Subgroups — #16743771

Order 3328.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128662	C₂	1	1	yes	maximal, characteristic, complemented
2	#13128637	C₂	1	1	yes	maximal, characteristic, complemented
3	#13127794	C₂	1	2	yes	maximal, complemented
4	#13127789	C₂	1	2	yes	maximal, complemented
5	#13127788	C₂	1	2	yes	maximal, complemented
6	#13127779	C₂	1	2	yes	maximal, complemented
7	#13127760	C₂	1	2	yes	maximal, complemented
8	#13127730	C₂	1	2	yes	maximal, complemented
9	#13127714	C₂	1	2	yes	maximal, complemented
10	#13127698	C₂	1	2	yes	maximal, complemented
11	#13125389	C₂	1	1	yes	maximal, characteristic, complemented
12	#13125376	C₂	1	1	yes	maximal, characteristic, complemented
13	#13125368	C₂	1	1	yes	maximal, characteristic, complemented
14	#13124696	C₂	1	1	yes	maximal, characteristic, complemented
15	#13124685	C₂	1	1	yes	maximal, characteristic, complemented
16	#13124670	C₂	1	1	yes	maximal, characteristic, complemented
17	#13124670	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11718508	C₂	1	1	yes	maximal, characteristic, complemented
19	#13123779	C₂	1	1	yes	maximal, characteristic, complemented
20	#13123671	C₂	1	1	yes	maximal, characteristic
21	#13123671	C₂	1	1	yes	maximal, characteristic
22	C₄×#88203	C₂	1	1	yes	maximal, characteristic
23	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	#11719532	C₂²	1	1	yes	characteristic
27	#11719532	C₂²	1	1	yes	characteristic
28	C₂×#88203	C₂²	1	1	yes	characteristic
29	#11719435	C₂²	1	2	yes	—
30	#11719432	C₂²	1	2	yes	—
31	#11719395	C₂²	1	2	yes	—
32	#11719395	C₂²	1	2	yes	—
33	#11719339	—	2	2	no	—
34	D₁₃×C₂²⋊Q₈	—	2	2	no	—
35	#11719284	—	2	1	no	—
36	#11719284	—	2	1	no	—
37	#11719284	—	2	1	no	—
38	Q₈×D₅₂	—	2	1	no	—
39	#11719274	C₂²	1	2	yes	complemented
40	#11719274	C₂²	1	2	yes	complemented
41	#11719244	—	2	2	no	—
42	#11719244	—	2	2	no	—
43	#11719244	C₂²	1	2	yes	complemented
44	#11719244	C₂²	1	2	yes	complemented
45	#11719226	C₂²	1	1	yes	characteristic
46	#11719226	C₂²	1	1	yes	characteristic
47	#11719224	—	2	1	no	—
48	#11719224	—	2	1	no	—
49	#11719224	C₂²	1	1	yes	characteristic
50	#11719224	C₂²	1	1	yes	characteristic
51	#11719224	C₂²	1	1	yes	characteristic
52	#11719224	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
54	#11719175	—	2	1	no	—
55	#11719175	C₂²	1	1	yes	characteristic
56	C₂×#88124	—	2	1	no	—
57	C₂×#88124	C₂²	1	1	yes	characteristic
58	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#427	C₂²	1	1	yes	characteristic
67	C₁₃×#427	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₃×#416	C₂²	1	1	yes	characteristic
70	C₁₃×#416	C₂²	1	1	yes	characteristic
71	#11718893	C₂²	1	1	yes	characteristic
72	C₂×#88061	C₂²	1	1	yes	characteristic
73	C₂×#88061	C₂²	1	1	yes	characteristic
74	C₂×#88058	C₂²	1	1	yes	characteristic
75	C₂×#88057	C₂²	1	1	yes	characteristic
76	#11718763	C₂²	1	1	yes	characteristic
77	#11718763	C₂²	1	1	yes	characteristic
78	#11718762	C₂²	1	1	yes	characteristic
79	#11718762	C₂²	1	1	yes	characteristic
80	#11718741	C₂²	1	2	yes	complemented
81	#11718741	C₂²	1	2	yes	complemented
82	#11718725	C₂²	1	2	yes	complemented
83	#11718725	C₂²	1	2	yes	complemented
84	#11718687	C₂²	1	2	yes	—
85	C₄×#6106	C₂²	1	2	yes	—
86	#11718675	C₂²	1	2	yes	—
87	C₄×#6104	C₂²	1	2	yes	—
88	#11718662	C₂²	1	1	yes	characteristic
89	#11718656	C₂²	1	1	yes	characteristic
90	#11718656	C₂²	1	1	yes	characteristic
91	#11718656	C₂²	1	1	yes	characteristic
92	#11718656	C₂²	1	1	yes	characteristic
93	#11718656	C₂²	1	1	yes	characteristic
94	C₄×#6099	C₂²	1	1	yes	characteristic
95	#11718552	C₂²	1	2	yes	—
96	#11718552	C₂²	1	2	yes	—
97	#11718551	C₂²	1	2	yes	—
98	#11718551	C₂²	1	2	yes	—
99	#11718539	C₂²	1	2	yes	complemented
100	#11718537	C₂²	1	2	yes	complemented
101	#11718537	C₂²	1	2	yes	complemented
102	#11718535	C₂²	1	2	yes	complemented
103	#11718532	C₂²	1	2	yes	—
104	#11718532	C₂²	1	2	yes	—
105	#11718531	C₂²	1	2	yes	—
106	#11718531	C₂²	1	2	yes	—
107	#11718519	C₂²	1	2	yes	complemented
108	#11718517	C₂²	1	2	yes	complemented
