Subgroups — #16744892

Order 3328.

1888 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128446	C₂	1	1	yes	maximal, characteristic
2	Q₈×#6127	C₂	1	1	yes	maximal, characteristic, complemented
3	#13127887	C₂	1	1	yes	maximal, characteristic, complemented
4	#13127744	C₂	1	1	yes	maximal, characteristic, complemented
5	#13127648	C₂	1	1	yes	maximal, characteristic, complemented
6	#13127615	C₂	1	1	yes	maximal, characteristic, complemented
7	#13127322	C₂	1	2	yes	maximal, complemented
8	#13127230	C₂	1	1	yes	maximal, characteristic, complemented
9	#13127008	C₂	1	2	yes	maximal, complemented
10	#13126918	C₂	1	2	yes	maximal, complemented
11	#13126714	C₂	1	1	yes	maximal, characteristic, complemented
12	#13126662	C₂	1	1	yes	maximal, characteristic, complemented
13	SD₁₆×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
14	#13126340	C₂	1	2	yes	maximal, complemented
15	#13125554	C₂	1	1	yes	maximal, characteristic, complemented
16	#13125543	C₂	1	2	yes	maximal, complemented
17	#13125011	C₂	1	2	yes	maximal, complemented
18	#13124998	C₂	1	1	yes	maximal, characteristic, complemented
19	#13124958	C₂	1	1	yes	maximal, characteristic, complemented
20	#13124933	C₂	1	2	yes	maximal, complemented
21	#13123851	C₂	1	1	yes	maximal, characteristic, complemented
22	D₁₃×#440	C₂	1	2	yes	maximal, complemented
23	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	#11719534	C₂²	1	2	yes	—
28	Q₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
29	C₂×SD₁₆×D₁₃	C₂²	1	2	yes	—
30	#11719290	C₂²	1	1	yes	characteristic
31	#11719285	C₂²	1	2	yes	—
32	#11719284	—	2	1	no	—
33	#11719284	C₂²	1	1	yes	characteristic
34	#11719284	C₂²	1	1	yes	characteristic
35	#11719283	—	2	2	no	—
36	#11719283	C₂²	1	2	yes	complemented
37	Q₈×D₅₂	C₂²	1	1	yes	characteristic
38	C₄×Q₈×D₁₃	C₂²	1	2	yes	complemented
39	#11719272	—	2	1	no	—
40	#11719272	C₂²	1	1	yes	characteristic, complemented
41	Q₈×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
42	#11719270	—	2	1	no	—
43	#11719255	—	2	1	no	—
44	D₄×D₅₂	C₂²	1	1	yes	characteristic
45	#11719252	—	2	2	no	—
46	C₄×D₄×D₁₃	C₂²	1	2	yes	—
47	#11719248	C₂²	1	1	yes	characteristic
48	#11719235	C₂²	1	2	yes	—
49	#11719232	—	2	2	no	—
50	#11719216	—	2	2	no	—
51	#11719216	C₂²	1	2	yes	complemented
52	#11719184	—	2	1	no	—
53	#11719182	C₂²	1	1	yes	characteristic
54	C₄×#6127	—	2	1	no	—
55	C₄×#6127	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₅₂	—	2	1	no	—
57	#11719175	—	2	1	no	—
58	#11719175	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#440	C₂²	1	1	yes	characteristic
62	C₁₃×#440	C₂²	1	1	yes	characteristic
63	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
65	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
67	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#417	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
71	#11718900	C₂²	1	2	yes	—
72	#11718888	C₂²	1	2	yes	complemented
73	#11718851	C₂²	1	2	yes	complemented
74	#11718849	C₂²	1	2	yes	complemented
75	#11718847	C₂²	1	2	yes	complemented
76	#11718846	C₂²	1	2	yes	complemented
77	#11718830	C₂²	1	2	yes	—
78	#11718825	C₂²	1	2	yes	—
79	#11718823	C₂²	1	2	yes	—
80	#11718795	C₂²	1	2	yes	complemented
81	#11718795	C₂²	1	2	yes	complemented
82	#11718788	C₂²	1	2	yes	complemented
83	#11718788	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	#11718688	C₂²	1	1	yes	characteristic
88	#11718687	C₂²	1	2	yes	complemented
89	#11718687	C₂²	1	2	yes	complemented
90	#11718682	C₂²	1	1	yes	characteristic, complemented
91	#11718682	C₂²	1	1	yes	characteristic, complemented
92	#11718682	C₂²	1	1	yes	characteristic, complemented
93	#11718680	C₂²	1	1	yes	characteristic
94	#11718679	C₂²	1	2	yes	—
95	#11718669	C₂²	1	1	yes	characteristic
96	#11718657	C₂²	1	2	yes	complemented
