Subgroups — C₁₃×#10876 #15697215

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
7	C₄×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
16	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
17	C₂×C₁₃×C₄⋊C₈	C₄	1	4	yes	complemented
18	C₂×C₄×C₈×C₁₃	—	2	2	no	—
19	C₂×C₄×C₈×C₁₃	—	2	2	no	—
20	C₂×C₄×C₈×C₁₃	—	2	2	no	—
21	C₂×C₁₃×#95	C₄	1	2	yes	—
22	C₂×C₁₃×#95	C₄	1	2	yes	—
23	C₁₃×#336	—	2	2	no	—
24	C₁₃×#336	—	2	2	no	—
25	C₁₃×#336	—	2	2	no	—
26	C₁₃×#336	C₄	1	4	yes	complemented
27	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
32	C₂²×C₈×C₁₃	—	2	1	no	—
33	C₂²×C₈×C₁₃	—	2	1	no	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₂²×C₈×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₂²×C₈×C₁₃	—	2	1	no	—
41	C₂²×C₈×C₁₃	—	2	1	no	—
42	C₂²×C₈×C₁₃	—	2	1	no	—
43	C₂²×C₈×C₁₃	—	2	1	no	—
44	C₂²×C₈×C₁₃	—	2	1	no	—
45	C₂²×C₈×C₁₃	—	2	1	no	—
46	C₂²×C₈×C₁₃	—	2	1	no	—
47	C₂²×C₈×C₁₃	—	2	1	no	—
48	C₂²×C₈×C₁₃	—	2	1	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₂²×C₈×C₁₃	—	2	1	no	—
51	C₂²×C₈×C₁₃	—	2	1	no	—
52	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
56	C₂²×C₈×C₁₃	D₄	1	2	yes	—
57	C₂²×C₈×C₁₃	D₄	1	2	yes	—
58	C₂²×C₈×C₁₃	D₄	1	2	yes	—
59	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	—	2	1	no	—
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₁₃	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
78	C₁₃×C₄⋊C₈	—	2	8	no	—
79	C₄×C₈×C₁₃	—	2	8	no	—
80	C₁₃×#95	—	2	4	no	—
81	C₁₃×#95	C₈	1	8	yes	complemented
82	#10876	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	—	2	1	no	—
85	C₂²×C₄×C₁₃	—	2	1	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
102	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
103	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
105	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
107	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	4	1	no	—
141	C₂×C₈×C₁₃	—	4	1	no	—
142	C₂×C₈×C₁₃	—	4	1	no	—
143	C₂×C₈×C₁₃	—	4	1	no	—
144	C₂×C₈×C₁₃	—	4	1	no	—
145	C₂×C₈×C₁₃	—	4	1	no	—
146	C₂×C₈×C₁₃	—	4	1	no	—
147	C₂×C₈×C₁₃	—	4	1	no	—
148	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
149	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	2	2	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	4	1	no	—
159	C₄²×C₁₃	—	4	1	no	—
160	C₄²×C₁₃	—	4	1	no	—
161	C₄²×C₁₃	—	4	1	no	—
162	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
163	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic
164	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
165	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
166	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
167	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
168	C₄×#95	C₂×C₁₃	1	1	yes	characteristic
169	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂³×C₁₃	#117	1	1	yes	characteristic
172	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
173	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
174	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
176	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
177	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
178	C₂³×C₁₃	#131	1	2	yes	—
179	C₂³×C₁₃	#131	1	2	yes	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	complemented
203	C₂×C₄×C₁₃	C₄⋊C₈	1	8	yes	complemented
204	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
207	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
217	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
224	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
225	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
226	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
228	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
229	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
230	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
232	C₈×C₁₃	—	2	4	no	—
233	C₈×C₁₃	—	2	4	no	—
234	C₈×C₁₃	—	4	2	no	—
235	C₈×C₁₃	—	4	2	no	—
236	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
241	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	—	2	2	no	—
244	C₂×C₄⋊C₈	—	2	2	no	—
245	C₂×C₄⋊C₈	C₄×C₁₃	1	4	yes	complemented
246	C₂×C₄×C₈	—	2	2	no	—
247	C₂×C₄×C₈	—	2	2	no	—
248	C₂×C₄×C₈	—	2	2	no	—
249	C₂×#95	C₄×C₁₃	1	2	yes	—
