Subgroups — #13128877

Order 1664.

1124 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719412	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719411	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719410	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719407	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	#11719395	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719393	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719367	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719364	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719363	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719361	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719360	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719360	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719359	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719355	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719345	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719342	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719341	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719338	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
23	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719315	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719303	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719269	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#88150	C₂	1	1	yes	maximal, characteristic, complemented
31	#11719209	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#6129	C₂²	1	1	yes	characteristic
34	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
36	C₂×#6127	C₂²	1	1	yes	characteristic
37	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
40	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#123	C₂²	1	1	yes	characteristic
46	C₁₃×#123	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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#121	C₂²	1	1	yes	characteristic
53	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	#88201	C₂²	1	1	yes	characteristic, complemented
57	#88200	C₂²	1	1	yes	characteristic
58	#88198	C₂²	1	1	yes	characteristic, complemented
59	#88193	C₂²	1	1	yes	characteristic
60	#88193	C₂²	1	1	yes	characteristic
61	#88193	C₂²	1	1	yes	characteristic, complemented
62	#88191	C₂²	1	1	yes	characteristic
63	#88191	C₂²	1	1	yes	characteristic
64	#88190	C₂²	1	1	yes	characteristic, complemented
65	#88189	C₂²	1	1	yes	characteristic
66	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
67	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
68	#88183	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
74	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
75	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
76	C₂×#6103	C₂²	1	1	yes	characteristic
77	C₂×#6103	C₂²	1	1	yes	characteristic
78	#88180	C₂²	1	1	yes	characteristic, complemented
79	#88178	C₂²	1	1	yes	characteristic, complemented
80	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
81	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
82	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
83	#88152	C₂²	1	1	yes	characteristic, complemented
84	#88152	C₂²	1	1	yes	characteristic, complemented
85	#88152	C₂²	1	1	yes	characteristic, complemented
86	#88152	C₂²	1	1	yes	characteristic, complemented
