Subgroups — C₁₃×#18283 #15704622

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 854 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×#3117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2604	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×#1606	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1605	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1603	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1602	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1506	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1500	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×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#484	C₂²	1	1	yes	characteristic
37	C₁₃×#484	C₂²	1	1	yes	characteristic
38	C₁₃×#484	C₂²	1	1	yes	characteristic
39	C₁₃×#481	C₂²	1	1	yes	characteristic
40	C₁₃×#479	—	2	1	no	—
41	C₁₃×#477	—	2	1	no	—
42	C₁₃×#464	—	2	1	no	—
43	C₁₃×#462	—	2	1	no	—
44	C₁₃×#451	C₂²	1	1	yes	characteristic
45	C₁₃×#451	C₂²	1	1	yes	characteristic
46	C₁₃×#451	C₂²	1	1	yes	characteristic
47	C₁₃×#448	C₂²	1	1	yes	characteristic
48	C₁₃×#441	—	2	1	no	—
49	C₁₃×#440	—	2	1	no	—
50	C₄×C₁₃×Q₁₆	—	2	1	no	—
51	C₄×C₁₃×Q₁₆	—	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×#395	C₂²	1	1	yes	characteristic
57	C₁₃×#393	C₂²	1	1	yes	characteristic
58	C₁₃×#389	—	2	1	no	—
59	C₁₃×#388	—	2	1	no	—
60	C₁₃×#388	—	2	1	no	—
61	C₁₃×#387	—	2	1	no	—
62	C₁₃×#376	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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×Q₁₆	—	2	1	no	—
77	C₂×C₁₃×Q₁₆	—	2	1	no	—
78	C₂×C₁₃×Q₁₆	—	2	1	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
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×#126	—	2	1	no	—
94	C₁₃×#126	—	2	1	no	—
95	C₁₃×#126	—	2	1	no	—
96	C₁₃×#126	—	2	1	no	—
97	C₁₃×#126	—	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	—	2	1	no	—
107	C₁₃×#125	D₄	1	1	yes	characteristic
108	C₁₃×#124	—	2	1	no	—
109	C₁₃×#124	—	2	1	no	—
110	C₁₃×#124	—	2	1	no	—
111	C₁₃×#124	D₄	1	1	yes	characteristic
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×#123	—	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	—	2	1	no	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
136	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
137	C₁₃×#121	—	2	1	no	—
138	C₁₃×#121	C₂³	1	1	yes	characteristic
139	C₁₃×#120	—	2	1	no	—
140	C₄×Q₈×C₁₃	—	2	1	no	—
141	C₄×Q₈×C₁₃	—	2	1	no	—
142	C₄×Q₈×C₁₃	—	2	1	no	—
143	C₄×Q₈×C₁₃	—	2	1	no	—
144	C₄×Q₈×C₁₃	—	2	1	no	—
145	C₄×Q₈×C₁₃	—	2	1	no	—
146	C₄×Q₈×C₁₃	—	2	1	no	—
147	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
149	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
150	C₄×D₄×C₁₃	—	2	1	no	—
151	C₄×D₄×C₁₃	—	2	1	no	—
152	C₄×D₄×C₁₃	—	2	1	no	—
153	C₄×D₄×C₁₃	—	2	1	no	—
154	C₄×D₄×C₁₃	—	2	1	no	—
155	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
156	C₁₃×#117	—	2	1	no	—
157	C₁₃×#117	—	2	1	no	—
158	C₁₃×#117	—	2	1	no	—
159	C₁₃×#117	—	2	1	no	—
160	C₁₃×#117	—	2	1	no	—
161	C₁₃×#117	—	2	1	no	—
162	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
167	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
174	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	—	2	1	no	—
