Subgroups — #16745640

Order 3328.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128908	C₂	1	2	yes	maximal, complemented
2	#13127825	C₂	1	1	yes	maximal, characteristic, complemented
3	#13127704	C₂	1	1	yes	maximal, characteristic, complemented
4	#13127665	C₂	1	2	yes	maximal, complemented
5	#13127267	C₂	1	1	yes	maximal, characteristic, complemented
6	#13127239	C₂	1	1	yes	maximal, characteristic, complemented
7	#13127205	C₂	1	1	yes	maximal, characteristic, complemented
8	#13127054	C₂	1	2	yes	maximal, complemented
9	#13126874	C₂	1	2	yes	maximal, complemented
10	#13126814	C₂	1	2	yes	maximal, complemented
11	#13126558	C₂	1	1	yes	maximal, characteristic, complemented
12	#13126523	C₂	1	1	yes	maximal, characteristic, complemented
13	#13126523	C₂	1	1	yes	maximal, characteristic, complemented
14	#13125495	C₂	1	1	yes	maximal, characteristic, complemented
15	#13125475	C₂	1	1	yes	maximal, characteristic, complemented
16	#13125406	C₂	1	1	yes	maximal, characteristic, complemented
17	#13125115	C₂	1	2	yes	maximal, complemented
18	#13125089	C₂	1	2	yes	maximal, complemented
19	#13124947	C₂	1	2	yes	maximal, complemented
20	#13123713	C₂	1	1	yes	maximal, characteristic, complemented
21	#13123689	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#88158	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#529	C₂²	1	1	yes	characteristic
25	C₂×#88158	C₂²	1	1	yes	characteristic
26	C₂×#88158	C₂²	1	1	yes	characteristic
27	C₂²×D₁₀₄	C₂²	1	1	yes	characteristic
28	#11719411	—	2	2	no	—
29	D₁₃×#126	—	2	2	no	—
30	#11719398	—	2	2	no	—
31	#11719384	—	2	2	no	—
32	#11719366	—	2	2	no	—
33	#11719364	—	2	2	no	—
34	#11719343	—	2	2	no	—
35	#11719318	—	2	2	no	—
36	#11719289	C₂²	1	2	yes	complemented
37	#11719284	C₂²	1	2	yes	complemented
38	#11719270	C₂²	1	2	yes	complemented
39	#11719256	C₂²	1	2	yes	complemented
40	#11719255	C₂²	1	2	yes	—
41	#11719255	C₂²	1	2	yes	—
42	#11719247	C₂²	1	2	yes	—
43	#11719246	C₂²	1	2	yes	—
44	#11719239	C₂²	1	2	yes	complemented
45	#11719228	C₂²	1	2	yes	complemented
46	#11719226	C₂²	1	2	yes	—
47	#11719223	C₂²	1	2	yes	—
48	#11719184	C₂²	1	2	yes	complemented
49	C₄×#6127	C₂²	1	2	yes	complemented
50	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
51	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#436	C₂²	1	1	yes	characteristic
53	C₁₃×#435	C₂²	1	1	yes	characteristic
54	C₁₃×#435	C₂²	1	1	yes	characteristic, complemented
55	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
56	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
57	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#433	C₂²	1	1	yes	characteristic
59	C₁₃×#433	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#405	C₂²	1	1	yes	characteristic
62	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
64	#11718798	C₂²	1	2	yes	—
65	#11718795	C₂²	1	2	yes	complemented
66	#11718794	C₂²	1	2	yes	complemented
67	#11718792	C₂²	1	2	yes	—
68	#11718777	C₂²	1	1	yes	characteristic
69	#11718777	C₂²	1	1	yes	characteristic
70	#11718777	C₂²	1	1	yes	characteristic, complemented
71	#11718777	C₂²	1	1	yes	characteristic, complemented
72	#11718776	C₂²	1	1	yes	characteristic
73	#11718776	C₂²	1	1	yes	characteristic
74	#11718775	C₂²	1	2	yes	complemented
75	#11718774	C₂²	1	2	yes	complemented
76	#11718767	C₂²	1	1	yes	characteristic
77	#11718767	C₂²	1	1	yes	characteristic, complemented
78	C₂×#88058	C₂²	1	1	yes	characteristic, complemented
79	#11718512	C₂²	1	2	yes	complemented
80	#11718508	C₂²	1	2	yes	complemented
81	#11718508	C₂²	1	2	yes	complemented
82	#11718508	C₂²	1	2	yes	complemented
83	#11718506	C₂²	1	2	yes	complemented
84	#11718506	C₂²	1	2	yes	complemented
85	#11718505	C₂²	1	2	yes	—
86	#11718505	C₂²	1	2	yes	—
87	#11718503	C₂²	1	2	yes	complemented
88	#11718502	C₂²	1	2	yes	complemented
89	#11718502	C₂²	1	2	yes	complemented
90	#11718490	C₂²	1	2	yes	complemented
91	#11718398	C₂²	1	2	yes	complemented
92	#11718396	C₂²	1	2	yes	complemented
93	#11718395	C₂²	1	2	yes	—
94	#11718395	C₂²	1	2	yes	—
95	#11718394	C₂²	1	2	yes	complemented
96	#11718394	C₂²	1	2	yes	complemented
97	#11718392	C₂²	1	2	yes	—
98	#11718392	C₂²	1	2	yes	—
99	#11718384	C₂²	1	2	yes	—
100	#11718384	C₂²	1	2	yes	—
101	#11718384	C₂²	1	2	yes	complemented
