Subgroups — #13128767

Order 1664.

1152 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×#553	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	#11719411	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719410	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719398	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719397	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719369	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719362	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719360	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719322	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719320	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719315	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719315	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	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719307	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719261	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719261	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719255	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
24	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
25	#11719250	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
27	#11719245	C₂	1	1	yes	maximal, characteristic, complemented
28	#11719233	C₂	1	1	yes	maximal, characteristic, complemented
29	#11719232	C₂	1	1	yes	maximal, characteristic, complemented
30	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#88148	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#6129	C₂²	1	1	yes	characteristic
33	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
37	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₅₂	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#121	C₂²	1	1	yes	characteristic
47	C₁₃×#121	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	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	#88194	C₂²	1	1	yes	characteristic
57	#88193	C₂²	1	1	yes	characteristic, complemented
58	#88193	C₂²	1	1	yes	characteristic, complemented
59	#88193	C₂²	1	1	yes	characteristic, complemented
60	#88193	C₂²	1	1	yes	characteristic, complemented
61	#88192	C₂²	1	1	yes	characteristic, complemented
62	#88191	C₂²	1	1	yes	characteristic
63	#88191	C₂²	1	1	yes	characteristic
64	#88191	C₂²	1	1	yes	characteristic, complemented
65	#88191	C₂²	1	1	yes	characteristic, complemented
66	#88191	C₂²	1	1	yes	characteristic, complemented
67	#88191	C₂²	1	1	yes	characteristic, complemented
68	#88189	C₂²	1	1	yes	characteristic, complemented
69	#88189	C₂²	1	1	yes	characteristic, complemented
70	#88189	C₂²	1	1	yes	characteristic, complemented
71	#88189	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
73	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
74	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
75	#88184	C₂²	1	1	yes	characteristic, complemented
76	#88183	C₂²	1	1	yes	characteristic, complemented
77	#88183	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
86	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
87	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
88	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
89	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