250	C₂×#95	C₄×C₁₃	1	2	yes	—
251	#336	—	2	2	no	—
252	#336	—	2	2	no	—
253	#336	—	2	2	no	—
254	#336	C₄×C₁₃	1	4	yes	complemented
255	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
257	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₁₃	#385	1	1	yes	characteristic
259	C₂²×C₁₃	#387	1	1	yes	characteristic
260	C₂²×C₁₃	#388	1	1	yes	characteristic
261	C₂²×C₁₃	#389	1	1	yes	characteristic
262	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
263	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
264	C₂²×C₁₃	#405	1	1	yes	characteristic
265	C₂²×C₁₃	#405	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
267	C₂²×C₁₃	#424	1	2	yes	—
268	C₂²×C₁₃	#431	1	2	yes	—
269	C₂²×C₁₃	#433	1	2	yes	—
270	C₂²×C₁₃	C₈×D₄	1	2	yes	—
271	C₂²×C₁₃	C₈×D₄	1	2	yes	—
272	C₂²×C₁₃	C₈×D₄	1	2	yes	—
273	C₂²×C₁₃	#435	1	2	yes	—
274	C₂²×C₁₃	#435	1	2	yes	—
275	C₂²×C₁₃	#436	1	2	yes	—
276	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
277	C₂²×C₁₃	#446	1	2	yes	—
278	C₄×C₁₃	—	2	8	no	—
279	C₄×C₁₃	—	2	4	no	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	#385	1	1	yes	characteristic
283	C₄×C₁₃	#386	1	1	yes	characteristic
284	C₄×C₁₃	#387	1	1	yes	characteristic
285	C₄×C₁₃	#387	1	1	yes	characteristic
286	C₄×C₁₃	#387	1	1	yes	characteristic
287	C₄×C₁₃	#388	1	1	yes	characteristic
288	C₄×C₁₃	#389	1	1	yes	characteristic
289	C₄×C₁₃	#391	1	1	yes	characteristic
290	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
291	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
292	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
293	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
294	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	—	2	1	no	—
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
316	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
317	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
318	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
319	C₂²×C₈	D₄×C₁₃	1	2	yes	—
320	C₂²×C₈	D₄×C₁₃	1	2	yes	—
321	C₂²×C₈	D₄×C₁₃	1	2	yes	—
322	C₂²×C₈	Q₈×C₁₃	1	2	yes	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
338	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
339	C₂×C₄²	D₄×C₁₃	1	2	yes	—
340	C₂×C₄²	Q₈×C₁₃	1	2	yes	—
341	C₄⋊C₈	—	2	8	no	—
342	C₄×C₈	—	2	8	no	—
343	#95	—	2	4	no	—
344	#95	C₈×C₁₃	1	8	yes	complemented
345	C₂×C₁₃	#1436	1	1	yes	characteristic
346	C₂×C₁₃	C₈×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₁₃	#1753	1	1	yes	characteristic
348	C₂×C₁₃	C₄×C₄⋊C₈	1	1	yes	characteristic
349	C₂×C₁₃	#1768	1	1	yes	characteristic
350	C₂×C₁₃	C₈×C₄⋊C₄	1	1	yes	characteristic
351	C₂×C₁₃	#1771	1	1	yes	characteristic
352	C₂×C₁₃	#1850	1	2	yes	—
353	C₂×C₁₃	#1916	1	2	yes	—
354	C₂×C₁₃	#1923	1	2	yes	—
355	C₂×C₁₃	#1939	1	2	yes	—
356	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	C₄²×C₁₃	1	2	yes	—
375	C₂²×C₄	C₄²×C₁₃	1	2	yes	—
376	C₂²×C₄	C₁₃×C₄⋊C₄	1	4	yes	—
377	C₂²×C₄	C₂×C₈×C₁₃	1	4	yes	—
378	C₂²×C₄	C₂×C₈×C₁₃	1	4	yes	—
379	C₂²×C₄	C₂×C₈×C₁₃	1	4	yes	—
380	C₂²×C₄	C₁₃×M₁₆	1	4	yes	—
381	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
390	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
391	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
392	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
393	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
394	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	4	1	no	—
414	C₂×C₈	—	4	1	no	—
415	C₂×C₈	—	4	1	no	—
416	C₂×C₈	—	4	1	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	—	4	1	no	—
419	C₂×C₈	—	4	1	no	—
420	C₂×C₈	—	4	1	no	—
421	C₂×C₈	C₁₃×C₂²⋊C₄	1	4	yes	—
422	C₂×C₈	C₁₃×C₄⋊C₄	1	4	yes	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	4	1	no	—
432	C₄²	—	4	1	no	—
433	C₄²	—	4	1	no	—
434	C₄²	—	4	1	no	—
435	C₁₃	#10876	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	C₂×C₄²×C₁₃	1	1	yes	characteristic
437	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
438	C₂³	C₁₃×#117	1	1	yes	characteristic
439	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
440	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
441	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
442	C₂³	C₄×Q₈×C₁₃	1	1	yes	characteristic
443	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
