Subgroups — #16745371

Order 3328.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128853	C₂	1	1	yes	maximal, characteristic, complemented
2	#13128797	C₂	1	1	yes	maximal, characteristic, complemented
3	#13127830	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#13127648	C₂	1	1	yes	maximal, characteristic, complemented
6	#13127552	C₂	1	1	yes	maximal, characteristic, complemented
7	#13127251	C₂	1	1	yes	maximal, characteristic, complemented
8	#13127245	C₂	1	2	yes	maximal, complemented
9	#13127121	C₂	1	1	yes	maximal, characteristic, complemented
10	#13127080	C₂	1	1	yes	maximal, characteristic, complemented
11	#13127018	C₂	1	2	yes	maximal, complemented
12	#13126868	C₂	1	2	yes	maximal, complemented
13	#13126537	C₂	1	2	yes	maximal, complemented
14	SD₁₆×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
15	#13125449	C₂	1	2	yes	maximal, complemented
16	#13125395	C₂	1	1	yes	maximal, characteristic, complemented
17	#13125071	C₂	1	2	yes	maximal, complemented
18	#13125016	C₂	1	2	yes	maximal, complemented
19	#13124998	C₂	1	1	yes	maximal, characteristic, complemented
20	#13124987	C₂	1	1	yes	maximal, characteristic, complemented
21	#13123811	C₂	1	1	yes	maximal, characteristic, complemented
22	#13123690	C₂	1	2	yes	maximal, complemented
23	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
27	#11719536	C₂²	1	2	yes	complemented
28	#11719534	C₂²	1	2	yes	—
29	C₂×SD₁₆×D₁₃	C₂²	1	2	yes	—
30	#11719290	C₂²	1	1	yes	characteristic
31	#11719289	C₂²	1	1	yes	characteristic
32	#11719287	C₂²	1	2	yes	—
33	Q₈×D₅₂	C₂²	1	1	yes	characteristic
34	#11719277	C₂²	1	2	yes	complemented
35	Q₈×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
36	#11719268	—	2	1	no	—
37	#11719268	C₂²	1	1	yes	characteristic
38	#11719266	—	2	2	no	—
39	#11719266	C₂²	1	2	yes	complemented
40	#11719265	—	2	2	no	—
41	#11719257	—	2	1	no	—
42	#11719255	—	2	1	no	—
43	D₄×D₅₂	C₂²	1	1	yes	characteristic
44	#11719250	C₂²	1	2	yes	—
45	#11719247	—	2	1	no	—
46	#11719247	C₂²	1	1	yes	characteristic, complemented
47	D₄×Dic₂₆	C₂²	1	1	yes	characteristic
48	#11719238	—	2	2	no	—
49	#11719238	C₂²	1	2	yes	complemented
50	#11719237	C₂²	1	2	yes	—
51	#11719232	—	2	2	no	—
52	#11719184	—	2	1	no	—
53	#11719184	—	2	1	no	—
54	#11719184	C₂²	1	1	yes	characteristic
55	#11719182	C₂²	1	1	yes	characteristic
56	C₂×#88129	—	2	1	no	—
57	#11719175	—	2	1	no	—
58	#11719175	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
61	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
62	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
63	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
65	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
67	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#416	C₂²	1	1	yes	characteristic
69	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
71	#11718900	C₂²	1	2	yes	—
72	#11718899	C₂²	1	2	yes	complemented
73	#11718847	C₂²	1	2	yes	complemented
74	#11718846	C₂²	1	2	yes	complemented
75	#11718832	C₂²	1	2	yes	complemented
76	#11718829	C₂²	1	2	yes	complemented
77	SD₁₆×Dic₁₃	C₂²	1	2	yes	—
78	#11718817	C₂²	1	2	yes	—
79	#11718814	C₂²	1	2	yes	—
80	#11718775	C₂²	1	2	yes	complemented
81	#11718775	C₂²	1	2	yes	complemented
82	#11718772	C₂²	1	2	yes	complemented
83	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
84	#11718692	C₂²	1	1	yes	characteristic, complemented
85	#11718691	C₂²	1	2	yes	complemented
86	#11718688	C₂²	1	1	yes	characteristic
87	#11718687	C₂²	1	2	yes	complemented
88	#11718682	C₂²	1	1	yes	characteristic, complemented
89	#11718681	C₂²	1	1	yes	characteristic, complemented
90	#11718680	C₂²	1	1	yes	characteristic
91	#11718679	C₂²	1	2	yes	—
92	#11718676	C₂²	1	1	yes	characteristic
93	#11718675	C₂²	1	2	yes	complemented
94	#11718669	C₂²	1	1	yes	characteristic
95	#11718668	C₂²	1	1	yes	characteristic, complemented
96	#11718664	C₂²	1	2	yes	complemented
97	#11718657	C₂²	1	2	yes	complemented
98	#11718587	C₂²	1	1	yes	characteristic, complemented
99	#11718551	C₂²	1	2	yes	complemented
100	#11718549	C₂²	1	2	yes	complemented
101	#11718546	C₂²	1	2	yes	—
102	#11718536	C₂²	1	2	yes	complemented
103	#11718525	C₂²	1	2	yes	—
104	#11718521	C₂²	1	2	yes	complemented
105	#11718516	C₂²	1	2	yes	complemented
106	#11718513	C₂²	1	2	yes	complemented
