Subgroups — #13129018

Order 1664.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719534	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719533	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719509	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719389	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719383	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719368	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719366	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719363	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719352	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719343	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719325	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719320	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719315	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719314	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719313	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719307	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719300	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719296	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719294	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719294	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719269	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719265	C₂	1	1	yes	maximal, characteristic, complemented
26	#11719263	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719255	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719200	C₂	1	1	yes	maximal, characteristic, complemented
29	#11719199	C₂	1	1	yes	maximal, characteristic, complemented
30	#11719195	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#88138	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊D₁₃	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, complemented
40	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
42	C₂²×D₅₂	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₁₃	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
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, complemented
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×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	#88207	C₂²	1	1	yes	characteristic
58	#88207	C₂²	1	1	yes	characteristic, complemented
59	#88207	C₂²	1	1	yes	characteristic, complemented
60	#88207	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
62	#88201	C₂²	1	1	yes	characteristic, complemented
63	#88200	C₂²	1	1	yes	characteristic, complemented
64	#88200	C₂²	1	1	yes	characteristic, complemented
65	#88200	C₂²	1	1	yes	characteristic, complemented
66	#88194	C₂²	1	1	yes	characteristic, complemented
67	#88194	C₂²	1	1	yes	characteristic, complemented
68	#88193	C₂²	1	1	yes	characteristic
69	#88193	C₂²	1	1	yes	characteristic, complemented
70	#88193	C₂²	1	1	yes	characteristic, complemented
71	#88193	C₂²	1	1	yes	characteristic, complemented
72	#88193	C₂²	1	1	yes	characteristic, complemented
73	#88193	C₂²	1	1	yes	characteristic, complemented
74	#88193	C₂²	1	1	yes	characteristic, complemented
75	#88193	C₂²	1	1	yes	characteristic, complemented
76	#88193	C₂²	1	1	yes	characteristic, complemented
77	#88192	C₂²	1	1	yes	characteristic, complemented
78	#88192	C₂²	1	1	yes	characteristic, complemented
79	#88192	C₂²	1	1	yes	characteristic, complemented
80	#88192	C₂²	1	1	yes	characteristic, complemented
81	#88192	C₂²	1	1	yes	characteristic, complemented
82	#88192	C₂²	1	1	yes	characteristic, complemented
83	#88191	C₂²	1	1	yes	characteristic
84	#88191	C₂²	1	1	yes	characteristic, complemented
85	#88191	C₂²	1	1	yes	characteristic, complemented
86	#88191	C₂²	1	1	yes	characteristic, complemented
87	#88191	C₂²	1	1	yes	characteristic, complemented
88	#88191	C₂²	1	1	yes	characteristic, complemented
89	#88191	C₂²	1	1	yes	characteristic, complemented
90	#88191	C₂²	1	1	yes	characteristic, complemented
91	#88189	C₂²	1	1	yes	characteristic, complemented
92	#88189	C₂²	1	1	yes	characteristic, complemented
93	#88189	C₂²	1	1	yes	characteristic, complemented
94	#88189	C₂²	1	1	yes	characteristic, complemented
95	#88189	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
97	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
98	#88184	C₂²	1	1	yes	characteristic, complemented
99	#88184	C₂²	1	1	yes	characteristic, complemented
100	#88184	C₂²	1	1	yes	characteristic, complemented
101	#88183	C₂²	1	1	yes	characteristic, complemented
102	#88183	C₂²	1	1	yes	characteristic, complemented
103	#88183	C₂²	1	1	yes	characteristic, complemented
104	#88183	C₂²	1	1	yes	characteristic, complemented
