Subgroups — #13129284

Order 1664.

932 conjugacy classes of subgroups.

The subgroup lattice has 918 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	#11719413	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719406	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	C₁₃⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719370	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719365	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719356	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719355	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719326	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719323	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719307	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719307	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719307	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719306	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719306	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719305	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719269	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719269	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719269	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719248	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719246	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719236	C₂	1	1	yes	maximal, characteristic, complemented
29	#11719223	C₂	1	1	yes	maximal, characteristic, complemented
30	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#88143	C₂	1	1	yes	maximal, characteristic, complemented
32	C₁₃×#126	C₂²	1	1	yes	characteristic
33	C₁₃×#126	C₂²	1	1	yes	characteristic
34	C₁₃×#125	C₂²	1	1	yes	characteristic
35	C₁₃×#123	C₂²	1	1	yes	characteristic
36	C₁₃×#123	C₂²	1	1	yes	characteristic
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
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
44	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#117	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	#88193	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	#88192	C₂²	1	1	yes	characteristic
53	#88190	C₂²	1	1	yes	characteristic
54	#88189	C₂²	1	1	yes	characteristic
55	#88189	C₂²	1	1	yes	characteristic
56	#88189	C₂²	1	1	yes	characteristic
57	#88189	C₂²	1	1	yes	characteristic
58	#88189	C₂²	1	1	yes	characteristic
59	#88189	C₂²	1	1	yes	characteristic
60	#88189	C₂²	1	1	yes	characteristic
61	#88189	C₂²	1	1	yes	characteristic
62	#88189	C₂²	1	1	yes	characteristic
63	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
64	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
65	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
66	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
67	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
68	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
69	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
70	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
71	#88183	C₂²	1	1	yes	characteristic
72	#88183	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
77	#88180	C₂²	1	1	yes	characteristic
78	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
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
84	#88178	C₂²	1	1	yes	characteristic
85	#88178	C₂²	1	1	yes	characteristic
86	#88178	C₂²	1	1	yes	characteristic
87	#88178	C₂²	1	1	yes	characteristic
88	C₂×#6101	C₂²	1	1	yes	characteristic
89	C₂×#6101	C₂²	1	1	yes	characteristic
90	C₂×#6101	C₂²	1	1	yes	characteristic
91	C₂×#6101	C₂²	1	1	yes	characteristic
92	C₂×#6101	C₂²	1	1	yes	characteristic
93	C₂×#6101	C₂²	1	1	yes	characteristic
94	C₂×C₄×Dic₁₃	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	#88151	C₂²	1	1	yes	characteristic
99	#88150	C₂²	1	1	yes	characteristic
100	#88150	C₂²	1	1	yes	characteristic
101	#88150	C₂²	1	1	yes	characteristic
102	#88150	C₂²	1	1	yes	characteristic
103	#88146	C₂²	1	1	yes	characteristic
104	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
105	#88144	C₂²	1	1	yes	characteristic
106	#88144	C₂²	1	1	yes	characteristic
107	#88144	C₂²	1	1	yes	characteristic
108	#88144	C₂²	1	1	yes	characteristic
109	#88144	C₂²	1	1	yes	characteristic
110	#88144	C₂²	1	1	yes	characteristic
111	#88143	C₂²	1	1	yes	characteristic
112	#88143	C₂²	1	1	yes	characteristic
113	#88143	C₂²	1	1	yes	characteristic
114	#88143	C₂²	1	1	yes	characteristic