109	#11718517	C₂²	1	2	yes	complemented
110	#11718516	C₂²	1	2	yes	complemented
111	#11718508	C₂²	1	2	yes	—
112	#11718508	C₂²	1	2	yes	—
113	#11718508	C₂²	1	2	yes	—
114	#11718508	C₂²	1	2	yes	—
115	#11718492	C₂²	1	2	yes	complemented
116	#11718491	C₂²	1	2	yes	complemented
117	#11718489	C₂²	1	2	yes	complemented
118	#11718489	C₂²	1	2	yes	complemented
119	#11718478	C₂²	1	2	yes	—
120	#11718478	C₂²	1	2	yes	—
121	#11718460	C₂²	1	2	yes	complemented
122	#11718457	C₂²	1	2	yes	complemented
123	#11718455	C₂²	1	2	yes	complemented
124	#11718452	C₂²	1	2	yes	complemented
125	#11718449	C₂²	1	2	yes	—
126	#11718449	C₂²	1	2	yes	—
127	#11718446	C₂²	1	2	yes	—
128	#11718446	C₂²	1	2	yes	—
129	#11718427	C₂²	1	2	yes	complemented
130	#11718424	C₂²	1	2	yes	complemented
131	#11718422	C₂²	1	2	yes	complemented
132	#11718420	C₂²	1	2	yes	complemented
133	#11718417	C₂²	1	2	yes	—
134	#11718417	C₂²	1	2	yes	—
135	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
136	C₂×Q₈×D₁₃	—	2	2	no	—
137	C₂²×D₅₂	C₂³	1	1	yes	characteristic
138	C₂²×C₄×D₁₃	—	2	1	no	—
139	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₁₃×#125	C₂³	1	1	yes	characteristic
144	C₁₃×#125	C₂³	1	1	yes	characteristic
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₄×Q₈×C₁₃	—	2	1	no	—
148	C₄×Q₈×C₁₃	—	2	1	no	—
149	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
151	C₄×D₄×C₁₃	—	2	1	no	—
152	C₄×D₄×C₁₃	—	2	1	no	—
153	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
154	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
155	C₁₃×#117	—	2	1	no	—
156	C₁₃×#117	C₂³	1	1	yes	characteristic
157	C₁₃×#117	C₂³	1	1	yes	characteristic
158	C₁₃×#117	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	—	2	1	no	—
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	#88203	Q₈	1	8	yes	complemented
162	#88200	—	2	2	no	—
163	#88200	—	2	2	no	—
164	#88200	—	2	2	no	—
165	Q₈×Dic₁₃	C₂³	1	2	yes	—
166	Q₈×Dic₁₃	C₂³	1	2	yes	—
167	C₂×#6106	C₂³	1	2	yes	—
168	D₄×Dic₁₃	—	2	2	no	—
169	D₄×Dic₁₃	—	2	2	no	—
170	D₄×Dic₁₃	C₂³	1	2	yes	—
171	D₄×Dic₁₃	C₂³	1	2	yes	—
172	C₂×#6104	C₂³	1	2	yes	—
173	C₂×#6103	—	2	1	no	—
174	#88180	—	2	1	no	—
175	#88180	—	2	1	no	—
176	#88180	C₂³	1	1	yes	characteristic
177	#88180	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊Dic₁₃	—	2	1	no	—
179	C₂×C₄⋊Dic₁₃	—	2	1	no	—
180	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	#88178	—	2	2	no	—
184	#88178	—	2	2	no	—
185	#88178	D₄	1	2	yes	—
186	#88178	D₄	1	2	yes	—
187	C₂×#6101	—	2	1	no	—
188	C₂×#6101	—	2	1	no	—
189	C₂×#6101	—	2	2	no	—
190	C₂×#6101	—	2	2	no	—
191	C₂×#6099	C₂³	1	1	yes	characteristic
192	C₂×#6099	C₂³	1	1	yes	characteristic
193	#88151	—	2	2	no	—
194	#88151	—	2	2	no	—
195	#88151	—	2	2	no	—
196	#88150	—	2	2	no	—
197	#88150	—	2	2	no	—
198	#88150	—	2	2	no	—
199	#88150	—	2	2	no	—
200	#88150	—	2	2	no	—
201	#88150	—	2	2	no	—
202	#88147	C₂³	1	2	yes	—
203	#88147	C₂³	1	2	yes	—
204	#88147	C₂³	1	2	yes	—
205	#88147	C₂³	1	2	yes	—
206	C₄⋊C₄×D₁₃	—	2	2	no	—
207	C₄⋊C₄×D₁₃	—	2	2	no	—
208	C₄⋊C₄×D₁₃	—	2	2	no	—
209	#88144	—	2	2	no	—
210	#88144	—	2	2	no	—
211	#88144	C₂³	1	2	yes	—
212	#88144	C₂³	1	2	yes	—
213	#88144	C₂³	1	2	yes	—
214	#88144	C₂³	1	2	yes	—
215	#88142	—	2	2	no	—
216	#88142	—	2	2	no	—
217	#88142	C₂³	1	2	yes	—
218	#88142	C₂³	1	2	yes	—
219	#88142	C₂³	1	2	yes	—
220	#88142	C₂³	1	2	yes	—
221	C₂²⋊C₄×D₁₃	—	2	2	no	—
222	C₂²⋊C₄×D₁₃	—	2	2	no	—
223	#88132	—	2	2	no	—
224	#88132	—	2	2	no	—
225	#88132	—	2	2	no	—
226	#88132	—	2	2	no	—
227	#88132	—	2	2	no	—
228	#88132	—	2	2	no	—
229	#88132	—	2	2	no	—
230	#88132	—	2	2	no	—
231	C₄×D₅₂	—	2	1	no	—
232	C₄×D₅₂	—	2	1	no	—
233	C₄×D₅₂	—	2	1	no	—
234	C₄×D₅₂	—	2	1	no	—
235	C₄×D₅₂	—	2	1	no	—
236	C₄×D₅₂	—	2	1	no	—
237	C₄×D₅₂	C₂³	1	2	yes	—
238	C₄×D₅₂	C₂³	1	2	yes	—
239	#88124	—	2	1	no	—
240	#88124	—	2	1	no	—
241	#88124	—	2	1	no	—
242	#88124	—	2	1	no	—
243	#88124	—	2	1	no	—
244	#88124	—	2	1	no	—
245	#88124	—	2	2	no	—
246	#88124	—	2	2	no	—
247	#88124	D₄	1	1	yes	characteristic
248	#88124	D₄	1	1	yes	characteristic
