Subgroups — C₁₃×#24540 #15710879

Order 3328.

940 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2499	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1825	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₁₃×#451	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₃×#419	—	2	4	no	—
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₃×#397	—	2	1	no	—
38	C₁₃×#397	—	2	1	no	—
39	C₁₃×#391	—	2	1	no	—
40	C₁₃×#391	—	2	1	no	—
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#391	C₂²	1	1	yes	characteristic
44	C₁₃×#391	C₂²	1	1	yes	characteristic
45	C₁₃×#387	—	2	1	no	—
46	C₁₃×#387	—	2	1	no	—
47	C₁₃×#384	C₂²	1	1	yes	characteristic
48	C₁₃×#382	C₂²	1	1	yes	characteristic
49	C₁₃×#380	—	2	1	no	—
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	—	2	1	no	—
62	C₂²×Q₈×C₁₃	—	2	2	no	—
63	C₂²×Q₈×C₁₃	—	2	2	no	—
64	C₂²×Q₈×C₁₃	—	2	2	no	—
65	C₂²×Q₈×C₁₃	—	4	1	no	—
66	C₂²×Q₈×C₁₃	—	4	1	no	—
67	C₂²×Q₈×C₁₃	D₄	1	4	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×Q₁₆	—	2	2	no	—
74	C₂×C₁₃×Q₁₆	—	2	2	no	—
75	C₂×C₁₃×Q₁₆	—	2	2	no	—
76	C₂×C₁₃×Q₁₆	—	2	2	no	—
77	C₂×C₁₃×Q₁₆	—	4	1	no	—
78	C₂×C₁₃×Q₁₆	—	4	1	no	—
79	C₂×C₁₃×M₁₆	—	2	2	no	—
80	C₂×C₁₃×M₁₆	—	4	1	no	—
81	C₂×C₁₃×M₁₆	—	4	1	no	—
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	4	1	no	—
91	C₄×Q₈×C₁₃	—	4	1	no	—
92	C₁₃×#117	—	2	2	no	—
93	C₁₃×#117	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	—	2	1	no	—
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	—	2	1	no	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	—	4	1	no	—
115	C₁₃×C₄⋊C₈	—	4	1	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	2	2	no	—
121	C₁₃×#103	—	2	2	no	—
122	C₁₃×#103	—	4	1	no	—
123	C₁₃×#103	—	4	1	no	—
124	C₁₃×C₂²⋊C₈	—	2	2	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	C₁₃×#95	—	2	1	no	—
134	C₁₃×#95	—	2	1	no	—
135	C₁₃×#95	—	2	1	no	—
136	C₁₃×#95	D₄	1	1	yes	characteristic
137	C₁₃×#95	D₄	1	1	yes	characteristic
138	#24540	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	8	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	4	2	no	—
157	C₂×Q₈×C₁₃	—	4	2	no	—
158	C₂×Q₈×C₁₃	—	4	4	no	—
159	C₂×Q₈×C₁₃	—	4	4	no	—
160	C₂×Q₈×C₁₃	—	4	4	no	—
161	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
162	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
163	C₂×Q₈×C₁₃	#41	1	2	yes	—
164	C₂×Q₈×C₁₃	#41	1	2	yes	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	—	4	2	no	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	#41	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₁₃×Q₁₆	—	4	4	no	—
189	C₁₃×Q₁₆	—	4	4	no	—
190	C₁₃×M₁₆	—	4	4	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	4	2	no	—
214	C₁₃×C₄⋊C₄	—	4	2	no	—
215	C₁₃×C₄⋊C₄	—	4	2	no	—
216	C₁₃×C₄⋊C₄	—	4	2	no	—
217	C₁₃×C₄⋊C₄	—	4	2	no	—
218	C₁₃×C₂²⋊C₄	—	2	2	no	—
219	C₁₃×C₂²⋊C₄	—	4	1	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	4	2	no	—
222	C₁₃×C₂²⋊C₄	—	4	2	no	—
