Subgroups — C₁₃×#9247 #15695586

Order 3328.

544 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic
2	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1486	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1292	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	C₄	1	2	yes	—
9	C₂²×C₁₃×M₁₆	—	2	1	no	—
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#461	—	2	1	no	—
13	C₁₃×#461	—	2	1	no	—
14	C₁₃×#461	—	2	1	no	—
15	C₁₃×#461	—	2	1	no	—
16	C₁₃×#436	—	2	1	no	—
17	C₁₃×#435	—	2	2	no	—
18	C₈×D₄×C₁₃	—	2	1	no	—
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	C₁₃×#423	C₂²	1	1	yes	characteristic
21	C₁₃×#423	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₄	1	2	yes	—
24	C₁₃×#407	—	2	1	no	—
25	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₁₃×#343	—	2	1	no	—
27	C₁₃×#343	—	2	1	no	—
28	C₁₃×#333	—	2	2	no	—
29	C₁₃×D₄⋊C₈	—	2	1	no	—
30	C₁₃×D₄⋊C₈	—	2	1	no	—
31	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	—	2	1	no	—
34	C₂×C₁₃×SD₁₆	—	2	2	no	—
35	C₂×C₁₃×SD₁₆	—	2	2	no	—
36	C₂×C₁₃×SD₁₆	—	4	4	no	—
37	C₂×C₁₃×M₁₆	—	2	2	no	—
38	C₂×C₁₃×M₁₆	—	2	1	no	—
39	C₂×C₁₃×M₁₆	—	2	1	no	—
40	C₂×C₁₃×M₁₆	—	4	2	no	—
41	C₂×C₁₃×M₁₆	—	4	2	no	—
42	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
43	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	C₁₃×C₄⋊Q₈	—	2	1	no	—
49	C₁₃×C₄⋊Q₈	—	2	1	no	—
50	C₄×D₄×C₁₃	—	2	1	no	—
51	C₄×D₄×C₁₃	—	2	1	no	—
52	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
53	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
54	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
55	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×C₄⋊C₈	—	2	1	no	—
62	C₁₃×C₄⋊C₈	—	2	1	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₁₃×C₄⋊C₈	—	2	1	no	—
66	C₁₃×C₄⋊C₈	—	2	1	no	—
67	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
68	C₁₃×#103	—	2	2	no	—
69	C₁₃×#103	—	2	2	no	—
70	C₁₃×C₂²⋊C₈	—	2	2	no	—
71	C₁₃×C₂²⋊C₈	—	2	2	no	—
72	C₁₃×C₂²⋊C₈	—	2	1	no	—
73	C₁₃×#97	—	2	1	no	—
74	C₄×C₈×C₁₃	—	2	1	no	—
75	C₄×C₈×C₁₃	—	2	1	no	—
76	#9247	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	1	no	—
78	C₂×Q₈×C₁₃	—	2	2	no	—
79	C₂×Q₈×C₁₃	—	2	2	no	—
80	C₂×Q₈×C₁₃	—	4	2	no	—
81	C₂×Q₈×C₁₃	—	4	2	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	1	no	—
84	C₂×D₄×C₁₃	—	4	1	no	—
85	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	4	1	no	—
94	C₂²×C₄×C₁₃	—	4	1	no	—
95	C₂²×C₄×C₁₃	—	4	1	no	—
96	C₂²×C₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
100	C₁₃×SD₁₆	—	4	4	no	—
101	C₁₃×SD₁₆	—	4	4	no	—
102	C₁₃×M₁₆	—	2	1	no	—
103	C₁₃×M₁₆	—	2	1	no	—
104	C₁₃×M₁₆	—	2	1	no	—
105	C₁₃×M₁₆	—	4	4	no	—
106	C₁₃×M₁₆	—	4	1	no	—
107	C₁₃×M₁₆	—	4	1	no	—
108	C₁₃×M₁₆	—	4	1	no	—
109	C₁₃×M₁₆	—	4	1	no	—
110	C₁₃×M₁₆	SD₁₆	1	2	yes	complemented
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	4	4	no	—
116	C₂×C₈×C₁₃	—	4	2	no	—
117	C₂×C₈×C₁₃	—	4	1	no	—
118	C₂×C₈×C₁₃	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
125	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
126	C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₁₃×C₂²⋊C₄	—	2	1	no	—
128	C₁₃×C₂²⋊C₄	—	2	1	no	—
129	C₁₃×C₂²⋊C₄	—	2	1	no	—
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	#41	1	1	yes	characteristic
134	C₂×#461	C₂×C₁₃	1	1	yes	characteristic
135	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
136	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#1548	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#1486	C₂×C₁₃	1	1	yes	characteristic
139	#1292	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1283	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂³×C₁₃	—	2	1	no	—
142	C₂³×C₁₃	—	2	1	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	—	4	1	no	—
145	C₂³×C₁₃	—	4	1	no	—
146	C₂³×C₁₃	—	8	1	no	—
147	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
148	Q₈×C₁₃	—	4	2	no	—
149	Q₈×C₁₃	—	4	2	no	—
150	Q₈×C₁₃	—	8	2	no	—
151	D₄×C₁₃	—	2	1	no	—
152	D₄×C₁₃	—	2	1	no	—
153	D₄×C₁₃	—	2	1	no	—
154	D₄×C₁₃	—	4	2	no	—
155	D₄×C₁₃	#100	1	2	yes	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	4	1	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	4	1	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	8	2	no	—
173	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
176	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
180	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
181	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
183	C₈×C₁₃	—	2	2	no	—
184	C₈×C₁₃	—	4	2	no	—
185	C₈×C₁₃	—	4	2	no	—
186	C₈×C₁₃	—	4	1	no	—
187	C₈×C₁₃	—	8	1	no	—
188	C₈×C₁₃	—	8	1	no	—
189	C₂²×SD₁₆	C₄×C₁₃	1	2	yes	—
190	C₂²×M₁₆	—	2	1	no	—
191	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