249	#88124	C₂³	1	2	yes	—
250	#88124	C₂³	1	2	yes	—
251	#88123	—	2	1	no	—
252	#88123	—	2	1	no	—
253	#88123	—	2	1	no	—
254	#88123	—	2	1	no	—
255	#88123	D₄	1	1	yes	characteristic
256	#88123	D₄	1	1	yes	characteristic
257	C₄×Dic₂₆	—	2	2	no	—
258	C₄×Dic₂₆	—	2	2	no	—
259	C₄×Dic₂₆	C₂³	1	2	yes	—
260	C₄×Dic₂₆	C₂³	1	2	yes	—
261	C₁₃×#107	C₂³	1	1	yes	characteristic
262	C₁₃×#107	C₂³	1	1	yes	characteristic
263	C₁₃×#107	C₂³	1	1	yes	characteristic
264	C₁₃×#107	C₂³	1	1	yes	characteristic
265	C₁₃×#106	C₂³	1	1	yes	characteristic
266	C₁₃×#106	C₂³	1	1	yes	characteristic
267	C₁₃×#106	C₂³	1	1	yes	characteristic
268	C₁₃×#106	C₂³	1	1	yes	characteristic
269	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₁₃×#103	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×#102	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	#88075	C₂³	1	2	yes	—
282	#88072	C₂³	1	2	yes	—
283	#88061	C₂³	1	2	yes	—
284	#88061	C₂³	1	2	yes	—
285	#88061	C₂³	1	2	yes	—
286	#88061	C₂³	1	2	yes	—
287	#88058	C₂³	1	2	yes	—
288	#88058	C₂³	1	2	yes	—
289	#88057	C₂³	1	2	yes	—
290	#88057	C₂³	1	2	yes	—
291	#88055	C₂³	1	2	yes	—
292	#88055	C₂³	1	2	yes	—
293	#88054	C₂³	1	2	yes	—
294	#88054	C₂³	1	2	yes	—
295	#88054	C₂³	1	2	yes	—
296	#88054	C₂³	1	2	yes	—
297	C₈×Dic₁₃	C₂³	1	2	yes	—
298	C₈×Dic₁₃	C₂³	1	2	yes	—
299	#88049	C₂³	1	2	yes	—
300	#88049	C₂³	1	2	yes	—
301	#88048	C₂³	1	2	yes	—
302	#88048	C₂³	1	2	yes	—
303	#88048	C₂³	1	2	yes	—
304	#88048	C₂³	1	2	yes	—
305	#88048	C₂³	1	2	yes	—
306	#88047	C₂³	1	2	yes	—
307	#88047	C₂³	1	2	yes	—
308	#88047	C₂³	1	2	yes	—
309	#88047	C₂³	1	2	yes	—
310	#88047	C₂³	1	2	yes	—
311	#88043	C₂³	1	2	yes	—
312	C₄×#1055	C₂³	1	2	yes	—
313	#61385	—	13	1	no	maximal, Sylow
314	C₂³×D₁₃	—	2	1	no	—
315	C₁₃×#41	—	2	2	no	—
316	C₁₃×#41	C₂×Q₈	1	4	yes	complemented
317	C₂×Q₈×C₁₃	—	2	1	no	—
318	C₂×Q₈×C₁₃	—	2	1	no	—
319	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₁₃	—	2	1	no	—
321	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃	—	2	1	no	—
323	C₂²×C₄×C₁₃	—	2	1	no	—
324	C₂²×C₄×C₁₃	—	2	1	no	—
325	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂²×Dic₁₃	—	2	1	no	—
329	C₂²×Dic₁₃	—	2	1	no	—
330	C₂²×Dic₁₃	—	2	1	no	—
331	C₂²×Dic₁₃	—	2	2	no	—
332	C₂²×Dic₁₃	—	2	2	no	—
333	Q₈×D₁₃	—	8	4	no	—
334	C₂×D₅₂	—	2	1	no	—
335	C₂×D₅₂	—	2	2	no	—
336	C₂×D₅₂	C₂×Q₈	1	4	yes	—
337	C₂×D₅₂	C₂⁴	1	2	yes	—
338	C₂×C₄×D₁₃	—	2	2	no	—
339	C₂×C₄×D₁₃	—	2	2	no	—
340	C₂×C₄×D₁₃	—	2	2	no	—
341	C₂×C₄×D₁₃	—	2	2	no	—
342	C₂×C₄×D₁₃	—	2	2	no	—
343	C₂×C₄×D₁₃	—	2	2	no	—
344	C₂×C₄×D₁₃	—	8	2	no	—
345	C₂×Dic₂₆	—	2	2	no	—
346	C₂×Dic₂₆	—	2	2	no	—
347	C₂×Dic₂₆	—	2	2	no	—
348	C₂×Dic₂₆	—	2	2	no	—
349	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
350	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
351	C₂×C₈×C₁₃	—	2	2	no	—
352	C₂×C₈×C₁₃	—	2	2	no	—
353	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₁₃×C₄⋊C₄	—	2	1	no	—
358	C₁₃×C₄⋊C₄	—	2	1	no	—
359	C₁₃×C₄⋊C₄	—	2	1	no	—
360	C₁₃×C₄⋊C₄	—	2	1	no	—
361	C₁₃×C₄⋊C₄	—	2	1	no	—
362	C₁₃×C₄⋊C₄	—	2	1	no	—
363	C₁₃×C₄⋊C₄	—	2	1	no	—
364	C₁₃×C₄⋊C₄	—	2	1	no	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
366	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
367	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
368	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
369	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
370	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
371	C₁₃×C₂²⋊C₄	—	2	1	no	—
372	C₁₃×C₂²⋊C₄	—	2	1	no	—
373	C₁₃×C₂²⋊C₄	—	2	1	no	—
374	C₁₃×C₂²⋊C₄	—	2	1	no	—
375	C₁₃×C₂²⋊C₄	—	2	1	no	—
376	C₄²×C₁₃	—	2	1	no	—
377	C₄²×C₁₃	—	2	1	no	—
378	C₄²×C₁₃	—	2	1	no	—
379	C₄²×C₁₃	—	2	1	no	—
380	C₄²×C₁₃	—	2	1	no	—
381	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂²⋊Dic₁₃	—	2	2	no	—
386	C₂²⋊Dic₁₃	—	2	2	no	—
387	C₂²⋊Dic₁₃	C₂×D₄	1	2	yes	—
388	C₂²⋊Dic₁₃	C₂×D₄	1	2	yes	—
389	#6106	C₂×Q₈	1	8	yes	complemented
390	#6104	C₂×Q₈	1	8	yes	complemented
391	#6103	—	2	2	no	—
392	#6103	—	2	2	no	—
393	#6103	—	2	2	no	—
394	#6103	—	2	2	no	—
395	#6103	—	2	2	no	—
396	#6103	—	2	2	no	—
