Subgroups — #13128789

Order 1664.

1142 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719415	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	#11719382	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719375	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719374	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719369	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719363	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719362	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719354	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719342	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719321	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719318	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719315	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719315	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719303	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719301	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719296	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719296	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719295	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719292	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719265	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719250	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719243	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#6129	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#88139	C₂	1	1	yes	maximal, characteristic, complemented
31	#11719191	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
34	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#6129	C₂²	1	1	yes	characteristic
36	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
37	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
39	C₂×D₄×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×#124	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#120	C₂²	1	1	yes	characteristic
52	C₁₃×#120	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
54	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
58	#88201	C₂²	1	1	yes	characteristic, complemented
59	#88200	C₂²	1	1	yes	characteristic, complemented
60	#88198	C₂²	1	1	yes	characteristic, complemented
61	#88194	C₂²	1	1	yes	characteristic
62	#88193	C₂²	1	1	yes	characteristic
63	#88193	C₂²	1	1	yes	characteristic
64	#88193	C₂²	1	1	yes	characteristic
65	#88193	C₂²	1	1	yes	characteristic, complemented
66	#88193	C₂²	1	1	yes	characteristic, complemented
67	#88193	C₂²	1	1	yes	characteristic, complemented
68	#88193	C₂²	1	1	yes	characteristic, complemented
69	#88192	C₂²	1	1	yes	characteristic, complemented
70	#88192	C₂²	1	1	yes	characteristic, complemented
71	#88191	C₂²	1	1	yes	characteristic
72	#88191	C₂²	1	1	yes	characteristic, complemented
73	#88191	C₂²	1	1	yes	characteristic, complemented
74	#88191	C₂²	1	1	yes	characteristic, complemented
75	#88190	C₂²	1	1	yes	characteristic, complemented
76	#88190	C₂²	1	1	yes	characteristic, complemented
77	#88189	C₂²	1	1	yes	characteristic, complemented
78	#88189	C₂²	1	1	yes	characteristic, complemented
79	#88189	C₂²	1	1	yes	characteristic, complemented
80	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
81	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
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
88	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
