Subgroups — #13129055

Order 1664.

1134 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#562	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719397	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719395	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719383	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719382	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719381	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719374	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719372	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719367	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719365	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719362	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719361	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719360	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719359	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719359	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719352	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719341	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719339	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719339	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719338	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719336	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719334	C₂	1	1	yes	maximal, characteristic, complemented
23	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719326	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719317	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719315	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719315	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719313	C₂	1	1	yes	maximal, characteristic, complemented
29	#11719313	C₂	1	1	yes	maximal, characteristic, complemented
30	D₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
31	#11719302	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
33	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
35	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
36	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
37	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
40	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
41	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
42	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#121	C₂²	1	1	yes	characteristic
56	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
59	#88201	C₂²	1	1	yes	characteristic, complemented
60	#88200	C₂²	1	1	yes	characteristic
61	#88200	C₂²	1	1	yes	characteristic
62	#88200	C₂²	1	1	yes	characteristic, complemented
63	#88200	C₂²	1	1	yes	characteristic, complemented
64	#88198	C₂²	1	1	yes	characteristic, complemented
65	#88193	C₂²	1	1	yes	characteristic
66	#88193	C₂²	1	1	yes	characteristic
67	#88193	C₂²	1	1	yes	characteristic, complemented
68	#88193	C₂²	1	1	yes	characteristic, complemented
69	#88193	C₂²	1	1	yes	characteristic, complemented
70	#88193	C₂²	1	1	yes	characteristic, complemented
71	#88193	C₂²	1	1	yes	characteristic, complemented
72	#88192	C₂²	1	1	yes	characteristic
73	#88192	C₂²	1	1	yes	characteristic, complemented
74	#88192	C₂²	1	1	yes	characteristic, complemented
75	#88192	C₂²	1	1	yes	characteristic, complemented
76	#88192	C₂²	1	1	yes	characteristic, complemented
77	#88191	C₂²	1	1	yes	characteristic
78	#88191	C₂²	1	1	yes	characteristic
79	#88191	C₂²	1	1	yes	characteristic
80	#88190	C₂²	1	1	yes	characteristic, complemented
81	#88189	C₂²	1	1	yes	characteristic, complemented
82	#88189	C₂²	1	1	yes	characteristic, complemented
83	#88184	C₂²	1	1	yes	characteristic
84	#88184	C₂²	1	1	yes	characteristic, complemented
85	#88183	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×#6103	C₂²	1	1	yes	characteristic
90	C₂×#6103	C₂²	1	1	yes	characteristic
91	#88178	C₂²	1	1	yes	characteristic, complemented
92	#88178	C₂²	1	1	yes	characteristic, complemented
93	#88178	C₂²	1	1	yes	characteristic, complemented
94	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
95	#88152	C₂²	1	1	yes	characteristic, complemented
96	#88151	C₂²	1	1	yes	characteristic
97	#88151	C₂²	1	1	yes	characteristic
