Subgroups — C₁₃×#10624725 #23744876

Order 9477.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6908	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6903	C₃	1	3	yes	maximal, complemented
3	C₃×C₁₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#6873	C₃	1	3	yes	maximal, complemented
5	C₁₃×#6872	C₃	1	3	yes	maximal, complemented
6	C₁₃×#6869	C₃	1	2	yes	maximal, complemented
7	C₁₃×#737	C₃²	1	3	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
9	C₁₃×#733	C₉	1	2	yes	—
10	C₁₃×#732	C₉	1	1	yes	characteristic
11	C₁₃×#731	C₉	1	3	yes	—
12	C₁₃×AΣL(1,𝔽₂₇)	C₉	1	3	yes	—
13	C₁₃×C₂₇⋊C₃	—	3	3	no	—
14	C₁₃×C₂₇⋊C₃	—	3	6	no	—
15	C₁₃×C₂₇⋊C₃	C₃²	1	6	yes	—
16	C₃×C₁₃×C₂₇	—	3	3	no	—
17	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
18	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
19	C₃×C₁₃×C₂₇	C₃²	1	1	yes	characteristic
20	#10624725	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₃³×C₁₃	C₃×C₉	1	1	yes	characteristic
22	C₁₃×3₋¹⁺²	—	3	6	no	—
23	C₁₃×3₋¹⁺²	C₃×C₉	1	6	yes	—
24	C₁₃×H(3,𝔽₃)	C₃×C₉	1	3	yes	—
25	C₃×C₉×C₁₃	—	3	3	no	—
26	C₃×C₉×C₁₃	—	3	1	no	—
27	C₃×C₉×C₁₃	—	3	2	no	—
28	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
29	C₃×C₉×C₁₃	C₃×C₉	1	1	yes	characteristic
30	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
31	C₁₃×C₂₇	—	3	6	no	—
32	C₁₃×C₂₇	—	3	1	no	—
33	C₁₃×C₂₇	—	3	1	no	—
34	C₁₃×C₂₇	H(3,𝔽₃)	1	3	yes	—
35	#6908	C₃×C₁₃	1	1	yes	characteristic
36	#6903	C₃×C₁₃	1	3	yes	complemented
37	C₃×C₂₇⋊C₃	C₃×C₁₃	1	1	yes	characteristic, complemented
38	#6873	C₃×C₁₃	1	3	yes	complemented
39	#6872	C₃×C₁₃	1	3	yes	complemented
40	#6869	C₃×C₁₃	1	2	yes	complemented
41	C₃²×C₁₃	—	3	1	no	—
42	C₃²×C₁₃	—	3	3	no	—
43	C₃²×C₁₃	—	9	1	no	—
44	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
45	C₉×C₁₃	—	3	1	no	—
46	C₉×C₁₃	—	3	1	no	—
47	C₉×C₁₃	—	3	6	no	—
48	C₉×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
49	C₉×C₁₃	#737	1	2	yes	—
50	#737	C₃²×C₁₃	1	3	yes	—
51	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
52	#733	C₉×C₁₃	1	2	yes	—
53	#732	C₉×C₁₃	1	1	yes	characteristic
54	#731	C₉×C₁₃	1	3	yes	—
55	AΣL(1,𝔽₂₇)	C₉×C₁₃	1	3	yes	—
56	C₂₇⋊C₃	—	3	3	no	—
57	C₂₇⋊C₃	—	3	6	no	—
58	C₂₇⋊C₃	C₃²×C₁₃	1	6	yes	—
59	C₃×C₂₇	—	3	3	no	—
60	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
61	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
62	C₃×C₂₇	C₃²×C₁₃	1	1	yes	characteristic
63	C₃×C₁₃	—	3	1	no	—
64	C₃×C₁₃	—	9	3	no	—
65	C₃×C₁₃	—	9	1	no	—
66	C₃×C₁₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
67	C₃³	C₃×C₉×C₁₃	1	1	yes	characteristic
68	3₋¹⁺²	—	3	6	no	—
69	3₋¹⁺²	C₃×C₉×C₁₃	1	6	yes	—
70	H(3,𝔽₃)	C₃×C₉×C₁₃	1	3	yes	—
71	C₃×C₉	—	3	3	no	—
72	C₃×C₉	—	3	1	no	—
73	C₃×C₉	—	3	2	no	—
74	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
75	C₃×C₉	C₃×C₉×C₁₃	1	1	yes	characteristic
76	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
77	C₂₇	—	3	6	no	—
78	C₂₇	—	3	1	no	—
79	C₂₇	—	3	1	no	—
80	C₂₇	C₁₃×H(3,𝔽₃)	1	3	yes	—
81	C₁₃	#10624725	1	1	yes	characteristic, direct product factor, Sylow
82	C₃²	—	3	1	no	—
83	C₃²	—	3	3	no	—
84	C₃²	—	9	1	no	—
85	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
86	C₉	—	3	1	no	—
87	C₉	—	3	1	no	—
88	C₉	—	3	6	no	—
89	C₉	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
90	C₉	C₁₃×#737	1	2	yes	—
91	C₃	—	3	1	no	—
92	C₃	—	9	1	no	—
93	C₃	—	9	3	no	—
94	C₃	C₉×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₉×C₁₃	C₃×H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₁₃
Frattini, cosocle	C₃×C₉	C₃³×C₁₃
socle	C₃×C₁₃	C₉×H(3,𝔽₃)
prime radical	C₁₃×#6908	C₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₃ ◁ C₃×C₁₃×C₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#6903	C₃	semidirect
3. C₃×C₁₃×C₂₇⋊C₃	C₃	semidirect
4. C₁₃×#6873	C₃	semidirect
5. C₁₃×#6872	C₃	semidirect
6. C₁₃×#6869	C₃	semidirect
20. #10624725	C₁₃	direct (N × H)
36. #6903	C₃×C₁₃	semidirect
37. C₃×C₂₇⋊C₃	C₃×C₁₃	semidirect
38. #6873	C₃×C₁₃	semidirect
39. #6872	C₃×C₁₃	semidirect
40. #6869	C₃×C₁₃	semidirect
81. C₁₃	#10624725	direct (N × H)

Subgroups — C13×#10624725 #23744876

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624725 #23744876