105	#88183	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
114	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
115	#88180	C₂²	1	1	yes	characteristic, complemented
116	#88178	C₂²	1	1	yes	characteristic, complemented
117	#88178	C₂²	1	1	yes	characteristic, complemented
118	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
119	#88152	C₂²	1	1	yes	characteristic, complemented
120	#88152	C₂²	1	1	yes	characteristic, complemented
121	#88151	C₂²	1	1	yes	characteristic, complemented
122	#88150	C₂²	1	1	yes	characteristic, complemented
123	#88149	C₂²	1	1	yes	characteristic, complemented
124	#88148	C₂²	1	1	yes	characteristic, complemented
125	#88148	C₂²	1	1	yes	characteristic, complemented
126	#88148	C₂²	1	1	yes	characteristic, complemented
127	#88148	C₂²	1	1	yes	characteristic, complemented
128	#88147	C₂²	1	1	yes	characteristic, complemented
129	#88146	C₂²	1	1	yes	characteristic, complemented
130	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
131	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
132	#88143	C₂²	1	1	yes	characteristic, complemented
133	#88143	C₂²	1	1	yes	characteristic, complemented
134	#88143	C₂²	1	1	yes	characteristic, complemented
135	#88140	C₂²	1	1	yes	characteristic, complemented
136	#88140	C₂²	1	1	yes	characteristic, complemented
137	#88140	C₂²	1	1	yes	characteristic, complemented
138	#88140	C₂²	1	1	yes	characteristic, complemented
139	#88139	C₂²	1	1	yes	characteristic, complemented
140	#88139	C₂²	1	1	yes	characteristic, complemented
141	#88139	C₂²	1	1	yes	characteristic, complemented
142	#88138	C₂²	1	1	yes	characteristic
143	#88138	C₂²	1	1	yes	characteristic, complemented
144	#88138	C₂²	1	1	yes	characteristic, complemented
145	#88138	C₂²	1	1	yes	characteristic, complemented
146	#88138	C₂²	1	1	yes	characteristic, complemented
147	#88138	C₂²	1	1	yes	characteristic, complemented
148	#88138	C₂²	1	1	yes	characteristic, complemented
149	#88138	C₂²	1	1	yes	characteristic, complemented
150	#88138	C₂²	1	1	yes	characteristic, complemented
151	#88138	C₂²	1	1	yes	characteristic, complemented
152	#88138	C₂²	1	1	yes	characteristic, complemented
153	#88138	C₂²	1	1	yes	characteristic, complemented
154	#88138	C₂²	1	1	yes	characteristic, complemented
155	#88138	C₂²	1	1	yes	characteristic, complemented
156	#88137	C₂²	1	1	yes	characteristic, complemented
157	#88137	C₂²	1	1	yes	characteristic, complemented
158	#88137	C₂²	1	1	yes	characteristic, complemented
159	#88137	C₂²	1	1	yes	characteristic, complemented
160	#88137	C₂²	1	1	yes	characteristic, complemented
161	#88137	C₂²	1	1	yes	characteristic, complemented
162	#88137	C₂²	1	1	yes	characteristic, complemented
163	#88137	C₂²	1	1	yes	characteristic, complemented
164	#88136	C₂²	1	1	yes	characteristic, complemented
165	#88136	C₂²	1	1	yes	characteristic, complemented
166	#88135	C₂²	1	1	yes	characteristic, complemented
167	#88135	C₂²	1	1	yes	characteristic, complemented
168	#88135	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
171	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
172	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
173	#88133	C₂²	1	1	yes	characteristic, complemented
174	#88133	C₂²	1	1	yes	characteristic, complemented
175	#88133	C₂²	1	1	yes	characteristic, complemented
176	#88133	C₂²	1	1	yes	characteristic, complemented
177	#88133	C₂²	1	1	yes	characteristic, complemented
178	#88132	C₂²	1	1	yes	characteristic, complemented
179	#88132	C₂²	1	1	yes	characteristic, complemented
180	#88132	C₂²	1	1	yes	characteristic, complemented
181	#88132	C₂²	1	1	yes	characteristic, complemented
182	#88131	C₂²	1	1	yes	characteristic, complemented
183	#88130	C₂²	1	1	yes	characteristic, complemented
184	#88129	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
186	#88124	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
188	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
189	C₂³×D₁₃	C₂³	1	1	yes	characteristic
190	C₂³×D₁₃	C₂³	1	1	yes	characteristic
191	C₂³×D₁₃	C₂³	1	1	yes	characteristic
192	C₂³×D₁₃	C₂³	1	1	yes	characteristic
193	C₁₃×#41	—	4	2	no	—
194	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₁₃	—	4	2	no	—
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	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
204	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₃	—	4	2	no	—
212	C₂×C₂²⋊D₁₃	—	4	2	no	—
213	C₂×C₂²⋊D₁₃	—	4	2	no	—
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	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
231	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
236	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
237	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