98	#88151	C₂²	1	1	yes	characteristic, complemented
99	#88151	C₂²	1	1	yes	characteristic, complemented
100	#88151	C₂²	1	1	yes	characteristic, complemented
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
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, complemented
115	#88149	C₂²	1	1	yes	characteristic, complemented
116	#88148	C₂²	1	1	yes	characteristic, complemented
117	#88148	C₂²	1	1	yes	characteristic, complemented
118	#88148	C₂²	1	1	yes	characteristic, complemented
119	#88148	C₂²	1	1	yes	characteristic, complemented
120	#88148	C₂²	1	1	yes	characteristic, complemented
121	#88147	C₂²	1	1	yes	characteristic
122	#88147	C₂²	1	1	yes	characteristic
123	#88147	C₂²	1	1	yes	characteristic, complemented
124	#88147	C₂²	1	1	yes	characteristic, complemented
125	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
126	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
127	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
128	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
129	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
130	#88144	C₂²	1	1	yes	characteristic, complemented
131	#88143	C₂²	1	1	yes	characteristic, complemented
132	#88143	C₂²	1	1	yes	characteristic, complemented
133	#88142	C₂²	1	1	yes	characteristic, complemented
134	#88141	C₂²	1	1	yes	characteristic, complemented
135	#88140	C₂²	1	1	yes	characteristic, complemented
136	#88139	C₂²	1	1	yes	characteristic, complemented
137	#88139	C₂²	1	1	yes	characteristic, complemented
138	#88139	C₂²	1	1	yes	characteristic, complemented
139	#88139	C₂²	1	1	yes	characteristic, complemented
140	#88139	C₂²	1	1	yes	characteristic, complemented
141	#88139	C₂²	1	1	yes	characteristic, complemented
142	#88138	C₂²	1	1	yes	characteristic
143	#88138	C₂²	1	1	yes	characteristic
144	#88138	C₂²	1	1	yes	characteristic
145	#88138	C₂²	1	1	yes	characteristic, complemented
146	#88138	C₂²	1	1	yes	characteristic, complemented
147	#88138	C₂²	1	1	yes	characteristic, complemented
148	#88138	C₂²	1	1	yes	characteristic, complemented
149	#88138	C₂²	1	1	yes	characteristic, complemented
150	#88138	C₂²	1	1	yes	characteristic, complemented
151	#88138	C₂²	1	1	yes	characteristic, complemented
152	#88138	C₂²	1	1	yes	characteristic, complemented
153	#88137	C₂²	1	1	yes	characteristic, complemented
154	#88137	C₂²	1	1	yes	characteristic, complemented
155	#88137	C₂²	1	1	yes	characteristic, complemented
156	#88137	C₂²	1	1	yes	characteristic, complemented
157	#88137	C₂²	1	1	yes	characteristic, complemented
158	#88136	C₂²	1	1	yes	characteristic
159	#88136	C₂²	1	1	yes	characteristic
160	#88136	C₂²	1	1	yes	characteristic
161	#88135	C₂²	1	1	yes	characteristic
162	#88135	C₂²	1	1	yes	characteristic
163	#88135	C₂²	1	1	yes	characteristic, complemented
164	#88135	C₂²	1	1	yes	characteristic, complemented
165	#88135	C₂²	1	1	yes	characteristic, complemented
166	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
172	#88133	C₂²	1	1	yes	characteristic, complemented
173	#88133	C₂²	1	1	yes	characteristic, complemented
174	#88132	C₂²	1	1	yes	characteristic, complemented
175	#88132	C₂²	1	1	yes	characteristic, complemented
176	#88132	C₂²	1	1	yes	characteristic, complemented
177	#88132	C₂²	1	1	yes	characteristic, complemented
178	#88132	C₂²	1	1	yes	characteristic, complemented
179	#88132	C₂²	1	1	yes	characteristic, complemented
180	#88132	C₂²	1	1	yes	characteristic, complemented
181	#88132	C₂²	1	1	yes	characteristic, complemented
182	#88131	C₂²	1	1	yes	characteristic, complemented
183	#88130	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₅₂	C₂²	1	1	yes	characteristic
185	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₃	C₂³	1	1	yes	characteristic
188	C₂³×D₁₃	C₂³	1	1	yes	characteristic
189	C₂³×D₁₃	C₂³	1	1	yes	characteristic
190	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×Q₈×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	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
196	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
197	C₂×D₄×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	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	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	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