97	#11718628	C₂²	1	2	yes	complemented
98	#11718587	C₂²	1	1	yes	characteristic, complemented
99	#11718551	C₂²	1	2	yes	complemented
100	#11718550	C₂²	1	2	yes	complemented
101	#11718545	C₂²	1	2	yes	complemented
102	D₁₃×#107	C₂²	1	2	yes	complemented
103	#11718525	C₂²	1	2	yes	—
104	#11718524	C₂²	1	2	yes	—
105	#11718518	C₂²	1	2	yes	complemented
106	#11718517	C₂²	1	2	yes	complemented
107	#11718479	C₂²	1	2	yes	complemented
108	#11718478	C₂²	1	2	yes	complemented
109	#11718474	C₂²	1	2	yes	complemented
110	#11718470	C₂²	1	2	yes	complemented
111	#11718470	C₂²	1	2	yes	complemented
112	#11718468	C₂²	1	2	yes	—
113	#11718467	C₂²	1	2	yes	—
114	D₁₃×#103	C₂²	1	2	yes	complemented
115	#11718459	C₂²	1	2	yes	complemented
116	#11718458	C₂²	1	2	yes	complemented
117	#11718457	C₂²	1	2	yes	complemented
118	#11718456	C₂²	1	2	yes	complemented
119	#11718437	C₂²	1	2	yes	—
120	D₁₃×#102	C₂²	1	2	yes	—
121	#11718420	C₂²	1	2	yes	—
122	#11718418	C₂²	1	2	yes	—
123	#11718371	C₂²	1	2	yes	complemented
124	#11718371	C₂²	1	2	yes	complemented
125	#11718366	C₂²	1	2	yes	complemented
126	D₁₃×#97	C₂²	1	2	yes	complemented
127	#11718355	C₂²	1	1	yes	characteristic
128	#11718354	C₂²	1	1	yes	characteristic
129	C₈×D₅₂	C₂²	1	1	yes	characteristic
130	C₈×D₅₂	C₂²	1	1	yes	characteristic
131	#11718343	C₂²	1	1	yes	characteristic, complemented
132	#11718342	C₂²	1	1	yes	characteristic, complemented
133	#11718340	C₂²	1	1	yes	characteristic, complemented
134	#11718340	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₁₃	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	C₂×#6127	D₄	1	1	yes	characteristic
141	C₂²×D₅₂	—	2	1	no	—
142	C₂²×C₄×D₁₃	—	2	2	no	—
143	C₁₃×#137	—	2	4	no	—
144	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
161	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
162	C₁₃×#117	—	2	1	no	—
163	C₁₃×#117	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	—	2	1	no	—
167	C₂×C₄²×C₁₃	—	2	1	no	—
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	#88201	C₂³	1	2	yes	—
170	#88200	—	2	2	no	—
171	#88200	C₂³	1	2	yes	—
172	#88200	C₂³	1	2	yes	—
173	Q₈×Dic₁₃	C₂³	1	2	yes	—
174	#88198	—	2	2	no	—
175	#88198	C₂³	1	2	yes	—
176	C₂×#6107	C₂³	1	2	yes	—
177	C₂×#6106	C₂³	1	2	yes	—
178	C₂×#6106	C₂³	1	2	yes	—
179	#88193	—	2	2	no	—
180	#88191	—	2	2	no	—
181	D₄×Dic₁₃	C₂³	1	2	yes	—
182	C₂×#6105	C₂³	1	2	yes	—
183	#88184	—	2	1	no	—
184	#88184	—	2	1	no	—
185	#88184	C₂³	1	2	yes	—
186	#88183	—	2	2	no	—
187	C₄×C₂²⋊D₁₃	—	2	2	no	—
188	C₄×C₂²⋊D₁₃	—	2	2	no	—
189	C₄×C₂²⋊D₁₃	—	2	2	no	—
190	C₄×C₂²⋊D₁₃	D₄	1	2	yes	—
191	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
192	C₂×#6103	—	2	2	no	—
193	#88180	—	2	1	no	—
194	#88180	D₄	1	1	yes	characteristic
195	C₂×C₄⋊Dic₁₃	—	2	1	no	—
196	#88178	—	2	1	no	—
197	#88178	—	2	1	no	—
198	#88178	—	2	2	no	—
199	#88178	—	2	2	no	—
200	#88178	C₂³	1	2	yes	—
201	SD₁₆×D₁₃	—	2	8	no	—
202	C₂×#6095	C₂³	1	2	yes	—
203	C₂×#6095	C₂³	1	2	yes	—
204	C₂×C₈×D₁₃	C₂³	1	2	yes	—
205	C₂×C₈×D₁₃	C₂³	1	2	yes	—
206	#88152	—	2	2	no	—
207	#88151	—	2	2	no	—
208	#88151	C₂³	1	2	yes	—
209	#88150	—	2	2	no	—
210	#88150	—	2	2	no	—
211	#88150	—	2	2	no	—
212	#88150	—	2	2	no	—
213	#88149	C₂³	1	2	yes	—
214	#88148	—	2	2	no	—
215	#88148	—	2	2	no	—
216	#88147	C₂³	1	2	yes	—
217	C₄⋊C₄×D₁₃	—	2	2	no	—
218	C₄⋊C₄×D₁₃	C₂³	1	2	yes	—
219	C₄⋊C₄×D₁₃	C₂³	1	2	yes	—
220	#88144	C₂³	1	2	yes	—
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	#88141	C₂³	1	2	yes	—
228	#88138	—	2	2	no	—
229	#88137	—	2	2	no	—
230	#88136	—	2	2	no	—
231	#88135	—	2	2	no	—
232	C₂²⋊C₄×D₁₃	—	2	2	no	—
233	#88132	—	2	2	no	—
234	#88130	—	2	2	no	—
235	#88129	—	2	1	no	—
236	#88129	—	2	1	no	—
237	#88128	C₂³	1	1	yes	characteristic
238	C₄×D₅₂	—	2	1	no	—
239	C₄×D₅₂	—	2	1	no	—
240	C₄×D₅₂	—	2	1	no	—