177	C₂×C₄²×C₁₃	—	2	1	no	—
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₁₃×#107	—	2	1	no	—
180	C₁₃×#107	—	2	1	no	—
181	C₁₃×#107	—	2	1	no	—
182	C₁₃×#106	—	2	1	no	—
183	C₁₃×C₄⋊C₈	—	2	1	no	—
184	C₁₃×C₄⋊C₈	—	2	1	no	—
185	C₁₃×#103	—	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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×#97	—	2	1	no	—
198	C₄×C₈×C₁₃	—	2	1	no	—
199	C₁₃×#95	—	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	#18283	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	—	2	1	no	—
212	C₂×Q₈×C₁₃	—	2	1	no	—
213	C₂×Q₈×C₁₃	—	4	2	no	—
214	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₁₃	—	2	1	no	—
218	C₂×D₄×C₁₃	—	2	1	no	—
219	C₂×D₄×C₁₃	—	2	1	no	—
220	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₁₃×Q₁₆	—	4	2	no	—
237	C₁₃×Q₁₆	—	4	2	no	—
238	C₁₃×Q₁₆	—	4	2	no	—
239	C₁₃×SD₁₆	—	4	2	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	2	1	no	—
242	C₂×C₈×C₁₃	—	2	1	no	—
243	C₂×C₈×C₁₃	—	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	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	4	2	no	—
277	C₁₃×C₄⋊C₄	—	4	1	no	—
278	C₁₃×C₄⋊C₄	—	4	1	no	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
280	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
281	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
282	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
303	C₁₃×C₂²⋊C₄	—	2	1	no	—
304	C₁₃×C₂²⋊C₄	—	4	2	no	—
305	C₁₃×C₂²⋊C₄	—	4	2	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	—	2	1	no	—
312	C₄²×C₁₃	—	2	1	no	—
313	C₄²×C₁₃	—	4	2	no	—
314	C₄²×C₁₃	—	4	1	no	—
315	C₄²×C₁₃	—	4	1	no	—
316	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
320	#3564	C₂×C₁₃	1	1	yes	characteristic
321	#3117	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#2604	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#1618	C₂×C₁₃	1	1	yes	characteristic
325	#1617	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#1615	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#1614	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#1606	C₂×C₁₃	1	1	yes	characteristic
329	#1605	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#1603	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#1602	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#1506	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#1500	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#1473	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂³×C₁₃	—	2	1	no	—
336	C₂³×C₁₃	—	2	1	no	—
337	C₂³×C₁₃	—	2	1	no	—
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	—	4	1	no	—
340	C₂³×C₁₃	—	4	1	no	—
341	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₁₃	—	2	2	no	—
343	Q₈×C₁₃	—	2	2	no	—
344	Q₈×C₁₃	—	4	1	no	—
345	Q₈×C₁₃	—	4	1	no	—
346	Q₈×C₁₃	—	4	1	no	—
347	Q₈×C₁₃	—	4	1	no	—
348	Q₈×C₁₃	—	4	1	no	—
349	Q₈×C₁₃	—	8	1	no	—
350	Q₈×C₁₃	—	8	1	no	—
351	Q₈×C₁₃	—	8	1	no	—
352	D₄×C₁₃	—	4	1	no	—
353	D₄×C₁₃	—	4	1	no	—
354	D₄×C₁₃	—	4	1	no	—
355	D₄×C₁₃	—	8	1	no	—
356	D₄×C₁₃	—	8	1	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	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	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	—	4	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	8	1	no	—
