Subgroups — #13129122

Order 1664.

1032 conjugacy classes of subgroups.

The subgroup lattice has 980 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	#11719429	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719405	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719401	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719398	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719397	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719352	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719351	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719349	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719349	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719345	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719345	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719341	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719341	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719338	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719334	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719287	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719265	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719265	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719257	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719245	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719245	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719220	C₂	1	1	yes	maximal, characteristic, complemented
29	#11719219	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#88150	C₂	1	1	yes	maximal, characteristic, complemented
31	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#6131	C₂²	1	1	yes	characteristic
33	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#6127	C₂²	1	1	yes	characteristic
35	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
37	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
38	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	#88201	C₂²	1	1	yes	characteristic
54	#88201	C₂²	1	1	yes	characteristic
55	#88201	C₂²	1	1	yes	characteristic
56	#88201	C₂²	1	1	yes	characteristic
57	#88200	C₂²	1	1	yes	characteristic
58	#88200	C₂²	1	1	yes	characteristic, complemented
59	#88200	C₂²	1	1	yes	characteristic, complemented
60	#88198	C₂²	1	1	yes	characteristic, complemented
61	#88198	C₂²	1	1	yes	characteristic, complemented
62	#88198	C₂²	1	1	yes	characteristic, complemented
63	#88193	C₂²	1	1	yes	characteristic
64	#88193	C₂²	1	1	yes	characteristic
65	#88193	C₂²	1	1	yes	characteristic
66	#88191	C₂²	1	1	yes	characteristic
67	#88184	C₂²	1	1	yes	characteristic
68	#88184	C₂²	1	1	yes	characteristic
69	#88184	C₂²	1	1	yes	characteristic
70	#88184	C₂²	1	1	yes	characteristic
71	#88184	C₂²	1	1	yes	characteristic
72	#88183	C₂²	1	1	yes	characteristic
73	#88183	C₂²	1	1	yes	characteristic
74	#88183	C₂²	1	1	yes	characteristic, complemented
75	#88183	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×#6103	C₂²	1	1	yes	characteristic
83	C₂×#6103	C₂²	1	1	yes	characteristic
84	#88178	C₂²	1	1	yes	characteristic, complemented
85	C₂×#6101	C₂²	1	1	yes	characteristic
86	C₂×#6101	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, complemented
94	#88152	C₂²	1	1	yes	characteristic, complemented