397	C₄⋊Dic₁₃	—	2	1	no	—
398	C₄⋊Dic₁₃	—	2	1	no	—
399	C₄⋊Dic₁₃	—	2	1	no	—
400	C₄⋊Dic₁₃	—	2	2	no	—
401	C₄⋊Dic₁₃	—	2	2	no	—
402	C₄⋊Dic₁₃	—	2	2	no	—
403	C₄⋊Dic₁₃	—	2	2	no	—
404	C₄⋊Dic₁₃	—	2	2	no	—
405	C₄⋊Dic₁₃	—	2	2	no	—
406	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
407	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
408	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
409	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
410	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
411	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
412	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
413	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
414	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
415	#6101	—	2	2	no	—
416	#6101	—	2	2	no	—
417	#6101	—	2	2	no	—
418	#6101	—	2	2	no	—
419	#6101	—	2	2	no	—
420	#6101	—	2	2	no	—
421	#6101	—	2	2	no	—
422	#6101	—	2	2	no	—
423	#6101	—	2	2	no	—
424	#6101	—	2	2	no	—
425	#6101	—	2	2	no	—
426	#6101	—	2	2	no	—
427	#6101	C₂×D₄	1	2	yes	—
428	#6101	C₂×D₄	1	2	yes	—
429	#6101	C₂×D₄	1	2	yes	—
430	#6101	C₂×D₄	1	2	yes	—
431	C₄×Dic₁₃	—	2	2	no	—
432	C₄×Dic₁₃	—	2	2	no	—
433	C₄×Dic₁₃	C₂⁴	1	2	yes	—
434	C₄×Dic₁₃	C₂⁴	1	2	yes	—
435	#6099	—	2	2	no	—
436	#6099	C₂×Q₈	1	4	yes	complemented
437	C₂×#1055	C₂⁴	1	2	yes	—
438	C₂×#1055	C₂⁴	1	2	yes	—
439	#3504	—	13	1	no	—
440	#3501	—	13	1	no	—
441	#3389	—	13	2	no	—
442	#3389	—	13	2	no	—
443	#3388	—	13	2	no	—
444	#3388	—	13	2	no	—
445	#3386	—	13	2	no	—
446	#3384	—	13	2	no	—
447	#3381	—	13	2	no	—
448	#3380	—	13	2	no	—
449	#3166	—	13	1	no	—
450	#3164	—	13	1	no	—
451	#3163	—	13	1	no	—
452	#3084	—	13	1	no	—
453	#3083	—	13	1	no	—
454	#3081	—	13	1	no	—
455	#3081	—	13	1	no	—
456	#3076	D₁₃	1	1	yes	characteristic, complemented
457	C₂×#478	—	13	1	no	—
458	#2962	—	13	1	no	—
459	#2946	—	13	1	no	—
460	#2946	—	13	1	no	—
461	C₄×AGL(1,ℤ/8)	—	13	1	no	—
462	C₂³×C₁₃	—	2	1	no	—
463	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
464	C₂²×D₁₃	—	2	2	no	—
465	C₂²×D₁₃	—	2	4	no	—
466	C₂²×D₁₃	—	8	1	no	—
467	C₂²×D₁₃	—	8	1	no	—
468	Q₈×C₁₃	—	2	1	no	—
469	Q₈×C₁₃	—	4	2	no	—
470	Q₈×C₁₃	—	8	1	no	—
471	Q₈×C₁₃	C₂²×Q₈	1	2	yes	—
472	D₄×C₁₃	—	2	4	no	—
473	D₄×C₁₃	—	2	1	no	—
474	D₄×C₁₃	C₂²×Q₈	1	2	yes	—
475	C₂×C₄×C₁₃	—	2	1	no	—
476	C₂×C₄×C₁₃	—	2	4	no	—
477	C₂×C₄×C₁₃	—	2	1	no	—
478	C₂×C₄×C₁₃	—	2	1	no	—
479	C₂×C₄×C₁₃	—	2	1	no	—
480	C₂×C₄×C₁₃	—	2	1	no	—
481	C₂×C₄×C₁₃	—	2	1	no	—
482	C₂×C₄×C₁₃	—	2	1	no	—
483	C₂×C₄×C₁₃	—	4	1	no	—
484	C₂×C₄×C₁₃	—	4	1	no	—
485	C₂×C₄×C₁₃	—	8	1	no	—
486	C₂×C₄×C₁₃	—	8	1	no	—
487	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
493	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
494	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
495	C₂×Dic₁₃	—	2	2	no	—
496	C₂×Dic₁₃	—	2	2	no	—
497	C₂×Dic₁₃	—	2	2	no	—
498	C₂×Dic₁₃	—	8	2	no	—
499	C₂×Dic₁₃	—	8	2	no	—
500	C₂×Dic₁₃	—	8	1	no	—
501	C₂×Dic₁₃	—	8	1	no	—
502	C₂×Dic₁₃	—	8	1	no	—
503	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
504	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
505	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
506	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
507	D₅₂	—	2	4	no	—
508	D₅₂	—	2	2	no	—
509	D₅₂	C₂²×Q₈	1	4	yes	—
510	C₄×D₁₃	—	4	4	no	—
511	C₄×D₁₃	—	8	2	no	—
512	C₄×D₁₃	—	8	2	no	—
513	C₄×D₁₃	—	8	2	no	—
514	C₄×D₁₃	—	8	2	no	—
515	C₄×D₁₃	—	8	2	no	—
516	Dic₂₆	—	4	2	no	—
517	Dic₂₆	—	4	2	no	—
518	Dic₂₆	—	8	2	no	—
519	Dic₂₆	—	8	2	no	—
520	Dic₂₆	—	8	2	no	—
521	Dic₂₆	—	8	2	no	—
522	C₈×C₁₃	—	2	1	no	—
523	C₈×C₁₃	—	2	1	no	—
524	C₈×C₁₃	—	2	1	no	—
525	C₈×C₁₃	—	2	1	no	—
526	#1055	—	2	2	no	—
527	#1055	C₂²×Q₈	1	4	yes	—
528	C₂×AGL(1,ℤ/8)	—	13	1	no	—
529	#557	—	13	2	no	—
530	#557	—	13	2	no	—
531	#554	—	13	2	no	—
532	#554	—	13	2	no	—
533	#554	—	13	2	no	—
534	#554	—	13	2	no	—
535	#554	—	13	2	no	—
536	#554	—	26	2	no	—
537	#554	—	26	2	no	—
538	#554	—	26	1	no	—
539	#554	—	26	1	no	—
540	#554	—	26	1	no	—
541	D₄×Q₈	—	13	2	no	—
542	D₄×Q₈	—	26	1	no	—
543	#544	—	13	1	no	—
