Subgroups — C₁₃×#10624908 #23745059

Order 9477.

618 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6900	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#6899	C₃	1	2	yes	maximal, complemented
3	C₁₃×#6899	C₃	1	2	yes	maximal, complemented
4	C₁₃×#6899	C₃	1	2	yes	maximal, complemented
5	C₁₃×#6899	C₃	1	2	yes	maximal, complemented
6	C₁₃×#6898	C₃	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#6898	C₃	1	2	yes	maximal, complemented
8	C₁₃×#6897	C₃	1	2	yes	maximal, complemented
9	C₁₃×#6897	C₃	1	2	yes	maximal, complemented
10	C₁₃×#6897	C₃	1	2	yes	maximal, complemented
11	C₁₃×#6896	C₃	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#6896	C₃	1	2	yes	maximal, complemented
13	C₁₃×#6896	C₃	1	2	yes	maximal, complemented
14	C₁₃×#6896	C₃	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#6895	C₃	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#6894	C₃	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#6894	C₃	1	2	yes	maximal, complemented
18	C₁₃×#6893	C₃	1	1	yes	maximal, characteristic
19	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
20	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	2	yes	maximal
21	C₉×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
22	C₉×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
23	C₉×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
24	C₁₃×#6887	C₃	1	2	yes	maximal, complemented
25	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
26	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
27	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
28	C₃×C₁₃×3₋¹⁺²	C₃²	1	2	yes	—
29	C₃×C₁₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
30	C₃×C₁₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
31	C₃×C₁₃×3₋¹⁺²	C₃²	1	1	yes	characteristic
32	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
33	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
34	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
35	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
36	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
37	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
38	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
39	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
40	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
41	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
42	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
43	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
44	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
45	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
46	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
47	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
48	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
49	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
50	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
51	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
52	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
53	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
54	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
55	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
56	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
57	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
58	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
59	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
60	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
61	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
62	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
63	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
64	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
65	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
66	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
67	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
68	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
69	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
70	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
71	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
