Subgroups — #16760469

Order 3328.

1756 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129324	C₂	1	1	yes	maximal, characteristic, complemented
2	#13128868	C₂	1	1	yes	maximal, characteristic
3	#13127744	C₂	1	1	yes	maximal, characteristic, complemented
4	#13127709	C₂	1	1	yes	maximal, characteristic, complemented
5	#13127563	C₂	1	1	yes	maximal, characteristic, complemented
6	#13127505	C₂	1	1	yes	maximal, characteristic, complemented
7	#13127464	C₂	1	1	yes	maximal, characteristic, complemented
8	#13127399	C₂	1	2	yes	maximal, complemented
9	#13127384	C₂	1	2	yes	maximal, complemented
10	#13127251	C₂	1	1	yes	maximal, characteristic, complemented
11	#13127069	C₂	1	1	yes	maximal, characteristic, complemented
12	#13127060	C₂	1	2	yes	maximal, complemented
13	#13126850	C₂	1	2	yes	maximal, complemented
14	#13126662	C₂	1	1	yes	maximal, characteristic, complemented
15	#13126279	C₂	1	2	yes	maximal, complemented
16	#13126219	C₂	1	1	yes	maximal, characteristic, complemented
17	#13126088	C₂	1	2	yes	maximal, complemented
18	#13125974	C₂	1	1	yes	maximal, characteristic, complemented
19	#13125086	C₂	1	2	yes	maximal, complemented
20	#13124662	C₂	1	2	yes	maximal, complemented
21	#13124633	C₂	1	1	yes	maximal, characteristic, complemented
22	#13123987	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	D₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
27	#11719496	—	2	1	no	—
28	C₂×#88184	—	2	1	no	—
29	#11719436	C₂²	1	2	yes	complemented
30	#11719434	C₂²	1	2	yes	complemented
31	#11719401	—	2	2	no	—
32	#11719351	—	2	2	no	—
33	#11719346	C₂²	1	2	yes	complemented
34	#11719344	C₂²	1	2	yes	complemented
35	#11719289	—	2	1	no	—
36	#11719289	C₂²	1	1	yes	characteristic, complemented
37	#11719284	C₂²	1	1	yes	characteristic, complemented
38	#11719275	C₂²	1	1	yes	characteristic, complemented
39	#11719272	—	2	1	no	—
40	Q₈×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
41	#11719270	—	2	1	no	—
42	#11719268	C₂²	1	1	yes	characteristic
43	#11719267	C₂²	1	2	yes	—
44	#11719265	—	2	2	no	—
45	#11719258	C₂²	1	1	yes	characteristic
46	#11719255	—	2	1	no	—
47	D₄×D₅₂	C₂²	1	1	yes	characteristic
48	#11719250	C₂²	1	2	yes	—
49	#11719248	C₂²	1	1	yes	characteristic
50	#11719239	—	2	1	no	—
51	#11719223	—	2	1	no	—
52	#11719219	C₂²	1	2	yes	—
53	#11719195	—	2	2	no	—
54	#11719184	C₂²	1	1	yes	characteristic
55	#11719182	C₂²	1	1	yes	characteristic
56	#11719175	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#483	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#483	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#476	C₂²	1	1	yes	characteristic
60	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#461	C₂²	1	1	yes	characteristic
62	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#450	C₂²	1	1	yes	characteristic
64	C₁₃×#450	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
67	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
70	#11718876	C₂²	1	2	yes	—
71	#11718835	C₂²	1	2	yes	complemented
72	#11718832	C₂²	1	2	yes	complemented
73	#11718830	C₂²	1	2	yes	—
74	#11718830	C₂²	1	2	yes	—
75	#11718825	C₂²	1	2	yes	—
76	#11718824	C₂²	1	2	yes	complemented
77	#11718824	C₂²	1	2	yes	complemented
78	SD₁₆×Dic₁₃	C₂²	1	2	yes	—
79	#11718748	C₂²	1	2	yes	complemented
80	#11718744	C₂²	1	2	yes	complemented
81	#11718710	C₂²	1	2	yes	complemented
82	#11718710	C₂²	1	2	yes	complemented
83	#11718688	C₂²	1	1	yes	characteristic, complemented
84	#11718688	C₂²	1	1	yes	characteristic, complemented
85	#11718682	C₂²	1	1	yes	characteristic, complemented
86	#11718682	C₂²	1	1	yes	characteristic, complemented
87	#11718670	C₂²	1	2	yes	—
88	#11718670	C₂²	1	2	yes	complemented
89	#11718669	C₂²	1	1	yes	characteristic
90	#11718669	C₂²	1	1	yes	characteristic, complemented
91	#11718668	C₂²	1	1	yes	characteristic
92	#11718668	C₂²	1	1	yes	characteristic, complemented
93	#11718625	C₂²	1	2	yes	complemented
94	#11718585	C₂²	1	1	yes	characteristic, complemented
95	#11718532	C₂²	1	2	yes	complemented
96	#11718531	C₂²	1	2	yes	complemented
97	#11718527	C₂²	1	2	yes	complemented
98	#11718524	C₂²	1	2	yes	complemented
99	#11718522	C₂²	1	2	yes	complemented
100	#11718521	C₂²	1	2	yes	complemented
