Subgroups — C₁₃×#18445 #15704784

Order 3328.

848 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3564	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3232	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2664	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1618	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1617	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1615	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1614	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1612	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1611	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1609	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1608	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1509	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1503	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1473	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#563	—	2	1	no	—
17	C₁₃×#563	—	2	1	no	—
18	C₁₃×#556	—	2	1	no	—
19	C₁₃×#554	—	2	1	no	—
20	C₁₃×#552	—	2	1	no	—
21	C₁₃×#552	—	2	1	no	—
22	C₁₃×#551	—	2	1	no	—
23	C₁₃×#551	—	2	1	no	—
24	C₁₃×#544	C₂²	1	1	yes	characteristic
25	C₁₃×#543	C₂²	1	1	yes	characteristic
26	C₁₃×#542	—	2	1	no	—
27	C₁₃×#541	—	2	1	no	—
28	C₁₃×#541	—	2	1	no	—
29	C₁₃×#539	—	2	1	no	—
30	C₁₃×#539	C₂²	1	1	yes	characteristic
31	C₁₃×#538	C₂²	1	1	yes	characteristic
32	C₁₃×#533	C₂²	1	1	yes	characteristic
33	C₁₃×#529	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#126	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
36	C₁₃×#501	—	2	1	no	—
37	C₁₃×#499	—	2	1	no	—
38	C₁₃×#491	—	2	1	no	—
39	C₁₃×#488	—	2	1	no	—
40	C₁₃×#484	C₂²	1	1	yes	characteristic
41	C₁₃×#484	C₂²	1	1	yes	characteristic
42	C₁₃×#484	C₂²	1	1	yes	characteristic
43	C₁₃×#483	C₂²	1	1	yes	characteristic
44	C₁₃×#483	C₂²	1	1	yes	characteristic
45	C₁₃×#483	C₂²	1	1	yes	characteristic
46	C₁₃×#481	C₂²	1	1	yes	characteristic
47	C₁₃×#480	C₂²	1	1	yes	characteristic
48	C₁₃×#479	—	2	1	no	—
49	C₁₃×#479	—	2	1	no	—
50	C₁₃×#479	—	2	1	no	—
51	C₁₃×#478	—	2	1	no	—
52	C₁₃×#432	C₂²	1	1	yes	characteristic
53	C₁₃×#431	C₂²	1	1	yes	characteristic
54	C₁₃×#400	C₂²	1	1	yes	characteristic
55	C₁₃×#399	C₂²	1	1	yes	characteristic
56	C₁₃×#398	—	2	1	no	—
57	C₁₃×#398	C₂²	1	1	yes	characteristic
58	C₁₃×#397	C₂²	1	1	yes	characteristic
59	C₁₃×#396	—	2	1	no	—
60	C₁₃×#389	—	2	1	no	—
61	C₁₃×#388	—	2	1	no	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
63	C₁₃×#328	C₂²	1	1	yes	characteristic
64	C₁₃×#328	C₂²	1	1	yes	characteristic
65	C₁₃×#328	C₂²	1	1	yes	characteristic
66	C₁₃×#328	C₂²	1	1	yes	characteristic
67	C₁₃×#328	C₂²	1	1	yes	characteristic
68	C₁₃×#328	C₂²	1	1	yes	characteristic
69	C₁₃×#327	C₂²	1	1	yes	characteristic
70	C₁₃×#327	C₂²	1	1	yes	characteristic
71	C₁₃×#324	C₂²	1	1	yes	characteristic
72	C₁₃×#324	C₂²	1	1	yes	characteristic
73	C₁₃×#323	C₂²	1	1	yes	characteristic
74	C₁₃×#323	C₂²	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	—	2	1	no	—
76	C₁₃×C₄⋊Q₈	—	2	1	no	—
77	C₁₃×C₄⋊Q₈	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