241	C₄×D₅₂	—	2	2	no	—
242	C₄×D₅₂	—	2	1	no	—
243	C₄×D₅₂	—	2	2	no	—
244	C₄×D₅₂	—	2	1	no	—
245	C₄×D₅₂	D₄	1	1	yes	characteristic
246	C₄×D₅₂	C₂³	1	1	yes	characteristic
247	C₄×D₅₂	C₂³	1	2	yes	—
248	#88126	—	2	2	no	—
249	#88126	—	2	2	no	—
250	#88126	D₄	1	2	yes	—
251	C₄²×D₁₃	—	2	2	no	—
252	C₄²×D₁₃	C₂³	1	2	yes	—
253	#88124	—	2	1	no	—
254	#88124	—	2	1	no	—
255	#88124	—	2	1	no	—
256	#88124	—	2	1	no	—
257	#88123	—	2	1	no	—
258	#88123	—	2	1	no	—
259	#88123	C₂³	1	1	yes	characteristic
260	#88123	C₂³	1	1	yes	characteristic
261	#88123	C₂³	1	1	yes	characteristic
262	C₄×Dic₂₆	—	2	1	no	—
263	C₄×Dic₂₆	—	2	1	no	—
264	C₄×Dic₂₆	—	2	1	no	—
265	C₄×Dic₂₆	—	2	2	no	—
266	C₄×Dic₂₆	—	2	2	no	—
267	C₄×Dic₂₆	D₄	1	1	yes	characteristic
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×#103	C₂³	1	1	yes	characteristic
279	C₁₃×#103	C₂³	1	1	yes	characteristic
280	C₁₃×#102	C₂³	1	1	yes	characteristic
281	C₁₃×#102	C₂³	1	1	yes	characteristic
282	C₁₃×#97	C₂³	1	1	yes	characteristic
283	C₁₃×#97	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	#88075	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	#88058	C₂³	1	2	yes	—
296	#88058	C₂³	1	2	yes	—
297	#88056	C₂³	1	2	yes	—
298	#88056	C₂³	1	2	yes	—
299	#88055	C₂³	1	2	yes	—
300	#88055	C₂³	1	2	yes	—
301	#88054	C₂³	1	2	yes	—
302	#88054	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	#88047	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	#61453	—	13	1	no	maximal, Sylow
315	C₂³×D₁₃	—	2	2	no	—
316	C₁₃×#41	—	2	2	no	—
317	C₁₃×#41	—	4	1	no	—
318	C₂×Q₈×C₁₃	—	2	1	no	—
319	C₂×Q₈×C₁₃	—	2	2	no	—
320	C₂×Q₈×C₁₃	—	4	1	no	—
321	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₁₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₂²⋊D₁₃	—	2	2	no	—
335	C₂×C₂²⋊D₁₃	—	2	2	no	—
336	C₂×C₂²⋊D₁₃	C₂×D₄	1	2	yes	—
337	C₂²×Dic₁₃	—	2	2	no	—
338	Q₈×D₁₃	—	2	4	no	—
339	Q₈×D₁₃	—	4	2	no	—
340	D₄×D₁₃	—	2	4	no	—
341	D₄×D₁₃	—	4	2	no	—
342	#6127	—	2	4	no	—
343	#6127	—	8	2	no	—
344	C₂×D₅₂	—	2	2	no	—
345	C₂×D₅₂	—	2	1	no	—
346	C₂×D₅₂	—	2	1	no	—
347	C₂×D₅₂	—	4	4	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	—	2	2	no	—
354	C₂×C₄×D₁₃	—	2	2	no	—
355	C₂×C₄×D₁₃	—	8	4	no	—
356	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
357	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
358	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
359	C₂×Dic₂₆	—	2	2	no	—
360	C₂×Dic₂₆	—	2	1	no	—
361	C₂×Dic₂₆	—	2	1	no	—
362	C₂×Dic₂₆	—	2	2	no	—
363	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
364	C₂×Dic₂₆	C₂⁴	1	2	yes	—
365	C₁₃×Q₁₆	—	2	2	no	—
366	C₁₃×Q₁₆	—	2	2	no	—
367	C₁₃×SD₁₆	—	2	2	no	—
368	C₁₃×SD₁₆	#41	1	4	yes	complemented
369	C₁₃×M₁₆	—	2	2	no	—
370	C₁₃×M₁₆	—	4	1	no	—
371	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₁₃×C₄⋊C₄	—	2	1	no	—
376	C₁₃×C₄⋊C₄	—	2	1	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	1	no	—
379	C₁₃×C₄⋊C₄	—	2	1	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
383	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
384	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
385	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
386	C₁₃×C₂²⋊C₄	—	2	1	no	—
387	C₁₃×C₂²⋊C₄	—	2	1	no	—
388	C₁₃×C₂²⋊C₄	—	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	—	2	1	no	—
394	C₄²×C₁₃	—	2	1	no	—
395	C₄²×C₁₃	—	2	1	no	—
396	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
399	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
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	#6106	—	4	2	no	—
406	#6105	—	2	4	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	C₂×D₄	1	2	yes	—
417	#6103	C₂×D₄	1	2	yes	—
418	C₄⋊Dic₁₃	—	2	1	no	—
419	C₄⋊Dic₁₃	—	2	1	no	—
420	C₄⋊Dic₁₃	—	2	1	no	—
421	C₄⋊Dic₁₃	—	2	1	no	—
422	C₄⋊Dic₁₃	—	2	2	no	—
423	C₄⋊Dic₁₃	—	2	2	no	—
424	C₄⋊Dic₁₃	—	2	2	no	—
