Subgroups — #13129489

Order 1664.

954 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719417	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719415	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719410	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719406	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	#11719369	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719365	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719363	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719354	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719326	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719326	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719325	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719324	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719321	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719318	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719318	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719307	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719266	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719265	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719263	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719261	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719245	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719239	C₂	1	1	yes	maximal, characteristic, complemented
29	#11719236	C₂	1	1	yes	maximal, characteristic, complemented
30	#11719220	C₂	1	1	yes	maximal, characteristic, complemented
31	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
32	C₁₃×#126	C₂²	1	1	yes	characteristic
33	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#123	C₂²	1	1	yes	characteristic
36	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₁₃×#121	C₂²	1	1	yes	characteristic
40	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
41	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
44	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	#88194	C₂²	1	1	yes	characteristic
48	#88193	C₂²	1	1	yes	characteristic
49	#88193	C₂²	1	1	yes	characteristic
50	#88193	C₂²	1	1	yes	characteristic
51	#88193	C₂²	1	1	yes	characteristic
52	#88193	C₂²	1	1	yes	characteristic
53	#88193	C₂²	1	1	yes	characteristic, complemented
54	#88192	C₂²	1	1	yes	characteristic
55	#88192	C₂²	1	1	yes	characteristic
56	#88192	C₂²	1	1	yes	characteristic
57	#88192	C₂²	1	1	yes	characteristic, complemented
58	#88191	C₂²	1	1	yes	characteristic
59	#88191	C₂²	1	1	yes	characteristic
60	#88191	C₂²	1	1	yes	characteristic
61	#88190	C₂²	1	1	yes	characteristic
62	#88190	C₂²	1	1	yes	characteristic
63	#88190	C₂²	1	1	yes	characteristic, complemented
64	#88189	C₂²	1	1	yes	characteristic
65	#88189	C₂²	1	1	yes	characteristic
66	#88189	C₂²	1	1	yes	characteristic
67	#88189	C₂²	1	1	yes	characteristic, complemented
68	#88189	C₂²	1	1	yes	characteristic, complemented
69	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
70	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