101	#11718519	C₂²	1	2	yes	complemented
102	#11718517	C₂²	1	2	yes	complemented
103	#11718508	C₂²	1	2	yes	complemented
104	#11718508	C₂²	1	2	yes	complemented
105	#11718501	C₂²	1	2	yes	complemented
106	#11718500	C₂²	1	2	yes	complemented
107	#11718478	C₂²	1	2	yes	complemented
108	#11718476	C₂²	1	2	yes	complemented
109	#11718475	C₂²	1	2	yes	complemented
110	#11718473	C₂²	1	2	yes	complemented
111	#11718468	C₂²	1	2	yes	complemented
112	#11718460	C₂²	1	2	yes	complemented
113	#11718457	C₂²	1	2	yes	complemented
114	#11718449	C₂²	1	2	yes	complemented
115	#11718440	C₂²	1	2	yes	complemented
116	#11718435	C₂²	1	2	yes	complemented
117	#11718431	C₂²	1	2	yes	—
118	D₁₃×#102	C₂²	1	2	yes	—
119	#11718425	C₂²	1	2	yes	complemented
120	#11718424	C₂²	1	2	yes	—
121	#11718421	C₂²	1	2	yes	complemented
122	#11718420	C₂²	1	2	yes	—
123	#11718398	C₂²	1	2	yes	complemented
124	#11718398	C₂²	1	2	yes	complemented
125	#11718390	C₂²	1	2	yes	complemented
126	#11718389	C₂²	1	2	yes	complemented
127	#11718355	C₂²	1	1	yes	characteristic, complemented
128	#11718355	C₂²	1	1	yes	characteristic, complemented
129	#11718349	C₂²	1	1	yes	characteristic, complemented
130	C₈×D₅₂	C₂²	1	1	yes	characteristic, complemented
131	#11718343	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	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₂²⋊D₁₃	—	2	2	no	—
138	C₂×D₄×D₁₃	C₂³	1	2	yes	—
139	C₂×#6127	—	2	1	no	—
140	C₂×#6127	—	2	1	no	—
141	C₂²×D₅₂	—	2	1	no	—
142	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
146	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
147	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
148	C₁₃×#125	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	1	no	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
151	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	#88207	—	2	2	no	—
166	#88200	—	2	2	no	—
167	#88200	C₂³	1	2	yes	—
168	#88200	C₂³	1	2	yes	—
169	Q₈×Dic₁₃	C₂³	1	2	yes	—
170	Q₈×Dic₁₃	C₂³	1	2	yes	—
171	#88198	—	2	2	no	—
172	C₂×#6106	C₂³	1	2	yes	—
173	C₂×#6106	C₂³	1	2	yes	—
174	#88194	C₂³	1	2	yes	—
175	#88193	—	2	2	no	—
176	#88192	C₂³	1	2	yes	—
177	#88191	—	2	2	no	—
178	D₄×Dic₁₃	C₂³	1	2	yes	—
179	#88184	—	2	1	no	—
180	#88184	—	2	2	no	—
181	#88184	—	2	1	no	—
182	#88184	—	2	2	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	D₄	1	2	yes	—
189	C₄×C₂²⋊D₁₃	—	2	2	no	—
190	C₄×C₂²⋊D₁₃	—	2	2	no	—
191	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
192	C₂×#6103	—	2	2	no	—
193	#88180	—	2	1	no	—
194	#88180	C₂³	1	2	yes	—
195	C₂×C₄⋊Dic₁₃	—	2	1	no	—
196	#88178	—	2	1	no	—
197	#88178	—	2	1	no	—
198	#88178	—	2	1	no	—
199	#88178	D₄	1	1	yes	characteristic
200	C₂×#6099	C₂³	1	2	yes	—
201	C₂×#6094	C₂³	1	2	yes	—
202	C₂×C₈×D₁₃	C₂³	1	2	yes	—
203	#88152	—	2	2	no	—
204	#88152	—	2	2	no	—
205	#88152	—	2	2	no	—
206	#88152	—	2	2	no	—
207	#88152	—	2	2	no	—
208	#88150	—	2	2	no	—
209	#88150	—	2	2	no	—
210	#88149	C₂³	1	2	yes	—
211	#88148	—	2	2	no	—
212	#88147	C₂³	1	2	yes	—
213	#88146	—	2	2	no	—
214	#88146	C₂³	1	2	yes	—
215	#88146	C₂³	1	2	yes	—
216	C₄⋊C₄×D₁₃	C₂³	1	2	yes	—
217	#88144	—	2	2	no	—
218	#88144	C₂³	1	2	yes	—
219	#88144	C₂³	1	2	yes	—
220	#88143	—	2	2	no	—
221	#88143	—	2	2	no	—
222	#88143	—	2	2	no	—
223	#88143	—	2	2	no	—
224	#88142	—	2	2	no	—
225	#88142	C₂³	1	2	yes	—
226	#88141	—	2	2	no	—
227	#88139	—	2	2	no	—
228	#88139	—	2	2	no	—
229	#88138	—	2	2	no	—
230	#88138	—	2	2	no	—
231	#88137	—	2	2	no	—
232	#88137	—	2	2	no	—
233	#88136	—	2	2	no	—
234	#88135	—	2	2	no	—
235	C₂²⋊C₄×D₁₃	—	2	2	no	—
236	#88133	—	2	2	no	—
237	#88133	—	2	2	no	—
238	#88132	—	2	2	no	—
239	#88130	D₄	1	2	yes	—
240	#88129	—	2	1	no	—
241	#88129	—	2	1	no	—
242	#88129	D₄	1	1	yes	characteristic
243	#88128	C₂³	1	1	yes	characteristic
244	C₄×D₅₂	—	2	1	no	—
245	C₄×D₅₂	—	2	1	no	—
246	C₄×D₅₂	C₂³	1	1	yes	characteristic
247	C₄×D₅₂	C₂³	1	2	yes	—
248	#88126	C₂³	1	2	yes	—
249	#88124	—	2	1	no	—
250	#88124	D₄	1	1	yes	characteristic
251	#88124	C₂³	1	2	yes	—
252	#88123	—	2	1	no	—
253	#88123	—	2	1	no	—
254	#88123	C₂³	1	1	yes	characteristic
255	#88123	C₂³	1	1	yes	characteristic
256	#88123	C₂³	1	1	yes	characteristic
257	C₄×Dic₂₆	—	2	1	no	—
258	C₄×Dic₂₆	—	2	1	no	—
259	C₄×Dic₂₆	—	2	1	no	—
260	C₄×Dic₂₆	—	2	1	no	—