238	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
239	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
240	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
241	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
242	#6129	—	4	2	no	—
243	D₄×D₁₃	—	4	2	no	—
244	D₄×D₁₃	—	4	2	no	—
245	D₄×D₁₃	—	4	2	no	—
246	#6127	—	4	2	no	—
247	C₂×D₅₂	—	4	2	no	—
248	C₂×D₅₂	C₂³	1	1	yes	characteristic
249	C₂×D₅₂	C₂³	1	1	yes	characteristic
250	C₂×D₅₂	C₂³	1	1	yes	characteristic
251	C₂×D₅₂	C₂³	1	1	yes	characteristic
252	C₂×D₅₂	C₂³	1	1	yes	characteristic
253	C₂×D₅₂	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₁₃	—	4	2	no	—
255	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
258	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
259	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
260	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
261	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
262	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
263	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
264	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
265	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
266	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
267	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
268	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₁₃×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	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₄²×C₁₃	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	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
292	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
293	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
294	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
295	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
296	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
297	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
298	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
299	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
300	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
301	#6103	C₂³	1	1	yes	characteristic
302	#6103	C₂³	1	1	yes	characteristic
303	#6103	C₂³	1	1	yes	characteristic
304	#6103	C₂³	1	1	yes	characteristic
305	#6103	C₂³	1	1	yes	characteristic
306	#6103	C₂³	1	1	yes	characteristic
307	#6103	C₂³	1	1	yes	characteristic
308	#6103	C₂³	1	1	yes	characteristic
309	#6103	C₂³	1	1	yes	characteristic
310	#6103	C₂³	1	1	yes	characteristic
311	#6103	C₂³	1	1	yes	characteristic
312	#6103	C₂³	1	1	yes	characteristic
313	#6103	C₂³	1	1	yes	characteristic
314	#6103	C₂³	1	1	yes	characteristic
315	#6103	C₂³	1	1	yes	characteristic
316	#6103	C₂³	1	1	yes	characteristic
317	#6103	C₂³	1	1	yes	characteristic
318	#6103	C₂³	1	1	yes	characteristic
319	#6103	C₂³	1	1	yes	characteristic
320	#6103	C₂³	1	1	yes	characteristic
321	#6103	C₂³	1	1	yes	characteristic
322	#6103	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
324	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
325	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
326	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
327	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
328	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
329	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
330	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
331	#6101	C₂³	1	1	yes	characteristic
332	#6101	C₂³	1	1	yes	characteristic
333	#6101	C₂³	1	1	yes	characteristic
334	#6101	C₂³	1	1	yes	characteristic
335	#6101	C₂³	1	1	yes	characteristic
336	#6101	C₂³	1	1	yes	characteristic
337	#6101	C₂³	1	1	yes	characteristic
338	#6101	C₂³	1	1	yes	characteristic
339	#6101	C₂³	1	1	yes	characteristic
340	#6101	C₂³	1	1	yes	characteristic
341	#6101	C₂³	1	1	yes	characteristic
342	#6101	C₂³	1	1	yes	characteristic
343	#6101	C₂³	1	1	yes	characteristic
344	#6101	C₂³	1	1	yes	characteristic
345	#6101	C₂³	1	1	yes	characteristic
346	#6101	C₂³	1	1	yes	characteristic
347	#6101	C₂³	1	1	yes	characteristic
348	#6101	C₂³	1	1	yes	characteristic
349	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
350	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
351	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
352	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
353	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
354	#3534	—	13	1	no	maximal, Sylow
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	4	1	no	—
357	C₂³×C₁₃	—	4	1	no	—
358	C₂³×C₁₃	—	4	1	no	—
359	C₂³×C₁₃	—	4	1	no	—
360	C₂³×C₁₃	—	4	1	no	—
361	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