216	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
217	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
218	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
219	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
220	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
221	#6131	—	4	2	no	—
222	Q₈×D₁₃	—	4	2	no	—
223	#6129	—	4	2	no	—
224	#6129	—	4	2	no	—
225	#6129	—	4	2	no	—
226	D₄×D₁₃	—	4	2	no	—
227	D₄×D₁₃	—	4	2	no	—
228	D₄×D₁₃	—	4	2	no	—
229	#6127	—	4	2	no	—
230	#6127	—	4	2	no	—
231	#6127	—	4	2	no	—
232	C₂×D₅₂	C₂³	1	1	yes	characteristic
233	C₂×D₅₂	C₂³	1	1	yes	characteristic
234	C₂×D₅₂	C₂³	1	1	yes	characteristic
235	C₂×D₅₂	C₂³	1	1	yes	characteristic
236	C₂×D₅₂	C₂³	1	1	yes	characteristic
237	C₂×D₅₂	C₂³	1	1	yes	characteristic
238	C₂×D₅₂	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₁₃	—	4	2	no	—
240	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
253	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
255	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
257	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
258	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
259	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
260	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
261	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
262	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
263	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
264	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₄²×C₁₃	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
289	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
290	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
291	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
292	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
293	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
294	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
295	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
296	C₂²⋊Dic₁₃	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	#6103	C₂³	1	1	yes	characteristic
308	#6103	C₂³	1	1	yes	characteristic
309	#6103	C₂³	1	1	yes	characteristic
310	#6103	C₂³	1	1	yes	characteristic
311	#6103	C₂³	1	1	yes	characteristic
312	#6103	C₂³	1	1	yes	characteristic
313	#6103	C₂³	1	1	yes	characteristic
314	#6103	C₂³	1	1	yes	characteristic
315	#6103	C₂³	1	1	yes	characteristic
316	#6103	C₂³	1	1	yes	characteristic
317	#6103	C₂³	1	1	yes	characteristic
318	#6103	C₂³	1	1	yes	characteristic
319	#6103	C₂³	1	1	yes	characteristic
320	#6103	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
324	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
325	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
326	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
327	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
328	C₄⋊Dic₁₃	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	#6101	C₂³	1	1	yes	characteristic
340	#6101	C₂³	1	1	yes	characteristic
341	#6101	C₂³	1	1	yes	characteristic
342	#6101	C₂³	1	1	yes	characteristic
343	#6101	C₂³	1	1	yes	characteristic
344	#6101	C₂³	1	1	yes	characteristic
345	#6101	C₂³	1	1	yes	characteristic
346	#6101	C₂³	1	1	yes	characteristic
347	#6101	C₂³	1	1	yes	characteristic
348	#6101	C₂³	1	1	yes	characteristic
349	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
350	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
351	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
352	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
353	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
354	#3536	—	13	1	no	maximal, Sylow
355	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂²×D₁₃	—	2	2	no	—
360	C₂²×D₁₃	—	2	2	no	—
361	C₂²×D₁₃	—	2	2	no	—
362	C₂²×D₁₃	—	2	2	no	—
363	C₂²×D₁₃	—	4	1	no	—
364	C₂²×D₁₃	—	4	1	no	—
365	C₂²×D₁₃	—	4	1	no	—
366	C₂²×D₁₃	—	4	1	no	—
367	C₂²×D₁₃	—	4	1	no	—
368	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
369	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
370	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
371	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