261	C₄×Dic₂₆	—	2	1	no	—
262	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
263	C₁₃×#106	C₂³	1	1	yes	characteristic
264	C₁₃×#106	C₂³	1	1	yes	characteristic
265	C₁₃×#106	C₂³	1	1	yes	characteristic
266	C₁₃×#106	C₂³	1	1	yes	characteristic
267	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₁₃×#103	C₂³	1	1	yes	characteristic
270	C₁₃×#103	C₂³	1	1	yes	characteristic
271	C₁₃×#103	C₂³	1	1	yes	characteristic
272	C₁₃×#103	C₂³	1	1	yes	characteristic
273	C₁₃×#102	C₂³	1	1	yes	characteristic
274	C₁₃×#102	C₂³	1	1	yes	characteristic
275	C₁₃×#102	C₂³	1	1	yes	characteristic
276	C₁₃×#102	C₂³	1	1	yes	characteristic
277	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
280	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
281	#88075	C₂³	1	2	yes	—
282	#88075	C₂³	1	2	yes	—
283	#88072	C₂³	1	2	yes	—
284	#88072	C₂³	1	2	yes	—
285	#88072	C₂³	1	2	yes	—
286	#88072	C₂³	1	2	yes	—
287	#88061	C₂³	1	2	yes	—
288	#88061	C₂³	1	2	yes	—
289	#88061	C₂³	1	2	yes	—
290	#88061	C₂³	1	2	yes	—
291	#88060	C₂³	1	2	yes	—
292	#88060	C₂³	1	2	yes	—
293	#88058	C₂³	1	2	yes	—
294	#88058	C₂³	1	2	yes	—
295	#88057	C₂³	1	2	yes	—
296	#88057	C₂³	1	2	yes	—
297	#88055	C₂³	1	2	yes	—
298	#88054	C₂³	1	2	yes	—
299	#88054	C₂³	1	2	yes	—
300	C₈×Dic₁₃	C₂³	1	2	yes	—
301	#88049	C₂³	1	2	yes	—
302	#88049	C₂³	1	2	yes	—
303	#88048	C₂³	1	2	yes	—
304	#88048	C₂³	1	2	yes	—
305	#88047	C₂³	1	2	yes	—
306	#88047	C₂³	1	2	yes	—
307	#88047	C₂³	1	2	yes	—
308	#88047	C₂³	1	2	yes	—
309	C₄⋊#1055	C₂³	1	1	yes	characteristic
310	C₄⋊#1055	C₂³	1	1	yes	characteristic
311	C₄⋊#1055	C₂³	1	2	yes	—
312	#62188	—	13	1	no	maximal, Sylow
313	C₂⁴×C₁₃	—	2	1	no	—
314	C₂³×D₁₃	—	2	2	no	—
315	C₂×Q₈×C₁₃	—	2	1	no	—
316	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
318	C₂×D₄×C₁₃	—	2	2	no	—
319	C₂×D₄×C₁₃	—	2	1	no	—
320	C₂×D₄×C₁₃	—	4	1	no	—
321	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₁₃	—	2	1	no	—
324	C₂²×C₄×C₁₃	—	2	1	no	—
325	C₂²×C₄×C₁₃	—	2	1	no	—
326	C₂²×C₄×C₁₃	—	2	1	no	—
327	C₂²×C₄×C₁₃	—	2	1	no	—
328	C₂²×C₄×C₁₃	—	8	2	no	—
329	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₂×C₂²⋊D₁₃	—	2	2	no	—
333	C₂×C₂²⋊D₁₃	—	2	2	no	—
334	C₂×C₂²⋊D₁₃	—	2	2	no	—
335	C₂×C₂²⋊D₁₃	—	2	2	no	—
336	C₂×C₂²⋊D₁₃	—	2	2	no	—
337	C₂×C₂²⋊D₁₃	—	8	4	no	—
338	C₂×C₂²⋊D₁₃	C₂×D₄	1	2	yes	—
339	C₂²×Dic₁₃	—	2	2	no	—
340	D₄×D₁₃	—	2	4	no	—
341	D₄×D₁₃	—	4	2	no	—
342	#6127	—	8	2	no	—
343	#6127	—	8	2	no	—
344	C₂×D₅₂	—	2	1	no	—
345	C₂×D₅₂	—	2	2	no	—
346	C₂×D₅₂	—	2	1	no	—
347	C₂×D₅₂	—	8	2	no	—
348	C₂×D₅₂	C₂×D₄	1	1	yes	characteristic
349	C₂×D₅₂	C₂⁴	1	2	yes	—
350	C₂×C₄×D₁₃	—	2	2	no	—
351	C₂×C₄×D₁₃	—	2	2	no	—
352	C₂×C₄×D₁₃	—	2	2	no	—
353	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
354	C₂×Dic₂₆	—	2	1	no	—
355	C₂×Dic₂₆	—	2	1	no	—
356	C₂×Dic₂₆	—	2	1	no	—
357	C₂×Dic₂₆	—	2	2	no	—
358	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
359	C₁₃×SD₁₆	—	2	2	no	—
360	C₁₃×SD₁₆	—	2	2	no	—
361	C₁₃×SD₁₆	—	4	1	no	—
362	C₁₃×SD₁₆	—	4	1	no	—
363	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₁₃×C₄⋊C₄	—	2	1	no	—
368	C₁₃×C₄⋊C₄	—	2	1	no	—
369	C₁₃×C₄⋊C₄	—	2	1	no	—
370	C₁₃×C₄⋊C₄	—	2	1	no	—
371	C₁₃×C₄⋊C₄	—	2	1	no	—
372	C₁₃×C₄⋊C₄	—	2	1	no	—
373	C₁₃×C₄⋊C₄	—	2	1	no	—
374	C₁₃×C₄⋊C₄	—	2	1	no	—
375	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
376	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
377	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
378	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
379	C₁₃×C₂²⋊C₄	—	2	1	no	—
380	C₁₃×C₂²⋊C₄	—	2	1	no	—
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	C₄²×C₁₃	—	2	1	no	—
386	C₄²×C₁₃	—	2	1	no	—
387	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
391	C₂²⋊Dic₁₃	—	2	2	no	—
392	C₂²⋊Dic₁₃	—	2	2	no	—
393	C₂²⋊Dic₁₃	—	2	2	no	—
394	C₂²⋊Dic₁₃	C₂×D₄	1	2	yes	—
395	#6106	—	4	2	no	—
396	#6106	—	4	2	no	—
397	#6103	—	2	2	no	—
398	#6103	—	2	2	no	—
399	#6103	—	2	2	no	—
400	#6103	—	2	2	no	—
401	#6103	—	2	2	no	—
402	#6103	—	2	2	no	—
403	#6103	—	2	2	no	—
404	#6103	—	2	2	no	—
405	#6103	C₂×D₄	1	2	yes	—
406	#6103	C₂×D₄	1	2	yes	—
407	#6103	C₂×D₄	1	2	yes	—
408	#6103	C₂×D₄	1	2	yes	—
409	C₄⋊Dic₁₃	—	2	1	no	—
410	C₄⋊Dic₁₃	—	2	1	no	—
411	C₄⋊Dic₁₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