102	#11718382	C₂²	1	2	yes	complemented
103	#11718377	C₂²	1	2	yes	complemented
104	#11718375	C₂²	1	2	yes	complemented
105	#11718372	C₂²	1	2	yes	—
106	#11718372	C₂²	1	2	yes	—
107	#11718371	C₂²	1	2	yes	complemented
108	#11718371	C₂²	1	2	yes	complemented
109	#11718371	C₂²	1	2	yes	complemented
110	#11718364	C₂²	1	2	yes	complemented
111	#11718360	C₂²	1	1	yes	characteristic, complemented
112	C₄×Dic₅₂	C₂²	1	1	yes	characteristic, complemented
113	C₄×Dic₅₂	C₂²	1	1	yes	characteristic, complemented
114	C₄×Dic₅₂	C₂²	1	1	yes	characteristic, complemented
115	C₄×Dic₅₂	C₂²	1	1	yes	characteristic, complemented
116	#11718358	C₂²	1	2	yes	complemented
117	#11718357	C₂²	1	1	yes	characteristic
118	#11718357	C₂²	1	1	yes	characteristic
119	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
120	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
121	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
122	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
123	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
124	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
125	C₄×#6095	C₂²	1	2	yes	complemented
126	C₄×#6095	C₂²	1	2	yes	complemented
127	C₄×#6095	C₂²	1	2	yes	complemented
128	#11718344	C₂²	1	1	yes	characteristic, complemented
129	#11718344	C₂²	1	1	yes	characteristic, complemented
130	#11718343	C₂²	1	1	yes	characteristic, complemented
131	C₂×#6127	C₂³	1	2	yes	—
132	C₂×#6127	C₂³	1	2	yes	—
133	C₂²×D₅₂	C₂³	1	2	yes	—
134	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
135	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₁₃×#126	D₄	1	1	yes	characteristic
141	C₁₃×#126	D₄	1	1	yes	characteristic
142	C₁₃×#125	D₄	1	1	yes	characteristic
143	C₁₃×#124	D₄	1	1	yes	characteristic
144	C₁₃×#123	D₄	1	1	yes	characteristic
145	C₁₃×#123	D₄	1	1	yes	characteristic
146	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
147	C₁₃×#121	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
150	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
151	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
152	C₁₃×#117	C₂³	1	1	yes	characteristic
153	C₁₃×#117	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
155	#88200	—	2	2	no	—
156	#88200	—	2	2	no	—
157	#88193	—	2	2	no	—
158	#88192	—	2	2	no	—
159	#88191	—	2	2	no	—
160	#88191	—	2	2	no	—
161	#88190	—	2	2	no	—
162	#88189	—	2	2	no	—
163	#88184	C₂³	1	2	yes	—
164	#88184	C₂³	1	2	yes	—
165	#88183	—	2	2	no	—
166	C₄×C₂²⋊D₁₃	—	2	2	no	—
167	C₄×C₂²⋊D₁₃	—	2	2	no	—
168	C₄×C₂²⋊D₁₃	—	2	2	no	—
169	#88180	C₂³	1	2	yes	—
170	#88180	C₂³	1	2	yes	—
171	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
172	#88178	C₂³	1	2	yes	—
173	#88178	C₂³	1	2	yes	—
174	#88178	C₂³	1	2	yes	—
175	#88178	C₂³	1	2	yes	—
176	C₂×Dic₅₂	C₂³	1	1	yes	characteristic
177	C₂×Dic₅₂	C₂³	1	1	yes	characteristic
178	C₂×Dic₅₂	C₂³	1	2	yes	—
179	#88158	—	2	4	no	—
180	#88158	—	2	4	no	—
181	C₂×D₁₀₄	—	2	4	no	—
182	C₂×D₁₀₄	C₂³	1	2	yes	—
183	C₂×D₁₀₄	C₂³	1	1	yes	characteristic
184	C₂×D₁₀₄	C₂³	1	1	yes	characteristic
185	C₂×#6095	C₂³	1	2	yes	—
186	C₂×#6095	C₂³	1	2	yes	—
187	C₂×#6095	C₂³	1	2	yes	—
188	C₂×#6095	C₂³	1	2	yes	—
189	#88152	—	2	2	no	—
190	#88152	—	2	2	no	—
191	#88152	—	2	2	no	—
192	#88152	—	2	2	no	—
193	#88150	—	2	2	no	—
194	#88150	—	2	2	no	—
195	#88150	—	2	2	no	—
196	#88148	—	2	2	no	—
197	#88148	—	2	2	no	—
198	#88147	—	2	2	no	—
199	#88147	—	2	2	no	—
200	#88146	—	2	2	no	—
201	#88146	—	2	2	no	—
202	C₄⋊C₄×D₁₃	—	2	2	no	—
203	C₄⋊C₄×D₁₃	—	2	2	no	—
204	C₄⋊C₄×D₁₃	—	2	2	no	—
205	#88143	—	2	2	no	—
206	#88143	—	2	2	no	—
207	#88143	—	2	2	no	—
208	#88141	—	2	2	no	—
209	#88139	—	2	2	no	—
210	#88138	—	2	2	no	—
211	#88138	—	2	2	no	—
212	#88137	—	2	2	no	—
213	#88137	—	2	2	no	—
214	#88137	—	2	2	no	—
215	#88137	—	2	2	no	—
216	#88135	—	2	2	no	—
217	#88135	—	2	2	no	—
218	#88135	—	2	2	no	—
219	C₂²⋊C₄×D₁₃	—	2	2	no	—
220	C₂²⋊C₄×D₁₃	—	2	2	no	—
221	C₂²⋊C₄×D₁₃	—	2	2	no	—
222	C₂²⋊C₄×D₁₃	—	2	2	no	—
223	#88133	—	2	2	no	—
224	#88133	—	2	2	no	—
225	#88133	—	2	2	no	—
226	#88133	—	2	2	no	—
227	#88133	—	2	2	no	—
228	#88131	—	2	2	no	—
229	#88130	—	2	2	no	—
230	#88129	C₂³	1	2	yes	—
231	#88129	C₂³	1	2	yes	—
232	C₄×D₅₂	C₂³	1	2	yes	—
233	C₄×D₅₂	C₂³	1	2	yes	—
234	C₄×D₅₂	C₂³	1	2	yes	—