107	#11718478	C₂²	1	2	yes	complemented
108	#11718477	C₂²	1	2	yes	complemented
109	#11718476	C₂²	1	2	yes	complemented
110	#11718467	C₂²	1	2	yes	—
111	#11718463	C₂²	1	2	yes	complemented
112	#11718459	C₂²	1	2	yes	complemented
113	#11718456	C₂²	1	2	yes	complemented
114	#11718452	C₂²	1	2	yes	complemented
115	#11718448	C₂²	1	2	yes	complemented
116	#11718443	C₂²	1	2	yes	—
117	#11718440	C₂²	1	2	yes	complemented
118	#11718437	C₂²	1	2	yes	—
119	#11718431	C₂²	1	2	yes	—
120	#11718426	C₂²	1	2	yes	complemented
121	#11718422	C₂²	1	2	yes	—
122	#11718418	C₂²	1	2	yes	—
123	#11718355	C₂²	1	1	yes	characteristic
124	#11718354	C₂²	1	1	yes	characteristic
125	C₄×#6095	C₂²	1	2	yes	complemented
126	C₄×#6095	C₂²	1	2	yes	complemented
127	#11718351	C₂²	1	2	yes	complemented
128	#11718350	C₂²	1	2	yes	complemented
129	#11718349	C₂²	1	1	yes	characteristic
130	C₈×D₅₂	C₂²	1	1	yes	characteristic
131	#11718342	C₂²	1	1	yes	characteristic, complemented
132	#11718341	C₂²	1	1	yes	characteristic, complemented
133	#11718340	C₂²	1	1	yes	characteristic, complemented
134	C₈×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
137	C₂×Q₈×D₁₃	C₂³	1	2	yes	—
138	C₂×D₄×D₁₃	C₂³	1	2	yes	—
139	C₂×#6127	—	2	1	no	—
140	C₂²×D₅₂	—	2	1	no	—
141	C₂²×Dic₂₆	—	2	1	no	—
142	C₁₃×#135	—	2	4	no	—
143	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
151	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
152	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₁₃	—	2	1	no	—
154	C₄×D₄×C₁₃	—	2	1	no	—
155	C₄×D₄×C₁₃	—	2	1	no	—
156	C₄×D₄×C₁₃	—	2	1	no	—
157	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
159	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
161	C₁₃×#117	—	2	1	no	—
162	C₁₃×#117	—	2	1	no	—
163	C₁₃×#117	C₂³	1	1	yes	characteristic
164	C₁₃×#117	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	—	2	1	no	—
166	C₂×C₄²×C₁₃	—	2	1	no	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	#88201	C₂³	1	2	yes	—
169	#88200	C₂³	1	2	yes	—
170	Q₈×Dic₁₃	C₂³	1	2	yes	—
171	C₂×#6107	C₂³	1	2	yes	—
172	C₂×#6106	C₂³	1	2	yes	—
173	#88193	—	2	2	no	—
174	#88192	—	2	2	no	—
175	#88192	C₂³	1	2	yes	—
176	#88191	—	2	2	no	—
177	#88190	—	2	2	no	—
178	#88190	C₂³	1	2	yes	—
179	D₄×Dic₁₃	C₂³	1	2	yes	—
180	C₂×#6105	C₂³	1	2	yes	—
181	C₂×#6104	C₂³	1	2	yes	—
182	#88184	—	2	1	no	—
183	#88184	—	2	1	no	—
184	#88184	—	2	1	no	—
185	#88184	D₄	1	1	yes	characteristic
186	#88184	C₂³	1	2	yes	—
187	#88183	—	2	2	no	—
188	#88183	—	2	2	no	—
189	#88183	D₄	1	2	yes	—
190	C₄×C₂²⋊D₁₃	—	2	2	no	—
191	C₄×C₂²⋊D₁₃	—	2	2	no	—
192	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
193	C₂×#6103	—	2	2	no	—
194	C₂×#6103	—	2	2	no	—
195	#88180	—	2	1	no	—
196	#88180	—	2	1	no	—
197	#88180	—	2	1	no	—
198	#88178	—	2	1	no	—
199	#88178	—	2	1	no	—
200	#88178	—	2	1	no	—
201	#88178	—	2	2	no	—
202	#88178	—	2	2	no	—
203	#88178	D₄	1	1	yes	characteristic
204	#88178	C₂³	1	2	yes	—
205	SD₁₆×D₁₃	—	2	8	no	—
206	C₂×#6095	C₂³	1	2	yes	—
207	C₂×#6095	C₂³	1	2	yes	—
208	C₂×#6094	C₂³	1	2	yes	—
209	C₂×C₈×D₁₃	C₂³	1	2	yes	—
210	#88152	—	2	2	no	—
211	#88151	—	2	2	no	—
212	#88151	C₂³	1	2	yes	—
213	#88150	—	2	2	no	—
214	#88149	C₂³	1	2	yes	—
215	#88148	—	2	2	no	—
216	#88148	—	2	2	no	—
217	#88147	C₂³	1	2	yes	—
218	#88146	—	2	2	no	—
219	#88146	C₂³	1	2	yes	—
220	#88146	C₂³	1	2	yes	—
221	#88142	—	2	2	no	—
222	#88142	C₂³	1	2	yes	—
223	#88142	C₂³	1	2	yes	—
224	#88141	—	2	2	no	—
225	#88141	C₂³	1	2	yes	—
226	#88139	—	2	2	no	—
227	#88139	—	2	2	no	—
228	#88139	—	2	2	no	—
229	#88139	—	2	2	no	—
230	#88138	—	2	2	no	—
231	#88136	—	2	2	no	—
232	#88135	—	2	2	no	—
233	C₂²⋊C₄×D₁₃	—	2	2	no	—
234	#88133	—	2	2	no	—
235	#88133	—	2	2	no	—
236	#88133	—	2	2	no	—
237	#88132	—	2	2	no	—
238	#88130	—	2	2	no	—
239	#88130	—	2	2	no	—
240	#88130	D₄	1	2	yes	—
241	#88129	—	2	1	no	—
242	#88129	—	2	1	no	—
243	#88129	—	2	1	no	—
244	#88129	—	2	2	no	—
245	#88129	—	2	2	no	—
246	#88129	D₄	1	1	yes	characteristic
247	#88128	C₂³	1	1	yes	characteristic
248	C₄×D₅₂	—	2	1	no	—
249	C₄×D₅₂	—	2	1	no	—
250	C₄×D₅₂	—	2	1	no	—
251	C₄×D₅₂	C₂³	1	1	yes	characteristic
252	C₄×D₅₂	C₂³	1	2	yes	—
253	#88126	—	2	2	no	—
254	#88126	—	2	2	no	—
255	#88126	C₂³	1	2	yes	—
256	#88124	—	2	1	no	—
257	#88124	D₄	1	1	yes	characteristic
258	#88123	—	2	1	no	—
259	#88123	—	2	1	no	—
260	#88123	C₂³	1	1	yes	characteristic
