Subgroups — #13129417

Order 1664.

1050 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719416	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719411	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719410	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719406	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719383	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719382	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719372	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719369	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719368	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719368	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719362	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719360	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719352	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719343	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719338	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719333	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719300	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719297	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719269	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719258	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719253	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719245	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719240	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719235	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719233	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719199	C₂	1	1	yes	maximal, characteristic, complemented
29	#11719199	C₂	1	1	yes	maximal, characteristic, complemented
30	#11719195	C₂	1	1	yes	maximal, characteristic, complemented
31	#11719195	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
33	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#6129	C₂²	1	1	yes	characteristic
35	C₂×#6127	C₂²	1	1	yes	characteristic
36	C₂×#6127	C₂²	1	1	yes	characteristic
37	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#126	C₂²	1	1	yes	characteristic
39	C₁₃×#126	C₂²	1	1	yes	characteristic
40	C₁₃×#124	C₂²	1	1	yes	characteristic
41	C₁₃×#123	C₂²	1	1	yes	characteristic
42	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#120	C₂²	1	1	yes	characteristic
47	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	#88207	C₂²	1	1	yes	characteristic
54	#88207	C₂²	1	1	yes	characteristic
55	#88207	C₂²	1	1	yes	characteristic
56	#88201	C₂²	1	1	yes	characteristic, complemented
57	#88200	C₂²	1	1	yes	characteristic, complemented
58	#88200	C₂²	1	1	yes	characteristic, complemented
59	#88194	C₂²	1	1	yes	characteristic
60	#88194	C₂²	1	1	yes	characteristic
61	#88194	C₂²	1	1	yes	characteristic, complemented
62	#88193	C₂²	1	1	yes	characteristic
63	#88193	C₂²	1	1	yes	characteristic
64	#88193	C₂²	1	1	yes	characteristic
65	#88193	C₂²	1	1	yes	characteristic, complemented
66	#88192	C₂²	1	1	yes	characteristic
67	#88192	C₂²	1	1	yes	characteristic, complemented
68	#88191	C₂²	1	1	yes	characteristic
69	#88189	C₂²	1	1	yes	characteristic, complemented
70	#88184	C₂²	1	1	yes	characteristic
71	#88184	C₂²	1	1	yes	characteristic
72	#88184	C₂²	1	1	yes	characteristic, complemented
73	#88184	C₂²	1	1	yes	characteristic, complemented
74	#88184	C₂²	1	1	yes	characteristic, complemented
75	#88183	C₂²	1	1	yes	characteristic
76	#88183	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
84	#88178	C₂²	1	1	yes	characteristic, complemented
85	#88178	C₂²	1	1	yes	characteristic, complemented
86	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
87	#88152	C₂²	1	1	yes	characteristic, complemented
88	#88151	C₂²	1	1	yes	characteristic, complemented
89	#88151	C₂²	1	1	yes	characteristic, complemented
90	#88150	C₂²	1	1	yes	characteristic, complemented