372	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
373	Q₈×C₁₃	—	4	1	no	—
374	Q₈×C₁₃	—	4	1	no	—
375	D₄×C₁₃	—	4	1	no	—
376	D₄×C₁₃	—	4	1	no	—
377	D₄×C₁₃	—	4	1	no	—
378	D₄×C₁₃	—	4	1	no	—
379	D₄×C₁₃	—	4	1	no	—
380	D₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
396	C₂²⋊D₁₃	—	2	2	no	—
397	C₂²⋊D₁₃	—	2	2	no	—
398	C₂²⋊D₁₃	—	2	2	no	—
399	C₂²⋊D₁₃	—	2	2	no	—
400	C₂²⋊D₁₃	—	2	2	no	—
401	C₂²⋊D₁₃	—	2	2	no	—
402	C₂²⋊D₁₃	—	4	1	no	—
403	C₂²⋊D₁₃	—	4	1	no	—
404	C₂²⋊D₁₃	—	4	1	no	—
405	C₂²⋊D₁₃	—	4	1	no	—
406	C₂²⋊D₁₃	—	4	1	no	—
407	C₂²⋊D₁₃	—	4	1	no	—
408	C₂²⋊D₁₃	—	4	1	no	—
409	C₂²⋊D₁₃	—	4	1	no	—
410	C₂×Dic₁₃	—	2	2	no	—
411	C₂×Dic₁₃	—	2	2	no	—
412	C₂×Dic₁₃	—	4	1	no	—
413	C₂×Dic₁₃	—	4	1	no	—
414	C₂×Dic₁₃	—	4	1	no	—
415	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
417	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
419	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
421	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
424	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
425	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
426	D₅₂	—	2	2	no	—
427	D₅₂	—	2	2	no	—
428	D₅₂	—	2	2	no	—
429	D₅₂	—	2	2	no	—
430	D₅₂	—	4	1	no	—
431	D₅₂	—	4	1	no	—
432	D₅₂	—	4	1	no	—
433	C₄×D₁₃	—	2	2	no	—
434	C₄×D₁₃	—	2	2	no	—
435	C₄×D₁₃	—	2	2	no	—
436	C₄×D₁₃	—	2	2	no	—
437	C₄×D₁₃	—	2	2	no	—
438	C₄×D₁₃	—	4	1	no	—
439	C₄×D₁₃	—	4	1	no	—
440	C₄×D₁₃	—	4	1	no	—
441	C₄×D₁₃	—	4	1	no	—
442	C₄×D₁₃	—	4	1	no	—
443	C₄×D₁₃	—	4	1	no	—
444	C₄×D₁₃	—	4	1	no	—
445	C₄×D₁₃	—	4	1	no	—
446	C₄×D₁₃	—	4	1	no	—
447	C₄×D₁₃	—	4	1	no	—
448	C₄×D₁₃	—	4	1	no	—
449	C₄×D₁₃	—	4	1	no	—
450	Dic₂₆	—	2	2	no	—
451	Dic₂₆	—	2	2	no	—
452	Dic₂₆	—	4	1	no	—
453	Dic₂₆	—	4	1	no	—
454	Dic₂₆	—	4	1	no	—
455	Dic₂₆	—	4	1	no	—
456	Dic₂₆	—	4	1	no	—
457	#562	—	13	1	no	—
458	#562	—	13	1	no	—
459	#562	—	13	1	no	—
460	#562	D₁₃	1	1	yes	characteristic, complemented
461	#554	—	13	1	no	—
462	#554	—	13	1	no	—
463	#548	—	13	1	no	—
464	#548	—	13	1	no	—
465	#547	—	13	1	no	—
466	#547	—	13	1	no	—
467	#546	—	13	1	no	—
468	#546	—	13	1	no	—
469	#546	—	13	1	no	—
470	#546	—	13	1	no	—
471	#546	—	13	1	no	—
472	#546	—	13	1	no	—
473	#543	—	13	1	no	—
474	#543	—	13	1	no	—
475	#542	—	13	1	no	—
476	#542	—	13	1	no	—
477	#539	—	13	1	no	—
478	#539	—	13	1	no	—
479	#538	—	13	1	no	—
480	#538	—	13	1	no	—
481	#537	—	13	1	no	—
482	#537	—	13	1	no	—
483	#537	—	13	1	no	—
484	#537	—	13	1	no	—
485	#525	—	13	1	no	—
486	C₂×C₂²⋊Q₈	—	13	1	no	—
487	C₂×#121	—	13	1	no	—
488	C₂²×C₁₃	—	2	1	no	—
489	C₂²×C₁₃	—	2	1	no	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	2	1	no	—
493	C₂²×C₁₃	—	2	1	no	—
494	C₂²×C₁₃	—	2	1	no	—
495	C₂²×C₁₃	—	2	1	no	—
496	C₂²×C₁₃	—	2	1	no	—
497	C₂²×C₁₃	—	2	1	no	—
498	C₂²×C₁₃	—	2	1	no	—
499	C₂²×C₁₃	—	2	1	no	—
500	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
501	C₂×D₁₃	—	2	1	no	—
502	C₂×D₁₃	—	2	1	no	—
503	C₂×D₁₃	—	2	1	no	—
504	C₂×D₁₃	—	2	1	no	—
505	C₂×D₁₃	—	2	1	no	—
506	C₂×D₁₃	—	2	1	no	—
507	C₂×D₁₃	—	2	1	no	—
508	C₂×D₁₃	—	2	1	no	—
509	C₂×D₁₃	—	2	1	no	—
510	C₂×D₁₃	—	2	1	no	—
511	C₂×D₁₃	—	2	1	no	—
512	C₂×D₁₃	—	2	1	no	—
513	C₂×D₁₃	—	2	1	no	—
514	C₂×D₁₃	—	4	4	no	—
515	C₂×D₁₃	—	8	2	no	—
516	C₂×D₁₃	—	8	2	no	—
517	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
518	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
519	C₄×C₁₃	—	2	1	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	1	no	—
522	C₄×C₁₃	—	2	1	no	—
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	2	1	no	—
525	C₄×C₁₃	—	2	1	no	—
526	C₄×C₁₃	—	2	1	no	—
527	C₄×C₁₃	—	2	1	no	—
528	C₄×C₁₃	—	2	1	no	—
529	C₄×C₁₃	—	2	1	no	—
530	Dic₁₃	—	2	1	no	—
531	Dic₁₃	—	2	1	no	—
532	Dic₁₃	—	2	1	no	—
533	Dic₁₃	—	2	1	no	—
534	Dic₁₃	—	2	1	no	—
535	Dic₁₃	—	2	1	no	—
536	Dic₁₃	—	2	1	no	—
537	Dic₁₃	—	2	1	no	—
538	Dic₁₃	—	2	1	no	—
539	Dic₁₃	—	2	1	no	—
540	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
541	C₂×#41	—	13	1	no	—
542	C₂×#41	—	13	1	no	—
543	C₂×#41	—	13	1	no	—
544	C₂×#41	—	13	1	no	—
545	C₂×#41	—	13	1	no	—
546	C₂×#41	—	13	1	no	—
547	C₂×#41	—	13	1	no	—
548	C₂²×Q₈	—	13	1	no	—
549	C₂²×D₄	—	13	1	no	—
550	C₂²×D₄	—	13	1	no	—
551	C₂²×D₄	—	13	1	no	—
552	C₂³×C₄	—	13	1	no	—
553	C₄⋊Q₈	—	13	1	no	—
554	C₄⋊Q₈	—	13	1	no	—
555	#126	—	13	1	no	—