261	#88123	C₂³	1	1	yes	characteristic
262	#88123	C₂³	1	1	yes	characteristic
263	C₄×Dic₂₆	—	2	1	no	—
264	C₄×Dic₂₆	—	2	1	no	—
265	C₄×Dic₂₆	—	2	1	no	—
266	C₄×Dic₂₆	—	2	2	no	—
267	C₄×Dic₂₆	—	2	2	no	—
268	C₄×Dic₂₆	C₂³	1	2	yes	—
269	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
270	C₁₃×#107	C₂³	1	1	yes	characteristic
271	C₁₃×#107	C₂³	1	1	yes	characteristic
272	C₁₃×#106	C₂³	1	1	yes	characteristic
273	C₁₃×#106	C₂³	1	1	yes	characteristic
274	C₁₃×#103	C₂³	1	1	yes	characteristic
275	C₁₃×#103	C₂³	1	1	yes	characteristic
276	C₁₃×#103	C₂³	1	1	yes	characteristic
277	C₁₃×#103	C₂³	1	1	yes	characteristic
278	C₁₃×#102	C₂³	1	1	yes	characteristic
279	C₁₃×#102	C₂³	1	1	yes	characteristic
280	C₁₃×#102	C₂³	1	1	yes	characteristic
281	C₁₃×#102	C₂³	1	1	yes	characteristic
282	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
283	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
284	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
285	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
286	#88075	C₂³	1	2	yes	—
287	#88075	C₂³	1	2	yes	—
288	#88072	C₂³	1	2	yes	—
289	#88072	C₂³	1	2	yes	—
290	C₂²⋊#1055	C₂³	1	2	yes	—
291	#88061	C₂³	1	2	yes	—
292	#88061	C₂³	1	2	yes	—
293	#88060	C₂³	1	2	yes	—
294	#88060	C₂³	1	2	yes	—
295	#88057	C₂³	1	2	yes	—
296	#88057	C₂³	1	2	yes	—
297	#88056	C₂³	1	2	yes	—
298	#88056	C₂³	1	2	yes	—
299	#88055	C₂³	1	2	yes	—
300	#88054	C₂³	1	2	yes	—
301	#88054	C₂³	1	2	yes	—
302	C₈×Dic₁₃	C₂³	1	2	yes	—
303	#88050	C₂³	1	2	yes	—
304	#88050	C₂³	1	2	yes	—
305	#88049	C₂³	1	2	yes	—
306	#88049	C₂³	1	2	yes	—
307	#88048	C₂³	1	2	yes	—
308	#88048	C₂³	1	2	yes	—
309	#88047	C₂³	1	2	yes	—
310	#88047	C₂³	1	2	yes	—
311	C₄⋊#1055	C₂³	1	1	yes	characteristic
312	C₄⋊#1055	C₂³	1	1	yes	characteristic
313	#88043	C₂³	1	2	yes	—
314	#61474	—	13	1	no	maximal, Sylow
315	C₂³×D₁₃	—	2	2	no	—
316	C₁₃×#41	—	2	2	no	—
317	C₁₃×#41	—	2	2	no	—
318	C₁₃×#41	—	4	1	no	—
319	C₁₃×#41	—	4	1	no	—
320	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₁₃	—	2	1	no	—
323	C₂×D₄×C₁₃	—	2	1	no	—
324	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	—	2	1	no	—
327	C₂²×C₄×C₁₃	—	2	1	no	—
328	C₂²×C₄×C₁₃	—	2	1	no	—
329	C₂²×C₄×C₁₃	—	2	1	no	—
330	C₂²×C₄×C₁₃	—	2	1	no	—
331	C₂²×C₄×C₁₃	—	2	1	no	—
332	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₂×C₂²⋊D₁₃	—	2	2	no	—
336	C₂×C₂²⋊D₁₃	—	2	2	no	—
337	C₂×C₂²⋊D₁₃	—	2	2	no	—
338	C₂×C₂²⋊D₁₃	C₂×D₄	1	2	yes	—
339	C₂²×Dic₁₃	—	2	2	no	—
340	Q₈×D₁₃	—	2	4	no	—
341	Q₈×D₁₃	—	4	2	no	—
342	D₄×D₁₃	—	2	4	no	—
343	D₄×D₁₃	—	4	2	no	—
344	#6127	—	8	2	no	—
345	C₂×D₅₂	—	2	1	no	—
346	C₂×D₅₂	—	2	2	no	—
347	C₂×D₅₂	—	2	1	no	—
348	C₂×D₅₂	—	8	2	no	—
349	C₂×D₅₂	C₂×D₄	1	1	yes	characteristic
350	C₂×D₅₂	C₂⁴	1	2	yes	—
351	C₂×C₄×D₁₃	—	2	2	no	—
352	C₂×C₄×D₁₃	—	2	2	no	—
353	C₂×C₄×D₁₃	—	2	2	no	—
354	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
355	C₂×Dic₂₆	—	2	1	no	—
356	C₂×Dic₂₆	—	2	2	no	—
357	C₂×Dic₂₆	—	2	1	no	—
358	C₂×Dic₂₆	—	2	2	no	—
359	C₂×Dic₂₆	—	2	2	no	—
360	C₂×Dic₂₆	—	8	2	no	—
361	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
362	C₂×Dic₂₆	C₂⁴	1	2	yes	—
363	C₁₃×Q₁₆	—	2	2	no	—
364	C₁₃×SD₁₆	—	2	2	no	—
365	C₁₃×SD₁₆	#41	1	4	yes	complemented
366	C₁₃×D₈	—	2	2	no	—
367	C₂×C₈×C₁₃	—	2	2	no	—
368	C₂×C₈×C₁₃	—	4	1	no	—
369	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₁₃×C₄⋊C₄	—	2	1	no	—
374	C₁₃×C₄⋊C₄	—	2	1	no	—
375	C₁₃×C₄⋊C₄	—	2	1	no	—
376	C₁₃×C₄⋊C₄	—	2	1	no	—
377	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
378	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
379	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
380	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
381	C₁₃×C₂²⋊C₄	—	2	1	no	—
382	C₁₃×C₂²⋊C₄	—	2	1	no	—
383	C₁₃×C₂²⋊C₄	—	2	1	no	—
384	C₁₃×C₂²⋊C₄	—	2	1	no	—
385	C₁₃×C₂²⋊C₄	—	2	1	no	—
386	C₁₃×C₂²⋊C₄	—	2	1	no	—
387	C₄²×C₁₃	—	2	1	no	—
388	C₄²×C₁₃	—	2	1	no	—
389	C₄²×C₁₃	—	2	1	no	—
390	C₄²×C₁₃	—	2	1	no	—
391	C₄²×C₁₃	—	2	1	no	—
392	C₄²×C₁₃	—	2	1	no	—
393	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
396	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
397	C₂²⋊Dic₁₃	—	2	2	no	—
398	C₂²⋊Dic₁₃	—	2	2	no	—
399	C₂²⋊Dic₁₃	—	2	2	no	—
400	C₂²⋊Dic₁₃	—	2	2	no	—
401	C₂²⋊Dic₁₃	—	2	2	no	—
402	C₂²⋊Dic₁₃	C₂×D₄	1	2	yes	—
403	#6107	—	4	2	no	—
404	#6106	—	2	4	no	—
405	#6105	—	2	4	no	—