94	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
95	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
96	#88180	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
99	#88152	C₂²	1	1	yes	characteristic, complemented
100	#88152	C₂²	1	1	yes	characteristic, complemented
101	#88152	C₂²	1	1	yes	characteristic, complemented
102	#88152	C₂²	1	1	yes	characteristic, complemented
103	#88151	C₂²	1	1	yes	characteristic, complemented
104	#88151	C₂²	1	1	yes	characteristic, complemented
105	#88150	C₂²	1	1	yes	characteristic, complemented
106	#88150	C₂²	1	1	yes	characteristic, complemented
107	#88150	C₂²	1	1	yes	characteristic, complemented
108	#88148	C₂²	1	1	yes	characteristic, complemented
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, complemented
113	#88147	C₂²	1	1	yes	characteristic, complemented
114	#88146	C₂²	1	1	yes	characteristic, complemented
115	#88146	C₂²	1	1	yes	characteristic, complemented
116	#88146	C₂²	1	1	yes	characteristic, complemented
117	#88143	C₂²	1	1	yes	characteristic, complemented
118	#88142	C₂²	1	1	yes	characteristic, complemented
119	#88142	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, complemented
129	#88139	C₂²	1	1	yes	characteristic, complemented
130	#88139	C₂²	1	1	yes	characteristic, complemented
131	#88139	C₂²	1	1	yes	characteristic, complemented
132	#88139	C₂²	1	1	yes	characteristic, complemented
133	#88139	C₂²	1	1	yes	characteristic, complemented
134	#88139	C₂²	1	1	yes	characteristic, complemented
135	#88139	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	#88138	C₂²	1	1	yes	characteristic
141	#88138	C₂²	1	1	yes	characteristic
142	#88138	C₂²	1	1	yes	characteristic, complemented
143	#88138	C₂²	1	1	yes	characteristic, complemented
144	#88137	C₂²	1	1	yes	characteristic, complemented
145	#88137	C₂²	1	1	yes	characteristic, complemented
146	#88136	C₂²	1	1	yes	characteristic
147	#88136	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	#88135	C₂²	1	1	yes	characteristic, complemented
154	#88135	C₂²	1	1	yes	characteristic, complemented
155	#88135	C₂²	1	1	yes	characteristic, complemented
156	#88135	C₂²	1	1	yes	characteristic, complemented
157	#88135	C₂²	1	1	yes	characteristic, complemented
158	#88135	C₂²	1	1	yes	characteristic, complemented
159	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
160	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
161	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
162	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
163	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
164	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
165	#88133	C₂²	1	1	yes	characteristic, complemented
166	#88133	C₂²	1	1	yes	characteristic, complemented
167	#88133	C₂²	1	1	yes	characteristic, complemented
168	#88132	C₂²	1	1	yes	characteristic, complemented
169	#88132	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	#88131	C₂²	1	1	yes	characteristic, complemented
175	#88131	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	#88129	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
182	#88126	C₂²	1	1	yes	characteristic, complemented
183	#88126	C₂²	1	1	yes	characteristic, complemented
184	C₄²×D₁₃	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	C₂³×D₁₃	C₂³	1	1	yes	characteristic