444	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
445	C₂³	C₁₃×#131	1	2	yes	—
446	C₂³	C₁₃×#131	1	2	yes	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	C₄×C₈×C₁₃	1	4	yes	complemented
470	C₂×C₄	C₁₃×C₄⋊C₈	1	8	yes	complemented
471	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
472	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
473	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
474	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
475	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
479	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
480	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
481	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
482	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
483	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
484	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
485	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
486	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
487	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
488	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
489	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
490	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
491	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
492	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
493	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
494	C₂×C₄	C₁₃×#125	1	1	yes	characteristic
495	C₂×C₄	C₁₃×#125	1	1	yes	characteristic
496	C₂×C₄	C₁₃×#126	1	1	yes	characteristic
497	C₂×C₄	C₁₃×#126	1	1	yes	characteristic
498	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
499	C₈	—	2	4	no	—
500	C₈	—	2	4	no	—
501	C₈	—	4	2	no	—
502	C₈	—	4	2	no	—
503	C₂²	C₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
504	C₂²	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
505	C₂²	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
506	C₂²	C₁₃×#385	1	1	yes	characteristic
507	C₂²	C₁₃×#387	1	1	yes	characteristic
508	C₂²	C₁₃×#388	1	1	yes	characteristic
509	C₂²	C₁₃×#389	1	1	yes	characteristic
510	C₂²	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
511	C₂²	C₄×C₁₃×M₁₆	1	1	yes	characteristic
512	C₂²	C₁₃×#405	1	1	yes	characteristic
513	C₂²	C₁₃×#405	1	1	yes	characteristic
514	C₂²	C₂×C₁₃×C₄⋊C₈	1	2	yes	—
515	C₂²	C₁₃×#424	1	2	yes	—
516	C₂²	C₁₃×#431	1	2	yes	—
517	C₂²	C₁₃×#433	1	2	yes	—
518	C₂²	C₈×D₄×C₁₃	1	2	yes	—
519	C₂²	C₈×D₄×C₁₃	1	2	yes	—
520	C₂²	C₈×D₄×C₁₃	1	2	yes	—
521	C₂²	C₁₃×#435	1	2	yes	—
522	C₂²	C₁₃×#435	1	2	yes	—
523	C₂²	C₁₃×#436	1	2	yes	—
524	C₂²	C₈×Q₈×C₁₃	1	2	yes	—
525	C₂²	C₁₃×#446	1	2	yes	—
526	C₄	—	2	4	no	—
527	C₄	—	2	8	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	4	no	—
530	C₄	C₁₃×#385	1	1	yes	characteristic
531	C₄	C₁₃×#386	1	1	yes	characteristic
532	C₄	C₁₃×#387	1	1	yes	characteristic
533	C₄	C₁₃×#387	1	1	yes	characteristic
534	C₄	C₁₃×#387	1	1	yes	characteristic
535	C₄	C₁₃×#388	1	1	yes	characteristic
536	C₄	C₁₃×#389	1	1	yes	characteristic
537	C₄	C₁₃×#391	1	1	yes	characteristic
538	C₂	C₁₃×#1436	1	1	yes	characteristic
539	C₂	C₈×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
540	C₂	C₁₃×#1753	1	1	yes	characteristic
541	C₂	C₄×C₁₃×C₄⋊C₈	1	1	yes	characteristic
542	C₂	C₁₃×#1768	1	1	yes	characteristic
543	C₂	C₈×C₁₃×C₄⋊C₄	1	1	yes	characteristic
544	C₂	C₁₃×#1771	1	1	yes	characteristic
545	C₂	C₁₃×#1850	1	2	yes	—
546	C₂	C₁₃×#1916	1	2	yes	—
547	C₂	C₁₃×#1923	1	2	yes	—
548	C₂	C₁₃×#1939	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator	C₂²	C₂×C₄×C₈×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
socle, prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
17. C₂×C₁₃×C₄⋊C₈	C₄	semidirect
26. C₁₃×#336	C₄	semidirect
81. C₁₃×#95	C₈	semidirect
82. #10876	C₁₃	direct (N × H)
202. C₂×C₄×C₁₃	C₄×C₈	semidirect
203. C₂×C₄×C₁₃	C₄⋊C₈	semidirect
245. C₂×C₄⋊C₈	C₄×C₁₃	semidirect
254. #336	C₄×C₁₃	semidirect
344. #95	C₈×C₁₃	semidirect
435. C₁₃	#10876	direct (N × H)
469. C₂×C₄	C₄×C₈×C₁₃	semidirect
470. C₂×C₄	C₁₃×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄⋊C₈	2
C₂²×C₄×C₈×C₁₃	2
C₂×C₁₃×#336	2
C₄×C₁₃×#95	2
#10876	13

Subgroups — C13×#10876 #15697215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10876 #15697215