Subgroups — C₂₇×#10587025 #28354857

Order 13851.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#10587025	C₃	1	1	yes	maximal, characteristic
2	#17987355	C₃	1	6	yes	maximal, complemented
3	C₃²⋊#10587018	C₃	1	2	yes	maximal
4	C₂₇×#4294	C₃	1	3	yes	maximal, complemented
5	C₃²×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic
6	C₃×#10587025	C₉	1	1	yes	characteristic
7	C₃×#10587018	C₃²	1	6	yes	—
8	#13095305	C₉	1	6	yes	—
9	C₃²⋊#4294	C₉	1	2	yes	—
10	C₉×#4294	C₃²	1	3	yes	—
11	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
12	C₃×C₁₉×C₂₇	—	3	3	no	—
13	C₃×C₁₉×C₂₇	C₃²	1	2	yes	—
14	C₃×C₁₉×C₂₇	C₃²	1	1	yes	characteristic
15	C₂₇×3₋¹⁺²	—	19	1	no	maximal, Sylow
16	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₁₉	—	3	1	no	—
18	C₃×C₉×C₁₉	—	3	2	no	—
19	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
20	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
21	#10587025	C₂₇	1	9	yes	direct product factor
22	C₃×#4294	C₃×C₉	1	6	yes	—
23	C₃×#4294	C₃×C₉	1	3	yes	—
24	C₁₉×C₂₇	—	3	2	no	—
25	C₁₉×C₂₇	3₋¹⁺²	1	3	yes	complemented
26	#10587018	—	3	6	no	—
27	C₃²×C₂₇	C₁₉⋊C₃	1	1	yes	characteristic
28	C₉×3₋¹⁺²	—	19	1	no	—
29	C₉⋊C₂₇	—	19	6	no	—
30	C₃²⋊C₂₇	—	19	2	no	—
31	C₉×C₂₇	—	19	3	no	—
32	C₃²×C₁₉	—	3	1	no	—
33	C₃²×C₁₉	—	3	2	no	—
34	C₃²×C₁₉	C₃×C₂₇	1	3	yes	—
35	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
36	C₉×C₁₉	—	3	2	no	—
37	C₉×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
38	C₉×C₁₉	#737	1	2	yes	—
39	#4294	—	3	6	no	—
40	#4294	C₃×C₂₇	1	9	yes	complemented
41	C₃×3₋¹⁺²	—	19	1	no	—
42	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
43	C₃×C₂₇	—	3	3	no	—
44	C₃×C₂₇	—	19	6	no	—
45	C₃×C₂₇	C₃×C₁₉⋊C₃	1	2	yes	—
46	C₃×C₂₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic
47	C₉⋊C₉	—	19	6	no	—
48	C₃²⋊C₉	—	19	2	no	—
49	C₉²	—	19	3	no	—
50	C₃×C₁₉	—	3	3	no	—
51	C₃×C₁₉	C₉×3₋¹⁺²	1	1	yes	characteristic
52	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
53	C₃×C₁₉	#6903	1	2	yes	—
54	C₃³	C₉×C₁₉⋊C₃	1	1	yes	characteristic
55	3₋¹⁺²	—	19	9	no	—
56	C₃×C₉	—	3	1	no	—
57	C₃×C₉	—	3	2	no	—
58	C₃×C₉	—	19	3	no	—
59	C₃×C₉	—	19	6	no	—
60	C₃×C₉	C₉×C₁₉⋊C₃	1	2	yes	—
61	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
62	C₂₇	—	3	2	no	—
63	C₂₇	—	57	6	no	—
64	C₂₇	#10587025	1	3	yes	direct product factor
65	C₁₉	C₂₇×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
66	C₃²	—	3	1	no	—
67	C₃²	—	3	2	no	—
68	C₃²	C₂₇×C₁₉⋊C₃	1	3	yes	—
69	C₃²	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
70	C₉	—	3	2	no	—
71	C₉	—	19	9	no	—
72	C₉	—	57	6	no	—
73	C₉	C₃×#10587025	1	1	yes	characteristic
74	C₉	#13095332	1	2	yes	—
75	C₃	—	3	3	no	—
76	C₃	C₉×#10587025	1	1	yes	characteristic
77	C₃	C₃×C₂₇×C₁₉⋊C₃	1	1	yes	characteristic
78	C₃	#17987479	1	2	yes	—

	subgroup	G/H
center	C₃×C₂₇	C₃×C₁₉⋊C₃
commutator	C₃×C₁₉	C₃²×C₂₇
Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
Fitting	C₃²×C₁₉×C₂₇	C₃
socle	C₃²×C₁₉	C₃²×C₉
prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃×C₉×C₁₉	C₃³
hypercenter	C₃²×C₂₇	C₁₉⋊C₃
hypocenter	C₁₉	C₂₇×3₋¹⁺²
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₂₇ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
2. #17987355	C₃	semidirect
4. C₂₇×#4294	C₃	semidirect
21. #10587025	C₂₇	direct (N × H)
25. C₁₉×C₂₇	3₋¹⁺²	semidirect
40. #4294	C₃×C₂₇	semidirect
64. C₂₇	#10587025	direct (N × H)
65. C₁₉	C₂₇×3₋¹⁺²	semidirect

Maximal subgroups

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

subgroup	index
C₉×#10587025	3
#17987355	3
C₃²⋊#10587018	3
C₂₇×#4294	3
C₃²×C₁₉×C₂₇	3
C₂₇×3₋¹⁺²	19

Subgroups — C27×#10587025 #28354857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₇×#10587025 #28354857