406	#6104	—	4	2	no	—
407	#6103	—	2	2	no	—
408	#6103	—	2	2	no	—
409	#6103	—	2	2	no	—
410	#6103	—	2	2	no	—
411	#6103	—	2	2	no	—
412	#6103	—	2	2	no	—
413	#6103	—	2	2	no	—
414	#6103	—	2	2	no	—
415	#6103	—	2	2	no	—
416	#6103	—	2	2	no	—
417	#6103	C₂×D₄	1	2	yes	—
418	#6103	C₂×D₄	1	2	yes	—
419	#6103	C₂×D₄	1	2	yes	—
420	#6103	C₂×D₄	1	2	yes	—
421	C₄⋊Dic₁₃	—	2	1	no	—
422	C₄⋊Dic₁₃	—	2	1	no	—
423	C₄⋊Dic₁₃	—	2	1	no	—
424	C₄⋊Dic₁₃	—	2	1	no	—
425	C₄⋊Dic₁₃	—	2	2	no	—
426	C₄⋊Dic₁₃	—	2	2	no	—
427	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
428	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
429	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
430	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
431	#6101	—	2	2	no	—
432	#6101	—	2	2	no	—
433	#6101	—	2	2	no	—
434	#6101	—	2	2	no	—
435	#6101	—	2	2	no	—
436	#6101	—	2	2	no	—
437	#6101	C₂×D₄	1	2	yes	—
438	#6101	C₂×D₄	1	2	yes	—
439	#6101	C₂×D₄	1	2	yes	—
440	#6101	C₂×D₄	1	2	yes	—
441	C₄×Dic₁₃	—	2	2	no	—
442	C₄×Dic₁₃	—	2	2	no	—
443	C₄×Dic₁₃	—	2	2	no	—
444	C₄×Dic₁₃	—	2	2	no	—
445	C₄×Dic₁₃	—	2	2	no	—
446	C₄×Dic₁₃	C₂⁴	1	2	yes	—
447	C₂×#1055	C₂⁴	1	2	yes	—
448	C₂×#1055	C₂⁴	1	2	yes	—
449	#6095	—	2	4	no	—
450	#6095	—	4	2	no	—
451	#6094	—	4	2	no	—
452	C₈×D₁₃	—	2	4	no	—
453	#3518	—	13	1	no	—
454	#3514	—	13	1	no	—
455	#3394	—	13	1	no	—
456	Q₈×SD₁₆	—	13	1	no	—
457	#3375	—	13	1	no	—
458	#3367	—	13	1	no	—
459	#3340	—	13	1	no	—
460	#3340	—	13	2	no	—
461	#3328	—	13	1	no	—
462	#3325	—	13	1	no	—
463	#3321	—	13	2	no	—
464	#3311	—	13	2	no	—
465	#3282	—	13	2	no	—
466	D₄×SD₁₆	—	13	1	no	—
467	#3173	—	13	2	no	—
468	#3167	—	13	1	no	—
469	#3121	—	13	2	no	—
470	#3118	—	13	2	no	—
471	#3116	—	13	1	no	—
472	#3115	—	13	1	no	—
473	#2966	—	13	1	no	—
474	#2949	—	13	2	no	—
475	C₄×#135	D₁₃	1	1	yes	characteristic, complemented
476	C₂³×C₁₃	—	2	1	no	—
477	C₂³×C₁₃	—	2	1	no	—
478	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
479	C₂²×D₁₃	—	2	2	no	—
480	C₂²×D₁₃	—	4	4	no	—
481	C₂²×D₁₃	—	8	2	no	—
482	C₂²×D₁₃	—	8	2	no	—
483	C₂²×D₁₃	C₂²×D₄	1	2	yes	—
484	Q₈×C₁₃	—	2	1	no	—
485	Q₈×C₁₃	—	2	1	no	—
486	Q₈×C₁₃	—	2	1	no	—
487	Q₈×C₁₃	C₂×#41	1	2	yes	—
488	D₄×C₁₃	—	2	1	no	—
489	D₄×C₁₃	—	2	1	no	—
490	D₄×C₁₃	—	2	1	no	—
491	D₄×C₁₃	—	4	2	no	—
492	D₄×C₁₃	—	4	2	no	—
493	D₄×C₁₃	C₂×#41	1	2	yes	—
494	C₂×C₄×C₁₃	—	2	1	no	—
495	C₂×C₄×C₁₃	—	2	2	no	—
496	C₂×C₄×C₁₃	—	2	1	no	—
497	C₂×C₄×C₁₃	—	2	1	no	—
498	C₂×C₄×C₁₃	—	2	1	no	—
499	C₂×C₄×C₁₃	—	2	1	no	—
500	C₂×C₄×C₁₃	—	2	1	no	—
501	C₂×C₄×C₁₃	—	2	1	no	—
502	C₂×C₄×C₁₃	—	2	1	no	—
503	C₂×C₄×C₁₃	—	4	1	no	—
504	C₂×C₄×C₁₃	—	4	2	no	—
505	C₂×C₄×C₁₃	—	4	2	no	—
506	C₂×C₄×C₁₃	—	4	2	no	—
507	C₂×C₄×C₁₃	—	4	2	no	—
508	C₂×C₄×C₁₃	—	8	1	no	—
509	C₂×C₄×C₁₃	—	8	1	no	—
510	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
516	C₂²⋊D₁₃	—	4	2	no	—
517	C₂²⋊D₁₃	—	4	4	no	—
518	C₂²⋊D₁₃	—	8	2	no	—
519	C₂²⋊D₁₃	—	8	2	no	—
520	C₂×Dic₁₃	—	2	2	no	—
521	C₂×Dic₁₃	—	2	2	no	—
522	C₂×Dic₁₃	—	2	2	no	—
523	C₂×Dic₁₃	—	8	2	no	—
524	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
525	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
526	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
527	D₅₂	—	2	2	no	—
528	D₅₂	—	2	2	no	—
529	D₅₂	—	2	2	no	—
530	D₅₂	—	4	2	no	—
531	D₅₂	—	8	1	no	—
532	D₅₂	—	8	2	no	—
533	C₄×D₁₃	—	2	2	no	—
534	C₄×D₁₃	—	2	2	no	—
535	C₄×D₁₃	—	4	4	no	—
536	C₄×D₁₃	—	8	2	no	—
537	C₄×D₁₃	—	8	2	no	—
538	Dic₂₆	—	2	2	no	—
539	Dic₂₆	—	2	2	no	—
540	Dic₂₆	—	2	2	no	—
541	Dic₂₆	—	4	4	no	—
542	Dic₂₆	—	4	2	no	—
543	Dic₂₆	—	8	2	no	—
544	Dic₂₆	—	8	2	no	—
545	Dic₂₆	—	8	1	no	—
546	C₈×C₁₃	—	2	1	no	—
547	C₈×C₁₃	—	2	1	no	—
548	C₈×C₁₃	—	2	1	no	—
549	C₈×C₁₃	C₂×#41	1	2	yes	—
550	#1055	—	2	2	no	—
551	#1055	—	2	2	no	—
552	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
553	C₂²×SD₁₆	—	13	2	no	—
554	#559	—	13	1	no	—
555	Q₈²	—	13	1	no	—
556	#556	—	13	1	no	—
557	#556	—	13	2	no	—
558	#556	—	13	1	no	—
559	#556	—	26	2	no	—
560	#556	—	26	1	no	—
561	#555	—	13	1	no	—
562	#555	—	13	2	no	—
563	#555	—	26	1	no	—
564	#551	—	26	2	no	—
565	D₄×Q₈	—	13	1	no	—
566	D₄×Q₈	—	13	1	no	—
567	#548	—	13	2	no	—
568	#548	—	26	1	no	—
569	#546	—	13	2	no	—
570	#546	—	26	1	no	—
571	D₄²	—	13	1	no	—
572	#542	—	13	2	no	—
573	#542	—	13	2	no	—
574	#542	—	26	2	no	—
575	#538	—	26	2	no	—
576	#533	—	13	1	no	—
577	#533	—	26	1	no	—