71	#88184	C₂²	1	1	yes	characteristic
72	#88184	C₂²	1	1	yes	characteristic
73	#88183	C₂²	1	1	yes	characteristic
74	#88183	C₂²	1	1	yes	characteristic
75	#88183	C₂²	1	1	yes	characteristic
76	#88183	C₂²	1	1	yes	characteristic
77	#88183	C₂²	1	1	yes	characteristic
78	#88183	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₂×#6103	C₂²	1	1	yes	characteristic
86	#88180	C₂²	1	1	yes	characteristic
87	#88180	C₂²	1	1	yes	characteristic, complemented
88	#88180	C₂²	1	1	yes	characteristic, complemented
89	#88178	C₂²	1	1	yes	characteristic
90	#88178	C₂²	1	1	yes	characteristic, complemented
91	#88178	C₂²	1	1	yes	characteristic, complemented
92	#88178	C₂²	1	1	yes	characteristic, complemented
93	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
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	#88151	C₂²	1	1	yes	characteristic
104	#88151	C₂²	1	1	yes	characteristic
105	#88150	C₂²	1	1	yes	characteristic
106	#88150	C₂²	1	1	yes	characteristic
107	#88150	C₂²	1	1	yes	characteristic
108	#88150	C₂²	1	1	yes	characteristic
109	#88150	C₂²	1	1	yes	characteristic, complemented
110	#88150	C₂²	1	1	yes	characteristic, complemented
111	#88148	C₂²	1	1	yes	characteristic
112	#88148	C₂²	1	1	yes	characteristic
113	#88148	C₂²	1	1	yes	characteristic
114	#88148	C₂²	1	1	yes	characteristic
115	#88147	C₂²	1	1	yes	characteristic
116	#88146	C₂²	1	1	yes	characteristic
117	#88146	C₂²	1	1	yes	characteristic
118	#88146	C₂²	1	1	yes	characteristic, complemented
119	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
120	#88144	C₂²	1	1	yes	characteristic, complemented
121	#88144	C₂²	1	1	yes	characteristic, complemented
122	#88143	C₂²	1	1	yes	characteristic, complemented
123	#88143	C₂²	1	1	yes	characteristic, complemented
124	#88143	C₂²	1	1	yes	characteristic, complemented
125	#88143	C₂²	1	1	yes	characteristic, complemented
126	#88143	C₂²	1	1	yes	characteristic, complemented
127	#88143	C₂²	1	1	yes	characteristic, complemented
128	#88143	C₂²	1	1	yes	characteristic, complemented
129	#88143	C₂²	1	1	yes	characteristic, complemented
130	#88142	C₂²	1	1	yes	characteristic, complemented
131	#88142	C₂²	1	1	yes	characteristic, complemented
132	#88141	C₂²	1	1	yes	characteristic, complemented
133	#88141	C₂²	1	1	yes	characteristic, complemented
134	#88141	C₂²	1	1	yes	characteristic, complemented
135	#88140	C₂²	1	1	yes	characteristic
136	#88140	C₂²	1	1	yes	characteristic
137	#88140	C₂²	1	1	yes	characteristic, complemented
138	#88139	C₂²	1	1	yes	characteristic
139	#88139	C₂²	1	1	yes	characteristic
140	#88139	C₂²	1	1	yes	characteristic
141	#88139	C₂²	1	1	yes	characteristic
142	#88139	C₂²	1	1	yes	characteristic
143	#88139	C₂²	1	1	yes	characteristic
144	#88139	C₂²	1	1	yes	characteristic, complemented
145	#88139	C₂²	1	1	yes	characteristic, complemented
146	#88138	C₂²	1	1	yes	characteristic
147	#88138	C₂²	1	1	yes	characteristic
148	#88137	C₂²	1	1	yes	characteristic
149	#88137	C₂²	1	1	yes	characteristic
150	#88137	C₂²	1	1	yes	characteristic
