Subgroups — #13129459

Order 1664.

936 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719440	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719436	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719404	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719401	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719401	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719398	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719351	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719351	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719348	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719347	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719346	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719345	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719343	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719342	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719342	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719339	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719328	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719327	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719288	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719269	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719265	C₂	1	1	yes	maximal, characteristic
24	#11719261	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719261	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719246	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719220	C₂	1	1	yes	maximal, characteristic, complemented
29	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#88152	C₂	1	1	yes	maximal, characteristic, complemented
31	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
32	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
42	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	#88201	C₂²	1	1	yes	characteristic
48	#88201	C₂²	1	1	yes	characteristic
49	#88200	C₂²	1	1	yes	characteristic
50	#88200	C₂²	1	1	yes	characteristic
51	#88200	C₂²	1	1	yes	characteristic
52	#88200	C₂²	1	1	yes	characteristic
53	#88200	C₂²	1	1	yes	characteristic, complemented
54	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
55	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
56	#88198	C₂²	1	1	yes	characteristic, complemented
57	#88198	C₂²	1	1	yes	characteristic, complemented
58	#88198	C₂²	1	1	yes	characteristic, complemented
59	#88193	C₂²	1	1	yes	characteristic
60	#88191	C₂²	1	1	yes	characteristic
61	#88189	C₂²	1	1	yes	characteristic
62	#88189	C₂²	1	1	yes	characteristic
63	#88184	C₂²	1	1	yes	characteristic
64	#88183	C₂²	1	1	yes	characteristic
65	#88183	C₂²	1	1	yes	characteristic
66	#88183	C₂²	1	1	yes	characteristic
67	#88183	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
74	C₂×#6103	C₂²	1	1	yes	characteristic
75	C₂×#6103	C₂²	1	1	yes	characteristic
76	C₂×#6103	C₂²	1	1	yes	characteristic
77	#88180	C₂²	1	1	yes	characteristic, complemented
78	#88180	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
80	#88178	C₂²	1	1	yes	characteristic
81	#88178	C₂²	1	1	yes	characteristic
82	#88178	C₂²	1	1	yes	characteristic
83	#88178	C₂²	1	1	yes	characteristic, complemented
84	#88178	C₂²	1	1	yes	characteristic, complemented
85	C₂×#6101	C₂²	1	1	yes	characteristic
86	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
87	#88152	C₂²	1	1	yes	characteristic
88	#88152	C₂²	1	1	yes	characteristic
89	#88152	C₂²	1	1	yes	characteristic
90	#88152	C₂²	1	1	yes	characteristic
91	#88152	C₂²	1	1	yes	characteristic
92	#88152	C₂²	1	1	yes	characteristic
93	#88152	C₂²	1	1	yes	characteristic
94	#88152	C₂²	1	1	yes	characteristic
95	#88152	C₂²	1	1	yes	characteristic
96	#88152	C₂²	1	1	yes	characteristic