90	#88178	C₂²	1	1	yes	characteristic, complemented
91	#88178	C₂²	1	1	yes	characteristic, complemented
92	#88178	C₂²	1	1	yes	characteristic, complemented
93	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
94	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
95	#88152	C₂²	1	1	yes	characteristic, complemented
96	#88152	C₂²	1	1	yes	characteristic, complemented
97	#88152	C₂²	1	1	yes	characteristic, complemented
98	#88152	C₂²	1	1	yes	characteristic, complemented
99	#88151	C₂²	1	1	yes	characteristic, complemented
100	#88151	C₂²	1	1	yes	characteristic, complemented
101	#88150	C₂²	1	1	yes	characteristic, complemented
102	#88150	C₂²	1	1	yes	characteristic, complemented
103	#88150	C₂²	1	1	yes	characteristic, complemented
104	#88150	C₂²	1	1	yes	characteristic, complemented
105	#88150	C₂²	1	1	yes	characteristic, complemented
106	#88150	C₂²	1	1	yes	characteristic, complemented
107	#88149	C₂²	1	1	yes	characteristic
108	#88148	C₂²	1	1	yes	characteristic
109	#88148	C₂²	1	1	yes	characteristic
110	#88148	C₂²	1	1	yes	characteristic
111	#88148	C₂²	1	1	yes	characteristic, complemented
112	#88148	C₂²	1	1	yes	characteristic, complemented
113	#88148	C₂²	1	1	yes	characteristic, complemented
114	#88148	C₂²	1	1	yes	characteristic, complemented
115	#88148	C₂²	1	1	yes	characteristic, complemented
116	#88148	C₂²	1	1	yes	characteristic, complemented
117	#88148	C₂²	1	1	yes	characteristic, complemented
118	#88148	C₂²	1	1	yes	characteristic, complemented
119	#88148	C₂²	1	1	yes	characteristic, complemented
120	#88147	C₂²	1	1	yes	characteristic
121	#88147	C₂²	1	1	yes	characteristic, complemented
122	#88147	C₂²	1	1	yes	characteristic, complemented
123	#88146	C₂²	1	1	yes	characteristic, complemented
124	#88146	C₂²	1	1	yes	characteristic, complemented
125	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
126	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
127	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
128	#88143	C₂²	1	1	yes	characteristic, complemented
129	#88143	C₂²	1	1	yes	characteristic, complemented
130	#88143	C₂²	1	1	yes	characteristic, complemented
131	#88143	C₂²	1	1	yes	characteristic, complemented
132	#88142	C₂²	1	1	yes	characteristic, complemented
133	#88141	C₂²	1	1	yes	characteristic, complemented
134	#88141	C₂²	1	1	yes	characteristic, complemented
135	#88140	C₂²	1	1	yes	characteristic, complemented
136	#88140	C₂²	1	1	yes	characteristic, complemented
137	#88139	C₂²	1	1	yes	characteristic, complemented
138	#88139	C₂²	1	1	yes	characteristic, complemented
139	#88139	C₂²	1	1	yes	characteristic, complemented
140	#88139	C₂²	1	1	yes	characteristic, complemented
141	#88139	C₂²	1	1	yes	characteristic, complemented
142	#88139	C₂²	1	1	yes	characteristic, complemented
143	#88138	C₂²	1	1	yes	characteristic
144	#88138	C₂²	1	1	yes	characteristic
145	#88138	C₂²	1	1	yes	characteristic
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	#88137	C₂²	1	1	yes	characteristic, complemented
150	#88137	C₂²	1	1	yes	characteristic, complemented
151	#88137	C₂²	1	1	yes	characteristic, complemented
152	#88137	C₂²	1	1	yes	characteristic, complemented
153	#88136	C₂²	1	1	yes	characteristic
154	#88136	C₂²	1	1	yes	characteristic
155	#88135	C₂²	1	1	yes	characteristic