363	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₂²×D₁₃	—	2	2	no	—
368	C₂²×D₁₃	—	2	2	no	—
369	C₂²×D₁₃	—	2	2	no	—
370	C₂²×D₁₃	—	2	2	no	—
371	C₂²×D₁₃	—	4	1	no	—
372	C₂²×D₁₃	—	4	1	no	—
373	C₂²×D₁₃	—	4	1	no	—
374	C₂²×D₁₃	—	4	1	no	—
375	C₂²×D₁₃	—	4	1	no	—
376	C₂²×D₁₃	—	4	1	no	—
377	C₂²×D₁₃	—	4	1	no	—
378	C₂²×D₁₃	—	4	1	no	—
379	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
380	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
381	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
382	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
383	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
384	Q₈×C₁₃	—	4	1	no	—
385	D₄×C₁₃	—	2	2	no	—
386	D₄×C₁₃	—	2	2	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	4	1	no	—
389	D₄×C₁₃	—	4	1	no	—
390	D₄×C₁₃	—	4	1	no	—
391	D₄×C₁₃	—	4	1	no	—
392	D₄×C₁₃	—	4	1	no	—
393	D₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	4	1	no	—
396	C₂×C₄×C₁₃	—	4	1	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	4	1	no	—
400	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
409	C₂²⋊D₁₃	—	2	2	no	—
410	C₂²⋊D₁₃	—	2	2	no	—
411	C₂²⋊D₁₃	—	2	2	no	—
412	C₂²⋊D₁₃	—	2	2	no	—
413	C₂²⋊D₁₃	—	2	2	no	—
414	C₂²⋊D₁₃	—	4	1	no	—
415	C₂²⋊D₁₃	—	4	1	no	—
416	C₂²⋊D₁₃	—	4	1	no	—
417	C₂²⋊D₁₃	—	4	1	no	—
418	C₂²⋊D₁₃	—	4	1	no	—
419	C₂²⋊D₁₃	—	4	1	no	—
420	C₂²⋊D₁₃	—	4	1	no	—
421	C₂²⋊D₁₃	—	4	1	no	—
422	C₂²⋊D₁₃	—	4	1	no	—
423	C₂²⋊D₁₃	—	4	1	no	—
424	C₂²⋊D₁₃	—	4	1	no	—
425	C₂²⋊D₁₃	—	4	1	no	—
426	C₂²⋊D₁₃	—	4	1	no	—
427	C₂²⋊D₁₃	—	4	1	no	—
428	C₂²⋊D₁₃	—	4	1	no	—
429	C₂²⋊D₁₃	—	4	1	no	—
430	C₂²⋊D₁₃	—	4	1	no	—
431	C₂×Dic₁₃	—	2	2	no	—
432	C₂×Dic₁₃	—	4	1	no	—
433	C₂×Dic₁₃	—	4	1	no	—
434	C₂×Dic₁₃	—	4	1	no	—
435	C₂×Dic₁₃	—	4	1	no	—
436	C₂×Dic₁₃	—	4	1	no	—
437	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
440	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
441	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
442	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
443	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
444	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
445	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
446	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
447	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
448	D₅₂	—	2	2	no	—
449	D₅₂	—	2	2	no	—
450	D₅₂	—	4	1	no	—
451	D₅₂	—	4	1	no	—
452	D₅₂	—	4	1	no	—
453	D₅₂	—	4	1	no	—
454	C₄×D₁₃	—	2	2	no	—
455	C₄×D₁₃	—	4	1	no	—
456	C₄×D₁₃	—	4	1	no	—
457	C₄×D₁₃	—	4	1	no	—
458	C₄×D₁₃	—	4	1	no	—
459	C₄×D₁₃	—	4	1	no	—
460	C₄×D₁₃	—	4	1	no	—
461	C₄×D₁₃	—	4	1	no	—
462	C₄×D₁₃	—	4	1	no	—
463	C₄×D₁₃	—	4	1	no	—
464	C₄×D₁₃	—	4	1	no	—
465	Dic₂₆	—	4	1	no	—
466	Dic₂₆	—	4	1	no	—
467	#562	—	13	1	no	—
468	#562	—	13	1	no	—
469	#560	—	13	1	no	—
470	#560	—	13	1	no	—
471	#553	—	13	1	no	—
472	#553	—	13	1	no	—
473	#551	—	13	1	no	—
474	#551	—	13	1	no	—
475	#546	—	13	1	no	—
476	#546	—	13	1	no	—
477	#546	—	13	1	no	—
478	#546	—	13	1	no	—
479	#546	—	13	1	no	—
480	#546	D₁₃	1	1	yes	characteristic, complemented
481	D₄²	—	13	1	no	—
482	D₄²	—	13	1	no	—
483	#540	—	13	1	no	—
484	#540	—	13	1	no	—
485	#539	—	13	1	no	—
486	#539	—	13	1	no	—
487	#539	—	13	1	no	—
488	#538	—	13	1	no	—
489	#538	—	13	1	no	—
490	#538	—	13	1	no	—
491	#537	—	13	1	no	—
492	#534	—	13	1	no	—
493	#534	—	13	1	no	—
494	#534	—	13	1	no	—
495	#525	—	13	1	no	—
496	C₂×#123	—	13	1	no	—
497	C₂×#121	—	13	1	no	—
498	C₂²×C₁₃	—	2	1	no	—
499	C₂²×C₁₃	—	2	1	no	—
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	1	no	—
507	C₂²×C₁₃	—	2	1	no	—
508	C₂²×C₁₃	—	2	1	no	—
509	C₂²×C₁₃	—	2	1	no	—
510	C₂²×C₁₃	—	2	1	no	—
511	C₂²×C₁₃	—	2	1	no	—
512	C₂²×C₁₃	—	2	1	no	—
513	C₂²×C₁₃	—	2	1	no	—
514	C₂²×C₁₃	—	2	1	no	—
515	C₂²×C₁₃	—	8	2	no	—
516	C₂²×C₁₃	—	8	2	no	—
517	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
518	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
519	C₂×D₁₃	—	2	1	no	—
520	C₂×D₁₃	—	2	1	no	—
521	C₂×D₁₃	—	2	1	no	—
522	C₂×D₁₃	—	2	1	no	—
523	C₂×D₁₃	—	2	1	no	—
524	C₂×D₁₃	—	2	1	no	—
525	C₂×D₁₃	—	2	1	no	—
526	C₂×D₁₃	—	2	1	no	—
527	C₂×D₁₃	—	2	1	no	—
528	C₂×D₁₃	—	2	1	no	—
529	C₂×D₁₃	—	2	1	no	—
530	C₂×D₁₃	—	2	1	no	—
531	C₂×D₁₃	—	2	1	no	—
532	C₂×D₁₃	—	2	1	no	—
533	C₂×D₁₃	—	4	4	no	—
534	C₂×D₁₃	—	8	2	no	—
535	C₂×D₁₃	—	8	2	no	—
536	C₂×D₁₃	—	8	2	no	—
537	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
538	C₄×C₁₃	—	2	1	no	—
539	C₄×C₁₃	—	2	1	no	—
540	C₄×C₁₃	—	2	1	no	—
541	C₄×C₁₃	—	2	1	no	—
542	C₄×C₁₃	—	2	1	no	—
543	C₄×C₁₃	—	2	1	no	—
544	C₄×C₁₃	—	2	1	no	—
545	C₄×C₁₃	—	2	1	no	—
546	C₄×C₁₃	—	2	1	no	—
547	Dic₁₃	—	2	1	no	—
548	Dic₁₃	—	2	1	no	—
549	Dic₁₃	—	2	1	no	—
550	Dic₁₃	—	2	1	no	—
551	Dic₁₃	—	2	1	no	—
552	Dic₁₃	—	2	1	no	—
553	Dic₁₃	—	2	1	no	—
554	Dic₁₃	—	2	1	no	—
555	Dic₁₃	—	2	1	no	—
