Subgroups — C₁₃×#18708 #15705047

Order 3328.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1649	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1648	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1641	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1626	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1621	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1557	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#562	—	2	2	no	—
17	C₁₃×#559	—	2	1	no	—
18	C₁₃×#559	C₂²	1	1	yes	characteristic
19	C₁₃×#557	C₂²	1	1	yes	characteristic
20	C₁₃×#554	—	2	1	no	—
21	C₁₃×#550	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#548	—	2	1	no	—
24	C₁₃×#547	—	2	1	no	—
25	C₁₃×#542	—	2	1	no	—
26	C₁₃×#542	—	2	1	no	—
27	C₁₃×#540	—	2	1	no	—
28	C₁₃×#539	—	2	2	no	—
29	C₁₃×#536	—	2	1	no	—
30	C₁₃×#533	C₂²	1	1	yes	characteristic
31	C₁₃×#532	C₂²	1	1	yes	characteristic
32	C₁₃×#532	C₂²	1	1	yes	characteristic
33	C₁₃×#529	C₂²	1	1	yes	characteristic
34	C₁₃×#500	C₂²	1	1	yes	characteristic
35	C₁₃×#497	—	2	1	no	—
36	C₁₃×#493	C₂²	1	1	yes	characteristic
37	C₁₃×#489	—	2	1	no	—
38	C₁₃×#486	C₂²	1	1	yes	characteristic
39	C₁₃×#486	C₂²	1	1	yes	characteristic
40	C₁₃×#478	—	2	1	no	—
41	C₁₃×#475	C₂²	1	1	yes	characteristic
42	C₁₃×#474	C₂²	1	1	yes	characteristic
43	C₁₃×#469	—	2	1	no	—
44	C₁₃×#468	—	2	1	no	—
45	C₁₃×#466	—	2	2	no	—
46	C₁₃×#463	—	2	1	no	—
47	C₁₃×#462	C₂²	1	1	yes	characteristic
48	C₁₃×#462	C₂²	1	1	yes	characteristic
49	C₁₃×#460	C₂²	1	1	yes	characteristic
50	C₁₃×#460	C₂²	1	1	yes	characteristic
51	C₁₃×#460	C₂²	1	1	yes	characteristic
52	C₁₃×#459	C₂²	1	1	yes	characteristic
53	C₁₃×#452	—	2	1	no	—
54	C₁₃×#452	—	2	1	no	—
55	C₄×C₁₃×D₈	—	2	2	no	—
56	C₁₃×#432	C₂²	1	1	yes	characteristic
57	C₁₃×#423	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
59	C₁₃×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×#331	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#41	—	2	1	no	—
72	C₂×C₁₃×#41	—	2	1	no	—
73	C₂×C₁₃×#41	—	2	1	no	—
74	C₂²×Q₈×C₁₃	—	2	1	no	—
75	C₂×C₁₃×Q₁₆	—	2	1	no	—
76	C₂×C₁₃×Q₁₆	—	2	1	no	—
77	C₂×C₁₃×SD₁₆	—	2	1	no	—
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×D₈	—	2	2	no	—
81	C₂×C₁₃×D₈	—	2	1	no	—
82	C₂×C₁₃×M₁₆	—	2	1	no	—
83	C₂²×C₈×C₁₃	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×C₄⋊Q₈	—	2	1	no	—
86	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
88	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₃×#127	—	2	1	no	—
91	C₁₃×#127	C₂³	1	1	yes	characteristic
92	C₁₃×#127	C₂³	1	1	yes	characteristic
93	C₁₃×#126	—	2	2	no	—
94	C₁₃×#126	—	2	1	no	—
95	C₁₃×#125	—	2	2	no	—
96	C₁₃×#125	—	2	1	no	—
97	C₁₃×#125	—	2	1	no	—
98	C₁₃×#125	D₄	1	1	yes	characteristic
99	C₁₃×#124	—	2	2	no	—
100	C₁₃×#124	—	2	2	no	—
101	C₁₃×#124	—	2	1	no	—
102	C₁₃×#124	—	2	1	no	—
103	C₁₃×#124	—	2	1	no	—
104	C₁₃×#124	—	2	1	no	—
105	C₁₃×#124	D₄	1	1	yes	characteristic
106	C₁₃×#123	—	2	2	no	—
107	C₁₃×#123	—	2	2	no	—
108	C₁₃×#123	—	2	2	no	—
109	C₁₃×#123	—	2	2	no	—
110	C₁₃×#123	—	2	2	no	—