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	#88135	C₂²	1	1	yes	characteristic, complemented
160	#88135	C₂²	1	1	yes	characteristic, complemented
161	#88135	C₂²	1	1	yes	characteristic, complemented
162	#88135	C₂²	1	1	yes	characteristic, complemented
163	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
164	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
165	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
166	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
169	#88133	C₂²	1	1	yes	characteristic, complemented
170	#88133	C₂²	1	1	yes	characteristic, complemented
171	#88132	C₂²	1	1	yes	characteristic, complemented
172	#88132	C₂²	1	1	yes	characteristic, complemented
173	#88131	C₂²	1	1	yes	characteristic, complemented
174	#88131	C₂²	1	1	yes	characteristic, complemented
175	#88130	C₂²	1	1	yes	characteristic, complemented
176	#88130	C₂²	1	1	yes	characteristic, complemented
177	#88129	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
181	#88126	C₂²	1	1	yes	characteristic, complemented
182	#88126	C₂²	1	1	yes	characteristic, complemented
183	#88126	C₂²	1	1	yes	characteristic, complemented
184	#88126	C₂²	1	1	yes	characteristic, complemented
185	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₃	C₂³	1	1	yes	characteristic
188	C₂³×D₁₃	C₂³	1	1	yes	characteristic
189	C₂³×D₁₃	C₂³	1	1	yes	characteristic
190	C₂³×D₁₃	C₂³	1	1	yes	characteristic
191	C₂×D₄×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	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
215	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
216	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
217	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
218	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
219	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
220	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
221	#6129	—	2	4	no	—
222	#6129	—	4	2	no	—
223	D₄×D₁₃	—	2	4	no	—
224	D₄×D₁₃	—	2	4	no	—
225	D₄×D₁₃	—	4	2	no	—
226	#6127	—	4	2	no	—
227	C₂×D₅₂	—	4	2	no	—
228	C₂×D₅₂	C₂³	1	1	yes	characteristic
229	C₂×D₅₂	C₂³	1	1	yes	characteristic
230	C₂×D₅₂	C₂³	1	1	yes	characteristic
231	C₂×D₅₂	C₂³	1	1	yes	characteristic
232	C₂×D₅₂	C₂³	1	1	yes	characteristic
233	C₂×D₅₂	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₁₃	—	4	2	no	—
235	C₂×C₄×D₁₃	—	4	2	no	—
236	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
251	C₂×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×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₁₃×C₄⋊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	C₄²×C₁₃	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	#6103	C₂³	1	1	yes	characteristic
289	#6103	C₂³	1	1	yes	characteristic
290	#6103	C₂³	1	1	yes	characteristic
291	#6103	C₂³	1	1	yes	characteristic
292	#6103	C₂³	1	1	yes	characteristic
293	#6103	C₂³	1	1	yes	characteristic
294	#6103	C₂³	1	1	yes	characteristic
295	#6103	C₂³	1	1	yes	characteristic
296	#6103	C₂³	1	1	yes	characteristic
297	#6103	C₂³	1	1	yes	characteristic
298	#6103	C₂³	1	1	yes	characteristic
299	#6103	C₂³	1	1	yes	characteristic
300	#6103	C₂³	1	1	yes	characteristic
301	#6103	C₂³	1	1	yes	characteristic
302	#6103	C₂³	1	1	yes	characteristic
303	#6103	C₂³	1	1	yes	characteristic