87	#88151	C₂²	1	1	yes	characteristic
88	#88151	C₂²	1	1	yes	characteristic, complemented
89	#88151	C₂²	1	1	yes	characteristic, complemented
90	#88150	C₂²	1	1	yes	characteristic
91	#88150	C₂²	1	1	yes	characteristic
92	#88150	C₂²	1	1	yes	characteristic
93	#88150	C₂²	1	1	yes	characteristic
94	#88150	C₂²	1	1	yes	characteristic
95	#88150	C₂²	1	1	yes	characteristic
96	#88150	C₂²	1	1	yes	characteristic
97	#88150	C₂²	1	1	yes	characteristic, complemented
98	#88150	C₂²	1	1	yes	characteristic, complemented
99	#88150	C₂²	1	1	yes	characteristic, complemented
100	#88150	C₂²	1	1	yes	characteristic, complemented
101	#88150	C₂²	1	1	yes	characteristic, complemented
102	#88150	C₂²	1	1	yes	characteristic, complemented
103	#88150	C₂²	1	1	yes	characteristic, complemented
104	#88150	C₂²	1	1	yes	characteristic, complemented
105	#88149	C₂²	1	1	yes	characteristic
106	#88148	C₂²	1	1	yes	characteristic
107	#88148	C₂²	1	1	yes	characteristic
108	#88148	C₂²	1	1	yes	characteristic
109	#88148	C₂²	1	1	yes	characteristic, complemented
110	#88148	C₂²	1	1	yes	characteristic, complemented
111	#88148	C₂²	1	1	yes	characteristic, complemented
112	#88147	C₂²	1	1	yes	characteristic
113	#88147	C₂²	1	1	yes	characteristic
114	#88147	C₂²	1	1	yes	characteristic
115	#88147	C₂²	1	1	yes	characteristic, complemented
116	#88147	C₂²	1	1	yes	characteristic, complemented
117	#88146	C₂²	1	1	yes	characteristic
118	#88146	C₂²	1	1	yes	characteristic
119	#88146	C₂²	1	1	yes	characteristic, complemented
120	#88146	C₂²	1	1	yes	characteristic, complemented
121	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
122	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
124	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
126	#88144	C₂²	1	1	yes	characteristic, complemented
127	#88143	C₂²	1	1	yes	characteristic, complemented
128	#88143	C₂²	1	1	yes	characteristic, complemented
129	#88143	C₂²	1	1	yes	characteristic, complemented
130	#88142	C₂²	1	1	yes	characteristic, complemented
131	#88142	C₂²	1	1	yes	characteristic, complemented
132	#88142	C₂²	1	1	yes	characteristic, complemented
133	#88141	C₂²	1	1	yes	characteristic, complemented
134	#88141	C₂²	1	1	yes	characteristic, complemented
135	#88141	C₂²	1	1	yes	characteristic, complemented
136	#88141	C₂²	1	1	yes	characteristic, complemented
137	#88141	C₂²	1	1	yes	characteristic, complemented
138	#88141	C₂²	1	1	yes	characteristic, complemented
139	#88140	C₂²	1	1	yes	characteristic, complemented
140	#88140	C₂²	1	1	yes	characteristic, complemented
141	#88139	C₂²	1	1	yes	characteristic
142	#88139	C₂²	1	1	yes	characteristic
143	#88139	C₂²	1	1	yes	characteristic, complemented
144	#88139	C₂²	1	1	yes	characteristic, complemented
145	#88139	C₂²	1	1	yes	characteristic, complemented
146	#88138	C₂²	1	1	yes	characteristic
147	#88138	C₂²	1	1	yes	characteristic
148	#88138	C₂²	1	1	yes	characteristic
149	#88138	C₂²	1	1	yes	characteristic, complemented
150	#88137	C₂²	1	1	yes	characteristic
151	#88137	C₂²	1	1	yes	characteristic, complemented
152	#88137	C₂²	1	1	yes	characteristic, complemented
153	#88137	C₂²	1	1	yes	characteristic, complemented
154	#88136	C₂²	1	1	yes	characteristic
155	#88136	C₂²	1	1	yes	characteristic
156	#88135	C₂²	1	1	yes	characteristic
157	#88135	C₂²	1	1	yes	characteristic
158	#88135	C₂²	1	1	yes	characteristic
159	#88135	C₂²	1	1	yes	characteristic