544	#544	—	13	1	no	—
545	#544	—	13	1	no	—
546	#544	—	13	1	no	—
547	#544	—	26	1	no	—
548	#544	—	26	1	no	—
549	#543	—	26	2	no	—
550	#533	—	13	1	no	—
551	#533	—	26	1	no	—
552	#533	C₂×D₁₃	1	1	yes	characteristic
553	C₂×#125	—	13	1	no	—
554	C₂×#125	—	26	1	no	—
555	C₂×C₂²⋊Q₈	—	26	2	no	—
556	#520	—	13	1	no	—
557	#520	—	13	1	no	—
558	#518	—	13	1	no	—
559	#518	—	13	1	no	—
560	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
561	C₂×C₄×D₄	—	13	1	no	—
562	#501	—	13	2	no	—
563	#501	—	13	2	no	—
564	#501	—	13	2	no	—
565	#501	—	13	2	no	—
566	#501	—	13	2	no	—
567	#501	—	13	2	no	—
568	#500	—	13	2	no	—
569	#499	—	13	2	no	—
570	#499	—	13	2	no	—
571	#499	—	13	2	no	—
572	#499	—	13	2	no	—
573	#498	—	13	2	no	—
574	#479	—	13	2	no	—
575	#479	—	13	2	no	—
576	#479	C₂×D₁₃	1	1	yes	characteristic, complemented
577	#479	C₂×D₁₃	1	1	yes	characteristic, complemented
578	#478	—	13	2	no	—
579	#478	—	13	2	no	—
580	#478	—	13	2	no	—
581	#478	—	13	2	no	—
582	#478	—	13	2	no	—
583	#478	—	13	2	no	—
584	#478	—	13	2	no	—
585	#478	—	13	2	no	—
586	#478	—	13	2	no	—
587	#478	—	13	2	no	—
588	#478	C₂×D₁₃	1	1	yes	characteristic, complemented
589	#478	C₂×D₁₃	1	1	yes	characteristic, complemented
590	#477	—	13	2	no	—
591	#477	C₂×D₁₃	1	1	yes	characteristic, complemented
592	#476	—	13	2	no	—
593	#476	—	13	2	no	—
594	#476	—	13	2	no	—
595	#476	C₂×D₁₃	1	1	yes	characteristic, complemented
596	#475	—	13	2	no	—
597	#475	C₂×D₁₃	1	1	yes	characteristic, complemented
598	#474	—	13	2	no	—
599	#474	—	13	2	no	—
600	#474	—	13	2	no	—
601	#474	C₂×D₁₃	1	1	yes	characteristic, complemented
602	#446	—	13	2	no	—
603	#446	—	13	2	no	—
604	#446	—	13	2	no	—
605	C₈×Q₈	—	13	2	no	—
606	#442	—	13	2	no	—
607	#442	—	13	2	no	—
608	#442	—	13	2	no	—
609	#440	—	13	2	no	—
610	#440	—	13	2	no	—
611	#440	—	13	2	no	—
612	C₄×SD₁₆	—	13	2	no	—
613	C₄×SD₁₆	—	13	2	no	—
614	C₄×SD₁₆	—	13	2	no	—
615	C₄×D₈	—	13	2	no	—
616	C₄×D₈	—	13	2	no	—
617	C₄×D₈	—	13	2	no	—
618	#428	—	13	1	no	—
619	#428	—	13	1	no	—
620	#428	—	13	1	no	—
621	#428	—	13	1	no	—
622	#428	—	13	1	no	—
623	#427	C₂×D₁₃	1	1	yes	characteristic
624	#427	C₂×D₁₃	1	1	yes	characteristic
625	C₂×#107	—	13	1	no	—
626	C₂×#106	—	13	1	no	—
627	#424	—	13	1	no	—
628	#424	—	13	1	no	—
629	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
630	#418	—	13	1	no	—
631	#417	—	13	1	no	—
632	#416	C₂×D₁₃	1	1	yes	characteristic
633	#416	C₂×D₁₃	1	1	yes	characteristic
634	C₂×#102	—	13	1	no	—
635	C₂×#102	—	13	1	no	—
636	#405	—	13	1	no	—
637	#405	—	13	1	no	—
638	C₄×M₁₆	—	13	1	no	—
639	C₂²×C₁₃	—	2	1	no	—
640	C₂²×C₁₃	—	2	1	no	—
641	C₂²×C₁₃	—	2	2	no	—
642	C₂²×C₁₃	—	4	1	no	—
643	C₂²×C₁₃	—	4	1	no	—
644	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
645	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
646	C₂×D₁₃	—	2	4	no	—
647	C₂×D₁₃	—	4	2	no	—
648	C₂×D₁₃	—	4	2	no	—
649	C₂×D₁₃	—	8	4	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	—	2	2	no	—
655	C₄×C₁₃	—	4	1	no	—
656	C₄×C₁₃	—	4	1	no	—
657	C₄×C₁₃	—	4	1	no	—
658	C₄×C₁₃	—	4	1	no	—
659	C₄×C₁₃	—	4	1	no	—
660	C₄×C₁₃	—	4	1	no	—
661	C₄×C₁₃	D₄×Q₈	1	2	yes	—
662	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
663	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
664	Dic₁₃	—	2	2	no	—
665	Dic₁₃	—	2	2	no	—
666	Dic₁₃	—	2	2	no	—
667	Dic₁₃	—	2	2	no	—
668	Dic₁₃	—	4	2	no	—
669	Dic₁₃	—	4	2	no	—
670	Dic₁₃	—	4	2	no	—
671	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
672	C₂²×Q₈	—	26	2	no	—
673	C₂²×D₄	—	13	1	no	—
674	C₂³×C₄	—	26	1	no	—
675	AGL(1,ℤ/8)	—	13	8	no	—
676	C₂×SD₁₆	—	13	2	no	—
677	C₂×D₈	—	13	2	no	—
678	C₂×M₁₆	—	13	1	no	—
679	C₂×M₁₆	—	13	1	no	—
680	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
681	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
682	C₄⋊Q₈	—	13	2	no	—
683	C₄⋊Q₈	—	13	2	no	—
684	C₄⋊Q₈	—	13	2	no	—
685	C₄⋊Q₈	—	13	2	no	—
686	C₄⋊Q₈	—	13	1	no	—
687	C₄⋊Q₈	—	13	1	no	—
688	C₄⋊Q₈	—	26	1	no	—
689	C₄⋊Q₈	—	26	1	no	—
690	C₄⋊Q₈	—	26	1	no	—
691	C₄⋊Q₈	—	26	1	no	—
692	C₄⋊Q₈	—	26	2	no	—
693	C₄⋊Q₈	—	26	2	no	—