304	#6103	C₂³	1	1	yes	characteristic
305	#6103	C₂³	1	1	yes	characteristic
306	#6103	C₂³	1	1	yes	characteristic
307	#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	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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
322	#6101	C₂³	1	1	yes	characteristic
323	#6101	C₂³	1	1	yes	characteristic
324	#6101	C₂³	1	1	yes	characteristic
325	#6101	C₂³	1	1	yes	characteristic
326	#6101	C₂³	1	1	yes	characteristic
327	#6101	C₂³	1	1	yes	characteristic
328	#6101	C₂³	1	1	yes	characteristic
329	#6101	C₂³	1	1	yes	characteristic
330	#6101	C₂³	1	1	yes	characteristic
331	#6101	C₂³	1	1	yes	characteristic
332	#6101	C₂³	1	1	yes	characteristic
333	#6101	C₂³	1	1	yes	characteristic
334	#6101	C₂³	1	1	yes	characteristic
335	#6101	C₂³	1	1	yes	characteristic
336	#6101	C₂³	1	1	yes	characteristic
337	#6101	C₂³	1	1	yes	characteristic
338	#6101	C₂³	1	1	yes	characteristic
339	#6101	C₂³	1	1	yes	characteristic
340	#6101	C₂³	1	1	yes	characteristic
341	#6101	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	#3513	—	13	1	no	maximal, Sylow
352	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂²×D₁₃	—	2	2	no	—
357	C₂²×D₁₃	—	2	2	no	—
358	C₂²×D₁₃	—	2	2	no	—
359	C₂²×D₁₃	—	2	2	no	—
360	C₂²×D₁₃	—	2	2	no	—
361	C₂²×D₁₃	—	2	2	no	—
362	C₂²×D₁₃	—	4	1	no	—
363	C₂²×D₁₃	—	4	1	no	—
364	C₂²×D₁₃	—	4	1	no	—
365	C₂²×D₁₃	—	4	1	no	—
366	C₂²×D₁₃	—	4	1	no	—
367	C₂²×D₁₃	—	4	1	no	—
368	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
369	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
370	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
371	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
372	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
373	D₄×C₁₃	—	2	2	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	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
396	C₂²⋊D₁₃	—	2	2	no	—
397	C₂²⋊D₁₃	—	2	2	no	—
398	C₂²⋊D₁₃	—	2	2	no	—
399	C₂²⋊D₁₃	—	2	2	no	—
400	C₂²⋊D₁₃	—	2	2	no	—
401	C₂²⋊D₁₃	—	4	1	no	—
402	C₂²⋊D₁₃	—	4	1	no	—
403	C₂²⋊D₁₃	—	4	1	no	—
404	C₂²⋊D₁₃	—	4	1	no	—
405	C₂²⋊D₁₃	—	4	1	no	—
406	C₂²⋊D₁₃	—	4	1	no	—
407	C₂²⋊D₁₃	#41	1	4	yes	complemented
408	C₂×Dic₁₃	—	2	2	no	—
409	C₂×Dic₁₃	—	2	2	no	—
410	C₂×Dic₁₃	—	4	1	no	—
411	C₂×Dic₁₃	—	4	1	no	—
412	C₂×Dic₁₃	—	4	1	no	—
413	C₂×Dic₁₃	—	4	1	no	—
414	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
417	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
419	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
421	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
424	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
425	D₅₂	—	2	2	no	—
426	D₅₂	—	2	2	no	—
427	D₅₂	—	2	2	no	—
428	D₅₂	—	2	2	no	—
429	D₅₂	—	4	1	no	—
430	D₅₂	—	4	1	no	—
431	C₄×D₁₃	—	2	2	no	—
432	C₄×D₁₃	—	2	2	no	—
433	C₄×D₁₃	—	2	2	no	—
434	C₄×D₁₃	—	2	2	no	—
435	C₄×D₁₃	—	2	2	no	—
436	C₄×D₁₃	—	2	2	no	—
437	C₄×D₁₃	—	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	C₄×D₁₃	—	4	1	no	—
444	C₄×D₁₃	—	4	1	no	—
445	C₄×D₁₃	—	4	1	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	#554	—	13	1	no	—
452	#553	—	13	1	no	—
453	#553	—	13	1	no	—
454	#553	D₁₃	1	1	yes	characteristic, complemented
455	#552	—	13	1	no	—
456	#551	—	13	1	no	—
457	#551	—	13	1	no	—
458	#551	—	13	1	no	—
459	#551	—	13	1	no	—