556	#126	—	13	1	no	—
557	#126	—	13	1	no	—
558	#126	—	13	1	no	—
559	#125	—	13	1	no	—
560	#125	—	13	1	no	—
561	#125	—	13	1	no	—
562	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
563	#124	—	13	1	no	—
564	#124	—	13	1	no	—
565	#124	—	13	1	no	—
566	#124	—	13	1	no	—
567	#124	—	13	1	no	—
568	#124	—	13	1	no	—
569	#124	—	13	1	no	—
570	#124	—	13	1	no	—
571	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
572	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
573	#123	—	13	1	no	—
574	#123	—	13	1	no	—
575	#123	—	13	1	no	—
576	#123	—	13	1	no	—
577	#123	—	13	1	no	—
578	#123	—	13	1	no	—
579	#123	—	13	1	no	—
580	#123	—	13	1	no	—
581	#123	—	13	1	no	—
582	#123	—	13	1	no	—
583	#123	—	13	1	no	—
584	#123	—	13	1	no	—
585	#123	—	13	1	no	—
586	#123	—	13	1	no	—
587	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
588	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
589	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
590	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
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	—	13	1	no	—
601	C₂²⋊Q₈	—	13	1	no	—
602	C₂²⋊Q₈	—	13	1	no	—
603	C₂²⋊Q₈	—	13	1	no	—
604	C₂²⋊Q₈	—	13	1	no	—
605	C₂²⋊Q₈	—	13	1	no	—
606	C₂²⋊Q₈	—	13	1	no	—
607	C₂²⋊Q₈	—	13	1	no	—
608	C₂²⋊Q₈	—	13	1	no	—
609	C₂²⋊Q₈	—	13	1	no	—
610	C₂²⋊Q₈	—	13	1	no	—
611	C₂²⋊Q₈	—	13	1	no	—
612	C₂²⋊Q₈	—	13	1	no	—
613	C₂²⋊Q₈	—	13	1	no	—
614	C₂²⋊Q₈	—	13	1	no	—
615	C₂²⋊Q₈	—	13	1	no	—
616	C₂²⋊Q₈	—	13	1	no	—
617	C₂²⋊Q₈	—	13	1	no	—
618	C₂²⋊Q₈	—	13	1	no	—
619	C₂²⋊Q₈	—	13	1	no	—
620	C₂²⋊Q₈	—	13	1	no	—
621	C₂²⋊Q₈	—	13	1	no	—
622	C₂²⋊Q₈	—	13	1	no	—
623	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
624	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
625	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
626	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
627	#121	—	13	1	no	—
628	#121	—	13	1	no	—
629	#121	—	13	1	no	—
630	#121	—	13	1	no	—
631	#121	—	13	1	no	—
632	#121	—	13	1	no	—
633	#121	—	13	1	no	—
634	#121	—	13	1	no	—
635	#121	—	13	1	no	—
636	#121	—	13	1	no	—
637	#121	—	13	1	no	—
638	#121	—	13	1	no	—
639	#121	—	13	1	no	—
640	#121	—	13	1	no	—
641	#121	—	13	1	no	—
642	#121	—	13	1	no	—
643	#121	—	13	1	no	—
644	#121	—	13	1	no	—
645	#121	—	13	1	no	—
646	#121	—	13	1	no	—
647	#121	—	13	1	no	—
648	#121	—	13	1	no	—
649	#121	—	13	1	no	—
650	#121	—	13	1	no	—
651	#121	—	13	1	no	—
652	#121	—	13	1	no	—
653	#121	—	13	1	no	—
654	#121	—	13	1	no	—
655	#121	C₂×D₁₃	1	1	yes	characteristic
656	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
657	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
658	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
659	#120	—	13	1	no	—
660	#120	—	13	1	no	—
661	#120	—	13	1	no	—
662	#120	—	13	1	no	—
663	#120	—	13	1	no	—
664	#120	—	13	1	no	—
665	C₄×Q₈	—	13	1	no	—
666	C₄×Q₈	—	13	1	no	—
667	C₄×D₄	—	13	1	no	—
668	C₄×D₄	—	13	1	no	—
669	C₄×D₄	—	13	1	no	—
670	C₄×D₄	—	13	1	no	—
671	C₄×D₄	—	13	1	no	—
672	C₄×D₄	—	13	1	no	—
673	C₄×D₄	—	13	1	no	—
674	C₄×D₄	—	13	1	no	—
675	C₄×D₄	—	13	1	no	—
676	C₄×D₄	—	13	1	no	—
677	C₄×D₄	—	13	1	no	—
678	C₄×D₄	—	13	1	no	—
679	C₄×D₄	—	13	1	no	—
680	C₄×D₄	—	13	1	no	—
681	#117	—	13	1	no	—
682	C₂×C₄⋊C₄	—	13	1	no	—
683	C₂×C₄⋊C₄	—	13	1	no	—
684	C₂×C₄⋊C₄	—	13	1	no	—
685	C₂×C₄⋊C₄	—	13	1	no	—
686	C₂×C₄⋊C₄	—	13	1	no	—
687	C₂×C₄⋊C₄	—	13	1	no	—
688	C₂×C₂²⋊C₄	—	13	1	no	—
689	C₂×C₂²⋊C₄	—	13	1	no	—
690	C₂×C₂²⋊C₄	—	13	1	no	—
691	C₂×C₂²⋊C₄	—	13	1	no	—
692	C₂×C₂²⋊C₄	—	13	1	no	—
693	C₂×C₂²⋊C₄	—	13	1	no	—
694	C₂×C₂²⋊C₄	—	13	1	no	—
695	C₂×C₂²⋊C₄	—	13	1	no	—
696	C₂×C₁₃	—	4	1	no	—
697	C₂×C₁₃	—	4	1	no	—
698	C₂×C₁₃	—	4	1	no	—
699	C₂×C₁₃	—	4	1	no	—
700	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
702	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
703	D₁₃	—	2	2	no	—
704	D₁₃	—	2	2	no	—
705	D₁₃	—	4	1	no	—
706	D₁₃	—	4	1	no	—
707	D₁₃	—	4	1	no	—
708	C₂⁴	—	13	1	no	—
709	C₂⁴	—	13	1	no	—
710	C₂⁴	—	13	1	no	—
711	#41	—	52	2	no	—
712	#41	—	52	2	no	—
713	#41	—	52	2	no	—
714	#41	—	52	2	no	—
715	#41	—	52	2	no	—
716	#41	—	52	2	no	—
717	#41	—	52	2	no	—
718	C₂×Q₈	—	13	1	no	—
719	C₂×Q₈	—	13	1	no	—
720	C₂×Q₈	—	13	1	no	—
721	C₂×Q₈	—	13	1	no	—
722	C₂×Q₈	—	13	1	no	—
723	C₂×Q₈	—	13	1	no	—
724	C₂×Q₈	—	13	1	no	—