235	C₄×D₅₂	C₂³	1	2	yes	—
236	C₄×D₅₂	C₂³	1	2	yes	—
237	C₄×D₅₂	C₂³	1	2	yes	—
238	#88126	—	2	2	no	—
239	#88126	—	2	2	no	—
240	C₄²×D₁₃	—	2	2	no	—
241	#88124	C₂³	1	2	yes	—
242	#88124	C₂³	1	2	yes	—
243	#88123	C₂³	1	2	yes	—
244	#88123	C₂³	1	2	yes	—
245	C₄×Dic₂₆	C₂³	1	2	yes	—
246	C₄×Dic₂₆	C₂³	1	2	yes	—
247	C₄×Dic₂₆	C₂³	1	2	yes	—
248	C₄×Dic₂₆	C₂³	1	2	yes	—
249	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
256	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
257	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
258	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
259	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
260	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
261	C₁₃×#97	C₂³	1	1	yes	characteristic
262	C₁₃×#97	C₂³	1	1	yes	characteristic
263	C₁₃×#97	C₂³	1	1	yes	characteristic
264	C₁₃×#97	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
266	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
267	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
268	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
269	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
271	#88061	C₂³	1	2	yes	—
272	#88061	C₂³	1	2	yes	—
273	#88061	C₂³	1	2	yes	—
274	#88061	C₂³	1	2	yes	—
275	#88061	C₂³	1	2	yes	—
276	#88061	C₂³	1	2	yes	—
277	#88061	C₂³	1	2	yes	—
278	#88061	C₂³	1	2	yes	—
279	#88058	C₂³	1	2	yes	—
280	#88058	C₂³	1	2	yes	—
281	#88058	C₂³	1	1	yes	characteristic
282	#88058	C₂³	1	1	yes	characteristic
283	#88058	C₂³	1	1	yes	characteristic
284	#88058	C₂³	1	1	yes	characteristic
285	#88057	C₂³	1	2	yes	—
286	#88057	C₂³	1	2	yes	—
287	#88057	C₂³	1	2	yes	—
288	#88057	C₂³	1	2	yes	—
289	#88056	C₂³	1	2	yes	—
290	#88056	C₂³	1	2	yes	—
291	#88056	C₂³	1	2	yes	—
292	#88056	C₂³	1	2	yes	—
293	#88056	C₂³	1	2	yes	—
294	#88056	C₂³	1	2	yes	—
295	#88056	C₂³	1	2	yes	—
296	#88056	C₂³	1	2	yes	—
297	#61487	—	13	1	no	maximal, Sylow
298	C₂³×D₁₃	—	2	2	no	—
299	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₂×C₂²⋊D₁₃	—	2	2	no	—
309	C₂×C₂²⋊D₁₃	—	2	2	no	—
310	C₂×C₂²⋊D₁₃	—	2	2	no	—
311	C₂×C₂²⋊D₁₃	—	2	2	no	—
312	C₂²×Dic₁₃	—	2	2	no	—
313	#6127	—	2	4	no	—
314	#6127	—	2	4	no	—
315	#6127	—	4	2	no	—
316	#6127	—	4	2	no	—
317	C₂×D₅₂	—	2	4	no	—
318	C₂×D₅₂	—	2	2	no	—
319	C₂×D₅₂	—	4	2	no	—
320	C₂×D₅₂	C₂⁴	1	2	yes	—
321	C₂×D₅₂	C₂⁴	1	2	yes	—
322	C₂×C₄×D₁₃	—	2	2	no	—
323	C₂×C₄×D₁₃	—	2	2	no	—
324	C₂×C₄×D₁₃	—	2	2	no	—
325	C₂×C₄×D₁₃	—	2	2	no	—
326	C₂×C₄×D₁₃	—	2	2	no	—
327	C₂×C₄×D₁₃	—	2	2	no	—
328	C₂×C₄×D₁₃	—	2	2	no	—
329	C₂×C₄×D₁₃	—	2	2	no	—
330	C₂×Dic₂₆	—	2	2	no	—
331	C₂×Dic₂₆	C₂⁴	1	2	yes	—
332	C₂×Dic₂₆	C₂⁴	1	2	yes	—
333	C₁₃×M₁₆	—	4	1	no	—
334	C₁₃×M₁₆	—	4	1	no	—
335	C₂×C₈×C₁₃	—	2	2	no	—
336	C₂×C₈×C₁₃	—	2	2	no	—
337	C₂×C₈×C₁₃	—	2	2	no	—
338	C₂×C₈×C₁₃	—	4	1	no	—
339	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
348	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
349	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
350	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
351	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
352	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
353	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
354	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
355	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
356	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
357	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
358	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
359	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
360	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
361	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
362	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
363	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
365	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
366	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂²⋊Dic₁₃	—	2	2	no	—
374	C₂²⋊Dic₁₃	—	2	2	no	—
375	C₂²⋊Dic₁₃	—	2	2	no	—
376	C₂²⋊Dic₁₃	—	2	2	no	—
377	C₂²⋊Dic₁₃	—	2	2	no	—
378	C₂²⋊Dic₁₃	—	2	2	no	—
379	#6103	—	2	2	no	—
380	#6103	—	2	2	no	—
381	#6103	—	2	2	no	—
382	#6103	—	2	2	no	—
383	#6103	—	2	2	no	—
384	#6103	—	2	2	no	—
385	#6103	—	2	2	no	—
386	#6103	—	2	2	no	—
387	#6103	—	2	2	no	—
388	#6103	—	2	2	no	—
