Subgroups — C₁₃×#10624877 #23745028

Order 9477.

662 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6899	C₃	1	6	yes	maximal, complemented
2	C₁₃×#6898	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6897	C₃	1	6	yes	maximal, complemented
4	C₁₃×#6896	C₃	1	3	yes	maximal, complemented
5	C₁₃×#6895	C₃	1	2	yes	maximal, complemented
6	C₁₃×#6894	C₃	1	4	yes	maximal, complemented
7	C₁₃×#6893	C₃	1	1	yes	maximal, characteristic
8	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	2	yes	maximal
9	C₉×C₁₃×3₋¹⁺²	C₃	1	6	yes	maximal, complemented
10	C₉×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
11	C₉×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
12	C₁₃×#6887	C₃	1	3	yes	maximal, complemented
13	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
14	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
15	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
16	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
17	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
18	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
19	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
20	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
21	C₁₃×C₉⋊C₉	C₃²	1	12	yes	—
22	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
23	C₁₃×C₉⋊C₉	C₃²	1	12	yes	—
24	C₁₃×C₉⋊C₉	C₃²	1	12	yes	—
25	C₁₃×C₉⋊C₉	C₃²	1	12	yes	—
26	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
27	C₁₃×C₉⋊C₉	C₃²	1	6	yes	—
28	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
29	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
30	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
31	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
32	C₁₃×C₃²⋊C₉	C₃²	1	3	yes	—
33	C₁₃×C₃²⋊C₉	C₃²	1	4	yes	—
34	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
35	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
36	C₉²×C₁₃	C₃²	1	1	yes	characteristic
37	C₉²×C₁₃	C₃²	1	2	yes	—
38	C₉²×C₁₃	C₃²	1	1	yes	characteristic
39	C₉²×C₁₃	C₃²	1	2	yes	—
40	C₉²×C₁₃	C₃²	1	1	yes	characteristic
41	C₉²×C₁₃	C₃²	1	2	yes	—
42	C₉²×C₁₃	C₃²	1	6	yes	—
43	#10624877	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₃³×C₁₃	C₃³	1	3	yes	—
45	C₃³×C₁₃	C₃³	1	1	yes	characteristic
46	C₁₃×3₋¹⁺²	—	3	6	no	—
47	C₁₃×3₋¹⁺²	—	3	18	no	—
48	C₁₃×H(3,𝔽₃)	—	3	3	no	—
49	C₃×C₉×C₁₃	—	3	3	no	—
50	C₃×C₉×C₁₃	—	3	3	no	—
51	C₃×C₉×C₁₃	—	3	9	no	—
52	C₃×C₉×C₁₃	—	3	6	no	—
53	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
54	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
55	C₃×C₉×C₁₃	C₃³	1	2	yes	—
56	C₃×C₉×C₁₃	C₃³	1	2	yes	—
57	C₃×C₉×C₁₃	C₃³	1	2	yes	—
58	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
59	C₃×C₉×C₁₃	C₃³	1	12	yes	—
60	C₃×C₉×C₁₃	C₃³	1	6	yes	—
61	C₃×C₉×C₁₃	C₃³	1	6	yes	—
62	C₃×C₉×C₁₃	C₃³	1	2	yes	—
63	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
64	#6899	C₃×C₁₃	1	6	yes	complemented
65	#6898	C₃×C₁₃	1	3	yes	complemented
66	#6897	C₃×C₁₃	1	6	yes	complemented
67	#6896	C₃×C₁₃	1	3	yes	complemented
68	#6895	C₃×C₁₃	1	2	yes	complemented
69	#6894	C₃×C₁₃	1	4	yes	complemented
70	#6893	C₃×C₁₃	1	1	yes	characteristic
71	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	2	yes	—
72	C₉×3₋¹⁺²	C₃×C₁₃	1	6	yes	complemented
73	C₉×3₋¹⁺²	C₃×C₁₃	1	2	yes	complemented
74	C₉×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
75	#6887	C₃×C₁₃	1	3	yes	complemented
76	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic, complemented
77	C₃²×C₁₃	—	3	1	no	—
78	C₃²×C₁₃	—	3	2	no	—
79	C₃²×C₁₃	—	3	3	no	—
80	C₃²×C₁₃	—	3	3	no	—
81	C₃²×C₁₃	—	3	6	no	—
82	C₃²×C₁₃	#737	1	3	yes	—
83	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
84	C₉×C₁₃	—	3	1	no	—
85	C₉×C₁₃	—	3	2	no	—
86	C₉×C₁₃	—	3	1	no	—
87	C₉×C₁₃	—	3	1	no	—
88	C₉×C₁₃	—	3	2	no	—
89	C₉×C₁₃	—	3	2	no	—
90	C₉×C₁₃	—	3	6	no	—
91	C₉×C₁₃	—	3	6	no	—
92	C₉×C₁₃	—	3	12	no	—
93	C₉×C₁₃	#737	1	3	yes	—