111	C₁₃×#123	—	2	2	no	—
112	C₁₃×#123	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	—	2	2	no	—
116	C₁₃×C₂²⋊Q₈	—	2	2	no	—
117	C₁₃×C₂²⋊Q₈	—	2	1	no	—
118	C₁₃×C₂²⋊Q₈	—	2	2	no	—
119	C₁₃×C₂²⋊Q₈	—	2	1	no	—
120	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
121	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
122	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
123	C₁₃×#121	—	2	2	no	—
124	C₁₃×#121	—	2	2	no	—
125	C₁₃×#121	—	2	2	no	—
126	C₁₃×#121	—	2	1	no	—
127	C₁₃×#121	—	2	1	no	—
128	C₁₃×#121	—	2	1	no	—
129	C₁₃×#121	—	2	1	no	—
130	C₁₃×#121	D₄	1	2	yes	—
131	C₁₃×#121	D₄	1	1	yes	characteristic
132	C₄×Q₈×C₁₃	—	2	1	no	—
133	C₄×Q₈×C₁₃	—	2	1	no	—
134	C₄×Q₈×C₁₃	—	2	1	no	—
135	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
136	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₄×D₄×C₁₃	—	2	2	no	—
139	C₄×D₄×C₁₃	—	2	1	no	—
140	C₄×D₄×C₁₃	—	2	1	no	—
141	C₄×D₄×C₁₃	—	2	1	no	—
142	C₄×D₄×C₁₃	—	2	1	no	—
143	C₄×D₄×C₁₃	—	2	1	no	—
144	C₄×D₄×C₁₃	—	2	1	no	—
145	C₄×D₄×C₁₃	—	2	1	no	—
146	C₄×D₄×C₁₃	—	2	1	no	—
147	C₄×D₄×C₁₃	D₄	1	2	yes	—
148	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
149	C₁₃×#117	—	2	1	no	—
150	C₁₃×#117	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
153	C₁₃×#107	—	2	2	no	—
154	C₁₃×#107	—	2	1	no	—
155	C₁₃×#106	—	2	1	no	—
156	C₁₃×C₄⋊C₈	—	2	1	no	—
157	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₁₃×#103	—	2	1	no	—
162	C₁₃×#103	—	2	1	no	—
163	C₁₃×#103	—	2	1	no	—
164	C₁₃×#102	—	2	2	no	—
165	C₁₃×#102	—	2	1	no	—
166	C₁₃×#102	—	2	2	no	—
167	C₁₃×#102	—	2	1	no	—
168	C₁₃×#102	—	2	1	no	—
169	C₁₃×#102	—	2	1	no	—
170	C₁₃×#102	—	2	1	no	—
171	C₁₃×C₂²⋊C₈	—	2	1	no	—
172	C₁₃×#97	—	2	1	no	—
173	C₄×C₈×C₁₃	—	2	1	no	—
174	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
176	#18708	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₁₃×#41	—	8	1	no	—
178	C₁₃×#41	—	8	1	no	—
179	C₁₃×#41	—	8	1	no	—
180	C₁₃×#41	—	8	1	no	—
181	C₁₃×#41	—	8	1	no	—
182	C₁₃×#41	—	8	1	no	—
183	C₂×Q₈×C₁₃	—	2	2	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	8	1	no	—
188	C₂×Q₈×C₁₃	—	8	1	no	—
189	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×D₄×C₁₃	—	2	2	no	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	2	no	—
196	C₂×D₄×C₁₃	—	2	1	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	4	1	no	—
202	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	4	1	no	—
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₁₃×Q₁₆	—	8	1	no	—
214	C₁₃×Q₁₆	—	8	1	no	—
215	C₁₃×SD₁₆	—	8	1	no	—
216	C₁₃×SD₁₆	—	8	1	no	—
217	C₁₃×SD₁₆	—	8	1	no	—
218	C₁₃×D₈	—	4	4	no	—
219	C₁₃×D₈	—	8	1	no	—
220	C₁₃×M₁₆	—	8	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	2	1	no	—
227	C₂×C₈×C₁₃	—	4	2	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₁₃×C₄⋊C₄	—	2	2	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
247	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
248	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
249	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