425	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
426	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
427	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
428	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
429	#6101	—	2	2	no	—
430	#6101	—	2	2	no	—
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	—	2	2	no	—
438	#6101	—	2	2	no	—
439	#6101	—	2	2	no	—
440	#6101	C₂×D₄	1	2	yes	—
441	#6101	C₂×D₄	1	2	yes	—
442	C₄×Dic₁₃	—	2	2	no	—
443	C₄×Dic₁₃	—	2	2	no	—
444	C₄×Dic₁₃	—	2	2	no	—
445	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
446	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
447	C₄×Dic₁₃	C₂⁴	1	2	yes	—
448	C₂×#1055	C₂⁴	1	2	yes	—
449	C₂×#1055	C₂⁴	1	2	yes	—
450	#6095	—	2	4	no	—
451	#6095	—	4	2	no	—
452	C₈×D₁₃	—	2	4	no	—
453	C₈×D₁₃	—	4	2	no	—
454	#3481	—	13	1	no	—
455	Q₈×#41	—	13	1	no	—
456	#3400	—	13	1	no	—
457	#3385	—	13	1	no	—
458	#3375	—	13	1	no	—
459	#3372	—	13	1	no	—
460	#3346	—	13	2	no	—
461	#3338	—	13	1	no	—
462	#3320	—	13	2	no	—
463	#3314	—	13	2	no	—
464	#3299	—	13	1	no	—
465	#3295	—	13	1	no	—
466	D₄×SD₁₆	—	13	1	no	—
467	#3266	—	13	2	no	—
468	#3182	—	13	1	no	—
469	#3181	—	13	2	no	—
470	#3117	—	13	2	no	—
471	#3116	—	13	1	no	—
472	#3112	—	13	1	no	—
473	#3110	—	13	2	no	—
474	#2970	—	13	1	no	—
475	C₄×#137	D₁₃	1	1	yes	characteristic, complemented
476	C₂×#440	—	13	2	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	—	4	4	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	—	2	1	no	—
488	Q₈×C₁₃	—	2	1	no	—
489	Q₈×C₁₃	—	4	2	no	—
490	Q₈×C₁₃	C₂×#41	1	2	yes	—
491	D₄×C₁₃	—	2	1	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	—	2	1	no	—
504	C₂×C₄×C₁₃	—	4	1	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	—	4	2	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	—	2	4	no	—
517	C₂²⋊D₁₃	—	4	4	no	—
518	C₂²⋊D₁₃	—	8	2	no	—
519	C₂×Dic₁₃	—	2	2	no	—
520	C₂×Dic₁₃	—	2	2	no	—
521	C₂×Dic₁₃	—	2	2	no	—
522	C₂×Dic₁₃	—	8	2	no	—
523	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
524	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
525	C₂×Dic₁₃	C₂²×D₄	1	2	yes	—
526	D₅₂	—	2	2	no	—
527	D₅₂	—	2	2	no	—
528	D₅₂	—	4	4	no	—
529	D₅₂	—	4	2	no	—
530	D₅₂	—	8	1	no	—
531	D₅₂	#137	1	4	yes	complemented
532	C₄×D₁₃	—	2	4	no	—
533	C₄×D₁₃	—	2	2	no	—
534	C₄×D₁₃	—	2	2	no	—
535	C₄×D₁₃	—	4	2	no	—
536	C₄×D₁₃	—	4	4	no	—
537	C₄×D₁₃	—	4	4	no	—
538	C₄×D₁₃	—	8	2	no	—
539	C₄×D₁₃	—	8	2	no	—
540	C₄×D₁₃	—	8	2	no	—
541	Dic₂₆	—	2	2	no	—
542	Dic₂₆	—	2	2	no	—
543	Dic₂₆	—	2	2	no	—
544	Dic₂₆	—	4	4	no	—
545	Dic₂₆	—	8	2	no	—
546	Dic₂₆	—	8	1	no	—
547	Dic₂₆	—	8	1	no	—
548	C₈×C₁₃	—	2	1	no	—
549	C₈×C₁₃	—	2	1	no	—
550	C₈×C₁₃	—	2	1	no	—
551	C₈×C₁₃	C₂×#41	1	2	yes	—
552	#1055	—	2	2	no	—
553	#1055	—	2	2	no	—
554	C₂×#137	C₂×D₁₃	1	1	yes	characteristic
555	C₂²×SD₁₆	—	13	2	no	—
556	#559	—	13	1	no	—
557	Q₈²	—	13	1	no	—
558	#557	—	13	1	no	—
559	#557	—	26	1	no	—
560	#554	—	13	1	no	—
561	#554	—	13	1	no	—
562	#554	—	13	2	no	—
563	#554	—	13	1	no	—
564	#554	—	26	2	no	—
565	#554	—	26	1	no	—
566	#553	—	13	2	no	—
567	#553	—	26	1	no	—
568	#551	—	26	2	no	—
569	D₄×Q₈	—	13	2	no	—
570	D₄×Q₈	—	13	1	no	—
571	#546	—	13	2	no	—
572	#546	—	26	1	no	—
573	D₄²	—	13	1	no	—
574	#533	—	13	2	no	—
575	#533	—	13	1	no	—
576	#533	—	26	1	no	—
577	#533	—	26	2	no	—
578	#532	—	13	1	no	—
579	#529	—	13	2	no	—
580	#529	—	26	1	no	—
581	#525	—	26	2	no	—
582	C₄×#41	—	13	1	no	—
583	C₄×#41	—	26	1	no	—
584	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
585	C₂×C₄×Q₈	—	13	2	no	—
586	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
587	C₂×C₄×D₄	—	13	2	no	—
588	C₂×C₄×D₄	—	26	1	no	—
589	#501	—	13	2	no	—
590	#500	—	13	1	no	—
591	#497	—	13	2	no	—
592	#492	—	13	1	no	—
593	#491	—	13	2	no	—
594	#489	—	13	2	no	—
595	#487	—	13	1	no	—