460	#547	—	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	#540	—	13	1	no	—
468	#539	—	13	1	no	—
469	#539	—	13	1	no	—
470	#538	—	13	1	no	—
471	#538	—	13	1	no	—
472	#529	—	13	1	no	—
473	#529	—	13	1	no	—
474	#525	—	13	1	no	—
475	#525	—	13	1	no	—
476	C₂×#123	—	13	1	no	—
477	C₂×#123	—	13	1	no	—
478	#520	—	13	1	no	—
479	#518	—	13	1	no	—
480	C₂×C₄×D₄	—	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	C₂×#41	1	2	yes	—
493	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
494	C₂×D₁₃	—	2	1	no	—
495	C₂×D₁₃	—	2	1	no	—
496	C₂×D₁₃	—	2	1	no	—
497	C₂×D₁₃	—	2	1	no	—
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	—	4	4	no	—
508	C₂×D₁₃	—	4	4	no	—
509	C₂×D₁₃	—	8	2	no	—
510	C₂×D₁₃	—	8	2	no	—
511	C₂×D₁₃	C₂×#41	1	2	yes	—
512	C₂×D₁₃	H(5,𝔽₂)	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	C₄×C₁₃	—	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	—	2	1	no	—
534	Dic₁₃	C₂×#41	1	2	yes	—
535	C₂×#41	—	13	1	no	—
536	C₂×#41	—	13	1	no	—
537	C₂×#41	—	13	1	no	—
538	C₂²×D₄	—	13	1	no	—
539	C₂²×D₄	—	13	1	no	—
540	C₂²×D₄	—	13	1	no	—
541	C₂²×D₄	—	13	1	no	—
542	C₂³×C₄	—	13	1	no	—
543	C₂³×C₄	—	13	1	no	—
544	C₄⋊Q₈	—	13	1	no	—
545	#127	—	13	1	no	—
546	#126	—	13	1	no	—
547	#126	—	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	C₂×D₁₃	1	1	yes	characteristic, complemented
555	#126	C₂×D₁₃	1	1	yes	characteristic, complemented
556	#125	—	13	1	no	—
557	#125	—	13	1	no	—
558	#125	—	13	1	no	—
559	#125	—	13	1	no	—
560	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
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	#123	—	13	1	no	—
569	#123	—	13	1	no	—
570	#123	—	13	1	no	—
571	#123	—	13	1	no	—
572	#123	—	13	1	no	—
573	#123	—	13	1	no	—
574	#123	—	13	1	no	—
575	#123	—	13	1	no	—
576	#123	—	13	1	no	—
577	#123	—	13	1	no	—
578	#123	—	13	1	no	—
579	#123	—	13	1	no	—
580	#123	—	13	1	no	—
581	#123	—	13	1	no	—
582	#123	—	13	1	no	—
583	#123	—	13	1	no	—
584	#123	—	13	1	no	—
585	#123	—	13	1	no	—
586	#123	—	13	1	no	—
587	#123	—	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	—	13	1	no	—
607	#121	—	13	1	no	—
608	#121	—	13	1	no	—
609	#121	—	13	1	no	—
610	#121	—	13	1	no	—
611	#121	—	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	C₂×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
631	#120	—	13	1	no	—
632	C₄×Q₈	—	13	1	no	—
633	C₄×Q₈	—	13	1	no	—
634	C₄×Q₈	—	13	1	no	—
635	C₄×D₄	—	13	1	no	—
636	C₄×D₄	—	13	1	no	—
637	C₄×D₄	—	13	1	no	—
638	C₄×D₄	—	13	1	no	—
639	C₄×D₄	—	13	1	no	—
640	C₄×D₄	—	13	1	no	—
641	C₄×D₄	—	13	1	no	—
642	C₄×D₄	—	13	1	no	—
643	C₄×D₄	—	13	1	no	—
644	C₄×D₄	—	13	1	no	—
645	C₄×D₄	—	13	1	no	—
646	C₄×D₄	—	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	C₂×D₁₃	1	1	yes	characteristic, complemented
661	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
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	C₂×D₁₃	1	1	yes	characteristic, complemented
673	C₂×C₄⋊C₄	—	13	1	no	—
674	C₂×C₄⋊C₄	—	13	1	no	—
675	C₂×C₄⋊C₄	—	13	1	no	—
676	C₂×C₄⋊C₄	—	13	1	no	—
677	C₂×C₄⋊C₄	—	13	1	no	—
678	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
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	—	13	1	no	—
687	C₂×C₂²⋊C₄	—	13	1	no	—
688	C₂×C₂²⋊C₄	—	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	C₂²×#41	1	1	yes	characteristic
695	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