388	C₂×C₄×C₁₃	—	8	1	no	—
389	C₂×C₄×C₁₃	—	8	1	no	—
390	C₂×C₄×C₁₃	—	8	1	no	—
391	C₂×C₄×C₁₃	—	8	1	no	—
392	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
393	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
394	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
395	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
396	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₈×C₁₃	—	4	1	no	—
399	C₈×C₁₃	—	4	1	no	—
400	C₈×C₁₃	—	4	1	no	—
401	C₈×C₁₃	—	4	1	no	—
402	#563	—	2	1	no	—
403	#563	—	2	1	no	—
404	#556	—	2	1	no	—
405	#554	—	2	1	no	—
406	#552	—	2	1	no	—
407	#552	—	2	1	no	—
408	#551	—	2	1	no	—
409	#551	—	2	1	no	—
410	#544	C₂²×C₁₃	1	1	yes	characteristic
411	#543	C₂²×C₁₃	1	1	yes	characteristic
412	#542	—	2	1	no	—
413	#541	—	2	1	no	—
414	#541	—	2	1	no	—
415	#539	—	2	1	no	—
416	#539	C₂²×C₁₃	1	1	yes	characteristic
417	#538	C₂²×C₁₃	1	1	yes	characteristic
418	#533	C₂²×C₁₃	1	1	yes	characteristic
419	#529	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#126	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
422	#484	C₂²×C₁₃	1	1	yes	characteristic
423	#484	C₂²×C₁₃	1	1	yes	characteristic
424	#484	C₂²×C₁₃	1	1	yes	characteristic
425	#481	C₂²×C₁₃	1	1	yes	characteristic
426	#479	—	2	1	no	—
427	#477	—	2	1	no	—
428	#464	—	2	1	no	—
429	#462	—	2	1	no	—
430	#451	C₂²×C₁₃	1	1	yes	characteristic
431	#451	C₂²×C₁₃	1	1	yes	characteristic
432	#451	C₂²×C₁₃	1	1	yes	characteristic
433	#448	C₂²×C₁₃	1	1	yes	characteristic
434	#441	—	2	1	no	—
435	#440	—	2	1	no	—
436	C₄×Q₁₆	—	2	1	no	—
437	C₄×Q₁₆	—	2	1	no	—
438	#432	C₂²×C₁₃	1	1	yes	characteristic
439	#431	C₂²×C₁₃	1	1	yes	characteristic
440	#400	C₂²×C₁₃	1	1	yes	characteristic
441	#399	C₂²×C₁₃	1	1	yes	characteristic
442	#395	C₂²×C₁₃	1	1	yes	characteristic
443	#393	C₂²×C₁₃	1	1	yes	characteristic
444	#389	—	2	1	no	—
445	#388	—	2	1	no	—
446	#388	—	2	1	no	—
447	#387	—	2	1	no	—
448	#376	C₂²×C₁₃	1	1	yes	characteristic
449	#328	C₂²×C₁₃	1	1	yes	characteristic
450	#328	C₂²×C₁₃	1	1	yes	characteristic
451	#328	C₂²×C₁₃	1	1	yes	characteristic
452	#328	C₂²×C₁₃	1	1	yes	characteristic
453	#328	C₂²×C₁₃	1	1	yes	characteristic
454	#328	C₂²×C₁₃	1	1	yes	characteristic
455	#327	C₂²×C₁₃	1	1	yes	characteristic
456	#327	C₂²×C₁₃	1	1	yes	characteristic
457	#324	C₂²×C₁₃	1	1	yes	characteristic
458	#324	C₂²×C₁₃	1	1	yes	characteristic
459	#323	C₂²×C₁₃	1	1	yes	characteristic
460	#323	C₂²×C₁₃	1	1	yes	characteristic
461	C₂²×C₁₃	—	2	1	no	—
462	C₂²×C₁₃	—	2	1	no	—
463	C₂²×C₁₃	—	4	1	no	—
464	C₂²×C₁₃	—	4	1	no	—
465	C₂²×C₁₃	—	4	1	no	—
466	C₂²×C₁₃	—	4	1	no	—
467	C₂²×C₁₃	—	4	1	no	—
468	C₂²×C₁₃	—	4	1	no	—
469	C₂²×C₁₃	—	8	1	no	—
470	C₂²×C₁₃	—	8	1	no	—
471	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
472	C₂²×C₁₃	#578	1	1	yes	characteristic
473	C₂²×C₁₃	#578	1	1	yes	characteristic
474	C₄×C₁₃	—	2	1	no	—
475	C₄×C₁₃	—	2	1	no	—
476	C₄×C₁₃	—	2	1	no	—
477	C₄×C₁₃	—	2	1	no	—
478	C₄×C₁₃	—	2	1	no	—
479	C₄×C₁₃	—	2	1	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	—	4	1	no	—
482	C₄×C₁₃	—	4	1	no	—
483	C₄×C₁₃	—	4	1	no	—
