Subgroups — #13128896

Order 1664.

1042 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719415	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719414	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719414	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719413	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719413	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719412	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719411	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719411	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719411	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719410	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719410	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719409	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719407	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719407	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719406	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719220	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719219	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719209	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719200	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719200	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719199	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719195	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719195	C₂	1	1	yes	maximal, characteristic, complemented
29	#11719191	C₂	1	1	yes	maximal, characteristic, complemented
30	#11719184	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
33	C₂×#6127	C₂²	1	1	yes	characteristic
34	C₂×#6127	C₂²	1	1	yes	characteristic
35	C₁₃×#126	C₂²	1	1	yes	characteristic
36	C₁₃×#126	C₂²	1	1	yes	characteristic
37	C₁₃×#126	C₂²	1	1	yes	characteristic
38	C₁₃×#126	C₂²	1	1	yes	characteristic
39	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#126	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	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
50	#88207	C₂²	1	1	yes	characteristic
51	#88207	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
53	#88184	C₂²	1	1	yes	characteristic
54	#88184	C₂²	1	1	yes	characteristic
55	#88184	C₂²	1	1	yes	characteristic, complemented
56	#88183	C₂²	1	1	yes	characteristic
57	#88183	C₂²	1	1	yes	characteristic
58	#88183	C₂²	1	1	yes	characteristic, complemented
59	#88183	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
70	#88180	C₂²	1	1	yes	characteristic, complemented
71	#88180	C₂²	1	1	yes	characteristic, complemented
72	#88178	C₂²	1	1	yes	characteristic, complemented
73	#88178	C₂²	1	1	yes	characteristic, complemented
74	#88178	C₂²	1	1	yes	characteristic, complemented
75	#88152	C₂²	1	1	yes	characteristic, complemented
76	#88152	C₂²	1	1	yes	characteristic, complemented
77	#88152	C₂²	1	1	yes	characteristic, complemented
78	#88152	C₂²	1	1	yes	characteristic, complemented
79	#88152	C₂²	1	1	yes	characteristic, complemented
80	#88152	C₂²	1	1	yes	characteristic, complemented
81	#88151	C₂²	1	1	yes	characteristic, complemented
82	#88151	C₂²	1	1	yes	characteristic, complemented
83	#88150	C₂²	1	1	yes	characteristic, complemented
84	#88150	C₂²	1	1	yes	characteristic, complemented
85	#88150	C₂²	1	1	yes	characteristic, complemented
86	#88150	C₂²	1	1	yes	characteristic, complemented
87	#88150	C₂²	1	1	yes	characteristic, complemented
88	#88150	C₂²	1	1	yes	characteristic, complemented
89	#88149	C₂²	1	1	yes	characteristic, complemented
