Subgroups — C₁₃×#9253 #15695592

Order 3328.

612 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic
2	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1292	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×D₈	C₄	1	2	yes	—
9	C₂²×C₁₃×M₁₆	—	2	1	no	—
10	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#459	—	2	1	no	—
13	C₁₃×#459	—	2	1	no	—
14	C₁₃×#459	—	2	1	no	—
15	C₁₃×#459	—	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×#102	C₄	1	2	yes	—
24	C₂×C₁₃×#100	—	2	1	no	—
25	C₂×C₁₃×#100	—	2	1	no	—
26	C₁₃×#407	—	2	1	no	—
27	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
28	C₁₃×#331	—	2	2	no	—
29	C₁₃×D₄⋊C₈	—	2	1	no	—
30	C₁₃×D₄⋊C₈	—	2	1	no	—
31	C₂²×D₄×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₃	—	2	1	no	—
36	C₂×C₁₃×D₈	—	2	2	no	—
37	C₂×C₁₃×D₈	—	2	2	no	—
38	C₂×C₁₃×D₈	—	4	4	no	—
39	C₂×C₁₃×M₁₆	—	2	2	no	—
40	C₂×C₁₃×M₁₆	—	2	1	no	—
41	C₂×C₁₃×M₁₆	—	2	1	no	—
42	C₂×C₁₃×M₁₆	—	4	2	no	—
43	C₂×C₁₃×M₁₆	—	4	2	no	—
44	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
48	C₁₃×#127	—	2	1	no	—
49	C₁₃×#127	—	2	1	no	—
50	C₁₃×#127	—	2	1	no	—
51	C₁₃×#127	—	2	1	no	—
52	C₄×D₄×C₁₃	—	2	1	no	—
53	C₄×D₄×C₁₃	—	2	1	no	—
54	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
55	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
56	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
57	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
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×#102	—	2	2	no	—
69	C₁₃×#102	—	2	2	no	—
70	C₁₃×#100	—	4	2	no	—
71	C₁₃×#100	—	4	2	no	—
72	C₁₃×C₂²⋊C₈	—	2	2	no	—
73	C₁₃×C₂²⋊C₈	—	2	2	no	—
74	C₁₃×C₂²⋊C₈	—	2	1	no	—
75	C₁₃×#97	—	2	1	no	—
76	C₄×C₈×C₁₃	—	2	1	no	—
77	C₄×C₈×C₁₃	—	2	1	no	—
78	#9253	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₃	—	2	1	no	—
80	C₂⁴×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	1	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	4	1	no	—
86	C₂×D₄×C₁₃	—	4	2	no	—
87	C₂×D₄×C₁₃	—	4	2	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	1	no	—
91	C₂×D₄×C₁₃	—	4	1	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	8	2	no	—
97	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	—	4	1	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
111	C₁₃×D₈	—	4	4	no	—
112	C₁₃×D₈	—	4	4	no	—
113	C₁₃×M₁₆	—	2	1	no	—
114	C₁₃×M₁₆	—	2	1	no	—
115	C₁₃×M₁₆	—	2	1	no	—
116	C₁₃×M₁₆	—	4	4	no	—
117	C₁₃×M₁₆	—	4	1	no	—
118	C₁₃×M₁₆	—	4	1	no	—
119	C₁₃×M₁₆	—	4	1	no	—
120	C₁₃×M₁₆	—	4	1	no	—
121	C₁₃×M₁₆	D₈	1	2	yes	complemented
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	4	4	no	—
127	C₂×C₈×C₁₃	—	4	2	no	—
128	C₂×C₈×C₁₃	—	4	1	no	—
129	C₂×C₈×C₁₃	—	4	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
132	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
133	C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	#41	1	1	yes	characteristic
141	C₂×#459	C₂×C₁₃	1	1	yes	characteristic
142	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1965	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#1545	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#1486	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#1292	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#1283	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂³×C₁₃	—	2	1	no	—