250	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
251	C₁₃×C₂²⋊C₄	—	2	2	no	—
252	C₁₃×C₂²⋊C₄	—	2	2	no	—
253	C₁₃×C₂²⋊C₄	—	2	2	no	—
254	C₁₃×C₂²⋊C₄	—	2	2	no	—
255	C₁₃×C₂²⋊C₄	—	2	2	no	—
256	C₁₃×C₂²⋊C₄	—	2	1	no	—
257	C₁₃×C₂²⋊C₄	—	2	1	no	—
258	C₁₃×C₂²⋊C₄	—	2	1	no	—
259	C₁₃×C₂²⋊C₄	—	2	1	no	—
260	C₁₃×C₂²⋊C₄	—	2	1	no	—
261	C₁₃×C₂²⋊C₄	—	2	1	no	—
262	C₁₃×C₂²⋊C₄	—	2	2	no	—
263	C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	1	no	—
265	C₁₃×C₂²⋊C₄	—	4	1	no	—
266	C₁₃×C₂²⋊C₄	—	4	1	no	—
267	C₄²×C₁₃	—	2	2	no	—
268	C₄²×C₁₃	—	2	1	no	—
269	C₄²×C₁₃	—	2	1	no	—
270	C₄²×C₁₃	—	2	1	no	—
271	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
275	#3554	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#3251	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1649	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1648	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1641	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1640	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1627	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1626	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1621	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1620	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1557	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#1494	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂³×C₁₃	—	2	1	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	4	1	no	—
293	C₂³×C₁₃	#120	1	1	yes	characteristic
294	Q₈×C₁₃	—	2	1	no	—
295	Q₈×C₁₃	—	2	1	no	—
296	Q₈×C₁₃	—	2	1	no	—
297	Q₈×C₁₃	—	2	1	no	—
298	Q₈×C₁₃	—	2	1	no	—
299	Q₈×C₁₃	—	2	1	no	—
300	Q₈×C₁₃	—	4	1	no	—
301	Q₈×C₁₃	—	4	1	no	—
302	Q₈×C₁₃	—	4	1	no	—
303	Q₈×C₁₃	—	4	1	no	—
304	Q₈×C₁₃	—	8	1	no	—
305	Q₈×C₁₃	—	8	2	no	—
306	D₄×C₁₃	—	2	1	no	—
307	D₄×C₁₃	—	2	1	no	—
308	D₄×C₁₃	—	4	2	no	—
309	D₄×C₁₃	—	4	2	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	4	1	no	—
313	D₄×C₁₃	—	4	1	no	—
314	D₄×C₁₃	—	4	1	no	—
315	D₄×C₁₃	—	4	1	no	—
316	D₄×C₁₃	—	4	1	no	—
317	D₄×C₁₃	—	4	1	no	—
318	D₄×C₁₃	—	8	1	no	—
319	D₄×C₁₃	—	8	2	no	—
320	D₄×C₁₃	—	8	2	no	—
321	D₄×C₁₃	—	8	2	no	—
322	D₄×C₁₃	—	8	2	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	4	1	no	—
338	C₂×C₄×C₁₃	—	4	1	no	—
339	C₂×C₄×C₁₃	—	8	2	no	—
340	C₂×C₄×C₁₃	—	8	2	no	—
341	C₂×C₄×C₁₃	—	8	2	no	—
342	C₂×C₄×C₁₃	—	8	2	no	—
343	C₂×C₄×C₁₃	—	8	2	no	—
344	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
345	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
346	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₈×C₁₃	—	2	2	no	—
351	C₈×C₁₃	—	4	1	no	—
352	C₈×C₁₃	—	4	1	no	—
353	C₈×C₁₃	—	4	1	no	—
354	C₈×C₁₃	—	4	1	no	—
355	C₈×C₁₃	—	4	1	no	—
356	#562	—	2	2	no	—
357	#559	—	2	1	no	—
358	#559	C₂²×C₁₃	1	1	yes	characteristic
359	#557	C₂²×C₁₃	1	1	yes	characteristic
360	#554	—	2	1	no	—
361	#550	C₂²×C₁₃	1	1	yes	characteristic
362	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
363	#548	—	2	1	no	—
364	#547	—	2	1	no	—
365	#542	—	2	1	no	—
366	#542	—	2	1	no	—
367	#540	—	2	1	no	—
