Subgroups — C₁₃×#7690 #15694029

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2850	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1272	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1270	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₁₃	—	2	1	no	—
7	C₂×C₁₃×#124	C₄	1	1	yes	characteristic
8	C₂×C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
9	C₂×C₁₃×#121	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
12	C₂×C₁₃×#97	—	2	1	no	—
13	C₁₃×#391	C₂²	1	1	yes	characteristic
14	C₁₃×#390	C₂²	1	1	yes	characteristic
15	C₁₃×#388	—	2	1	no	—
16	C₁₃×#388	—	2	1	no	—
17	C₁₃×#386	—	2	1	no	—
18	C₁₃×#386	—	2	1	no	—
19	C₁₃×#382	C₄	1	1	yes	characteristic
20	C₁₃×#336	—	2	1	no	—
21	C₁₃×#336	C₂²	1	2	yes	—
22	C₁₃×#336	C₂²	1	2	yes	—
23	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×D₄×C₁₃	—	2	1	no	—
25	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	—	2	4	no	—
30	C₂²×C₈×C₁₃	—	2	2	no	—
31	C₂²×C₈×C₁₃	—	2	2	no	—
32	C₂²×C₈×C₁₃	—	4	2	no	—
33	C₂²×C₈×C₁₃	—	4	2	no	—
34	C₁₃×#124	—	4	2	no	—
35	C₁₃×C₂²⋊Q₈	—	4	2	no	—
36	C₁₃×#121	—	4	2	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
38	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
41	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
42	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
43	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
44	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
45	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
46	C₂×C₄²×C₁₃	—	4	2	no	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×C₂²⋊C₈	—	2	4	no	—
52	C₁₃×#97	—	4	2	no	—
53	C₁₃×#95	—	2	1	no	—
54	C₁₃×#95	—	2	1	no	—
55	C₁₃×#95	—	2	1	no	—
56	C₁₃×#95	—	2	1	no	—
57	#7690	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂⁴×C₁₃	—	2	1	no	—
59	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×Q₈×C₁₃	—	2	2	no	—
61	C₂×Q₈×C₁₃	—	4	1	no	—
62	C₂×Q₈×C₁₃	—	4	1	no	—
63	C₂×D₄×C₁₃	—	2	2	no	—
64	C₂×D₄×C₁₃	—	4	1	no	—
65	C₂×D₄×C₁₃	—	4	1	no	—
66	C₂×D₄×C₁₃	—	4	2	no	—
67	C₂×D₄×C₁₃	—	4	2	no	—
68	C₂×D₄×C₁₃	—	4	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	1	no	—
72	C₂²×C₄×C₁₃	—	2	1	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	1	no	—
78	C₂²×C₄×C₁₃	—	2	1	no	—
79	C₂²×C₄×C₁₃	—	2	1	no	—
80	C₂²×C₄×C₁₃	—	4	1	no	—
81	C₂²×C₄×C₁₃	—	4	1	no	—
82	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₁₃	—	2	4	no	—
89	C₂×C₈×C₁₃	—	2	4	no	—
90	C₂×C₈×C₁₃	—	4	2	no	—
91	C₂×C₈×C₁₃	—	4	8	no	—
92	C₂×C₈×C₁₃	—	4	2	no	—
93	C₂×C₈×C₁₃	—	4	2	no	—
94	C₂×C₈×C₁₃	—	4	2	no	—
95	C₁₃×C₄⋊C₄	—	4	1	no	—
96	C₁₃×C₄⋊C₄	—	4	1	no	—
97	C₁₃×C₄⋊C₄	—	4	2	no	—
98	C₁₃×C₂²⋊C₄	—	4	2	no	—
99	C₁₃×C₂²⋊C₄	—	4	2	no	—
100	C₁₃×C₂²⋊C₄	—	4	2	no	—
101	C₁₃×C₂²⋊C₄	—	4	2	no	—
102	C₁₃×C₂²⋊C₄	—	4	2	no	—
103	C₁₃×C₂²⋊C₄	—	4	1	no	—
104	C₁₃×C₂²⋊C₄	—	4	1	no	—
105	C₄²×C₁₃	—	2	2	no	—
106	C₄²×C₁₃	—	2	2	no	—
107	C₄²×C₁₃	—	4	1	no	—
108	C₄²×C₁₃	—	4	1	no	—
109	#2850	C₂×C₁₃	1	1	yes	characteristic
110	#1749	C₂×C₁₃	1	1	yes	characteristic, complemented
111	C₂×#336	C₂×C₁₃	1	1	yes	characteristic, complemented