151	#88137	C₂²	1	1	yes	characteristic, complemented
152	#88136	C₂²	1	1	yes	characteristic
153	#88135	C₂²	1	1	yes	characteristic
154	#88135	C₂²	1	1	yes	characteristic
155	#88135	C₂²	1	1	yes	characteristic
156	#88135	C₂²	1	1	yes	characteristic, complemented
157	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
158	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
159	#88133	C₂²	1	1	yes	characteristic
160	#88133	C₂²	1	1	yes	characteristic
161	#88133	C₂²	1	1	yes	characteristic
162	#88133	C₂²	1	1	yes	characteristic
163	#88133	C₂²	1	1	yes	characteristic, complemented
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	#88132	C₂²	1	1	yes	characteristic
168	#88132	C₂²	1	1	yes	characteristic
169	#88132	C₂²	1	1	yes	characteristic, complemented
170	#88132	C₂²	1	1	yes	characteristic, complemented
171	#88132	C₂²	1	1	yes	characteristic, complemented
172	#88132	C₂²	1	1	yes	characteristic, complemented
173	#88131	C₂²	1	1	yes	characteristic
174	#88131	C₂²	1	1	yes	characteristic, complemented
175	#88130	C₂²	1	1	yes	characteristic
176	#88130	C₂²	1	1	yes	characteristic
177	#88129	C₂²	1	1	yes	characteristic
178	C₄×D₅₂	C₂²	1	1	yes	characteristic
179	#88126	C₂²	1	1	yes	characteristic
180	#88126	C₂²	1	1	yes	characteristic
181	#88126	C₂²	1	1	yes	characteristic, complemented
182	#88124	C₂²	1	1	yes	characteristic, complemented
183	#88123	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₂₆	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×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₂×D₄×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	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
210	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
211	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
212	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
213	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
214	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
215	C₂×D₅₂	C₂³	1	1	yes	characteristic
216	C₂×D₅₂	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
224	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
225	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
226	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
227	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
228	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
229	C₂×Dic₂₆	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₁₃×C₄⋊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	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₄²×C₁₃	C₂³	1	1	yes	characteristic
251	C₄²×C₁₃	C₂³	1	1	yes	characteristic
252	C₄²×C₁₃	C₂³	1	1	yes	characteristic
253	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
254	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
255	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
256	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
257	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₁₃	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	#6103	C₂³	1	1	yes	characteristic
