Subgroups — C₃²×C₁₉×C₈₁ #28353027

Order 13851.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₉×C₈₁	C₃	1	12	yes	maximal, direct product factor
3	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
4	C₃×C₁₉×C₂₇	C₉	1	8	yes	—
5	C₃×C₁₉×C₂₇	C₃²	1	4	yes	—
6	C₁₉×C₈₁	C₃²	1	9	yes	direct product factor
7	C₃²×C₈₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃³×C₁₉	C₂₇	1	1	yes	characteristic
9	C₃×C₉×C₁₉	C₂₇	1	8	yes	—
10	C₃×C₉×C₁₉	C₃×C₉	1	4	yes	—
11	C₁₉×C₂₇	C₃×C₉	1	8	yes	—
12	C₁₉×C₂₇	C₃³	1	1	yes	characteristic
13	C₃²×C₂₇	C₃×C₁₉	1	1	yes	characteristic
14	C₃×C₈₁	C₃×C₁₉	1	12	yes	direct product factor
15	C₃²×C₁₉	C₈₁	1	9	yes	direct product factor
16	C₃²×C₁₉	C₃×C₂₇	1	4	yes	—
17	C₉×C₁₉	C₃×C₂₇	1	8	yes	—
18	C₉×C₁₉	C₃²×C₉	1	1	yes	characteristic
19	C₃²×C₉	C₉×C₁₉	1	1	yes	characteristic
20	C₃×C₂₇	C₉×C₁₉	1	8	yes	—
21	C₃×C₂₇	C₃²×C₁₉	1	4	yes	—
22	C₈₁	C₃²×C₁₉	1	9	yes	direct product factor
23	C₃×C₁₉	C₃×C₈₁	1	12	yes	direct product factor
24	C₃×C₁₉	C₃²×C₂₇	1	1	yes	characteristic
25	C₃³	C₁₉×C₂₇	1	1	yes	characteristic
26	C₃×C₉	C₁₉×C₂₇	1	8	yes	—
27	C₃×C₉	C₃×C₉×C₁₉	1	4	yes	—
28	C₂₇	C₃×C₉×C₁₉	1	8	yes	—
29	C₂₇	C₃³×C₁₉	1	1	yes	characteristic
30	C₁₉	C₃²×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₃²	C₁₉×C₈₁	1	9	yes	direct product factor
32	C₃²	C₃×C₁₉×C₂₇	1	4	yes	—
33	C₉	C₃×C₁₉×C₂₇	1	8	yes	—
34	C₉	C₃²×C₉×C₁₉	1	1	yes	characteristic
35	C₃	C₃×C₁₉×C₈₁	1	12	yes	direct product factor
36	C₃	C₃²×C₁₉×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₃³×C₁₉
socle, prime radical	C₃³×C₁₉	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₉×C₈₁	C₃	direct (N × H)
6. C₁₉×C₈₁	C₃²	direct (N × H)
7. C₃²×C₈₁	C₁₉	direct (N × H)
14. C₃×C₈₁	C₃×C₁₉	direct (N × H)
15. C₃²×C₁₉	C₈₁	direct (N × H)
22. C₈₁	C₃²×C₁₉	direct (N × H)
23. C₃×C₁₉	C₃×C₈₁	direct (N × H)
30. C₁₉	C₃²×C₈₁	direct (N × H)
31. C₃²	C₁₉×C₈₁	direct (N × H)
35. C₃	C₃×C₁₉×C₈₁	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×C₁₉×C₈₁	3
C₃²×C₈₁	19

Subgroups — C32×C19×C81 #28353027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₉×C₈₁ #28353027