115	#88143	C₂²	1	1	yes	characteristic
116	#88143	C₂²	1	1	yes	characteristic
117	#88143	C₂²	1	1	yes	characteristic
118	#88143	C₂²	1	1	yes	characteristic
119	#88143	C₂²	1	1	yes	characteristic
120	#88143	C₂²	1	1	yes	characteristic
121	#88143	C₂²	1	1	yes	characteristic
122	#88143	C₂²	1	1	yes	characteristic
123	#88143	C₂²	1	1	yes	characteristic
124	#88143	C₂²	1	1	yes	characteristic
125	#88143	C₂²	1	1	yes	characteristic
126	#88143	C₂²	1	1	yes	characteristic
127	#88143	C₂²	1	1	yes	characteristic
128	#88143	C₂²	1	1	yes	characteristic
129	#88143	C₂²	1	1	yes	characteristic
130	#88142	C₂²	1	1	yes	characteristic
131	#88142	C₂²	1	1	yes	characteristic
132	#88142	C₂²	1	1	yes	characteristic
133	#88141	C₂²	1	1	yes	characteristic
134	#88141	C₂²	1	1	yes	characteristic
135	#88140	C₂²	1	1	yes	characteristic
136	#88140	C₂²	1	1	yes	characteristic
137	#88140	C₂²	1	1	yes	characteristic
138	#88139	C₂²	1	1	yes	characteristic
139	#88137	C₂²	1	1	yes	characteristic
140	#88137	C₂²	1	1	yes	characteristic
141	#88137	C₂²	1	1	yes	characteristic
142	#88137	C₂²	1	1	yes	characteristic
143	#88135	C₂²	1	1	yes	characteristic
144	#88135	C₂²	1	1	yes	characteristic
145	#88133	C₂²	1	1	yes	characteristic
146	#88133	C₂²	1	1	yes	characteristic
147	#88133	C₂²	1	1	yes	characteristic
148	#88133	C₂²	1	1	yes	characteristic
149	#88133	C₂²	1	1	yes	characteristic
150	#88133	C₂²	1	1	yes	characteristic
151	#88133	C₂²	1	1	yes	characteristic
152	#88133	C₂²	1	1	yes	characteristic
153	#88133	C₂²	1	1	yes	characteristic
154	#88133	C₂²	1	1	yes	characteristic
155	#88133	C₂²	1	1	yes	characteristic
156	#88133	C₂²	1	1	yes	characteristic
157	#88133	C₂²	1	1	yes	characteristic
158	#88132	C₂²	1	1	yes	characteristic
159	#88132	C₂²	1	1	yes	characteristic
160	#88132	C₂²	1	1	yes	characteristic
161	#88132	C₂²	1	1	yes	characteristic
162	#88132	C₂²	1	1	yes	characteristic
163	#88132	C₂²	1	1	yes	characteristic
164	#88132	C₂²	1	1	yes	characteristic
165	#88132	C₂²	1	1	yes	characteristic
166	#88132	C₂²	1	1	yes	characteristic
167	#88132	C₂²	1	1	yes	characteristic
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	#88126	C₂²	1	1	yes	characteristic
178	#88124	C₂²	1	1	yes	characteristic
179	#88124	C₂²	1	1	yes	characteristic
180	#88124	C₂²	1	1	yes	characteristic
181	#88124	C₂²	1	1	yes	characteristic
182	#88123	C₂²	1	1	yes	characteristic
183	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
184	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
185	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
186	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
187	C₂×D₄×C₁₃	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	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	C₂²×C₄×C₁₃	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	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
203	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
204	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
205	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
206	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
207	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
208	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
209	C₂²×Dic₁₃	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	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₁₃	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	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
221	C₂×Dic₂₆	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₁₃×C₂²⋊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	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	#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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
272	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
273	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
274	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
275	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
276	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
277	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
278	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
279	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
280	C₄⋊Dic₁₃	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	#6101	C₂³	1	1	yes	characteristic
290	#6101	C₂³	1	1	yes	characteristic
291	#6101	C₂³	1	1	yes	characteristic