282	#6103	C₂³	1	1	yes	characteristic
283	#6103	C₂³	1	1	yes	characteristic
284	#6103	C₂³	1	1	yes	characteristic
285	#6103	C₂³	1	1	yes	characteristic
286	#6103	C₂³	1	1	yes	characteristic
287	#6103	C₂³	1	1	yes	characteristic
288	#6103	C₂³	1	1	yes	characteristic
289	#6103	C₂³	1	1	yes	characteristic
290	#6103	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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
296	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₁₃	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	#6101	C₂³	1	1	yes	characteristic
328	#6101	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	#3566	—	13	1	no	maximal, Sylow
343	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂²×D₁₃	—	4	1	no	—
348	C₂²×D₁₃	—	4	1	no	—
349	C₂²×D₁₃	—	4	1	no	—
350	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
351	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
352	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
353	D₄×C₁₃	—	4	1	no	—
354	D₄×C₁₃	—	4	1	no	—
355	D₄×C₁₃	—	4	1	no	—
356	D₄×C₁₃	—	4	1	no	—
357	D₄×C₁₃	—	4	1	no	—
358	D₄×C₁₃	—	4	1	no	—
359	C₂×C₄×C₁₃	—	4	1	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
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	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₂²⋊D₁₃	—	4	1	no	—
377	C₂²⋊D₁₃	—	4	1	no	—
378	C₂²⋊D₁₃	—	4	1	no	—
379	C₂²⋊D₁₃	—	4	1	no	—
380	C₂²⋊D₁₃	—	4	1	no	—
381	C₂²⋊D₁₃	—	4	1	no	—
382	C₂²⋊D₁₃	—	4	1	no	—
383	C₂²⋊D₁₃	—	4	1	no	—
384	C₂²⋊D₁₃	—	4	1	no	—
385	C₂²⋊D₁₃	—	4	1	no	—
386	C₂×Dic₁₃	—	4	1	no	—
387	C₂×Dic₁₃	—	4	1	no	—
388	C₂×Dic₁₃	—	4	1	no	—
389	C₂×Dic₁₃	—	4	1	no	—
390	C₂×Dic₁₃	—	4	1	no	—
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	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
404	D₅₂	—	4	1	no	—
405	D₅₂	—	4	1	no	—
406	C₄×D₁₃	—	4	1	no	—
407	C₄×D₁₃	—	4	1	no	—
408	C₄×D₁₃	—	4	1	no	—
409	C₄×D₁₃	—	4	1	no	—
410	C₄×D₁₃	—	4	1	no	—
411	C₄×D₁₃	—	4	1	no	—
412	C₄×D₁₃	—	4	1	no	—
413	Dic₂₆	—	4	1	no	—
414	Dic₂₆	—	4	1	no	—
415	Dic₂₆	—	4	1	no	—
416	Dic₂₆	—	4	1	no	—
417	Dic₂₆	—	4	1	no	—
418	Dic₂₆	—	4	1	no	—
419	#563	—	13	1	no	—
420	#562	—	13	1	no	—
421	#562	—	13	1	no	—
422	#560	—	13	1	no	—
423	#559	—	13	1	no	—
424	#556	—	13	1	no	—
425	#555	—	13	1	no	—
426	#553	—	13	1	no	—
427	#553	—	13	1	no	—
428	#553	D₁₃	1	1	yes	characteristic, complemented
429	#552	—	13	1	no	—
430	#552	—	13	1	no	—
431	#552	—	13	1	no	—
432	#551	—	13	1	no	—
433	#551	—	13	1	no	—
434	#551	—	13	1	no	—
435	#542	—	13	1	no	—
436	#542	—	13	1	no	—
437	#542	—	13	1	no	—
438	#541	—	13	1	no	—
439	#541	—	13	1	no	—
440	#540	—	13	1	no	—
441	#539	—	13	1	no	—
442	#539	—	13	1	no	—
443	#539	—	13	1	no	—
444	#538	—	13	1	no	—
445	#538	—	13	1	no	—
446	#538	—	13	1	no	—
447	#529	—	13	1	no	—
448	#529	—	13	1	no	—
449	#529	—	13	1	no	—
450	C₂²×C₁₃	—	2	1	no	—
451	C₂²×C₁₃	—	2	1	no	—
452	C₂²×C₁₃	—	2	1	no	—
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	2	1	no	—
456	C₂²×C₁₃	—	2	1	no	—
457	C₂²×C₁₃	—	2	1	no	—
458	C₂²×C₁₃	—	2	1	no	—
459	C₂²×C₁₃	—	2	1	no	—
460	C₂²×C₁₃	—	2	1	no	—