368	#539	—	2	2	no	—
369	#536	—	2	1	no	—
370	#533	C₂²×C₁₃	1	1	yes	characteristic
371	#532	C₂²×C₁₃	1	1	yes	characteristic
372	#532	C₂²×C₁₃	1	1	yes	characteristic
373	#529	C₂²×C₁₃	1	1	yes	characteristic
374	#500	C₂²×C₁₃	1	1	yes	characteristic
375	#497	—	2	1	no	—
376	#493	C₂²×C₁₃	1	1	yes	characteristic
377	#489	—	2	1	no	—
378	#486	C₂²×C₁₃	1	1	yes	characteristic
379	#486	C₂²×C₁₃	1	1	yes	characteristic
380	#478	—	2	1	no	—
381	#475	C₂²×C₁₃	1	1	yes	characteristic
382	#474	C₂²×C₁₃	1	1	yes	characteristic
383	#469	—	2	1	no	—
384	#468	—	2	1	no	—
385	#466	—	2	2	no	—
386	#463	—	2	1	no	—
387	#462	C₂²×C₁₃	1	1	yes	characteristic
388	#462	C₂²×C₁₃	1	1	yes	characteristic
389	#460	C₂²×C₁₃	1	1	yes	characteristic
390	#460	C₂²×C₁₃	1	1	yes	characteristic
391	#460	C₂²×C₁₃	1	1	yes	characteristic
392	#459	C₂²×C₁₃	1	1	yes	characteristic
393	#452	—	2	1	no	—
394	#452	—	2	1	no	—
395	C₄×D₈	—	2	2	no	—
396	#432	C₂²×C₁₃	1	1	yes	characteristic
397	#423	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
399	#332	C₂²×C₁₃	1	1	yes	characteristic
400	#332	C₂²×C₁₃	1	1	yes	characteristic
401	#331	C₂²×C₁₃	1	1	yes	characteristic
402	#331	C₂²×C₁₃	1	1	yes	characteristic
403	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
404	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
405	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
406	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
407	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
408	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
409	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
410	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
411	C₂²×C₁₃	—	2	1	no	—
412	C₂²×C₁₃	—	2	1	no	—
413	C₂²×C₁₃	—	2	1	no	—
414	C₂²×C₁₃	—	4	1	no	—
415	C₂²×C₁₃	—	4	2	no	—
416	C₂²×C₁₃	—	4	1	no	—
417	C₂²×C₁₃	—	4	2	no	—
418	C₂²×C₁₃	—	4	2	no	—
419	C₂²×C₁₃	—	4	1	no	—
420	C₂²×C₁₃	—	8	1	no	—
421	C₂²×C₁₃	—	8	1	no	—
422	C₂²×C₁₃	—	8	1	no	—
423	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
424	C₄×C₁₃	—	2	1	no	—
425	C₄×C₁₃	—	2	1	no	—
426	C₄×C₁₃	—	2	1	no	—
427	C₄×C₁₃	—	2	1	no	—
428	C₄×C₁₃	—	4	1	no	—
429	C₄×C₁₃	—	4	1	no	—
430	C₄×C₁₃	—	4	2	no	—
431	C₄×C₁₃	—	4	1	no	—
432	C₄×C₁₃	—	4	1	no	—
433	C₄×C₁₃	—	4	1	no	—
434	C₄×C₁₃	—	4	1	no	—
435	C₄×C₁₃	—	4	1	no	—
436	C₄×C₁₃	—	8	1	no	—
437	C₄×C₁₃	#576	1	1	yes	characteristic
438	C₄×C₁₃	#576	1	1	yes	characteristic
439	C₄×C₁₃	#577	1	1	yes	characteristic
440	C₄×C₁₃	#578	1	1	yes	characteristic
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	2	1	no	—
443	C₂×#41	—	2	1	no	—
444	C₂²×Q₈	—	2	1	no	—
445	C₂×Q₁₆	—	2	1	no	—
446	C₂×Q₁₆	—	2	1	no	—
447	C₂×SD₁₆	—	2	1	no	—
448	C₂×SD₁₆	—	2	1	no	—
449	C₂×SD₁₆	—	2	1	no	—
450	C₂×D₈	—	2	2	no	—
451	C₂×D₈	—	2	1	no	—
452	C₂×M₁₆	—	2	1	no	—
453	C₂²×C₈	—	2	1	no	—
454	C₄⋊Q₈	—	2	1	no	—
455	C₄⋊Q₈	—	2	1	no	—
456	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
457	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
458	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
460	#127	—	2	1	no	—
