Subgroups — C₁₃×C₃²⋊C₈₁ #23744652

Order 9477.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₈₁	C₃	1	3	yes	maximal, complemented
3	C₃²×C₉×C₁₃	C₉	1	1	yes	characteristic
4	C₃×C₁₃×C₂₇	—	3	1	no	—
5	C₃×C₁₃×C₂₇	—	3	2	no	—
6	C₃×C₁₃×C₂₇	C₉	1	2	yes	—
7	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
8	C₁₃×C₈₁	—	3	3	no	—
9	C₃²⋊C₈₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃³×C₁₃	C₂₇	1	1	yes	characteristic
11	C₃×C₉×C₁₃	—	3	1	no	—
12	C₃×C₉×C₁₃	—	3	2	no	—
13	C₃×C₉×C₁₃	C₂₇	1	2	yes	—
14	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
15	C₁₃×C₂₇	—	3	2	no	—
16	C₁₃×C₂₇	H(3,𝔽₃)	1	1	yes	characteristic
17	C₁₃×C₂₇	3₋¹⁺²	1	2	yes	—
18	C₃²×C₂₇	C₃×C₁₃	1	1	yes	characteristic
19	C₃×C₈₁	C₃×C₁₃	1	3	yes	complemented
20	C₃²×C₁₃	—	3	1	no	—
21	C₃²×C₁₃	—	3	2	no	—
22	C₃²×C₁₃	C₈₁	1	3	yes	complemented
23	C₃²×C₁₃	C₃×C₂₇	1	1	yes	characteristic
24	C₉×C₁₃	—	3	2	no	—
25	C₉×C₁₃	C₃²⋊C₉	1	1	yes	characteristic
26	C₉×C₁₃	C₂₇⋊C₃	1	2	yes	—
27	C₃²×C₉	C₉×C₁₃	1	1	yes	characteristic
28	C₃×C₂₇	—	3	1	no	—
29	C₃×C₂₇	—	3	2	no	—
30	C₃×C₂₇	C₉×C₁₃	1	2	yes	—
31	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
32	C₈₁	—	3	3	no	—
33	C₃×C₁₃	—	3	3	no	—
34	C₃×C₁₃	C₃²⋊C₂₇	1	1	yes	characteristic
35	C₃×C₁₃	C₃×C₈₁	1	1	yes	characteristic
36	C₃×C₁₃	C₈₁⋊C₃	1	2	yes	—
37	C₃³	C₁₃×C₂₇	1	1	yes	characteristic
38	C₃×C₉	—	3	1	no	—
39	C₃×C₉	—	3	2	no	—
40	C₃×C₉	C₁₃×C₂₇	1	2	yes	—
41	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
42	C₂₇	—	3	2	no	—
43	C₂₇	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
44	C₂₇	C₁₃×3₋¹⁺²	1	2	yes	—
45	C₁₃	C₃²⋊C₈₁	1	1	yes	characteristic, direct product factor, Sylow
46	C₃²	—	3	1	no	—
47	C₃²	—	3	2	no	—
48	C₃²	C₁₃×C₈₁	1	3	yes	complemented
49	C₃²	C₃×C₁₃×C₂₇	1	1	yes	characteristic
50	C₉	—	3	2	no	—
51	C₉	C₁₃×C₃²⋊C₉	1	1	yes	characteristic
52	C₉	C₁₃×C₂₇⋊C₃	1	2	yes	—
53	C₃	—	3	3	no	—
54	C₃	C₁₃×C₃²⋊C₂₇	1	1	yes	characteristic
55	C₃	C₃×C₁₃×C₈₁	1	1	yes	characteristic
56	C₃	C₁₃×C₈₁⋊C₃	1	2	yes	—

	subgroup	G/H
center	C₃×C₁₃×C₂₇	C₃²
commutator	C₃	C₃×C₁₃×C₈₁
Frattini, cosocle	C₃×C₂₇	C₃²×C₁₃
socle	C₃²×C₁₃	C₃×C₂₇
prime radical	C₃³×C₁₃	C₂₇
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃×C₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×C₈₁	C₃	semidirect
9. C₃²⋊C₈₁	C₁₃	direct (N × H)
19. C₃×C₈₁	C₃×C₁₃	semidirect
22. C₃²×C₁₃	C₈₁	semidirect
45. C₁₃	C₃²⋊C₈₁	direct (N × H)
48. C₃²	C₁₃×C₈₁	semidirect

Subgroups — C13×C32⋊C81 #23744652

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×C₃²⋊C₈₁ #23744652