97	#88152	C₂²	1	1	yes	characteristic
98	#88152	C₂²	1	1	yes	characteristic
99	#88152	C₂²	1	1	yes	characteristic
100	#88152	C₂²	1	1	yes	characteristic
101	#88152	C₂²	1	1	yes	characteristic
102	#88152	C₂²	1	1	yes	characteristic, complemented
103	#88152	C₂²	1	1	yes	characteristic, complemented
104	#88152	C₂²	1	1	yes	characteristic, complemented
105	#88151	C₂²	1	1	yes	characteristic
106	#88151	C₂²	1	1	yes	characteristic
107	#88151	C₂²	1	1	yes	characteristic, complemented
108	#88150	C₂²	1	1	yes	characteristic
109	#88150	C₂²	1	1	yes	characteristic
110	#88150	C₂²	1	1	yes	characteristic
111	#88150	C₂²	1	1	yes	characteristic
112	#88150	C₂²	1	1	yes	characteristic
113	#88150	C₂²	1	1	yes	characteristic
114	#88150	C₂²	1	1	yes	characteristic, complemented
115	#88150	C₂²	1	1	yes	characteristic, complemented
116	#88150	C₂²	1	1	yes	characteristic, complemented
117	#88148	C₂²	1	1	yes	characteristic
118	#88148	C₂²	1	1	yes	characteristic
119	#88148	C₂²	1	1	yes	characteristic
120	#88148	C₂²	1	1	yes	characteristic
121	#88148	C₂²	1	1	yes	characteristic
122	#88147	C₂²	1	1	yes	characteristic
123	#88147	C₂²	1	1	yes	characteristic
124	#88146	C₂²	1	1	yes	characteristic
125	#88146	C₂²	1	1	yes	characteristic
126	#88146	C₂²	1	1	yes	characteristic, complemented
127	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
128	#88144	C₂²	1	1	yes	characteristic, complemented
129	#88144	C₂²	1	1	yes	characteristic, complemented
130	#88144	C₂²	1	1	yes	characteristic, complemented
131	#88143	C₂²	1	1	yes	characteristic, complemented
132	#88143	C₂²	1	1	yes	characteristic, complemented
133	#88143	C₂²	1	1	yes	characteristic, complemented
134	#88143	C₂²	1	1	yes	characteristic, complemented
135	#88143	C₂²	1	1	yes	characteristic, complemented
136	#88143	C₂²	1	1	yes	characteristic, complemented
137	#88143	C₂²	1	1	yes	characteristic, complemented
138	#88143	C₂²	1	1	yes	characteristic, complemented
139	#88143	C₂²	1	1	yes	characteristic, complemented
140	#88143	C₂²	1	1	yes	characteristic, complemented
141	#88143	C₂²	1	1	yes	characteristic, complemented
142	#88143	C₂²	1	1	yes	characteristic, complemented
143	#88142	C₂²	1	1	yes	characteristic, complemented
144	#88142	C₂²	1	1	yes	characteristic, complemented
145	#88142	C₂²	1	1	yes	characteristic, complemented
146	#88142	C₂²	1	1	yes	characteristic, complemented
147	#88141	C₂²	1	1	yes	characteristic, complemented
148	#88141	C₂²	1	1	yes	characteristic, complemented
149	#88141	C₂²	1	1	yes	characteristic, complemented
150	#88141	C₂²	1	1	yes	characteristic, complemented
151	#88140	C₂²	1	1	yes	characteristic
152	#88140	C₂²	1	1	yes	characteristic
153	#88139	C₂²	1	1	yes	characteristic
154	#88139	C₂²	1	1	yes	characteristic
155	#88139	C₂²	1	1	yes	characteristic
156	#88139	C₂²	1	1	yes	characteristic, complemented
157	#88138	C₂²	1	1	yes	characteristic
158	#88137	C₂²	1	1	yes	characteristic
159	#88137	C₂²	1	1	yes	characteristic
160	#88137	C₂²	1	1	yes	characteristic, complemented
161	#88136	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
164	#88133	C₂²	1	1	yes	characteristic, complemented
165	#88133	C₂²	1	1	yes	characteristic, complemented
166	#88133	C₂²	1	1	yes	characteristic, complemented
167	#88133	C₂²	1	1	yes	characteristic, complemented
168	#88132	C₂²	1	1	yes	characteristic
169	#88132	C₂²	1	1	yes	characteristic
170	#88132	C₂²	1	1	yes	characteristic
171	#88131	C₂²	1	1	yes	characteristic
172	#88131	C₂²	1	1	yes	characteristic
173	#88131	C₂²	1	1	yes	characteristic
174	#88131	C₂²	1	1	yes	characteristic
175	#88130	C₂²	1	1	yes	characteristic
176	#88130	C₂²	1	1	yes	characteristic
177	#88130	C₂²	1	1	yes	characteristic
178	#88130	C₂²	1	1	yes	characteristic, complemented
179	#88129	C₂²	1	1	yes	characteristic
180	#88126	C₂²	1	1	yes	characteristic
