Subgroups — C₃×C₉×C₁₉×C₂₇ #28352874

Order 13851.

404 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₂₇	C₃	1	3	yes	maximal
2	C₃×C₉²×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₉×C₂₇	C₃	1	9	yes	maximal, direct product factor
4	C₃²×C₉×C₁₉	C₉	1	3	yes	—
5	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
6	C₃×C₁₉×C₂₇	C₉	1	27	yes	direct product factor
7	C₃×C₁₉×C₂₇	C₃²	1	9	yes	—
8	C₉²×C₁₉	C₉	1	6	yes	—
9	C₉²×C₁₉	C₃²	1	3	yes	—
10	C₃×C₉×C₂₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
12	C₃×C₉×C₁₉	C₂₇	1	27	yes	direct product factor
13	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
14	C₃×C₉×C₁₉	C₃×C₉	1	9	yes	—
15	C₃×C₉×C₁₉	C₃×C₉	1	9	yes	—
16	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
17	C₁₉×C₂₇	C₃×C₉	1	27	yes	direct product factor
18	C₃²×C₂₇	C₃×C₁₉	1	3	yes	—
19	C₃×C₉²	C₃×C₁₉	1	1	yes	characteristic
20	C₉×C₂₇	C₃×C₁₉	1	9	yes	direct product factor
21	C₃²×C₁₉	C₉²	1	3	yes	—
22	C₃²×C₁₉	C₃×C₂₇	1	9	yes	—
23	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
24	C₉×C₁₉	C₉²	1	6	yes	—
25	C₉×C₁₉	C₃×C₂₇	1	27	yes	direct product factor
26	C₉×C₁₉	C₃²×C₉	1	3	yes	—
27	C₃²×C₉	C₉×C₁₉	1	3	yes	—
28	C₃²×C₉	C₃²×C₁₉	1	1	yes	characteristic
29	C₃×C₂₇	C₉×C₁₉	1	27	yes	direct product factor
30	C₃×C₂₇	C₃²×C₁₉	1	9	yes	—
31	C₉²	C₉×C₁₉	1	6	yes	—
32	C₉²	C₃²×C₁₉	1	3	yes	—
33	C₃×C₁₉	C₉×C₂₇	1	9	yes	direct product factor
34	C₃×C₁₉	C₃×C₉²	1	1	yes	characteristic
35	C₃×C₁₉	C₃²×C₂₇	1	3	yes	—
36	C₃³	C₃×C₉×C₁₉	1	1	yes	characteristic
37	C₃×C₉	C₁₉×C₂₇	1	27	yes	direct product factor
38	C₃×C₉	C₃×C₉×C₁₉	1	2	yes	—
39	C₃×C₉	C₃×C₉×C₁₉	1	9	yes	—
40	C₃×C₉	C₃×C₉×C₁₉	1	9	yes	—
41	C₃×C₉	C₃³×C₁₉	1	1	yes	characteristic
42	C₂₇	C₃×C₉×C₁₉	1	27	yes	direct product factor
43	C₁₉	C₃×C₉×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₃²	C₉²×C₁₉	1	3	yes	—
45	C₃²	C₃×C₁₉×C₂₇	1	9	yes	—
46	C₃²	C₃²×C₉×C₁₉	1	1	yes	characteristic
47	C₉	C₉²×C₁₉	1	6	yes	—
48	C₉	C₃×C₁₉×C₂₇	1	27	yes	direct product factor
49	C₉	C₃²×C₉×C₁₉	1	3	yes	—
50	C₃	C₉×C₁₉×C₂₇	1	9	yes	direct product factor
51	C₃	C₃×C₉²×C₁₉	1	1	yes	characteristic
52	C₃	C₃²×C₁₉×C₂₇	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₉	C₃³×C₁₉
socle, prime radical	C₃³×C₁₉	C₃×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₉×C₂₇	C₃	direct (N × H)
6. C₃×C₁₉×C₂₇	C₉	direct (N × H)
10. C₃×C₉×C₂₇	C₁₉	direct (N × H)
12. C₃×C₉×C₁₉	C₂₇	direct (N × H)
17. C₁₉×C₂₇	C₃×C₉	direct (N × H)
20. C₉×C₂₇	C₃×C₁₉	direct (N × H)
25. C₉×C₁₉	C₃×C₂₇	direct (N × H)
29. C₃×C₂₇	C₉×C₁₉	direct (N × H)
33. C₃×C₁₉	C₉×C₂₇	direct (N × H)
37. C₃×C₉	C₁₉×C₂₇	direct (N × H)
42. C₂₇	C₃×C₉×C₁₉	direct (N × H)
43. C₁₉	C₃×C₉×C₂₇	direct (N × H)
48. C₉	C₃×C₁₉×C₂₇	direct (N × H)
50. C₃	C₉×C₁₉×C₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₉×C₂₇	3
C₃×C₉²×C₁₉	3
C₉×C₁₉×C₂₇	3
C₃×C₉×C₂₇	19

Subgroups — C3×C9×C19×C27 #28352874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×C₁₉×C₂₇ #28352874