160	#88135	C₂²	1	1	yes	characteristic
161	#88135	C₂²	1	1	yes	characteristic, complemented
162	#88135	C₂²	1	1	yes	characteristic, complemented
163	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
164	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
165	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
166	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
167	#88133	C₂²	1	1	yes	characteristic, complemented
168	#88133	C₂²	1	1	yes	characteristic, complemented
169	#88133	C₂²	1	1	yes	characteristic, complemented
170	#88132	C₂²	1	1	yes	characteristic, complemented
171	#88132	C₂²	1	1	yes	characteristic, complemented
172	#88132	C₂²	1	1	yes	characteristic, complemented
173	#88132	C₂²	1	1	yes	characteristic, complemented
174	#88132	C₂²	1	1	yes	characteristic, complemented
175	#88132	C₂²	1	1	yes	characteristic, complemented
176	#88131	C₂²	1	1	yes	characteristic, complemented
177	#88131	C₂²	1	1	yes	characteristic, complemented
178	#88131	C₂²	1	1	yes	characteristic, complemented
179	#88130	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₅₂	C₂²	1	1	yes	characteristic
181	C₄×D₅₂	C₂²	1	1	yes	characteristic
182	#88126	C₂²	1	1	yes	characteristic, complemented
183	#88126	C₂²	1	1	yes	characteristic, complemented
184	C₄²×D₁₃	C₂²	1	1	yes	characteristic
185	#88124	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	C₂×Q₈×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	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	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
210	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
211	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
212	Q₈×D₁₃	—	4	2	no	—
213	#6129	—	2	4	no	—
214	#6129	—	4	2	no	—
215	D₄×D₁₃	—	2	4	no	—
216	#6127	—	2	4	no	—
217	#6127	—	4	2	no	—
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	—	4	2	no	—
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×C₄×D₁₃	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
240	C₂×Dic₂₆	—	4	2	no	—
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	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
245	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
246	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
247	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
248	C₂×Dic₂₆	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₁₃×C₄⋊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	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₄²×C₁₃	C₂³	1	1	yes	characteristic
274	C₄²×C₁₃	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₁₃	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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₁₃	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	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
349	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
350	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
351	#3520	—	13	1	no	maximal, Sylow
352	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂²×D₁₃	—	2	2	no	—
356	C₂²×D₁₃	—	2	2	no	—
357	C₂²×D₁₃	—	2	2	no	—
358	C₂²×D₁₃	—	2	2	no	—
359	C₂²×D₁₃	—	4	1	no	—
360	C₂²×D₁₃	—	4	1	no	—
361	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
362	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
363	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
364	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