596	#486	—	13	1	no	—
597	#485	—	13	2	no	—
598	#484	—	13	2	no	—
599	#484	—	13	2	no	—
600	#484	—	13	2	no	—
601	#481	—	13	2	no	—
602	#480	—	13	2	no	—
603	#479	—	13	2	no	—
604	#479	—	13	2	no	—
605	#477	—	13	1	no	—
606	#477	—	13	1	no	—
607	#477	—	13	1	no	—
608	#476	—	13	1	no	—
609	#474	—	13	2	no	—
610	#474	—	13	2	no	—
611	#468	—	13	2	no	—
612	#468	—	13	2	no	—
613	#467	—	13	2	no	—
614	#467	—	13	2	no	—
615	#465	—	13	2	no	—
616	#465	—	13	2	no	—
617	#464	—	13	2	no	—
618	#464	—	13	2	no	—
619	#462	—	13	1	no	—
620	#461	—	13	2	no	—
621	#461	—	13	1	no	—
622	#461	—	13	2	no	—
623	#460	—	13	1	no	—
624	#460	—	13	1	no	—
625	#452	—	13	2	no	—
626	#451	—	13	2	no	—
627	#450	—	13	2	no	—
628	#450	—	13	2	no	—
629	#448	—	13	2	no	—
630	#448	—	13	2	no	—
631	#446	—	13	1	no	—
632	#446	—	13	1	no	—
633	#441	—	13	2	no	—
634	#441	C₂×D₁₃	1	1	yes	characteristic, complemented
635	#441	C₂×D₁₃	1	1	yes	characteristic, complemented
636	#440	—	13	2	no	—
637	#440	—	13	2	no	—
638	#440	—	13	2	no	—
639	#440	—	13	2	no	—
640	#440	—	13	2	no	—
641	#440	—	13	2	no	—
642	#440	—	13	2	no	—
643	#440	—	13	2	no	—
644	#440	—	13	2	no	—
645	#440	C₂×D₁₃	1	1	yes	characteristic
646	#440	C₂×D₁₃	1	1	yes	characteristic
647	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
648	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
649	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
650	C₄×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
651	#435	—	13	2	no	—
652	#435	—	13	2	no	—
653	C₈×D₄	—	13	1	no	—
654	C₈×D₄	—	13	1	no	—
655	#432	—	13	1	no	—
656	#432	—	13	2	no	—
657	#428	C₂×D₁₃	1	1	yes	characteristic, complemented
658	C₂×#107	—	13	2	no	—
659	#419	C₂×D₁₃	1	1	yes	characteristic, complemented
660	#417	C₂×D₁₃	1	1	yes	characteristic
661	C₂×#103	—	13	2	no	—
662	C₂×#102	—	13	2	no	—
663	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
664	C₂×#97	—	13	2	no	—
665	C₂²×C₁₃	—	2	1	no	—
666	C₂²×C₁₃	—	2	2	no	—
667	C₂²×C₁₃	—	2	1	no	—
668	C₂²×C₁₃	—	2	1	no	—
669	C₂²×C₁₃	—	4	1	no	—
670	C₂²×C₁₃	—	4	1	no	—
671	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
672	C₂×D₁₃	—	2	2	no	—
673	C₂×D₁₃	—	2	2	no	—
674	C₂×D₁₃	—	4	2	no	—
675	C₂×D₁₃	—	4	2	no	—
676	C₂×D₁₃	—	4	2	no	—
677	C₂×D₁₃	—	8	8	no	—
678	C₂×D₁₃	C₂×#137	1	4	yes	—
679	C₄×C₁₃	—	2	1	no	—
680	C₄×C₁₃	—	2	1	no	—
681	C₄×C₁₃	—	2	2	no	—
682	C₄×C₁₃	—	2	1	no	—
683	C₄×C₁₃	—	2	1	no	—
684	C₄×C₁₃	—	4	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	C₂×#137	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	—	13	1	no	—
700	C₂×#41	—	26	1	no	—
701	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
702	C₂²×Q₈	—	13	2	no	—
703	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
704	C₂²×D₄	—	13	2	no	—
705	C₂²×D₄	—	26	1	no	—
706	C₂³×C₄	—	26	2	no	—
707	#137	—	2	4	no	—
708	C₂×Q₁₆	—	13	2	no	—
709	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
710	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
711	C₂×SD₁₆	—	13	2	no	—
712	C₂×SD₁₆	—	13	2	no	—
713	C₂×SD₁₆	—	13	2	no	—
714	C₂×SD₁₆	—	13	2	no	—
715	C₂×SD₁₆	—	13	2	no	—
716	C₂×SD₁₆	—	26	8	no	—
717	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
718	C₂×SD₁₆	C₂²×D₁₃	1	1	yes	characteristic
719	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
720	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
721	C₂²×C₈	—	13	2	no	—
722	C₂²×C₈	—	13	2	no	—
723	C₄⋊Q₈	—	13	2	no	—
724	C₄⋊Q₈	—	13	2	no	—
725	C₄⋊Q₈	—	13	1	no	—
726	C₄⋊Q₈	—	13	1	no	—
727	C₄⋊Q₈	—	13	1	no	—
728	C₄⋊Q₈	—	26	1	no	—
729	C₄⋊Q₈	—	26	1	no	—
730	C₄⋊Q₈	—	26	2	no	—
731	C₄⋊Q₈	—	26	2	no	—
732	#127	—	13	1	no	—
733	#126	—	26	2	no	—
734	#126	—	26	2	no	—
735	#125	—	13	2	no	—
736	#125	—	26	1	no	—
737	#125	—	26	1	no	—
738	#125	—	26	1	no	—
739	#125	—	26	2	no	—
740	#125	—	26	2	no	—
741	#125	—	26	2	no	—
742	#125	—	26	1	no	—