461	#127	C₂³×C₁₃	1	1	yes	characteristic
462	#127	C₂³×C₁₃	1	1	yes	characteristic
463	#126	—	2	2	no	—
464	#126	—	2	1	no	—
465	#125	—	2	2	no	—
466	#125	—	2	1	no	—
467	#125	—	2	1	no	—
468	#125	D₄×C₁₃	1	1	yes	characteristic
469	#124	—	2	2	no	—
470	#124	—	2	2	no	—
471	#124	—	2	1	no	—
472	#124	—	2	1	no	—
473	#124	—	2	1	no	—
474	#124	—	2	1	no	—
475	#124	D₄×C₁₃	1	1	yes	characteristic
476	#123	—	2	2	no	—
477	#123	—	2	2	no	—
478	#123	—	2	2	no	—
479	#123	—	2	2	no	—
480	#123	—	2	2	no	—
481	#123	—	2	2	no	—
482	#123	—	2	1	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	1	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
491	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
492	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	1	no	—
497	#121	—	2	1	no	—
498	#121	—	2	1	no	—
499	#121	—	2	1	no	—
500	#121	D₄×C₁₃	1	1	yes	characteristic
501	#121	D₄×C₁₃	1	2	yes	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
506	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	D₄×C₁₃	1	2	yes	—
518	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
519	#117	—	2	1	no	—
520	#117	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	2	no	—
522	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
523	#107	—	2	2	no	—
524	#107	—	2	1	no	—
525	#106	—	2	1	no	—
526	C₄⋊C₈	—	2	1	no	—
527	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
528	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
529	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
530	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
531	#103	—	2	1	no	—
532	#103	—	2	1	no	—
533	#103	—	2	1	no	—
534	#102	—	2	2	no	—
535	#102	—	2	1	no	—
536	#102	—	2	2	no	—
537	#102	—	2	1	no	—
538	#102	—	2	1	no	—
539	#102	—	2	1	no	—
540	#102	—	2	1	no	—
541	C₂²⋊C₈	—	2	1	no	—
542	#97	—	2	1	no	—
543	C₄×C₈	—	2	1	no	—
544	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×C₁₃	—	4	1	no	—
547	C₂×C₁₃	—	8	1	no	—
548	C₂×C₁₃	—	8	2	no	—
549	C₂×C₁₃	—	16	1	no	—
550	C₂×C₁₃	#3008	1	1	yes	characteristic
551	C₂×C₁₃	#3013	1	1	yes	characteristic
552	C₂×C₁₃	#3018	1	1	yes	characteristic
553	#41	—	8	1	no	—
554	#41	—	8	1	no	—
555	#41	—	8	1	no	—
556	#41	—	8	1	no	—
557	#41	—	8	1	no	—
558	#41	—	8	1	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	8	1	no	—
564	C₂×Q₈	—	8	1	no	—
565	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
579	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
589	Q₁₆	—	8	1	no	—
590	Q₁₆	—	8	1	no	—
591	SD₁₆	—	8	1	no	—
592	SD₁₆	—	8	1	no	—
593	SD₁₆	—	8	1	no	—
594	D₈	—	4	4	no	—
595	D₈	—	8	1	no	—
596	M₁₆	—	8	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	4	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
623	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
624	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
626	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	4	1	no	—
642	C₂²⋊C₄	—	4	1	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	2	1	no	—
646	C₄²	—	2	1	no	—
647	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