365	Q₈×C₁₃	—	4	1	no	—
366	D₄×C₁₃	—	2	2	no	—
367	D₄×C₁₃	—	2	2	no	—
368	D₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
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	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂²⋊D₁₃	—	2	2	no	—
387	C₂²⋊D₁₃	—	2	2	no	—
388	C₂²⋊D₁₃	—	2	2	no	—
389	C₂²⋊D₁₃	—	2	2	no	—
390	C₂²⋊D₁₃	—	2	2	no	—
391	C₂²⋊D₁₃	—	4	1	no	—
392	C₂²⋊D₁₃	—	4	1	no	—
393	C₂²⋊D₁₃	#41	1	4	yes	complemented
394	C₂×Dic₁₃	—	2	2	no	—
395	C₂×Dic₁₃	—	2	2	no	—
396	C₂×Dic₁₃	—	2	2	no	—
397	C₂×Dic₁₃	—	2	2	no	—
398	C₂×Dic₁₃	—	4	1	no	—
399	C₂×Dic₁₃	—	4	1	no	—
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	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
412	D₅₂	—	2	2	no	—
413	D₅₂	—	2	2	no	—
414	D₅₂	—	2	2	no	—
415	D₅₂	—	4	1	no	—
416	C₄×D₁₃	—	2	2	no	—
417	C₄×D₁₃	—	2	2	no	—
418	C₄×D₁₃	—	2	2	no	—
419	C₄×D₁₃	—	2	2	no	—
420	C₄×D₁₃	—	2	2	no	—
421	C₄×D₁₃	—	2	2	no	—
422	C₄×D₁₃	—	2	2	no	—
423	C₄×D₁₃	—	2	2	no	—
424	C₄×D₁₃	—	4	1	no	—
425	C₄×D₁₃	—	4	1	no	—
426	C₄×D₁₃	—	4	1	no	—
427	C₄×D₁₃	—	4	1	no	—
428	C₄×D₁₃	—	4	1	no	—
429	C₄×D₁₃	—	4	1	no	—
430	C₄×D₁₃	—	4	1	no	—
431	C₄×D₁₃	—	4	1	no	—
432	Dic₂₆	—	2	2	no	—
433	Dic₂₆	—	2	2	no	—
434	Dic₂₆	—	2	2	no	—
435	Dic₂₆	—	2	2	no	—
436	Dic₂₆	—	2	2	no	—
437	Dic₂₆	—	4	1	no	—
438	Dic₂₆	—	4	1	no	—
439	Dic₂₆	—	4	1	no	—
440	#556	—	13	1	no	—
441	#554	—	13	1	no	—
442	#554	—	13	1	no	—
443	#552	—	13	1	no	—
444	#552	—	13	1	no	—
445	#551	—	13	1	no	—
446	#551	—	13	1	no	—
447	#551	—	13	1	no	—
448	#551	—	13	1	no	—
449	D₄×Q₈	—	13	1	no	—
450	#548	—	13	1	no	—
451	#548	—	13	1	no	—
452	#547	—	13	1	no	—
453	#547	—	13	1	no	—
454	#546	—	13	1	no	—
455	#546	—	13	1	no	—
456	#542	—	13	1	no	—
457	#542	—	13	1	no	—
458	#539	—	13	1	no	—
459	#539	—	13	1	no	—
460	#539	—	13	1	no	—
461	#539	D₁₃	1	1	yes	characteristic, complemented
462	#533	—	13	1	no	—
463	#529	—	13	1	no	—
464	#525	—	13	1	no	—
465	#525	—	13	1	no	—
466	C₂×C₂²⋊Q₈	—	13	1	no	—
467	C₂×C₂²⋊Q₈	—	13	1	no	—
468	#520	—	13	1	no	—
469	#520	—	13	1	no	—
470	C₂×C₄×D₄	—	13	1	no	—
471	C₂²×C₁₃	—	2	1	no	—
472	C₂²×C₁₃	—	2	1	no	—
473	C₂²×C₁₃	—	2	1	no	—
474	C₂²×C₁₃	—	2	1	no	—
475	C₂²×C₁₃	—	2	1	no	—
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	2	1	no	—
478	C₂²×C₁₃	—	2	1	no	—
479	C₂²×C₁₃	C₂×#41	1	2	yes	—
480	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
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	—	2	1	no	—
487	C₂×D₁₃	—	2	1	no	—
488	C₂×D₁₃	—	2	1	no	—
489	C₂×D₁₃	—	2	1	no	—
490	C₂×D₁₃	—	2	1	no	—
491	C₂×D₁₃	—	4	4	no	—
492	C₂×D₁₃	—	4	4	no	—
493	C₂×D₁₃	C₂×#41	1	2	yes	—
494	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
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	C₄×C₁₃	—	2	1	no	—
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	2	1	no	—
503	C₄×C₁₃	—	2	1	no	—
504	C₄×C₁₃	—	2	1	no	—
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	1	no	—
507	Dic₁₃	—	2	1	no	—
508	Dic₁₃	—	2	1	no	—
509	Dic₁₃	—	2	1	no	—
510	Dic₁₃	—	2	1	no	—
511	Dic₁₃	—	2	1	no	—
512	Dic₁₃	—	2	1	no	—
513	Dic₁₃	—	2	1	no	—
514	Dic₁₃	—	2	1	no	—
515	Dic₁₃	—	2	1	no	—
516	Dic₁₃	—	2	1	no	—
517	Dic₁₃	C₂×#41	1	2	yes	—
518	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
519	C₂×#41	—	13	1	no	—
520	C₂×#41	—	13	1	no	—
521	C₂×#41	—	13	1	no	—
522	C₂×#41	—	13	1	no	—
523	C₂²×Q₈	—	13	1	no	—
524	C₂²×Q₈	—	13	1	no	—
525	C₂²×D₄	—	13	1	no	—
526	C₂³×C₄	—	13	1	no	—
527	C₂³×C₄	—	13	1	no	—