181	#88126	C₂²	1	1	yes	characteristic
182	#88126	C₂²	1	1	yes	characteristic, complemented
183	#88124	C₂²	1	1	yes	characteristic, complemented
184	#88124	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₃	C₂³	1	1	yes	characteristic
188	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
202	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
203	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
204	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
205	C₂×D₅₂	C₂³	1	1	yes	characteristic
206	C₂×D₅₂	C₂³	1	1	yes	characteristic
207	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
214	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
215	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
216	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
217	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
218	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
219	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
220	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
221	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
224	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₄²×C₁₃	C₂³	1	1	yes	characteristic
243	C₄²×C₁₃	C₂³	1	1	yes	characteristic
244	C₄²×C₁₃	C₂³	1	1	yes	characteristic
245	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
246	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
247	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
248	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
249	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
250	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
251	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
252	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
253	#6103	C₂³	1	1	yes	characteristic
254	#6103	C₂³	1	1	yes	characteristic
255	#6103	C₂³	1	1	yes	characteristic
256	#6103	C₂³	1	1	yes	characteristic
257	#6103	C₂³	1	1	yes	characteristic
258	#6103	C₂³	1	1	yes	characteristic
259	#6103	C₂³	1	1	yes	characteristic
260	#6103	C₂³	1	1	yes	characteristic
261	#6103	C₂³	1	1	yes	characteristic
262	#6103	C₂³	1	1	yes	characteristic
263	#6103	C₂³	1	1	yes	characteristic
264	#6103	C₂³	1	1	yes	characteristic
265	#6103	C₂³	1	1	yes	characteristic
266	#6103	C₂³	1	1	yes	characteristic
267	#6103	C₂³	1	1	yes	characteristic
268	#6103	C₂³	1	1	yes	characteristic
269	#6103	C₂³	1	1	yes	characteristic
270	#6103	C₂³	1	1	yes	characteristic
271	#6103	C₂³	1	1	yes	characteristic
272	#6103	C₂³	1	1	yes	characteristic
273	#6103	C₂³	1	1	yes	characteristic
274	#6103	C₂³	1	1	yes	characteristic
275	#6103	C₂³	1	1	yes	characteristic
276	#6103	C₂³	1	1	yes	characteristic
277	#6103	C₂³	1	1	yes	characteristic
278	#6103	C₂³	1	1	yes	characteristic
279	#6103	C₂³	1	1	yes	characteristic
280	#6103	C₂³	1	1	yes	characteristic
281	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
282	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
283	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
284	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
285	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
286	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
287	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
288	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
289	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
290	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
291	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
292	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
293	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
295	#6101	C₂³	1	1	yes	characteristic
296	#6101	C₂³	1	1	yes	characteristic
297	#6101	C₂³	1	1	yes	characteristic
298	#6101	C₂³	1	1	yes	characteristic
299	#6101	C₂³	1	1	yes	characteristic
300	#6101	C₂³	1	1	yes	characteristic
