Subgroups — C₁₃×#9680 #15696019

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2856	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#327	C₂	1	4	yes	maximal, complemented
4	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#127	C₄	1	1	yes	characteristic, complemented
6	C₂×C₁₃×#121	—	2	1	no	—
7	C₂×C₁₃×#121	—	2	1	no	—
8	C₂×C₁₃×#121	C₂²	1	2	yes	—
9	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₃	—	2	1	no	—
13	C₁₃×#390	—	2	1	no	—
14	C₁₃×#390	—	2	1	no	—
15	C₁₃×#390	C₄	1	2	yes	complemented
16	C₁₃×#384	C₄	1	1	yes	characteristic, complemented
17	C₂×C₁₃×#95	—	2	1	no	—
18	C₂×C₁₃×#95	C₂²	1	2	yes	—
19	C₁₃×#336	—	2	1	no	—
20	C₁₃×#327	—	2	8	no	—
21	C₂²×D₄×C₁₃	—	2	2	no	—
22	C₂²×D₄×C₁₃	—	2	1	no	—
23	C₂²×D₄×C₁₃	—	2	1	no	—
24	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₃	—	2	2	no	—
26	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	—	2	2	no	—
30	C₁₃×#127	—	4	2	no	—
31	C₁₃×#121	—	2	4	no	—
32	C₁₃×#121	—	2	4	no	—
33	C₁₃×#121	—	4	2	no	—
34	C₁₃×#121	—	4	2	no	—
35	C₁₃×#121	—	4	2	no	—
36	C₁₃×#121	—	4	2	no	—
37	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
40	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
41	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
44	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
45	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
46	C₂×C₄²×C₁₃	—	4	2	no	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
51	C₁₃×C₂²⋊C₈	—	2	2	no	—
52	C₁₃×C₂²⋊C₈	D₄	1	4	yes	complemented
53	C₄×C₈×C₁₃	—	4	2	no	—
54	C₁₃×#95	—	2	4	no	—
55	C₁₃×#95	—	4	2	no	—
56	#9680	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂⁴×C₁₃	—	2	2	no	—
58	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂×D₄×C₁₃	—	2	4	no	—
60	C₂×D₄×C₁₃	—	4	2	no	—
61	C₂×D₄×C₁₃	—	4	2	no	—
62	C₂×D₄×C₁₃	—	4	2	no	—
63	C₂×D₄×C₁₃	—	4	2	no	—
64	C₂×D₄×C₁₃	—	4	2	no	—
65	C₂×D₄×C₁₃	—	4	2	no	—
66	C₂×D₄×C₁₃	—	4	2	no	—
67	C₂×D₄×C₁₃	—	4	2	no	—
68	C₂×D₄×C₁₃	—	4	2	no	—
69	C₂×D₄×C₁₃	—	4	2	no	—
70	C₂×D₄×C₁₃	—	4	2	no	—
71	C₂×D₄×C₁₃	—	4	2	no	—
72	C₂×D₄×C₁₃	—	4	2	no	—
73	C₂×D₄×C₁₃	—	4	2	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	4	1	no	—
79	C₂²×C₄×C₁₃	—	4	1	no	—
80	C₂²×C₄×C₁₃	—	4	1	no	—
81	C₂²×C₄×C₁₃	—	4	1	no	—
82	C₂²×C₄×C₁₃	—	4	2	no	—
83	C₂²×C₄×C₁₃	—	4	2	no	—
84	C₂²×C₄×C₁₃	—	4	2	no	—
85	C₂²×C₄×C₁₃	—	4	2	no	—
86	C₂²×C₄×C₁₃	—	4	2	no	—
87	C₂²×C₄×C₁₃	—	4	2	no	—
88	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	D₈	1	2	yes	—
93	C₂²×C₄×C₁₃	D₈	1	2	yes	—
94	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
95	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	#41	1	2	yes	—
100	C₂×C₈×C₁₃	—	2	4	no	—
101	C₂×C₈×C₁₃	—	4	2	no	—
102	C₂×C₈×C₁₃	—	4	2	no	—
103	C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₁₃×C₄⋊C₄	—	4	8	no	—
105	C₁₃×C₄⋊C₄	—	4	2	no	—
106	C₁₃×C₄⋊C₄	—	4	2	no	—
107	C₁₃×C₂²⋊C₄	—	4	4	no	—
108	C₁₃×C₂²⋊C₄	—	4	4	no	—
109	C₁₃×C₂²⋊C₄	—	4	4	no	—
110	C₄²×C₁₃	—	2	2	no	—
111	C₄²×C₁₃	—	2	2	no	—
112	C₄²×C₁₃	—	4	1	no	—
113	C₄²×C₁₃	—	4	1	no	—
114	#2856	C₂×C₁₃	1	1	yes	characteristic
115	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
116	C₂×#327	C₂×C₁₃	1	4	yes	complemented
117	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic, complemented
118	C₂³×C₁₃	—	2	1	no	—
119	C₂³×C₁₃	—	2	1	no	—
120	C₂³×C₁₃	—	2	1	no	—
121	C₂³×C₁₃	—	2	1	no	—
122	C₂³×C₁₃	—	4	2	no	—
123	C₂³×C₁₃	—	4	2	no	—
124	C₂³×C₁₃	—	4	2	no	—
125	C₂³×C₁₃	—	4	2	no	—
126	C₂³×C₁₃	—	4	2	no	—
127	C₂³×C₁₃	—	4	2	no	—
128	C₂³×C₁₃	—	4	2	no	—
129	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₃	#124	1	1	yes	characteristic
131	C₂³×C₁₃	#127	1	1	yes	characteristic