484	C₄×C₁₃	—	4	1	no	—
485	C₄×C₁₃	—	4	1	no	—
486	C₄×C₁₃	—	4	1	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	—	4	1	no	—
489	C₄×C₁₃	—	4	1	no	—
490	C₄×C₁₃	—	4	1	no	—
491	C₄×C₁₃	—	4	1	no	—
492	C₄×C₁₃	—	8	1	no	—
493	C₄×C₁₃	—	8	1	no	—
494	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
495	C₂×Q₁₆	—	2	1	no	—
496	C₂×Q₁₆	—	2	1	no	—
497	C₂×Q₁₆	—	2	1	no	—
498	C₂×SD₁₆	—	2	1	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	—	2	1	no	—
501	C₄⋊Q₈	—	2	1	no	—
502	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
504	#126	—	2	1	no	—
505	#126	—	2	1	no	—
506	#126	—	2	1	no	—
507	#126	—	2	1	no	—
508	#126	—	2	1	no	—
509	#126	—	2	1	no	—
510	#126	—	2	1	no	—
511	#126	—	2	1	no	—
512	#126	—	2	1	no	—
513	#126	—	2	1	no	—
514	#126	—	2	1	no	—
515	#126	—	2	1	no	—
516	#126	—	2	1	no	—
517	#125	—	2	1	no	—
518	#125	—	2	1	no	—
519	#125	—	2	1	no	—
520	#125	—	2	1	no	—
521	#125	—	2	1	no	—
522	#125	—	2	1	no	—
523	#125	—	2	1	no	—
524	#125	—	2	1	no	—
525	#125	—	2	1	no	—
526	#125	D₄×C₁₃	1	1	yes	characteristic
527	#124	—	2	1	no	—
528	#124	—	2	1	no	—
529	#124	—	2	1	no	—
530	#124	D₄×C₁₃	1	1	yes	characteristic
531	#123	—	2	1	no	—
532	#123	—	2	1	no	—
533	#123	—	2	1	no	—
534	#123	—	2	1	no	—
535	#123	—	2	1	no	—
536	#123	—	2	1	no	—
537	#123	—	2	1	no	—
538	#123	—	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	—	2	1	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	1	no	—
553	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
554	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	#121	—	2	1	no	—
557	#121	C₂³×C₁₃	1	1	yes	characteristic
558	#120	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	—	2	1	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
567	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
568	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
575	#117	—	2	1	no	—
576	#117	—	2	1	no	—
577	#117	—	2	1	no	—
578	#117	—	2	1	no	—
579	#117	—	2	1	no	—
580	#117	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄²	—	2	1	no	—
596	C₂×C₄²	—	2	1	no	—
597	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
598	#107	—	2	1	no	—
599	#107	—	2	1	no	—
600	#107	—	2	1	no	—
601	#106	—	2	1	no	—
602	C₄⋊C₈	—	2	1	no	—
603	C₄⋊C₈	—	2	1	no	—
604	#103	—	2	1	no	—
605	#103	—	2	1	no	—
606	#103	—	2	1	no	—
607	#103	—	2	1	no	—
608	#103	—	2	1	no	—
609	#103	—	2	1	no	—
610	#103	—	2	1	no	—
611	#102	—	2	1	no	—
612	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
614	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
615	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
616	#97	—	2	1	no	—
617	C₄×C₈	—	2	1	no	—
618	#95	—	2	1	no	—
619	#95	—	2	1	no	—
620	#95	—	2	1	no	—
621	#95	—	2	1	no	—
622	#95	—	2	1	no	—
623	#95	C₂³×C₁₃	1	1	yes	characteristic
624	#95	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₁₃	—	2	1	no	—
626	C₂×C₁₃	—	2	1	no	—
627	C₂×C₁₃	—	8	1	no	—
628	C₂×C₁₃	—	8	1	no	—
629	C₂×C₁₃	#3011	1	1	yes	characteristic
630	C₂×C₁₃	#3018	1	1	yes	characteristic
631	C₂×C₁₃	#3025	1	1	yes	characteristic
632	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	1	no	—
635	C₂×Q₈	—	2	1	no	—
636	C₂×Q₈	—	2	1	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	4	2	no	—