578	#532	—	13	1	no	—
579	#529	—	13	1	no	—
580	#529	—	26	1	no	—
581	#529	—	26	1	no	—
582	C₂×#124	—	26	1	no	—
583	#519	—	13	2	no	—
584	#518	—	13	2	no	—
585	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
586	C₄×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
587	#498	—	13	2	no	—
588	#498	—	13	1	no	—
589	#495	—	13	2	no	—
590	#492	—	13	1	no	—
591	#489	—	13	2	no	—
592	#489	—	13	2	no	—
593	#487	—	13	1	no	—
594	#486	—	13	1	no	—
595	#485	—	13	2	no	—
596	#485	—	13	2	no	—
597	#485	—	13	2	no	—
598	#482	—	13	2	no	—
599	#482	—	13	2	no	—
600	#482	—	13	2	no	—
601	#477	—	13	1	no	—
602	#477	—	13	2	no	—
603	#476	—	13	1	no	—
604	#476	—	13	2	no	—
605	#475	—	13	1	no	—
606	#475	—	13	2	no	—
607	#474	—	13	1	no	—
608	#474	—	13	2	no	—
609	#470	—	13	2	no	—
610	#469	—	13	2	no	—
611	#465	—	13	2	no	—
612	#465	—	13	2	no	—
613	#465	—	13	2	no	—
614	#465	—	13	2	no	—
615	#464	—	13	2	no	—
616	#464	—	13	2	no	—
617	#463	—	13	2	no	—
618	#463	—	13	2	no	—
619	#462	—	13	1	no	—
620	#461	—	13	1	no	—
621	#460	—	13	1	no	—
622	#459	—	13	1	no	—
623	#452	—	13	2	no	—
624	#451	—	13	2	no	—
625	#450	—	13	2	no	—
626	#449	—	13	2	no	—
627	#448	—	13	2	no	—
628	#447	—	13	2	no	—
629	#446	—	13	1	no	—
630	C₈×Q₈	—	13	1	no	—
631	#442	—	13	2	no	—
632	#441	—	13	2	no	—
633	#440	—	13	2	no	—
634	#440	—	13	2	no	—
635	#440	—	13	2	no	—
636	#440	—	13	2	no	—
637	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
638	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
639	C₄×SD₁₆	—	13	2	no	—
640	C₄×SD₁₆	—	13	2	no	—
641	C₄×SD₁₆	—	13	2	no	—
642	C₄×SD₁₆	—	13	2	no	—
643	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
644	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
645	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
646	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
647	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
648	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
649	#436	—	13	1	no	—
650	#435	—	13	2	no	—
651	C₈×D₄	—	13	2	no	—
652	C₈×D₄	—	13	1	no	—
653	#433	—	13	2	no	—
654	#432	—	13	1	no	—
655	#427	—	13	2	no	—
656	#427	C₂×D₁₃	1	1	yes	characteristic, complemented
657	#419	—	13	2	no	—
658	#418	—	13	2	no	—
659	#416	C₂×D₁₃	1	1	yes	characteristic
660	#416	C₂×D₁₃	1	1	yes	characteristic, complemented
661	#405	—	13	2	no	—
662	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
663	C₂²×C₁₃	—	2	1	no	—
664	C₂²×C₁₃	—	2	2	no	—
665	C₂²×C₁₃	—	2	1	no	—
666	C₂²×C₁₃	—	2	1	no	—
667	C₂²×C₁₃	—	4	1	no	—
668	C₂²×C₁₃	—	4	1	no	—
669	C₂²×C₁₃	—	4	1	no	—
670	C₂²×C₁₃	—	4	1	no	—
671	C₂²×C₁₃	—	4	1	no	—
672	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
673	C₂×D₁₃	—	2	2	no	—
674	C₂×D₁₃	—	2	2	no	—
675	C₂×D₁₃	—	2	2	no	—
676	C₂×D₁₃	—	4	2	no	—
677	C₂×D₁₃	—	4	2	no	—
678	C₂×D₁₃	—	4	2	no	—
679	C₂×D₁₃	—	16	4	no	—
680	C₄×C₁₃	—	2	1	no	—
681	C₄×C₁₃	—	2	1	no	—
682	C₄×C₁₃	—	2	2	no	—
683	C₄×C₁₃	—	2	1	no	—
684	C₄×C₁₃	—	2	1	no	—
685	C₄×C₁₃	—	4	1	no	—
686	C₄×C₁₃	—	4	1	no	—
687	C₄×C₁₃	—	4	1	no	—
688	C₄×C₁₃	—	4	1	no	—
689	C₄×C₁₃	—	4	1	no	—
690	C₄×C₁₃	#577	1	2	yes	—
691	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
692	C₄×C₁₃	#585	1	1	yes	characteristic
693	Dic₁₃	—	2	2	no	—
694	Dic₁₃	—	2	2	no	—
695	Dic₁₃	—	2	2	no	—
696	Dic₁₃	—	4	2	no	—
697	Dic₁₃	—	4	2	no	—
698	Dic₁₃	—	4	2	no	—
699	C₂×#41	—	26	1	no	—
700	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
701	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
702	C₂²×Q₈	—	13	2	no	—
703	C₂²×Q₈	—	26	1	no	—
704	C₂²×D₄	—	13	2	no	—
705	C₂²×D₄	—	26	1	no	—
706	#135	—	2	4	no	—
707	C₂×Q₁₆	—	13	2	no	—
708	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
709	C₂×SD₁₆	—	13	2	no	—
710	C₂×SD₁₆	—	13	2	no	—
711	C₂×SD₁₆	—	13	2	no	—
712	C₂×SD₁₆	—	13	2	no	—
713	C₂×SD₁₆	—	26	8	no	—
714	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
715	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
716	C₂×D₈	—	13	2	no	—
717	C₂×D₈	C₂²×D₁₃	1	1	yes	characteristic
718	C₂×M₁₆	—	13	2	no	—
719	C₂²×C₈	—	13	2	no	—
720	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
721	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
722	C₄⋊Q₈	—	13	2	no	—
723	C₄⋊Q₈	—	13	2	no	—
724	C₄⋊Q₈	—	13	1	no	—
725	C₄⋊Q₈	—	13	1	no	—
726	C₄⋊Q₈	—	13	1	no	—
727	C₄⋊Q₈	—	26	1	no	—
728	C₄⋊Q₈	—	26	1	no	—
729	C₄⋊Q₈	—	26	2	no	—