461	C₂²×C₁₃	—	2	1	no	—
462	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
463	C₂×D₁₃	—	2	1	no	—
464	C₂×D₁₃	—	2	1	no	—
465	C₂×D₁₃	—	2	1	no	—
466	C₂×D₁₃	—	2	1	no	—
467	C₂×D₁₃	—	2	1	no	—
468	C₂×D₁₃	—	2	1	no	—
469	C₂×D₁₃	—	2	1	no	—
470	C₂×D₁₃	—	2	1	no	—
471	C₂×D₁₃	—	2	1	no	—
472	C₂×D₁₃	—	8	2	no	—
473	C₄×C₁₃	—	2	1	no	—
474	C₄×C₁₃	—	2	1	no	—
475	C₄×C₁₃	—	2	1	no	—
476	C₄×C₁₃	—	2	1	no	—
477	C₄×C₁₃	—	2	1	no	—
478	C₄×C₁₃	—	2	1	no	—
479	C₄×C₁₃	—	2	1	no	—
480	C₄×C₁₃	—	2	1	no	—
481	C₄×C₁₃	—	2	1	no	—
482	C₄×C₁₃	—	2	1	no	—
483	C₄×C₁₃	—	2	1	no	—
484	Dic₁₃	—	2	1	no	—
485	Dic₁₃	—	2	1	no	—
486	Dic₁₃	—	2	1	no	—
487	Dic₁₃	—	2	1	no	—
488	Dic₁₃	—	2	1	no	—
489	Dic₁₃	—	2	1	no	—
490	Dic₁₃	—	2	1	no	—
491	Dic₁₃	—	2	1	no	—
492	Dic₁₃	—	2	1	no	—
493	Dic₁₃	—	2	1	no	—
494	Dic₁₃	—	2	1	no	—
495	Dic₁₃	—	2	1	no	—
496	Dic₁₃	—	2	1	no	—
497	C₄⋊Q₈	—	13	1	no	—
498	C₄⋊Q₈	—	13	1	no	—
499	C₄⋊Q₈	—	13	1	no	—
500	#127	—	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	#126	—	13	1	no	—
518	#126	—	13	1	no	—
519	#126	C₂×D₁₃	1	1	yes	characteristic
520	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
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	C₂×D₁₃	1	1	yes	characteristic, complemented
533	#124	—	13	1	no	—
534	#124	—	13	1	no	—
535	#124	—	13	1	no	—
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	#124	—	13	1	no	—
544	#124	—	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	#123	—	13	1	no	—
560	#123	—	13	1	no	—
561	#123	—	13	1	no	—
562	#123	—	13	1	no	—
563	#123	—	13	1	no	—
564	#123	—	13	1	no	—
565	#123	—	13	1	no	—
566	#123	—	13	1	no	—
567	#123	C₂×D₁₃	1	1	yes	characteristic
568	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
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	—	13	1	no	—
585	C₂²⋊Q₈	—	13	1	no	—
586	C₂²⋊Q₈	—	13	1	no	—
587	#121	—	13	1	no	—
588	#121	—	13	1	no	—
589	#121	—	13	1	no	—
590	#121	—	13	1	no	—
591	#121	—	13	1	no	—
592	#121	—	13	1	no	—
593	#121	—	13	1	no	—
594	#121	—	13	1	no	—
595	#121	—	13	1	no	—
596	#121	—	13	1	no	—
597	#121	—	13	1	no	—
598	#121	—	13	1	no	—
599	#121	—	13	1	no	—
600	#121	—	13	1	no	—
601	#121	C₂×D₁₃	1	1	yes	characteristic
602	#121	C₂×D₁₃	1	1	yes	characteristic
603	#121	C₂×D₁₃	1	1	yes	characteristic
604	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
605	#120	—	13	1	no	—
606	#120	—	13	1	no	—
607	#120	—	13	1	no	—
608	#120	—	13	1	no	—
609	C₄×Q₈	—	13	1	no	—
610	C₄×Q₈	—	13	1	no	—
611	C₄×Q₈	—	13	1	no	—
612	C₄×Q₈	—	13	1	no	—
613	C₄×Q₈	—	13	1	no	—
614	C₄×Q₈	—	13	1	no	—
615	C₄×D₄	—	13	1	no	—
616	C₄×D₄	—	13	1	no	—
617	C₄×D₄	—	13	1	no	—
618	C₄×D₄	—	13	1	no	—
619	C₄×D₄	—	13	1	no	—
620	C₄×D₄	—	13	1	no	—
621	C₄×D₄	—	13	1	no	—
622	C₄×D₄	—	13	1	no	—
623	C₄×D₄	—	13	1	no	—
624	C₄×D₄	—	13	1	no	—
625	C₄×D₄	—	13	1	no	—
626	C₄×D₄	—	13	1	no	—
627	C₄×D₄	—	13	1	no	—
628	C₄×D₄	—	13	1	no	—
629	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
630	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
631	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
632	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