301	#6101	C₂³	1	1	yes	characteristic
302	#6101	C₂³	1	1	yes	characteristic
303	#6101	C₂³	1	1	yes	characteristic
304	#6101	C₂³	1	1	yes	characteristic
305	#6101	C₂³	1	1	yes	characteristic
306	#6101	C₂³	1	1	yes	characteristic
307	#6101	C₂³	1	1	yes	characteristic
308	#6101	C₂³	1	1	yes	characteristic
309	#6101	C₂³	1	1	yes	characteristic
310	#6101	C₂³	1	1	yes	characteristic
311	#6101	C₂³	1	1	yes	characteristic
312	#6101	C₂³	1	1	yes	characteristic
313	#6101	C₂³	1	1	yes	characteristic
314	#6101	C₂³	1	1	yes	characteristic
315	#6101	C₂³	1	1	yes	characteristic
316	#6101	C₂³	1	1	yes	characteristic
317	#6101	C₂³	1	1	yes	characteristic
318	#6101	C₂³	1	1	yes	characteristic
319	#6101	C₂³	1	1	yes	characteristic
320	#6101	C₂³	1	1	yes	characteristic
321	#6101	C₂³	1	1	yes	characteristic
322	#6101	C₂³	1	1	yes	characteristic
323	#6101	C₂³	1	1	yes	characteristic
324	#6101	C₂³	1	1	yes	characteristic
325	#6101	C₂³	1	1	yes	characteristic
326	#6101	C₂³	1	1	yes	characteristic
327	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
328	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
329	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
330	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
331	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
332	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
333	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
334	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
335	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
336	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
337	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
338	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
339	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
340	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
341	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
342	#3564	—	13	1	no	maximal, Sylow
343	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₂²×D₁₃	—	2	2	no	—
346	C₂²×D₁₃	—	4	1	no	—
347	C₂²×D₁₃	—	4	1	no	—
348	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
349	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
350	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
351	Q₈×C₁₃	—	4	1	no	—
352	Q₈×C₁₃	—	4	1	no	—
353	Q₈×C₁₃	—	4	1	no	—
354	D₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	4	1	no	—
356	C₂×C₄×C₁₃	—	4	1	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	1	no	—
359	C₂×C₄×C₁₃	—	4	1	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₂²⋊D₁₃	—	2	2	no	—
375	C₂²⋊D₁₃	—	4	1	no	—
376	C₂²⋊D₁₃	—	4	1	no	—
377	C₂²⋊D₁₃	—	4	1	no	—
378	C₂×Dic₁₃	—	2	2	no	—
379	C₂×Dic₁₃	—	2	2	no	—
380	C₂×Dic₁₃	—	4	1	no	—
381	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
394	D₅₂	—	4	1	no	—
395	D₅₂	—	4	1	no	—
396	C₄×D₁₃	—	4	1	no	—
397	C₄×D₁₃	—	4	1	no	—
398	C₄×D₁₃	—	4	1	no	—
399	C₄×D₁₃	—	4	1	no	—
400	C₄×D₁₃	—	4	1	no	—
401	C₄×D₁₃	—	4	1	no	—
402	C₄×D₁₃	—	4	1	no	—
403	Dic₂₆	—	4	1	no	—
404	Dic₂₆	—	4	1	no	—
405	Dic₂₆	—	4	1	no	—
406	Dic₂₆	—	4	1	no	—
407	Dic₂₆	—	4	1	no	—
408	Dic₂₆	—	4	1	no	—
409	#563	—	13	1	no	—
410	#563	—	13	1	no	—
411	#563	—	13	1	no	—
412	#563	—	13	1	no	—
413	#556	—	13	1	no	—
414	#556	—	13	1	no	—
415	#554	—	13	1	no	—
416	#554	D₁₃	1	1	yes	characteristic, complemented
417	#552	—	13	1	no	—
418	#552	—	13	1	no	—
419	#552	—	13	1	no	—
420	#552	—	13	1	no	—
421	#551	—	13	1	no	—
422	#551	—	13	1	no	—
423	#551	—	13	1	no	—
424	#551	—	13	1	no	—
425	#544	—	13	1	no	—
426	#543	—	13	1	no	—
427	#542	—	13	1	no	—
428	#542	—	13	1	no	—
429	#541	—	13	1	no	—
430	#541	—	13	1	no	—
431	#541	—	13	1	no	—
432	#541	—	13	1	no	—
433	#539	—	13	1	no	—
434	#539	—	13	1	no	—
435	#539	—	13	1	no	—
436	#538	—	13	1	no	—
437	#533	—	13	1	no	—
438	#529	—	13	1	no	—
439	C₂×#126	—	13	1	no	—