79	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
80	C₁₃×#126	—	2	1	no	—
81	C₁₃×#126	—	2	1	no	—
82	C₁₃×#126	—	2	1	no	—
83	C₁₃×#126	—	2	1	no	—
84	C₁₃×#126	—	2	1	no	—
85	C₁₃×#126	—	2	1	no	—
86	C₁₃×#126	—	2	1	no	—
87	C₁₃×#126	—	2	1	no	—
88	C₁₃×#126	—	2	1	no	—
89	C₁₃×#126	—	2	1	no	—
90	C₁₃×#126	—	2	1	no	—
91	C₁₃×#126	—	2	1	no	—
92	C₁₃×#126	—	2	1	no	—
93	C₁₃×#125	—	2	1	no	—
94	C₁₃×#125	—	2	1	no	—
95	C₁₃×#125	—	2	1	no	—
96	C₁₃×#125	—	2	1	no	—
97	C₁₃×#125	—	2	1	no	—
98	C₁₃×#125	—	2	1	no	—
99	C₁₃×#125	—	2	1	no	—
100	C₁₃×#125	—	2	1	no	—
101	C₁₃×#125	—	2	1	no	—
102	C₁₃×#125	—	2	1	no	—
103	C₁₃×#125	—	2	1	no	—
104	C₁₃×#125	—	2	1	no	—
105	C₁₃×#125	—	2	1	no	—
106	C₁₃×#125	D₄	1	1	yes	characteristic
107	C₁₃×#124	—	2	1	no	—
108	C₁₃×#124	—	2	1	no	—
109	C₁₃×#124	—	2	1	no	—
110	C₁₃×#124	D₄	1	1	yes	characteristic
111	C₁₃×#123	—	2	1	no	—
112	C₁₃×#123	—	2	1	no	—
113	C₁₃×#123	—	2	1	no	—
114	C₁₃×#123	—	2	1	no	—
115	C₁₃×#123	—	2	1	no	—
116	C₁₃×#123	—	2	1	no	—
117	C₁₃×#123	—	2	1	no	—
118	C₁₃×#123	—	2	1	no	—
119	C₁₃×C₂²⋊Q₈	—	2	1	no	—
120	C₁₃×C₂²⋊Q₈	—	2	1	no	—
121	C₁₃×C₂²⋊Q₈	—	2	1	no	—
122	C₁₃×C₂²⋊Q₈	—	2	1	no	—
123	C₁₃×C₂²⋊Q₈	—	2	1	no	—
124	C₁₃×C₂²⋊Q₈	—	2	1	no	—
125	C₁₃×C₂²⋊Q₈	—	2	1	no	—
126	C₁₃×C₂²⋊Q₈	—	2	1	no	—
127	C₁₃×C₂²⋊Q₈	—	2	1	no	—
128	C₁₃×C₂²⋊Q₈	—	2	1	no	—
129	C₁₃×C₂²⋊Q₈	—	2	1	no	—
130	C₁₃×C₂²⋊Q₈	—	2	1	no	—
131	C₁₃×C₂²⋊Q₈	—	2	1	no	—
132	C₁₃×C₂²⋊Q₈	—	2	1	no	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
134	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
136	C₁₃×#121	—	2	1	no	—
137	C₁₃×#121	C₂³	1	1	yes	characteristic
138	C₁₃×#120	—	2	1	no	—
139	C₄×Q₈×C₁₃	—	2	1	no	—
140	C₄×Q₈×C₁₃	—	2	1	no	—
141	C₄×Q₈×C₁₃	—	2	1	no	—
142	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
143	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
144	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
145	C₄×D₄×C₁₃	—	2	1	no	—
146	C₄×D₄×C₁₃	—	2	1	no	—
147	C₄×D₄×C₁₃	—	2	1	no	—
148	C₄×D₄×C₁₃	—	2	1	no	—
149	C₄×D₄×C₁₃	—	2	1	no	—
150	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
151	C₁₃×#117	—	2	1	no	—
152	C₁₃×#117	—	2	1	no	—
153	C₁₃×#117	—	2	1	no	—
154	C₁₃×#117	—	2	1	no	—
155	C₁₃×#117	—	2	1	no	—
156	C₁₃×#117	—	2	1	no	—
157	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
164	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
170	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
172	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃	—	2	1	no	—
175	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₁₃×#107	—	2	1	no	—
177	C₁₃×#107	—	2	1	no	—
178	C₁₃×#107	—	2	1	no	—
179	C₁₃×#107	—	2	1	no	—
180	C₁₃×#106	—	2	1	no	—
181	C₁₃×#106	—	2	1	no	—
182	C₁₃×#106	—	2	1	no	—
183	C₁₃×#106	—	2	1	no	—
184	C₁₃×C₄⋊C₈	—	2	1	no	—
185	C₁₃×C₄⋊C₈	—	2	1	no	—
186	C₁₃×#103	—	2	1	no	—
187	C₁₃×#103	—	2	1	no	—
188	C₁₃×#103	—	2	1	no	—
189	C₁₃×#103	—	2	1	no	—
190	C₁₃×#103	—	2	1	no	—
191	C₁₃×#103	—	2	1	no	—
192	C₁₃×#102	—	2	1	no	—
193	C₁₃×#102	—	2	1	no	—
194	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