112	#1272	C₂×C₁₃	1	2	yes	complemented
113	#1270	C₂×C₁₃	1	2	yes	complemented
114	C₂³×C₁₃	—	2	1	no	—
115	C₂³×C₁₃	—	2	1	no	—
116	C₂³×C₁₃	—	2	1	no	—
117	C₂³×C₁₃	—	2	1	no	—
118	C₂³×C₁₃	—	4	1	no	—
119	C₂³×C₁₃	—	4	1	no	—
120	C₂³×C₁₃	—	4	1	no	—
121	C₂³×C₁₃	—	4	1	no	—
122	C₂³×C₁₃	—	4	1	no	—
123	C₂³×C₁₃	—	4	1	no	—
124	C₂³×C₁₃	—	4	1	no	—
125	C₂³×C₁₃	#100	1	2	yes	—
126	C₂³×C₁₃	#104	1	2	yes	—
127	C₂³×C₁₃	#104	1	2	yes	—
128	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	Q₈×C₁₃	—	8	2	no	—
130	D₄×C₁₃	—	8	2	no	—
131	D₄×C₁₃	—	8	4	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	2	4	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	4	4	no	—
149	C₂×C₄×C₁₃	—	4	4	no	—
150	C₂×C₄×C₁₃	—	4	1	no	—
151	C₂×C₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	4	1	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	#99	1	2	yes	—
160	C₂×C₄×C₁₃	#131	1	2	yes	—
161	C₂×C₄×C₁₃	#135	1	2	yes	—
162	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
164	C₈×C₁₃	—	4	4	no	—
165	C₈×C₁₃	—	4	4	no	—
166	C₂³×C₈	—	2	1	no	—
167	C₂×#124	C₄×C₁₃	1	1	yes	characteristic
168	C₂×C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
169	C₂×#121	C₄×C₁₃	1	1	yes	characteristic
170	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×C₂²⋊C₈	—	2	1	no	—
172	C₂×#97	—	2	1	no	—
173	#391	C₂²×C₁₃	1	1	yes	characteristic
174	#390	C₂²×C₁₃	1	1	yes	characteristic
175	#388	—	2	1	no	—
176	#388	—	2	1	no	—
177	#386	—	2	1	no	—
178	#386	—	2	1	no	—
179	#382	C₄×C₁₃	1	1	yes	characteristic
180	#336	—	2	1	no	—
181	#336	C₂²×C₁₃	1	2	yes	—
182	#336	C₂²×C₁₃	1	2	yes	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	—	2	2	no	—
185	C₂²×C₁₃	—	2	2	no	—
186	C₂²×C₁₃	—	2	2	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	8	1	no	—
190	C₂²×C₁₃	—	8	1	no	—
191	C₂²×C₁₃	—	8	1	no	—
192	C₂²×C₁₃	—	8	1	no	—
193	C₂²×C₁₃	—	8	1	no	—
194	C₂²×C₁₃	—	8	1	no	—
195	C₂²×C₁₃	—	8	1	no	—
196	C₂²×C₁₃	#329	1	4	yes	—
197	C₂²×C₁₃	#408	1	1	yes	characteristic
198	C₂²×C₁₃	C₂×#99	1	1	yes	characteristic
199	C₂²×C₁₃	C₂×#100	1	1	yes	characteristic
200	C₂²×C₁₃	#416	1	1	yes	characteristic
201	C₂²×C₁₃	#417	1	1	yes	characteristic
202	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
203	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
204	C₄×C₁₃	—	2	2	no	—
205	C₄×C₁₃	—	2	2	no	—
206	C₄×C₁₃	—	2	1	no	—
207	C₄×C₁₃	—	2	2	no	—
208	C₄×C₁₃	—	2	1	no	—
209	C₄×C₁₃	—	4	1	no	—
210	C₄×C₁₃	—	4	1	no	—
211	C₄×C₁₃	—	8	1	no	—
212	C₄×C₁₃	—	8	1	no	—
213	C₄×C₁₃	—	8	1	no	—
214	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
215	C₂²×D₄	—	2	1	no	—
216	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
217	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
218	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
219	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	4	2	no	—
224	C₂²×C₈	—	4	2	no	—
225	#124	—	4	2	no	—
226	C₂²⋊Q₈	—	4	2	no	—
227	#121	—	4	2	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₂²⋊C₄	—	2	1	no	—
233	C₂×C₂²⋊C₄	—	2	1	no	—
234	C₂×C₂²⋊C₄	—	2	1	no	—
