Subgroups — C₃²×C₇×C₈₁ #19100240

Order 5103.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₃×C₇×C₈₁	C₃	1	12	yes	maximal, direct product factor
3	C₃²×C₈₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃²×C₇×C₉	C₉	1	1	yes	characteristic
5	C₃×C₇×C₂₇	C₉	1	8	yes	—
6	C₃×C₇×C₂₇	C₃²	1	4	yes	—
7	C₇×C₈₁	C₃²	1	9	yes	direct product factor
8	C₃²×C₂₇	C₃×C₇	1	1	yes	characteristic
9	C₃×C₈₁	C₃×C₇	1	12	yes	direct product factor
10	C₃³×C₇	C₂₇	1	1	yes	characteristic
11	C₃×C₇×C₉	C₂₇	1	8	yes	—
12	C₃×C₇×C₉	C₃×C₉	1	4	yes	—
13	C₇×C₂₇	C₃×C₉	1	8	yes	—
14	C₇×C₂₇	C₃³	1	1	yes	characteristic
15	C₃²×C₉	C₇×C₉	1	1	yes	characteristic
16	C₃×C₂₇	C₇×C₉	1	8	yes	—
17	C₃×C₂₇	C₃²×C₇	1	4	yes	—
18	C₈₁	C₃²×C₇	1	9	yes	direct product factor
19	C₃²×C₇	C₈₁	1	9	yes	direct product factor
20	C₃²×C₇	C₃×C₂₇	1	4	yes	—
21	C₇×C₉	C₃×C₂₇	1	8	yes	—
22	C₇×C₉	C₃²×C₉	1	1	yes	characteristic
23	C₃³	C₇×C₂₇	1	1	yes	characteristic
24	C₃×C₉	C₇×C₂₇	1	8	yes	—
25	C₃×C₉	C₃×C₇×C₉	1	4	yes	—
26	C₂₇	C₃×C₇×C₉	1	8	yes	—
27	C₂₇	C₃³×C₇	1	1	yes	characteristic
28	C₃×C₇	C₃×C₈₁	1	12	yes	direct product factor
29	C₃×C₇	C₃²×C₂₇	1	1	yes	characteristic
30	C₃²	C₇×C₈₁	1	9	yes	direct product factor
31	C₃²	C₃×C₇×C₂₇	1	4	yes	—
32	C₉	C₃×C₇×C₂₇	1	8	yes	—
33	C₉	C₃²×C₇×C₉	1	1	yes	characteristic
34	C₇	C₃²×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
35	C₃	C₃×C₇×C₈₁	1	12	yes	direct product factor
36	C₃	C₃²×C₇×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂₇	C₃³×C₇
socle	C₃³×C₇	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×C₇×C₈₁	C₃	direct (N × H)
3. C₃²×C₈₁	C₇	direct (N × H)
7. C₇×C₈₁	C₃²	direct (N × H)
9. C₃×C₈₁	C₃×C₇	direct (N × H)
18. C₈₁	C₃²×C₇	direct (N × H)
19. C₃²×C₇	C₈₁	direct (N × H)
28. C₃×C₇	C₃×C₈₁	direct (N × H)
30. C₃²	C₇×C₈₁	direct (N × H)
34. C₇	C₃²×C₈₁	direct (N × H)
35. C₃	C₃×C₇×C₈₁	direct (N × H)

Subgroups — C32×C7×C81 #19100240

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₇×C₈₁ #19100240