696	C₂×C₁₃	#585	1	1	yes	characteristic
697	D₁₃	—	2	2	no	—
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	—	13	1	no	—
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×D₄	—	13	1	no	—
714	C₂×D₄	—	13	1	no	—
715	C₂×D₄	—	13	1	no	—
716	C₂×D₄	—	13	1	no	—
717	C₂×D₄	—	13	1	no	—
718	C₂×D₄	—	13	1	no	—
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	—	26	4	no	—
732	C₂×D₄	—	26	4	no	—
733	C₂×D₄	—	52	2	no	—
734	C₂×D₄	—	52	2	no	—
735	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
736	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
737	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
738	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
739	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
740	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
741	C₂²×C₄	—	13	1	no	—
742	C₂²×C₄	—	13	1	no	—
743	C₂²×C₄	—	13	1	no	—
744	C₂²×C₄	—	13	1	no	—
745	C₂²×C₄	—	13	1	no	—
746	C₂²×C₄	—	13	1	no	—
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	—	52	2	no	—
763	C₂²×C₄	—	52	2	no	—
764	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
765	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
793	C₄⋊C₄	—	13	1	no	—
794	C₄⋊C₄	—	13	1	no	—
795	C₄⋊C₄	—	13	1	no	—
796	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
797	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
799	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
800	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
801	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
802	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
803	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
804	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
805	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
837	C₂²⋊C₄	—	13	1	no	—
838	C₂²⋊C₄	—	13	1	no	—
839	C₂²⋊C₄	—	13	1	no	—
840	C₂²⋊C₄	—	13	1	no	—
841	C₂²⋊C₄	—	13	1	no	—
842	C₂²⋊C₄	—	13	1	no	—
843	C₂²⋊C₄	—	13	1	no	—
844	C₂²⋊C₄	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	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
851	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
852	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
853	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	C₂²×D₁₃	1	1	yes	characteristic
864	C₄²	C₂²×D₁₃	1	1	yes	characteristic
865	C₄²	C₂²×D₁₃	1	1	yes	characteristic
866	C₁₃	#3513	1	1	yes	characteristic, complemented, Sylow
867	C₂³	—	13	1	no	—
868	C₂³	—	13	1	no	—
869	C₂³	—	13	1	no	—
870	C₂³	—	13	1	no	—
871	C₂³	—	13	1	no	—
872	C₂³	—	26	2	no	—
873	C₂³	—	26	2	no	—
874	C₂³	—	26	2	no	—
875	C₂³	—	26	2	no	—
876	C₂³	—	26	2	no	—
877	C₂³	—	26	2	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	—	52	1	no	—
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	—	26	2	no	—
889	Q₈	—	52	1	no	—
890	Q₈	—	52	1	no	—
891	Q₈	—	52	1	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	2	2	no	—
895	D₄	—	4	1	no	—
896	D₄	—	4	1	no	—
897	D₄	—	4	1	no	—
898	D₄	—	13	4	no	—
899	D₄	—	26	2	no	—
900	D₄	—	26	2	no	—
901	D₄	—	26	2	no	—
902	D₄	—	26	2	no	—
903	D₄	—	26	2	no	—
904	D₄	—	26	2	no	—
905	D₄	—	26	2	no	—
906	D₄	—	26	2	no	—
907	D₄	—	26	2	no	—
908	D₄	—	52	1	no	—
909	D₄	—	52	1	no	—
910	D₄	—	52	1	no	—
911	D₄	—	52	1	no	—
912	D₄	—	52	1	no	—
913	D₄	—	52	1	no	—
914	D₄	—	52	1	no	—