440	C₂²×C₁₃	—	2	1	no	—
441	C₂²×C₁₃	—	2	1	no	—
442	C₂²×C₁₃	—	2	1	no	—
443	C₂²×C₁₃	—	2	1	no	—
444	C₂²×C₁₃	—	2	1	no	—
445	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
446	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
447	C₂×D₁₃	—	2	1	no	—
448	C₂×D₁₃	—	2	1	no	—
449	C₂×D₁₃	—	2	1	no	—
450	C₂×D₁₃	—	2	1	no	—
451	C₂×D₁₃	—	2	1	no	—
452	C₂×D₁₃	—	2	1	no	—
453	C₂×D₁₃	—	2	1	no	—
454	C₂×D₁₃	—	2	1	no	—
455	C₂×D₁₃	—	2	1	no	—
456	C₂×D₁₃	—	8	2	no	—
457	C₄×C₁₃	—	2	1	no	—
458	C₄×C₁₃	—	2	1	no	—
459	C₄×C₁₃	—	2	1	no	—
460	C₄×C₁₃	—	2	1	no	—
461	C₄×C₁₃	—	2	1	no	—
462	C₄×C₁₃	—	2	1	no	—
463	C₄×C₁₃	—	2	1	no	—
464	C₄×C₁₃	—	2	1	no	—
465	C₄×C₁₃	—	2	1	no	—
466	C₄×C₁₃	—	2	1	no	—
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	1	no	—
470	Dic₁₃	—	2	1	no	—
471	Dic₁₃	—	2	1	no	—
472	Dic₁₃	—	2	1	no	—
473	Dic₁₃	—	2	1	no	—
474	Dic₁₃	—	2	1	no	—
475	Dic₁₃	—	2	1	no	—
476	Dic₁₃	—	2	1	no	—
477	Dic₁₃	—	2	1	no	—
478	Dic₁₃	—	2	1	no	—
479	Dic₁₃	—	2	1	no	—
480	Dic₁₃	—	2	1	no	—
481	Dic₁₃	—	2	1	no	—
482	Dic₁₃	—	2	1	no	—
483	C₄⋊Q₈	—	13	1	no	—
484	C₄⋊Q₈	—	13	1	no	—
485	C₄⋊Q₈	—	13	1	no	—
486	C₄⋊Q₈	—	13	1	no	—
487	C₄⋊Q₈	—	13	1	no	—
488	C₄⋊Q₈	—	13	1	no	—
489	C₄⋊Q₈	—	13	1	no	—
490	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
491	#126	—	13	1	no	—
492	#126	—	13	1	no	—
493	#126	—	13	1	no	—
494	#126	—	13	1	no	—
495	#126	—	13	1	no	—
496	#126	—	13	1	no	—
497	#126	—	13	1	no	—
498	#126	—	13	1	no	—
499	#126	—	13	1	no	—
500	#126	—	13	1	no	—
501	#126	—	13	1	no	—
502	#126	—	13	1	no	—
503	#126	—	13	1	no	—
504	#126	—	13	1	no	—
505	#126	—	13	1	no	—
506	#126	—	13	1	no	—
507	#126	—	13	1	no	—
508	#126	—	13	1	no	—
509	#126	—	13	1	no	—
510	#126	—	13	1	no	—
511	#126	—	13	1	no	—
512	#126	—	13	1	no	—
513	#126	—	13	1	no	—
514	#126	—	13	1	no	—
515	#126	—	13	1	no	—
516	#126	—	13	1	no	—
517	#125	—	13	1	no	—
518	#125	—	13	1	no	—
519	#125	—	13	1	no	—
520	#125	—	13	1	no	—
521	#125	—	13	1	no	—
522	#125	—	13	1	no	—
523	#125	—	13	1	no	—
524	#125	—	13	1	no	—
525	#125	—	13	1	no	—
526	#125	—	13	1	no	—
527	#125	—	13	1	no	—
528	#125	—	13	1	no	—
529	#125	—	13	1	no	—
530	#125	—	13	1	no	—
531	#125	—	13	1	no	—
532	#125	—	13	1	no	—
533	#125	—	13	1	no	—
534	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
535	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
536	#124	—	13	1	no	—
537	#124	—	13	1	no	—
538	#124	—	13	1	no	—
539	#124	—	13	1	no	—
540	#124	—	13	1	no	—
541	#124	—	13	1	no	—
542	#124	—	13	1	no	—
543	#123	—	13	1	no	—
544	#123	—	13	1	no	—
545	#123	—	13	1	no	—
546	#123	—	13	1	no	—
547	#123	—	13	1	no	—
548	#123	—	13	1	no	—
549	#123	—	13	1	no	—
550	#123	—	13	1	no	—
551	#123	—	13	1	no	—
552	#123	—	13	1	no	—
553	#123	—	13	1	no	—
554	#123	—	13	1	no	—
555	#123	—	13	1	no	—
556	#123	—	13	1	no	—
557	#123	—	13	1	no	—
558	#123	—	13	1	no	—
559	C₂²⋊Q₈	—	13	1	no	—
560	C₂²⋊Q₈	—	13	1	no	—
561	C₂²⋊Q₈	—	13	1	no	—
562	C₂²⋊Q₈	—	13	1	no	—
563	C₂²⋊Q₈	—	13	1	no	—
564	C₂²⋊Q₈	—	13	1	no	—
565	C₂²⋊Q₈	—	13	1	no	—
566	C₂²⋊Q₈	—	13	1	no	—
567	C₂²⋊Q₈	—	13	1	no	—
568	C₂²⋊Q₈	—	13	1	no	—
569	C₂²⋊Q₈	—	13	1	no	—
570	C₂²⋊Q₈	—	13	1	no	—
571	C₂²⋊Q₈	—	13	1	no	—
572	C₂²⋊Q₈	—	13	1	no	—
573	C₂²⋊Q₈	—	13	1	no	—
574	C₂²⋊Q₈	—	13	1	no	—
575	C₂²⋊Q₈	—	13	1	no	—
576	C₂²⋊Q₈	—	13	1	no	—
577	C₂²⋊Q₈	—	13	1	no	—
578	C₂²⋊Q₈	—	13	1	no	—
579	C₂²⋊Q₈	—	13	1	no	—
580	C₂²⋊Q₈	—	13	1	no	—
581	C₂²⋊Q₈	—	13	1	no	—
582	C₂²⋊Q₈	—	13	1	no	—
583	C₂²⋊Q₈	—	13	1	no	—
584	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
585	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
586	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
587	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
588	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
589	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
590	#121	—	13	1	no	—
591	#121	—	13	1	no	—