743	#124	—	13	2	no	—
744	#124	—	26	1	no	—
745	#124	—	26	1	no	—
746	#123	—	26	2	no	—
747	#123	—	26	2	no	—
748	#123	—	26	2	no	—
749	#123	—	26	2	no	—
750	C₂²⋊Q₈	—	13	2	no	—
751	C₂²⋊Q₈	—	13	2	no	—
752	C₂²⋊Q₈	—	13	2	no	—
753	C₂²⋊Q₈	—	13	2	no	—
754	C₂²⋊Q₈	—	26	2	no	—
755	C₂²⋊Q₈	—	26	2	no	—
756	C₂²⋊Q₈	—	26	2	no	—
757	C₂²⋊Q₈	—	26	2	no	—
758	C₂²⋊Q₈	—	26	2	no	—
759	C₂²⋊Q₈	—	26	2	no	—
760	C₂²⋊Q₈	—	26	2	no	—
761	C₂²⋊Q₈	—	26	2	no	—
762	C₂²⋊Q₈	—	26	2	no	—
763	C₂²⋊Q₈	—	26	1	no	—
764	C₂²⋊Q₈	—	26	1	no	—
765	#121	—	13	2	no	—
766	#121	—	13	2	no	—
767	#121	—	26	2	no	—
768	#121	—	26	2	no	—
769	#121	—	26	1	no	—
770	#121	—	26	1	no	—
771	#120	—	26	2	no	—
772	#120	—	26	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	13	1	no	—
776	C₄×Q₈	—	13	1	no	—
777	C₄×Q₈	—	13	2	no	—
778	C₄×Q₈	—	13	2	no	—
779	C₄×Q₈	—	13	2	no	—
780	C₄×Q₈	—	26	2	no	—
781	C₄×Q₈	—	26	2	no	—
782	C₄×Q₈	—	26	1	no	—
783	C₄×Q₈	—	26	1	no	—
784	C₄×Q₈	—	26	2	no	—
785	C₄×Q₈	—	26	1	no	—
786	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
787	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
788	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
789	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
790	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
791	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	13	2	no	—
795	C₄×D₄	—	13	2	no	—
796	C₄×D₄	—	13	2	no	—
797	C₄×D₄	—	13	2	no	—
798	C₄×D₄	—	13	1	no	—
799	C₄×D₄	—	13	1	no	—
800	C₄×D₄	—	13	2	no	—
801	C₄×D₄	—	26	2	no	—
802	C₄×D₄	—	26	1	no	—
803	C₄×D₄	—	26	2	no	—
804	C₄×D₄	—	26	1	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	2	no	—
811	C₄×D₄	—	26	1	no	—
812	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
813	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
814	#117	—	2	1	no	—
815	#117	—	13	1	no	—
816	#117	—	13	2	no	—
817	#117	—	26	2	no	—
818	#117	—	26	2	no	—
819	#117	—	26	1	no	—
820	#117	C₂²×D₁₃	1	1	yes	characteristic
821	C₂×C₄⋊C₄	—	2	1	no	—
822	C₂×C₄⋊C₄	—	13	2	no	—
823	C₂×C₄⋊C₄	—	13	2	no	—
824	C₂×C₄⋊C₄	—	26	2	no	—
825	C₂×C₄⋊C₄	—	26	1	no	—
826	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
827	C₂×C₂²⋊C₄	—	26	2	no	—
828	C₂×C₂²⋊C₄	—	26	2	no	—
829	C₂×C₄²	—	2	1	no	—
830	C₂×C₄²	—	2	1	no	—
831	C₂×C₄²	—	13	2	no	—
832	C₂×C₄²	—	26	2	no	—
833	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
834	#107	—	13	2	no	—
835	#107	—	13	2	no	—
836	#107	—	13	2	no	—
837	#107	—	13	2	no	—
838	#107	—	13	2	no	—
839	#107	C₂²×D₁₃	1	1	yes	characteristic
840	#107	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	2	no	—
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	#103	C₂²×D₁₃	1	1	yes	characteristic
859	#103	C₂²×D₁₃	1	1	yes	characteristic
860	#103	C₂²×D₁₃	1	1	yes	characteristic
861	#102	—	13	2	no	—
862	#102	—	13	2	no	—
863	#102	—	13	2	no	—
864	#102	—	13	2	no	—
865	#102	—	13	2	no	—
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	#97	—	13	2	no	—
874	#97	C₂²×D₁₃	1	1	yes	characteristic
875	#97	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	D₄×#41	1	1	yes	characteristic
881	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
882	C₂×C₁₃	#3585	1	1	yes	characteristic
883	D₁₃	—	2	4	no	—
884	D₁₃	—	8	2	no	—
885	C₂⁴	—	26	2	no	—
886	#41	—	2	2	no	—
887	#41	—	4	1	no	—
888	#41	—	26	4	no	—
889	#41	—	104	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	4	1	no	—
893	C₂×Q₈	—	13	1	no	—
894	C₂×Q₈	—	13	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	C₂³×D₁₃	1	1	yes	characteristic
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	—	13	2	no	—
906	C₂×D₄	—	13	1	no	—
907	C₂×D₄	—	13	2	no	—
908	C₂×D₄	—	26	2	no	—
909	C₂×D₄	—	26	2	no	—
910	C₂×D₄	—	26	4	no	—
911	C₂×D₄	—	26	2	no	—
912	C₂×D₄	—	26	1	no	—
913	C₂×D₄	—	26	1	no	—
914	C₂×D₄	—	52	4	no	—
915	C₂×D₄	—	52	2	no	—