633	#117	—	13	1	no	—
634	#117	—	13	1	no	—
635	#117	—	13	1	no	—
636	#117	—	13	1	no	—
637	#117	—	13	1	no	—
638	#117	—	13	1	no	—
639	#117	—	13	1	no	—
640	#117	—	13	1	no	—
641	#117	—	13	1	no	—
642	#117	—	13	1	no	—
643	#117	—	13	1	no	—
644	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
645	C₂×C₄⋊C₄	—	13	1	no	—
646	C₂×C₄⋊C₄	—	13	1	no	—
647	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
648	C₂×C₂²⋊C₄	—	13	1	no	—
649	C₂×C₂²⋊C₄	—	13	1	no	—
650	C₂×C₂²⋊C₄	—	13	1	no	—
651	C₂×C₄²	—	13	1	no	—
652	C₂×C₁₃	—	4	1	no	—
653	C₂×C₁₃	—	4	1	no	—
654	C₂×C₁₃	—	4	1	no	—
655	C₂×C₁₃	—	4	1	no	—
656	C₂×C₁₃	#585	1	1	yes	characteristic
657	C₂×C₁₃	#585	1	1	yes	characteristic
658	C₂×C₁₃	#585	1	1	yes	characteristic
659	D₁₃	—	4	1	no	—
660	D₁₃	—	4	1	no	—
661	D₁₃	—	4	1	no	—
662	C₂⁴	—	13	1	no	—
663	C₂×Q₈	—	13	1	no	—
664	C₂×Q₈	—	13	1	no	—
665	C₂×Q₈	—	13	1	no	—
666	C₂×Q₈	—	13	1	no	—
667	C₂×Q₈	—	13	1	no	—
668	C₂×Q₈	—	13	1	no	—
669	C₂×D₄	—	13	1	no	—
670	C₂×D₄	—	13	1	no	—
671	C₂×D₄	—	13	1	no	—
672	C₂×D₄	—	13	1	no	—
673	C₂×D₄	—	13	1	no	—
674	C₂×D₄	—	13	1	no	—
675	C₂×D₄	—	13	1	no	—
676	C₂×D₄	—	13	1	no	—
677	C₂×D₄	—	13	1	no	—
678	C₂×D₄	—	13	1	no	—
679	C₂×D₄	—	13	1	no	—
680	C₂×D₄	—	13	1	no	—
681	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
682	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
683	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
684	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
685	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
686	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
687	C₂²×C₄	—	13	1	no	—
688	C₂²×C₄	—	13	1	no	—
689	C₂²×C₄	—	13	1	no	—
690	C₂²×C₄	—	13	1	no	—
691	C₂²×C₄	—	13	1	no	—
692	C₂²×C₄	—	13	1	no	—
693	C₂²×C₄	—	13	1	no	—
694	C₂²×C₄	—	13	1	no	—
695	C₂²×C₄	—	13	1	no	—
696	C₂²×C₄	—	13	1	no	—
697	C₂²×C₄	—	13	1	no	—
698	C₂²×C₄	—	13	1	no	—
699	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
701	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
702	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
726	C₄⋊C₄	—	13	1	no	—
727	C₄⋊C₄	—	13	1	no	—
728	C₄⋊C₄	—	13	1	no	—
729	C₄⋊C₄	—	13	1	no	—
730	C₄⋊C₄	—	13	1	no	—
731	C₄⋊C₄	—	13	1	no	—
732	C₄⋊C₄	—	13	1	no	—
733	C₄⋊C₄	—	13	1	no	—
734	C₄⋊C₄	—	13	1	no	—
735	C₄⋊C₄	—	13	1	no	—
736	C₄⋊C₄	—	13	1	no	—
737	C₄⋊C₄	—	13	1	no	—
738	C₄⋊C₄	—	13	1	no	—
739	C₄⋊C₄	—	13	1	no	—
740	C₄⋊C₄	—	13	1	no	—
741	C₄⋊C₄	—	13	1	no	—
742	C₄⋊C₄	—	13	1	no	—
743	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
778	C₂²⋊C₄	—	13	1	no	—
779	C₂²⋊C₄	—	13	1	no	—
780	C₂²⋊C₄	—	13	1	no	—
781	C₂²⋊C₄	—	13	1	no	—
782	C₂²⋊C₄	—	13	1	no	—
783	C₂²⋊C₄	—	13	1	no	—
784	C₂²⋊C₄	—	13	1	no	—
785	C₂²⋊C₄	—	13	1	no	—
786	C₂²⋊C₄	—	13	1	no	—
787	C₂²⋊C₄	—	13	1	no	—
788	C₂²⋊C₄	—	13	1	no	—
789	C₂²⋊C₄	—	13	1	no	—
790	C₂²⋊C₄	—	13	1	no	—
791	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
792	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
801	C₄²	—	13	1	no	—
802	C₄²	—	13	1	no	—
803	C₄²	—	13	1	no	—
804	C₄²	—	13	1	no	—
805	C₄²	—	13	1	no	—
806	C₄²	—	13	1	no	—