95	#88151	C₂²	1	1	yes	characteristic, complemented
96	#88150	C₂²	1	1	yes	characteristic
97	#88150	C₂²	1	1	yes	characteristic
98	#88150	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	#88150	C₂²	1	1	yes	characteristic
104	#88150	C₂²	1	1	yes	characteristic
105	#88150	C₂²	1	1	yes	characteristic, complemented
106	#88150	C₂²	1	1	yes	characteristic, complemented
107	#88150	C₂²	1	1	yes	characteristic, complemented
108	#88150	C₂²	1	1	yes	characteristic, complemented
109	#88150	C₂²	1	1	yes	characteristic, complemented
110	#88150	C₂²	1	1	yes	characteristic, complemented
111	#88150	C₂²	1	1	yes	characteristic, complemented
112	#88150	C₂²	1	1	yes	characteristic, complemented
113	#88149	C₂²	1	1	yes	characteristic
114	#88149	C₂²	1	1	yes	characteristic
115	#88149	C₂²	1	1	yes	characteristic
116	#88149	C₂²	1	1	yes	characteristic
117	#88149	C₂²	1	1	yes	characteristic
118	#88149	C₂²	1	1	yes	characteristic, complemented
119	#88148	C₂²	1	1	yes	characteristic
120	#88148	C₂²	1	1	yes	characteristic
121	#88148	C₂²	1	1	yes	characteristic
122	#88148	C₂²	1	1	yes	characteristic
123	#88148	C₂²	1	1	yes	characteristic
124	#88148	C₂²	1	1	yes	characteristic
125	#88148	C₂²	1	1	yes	characteristic
126	#88148	C₂²	1	1	yes	characteristic
127	#88148	C₂²	1	1	yes	characteristic
128	#88148	C₂²	1	1	yes	characteristic, complemented
129	#88148	C₂²	1	1	yes	characteristic, complemented
130	#88148	C₂²	1	1	yes	characteristic, complemented
131	#88148	C₂²	1	1	yes	characteristic, complemented
132	#88147	C₂²	1	1	yes	characteristic
133	#88147	C₂²	1	1	yes	characteristic
134	#88147	C₂²	1	1	yes	characteristic, complemented
135	#88146	C₂²	1	1	yes	characteristic
136	#88146	C₂²	1	1	yes	characteristic, complemented
137	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
138	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
139	#88144	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	#88143	C₂²	1	1	yes	characteristic, complemented
144	#88143	C₂²	1	1	yes	characteristic, complemented
145	#88143	C₂²	1	1	yes	characteristic, complemented
146	#88142	C₂²	1	1	yes	characteristic, complemented
147	#88142	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	#88139	C₂²	1	1	yes	characteristic
152	#88139	C₂²	1	1	yes	characteristic
153	#88139	C₂²	1	1	yes	characteristic, complemented
154	#88139	C₂²	1	1	yes	characteristic, complemented
155	#88138	C₂²	1	1	yes	characteristic
156	#88138	C₂²	1	1	yes	characteristic
157	#88138	C₂²	1	1	yes	characteristic
158	#88138	C₂²	1	1	yes	characteristic, complemented
159	#88138	C₂²	1	1	yes	characteristic, complemented
160	#88137	C₂²	1	1	yes	characteristic
161	#88136	C₂²	1	1	yes	characteristic
162	#88136	C₂²	1	1	yes	characteristic
163	#88136	C₂²	1	1	yes	characteristic
164	#88135	C₂²	1	1	yes	characteristic
165	#88135	C₂²	1	1	yes	characteristic
166	#88135	C₂²	1	1	yes	characteristic
167	#88135	C₂²	1	1	yes	characteristic
168	#88135	C₂²	1	1	yes	characteristic
169	#88135	C₂²	1	1	yes	characteristic
170	#88133	C₂²	1	1	yes	characteristic, complemented
171	#88133	C₂²	1	1	yes	characteristic, complemented
172	#88132	C₂²	1	1	yes	characteristic
173	#88132	C₂²	1	1	yes	characteristic
174	#88132	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, complemented