91	#88150	C₂²	1	1	yes	characteristic, complemented
92	#88150	C₂²	1	1	yes	characteristic, complemented
93	#88149	C₂²	1	1	yes	characteristic, complemented
94	#88149	C₂²	1	1	yes	characteristic, complemented
95	#88149	C₂²	1	1	yes	characteristic, complemented
96	#88148	C₂²	1	1	yes	characteristic, complemented
97	#88148	C₂²	1	1	yes	characteristic, complemented
98	#88148	C₂²	1	1	yes	characteristic, complemented
99	#88148	C₂²	1	1	yes	characteristic, complemented
100	#88148	C₂²	1	1	yes	characteristic, complemented
101	#88148	C₂²	1	1	yes	characteristic, complemented
102	#88148	C₂²	1	1	yes	characteristic, complemented
103	#88148	C₂²	1	1	yes	characteristic, complemented
104	#88147	C₂²	1	1	yes	characteristic, complemented
105	#88147	C₂²	1	1	yes	characteristic, complemented
106	#88147	C₂²	1	1	yes	characteristic, complemented
107	#88146	C₂²	1	1	yes	characteristic, complemented
108	#88146	C₂²	1	1	yes	characteristic, complemented
109	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
110	#88144	C₂²	1	1	yes	characteristic, complemented
111	#88143	C₂²	1	1	yes	characteristic, complemented
112	#88143	C₂²	1	1	yes	characteristic, complemented
113	#88143	C₂²	1	1	yes	characteristic, complemented
114	#88143	C₂²	1	1	yes	characteristic, complemented
115	#88142	C₂²	1	1	yes	characteristic, complemented
116	#88142	C₂²	1	1	yes	characteristic, complemented
117	#88141	C₂²	1	1	yes	characteristic, complemented
118	#88141	C₂²	1	1	yes	characteristic, complemented
119	#88140	C₂²	1	1	yes	characteristic, complemented
120	#88140	C₂²	1	1	yes	characteristic, complemented
121	#88139	C₂²	1	1	yes	characteristic
122	#88139	C₂²	1	1	yes	characteristic
123	#88139	C₂²	1	1	yes	characteristic
124	#88139	C₂²	1	1	yes	characteristic
125	#88139	C₂²	1	1	yes	characteristic
126	#88139	C₂²	1	1	yes	characteristic
127	#88139	C₂²	1	1	yes	characteristic, complemented
128	#88139	C₂²	1	1	yes	characteristic, complemented
129	#88139	C₂²	1	1	yes	characteristic, complemented
130	#88139	C₂²	1	1	yes	characteristic, complemented
131	#88138	C₂²	1	1	yes	characteristic
132	#88138	C₂²	1	1	yes	characteristic
133	#88138	C₂²	1	1	yes	characteristic
134	#88138	C₂²	1	1	yes	characteristic
135	#88138	C₂²	1	1	yes	characteristic
136	#88138	C₂²	1	1	yes	characteristic
137	#88138	C₂²	1	1	yes	characteristic
138	#88138	C₂²	1	1	yes	characteristic
139	#88138	C₂²	1	1	yes	characteristic
140	#88138	C₂²	1	1	yes	characteristic, complemented
141	#88138	C₂²	1	1	yes	characteristic, complemented
142	#88138	C₂²	1	1	yes	characteristic, complemented
143	#88138	C₂²	1	1	yes	characteristic, complemented
144	#88138	C₂²	1	1	yes	characteristic, complemented
145	#88138	C₂²	1	1	yes	characteristic, complemented
146	#88138	C₂²	1	1	yes	characteristic, complemented
147	#88137	C₂²	1	1	yes	characteristic
148	#88137	C₂²	1	1	yes	characteristic
149	#88137	C₂²	1	1	yes	characteristic
150	#88137	C₂²	1	1	yes	characteristic
151	#88137	C₂²	1	1	yes	characteristic, complemented
152	#88137	C₂²	1	1	yes	characteristic, complemented
153	#88137	C₂²	1	1	yes	characteristic, complemented
154	#88137	C₂²	1	1	yes	characteristic, complemented
155	#88136	C₂²	1	1	yes	characteristic
156	#88136	C₂²	1	1	yes	characteristic
157	#88136	C₂²	1	1	yes	characteristic
158	#88135	C₂²	1	1	yes	characteristic
159	#88135	C₂²	1	1	yes	characteristic
160	#88135	C₂²	1	1	yes	characteristic, complemented
161	#88135	C₂²	1	1	yes	characteristic, complemented
162	#88135	C₂²	1	1	yes	characteristic, complemented
163	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
164	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
165	#88133	C₂²	1	1	yes	characteristic
166	#88133	C₂²	1	1	yes	characteristic
167	#88133	C₂²	1	1	yes	characteristic
168	#88133	C₂²	1	1	yes	characteristic, complemented
169	#88133	C₂²	1	1	yes	characteristic, complemented
170	#88133	C₂²	1	1	yes	characteristic, complemented