193	#461	—	2	1	no	—
194	#461	—	2	1	no	—
195	#461	—	2	1	no	—
196	#461	—	2	1	no	—
197	#436	—	2	1	no	—
198	#435	—	2	2	no	—
199	C₈×D₄	—	2	1	no	—
200	#431	C₂²×C₁₃	1	1	yes	characteristic
201	#423	C₂²×C₁₃	1	1	yes	characteristic
202	#423	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#103	C₄×C₁₃	1	2	yes	—
205	#407	—	2	1	no	—
206	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
207	#343	—	2	1	no	—
208	#343	—	2	1	no	—
209	#333	—	2	2	no	—
210	D₄⋊C₈	—	2	1	no	—
211	D₄⋊C₈	—	2	1	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	2	1	no	—
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	—	4	1	no	—
216	C₂²×C₁₃	—	4	1	no	—
217	C₂²×C₁₃	—	4	1	no	—
218	C₂²×C₁₃	—	4	1	no	—
219	C₂²×C₁₃	—	4	1	no	—
220	C₂²×C₁₃	—	8	2	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	#386	1	1	yes	characteristic
223	C₂²×C₁₃	C₄×SD₁₆	1	1	yes	characteristic
224	C₂²×C₁₃	#440	1	1	yes	characteristic
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	4	1	no	—
229	C₄×C₁₃	—	4	1	no	—
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	C₂×#100	1	1	yes	characteristic
232	C₄×C₁₃	#413	1	1	yes	characteristic
233	C₄×C₁₃	#450	1	1	yes	characteristic
234	C₄×C₁₃	#452	1	1	yes	characteristic
235	C₄×C₁₃	#461	1	1	yes	characteristic
236	C₄×C₁₃	#463	1	1	yes	characteristic
237	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
238	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₂³×C₄	—	2	1	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	4	4	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	4	2	no	—
247	C₂×M₁₆	—	4	2	no	—
248	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
249	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
259	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
260	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
261	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	2	1	no	—
279	#97	—	2	1	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₂×C₁₃	—	2	1	no	—
283	C₂×C₁₃	—	2	1	no	—
284	C₂×C₁₃	—	4	2	no	—
285	C₂×C₁₃	—	8	1	no	—
286	C₂×C₁₃	#1877	1	1	yes	characteristic
287	C₂×C₁₃	#1900	1	1	yes	characteristic
288	C₂×C₁₃	#1902	1	1	yes	characteristic
289	C₂⁴	—	2	1	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
312	SD₁₆	—	4	4	no	—
313	SD₁₆	—	4	4	no	—
314	M₁₆	—	2	1	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	4	4	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	4	1	no	—
320	M₁₆	—	4	1	no	—
321	M₁₆	—	4	1	no	—
322	M₁₆	C₁₃×SD₁₆	1	2	yes	complemented
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	4	4	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
337	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₄²	C₁₃×#41	1	1	yes	characteristic
346	C₁₃	#9247	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	8	1	no	—
353	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	8	2	no	—
357	D₄	—	2	1	no	—
358	D₄	—	2	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	4	2	no	—
361	D₄	C₁₃×#100	1	2	yes	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
380	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
382	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
383	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
384	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
386	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
387	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	8	1	no	—
394	C₈	—	8	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	C₁₃×#386	1	1	yes	characteristic
406	C₂²	C₄×C₁₃×SD₁₆	1	1	yes	characteristic
407	C₂²	C₁₃×#440	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	8	2	no	—
414	C₄	C₂×C₁₃×#100	1	1	yes	characteristic
415	C₄	C₁₃×#413	1	1	yes	characteristic
416	C₄	C₁₃×#450	1	1	yes	characteristic
417	C₄	C₁₃×#452	1	1	yes	characteristic
418	C₄	C₁₃×#461	1	1	yes	characteristic
419	C₄	C₁₃×#463	1	1	yes	characteristic
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	4	2	no	—
423	C₂	—	8	1	no	—
424	C₂	C₁₃×#1877	1	1	yes	characteristic
425	C₂	C₁₃×#1900	1	1	yes	characteristic
426	C₂	C₁₃×#1902	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1997	C₂	semidirect
4. C₁₃×#1548	C₂	semidirect
6. C₁₃×#1292	C₂	semidirect
7. C₁₃×#1283	C₂	semidirect
76. #9247	C₁₃	direct (N × H)
110. C₁₃×M₁₆	SD₁₆	semidirect
136. #1997	C₂×C₁₃	semidirect
137. #1548	C₂×C₁₃	semidirect
139. #1292	C₂×C₁₃	semidirect
140. #1283	C₂×C₁₃	semidirect
322. M₁₆	C₁₃×SD₁₆	semidirect
346. C₁₃	#9247	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#461	2
D₄×C₁₃×M₁₆	2
C₁₃×#1997	2
C₁₃×#1548	2
C₁₃×#1486	2
C₁₃×#1292	2
C₁₃×#1283	2
#9247	13

Subgroups — C13×#9247 #15695586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9247 #15695586