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
44	C₃×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
45	C₃×C₁₉	#737	1	2	yes	—
46	C₁₉⋊C₃	—	9	1	no	—
47	C₃³	—	19	1	no	—
48	3₋¹⁺²	—	57	3	no	—
49	3₋¹⁺²	—	57	3	no	—
50	C₃×C₉	—	19	1	no	—
51	C₃×C₉	—	19	2	no	—
52	C₃×C₉	—	19	2	no	—
53	C₃×C₉	—	19	1	no	—
54	C₃×C₉	—	19	2	no	—
55	C₃×C₉	C₃×C₁₉⋊C₃	1	2	yes	—
56	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
57	C₃×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
58	C₁₉	#6896	1	1	yes	characteristic, complemented, Sylow
59	C₃²	—	57	1	no	—
60	C₃²	—	57	1	no	—
61	C₃²	—	57	2	no	—
62	C₃²	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
63	C₉	—	3	1	no	—
64	C₉	—	3	2	no	—
65	C₉	—	19	3	no	—
66	C₉	—	57	1	no	—
67	C₉	—	57	2	no	—
68	C₉	—	57	2	no	—
69	C₉	—	57	2	no	—
70	C₉	#10587023	1	3	yes	complemented
71	C₃	—	171	1	no	—
72	C₃	3₋¹⁺²×C₁₉⋊C₃	1	1	yes	characteristic
73	C₃	C₃×#10587023	1	1	yes	characteristic
74	C₃	#13095333	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₉	C₃³
Fitting	C₁₉×C₉⋊C₉	C₃
prime radical	C₃²×C₁₉⋊C₃	C₃²
hypercenter	C₉⋊C₉	C₁₉⋊C₃
hypocenter	C₁₉	#6896
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
3. #13095307	C₃	semidirect
4. #13095307	C₃	semidirect
5. #13095305	C₃	semidirect
6. #13095305	C₃	semidirect
8. C₉×#4294	C₃	semidirect
9. C₁₉×C₉⋊C₉	C₃	semidirect
28. C₉×C₁₉	3₋¹⁺²	semidirect
33. #4294	3₋¹⁺²	semidirect
40. C₉⋊C₉	C₁₉⋊C₃	semidirect
58. C₁₉	#6896	semidirect
70. C₉	#10587023	semidirect

Maximal subgroups

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

subgroup	index
C₃×#10587022	3
C₃×#10587023	3
#13095307	3
#13095305	3
#13095303	3
C₉×#4294	3
C₁₉×C₉⋊C₉	3
#6896	19