592	#121	—	13	1	no	—
593	#120	—	13	1	no	—
594	#120	—	13	1	no	—
595	C₄×Q₈	—	13	1	no	—
596	C₄×Q₈	—	13	1	no	—
597	C₄×Q₈	—	13	1	no	—
598	C₄×Q₈	—	13	1	no	—
599	C₄×Q₈	—	13	1	no	—
600	C₄×Q₈	—	13	1	no	—
601	C₄×Q₈	—	13	1	no	—
602	C₄×Q₈	—	13	1	no	—
603	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
604	C₄×D₄	—	13	1	no	—
605	C₄×D₄	—	13	1	no	—
606	C₄×D₄	—	13	1	no	—
607	C₄×D₄	—	13	1	no	—
608	C₄×D₄	—	13	1	no	—
609	C₄×D₄	—	13	1	no	—
610	C₄×D₄	—	13	1	no	—
611	C₄×D₄	—	13	1	no	—
612	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
613	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
614	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
615	#117	—	13	1	no	—
616	#117	—	13	1	no	—
617	#117	—	13	1	no	—
618	#117	—	13	1	no	—
619	#117	—	13	1	no	—
620	#117	—	13	1	no	—
621	#117	—	13	1	no	—
622	#117	—	13	1	no	—
623	#117	—	13	1	no	—
624	#117	—	13	1	no	—
625	#117	—	13	1	no	—
626	#117	—	13	1	no	—
627	C₂×C₄⋊C₄	—	13	1	no	—
628	C₂×C₄⋊C₄	—	13	1	no	—
629	C₂×C₄⋊C₄	—	13	1	no	—
630	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
632	C₂×C₂²⋊C₄	—	13	1	no	—
633	C₂×C₂²⋊C₄	—	13	1	no	—
634	C₂×C₂²⋊C₄	—	13	1	no	—
635	C₂×C₂²⋊C₄	—	13	1	no	—
636	C₂×C₂²⋊C₄	—	13	1	no	—
637	C₂×C₄²	—	13	1	no	—
638	C₂×C₁₃	—	2	2	no	—
639	C₂×C₁₃	—	4	1	no	—
640	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
641	C₂×C₁₃	#585	1	1	yes	characteristic
642	C₂×C₁₃	#585	1	1	yes	characteristic
643	D₁₃	—	4	1	no	—
644	D₁₃	—	4	1	no	—
645	D₁₃	—	4	1	no	—
646	C₂⁴	—	13	1	no	—
647	C₂×Q₈	—	13	1	no	—
648	C₂×Q₈	—	13	1	no	—
649	C₂×Q₈	—	13	1	no	—
650	C₂×Q₈	—	13	1	no	—
651	C₂×Q₈	—	13	1	no	—
652	C₂×Q₈	—	13	1	no	—
653	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
654	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
655	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
656	C₂×D₄	—	13	1	no	—
657	C₂×D₄	—	13	1	no	—
658	C₂×D₄	—	13	1	no	—
659	C₂×D₄	—	13	1	no	—
660	C₂×D₄	—	13	1	no	—
661	C₂×D₄	—	13	1	no	—
662	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
663	C₂²×C₄	—	13	1	no	—
664	C₂²×C₄	—	13	1	no	—
665	C₂²×C₄	—	13	1	no	—
666	C₂²×C₄	—	13	1	no	—
667	C₂²×C₄	—	13	1	no	—
668	C₂²×C₄	—	13	1	no	—
669	C₂²×C₄	—	13	1	no	—
670	C₂²×C₄	—	13	1	no	—
671	C₂²×C₄	—	13	1	no	—
672	C₂²×C₄	—	13	1	no	—
673	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
676	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
677	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
679	C₄⋊C₄	—	13	1	no	—
680	C₄⋊C₄	—	13	1	no	—
681	C₄⋊C₄	—	13	1	no	—
682	C₄⋊C₄	—	13	1	no	—
683	C₄⋊C₄	—	13	1	no	—
684	C₄⋊C₄	—	13	1	no	—
685	C₄⋊C₄	—	13	1	no	—
686	C₄⋊C₄	—	13	1	no	—
687	C₄⋊C₄	—	13	1	no	—
688	C₄⋊C₄	—	13	1	no	—
689	C₄⋊C₄	—	13	1	no	—
690	C₄⋊C₄	—	13	1	no	—
691	C₄⋊C₄	—	13	1	no	—
692	C₄⋊C₄	—	13	1	no	—
693	C₄⋊C₄	—	13	1	no	—
694	C₄⋊C₄	—	13	1	no	—
695	C₄⋊C₄	—	13	1	no	—
696	C₄⋊C₄	—	13	1	no	—
697	C₄⋊C₄	—	13	1	no	—
698	C₄⋊C₄	—	13	1	no	—
699	C₄⋊C₄	—	13	1	no	—
700	C₄⋊C₄	—	13	1	no	—
701	C₄⋊C₄	—	13	1	no	—
702	C₄⋊C₄	—	13	1	no	—
703	C₄⋊C₄	—	13	1	no	—
704	C₄⋊C₄	—	13	1	no	—
705	C₄⋊C₄	—	13	1	no	—
706	C₄⋊C₄	—	13	1	no	—
707	C₄⋊C₄	—	13	1	no	—
708	C₄⋊C₄	—	13	1	no	—
709	C₄⋊C₄	—	13	1	no	—
710	C₄⋊C₄	—	13	1	no	—
711	C₄⋊C₄	—	13	1	no	—
712	C₄⋊C₄	—	13	1	no	—
713	C₄⋊C₄	—	13	1	no	—
714	C₄⋊C₄	—	13	1	no	—
715	C₄⋊C₄	—	13	1	no	—
716	C₄⋊C₄	—	13	1	no	—
717	C₄⋊C₄	—	13	1	no	—
718	C₄⋊C₄	—	13	1	no	—
719	C₄⋊C₄	—	13	1	no	—
720	C₄⋊C₄	—	13	1	no	—
721	C₄⋊C₄	—	13	1	no	—
722	C₄⋊C₄	—	13	1	no	—
723	C₄⋊C₄	—	13	1	no	—
724	C₄⋊C₄	—	13	1	no	—
725	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
731	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
741	C₂²⋊C₄	—	13	1	no	—
742	C₂²⋊C₄	—	13	1	no	—
743	C₂²⋊C₄	—	13	1	no	—
744	C₂²⋊C₄	—	13	1	no	—
745	C₂²⋊C₄	—	13	1	no	—
746	C₂²⋊C₄	—	13	1	no	—
747	C₂²⋊C₄	—	13	1	no	—
748	C₂²⋊C₄	—	13	1	no	—
749	C₂²⋊C₄	—	13	1	no	—