72	C₁₃×C₉⋊C₉	C₃²	1	2	yes	—
73	C₁₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
74	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
75	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
76	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
77	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
78	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
79	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
80	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
81	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
82	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
83	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
84	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
85	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
86	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
87	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
88	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
89	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
90	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
91	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
92	C₉²×C₁₃	C₃²	1	1	yes	characteristic
93	C₉²×C₁₃	C₃²	1	2	yes	—
94	C₉²×C₁₃	C₃²	1	2	yes	—
95	C₉²×C₁₃	C₃²	1	2	yes	—
96	C₉²×C₁₃	C₃²	1	2	yes	—
97	C₉²×C₁₃	C₃²	1	1	yes	characteristic
98	C₉²×C₁₃	C₃²	1	2	yes	—
99	#10624908	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₃³×C₁₃	C₃³	1	2	yes	—
101	C₃³×C₁₃	C₃³	1	1	yes	characteristic
102	C₃³×C₁₃	C₃³	1	1	yes	characteristic
103	C₁₃×3₋¹⁺²	—	3	6	no	—
104	C₁₃×3₋¹⁺²	—	3	6	no	—
105	C₁₃×3₋¹⁺²	—	3	6	no	—
106	C₁₃×3₋¹⁺²	—	9	2	no	—
107	C₁₃×3₋¹⁺²	—	9	1	no	—
108	C₁₃×3₋¹⁺²	—	9	1	no	—
109	C₁₃×3₋¹⁺²	—	9	1	no	—
110	C₁₃×H(3,𝔽₃)	—	9	1	no	—
111	C₃×C₉×C₁₃	—	3	6	no	—
112	C₃×C₉×C₁₃	—	9	1	no	—
113	C₃×C₉×C₁₃	—	9	1	no	—
114	C₃×C₉×C₁₃	C₃³	1	2	yes	—
115	C₃×C₉×C₁₃	C₃³	1	2	yes	—
116	C₃×C₉×C₁₃	C₃³	1	2	yes	—
117	C₃×C₉×C₁₃	C₃³	1	2	yes	—
118	C₃×C₉×C₁₃	C₃³	1	2	yes	—
119	C₃×C₉×C₁₃	C₃³	1	2	yes	—
120	C₃×C₉×C₁₃	C₃³	1	2	yes	—
121	C₃×C₉×C₁₃	C₃³	1	2	yes	—
122	C₃×C₉×C₁₃	C₃³	1	2	yes	—
123	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
124	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
125	C₃×C₉×C₁₃	C₃³	1	2	yes	—
126	C₃×C₉×C₁₃	C₃³	1	2	yes	—
127	C₃×C₉×C₁₃	C₃³	1	2	yes	—
128	C₃×C₉×C₁₃	C₃³	1	2	yes	—
129	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
130	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
131	C₃×C₉×C₁₃	C₃³	1	2	yes	—
132	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
133	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
134	C₃×C₉×C₁₃	C₃³	1	2	yes	—
135	#6900	C₃×C₁₃	1	1	yes	characteristic, complemented
136	#6899	C₃×C₁₃	1	2	yes	complemented
137	#6899	C₃×C₁₃	1	2	yes	complemented
138	#6899	C₃×C₁₃	1	2	yes	complemented
139	#6899	C₃×C₁₃	1	2	yes	complemented
140	#6898	C₃×C₁₃	1	1	yes	characteristic, complemented
141	#6898	C₃×C₁₃	1	2	yes	complemented
142	#6897	C₃×C₁₃	1	2	yes	complemented
143	#6897	C₃×C₁₃	1	2	yes	complemented
144	#6897	C₃×C₁₃	1	2	yes	complemented
145	#6896	C₃×C₁₃	1	1	yes	characteristic, complemented
146	#6896	C₃×C₁₃	1	2	yes	complemented
147	#6896	C₃×C₁₃	1	2	yes	complemented
148	#6896	C₃×C₁₃	1	1	yes	characteristic, complemented
149	#6895	C₃×C₁₃	1	1	yes	characteristic, complemented
150	#6894	C₃×C₁₃	1	1	yes	characteristic, complemented
151	#6894	C₃×C₁₃	1	2	yes	complemented
152	#6893	C₃×C₁₃	1	1	yes	characteristic
153	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
154	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	2	yes	—
155	C₉×3₋¹⁺²	C₃×C₁₃	1	2	yes	complemented
156	C₉×3₋¹⁺²	C₃×C₁₃	1	2	yes	complemented
157	C₉×3₋¹⁺²	C₃×C₁₃	1	2	yes	complemented
158	#6887	C₃×C₁₃	1	2	yes	complemented
159	C₃²×C₁₃	—	3	2	no	—
160	C₃²×C₁₃	—	3	2	no	—
161	C₃²×C₁₃	—	3	2	no	—
162	C₃²×C₁₃	—	3	2	no	—
163	C₃²×C₁₃	—	3	1	no	—
164	C₃²×C₁₃	—	3	1	no	—
165	C₃²×C₁₃	—	3	2	no	—
166	C₃²×C₁₃	—	3	1	no	—
167	C₃²×C₁₃	—	3	2	no	—
168	C₃²×C₁₃	—	3	1	no	—
169	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
170	C₉×C₁₃	—	3	2	no	—
171	C₉×C₁₃	—	3	2	no	—
172	C₉×C₁₃	—	3	2	no	—
173	C₉×C₁₃	—	3	2	no	—
174	C₉×C₁₃	—	3	2	no	—
175	C₉×C₁₃	—	3	2	no	—