171	#88132	C₂²	1	1	yes	characteristic
172	#88132	C₂²	1	1	yes	characteristic
173	#88132	C₂²	1	1	yes	characteristic, complemented
174	#88131	C₂²	1	1	yes	characteristic
175	#88130	C₂²	1	1	yes	characteristic, complemented
176	#88130	C₂²	1	1	yes	characteristic, complemented
177	#88130	C₂²	1	1	yes	characteristic, complemented
178	#88128	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
182	#88126	C₂²	1	1	yes	characteristic, complemented
183	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
184	#88124	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
188	C₂³×D₁₃	C₂³	1	1	yes	characteristic
189	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₁₃	—	4	2	no	—
199	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
217	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
218	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
219	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
220	Q₈×D₁₃	—	4	2	no	—
221	#6129	—	4	2	no	—
222	#6127	—	4	2	no	—
223	#6127	—	4	2	no	—
224	#6127	—	4	2	no	—
225	C₂×D₅₂	C₂³	1	1	yes	characteristic
226	C₂×D₅₂	C₂³	1	1	yes	characteristic
227	C₂×D₅₂	C₂³	1	1	yes	characteristic
228	C₂×D₅₂	C₂³	1	1	yes	characteristic
229	C₂×D₅₂	C₂³	1	1	yes	characteristic
230	C₂×D₅₂	C₂³	1	1	yes	characteristic
231	C₂×D₅₂	C₂³	1	1	yes	characteristic
232	C₂×D₅₂	C₂³	1	1	yes	characteristic
233	C₂×D₅₂	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
247	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
248	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
249	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
250	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
251	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
252	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₄²×C₁₃	C₂³	1	1	yes	characteristic
275	C₄²×C₁₃	C₂³	1	1	yes	characteristic
276	C₄²×C₁₃	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
287	#6103	C₂³	1	1	yes	characteristic
288	#6103	C₂³	1	1	yes	characteristic
289	#6103	C₂³	1	1	yes	characteristic
290	#6103	C₂³	1	1	yes	characteristic
291	#6103	C₂³	1	1	yes	characteristic
292	#6103	C₂³	1	1	yes	characteristic
293	#6103	C₂³	1	1	yes	characteristic
294	#6103	C₂³	1	1	yes	characteristic
295	#6103	C₂³	1	1	yes	characteristic
296	#6103	C₂³	1	1	yes	characteristic
297	#6103	C₂³	1	1	yes	characteristic
298	#6103	C₂³	1	1	yes	characteristic
299	#6103	C₂³	1	1	yes	characteristic
300	#6103	C₂³	1	1	yes	characteristic
301	#6103	C₂³	1	1	yes	characteristic
302	#6103	C₂³	1	1	yes	characteristic
303	#6103	C₂³	1	1	yes	characteristic
304	#6103	C₂³	1	1	yes	characteristic
305	#6103	C₂³	1	1	yes	characteristic
306	#6103	C₂³	1	1	yes	characteristic
307	#6103	C₂³	1	1	yes	characteristic
308	#6103	C₂³	1	1	yes	characteristic
309	#6103	C₂³	1	1	yes	characteristic
310	#6103	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
315	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
316	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
319	#6101	C₂³	1	1	yes	characteristic
320	#6101	C₂³	1	1	yes	characteristic
321	#6101	C₂³	1	1	yes	characteristic
322	#6101	C₂³	1	1	yes	characteristic
323	#6101	C₂³	1	1	yes	characteristic
324	#6101	C₂³	1	1	yes	characteristic
325	#6101	C₂³	1	1	yes	characteristic
326	#6101	C₂³	1	1	yes	characteristic
327	#6101	C₂³	1	1	yes	characteristic
328	#6101	C₂³	1	1	yes	characteristic
329	#6101	C₂³	1	1	yes	characteristic
330	#6101	C₂³	1	1	yes	characteristic
331	#6101	C₂³	1	1	yes	characteristic
332	#6101	C₂³	1	1	yes	characteristic
333	#6101	C₂³	1	1	yes	characteristic
334	#6101	C₂³	1	1	yes	characteristic
335	#6101	C₂³	1	1	yes	characteristic
336	#6101	C₂³	1	1	yes	characteristic
337	#6101	C₂³	1	1	yes	characteristic
338	#6101	C₂³	1	1	yes	characteristic
339	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
340	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
341	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