915	D₄	—	52	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	13	1	no	—
923	C₂×C₄	—	13	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	—	26	2	no	—
934	C₂×C₄	—	26	2	no	—
935	C₂×C₄	—	26	2	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	—	52	1	no	—
942	C₂×C₄	—	52	1	no	—
943	C₂×C₄	—	52	1	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	C₂³×D₁₃	1	1	yes	characteristic
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	—	13	2	no	—
977	C₂²	—	13	2	no	—
978	C₂²	—	26	1	no	—
979	C₂²	—	26	1	no	—
980	C₂²	—	26	1	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	—	52	4	no	—
992	C₂²	—	52	4	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	—	2	1	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	—	26	2	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	#11719648	1	1	yes	characteristic
1030	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×#553	C₂
hypercenter	#553	D₁₃
hypocenter	C₁₃	#3513
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₁₃×#553	C₂	semidirect
2. #11719415	C₂	semidirect
3. #11719414	C₂	semidirect
4. #11719411	C₂	semidirect
5. #11719410	C₂	semidirect
6. #11719398	C₂	semidirect
7. #11719397	C₂	semidirect
8. #11719369	C₂	semidirect
9. #11719362	C₂	semidirect
10. #11719360	C₂	semidirect
11. D₁₃×#123	C₂	semidirect
12. #11719322	C₂	semidirect
13. #11719320	C₂	semidirect
14. #11719315	C₂	semidirect
15. #11719315	C₂	semidirect
16. #11719315	C₂	semidirect
17. #11719314	C₂	semidirect
18. #11719311	C₂	semidirect
19. #11719307	C₂	semidirect
20. #11719261	C₂	semidirect
21. #11719261	C₂	semidirect
22. #11719255	C₂	semidirect
23. #11719252	C₂	semidirect
24. #11719251	C₂	semidirect
25. #11719250	C₂	semidirect
26. C₄×D₄×D₁₃	C₂	semidirect
27. #11719245	C₂	semidirect
28. #11719233	C₂	semidirect
29. #11719232	C₂	semidirect
30. #11719216	C₂	semidirect
31. C₂×#88148	C₂	semidirect
33. C₂×#6129	C₂²	semidirect
37. C₂×#6127	C₂²	semidirect
39. C₂²×C₄×D₁₃	C₂²	semidirect
40. C₂²×C₄×D₁₃	C₂²	semidirect
41. C₁₃×#126	C₂²	semidirect
42. C₁₃×#126	C₂²	semidirect
43. C₁₃×#125	C₂²	semidirect
44. C₁₃×#123	C₂²	semidirect
45. C₁₃×#123	C₂²	semidirect
47. C₁₃×#121	C₂²	semidirect
48. C₁₃×#121	C₂²	semidirect
49. C₁₃×#121	C₂²	semidirect
50. C₄×D₄×C₁₃	C₂²	semidirect
51. C₄×D₄×C₁₃	C₂²	semidirect
52. C₄×D₄×C₁₃	C₂²	semidirect
53. C₄×D₄×C₁₃	C₂²	semidirect
54. C₁₃×#117	C₂²	semidirect
55. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
57. #88193	C₂²	semidirect
58. #88193	C₂²	semidirect
59. #88193	C₂²	semidirect
60. #88193	C₂²	semidirect
61. #88192	C₂²	semidirect
64. #88191	C₂²	semidirect
65. #88191	C₂²	semidirect
66. #88191	C₂²	semidirect
67. #88191	C₂²	semidirect
68. #88189	C₂²	semidirect
69. #88189	C₂²	semidirect
70. #88189	C₂²	semidirect
71. #88189	C₂²	semidirect
72. D₄×Dic₁₃	C₂²	semidirect
73. D₄×Dic₁₃	C₂²	semidirect
74. D₄×Dic₁₃	C₂²	semidirect
75. #88184	C₂²	semidirect
76. #88183	C₂²	semidirect
77. #88183	C₂²	semidirect
81. C₄×C₂²⋊D₁₃	C₂²	semidirect
82. C₄×C₂²⋊D₁₃	C₂²	semidirect
83. C₄×C₂²⋊D₁₃	C₂²	semidirect
84. C₄×C₂²⋊D₁₃	C₂²	semidirect
85. C₄×C₂²⋊D₁₃	C₂²	semidirect
86. C₂×#6103	C₂²	semidirect
87. C₂×#6103	C₂²	semidirect
88. C₂×#6103	C₂²	semidirect
89. C₂×#6103	C₂²	semidirect
90. #88178	C₂²	semidirect
91. #88178	C₂²	semidirect