556	Dic₁₃	—	2	1	no	—
557	Dic₁₃	—	2	1	no	—
558	C₂×#41	—	13	1	no	—
559	C₂×#41	—	13	1	no	—
560	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
561	C₂²×D₄	—	13	1	no	—
562	C₂²×D₄	—	13	1	no	—
563	C₂²×D₄	—	13	1	no	—
564	C₂²×D₄	—	13	1	no	—
565	C₂²×D₄	—	13	1	no	—
566	C₂²×D₄	—	13	1	no	—
567	C₂²×D₄	—	13	1	no	—
568	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
569	C₂³×C₄	—	13	1	no	—
570	#127	—	13	1	no	—
571	#127	—	13	1	no	—
572	#126	—	13	1	no	—
573	#126	—	13	1	no	—
574	#126	—	13	1	no	—
575	#126	—	13	1	no	—
576	#126	—	13	1	no	—
577	#126	—	13	1	no	—
578	#126	—	13	1	no	—
579	#126	—	13	1	no	—
580	#125	—	13	1	no	—
581	#125	—	13	1	no	—
582	#125	—	13	1	no	—
583	#125	—	13	1	no	—
584	#124	—	13	1	no	—
585	#124	—	13	1	no	—
586	#124	—	13	1	no	—
587	#124	—	13	1	no	—
588	#124	—	13	1	no	—
589	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
590	#123	—	13	1	no	—
591	#123	—	13	1	no	—
592	#123	—	13	1	no	—
593	#123	—	13	1	no	—
594	#123	—	13	1	no	—
595	#123	—	13	1	no	—
596	#123	—	13	1	no	—
597	#123	—	13	1	no	—
598	#123	—	13	1	no	—
599	#123	—	13	1	no	—
600	#123	—	13	1	no	—
601	#123	—	13	1	no	—
602	#123	—	13	1	no	—
603	#123	—	13	1	no	—
604	#123	—	13	1	no	—
605	#123	—	13	1	no	—
606	#123	—	13	1	no	—
607	#123	—	13	1	no	—
608	#123	—	13	1	no	—
609	#123	—	13	1	no	—
610	#123	—	13	1	no	—
611	#123	—	13	1	no	—
612	#123	—	13	1	no	—
613	#123	—	13	1	no	—
614	#123	—	13	1	no	—
615	#123	—	13	1	no	—
616	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
617	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
618	C₂²⋊Q₈	—	13	1	no	—
619	C₂²⋊Q₈	—	13	1	no	—
620	C₂²⋊Q₈	—	13	1	no	—
621	C₂²⋊Q₈	—	13	1	no	—
622	C₂²⋊Q₈	—	13	1	no	—
623	C₂²⋊Q₈	—	13	1	no	—
624	C₂²⋊Q₈	—	13	1	no	—
625	C₂²⋊Q₈	—	13	1	no	—
626	C₂²⋊Q₈	—	13	1	no	—
627	C₂²⋊Q₈	—	13	1	no	—
628	C₂²⋊Q₈	—	13	1	no	—
629	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
630	#121	—	13	1	no	—
631	#121	—	13	1	no	—
632	#121	—	13	1	no	—
633	#121	—	13	1	no	—
634	#121	—	13	1	no	—
635	#121	—	13	1	no	—
636	#121	—	13	1	no	—
637	#121	—	13	1	no	—
638	#121	—	13	1	no	—
639	#121	—	13	1	no	—
640	#121	—	13	1	no	—
641	#121	—	13	1	no	—
642	#121	—	13	1	no	—
643	#121	—	13	1	no	—
644	#121	—	13	1	no	—
645	#121	—	13	1	no	—
646	#121	—	13	1	no	—
647	#121	—	13	1	no	—
648	#121	—	13	1	no	—
649	#121	—	13	1	no	—
650	#121	—	13	1	no	—
651	#121	—	13	1	no	—
652	#121	—	13	1	no	—
653	#121	—	13	1	no	—
654	#121	—	13	1	no	—
655	#121	—	13	1	no	—
656	#121	—	13	1	no	—
657	#121	—	13	1	no	—
658	#121	—	13	1	no	—
659	#121	—	13	1	no	—
660	#121	—	13	1	no	—
661	#121	—	13	1	no	—
662	#121	—	13	1	no	—
663	#121	C₂×D₁₃	1	1	yes	characteristic
664	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
665	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
666	#120	—	13	1	no	—
667	#120	—	13	1	no	—
668	#120	—	13	1	no	—
669	#120	—	13	1	no	—
670	#120	—	13	1	no	—
671	#120	—	13	1	no	—
672	#120	—	13	1	no	—
673	#120	—	13	1	no	—
674	#120	—	13	1	no	—
675	#120	—	13	1	no	—
676	#120	—	13	1	no	—
677	#120	—	13	1	no	—
678	#120	—	13	1	no	—
679	#120	—	13	1	no	—
680	#120	C₂×D₁₃	1	1	yes	characteristic, complemented
681	#120	C₂×D₁₃	1	1	yes	characteristic, complemented
682	C₄×D₄	—	13	1	no	—
683	C₄×D₄	—	13	1	no	—
684	C₄×D₄	—	13	1	no	—
685	C₄×D₄	—	13	1	no	—
686	C₄×D₄	—	13	1	no	—
687	C₄×D₄	—	13	1	no	—
688	C₄×D₄	—	13	1	no	—
689	C₄×D₄	—	13	1	no	—
690	C₄×D₄	—	13	1	no	—
691	C₄×D₄	—	13	1	no	—
692	C₄×D₄	—	13	1	no	—
693	C₄×D₄	—	13	1	no	—
694	C₄×D₄	—	13	1	no	—
695	C₄×D₄	—	13	1	no	—
696	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
697	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
698	#117	—	13	1	no	—
699	#117	—	13	1	no	—
700	#117	—	13	1	no	—
701	C₂×C₄⋊C₄	—	13	1	no	—
702	C₂×C₄⋊C₄	—	13	1	no	—
703	C₂×C₄⋊C₄	—	13	1	no	—
704	C₂×C₂²⋊C₄	—	13	1	no	—
705	C₂×C₂²⋊C₄	—	13	1	no	—
706	C₂×C₂²⋊C₄	—	13	1	no	—
707	C₂×C₂²⋊C₄	—	13	1	no	—
708	C₂×C₂²⋊C₄	—	13	1	no	—
709	C₂×C₂²⋊C₄	—	13	1	no	—
710	C₂×C₂²⋊C₄	—	13	1	no	—
711	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
712	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
713	C₂×C₁₃	—	2	2	no	—
714	C₂×C₁₃	—	4	1	no	—
715	C₂×C₁₃	—	4	1	no	—
716	C₂×C₁₃	—	4	1	no	—
717	C₂×C₁₃	—	4	1	no	—
718	C₂×C₁₃	—	4	1	no	—
719	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
720	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
721	C₂×C₁₃	#585	1	1	yes	characteristic
722	D₁₃	—	2	2	no	—
723	D₁₃	—	4	1	no	—
724	D₁₃	—	4	1	no	—
725	D₁₃	—	4	1	no	—
726	D₁₃	—	4	1	no	—
727	C₂⁴	—	13	1	no	—
728	C₂⁴	—	13	1	no	—
729	C₂⁴	—	13	1	no	—
730	C₂⁴	—	13	1	no	—
731	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
732	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
733	#41	—	4	2	no	—
734	#41	—	52	2	no	—
735	#41	—	52	2	no	—