292	#6101	C₂³	1	1	yes	characteristic
293	#6101	C₂³	1	1	yes	characteristic
294	#6101	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	#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	#3553	—	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	C₂⁴	1	1	yes	characteristic
348	D₄×C₁₃	—	2	2	no	—
349	D₄×C₁₃	—	2	2	no	—
350	D₄×C₁₃	—	2	2	no	—
351	D₄×C₁₃	—	4	1	no	—
352	D₄×C₁₃	—	4	1	no	—
353	D₄×C₁₃	—	4	1	no	—
354	C₂×C₄×C₁₃	—	4	1	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	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₁₃	—	2	2	no	—
372	C₂²⋊D₁₃	—	4	1	no	—
373	C₂²⋊D₁₃	—	4	1	no	—
374	C₂²⋊D₁₃	—	4	1	no	—
375	C₂×Dic₁₃	—	2	2	no	—
376	C₂×Dic₁₃	—	4	1	no	—
377	C₂×Dic₁₃	—	4	1	no	—
378	C₂×Dic₁₃	—	4	1	no	—
379	C₂×Dic₁₃	—	4	1	no	—
380	C₂×Dic₁₃	—	4	1	no	—
381	C₂×Dic₁₃	—	4	1	no	—
382	C₂×Dic₁₃	—	4	1	no	—
383	C₂×Dic₁₃	—	4	1	no	—
384	C₂×Dic₁₃	—	4	1	no	—
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	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	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	#564	—	13	1	no	—
410	#563	—	13	1	no	—
411	#563	—	13	1	no	—
412	#562	—	13	1	no	—
413	#554	—	13	1	no	—
414	#554	—	13	1	no	—
415	#554	—	13	1	no	—
416	#554	—	13	1	no	—
417	#553	—	13	1	no	—
418	#553	—	13	1	no	—
419	#553	—	13	1	no	—
420	#553	D₁₃	1	1	yes	characteristic, complemented
421	#552	—	13	1	no	—
422	#552	—	13	1	no	—
423	#552	—	13	1	no	—
424	#552	—	13	1	no	—
425	#541	—	13	1	no	—
426	#541	—	13	1	no	—
427	#541	—	13	1	no	—
428	#541	—	13	1	no	—
429	#539	—	13	1	no	—
430	#539	—	13	1	no	—
431	#539	—	13	1	no	—
432	#539	—	13	1	no	—
433	#539	—	13	1	no	—
434	#539	—	13	1	no	—
435	#539	—	13	1	no	—
436	#539	—	13	1	no	—
437	#529	—	13	1	no	—
438	#529	—	13	1	no	—
439	C₂×#125	—	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	no	—
446	C₂²×C₁₃	—	2	1	no	—
447	C₂²×C₁₃	—	2	1	no	—
448	C₂²×C₁₃	—	2	1	no	—
449	C₂²×C₁₃	—	2	1	no	—
450	C₂²×C₁₃	—	2	1	no	—
451	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
452	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
453	C₂×D₁₃	—	2	1	no	—
454	C₂×D₁₃	—	2	1	no	—
455	C₂×D₁₃	—	2	1	no	—
456	C₄×C₁₃	—	2	1	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	Dic₁₃	—	2	1	no	—
468	Dic₁₃	—	2	1	no	—
469	Dic₁₃	—	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	C₄⋊Q₈	—	13	1	no	—
483	C₄⋊Q₈	—	13	1	no	—
484	C₄⋊Q₈	—	13	1	no	—
485	C₄⋊Q₈	—	13	1	no	—
486	#126	—	13	1	no	—
487	#126	—	13	1	no	—
488	#126	—	13	1	no	—
489	#126	—	13	1	no	—
490	#126	—	13	1	no	—
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	C₂×D₁₃	1	1	yes	characteristic
505	#126	C₂×D₁₃	1	1	yes	characteristic
506	#125	—	13	1	no	—
507	#125	—	13	1	no	—
508	#125	—	13	1	no	—
509	#125	—	13	1	no	—
510	#125	—	13	1	no	—
511	#125	—	13	1	no	—
512	#125	—	13	1	no	—
513	#125	—	13	1	no	—
514	#125	—	13	1	no	—
515	#125	—	13	1	no	—
516	#125	—	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	—	13	1	no	—
535	#125	C₂×D₁₃	1	1	yes	characteristic
536	#124	—	13	1	no	—
537	#124	—	13	1	no	—
538	#123	—	13	1	no	—
539	#123	—	13	1	no	—
540	#123	—	13	1	no	—
541	#123	—	13	1	no	—
542	#123	—	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	C₂×D₁₃	1	1	yes	characteristic
557	#123	C₂×D₁₃	1	1	yes	characteristic
558	C₂²⋊Q₈	—	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	#121	—	13	1	no	—
585	#121	—	13	1	no	—
586	#121	—	13	1	no	—
587	#121	—	13	1	no	—
588	#121	—	13	1	no	—
589	#121	—	13	1	no	—
590	#121	C₂×D₁₃	1	1	yes	characteristic
591	#121	C₂×D₁₃	1	1	yes	characteristic
592	#121	C₂×D₁₃	1	1	yes	characteristic
593	#121	C₂×D₁₃	1	1	yes	characteristic
594	C₄×Q₈	—	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×D₄	—	13	1	no	—
601	C₄×D₄	—	13	1	no	—
602	C₄×D₄	—	13	1	no	—
603	C₄×D₄	—	13	1	no	—
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	—	13	1	no	—
613	C₄×D₄	—	13	1	no	—
614	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
615	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
616	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
617	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
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	C₂×D₁₃	1	1	yes	characteristic
626	C₂×C₄⋊C₄	—	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	—	13	1	no	—
631	C₂×C₄⋊C₄	—	13	1	no	—
632	C₂×C₄⋊C₄	—	13	1	no	—
633	C₂×C₄⋊C₄	—	13	1	no	—
634	C₂×C₄⋊C₄	—	13	1	no	—
635	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