90	#88149	C₂²	1	1	yes	characteristic, complemented
91	#88148	C₂²	1	1	yes	characteristic, complemented
92	#88148	C₂²	1	1	yes	characteristic, complemented
93	#88148	C₂²	1	1	yes	characteristic, complemented
94	#88148	C₂²	1	1	yes	characteristic, complemented
95	#88148	C₂²	1	1	yes	characteristic, complemented
96	#88148	C₂²	1	1	yes	characteristic, complemented
97	#88147	C₂²	1	1	yes	characteristic, complemented
98	#88147	C₂²	1	1	yes	characteristic, complemented
99	#88147	C₂²	1	1	yes	characteristic, complemented
100	#88147	C₂²	1	1	yes	characteristic, complemented
101	#88146	C₂²	1	1	yes	characteristic, complemented
102	#88146	C₂²	1	1	yes	characteristic, complemented
103	#88146	C₂²	1	1	yes	characteristic, complemented
104	#88146	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
108	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
109	#88144	C₂²	1	1	yes	characteristic, complemented
110	#88144	C₂²	1	1	yes	characteristic, complemented
111	#88143	C₂²	1	1	yes	characteristic, complemented
112	#88143	C₂²	1	1	yes	characteristic, complemented
113	#88143	C₂²	1	1	yes	characteristic, complemented
114	#88143	C₂²	1	1	yes	characteristic, complemented
115	#88143	C₂²	1	1	yes	characteristic, complemented
116	#88143	C₂²	1	1	yes	characteristic, complemented
117	#88142	C₂²	1	1	yes	characteristic, complemented
118	#88142	C₂²	1	1	yes	characteristic, complemented
119	#88141	C₂²	1	1	yes	characteristic, complemented
120	#88141	C₂²	1	1	yes	characteristic, complemented
121	#88141	C₂²	1	1	yes	characteristic, complemented
122	#88141	C₂²	1	1	yes	characteristic, complemented
123	#88140	C₂²	1	1	yes	characteristic, complemented
124	#88140	C₂²	1	1	yes	characteristic, complemented
125	#88139	C₂²	1	1	yes	characteristic
126	#88139	C₂²	1	1	yes	characteristic
127	#88139	C₂²	1	1	yes	characteristic
128	#88139	C₂²	1	1	yes	characteristic
129	#88139	C₂²	1	1	yes	characteristic
130	#88139	C₂²	1	1	yes	characteristic, complemented
131	#88138	C₂²	1	1	yes	characteristic
132	#88138	C₂²	1	1	yes	characteristic
133	#88138	C₂²	1	1	yes	characteristic
134	#88138	C₂²	1	1	yes	characteristic
135	#88138	C₂²	1	1	yes	characteristic
136	#88138	C₂²	1	1	yes	characteristic, complemented
137	#88137	C₂²	1	1	yes	characteristic
138	#88137	C₂²	1	1	yes	characteristic
139	#88137	C₂²	1	1	yes	characteristic
140	#88137	C₂²	1	1	yes	characteristic
141	#88137	C₂²	1	1	yes	characteristic
142	#88137	C₂²	1	1	yes	characteristic, complemented
143	#88136	C₂²	1	1	yes	characteristic
144	#88136	C₂²	1	1	yes	characteristic
145	#88135	C₂²	1	1	yes	characteristic
146	#88135	C₂²	1	1	yes	characteristic
147	#88135	C₂²	1	1	yes	characteristic
148	#88135	C₂²	1	1	yes	characteristic
149	#88135	C₂²	1	1	yes	characteristic
150	#88135	C₂²	1	1	yes	characteristic
151	#88135	C₂²	1	1	yes	characteristic, complemented
152	#88135	C₂²	1	1	yes	characteristic, complemented
153	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
154	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
155	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
156	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
157	#88133	C₂²	1	1	yes	characteristic
158	#88133	C₂²	1	1	yes	characteristic
159	#88133	C₂²	1	1	yes	characteristic
160	#88133	C₂²	1	1	yes	characteristic
161	#88133	C₂²	1	1	yes	characteristic
162	#88133	C₂²	1	1	yes	characteristic, complemented
163	#88132	C₂²	1	1	yes	characteristic
164	#88132	C₂²	1	1	yes	characteristic
165	#88132	C₂²	1	1	yes	characteristic, complemented