736	C₂×Q₈	—	13	1	no	—
737	C₂×Q₈	—	13	1	no	—
738	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	13	1	no	—
741	C₂×D₄	—	13	1	no	—
742	C₂×D₄	—	13	1	no	—
743	C₂×D₄	—	13	1	no	—
744	C₂×D₄	—	13	1	no	—
745	C₂×D₄	—	13	1	no	—
746	C₂×D₄	—	13	1	no	—
747	C₂×D₄	—	13	1	no	—
748	C₂×D₄	—	13	1	no	—
749	C₂×D₄	—	13	1	no	—
750	C₂×D₄	—	13	1	no	—
751	C₂×D₄	—	13	1	no	—
752	C₂×D₄	—	13	1	no	—
753	C₂×D₄	—	13	1	no	—
754	C₂×D₄	—	13	1	no	—
755	C₂×D₄	—	13	1	no	—
756	C₂×D₄	—	13	1	no	—
757	C₂×D₄	—	13	1	no	—
758	C₂×D₄	—	13	1	no	—
759	C₂×D₄	—	13	1	no	—
760	C₂×D₄	—	13	1	no	—
761	C₂×D₄	—	13	1	no	—
762	C₂×D₄	—	13	1	no	—
763	C₂×D₄	—	13	1	no	—
764	C₂×D₄	—	13	1	no	—
765	C₂×D₄	—	13	1	no	—
766	C₂×D₄	—	13	1	no	—
767	C₂×D₄	—	13	1	no	—
768	C₂×D₄	—	52	2	no	—
769	C₂×D₄	—	52	2	no	—
770	C₂×D₄	—	52	2	no	—
771	C₂×D₄	—	52	2	no	—
772	C₂×D₄	—	52	2	no	—
773	C₂×D₄	—	52	2	no	—
774	C₂×D₄	—	52	2	no	—
775	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
776	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
777	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
778	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
779	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
780	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
781	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
782	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
783	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
784	C₂²×C₄	—	13	1	no	—
785	C₂²×C₄	—	13	1	no	—
786	C₂²×C₄	—	13	1	no	—
787	C₂²×C₄	—	13	1	no	—
788	C₂²×C₄	—	13	1	no	—
789	C₂²×C₄	—	13	1	no	—
790	C₂²×C₄	—	13	1	no	—
791	C₂²×C₄	—	13	1	no	—
792	C₂²×C₄	—	13	1	no	—
793	C₂²×C₄	—	13	1	no	—
794	C₂²×C₄	—	13	1	no	—
795	C₂²×C₄	—	13	1	no	—
796	C₂²×C₄	—	13	1	no	—
797	C₂²×C₄	—	13	1	no	—
798	C₂²×C₄	—	13	1	no	—
799	C₂²×C₄	—	13	1	no	—
800	C₂²×C₄	—	13	1	no	—
801	C₂²×C₄	—	52	2	no	—
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	C₄⋊C₄	—	13	1	no	—
809	C₄⋊C₄	—	13	1	no	—
810	C₄⋊C₄	—	13	1	no	—
811	C₄⋊C₄	—	13	1	no	—
812	C₄⋊C₄	—	13	1	no	—
813	C₄⋊C₄	—	13	1	no	—
814	C₄⋊C₄	—	13	1	no	—
815	C₄⋊C₄	—	13	1	no	—
816	C₄⋊C₄	—	13	1	no	—
817	C₄⋊C₄	—	13	1	no	—
818	C₄⋊C₄	—	13	1	no	—
819	C₄⋊C₄	—	13	1	no	—
820	C₄⋊C₄	—	13	1	no	—
821	C₄⋊C₄	—	13	1	no	—
822	C₄⋊C₄	—	13	1	no	—
823	C₄⋊C₄	—	13	1	no	—
824	C₄⋊C₄	—	13	1	no	—
825	C₄⋊C₄	—	13	1	no	—
826	C₄⋊C₄	—	13	1	no	—
827	C₄⋊C₄	—	13	1	no	—
828	C₄⋊C₄	—	13	1	no	—
829	C₄⋊C₄	—	13	1	no	—
830	C₄⋊C₄	—	13	1	no	—
831	C₄⋊C₄	—	13	1	no	—
832	C₄⋊C₄	—	13	1	no	—
833	C₄⋊C₄	—	13	1	no	—
834	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
835	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
838	C₂²⋊C₄	—	13	1	no	—
839	C₂²⋊C₄	—	13	1	no	—
840	C₂²⋊C₄	—	13	1	no	—
841	C₂²⋊C₄	—	13	1	no	—
842	C₂²⋊C₄	—	13	1	no	—
843	C₂²⋊C₄	—	13	1	no	—
844	C₂²⋊C₄	—	13	1	no	—
845	C₂²⋊C₄	—	13	1	no	—
846	C₂²⋊C₄	—	13	1	no	—
847	C₂²⋊C₄	—	13	1	no	—
848	C₂²⋊C₄	—	13	1	no	—
849	C₂²⋊C₄	—	13	1	no	—
850	C₂²⋊C₄	—	13	1	no	—
851	C₂²⋊C₄	—	13	1	no	—
852	C₂²⋊C₄	—	13	1	no	—
853	C₂²⋊C₄	—	13	1	no	—
854	C₂²⋊C₄	—	13	1	no	—
855	C₂²⋊C₄	—	13	1	no	—
856	C₂²⋊C₄	—	13	1	no	—
857	C₂²⋊C₄	—	13	1	no	—
858	C₂²⋊C₄	—	13	1	no	—
859	C₂²⋊C₄	—	13	1	no	—
860	C₂²⋊C₄	—	13	1	no	—
861	C₂²⋊C₄	—	13	1	no	—
862	C₂²⋊C₄	—	13	1	no	—
863	C₂²⋊C₄	—	13	1	no	—
864	C₂²⋊C₄	—	13	1	no	—
865	C₂²⋊C₄	—	13	1	no	—
866	C₂²⋊C₄	—	13	1	no	—
867	C₂²⋊C₄	—	13	1	no	—
868	C₂²⋊C₄	—	13	1	no	—
869	C₂²⋊C₄	—	13	1	no	—
870	C₂²⋊C₄	—	13	1	no	—
871	C₂²⋊C₄	—	13	1	no	—
872	C₂²⋊C₄	—	13	1	no	—
873	C₂²⋊C₄	—	13	1	no	—
874	C₂²⋊C₄	—	13	1	no	—
875	C₂²⋊C₄	—	13	1	no	—
876	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
877	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
878	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
879	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
880	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
881	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
882	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
883	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
884	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
885	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
886	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
887	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
888	C₄²	—	13	1	no	—
889	C₄²	—	13	1	no	—
890	C₄²	—	13	1	no	—
891	C₄²	—	13	1	no	—
892	C₄²	—	13	1	no	—
893	C₄²	C₂²×D₁₃	1	1	yes	characteristic
894	C₁₃	#3534	1	1	yes	characteristic, complemented, Sylow
895	C₂³	—	2	2	no	—
896	C₂³	—	4	1	no	—
897	C₂³	—	4	1	no	—
898	C₂³	—	4	1	no	—
899	C₂³	—	4	1	no	—
900	C₂³	—	4	1	no	—
901	C₂³	—	13	1	no	—
902	C₂³	—	13	1	no	—
903	C₂³	—	13	1	no	—
904	C₂³	—	13	1	no	—
905	C₂³	—	13	1	no	—
906	C₂³	—	26	2	no	—
907	C₂³	—	26	2	no	—