132	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
133	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
134	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
135	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
136	D₄×C₁₃	—	8	4	no	—
137	D₄×C₁₃	—	8	4	no	—
138	D₄×C₁₃	—	8	2	no	—
139	D₄×C₁₃	—	8	2	no	—
140	D₄×C₁₃	—	8	2	no	—
141	D₄×C₁₃	—	8	2	no	—
142	D₄×C₁₃	—	8	4	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	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	4	no	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	4	no	—
160	C₂×C₄×C₁₃	—	4	4	no	—
161	C₂×C₄×C₁₃	—	4	4	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	8	2	no	—
166	C₂×C₄×C₁₃	—	8	2	no	—
167	C₂×C₄×C₁₃	—	8	2	no	—
168	C₂×C₄×C₁₃	—	8	2	no	—
169	C₂×C₄×C₁₃	#99	1	2	yes	—
170	C₂×C₄×C₁₃	#102	1	2	yes	—
171	C₂×C₄×C₁₃	#102	1	2	yes	—
172	C₂×C₄×C₁₃	#102	1	2	yes	—
173	C₂×C₄×C₁₃	#102	1	2	yes	—
174	C₂×C₄×C₁₃	#104	1	2	yes	—
175	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₁₃	#121	1	2	yes	—
177	C₈×C₁₃	—	4	4	no	—
178	C₂×#127	C₄×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#121	—	2	1	no	—
180	C₂×#121	—	2	1	no	—
181	C₂×#121	C₂²×C₁₃	1	2	yes	—
182	C₂²×C₄⋊C₄	—	2	1	no	—
183	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
185	C₂×C₄×C₈	—	2	1	no	—
186	#390	—	2	1	no	—
187	#390	—	2	1	no	—
188	#390	C₄×C₁₃	1	2	yes	complemented
189	#384	C₄×C₁₃	1	1	yes	characteristic, complemented
190	C₂×#95	—	2	1	no	—
191	C₂×#95	C₂²×C₁₃	1	2	yes	—
192	#336	—	2	1	no	—
193	#327	—	2	8	no	—
194	C₂²×C₁₃	—	2	1	no	—
195	C₂²×C₁₃	—	2	1	no	—
196	C₂²×C₁₃	—	2	1	no	—
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	1	no	—
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	—	2	1	no	—
204	C₂²×C₁₃	—	2	1	no	—
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	—	8	2	no	—
207	C₂²×C₁₃	—	8	2	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	—	8	2	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	—	8	2	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	#390	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×#99	1	1	yes	characteristic
215	C₂²×C₁₃	#410	1	1	yes	characteristic
216	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
217	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
218	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
219	C₂²×C₁₃	#421	1	1	yes	characteristic
220	C₂²×C₁₃	#486	1	1	yes	characteristic
221	C₂²×C₁₃	#486	1	1	yes	characteristic
222	C₂²×C₁₃	#492	1	1	yes	characteristic
223	C₂²×C₁₃	#493	1	1	yes	characteristic
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	8	4	no	—
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	#327	1	4	yes	complemented
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
238	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
240	C₂²×C₈	—	2	2	no	—
241	#127	—	4	2	no	—
242	#121	—	2	4	no	—
243	#121	—	2	4	no	—
244	#121	—	4	2	no	—
245	#121	—	4	2	no	—
246	#121	—	4	2	no	—
247	#121	—	4	2	no	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	4	2	no	—
252	C₂×C₄⋊C₄	—	4	2	no	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	4	2	no	—
258	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	D₄×C₁₃	1	4	yes	complemented
264	C₄×C₈	—	4	2	no	—
265	#95	—	2	4	no	—
266	#95	—	4	2	no	—
267	C₂×C₁₃	—	2	1	no	—
268	C₂×C₁₃	—	2	1	no	—
269	C₂×C₁₃	—	2	1	no	—
270	C₂×C₁₃	—	2	1	no	—
271	C₂×C₁₃	—	16	2	no	—
272	C₂×C₁₃	C₂×#327	1	1	yes	characteristic
273	C₂×C₁₃	#1502	1	1	yes	characteristic
274	C₂×C₁₃	#1517	1	1	yes	characteristic
275	C₂×C₁₃	#1519	1	1	yes	characteristic
276	C₂×C₁₃	#1957	1	1	yes	characteristic