190	C₂³×D₁₃	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	C₂×D₄×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	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₃	—	2	4	no	—
204	C₂×C₂²⋊D₁₃	—	4	2	no	—
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	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
219	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
220	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
221	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
222	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
225	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
228	Q₈×D₁₃	—	4	2	no	—
229	#6129	—	2	4	no	—
230	#6129	—	4	2	no	—
231	#6129	—	4	2	no	—
232	D₄×D₁₃	—	2	4	no	—
233	D₄×D₁₃	—	4	2	no	—
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×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×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×Dic₂₆	—	4	2	no	—
248	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
249	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
250	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
251	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
252	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
253	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
254	C₂×Dic₂₆	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
266	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	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₄²×C₁₃	C₂³	1	1	yes	characteristic
276	C₄²×C₁₃	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	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₁₃	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	#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	#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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
316	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₁₃	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	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	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	#3514	—	13	1	no	maximal, Sylow
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	4	1	no	—
354	C₂³×C₁₃	—	4	1	no	—
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	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
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	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	2	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	C₂²⋊D₁₃	—	2	2	no	—
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	—	2	2	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	#41	1	4	yes	complemented
409	C₂×Dic₁₃	—	2	2	no	—
410	C₂×Dic₁₃	—	2	2	no	—
411	C₂×Dic₁₃	—	2	2	no	—
412	C₂×Dic₁₃	—	2	2	no	—
413	C₂×Dic₁₃	—	2	2	no	—
414	C₂×Dic₁₃	—	4	1	no	—
415	C₂×Dic₁₃	—	4	1	no	—
416	C₂×Dic₁₃	—	4	1	no	—
417	C₂×Dic₁₃	—	4	1	no	—
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	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
427	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
430	D₅₂	—	2	2	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	—	4	1	no	—
437	C₄×D₁₃	—	4	1	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	Dic₂₆	—	2	2	no	—
444	Dic₂₆	—	2	2	no	—
445	Dic₂₆	—	2	2	no	—
446	Dic₂₆	—	2	2	no	—
447	Dic₂₆	—	4	1	no	—
448	Dic₂₆	—	4	1	no	—
449	Dic₂₆	—	4	1	no	—
450	#559	—	13	1	no	—
451	#556	—	13	1	no	—
452	#555	—	13	1	no	—
453	#555	—	13	1	no	—
454	#551	—	13	1	no	—
455	#551	—	13	1	no	—
456	#551	—	13	1	no	—