916	C₂×D₄	C₂³×D₁₃	1	1	yes	characteristic
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	13	2	no	—
923	C₂²×C₄	—	13	2	no	—
924	C₂²×C₄	—	13	2	no	—
925	C₂²×C₄	—	26	2	no	—
926	C₂²×C₄	—	26	2	no	—
927	C₂²×C₄	—	26	2	no	—
928	C₂²×C₄	—	26	2	no	—
929	C₂²×C₄	—	26	2	no	—
930	C₂²×C₄	—	26	2	no	—
931	C₂²×C₄	—	104	4	no	—
932	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
933	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
934	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
935	Q₁₆	—	2	2	no	—
936	Q₁₆	—	2	2	no	—
937	Q₁₆	—	52	2	no	—
938	SD₁₆	—	2	2	no	—
939	SD₁₆	—	26	4	no	—
940	SD₁₆	—	26	4	no	—
941	SD₁₆	—	26	4	no	—
942	SD₁₆	—	52	2	no	—
943	SD₁₆	—	52	2	no	—
944	SD₁₆	#6127	1	4	yes	complemented
945	M₁₆	—	2	2	no	—
946	M₁₆	—	4	1	no	—
947	C₂×C₈	—	13	2	no	—
948	C₂×C₈	—	13	2	no	—
949	C₂×C₈	—	26	4	no	—
950	C₂×C₈	—	52	2	no	—
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	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	13	1	no	—
963	C₄⋊C₄	—	13	1	no	—
964	C₄⋊C₄	—	13	2	no	—
965	C₄⋊C₄	—	13	2	no	—
966	C₄⋊C₄	—	13	2	no	—
967	C₄⋊C₄	—	13	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	2	no	—
973	C₄⋊C₄	—	26	2	no	—
974	C₄⋊C₄	—	26	2	no	—
975	C₄⋊C₄	—	26	2	no	—
976	C₄⋊C₄	—	26	2	no	—
977	C₄⋊C₄	—	26	2	no	—
978	C₄⋊C₄	—	26	2	no	—
979	C₄⋊C₄	—	26	2	no	—
980	C₄⋊C₄	—	26	1	no	—
981	C₄⋊C₄	—	26	2	no	—
982	C₄⋊C₄	—	26	1	no	—
983	C₄⋊C₄	—	26	1	no	—
984	C₄⋊C₄	—	26	2	no	—
985	C₄⋊C₄	—	26	1	no	—
986	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂³×D₁₃	1	1	yes	characteristic
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	13	2	no	—
994	C₂²⋊C₄	—	13	2	no	—
995	C₂²⋊C₄	—	13	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	C₄²	—	2	1	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	—	13	2	no	—
1016	C₄²	—	13	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	#61453	1	1	yes	characteristic, complemented, Sylow
1025	C₂³	—	2	1	no	—
1026	C₂³	—	13	2	no	—
1027	C₂³	—	26	2	no	—
1028	C₂³	—	52	4	no	—
1029	C₂³	—	52	4	no	—
1030	C₂³	—	104	2	no	—
1031	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
1032	Q₈	—	2	1	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	4	2	no	—
1038	Q₈	—	26	2	no	—
1039	Q₈	—	26	2	no	—
1040	Q₈	—	26	2	no	—
1041	Q₈	—	52	4	no	—
1042	Q₈	—	104	1	no	—
1043	Q₈	—	104	1	no	—
1044	Q₈	—	104	2	no	—
1045	Q₈	C₂×#6127	1	2	yes	—
1046	D₄	—	2	1	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	13	4	no	—
1049	D₄	—	26	4	no	—
1050	D₄	—	26	2	no	—
1051	D₄	—	26	2	no	—
1052	D₄	—	52	4	no	—
1053	D₄	—	52	4	no	—
1054	D₄	—	52	2	no	—
1055	D₄	—	104	1	no	—
1056	D₄	—	104	2	no	—
1057	D₄	C₂×#6127	1	2	yes	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	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	—	4	1	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	13	2	no	—
1075	C₂×C₄	—	13	2	no	—
1076	C₂×C₄	—	13	2	no	—
1077	C₂×C₄	—	26	4	no	—
1078	C₂×C₄	—	26	2	no	—
1079	C₂×C₄	—	26	2	no	—
1080	C₂×C₄	—	26	2	no	—
1081	C₂×C₄	—	26	2	no	—
1082	C₂×C₄	—	26	2	no	—
1083	C₂×C₄	—	52	2	no	—
1084	C₂×C₄	—	52	4	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	—	104	2	no	—
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	C₂×D₄×D₁₃	1	1	yes	characteristic
1095	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1096	C₈	—	2	1	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	26	2	no	—
1100	C₈	—	26	2	no	—
1101	C₈	C₂×#6127	1	2	yes	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	13	4	no	—
1109	C₂²	—	26	2	no	—
1110	C₂²	—	26	2	no	—
1111	C₂²	—	52	2	no	—
1112	C₂²	—	52	2	no	—
1113	C₂²	—	52	2	no	—
1114	C₂²	—	104	8	no	—
1115	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	26	2	no	—
1128	C₄	—	26	2	no	—
1129	C₄	—	26	2	no	—
1130	C₄	—	52	2	no	—
1131	C₄	—	52	2	no	—
1132	C₄	—	52	2	no	—