166	#88132	C₂²	1	1	yes	characteristic, complemented
167	#88131	C₂²	1	1	yes	characteristic
168	#88131	C₂²	1	1	yes	characteristic
169	#88131	C₂²	1	1	yes	characteristic, complemented
170	#88131	C₂²	1	1	yes	characteristic, complemented
171	#88130	C₂²	1	1	yes	characteristic, complemented
172	#88130	C₂²	1	1	yes	characteristic, complemented
173	#88129	C₂²	1	1	yes	characteristic, complemented
174	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
175	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
176	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
177	#88126	C₂²	1	1	yes	characteristic, complemented
178	#88126	C₂²	1	1	yes	characteristic, complemented
179	#88126	C₂²	1	1	yes	characteristic, complemented
180	#88126	C₂²	1	1	yes	characteristic, complemented
181	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
182	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
183	#88124	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
188	C₂³×D₁₃	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₂²×C₄×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	C₂×C₂²⋊D₁₃	—	2	4	no	—
196	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₁₃	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	#6127	—	2	4	no	—
210	#6127	—	2	4	no	—
211	C₂×D₅₂	C₂³	1	1	yes	characteristic
212	C₂×D₅₂	C₂³	1	1	yes	characteristic
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×C₄×D₁₃	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
224	C₂×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×Dic₂₆	C₂³	1	1	yes	characteristic
231	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
232	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
233	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
234	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
235	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₁₃×C₄⋊C₄	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
253	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₄²×C₁₃	C₂³	1	1	yes	characteristic
260	C₄²×C₁₃	C₂³	1	1	yes	characteristic
261	C₄²×C₁₃	C₂³	1	1	yes	characteristic
262	C₄²×C₁₃	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
269	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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
307	#6101	C₂³	1	1	yes	characteristic
308	#6101	C₂³	1	1	yes	characteristic
309	#6101	C₂³	1	1	yes	characteristic
310	#6101	C₂³	1	1	yes	characteristic
311	#6101	C₂³	1	1	yes	characteristic
312	#6101	C₂³	1	1	yes	characteristic
313	#6101	C₂³	1	1	yes	characteristic
314	#6101	C₂³	1	1	yes	characteristic
315	#6101	C₂³	1	1	yes	characteristic
316	#6101	C₂³	1	1	yes	characteristic
317	#6101	C₂³	1	1	yes	characteristic
318	#6101	C₂³	1	1	yes	characteristic
319	#6101	C₂³	1	1	yes	characteristic
320	#6101	C₂³	1	1	yes	characteristic
321	#6101	C₂³	1	1	yes	characteristic
322	#6101	C₂³	1	1	yes	characteristic
323	#6101	C₂³	1	1	yes	characteristic
324	#6101	C₂³	1	1	yes	characteristic
325	#6101	C₂³	1	1	yes	characteristic
326	#6101	C₂³	1	1	yes	characteristic
327	#6101	C₂³	1	1	yes	characteristic
328	#6101	C₂³	1	1	yes	characteristic
329	#6101	C₂³	1	1	yes	characteristic
330	#6101	C₂³	1	1	yes	characteristic
331	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
332	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
333	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
334	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
335	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
336	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