457	#551	—	13	1	no	—
458	D₄×Q₈	—	13	1	no	—
459	#548	—	13	1	no	—
460	#548	—	13	1	no	—
461	#546	—	13	1	no	—
462	#546	—	13	1	no	—
463	#546	—	13	1	no	—
464	#546	—	13	1	no	—
465	D₄²	—	13	1	no	—
466	#542	—	13	1	no	—
467	#542	—	13	1	no	—
468	#538	—	13	1	no	—
469	#538	—	13	1	no	—
470	#538	—	13	1	no	—
471	#538	D₁₃	1	1	yes	characteristic, complemented
472	#532	—	13	1	no	—
473	#529	—	13	1	no	—
474	#529	—	13	1	no	—
475	#529	—	13	1	no	—
476	C₂×#124	—	13	1	no	—
477	C₂×#124	—	13	1	no	—
478	#518	—	13	1	no	—
479	#518	—	13	1	no	—
480	C₄×#41	—	13	1	no	—
481	C₂²×C₁₃	—	2	1	no	—
482	C₂²×C₁₃	—	2	1	no	—
483	C₂²×C₁₃	—	2	1	no	—
484	C₂²×C₁₃	—	2	1	no	—
485	C₂²×C₁₃	—	2	1	no	—
486	C₂²×C₁₃	—	2	1	no	—
487	C₂²×C₁₃	—	2	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	—	8	2	no	—
496	C₂²×C₁₃	C₂×#41	1	2	yes	—
497	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
498	C₂×D₁₃	—	2	1	no	—
499	C₂×D₁₃	—	2	1	no	—
500	C₂×D₁₃	—	2	1	no	—
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	—	8	2	no	—
510	C₂×D₁₃	—	8	2	no	—
511	C₂×D₁₃	—	8	2	no	—
512	C₂×D₁₃	C₂×#41	1	2	yes	—
513	C₄×C₁₃	—	2	1	no	—
514	C₄×C₁₃	—	2	1	no	—
515	C₄×C₁₃	—	2	1	no	—
516	C₄×C₁₃	—	2	1	no	—
517	C₄×C₁₃	—	2	1	no	—
518	C₄×C₁₃	—	2	1	no	—
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	Dic₁₃	—	2	1	no	—
524	Dic₁₃	—	2	1	no	—
525	Dic₁₃	—	2	1	no	—
526	Dic₁₃	—	2	1	no	—
527	Dic₁₃	—	2	1	no	—
528	Dic₁₃	—	2	1	no	—
529	Dic₁₃	—	2	1	no	—
530	Dic₁₃	—	2	1	no	—
531	Dic₁₃	—	2	1	no	—
532	Dic₁₃	—	2	1	no	—
533	Dic₁₃	C₂×#41	1	2	yes	—
534	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
535	C₂×#41	—	13	1	no	—
536	C₂×#41	—	13	1	no	—
537	C₂×#41	—	13	1	no	—
538	C₂²×Q₈	—	13	1	no	—
539	C₂²×Q₈	—	13	1	no	—
540	C₂²×D₄	—	13	1	no	—
541	C₂²×D₄	—	13	1	no	—
542	C₂²×D₄	—	13	1	no	—
543	C₂²×D₄	—	13	1	no	—
544	C₄⋊Q₈	—	13	1	no	—
545	C₄⋊Q₈	—	13	1	no	—
546	C₄⋊Q₈	—	13	1	no	—
547	#127	—	13	1	no	—
548	#126	—	13	1	no	—
549	#126	—	13	1	no	—
550	#126	—	13	1	no	—
551	#126	—	13	1	no	—
552	#126	—	13	1	no	—
553	#126	—	13	1	no	—
554	#126	—	13	1	no	—
555	#126	—	13	1	no	—
556	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
557	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
558	#125	—	13	1	no	—
559	#124	—	13	1	no	—
560	#124	—	13	1	no	—
561	#124	—	13	1	no	—
562	#124	—	13	1	no	—
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	—	13	1	no	—
572	#124	—	13	1	no	—
573	#124	—	13	1	no	—
574	#124	—	13	1	no	—
575	#124	—	13	1	no	—
576	#124	—	13	1	no	—
577	#124	—	13	1	no	—
578	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
579	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
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	—	13	1	no	—
588	#123	—	13	1	no	—
589	#123	—	13	1	no	—
590	#123	—	13	1	no	—
591	#123	—	13	1	no	—
592	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
593	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
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	C₂×D₁₃	1	1	yes	characteristic, complemented
607	#121	—	13	1	no	—
608	#121	—	13	1	no	—
609	#121	—	13	1	no	—
610	#121	—	13	1	no	—
611	#121	—	13	1	no	—
612	#121	—	13	1	no	—
613	#121	—	13	1	no	—
614	#121	—	13	1	no	—
615	#121	—	13	1	no	—
616	#121	—	13	1	no	—
617	#121	—	13	1	no	—
618	#121	—	13	1	no	—
619	#121	—	13	1	no	—
620	#121	—	13	1	no	—
621	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
622	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
623	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