178	#88130	C₂²	1	1	yes	characteristic, complemented
179	#88129	C₂²	1	1	yes	characteristic
180	#88129	C₂²	1	1	yes	characteristic
181	#88129	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₅₂	C₂²	1	1	yes	characteristic
183	#88126	C₂²	1	1	yes	characteristic
184	#88126	C₂²	1	1	yes	characteristic, complemented
185	#88126	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	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	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
207	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
208	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
209	#6131	—	4	2	no	—
210	Q₈×D₁₃	—	4	2	no	—
211	#6127	—	4	2	no	—
212	#6127	—	4	2	no	—
213	C₂×D₅₂	C₂³	1	1	yes	characteristic
214	C₂×D₅₂	C₂³	1	1	yes	characteristic
215	C₂×D₅₂	C₂³	1	1	yes	characteristic
216	C₂×D₅₂	C₂³	1	1	yes	characteristic
217	C₂×D₅₂	C₂³	1	1	yes	characteristic
218	C₂×D₅₂	C₂³	1	1	yes	characteristic
219	C₂×D₅₂	C₂³	1	1	yes	characteristic
220	C₂×D₅₂	C₂³	1	1	yes	characteristic
221	C₂×D₅₂	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₁₃	—	4	2	no	—
223	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
236	C₂×Dic₂₆	—	4	2	no	—
237	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
238	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
239	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
240	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
241	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
242	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
243	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
244	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	C₄²×C₁₃	C₂³	1	1	yes	characteristic
267	C₄²×C₁₃	C₂³	1	1	yes	characteristic
268	C₄²×C₁₃	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₁₃	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	#6103	C₂³	1	1	yes	characteristic
292	#6103	C₂³	1	1	yes	characteristic
293	#6103	C₂³	1	1	yes	characteristic
294	#6103	C₂³	1	1	yes	characteristic
295	#6103	C₂³	1	1	yes	characteristic
296	#6103	C₂³	1	1	yes	characteristic
297	#6103	C₂³	1	1	yes	characteristic
298	#6103	C₂³	1	1	yes	characteristic
299	#6103	C₂³	1	1	yes	characteristic
300	#6103	C₂³	1	1	yes	characteristic
301	#6103	C₂³	1	1	yes	characteristic
302	#6103	C₂³	1	1	yes	characteristic
303	#6103	C₂³	1	1	yes	characteristic
304	#6103	C₂³	1	1	yes	characteristic
305	#6103	C₂³	1	1	yes	characteristic
306	#6103	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
309	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
310	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₁₃	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	#6101	C₂³	1	1	yes	characteristic
330	#6101	C₂³	1	1	yes	characteristic
331	#6101	C₂³	1	1	yes	characteristic
332	#6101	C₂³	1	1	yes	characteristic
333	#6101	C₂³	1	1	yes	characteristic
334	#6101	C₂³	1	1	yes	characteristic
335	#6101	C₂³	1	1	yes	characteristic
336	#6101	C₂³	1	1	yes	characteristic
337	#6101	C₂³	1	1	yes	characteristic
338	#6101	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	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
343	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
344	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