528	C₄⋊Q₈	—	13	1	no	—
529	C₄⋊Q₈	—	13	1	no	—
530	C₄⋊Q₈	—	13	1	no	—
531	C₄⋊Q₈	—	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	#126	—	13	1	no	—
538	#126	—	13	1	no	—
539	#126	—	13	1	no	—
540	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
541	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
542	#125	—	13	1	no	—
543	#125	—	13	1	no	—
544	#125	—	13	1	no	—
545	#125	—	13	1	no	—
546	#125	—	13	1	no	—
547	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
548	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
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	#123	—	13	1	no	—
557	#123	—	13	1	no	—
558	#123	—	13	1	no	—
559	#123	—	13	1	no	—
560	#123	—	13	1	no	—
561	#123	—	13	1	no	—
562	#123	—	13	1	no	—
563	#123	—	13	1	no	—
564	#123	—	13	1	no	—
565	#123	—	13	1	no	—
566	#123	—	13	1	no	—
567	#123	—	13	1	no	—
568	#123	—	13	1	no	—
569	#123	—	13	1	no	—
570	#123	C₂×D₁₃	1	1	yes	characteristic
571	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
572	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
573	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
574	C₂²⋊Q₈	—	13	1	no	—
575	C₂²⋊Q₈	—	13	1	no	—
576	C₂²⋊Q₈	—	13	1	no	—
577	C₂²⋊Q₈	—	13	1	no	—
578	C₂²⋊Q₈	—	13	1	no	—
579	C₂²⋊Q₈	—	13	1	no	—
580	C₂²⋊Q₈	—	13	1	no	—
581	C₂²⋊Q₈	—	13	1	no	—
582	C₂²⋊Q₈	—	13	1	no	—
583	C₂²⋊Q₈	—	13	1	no	—
584	C₂²⋊Q₈	—	13	1	no	—
585	C₂²⋊Q₈	—	13	1	no	—
586	C₂²⋊Q₈	—	13	1	no	—
587	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, complemented
601	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
602	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
603	#121	—	13	1	no	—
604	#121	—	13	1	no	—
605	#121	—	13	1	no	—
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	C₂×D₁₃	1	1	yes	characteristic
612	#120	—	13	1	no	—
613	#120	—	13	1	no	—
614	#120	—	13	1	no	—
615	#120	—	13	1	no	—
616	C₄×Q₈	—	13	1	no	—
617	C₄×Q₈	—	13	1	no	—
618	C₄×Q₈	—	13	1	no	—
619	C₄×Q₈	—	13	1	no	—
620	C₄×Q₈	—	13	1	no	—
621	C₄×Q₈	—	13	1	no	—
622	C₄×Q₈	—	13	1	no	—
623	C₄×D₄	—	13	1	no	—
624	C₄×D₄	—	13	1	no	—
625	C₄×D₄	—	13	1	no	—
626	C₄×D₄	—	13	1	no	—
627	C₄×D₄	—	13	1	no	—
628	C₄×D₄	—	13	1	no	—
629	C₄×D₄	—	13	1	no	—
630	C₄×D₄	—	13	1	no	—
631	C₄×D₄	—	13	1	no	—
632	C₄×D₄	—	13	1	no	—
633	C₄×D₄	—	13	1	no	—
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	C₂×D₁₃	1	1	yes	characteristic
647	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
648	#117	—	13	1	no	—
649	#117	—	13	1	no	—
650	#117	—	13	1	no	—
651	#117	—	13	1	no	—
652	#117	—	13	1	no	—
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	—	13	1	no	—
663	C₂×C₄⋊C₄	—	13	1	no	—
664	C₂×C₄⋊C₄	—	13	1	no	—
665	C₂×C₄⋊C₄	—	13	1	no	—
666	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
667	C₂×C₂²⋊C₄	—	13	1	no	—
668	C₂×C₂²⋊C₄	—	13	1	no	—
669	C₂×C₂²⋊C₄	—	13	1	no	—
670	C₂×C₂²⋊C₄	—	13	1	no	—
671	C₂×C₂²⋊C₄	—	13	1	no	—
672	C₂×C₂²⋊C₄	—	13	1	no	—
673	C₂×C₄²	—	13	1	no	—
674	C₂×C₁₃	—	2	2	no	—
675	C₂×C₁₃	—	4	1	no	—
676	C₂×C₁₃	—	4	1	no	—
677	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
678	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
680	D₁₃	—	2	2	no	—
681	D₁₃	—	2	2	no	—
682	D₁₃	—	4	1	no	—
683	D₁₃	—	4	1	no	—
684	C₂⁴	—	13	1	no	—
685	C₂⁴	—	13	1	no	—
686	#41	—	26	4	no	—
687	#41	—	26	4	no	—
688	#41	—	52	2	no	—
689	#41	—	52	2	no	—
690	C₂×Q₈	—	13	1	no	—
691	C₂×Q₈	—	13	1	no	—
692	C₂×Q₈	—	13	1	no	—
693	C₂×Q₈	—	13	1	no	—