389	#6103	—	2	2	no	—
390	#6103	—	2	2	no	—
391	C₄⋊Dic₁₃	—	2	2	no	—
392	C₄⋊Dic₁₃	—	2	2	no	—
393	C₄⋊Dic₁₃	—	2	2	no	—
394	C₄⋊Dic₁₃	—	2	2	no	—
395	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
396	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
397	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
398	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
399	#6101	—	2	2	no	—
400	#6101	—	2	2	no	—
401	#6101	—	2	2	no	—
402	#6101	—	2	2	no	—
403	#6101	—	2	2	no	—
404	#6101	—	2	2	no	—
405	#6101	—	2	2	no	—
406	#6101	—	2	2	no	—
407	#6101	—	2	2	no	—
408	#6101	—	2	2	no	—
409	#6101	—	2	2	no	—
410	#6101	—	2	2	no	—
411	C₄×Dic₁₃	—	2	2	no	—
412	C₄×Dic₁₃	—	2	2	no	—
413	C₄×Dic₁₃	—	2	2	no	—
414	C₄×Dic₁₃	—	2	2	no	—
415	C₄×Dic₁₃	—	2	2	no	—
416	C₄×Dic₁₃	—	2	2	no	—
417	Dic₅₂	—	2	2	no	—
418	Dic₅₂	—	2	2	no	—
419	Dic₅₂	—	4	2	no	—
420	D₁₀₄	—	2	4	no	—
421	D₁₀₄	—	2	2	no	—
422	D₁₀₄	#41	1	4	yes	—
423	#6095	—	2	4	no	—
424	#6095	—	2	4	no	—
425	#6095	—	4	2	no	—
426	#6095	—	4	2	no	—
427	#3521	—	13	2	no	—
428	#3393	—	13	1	no	—
429	#3380	—	13	1	no	—
430	#3376	—	13	2	no	—
431	#3342	—	13	1	no	—
432	#3339	—	13	1	no	—
433	#3336	—	13	1	no	—
434	#3323	—	13	2	no	—
435	#3311	—	13	2	no	—
436	#3307	—	13	2	no	—
437	#3283	—	13	1	no	—
438	#3280	—	13	1	no	—
439	#3280	—	13	1	no	—
440	#3177	—	13	1	no	—
441	#3175	—	13	1	no	—
442	#3168	—	13	1	no	—
443	#3125	—	13	2	no	—
444	#3123	—	13	2	no	—
445	#3111	—	13	2	no	—
446	#2966	D₁₃	1	1	yes	characteristic, complemented
447	#2951	—	13	1	no	—
448	#2948	—	13	1	no	—
449	C₄×#135	—	13	1	no	—
450	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
452	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
453	C₂²×D₁₃	—	2	2	no	—
454	C₂²×D₁₃	—	2	2	no	—
455	C₂²×D₁₃	—	4	4	no	—
456	C₂²×D₁₃	—	8	2	no	—
457	C₂²×D₁₃	—	8	2	no	—
458	Q₈×C₁₃	—	4	1	no	—
459	D₄×C₁₃	—	4	1	no	—
460	D₄×C₁₃	—	4	1	no	—
461	D₄×C₁₃	—	4	1	no	—
462	C₂×C₄×C₁₃	—	2	1	no	—
463	C₂×C₄×C₁₃	—	2	1	no	—
464	C₂×C₄×C₁₃	—	2	1	no	—
465	C₂×C₄×C₁₃	—	2	1	no	—
466	C₂×C₄×C₁₃	—	2	1	no	—
467	C₂×C₄×C₁₃	—	2	1	no	—
468	C₂×C₄×C₁₃	—	4	1	no	—
469	C₂×C₄×C₁₃	—	4	1	no	—
470	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
482	C₂²⋊D₁₃	—	4	4	no	—
483	C₂²⋊D₁₃	—	4	4	no	—
484	C₂²⋊D₁₃	—	8	2	no	—
485	C₂²⋊D₁₃	—	8	2	no	—
486	C₂×Dic₁₃	—	2	2	no	—
487	C₂×Dic₁₃	—	2	2	no	—
488	C₂×Dic₁₃	—	2	2	no	—
489	C₂×Dic₁₃	—	2	2	no	—
490	C₂×Dic₁₃	—	2	2	no	—
491	C₂×Dic₁₃	—	2	2	no	—
492	C₂×Dic₁₃	—	8	2	no	—
493	D₅₂	—	2	2	no	—
494	D₅₂	—	2	2	no	—
495	D₅₂	—	2	2	no	—
496	D₅₂	—	4	4	no	—
497	D₅₂	C₂×#41	1	4	yes	—
498	C₄×D₁₃	—	4	4	no	—
499	C₄×D₁₃	—	4	4	no	—
500	C₄×D₁₃	—	8	2	no	—
501	C₄×D₁₃	—	8	2	no	—
502	C₄×D₁₃	—	8	2	no	—
503	C₄×D₁₃	—	8	2	no	—
504	C₄×D₁₃	—	8	2	no	—
505	C₄×D₁₃	—	8	2	no	—
506	Dic₂₆	—	2	2	no	—
507	Dic₂₆	—	2	2	no	—
508	Dic₂₆	—	2	2	no	—
509	Dic₂₆	—	2	2	no	—
510	Dic₂₆	—	8	2	no	—
511	C₈×C₁₃	—	2	1	no	—
512	C₈×C₁₃	—	2	1	no	—
513	C₈×C₁₃	—	2	1	no	—
514	C₈×C₁₃	—	2	1	no	—
515	C₈×C₁₃	—	2	1	no	—
516	C₈×C₁₃	—	2	1	no	—
517	C₈×C₁₃	—	2	1	no	—
518	C₈×C₁₃	C₂×#41	1	2	yes	—
519	C₂×#135	—	13	1	no	—
520	C₂×#135	—	13	1	no	—
521	C₂²×D₈	—	13	1	no	—
522	#556	—	13	2	no	—
523	#556	—	13	2	no	—
524	#554	—	13	2	no	—
525	#553	—	13	2	no	—
526	#553	—	26	2	no	—
527	#552	—	13	2	no	—
528	#552	—	26	2	no	—
529	#551	—	26	2	no	—
530	#551	—	26	2	no	—
531	#547	—	13	2	no	—
532	#546	—	13	2	no	—
533	#546	—	13	2	no	—
534	#542	—	13	2	no	—
535	#541	—	13	2	no	—
536	#539	—	26	2	no	—
537	#538	—	26	2	no	—
538	#529	—	13	2	no	—
539	#529	—	26	2	no	—
540	#529	C₂×D₁₃	1	1	yes	characteristic
541	C₂×#126	—	26	2	no	—
542	#520	—	13	2	no	—
543	#518	—	13	2	no	—
544	C₄×#41	—	13	2	no	—
545	#500	—	13	1	no	—
546	#499	—	13	1	no	—
547	#499	—	13	1	no	—
548	#495	—	13	1	no	—
549	#495	—	13	1	no	—
550	#494	—	13	1	no	—
551	#491	—	13	2	no	—
552	#489	—	13	2	no	—
553	#488	—	13	2	no	—
554	#485	—	13	2	no	—
555	#485	—	13	2	no	—
556	#485	—	13	2	no	—
557	#483	—	13	2	no	—
558	#482	—	13	2	no	—
559	#481	—	13	2	no	—
560	#479	—	13	2	no	—
561	#478	—	13	2	no	—
562	#478	—	13	2	no	—
563	#478	—	13	2	no	—
564	#476	—	13	2	no	—
565	#475	—	13	2	no	—
566	#470	—	13	2	no	—
567	#468	—	13	2	no	—
568	#467	—	13	1	no	—
569	#467	—	13	1	no	—
570	#467	—	13	1	no	—
571	#467	—	13	1	no	—
572	#466	—	13	1	no	—
573	#466	—	13	1	no	—