345	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
346	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
347	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
348	#3541	—	13	1	no	maximal, Sylow
349	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂²×D₁₃	—	2	2	no	—
352	C₂²×D₁₃	—	4	1	no	—
353	C₂²×D₁₃	—	4	1	no	—
354	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
355	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
356	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
357	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
358	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
359	Q₈×C₁₃	—	4	1	no	—
360	Q₈×C₁₃	—	4	1	no	—
361	Q₈×C₁₃	—	4	1	no	—
362	D₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
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	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂²⋊D₁₃	—	2	2	no	—
383	C₂²⋊D₁₃	—	2	2	no	—
384	C₂²⋊D₁₃	—	2	2	no	—
385	C₂²⋊D₁₃	—	2	2	no	—
386	C₂²⋊D₁₃	—	4	1	no	—
387	C₂²⋊D₁₃	—	4	1	no	—
388	C₂²⋊D₁₃	—	4	1	no	—
389	C₂²⋊D₁₃	—	4	1	no	—
390	C₂×Dic₁₃	—	2	2	no	—
391	C₂×Dic₁₃	—	4	1	no	—
392	C₂×Dic₁₃	—	4	1	no	—
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	D₅₂	—	4	1	no	—
407	D₅₂	—	4	1	no	—
408	D₅₂	—	4	1	no	—
409	D₅₂	—	4	1	no	—
410	D₅₂	—	4	1	no	—
411	D₅₂	—	4	1	no	—
412	D₅₂	—	4	1	no	—
413	C₄×D₁₃	—	2	2	no	—
414	C₄×D₁₃	—	2	2	no	—
415	C₄×D₁₃	—	2	2	no	—
416	C₄×D₁₃	—	2	2	no	—
417	C₄×D₁₃	—	4	1	no	—
418	C₄×D₁₃	—	4	1	no	—
419	C₄×D₁₃	—	4	1	no	—
420	C₄×D₁₃	—	4	1	no	—
421	C₄×D₁₃	—	4	1	no	—
422	C₄×D₁₃	—	4	1	no	—
423	C₄×D₁₃	—	4	1	no	—
424	C₄×D₁₃	—	4	1	no	—
425	C₄×D₁₃	—	4	1	no	—
426	Dic₂₆	—	2	2	no	—
427	Dic₂₆	—	2	2	no	—
428	Dic₂₆	—	2	2	no	—
429	Dic₂₆	—	4	1	no	—
430	Dic₂₆	—	4	1	no	—
431	Dic₂₆	—	4	1	no	—
432	Dic₂₆	—	4	1	no	—
433	#563	—	13	1	no	—
434	#563	—	13	1	no	—
435	#562	—	13	1	no	—
436	#562	—	13	1	no	—
437	#556	—	13	1	no	—
438	#554	—	13	1	no	—
439	#554	—	13	1	no	—
440	#554	D₁₃	1	1	yes	characteristic, complemented
441	#553	—	13	1	no	—
442	#553	—	13	1	no	—
443	#553	—	13	1	no	—
444	#552	—	13	1	no	—
445	D₄×Q₈	—	13	1	no	—
446	#548	—	13	1	no	—
447	#548	—	13	1	no	—
448	#547	—	13	1	no	—
449	#542	—	13	1	no	—
450	#542	—	13	1	no	—
451	#542	—	13	1	no	—
452	#541	—	13	1	no	—
453	#539	—	13	1	no	—
454	#539	—	13	1	no	—
455	#538	—	13	1	no	—
456	#538	—	13	1	no	—
457	#538	—	13	1	no	—
458	#538	—	13	1	no	—
459	#537	—	13	1	no	—
460	#536	—	13	1	no	—
461	#525	—	13	1	no	—
462	#525	—	13	1	no	—
463	C₂×C₂²⋊Q₈	—	13	1	no	—
464	C₂²×C₁₃	—	2	1	no	—
465	C₂²×C₁₃	—	2	1	no	—
466	C₂²×C₁₃	—	2	1	no	—
467	C₂²×C₁₃	—	2	1	no	—
468	C₂²×C₁₃	—	2	1	no	—
469	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
470	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
471	C₂×D₁₃	—	2	1	no	—
472	C₂×D₁₃	—	2	1	no	—
473	C₂×D₁₃	—	2	1	no	—
474	C₂×D₁₃	—	2	1	no	—
475	C₂×D₁₃	—	2	1	no	—
476	C₂×D₁₃	—	2	1	no	—
477	C₂×D₁₃	—	2	1	no	—
478	C₂×D₁₃	—	2	1	no	—
479	C₂×D₁₃	—	2	1	no	—
480	C₂×D₁₃	—	2	1	no	—
481	C₂×D₁₃	—	2	1	no	—
482	C₂×D₁₃	—	2	1	no	—
483	C₂×D₁₃	—	2	1	no	—
484	C₂×D₁₃	—	2	1	no	—
485	C₂×D₁₃	—	2	1	no	—
486	C₂×D₁₃	—	4	4	no	—
487	C₄×C₁₃	—	2	1	no	—
488	C₄×C₁₃	—	2	1	no	—
489	C₄×C₁₃	—	2	1	no	—
490	C₄×C₁₃	—	2	1	no	—
491	C₄×C₁₃	—	2	1	no	—
492	C₄×C₁₃	—	2	1	no	—
493	C₄×C₁₃	—	2	1	no	—
494	C₄×C₁₃	—	2	1	no	—
495	C₄×C₁₃	—	2	1	no	—
496	C₄×C₁₃	—	2	1	no	—