730	#127	—	13	1	no	—
731	#126	—	13	2	no	—
732	#126	—	26	2	no	—
733	#126	—	26	2	no	—
734	#126	—	26	2	no	—
735	#126	—	26	2	no	—
736	#126	—	26	2	no	—
737	#126	—	26	2	no	—
738	#125	—	13	1	no	—
739	#125	—	26	1	no	—
740	#124	—	13	2	no	—
741	#124	—	13	2	no	—
742	#124	—	13	1	no	—
743	#124	—	26	2	no	—
744	#124	—	26	2	no	—
745	#124	—	26	1	no	—
746	#124	—	26	1	no	—
747	#124	—	26	2	no	—
748	#124	—	26	2	no	—
749	#124	—	26	2	no	—
750	#124	—	26	2	no	—
751	#124	—	26	2	no	—
752	#124	—	26	1	no	—
753	#123	—	13	2	no	—
754	#123	—	26	2	no	—
755	#123	—	26	2	no	—
756	#123	—	26	2	no	—
757	#123	—	26	2	no	—
758	C₂²⋊Q₈	—	13	1	no	—
759	C₂²⋊Q₈	—	13	2	no	—
760	C₂²⋊Q₈	—	13	2	no	—
761	C₂²⋊Q₈	—	13	2	no	—
762	C₂²⋊Q₈	—	26	2	no	—
763	C₂²⋊Q₈	—	26	2	no	—
764	C₂²⋊Q₈	—	26	2	no	—
765	C₂²⋊Q₈	—	26	1	no	—
766	C₂²⋊Q₈	—	26	2	no	—
767	C₂²⋊Q₈	—	26	2	no	—
768	C₂²⋊Q₈	—	26	1	no	—
769	C₂²⋊Q₈	—	26	1	no	—
770	#121	—	13	1	no	—
771	#121	—	13	2	no	—
772	#121	—	13	2	no	—
773	#121	—	13	2	no	—
774	#121	—	26	2	no	—
775	#121	—	26	2	no	—
776	#121	—	26	1	no	—
777	#121	—	26	1	no	—
778	#121	—	26	2	no	—
779	#121	—	26	1	no	—
780	#120	—	26	2	no	—
781	#120	—	26	2	no	—
782	C₄×Q₈	—	13	1	no	—
783	C₄×Q₈	—	13	2	no	—
784	C₄×Q₈	—	13	2	no	—
785	C₄×Q₈	—	13	2	no	—
786	C₄×Q₈	—	26	2	no	—
787	C₄×Q₈	—	26	1	no	—
788	C₄×Q₈	—	26	2	no	—
789	C₄×Q₈	—	26	1	no	—
790	C₄×Q₈	—	26	2	no	—
791	C₄×Q₈	—	26	1	no	—
792	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
793	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
794	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
795	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	13	2	no	—
801	C₄×D₄	—	13	2	no	—
802	C₄×D₄	—	13	2	no	—
803	C₄×D₄	—	13	1	no	—
804	C₄×D₄	—	13	2	no	—
805	C₄×D₄	—	26	1	no	—
806	C₄×D₄	—	26	1	no	—
807	C₄×D₄	—	26	2	no	—
808	C₄×D₄	—	26	2	no	—
809	C₄×D₄	—	26	2	no	—
810	C₄×D₄	—	26	1	no	—
811	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
812	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
813	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
814	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	—	13	2	no	—
818	#117	—	13	2	no	—
819	#117	—	13	2	no	—
820	#117	—	26	2	no	—
821	#117	—	26	2	no	—
822	#117	—	26	2	no	—
823	#117	—	26	1	no	—
824	#117	—	26	1	no	—
825	#117	—	26	1	no	—
826	#117	C₂²×D₁₃	1	1	yes	characteristic
827	#117	C₂²×D₁₃	1	1	yes	characteristic
828	C₂×C₂²⋊C₄	—	26	2	no	—
829	C₂×C₂²⋊C₄	—	26	2	no	—
830	C₂×C₂²⋊C₄	—	26	2	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
834	#107	—	13	2	no	—
835	#107	—	13	2	no	—
836	#107	C₂²×D₁₃	1	1	yes	characteristic
837	#107	C₂²×D₁₃	1	1	yes	characteristic
838	#106	—	13	2	no	—
839	#106	—	13	2	no	—
840	#106	—	13	2	no	—
841	#106	—	13	2	no	—
842	#106	C₂²×D₁₃	1	1	yes	characteristic
843	#106	C₂²×D₁₃	1	1	yes	characteristic
844	C₄⋊C₈	—	13	2	no	—
845	C₄⋊C₈	—	13	2	no	—
846	C₄⋊C₈	—	13	1	no	—
847	C₄⋊C₈	—	13	1	no	—
848	#103	—	13	2	no	—
849	#103	—	13	2	no	—
850	#103	—	13	2	no	—
851	#103	—	13	2	no	—
852	#103	—	13	2	no	—
853	#103	—	13	2	no	—
854	#103	C₂²×D₁₃	1	1	yes	characteristic
855	#103	C₂²×D₁₃	1	1	yes	characteristic
856	#103	C₂²×D₁₃	1	1	yes	characteristic
857	#103	C₂²×D₁₃	1	1	yes	characteristic
858	#102	—	13	2	no	—
859	#102	—	13	2	no	—
860	#102	—	13	2	no	—
861	#102	—	13	2	no	—
862	#102	—	13	2	no	—
863	#102	—	13	2	no	—
864	#102	C₂²×D₁₃	1	1	yes	characteristic
865	#102	C₂²×D₁₃	1	1	yes	characteristic
866	#102	C₂²×D₁₃	1	1	yes	characteristic
867	#102	C₂²×D₁₃	1	1	yes	characteristic
868	C₂²⋊C₈	—	13	2	no	—
869	C₂²⋊C₈	—	13	2	no	—
870	C₂²⋊C₈	—	13	2	no	—
871	#97	—	13	2	no	—
872	#97	—	13	2	no	—
873	C₄×C₈	—	13	2	no	—
874	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
875	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
876	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
877	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
878	C₂×C₁₃	—	4	2	no	—
879	C₂×C₁₃	—	4	1	no	—
880	C₂×C₁₃	—	8	1	no	—
881	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
882	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
883	C₂×C₁₃	#3584	1	1	yes	characteristic
884	D₁₃	—	4	2	no	—
885	D₁₃	—	8	2	no	—
886	C₂⁴	—	26	2	no	—
887	#41	—	2	2	no	—
888	#41	—	2	2	no	—
889	#41	—	4	1	no	—
890	#41	—	4	1	no	—
891	#41	—	104	2	no	—
892	C₂×Q₈	—	13	1	no	—
893	C₂×Q₈	—	13	2	no	—
894	C₂×Q₈	—	26	2	no	—