417	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
418	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
419	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
420	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
428	#6101	—	2	2	no	—
429	#6101	C₂×D₄	1	2	yes	—
430	#6101	C₂×D₄	1	2	yes	—
431	#6101	C₂×D₄	1	2	yes	—
432	#6101	C₂×D₄	1	2	yes	—
433	C₄×Dic₁₃	—	2	2	no	—
434	C₄×Dic₁₃	—	2	2	no	—
435	C₄×Dic₁₃	—	2	2	no	—
436	C₄×Dic₁₃	—	2	2	no	—
437	C₄×Dic₁₃	—	2	2	no	—
438	C₄×Dic₁₃	C₂⁴	1	2	yes	—
439	#6099	—	4	2	no	—
440	C₂×#1055	C₂⁴	1	2	yes	—
441	C₂×#1055	C₂⁴	1	2	yes	—
442	#6094	—	4	2	no	—
443	C₈×D₁₃	—	4	2	no	—
444	#3555	—	13	1	no	—
445	#3519	—	13	1	no	—
446	#3385	—	13	1	no	—
447	#3381	—	13	1	no	—
448	#3368	—	13	1	no	—
449	#3362	—	13	1	no	—
450	#3357	—	13	1	no	—
451	#3351	—	13	2	no	—
452	#3350	—	13	2	no	—
453	#3340	—	13	1	no	—
454	#3324	—	13	2	no	—
455	#3324	—	13	1	no	—
456	#3310	—	13	2	no	—
457	#3295	—	13	1	no	—
458	#3260	—	13	2	no	—
459	#3254	—	13	1	no	—
460	#3241	—	13	2	no	—
461	#3228	—	13	1	no	—
462	#3123	—	13	2	no	—
463	#3101	D₁₃	1	1	yes	characteristic, complemented
464	#3081	—	13	2	no	—
465	#3077	—	13	1	no	—
466	#2993	—	13	1	no	—
467	C₂³×C₁₃	—	2	1	no	—
468	C₂³×C₁₃	—	2	1	no	—
469	C₂³×C₁₃	—	4	2	no	—
470	C₂³×C₁₃	—	4	2	no	—
471	C₂³×C₁₃	—	8	1	no	—
472	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
473	C₂²×D₁₃	—	2	2	no	—
474	C₂²×D₁₃	—	4	4	no	—
475	C₂²×D₁₃	—	8	2	no	—
476	C₂²×D₁₃	—	8	2	no	—
477	C₂²×D₁₃	C₂²×D₄	1	2	yes	—
478	Q₈×C₁₃	—	2	1	no	—
479	Q₈×C₁₃	—	2	1	no	—
480	Q₈×C₁₃	—	2	1	no	—
481	Q₈×C₁₃	—	2	1	no	—
482	Q₈×C₁₃	—	8	1	no	—
483	D₄×C₁₃	—	2	1	no	—
484	D₄×C₁₃	—	2	1	no	—
485	D₄×C₁₃	—	2	1	no	—
486	D₄×C₁₃	—	4	2	no	—
487	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
488	C₂×C₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	1	no	—
490	C₂×C₄×C₁₃	—	2	1	no	—
491	C₂×C₄×C₁₃	—	2	1	no	—
492	C₂×C₄×C₁₃	—	2	1	no	—
493	C₂×C₄×C₁₃	—	2	1	no	—
494	C₂×C₄×C₁₃	—	2	1	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	1	no	—
497	C₂×C₄×C₁₃	—	4	1	no	—
498	C₂×C₄×C₁₃	—	4	2	no	—
499	C₂×C₄×C₁₃	—	4	2	no	—
500	C₂×C₄×C₁₃	—	8	1	no	—
501	C₂×C₄×C₁₃	—	8	1	no	—
502	C₂×C₄×C₁₃	—	8	1	no	—
503	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
509	C₂²⋊D₁₃	—	4	2	no	—
510	C₂²⋊D₁₃	—	4	4	no	—
511	C₂²⋊D₁₃	—	4	4	no	—
512	C₂²⋊D₁₃	—	8	2	no	—
513	C₂²⋊D₁₃	—	8	2	no	—
514	C₂²⋊D₁₃	—	8	2	no	—
515	C₂×Dic₁₃	—	2	2	no	—
516	C₂×Dic₁₃	—	2	2	no	—
517	C₂×Dic₁₃	—	2	2	no	—
518	C₂×Dic₁₃	—	8	2	no	—
519	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
520	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
521	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
522	D₅₂	—	2	2	no	—
523	D₅₂	—	2	2	no	—
524	D₅₂	—	2	2	no	—
525	D₅₂	—	4	2	no	—
526	D₅₂	—	8	1	no	—
527	D₅₂	—	8	2	no	—
528	C₄×D₁₃	—	2	2	no	—
529	C₄×D₁₃	—	2	2	no	—
530	C₄×D₁₃	—	8	2	no	—
531	C₄×D₁₃	—	8	2	no	—
532	C₄×D₁₃	—	8	2	no	—
533	Dic₂₆	—	2	2	no	—
534	Dic₂₆	—	4	2	no	—
535	Dic₂₆	—	8	2	no	—
536	Dic₂₆	—	8	1	no	—
537	Dic₂₆	—	8	1	no	—
538	C₈×C₁₃	—	2	1	no	—
539	C₈×C₁₃	—	2	1	no	—
540	C₈×C₁₃	—	2	1	no	—
541	C₈×C₁₃	—	2	1	no	—
542	#1055	—	2	2	no	—
543	#1055	—	2	2	no	—
544	#563	—	26	2	no	—
545	Q₈²	—	13	1	no	—
546	#557	—	13	1	no	—
547	#557	—	26	1	no	—
548	#556	—	13	2	no	—
549	#556	—	13	1	no	—
550	#556	—	26	1	no	—
551	#555	—	13	1	no	—
552	#554	—	13	1	no	—
553	#554	—	13	1	no	—
554	#553	—	13	2	no	—
555	#553	—	26	1	no	—
556	#552	—	13	2	no	—
557	#550	—	13	1	no	—
558	#546	—	26	2	no	—
559	#546	—	26	1	no	—
560	D₄²	—	13	2	no	—
561	D₄²	—	13	1	no	—
562	#544	—	13	2	no	—
563	#542	—	26	1	no	—
564	#541	—	13	2	no	—
565	#541	—	26	1	no	—
566	#541	—	26	2	no	—
567	#540	—	13	2	no	—
568	#538	—	26	2	no	—
569	#533	—	13	1	no	—
570	#533	C₂×D₁₃	1	1	yes	characteristic, complemented
571	#532	—	13	1	no	—
572	#529	—	13	1	no	—
573	#525	—	26	1	no	—
574	C₂×#121	—	26	1	no	—
575	#518	—	13	2	no	—
576	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
577	#501	—	13	2	no	—
578	#500	—	13	1	no	—
579	#499	—	13	2	no	—
580	#498	—	13	1	no	—
581	#490	—	13	2	no	—
582	#486	—	13	2	no	—
583	#486	—	13	1	no	—
584	#486	—	13	1	no	—
585	#485	—	13	2	no	—
586	#485	—	13	2	no	—
587	#483	C₂×D₁₃	1	1	yes	characteristic, complemented
588	#483	C₂×D₁₃	1	1	yes	characteristic, complemented