694	C₂×Q₈	—	13	1	no	—
695	C₂×Q₈	—	13	1	no	—
696	C₂×Q₈	—	13	1	no	—
697	C₂×Q₈	—	13	1	no	—
698	C₂×Q₈	—	52	2	no	—
699	C₂×Q₈	—	52	2	no	—
700	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
710	C₂×D₄	—	13	1	no	—
711	C₂×D₄	—	13	1	no	—
712	C₂×D₄	—	13	1	no	—
713	C₂×D₄	—	26	4	no	—
714	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
715	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
716	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
727	C₂²×C₄	—	13	1	no	—
728	C₂²×C₄	—	13	1	no	—
729	C₂²×C₄	—	13	1	no	—
730	C₂²×C₄	—	13	1	no	—
731	C₂²×C₄	—	13	1	no	—
732	C₂²×C₄	—	13	1	no	—
733	C₂²×C₄	—	13	1	no	—
734	C₂²×C₄	—	13	1	no	—
735	C₂²×C₄	—	13	1	no	—
736	C₂²×C₄	—	13	1	no	—
737	C₂²×C₄	—	13	1	no	—
738	C₂²×C₄	—	13	1	no	—
739	C₂²×C₄	—	52	2	no	—
740	C₂²×C₄	—	52	2	no	—
741	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
742	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
744	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
766	C₄⋊C₄	—	13	1	no	—
767	C₄⋊C₄	—	13	1	no	—
768	C₄⋊C₄	—	13	1	no	—
769	C₄⋊C₄	—	13	1	no	—
770	C₄⋊C₄	—	13	1	no	—
771	C₄⋊C₄	—	13	1	no	—
772	C₄⋊C₄	—	13	1	no	—
773	C₄⋊C₄	—	13	1	no	—
774	C₄⋊C₄	—	13	1	no	—
775	C₄⋊C₄	—	13	1	no	—
776	C₄⋊C₄	—	13	1	no	—
777	C₄⋊C₄	—	13	1	no	—
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	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
783	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
784	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
786	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
820	C₂²⋊C₄	—	13	1	no	—
821	C₂²⋊C₄	—	13	1	no	—
822	C₂²⋊C₄	—	13	1	no	—
823	C₂²⋊C₄	—	13	1	no	—
824	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
829	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
830	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
831	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
832	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
834	C₄²	—	13	1	no	—
835	C₄²	—	13	1	no	—
836	C₄²	—	13	1	no	—
837	C₄²	—	13	1	no	—
838	C₄²	—	13	1	no	—
839	C₄²	—	13	1	no	—
840	C₄²	—	13	1	no	—
841	C₄²	—	13	1	no	—
842	C₄²	—	13	1	no	—
843	C₄²	—	13	1	no	—
844	C₄²	—	13	1	no	—
845	C₄²	—	13	1	no	—
846	C₄²	C₂²×D₁₃	1	1	yes	characteristic
847	C₄²	C₂²×D₁₃	1	1	yes	characteristic
848	C₁₃	#3520	1	1	yes	characteristic, complemented, Sylow
849	C₂³	—	13	1	no	—
850	C₂³	—	13	1	no	—
851	C₂³	—	13	1	no	—
852	C₂³	—	13	1	no	—
853	C₂³	—	26	2	no	—
854	C₂³	—	26	2	no	—
855	C₂³	—	26	2	no	—
856	C₂³	—	26	2	no	—
857	C₂³	—	52	1	no	—
858	C₂³	—	52	1	no	—
859	C₂³	C₂³×D₁₃	1	1	yes	characteristic
860	C₂³	C₂³×D₁₃	1	1	yes	characteristic
861	C₂³	C₂³×D₁₃	1	1	yes	characteristic
862	Q₈	—	4	1	no	—
863	Q₈	—	26	2	no	—
864	Q₈	—	26	2	no	—
865	Q₈	—	26	2	no	—
866	Q₈	—	26	2	no	—
867	Q₈	—	26	2	no	—
868	Q₈	—	52	1	no	—
869	Q₈	—	52	1	no	—
870	Q₈	—	52	1	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	4	1	no	—
874	D₄	—	13	4	no	—
875	D₄	—	26	2	no	—
876	D₄	—	26	2	no	—
877	D₄	—	26	2	no	—
878	D₄	—	26	2	no	—
879	D₄	—	26	2	no	—
880	D₄	—	26	2	no	—
881	D₄	—	26	2	no	—
882	D₄	—	26	2	no	—
883	D₄	—	52	1	no	—
884	D₄	—	52	1	no	—
885	D₄	—	52	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	13	1	no	—
892	C₂×C₄	—	13	1	no	—
893	C₂×C₄	—	13	1	no	—
894	C₂×C₄	—	13	1	no	—
895	C₂×C₄	—	13	1	no	—
896	C₂×C₄	—	13	1	no	—
897	C₂×C₄	—	13	1	no	—
898	C₂×C₄	—	13	1	no	—
899	C₂×C₄	—	13	1	no	—
900	C₂×C₄	—	13	1	no	—
901	C₂×C₄	—	13	1	no	—