497	C₄×C₁₃	—	2	1	no	—
498	C₄×C₁₃	—	2	1	no	—
499	C₄×C₁₃	—	2	1	no	—
500	Dic₁₃	—	2	1	no	—
501	Dic₁₃	—	2	1	no	—
502	Dic₁₃	—	2	1	no	—
503	Dic₁₃	—	2	1	no	—
504	Dic₁₃	—	2	1	no	—
505	Dic₁₃	—	2	1	no	—
506	Dic₁₃	—	2	1	no	—
507	Dic₁₃	—	2	1	no	—
508	Dic₁₃	—	2	1	no	—
509	Dic₁₃	—	2	1	no	—
510	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
511	C₂×#41	—	13	1	no	—
512	C₂×#41	—	13	1	no	—
513	C₂×#41	—	13	1	no	—
514	C₂²×Q₈	—	13	1	no	—
515	C₂²×Q₈	—	13	1	no	—
516	C₂³×C₄	—	13	1	no	—
517	C₄⋊Q₈	—	13	1	no	—
518	C₄⋊Q₈	—	13	1	no	—
519	C₄⋊Q₈	—	13	1	no	—
520	C₄⋊Q₈	—	13	1	no	—
521	C₄⋊Q₈	—	13	1	no	—
522	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
523	#126	—	13	1	no	—
524	#126	—	13	1	no	—
525	#126	—	13	1	no	—
526	#126	—	13	1	no	—
527	#126	—	13	1	no	—
528	#126	—	13	1	no	—
529	#126	—	13	1	no	—
530	#126	—	13	1	no	—
531	#126	—	13	1	no	—
532	#126	—	13	1	no	—
533	#126	—	13	1	no	—
534	#126	—	13	1	no	—
535	#126	—	13	1	no	—
536	#126	—	13	1	no	—
537	#125	—	13	1	no	—
538	#125	—	13	1	no	—
539	#125	—	13	1	no	—
540	#125	—	13	1	no	—
541	#125	—	13	1	no	—
542	#125	—	13	1	no	—
543	#125	—	13	1	no	—
544	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
545	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
546	#124	—	13	1	no	—
547	#124	—	13	1	no	—
548	#124	—	13	1	no	—
549	#124	—	13	1	no	—
550	#124	—	13	1	no	—
551	#124	—	13	1	no	—
552	#124	—	13	1	no	—
553	#124	—	13	1	no	—
554	#124	—	13	1	no	—
555	#124	—	13	1	no	—
556	#124	—	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	—	13	1	no	—
568	#123	—	13	1	no	—
569	#123	—	13	1	no	—
570	#123	—	13	1	no	—
571	#123	—	13	1	no	—
572	#123	—	13	1	no	—
573	#123	—	13	1	no	—
574	#123	—	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	C₂²⋊Q₈	—	13	1	no	—
588	C₂²⋊Q₈	—	13	1	no	—
589	C₂²⋊Q₈	—	13	1	no	—
590	C₂²⋊Q₈	—	13	1	no	—
591	C₂²⋊Q₈	—	13	1	no	—
592	C₂²⋊Q₈	—	13	1	no	—
593	C₂²⋊Q₈	—	13	1	no	—
594	C₂²⋊Q₈	—	13	1	no	—
595	C₂²⋊Q₈	—	13	1	no	—
596	C₂²⋊Q₈	—	13	1	no	—
597	C₂²⋊Q₈	—	13	1	no	—
598	C₂²⋊Q₈	—	13	1	no	—
599	C₂²⋊Q₈	—	13	1	no	—
600	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
601	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
602	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
603	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
604	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
605	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
606	#121	—	13	1	no	—
607	#121	—	13	1	no	—
608	#121	—	13	1	no	—
609	#121	—	13	1	no	—
610	#121	—	13	1	no	—
611	#121	—	13	1	no	—
612	#121	—	13	1	no	—
613	#121	—	13	1	no	—
614	#121	—	13	1	no	—
615	#121	—	13	1	no	—
616	#121	—	13	1	no	—
617	#121	—	13	1	no	—
618	#121	—	13	1	no	—
619	#121	—	13	1	no	—
620	#121	—	13	1	no	—
621	#121	—	13	1	no	—
622	#121	—	13	1	no	—
623	#121	—	13	1	no	—
624	#121	—	13	1	no	—
625	#120	—	13	1	no	—
626	#120	—	13	1	no	—
627	#120	—	13	1	no	—
628	#120	—	13	1	no	—
629	C₄×Q₈	—	13	1	no	—
630	C₄×Q₈	—	13	1	no	—
631	C₄×Q₈	—	13	1	no	—
632	C₄×Q₈	—	13	1	no	—
633	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
634	C₄×D₄	—	13	1	no	—
635	C₄×D₄	—	13	1	no	—
636	C₄×D₄	—	13	1	no	—
637	C₄×D₄	—	13	1	no	—
638	C₄×D₄	—	13	1	no	—
639	C₄×D₄	—	13	1	no	—
640	C₄×D₄	—	13	1	no	—
641	C₄×D₄	—	13	1	no	—
642	C₄×D₄	—	13	1	no	—
643	C₄×D₄	—	13	1	no	—
644	C₄×D₄	—	13	1	no	—