807	C₄²	—	13	1	no	—
808	C₄²	—	13	1	no	—
809	C₄²	—	13	1	no	—
810	C₄²	—	13	1	no	—
811	C₄²	—	13	1	no	—
812	C₄²	—	13	1	no	—
813	C₄²	—	13	1	no	—
814	C₄²	C₂²×D₁₃	1	1	yes	characteristic
815	C₄²	C₂²×D₁₃	1	1	yes	characteristic
816	C₄²	C₂²×D₁₃	1	1	yes	characteristic
817	C₁₃	#3566	1	1	yes	characteristic, complemented, Sylow
818	C₂³	—	13	1	no	—
819	C₂³	—	13	1	no	—
820	C₂³	—	13	1	no	—
821	C₂³	—	52	1	no	—
822	C₂³	—	52	1	no	—
823	C₂³	—	52	1	no	—
824	C₂³	C₂³×D₁₃	1	1	yes	characteristic
825	C₂³	C₂³×D₁₃	1	1	yes	characteristic
826	C₂³	C₂³×D₁₃	1	1	yes	characteristic
827	C₂³	C₂³×D₁₃	1	1	yes	characteristic
828	Q₈	—	52	1	no	—
829	Q₈	—	52	1	no	—
830	Q₈	—	52	1	no	—
831	Q₈	—	52	1	no	—
832	Q₈	—	52	1	no	—
833	Q₈	—	52	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	52	1	no	—
841	D₄	—	52	1	no	—
842	D₄	—	52	1	no	—
843	D₄	—	52	1	no	—
844	D₄	—	52	1	no	—
845	D₄	—	52	1	no	—
846	D₄	—	52	1	no	—
847	D₄	—	52	1	no	—
848	D₄	—	52	1	no	—
849	D₄	—	52	1	no	—
850	D₄	—	52	1	no	—
851	D₄	—	52	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	13	1	no	—
859	C₂×C₄	—	13	1	no	—
860	C₂×C₄	—	13	1	no	—
861	C₂×C₄	—	13	1	no	—
862	C₂×C₄	—	13	1	no	—
863	C₂×C₄	—	13	1	no	—
864	C₂×C₄	—	13	1	no	—
865	C₂×C₄	—	13	1	no	—
866	C₂×C₄	—	13	1	no	—
867	C₂×C₄	—	13	1	no	—
868	C₂×C₄	—	13	1	no	—
869	C₂×C₄	—	13	1	no	—
870	C₂×C₄	—	13	1	no	—
871	C₂×C₄	—	52	1	no	—
872	C₂×C₄	—	52	1	no	—
873	C₂×C₄	—	52	1	no	—
874	C₂×C₄	—	52	1	no	—
875	C₂×C₄	—	52	1	no	—
876	C₂×C₄	—	52	1	no	—
877	C₂×C₄	—	52	1	no	—
878	C₂×C₄	—	52	1	no	—
879	C₂×C₄	—	52	1	no	—
880	C₂×C₄	—	52	1	no	—
881	C₂×C₄	—	52	1	no	—
882	C₂×C₄	—	52	1	no	—
883	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
884	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
885	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	26	1	no	—
907	C₂²	—	26	1	no	—
908	C₂²	—	26	1	no	—
909	C₂²	—	26	1	no	—
910	C₂²	—	26	1	no	—
911	C₂²	—	26	1	no	—
912	C₂²	—	26	1	no	—
913	C₂²	—	26	1	no	—
914	C₂²	—	26	1	no	—
915	C₂²	—	104	2	no	—
916	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	26	1	no	—
929	C₄	—	26	1	no	—
930	C₄	—	26	1	no	—
931	C₄	—	26	1	no	—
932	C₄	—	26	1	no	—
933	C₄	—	26	1	no	—
934	C₄	—	26	1	no	—
935	C₄	—	26	1	no	—
936	C₄	—	26	1	no	—
937	C₄	—	26	1	no	—
938	C₄	—	26	1	no	—
939	C₄	—	26	1	no	—
940	C₄	—	26	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	1	no	—
943	C₂	—	4	1	no	—
944	C₂	—	4	1	no	—
945	C₂	—	52	1	no	—
946	C₂	—	52	1	no	—
947	C₂	—	52	1	no	—
948	C₂	#11719648	1	1	yes	characteristic
949	C₂	#11719648	1	1	yes	characteristic
950	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#553	C₂
hypercenter	#553	D₁₃
hypocenter	C₁₃	#3566
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₁₃×#553	C₂	semidirect
2. #11719417	C₂	semidirect
3. #11719415	C₂	semidirect
4. #11719410	C₂	semidirect
5. #11719406	C₂	semidirect
6. #11719401	C₂	semidirect
7. #11719398	C₂	semidirect
8. #11719369	C₂	semidirect
9. #11719365	C₂	semidirect
10. #11719363	C₂	semidirect
11. #11719354	C₂	semidirect
12. #11719326	C₂	semidirect
13. #11719326	C₂	semidirect