223	C₄²×C₁₃	—	2	1	no	—
224	C₄²×C₁₃	—	2	1	no	—
225	C₄²×C₁₃	—	2	1	no	—
226	C₄²×C₁₃	—	2	1	no	—
227	C₄²×C₁₃	—	4	2	no	—
228	C₄²×C₁₃	—	4	2	no	—
229	C₄²×C₁₃	—	4	2	no	—
230	C₂×#451	C₂×C₁₃	1	1	yes	characteristic
231	C₂×#419	C₂×C₁₃	1	1	yes	characteristic
232	#2499	C₂×C₁₃	1	1	yes	characteristic
233	Q₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
234	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#1894	C₂×C₁₃	1	1	yes	characteristic
239	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#1851	C₂×C₁₃	1	1	yes	characteristic
242	#1825	C₂×C₁₃	1	1	yes	characteristic
243	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	2	1	no	—
248	C₂³×C₁₃	—	2	1	no	—
249	C₂³×C₁₃	—	2	1	no	—
250	C₂³×C₁₃	—	2	1	no	—
251	C₂³×C₁₃	#121	1	2	yes	—
252	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	Q₈×C₁₃	—	2	2	no	—
254	Q₈×C₁₃	—	2	2	no	—
255	Q₈×C₁₃	—	2	2	no	—
256	Q₈×C₁₃	—	2	2	no	—
257	Q₈×C₁₃	—	2	2	no	—
258	Q₈×C₁₃	—	4	8	no	—
259	Q₈×C₁₃	—	4	1	no	—
260	Q₈×C₁₃	—	4	1	no	—
261	Q₈×C₁₃	—	4	1	no	—
262	Q₈×C₁₃	—	4	1	no	—
263	Q₈×C₁₃	—	4	1	no	—
264	Q₈×C₁₃	—	4	1	no	—
265	Q₈×C₁₃	#123	1	4	yes	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	4	8	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	#121	1	2	yes	—
309	C₂×C₄×C₁₃	#137	1	2	yes	—
310	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
312	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
313	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
314	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
316	C₈×C₁₃	—	4	1	no	—
317	C₈×C₁₃	—	4	1	no	—
318	C₈×C₁₃	—	4	1	no	—
319	C₈×C₁₃	—	4	1	no	—
320	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
321	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
323	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
328	#451	—	2	4	no	—
329	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
331	#419	—	2	4	no	—
332	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
341	#397	—	2	1	no	—
342	#397	—	2	1	no	—
343	#391	—	2	1	no	—
344	#391	—	2	1	no	—
345	#391	C₂²×C₁₃	1	1	yes	characteristic
346	#391	C₂²×C₁₃	1	1	yes	characteristic
347	#391	C₂²×C₁₃	1	1	yes	characteristic
348	#391	C₂²×C₁₃	1	1	yes	characteristic
349	#387	—	2	1	no	—
350	#387	—	2	1	no	—
351	#384	C₂²×C₁₃	1	1	yes	characteristic
352	#382	C₂²×C₁₃	1	1	yes	characteristic
353	#380	—	2	1	no	—
354	#380	C₂²×C₁₃	1	1	yes	characteristic
355	C₄×C₂²⋊C₄	—	2	1	no	—
356	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
357	#340	C₂²×C₁₃	1	1	yes	characteristic
358	#340	C₂²×C₁₃	1	1	yes	characteristic
359	#340	C₂²×C₁₃	1	1	yes	characteristic
360	#340	C₂²×C₁₃	1	1	yes	characteristic
361	#340	C₂²×C₁₃	1	1	yes	characteristic
362	#340	C₂²×C₁₃	1	1	yes	characteristic
363	#336	C₂²×C₁₃	1	1	yes	characteristic
364	#336	C₂²×C₁₃	1	1	yes	characteristic
365	C₂²×C₁₃	—	2	2	no	—
366	C₂²×C₁₃	—	2	2	no	—
367	C₂²×C₁₃	—	2	2	no	—
368	C₂²×C₁₃	—	4	1	no	—