694	C₄⋊Q₈	C₂²×D₁₃	1	1	yes	characteristic
695	C₄⋊Q₈	C₂²×D₁₃	1	1	yes	characteristic
696	#125	—	13	2	no	—
697	#125	—	13	2	no	—
698	#125	—	13	2	no	—
699	#125	—	13	2	no	—
700	#125	—	13	1	no	—
701	#125	—	13	1	no	—
702	#125	—	13	2	no	—
703	#125	—	13	2	no	—
704	#125	—	26	1	no	—
705	#125	—	26	1	no	—
706	#125	—	26	2	no	—
707	#125	—	26	2	no	—
708	#125	—	26	1	no	—
709	#125	—	26	1	no	—
710	#125	—	26	2	no	—
711	#125	—	26	2	no	—
712	#125	—	26	1	no	—
713	#125	—	26	1	no	—
714	#125	C₂²×D₁₃	1	1	yes	characteristic
715	#125	C₂²×D₁₃	1	1	yes	characteristic
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	1	no	—
718	C₂²⋊Q₈	—	13	2	no	—
719	C₂²⋊Q₈	—	13	2	no	—
720	C₂²⋊Q₈	—	26	2	no	—
721	C₂²⋊Q₈	—	26	2	no	—
722	C₂²⋊Q₈	—	26	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	—	26	2	no	—
729	C₂²⋊Q₈	—	26	2	no	—
730	C₂²⋊Q₈	—	26	2	no	—
731	C₂²⋊Q₈	—	26	2	no	—
732	C₂²⋊Q₈	—	26	2	no	—
733	C₂²⋊Q₈	—	26	2	no	—
734	C₂²⋊Q₈	—	26	2	no	—
735	C₂²⋊Q₈	—	26	2	no	—
736	C₂²⋊Q₈	—	26	2	no	—
737	C₂²⋊Q₈	—	26	2	no	—
738	C₂²⋊Q₈	—	26	2	no	—
739	C₂²⋊Q₈	—	26	2	no	—
740	C₂²⋊Q₈	—	26	2	no	—
741	C₂²⋊Q₈	—	26	2	no	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	13	2	no	—
745	C₄×Q₈	—	13	2	no	—
746	C₄×Q₈	—	13	2	no	—
747	C₄×Q₈	—	13	2	no	—
748	C₄×Q₈	—	26	2	no	—
749	C₄×Q₈	—	26	2	no	—
750	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
751	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
752	C₄×D₄	—	2	1	no	—
753	C₄×D₄	—	2	1	no	—
754	C₄×D₄	—	13	2	no	—
755	C₄×D₄	—	13	2	no	—
756	C₄×D₄	—	13	2	no	—
757	C₄×D₄	—	13	2	no	—
758	C₄×D₄	—	13	2	no	—
759	C₄×D₄	—	13	2	no	—
760	C₄×D₄	—	13	2	no	—
761	C₄×D₄	—	13	2	no	—
762	C₄×D₄	—	26	1	no	—
763	C₄×D₄	—	26	1	no	—
764	C₄×D₄	—	26	1	no	—
765	C₄×D₄	—	26	1	no	—
766	C₄×D₄	—	26	2	no	—
767	C₄×D₄	—	26	2	no	—
768	C₄×D₄	—	26	1	no	—
769	C₄×D₄	—	26	1	no	—
770	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
771	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
772	#117	—	2	1	no	—
773	#117	—	13	1	no	—
774	#117	—	13	1	no	—
775	#117	—	26	1	no	—
776	#117	—	26	1	no	—
777	#117	C₂²×D₁₃	1	1	yes	characteristic
778	#117	C₂²×D₁₃	1	1	yes	characteristic
779	#117	C₂²×D₁₃	1	1	yes	characteristic
780	C₂×C₄⋊C₄	—	13	1	no	—
781	C₂×C₄⋊C₄	—	13	1	no	—
782	C₂×C₄⋊C₄	—	13	1	no	—
783	C₂×C₄⋊C₄	—	26	2	no	—
784	C₂×C₄⋊C₄	—	26	2	no	—
785	C₂×C₄⋊C₄	—	26	2	no	—
786	C₂×C₄⋊C₄	—	26	1	no	—
787	C₂×C₄⋊C₄	—	26	1	no	—
788	C₂×C₄⋊C₄	—	26	2	no	—
789	C₂×C₄⋊C₄	—	26	2	no	—
790	C₂×C₄⋊C₄	—	26	1	no	—
791	C₂×C₄⋊C₄	—	26	1	no	—
792	C₂×C₂²⋊C₄	—	26	2	no	—
793	C₂×C₂²⋊C₄	—	26	2	no	—
794	C₂×C₂²⋊C₄	—	26	1	no	—
795	C₂×C₄²	—	2	1	no	—
796	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
797	#107	—	13	2	no	—
798	#107	—	13	2	no	—
799	#107	—	13	2	no	—
800	#107	—	13	2	no	—
801	#107	—	13	2	no	—
802	#107	—	13	2	no	—
803	#107	—	13	2	no	—
804	#107	C₂²×D₁₃	1	1	yes	characteristic
805	#107	C₂²×D₁₃	1	1	yes	characteristic
806	#107	C₂²×D₁₃	1	1	yes	characteristic
807	#107	C₂²×D₁₃	1	1	yes	characteristic
808	#106	—	13	2	no	—
809	#106	—	13	2	no	—
810	#106	—	13	2	no	—
811	#106	—	13	2	no	—
812	#106	—	13	2	no	—
813	#106	—	13	2	no	—
814	#106	—	13	2	no	—
815	#106	C₂²×D₁₃	1	1	yes	characteristic
816	#106	C₂²×D₁₃	1	1	yes	characteristic
817	#106	C₂²×D₁₃	1	1	yes	characteristic
818	#106	C₂²×D₁₃	1	1	yes	characteristic
819	C₄⋊C₈	—	13	2	no	—
820	C₄⋊C₈	—	13	2	no	—
821	C₄⋊C₈	—	13	2	no	—
822	C₄⋊C₈	—	13	2	no	—
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	#103	—	13	2	no	—
828	#103	C₂²×D₁₃	1	1	yes	characteristic
829	#103	C₂²×D₁₃	1	1	yes	characteristic
830	#103	C₂²×D₁₃	1	1	yes	characteristic
831	#103	C₂²×D₁₃	1	1	yes	characteristic
832	#102	—	13	2	no	—
833	#102	—	13	2	no	—
834	#102	—	13	2	no	—
835	#102	—	13	2	no	—
836	#102	—	13	2	no	—
837	#102	—	13	2	no	—
838	#102	—	13	2	no	—
839	#102	C₂²×D₁₃	1	1	yes	characteristic
840	#102	C₂²×D₁₃	1	1	yes	characteristic
841	#102	C₂²×D₁₃	1	1	yes	characteristic
842	#102	C₂²×D₁₃	1	1	yes	characteristic
843	#97	—	13	2	no	—
844	#97	—	13	2	no	—
845	#97	—	13	2	no	—
846	C₄×C₈	—	13	2	no	—
847	C₄×C₈	—	13	2	no	—
848	C₄×C₈	—	13	2	no	—