639	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
661	Q₁₆	—	4	2	no	—
662	Q₁₆	—	4	2	no	—
663	Q₁₆	—	4	2	no	—
664	SD₁₆	—	4	2	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	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	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	1	no	—
703	C₄⋊C₄	—	4	1	no	—
704	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
706	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₄²	—	2	1	no	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	4	2	no	—
739	C₄²	—	4	1	no	—
740	C₄²	—	4	1	no	—
741	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₁₃	#18283	1	1	yes	characteristic, direct product factor, Sylow
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
753	Q₈	—	2	2	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	4	1	no	—
756	Q₈	—	4	1	no	—
757	Q₈	—	4	1	no	—
758	Q₈	—	4	1	no	—
759	Q₈	—	4	1	no	—
760	Q₈	—	8	1	no	—
761	Q₈	—	8	1	no	—
762	Q₈	—	8	1	no	—
763	D₄	—	4	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	8	1	no	—
767	D₄	—	8	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	8	1	no	—
799	C₂×C₄	—	8	1	no	—
800	C₂×C₄	—	8	1	no	—
801	C₂×C₄	—	8	1	no	—
802	C₂×C₄	—	8	1	no	—
803	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
804	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
805	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
806	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
809	C₈	—	4	1	no	—
810	C₈	—	4	1	no	—
811	C₈	—	4	1	no	—
812	C₈	—	4	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	8	1	no	—
822	C₂²	—	8	1	no	—
823	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
824	C₂²	C₁₃×#578	1	1	yes	characteristic
825	C₂²	C₁₃×#578	1	1	yes	characteristic
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	1	no	—
844	C₄	—	8	1	no	—
845	C₄	—	8	1	no	—
846	C₂	—	2	1	no	—
847	C₂	—	2	1	no	—
848	C₂	—	8	1	no	—
849	C₂	—	8	1	no	—
850	C₂	C₁₃×#3011	1	1	yes	characteristic
851	C₂	C₁₃×#3018	1	1	yes	characteristic
852	C₂	C₁₃×#3025	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×#3117	C₂	semidirect
3. C₁₃×#3104	C₂	semidirect
4. C₁₃×#2604	C₂	semidirect
6. C₁₃×#1617	C₂	semidirect
7. C₁₃×#1615	C₂	semidirect
8. C₁₃×#1614	C₂	semidirect
10. C₁₃×#1605	C₂	semidirect
11. C₁₃×#1603	C₂	semidirect
12. C₁₃×#1602	C₂	semidirect
13. C₁₃×#1506	C₂	semidirect
14. C₁₃×#1500	C₂	semidirect
15. C₁₃×#1473	C₂	semidirect
206. #18283	C₁₃	direct (N × H)
321. #3117	C₂×C₁₃	semidirect
322. #3104	C₂×C₁₃	semidirect
323. #2604	C₂×C₁₃	semidirect
325. #1617	C₂×C₁₃	semidirect
326. #1615	C₂×C₁₃	semidirect
327. #1614	C₂×C₁₃	semidirect
329. #1605	C₂×C₁₃	semidirect
330. #1603	C₂×C₁₃	semidirect
331. #1602	C₂×C₁₃	semidirect
332. #1506	C₂×C₁₃	semidirect
333. #1500	C₂×C₁₃	semidirect
334. #1473	C₂×C₁₃	semidirect
745. C₁₃	#18283	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×#3117	2
C₁₃×#3104	2
C₁₃×#2604	2
C₁₃×#1618	2
C₁₃×#1617	2
C₁₃×#1615	2
C₁₃×#1614	2
C₁₃×#1606	2
C₁₃×#1605	2
C₁₃×#1603	2
C₁₃×#1602	2
C₁₃×#1506	2
C₁₃×#1500	2
C₁₃×#1473	2
#18283	13

Subgroups — C13×#18283 #15704622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18283 #15704622