908	C₂³	—	26	2	no	—
909	C₂³	—	26	2	no	—
910	C₂³	—	52	1	no	—
911	C₂³	—	52	1	no	—
912	C₂³	—	52	1	no	—
913	C₂³	—	52	1	no	—
914	C₂³	—	52	1	no	—
915	C₂³	—	52	1	no	—
916	C₂³	—	52	1	no	—
917	C₂³	—	52	1	no	—
918	C₂³	C₂³×D₁₃	1	1	yes	characteristic
919	C₂³	C₂³×D₁₃	1	1	yes	characteristic
920	C₂³	C₂³×D₁₃	1	1	yes	characteristic
921	C₂³	C₂³×D₁₃	1	1	yes	characteristic
922	C₂³	C₂³×D₁₃	1	1	yes	characteristic
923	C₂³	C₂³×D₁₃	1	1	yes	characteristic
924	Q₈	—	4	1	no	—
925	Q₈	—	52	1	no	—
926	Q₈	—	52	1	no	—
927	D₄	—	2	2	no	—
928	D₄	—	2	2	no	—
929	D₄	—	2	2	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	1	no	—
936	D₄	—	26	2	no	—
937	D₄	—	26	2	no	—
938	D₄	—	26	2	no	—
939	D₄	—	26	2	no	—
940	D₄	—	26	2	no	—
941	D₄	—	26	2	no	—
942	D₄	—	26	2	no	—
943	D₄	—	52	1	no	—
944	D₄	—	52	1	no	—
945	D₄	—	52	1	no	—
946	D₄	—	52	1	no	—
947	D₄	—	52	1	no	—
948	D₄	—	52	1	no	—
949	D₄	—	52	1	no	—
950	D₄	—	52	1	no	—
951	D₄	—	52	1	no	—
952	D₄	—	52	1	no	—
953	D₄	—	52	1	no	—
954	D₄	—	52	1	no	—
955	D₄	—	52	1	no	—
956	D₄	—	52	1	no	—
957	D₄	—	52	1	no	—
958	D₄	—	52	1	no	—
959	D₄	—	52	1	no	—
960	D₄	—	52	1	no	—
961	D₄	—	52	1	no	—
962	D₄	—	52	1	no	—
963	D₄	—	52	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	13	1	no	—
971	C₂×C₄	—	13	1	no	—
972	C₂×C₄	—	13	1	no	—
973	C₂×C₄	—	13	1	no	—
974	C₂×C₄	—	13	1	no	—
975	C₂×C₄	—	13	1	no	—
976	C₂×C₄	—	13	1	no	—
977	C₂×C₄	—	13	1	no	—
978	C₂×C₄	—	13	1	no	—
979	C₂×C₄	—	13	1	no	—
980	C₂×C₄	—	13	1	no	—
981	C₂×C₄	—	26	2	no	—
982	C₂×C₄	—	26	2	no	—
983	C₂×C₄	—	52	1	no	—
984	C₂×C₄	—	52	1	no	—
985	C₂×C₄	—	52	1	no	—
986	C₂×C₄	—	52	1	no	—
987	C₂×C₄	—	52	1	no	—
988	C₂×C₄	—	52	1	no	—
989	C₂×C₄	—	52	1	no	—
990	C₂×C₄	—	52	1	no	—
991	C₂×C₄	—	52	1	no	—
992	C₂×C₄	—	52	1	no	—
993	C₂×C₄	—	52	1	no	—
994	C₂×C₄	—	52	1	no	—
995	C₂×C₄	—	52	1	no	—
996	C₂×C₄	—	52	1	no	—
997	C₂×C₄	—	52	1	no	—
998	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
999	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
1004	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
1005	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
1006	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	2	1	no	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	8	2	no	—
1025	C₂²	—	8	2	no	—
1026	C₂²	—	13	2	no	—
1027	C₂²	—	26	1	no	—
1028	C₂²	—	26	1	no	—
1029	C₂²	—	26	1	no	—
1030	C₂²	—	26	1	no	—
1031	C₂²	—	26	1	no	—
1032	C₂²	—	26	1	no	—
1033	C₂²	—	26	1	no	—
1034	C₂²	—	26	1	no	—
1035	C₂²	—	26	1	no	—
1036	C₂²	—	26	1	no	—
1037	C₂²	—	26	1	no	—
1038	C₂²	—	26	1	no	—
1039	C₂²	—	26	1	no	—
1040	C₂²	—	26	1	no	—
1041	C₂²	—	52	4	no	—
1042	C₂²	—	104	2	no	—
1043	C₂²	—	104	2	no	—
1044	C₂²	—	104	2	no	—
1045	C₂²	#88251	1	2	yes	—
1046	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	26	1	no	—
1057	C₄	—	26	1	no	—
1058	C₄	—	26	1	no	—
1059	C₄	—	26	1	no	—
1060	C₄	—	26	1	no	—
1061	C₄	—	26	1	no	—
1062	C₄	—	26	1	no	—
1063	C₄	—	26	1	no	—
1064	C₄	—	26	1	no	—
1065	C₄	—	26	1	no	—
1066	C₄	—	26	1	no	—
1067	C₂	—	2	2	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	4	1	no	—
1072	C₂	—	4	1	no	—
1073	C₂	—	26	2	no	—
1074	C₂	—	52	1	no	—
1075	C₂	—	52	1	no	—
1076	C₂	—	52	1	no	—
1077	C₂	—	52	1	no	—
1078	C₂	C₂×#88251	1	1	yes	characteristic
1079	C₂	#11719648	1	1	yes	characteristic
1080	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#546	C₂
hypercenter	#546	D₁₃
hypocenter	C₁₃	#3534
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₁₃×#546	C₂	semidirect
2. #11719534	C₂	semidirect
3. #11719533	C₂	semidirect
4. #11719509	C₂	semidirect
5. D₄×C₂²⋊D₁₃	C₂	semidirect
6. #11719389	C₂	semidirect
7. #11719383	C₂	semidirect
8. #11719368	C₂	semidirect
9. #11719366	C₂	semidirect
10. #11719363	C₂	semidirect
11. D₁₃×#123	C₂	semidirect
12. #11719352	C₂	semidirect
13. #11719343	C₂	semidirect
14. #11719325	C₂	semidirect
15. #11719320	C₂	semidirect
16. #11719315	C₂	semidirect
17. #11719314	C₂	semidirect
18. #11719313	C₂	semidirect
19. #11719307	C₂	semidirect
20. #11719300	C₂	semidirect
21. #11719296	C₂	semidirect
22. #11719294	C₂	semidirect
23. #11719294	C₂	semidirect
24. #11719269	C₂	semidirect
25. #11719265	C₂	semidirect
26. #11719263	C₂	semidirect
27. #11719255	C₂	semidirect
28. #11719200	C₂	semidirect
29. #11719199	C₂	semidirect
30. #11719195	C₂	semidirect
31. C₂×#88138	C₂	semidirect
32. C₂×C₁₃×#41	C₂²	semidirect
33. C₂²×D₄×C₁₃	C₂²	semidirect
34. C₂²×C₂²⋊D₁₃	C₂²	semidirect
35. C₂²×C₂²⋊D₁₃	C₂²	semidirect
36. C₂²×C₂²⋊D₁₃	C₂²	semidirect
37. C₂×#6129	C₂²	semidirect
39. C₂×D₄×D₁₃	C₂²	semidirect
40. C₂×D₄×D₁₃	C₂²	semidirect
41. C₂×#6127	C₂²	semidirect
42. C₂²×D₅₂	C₂²	semidirect
43. C₂²×C₄×D₁₃	C₂²	semidirect
44. C₁₃×#124	C₂²	semidirect
45. C₁₃×#123	C₂²	semidirect
46. C₁₃×#123	C₂²	semidirect