849	C₂×C₁₃	—	2	2	no	—
850	C₂×C₁₃	—	4	2	no	—
851	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
852	C₂×C₁₃	#3584	1	1	yes	characteristic
853	C₂×C₁₃	#3585	1	1	yes	characteristic
854	D₁₃	—	4	4	no	—
855	C₂⁴	—	26	1	no	—
856	#41	—	2	2	no	—
857	#41	Q₈×D₁₃	1	4	yes	complemented
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	13	2	no	—
861	C₂×Q₈	—	13	2	no	—
862	C₂×Q₈	—	26	2	no	—
863	C₂×Q₈	—	26	2	no	—
864	C₂×Q₈	—	26	2	no	—
865	C₂×Q₈	—	26	2	no	—
866	C₂×Q₈	—	104	4	no	—
867	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	13	4	no	—
870	C₂×D₄	—	13	2	no	—
871	C₂×D₄	—	26	1	no	—
872	C₂×D₄	—	26	2	no	—
873	C₂×D₄	C₂³×D₁₃	1	1	yes	characteristic
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	26	2	no	—
878	C₂²×C₄	—	26	2	no	—
879	C₂²×C₄	—	26	2	no	—
880	C₂²×C₄	—	26	2	no	—
881	C₂²×C₄	—	26	2	no	—
882	C₂²×C₄	—	26	2	no	—
883	C₂²×C₄	—	26	1	no	—
884	C₂²×C₄	—	26	1	no	—
885	C₂²×C₄	—	26	1	no	—
886	C₂²×C₄	—	26	2	no	—
887	C₂²×C₄	—	26	2	no	—
888	C₂²×C₄	—	104	2	no	—
889	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
890	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
891	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
892	SD₁₆	—	13	8	no	—
893	D₈	—	13	8	no	—
894	M₁₆	—	13	4	no	—
895	M₁₆	—	26	2	no	—
896	C₂×C₈	—	2	2	no	—
897	C₂×C₈	—	2	2	no	—
898	C₂×C₈	—	13	2	no	—
899	C₂×C₈	—	13	2	no	—
900	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
901	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
902	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
903	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	13	2	no	—
913	C₄⋊C₄	—	13	1	no	—
914	C₄⋊C₄	—	13	1	no	—
915	C₄⋊C₄	—	13	2	no	—
916	C₄⋊C₄	—	13	2	no	—
917	C₄⋊C₄	—	13	2	no	—
918	C₄⋊C₄	—	13	1	no	—
919	C₄⋊C₄	—	13	1	no	—
920	C₄⋊C₄	—	13	2	no	—
921	C₄⋊C₄	—	13	2	no	—
922	C₄⋊C₄	—	13	2	no	—
923	C₄⋊C₄	—	13	2	no	—
924	C₄⋊C₄	—	13	2	no	—
925	C₄⋊C₄	—	26	2	no	—
926	C₄⋊C₄	—	26	2	no	—
927	C₄⋊C₄	—	26	2	no	—
928	C₄⋊C₄	—	26	2	no	—
929	C₄⋊C₄	—	26	2	no	—
930	C₄⋊C₄	—	26	2	no	—
931	C₄⋊C₄	—	26	2	no	—
932	C₄⋊C₄	—	26	2	no	—
933	C₄⋊C₄	—	26	2	no	—
934	C₄⋊C₄	—	26	2	no	—
935	C₄⋊C₄	—	26	2	no	—
936	C₄⋊C₄	—	26	2	no	—
937	C₄⋊C₄	—	26	2	no	—
938	C₄⋊C₄	—	26	2	no	—
939	C₄⋊C₄	—	26	1	no	—
940	C₄⋊C₄	—	26	1	no	—
941	C₄⋊C₄	—	26	1	no	—
942	C₄⋊C₄	—	26	2	no	—
943	C₄⋊C₄	—	26	2	no	—
944	C₄⋊C₄	—	26	2	no	—
945	C₄⋊C₄	—	26	2	no	—
946	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
949	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	13	2	no	—
958	C₂²⋊C₄	—	13	2	no	—
959	C₂²⋊C₄	—	26	2	no	—
960	C₂²⋊C₄	—	26	2	no	—
961	C₂²⋊C₄	—	26	2	no	—
962	C₂²⋊C₄	—	26	2	no	—
963	C₂²⋊C₄	—	26	2	no	—
964	C₂²⋊C₄	—	26	2	no	—
965	C₂²⋊C₄	—	26	2	no	—
966	C₂²⋊C₄	—	26	2	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	13	2	no	—
973	C₄²	—	13	2	no	—
974	C₄²	—	26	2	no	—
975	C₄²	—	26	2	no	—
976	C₄²	D₄×D₁₃	1	1	yes	characteristic
977	C₄²	D₄×D₁₃	1	1	yes	characteristic
978	C₄²	C₂³×D₁₃	1	1	yes	characteristic
979	C₄²	C₂³×D₁₃	1	1	yes	characteristic
980	C₁₃	#61385	1	1	yes	characteristic, complemented, Sylow
981	C₂³	—	2	1	no	—
982	C₂³	—	26	2	no	—
983	C₂³	—	26	4	no	—
984	C₂³	—	104	1	no	—
985	C₂³	—	104	1	no	—
986	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
987	Q₈	—	2	1	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	8	1	no	—
990	Q₈	—	52	2	no	—
991	Q₈	—	52	2	no	—
992	Q₈	—	104	2	no	—
993	Q₈	—	104	2	no	—
994	Q₈	—	104	2	no	—
995	Q₈	—	104	2	no	—
996	Q₈	C₂×Q₈×D₁₃	1	2	yes	—
997	D₄	—	2	4	no	—
998	D₄	—	2	1	no	—
999	D₄	—	13	4	no	—
1000	D₄	—	26	4	no	—
1001	D₄	—	26	2	no	—
1002	D₄	C₂×Q₈×D₁₃	1	2	yes	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	4	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	8	1	no	—
1014	C₂×C₄	—	8	1	no	—
1015	C₂×C₄	—	13	2	no	—
1016	C₂×C₄	—	13	2	no	—
1017	C₂×C₄	—	13	2	no	—
1018	C₂×C₄	—	13	2	no	—
1019	C₂×C₄	—	26	2	no	—
1020	C₂×C₄	—	26	2	no	—
1021	C₂×C₄	—	26	2	no	—
1022	C₂×C₄	—	52	4	no	—
1023	C₂×C₄	—	104	2	no	—
1024	C₂×C₄	—	104	2	no	—
1025	C₂×C₄	—	104	2	no	—
1026	C₂×C₄	—	104	2	no	—
1027	C₂×C₄	—	104	2	no	—