574	#465	—	13	2	no	—
575	#464	—	13	2	no	—
576	#464	—	13	2	no	—
577	#463	—	13	2	no	—
578	#463	—	13	2	no	—
579	#461	—	13	2	no	—
580	#461	—	13	2	no	—
581	#452	—	13	2	no	—
582	#452	—	13	2	no	—
583	#450	—	13	2	no	—
584	#450	—	13	2	no	—
585	#449	—	13	2	no	—
586	#449	—	13	2	no	—
587	#446	C₂×D₁₃	1	1	yes	characteristic, complemented
588	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
589	#442	—	13	2	no	—
590	#442	—	13	2	no	—
591	#441	—	13	2	no	—
592	#440	—	13	2	no	—
593	#440	—	13	2	no	—
594	#440	—	13	2	no	—
595	C₄×Q₁₆	—	13	1	no	—
596	C₄×Q₁₆	—	13	1	no	—
597	C₄×Q₁₆	—	13	1	no	—
598	C₄×Q₁₆	—	13	1	no	—
599	C₄×SD₁₆	—	13	2	no	—
600	C₄×SD₁₆	—	13	2	no	—
601	C₄×SD₁₆	—	13	2	no	—
602	C₄×D₈	—	13	1	no	—
603	C₄×D₈	—	13	1	no	—
604	C₄×D₈	—	13	1	no	—
605	C₄×D₈	—	13	1	no	—
606	C₄×D₈	—	13	1	no	—
607	C₄×D₈	—	13	1	no	—
608	#436	C₂×D₁₃	1	1	yes	characteristic
609	#435	C₂×D₁₃	1	1	yes	characteristic
610	#435	C₂×D₁₃	1	1	yes	characteristic, complemented
611	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
612	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
613	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
614	#433	C₂×D₁₃	1	1	yes	characteristic
615	#433	C₂×D₁₃	1	1	yes	characteristic, complemented
616	#432	C₂×D₁₃	1	1	yes	characteristic, complemented
617	#427	—	13	1	no	—
618	#427	—	13	1	no	—
619	C₂×#107	—	13	1	no	—
620	#418	—	13	2	no	—
621	#417	—	13	2	no	—
622	#416	—	13	2	no	—
623	#405	C₂×D₁₃	1	1	yes	characteristic
624	#405	C₂×D₁₃	1	1	yes	characteristic, complemented
625	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
626	C₂²×C₁₃	—	2	1	no	—
627	C₂²×C₁₃	—	2	1	no	—
628	C₂²×C₁₃	—	2	1	no	—
629	C₂²×C₁₃	—	2	1	no	—
630	C₂²×C₁₃	—	2	1	no	—
631	C₂²×C₁₃	—	2	1	no	—
632	C₂²×C₁₃	—	2	1	no	—
633	C₂²×C₁₃	—	2	1	no	—
634	C₂²×C₁₃	—	2	1	no	—
635	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
636	C₂×D₁₃	—	2	4	no	—
637	C₂×D₁₃	—	4	2	no	—
638	C₂×D₁₃	—	4	2	no	—
639	C₂×D₁₃	—	4	2	no	—
640	C₂×D₁₃	—	4	2	no	—
641	C₂×D₁₃	—	4	2	no	—
642	C₂×D₁₃	—	16	4	no	—
643	C₄×C₁₃	—	2	1	no	—
644	C₄×C₁₃	—	2	1	no	—
645	C₄×C₁₃	—	2	1	no	—
646	C₄×C₁₃	—	2	1	no	—
647	C₄×C₁₃	—	2	1	no	—
648	C₄×C₁₃	—	2	1	no	—
649	C₄×C₁₃	—	2	1	no	—
650	C₄×C₁₃	—	2	1	no	—
651	C₄×C₁₃	—	2	1	no	—
652	C₄×C₁₃	—	2	1	no	—
653	C₄×C₁₃	—	2	1	no	—
654	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
655	C₄×C₁₃	#585	1	1	yes	characteristic
656	Dic₁₃	—	4	2	no	—
657	Dic₁₃	—	4	2	no	—
658	Dic₁₃	—	4	2	no	—
659	Dic₁₃	—	4	2	no	—
660	Dic₁₃	—	4	2	no	—
661	Dic₁₃	—	4	2	no	—
662	C₂×#41	—	13	2	no	—
663	C₂×#41	—	13	2	no	—
664	C₂²×D₄	—	13	2	no	—
665	#135	—	26	4	no	—
666	#135	—	26	4	no	—
667	C₂×Q₁₆	—	13	1	no	—
668	C₂×Q₁₆	—	13	1	no	—
669	C₂×Q₁₆	—	13	2	no	—
670	C₂×SD₁₆	—	13	2	no	—
671	C₂×SD₁₆	—	13	2	no	—
672	C₂×SD₁₆	—	13	2	no	—
673	C₂×SD₁₆	—	13	2	no	—
674	C₂×D₈	—	13	1	no	—
675	C₂×D₈	—	13	1	no	—
676	C₂×D₈	—	13	2	no	—
677	C₂×D₈	—	26	4	no	—
678	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
679	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
680	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
681	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
682	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
683	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
684	C₄⋊Q₈	—	13	2	no	—
685	C₄⋊Q₈	—	13	2	no	—
686	#126	—	26	2	no	—
687	#126	—	26	2	no	—
688	#126	—	26	2	no	—
689	#126	—	26	2	no	—
690	#126	—	26	2	no	—
691	#126	—	26	2	no	—
692	#126	—	26	2	no	—
693	#126	—	26	2	no	—
694	#126	—	26	2	no	—
695	#126	—	26	2	no	—
696	#126	D₅₂	1	1	yes	characteristic
697	#126	D₅₂	1	1	yes	characteristic
698	#125	—	13	2	no	—
699	#125	—	13	2	no	—
700	#125	—	26	2	no	—
701	#125	—	26	2	no	—
702	#125	—	26	2	no	—
703	#125	D₅₂	1	1	yes	characteristic
704	#124	—	13	2	no	—
705	#124	—	13	2	no	—
706	#124	—	26	2	no	—
707	#124	—	26	2	no	—
708	#124	D₅₂	1	1	yes	characteristic
709	#123	—	26	2	no	—
710	#123	—	26	2	no	—
711	#123	—	26	2	no	—
712	#123	—	26	2	no	—
713	#123	—	26	2	no	—
714	#123	—	26	2	no	—
715	#123	—	26	2	no	—
716	#123	—	26	2	no	—
717	#123	D₅₂	1	1	yes	characteristic
718	#123	D₅₂	1	1	yes	characteristic
719	C₂²⋊Q₈	—	13	2	no	—
720	C₂²⋊Q₈	—	13	2	no	—
721	C₂²⋊Q₈	—	13	2	no	—
722	C₂²⋊Q₈	—	13	2	no	—
723	C₂²⋊Q₈	—	26	2	no	—
724	C₂²⋊Q₈	—	26	2	no	—
725	C₂²⋊Q₈	—	26	2	no	—