94	C₉×C₁₃	#737	1	6	yes	—
95	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
96	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
97	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
98	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
99	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
100	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
101	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
102	C₉⋊C₉	C₃²×C₁₃	1	12	yes	—
103	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
104	C₉⋊C₉	C₃²×C₁₃	1	12	yes	—
105	C₉⋊C₉	C₃²×C₁₃	1	12	yes	—
106	C₉⋊C₉	C₃²×C₁₃	1	12	yes	—
107	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
108	C₉⋊C₉	C₃²×C₁₃	1	6	yes	—
109	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
110	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
111	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
112	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
113	C₃²⋊C₉	C₃²×C₁₃	1	3	yes	—
114	C₃²⋊C₉	C₃²×C₁₃	1	4	yes	—
115	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
116	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
117	C₉²	C₃²×C₁₃	1	1	yes	characteristic
118	C₉²	C₃²×C₁₃	1	2	yes	—
119	C₉²	C₃²×C₁₃	1	1	yes	characteristic
120	C₉²	C₃²×C₁₃	1	2	yes	—
121	C₉²	C₃²×C₁₃	1	1	yes	characteristic
122	C₉²	C₃²×C₁₃	1	2	yes	—
123	C₉²	C₃²×C₁₃	1	6	yes	—
124	C₃×C₁₃	—	3	3	no	—
125	C₃×C₁₃	—	9	3	no	—
126	C₃×C₁₃	C₃×#737	1	1	yes	characteristic
127	C₃×C₁₃	C₃×#737	1	1	yes	characteristic
128	C₃×C₁₃	C₃×#737	1	2	yes	—
129	C₃³	C₃³×C₁₃	1	3	yes	—
130	C₃³	C₃³×C₁₃	1	1	yes	characteristic
131	3₋¹⁺²	—	3	6	no	—
132	3₋¹⁺²	—	3	18	no	—
133	H(3,𝔽₃)	—	3	3	no	—
134	C₃×C₉	—	3	3	no	—
135	C₃×C₉	—	3	3	no	—
136	C₃×C₉	—	3	9	no	—
137	C₃×C₉	—	3	6	no	—
138	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
139	C₃×C₉	C₃³×C₁₃	1	2	yes	—
140	C₃×C₉	C₃³×C₁₃	1	2	yes	—
141	C₃×C₉	C₃³×C₁₃	1	2	yes	—
142	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
143	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
144	C₃×C₉	C₃³×C₁₃	1	12	yes	—
145	C₃×C₉	C₃³×C₁₃	1	6	yes	—
146	C₃×C₉	C₃³×C₁₃	1	6	yes	—
147	C₃×C₉	C₃³×C₁₃	1	2	yes	—
148	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
149	C₁₃	#10624877	1	1	yes	characteristic, direct product factor, Sylow
150	C₃²	—	3	1	no	—
151	C₃²	—	3	2	no	—
152	C₃²	—	3	3	no	—
153	C₃²	—	3	3	no	—
154	C₃²	—	3	6	no	—
155	C₃²	C₁₃×#737	1	3	yes	—
156	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
157	C₉	—	3	1	no	—
158	C₉	—	3	2	no	—
159	C₉	—	3	1	no	—
160	C₉	—	3	1	no	—
161	C₉	—	3	2	no	—
162	C₉	—	3	2	no	—
163	C₉	—	3	6	no	—
164	C₉	—	3	6	no	—
165	C₉	—	3	12	no	—
166	C₉	C₁₃×#737	1	3	yes	—
167	C₉	C₁₃×#737	1	6	yes	—
168	C₃	—	3	3	no	—
169	C₃	—	9	3	no	—
170	C₃	C₃×C₁₃×#737	1	1	yes	characteristic
171	C₃	C₃×C₁₃×#737	1	1	yes	characteristic
172	C₃	C₃×C₁₃×#737	1	2	yes	—

	subgroup	G/H
center	C₃×C₉×C₁₃	C₃³
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
socle	C₃²×C₁₃	C₃⁴
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#6899	C₃	semidirect
2. C₁₃×#6898	C₃	semidirect
3. C₁₃×#6897	C₃	semidirect
4. C₁₃×#6896	C₃	semidirect
5. C₁₃×#6895	C₃	semidirect
6. C₁₃×#6894	C₃	semidirect
9. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
10. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
12. C₁₃×#6887	C₃	semidirect
13. C₃×C₉²×C₁₃	C₃	semidirect
43. #10624877	C₁₃	direct (N × H)
64. #6899	C₃×C₁₃	semidirect
65. #6898	C₃×C₁₃	semidirect
66. #6897	C₃×C₁₃	semidirect
67. #6896	C₃×C₁₃	semidirect
68. #6895	C₃×C₁₃	semidirect
69. #6894	C₃×C₁₃	semidirect
72. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
73. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
75. #6887	C₃×C₁₃	semidirect
76. C₃×C₉²	C₃×C₁₃	semidirect
149. C₁₃	#10624877	direct (N × H)

Subgroups — C13×#10624877 #23745028

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624877 #23745028