342	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
343	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
344	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
345	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
346	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
347	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
348	#3562	—	13	1	no	maximal, Sylow
349	C₂³×C₁₃	—	4	1	no	—
350	C₂³×C₁₃	—	4	1	no	—
351	C₂³×C₁₃	—	4	1	no	—
352	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂²×D₁₃	—	4	1	no	—
357	C₂²×D₁₃	—	4	1	no	—
358	C₂²×D₁₃	—	4	1	no	—
359	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
360	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
361	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
362	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
363	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
364	Q₈×C₁₃	—	4	1	no	—
365	D₄×C₁₃	—	4	1	no	—
366	D₄×C₁₃	—	4	1	no	—
367	D₄×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	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂²⋊D₁₃	—	2	2	no	—
385	C₂²⋊D₁₃	—	2	2	no	—
386	C₂²⋊D₁₃	—	2	2	no	—
387	C₂²⋊D₁₃	—	4	1	no	—
388	C₂²⋊D₁₃	—	4	1	no	—
389	C₂²⋊D₁₃	—	4	1	no	—
390	C₂²⋊D₁₃	—	4	1	no	—
391	C₂²⋊D₁₃	—	4	1	no	—
392	C₂²⋊D₁₃	—	4	1	no	—
393	C₂²⋊D₁₃	—	4	1	no	—
394	C₂²⋊D₁₃	—	4	1	no	—
395	C₂²⋊D₁₃	—	4	1	no	—
396	C₂²⋊D₁₃	—	4	1	no	—
397	C₂²⋊D₁₃	—	4	1	no	—
398	C₂²⋊D₁₃	—	4	1	no	—
399	C₂²⋊D₁₃	—	4	1	no	—
400	C₂²⋊D₁₃	—	4	1	no	—
401	C₂²⋊D₁₃	—	4	1	no	—
402	C₂×Dic₁₃	—	2	2	no	—
403	C₂×Dic₁₃	—	4	1	no	—
404	C₂×Dic₁₃	—	4	1	no	—
405	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
416	D₅₂	—	4	1	no	—
417	D₅₂	—	4	1	no	—
418	D₅₂	—	4	1	no	—
419	D₅₂	—	4	1	no	—
420	D₅₂	—	4	1	no	—
421	D₅₂	—	4	1	no	—
422	D₅₂	—	4	1	no	—
423	D₅₂	—	4	1	no	—
424	D₅₂	—	4	1	no	—
425	C₄×D₁₃	—	2	2	no	—
426	C₄×D₁₃	—	2	2	no	—
427	C₄×D₁₃	—	4	1	no	—
428	C₄×D₁₃	—	4	1	no	—
429	C₄×D₁₃	—	4	1	no	—
430	C₄×D₁₃	—	4	1	no	—
431	C₄×D₁₃	—	4	1	no	—
432	C₄×D₁₃	—	4	1	no	—
433	C₄×D₁₃	—	4	1	no	—
434	C₄×D₁₃	—	4	1	no	—
435	C₄×D₁₃	—	4	1	no	—
436	C₄×D₁₃	—	4	1	no	—
437	C₄×D₁₃	—	4	1	no	—
438	Dic₂₆	—	2	2	no	—
439	Dic₂₆	—	2	2	no	—
440	Dic₂₆	—	2	2	no	—
441	Dic₂₆	—	4	1	no	—
442	Dic₂₆	—	4	1	no	—
443	#562	—	13	1	no	—
444	#562	—	13	1	no	—
445	#560	—	13	1	no	—
446	#560	—	13	1	no	—
447	#559	—	13	1	no	—
448	#556	—	13	1	no	—
449	#553	—	13	1	no	—
450	#553	—	13	1	no	—
451	#551	—	13	1	no	—
452	#551	D₁₃	1	1	yes	characteristic, complemented
453	#550	—	13	1	no	—
454	#548	—	13	1	no	—
455	#548	—	13	1	no	—
456	#547	—	13	1	no	—
457	#546	—	13	1	no	—
458	#546	—	13	1	no	—
459	#541	—	13	1	no	—
460	#540	—	13	1	no	—
461	#540	—	13	1	no	—
462	#540	—	13	1	no	—
463	#539	—	13	1	no	—
464	#539	—	13	1	no	—
465	#538	—	13	1	no	—
466	#538	—	13	1	no	—
467	#538	—	13	1	no	—
468	#538	—	13	1	no	—
469	#536	—	13	1	no	—
470	#535	—	13	1	no	—
471	#532	—	13	1	no	—
472	#529	—	13	1	no	—
473	#529	—	13	1	no	—
474	C₂²×C₁₃	—	2	1	no	—
475	C₂²×C₁₃	—	2	1	no	—
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	2	1	no	—
478	C₂²×C₁₃	—	2	1	no	—
479	C₂²×C₁₃	—	2	1	no	—
480	C₂²×C₁₃	—	2	1	no	—
481	C₂²×C₁₃	—	2	1	no	—
482	C₂²×C₁₃	—	2	1	no	—
483	C₂²×C₁₃	—	2	1	no	—
484	C₂²×C₁₃	—	2	1	no	—
485	C₂²×C₁₃	—	2	1	no	—
486	C₂²×C₁₃	—	8	2	no	—
487	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
488	C₂×D₁₃	—	2	1	no	—
489	C₂×D₁₃	—	2	1	no	—
490	C₂×D₁₃	—	2	1	no	—
491	C₂×D₁₃	—	2	1	no	—
492	C₂×D₁₃	—	2	1	no	—
493	C₂×D₁₃	—	2	1	no	—
494	C₂×D₁₃	—	2	1	no	—
495	C₂×D₁₃	—	2	1	no	—
496	C₂×D₁₃	—	2	1	no	—
497	C₂×D₁₃	—	2	1	no	—
498	C₂×D₁₃	—	2	1	no	—
499	C₂×D₁₃	—	2	1	no	—
500	C₂×D₁₃	—	2	1	no	—
501	C₂×D₁₃	—	2	1	no	—
502	C₂×D₁₃	—	2	1	no	—
503	C₂×D₁₃	—	8	2	no	—
504	C₄×C₁₃	—	2	1	no	—
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	1	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	1	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	1	no	—
511	C₄×C₁₃	—	2	1	no	—
