Subgroups — C₃²×C₇×C₂₇⋊C₃ #19100325

Order 5103.

944 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₇×C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₇×C₂₇⋊C₃	C₃	1	36	yes	maximal, direct product factor
3	C₃²×C₇×C₂₇	C₃	1	3	yes	maximal, complemented
4	C₃²×C₂₇⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃⁴×C₇	C₉	1	1	yes	characteristic
6	C₃²×C₇×C₉	C₉	1	2	yes	—
7	C₃²×C₇×C₉	C₉	1	24	yes	—
8	C₃²×C₇×C₉	C₃²	1	12	yes	—
9	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
10	C₇×C₂₇⋊C₃	C₃²	1	81	yes	direct product factor
11	C₃×C₇×C₂₇	C₃²	1	36	yes	complemented
12	C₃³×C₉	C₃×C₇	1	1	yes	characteristic
13	C₃×C₂₇⋊C₃	C₃×C₇	1	36	yes	direct product factor
14	C₃²×C₂₇	C₃×C₇	1	3	yes	complemented
15	C₃³×C₇	—	3	9	no	—
16	C₃³×C₇	C₃×C₉	1	12	yes	—
17	C₃³×C₇	C₃×C₉	1	1	yes	characteristic
18	C₃×C₇×C₉	C₃×C₉	1	72	yes	—
19	C₃×C₇×C₉	C₃×C₉	1	24	yes	—
20	C₃×C₇×C₉	C₃×C₉	1	8	yes	—
21	C₃×C₇×C₉	C₃³	1	4	yes	—
22	C₃×C₇×C₉	C₃³	1	9	yes	—
23	C₇×C₂₇	C₃³	1	27	yes	complemented
24	C₃⁴	C₇×C₉	1	1	yes	characteristic
25	C₃²×C₉	C₇×C₉	1	24	yes	—
26	C₃²×C₉	C₇×C₉	1	2	yes	—
27	C₃²×C₉	C₃²×C₇	1	12	yes	—
28	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
29	C₂₇⋊C₃	C₃²×C₇	1	81	yes	direct product factor
30	C₃×C₂₇	C₃²×C₇	1	36	yes	complemented
31	C₃²×C₇	—	3	36	no	—
32	C₃²×C₇	C₂₇⋊C₃	1	9	yes	direct product factor
33	C₃²×C₇	C₃²×C₉	1	9	yes	—
34	C₃²×C₇	C₃²×C₉	1	4	yes	—
35	C₇×C₉	C₃²×C₉	1	18	yes	—
36	C₇×C₉	C₃²×C₉	1	8	yes	—
37	C₇×C₉	C₃⁴	1	1	yes	characteristic
38	C₃³	—	3	9	no	—
39	C₃³	C₃×C₇×C₉	1	12	yes	—
40	C₃³	C₃×C₇×C₉	1	1	yes	characteristic
41	C₃×C₉	C₃×C₇×C₉	1	72	yes	—
42	C₃×C₉	C₃×C₇×C₉	1	24	yes	—
43	C₃×C₉	C₃×C₇×C₉	1	8	yes	—
44	C₃×C₉	C₃³×C₇	1	4	yes	—
45	C₃×C₉	C₃³×C₇	1	9	yes	—
46	C₂₇	C₃³×C₇	1	27	yes	complemented
47	C₃×C₇	—	3	9	no	—
48	C₃×C₇	C₃×C₂₇⋊C₃	1	12	yes	direct product factor
49	C₃×C₇	C₃³×C₉	1	1	yes	characteristic
50	C₃²	—	3	36	no	—
51	C₃²	C₇×C₂₇⋊C₃	1	9	yes	direct product factor
52	C₃²	C₃²×C₇×C₉	1	9	yes	—
53	C₃²	C₃²×C₇×C₉	1	4	yes	—
54	C₉	C₃²×C₇×C₉	1	8	yes	—
55	C₉	C₃²×C₇×C₉	1	18	yes	—
56	C₉	C₃⁴×C₇	1	1	yes	characteristic
57	C₇	C₃²×C₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
58	C₃	—	3	9	no	—
59	C₃	C₃×C₇×C₂₇⋊C₃	1	12	yes	direct product factor
60	C₃	C₃³×C₇×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃²×C₇×C₉	C₃²
commutator	C₃	C₃³×C₇×C₉
Frattini	C₉	C₃⁴×C₇
socle	C₃³×C₇	C₃×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₇×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×C₂₇⋊C₃	C₃	direct (N × H)
3. C₃²×C₇×C₂₇	C₃	semidirect
4. C₃²×C₂₇⋊C₃	C₇	direct (N × H)
10. C₇×C₂₇⋊C₃	C₃²	direct (N × H)
11. C₃×C₇×C₂₇	C₃²	semidirect
13. C₃×C₂₇⋊C₃	C₃×C₇	direct (N × H)
14. C₃²×C₂₇	C₃×C₇	semidirect
23. C₇×C₂₇	C₃³	semidirect
29. C₂₇⋊C₃	C₃²×C₇	direct (N × H)
30. C₃×C₂₇	C₃²×C₇	semidirect
32. C₃²×C₇	C₂₇⋊C₃	direct (N × H)
46. C₂₇	C₃³×C₇	semidirect
48. C₃×C₇	C₃×C₂₇⋊C₃	direct (N × H)
51. C₃²	C₇×C₂₇⋊C₃	direct (N × H)
57. C₇	C₃²×C₂₇⋊C₃	direct (N × H)
59. C₃	C₃×C₇×C₂₇⋊C₃	direct (N × H)

Subgroups — C32×C7×C27⋊C3 #19100325

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₇×C₂₇⋊C₃ #19100325