750	C₂²⋊C₄	—	13	1	no	—
751	C₂²⋊C₄	—	13	1	no	—
752	C₂²⋊C₄	—	13	1	no	—
753	C₂²⋊C₄	—	13	1	no	—
754	C₂²⋊C₄	—	13	1	no	—
755	C₂²⋊C₄	—	13	1	no	—
756	C₂²⋊C₄	—	13	1	no	—
757	C₂²⋊C₄	—	13	1	no	—
758	C₂²⋊C₄	—	13	1	no	—
759	C₂²⋊C₄	—	13	1	no	—
760	C₂²⋊C₄	—	13	1	no	—
761	C₂²⋊C₄	—	13	1	no	—
762	C₂²⋊C₄	—	13	1	no	—
763	C₂²⋊C₄	—	13	1	no	—
764	C₂²⋊C₄	—	13	1	no	—
765	C₂²⋊C₄	—	13	1	no	—
766	C₂²⋊C₄	—	13	1	no	—
767	C₂²⋊C₄	—	13	1	no	—
768	C₂²⋊C₄	—	13	1	no	—
769	C₂²⋊C₄	—	13	1	no	—
770	C₂²⋊C₄	—	13	1	no	—
771	C₂²⋊C₄	—	13	1	no	—
772	C₂²⋊C₄	—	13	1	no	—
773	C₂²⋊C₄	—	13	1	no	—
774	C₂²⋊C₄	—	13	1	no	—
775	C₂²⋊C₄	—	13	1	no	—
776	C₂²⋊C₄	—	13	1	no	—
777	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
778	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
779	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
780	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
781	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
782	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
783	C₄²	—	13	1	no	—
784	C₄²	—	13	1	no	—
785	C₄²	—	13	1	no	—
786	C₄²	—	13	1	no	—
787	C₄²	—	13	1	no	—
788	C₄²	—	13	1	no	—
789	C₄²	—	13	1	no	—
790	C₄²	—	13	1	no	—
791	C₄²	—	13	1	no	—
792	C₄²	—	13	1	no	—
793	C₄²	—	13	1	no	—
794	C₄²	—	13	1	no	—
795	C₄²	—	13	1	no	—
796	C₄²	—	13	1	no	—
797	C₄²	—	13	1	no	—
798	C₄²	C₂²×D₁₃	1	1	yes	characteristic
799	C₄²	C₂²×D₁₃	1	1	yes	characteristic
800	C₄²	C₂²×D₁₃	1	1	yes	characteristic
801	C₁₃	#3564	1	1	yes	characteristic, complemented, Sylow
802	C₂³	—	13	1	no	—
803	C₂³	—	13	1	no	—
804	C₂³	—	13	1	no	—
805	C₂³	—	26	2	no	—
806	C₂³	—	52	1	no	—
807	C₂³	—	52	1	no	—
808	C₂³	C₂³×D₁₃	1	1	yes	characteristic
809	C₂³	C₂³×D₁₃	1	1	yes	characteristic
810	Q₈	—	4	1	no	—
811	Q₈	—	4	1	no	—
812	Q₈	—	4	1	no	—
813	Q₈	—	52	1	no	—
814	Q₈	—	52	1	no	—
815	Q₈	—	52	1	no	—
816	Q₈	—	52	1	no	—
817	Q₈	—	52	1	no	—
818	Q₈	—	52	1	no	—
819	D₄	—	2	2	no	—
820	D₄	—	26	2	no	—
821	D₄	—	52	1	no	—
822	D₄	—	52	1	no	—
823	D₄	—	52	1	no	—
824	D₄	—	52	1	no	—
825	D₄	—	52	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	13	1	no	—
833	C₂×C₄	—	13	1	no	—
834	C₂×C₄	—	13	1	no	—
835	C₂×C₄	—	13	1	no	—
836	C₂×C₄	—	13	1	no	—
837	C₂×C₄	—	13	1	no	—
838	C₂×C₄	—	13	1	no	—
839	C₂×C₄	—	13	1	no	—
840	C₂×C₄	—	13	1	no	—
841	C₂×C₄	—	13	1	no	—
842	C₂×C₄	—	13	1	no	—
843	C₂×C₄	—	13	1	no	—
844	C₂×C₄	—	13	1	no	—
845	C₂×C₄	—	26	2	no	—
846	C₂×C₄	—	26	2	no	—
847	C₂×C₄	—	52	1	no	—
848	C₂×C₄	—	52	1	no	—
849	C₂×C₄	—	52	1	no	—
850	C₂×C₄	—	52	1	no	—
851	C₂×C₄	—	52	1	no	—
852	C₂×C₄	—	52	1	no	—
853	C₂×C₄	—	52	1	no	—
854	C₂×C₄	—	52	1	no	—
855	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
857	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
858	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
859	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
860	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
861	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
862	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
863	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
864	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
865	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
866	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
867	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	26	1	no	—
874	C₂²	—	26	1	no	—
875	C₂²	—	26	1	no	—
876	C₂²	—	26	1	no	—
877	C₂²	—	26	1	no	—
878	C₂²	—	26	1	no	—
879	C₂²	—	26	1	no	—
880	C₂²	—	26	1	no	—
881	C₂²	—	26	1	no	—
882	C₂²	—	104	2	no	—
883	C₂²	#88254	1	2	yes	—
884	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	26	1	no	—
899	C₄	—	26	1	no	—
900	C₄	—	26	1	no	—
901	C₄	—	26	1	no	—
902	C₄	—	26	1	no	—
903	C₄	—	26	1	no	—
904	C₄	—	26	1	no	—
905	C₄	—	26	1	no	—
906	C₄	—	26	1	no	—
907	C₄	—	26	1	no	—
908	C₄	—	26	1	no	—
909	C₄	—	26	1	no	—
910	C₄	—	26	1	no	—