176	C₉×C₁₃	—	3	2	no	—
177	C₉×C₁₃	—	3	2	no	—
178	C₉×C₁₃	—	3	2	no	—
179	C₉×C₁₃	—	3	2	no	—
180	C₉×C₁₃	—	3	1	no	—
181	C₉×C₁₃	—	3	1	no	—
182	C₉×C₁₃	—	3	1	no	—
183	C₉×C₁₃	—	3	2	no	—
184	C₉×C₁₃	—	3	2	no	—
185	C₉×C₁₃	—	3	1	no	—
186	C₉×C₁₃	—	3	1	no	—
187	C₉×C₁₃	—	3	2	no	—
188	C₉×C₁₃	—	3	2	no	—
189	C₉×C₁₃	—	3	1	no	—
190	C₉×C₁₃	#737	1	6	yes	—
191	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
192	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
193	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
194	C₃×3₋¹⁺²	C₃²×C₁₃	1	2	yes	—
195	C₃×3₋¹⁺²	C₃²×C₁₃	1	1	yes	characteristic
196	C₃×3₋¹⁺²	C₃²×C₁₃	1	1	yes	characteristic
197	C₃×3₋¹⁺²	C₃²×C₁₃	1	1	yes	characteristic
198	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
199	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
200	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
201	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
202	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
203	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
204	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
205	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
206	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
207	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
208	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
209	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
210	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
211	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
212	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
213	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
214	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
215	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
216	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
217	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
218	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
219	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
220	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
221	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
222	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
223	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
224	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
225	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
226	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
227	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
228	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
229	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
230	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
231	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
232	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
233	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
234	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
235	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
236	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
237	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
238	C₉⋊C₉	C₃²×C₁₃	1	2	yes	—
239	C₉⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
240	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
241	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
242	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
243	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
244	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
245	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
246	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
247	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
248	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
249	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
250	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
251	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
252	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
253	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
254	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
255	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