645	C₄×D₄	—	13	1	no	—
646	C₄×D₄	—	13	1	no	—
647	C₄×D₄	—	13	1	no	—
648	C₄×D₄	—	13	1	no	—
649	C₄×D₄	—	13	1	no	—
650	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
651	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
652	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
653	#117	—	13	1	no	—
654	#117	—	13	1	no	—
655	#117	—	13	1	no	—
656	#117	—	13	1	no	—
657	#117	—	13	1	no	—
658	C₂×C₄⋊C₄	—	13	1	no	—
659	C₂×C₄⋊C₄	—	13	1	no	—
660	C₂×C₄⋊C₄	—	13	1	no	—
661	C₂×C₄⋊C₄	—	13	1	no	—
662	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
664	C₂×C₂²⋊C₄	—	13	1	no	—
665	C₂×C₂²⋊C₄	—	13	1	no	—
666	C₂×C₁₃	—	2	2	no	—
667	C₂×C₁₃	—	4	1	no	—
668	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
670	C₂×C₁₃	#585	1	1	yes	characteristic
671	D₁₃	—	4	1	no	—
672	D₁₃	—	4	1	no	—
673	D₁₃	—	4	1	no	—
674	D₁₃	—	4	1	no	—
675	D₁₃	—	4	1	no	—
676	C₂⁴	—	13	1	no	—
677	#41	—	52	2	no	—
678	#41	—	52	2	no	—
679	#41	—	52	2	no	—
680	C₂×Q₈	—	13	1	no	—
681	C₂×Q₈	—	13	1	no	—
682	C₂×Q₈	—	13	1	no	—
683	C₂×Q₈	—	13	1	no	—
684	C₂×Q₈	—	13	1	no	—
685	C₂×Q₈	—	13	1	no	—
686	C₂×Q₈	—	13	1	no	—
687	C₂×Q₈	—	52	2	no	—
688	C₂×Q₈	—	52	2	no	—
689	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
690	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
691	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
692	C₂×D₄	—	13	1	no	—
693	C₂×D₄	—	13	1	no	—
694	C₂×D₄	—	13	1	no	—
695	C₂×D₄	—	13	1	no	—
696	C₂×D₄	—	13	1	no	—
697	C₂×D₄	—	13	1	no	—
698	C₂×D₄	—	13	1	no	—
699	C₂×D₄	—	13	1	no	—
700	C₂×D₄	—	13	1	no	—
701	C₂×D₄	—	13	1	no	—
702	C₂×D₄	—	13	1	no	—
703	C₂×D₄	—	13	1	no	—
704	C₂×D₄	—	13	1	no	—
705	C₂×D₄	—	13	1	no	—
706	C₂×D₄	—	13	1	no	—
707	C₂×D₄	—	13	1	no	—
708	C₂×D₄	—	13	1	no	—
709	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
710	C₂²×C₄	—	13	1	no	—
711	C₂²×C₄	—	13	1	no	—
712	C₂²×C₄	—	13	1	no	—
713	C₂²×C₄	—	13	1	no	—
714	C₂²×C₄	—	13	1	no	—
715	C₂²×C₄	—	13	1	no	—
716	C₂²×C₄	—	13	1	no	—
717	C₂²×C₄	—	13	1	no	—
718	C₂²×C₄	—	13	1	no	—
719	C₂²×C₄	—	13	1	no	—
720	C₂²×C₄	—	13	1	no	—
721	C₂²×C₄	—	13	1	no	—
722	C₂²×C₄	—	13	1	no	—
723	C₂²×C₄	—	13	1	no	—
724	C₂²×C₄	—	13	1	no	—
725	C₂²×C₄	—	13	1	no	—
726	C₂²×C₄	—	52	2	no	—
727	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
729	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
744	C₄⋊C₄	—	13	1	no	—
745	C₄⋊C₄	—	13	1	no	—
746	C₄⋊C₄	—	13	1	no	—
747	C₄⋊C₄	—	13	1	no	—
748	C₄⋊C₄	—	13	1	no	—
749	C₄⋊C₄	—	13	1	no	—
750	C₄⋊C₄	—	13	1	no	—
751	C₄⋊C₄	—	13	1	no	—
752	C₄⋊C₄	—	13	1	no	—
753	C₄⋊C₄	—	13	1	no	—
754	C₄⋊C₄	—	13	1	no	—
755	C₄⋊C₄	—	13	1	no	—
756	C₄⋊C₄	—	13	1	no	—
757	C₄⋊C₄	—	13	1	no	—
758	C₄⋊C₄	—	13	1	no	—
759	C₄⋊C₄	—	13	1	no	—
760	C₄⋊C₄	—	13	1	no	—
761	C₄⋊C₄	—	13	1	no	—
762	C₄⋊C₄	—	13	1	no	—
763	C₄⋊C₄	—	13	1	no	—
764	C₄⋊C₄	—	13	1	no	—
765	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
766	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
792	C₂²⋊C₄	—	13	1	no	—
793	C₂²⋊C₄	—	13	1	no	—
794	C₂²⋊C₄	—	13	1	no	—
795	C₂²⋊C₄	—	13	1	no	—
796	C₂²⋊C₄	—	13	1	no	—
797	C₂²⋊C₄	—	13	1	no	—
798	C₂²⋊C₄	—	13	1	no	—
799	C₂²⋊C₄	—	13	1	no	—
800	C₂²⋊C₄	—	13	1	no	—
801	C₂²⋊C₄	—	13	1	no	—
802	C₂²⋊C₄	—	13	1	no	—
803	C₂²⋊C₄	—	13	1	no	—
804	C₂²⋊C₄	—	13	1	no	—
805	C₂²⋊C₄	—	13	1	no	—
806	C₂²⋊C₄	—	13	1	no	—
807	C₂²⋊C₄	—	13	1	no	—