624	#120	—	13	1	no	—
625	#120	—	13	1	no	—
626	#120	—	13	1	no	—
627	#120	—	13	1	no	—
628	#120	—	13	1	no	—
629	#120	—	13	1	no	—
630	#120	C₂×D₁₃	1	1	yes	characteristic
631	#120	C₂×D₁₃	1	1	yes	characteristic, complemented
632	C₄×Q₈	—	13	1	no	—
633	C₄×Q₈	—	13	1	no	—
634	C₄×Q₈	—	13	1	no	—
635	C₄×Q₈	—	13	1	no	—
636	C₄×Q₈	—	13	1	no	—
637	C₄×D₄	—	13	1	no	—
638	C₄×D₄	—	13	1	no	—
639	C₄×D₄	—	13	1	no	—
640	C₄×D₄	—	13	1	no	—
641	C₄×D₄	—	13	1	no	—
642	C₄×D₄	—	13	1	no	—
643	C₄×D₄	—	13	1	no	—
644	C₄×D₄	—	13	1	no	—
645	C₄×D₄	—	13	1	no	—
646	C₄×D₄	—	13	1	no	—
647	C₄×D₄	—	13	1	no	—
648	C₄×D₄	—	13	1	no	—
649	C₄×D₄	—	13	1	no	—
650	C₄×D₄	—	13	1	no	—
651	C₄×D₄	—	13	1	no	—
652	C₄×D₄	—	13	1	no	—
653	C₄×D₄	—	13	1	no	—
654	C₄×D₄	—	13	1	no	—
655	C₄×D₄	—	13	1	no	—
656	C₄×D₄	—	13	1	no	—
657	C₄×D₄	—	13	1	no	—
658	C₄×D₄	—	13	1	no	—
659	C₄×D₄	—	13	1	no	—
660	C₄×D₄	—	13	1	no	—
661	C₄×D₄	—	13	1	no	—
662	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
663	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
664	#117	—	13	1	no	—
665	#117	—	13	1	no	—
666	#117	—	13	1	no	—
667	#117	—	13	1	no	—
668	#117	—	13	1	no	—
669	#117	—	13	1	no	—
670	#117	—	13	1	no	—
671	#117	—	13	1	no	—
672	#117	—	13	1	no	—
673	#117	—	13	1	no	—
674	#117	—	13	1	no	—
675	C₂×C₂²⋊C₄	—	13	1	no	—
676	C₂×C₂²⋊C₄	—	13	1	no	—
677	C₂×C₂²⋊C₄	—	13	1	no	—
678	C₂×C₂²⋊C₄	—	13	1	no	—
679	C₂×C₂²⋊C₄	—	13	1	no	—
680	C₂×C₂²⋊C₄	—	13	1	no	—
681	C₂×C₂²⋊C₄	—	13	1	no	—
682	C₂×C₂²⋊C₄	—	13	1	no	—
683	C₂×C₂²⋊C₄	—	13	1	no	—
684	C₂×C₂²⋊C₄	—	13	1	no	—
685	C₂×C₂²⋊C₄	—	13	1	no	—
686	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
687	C₂×C₄²	—	13	1	no	—
688	C₂×C₄²	—	13	1	no	—
689	C₂×C₄²	—	13	1	no	—
690	C₂×C₁₃	—	2	2	no	—
691	C₂×C₁₃	—	4	1	no	—
692	C₂×C₁₃	—	4	1	no	—
693	C₂×C₁₃	—	4	1	no	—
694	C₂×C₁₃	—	4	1	no	—
695	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
696	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
697	C₂×C₁₃	#585	1	1	yes	characteristic
698	D₁₃	—	2	2	no	—
699	D₁₃	—	4	1	no	—
700	D₁₃	—	4	1	no	—
701	D₁₃	—	4	1	no	—
702	C₂⁴	—	13	1	no	—
703	C₂⁴	—	13	1	no	—
704	C₂⁴	—	13	1	no	—
705	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
706	#41	—	26	4	no	—
707	#41	—	52	2	no	—
708	#41	—	52	2	no	—
709	C₂×Q₈	—	13	1	no	—
710	C₂×Q₈	—	13	1	no	—
711	C₂×Q₈	—	13	1	no	—
712	C₂×Q₈	—	13	1	no	—
713	C₂×Q₈	—	13	1	no	—
714	C₂×Q₈	—	13	1	no	—
715	C₂×Q₈	—	13	1	no	—
716	C₂×Q₈	—	52	2	no	—
717	C₂×Q₈	—	52	2	no	—
718	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
719	C₂×D₄	—	13	1	no	—
720	C₂×D₄	—	13	1	no	—
721	C₂×D₄	—	13	1	no	—
722	C₂×D₄	—	13	1	no	—
723	C₂×D₄	—	13	1	no	—
724	C₂×D₄	—	13	1	no	—
725	C₂×D₄	—	13	1	no	—
726	C₂×D₄	—	13	1	no	—
727	C₂×D₄	—	13	1	no	—
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	—	26	4	no	—
737	C₂×D₄	—	26	4	no	—
738	C₂×D₄	—	52	2	no	—
739	C₂×D₄	—	52	2	no	—
740	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
741	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
742	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
743	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
744	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
745	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
746	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
747	C₂²×C₄	—	13	1	no	—
748	C₂²×C₄	—	13	1	no	—
749	C₂²×C₄	—	13	1	no	—
750	C₂²×C₄	—	13	1	no	—
751	C₂²×C₄	—	13	1	no	—
752	C₂²×C₄	—	13	1	no	—
753	C₂²×C₄	—	13	1	no	—