911	C₂	—	2	2	no	—
912	C₂	—	4	1	no	—
913	C₂	—	52	1	no	—
914	C₂	—	52	1	no	—
915	C₂	—	52	1	no	—
916	C₂	C₂×#88254	1	1	yes	characteristic
917	C₂	#11719648	1	1	yes	characteristic
918	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#554	C₂
prime radical	#11719265	C₂
hypercenter	#554	D₁₃
hypocenter	C₁₃	#3564
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₁₃×#554	C₂	semidirect
2. #11719440	C₂	semidirect
3. #11719436	C₂	semidirect
4. #11719404	C₂	semidirect
5. #11719401	C₂	semidirect
6. #11719401	C₂	semidirect
7. #11719398	C₂	semidirect
8. #11719351	C₂	semidirect
9. #11719351	C₂	semidirect
10. #11719348	C₂	semidirect
11. #11719347	C₂	semidirect
12. #11719346	C₂	semidirect
13. #11719345	C₂	semidirect
14. #11719343	C₂	semidirect
15. #11719342	C₂	semidirect
16. #11719342	C₂	semidirect
17. #11719339	C₂	semidirect
18. #11719328	C₂	semidirect
19. #11719327	C₂	semidirect
20. #11719288	C₂	semidirect
21. #11719273	C₂	semidirect
22. #11719269	C₂	semidirect
24. #11719261	C₂	semidirect
25. #11719261	C₂	semidirect
26. #11719246	C₂	semidirect
27. #11719243	C₂	semidirect
28. #11719220	C₂	semidirect
29. #11719218	C₂	semidirect
30. C₂×#88152	C₂	semidirect
31. #11719216	C₂	semidirect
32. C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₁₃×#125	C₂²	semidirect
34. C₁₃×#125	C₂²	semidirect
38. C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₁₃×C₂²⋊Q₈	C₂²	semidirect
40. C₁₃×C₂²⋊Q₈	C₂²	semidirect
41. C₄×Q₈×C₁₃	C₂²	semidirect
46. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
53. #88200	C₂²	semidirect
54. Q₈×Dic₁₃	C₂²	semidirect
55. Q₈×Dic₁₃	C₂²	semidirect
56. #88198	C₂²	semidirect
57. #88198	C₂²	semidirect
58. #88198	C₂²	semidirect
67. #88183	C₂²	semidirect
73. C₄×C₂²⋊D₁₃	C₂²	semidirect
77. #88180	C₂²	semidirect
78. #88180	C₂²	semidirect
83. #88178	C₂²	semidirect
84. #88178	C₂²	semidirect
102. #88152	C₂²	semidirect
103. #88152	C₂²	semidirect
104. #88152	C₂²	semidirect
107. #88151	C₂²	semidirect
114. #88150	C₂²	semidirect
115. #88150	C₂²	semidirect
116. #88150	C₂²	semidirect
126. #88146	C₂²	semidirect
127. C₄⋊C₄×D₁₃	C₂²	semidirect
128. #88144	C₂²	semidirect
129. #88144	C₂²	semidirect
130. #88144	C₂²	semidirect
131. #88143	C₂²	semidirect
132. #88143	C₂²	semidirect
133. #88143	C₂²	semidirect
134. #88143	C₂²	semidirect
135. #88143	C₂²	semidirect
136. #88143	C₂²	semidirect
137. #88143	C₂²	semidirect
138. #88143	C₂²	semidirect
139. #88143	C₂²	semidirect
140. #88143	C₂²	semidirect
141. #88143	C₂²	semidirect
142. #88143	C₂²	semidirect
143. #88142	C₂²	semidirect
144. #88142	C₂²	semidirect
145. #88142	C₂²	semidirect
146. #88142	C₂²	semidirect
147. #88141	C₂²	semidirect
148. #88141	C₂²	semidirect
149. #88141	C₂²	semidirect
150. #88141	C₂²	semidirect
156. #88139	C₂²	semidirect
160. #88137	C₂²	semidirect
164. #88133	C₂²	semidirect
165. #88133	C₂²	semidirect
166. #88133	C₂²	semidirect
167. #88133	C₂²	semidirect
178. #88130	C₂²	semidirect
182. #88126	C₂²	semidirect
183. #88124	C₂²	semidirect
184. #88124	C₂²	semidirect
185. C₄×Dic₂₆	C₂²	semidirect
186. C₄×Dic₂₆	C₂²	semidirect
416. #554	D₁₃	semidirect
490. C₄⋊Q₈	C₂×D₁₃	semidirect
534. #125	C₂×D₁₃	semidirect
535. #125	C₂×D₁₃	semidirect
587. C₂²⋊Q₈	C₂×D₁₃	semidirect
588. C₂²⋊Q₈	C₂×D₁₃	semidirect
589. C₂²⋊Q₈	C₂×D₁₃	semidirect
603. C₄×Q₈	C₂×D₁₃	semidirect
631. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
801. C₁₃	#3564	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#554	2
#11719440	2
#11719436	2
#11719404	2
#11719401	2
#11719398	2
#11719351	2
#11719348	2
#11719347	2
#11719346	2
#11719345	2
#11719343	2
#11719342	2
#11719339	2
#11719328	2
#11719327	2
#11719288	2
#11719273	2
#11719269	2
#11719265	2
#11719261	2
#11719246	2
#11719243	2
#11719220	2
#11719218	2
C₂×#88152	2
#11719216	2
#3564	13