808	C₂²⋊C₄	—	13	1	no	—
809	C₂²⋊C₄	—	13	1	no	—
810	C₂²⋊C₄	—	13	1	no	—
811	C₂²⋊C₄	—	13	1	no	—
812	C₂²⋊C₄	—	13	1	no	—
813	C₂²⋊C₄	—	13	1	no	—
814	C₂²⋊C₄	—	13	1	no	—
815	C₂²⋊C₄	—	13	1	no	—
816	C₂²⋊C₄	—	13	1	no	—
817	C₂²⋊C₄	—	13	1	no	—
818	C₂²⋊C₄	—	13	1	no	—
819	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
825	C₄²	—	13	1	no	—
826	C₄²	—	13	1	no	—
827	C₄²	—	13	1	no	—
828	C₄²	—	13	1	no	—
829	C₄²	—	13	1	no	—
830	C₄²	—	13	1	no	—
831	C₄²	—	13	1	no	—
832	C₄²	—	13	1	no	—
833	C₄²	—	13	1	no	—
834	C₄²	C₂²×D₁₃	1	1	yes	characteristic
835	C₄²	C₂²×D₁₃	1	1	yes	characteristic
836	C₄²	C₂²×D₁₃	1	1	yes	characteristic
837	C₁₃	#3541	1	1	yes	characteristic, complemented, Sylow
838	C₂³	—	13	1	no	—
839	C₂³	—	13	1	no	—
840	C₂³	—	13	1	no	—
841	C₂³	—	13	1	no	—
842	C₂³	—	13	1	no	—
843	C₂³	—	26	2	no	—
844	C₂³	—	52	1	no	—
845	C₂³	—	52	1	no	—
846	C₂³	C₂³×D₁₃	1	1	yes	characteristic
847	C₂³	C₂³×D₁₃	1	1	yes	characteristic
848	Q₈	—	4	1	no	—
849	Q₈	—	4	1	no	—
850	Q₈	—	4	1	no	—
851	Q₈	—	26	2	no	—
852	Q₈	—	26	2	no	—
853	Q₈	—	26	2	no	—
854	Q₈	—	52	1	no	—
855	Q₈	—	52	1	no	—
856	Q₈	—	52	1	no	—
857	Q₈	—	52	1	no	—
858	D₄	—	2	2	no	—
859	D₄	—	26	2	no	—
860	D₄	—	26	2	no	—
861	D₄	—	26	2	no	—
862	D₄	—	26	2	no	—
863	D₄	—	52	1	no	—
864	D₄	—	52	1	no	—
865	D₄	—	52	1	no	—
866	D₄	—	52	1	no	—
867	D₄	—	52	1	no	—
868	D₄	—	52	1	no	—
869	D₄	—	52	1	no	—
870	D₄	—	52	1	no	—
871	D₄	—	52	1	no	—
872	D₄	—	52	1	no	—
873	D₄	—	52	1	no	—
874	D₄	—	52	1	no	—
875	D₄	—	52	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	13	1	no	—
883	C₂×C₄	—	13	1	no	—
884	C₂×C₄	—	13	1	no	—
885	C₂×C₄	—	13	1	no	—
886	C₂×C₄	—	13	1	no	—
887	C₂×C₄	—	13	1	no	—
888	C₂×C₄	—	13	1	no	—
889	C₂×C₄	—	13	1	no	—
890	C₂×C₄	—	13	1	no	—
891	C₂×C₄	—	13	1	no	—
892	C₂×C₄	—	13	1	no	—
893	C₂×C₄	—	26	2	no	—
894	C₂×C₄	—	26	2	no	—
895	C₂×C₄	—	26	2	no	—
896	C₂×C₄	—	26	2	no	—
897	C₂×C₄	—	26	2	no	—
898	C₂×C₄	—	52	1	no	—
899	C₂×C₄	—	52	1	no	—
900	C₂×C₄	—	52	1	no	—
901	C₂×C₄	—	52	1	no	—
902	C₂×C₄	—	52	1	no	—
903	C₂×C₄	—	52	1	no	—
904	C₂×C₄	—	52	1	no	—
905	C₂×C₄	—	52	1	no	—
906	C₂×C₄	—	52	1	no	—
907	C₂×C₄	—	52	1	no	—
908	C₂×C₄	—	52	1	no	—
909	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
910	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	26	1	no	—
928	C₂²	—	26	1	no	—
929	C₂²	—	26	1	no	—
930	C₂²	—	26	1	no	—
931	C₂²	—	26	1	no	—
932	C₂²	—	26	1	no	—
933	C₂²	—	26	1	no	—
934	C₂²	—	26	1	no	—
935	C₂²	—	26	1	no	—
936	C₂²	—	26	1	no	—
937	C₂²	—	26	1	no	—
938	C₂²	—	26	1	no	—
939	C₂²	—	26	1	no	—
940	C₂²	—	26	1	no	—
941	C₂²	—	26	1	no	—
942	C₂²	—	52	4	no	—
943	C₂²	#88254	1	2	yes	—
944	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	13	2	no	—
959	C₄	—	26	1	no	—
960	C₄	—	26	1	no	—
961	C₄	—	26	1	no	—
962	C₄	—	26	1	no	—
963	C₄	—	26	1	no	—
964	C₄	—	26	1	no	—
965	C₄	—	26	1	no	—
966	C₄	—	26	1	no	—
967	C₄	—	26	1	no	—
968	C₄	—	26	1	no	—
969	C₂	—	2	2	no	—
970	C₂	—	4	1	no	—
971	C₂	—	52	1	no	—
972	C₂	—	52	1	no	—
973	C₂	—	52	1	no	—
974	C₂	—	52	1	no	—
975	C₂	—	52	1	no	—
976	C₂	C₂×#88254	1	1	yes	characteristic
977	C₂	#11719648	1	1	yes	characteristic
978	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#554	C₂
hypercenter	#554	D₁₃
hypocenter	C₁₃	#3541
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. #11719429	C₂	semidirect
4. #11719405	C₂	semidirect