512	C₄×C₁₃	—	2	1	no	—
513	C₄×C₁₃	—	2	1	no	—
514	C₄×C₁₃	—	2	1	no	—
515	Dic₁₃	—	2	1	no	—
516	Dic₁₃	—	2	1	no	—
517	Dic₁₃	—	2	1	no	—
518	Dic₁₃	—	2	1	no	—
519	Dic₁₃	—	2	1	no	—
520	Dic₁₃	—	2	1	no	—
521	Dic₁₃	—	2	1	no	—
522	Dic₁₃	—	2	1	no	—
523	Dic₁₃	—	2	1	no	—
524	Dic₁₃	—	2	1	no	—
525	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
526	C₂×#41	—	13	1	no	—
527	C₂×#41	—	13	1	no	—
528	C₂×#41	—	13	1	no	—
529	C₂×#41	—	13	1	no	—
530	C₂²×Q₈	—	13	1	no	—
531	C₂²×D₄	—	13	1	no	—
532	C₄⋊Q₈	—	13	1	no	—
533	C₄⋊Q₈	—	13	1	no	—
534	#127	—	13	1	no	—
535	#127	—	13	1	no	—
536	#127	—	13	1	no	—
537	#127	—	13	1	no	—
538	#126	—	13	1	no	—
539	#126	—	13	1	no	—
540	#126	—	13	1	no	—
541	#126	—	13	1	no	—
542	#126	—	13	1	no	—
543	#126	—	13	1	no	—
544	#126	—	13	1	no	—
545	#126	—	13	1	no	—
546	#126	—	13	1	no	—
547	#126	—	13	1	no	—
548	#126	C₂×D₁₃	1	1	yes	characteristic
549	#126	C₂×D₁₃	1	1	yes	characteristic
550	#125	—	13	1	no	—
551	#125	—	13	1	no	—
552	#125	—	13	1	no	—
553	#125	—	13	1	no	—
554	#125	—	13	1	no	—
555	#125	—	13	1	no	—
556	#124	—	13	1	no	—
557	#124	—	13	1	no	—
558	#124	—	13	1	no	—
559	#124	—	13	1	no	—
560	#124	—	13	1	no	—
561	#124	—	13	1	no	—
562	#124	—	13	1	no	—
563	#124	—	13	1	no	—
564	#124	—	13	1	no	—
565	#124	—	13	1	no	—
566	#124	—	13	1	no	—
567	#124	C₂×D₁₃	1	1	yes	characteristic
568	#123	—	13	1	no	—
569	#123	—	13	1	no	—
570	#123	—	13	1	no	—
571	#123	—	13	1	no	—
572	#123	—	13	1	no	—
573	#123	—	13	1	no	—
574	#123	—	13	1	no	—
575	#123	—	13	1	no	—
576	#123	—	13	1	no	—
577	#123	—	13	1	no	—
578	#123	—	13	1	no	—
579	#123	—	13	1	no	—
580	#123	—	13	1	no	—
581	#123	—	13	1	no	—
582	#123	—	13	1	no	—
583	#123	—	13	1	no	—
584	#123	—	13	1	no	—
585	#123	—	13	1	no	—
586	#123	—	13	1	no	—
587	#123	—	13	1	no	—
588	#123	—	13	1	no	—
589	#123	C₂×D₁₃	1	1	yes	characteristic
590	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
591	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
592	C₂²⋊Q₈	—	13	1	no	—
593	C₂²⋊Q₈	—	13	1	no	—
594	C₂²⋊Q₈	—	13	1	no	—
595	C₂²⋊Q₈	—	13	1	no	—
596	C₂²⋊Q₈	—	13	1	no	—
597	C₂²⋊Q₈	—	13	1	no	—
598	C₂²⋊Q₈	—	13	1	no	—
599	C₂²⋊Q₈	—	13	1	no	—
600	C₂²⋊Q₈	—	13	1	no	—
601	C₂²⋊Q₈	—	13	1	no	—
602	C₂²⋊Q₈	—	13	1	no	—
603	C₂²⋊Q₈	—	13	1	no	—
604	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
605	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
606	#121	—	13	1	no	—
607	#121	—	13	1	no	—
608	#121	—	13	1	no	—
609	#121	—	13	1	no	—
610	#121	—	13	1	no	—
611	#121	—	13	1	no	—
612	#121	—	13	1	no	—
613	#121	—	13	1	no	—
614	#121	—	13	1	no	—
615	#121	—	13	1	no	—
616	#121	—	13	1	no	—
617	#121	—	13	1	no	—
618	#121	—	13	1	no	—
619	#121	—	13	1	no	—
620	#121	—	13	1	no	—
621	#121	—	13	1	no	—
622	#121	—	13	1	no	—
623	#121	—	13	1	no	—
624	#121	—	13	1	no	—
625	#121	—	13	1	no	—
626	#121	—	13	1	no	—
627	#121	—	13	1	no	—
628	#121	—	13	1	no	—
629	#121	—	13	1	no	—
630	#121	—	13	1	no	—
631	#121	—	13	1	no	—
632	#121	—	13	1	no	—
633	#121	—	13	1	no	—
634	#121	—	13	1	no	—
635	#121	—	13	1	no	—
636	#120	—	13	1	no	—
637	#120	—	13	1	no	—
638	#120	—	13	1	no	—
639	#120	—	13	1	no	—
640	#120	—	13	1	no	—
641	#120	—	13	1	no	—
642	#120	—	13	1	no	—
643	#120	C₂×D₁₃	1	1	yes	characteristic
644	C₄×Q₈	—	13	1	no	—
645	C₄×Q₈	—	13	1	no	—
646	C₄×Q₈	—	13	1	no	—
647	C₄×Q₈	—	13	1	no	—
648	C₄×D₄	—	13	1	no	—
649	C₄×D₄	—	13	1	no	—
650	C₄×D₄	—	13	1	no	—
651	C₄×D₄	—	13	1	no	—
652	C₄×D₄	—	13	1	no	—
653	C₄×D₄	—	13	1	no	—
654	C₄×D₄	—	13	1	no	—
655	C₄×D₄	—	13	1	no	—
656	C₄×D₄	—	13	1	no	—
657	C₄×D₄	—	13	1	no	—
658	C₄×D₄	—	13	1	no	—
659	C₄×D₄	—	13	1	no	—
660	C₄×D₄	—	13	1	no	—
661	C₄×D₄	—	13	1	no	—
662	C₄×D₄	—	13	1	no	—
663	C₄×D₄	—	13	1	no	—
664	C₄×D₄	—	13	1	no	—
665	C₄×D₄	—	13	1	no	—
666	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
667	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
668	#117	—	13	1	no	—
669	#117	—	13	1	no	—
670	#117	—	13	1	no	—
671	#117	—	13	1	no	—