337	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
338	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
339	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
340	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
341	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
342	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
343	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
344	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
345	#3521	—	13	1	no	maximal, Sylow
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	—	4	1	no	—
348	C₂³×C₁₃	—	4	1	no	—
349	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂²×D₁₃	—	2	2	no	—
353	C₂²×D₁₃	—	4	1	no	—
354	C₂²×D₁₃	—	4	1	no	—
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	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂²⋊D₁₃	—	2	2	no	—
378	C₂²⋊D₁₃	—	2	2	no	—
379	C₂²⋊D₁₃	—	2	2	no	—
380	C₂²⋊D₁₃	—	2	2	no	—
381	C₂²⋊D₁₃	—	2	2	no	—
382	C₂²⋊D₁₃	—	4	1	no	—
383	C₂²⋊D₁₃	—	4	1	no	—
384	C₂²⋊D₁₃	—	4	1	no	—
385	C₂²⋊D₁₃	—	4	1	no	—
386	C₂²⋊D₁₃	#41	1	4	yes	—
387	C₂×Dic₁₃	—	2	2	no	—
388	C₂×Dic₁₃	—	4	1	no	—
389	C₂×Dic₁₃	—	4	1	no	—
390	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
402	D₅₂	—	2	2	no	—
403	D₅₂	—	2	2	no	—
404	D₅₂	—	4	1	no	—
405	D₅₂	—	4	1	no	—
406	D₅₂	—	4	1	no	—
407	C₄×D₁₃	—	2	2	no	—
408	C₄×D₁₃	—	2	2	no	—
409	C₄×D₁₃	—	2	2	no	—
410	C₄×D₁₃	—	2	2	no	—
411	C₄×D₁₃	—	4	1	no	—
412	C₄×D₁₃	—	4	1	no	—
413	C₄×D₁₃	—	4	1	no	—
414	C₄×D₁₃	—	4	1	no	—
415	C₄×D₁₃	—	4	1	no	—
416	C₄×D₁₃	—	4	1	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	Dic₂₆	—	2	2	no	—
422	Dic₂₆	—	2	2	no	—
423	Dic₂₆	—	4	1	no	—
424	Dic₂₆	—	4	1	no	—
425	Dic₂₆	—	4	1	no	—
426	#556	—	13	1	no	—
427	#556	—	13	1	no	—
428	#554	—	13	1	no	—
429	#553	—	13	1	no	—
430	#553	—	13	1	no	—
431	#553	—	13	1	no	—
432	#552	—	13	1	no	—
433	#552	—	13	1	no	—
434	#552	—	13	1	no	—
435	#551	—	13	1	no	—
436	#551	—	13	1	no	—
437	#551	—	13	1	no	—
438	#551	—	13	1	no	—
439	#547	—	13	1	no	—
440	#546	—	13	1	no	—
441	#546	—	13	1	no	—
442	#542	—	13	1	no	—
443	#541	—	13	1	no	—
444	#539	—	13	1	no	—
445	#539	—	13	1	no	—
446	#538	—	13	1	no	—
447	#538	—	13	1	no	—
448	#529	—	13	1	no	—
449	#529	—	13	1	no	—
450	#529	—	13	1	no	—
451	#529	—	13	1	no	—
452	C₂×#126	—	13	1	no	—
453	C₂×#126	D₁₃	1	1	yes	characteristic, complemented
454	#520	—	13	1	no	—
455	#518	—	13	1	no	—
456	C₄×#41	—	13	1	no	—
457	C₂²×C₁₃	—	2	1	no	—
458	C₂²×C₁₃	—	2	1	no	—
459	C₂²×C₁₃	—	2	1	no	—
460	C₂²×C₁₃	—	2	1	no	—
461	C₂²×C₁₃	—	2	1	no	—
462	C₂²×C₁₃	—	2	1	no	—
463	C₂²×C₁₃	—	2	1	no	—
464	C₂²×C₁₃	—	2	1	no	—
465	C₂²×C₁₃	—	8	2	no	—
466	C₂²×C₁₃	C₂×#41	1	2	yes	—
467	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
468	C₂×D₁₃	—	2	1	no	—
469	C₂×D₁₃	—	2	1	no	—
470	C₂×D₁₃	—	2	1	no	—
471	C₂×D₁₃	—	2	1	no	—
472	C₂×D₁₃	—	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	—	8	2	no	—
480	C₂×D₁₃	C₂×#41	1	2	yes	—
481	C₄×C₁₃	—	2	1	no	—
482	C₄×C₁₃	—	2	1	no	—
483	C₄×C₁₃	—	2	1	no	—
484	C₄×C₁₃	—	2	1	no	—
485	C₄×C₁₃	—	2	1	no	—
486	C₄×C₁₃	—	2	1	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	Dic₁₃	—	2	1	no	—
494	Dic₁₃	—	2	1	no	—
495	Dic₁₃	—	2	1	no	—
496	Dic₁₃	—	2	1	no	—
497	Dic₁₃	—	2	1	no	—
498	Dic₁₃	—	2	1	no	—
499	Dic₁₃	—	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	C₂×#41	1	2	yes	—
505	C₂×#41	—	13	1	no	—
506	C₂×#41	—	13	1	no	—
507	C₂²×D₄	—	13	1	no	—
508	C₄⋊Q₈	—	13	1	no	—
509	C₄⋊Q₈	—	13	1	no	—
510	#126	—	13	1	no	—
511	#126	—	13	1	no	—
512	#126	—	13	1	no	—
513	#126	—	13	1	no	—
514	#126	—	13	1	no	—