649	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
651	C₁₃	#18708	1	1	yes	characteristic, direct product factor, Sylow
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	1	no	—
655	C₂³	C₁₃×#120	1	1	yes	characteristic
656	Q₈	—	2	1	no	—
657	Q₈	—	2	1	no	—
658	Q₈	—	2	1	no	—
659	Q₈	—	2	1	no	—
660	Q₈	—	2	1	no	—
661	Q₈	—	2	1	no	—
662	Q₈	—	4	1	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	4	1	no	—
665	Q₈	—	4	1	no	—
666	Q₈	—	8	1	no	—
667	Q₈	—	8	2	no	—
668	D₄	—	2	1	no	—
669	D₄	—	2	1	no	—
670	D₄	—	4	2	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	D₄	—	4	1	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	8	1	no	—
681	D₄	—	8	2	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	2	no	—
684	D₄	—	8	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	8	2	no	—
702	C₂×C₄	—	8	2	no	—
703	C₂×C₄	—	8	2	no	—
704	C₂×C₄	—	8	2	no	—
705	C₂×C₄	—	8	2	no	—
706	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
707	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
708	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
712	C₈	—	2	2	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₈	—	4	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	8	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	8	1	no	—
744	C₄	C₁₃×#576	1	1	yes	characteristic
745	C₄	C₁₃×#576	1	1	yes	characteristic
746	C₄	C₁₃×#577	1	1	yes	characteristic
747	C₄	C₁₃×#578	1	1	yes	characteristic
748	C₂	—	4	1	no	—
749	C₂	—	8	1	no	—
750	C₂	—	8	2	no	—
751	C₂	—	16	1	no	—
752	C₂	C₁₃×#3008	1	1	yes	characteristic
753	C₂	C₁₃×#3013	1	1	yes	characteristic
754	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
LCS	G ▷ C₄² ▷ 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
1. C₁₃×#3554	C₂	semidirect
2. C₁₃×#3251	C₂	semidirect
3. C₁₃×#3216	C₂	semidirect
4. C₁₃×#3169	C₂	semidirect
5. C₁₃×#1649	C₂	semidirect
6. C₁₃×#1648	C₂	semidirect
7. C₁₃×#1641	C₂	semidirect
8. C₁₃×#1640	C₂	semidirect
9. C₁₃×#1627	C₂	semidirect
10. C₁₃×#1626	C₂	semidirect
11. C₁₃×#1621	C₂	semidirect
12. C₁₃×#1620	C₂	semidirect
13. C₁₃×#1557	C₂	semidirect
14. C₁₃×#1494	C₂	semidirect
15. C₁₃×#1493	C₂	semidirect
176. #18708	C₁₃	direct (N × H)
275. #3554	C₂×C₁₃	semidirect
276. #3251	C₂×C₁₃	semidirect
277. #3216	C₂×C₁₃	semidirect
278. #3169	C₂×C₁₃	semidirect
279. #1649	C₂×C₁₃	semidirect
280. #1648	C₂×C₁₃	semidirect
281. #1641	C₂×C₁₃	semidirect
282. #1640	C₂×C₁₃	semidirect
283. #1627	C₂×C₁₃	semidirect
284. #1626	C₂×C₁₃	semidirect
285. #1621	C₂×C₁₃	semidirect
286. #1620	C₂×C₁₃	semidirect
287. #1557	C₂×C₁₃	semidirect
288. #1494	C₂×C₁₃	semidirect
289. #1493	C₂×C₁₃	semidirect
651. C₁₃	#18708	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3554	2
C₁₃×#3251	2
C₁₃×#3216	2
C₁₃×#3169	2
C₁₃×#1649	2
C₁₃×#1648	2
C₁₃×#1641	2
C₁₃×#1640	2
C₁₃×#1627	2
C₁₃×#1626	2
C₁₃×#1621	2
C₁₃×#1620	2
C₁₃×#1557	2
C₁₃×#1494	2
C₁₃×#1493	2
#18708	13

Subgroups — C13×#18708 #15705047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18708 #15705047