149	C₂³×C₁₃	—	2	1	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	4	1	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	—	4	2	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	—	8	1	no	—
157	C₂³×C₁₃	—	8	2	no	—
158	C₂³×C₁₃	—	8	2	no	—
159	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
160	D₄×C₁₃	—	2	1	no	—
161	D₄×C₁₃	—	2	1	no	—
162	D₄×C₁₃	—	2	1	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	8	2	no	—
167	D₄×C₁₃	—	8	2	no	—
168	D₄×C₁₃	—	8	2	no	—
169	D₄×C₁₃	—	8	1	no	—
170	D₄×C₁₃	—	8	1	no	—
171	D₄×C₁₃	—	8	1	no	—
172	D₄×C₁₃	—	8	1	no	—
173	D₄×C₁₃	#100	1	2	yes	complemented
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
192	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
197	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₈×C₁₃	—	2	2	no	—
200	C₈×C₁₃	—	4	2	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₈×C₁₃	—	4	1	no	—
203	C₈×C₁₃	—	8	1	no	—
204	C₈×C₁₃	—	8	1	no	—
205	C₂²×D₈	C₄×C₁₃	1	2	yes	—
206	C₂²×M₁₆	—	2	1	no	—
207	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
209	#459	—	2	1	no	—
210	#459	—	2	1	no	—
211	#459	—	2	1	no	—
212	#459	—	2	1	no	—
213	#436	—	2	1	no	—
214	#435	—	2	2	no	—
215	C₈×D₄	—	2	1	no	—
216	#431	C₂²×C₁₃	1	1	yes	characteristic
217	#423	C₂²×C₁₃	1	1	yes	characteristic
218	#423	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#102	C₄×C₁₃	1	2	yes	—
221	C₂×#100	—	2	1	no	—
222	C₂×#100	—	2	1	no	—
223	#407	—	2	1	no	—
224	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
225	#331	—	2	2	no	—
226	D₄⋊C₈	—	2	1	no	—
227	D₄⋊C₈	—	2	1	no	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	2	no	—
231	C₂²×C₁₃	—	4	1	no	—
232	C₂²×C₁₃	—	4	1	no	—
233	C₂²×C₁₃	—	4	1	no	—
234	C₂²×C₁₃	—	4	1	no	—
235	C₂²×C₁₃	—	4	1	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	8	2	no	—
240	C₂²×C₁₃	—	8	2	no	—
241	C₂²×C₁₃	—	16	2	no	—
242	C₂²×C₁₃	—	16	2	no	—
243	C₂²×C₁₃	#386	1	1	yes	characteristic
244	C₂²×C₁₃	C₄×D₈	1	1	yes	characteristic
245	C₂²×C₁₃	#442	1	1	yes	characteristic
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	—	4	1	no	—
251	C₄×C₁₃	C₂×#100	1	1	yes	characteristic
252	C₄×C₁₃	#413	1	1	yes	characteristic
253	C₄×C₁₃	#447	1	1	yes	characteristic
254	C₄×C₁₃	#449	1	1	yes	characteristic
255	C₄×C₁₃	#459	1	1	yes	characteristic
256	C₄×C₁₃	#463	1	1	yes	characteristic
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
260	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
261	C₂³×C₄	—	2	1	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×D₈	—	4	4	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	4	2	no	—
269	C₂×M₁₆	—	4	2	no	—
270	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
271	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
274	#127	—	2	1	no	—
275	#127	—	2	1	no	—
276	#127	—	2	1	no	—
277	#127	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
281	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
282	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
283	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
294	#102	—	2	2	no	—
295	#102	—	2	2	no	—
296	#100	—	4	2	no	—
297	#100	—	4	2	no	—
298	C₂²⋊C₈	—	2	2	no	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	2	1	no	—
301	#97	—	2	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	—	2	1	no	—
304	C₂×C₁₃	—	2	1	no	—
305	C₂×C₁₃	—	2	1	no	—
306	C₂×C₁₃	—	4	2	no	—
307	C₂×C₁₃	—	8	1	no	—
308	C₂×C₁₃	—	16	2	no	—
309	C₂×C₁₃	#1879	1	1	yes	characteristic