515	#126	—	13	1	no	—
516	#126	—	13	1	no	—
517	#126	—	13	1	no	—
518	#126	—	13	1	no	—
519	#126	—	13	1	no	—
520	#126	—	13	1	no	—
521	#126	—	13	1	no	—
522	#126	—	13	1	no	—
523	#126	—	13	1	no	—
524	#126	C₂×D₁₃	1	1	yes	characteristic
525	#126	C₂×D₁₃	1	1	yes	characteristic
526	#126	C₂×D₁₃	1	1	yes	characteristic
527	#126	C₂×D₁₃	1	1	yes	characteristic
528	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
529	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
530	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
531	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
532	#125	—	13	1	no	—
533	#125	—	13	1	no	—
534	#125	—	13	1	no	—
535	#125	—	13	1	no	—
536	#125	—	13	1	no	—
537	#125	—	13	1	no	—
538	#125	—	13	1	no	—
539	#125	—	13	1	no	—
540	#125	—	13	1	no	—
541	#124	—	13	1	no	—
542	#124	—	13	1	no	—
543	#124	—	13	1	no	—
544	#124	—	13	1	no	—
545	#124	—	13	1	no	—
546	#124	—	13	1	no	—
547	#124	—	13	1	no	—
548	#123	—	13	1	no	—
549	#123	—	13	1	no	—
550	#123	—	13	1	no	—
551	#123	—	13	1	no	—
552	#123	—	13	1	no	—
553	#123	—	13	1	no	—
554	#123	—	13	1	no	—
555	#123	—	13	1	no	—
556	#123	—	13	1	no	—
557	#123	—	13	1	no	—
558	#123	—	13	1	no	—
559	#123	—	13	1	no	—
560	#123	—	13	1	no	—
561	#123	—	13	1	no	—
562	#123	—	13	1	no	—
563	#123	—	13	1	no	—
564	#123	—	13	1	no	—
565	#123	—	13	1	no	—
566	C₂²⋊Q₈	—	13	1	no	—
567	C₂²⋊Q₈	—	13	1	no	—
568	C₂²⋊Q₈	—	13	1	no	—
569	C₂²⋊Q₈	—	13	1	no	—
570	C₂²⋊Q₈	—	13	1	no	—
571	C₂²⋊Q₈	—	13	1	no	—
572	C₂²⋊Q₈	—	13	1	no	—
573	C₂²⋊Q₈	—	13	1	no	—
574	C₂²⋊Q₈	—	13	1	no	—
575	C₂²⋊Q₈	—	13	1	no	—
576	C₂²⋊Q₈	—	13	1	no	—
577	C₂²⋊Q₈	—	13	1	no	—
578	C₂²⋊Q₈	—	13	1	no	—
579	C₂²⋊Q₈	—	13	1	no	—
580	C₂²⋊Q₈	—	13	1	no	—
581	#121	—	13	1	no	—
582	#121	—	13	1	no	—
583	#121	—	13	1	no	—
584	#121	—	13	1	no	—
585	#121	—	13	1	no	—
586	#121	—	13	1	no	—
587	#121	—	13	1	no	—
588	#121	—	13	1	no	—
589	#121	—	13	1	no	—
590	#121	—	13	1	no	—
591	#121	—	13	1	no	—
592	#120	—	13	1	no	—
593	#120	—	13	1	no	—
594	#120	—	13	1	no	—
595	#120	—	13	1	no	—
596	C₄×Q₈	—	13	1	no	—
597	C₄×Q₈	—	13	1	no	—
598	C₄×Q₈	—	13	1	no	—
599	C₄×Q₈	—	13	1	no	—
600	C₄×Q₈	—	13	1	no	—
601	C₄×Q₈	—	13	1	no	—
602	C₄×Q₈	—	13	1	no	—
603	C₄×D₄	—	13	1	no	—
604	C₄×D₄	—	13	1	no	—
605	C₄×D₄	—	13	1	no	—
606	C₄×D₄	—	13	1	no	—
607	C₄×D₄	—	13	1	no	—
608	C₄×D₄	—	13	1	no	—
609	C₄×D₄	—	13	1	no	—
610	C₄×D₄	—	13	1	no	—
611	C₄×D₄	—	13	1	no	—
612	C₄×D₄	—	13	1	no	—
613	C₄×D₄	—	13	1	no	—
614	C₄×D₄	—	13	1	no	—
615	C₄×D₄	—	13	1	no	—
616	C₄×D₄	—	13	1	no	—
617	C₄×D₄	—	13	1	no	—
618	C₄×D₄	—	13	1	no	—
619	C₄×D₄	—	13	1	no	—
620	C₄×D₄	—	13	1	no	—
621	C₄×D₄	—	13	1	no	—
622	C₄×D₄	—	13	1	no	—
623	C₄×D₄	—	13	1	no	—
624	C₄×D₄	—	13	1	no	—
625	C₄×D₄	—	13	1	no	—
626	C₄×D₄	—	13	1	no	—
627	C₄×D₄	—	13	1	no	—
628	#117	—	13	1	no	—
629	#117	—	13	1	no	—
630	#117	—	13	1	no	—
631	#117	—	13	1	no	—
632	#117	—	13	1	no	—
633	#117	—	13	1	no	—
634	#117	—	13	1	no	—
635	#117	—	13	1	no	—
636	#117	—	13	1	no	—
637	#117	—	13	1	no	—
638	#117	—	13	1	no	—
639	#117	—	13	1	no	—
640	#117	—	13	1	no	—
641	#117	—	13	1	no	—
642	C₂×C₄⋊C₄	—	13	1	no	—
643	C₂×C₄⋊C₄	—	13	1	no	—
644	C₂×C₄⋊C₄	—	13	1	no	—
645	C₂×C₄⋊C₄	—	13	1	no	—
646	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
647	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
648	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
649	C₂×C₂²⋊C₄	—	13	1	no	—
650	C₂×C₂²⋊C₄	—	13	1	no	—
651	C₂×C₂²⋊C₄	—	13	1	no	—
652	C₂×C₂²⋊C₄	—	13	1	no	—
653	C₂×C₂²⋊C₄	—	13	1	no	—
654	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
657	C₂×C₄²	—	13	1	no	—