902	C₂×C₄	—	13	1	no	—
903	C₂×C₄	—	26	2	no	—
904	C₂×C₄	—	26	2	no	—
905	C₂×C₄	—	26	2	no	—
906	C₂×C₄	—	26	2	no	—
907	C₂×C₄	—	26	2	no	—
908	C₂×C₄	—	26	2	no	—
909	C₂×C₄	—	26	2	no	—
910	C₂×C₄	—	26	2	no	—
911	C₂×C₄	—	26	2	no	—
912	C₂×C₄	—	26	2	no	—
913	C₂×C₄	—	26	2	no	—
914	C₂×C₄	—	26	2	no	—
915	C₂×C₄	—	52	1	no	—
916	C₂×C₄	—	52	1	no	—
917	C₂×C₄	—	52	1	no	—
918	C₂×C₄	—	52	1	no	—
919	C₂×C₄	—	52	1	no	—
920	C₂×C₄	—	52	1	no	—
921	C₂×C₄	—	52	1	no	—
922	C₂×C₄	—	52	1	no	—
923	C₂×C₄	—	52	1	no	—
924	C₂×C₄	—	52	1	no	—
925	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
926	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
927	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
928	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
929	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
930	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
931	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
932	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
933	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
934	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
935	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
936	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	13	2	no	—
946	C₂²	—	13	2	no	—
947	C₂²	—	26	1	no	—
948	C₂²	—	26	1	no	—
949	C₂²	—	26	1	no	—
950	C₂²	—	26	1	no	—
951	C₂²	—	26	1	no	—
952	C₂²	—	26	1	no	—
953	C₂²	—	26	1	no	—
954	C₂²	—	26	1	no	—
955	C₂²	—	26	1	no	—
956	C₂²	—	26	1	no	—
957	C₂²	—	52	4	no	—
958	C₂²	—	52	4	no	—
959	C₂²	#41×D₁₃	1	2	yes	—
960	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	2	1	no	—
973	C₄	—	13	2	no	—
974	C₄	—	13	2	no	—
975	C₄	—	26	1	no	—
976	C₄	—	26	1	no	—
977	C₄	—	26	1	no	—
978	C₄	—	26	1	no	—
979	C₄	—	26	1	no	—
980	C₄	—	26	1	no	—
981	C₄	—	26	1	no	—
982	C₄	—	26	1	no	—
983	C₄	—	26	1	no	—
984	C₄	—	26	1	no	—
985	C₂	—	2	2	no	—
986	C₂	—	4	1	no	—
987	C₂	—	4	1	no	—
988	C₂	—	26	2	no	—
989	C₂	—	26	2	no	—
990	C₂	—	52	1	no	—
991	C₂	—	52	1	no	—
992	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
993	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
994	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×#539	C₂
hypercenter	#539	D₁₃
hypocenter	C₁₃	#3520
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. C₁₃×#539	C₂	semidirect
2. #11719412	C₂	semidirect
3. #11719411	C₂	semidirect
4. #11719410	C₂	semidirect
5. #11719407	C₂	semidirect
6. #11719398	C₂	semidirect
7. #11719397	C₂	semidirect
8. #11719395	C₂	semidirect
9. #11719393	C₂	semidirect
10. #11719367	C₂	semidirect
11. #11719364	C₂	semidirect
12. #11719363	C₂	semidirect
13. #11719361	C₂	semidirect
14. #11719360	C₂	semidirect
15. #11719360	C₂	semidirect
16. #11719359	C₂	semidirect
17. #11719355	C₂	semidirect
18. #11719345	C₂	semidirect
19. #11719342	C₂	semidirect
20. #11719341	C₂	semidirect
21. #11719338	C₂	semidirect
22. #11719337	C₂	semidirect
23. D₁₃×C₂²⋊Q₈	C₂	semidirect
24. #11719315	C₂	semidirect
25. #11719303	C₂	semidirect
26. #11719269	C₂	semidirect
27. #11719252	C₂	semidirect
28. #11719251	C₂	semidirect
29. C₄×D₄×D₁₃	C₂	semidirect
30. C₂×#88150	C₂	semidirect
31. #11719209	C₂	semidirect
32. C₂×Q₈×D₁₃	C₂²	semidirect
34. C₂×#6129	C₂²	semidirect
37. C₂×#6127	C₂²	semidirect
40. C₂²×Dic₂₆	C₂²	semidirect
41. C₁₃×#126	C₂²	semidirect
42. C₁₃×#126	C₂²	semidirect
43. C₁₃×#125	C₂²	semidirect
44. C₁₃×#125	C₂²	semidirect