589	#482	—	13	2	no	—
590	#482	—	13	2	no	—
591	#482	—	13	2	no	—
592	#482	—	13	2	no	—
593	#481	—	13	2	no	—
594	#480	—	13	2	no	—
595	#479	—	13	2	no	—
596	#479	—	13	2	no	—
597	#478	—	13	2	no	—
598	#478	—	13	2	no	—
599	#478	—	13	2	no	—
600	#478	—	13	2	no	—
601	#478	—	13	2	no	—
602	#478	—	13	2	no	—
603	#477	—	13	1	no	—
604	#477	—	13	1	no	—
605	#476	—	13	1	no	—
606	#476	—	13	1	no	—
607	#476	—	13	2	no	—
608	#476	C₂×D₁₃	1	1	yes	characteristic
609	#476	C₂×D₁₃	1	1	yes	characteristic, complemented
610	#474	—	13	2	no	—
611	#474	—	13	1	no	—
612	#474	—	13	1	no	—
613	#474	—	13	2	no	—
614	#468	—	13	2	no	—
615	#468	—	13	2	no	—
616	#468	—	13	2	no	—
617	#468	—	13	2	no	—
618	#465	—	13	2	no	—
619	#465	—	13	2	no	—
620	#461	—	13	2	no	—
621	#461	C₂×D₁₃	1	1	yes	characteristic
622	#461	C₂×D₁₃	1	1	yes	characteristic, complemented
623	#460	—	13	2	no	—
624	#460	—	13	2	no	—
625	#460	—	13	1	no	—
626	#460	—	13	1	no	—
627	#450	—	13	2	no	—
628	#450	—	13	2	no	—
629	#450	C₂×D₁₃	1	1	yes	characteristic
630	#450	C₂×D₁₃	1	1	yes	characteristic
631	#446	—	13	1	no	—
632	C₈×Q₈	—	13	1	no	—
633	#440	—	13	2	no	—
634	#440	—	13	2	no	—
635	C₄×SD₁₆	—	13	2	no	—
636	C₄×SD₁₆	—	13	2	no	—
637	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
638	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
639	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
640	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
641	#436	—	13	2	no	—
642	#436	—	13	1	no	—
643	#435	—	13	2	no	—
644	C₈×D₄	—	13	1	no	—
645	#433	—	13	2	no	—
646	#431	C₂×D₁₃	1	1	yes	characteristic, complemented
647	#428	—	13	2	no	—
648	#428	—	13	2	no	—
649	#427	—	13	2	no	—
650	#424	—	13	2	no	—
651	#423	—	13	1	no	—
652	#418	—	13	2	no	—
653	#418	—	13	2	no	—
654	C₂×#102	—	13	2	no	—
655	C₂²×C₁₃	—	2	1	no	—
656	C₂²×C₁₃	—	2	2	no	—
657	C₂²×C₁₃	—	2	1	no	—
658	C₂²×C₁₃	—	2	1	no	—
659	C₂²×C₁₃	—	4	1	no	—
660	C₂²×C₁₃	—	4	1	no	—
661	C₂²×C₁₃	—	4	1	no	—
662	C₂²×C₁₃	—	4	1	no	—
663	C₂²×C₁₃	—	4	1	no	—
664	C₂²×C₁₃	—	8	4	no	—
665	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
666	C₂×D₁₃	—	2	2	no	—
667	C₂×D₁₃	—	2	2	no	—
668	C₂×D₁₃	—	2	2	no	—
669	C₂×D₁₃	—	4	2	no	—
670	C₂×D₁₃	—	4	2	no	—
671	C₂×D₁₃	—	4	2	no	—
672	C₂×D₁₃	—	16	4	no	—
673	C₄×C₁₃	—	2	1	no	—
674	C₄×C₁₃	—	2	1	no	—
675	C₄×C₁₃	—	2	1	no	—
676	C₄×C₁₃	—	2	1	no	—
677	C₄×C₁₃	—	4	1	no	—
678	C₄×C₁₃	—	4	1	no	—
679	C₄×C₁₃	—	4	1	no	—
680	C₄×C₁₃	—	4	1	no	—
681	C₄×C₁₃	—	4	1	no	—
682	C₄×C₁₃	—	4	1	no	—
683	C₄×C₁₃	#577	1	2	yes	—
684	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
685	C₄×C₁₃	#585	1	1	yes	characteristic
686	Dic₁₃	—	2	2	no	—
687	Dic₁₃	—	2	2	no	—
688	Dic₁₃	—	2	2	no	—
689	Dic₁₃	—	4	2	no	—
690	Dic₁₃	—	4	2	no	—
691	Dic₁₃	—	4	2	no	—
692	C₂×#41	—	26	1	no	—
693	C₂×#41	—	26	1	no	—
694	C₂²×D₄	—	13	2	no	—
695	C₂²×D₄	—	26	1	no	—
696	C₂²×D₄	—	26	2	no	—
697	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
698	C₂³×C₄	—	2	1	no	—
699	C₂×SD₁₆	—	13	2	no	—
700	C₂×SD₁₆	—	13	2	no	—
701	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
702	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
703	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
704	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
705	C₂×M₁₆	—	13	2	no	—
706	C₂×M₁₆	—	13	2	no	—
707	C₂²×C₈	—	13	2	no	—
708	C₄⋊Q₈	—	13	2	no	—
709	C₄⋊Q₈	—	13	1	no	—
710	C₄⋊Q₈	—	13	1	no	—
711	C₄⋊Q₈	—	13	1	no	—
712	C₄⋊Q₈	—	26	1	no	—
713	C₄⋊Q₈	—	26	1	no	—
714	C₄⋊Q₈	—	26	2	no	—
715	C₄⋊Q₈	—	26	2	no	—
716	C₄⋊Q₈	C₂²×D₁₃	1	1	yes	characteristic
717	C₄⋊Q₈	C₂²×D₁₃	1	1	yes	characteristic
718	#127	—	13	2	no	—
719	#127	—	13	1	no	—
720	#126	—	13	2	no	—
721	#126	—	26	2	no	—
722	#126	—	26	2	no	—
723	#126	—	26	2	no	—
724	#126	—	26	2	no	—
725	#126	—	26	2	no	—
726	#126	—	26	2	no	—
727	#126	—	26	2	no	—
728	#125	—	2	1	no	—
729	#125	—	13	2	no	—
730	#125	—	13	2	no	—
731	#125	—	13	1	no	—
732	#125	—	13	2	no	—
733	#125	—	26	1	no	—
734	#125	—	26	2	no	—
735	#125	—	26	2	no	—
736	#125	—	26	2	no	—
737	#125	—	26	2	no	—
738	#125	—	26	2	no	—
739	#124	—	13	1	no	—
740	#124	—	26	1	no	—
741	#124	—	26	2	no	—
742	#124	—	26	2	no	—
743	#124	—	26	1	no	—
744	#123	—	13	2	no	—
745	#123	—	26	2	no	—
746	#123	—	26	2	no	—
747	#123	—	26	2	no	—