310	C₂×C₁₃	#1900	1	1	yes	characteristic
311	C₂×C₁₃	#1903	1	1	yes	characteristic
312	C₂⁴	—	2	1	no	—
313	C₂⁴	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	8	2	no	—
330	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
331	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
344	D₈	—	4	4	no	—
345	D₈	—	4	4	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	2	1	no	—
349	M₁₆	—	4	4	no	—
350	M₁₆	—	4	1	no	—
351	M₁₆	—	4	1	no	—
352	M₁₆	—	4	1	no	—
353	M₁₆	—	4	1	no	—
354	M₁₆	C₁₃×D₈	1	2	yes	complemented
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	4	no	—
360	C₂×C₈	—	4	2	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
365	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₄²	C₁₃×#41	1	1	yes	characteristic
374	C₁₃	#9253	1	1	yes	characteristic, direct product factor, Sylow
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	8	1	no	—
384	C₂³	—	8	2	no	—
385	C₂³	—	8	2	no	—
386	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
387	D₄	—	2	1	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	1	no	—
397	D₄	—	8	1	no	—
398	D₄	—	8	1	no	—
399	D₄	—	8	1	no	—
400	D₄	C₁₃×#100	1	2	yes	complemented
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
417	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
419	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
420	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
421	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
422	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
423	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
424	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
425	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	4	2	no	—
428	C₈	—	4	2	no	—
429	C₈	—	4	1	no	—
430	C₈	—	8	1	no	—
431	C₈	—	8	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	16	2	no	—
446	C₂²	—	16	2	no	—
447	C₂²	C₁₃×#386	1	1	yes	characteristic
448	C₂²	C₄×C₁₃×D₈	1	1	yes	characteristic
449	C₂²	C₁₃×#442	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	1	no	—
455	C₄	C₂×C₁₃×#100	1	1	yes	characteristic
456	C₄	C₁₃×#413	1	1	yes	characteristic
457	C₄	C₁₃×#447	1	1	yes	characteristic
458	C₄	C₁₃×#449	1	1	yes	characteristic
459	C₄	C₁₃×#459	1	1	yes	characteristic
460	C₄	C₁₃×#463	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	4	2	no	—
464	C₂	—	8	1	no	—
465	C₂	—	16	2	no	—
466	C₂	C₁₃×#1879	1	1	yes	characteristic
467	C₂	C₁₃×#1900	1	1	yes	characteristic
468	C₂	C₁₃×#1903	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	C₂×C₁₃×#459	C₂
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
2. D₄×C₁₃×M₁₆	C₂	semidirect
3. C₁₃×#1965	C₂	semidirect
4. C₁₃×#1545	C₂	semidirect
5. C₁₃×#1486	C₂	semidirect
6. C₁₃×#1292	C₂	semidirect
7. C₁₃×#1283	C₂	semidirect
78. #9253	C₁₃	direct (N × H)
121. C₁₃×M₁₆	D₈	semidirect
142. D₄×M₁₆	C₂×C₁₃	semidirect
143. #1965	C₂×C₁₃	semidirect
144. #1545	C₂×C₁₃	semidirect
145. #1486	C₂×C₁₃	semidirect
146. #1292	C₂×C₁₃	semidirect
147. #1283	C₂×C₁₃	semidirect
173. D₄×C₁₃	#100	semidirect
354. M₁₆	C₁₃×D₈	semidirect
374. C₁₃	#9253	direct (N × H)
400. D₄	C₁₃×#100	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#459	2
D₄×C₁₃×M₁₆	2
C₁₃×#1965	2
C₁₃×#1545	2
C₁₃×#1486	2
C₁₃×#1292	2
C₁₃×#1283	2
#9253	13

Subgroups — C13×#9253 #15695592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9253 #15695592