47. C₁₃×C₂²⋊Q₈	C₂²	semidirect
49. C₁₃×#121	C₂²	semidirect
50. C₁₃×#121	C₂²	semidirect
51. C₁₃×#120	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×C₁₃×C₂²⋊C₄	C₂²	semidirect
58. #88207	C₂²	semidirect
59. #88207	C₂²	semidirect
60. #88207	C₂²	semidirect
61. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
62. #88201	C₂²	semidirect
63. #88200	C₂²	semidirect
64. #88200	C₂²	semidirect
65. #88200	C₂²	semidirect
66. #88194	C₂²	semidirect
67. #88194	C₂²	semidirect
69. #88193	C₂²	semidirect
70. #88193	C₂²	semidirect
71. #88193	C₂²	semidirect
72. #88193	C₂²	semidirect
73. #88193	C₂²	semidirect
74. #88193	C₂²	semidirect
75. #88193	C₂²	semidirect
76. #88193	C₂²	semidirect
77. #88192	C₂²	semidirect
78. #88192	C₂²	semidirect
79. #88192	C₂²	semidirect
80. #88192	C₂²	semidirect
81. #88192	C₂²	semidirect
82. #88192	C₂²	semidirect
84. #88191	C₂²	semidirect
85. #88191	C₂²	semidirect
86. #88191	C₂²	semidirect
87. #88191	C₂²	semidirect
88. #88191	C₂²	semidirect
89. #88191	C₂²	semidirect
90. #88191	C₂²	semidirect
91. #88189	C₂²	semidirect
92. #88189	C₂²	semidirect
93. #88189	C₂²	semidirect
94. #88189	C₂²	semidirect
95. #88189	C₂²	semidirect
96. D₄×Dic₁₃	C₂²	semidirect
97. D₄×Dic₁₃	C₂²	semidirect
98. #88184	C₂²	semidirect
99. #88184	C₂²	semidirect
100. #88184	C₂²	semidirect
101. #88183	C₂²	semidirect
102. #88183	C₂²	semidirect
103. #88183	C₂²	semidirect
104. #88183	C₂²	semidirect
105. #88183	C₂²	semidirect
106. C₄×C₂²⋊D₁₃	C₂²	semidirect
107. C₄×C₂²⋊D₁₃	C₂²	semidirect
108. C₄×C₂²⋊D₁₃	C₂²	semidirect
109. C₄×C₂²⋊D₁₃	C₂²	semidirect
110. C₄×C₂²⋊D₁₃	C₂²	semidirect
111. C₄×C₂²⋊D₁₃	C₂²	semidirect
112. C₄×C₂²⋊D₁₃	C₂²	semidirect
113. C₂×#6103	C₂²	semidirect
114. C₂×#6103	C₂²	semidirect
115. #88180	C₂²	semidirect
116. #88178	C₂²	semidirect
117. #88178	C₂²	semidirect
118. C₂×#6101	C₂²	semidirect
119. #88152	C₂²	semidirect
120. #88152	C₂²	semidirect
121. #88151	C₂²	semidirect
122. #88150	C₂²	semidirect
123. #88149	C₂²	semidirect
124. #88148	C₂²	semidirect
125. #88148	C₂²	semidirect
126. #88148	C₂²	semidirect
127. #88148	C₂²	semidirect
128. #88147	C₂²	semidirect
129. #88146	C₂²	semidirect
130. C₄⋊C₄×D₁₃	C₂²	semidirect
131. C₄⋊C₄×D₁₃	C₂²	semidirect
132. #88143	C₂²	semidirect
133. #88143	C₂²	semidirect
134. #88143	C₂²	semidirect
135. #88140	C₂²	semidirect
136. #88140	C₂²	semidirect
137. #88140	C₂²	semidirect
138. #88140	C₂²	semidirect
139. #88139	C₂²	semidirect
140. #88139	C₂²	semidirect
141. #88139	C₂²	semidirect
143. #88138	C₂²	semidirect
144. #88138	C₂²	semidirect
145. #88138	C₂²	semidirect
146. #88138	C₂²	semidirect
147. #88138	C₂²	semidirect
148. #88138	C₂²	semidirect
149. #88138	C₂²	semidirect
150. #88138	C₂²	semidirect
151. #88138	C₂²	semidirect
152. #88138	C₂²	semidirect
153. #88138	C₂²	semidirect
154. #88138	C₂²	semidirect
155. #88138	C₂²	semidirect
156. #88137	C₂²	semidirect
157. #88137	C₂²	semidirect
158. #88137	C₂²	semidirect
159. #88137	C₂²	semidirect
160. #88137	C₂²	semidirect
161. #88137	C₂²	semidirect
162. #88137	C₂²	semidirect
163. #88137	C₂²	semidirect
164. #88136	C₂²	semidirect
165. #88136	C₂²	semidirect
166. #88135	C₂²	semidirect
167. #88135	C₂²	semidirect
168. #88135	C₂²	semidirect
169. C₂²⋊C₄×D₁₃	C₂²	semidirect
170. C₂²⋊C₄×D₁₃	C₂²	semidirect
171. C₂²⋊C₄×D₁₃	C₂²	semidirect
172. C₂²⋊C₄×D₁₃	C₂²	semidirect
173. #88133	C₂²	semidirect
174. #88133	C₂²	semidirect
175. #88133	C₂²	semidirect
176. #88133	C₂²	semidirect
177. #88133	C₂²	semidirect
178. #88132	C₂²	semidirect
179. #88132	C₂²	semidirect
180. #88132	C₂²	semidirect
181. #88132	C₂²	semidirect
182. #88131	C₂²	semidirect
183. #88130	C₂²	semidirect
184. #88129	C₂²	semidirect
185. C₄×D₅₂	C₂²	semidirect
186. #88124	C₂²	semidirect
480. #546	D₁₃	semidirect
560. C₂×#41	C₂×D₁₃	semidirect
568. C₂²×D₄	C₂×D₁₃	semidirect
589. #124	C₂×D₁₃	semidirect
616. #123	C₂×D₁₃	semidirect
617. #123	C₂×D₁₃	semidirect
629. C₂²⋊Q₈	C₂×D₁₃	semidirect
664. #121	C₂×D₁₃	semidirect
665. #121	C₂×D₁₃	semidirect
680. #120	C₂×D₁₃	semidirect
681. #120	C₂×D₁₃	semidirect
696. C₄×D₄	C₂×D₁₃	semidirect
697. C₄×D₄	C₂×D₁₃	semidirect
711. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
712. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
894. C₁₃	#3534	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#546	2
#11719534	2
#11719533	2
#11719509	2
D₄×C₂²⋊D₁₃	2
#11719389	2
#11719383	2
#11719368	2
#11719366	2
#11719363	2
D₁₃×#123	2
#11719352	2
#11719343	2
#11719325	2
#11719320	2
#11719315	2
#11719314	2
#11719313	2
#11719307	2
#11719300	2
#11719296	2
#11719294	2
#11719269	2
#11719265	2
#11719263	2
#11719255	2
#11719200	2
#11719199	2
#11719195	2
C₂×#88138	2
#3534	13