748	#123	—	26	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	13	1	no	—
751	C₂²⋊Q₈	—	13	2	no	—
752	C₂²⋊Q₈	—	13	2	no	—
753	C₂²⋊Q₈	—	26	2	no	—
754	C₂²⋊Q₈	—	26	2	no	—
755	C₂²⋊Q₈	—	26	2	no	—
756	C₂²⋊Q₈	—	26	2	no	—
757	C₂²⋊Q₈	—	26	1	no	—
758	C₂²⋊Q₈	—	26	1	no	—
759	C₂²⋊Q₈	—	26	1	no	—
760	C₂²⋊Q₈	C₂²×D₁₃	1	1	yes	characteristic
761	C₂²⋊Q₈	C₂²×D₁₃	1	1	yes	characteristic
762	#121	—	13	1	no	—
763	#121	—	13	2	no	—
764	#121	—	13	2	no	—
765	#121	—	13	2	no	—
766	#121	—	26	2	no	—
767	#121	—	26	2	no	—
768	#121	—	26	2	no	—
769	#121	—	26	1	no	—
770	#121	—	26	1	no	—
771	#121	—	26	2	no	—
772	#121	—	26	2	no	—
773	#121	—	26	1	no	—
774	#121	—	26	1	no	—
775	#120	—	26	2	no	—
776	#120	—	26	2	no	—
777	#120	—	26	2	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	13	1	no	—
780	C₄×Q₈	—	13	2	no	—
781	C₄×Q₈	—	13	2	no	—
782	C₄×Q₈	—	26	1	no	—
783	C₄×Q₈	—	26	1	no	—
784	C₄×Q₈	—	26	1	no	—
785	C₄×Q₈	—	26	2	no	—
786	C₄×Q₈	—	26	1	no	—
787	C₄×Q₈	—	26	1	no	—
788	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
789	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	13	2	no	—
793	C₄×D₄	—	13	2	no	—
794	C₄×D₄	—	13	2	no	—
795	C₄×D₄	—	13	1	no	—
796	C₄×D₄	—	13	2	no	—
797	C₄×D₄	—	26	1	no	—
798	C₄×D₄	—	26	2	no	—
799	C₄×D₄	—	26	2	no	—
800	C₄×D₄	—	26	2	no	—
801	C₄×D₄	—	26	1	no	—
802	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
803	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
804	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
805	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
806	#117	—	2	1	no	—
807	#117	—	13	2	no	—
808	#117	—	13	2	no	—
809	#117	—	13	2	no	—
810	#117	—	13	2	no	—
811	#117	—	26	2	no	—
812	#117	—	26	1	no	—
813	C₂×C₄⋊C₄	—	13	2	no	—
814	C₂×C₄⋊C₄	—	26	1	no	—
815	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	—	2	1	no	—
817	C₂×C₂²⋊C₄	—	26	2	no	—
818	C₂×C₂²⋊C₄	—	26	2	no	—
819	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
820	#107	—	13	2	no	—
821	#107	—	13	2	no	—
822	#107	—	13	2	no	—
823	#107	—	13	2	no	—
824	#107	—	13	2	no	—
825	#107	—	13	2	no	—
826	#106	—	13	2	no	—
827	#106	—	13	2	no	—
828	#106	—	13	2	no	—
829	#106	—	13	2	no	—
830	#106	C₂²×D₁₃	1	1	yes	characteristic
831	#106	C₂²×D₁₃	1	1	yes	characteristic
832	#106	C₂²×D₁₃	1	1	yes	characteristic
833	#106	C₂²×D₁₃	1	1	yes	characteristic
834	C₄⋊C₈	—	13	2	no	—
835	C₄⋊C₈	—	13	2	no	—
836	C₄⋊C₈	—	13	2	no	—
837	C₄⋊C₈	—	13	1	no	—
838	C₄⋊C₈	—	13	1	no	—
839	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
840	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
841	#103	—	13	2	no	—
842	#103	—	13	2	no	—
843	#103	C₂²×D₁₃	1	1	yes	characteristic
844	#103	C₂²×D₁₃	1	1	yes	characteristic
845	#103	C₂²×D₁₃	1	1	yes	characteristic
846	#103	C₂²×D₁₃	1	1	yes	characteristic
847	#102	—	13	2	no	—
848	#102	—	13	2	no	—
849	#102	—	13	2	no	—
850	#102	—	13	2	no	—
851	#102	—	13	2	no	—
852	#102	—	13	2	no	—
853	#102	—	13	2	no	—
854	#102	—	13	2	no	—
855	#102	—	13	2	no	—
856	#102	—	13	2	no	—
857	#102	C₂²×D₁₃	1	1	yes	characteristic
858	#102	C₂²×D₁₃	1	1	yes	characteristic
859	#102	C₂²×D₁₃	1	1	yes	characteristic
860	#102	C₂²×D₁₃	1	1	yes	characteristic
861	C₂²⋊C₈	—	13	2	no	—
862	C₂²⋊C₈	—	13	2	no	—
863	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
864	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
865	#97	—	13	2	no	—
866	C₄×C₈	—	13	2	no	—
867	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
868	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
869	C₂×C₁₃	—	4	2	no	—
870	C₂×C₁₃	—	4	1	no	—
871	C₂×C₁₃	—	8	1	no	—
872	C₂×C₁₃	#3489	1	1	yes	characteristic
873	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
874	C₂×C₁₃	#3585	1	1	yes	characteristic
875	D₁₃	—	4	2	no	—
876	D₁₃	—	8	2	no	—
877	C₂⁴	—	2	1	no	—
878	C₂⁴	—	26	2	no	—
879	#41	—	104	2	no	—
880	#41	—	104	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	13	1	no	—
883	C₂×Q₈	—	26	2	no	—
884	C₂×Q₈	—	26	1	no	—
885	C₂×Q₈	—	26	1	no	—
886	C₂×Q₈	—	26	1	no	—
887	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
888	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	4	1	no	—
892	C₂×D₄	—	13	2	no	—
893	C₂×D₄	—	13	1	no	—
894	C₂×D₄	—	13	2	no	—
895	C₂×D₄	—	26	2	no	—
896	C₂×D₄	—	26	2	no	—
897	C₂×D₄	—	26	2	no	—
898	C₂×D₄	—	26	2	no	—