369	C₂²×C₁₃	—	4	1	no	—
370	C₂²×C₁₃	—	4	1	no	—
371	C₂²×C₁₃	—	4	1	no	—
372	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
373	C₂²×C₁₃	#546	1	1	yes	characteristic
374	C₂²×C₁₃	#546	1	1	yes	characteristic
375	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
376	C₂²×C₁₃	#575	1	1	yes	characteristic
377	C₂²×C₁₃	#578	1	1	yes	characteristic
378	C₂²×C₁₃	#578	1	1	yes	characteristic
379	C₄×C₁₃	—	2	2	no	—
380	C₄×C₁₃	—	2	4	no	—
381	C₄×C₁₃	—	2	2	no	—
382	C₄×C₁₃	—	4	1	no	—
383	C₄×C₁₃	—	4	2	no	—
384	C₄×C₁₃	—	4	1	no	—
385	C₄×C₁₃	—	4	1	no	—
386	C₄×C₁₃	—	8	1	no	—
387	C₄×C₁₃	—	8	1	no	—
388	C₄×C₁₃	—	8	1	no	—
389	C₄×C₁₃	—	8	1	no	—
390	C₄×C₁₃	—	8	1	no	—
391	C₄×C₁₃	—	8	1	no	—
392	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
393	C₄×C₁₃	#534	1	1	yes	characteristic
394	C₄×C₁₃	#551	1	1	yes	characteristic
395	C₄×C₁₃	#551	1	1	yes	characteristic
396	C₂²×Q₈	—	2	1	no	—
397	C₂²×Q₈	—	2	2	no	—
398	C₂²×Q₈	—	2	2	no	—
399	C₂²×Q₈	—	2	2	no	—
400	C₂²×Q₈	—	4	1	no	—
401	C₂²×Q₈	—	4	1	no	—
402	C₂²×Q₈	D₄×C₁₃	1	4	yes	—
403	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₂³×C₄	—	2	1	no	—
407	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×Q₁₆	—	2	2	no	—
409	C₂×Q₁₆	—	2	2	no	—
410	C₂×Q₁₆	—	2	2	no	—
411	C₂×Q₁₆	—	2	2	no	—
412	C₂×Q₁₆	—	4	1	no	—
413	C₂×Q₁₆	—	4	1	no	—
414	C₂×M₁₆	—	2	2	no	—
415	C₂×M₁₆	—	4	1	no	—
416	C₂×M₁₆	—	4	1	no	—
417	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₄×Q₈	—	2	2	no	—
424	C₄×Q₈	—	2	2	no	—
425	C₄×Q₈	—	4	1	no	—
426	C₄×Q₈	—	4	1	no	—
427	#117	—	2	2	no	—
428	#117	—	2	2	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
449	C₄⋊C₈	—	4	1	no	—
450	C₄⋊C₈	—	4	1	no	—
451	#103	—	2	2	no	—
452	#103	—	2	2	no	—
453	#103	—	2	2	no	—
454	#103	—	2	2	no	—
455	#103	—	2	2	no	—
456	#103	—	2	2	no	—
457	#103	—	4	1	no	—
458	#103	—	4	1	no	—
459	C₂²⋊C₈	—	2	2	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	D₄×C₁₃	1	1	yes	characteristic
472	#95	D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₁₃	—	4	2	no	—
474	C₂×C₁₃	#2412	1	1	yes	characteristic
475	C₂×C₁₃	#3037	1	1	yes	characteristic
476	C₂×C₁₃	#3044	1	1	yes	characteristic
477	C₂×C₁₃	#3312	1	1	yes	characteristic
478	C₂×C₁₃	#3313	1	1	yes	characteristic
479	C₂×C₁₃	#3327	1	1	yes	characteristic
480	C₂×C₁₃	#3328	1	1	yes	characteristic
481	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂×Q₈	—	2	4	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	8	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	4	2	no	—
499	C₂×Q₈	—	4	2	no	—
500	C₂×Q₈	—	4	4	no	—
501	C₂×Q₈	—	4	4	no	—
502	C₂×Q₈	—	4	4	no	—
503	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
504	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
505	C₂×Q₈	C₁₃×#41	1	2	yes	—
506	C₂×Q₈	C₁₃×#41	1	2	yes	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	C₁₃×#41	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
530	Q₁₆	—	4	4	no	—