725	C₂×Q₈	—	52	2	no	—
726	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
727	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
728	C₂×D₄	—	13	1	no	—
729	C₂×D₄	—	13	1	no	—
730	C₂×D₄	—	13	1	no	—
731	C₂×D₄	—	13	1	no	—
732	C₂×D₄	—	13	1	no	—
733	C₂×D₄	—	13	1	no	—
734	C₂×D₄	—	13	1	no	—
735	C₂×D₄	—	13	1	no	—
736	C₂×D₄	—	13	1	no	—
737	C₂×D₄	—	13	1	no	—
738	C₂×D₄	—	13	1	no	—
739	C₂×D₄	—	13	1	no	—
740	C₂×D₄	—	13	1	no	—
741	C₂×D₄	—	13	1	no	—
742	C₂×D₄	—	13	1	no	—
743	C₂×D₄	—	13	1	no	—
744	C₂×D₄	—	13	1	no	—
745	C₂×D₄	—	13	1	no	—
746	C₂×D₄	—	13	1	no	—
747	C₂×D₄	—	13	1	no	—
748	C₂×D₄	—	13	1	no	—
749	C₂×D₄	—	52	2	no	—
750	C₂×D₄	—	52	2	no	—
751	C₂×D₄	—	52	2	no	—
752	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
753	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
754	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
755	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
756	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
757	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	52	2	no	—
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	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
785	C₄⋊C₄	—	13	1	no	—
786	C₄⋊C₄	—	13	1	no	—
787	C₄⋊C₄	—	13	1	no	—
788	C₄⋊C₄	—	13	1	no	—
789	C₄⋊C₄	—	13	1	no	—
790	C₄⋊C₄	—	13	1	no	—
791	C₄⋊C₄	—	13	1	no	—
792	C₄⋊C₄	—	13	1	no	—
793	C₄⋊C₄	—	13	1	no	—
794	C₄⋊C₄	—	13	1	no	—
795	C₄⋊C₄	—	13	1	no	—
796	C₄⋊C₄	—	13	1	no	—
797	C₄⋊C₄	—	13	1	no	—
798	C₄⋊C₄	—	13	1	no	—
799	C₄⋊C₄	—	13	1	no	—
800	C₄⋊C₄	—	13	1	no	—
801	C₄⋊C₄	—	13	1	no	—
802	C₄⋊C₄	—	13	1	no	—
803	C₄⋊C₄	—	13	1	no	—
804	C₄⋊C₄	—	13	1	no	—
805	C₄⋊C₄	—	13	1	no	—
806	C₄⋊C₄	—	13	1	no	—
807	C₄⋊C₄	—	13	1	no	—
808	C₄⋊C₄	—	13	1	no	—
809	C₄⋊C₄	—	13	1	no	—
810	C₄⋊C₄	—	13	1	no	—
811	C₄⋊C₄	—	13	1	no	—
812	C₄⋊C₄	—	13	1	no	—
813	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
814	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
815	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
816	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
817	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
818	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
819	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
820	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
821	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
822	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
823	C₂²⋊C₄	—	13	1	no	—
824	C₂²⋊C₄	—	13	1	no	—
825	C₂²⋊C₄	—	13	1	no	—
826	C₂²⋊C₄	—	13	1	no	—
827	C₂²⋊C₄	—	13	1	no	—
828	C₂²⋊C₄	—	13	1	no	—
829	C₂²⋊C₄	—	13	1	no	—
830	C₂²⋊C₄	—	13	1	no	—
831	C₂²⋊C₄	—	13	1	no	—
832	C₂²⋊C₄	—	13	1	no	—
833	C₂²⋊C₄	—	13	1	no	—
834	C₂²⋊C₄	—	13	1	no	—
835	C₂²⋊C₄	—	13	1	no	—
836	C₂²⋊C₄	—	13	1	no	—
837	C₂²⋊C₄	—	13	1	no	—
838	C₂²⋊C₄	—	13	1	no	—
839	C₂²⋊C₄	—	13	1	no	—
840	C₂²⋊C₄	—	13	1	no	—
841	C₂²⋊C₄	—	13	1	no	—
842	C₂²⋊C₄	—	13	1	no	—
843	C₂²⋊C₄	—	13	1	no	—
844	C₂²⋊C₄	—	13	1	no	—
845	C₂²⋊C₄	—	13	1	no	—
846	C₂²⋊C₄	—	13	1	no	—
847	C₂²⋊C₄	—	13	1	no	—
848	C₂²⋊C₄	—	13	1	no	—
849	C₂²⋊C₄	—	13	1	no	—
850	C₂²⋊C₄	—	13	1	no	—
851	C₂²⋊C₄	—	13	1	no	—
852	C₂²⋊C₄	—	13	1	no	—
853	C₂²⋊C₄	—	13	1	no	—
854	C₂²⋊C₄	—	13	1	no	—
855	C₂²⋊C₄	—	13	1	no	—
856	C₂²⋊C₄	—	13	1	no	—
857	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
858	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
859	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
860	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
861	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
862	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
863	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
864	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
865	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
866	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
867	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
868	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
869	C₄²	—	13	1	no	—
870	C₄²	—	13	1	no	—
871	C₄²	—	13	1	no	—
872	C₄²	—	13	1	no	—
873	C₄²	—	13	1	no	—
874	C₄²	C₂²×D₁₃	1	1	yes	characteristic
875	C₁₃	#3536	1	1	yes	characteristic, complemented, Sylow
876	C₂³	—	13	1	no	—
877	C₂³	—	13	1	no	—
878	C₂³	—	13	1	no	—
879	C₂³	—	13	1	no	—