899	C₂×D₄	—	26	4	no	—
900	C₂×D₄	—	26	2	no	—
901	C₂×D₄	—	26	2	no	—
902	C₂×D₄	—	26	1	no	—
903	C₂×D₄	—	26	1	no	—
904	C₂×D₄	—	52	2	no	—
905	C₂×D₄	—	104	2	no	—
906	C₂×D₄	—	104	4	no	—
907	C₂×D₄	C₂³×D₁₃	1	1	yes	characteristic
908	C₂×D₄	C₂³×D₁₃	1	1	yes	characteristic
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	8	2	no	—
915	C₂²×C₄	—	13	2	no	—
916	C₂²×C₄	—	26	2	no	—
917	C₂²×C₄	—	26	2	no	—
918	C₂²×C₄	—	26	2	no	—
919	C₂²×C₄	—	26	2	no	—
920	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
921	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
922	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
923	SD₁₆	—	2	2	no	—
924	SD₁₆	—	2	2	no	—
925	SD₁₆	—	4	1	no	—
926	SD₁₆	—	4	1	no	—
927	SD₁₆	—	52	2	no	—
928	SD₁₆	—	52	2	no	—
929	M₁₆	—	52	2	no	—
930	M₁₆	—	52	2	no	—
931	C₂×C₈	—	13	2	no	—
932	C₂×C₈	—	13	2	no	—
933	C₂×C₈	—	52	2	no	—
934	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
935	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
936	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
937	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	13	1	no	—
947	C₄⋊C₄	—	13	2	no	—
948	C₄⋊C₄	—	13	2	no	—
949	C₄⋊C₄	—	13	1	no	—
950	C₄⋊C₄	—	13	2	no	—
951	C₄⋊C₄	—	13	2	no	—
952	C₄⋊C₄	—	13	2	no	—
953	C₄⋊C₄	—	13	2	no	—
954	C₄⋊C₄	—	13	2	no	—
955	C₄⋊C₄	—	26	2	no	—
956	C₄⋊C₄	—	26	2	no	—
957	C₄⋊C₄	—	26	2	no	—
958	C₄⋊C₄	—	26	2	no	—
959	C₄⋊C₄	—	26	2	no	—
960	C₄⋊C₄	—	26	2	no	—
961	C₄⋊C₄	—	26	2	no	—
962	C₄⋊C₄	—	26	2	no	—
963	C₄⋊C₄	—	26	2	no	—
964	C₄⋊C₄	—	26	2	no	—
965	C₄⋊C₄	—	26	1	no	—
966	C₄⋊C₄	—	26	1	no	—
967	C₄⋊C₄	—	26	2	no	—
968	C₄⋊C₄	—	26	2	no	—
969	C₄⋊C₄	—	26	1	no	—
970	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	13	2	no	—
981	C₂²⋊C₄	—	13	2	no	—
982	C₂²⋊C₄	—	13	2	no	—
983	C₂²⋊C₄	—	13	2	no	—
984	C₂²⋊C₄	—	13	2	no	—
985	C₂²⋊C₄	—	26	2	no	—
986	C₂²⋊C₄	—	26	2	no	—
987	C₂²⋊C₄	—	26	2	no	—
988	C₂²⋊C₄	—	26	2	no	—
989	C₂²⋊C₄	—	26	2	no	—
990	C₂²⋊C₄	—	26	2	no	—
991	C₂²⋊C₄	—	26	2	no	—
992	C₂²⋊C₄	—	26	2	no	—
993	C₂²⋊C₄	—	26	2	no	—
994	C₂²⋊C₄	—	26	2	no	—
995	C₂²⋊C₄	—	26	2	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	13	2	no	—
999	C₄²	—	26	2	no	—
1000	C₄²	—	26	2	no	—
1001	C₄²	—	26	2	no	—
1002	C₄²	—	26	2	no	—
1003	C₄²	—	26	2	no	—
1004	C₄²	D₄×D₁₃	1	1	yes	characteristic
1005	C₄²	D₄×D₁₃	1	1	yes	characteristic
1006	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1007	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1008	C₁₃	#62188	1	1	yes	characteristic, complemented, Sylow
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	4	2	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	8	1	no	—
1014	C₂³	—	13	2	no	—
1015	C₂³	—	26	2	no	—
1016	C₂³	—	52	4	no	—
1017	C₂³	—	104	2	no	—
1018	C₂³	—	104	2	no	—
1019	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	8	1	no	—
1025	Q₈	—	26	2	no	—
1026	Q₈	—	52	2	no	—
1027	Q₈	—	104	1	no	—
1028	Q₈	—	104	1	no	—
1029	Q₈	—	104	2	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	26	2	no	—
1035	D₄	—	26	2	no	—
1036	D₄	—	26	2	no	—
1037	D₄	—	52	2	no	—
1038	D₄	—	52	4	no	—
1039	D₄	—	52	4	no	—
1040	D₄	—	52	2	no	—
1041	D₄	—	104	1	no	—
1042	D₄	—	104	2	no	—
1043	D₄	—	104	2	no	—
1044	D₄	—	104	2	no	—
1045	D₄	—	104	2	no	—
1046	D₄	#88257	1	2	yes	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	—	13	2	no	—
1063	C₂×C₄	—	13	2	no	—
1064	C₂×C₄	—	13	2	no	—
1065	C₂×C₄	—	26	2	no	—
1066	C₂×C₄	—	26	2	no	—
1067	C₂×C₄	—	26	2	no	—
1068	C₂×C₄	—	26	2	no	—
1069	C₂×C₄	—	26	2	no	—
1070	C₂×C₄	—	104	2	no	—
1071	C₂×C₄	—	104	2	no	—
1072	C₂×C₄	—	104	2	no	—
1073	C₂×C₄	—	104	2	no	—
1074	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1075	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1076	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1077	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1078	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
1079	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1080	C₈	—	2	1	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	26	2	no	—
1085	C₈	—	26	2	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	8	4	no	—
1096	C₂²	—	26	2	no	—
1097	C₂²	—	26	2	no	—
1098	C₂²	—	26	2	no	—
1099	C₂²	—	52	2	no	—
1100	C₂²	—	52	2	no	—
1101	C₂²	—	52	2	no	—
1102	C₂²	—	208	4	no	—