754	C₂²×C₄	—	13	1	no	—
755	C₂²×C₄	—	13	1	no	—
756	C₂²×C₄	—	13	1	no	—
757	C₂²×C₄	—	13	1	no	—
758	C₂²×C₄	—	13	1	no	—
759	C₂²×C₄	—	13	1	no	—
760	C₂²×C₄	—	13	1	no	—
761	C₂²×C₄	—	13	1	no	—
762	C₂²×C₄	—	13	1	no	—
763	C₂²×C₄	—	13	1	no	—
764	C₂²×C₄	—	13	1	no	—
765	C₂²×C₄	—	13	1	no	—
766	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
769	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
779	C₄⋊C₄	—	13	1	no	—
780	C₄⋊C₄	—	13	1	no	—
781	C₄⋊C₄	—	13	1	no	—
782	C₄⋊C₄	—	13	1	no	—
783	C₄⋊C₄	—	13	1	no	—
784	C₄⋊C₄	—	13	1	no	—
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	C₂²×D₁₃	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
796	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
797	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	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	C₂²×D₁₃	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
846	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
847	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
848	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
849	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
850	C₄²	—	13	1	no	—
851	C₄²	—	13	1	no	—
852	C₄²	—	13	1	no	—
853	C₄²	—	13	1	no	—
854	C₄²	—	13	1	no	—
855	C₄²	—	13	1	no	—
856	C₄²	—	13	1	no	—
857	C₄²	—	13	1	no	—
858	C₄²	—	13	1	no	—
859	C₄²	—	13	1	no	—
860	C₄²	—	13	1	no	—
861	C₄²	—	13	1	no	—
862	C₄²	—	13	1	no	—
863	C₄²	—	13	1	no	—
864	C₄²	C₂²×D₁₃	1	1	yes	characteristic
865	C₄²	C₂²×D₁₃	1	1	yes	characteristic
866	C₁₃	#3514	1	1	yes	characteristic, complemented, Sylow
867	C₂³	—	2	2	no	—
868	C₂³	—	4	1	no	—
869	C₂³	—	4	1	no	—
870	C₂³	—	13	1	no	—
871	C₂³	—	13	1	no	—
872	C₂³	—	13	1	no	—
873	C₂³	—	13	1	no	—
874	C₂³	—	26	2	no	—
875	C₂³	—	26	2	no	—
876	C₂³	—	26	2	no	—
877	C₂³	—	52	1	no	—
878	C₂³	—	52	1	no	—
879	C₂³	—	52	1	no	—
880	C₂³	—	52	1	no	—
881	C₂³	—	52	1	no	—
882	C₂³	—	52	1	no	—
883	C₂³	C₂³×D₁₃	1	1	yes	characteristic
884	C₂³	C₂³×D₁₃	1	1	yes	characteristic
885	C₂³	C₂³×D₁₃	1	1	yes	characteristic
886	C₂³	C₂³×D₁₃	1	1	yes	characteristic
887	C₂³	C₂³×D₁₃	1	1	yes	characteristic
888	Q₈	—	4	1	no	—
889	Q₈	—	26	2	no	—
890	Q₈	—	26	2	no	—
891	Q₈	—	26	2	no	—
892	Q₈	—	26	2	no	—
893	Q₈	—	52	1	no	—
894	Q₈	—	52	1	no	—
895	Q₈	—	52	1	no	—
896	D₄	—	2	2	no	—
897	D₄	—	2	2	no	—
898	D₄	—	4	1	no	—
899	D₄	—	4	1	no	—
900	D₄	—	4	1	no	—
901	D₄	—	4	1	no	—
902	D₄	—	4	1	no	—
903	D₄	—	13	4	no	—
904	D₄	—	26	2	no	—
905	D₄	—	26	2	no	—
906	D₄	—	26	2	no	—
907	D₄	—	26	2	no	—
908	D₄	—	26	2	no	—
909	D₄	—	26	2	no	—
910	D₄	—	26	2	no	—
911	D₄	—	26	2	no	—
912	D₄	—	26	2	no	—
913	D₄	—	52	1	no	—
914	D₄	—	52	1	no	—
915	D₄	—	52	1	no	—
916	D₄	—	52	1	no	—
917	D₄	—	52	1	no	—
918	D₄	—	52	1	no	—
919	D₄	—	52	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	13	1	no	—
925	C₂×C₄	—	13	1	no	—
926	C₂×C₄	—	13	1	no	—
927	C₂×C₄	—	13	1	no	—
928	C₂×C₄	—	13	1	no	—
929	C₂×C₄	—	13	1	no	—
930	C₂×C₄	—	13	1	no	—
931	C₂×C₄	—	13	1	no	—
932	C₂×C₄	—	13	1	no	—
933	C₂×C₄	—	13	1	no	—
934	C₂×C₄	—	13	1	no	—
935	C₂×C₄	—	13	1	no	—
936	C₂×C₄	—	26	2	no	—
937	C₂×C₄	—	26	2	no	—
938	C₂×C₄	—	26	2	no	—
939	C₂×C₄	—	26	2	no	—
940	C₂×C₄	—	26	2	no	—
941	C₂×C₄	—	26	2	no	—
942	C₂×C₄	—	26	2	no	—
943	C₂×C₄	—	26	2	no	—
944	C₂×C₄	—	52	1	no	—
945	C₂×C₄	—	52	1	no	—
946	C₂×C₄	—	52	1	no	—
947	C₂×C₄	—	52	1	no	—
948	C₂×C₄	—	52	1	no	—
949	C₂×C₄	—	52	1	no	—
950	C₂×C₄	—	52	1	no	—
951	C₂×C₄	—	52	1	no	—
952	C₂×C₄	—	52	1	no	—
953	C₂×C₄	—	52	1	no	—