726	C₂²⋊Q₈	—	26	2	no	—
727	C₂²⋊Q₈	—	26	2	no	—
728	C₂²⋊Q₈	D₅₂	1	1	yes	characteristic
729	#121	—	13	2	no	—
730	#121	—	13	2	no	—
731	#121	—	26	2	no	—
732	#121	—	26	2	no	—
733	#121	—	26	2	no	—
734	#121	—	26	2	no	—
735	#121	D₅₂	1	1	yes	characteristic
736	#120	—	26	2	no	—
737	#120	—	26	2	no	—
738	C₄×Q₈	—	13	2	no	—
739	C₄×Q₈	—	13	2	no	—
740	C₄×Q₈	—	13	2	no	—
741	C₄×Q₈	—	13	2	no	—
742	C₄×Q₈	—	26	2	no	—
743	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
744	C₄×D₄	—	13	2	no	—
745	C₄×D₄	—	13	2	no	—
746	C₄×D₄	—	13	2	no	—
747	C₄×D₄	—	13	2	no	—
748	C₄×D₄	—	13	2	no	—
749	C₄×D₄	—	13	2	no	—
750	C₄×D₄	—	26	2	no	—
751	C₄×D₄	—	26	2	no	—
752	C₄×D₄	—	26	2	no	—
753	C₄×D₄	—	26	2	no	—
754	C₄×D₄	—	26	2	no	—
755	C₄×D₄	—	26	2	no	—
756	C₄×D₄	—	26	2	no	—
757	C₄×D₄	—	26	2	no	—
758	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
759	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
760	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
761	#117	—	13	2	no	—
762	#117	—	13	2	no	—
763	#117	—	26	2	no	—
764	#117	—	26	2	no	—
765	#117	—	26	2	no	—
766	#117	—	26	2	no	—
767	#117	—	26	2	no	—
768	#117	C₂²×D₁₃	1	1	yes	characteristic
769	#117	C₂²×D₁₃	1	1	yes	characteristic
770	C₂×C₄⋊C₄	—	13	2	no	—
771	C₂×C₄⋊C₄	—	26	2	no	—
772	C₂×C₄⋊C₄	—	26	2	no	—
773	C₂×C₄⋊C₄	—	26	2	no	—
774	C₂×C₂²⋊C₄	—	26	2	no	—
775	C₂×C₂²⋊C₄	—	26	2	no	—
776	C₂×C₂²⋊C₄	—	26	2	no	—
777	C₂×C₂²⋊C₄	—	26	2	no	—
778	C₂×C₄²	—	26	2	no	—
779	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
780	#107	—	13	1	no	—
781	#107	—	13	1	no	—
782	#107	—	13	2	no	—
783	#107	—	13	1	no	—
784	#107	—	13	1	no	—
785	#107	—	13	2	no	—
786	#106	—	13	2	no	—
787	#106	—	13	2	no	—
788	#106	—	13	2	no	—
789	#106	—	13	2	no	—
790	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
791	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
792	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
793	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
794	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
795	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
796	#103	—	13	2	no	—
797	#103	—	13	2	no	—
798	#103	—	13	2	no	—
799	#103	—	13	2	no	—
800	#103	—	13	2	no	—
801	#103	—	13	2	no	—
802	#103	—	13	2	no	—
803	#103	—	13	2	no	—
804	#102	—	13	2	no	—
805	#102	—	13	2	no	—
806	#102	—	13	2	no	—
807	#102	—	13	2	no	—
808	#102	—	13	2	no	—
809	#102	—	13	2	no	—
810	#102	—	13	2	no	—
811	#102	—	13	2	no	—
812	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
813	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
814	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
815	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
816	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
817	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
818	#97	C₂²×D₁₃	1	1	yes	characteristic
819	#97	C₂²×D₁₃	1	1	yes	characteristic
820	#97	C₂²×D₁₃	1	1	yes	characteristic
821	#97	C₂²×D₁₃	1	1	yes	characteristic
822	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
823	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
824	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
825	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
826	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
827	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
828	C₂×C₁₃	—	4	1	no	—
829	C₂×C₁₃	—	4	1	no	—
830	C₂×C₁₃	—	4	1	no	—
831	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
832	C₂×C₁₃	#3584	1	1	yes	characteristic
833	C₂×C₁₃	#3584	1	1	yes	characteristic
834	D₁₃	—	4	4	no	—
835	D₁₃	—	8	2	no	—
836	C₂⁴	—	26	2	no	—
837	#41	—	26	4	no	—
838	#41	—	26	4	no	—
839	#41	—	52	2	no	—
840	#41	—	52	2	no	—
841	C₂×Q₈	—	13	2	no	—
842	C₂×Q₈	—	13	2	no	—
843	C₂×Q₈	—	26	2	no	—
844	C₂×Q₈	C₂×D₅₂	1	1	yes	characteristic
845	C₂×D₄	—	13	2	no	—
846	C₂×D₄	—	13	2	no	—
847	C₂×D₄	—	26	4	no	—
848	C₂×D₄	—	26	2	no	—
849	C₂×D₄	—	26	2	no	—
850	C₂×D₄	—	26	2	no	—
851	C₂×D₄	—	26	2	no	—
852	C₂×D₄	—	26	2	no	—
853	C₂×D₄	—	52	2	no	—
854	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
855	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
856	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
857	C₂²×C₄	—	26	2	no	—
858	C₂²×C₄	—	26	2	no	—
859	C₂²×C₄	—	26	2	no	—
860	C₂²×C₄	—	26	2	no	—