46. C₁₃×#123	C₂²	semidirect
47. C₁₃×#123	C₂²	semidirect
48. C₁₃×#123	C₂²	semidirect
49. C₁₃×C₂²⋊Q₈	C₂²	semidirect
50. C₁₃×C₂²⋊Q₈	C₂²	semidirect
51. C₁₃×C₂²⋊Q₈	C₂²	semidirect
54. C₄×D₄×C₁₃	C₂²	semidirect
55. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
56. #88201	C₂²	semidirect
58. #88198	C₂²	semidirect
61. #88193	C₂²	semidirect
64. #88190	C₂²	semidirect
67. D₄×Dic₁₃	C₂²	semidirect
68. #88183	C₂²	semidirect
73. C₄×C₂²⋊D₁₃	C₂²	semidirect
74. C₄×C₂²⋊D₁₃	C₂²	semidirect
75. C₄×C₂²⋊D₁₃	C₂²	semidirect
78. #88180	C₂²	semidirect
79. #88178	C₂²	semidirect
80. C₂×#6101	C₂²	semidirect
81. C₂×#6101	C₂²	semidirect
82. C₂×#6101	C₂²	semidirect
83. #88152	C₂²	semidirect
84. #88152	C₂²	semidirect
85. #88152	C₂²	semidirect
86. #88152	C₂²	semidirect
88. #88151	C₂²	semidirect
89. #88151	C₂²	semidirect
97. #88150	C₂²	semidirect
98. #88150	C₂²	semidirect
99. #88150	C₂²	semidirect
100. #88150	C₂²	semidirect
101. #88150	C₂²	semidirect
102. #88150	C₂²	semidirect
103. #88150	C₂²	semidirect
104. #88150	C₂²	semidirect
109. #88148	C₂²	semidirect
110. #88148	C₂²	semidirect
111. #88148	C₂²	semidirect
115. #88147	C₂²	semidirect
116. #88147	C₂²	semidirect
119. #88146	C₂²	semidirect
120. #88146	C₂²	semidirect
122. C₄⋊C₄×D₁₃	C₂²	semidirect
123. C₄⋊C₄×D₁₃	C₂²	semidirect
124. C₄⋊C₄×D₁₃	C₂²	semidirect
125. C₄⋊C₄×D₁₃	C₂²	semidirect
126. #88144	C₂²	semidirect
127. #88143	C₂²	semidirect
128. #88143	C₂²	semidirect
129. #88143	C₂²	semidirect
130. #88142	C₂²	semidirect
131. #88142	C₂²	semidirect
132. #88142	C₂²	semidirect
133. #88141	C₂²	semidirect
134. #88141	C₂²	semidirect
135. #88141	C₂²	semidirect
136. #88141	C₂²	semidirect
137. #88141	C₂²	semidirect
138. #88141	C₂²	semidirect
139. #88140	C₂²	semidirect
140. #88140	C₂²	semidirect
143. #88139	C₂²	semidirect
144. #88139	C₂²	semidirect
145. #88139	C₂²	semidirect
149. #88138	C₂²	semidirect
151. #88137	C₂²	semidirect
152. #88137	C₂²	semidirect
153. #88137	C₂²	semidirect
161. #88135	C₂²	semidirect
162. #88135	C₂²	semidirect
167. #88133	C₂²	semidirect
168. #88133	C₂²	semidirect
169. #88133	C₂²	semidirect
170. #88132	C₂²	semidirect
171. #88132	C₂²	semidirect
172. #88132	C₂²	semidirect
173. #88132	C₂²	semidirect
174. #88132	C₂²	semidirect
175. #88132	C₂²	semidirect
176. #88131	C₂²	semidirect
177. #88131	C₂²	semidirect
178. #88131	C₂²	semidirect
179. #88130	C₂²	semidirect
182. #88126	C₂²	semidirect
183. #88126	C₂²	semidirect
185. #88124	C₂²	semidirect
186. C₄×Dic₂₆	C₂²	semidirect
393. C₂²⋊D₁₃	#41	semidirect
461. #539	D₁₃	semidirect
540. #126	C₂×D₁₃	semidirect
541. #126	C₂×D₁₃	semidirect
547. #125	C₂×D₁₃	semidirect
548. #125	C₂×D₁₃	semidirect
571. #123	C₂×D₁₃	semidirect
572. #123	C₂×D₁₃	semidirect
573. #123	C₂×D₁₃	semidirect
600. C₂²⋊Q₈	C₂×D₁₃	semidirect
601. C₂²⋊Q₈	C₂×D₁₃	semidirect
602. C₂²⋊Q₈	C₂×D₁₃	semidirect
647. C₄×D₄	C₂×D₁₃	semidirect
666. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
848. C₁₃	#3520	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#539	2
#11719412	2
#11719411	2
#11719410	2
#11719407	2
#11719398	2
#11719397	2
#11719395	2
#11719393	2
#11719367	2
#11719364	2
#11719363	2
#11719361	2
#11719360	2
#11719359	2
#11719355	2
#11719345	2
#11719342	2
#11719341	2
#11719338	2
#11719337	2
D₁₃×C₂²⋊Q₈	2
#11719315	2
#11719303	2
#11719269	2
#11719252	2
#11719251	2
C₄×D₄×D₁₃	2
C₂×#88150	2
#11719209	2
#3520	13