1133	C₄	D₁₃×#137	1	2	yes	—
1134	C₄	C₂²×#6127	1	1	yes	characteristic
1135	C₄	#11719648	1	1	yes	characteristic
1136	C₂	—	4	1	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	26	4	no	—
1139	C₂	—	104	2	no	—
1140	C₂	D₄×#6127	1	1	yes	characteristic
1141	C₂	C₂×D₁₃×#137	1	1	yes	characteristic
1142	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	C₄×C₁₃×#137	C₂
socle	C₂²×C₁₃	C₂³×D₄
prime radical	#13128446	C₂
hypercenter	C₄×#137	D₁₃
hypocenter	C₁₃	#61453
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#137

Complements

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

N	H ≅ G/N	type
2. Q₈×#6127	C₂	semidirect
3. #13127887	C₂	semidirect
4. #13127744	C₂	semidirect
5. #13127648	C₂	semidirect
6. #13127615	C₂	semidirect
7. #13127322	C₂	semidirect
8. #13127230	C₂	semidirect
9. #13127008	C₂	semidirect
10. #13126918	C₂	semidirect
11. #13126714	C₂	semidirect
12. #13126662	C₂	semidirect
13. SD₁₆×D₅₂	C₂	semidirect
14. #13126340	C₂	semidirect
15. #13125554	C₂	semidirect
16. #13125543	C₂	semidirect
17. #13125011	C₂	semidirect
18. #13124998	C₂	semidirect
19. #13124958	C₂	semidirect
20. #13124933	C₂	semidirect
21. #13123851	C₂	semidirect
22. D₁₃×#440	C₂	semidirect
23. C₄×C₁₃×#137	C₂	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. Q₈×C₂²⋊D₁₃	C₂²	semidirect
36. #11719283	C₂²	semidirect
38. C₄×Q₈×D₁₃	C₂²	semidirect
40. #11719272	C₂²	semidirect
41. Q₈×Dic₂₆	C₂²	semidirect
51. #11719216	C₂²	semidirect
58. #11719175	C₂²	semidirect
59. C₁₃×#441	C₂²	semidirect
60. C₁₃×#441	C₂²	semidirect
63. C₄×C₁₃×Q₁₆	C₂²	semidirect
64. C₄×C₁₃×Q₁₆	C₂²	semidirect
67. C₁₃×#428	C₂²	semidirect
68. C₁₃×#419	C₂²	semidirect
70. C₄×C₁₃×M₁₆	C₂²	semidirect
72. #11718888	C₂²	semidirect
73. #11718851	C₂²	semidirect
74. #11718849	C₂²	semidirect
75. #11718847	C₂²	semidirect
76. #11718846	C₂²	semidirect
80. #11718795	C₂²	semidirect
81. #11718795	C₂²	semidirect
82. #11718788	C₂²	semidirect
83. #11718788	C₂²	semidirect
84. #11718692	C₂²	semidirect
85. #11718691	C₂²	semidirect
88. #11718687	C₂²	semidirect
89. #11718687	C₂²	semidirect
90. #11718682	C₂²	semidirect
91. #11718682	C₂²	semidirect
92. #11718682	C₂²	semidirect
96. #11718657	C₂²	semidirect
97. #11718628	C₂²	semidirect
98. #11718587	C₂²	semidirect
99. #11718551	C₂²	semidirect
100. #11718550	C₂²	semidirect
101. #11718545	C₂²	semidirect
102. D₁₃×#107	C₂²	semidirect
105. #11718518	C₂²	semidirect
106. #11718517	C₂²	semidirect
107. #11718479	C₂²	semidirect
108. #11718478	C₂²	semidirect
109. #11718474	C₂²	semidirect
110. #11718470	C₂²	semidirect
111. #11718470	C₂²	semidirect
114. D₁₃×#103	C₂²	semidirect
115. #11718459	C₂²	semidirect
116. #11718458	C₂²	semidirect
117. #11718457	C₂²	semidirect
118. #11718456	C₂²	semidirect
123. #11718371	C₂²	semidirect
124. #11718371	C₂²	semidirect
125. #11718366	C₂²	semidirect
126. D₁₃×#97	C₂²	semidirect
131. #11718343	C₂²	semidirect
132. #11718342	C₂²	semidirect
133. #11718340	C₂²	semidirect
134. #11718340	C₂²	semidirect
368. C₁₃×SD₁₆	#41	semidirect
475. C₄×#137	D₁₃	semidirect
531. D₅₂	#137	semidirect
586. C₂×C₄×Q₈	C₂×D₁₃	semidirect
634. #441	C₂×D₁₃	semidirect
635. #441	C₂×D₁₃	semidirect
647. C₄×Q₁₆	C₂×D₁₃	semidirect
648. C₄×Q₁₆	C₂×D₁₃	semidirect
657. #428	C₂×D₁₃	semidirect
659. #419	C₂×D₁₃	semidirect
663. C₄×M₁₆	C₂×D₁₃	semidirect
944. SD₁₆	#6127	semidirect
1024. C₁₃	#61453	semidirect

Maximal subgroups

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

subgroup	index
#13128446	2
Q₈×#6127	2
#13127887	2
#13127744	2
#13127648	2
#13127615	2
#13127322	2
#13127230	2
#13127008	2
#13126918	2
#13126714	2
#13126662	2
SD₁₆×D₅₂	2
#13126340	2
#13125554	2
#13125543	2
#13125011	2
#13124998	2
#13124958	2
#13124933	2
#13123851	2
D₁₃×#440	2
C₄×C₁₃×#137	2
#61453	13