658	C₂×C₄²	—	13	1	no	—
659	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
660	C₂×C₁₃	—	2	2	no	—
661	C₂×C₁₃	—	4	1	no	—
662	C₂×C₁₃	—	4	1	no	—
663	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
664	C₂×C₁₃	#585	1	1	yes	characteristic
665	C₂×C₁₃	#585	1	1	yes	characteristic
666	D₁₃	—	2	2	no	—
667	D₁₃	—	4	1	no	—
668	D₁₃	—	4	1	no	—
669	D₁₃	—	4	1	no	—
670	C₂⁴	—	13	1	no	—
671	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
672	#41	—	26	4	no	—
673	#41	—	26	4	no	—
674	C₂×Q₈	—	13	1	no	—
675	C₂×Q₈	—	13	1	no	—
676	C₂×Q₈	—	13	1	no	—
677	C₂×Q₈	—	13	1	no	—
678	C₂×Q₈	—	13	1	no	—
679	C₂×D₄	—	13	1	no	—
680	C₂×D₄	—	13	1	no	—
681	C₂×D₄	—	13	1	no	—
682	C₂×D₄	—	13	1	no	—
683	C₂×D₄	—	13	1	no	—
684	C₂×D₄	—	13	1	no	—
685	C₂×D₄	—	13	1	no	—
686	C₂×D₄	—	13	1	no	—
687	C₂×D₄	—	13	1	no	—
688	C₂×D₄	—	13	1	no	—
689	C₂×D₄	—	13	1	no	—
690	C₂×D₄	—	13	1	no	—
691	C₂×D₄	—	13	1	no	—
692	C₂×D₄	—	13	1	no	—
693	C₂×D₄	—	13	1	no	—
694	C₂×D₄	—	26	4	no	—
695	C₂²×C₄	—	13	1	no	—
696	C₂²×C₄	—	13	1	no	—
697	C₂²×C₄	—	13	1	no	—
698	C₂²×C₄	—	13	1	no	—
699	C₂²×C₄	—	13	1	no	—
700	C₂²×C₄	—	13	1	no	—
701	C₂²×C₄	—	13	1	no	—
702	C₂²×C₄	—	13	1	no	—
703	C₂²×C₄	—	13	1	no	—
704	C₂²×C₄	—	13	1	no	—
705	C₂²×C₄	—	13	1	no	—
706	C₂²×C₄	—	13	1	no	—
707	C₂²×C₄	—	13	1	no	—
708	C₂²×C₄	—	13	1	no	—
709	C₂²×C₄	—	13	1	no	—
710	C₂²×C₄	—	13	1	no	—
711	C₂²×C₄	—	13	1	no	—
712	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
715	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
716	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
718	C₄⋊C₄	—	13	1	no	—
719	C₄⋊C₄	—	13	1	no	—
720	C₄⋊C₄	—	13	1	no	—
721	C₄⋊C₄	—	13	1	no	—
722	C₄⋊C₄	—	13	1	no	—
723	C₄⋊C₄	—	13	1	no	—
724	C₄⋊C₄	—	13	1	no	—
725	C₄⋊C₄	—	13	1	no	—
726	C₄⋊C₄	—	13	1	no	—
727	C₄⋊C₄	—	13	1	no	—
728	C₄⋊C₄	—	13	1	no	—
729	C₄⋊C₄	—	13	1	no	—
730	C₄⋊C₄	—	13	1	no	—
731	C₄⋊C₄	—	13	1	no	—
732	C₄⋊C₄	—	13	1	no	—
733	C₄⋊C₄	—	13	1	no	—
734	C₄⋊C₄	—	13	1	no	—
735	C₄⋊C₄	—	13	1	no	—
736	C₄⋊C₄	—	13	1	no	—
737	C₄⋊C₄	—	13	1	no	—
738	C₄⋊C₄	—	13	1	no	—
739	C₄⋊C₄	—	13	1	no	—
740	C₄⋊C₄	—	13	1	no	—
741	C₄⋊C₄	—	13	1	no	—
742	C₄⋊C₄	—	13	1	no	—
743	C₄⋊C₄	—	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	C₂²×D₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
764	C₂²⋊C₄	—	13	1	no	—
765	C₂²⋊C₄	—	13	1	no	—
766	C₂²⋊C₄	—	13	1	no	—
767	C₂²⋊C₄	—	13	1	no	—
768	C₂²⋊C₄	—	13	1	no	—
769	C₂²⋊C₄	—	13	1	no	—
770	C₂²⋊C₄	—	13	1	no	—
771	C₂²⋊C₄	—	13	1	no	—
772	C₂²⋊C₄	—	13	1	no	—
773	C₂²⋊C₄	—	13	1	no	—
774	C₂²⋊C₄	—	13	1	no	—
775	C₂²⋊C₄	—	13	1	no	—
776	C₂²⋊C₄	—	13	1	no	—
777	C₂²⋊C₄	—	13	1	no	—
778	C₂²⋊C₄	—	13	1	no	—
779	C₂²⋊C₄	—	13	1	no	—
780	C₂²⋊C₄	—	13	1	no	—
781	C₂²⋊C₄	—	13	1	no	—
782	C₂²⋊C₄	—	13	1	no	—
783	C₂²⋊C₄	—	13	1	no	—
784	C₂²⋊C₄	—	13	1	no	—
785	C₂²⋊C₄	—	13	1	no	—
786	C₂²⋊C₄	—	13	1	no	—
787	C₂²⋊C₄	—	13	1	no	—
788	C₂²⋊C₄	—	13	1	no	—
789	C₂²⋊C₄	—	13	1	no	—
790	C₂²⋊C₄	—	13	1	no	—
791	C₂²⋊C₄	—	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	C₂²×D₁₃	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
808	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
810	C₄²	—	13	1	no	—
811	C₄²	—	13	1	no	—
812	C₄²	—	13	1	no	—
813	C₄²	—	13	1	no	—
814	C₄²	—	13	1	no	—
815	C₄²	—	13	1	no	—
816	C₄²	—	13	1	no	—
817	C₄²	—	13	1	no	—
818	C₄²	—	13	1	no	—
819	C₄²	—	13	1	no	—
820	C₄²	—	13	1	no	—
821	C₄²	—	13	1	no	—
822	C₄²	—	13	1	no	—
823	C₄²	—	13	1	no	—
824	C₄²	C₂²×D₁₃	1	1	yes	characteristic
825	C₄²	C₂²×D₁₃	1	1	yes	characteristic
826	C₄²	C₂²×D₁₃	1	1	yes	characteristic
827	C₄²	C₂²×D₁₃	1	1	yes	characteristic