895	C₂×Q₈	—	26	2	no	—
896	C₂×Q₈	—	26	2	no	—
897	C₂×Q₈	—	26	1	no	—
898	C₂×Q₈	—	26	1	no	—
899	C₂×Q₈	—	26	4	no	—
900	C₂×Q₈	—	52	2	no	—
901	C₂×Q₈	—	104	2	no	—
902	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
903	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	13	2	no	—
907	C₂×D₄	—	13	1	no	—
908	C₂×D₄	—	13	2	no	—
909	C₂×D₄	—	26	2	no	—
910	C₂×D₄	—	26	2	no	—
911	C₂×D₄	—	26	4	no	—
912	C₂×D₄	—	26	2	no	—
913	C₂×D₄	—	26	2	no	—
914	C₂×D₄	—	26	1	no	—
915	C₂×D₄	—	26	1	no	—
916	C₂×D₄	—	52	2	no	—
917	C₂×D₄	—	104	2	no	—
918	C₂×D₄	C₂³×D₁₃	1	1	yes	characteristic
919	C₂×D₄	C₂³×D₁₃	1	1	yes	characteristic
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	13	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	D₄×D₁₃	1	1	yes	characteristic
932	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
933	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
934	Q₁₆	—	2	2	no	—
935	Q₁₆	—	52	2	no	—
936	SD₁₆	—	2	2	no	—
937	SD₁₆	—	26	4	no	—
938	SD₁₆	—	26	4	no	—
939	SD₁₆	—	26	4	no	—
940	SD₁₆	—	52	2	no	—
941	SD₁₆	#6127	1	4	yes	complemented
942	D₈	—	2	2	no	—
943	D₈	—	52	2	no	—
944	M₁₆	—	52	2	no	—
945	C₂×C₈	—	2	2	no	—
946	C₂×C₈	—	4	1	no	—
947	C₂×C₈	—	13	2	no	—
948	C₂×C₈	—	13	2	no	—
949	C₂×C₈	—	26	4	no	—
950	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
951	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
952	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
953	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	13	2	no	—
959	C₄⋊C₄	—	13	2	no	—
960	C₄⋊C₄	—	13	1	no	—
961	C₄⋊C₄	—	13	2	no	—
962	C₄⋊C₄	—	13	1	no	—
963	C₄⋊C₄	—	13	2	no	—
964	C₄⋊C₄	—	13	2	no	—
965	C₄⋊C₄	—	13	2	no	—
966	C₄⋊C₄	—	26	2	no	—
967	C₄⋊C₄	—	26	2	no	—
968	C₄⋊C₄	—	26	2	no	—
969	C₄⋊C₄	—	26	2	no	—
970	C₄⋊C₄	—	26	2	no	—
971	C₄⋊C₄	—	26	2	no	—
972	C₄⋊C₄	—	26	1	no	—
973	C₄⋊C₄	—	26	1	no	—
974	C₄⋊C₄	—	26	2	no	—
975	C₄⋊C₄	—	26	2	no	—
976	C₄⋊C₄	—	26	1	no	—
977	C₄⋊C₄	—	26	1	no	—
978	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
980	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	13	2	no	—
989	C₂²⋊C₄	—	13	2	no	—
990	C₂²⋊C₄	—	13	2	no	—
991	C₂²⋊C₄	—	13	2	no	—
992	C₂²⋊C₄	—	13	2	no	—
993	C₂²⋊C₄	—	26	2	no	—
994	C₂²⋊C₄	—	26	2	no	—
995	C₂²⋊C₄	—	26	2	no	—
996	C₂²⋊C₄	—	26	2	no	—
997	C₂²⋊C₄	—	26	2	no	—
998	C₂²⋊C₄	—	26	2	no	—
999	C₂²⋊C₄	—	26	2	no	—
1000	C₂²⋊C₄	—	26	2	no	—
1001	C₂²⋊C₄	—	26	2	no	—
1002	C₂²⋊C₄	—	26	2	no	—
1003	C₂²⋊C₄	—	26	2	no	—
1004	C₂²⋊C₄	—	26	2	no	—
1005	C₂²⋊C₄	—	26	2	no	—
1006	C₂²⋊C₄	—	26	2	no	—
1007	C₂²⋊C₄	—	26	2	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	13	2	no	—
1015	C₄²	—	26	2	no	—
1016	C₄²	—	26	2	no	—
1017	C₄²	—	26	2	no	—
1018	C₄²	—	26	2	no	—
1019	C₄²	—	26	2	no	—
1020	C₄²	D₄×D₁₃	1	1	yes	characteristic
1021	C₄²	D₄×D₁₃	1	1	yes	characteristic
1022	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1023	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1024	C₁₃	#61474	1	1	yes	characteristic, complemented, Sylow
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	13	2	no	—
1028	C₂³	—	26	2	no	—
1029	C₂³	—	52	4	no	—
1030	C₂³	—	104	2	no	—
1031	C₂³	—	104	2	no	—
1032	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	26	2	no	—
1037	Q₈	—	26	2	no	—
1038	Q₈	—	26	2	no	—
1039	Q₈	—	52	4	no	—
1040	Q₈	—	52	2	no	—
1041	Q₈	—	104	1	no	—
1042	Q₈	—	104	2	no	—
1043	Q₈	—	104	2	no	—
1044	Q₈	C₂×#6127	1	2	yes	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	26	2	no	—
1051	D₄	—	26	2	no	—
1052	D₄	—	26	2	no	—
1053	D₄	—	52	2	no	—
1054	D₄	—	52	4	no	—
1055	D₄	—	52	2	no	—
1056	D₄	—	104	1	no	—
1057	D₄	—	104	2	no	—
1058	D₄	—	104	2	no	—
1059	D₄	—	104	2	no	—
1060	D₄	C₂×#6127	1	2	yes	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	8	1	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	13	2	no	—
1078	C₂×C₄	—	13	2	no	—
1079	C₂×C₄	—	13	2	no	—
1080	C₂×C₄	—	26	2	no	—
1081	C₂×C₄	—	26	2	no	—
1082	C₂×C₄	—	26	2	no	—
1083	C₂×C₄	—	26	2	no	—
1084	C₂×C₄	—	26	2	no	—
1085	C₂×C₄	—	52	4	no	—
1086	C₂×C₄	—	104	2	no	—
1087	C₂×C₄	—	104	2	no	—
1088	C₂×C₄	—	104	2	no	—
1089	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1090	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1091	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1092	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1093	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1094	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1095	C₈	—	2	1	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	26	2	no	—