672	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
673	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
674	C₂×C₄⋊C₄	—	13	1	no	—
675	C₂×C₄⋊C₄	—	13	1	no	—
676	C₂×C₂²⋊C₄	—	13	1	no	—
677	C₂×C₂²⋊C₄	—	13	1	no	—
678	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
680	C₂×C₄²	—	13	1	no	—
681	C₂×C₁₃	—	4	1	no	—
682	C₂×C₁₃	—	4	1	no	—
683	C₂×C₁₃	—	4	1	no	—
684	C₂×C₁₃	—	4	1	no	—
685	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
686	C₂×C₁₃	#585	1	1	yes	characteristic
687	C₂×C₁₃	#585	1	1	yes	characteristic
688	D₁₃	—	4	1	no	—
689	D₁₃	—	4	1	no	—
690	D₁₃	—	4	1	no	—
691	D₁₃	—	4	1	no	—
692	D₁₃	—	4	1	no	—
693	C₂⁴	—	13	1	no	—
694	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
695	#41	—	52	2	no	—
696	#41	—	52	2	no	—
697	#41	—	52	2	no	—
698	#41	—	52	2	no	—
699	C₂×Q₈	—	13	1	no	—
700	C₂×Q₈	—	13	1	no	—
701	C₂×Q₈	—	13	1	no	—
702	C₂×Q₈	—	13	1	no	—
703	C₂×Q₈	—	13	1	no	—
704	C₂×Q₈	—	52	2	no	—
705	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
706	C₂×D₄	—	13	1	no	—
707	C₂×D₄	—	13	1	no	—
708	C₂×D₄	—	13	1	no	—
709	C₂×D₄	—	13	1	no	—
710	C₂×D₄	—	13	1	no	—
711	C₂×D₄	—	13	1	no	—
712	C₂×D₄	—	13	1	no	—
713	C₂×D₄	—	13	1	no	—
714	C₂×D₄	—	13	1	no	—
715	C₂×D₄	—	13	1	no	—
716	C₂×D₄	—	13	1	no	—
717	C₂×D₄	—	13	1	no	—
718	C₂×D₄	—	13	1	no	—
719	C₂×D₄	—	13	1	no	—
720	C₂×D₄	—	13	1	no	—
721	C₂×D₄	—	13	1	no	—
722	C₂×D₄	—	13	1	no	—
723	C₂×D₄	—	13	1	no	—
724	C₂×D₄	—	13	1	no	—
725	C₂×D₄	—	13	1	no	—
726	C₂×D₄	—	13	1	no	—
727	C₂×D₄	—	13	1	no	—
728	C₂×D₄	—	13	1	no	—
729	C₂×D₄	—	13	1	no	—
730	C₂×D₄	—	13	1	no	—
731	C₂×D₄	—	13	1	no	—
732	C₂×D₄	—	13	1	no	—
733	C₂×D₄	—	52	2	no	—
734	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
735	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
736	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
737	C₂²×C₄	—	13	1	no	—
738	C₂²×C₄	—	13	1	no	—
739	C₂²×C₄	—	13	1	no	—
740	C₂²×C₄	—	13	1	no	—
741	C₂²×C₄	—	13	1	no	—
742	C₂²×C₄	—	13	1	no	—
743	C₂²×C₄	—	13	1	no	—
744	C₂²×C₄	—	13	1	no	—
745	C₂²×C₄	—	13	1	no	—
746	C₂²×C₄	—	13	1	no	—
747	C₂²×C₄	—	13	1	no	—
748	C₂²×C₄	—	13	1	no	—
749	C₂²×C₄	—	13	1	no	—
750	C₂²×C₄	—	13	1	no	—
751	C₂²×C₄	—	13	1	no	—
752	C₂²×C₄	—	13	1	no	—
753	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
754	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
758	C₄⋊C₄	—	13	1	no	—
759	C₄⋊C₄	—	13	1	no	—
760	C₄⋊C₄	—	13	1	no	—
761	C₄⋊C₄	—	13	1	no	—
762	C₄⋊C₄	—	13	1	no	—
763	C₄⋊C₄	—	13	1	no	—
764	C₄⋊C₄	—	13	1	no	—
765	C₄⋊C₄	—	13	1	no	—
766	C₄⋊C₄	—	13	1	no	—
767	C₄⋊C₄	—	13	1	no	—
768	C₄⋊C₄	—	13	1	no	—
769	C₄⋊C₄	—	13	1	no	—
770	C₄⋊C₄	—	13	1	no	—
771	C₄⋊C₄	—	13	1	no	—
772	C₄⋊C₄	—	13	1	no	—
773	C₄⋊C₄	—	13	1	no	—
774	C₄⋊C₄	—	13	1	no	—
775	C₄⋊C₄	—	13	1	no	—
776	C₄⋊C₄	—	13	1	no	—
777	C₄⋊C₄	—	13	1	no	—
778	C₄⋊C₄	—	13	1	no	—
779	C₄⋊C₄	—	13	1	no	—
780	C₄⋊C₄	—	13	1	no	—
781	C₄⋊C₄	—	13	1	no	—
782	C₄⋊C₄	—	13	1	no	—
783	C₄⋊C₄	—	13	1	no	—
784	C₄⋊C₄	—	13	1	no	—
785	C₄⋊C₄	—	13	1	no	—
786	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
794	C₂²⋊C₄	—	13	1	no	—
795	C₂²⋊C₄	—	13	1	no	—
796	C₂²⋊C₄	—	13	1	no	—
797	C₂²⋊C₄	—	13	1	no	—
798	C₂²⋊C₄	—	13	1	no	—
799	C₂²⋊C₄	—	13	1	no	—
800	C₂²⋊C₄	—	13	1	no	—
801	C₂²⋊C₄	—	13	1	no	—
802	C₂²⋊C₄	—	13	1	no	—
803	C₂²⋊C₄	—	13	1	no	—
804	C₂²⋊C₄	—	13	1	no	—
805	C₂²⋊C₄	—	13	1	no	—
806	C₂²⋊C₄	—	13	1	no	—
807	C₂²⋊C₄	—	13	1	no	—
808	C₂²⋊C₄	—	13	1	no	—
809	C₂²⋊C₄	—	13	1	no	—
810	C₂²⋊C₄	—	13	1	no	—
811	C₂²⋊C₄	—	13	1	no	—
812	C₂²⋊C₄	—	13	1	no	—
813	C₂²⋊C₄	—	13	1	no	—
814	C₂²⋊C₄	—	13	1	no	—
815	C₂²⋊C₄	—	13	1	no	—
816	C₂²⋊C₄	—	13	1	no	—
817	C₂²⋊C₄	—	13	1	no	—
818	C₂²⋊C₄	—	13	1	no	—
819	C₂²⋊C₄	—	13	1	no	—
820	C₂²⋊C₄	—	13	1	no	—
821	C₂²⋊C₄	—	13	1	no	—
822	C₂²⋊C₄	—	13	1	no	—
823	C₂²⋊C₄	—	13	1	no	—
824	C₂²⋊C₄	—	13	1	no	—
825	C₂²⋊C₄	—	13	1	no	—
826	C₂²⋊C₄	—	13	1	no	—
827	C₂²⋊C₄	—	13	1	no	—
828	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
829	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