277	C₂×C₁₃	#1964	1	1	yes	characteristic
278	C₂×C₁₃	#1980	1	1	yes	characteristic
279	C₂⁴	—	2	2	no	—
280	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
311	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
312	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
313	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
314	C₂²×C₄	C₁₃×D₈	1	2	yes	—
315	C₂²×C₄	C₁₃×D₈	1	2	yes	—
316	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
317	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
318	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
321	C₂²×C₄	C₁₃×#41	1	2	yes	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	4	2	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	4	8	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	4	4	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	4	1	no	—
335	C₄²	—	4	1	no	—
336	C₁₃	#9680	1	1	yes	characteristic, direct product factor, Sylow
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
349	C₂³	C₁₃×#124	1	1	yes	characteristic
350	C₂³	C₁₃×#127	1	1	yes	characteristic
351	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
352	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
353	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
354	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
355	D₄	—	8	4	no	—
356	D₄	—	8	4	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	4	no	—
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	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	C₁₃×#99	1	2	yes	—
389	C₂×C₄	C₁₃×#102	1	2	yes	—
390	C₂×C₄	C₁₃×#102	1	2	yes	—
391	C₂×C₄	C₁₃×#102	1	2	yes	—
392	C₂×C₄	C₁₃×#102	1	2	yes	—
393	C₂×C₄	C₁₃×#104	1	2	yes	—
394	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
395	C₂×C₄	C₁₃×#121	1	2	yes	—
396	C₈	—	4	4	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	C₁₃×#390	1	1	yes	characteristic
417	C₂²	C₂×C₁₃×#99	1	1	yes	characteristic
418	C₂²	C₁₃×#410	1	1	yes	characteristic
419	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
420	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
421	C₂²	C₂×C₁₃×#104	1	1	yes	characteristic
422	C₂²	C₁₃×#421	1	1	yes	characteristic
423	C₂²	C₁₃×#486	1	1	yes	characteristic
424	C₂²	C₁₃×#486	1	1	yes	characteristic
425	C₂²	C₁₃×#492	1	1	yes	characteristic
426	C₂²	C₁₃×#493	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	8	4	no	—
433	C₄	—	8	2	no	—
434	C₄	C₁₃×#327	1	4	yes	complemented
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×C₁₃×#327	1	1	yes	characteristic
441	C₂	C₁₃×#1502	1	1	yes	characteristic
442	C₂	C₁₃×#1517	1	1	yes	characteristic
443	C₂	C₁₃×#1519	1	1	yes	characteristic
444	C₂	C₁₃×#1957	1	1	yes	characteristic
445	C₂	C₁₃×#1964	1	1	yes	characteristic
446	C₂	C₁₃×#1980	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₁₃×#2856	C₂
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. C₄×C₁₃×C₂²⋊C₈	C₂	semidirect
3. C₂×C₁₃×#327	C₂	semidirect
4. C₁₃×C₄⋊#95	C₂	semidirect
5. C₂×C₁₃×#127	C₄	semidirect
15. C₁₃×#390	C₄	semidirect
16. C₁₃×#384	C₄	semidirect
52. C₁₃×C₂²⋊C₈	D₄	semidirect
56. #9680	C₁₃	direct (N × H)
115. C₄×C₂²⋊C₈	C₂×C₁₃	semidirect
116. C₂×#327	C₂×C₁₃	semidirect
117. C₄⋊#95	C₂×C₁₃	semidirect
178. C₂×#127	C₄×C₁₃	semidirect
188. #390	C₄×C₁₃	semidirect
189. #384	C₄×C₁₃	semidirect
231. C₄×C₁₃	#327	semidirect
263. C₂²⋊C₈	D₄×C₁₃	semidirect
336. C₁₃	#9680	direct (N × H)
434. C₄	C₁₃×#327	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#2856	2
C₄×C₁₃×C₂²⋊C₈	2
C₂×C₁₃×#327	2
C₁₃×C₄⋊#95	2
#9680	13

Subgroups — C13×#9680 #15696019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9680 #15696019