636	C₂×C₄²	—	13	1	no	—
637	C₂×C₁₃	—	2	2	no	—
638	C₂×C₁₃	—	4	1	no	—
639	C₂×C₁₃	—	4	1	no	—
640	C₂×C₁₃	—	4	1	no	—
641	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
642	C₂×C₁₃	#585	1	1	yes	characteristic
643	C₂×C₁₃	#585	1	1	yes	characteristic
644	D₁₃	—	4	1	no	—
645	C₂×Q₈	—	13	1	no	—
646	C₂×Q₈	—	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×D₄	—	13	1	no	—
652	C₂×D₄	—	13	1	no	—
653	C₂×D₄	—	13	1	no	—
654	C₂×D₄	—	13	1	no	—
655	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
656	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
657	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
658	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
659	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
660	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
661	C₂²×C₄	—	13	1	no	—
662	C₂²×C₄	—	13	1	no	—
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	—	13	1	no	—
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	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	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	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	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	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	C₂²×D₁₃	1	1	yes	characteristic
775	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
776	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	C₂²×D₁₃	1	1	yes	characteristic
798	C₄²	C₂²×D₁₃	1	1	yes	characteristic
799	C₄²	C₂²×D₁₃	1	1	yes	characteristic
800	C₁₃	#3553	1	1	yes	characteristic, complemented, Sylow
801	C₂³	—	13	1	no	—
802	C₂³	C₂³×D₁₃	1	1	yes	characteristic
803	C₂³	C₂³×D₁₃	1	1	yes	characteristic
804	C₂³	C₂³×D₁₃	1	1	yes	characteristic
805	C₂³	C₂³×D₁₃	1	1	yes	characteristic
806	Q₈	—	52	1	no	—
807	Q₈	—	52	1	no	—
808	Q₈	—	52	1	no	—
809	Q₈	—	52	1	no	—
810	Q₈	—	52	1	no	—
811	Q₈	—	52	1	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	4	1	no	—
816	D₄	—	4	1	no	—
817	D₄	—	4	1	no	—
818	D₄	—	26	2	no	—
819	D₄	—	52	1	no	—
820	D₄	—	52	1	no	—
821	D₄	—	52	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	13	1	no	—
829	C₂×C₄	—	13	1	no	—
830	C₂×C₄	—	13	1	no	—
831	C₂×C₄	—	13	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	—	26	2	no	—
844	C₂×C₄	—	52	1	no	—
845	C₂×C₄	—	52	1	no	—
846	C₂×C₄	—	52	1	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	—	52	1	no	—
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	C₂²	—	2	1	no	—
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	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	1	no	—
877	C₂²	—	2	1	no	—
878	C₂²	—	26	1	no	—
879	C₂²	—	26	1	no	—
880	C₂²	—	26	1	no	—
881	C₂²	#88257	1	2	yes	—
882	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
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	—	26	1	no	—
895	C₄	—	26	1	no	—
896	C₄	—	26	1	no	—
897	C₄	—	26	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	C₂	—	2	2	no	—
910	C₂	—	4	1	no	—
911	C₂	—	4	1	no	—
912	C₂	—	4	1	no	—
913	C₂	—	52	1	no	—
914	C₂	C₂×#88257	1	1	yes	characteristic
915	C₂	#11719648	1	1	yes	characteristic
916	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	#3553
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. #11719413	C₂	semidirect
4. #11719406	C₂	semidirect
5. #11719406	C₂	semidirect
6. #11719401	C₂	semidirect
7. C₁₃⋊#564	C₂	semidirect
8. #11719370	C₂	semidirect
9. #11719365	C₂	semidirect
10. #11719356	C₂	semidirect
11. #11719355	C₂	semidirect
12. #11719326	C₂	semidirect
13. #11719323	C₂	semidirect
14. #11719307	C₂	semidirect
15. #11719307	C₂	semidirect
16. #11719307	C₂	semidirect
17. #11719306	C₂	semidirect
18. #11719306	C₂	semidirect
19. #11719305	C₂	semidirect
20. #11719269	C₂	semidirect
21. #11719269	C₂	semidirect
22. #11719269	C₂	semidirect
23. #11719248	C₂	semidirect
24. #11719246	C₂	semidirect
25. #11719244	C₂	semidirect
26. #11719244	C₂	semidirect
27. #11719243	C₂	semidirect
28. #11719236	C₂	semidirect
29. #11719223	C₂	semidirect
30. #11719216	C₂	semidirect
31. C₂×#88143	C₂	semidirect
420. #553	D₁₃	semidirect
800. C₁₃	#3553	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
#11719413	2
#11719406	2
#11719401	2
C₁₃⋊#564	2
#11719370	2
#11719365	2
#11719356	2
#11719355	2
#11719326	2
#11719323	2
#11719307	2
#11719306	2
#11719305	2
#11719269	2
#11719248	2
#11719246	2
#11719244	2
#11719243	2
#11719236	2
#11719223	2
#11719216	2
C₂×#88143	2
#3553	13