195	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
196	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
197	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
198	C₁₃×#97	—	2	1	no	—
199	C₄×C₈×C₁₃	—	2	1	no	—
200	C₁₃×#95	—	2	1	no	—
201	C₁₃×#95	—	2	1	no	—
202	C₁₃×#95	—	2	1	no	—
203	C₁₃×#95	—	2	1	no	—
204	C₁₃×#95	C₂³	1	1	yes	characteristic
205	C₁₃×#95	C₂³	1	1	yes	characteristic
206	#18445	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₃	—	2	1	no	—
209	C₂×Q₈×C₁₃	—	2	1	no	—
210	C₂×Q₈×C₁₃	—	2	1	no	—
211	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₈×C₁₃	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	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	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	4	2	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	—	4	1	no	—
273	C₁₃×C₄⋊C₄	—	4	1	no	—
274	C₁₃×C₄⋊C₄	—	4	1	no	—
275	C₁₃×C₄⋊C₄	—	4	1	no	—
276	C₁₃×C₄⋊C₄	—	8	1	no	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
278	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
279	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
280	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
281	C₁₃×C₂²⋊C₄	—	2	1	no	—
282	C₁₃×C₂²⋊C₄	—	2	1	no	—
283	C₁₃×C₂²⋊C₄	—	2	1	no	—
284	C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	1	no	—
291	C₁₃×C₂²⋊C₄	—	2	1	no	—
292	C₁₃×C₂²⋊C₄	—	2	1	no	—
293	C₁₃×C₂²⋊C₄	—	2	1	no	—
294	C₁₃×C₂²⋊C₄	—	2	1	no	—
295	C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₁₃×C₂²⋊C₄	—	2	1	no	—
297	C₁₃×C₂²⋊C₄	—	2	1	no	—
298	C₁₃×C₂²⋊C₄	—	2	1	no	—
299	C₁₃×C₂²⋊C₄	—	2	1	no	—
300	C₁₃×C₂²⋊C₄	—	2	1	no	—
301	C₁₃×C₂²⋊C₄	—	2	1	no	—
302	C₁₃×C₂²⋊C₄	—	4	2	no	—
303	C₁₃×C₂²⋊C₄	—	8	1	no	—
304	C₄²×C₁₃	—	2	1	no	—
305	C₄²×C₁₃	—	2	1	no	—
306	C₄²×C₁₃	—	2	1	no	—
307	C₄²×C₁₃	—	2	1	no	—
308	C₄²×C₁₃	—	2	1	no	—
309	C₄²×C₁₃	—	2	1	no	—
310	C₄²×C₁₃	—	2	1	no	—
311	C₄²×C₁₃	—	8	1	no	—
312	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
316	#3564	C₂×C₁₃	1	1	yes	characteristic
317	#3236	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#3232	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#2664	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#1618	C₂×C₁₃	1	1	yes	characteristic
321	#1617	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#1615	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#1614	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#1612	C₂×C₁₃	1	1	yes	characteristic
325	#1611	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#1609	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#1608	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#1509	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#1503	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#1473	C₂×C₁₃	1	1	yes	characteristic, complemented
331	C₂³×C₁₃	—	2	1	no	—
332	C₂³×C₁₃	—	2	1	no	—
333	C₂³×C₁₃	—	2	1	no	—
334	C₂³×C₁₃	—	2	1	no	—
335	C₂³×C₁₃	—	4	1	no	—
336	C₂³×C₁₃	—	4	1	no	—
337	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
338	Q₈×C₁₃	—	4	1	no	—
339	Q₈×C₁₃	—	4	1	no	—