861	C₂²×C₄	—	26	2	no	—
862	C₂²×C₄	—	26	2	no	—
863	C₂²×C₄	—	26	2	no	—
864	C₂²×C₄	—	26	2	no	—
865	C₂²×C₄	—	26	2	no	—
866	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
867	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
868	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
869	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
870	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
871	Q₁₆	—	26	2	no	—
872	Q₁₆	—	26	2	no	—
873	Q₁₆	—	52	2	no	—
874	SD₁₆	—	26	4	no	—
875	SD₁₆	—	26	4	no	—
876	SD₁₆	—	52	2	no	—
877	SD₁₆	—	52	2	no	—
878	D₈	—	13	4	no	—
879	D₈	—	26	4	no	—
880	D₈	—	26	2	no	—
881	M₁₆	—	4	1	no	—
882	M₁₆	—	4	1	no	—
883	C₂×C₈	—	2	2	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	4	1	no	—
887	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
888	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
889	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
892	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
893	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
894	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
895	C₄⋊C₄	—	13	2	no	—
896	C₄⋊C₄	—	13	2	no	—
897	C₄⋊C₄	—	13	2	no	—
898	C₄⋊C₄	—	13	2	no	—
899	C₄⋊C₄	—	26	2	no	—
900	C₄⋊C₄	—	26	2	no	—
901	C₄⋊C₄	—	26	2	no	—
902	C₄⋊C₄	—	26	2	no	—
903	C₄⋊C₄	—	26	2	no	—
904	C₄⋊C₄	—	26	2	no	—
905	C₄⋊C₄	—	26	2	no	—
906	C₄⋊C₄	—	26	2	no	—
907	C₄⋊C₄	—	26	2	no	—
908	C₄⋊C₄	—	26	2	no	—
909	C₄⋊C₄	—	26	2	no	—
910	C₄⋊C₄	—	26	2	no	—
911	C₄⋊C₄	—	26	2	no	—
912	C₄⋊C₄	—	26	2	no	—
913	C₄⋊C₄	—	26	2	no	—
914	C₄⋊C₄	—	26	2	no	—
915	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
916	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
921	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
922	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
923	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
924	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
925	C₂²⋊C₄	—	26	2	no	—
926	C₂²⋊C₄	—	26	2	no	—
927	C₂²⋊C₄	—	26	2	no	—
928	C₂²⋊C₄	—	26	2	no	—
929	C₂²⋊C₄	—	26	2	no	—
930	C₂²⋊C₄	—	26	2	no	—
931	C₂²⋊C₄	—	26	2	no	—
932	C₂²⋊C₄	—	26	2	no	—
933	C₂²⋊C₄	—	26	2	no	—
934	C₂²⋊C₄	—	26	2	no	—
935	C₂²⋊C₄	—	26	2	no	—
936	C₂²⋊C₄	—	26	2	no	—
937	C₂²⋊C₄	—	26	2	no	—
938	C₂²⋊C₄	—	26	2	no	—
939	C₂²⋊C₄	—	26	2	no	—
940	C₂²⋊C₄	—	26	2	no	—
941	C₂²⋊C₄	—	26	2	no	—
942	C₂²⋊C₄	—	26	2	no	—
943	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
944	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
945	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
946	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
947	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
948	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
949	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
950	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
951	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
952	C₂²⋊C₄	C₂×D₅₂	1	1	yes	characteristic
953	C₄²	—	26	2	no	—
954	C₄²	—	26	2	no	—
955	C₄²	—	26	2	no	—
956	C₄²	—	26	2	no	—
957	C₄²	—	26	2	no	—
958	C₄²	—	26	2	no	—
959	C₄²	C₂×D₅₂	1	1	yes	characteristic
960	C₄²	C₂×D₅₂	1	1	yes	characteristic
961	C₄²	C₂³×D₁₃	1	1	yes	characteristic
962	C₄²	C₂³×D₁₃	1	1	yes	characteristic
963	C₄²	C₂³×D₁₃	1	1	yes	characteristic
964	C₄²	C₂³×D₁₃	1	1	yes	characteristic
965	C₁₃	#61487	1	1	yes	characteristic, complemented, Sylow
966	C₂³	—	26	2	no	—
967	C₂³	—	26	2	no	—
968	C₂³	—	52	4	no	—
969	C₂³	—	104	2	no	—
970	C₂³	—	104	2	no	—
971	C₂³	C₂²×D₅₂	1	1	yes	characteristic
972	C₂³	C₂²×D₅₂	1	1	yes	characteristic
973	C₂³	C₂²×D₅₂	1	1	yes	characteristic
974	Q₈	—	4	1	no	—
975	Q₈	—	26	2	no	—
976	Q₈	—	26	2	no	—
977	Q₈	—	26	2	no	—
978	Q₈	—	26	2	no	—
979	Q₈	—	104	2	no	—
980	D₄	—	4	1	no	—
981	D₄	—	4	1	no	—
982	D₄	—	4	1	no	—
983	D₄	—	13	4	no	—
984	D₄	—	26	2	no	—
985	D₄	—	26	2	no	—
986	D₄	—	26	2	no	—
987	D₄	—	52	4	no	—
988	D₄	—	52	4	no	—
989	D₄	—	52	4	no	—
990	D₄	—	104	2	no	—
991	D₄	—	104	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	4	1	no	—
1000	C₂×C₄	—	26	2	no	—
1001	C₂×C₄	—	26	2	no	—
1002	C₂×C₄	—	26	2	no	—
1003	C₂×C₄	—	26	2	no	—
1004	C₂×C₄	—	26	2	no	—
1005	C₂×C₄	—	26	2	no	—
1006	C₂×C₄	—	52	4	no	—
1007	C₂×C₄	—	52	4	no	—
1008	C₂×C₄	—	104	2	no	—
1009	C₂×C₄	—	104	2	no	—
1010	C₂×C₄	—	104	2	no	—