256	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
257	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
258	C₉²	C₃²×C₁₃	1	1	yes	characteristic
259	C₉²	C₃²×C₁₃	1	2	yes	—
260	C₉²	C₃²×C₁₃	1	2	yes	—
261	C₉²	C₃²×C₁₃	1	2	yes	—
262	C₉²	C₃²×C₁₃	1	2	yes	—
263	C₉²	C₃²×C₁₃	1	1	yes	characteristic
264	C₉²	C₃²×C₁₃	1	2	yes	—
265	C₃×C₁₃	—	9	2	no	—
266	C₃×C₁₃	—	9	1	no	—
267	C₃×C₁₃	—	9	1	no	—
268	C₃×C₁₃	C₃×#737	1	2	yes	—
269	C₃×C₁₃	3₋¹⁺⁴	1	1	yes	characteristic
270	C₃×C₁₃	3₋¹⁺⁴	1	1	yes	characteristic
271	C₃³	C₃³×C₁₃	1	2	yes	—
272	C₃³	C₃³×C₁₃	1	1	yes	characteristic
273	C₃³	C₃³×C₁₃	1	1	yes	characteristic
274	3₋¹⁺²	—	3	6	no	—
275	3₋¹⁺²	—	3	6	no	—
276	3₋¹⁺²	—	3	6	no	—
277	3₋¹⁺²	—	9	2	no	—
278	3₋¹⁺²	—	9	1	no	—
279	3₋¹⁺²	—	9	1	no	—
280	3₋¹⁺²	—	9	1	no	—
281	H(3,𝔽₃)	—	9	1	no	—
282	C₃×C₉	—	3	6	no	—
283	C₃×C₉	—	9	1	no	—
284	C₃×C₉	—	9	1	no	—
285	C₃×C₉	C₃³×C₁₃	1	2	yes	—
286	C₃×C₉	C₃³×C₁₃	1	2	yes	—
287	C₃×C₉	C₃³×C₁₃	1	2	yes	—
288	C₃×C₉	C₃³×C₁₃	1	2	yes	—
289	C₃×C₉	C₃³×C₁₃	1	2	yes	—
290	C₃×C₉	C₃³×C₁₃	1	2	yes	—
291	C₃×C₉	C₃³×C₁₃	1	2	yes	—
292	C₃×C₉	C₃³×C₁₃	1	2	yes	—
293	C₃×C₉	C₃³×C₁₃	1	2	yes	—
294	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
295	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
296	C₃×C₉	C₃³×C₁₃	1	2	yes	—
297	C₃×C₉	C₃³×C₁₃	1	2	yes	—
298	C₃×C₉	C₃³×C₁₃	1	2	yes	—
299	C₃×C₉	C₃³×C₁₃	1	2	yes	—
300	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
301	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
302	C₃×C₉	C₃³×C₁₃	1	2	yes	—
303	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
304	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
305	C₃×C₉	C₃³×C₁₃	1	2	yes	—
306	C₁₃	#10624908	1	1	yes	characteristic, direct product factor, Sylow
307	C₃²	—	3	2	no	—
308	C₃²	—	3	2	no	—
309	C₃²	—	3	2	no	—
310	C₃²	—	3	2	no	—
311	C₃²	—	3	1	no	—
312	C₃²	—	3	1	no	—
313	C₃²	—	3	2	no	—
314	C₃²	—	3	1	no	—
315	C₃²	—	3	2	no	—
316	C₃²	—	3	1	no	—
317	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
318	C₉	—	3	2	no	—
319	C₉	—	3	2	no	—
320	C₉	—	3	2	no	—
321	C₉	—	3	2	no	—
322	C₉	—	3	2	no	—
323	C₉	—	3	2	no	—
324	C₉	—	3	2	no	—
325	C₉	—	3	2	no	—
326	C₉	—	3	1	no	—
327	C₉	—	3	2	no	—
328	C₉	—	3	2	no	—
329	C₉	—	3	1	no	—
330	C₉	—	3	1	no	—
331	C₉	—	3	2	no	—
332	C₉	—	3	2	no	—
333	C₉	—	3	1	no	—
334	C₉	—	3	1	no	—
335	C₉	—	3	2	no	—
336	C₉	—	3	2	no	—
337	C₉	—	3	1	no	—
338	C₉	C₁₃×#737	1	6	yes	—
339	C₃	—	9	2	no	—
340	C₃	—	9	1	no	—
341	C₃	—	9	1	no	—
342	C₃	C₃×C₁₃×#737	1	2	yes	—
343	C₃	C₁₃×3₋¹⁺⁴	1	1	yes	characteristic
344	C₃	C₁₃×3₋¹⁺⁴	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#6900	C₃	semidirect
2. C₁₃×#6899	C₃	semidirect
3. C₁₃×#6899	C₃	semidirect
4. C₁₃×#6899	C₃	semidirect
5. C₁₃×#6899	C₃	semidirect
6. C₁₃×#6898	C₃	semidirect
7. C₁₃×#6898	C₃	semidirect
8. C₁₃×#6897	C₃	semidirect
9. C₁₃×#6897	C₃	semidirect
10. C₁₃×#6897	C₃	semidirect
11. C₁₃×#6896	C₃	semidirect
12. C₁₃×#6896	C₃	semidirect
13. C₁₃×#6896	C₃	semidirect
14. C₁₃×#6896	C₃	semidirect
15. C₁₃×#6895	C₃	semidirect
16. C₁₃×#6894	C₃	semidirect
17. C₁₃×#6894	C₃	semidirect
21. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
22. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
23. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
24. C₁₃×#6887	C₃	semidirect
99. #10624908	C₁₃	direct (N × H)
135. #6900	C₃×C₁₃	semidirect
136. #6899	C₃×C₁₃	semidirect
137. #6899	C₃×C₁₃	semidirect
138. #6899	C₃×C₁₃	semidirect
139. #6899	C₃×C₁₃	semidirect
140. #6898	C₃×C₁₃	semidirect
141. #6898	C₃×C₁₃	semidirect
142. #6897	C₃×C₁₃	semidirect
143. #6897	C₃×C₁₃	semidirect
144. #6897	C₃×C₁₃	semidirect
145. #6896	C₃×C₁₃	semidirect
146. #6896	C₃×C₁₃	semidirect
147. #6896	C₃×C₁₃	semidirect
148. #6896	C₃×C₁₃	semidirect
149. #6895	C₃×C₁₃	semidirect
150. #6894	C₃×C₁₃	semidirect
151. #6894	C₃×C₁₃	semidirect
155. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
156. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
157. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
158. #6887	C₃×C₁₃	semidirect
306. C₁₃	#10624908	direct (N × H)

Subgroups — C13×#10624908 #23745059

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624908 #23745059