954	C₂×C₄	—	52	1	no	—
955	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
964	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	8	2	no	—
980	C₂²	—	13	2	no	—
981	C₂²	—	26	1	no	—
982	C₂²	—	26	1	no	—
983	C₂²	—	26	1	no	—
984	C₂²	—	26	1	no	—
985	C₂²	—	26	1	no	—
986	C₂²	—	26	1	no	—
987	C₂²	—	26	1	no	—
988	C₂²	—	26	1	no	—
989	C₂²	—	26	1	no	—
990	C₂²	—	26	1	no	—
991	C₂²	—	26	1	no	—
992	C₂²	—	104	2	no	—
993	C₂²	—	104	2	no	—
994	C₂²	—	104	2	no	—
995	C₂²	#41×D₁₃	1	2	yes	—
996	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	13	2	no	—
1008	C₄	—	13	2	no	—
1009	C₄	—	26	1	no	—
1010	C₄	—	26	1	no	—
1011	C₄	—	26	1	no	—
1012	C₄	—	26	1	no	—
1013	C₄	—	26	1	no	—
1014	C₄	—	26	1	no	—
1015	C₄	—	26	1	no	—
1016	C₄	—	26	1	no	—
1017	C₄	—	26	1	no	—
1018	C₄	—	26	1	no	—
1019	C₂	—	2	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	4	1	no	—
1024	C₂	—	26	2	no	—
1025	C₂	—	52	1	no	—
1026	C₂	—	52	1	no	—
1027	C₂	—	52	1	no	—
1028	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
1029	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1030	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#538	C₂
hypercenter	#538	D₁₃
hypocenter	C₁₃	#3514
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. C₁₃×#538	C₂	semidirect
2. #11719415	C₂	semidirect
3. #11719411	C₂	semidirect
4. #11719410	C₂	semidirect
5. #11719407	C₂	semidirect
6. #11719382	C₂	semidirect
7. D₁₃×#124	C₂	semidirect
8. #11719375	C₂	semidirect
9. #11719374	C₂	semidirect
10. #11719369	C₂	semidirect
11. #11719363	C₂	semidirect
12. #11719362	C₂	semidirect
13. #11719354	C₂	semidirect
14. #11719342	C₂	semidirect
15. #11719337	C₂	semidirect
16. #11719321	C₂	semidirect
17. #11719318	C₂	semidirect
18. #11719315	C₂	semidirect
19. #11719315	C₂	semidirect
20. #11719303	C₂	semidirect
21. #11719301	C₂	semidirect
22. #11719296	C₂	semidirect
23. #11719296	C₂	semidirect
24. #11719295	C₂	semidirect
25. #11719292	C₂	semidirect
26. #11719265	C₂	semidirect
27. #11719250	C₂	semidirect
28. #11719243	C₂	semidirect
29. C₄×#6129	C₂	semidirect
30. C₂×#88139	C₂	semidirect
31. #11719191	C₂	semidirect
34. C₂×Q₈×D₁₃	C₂²	semidirect
36. C₂×#6129	C₂²	semidirect
37. C₂×#6129	C₂²	semidirect
40. C₂²×Dic₂₆	C₂²	semidirect
41. C₁₃×#126	C₂²	semidirect
42. C₁₃×#126	C₂²	semidirect
43. C₁₃×#124	C₂²	semidirect
44. C₁₃×#124	C₂²	semidirect
45. C₁₃×#123	C₂²	semidirect
46. C₁₃×#123	C₂²	semidirect
47. C₁₃×C₂²⋊Q₈	C₂²	semidirect
48. C₁₃×#121	C₂²	semidirect
49. C₁₃×#121	C₂²	semidirect
50. C₁₃×#121	C₂²	semidirect
52. C₁₃×#120	C₂²	semidirect
53. C₄×D₄×C₁₃	C₂²	semidirect
54. C₄×D₄×C₁₃	C₂²	semidirect
55. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
56. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
57. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
58. #88201	C₂²	semidirect
59. #88200	C₂²	semidirect
60. #88198	C₂²	semidirect
65. #88193	C₂²	semidirect
66. #88193	C₂²	semidirect
67. #88193	C₂²	semidirect
68. #88193	C₂²	semidirect
69. #88192	C₂²	semidirect
70. #88192	C₂²	semidirect
72. #88191	C₂²	semidirect
73. #88191	C₂²	semidirect
74. #88191	C₂²	semidirect
75. #88190	C₂²	semidirect
76. #88190	C₂²	semidirect
77. #88189	C₂²	semidirect
78. #88189	C₂²	semidirect
79. #88189	C₂²	semidirect
80. D₄×Dic₁₃	C₂²	semidirect
81. D₄×Dic₁₃	C₂²	semidirect
82. D₄×Dic₁₃	C₂²	semidirect
83. D₄×Dic₁₃	C₂²	semidirect
84. #88184	C₂²	semidirect
85. #88183	C₂²	semidirect
88. C₄×C₂²⋊D₁₃	C₂²	semidirect