1028	C₂×C₄	—	104	2	no	—
1029	C₂×C₄	—	104	2	no	—
1030	C₂×C₄	—	104	1	no	—
1031	C₂×C₄	—	104	1	no	—
1032	C₂×C₄	—	104	1	no	—
1033	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1034	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1035	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1036	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1037	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1038	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
1039	C₂×C₄	#88257	1	2	yes	—
1040	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	13	4	no	—
1046	C₈	—	26	2	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	26	4	no	—
1053	C₂²	—	52	2	no	—
1054	C₂²	—	52	2	no	—
1055	C₂²	—	104	4	no	—
1056	C₂²	#11719337	1	2	yes	—
1057	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
1058	C₄	—	2	2	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	26	2	no	—
1070	C₄	—	26	2	no	—
1071	C₄	—	26	2	no	—
1072	C₄	—	26	2	no	—
1073	C₄	—	52	2	no	—
1074	C₄	—	52	2	no	—
1075	C₄	—	52	2	no	—
1076	C₄	#11719337	1	2	yes	—
1077	C₄	C₂²×Q₈×D₁₃	1	1	yes	characteristic
1078	C₄	C₂×#88257	1	1	yes	characteristic
1079	C₂	—	2	2	no	—
1080	C₂	—	4	2	no	—
1081	C₂	—	52	4	no	—
1082	C₂	C₂×#11719337	1	1	yes	characteristic
1083	C₂	#13129605	1	1	yes	characteristic
1084	C₂	#13129613	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₁₃×#3076	C₂
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₂×#88203	C₂²
hypercenter	#3076	D₁₃
hypocenter	C₁₃	#61385
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #13128662	C₂	semidirect
2. #13128637	C₂	semidirect
3. #13127794	C₂	semidirect
4. #13127789	C₂	semidirect
5. #13127788	C₂	semidirect
6. #13127779	C₂	semidirect
7. #13127760	C₂	semidirect
8. #13127730	C₂	semidirect
9. #13127714	C₂	semidirect
10. #13127698	C₂	semidirect
11. #13125389	C₂	semidirect
12. #13125376	C₂	semidirect
13. #13125368	C₂	semidirect
14. #13124696	C₂	semidirect
15. #13124685	C₂	semidirect
16. #13124670	C₂	semidirect
17. #13124670	C₂	semidirect
18. C₂×#11718508	C₂	semidirect
19. #13123779	C₂	semidirect
23. C₁₃×#3076	C₂	semidirect
39. #11719274	C₂²	semidirect
40. #11719274	C₂²	semidirect
43. #11719244	C₂²	semidirect
44. #11719244	C₂²	semidirect
58. C₁₃×#479	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
60. C₁₃×#478	C₂²	semidirect
61. C₁₃×#478	C₂²	semidirect
62. C₁₃×#477	C₂²	semidirect
63. C₁₃×#476	C₂²	semidirect
64. C₁₃×#475	C₂²	semidirect
65. C₁₃×#474	C₂²	semidirect
80. #11718741	C₂²	semidirect
81. #11718741	C₂²	semidirect
82. #11718725	C₂²	semidirect
83. #11718725	C₂²	semidirect
99. #11718539	C₂²	semidirect
100. #11718537	C₂²	semidirect
101. #11718537	C₂²	semidirect
102. #11718535	C₂²	semidirect
107. #11718519	C₂²	semidirect
108. #11718517	C₂²	semidirect
109. #11718517	C₂²	semidirect
110. #11718516	C₂²	semidirect
115. #11718492	C₂²	semidirect
116. #11718491	C₂²	semidirect
117. #11718489	C₂²	semidirect
118. #11718489	C₂²	semidirect
121. #11718460	C₂²	semidirect
122. #11718457	C₂²	semidirect
123. #11718455	C₂²	semidirect
124. #11718452	C₂²	semidirect
129. #11718427	C₂²	semidirect
130. #11718424	C₂²	semidirect
131. #11718422	C₂²	semidirect
132. #11718420	C₂²	semidirect
161. #88203	Q₈	semidirect
316. C₁₃×#41	C₂×Q₈	semidirect
389. #6106	C₂×Q₈	semidirect
390. #6104	C₂×Q₈	semidirect
436. #6099	C₂×Q₈	semidirect
456. #3076	D₁₃	semidirect
576. #479	C₂×D₁₃	semidirect
577. #479	C₂×D₁₃	semidirect
588. #478	C₂×D₁₃	semidirect
589. #478	C₂×D₁₃	semidirect
591. #477	C₂×D₁₃	semidirect
595. #476	C₂×D₁₃	semidirect
597. #475	C₂×D₁₃	semidirect
601. #474	C₂×D₁₃	semidirect
857. #41	Q₈×D₁₃	semidirect
980. C₁₃	#61385	semidirect

Maximal subgroups

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

subgroup	index
#13128662	2
#13128637	2
#13127794	2
#13127789	2
#13127788	2
#13127779	2
#13127760	2
#13127730	2
#13127714	2
#13127698	2
#13125389	2
#13125376	2
#13125368	2
#13124696	2
#13124685	2
#13124670	2
C₂×#11718508	2
#13123779	2
#13123671	2
C₄×#88203	2
C₁₃×#3076	2
#61385	13