880	C₂³	—	13	1	no	—
881	C₂³	—	26	2	no	—
882	C₂³	—	26	2	no	—
883	C₂³	—	26	2	no	—
884	C₂³	—	26	2	no	—
885	C₂³	—	52	1	no	—
886	C₂³	—	52	1	no	—
887	C₂³	—	52	1	no	—
888	C₂³	—	52	1	no	—
889	C₂³	—	52	1	no	—
890	C₂³	C₂³×D₁₃	1	1	yes	characteristic
891	C₂³	C₂³×D₁₃	1	1	yes	characteristic
892	C₂³	C₂³×D₁₃	1	1	yes	characteristic
893	C₂³	C₂³×D₁₃	1	1	yes	characteristic
894	Q₈	—	4	1	no	—
895	Q₈	—	4	1	no	—
896	Q₈	—	26	2	no	—
897	Q₈	—	26	2	no	—
898	Q₈	—	52	1	no	—
899	Q₈	—	52	1	no	—
900	Q₈	—	52	1	no	—
901	Q₈	—	52	1	no	—
902	Q₈	—	52	1	no	—
903	D₄	—	4	1	no	—
904	D₄	—	4	1	no	—
905	D₄	—	4	1	no	—
906	D₄	—	4	1	no	—
907	D₄	—	4	1	no	—
908	D₄	—	4	1	no	—
909	D₄	—	26	2	no	—
910	D₄	—	26	2	no	—
911	D₄	—	26	2	no	—
912	D₄	—	26	2	no	—
913	D₄	—	26	2	no	—
914	D₄	—	26	2	no	—
915	D₄	—	26	2	no	—
916	D₄	—	26	2	no	—
917	D₄	—	26	2	no	—
918	D₄	—	26	2	no	—
919	D₄	—	52	1	no	—
920	D₄	—	52	1	no	—
921	D₄	—	52	1	no	—
922	D₄	—	52	1	no	—
923	D₄	—	52	1	no	—
924	D₄	—	52	1	no	—
925	D₄	—	52	1	no	—
926	D₄	—	52	1	no	—
927	D₄	—	52	1	no	—
928	D₄	—	52	1	no	—
929	D₄	—	52	1	no	—
930	C₂×C₄	—	4	1	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	13	1	no	—
935	C₂×C₄	—	13	1	no	—
936	C₂×C₄	—	13	1	no	—
937	C₂×C₄	—	13	1	no	—
938	C₂×C₄	—	13	1	no	—
939	C₂×C₄	—	13	1	no	—
940	C₂×C₄	—	13	1	no	—
941	C₂×C₄	—	13	1	no	—
942	C₂×C₄	—	13	1	no	—
943	C₂×C₄	—	13	1	no	—
944	C₂×C₄	—	13	1	no	—
945	C₂×C₄	—	26	2	no	—
946	C₂×C₄	—	26	2	no	—
947	C₂×C₄	—	26	2	no	—
948	C₂×C₄	—	26	2	no	—
949	C₂×C₄	—	26	2	no	—
950	C₂×C₄	—	26	2	no	—
951	C₂×C₄	—	26	2	no	—
952	C₂×C₄	—	52	1	no	—
953	C₂×C₄	—	52	1	no	—
954	C₂×C₄	—	52	1	no	—
955	C₂×C₄	—	52	1	no	—
956	C₂×C₄	—	52	1	no	—
957	C₂×C₄	—	52	1	no	—
958	C₂×C₄	—	52	1	no	—
959	C₂×C₄	—	52	1	no	—
960	C₂×C₄	—	52	1	no	—
961	C₂×C₄	—	52	1	no	—
962	C₂×C₄	—	52	1	no	—
963	C₂×C₄	—	52	1	no	—
964	C₂×C₄	—	52	1	no	—
965	C₂×C₄	—	52	1	no	—
966	C₂×C₄	—	52	1	no	—
967	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
968	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
969	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
970	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
971	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
972	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
973	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
974	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
975	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
976	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
977	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	1	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	13	2	no	—
991	C₂²	—	13	2	no	—
992	C₂²	—	26	1	no	—
993	C₂²	—	26	1	no	—
994	C₂²	—	26	1	no	—
995	C₂²	—	26	1	no	—
996	C₂²	—	26	1	no	—
997	C₂²	—	26	1	no	—
998	C₂²	—	26	1	no	—
999	C₂²	—	26	1	no	—
1000	C₂²	—	26	1	no	—
1001	C₂²	—	26	1	no	—
1002	C₂²	—	26	1	no	—
1003	C₂²	—	26	1	no	—
1004	C₂²	—	26	1	no	—
1005	C₂²	—	52	4	no	—
1006	C₂²	—	104	2	no	—
1007	C₂²	—	104	2	no	—
1008	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	13	2	no	—
1021	C₄	—	26	1	no	—
1022	C₄	—	26	1	no	—
1023	C₄	—	26	1	no	—
1024	C₄	—	26	1	no	—
1025	C₄	—	26	1	no	—
1026	C₄	—	26	1	no	—
1027	C₄	—	26	1	no	—
1028	C₄	—	26	1	no	—
1029	C₄	—	26	1	no	—
1030	C₄	—	26	1	no	—
1031	C₂	—	4	1	no	—
1032	C₂	—	4	1	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	1	no	—
1035	C₂	—	26	2	no	—
1036	C₂	—	26	2	no	—
1037	C₂	—	52	1	no	—
1038	C₂	—	52	1	no	—
1039	C₂	—	52	1	no	—
1040	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1041	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1042	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#562	C₂
hypercenter	#562	D₁₃
hypocenter	C₁₃	#3536
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. C₁₃×#562	C₂	semidirect
2. #11719397	C₂	semidirect
3. #11719395	C₂	semidirect
4. #11719383	C₂	semidirect
5. #11719382	C₂	semidirect
6. #11719381	C₂	semidirect
7. #11719374	C₂	semidirect
8. #11719372	C₂	semidirect
9. #11719367	C₂	semidirect
10. #11719365	C₂	semidirect
11. #11719362	C₂	semidirect
12. #11719361	C₂	semidirect
13. #11719360	C₂	semidirect
14. #11719359	C₂	semidirect
15. #11719359	C₂	semidirect
16. #11719352	C₂	semidirect
17. #11719341	C₂	semidirect
18. #11719339	C₂	semidirect