340	Q₈×C₁₃	—	4	1	no	—
341	Q₈×C₁₃	—	8	1	no	—
342	Q₈×C₁₃	—	8	1	no	—
343	Q₈×C₁₃	—	8	1	no	—
344	D₄×C₁₃	—	4	1	no	—
345	D₄×C₁₃	—	4	1	no	—
346	D₄×C₁₃	—	4	1	no	—
347	D₄×C₁₃	—	8	1	no	—
348	D₄×C₁₃	—	8	1	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	2	1	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	1	no	—
376	C₂×C₄×C₁₃	—	4	1	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	8	1	no	—
380	C₂×C₄×C₁₃	—	8	1	no	—
381	C₂×C₄×C₁₃	—	8	1	no	—
382	C₂×C₄×C₁₃	—	8	1	no	—
383	C₂×C₄×C₁₃	—	8	1	no	—
384	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
385	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
386	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
387	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
390	C₈×C₁₃	—	4	1	no	—
391	C₈×C₁₃	—	4	1	no	—
392	C₈×C₁₃	—	4	1	no	—
393	C₈×C₁₃	—	4	1	no	—
394	#563	—	2	1	no	—
395	#563	—	2	1	no	—
396	#556	—	2	1	no	—
397	#554	—	2	1	no	—
398	#552	—	2	1	no	—
399	#552	—	2	1	no	—
400	#551	—	2	1	no	—
401	#551	—	2	1	no	—
402	#544	C₂²×C₁₃	1	1	yes	characteristic
403	#543	C₂²×C₁₃	1	1	yes	characteristic
404	#542	—	2	1	no	—
405	#541	—	2	1	no	—
406	#541	—	2	1	no	—
407	#539	—	2	1	no	—
408	#539	C₂²×C₁₃	1	1	yes	characteristic
409	#538	C₂²×C₁₃	1	1	yes	characteristic
410	#533	C₂²×C₁₃	1	1	yes	characteristic
411	#529	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#126	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
414	#501	—	2	1	no	—
415	#499	—	2	1	no	—
416	#491	—	2	1	no	—
417	#488	—	2	1	no	—
418	#484	C₂²×C₁₃	1	1	yes	characteristic
419	#484	C₂²×C₁₃	1	1	yes	characteristic
420	#484	C₂²×C₁₃	1	1	yes	characteristic
421	#483	C₂²×C₁₃	1	1	yes	characteristic
422	#483	C₂²×C₁₃	1	1	yes	characteristic
423	#483	C₂²×C₁₃	1	1	yes	characteristic
424	#481	C₂²×C₁₃	1	1	yes	characteristic
425	#480	C₂²×C₁₃	1	1	yes	characteristic
426	#479	—	2	1	no	—
427	#479	—	2	1	no	—
428	#479	—	2	1	no	—
429	#478	—	2	1	no	—
430	#432	C₂²×C₁₃	1	1	yes	characteristic
431	#431	C₂²×C₁₃	1	1	yes	characteristic
432	#400	C₂²×C₁₃	1	1	yes	characteristic
433	#399	C₂²×C₁₃	1	1	yes	characteristic
434	#398	—	2	1	no	—
435	#398	C₂²×C₁₃	1	1	yes	characteristic
436	#397	C₂²×C₁₃	1	1	yes	characteristic
437	#396	—	2	1	no	—
438	#389	—	2	1	no	—
439	#388	—	2	1	no	—
440	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
441	#328	C₂²×C₁₃	1	1	yes	characteristic
442	#328	C₂²×C₁₃	1	1	yes	characteristic
443	#328	C₂²×C₁₃	1	1	yes	characteristic
444	#328	C₂²×C₁₃	1	1	yes	characteristic
445	#328	C₂²×C₁₃	1	1	yes	characteristic
446	#328	C₂²×C₁₃	1	1	yes	characteristic
447	#327	C₂²×C₁₃	1	1	yes	characteristic
448	#327	C₂²×C₁₃	1	1	yes	characteristic
449	#324	C₂²×C₁₃	1	1	yes	characteristic
450	#324	C₂²×C₁₃	1	1	yes	characteristic
451	#323	C₂²×C₁₃	1	1	yes	characteristic
452	#323	C₂²×C₁₃	1	1	yes	characteristic
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	4	1	no	—
456	C₂²×C₁₃	—	4	1	no	—
457	C₂²×C₁₃	—	4	1	no	—
458	C₂²×C₁₃	—	4	1	no	—
459	C₂²×C₁₃	—	4	1	no	—
460	C₂²×C₁₃	—	4	1	no	—
461	C₂²×C₁₃	—	8	1	no	—
462	C₂²×C₁₃	—	8	1	no	—