1011	C₂×C₄	—	104	2	no	—
1012	C₂×C₄	—	104	2	no	—
1013	C₂×C₄	—	104	2	no	—
1014	C₂×C₄	—	104	2	no	—
1015	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
1026	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	1	no	—
1034	C₈	#41×D₁₃	1	2	yes	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	26	4	no	—
1045	C₂²	—	52	2	no	—
1046	C₂²	—	52	2	no	—
1047	C₂²	—	52	2	no	—
1048	C₂²	—	52	2	no	—
1049	C₂²	—	52	2	no	—
1050	C₂²	—	208	4	no	—
1051	C₂²	C₂³×D₅₂	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	52	2	no	—
1064	C₄	—	52	2	no	—
1065	C₄	—	52	2	no	—
1066	C₄	—	52	2	no	—
1067	C₄	—	52	2	no	—
1068	C₄	—	52	2	no	—
1069	C₄	C₂×#41×D₁₃	1	1	yes	characteristic
1070	C₄	#11719648	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	4	1	no	—
1073	C₂	—	4	1	no	—
1074	C₂	—	52	4	no	—
1075	C₂	—	104	2	no	—
1076	C₂	#41×D₅₂	1	1	yes	characteristic
1077	C₂	#13129610	1	1	yes	characteristic
1078	C₂	#13129610	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₅₂
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₁₃×#2966	C₂
socle	C₂²×C₁₃	C₂³×D₄
hypercenter	#2966	D₁₃
hypocenter	C₁₃	#61487
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #13128908	C₂	semidirect
2. #13127825	C₂	semidirect
3. #13127704	C₂	semidirect
4. #13127665	C₂	semidirect
5. #13127267	C₂	semidirect
6. #13127239	C₂	semidirect
7. #13127205	C₂	semidirect
8. #13127054	C₂	semidirect
9. #13126874	C₂	semidirect
10. #13126814	C₂	semidirect
11. #13126558	C₂	semidirect
12. #13126523	C₂	semidirect
13. #13126523	C₂	semidirect
14. #13125495	C₂	semidirect
15. #13125475	C₂	semidirect
16. #13125406	C₂	semidirect
17. #13125115	C₂	semidirect
18. #13125089	C₂	semidirect
19. #13124947	C₂	semidirect
20. #13123713	C₂	semidirect
21. #13123689	C₂	semidirect
22. C₄×#88158	C₂	semidirect
23. C₁₃×#2966	C₂	semidirect
36. #11719289	C₂²	semidirect
37. #11719284	C₂²	semidirect
38. #11719270	C₂²	semidirect
39. #11719256	C₂²	semidirect
44. #11719239	C₂²	semidirect
45. #11719228	C₂²	semidirect
48. #11719184	C₂²	semidirect
49. C₄×#6127	C₂²	semidirect
50. C₁₃×#446	C₂²	semidirect
51. C₈×Q₈×C₁₃	C₂²	semidirect
54. C₁₃×#435	C₂²	semidirect
57. C₈×D₄×C₁₃	C₂²	semidirect
59. C₁₃×#433	C₂²	semidirect
60. C₁₃×#432	C₂²	semidirect
62. C₁₃×#405	C₂²	semidirect
63. C₂×C₄×C₈×C₁₃	C₂²	semidirect
65. #11718795	C₂²	semidirect
66. #11718794	C₂²	semidirect
70. #11718777	C₂²	semidirect
71. #11718777	C₂²	semidirect
74. #11718775	C₂²	semidirect
75. #11718774	C₂²	semidirect
77. #11718767	C₂²	semidirect
78. C₂×#88058	C₂²	semidirect
79. #11718512	C₂²	semidirect
80. #11718508	C₂²	semidirect
81. #11718508	C₂²	semidirect
82. #11718508	C₂²	semidirect
83. #11718506	C₂²	semidirect
84. #11718506	C₂²	semidirect
87. #11718503	C₂²	semidirect
88. #11718502	C₂²	semidirect
89. #11718502	C₂²	semidirect
90. #11718490	C₂²	semidirect
91. #11718398	C₂²	semidirect
92. #11718396	C₂²	semidirect
95. #11718394	C₂²	semidirect
96. #11718394	C₂²	semidirect
101. #11718384	C₂²	semidirect
102. #11718382	C₂²	semidirect
103. #11718377	C₂²	semidirect
104. #11718375	C₂²	semidirect
107. #11718371	C₂²	semidirect
108. #11718371	C₂²	semidirect
109. #11718371	C₂²	semidirect
110. #11718364	C₂²	semidirect
111. #11718360	C₂²	semidirect
112. C₄×Dic₅₂	C₂²	semidirect
113. C₄×Dic₅₂	C₂²	semidirect
114. C₄×Dic₅₂	C₂²	semidirect
115. C₄×Dic₅₂	C₂²	semidirect
116. #11718358	C₂²	semidirect
125. C₄×#6095	C₂²	semidirect
126. C₄×#6095	C₂²	semidirect
127. C₄×#6095	C₂²	semidirect
128. #11718344	C₂²	semidirect
129. #11718344	C₂²	semidirect
130. #11718343	C₂²	semidirect
446. #2966	D₁₃	semidirect
587. #446	C₂×D₁₃	semidirect
588. C₈×Q₈	C₂×D₁₃	semidirect
610. #435	C₂×D₁₃	semidirect
613. C₈×D₄	C₂×D₁₃	semidirect
615. #433	C₂×D₁₃	semidirect
616. #432	C₂×D₁₃	semidirect
624. #405	C₂×D₁₃	semidirect
625. C₂×C₄×C₈	C₂×D₁₃	semidirect
965. C₁₃	#61487	semidirect

Maximal subgroups

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

subgroup	index
#13128908	2
#13127825	2
#13127704	2
#13127665	2
#13127267	2
#13127239	2
#13127205	2
#13127054	2
#13126874	2
#13126814	2
#13126558	2
#13126523	2
#13125495	2
#13125475	2
#13125406	2
#13125115	2
#13125089	2
#13124947	2
#13123713	2
#13123689	2
C₄×#88158	2
C₁₃×#2966	2
#61487	13