828	C₁₃	#3521	1	1	yes	characteristic, complemented, Sylow
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	1	no	—
832	C₂³	—	13	1	no	—
833	C₂³	—	13	1	no	—
834	C₂³	—	13	1	no	—
835	C₂³	—	13	1	no	—
836	C₂³	—	26	2	no	—
837	C₂³	—	52	1	no	—
838	C₂³	—	52	1	no	—
839	C₂³	C₂³×D₁₃	1	1	yes	characteristic
840	C₂³	C₂³×D₁₃	1	1	yes	characteristic
841	C₂³	C₂³×D₁₃	1	1	yes	characteristic
842	Q₈	—	26	2	no	—
843	Q₈	—	26	2	no	—
844	Q₈	—	52	1	no	—
845	Q₈	—	52	1	no	—
846	Q₈	—	52	1	no	—
847	D₄	—	13	4	no	—
848	D₄	—	26	2	no	—
849	D₄	—	26	2	no	—
850	D₄	—	26	2	no	—
851	D₄	—	26	2	no	—
852	D₄	—	26	2	no	—
853	D₄	—	26	2	no	—
854	D₄	—	26	2	no	—
855	D₄	—	52	1	no	—
856	D₄	—	52	1	no	—
857	D₄	—	52	1	no	—
858	D₄	—	52	1	no	—
859	D₄	—	52	1	no	—
860	D₄	—	52	1	no	—
861	D₄	—	52	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	13	1	no	—
869	C₂×C₄	—	13	1	no	—
870	C₂×C₄	—	13	1	no	—
871	C₂×C₄	—	13	1	no	—
872	C₂×C₄	—	13	1	no	—
873	C₂×C₄	—	13	1	no	—
874	C₂×C₄	—	13	1	no	—
875	C₂×C₄	—	13	1	no	—
876	C₂×C₄	—	13	1	no	—
877	C₂×C₄	—	13	1	no	—
878	C₂×C₄	—	13	1	no	—
879	C₂×C₄	—	13	1	no	—
880	C₂×C₄	—	26	2	no	—
881	C₂×C₄	—	26	2	no	—
882	C₂×C₄	—	26	2	no	—
883	C₂×C₄	—	26	2	no	—
884	C₂×C₄	—	26	2	no	—
885	C₂×C₄	—	52	1	no	—
886	C₂×C₄	—	52	1	no	—
887	C₂×C₄	—	52	1	no	—
888	C₂×C₄	—	52	1	no	—
889	C₂×C₄	—	52	1	no	—
890	C₂×C₄	—	52	1	no	—
891	C₂×C₄	—	52	1	no	—
892	C₂×C₄	—	52	1	no	—
893	C₂×C₄	—	52	1	no	—
894	C₂×C₄	—	52	1	no	—
895	C₂×C₄	—	52	1	no	—
896	C₂×C₄	—	52	1	no	—
897	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
898	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
899	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
908	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	8	2	no	—
918	C₂²	—	13	2	no	—
919	C₂²	—	26	1	no	—
920	C₂²	—	26	1	no	—
921	C₂²	—	26	1	no	—
922	C₂²	—	26	1	no	—
923	C₂²	—	26	1	no	—
924	C₂²	—	26	1	no	—
925	C₂²	—	26	1	no	—
926	C₂²	—	26	1	no	—
927	C₂²	—	26	1	no	—
928	C₂²	—	26	1	no	—
929	C₂²	—	26	1	no	—
930	C₂²	—	104	2	no	—
931	C₂²	#41×D₁₃	1	2	yes	—
932	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	1	no	—
945	C₄	—	13	2	no	—
946	C₄	—	26	1	no	—
947	C₄	—	26	1	no	—
948	C₄	—	26	1	no	—
949	C₄	—	26	1	no	—
950	C₄	—	26	1	no	—
951	C₄	—	26	1	no	—
952	C₄	—	26	1	no	—
953	C₄	—	26	1	no	—
954	C₄	—	26	1	no	—
955	C₄	—	26	1	no	—
956	C₄	—	26	1	no	—
957	C₂	—	2	2	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	26	2	no	—
961	C₂	—	52	1	no	—
962	C₂	—	52	1	no	—
963	C₂	—	52	1	no	—
964	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
965	C₂	#11719648	1	1	yes	characteristic
966	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₂×C₁₃×#126	C₂
hypercenter	C₂×#126	D₁₃
hypocenter	C₁₃	#3521
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#126	C₂	semidirect
2. #11719415	C₂	semidirect
3. #11719414	C₂	semidirect
4. #11719414	C₂	semidirect
5. #11719413	C₂	semidirect
6. #11719413	C₂	semidirect
7. #11719412	C₂	semidirect
8. #11719411	C₂	semidirect
9. #11719411	C₂	semidirect
10. #11719411	C₂	semidirect
11. #11719410	C₂	semidirect
12. #11719410	C₂	semidirect
13. #11719409	C₂	semidirect
14. D₁₃×#126	C₂	semidirect
15. #11719407	C₂	semidirect
16. #11719407	C₂	semidirect
17. #11719406	C₂	semidirect
18. #11719220	C₂	semidirect
19. #11719219	C₂	semidirect
20. #11719218	C₂	semidirect
21. #11719216	C₂	semidirect
22. #11719212	C₂	semidirect
23. #11719209	C₂	semidirect
24. #11719200	C₂	semidirect
25. #11719200	C₂	semidirect
26. #11719199	C₂	semidirect
27. #11719195	C₂	semidirect
28. #11719195	C₂	semidirect
29. #11719191	C₂	semidirect