463	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
464	C₂²×C₁₃	#577	1	1	yes	characteristic
465	C₂²×C₁₃	#578	1	1	yes	characteristic
466	C₄×C₁₃	—	2	1	no	—
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	1	no	—
470	C₄×C₁₃	—	2	1	no	—
471	C₄×C₁₃	—	2	1	no	—
472	C₄×C₁₃	—	4	2	no	—
473	C₄×C₁₃	—	4	1	no	—
474	C₄×C₁₃	—	4	1	no	—
475	C₄×C₁₃	—	4	1	no	—
476	C₄×C₁₃	—	4	1	no	—
477	C₄×C₁₃	—	4	1	no	—
478	C₄×C₁₃	—	4	1	no	—
479	C₄×C₁₃	—	4	1	no	—
480	C₄×C₁₃	—	4	1	no	—
481	C₄×C₁₃	—	4	1	no	—
482	C₄×C₁₃	—	4	1	no	—
483	C₄×C₁₃	—	8	1	no	—
484	C₄×C₁₃	—	8	1	no	—
485	C₄×C₁₃	—	8	1	no	—
486	C₄⋊Q₈	—	2	1	no	—
487	C₄⋊Q₈	—	2	1	no	—
488	C₄⋊Q₈	—	2	1	no	—
489	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
490	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
491	#126	—	2	1	no	—
492	#126	—	2	1	no	—
493	#126	—	2	1	no	—
494	#126	—	2	1	no	—
495	#126	—	2	1	no	—
496	#126	—	2	1	no	—
497	#126	—	2	1	no	—
498	#126	—	2	1	no	—
499	#126	—	2	1	no	—
500	#126	—	2	1	no	—
501	#126	—	2	1	no	—
502	#126	—	2	1	no	—
503	#126	—	2	1	no	—
504	#125	—	2	1	no	—
505	#125	—	2	1	no	—
506	#125	—	2	1	no	—
507	#125	—	2	1	no	—
508	#125	—	2	1	no	—
509	#125	—	2	1	no	—
510	#125	—	2	1	no	—
511	#125	—	2	1	no	—
512	#125	—	2	1	no	—
513	#125	—	2	1	no	—
514	#125	—	2	1	no	—
515	#125	—	2	1	no	—
516	#125	—	2	1	no	—
517	#125	D₄×C₁₃	1	1	yes	characteristic
518	#124	—	2	1	no	—
519	#124	—	2	1	no	—
520	#124	—	2	1	no	—
521	#124	D₄×C₁₃	1	1	yes	characteristic
522	#123	—	2	1	no	—
523	#123	—	2	1	no	—
524	#123	—	2	1	no	—
525	#123	—	2	1	no	—
526	#123	—	2	1	no	—
527	#123	—	2	1	no	—
528	#123	—	2	1	no	—
529	#123	—	2	1	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
547	#121	—	2	1	no	—
548	#121	C₂³×C₁₃	1	1	yes	characteristic
549	#120	—	2	1	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
554	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
555	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
562	#117	—	2	1	no	—
563	#117	—	2	1	no	—
564	#117	—	2	1	no	—
565	#117	—	2	1	no	—
566	#117	—	2	1	no	—
567	#117	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
587	#107	—	2	1	no	—
588	#107	—	2	1	no	—
589	#107	—	2	1	no	—
590	#107	—	2	1	no	—
591	#106	—	2	1	no	—
592	#106	—	2	1	no	—
593	#106	—	2	1	no	—
594	#106	—	2	1	no	—
595	C₄⋊C₈	—	2	1	no	—
596	C₄⋊C₈	—	2	1	no	—
597	#103	—	2	1	no	—
598	#103	—	2	1	no	—
599	#103	—	2	1	no	—
600	#103	—	2	1	no	—
601	#103	—	2	1	no	—
602	#103	—	2	1	no	—
603	#102	—	2	1	no	—
604	#102	—	2	1	no	—
605	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
607	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
608	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
609	#97	—	2	1	no	—
610	C₄×C₈	—	2	1	no	—
611	#95	—	2	1	no	—
612	#95	—	2	1	no	—
613	#95	—	2	1	no	—
614	#95	—	2	1	no	—
615	#95	C₂³×C₁₃	1	1	yes	characteristic
616	#95	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×C₁₃	—	2	1	no	—
618	C₂×C₁₃	—	2	1	no	—
619	C₂×C₁₃	—	8	1	no	—
620	C₂×C₁₃	—	8	1	no	—
621	C₂×C₁₃	#3013	1	1	yes	characteristic
622	C₂×C₁₃	#3018	1	1	yes	characteristic
623	C₂×C₁₃	#3028	1	1	yes	characteristic