19. #11719339	C₂	semidirect
20. #11719338	C₂	semidirect
21. #11719336	C₂	semidirect
22. #11719334	C₂	semidirect
23. D₁₃×C₂²⋊Q₈	C₂	semidirect
24. #11719326	C₂	semidirect
25. #11719317	C₂	semidirect
26. #11719315	C₂	semidirect
27. #11719315	C₂	semidirect
28. #11719313	C₂	semidirect
29. #11719313	C₂	semidirect
30. D₁₃×#121	C₂	semidirect
31. #11719302	C₂	semidirect
32. C₂×#6131	C₂²	semidirect
33. C₂×Q₈×D₁₃	C₂²	semidirect
34. C₂×#6129	C₂²	semidirect
35. C₂×#6129	C₂²	semidirect
36. C₂×#6129	C₂²	semidirect
40. C₂×#6127	C₂²	semidirect
41. C₂×#6127	C₂²	semidirect
42. C₂×#6127	C₂²	semidirect
44. C₁₃×#125	C₂²	semidirect
45. C₁₃×#124	C₂²	semidirect
46. C₁₃×#124	C₂²	semidirect
47. C₁₃×#123	C₂²	semidirect
48. C₁₃×#123	C₂²	semidirect
49. C₁₃×#123	C₂²	semidirect
50. C₁₃×#123	C₂²	semidirect
51. C₁₃×C₂²⋊Q₈	C₂²	semidirect
52. C₁₃×C₂²⋊Q₈	C₂²	semidirect
53. C₁₃×C₂²⋊Q₈	C₂²	semidirect
54. C₁₃×C₂²⋊Q₈	C₂²	semidirect
56. C₁₃×#121	C₂²	semidirect
57. C₁₃×#121	C₂²	semidirect
58. C₁₃×#121	C₂²	semidirect
59. #88201	C₂²	semidirect
62. #88200	C₂²	semidirect
63. #88200	C₂²	semidirect
64. #88198	C₂²	semidirect
67. #88193	C₂²	semidirect
68. #88193	C₂²	semidirect
69. #88193	C₂²	semidirect
70. #88193	C₂²	semidirect
71. #88193	C₂²	semidirect
73. #88192	C₂²	semidirect
74. #88192	C₂²	semidirect
75. #88192	C₂²	semidirect
76. #88192	C₂²	semidirect
80. #88190	C₂²	semidirect
81. #88189	C₂²	semidirect
82. #88189	C₂²	semidirect
84. #88184	C₂²	semidirect
85. #88183	C₂²	semidirect
87. C₄×C₂²⋊D₁₃	C₂²	semidirect
88. C₄×C₂²⋊D₁₃	C₂²	semidirect
91. #88178	C₂²	semidirect
92. #88178	C₂²	semidirect
93. #88178	C₂²	semidirect
94. C₂×#6101	C₂²	semidirect
95. #88152	C₂²	semidirect
98. #88151	C₂²	semidirect
99. #88151	C₂²	semidirect
100. #88151	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
114. #88149	C₂²	semidirect
115. #88149	C₂²	semidirect
116. #88148	C₂²	semidirect
117. #88148	C₂²	semidirect
118. #88148	C₂²	semidirect
119. #88148	C₂²	semidirect
120. #88148	C₂²	semidirect
123. #88147	C₂²	semidirect
124. #88147	C₂²	semidirect
126. C₄⋊C₄×D₁₃	C₂²	semidirect
127. C₄⋊C₄×D₁₃	C₂²	semidirect
128. C₄⋊C₄×D₁₃	C₂²	semidirect
129. C₄⋊C₄×D₁₃	C₂²	semidirect
130. #88144	C₂²	semidirect
131. #88143	C₂²	semidirect
132. #88143	C₂²	semidirect
133. #88142	C₂²	semidirect
134. #88141	C₂²	semidirect
135. #88140	C₂²	semidirect
136. #88139	C₂²	semidirect
137. #88139	C₂²	semidirect
138. #88139	C₂²	semidirect
139. #88139	C₂²	semidirect
140. #88139	C₂²	semidirect
141. #88139	C₂²	semidirect
145. #88138	C₂²	semidirect
146. #88138	C₂²	semidirect
147. #88138	C₂²	semidirect
148. #88138	C₂²	semidirect
149. #88138	C₂²	semidirect
150. #88138	C₂²	semidirect
151. #88138	C₂²	semidirect
152. #88138	C₂²	semidirect
153. #88137	C₂²	semidirect
154. #88137	C₂²	semidirect
155. #88137	C₂²	semidirect
156. #88137	C₂²	semidirect
157. #88137	C₂²	semidirect
163. #88135	C₂²	semidirect
164. #88135	C₂²	semidirect
165. #88135	C₂²	semidirect
172. #88133	C₂²	semidirect
173. #88133	C₂²	semidirect
174. #88132	C₂²	semidirect
175. #88132	C₂²	semidirect
176. #88132	C₂²	semidirect
177. #88132	C₂²	semidirect
178. #88132	C₂²	semidirect
179. #88132	C₂²	semidirect
180. #88132	C₂²	semidirect
181. #88132	C₂²	semidirect
182. #88131	C₂²	semidirect
183. #88130	C₂²	semidirect
185. C₄×D₅₂	C₂²	semidirect
186. C₄×Dic₂₆	C₂²	semidirect
460. #562	D₁₃	semidirect
562. #125	C₂×D₁₃	semidirect
571. #124	C₂×D₁₃	semidirect
572. #124	C₂×D₁₃	semidirect
587. #123	C₂×D₁₃	semidirect
588. #123	C₂×D₁₃	semidirect
589. #123	C₂×D₁₃	semidirect
590. #123	C₂×D₁₃	semidirect
623. C₂²⋊Q₈	C₂×D₁₃	semidirect
624. C₂²⋊Q₈	C₂×D₁₃	semidirect
625. C₂²⋊Q₈	C₂×D₁₃	semidirect
626. C₂²⋊Q₈	C₂×D₁₃	semidirect
656. #121	C₂×D₁₃	semidirect
657. #121	C₂×D₁₃	semidirect
658. #121	C₂×D₁₃	semidirect
875. C₁₃	#3536	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#562	2
#11719397	2
#11719395	2
#11719383	2
#11719382	2
#11719381	2
#11719374	2
#11719372	2
#11719367	2
#11719365	2
#11719362	2
#11719361	2
#11719360	2
#11719359	2
#11719352	2
#11719341	2
#11719339	2
#11719338	2
#11719336	2
#11719334	2
D₁₃×C₂²⋊Q₈	2
#11719326	2
#11719317	2
#11719315	2
#11719313	2
D₁₃×#121	2
#11719302	2
#3536	13