14. #11719325	C₂	semidirect
15. #11719324	C₂	semidirect
16. #11719321	C₂	semidirect
17. #11719318	C₂	semidirect
18. #11719318	C₂	semidirect
19. #11719307	C₂	semidirect
20. #11719266	C₂	semidirect
21. #11719265	C₂	semidirect
22. #11719263	C₂	semidirect
23. #11719261	C₂	semidirect
24. #11719247	C₂	semidirect
25. #11719245	C₂	semidirect
26. #11719243	C₂	semidirect
27. #11719243	C₂	semidirect
28. #11719239	C₂	semidirect
29. #11719236	C₂	semidirect
30. #11719220	C₂	semidirect
31. #11719218	C₂	semidirect
33. C₁₃×#126	C₂²	semidirect
34. C₁₃×#125	C₂²	semidirect
36. C₁₃×#123	C₂²	semidirect
40. C₁₃×#121	C₂²	semidirect
43. C₄×D₄×C₁₃	C₂²	semidirect
44. C₄×D₄×C₁₃	C₂²	semidirect
45. C₁₃×#117	C₂²	semidirect
46. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
53. #88193	C₂²	semidirect
57. #88192	C₂²	semidirect
63. #88190	C₂²	semidirect
67. #88189	C₂²	semidirect
68. #88189	C₂²	semidirect
70. D₄×Dic₁₃	C₂²	semidirect
78. #88183	C₂²	semidirect
83. C₄×C₂²⋊D₁₃	C₂²	semidirect
84. C₄×C₂²⋊D₁₃	C₂²	semidirect
87. #88180	C₂²	semidirect
88. #88180	C₂²	semidirect
90. #88178	C₂²	semidirect
91. #88178	C₂²	semidirect
92. #88178	C₂²	semidirect
93. C₂×#6101	C₂²	semidirect
94. C₂×C₄×Dic₁₃	C₂²	semidirect
102. #88152	C₂²	semidirect
109. #88150	C₂²	semidirect
110. #88150	C₂²	semidirect
118. #88146	C₂²	semidirect
119. C₄⋊C₄×D₁₃	C₂²	semidirect
120. #88144	C₂²	semidirect
121. #88144	C₂²	semidirect
122. #88143	C₂²	semidirect
123. #88143	C₂²	semidirect
124. #88143	C₂²	semidirect
125. #88143	C₂²	semidirect
126. #88143	C₂²	semidirect
127. #88143	C₂²	semidirect
128. #88143	C₂²	semidirect
129. #88143	C₂²	semidirect
130. #88142	C₂²	semidirect
131. #88142	C₂²	semidirect
132. #88141	C₂²	semidirect
133. #88141	C₂²	semidirect
134. #88141	C₂²	semidirect
137. #88140	C₂²	semidirect
144. #88139	C₂²	semidirect
145. #88139	C₂²	semidirect
151. #88137	C₂²	semidirect
156. #88135	C₂²	semidirect
163. #88133	C₂²	semidirect
164. #88133	C₂²	semidirect
165. #88133	C₂²	semidirect
166. #88133	C₂²	semidirect
169. #88132	C₂²	semidirect
170. #88132	C₂²	semidirect
171. #88132	C₂²	semidirect
172. #88132	C₂²	semidirect
174. #88131	C₂²	semidirect
181. #88126	C₂²	semidirect
182. #88124	C₂²	semidirect
183. #88123	C₂²	semidirect
184. C₄×Dic₂₆	C₂²	semidirect
185. C₄×Dic₂₆	C₂²	semidirect
186. C₄×Dic₂₆	C₂²	semidirect
428. #553	D₁₃	semidirect
520. #126	C₂×D₁₃	semidirect
532. #125	C₂×D₁₃	semidirect
568. #123	C₂×D₁₃	semidirect
604. #121	C₂×D₁₃	semidirect
631. C₄×D₄	C₂×D₁₃	semidirect
632. C₄×D₄	C₂×D₁₃	semidirect
644. #117	C₂×D₁₃	semidirect
647. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
817. C₁₃	#3566	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#553	2
#11719417	2
#11719415	2
#11719410	2
#11719406	2
#11719401	2
#11719398	2
#11719369	2
#11719365	2
#11719363	2
#11719354	2
#11719326	2
#11719325	2
#11719324	2
#11719321	2
#11719318	2
#11719307	2
#11719266	2
#11719265	2
#11719263	2
#11719261	2
#11719247	2
#11719245	2
#11719243	2
#11719239	2
#11719236	2
#11719220	2
#11719218	2
#3566	13