830	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
832	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
834	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
842	C₄²	—	13	1	no	—
843	C₄²	—	13	1	no	—
844	C₄²	—	13	1	no	—
845	C₄²	—	13	1	no	—
846	C₄²	—	13	1	no	—
847	C₄²	—	13	1	no	—
848	C₄²	—	13	1	no	—
849	C₄²	—	13	1	no	—
850	C₄²	—	13	1	no	—
851	C₄²	C₂²×D₁₃	1	1	yes	characteristic
852	C₄²	C₂²×D₁₃	1	1	yes	characteristic
853	C₄²	C₂²×D₁₃	1	1	yes	characteristic
854	C₁₃	#3562	1	1	yes	characteristic, complemented, Sylow
855	C₂³	—	4	1	no	—
856	C₂³	—	4	1	no	—
857	C₂³	—	4	1	no	—
858	C₂³	—	13	1	no	—
859	C₂³	—	13	1	no	—
860	C₂³	—	13	1	no	—
861	C₂³	—	13	1	no	—
862	C₂³	—	13	1	no	—
863	C₂³	—	52	1	no	—
864	C₂³	—	52	1	no	—
865	C₂³	—	52	1	no	—
866	C₂³	C₂³×D₁₃	1	1	yes	characteristic
867	C₂³	C₂³×D₁₃	1	1	yes	characteristic
868	C₂³	C₂³×D₁₃	1	1	yes	characteristic
869	C₂³	C₂³×D₁₃	1	1	yes	characteristic
870	Q₈	—	4	1	no	—
871	Q₈	—	26	2	no	—
872	Q₈	—	26	2	no	—
873	Q₈	—	26	2	no	—
874	Q₈	—	52	1	no	—
875	Q₈	—	52	1	no	—
876	D₄	—	4	1	no	—
877	D₄	—	4	1	no	—
878	D₄	—	4	1	no	—
879	D₄	—	26	2	no	—
880	D₄	—	26	2	no	—
881	D₄	—	26	2	no	—
882	D₄	—	52	1	no	—
883	D₄	—	52	1	no	—
884	D₄	—	52	1	no	—
885	D₄	—	52	1	no	—
886	D₄	—	52	1	no	—
887	D₄	—	52	1	no	—
888	D₄	—	52	1	no	—
889	D₄	—	52	1	no	—
890	D₄	—	52	1	no	—
891	D₄	—	52	1	no	—
892	D₄	—	52	1	no	—
893	D₄	—	52	1	no	—
894	D₄	—	52	1	no	—
895	D₄	—	52	1	no	—
896	D₄	—	52	1	no	—
897	D₄	—	52	1	no	—
898	D₄	—	52	1	no	—
899	D₄	—	52	1	no	—
900	D₄	—	52	1	no	—
901	D₄	—	52	1	no	—
902	D₄	—	52	1	no	—
903	D₄	—	52	1	no	—
904	D₄	—	52	1	no	—
905	D₄	—	52	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	13	1	no	—
912	C₂×C₄	—	13	1	no	—
913	C₂×C₄	—	13	1	no	—
914	C₂×C₄	—	13	1	no	—
915	C₂×C₄	—	13	1	no	—
916	C₂×C₄	—	13	1	no	—
917	C₂×C₄	—	13	1	no	—
918	C₂×C₄	—	13	1	no	—
919	C₂×C₄	—	13	1	no	—
920	C₂×C₄	—	13	1	no	—
921	C₂×C₄	—	13	1	no	—
922	C₂×C₄	—	26	2	no	—
923	C₂×C₄	—	26	2	no	—
924	C₂×C₄	—	26	2	no	—
925	C₂×C₄	—	52	1	no	—
926	C₂×C₄	—	52	1	no	—
927	C₂×C₄	—	52	1	no	—
928	C₂×C₄	—	52	1	no	—
929	C₂×C₄	—	52	1	no	—
930	C₂×C₄	—	52	1	no	—
931	C₂×C₄	—	52	1	no	—
932	C₂×C₄	—	52	1	no	—
933	C₂×C₄	—	52	1	no	—
934	C₂×C₄	—	52	1	no	—
935	C₂×C₄	—	52	1	no	—
936	C₂×C₄	—	52	1	no	—
937	C₂×C₄	—	52	1	no	—
938	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
939	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
949	C₂²	—	2	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	8	2	no	—
962	C₂²	—	26	1	no	—
963	C₂²	—	26	1	no	—
964	C₂²	—	26	1	no	—
965	C₂²	—	26	1	no	—
966	C₂²	—	26	1	no	—
967	C₂²	—	26	1	no	—
968	C₂²	—	26	1	no	—
969	C₂²	—	26	1	no	—
970	C₂²	—	26	1	no	—
971	C₂²	—	26	1	no	—
972	C₂²	—	26	1	no	—
973	C₂²	—	26	1	no	—
974	C₂²	—	26	1	no	—
975	C₂²	—	26	1	no	—
976	C₂²	—	26	1	no	—
977	C₂²	—	104	2	no	—
978	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	13	2	no	—
991	C₄	—	26	1	no	—
992	C₄	—	26	1	no	—
993	C₄	—	26	1	no	—
994	C₄	—	26	1	no	—
995	C₄	—	26	1	no	—
996	C₄	—	26	1	no	—
997	C₄	—	26	1	no	—
998	C₄	—	26	1	no	—
999	C₄	—	26	1	no	—
1000	C₄	—	26	1	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	4	1	no	—
1003	C₂	—	4	1	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	52	1	no	—
1006	C₂	—	52	1	no	—
1007	C₂	—	52	1	no	—
1008	C₂	—	52	1	no	—
1009	C₂	—	52	1	no	—
1010	C₂	#11719648	1	1	yes	characteristic
1011	C₂	#11719648	1	1	yes	characteristic
1012	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#551	C₂
hypercenter	#551	D₁₃
hypocenter	C₁₃	#3562
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. C₁₃×#551	C₂	semidirect
2. #11719416	C₂	semidirect
3. #11719411	C₂	semidirect
4. #11719410	C₂	semidirect
5. #11719406	C₂	semidirect
6. #11719383	C₂	semidirect
7. #11719382	C₂	semidirect
8. #11719372	C₂	semidirect
9. #11719369	C₂	semidirect
10. #11719368	C₂	semidirect
11. #11719368	C₂	semidirect
12. #11719362	C₂	semidirect
13. #11719360	C₂	semidirect