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₄²	—	4	2	no	—
238	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
240	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
242	C₂²⋊C₈	—	2	4	no	—
243	#97	—	4	2	no	—
244	#95	—	2	1	no	—
245	#95	—	2	1	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	C₂×C₁₃	—	2	4	no	—
249	C₂×C₁₃	—	16	1	no	—
250	C₂×C₁₃	#1471	1	1	yes	characteristic
251	C₂×C₁₃	#1483	1	1	yes	characteristic
252	C₂×C₁₃	#1494	1	1	yes	characteristic
253	C₂×C₁₃	#1501	1	1	yes	characteristic
254	C₂×C₁₃	#1504	1	1	yes	characteristic
255	C₂×C₁₃	C₂×#329	1	1	yes	characteristic
256	C₂×C₁₃	#1551	1	1	yes	characteristic
257	C₂⁴	—	2	1	no	—
258	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	4	1	no	—
261	C₂×Q₈	—	4	1	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	4	8	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₂²⋊C₄	—	4	2	no	—
302	C₂²⋊C₄	—	4	1	no	—
303	C₂²⋊C₄	—	4	1	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₁₃	#7690	1	1	yes	characteristic, direct product factor, Sylow
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	1	no	—
319	C₂³	—	4	1	no	—
320	C₂³	C₁₃×#100	1	2	yes	—
321	C₂³	C₁₃×#104	1	2	yes	—
322	C₂³	C₁₃×#104	1	2	yes	—
323	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
324	Q₈	—	8	2	no	—
325	D₄	—	8	2	no	—
326	D₄	—	8	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	C₁₃×#99	1	2	yes	—
355	C₂×C₄	C₁₃×#131	1	2	yes	—
356	C₂×C₄	C₁₃×#135	1	2	yes	—
357	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
358	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
359	C₈	—	4	4	no	—
360	C₈	—	4	4	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	—	8	1	no	—
372	C₂²	—	8	1	no	—
373	C₂²	—	8	1	no	—
374	C₂²	C₁₃×#329	1	4	yes	—
375	C₂²	C₁₃×#408	1	1	yes	characteristic
376	C₂²	C₂×C₁₃×#99	1	1	yes	characteristic
377	C₂²	C₂×C₁₃×#100	1	1	yes	characteristic
378	C₂²	C₁₃×#416	1	1	yes	characteristic
379	C₂²	C₁₃×#417	1	1	yes	characteristic
380	C₂²	C₂×C₁₃×#104	1	1	yes	characteristic
381	C₂²	C₂×C₁₃×#104	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	8	1	no	—
390	C₄	—	8	1	no	—
391	C₄	—	8	1	no	—
392	C₂	—	2	4	no	—
393	C₂	—	16	1	no	—
394	C₂	C₁₃×#1471	1	1	yes	characteristic
395	C₂	C₁₃×#1483	1	1	yes	characteristic
396	C₂	C₁₃×#1494	1	1	yes	characteristic
397	C₂	C₁₃×#1501	1	1	yes	characteristic
398	C₂	C₁₃×#1504	1	1	yes	characteristic
399	C₂	C₂×C₁₃×#329	1	1	yes	characteristic
400	C₂	C₁₃×#1551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#121	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1749	C₂	semidirect
3. C₂×C₁₃×#336	C₂	semidirect
4. C₁₃×#1272	C₂	semidirect
5. C₁₃×#1270	C₂	semidirect
57. #7690	C₁₃	direct (N × H)
110. #1749	C₂×C₁₃	semidirect
111. C₂×#336	C₂×C₁₃	semidirect
112. #1272	C₂×C₁₃	semidirect
113. #1270	C₂×C₁₃	semidirect
308. C₁₃	#7690	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#2850	2
C₁₃×#1749	2
C₂×C₁₃×#336	2
C₁₃×#1272	2
C₁₃×#1270	2
#7690	13

Subgroups — C13×#7690 #15694029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#7690 #15694029