1103	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	26	2	no	—
1115	C₄	—	26	2	no	—
1116	C₄	—	26	2	no	—
1117	C₄	—	52	2	no	—
1118	C₄	—	52	2	no	—
1119	C₄	—	52	2	no	—
1120	C₄	#11719467	1	2	yes	—
1121	C₄	C₂×#88257	1	1	yes	characteristic
1122	C₄	#11719648	1	1	yes	characteristic
1123	C₂	—	4	1	no	—
1124	C₂	—	4	2	no	—
1125	C₂	—	8	1	no	—
1126	C₂	—	52	2	no	—
1127	C₂	—	104	2	no	—
1128	C₂	#13128508	1	1	yes	characteristic
1129	C₂	C₂×#11719467	1	1	yes	characteristic
1130	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×#3101	C₂
socle	C₂²×C₁₃	C₂³×D₄
prime radical	#13128868	C₂
hypercenter	#3101	D₁₃
hypocenter	C₁₃	#62188
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3101

Complements

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

N	H ≅ G/N	type
1. #13129324	C₂	semidirect
3. #13127744	C₂	semidirect
4. #13127709	C₂	semidirect
5. #13127563	C₂	semidirect
6. #13127505	C₂	semidirect
7. #13127464	C₂	semidirect
8. #13127399	C₂	semidirect
9. #13127384	C₂	semidirect
10. #13127251	C₂	semidirect
11. #13127069	C₂	semidirect
12. #13127060	C₂	semidirect
13. #13126850	C₂	semidirect
14. #13126662	C₂	semidirect
15. #13126279	C₂	semidirect
16. #13126219	C₂	semidirect
17. #13126088	C₂	semidirect
18. #13125974	C₂	semidirect
19. #13125086	C₂	semidirect
20. #13124662	C₂	semidirect
21. #13124633	C₂	semidirect
22. #13123987	C₂	semidirect
23. C₁₃×#3101	C₂	semidirect
24. C₁₃×#533	C₂²	semidirect
29. #11719436	C₂²	semidirect
30. #11719434	C₂²	semidirect
33. #11719346	C₂²	semidirect
34. #11719344	C₂²	semidirect
36. #11719289	C₂²	semidirect
37. #11719284	C₂²	semidirect
38. #11719275	C₂²	semidirect
40. Q₈×Dic₂₆	C₂²	semidirect
56. #11719175	C₂²	semidirect
57. C₁₃×#483	C₂²	semidirect
58. C₁₃×#483	C₂²	semidirect
60. C₁₃×#476	C₂²	semidirect
62. C₁₃×#461	C₂²	semidirect
67. C₄×C₁₃×SD₁₆	C₂²	semidirect
68. C₄×C₁₃×SD₁₆	C₂²	semidirect
69. C₁₃×#431	C₂²	semidirect
71. #11718835	C₂²	semidirect
72. #11718832	C₂²	semidirect
76. #11718824	C₂²	semidirect
77. #11718824	C₂²	semidirect
79. #11718748	C₂²	semidirect
80. #11718744	C₂²	semidirect
81. #11718710	C₂²	semidirect
82. #11718710	C₂²	semidirect
83. #11718688	C₂²	semidirect
84. #11718688	C₂²	semidirect
85. #11718682	C₂²	semidirect
86. #11718682	C₂²	semidirect
88. #11718670	C₂²	semidirect
90. #11718669	C₂²	semidirect
92. #11718668	C₂²	semidirect
93. #11718625	C₂²	semidirect
94. #11718585	C₂²	semidirect
95. #11718532	C₂²	semidirect
96. #11718531	C₂²	semidirect
97. #11718527	C₂²	semidirect
98. #11718524	C₂²	semidirect
99. #11718522	C₂²	semidirect
100. #11718521	C₂²	semidirect
101. #11718519	C₂²	semidirect
102. #11718517	C₂²	semidirect
103. #11718508	C₂²	semidirect
104. #11718508	C₂²	semidirect
105. #11718501	C₂²	semidirect
106. #11718500	C₂²	semidirect
107. #11718478	C₂²	semidirect
108. #11718476	C₂²	semidirect
109. #11718475	C₂²	semidirect
110. #11718473	C₂²	semidirect
111. #11718468	C₂²	semidirect
112. #11718460	C₂²	semidirect
113. #11718457	C₂²	semidirect
114. #11718449	C₂²	semidirect
115. #11718440	C₂²	semidirect
116. #11718435	C₂²	semidirect
119. #11718425	C₂²	semidirect
121. #11718421	C₂²	semidirect
123. #11718398	C₂²	semidirect
124. #11718398	C₂²	semidirect
125. #11718390	C₂²	semidirect
126. #11718389	C₂²	semidirect
127. #11718355	C₂²	semidirect
128. #11718355	C₂²	semidirect
129. #11718349	C₂²	semidirect
130. C₈×D₅₂	C₂²	semidirect
131. #11718343	C₂²	semidirect
132. #11718341	C₂²	semidirect
133. #11718340	C₂²	semidirect
134. C₈×Dic₂₆	C₂²	semidirect
463. #3101	D₁₃	semidirect
570. #533	C₂×D₁₃	semidirect
587. #483	C₂×D₁₃	semidirect
588. #483	C₂×D₁₃	semidirect
609. #476	C₂×D₁₃	semidirect
622. #461	C₂×D₁₃	semidirect
639. C₄×SD₁₆	C₂×D₁₃	semidirect
640. C₄×SD₁₆	C₂×D₁₃	semidirect
646. #431	C₂×D₁₃	semidirect
1008. C₁₃	#62188	semidirect

Maximal subgroups

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

subgroup	index
#13129324	2
#13128868	2
#13127744	2
#13127709	2
#13127563	2
#13127505	2
#13127464	2
#13127399	2
#13127384	2
#13127251	2
#13127069	2
#13127060	2
#13126850	2
#13126662	2
#13126279	2
#13126219	2
#13126088	2
#13125974	2
#13125086	2
#13124662	2
#13124633	2
#13123987	2
C₁₃×#3101	2
#62188	13