624	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
630	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	—	4	2	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₄⋊C₄	—	4	1	no	—
691	C₄⋊C₄	—	4	1	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	8	1	no	—
694	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	1	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	8	1	no	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	2	1	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₄²	—	2	1	no	—
728	C₄²	—	8	1	no	—
729	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
730	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₁₃	#18445	1	1	yes	characteristic, direct product factor, Sylow
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
741	Q₈	—	4	1	no	—
742	Q₈	—	4	1	no	—
743	Q₈	—	4	1	no	—
744	Q₈	—	8	1	no	—
745	Q₈	—	8	1	no	—
746	Q₈	—	8	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	8	1	no	—
751	D₄	—	8	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	8	1	no	—
783	C₂×C₄	—	8	1	no	—
784	C₂×C₄	—	8	1	no	—
785	C₂×C₄	—	8	1	no	—
786	C₂×C₄	—	8	1	no	—
787	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
788	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
789	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
790	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
793	C₈	—	4	1	no	—
794	C₈	—	4	1	no	—
795	C₈	—	4	1	no	—
796	C₈	—	4	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
808	C₂²	C₁₃×#577	1	1	yes	characteristic
809	C₂²	C₁₃×#578	1	1	yes	characteristic
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	8	1	no	—
828	C₄	—	8	1	no	—
829	C₄	—	8	1	no	—
830	C₂	—	2	1	no	—
831	C₂	—	2	1	no	—
832	C₂	—	8	1	no	—
833	C₂	—	8	1	no	—
834	C₂	C₁₃×#3013	1	1	yes	characteristic
835	C₂	C₁₃×#3018	1	1	yes	characteristic
836	C₂	C₁₃×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#538	C₂²
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. C₁₃×#3236	C₂	semidirect
3. C₁₃×#3232	C₂	semidirect
4. C₁₃×#2664	C₂	semidirect
6. C₁₃×#1617	C₂	semidirect
7. C₁₃×#1615	C₂	semidirect
8. C₁₃×#1614	C₂	semidirect
10. C₁₃×#1611	C₂	semidirect
11. C₁₃×#1609	C₂	semidirect
12. C₁₃×#1608	C₂	semidirect
13. C₁₃×#1509	C₂	semidirect
14. C₁₃×#1503	C₂	semidirect
15. C₁₃×#1473	C₂	semidirect
206. #18445	C₁₃	direct (N × H)
317. #3236	C₂×C₁₃	semidirect
318. #3232	C₂×C₁₃	semidirect
319. #2664	C₂×C₁₃	semidirect
321. #1617	C₂×C₁₃	semidirect
322. #1615	C₂×C₁₃	semidirect
323. #1614	C₂×C₁₃	semidirect
325. #1611	C₂×C₁₃	semidirect
326. #1609	C₂×C₁₃	semidirect
327. #1608	C₂×C₁₃	semidirect
328. #1509	C₂×C₁₃	semidirect
329. #1503	C₂×C₁₃	semidirect
330. #1473	C₂×C₁₃	semidirect
733. C₁₃	#18445	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×#3564	2
C₁₃×#3236	2
C₁₃×#3232	2
C₁₃×#2664	2
C₁₃×#1618	2
C₁₃×#1617	2
C₁₃×#1615	2
C₁₃×#1614	2
C₁₃×#1612	2
C₁₃×#1611	2
C₁₃×#1609	2
C₁₃×#1608	2
C₁₃×#1509	2
C₁₃×#1503	2
C₁₃×#1473	2
#18445	13

Subgroups — C13×#18445 #15704784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18445 #15704784