1099	C₈	—	26	2	no	—
1100	C₈	C₂×#6127	1	2	yes	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	26	2	no	—
1111	C₂²	—	26	2	no	—
1112	C₂²	—	26	2	no	—
1113	C₂²	—	52	2	no	—
1114	C₂²	—	52	2	no	—
1115	C₂²	—	52	2	no	—
1116	C₂²	—	208	4	no	—
1117	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	26	2	no	—
1129	C₄	—	26	2	no	—
1130	C₄	—	26	2	no	—
1131	C₄	—	52	2	no	—
1132	C₄	—	52	2	no	—
1133	C₄	—	52	2	no	—
1134	C₄	#11719475	1	2	yes	—
1135	C₄	C₂²×#6127	1	1	yes	characteristic
1136	C₄	#11719648	1	1	yes	characteristic
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	8	1	no	—
1140	C₂	—	52	2	no	—
1141	C₂	—	104	2	no	—
1142	C₂	D₄×#6127	1	1	yes	characteristic
1143	C₂	C₂×#11719475	1	1	yes	characteristic
1144	C₂	#13129605	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₄×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂³×D₄
hypercenter	C₄×#135	D₁₃
hypocenter	C₁₃	#61474
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #13128853	C₂	semidirect
2. #13128797	C₂	semidirect
3. #13127830	C₂	semidirect
4. SD₁₆×Dic₂₆	C₂	semidirect
5. #13127648	C₂	semidirect
6. #13127552	C₂	semidirect
7. #13127251	C₂	semidirect
8. #13127245	C₂	semidirect
9. #13127121	C₂	semidirect
10. #13127080	C₂	semidirect
11. #13127018	C₂	semidirect
12. #13126868	C₂	semidirect
13. #13126537	C₂	semidirect
14. SD₁₆×D₅₂	C₂	semidirect
15. #13125449	C₂	semidirect
16. #13125395	C₂	semidirect
17. #13125071	C₂	semidirect
18. #13125016	C₂	semidirect
19. #13124998	C₂	semidirect
20. #13124987	C₂	semidirect
21. #13123811	C₂	semidirect
22. #13123690	C₂	semidirect
23. C₄×C₁₃×#135	C₂	semidirect
26. C₄×C₁₃×#41	C₂²	semidirect
27. #11719536	C₂²	semidirect
34. #11719277	C₂²	semidirect
35. Q₈×Dic₂₆	C₂²	semidirect
39. #11719266	C₂²	semidirect
46. #11719247	C₂²	semidirect
49. #11719238	C₂²	semidirect
58. #11719175	C₂²	semidirect
59. C₄×C₁₃×Q₁₆	C₂²	semidirect
60. C₄×C₁₃×Q₁₆	C₂²	semidirect
63. C₄×C₁₃×SD₁₆	C₂²	semidirect
64. C₄×C₁₃×SD₁₆	C₂²	semidirect
67. C₁₃×#427	C₂²	semidirect
69. C₁₃×#416	C₂²	semidirect
70. C₂×C₄×C₈×C₁₃	C₂²	semidirect
72. #11718899	C₂²	semidirect
73. #11718847	C₂²	semidirect
74. #11718846	C₂²	semidirect
75. #11718832	C₂²	semidirect
76. #11718829	C₂²	semidirect
80. #11718775	C₂²	semidirect
81. #11718775	C₂²	semidirect
82. #11718772	C₂²	semidirect
83. C₈×C₂²⋊D₁₃	C₂²	semidirect
84. #11718692	C₂²	semidirect
85. #11718691	C₂²	semidirect
87. #11718687	C₂²	semidirect
88. #11718682	C₂²	semidirect
89. #11718681	C₂²	semidirect
93. #11718675	C₂²	semidirect
95. #11718668	C₂²	semidirect
96. #11718664	C₂²	semidirect
97. #11718657	C₂²	semidirect
98. #11718587	C₂²	semidirect
99. #11718551	C₂²	semidirect
100. #11718549	C₂²	semidirect
102. #11718536	C₂²	semidirect
104. #11718521	C₂²	semidirect
105. #11718516	C₂²	semidirect
106. #11718513	C₂²	semidirect
107. #11718478	C₂²	semidirect
108. #11718477	C₂²	semidirect
109. #11718476	C₂²	semidirect
111. #11718463	C₂²	semidirect
112. #11718459	C₂²	semidirect
113. #11718456	C₂²	semidirect
114. #11718452	C₂²	semidirect
115. #11718448	C₂²	semidirect
117. #11718440	C₂²	semidirect
120. #11718426	C₂²	semidirect
125. C₄×#6095	C₂²	semidirect
126. C₄×#6095	C₂²	semidirect
127. #11718351	C₂²	semidirect
128. #11718350	C₂²	semidirect
131. #11718342	C₂²	semidirect
132. #11718341	C₂²	semidirect
133. #11718340	C₂²	semidirect
134. C₈×Dic₂₆	C₂²	semidirect
365. C₁₃×SD₁₆	#41	semidirect
475. C₄×#135	D₁₃	semidirect
586. C₄×#41	C₂×D₁₃	semidirect
637. C₄×Q₁₆	C₂×D₁₃	semidirect
638. C₄×Q₁₆	C₂×D₁₃	semidirect
645. C₄×SD₁₆	C₂×D₁₃	semidirect
646. C₄×SD₁₆	C₂×D₁₃	semidirect
656. #427	C₂×D₁₃	semidirect
660. #416	C₂×D₁₃	semidirect
662. C₂×C₄×C₈	C₂×D₁₃	semidirect
941. SD₁₆	#6127	semidirect
1024. C₁₃	#61474	semidirect

Maximal subgroups

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

subgroup	index
#13128853	2
#13128797	2
#13127830	2
SD₁₆×Dic₂₆	2
#13127648	2
#13127552	2
#13127251	2
#13127245	2
#13127121	2
#13127080	2
#13127018	2
#13126868	2
#13126537	2
SD₁₆×D₅₂	2
#13125449	2
#13125395	2
#13125071	2
#13125016	2
#13124998	2
#13124987	2
#13123811	2
#13123690	2
C₄×C₁₃×#135	2
#61474	13