30. #11719184	C₂	semidirect
31. C₄×#6127	C₂	semidirect
39. C₁₃×#126	C₂²	semidirect
40. C₁₃×#126	C₂²	semidirect
41. C₁₃×#126	C₂²	semidirect
42. C₁₃×#126	C₂²	semidirect
43. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
44. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
45. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
49. C₂×C₄²×C₁₃	C₂²	semidirect
55. #88184	C₂²	semidirect
58. #88183	C₂²	semidirect
59. #88183	C₂²	semidirect
66. C₄×C₂²⋊D₁₃	C₂²	semidirect
67. C₄×C₂²⋊D₁₃	C₂²	semidirect
68. C₄×C₂²⋊D₁₃	C₂²	semidirect
69. C₄×C₂²⋊D₁₃	C₂²	semidirect
70. #88180	C₂²	semidirect
71. #88180	C₂²	semidirect
72. #88178	C₂²	semidirect
73. #88178	C₂²	semidirect
74. #88178	C₂²	semidirect
75. #88152	C₂²	semidirect
76. #88152	C₂²	semidirect
77. #88152	C₂²	semidirect
78. #88152	C₂²	semidirect
79. #88152	C₂²	semidirect
80. #88152	C₂²	semidirect
81. #88151	C₂²	semidirect
82. #88151	C₂²	semidirect
83. #88150	C₂²	semidirect
84. #88150	C₂²	semidirect
85. #88150	C₂²	semidirect
86. #88150	C₂²	semidirect
87. #88150	C₂²	semidirect
88. #88150	C₂²	semidirect
89. #88149	C₂²	semidirect
90. #88149	C₂²	semidirect
91. #88148	C₂²	semidirect
92. #88148	C₂²	semidirect
93. #88148	C₂²	semidirect
94. #88148	C₂²	semidirect
95. #88148	C₂²	semidirect
96. #88148	C₂²	semidirect
97. #88147	C₂²	semidirect
98. #88147	C₂²	semidirect
99. #88147	C₂²	semidirect
100. #88147	C₂²	semidirect
101. #88146	C₂²	semidirect
102. #88146	C₂²	semidirect
103. #88146	C₂²	semidirect
104. #88146	C₂²	semidirect
105. C₄⋊C₄×D₁₃	C₂²	semidirect
106. C₄⋊C₄×D₁₃	C₂²	semidirect
107. C₄⋊C₄×D₁₃	C₂²	semidirect
108. C₄⋊C₄×D₁₃	C₂²	semidirect
109. #88144	C₂²	semidirect
110. #88144	C₂²	semidirect
111. #88143	C₂²	semidirect
112. #88143	C₂²	semidirect
113. #88143	C₂²	semidirect
114. #88143	C₂²	semidirect
115. #88143	C₂²	semidirect
116. #88143	C₂²	semidirect
117. #88142	C₂²	semidirect
118. #88142	C₂²	semidirect
119. #88141	C₂²	semidirect
120. #88141	C₂²	semidirect
121. #88141	C₂²	semidirect
122. #88141	C₂²	semidirect
123. #88140	C₂²	semidirect
124. #88140	C₂²	semidirect
130. #88139	C₂²	semidirect
136. #88138	C₂²	semidirect
142. #88137	C₂²	semidirect
151. #88135	C₂²	semidirect
152. #88135	C₂²	semidirect
162. #88133	C₂²	semidirect
165. #88132	C₂²	semidirect
166. #88132	C₂²	semidirect
169. #88131	C₂²	semidirect
170. #88131	C₂²	semidirect
171. #88130	C₂²	semidirect
172. #88130	C₂²	semidirect
173. #88129	C₂²	semidirect
174. C₄×D₅₂	C₂²	semidirect
175. C₄×D₅₂	C₂²	semidirect
176. C₄×D₅₂	C₂²	semidirect
177. #88126	C₂²	semidirect
178. #88126	C₂²	semidirect
179. #88126	C₂²	semidirect
180. #88126	C₂²	semidirect
181. C₄²×D₁₃	C₂²	semidirect
182. C₄²×D₁₃	C₂²	semidirect
183. #88124	C₂²	semidirect
184. C₄×Dic₂₆	C₂²	semidirect
185. C₄×Dic₂₆	C₂²	semidirect
186. C₄×Dic₂₆	C₂²	semidirect
453. C₂×#126	D₁₃	semidirect
528. #126	C₂×D₁₃	semidirect
529. #126	C₂×D₁₃	semidirect
530. #126	C₂×D₁₃	semidirect
531. #126	C₂×D₁₃	semidirect
646. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
647. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
648. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
659. C₂×C₄²	C₂×D₁₃	semidirect
828. C₁₃	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#126	2
#11719415	2
#11719414	2
#11719413	2
#11719412	2
#11719411	2
#11719410	2
#11719409	2
D₁₃×#126	2
#11719407	2
#11719406	2
#11719220	2
#11719219	2
#11719218	2
#11719216	2
#11719212	2
#11719209	2
#11719200	2
#11719199	2
#11719195	2
#11719191	2
#11719184	2
C₄×#6127	2
#3521	13