89. C₄×C₂²⋊D₁₃	C₂²	semidirect
90. C₄×C₂²⋊D₁₃	C₂²	semidirect
91. C₄×C₂²⋊D₁₃	C₂²	semidirect
92. C₄×C₂²⋊D₁₃	C₂²	semidirect
93. C₂×#6103	C₂²	semidirect
94. C₂×#6103	C₂²	semidirect
95. C₂×#6103	C₂²	semidirect
96. #88180	C₂²	semidirect
97. C₂×C₄×Dic₁₃	C₂²	semidirect
98. C₂×C₄×Dic₁₃	C₂²	semidirect
99. #88152	C₂²	semidirect
100. #88152	C₂²	semidirect
101. #88152	C₂²	semidirect
102. #88152	C₂²	semidirect
103. #88151	C₂²	semidirect
104. #88151	C₂²	semidirect
105. #88150	C₂²	semidirect
106. #88150	C₂²	semidirect
107. #88150	C₂²	semidirect
108. #88148	C₂²	semidirect
109. #88148	C₂²	semidirect
110. #88148	C₂²	semidirect
111. #88148	C₂²	semidirect
112. #88147	C₂²	semidirect
113. #88147	C₂²	semidirect
114. #88146	C₂²	semidirect
115. #88146	C₂²	semidirect
116. #88146	C₂²	semidirect
117. #88143	C₂²	semidirect
118. #88142	C₂²	semidirect
119. #88142	C₂²	semidirect
120. #88141	C₂²	semidirect
121. #88141	C₂²	semidirect
122. #88141	C₂²	semidirect
123. #88140	C₂²	semidirect
124. #88140	C₂²	semidirect
128. #88139	C₂²	semidirect
129. #88139	C₂²	semidirect
130. #88139	C₂²	semidirect
131. #88139	C₂²	semidirect
132. #88139	C₂²	semidirect
133. #88139	C₂²	semidirect
134. #88139	C₂²	semidirect
135. #88139	C₂²	semidirect
136. #88139	C₂²	semidirect
137. #88139	C₂²	semidirect
138. #88139	C₂²	semidirect
139. #88139	C₂²	semidirect
142. #88138	C₂²	semidirect
143. #88138	C₂²	semidirect
144. #88137	C₂²	semidirect
145. #88137	C₂²	semidirect
151. #88135	C₂²	semidirect
152. #88135	C₂²	semidirect
153. #88135	C₂²	semidirect
154. #88135	C₂²	semidirect
155. #88135	C₂²	semidirect
156. #88135	C₂²	semidirect
157. #88135	C₂²	semidirect
158. #88135	C₂²	semidirect
159. C₂²⋊C₄×D₁₃	C₂²	semidirect
160. C₂²⋊C₄×D₁₃	C₂²	semidirect
161. C₂²⋊C₄×D₁₃	C₂²	semidirect
162. C₂²⋊C₄×D₁₃	C₂²	semidirect
163. C₂²⋊C₄×D₁₃	C₂²	semidirect
164. C₂²⋊C₄×D₁₃	C₂²	semidirect
165. #88133	C₂²	semidirect
166. #88133	C₂²	semidirect
167. #88133	C₂²	semidirect
168. #88132	C₂²	semidirect
169. #88132	C₂²	semidirect
170. #88132	C₂²	semidirect
171. #88132	C₂²	semidirect
172. #88132	C₂²	semidirect
173. #88132	C₂²	semidirect
174. #88131	C₂²	semidirect
175. #88131	C₂²	semidirect
176. #88131	C₂²	semidirect
177. #88131	C₂²	semidirect
178. #88131	C₂²	semidirect
179. #88130	C₂²	semidirect
180. #88129	C₂²	semidirect
181. C₄×D₅₂	C₂²	semidirect
182. #88126	C₂²	semidirect
183. #88126	C₂²	semidirect
184. C₄²×D₁₃	C₂²	semidirect
185. C₄×Dic₂₆	C₂²	semidirect
186. C₄×Dic₂₆	C₂²	semidirect
408. C₂²⋊D₁₃	#41	semidirect
471. #538	D₁₃	semidirect
556. #126	C₂×D₁₃	semidirect
557. #126	C₂×D₁₃	semidirect
578. #124	C₂×D₁₃	semidirect
579. #124	C₂×D₁₃	semidirect
592. #123	C₂×D₁₃	semidirect
593. #123	C₂×D₁₃	semidirect
606. C₂²⋊Q₈	C₂×D₁₃	semidirect
621. #121	C₂×D₁₃	semidirect
622. #121	C₂×D₁₃	semidirect
623. #121	C₂×D₁₃	semidirect
631. #120	C₂×D₁₃	semidirect
662. C₄×D₄	C₂×D₁₃	semidirect
663. C₄×D₄	C₂×D₁₃	semidirect
686. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
866. C₁₃	#3514	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#538	2
#11719415	2
#11719411	2
#11719410	2
#11719407	2
#11719382	2
D₁₃×#124	2
#11719375	2
#11719374	2
#11719369	2
#11719363	2
#11719362	2
#11719354	2
#11719342	2
#11719337	2
#11719321	2
#11719318	2
#11719315	2
#11719303	2
#11719301	2
#11719296	2
#11719295	2
#11719292	2
#11719265	2
#11719250	2
#11719243	2
C₄×#6129	2
C₂×#88139	2
#11719191	2
#3514	13