5. #11719401	C₂	semidirect
6. #11719398	C₂	semidirect
7. #11719397	C₂	semidirect
8. #11719352	C₂	semidirect
9. #11719351	C₂	semidirect
10. #11719349	C₂	semidirect
11. #11719349	C₂	semidirect
12. #11719345	C₂	semidirect
13. #11719345	C₂	semidirect
14. #11719341	C₂	semidirect
15. #11719341	C₂	semidirect
16. #11719338	C₂	semidirect
17. #11719337	C₂	semidirect
18. #11719334	C₂	semidirect
19. #11719332	C₂	semidirect
20. #11719287	C₂	semidirect
21. #11719273	C₂	semidirect
22. #11719265	C₂	semidirect
23. #11719265	C₂	semidirect
24. #11719257	C₂	semidirect
25. #11719252	C₂	semidirect
26. #11719245	C₂	semidirect
27. #11719245	C₂	semidirect
28. #11719220	C₂	semidirect
29. #11719219	C₂	semidirect
30. C₂×#88150	C₂	semidirect
31. #11719212	C₂	semidirect
33. C₂×Q₈×D₁₃	C₂²	semidirect
35. C₂×#6127	C₂²	semidirect
38. C₁₃×C₄⋊Q₈	C₂²	semidirect
39. C₁₃×#125	C₂²	semidirect
40. C₁₃×#125	C₂²	semidirect
44. C₁₃×C₂²⋊Q₈	C₂²	semidirect
45. C₁₃×C₂²⋊Q₈	C₂²	semidirect
46. C₁₃×C₂²⋊Q₈	C₂²	semidirect
47. C₄×Q₈×C₁₃	C₂²	semidirect
52. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
58. #88200	C₂²	semidirect
59. #88200	C₂²	semidirect
60. #88198	C₂²	semidirect
61. #88198	C₂²	semidirect
62. #88198	C₂²	semidirect
74. #88183	C₂²	semidirect
75. #88183	C₂²	semidirect
80. C₄×C₂²⋊D₁₃	C₂²	semidirect
81. C₄×C₂²⋊D₁₃	C₂²	semidirect
84. #88178	C₂²	semidirect
93. #88152	C₂²	semidirect
94. #88152	C₂²	semidirect
95. #88151	C₂²	semidirect
105. #88150	C₂²	semidirect
106. #88150	C₂²	semidirect
107. #88150	C₂²	semidirect
108. #88150	C₂²	semidirect
109. #88150	C₂²	semidirect
110. #88150	C₂²	semidirect
111. #88150	C₂²	semidirect
112. #88150	C₂²	semidirect
118. #88149	C₂²	semidirect
128. #88148	C₂²	semidirect
129. #88148	C₂²	semidirect
130. #88148	C₂²	semidirect
131. #88148	C₂²	semidirect
134. #88147	C₂²	semidirect
136. #88146	C₂²	semidirect
137. C₄⋊C₄×D₁₃	C₂²	semidirect
138. C₄⋊C₄×D₁₃	C₂²	semidirect
139. #88144	C₂²	semidirect
140. #88143	C₂²	semidirect
141. #88143	C₂²	semidirect
142. #88143	C₂²	semidirect
143. #88143	C₂²	semidirect
144. #88143	C₂²	semidirect
145. #88143	C₂²	semidirect
146. #88142	C₂²	semidirect
147. #88142	C₂²	semidirect
148. #88141	C₂²	semidirect
149. #88141	C₂²	semidirect
150. #88141	C₂²	semidirect
153. #88139	C₂²	semidirect
154. #88139	C₂²	semidirect
158. #88138	C₂²	semidirect
159. #88138	C₂²	semidirect
170. #88133	C₂²	semidirect
171. #88133	C₂²	semidirect
177. #88130	C₂²	semidirect
178. #88130	C₂²	semidirect
181. #88129	C₂²	semidirect
184. #88126	C₂²	semidirect
185. #88126	C₂²	semidirect
186. C₄×Dic₂₆	C₂²	semidirect
440. #554	D₁₃	semidirect
522. C₄⋊Q₈	C₂×D₁₃	semidirect
544. #125	C₂×D₁₃	semidirect
545. #125	C₂×D₁₃	semidirect
603. C₂²⋊Q₈	C₂×D₁₃	semidirect
604. C₂²⋊Q₈	C₂×D₁₃	semidirect
605. C₂²⋊Q₈	C₂×D₁₃	semidirect
633. C₄×Q₈	C₂×D₁₃	semidirect
663. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
837. C₁₃	#3541	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
#11719429	2
#11719405	2
#11719401	2
#11719398	2
#11719397	2
#11719352	2
#11719351	2
#11719349	2
#11719345	2
#11719341	2
#11719338	2
#11719337	2
#11719334	2
#11719332	2
#11719287	2
#11719273	2
#11719265	2
#11719257	2
#11719252	2
#11719245	2
#11719220	2
#11719219	2
C₂×#88150	2
#11719212	2
#3541	13