14. #11719352	C₂	semidirect
15. #11719343	C₂	semidirect
16. #11719338	C₂	semidirect
17. #11719333	C₂	semidirect
18. #11719300	C₂	semidirect
19. #11719297	C₂	semidirect
20. #11719269	C₂	semidirect
21. #11719258	C₂	semidirect
22. #11719253	C₂	semidirect
23. #11719245	C₂	semidirect
24. #11719240	C₂	semidirect
25. #11719238	C₂	semidirect
26. #11719235	C₂	semidirect
27. #11719233	C₂	semidirect
28. #11719199	C₂	semidirect
29. #11719199	C₂	semidirect
30. #11719195	C₂	semidirect
31. #11719195	C₂	semidirect
33. C₂×Q₈×D₁₃	C₂²	semidirect
37. C₂×#6127	C₂²	semidirect
42. C₁₃×#123	C₂²	semidirect
43. C₁₃×#123	C₂²	semidirect
44. C₁₃×C₂²⋊Q₈	C₂²	semidirect
45. C₁₃×C₂²⋊Q₈	C₂²	semidirect
47. C₄×D₄×C₁₃	C₂²	semidirect
48. C₄×D₄×C₁₃	C₂²	semidirect
49. C₁₃×#117	C₂²	semidirect
50. C₁₃×#117	C₂²	semidirect
56. #88201	C₂²	semidirect
57. #88200	C₂²	semidirect
58. #88200	C₂²	semidirect
61. #88194	C₂²	semidirect
65. #88193	C₂²	semidirect
67. #88192	C₂²	semidirect
69. #88189	C₂²	semidirect
72. #88184	C₂²	semidirect
73. #88184	C₂²	semidirect
74. #88184	C₂²	semidirect
79. C₄×C₂²⋊D₁₃	C₂²	semidirect
80. C₄×C₂²⋊D₁₃	C₂²	semidirect
81. C₄×C₂²⋊D₁₃	C₂²	semidirect
82. C₄×C₂²⋊D₁₃	C₂²	semidirect
83. C₄×C₂²⋊D₁₃	C₂²	semidirect
84. #88178	C₂²	semidirect
85. #88178	C₂²	semidirect
86. C₂×#6101	C₂²	semidirect
87. #88152	C₂²	semidirect
88. #88151	C₂²	semidirect
89. #88151	C₂²	semidirect
90. #88150	C₂²	semidirect
91. #88150	C₂²	semidirect
92. #88150	C₂²	semidirect
93. #88149	C₂²	semidirect
94. #88149	C₂²	semidirect
95. #88149	C₂²	semidirect
96. #88148	C₂²	semidirect
97. #88148	C₂²	semidirect
98. #88148	C₂²	semidirect
99. #88148	C₂²	semidirect
100. #88148	C₂²	semidirect
101. #88148	C₂²	semidirect
102. #88148	C₂²	semidirect
103. #88148	C₂²	semidirect
104. #88147	C₂²	semidirect
105. #88147	C₂²	semidirect
106. #88147	C₂²	semidirect
107. #88146	C₂²	semidirect
108. #88146	C₂²	semidirect
109. C₄⋊C₄×D₁₃	C₂²	semidirect
110. #88144	C₂²	semidirect
111. #88143	C₂²	semidirect
112. #88143	C₂²	semidirect
113. #88143	C₂²	semidirect
114. #88143	C₂²	semidirect
115. #88142	C₂²	semidirect
116. #88142	C₂²	semidirect
117. #88141	C₂²	semidirect
118. #88141	C₂²	semidirect
119. #88140	C₂²	semidirect
120. #88140	C₂²	semidirect
127. #88139	C₂²	semidirect
128. #88139	C₂²	semidirect
129. #88139	C₂²	semidirect
130. #88139	C₂²	semidirect
140. #88138	C₂²	semidirect
141. #88138	C₂²	semidirect
142. #88138	C₂²	semidirect
143. #88138	C₂²	semidirect
144. #88138	C₂²	semidirect
145. #88138	C₂²	semidirect
146. #88138	C₂²	semidirect
151. #88137	C₂²	semidirect
152. #88137	C₂²	semidirect
153. #88137	C₂²	semidirect
154. #88137	C₂²	semidirect
160. #88135	C₂²	semidirect
161. #88135	C₂²	semidirect
162. #88135	C₂²	semidirect
168. #88133	C₂²	semidirect
169. #88133	C₂²	semidirect
170. #88133	C₂²	semidirect
173. #88132	C₂²	semidirect
175. #88130	C₂²	semidirect
176. #88130	C₂²	semidirect
177. #88130	C₂²	semidirect
178. #88128	C₂²	semidirect
179. C₄×D₅₂	C₂²	semidirect
180. C₄×D₅₂	C₂²	semidirect
181. C₄×D₅₂	C₂²	semidirect
182. #88126	C₂²	semidirect
183. C₄²×D₁₃	C₂²	semidirect
184. #88124	C₂²	semidirect
185. C₄×Dic₂₆	C₂²	semidirect
186. C₄×Dic₂₆	C₂²	semidirect
452. #551	D₁₃	semidirect
590. #123	C₂×D₁₃	semidirect
591. #123	C₂×D₁₃	semidirect
604. C₂²⋊Q₈	C₂×D₁₃	semidirect
605. C₂²⋊Q₈	C₂×D₁₃	semidirect
666. C₄×D₄	C₂×D₁₃	semidirect
667. C₄×D₄	C₂×D₁₃	semidirect
672. #117	C₂×D₁₃	semidirect
673. #117	C₂×D₁₃	semidirect
854. C₁₃	#3562	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#551	2
#11719416	2
#11719411	2
#11719410	2
#11719406	2
#11719383	2
#11719382	2
#11719372	2
#11719369	2
#11719368	2
#11719362	2
#11719360	2
#11719352	2
#11719343	2
#11719338	2
#11719333	2
#11719300	2
#11719297	2
#11719269	2
#11719258	2
#11719253	2
#11719245	2
#11719240	2
#11719238	2
#11719235	2
#11719233	2
#11719199	2
#11719195	2
#3562	13