531	Q₁₆	—	4	4	no	—
532	M₁₆	—	4	4	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	4	1	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	4	2	no	—
570	C₄²	—	4	2	no	—
571	C₄²	—	4	2	no	—
572	C₁₃	#24540	1	1	yes	characteristic, direct product factor, Sylow
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	C₁₃×#121	1	2	yes	—
580	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
581	Q₈	—	2	2	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	2	2	no	—
584	Q₈	—	2	2	no	—
585	Q₈	—	2	2	no	—
586	Q₈	—	4	8	no	—
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	Q₈	—	4	1	no	—
592	Q₈	—	4	1	no	—
593	Q₈	C₁₃×#123	1	4	yes	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	8	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	C₁₃×#121	1	2	yes	—
637	C₂×C₄	C₁₃×#137	1	2	yes	—
638	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
639	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
640	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
641	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
642	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
644	C₈	—	4	1	no	—
645	C₈	—	4	1	no	—
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
656	C₂²	C₁₃×#546	1	1	yes	characteristic
657	C₂²	C₁₃×#546	1	1	yes	characteristic
658	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
659	C₂²	C₁₃×#575	1	1	yes	characteristic
660	C₂²	C₁₃×#578	1	1	yes	characteristic
661	C₂²	C₁₃×#578	1	1	yes	characteristic
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	4	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
676	C₄	C₁₃×#534	1	1	yes	characteristic
677	C₄	C₁₃×#551	1	1	yes	characteristic
678	C₄	C₁₃×#551	1	1	yes	characteristic
679	C₂	—	4	2	no	—
680	C₂	C₁₃×#2412	1	1	yes	characteristic
681	C₂	C₁₃×#3037	1	1	yes	characteristic
682	C₂	C₁₃×#3044	1	1	yes	characteristic
683	C₂	C₁₃×#3312	1	1	yes	characteristic
684	C₂	C₁₃×#3313	1	1	yes	characteristic
685	C₂	C₁₃×#3327	1	1	yes	characteristic
686	C₂	C₁₃×#3328	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₃×#2074	C₂	semidirect
6. C₁₃×#2072	C₂	semidirect
7. C₁₃×#2056	C₂	semidirect
8. C₁₃×#2056	C₂	semidirect
10. C₁₃×#1878	C₂	semidirect
11. C₁₃×#1878	C₂	semidirect
14. C₁₃×#1805	C₂	semidirect
15. C₁₃×#1803	C₂	semidirect
138. #24540	C₁₃	direct (N × H)
234. #2074	C₂×C₁₃	semidirect
235. #2072	C₂×C₁₃	semidirect
236. #2056	C₂×C₁₃	semidirect
237. #2056	C₂×C₁₃	semidirect
239. #1878	C₂×C₁₃	semidirect
240. #1878	C₂×C₁₃	semidirect
243. #1805	C₂×C₁₃	semidirect
244. #1803	C₂×C₁₃	semidirect
572. C₁₃	#24540	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×#451	2
C₂×C₁₃×#419	2
C₁₃×#2499	2
Q₈×C₁₃×C₂²⋊C₄	2
C₁₃×#2074	2
C₁₃×#2072	2
C₁₃×#2056	2
C₁₃×#1894	2
C₁₃×#1878	2
C₁₃×#1851	2
C₁₃×#1825	2
C₁₃×#1805	2
C₁₃×#1803	2
#24540	13

Subgroups — C13×#24540 #15710879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24540 #15710879