92. #88178	C₂²	semidirect
93. C₂×#6101	C₂²	semidirect
94. C₂×#6101	C₂²	semidirect
95. #88152	C₂²	semidirect
96. #88152	C₂²	semidirect
97. #88152	C₂²	semidirect
98. #88152	C₂²	semidirect
99. #88151	C₂²	semidirect
100. #88151	C₂²	semidirect
101. #88150	C₂²	semidirect
102. #88150	C₂²	semidirect
103. #88150	C₂²	semidirect
104. #88150	C₂²	semidirect
105. #88150	C₂²	semidirect
106. #88150	C₂²	semidirect
111. #88148	C₂²	semidirect
112. #88148	C₂²	semidirect
113. #88148	C₂²	semidirect
114. #88148	C₂²	semidirect
115. #88148	C₂²	semidirect
116. #88148	C₂²	semidirect
117. #88148	C₂²	semidirect
118. #88148	C₂²	semidirect
119. #88148	C₂²	semidirect
121. #88147	C₂²	semidirect
122. #88147	C₂²	semidirect
123. #88146	C₂²	semidirect
124. #88146	C₂²	semidirect
125. C₄⋊C₄×D₁₃	C₂²	semidirect
126. C₄⋊C₄×D₁₃	C₂²	semidirect
127. C₄⋊C₄×D₁₃	C₂²	semidirect
128. #88143	C₂²	semidirect
129. #88143	C₂²	semidirect
130. #88143	C₂²	semidirect
131. #88143	C₂²	semidirect
132. #88142	C₂²	semidirect
133. #88141	C₂²	semidirect
134. #88141	C₂²	semidirect
135. #88140	C₂²	semidirect
136. #88140	C₂²	semidirect
137. #88139	C₂²	semidirect
138. #88139	C₂²	semidirect
139. #88139	C₂²	semidirect
140. #88139	C₂²	semidirect
141. #88139	C₂²	semidirect
142. #88139	C₂²	semidirect
146. #88138	C₂²	semidirect
147. #88138	C₂²	semidirect
148. #88138	C₂²	semidirect
149. #88137	C₂²	semidirect
150. #88137	C₂²	semidirect
151. #88137	C₂²	semidirect
152. #88137	C₂²	semidirect
156. #88135	C₂²	semidirect
157. #88135	C₂²	semidirect
158. #88135	C₂²	semidirect
159. #88135	C₂²	semidirect
160. #88135	C₂²	semidirect
161. #88135	C₂²	semidirect
162. #88135	C₂²	semidirect
163. C₂²⋊C₄×D₁₃	C₂²	semidirect
164. C₂²⋊C₄×D₁₃	C₂²	semidirect
165. C₂²⋊C₄×D₁₃	C₂²	semidirect
166. C₂²⋊C₄×D₁₃	C₂²	semidirect
167. C₂²⋊C₄×D₁₃	C₂²	semidirect
168. C₂²⋊C₄×D₁₃	C₂²	semidirect
169. #88133	C₂²	semidirect
170. #88133	C₂²	semidirect
171. #88132	C₂²	semidirect
172. #88132	C₂²	semidirect
173. #88131	C₂²	semidirect
174. #88131	C₂²	semidirect
175. #88130	C₂²	semidirect
176. #88130	C₂²	semidirect
177. #88129	C₂²	semidirect
178. C₄×D₅₂	C₂²	semidirect
179. C₄×D₅₂	C₂²	semidirect
180. C₄×D₅₂	C₂²	semidirect
181. #88126	C₂²	semidirect
182. #88126	C₂²	semidirect
183. #88126	C₂²	semidirect
184. #88126	C₂²	semidirect
185. C₄²×D₁₃	C₂²	semidirect
186. C₄×Dic₂₆	C₂²	semidirect
407. C₂²⋊D₁₃	#41	semidirect
454. #553	D₁₃	semidirect
554. #126	C₂×D₁₃	semidirect
555. #126	C₂×D₁₃	semidirect
560. #125	C₂×D₁₃	semidirect
592. #123	C₂×D₁₃	semidirect
593. #123	C₂×D₁₃	semidirect
621. #121	C₂×D₁₃	semidirect
622. #121	C₂×D₁₃	semidirect
623. #121	C₂×D₁₃	semidirect
660. C₄×D₄	C₂×D₁₃	semidirect
661. C₄×D₄	C₂×D₁₃	semidirect
662. C₄×D₄	C₂×D₁₃	semidirect
663. C₄×D₄	C₂×D₁₃	semidirect
672. #117	C₂×D₁₃	semidirect
678. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
866. C₁₃	#3513	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#553	2
#11719415	2
#11719414	2
#11719411	2
#11719410	2
#11719398	2
#11719397	2
#11719369	2
#11719362	2
#11719360	2
D₁₃×#123	2
#11719322	2
#11719320	2
#11719315	2
#11719314	2
#11719311	2
#11719307	2
#11719261	2
#11719255	2
#11719252	2
#11719251	2
#11719250	2
C₄×D₄×D₁₃	2
#11719245	2
#11719233	2
#11719232	2
#11719216	2
C₂×#88148	2
#3513	13