Subgroups — #16728145

Order 3328.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128392	C₂	1	1	yes	maximal, characteristic
2	#13123994	C₂	1	2	yes	maximal, complemented
3	#13123991	C₂	1	1	yes	maximal, characteristic, complemented
4	#13123991	C₂	1	2	yes	maximal, complemented
5	#13123985	C₂	1	1	yes	maximal, characteristic, complemented
6	#13123980	C₂	1	1	yes	maximal, characteristic, complemented
7	#13123971	C₂	1	2	yes	maximal, complemented
8	#13123970	C₂	1	2	yes	maximal, complemented
9	#13123960	C₂	1	1	yes	maximal, characteristic, complemented
10	#13123957	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123946	C₂	1	1	yes	maximal, characteristic, complemented
12	#13123945	C₂	1	1	yes	maximal, characteristic, complemented
13	#13123778	C₂	1	1	yes	maximal, characteristic, complemented
14	#13123767	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123572	C₂	1	1	yes	maximal, characteristic, complemented
16	#13123559	C₂	1	2	yes	maximal, complemented
17	#13123525	C₂	1	2	yes	maximal, complemented
18	C₈×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#13123492	C₂	1	2	yes	maximal, complemented
20	#13123475	C₂	1	1	yes	maximal, characteristic, complemented
21	#13123401	C₂	1	1	yes	maximal, characteristic, complemented
22	D₁₃×#424	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#529	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
26	C₂×#88155	C₂²	1	2	yes	—
27	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
28	#11719413	C₄	1	2	yes	—
29	#11719410	C₄	1	2	yes	—
30	#11719399	C₄	1	1	yes	characteristic
31	#11719395	C₄	1	1	yes	characteristic
32	#11719381	C₄	1	1	yes	characteristic
33	#11719376	C₄	1	1	yes	characteristic
34	#11719366	C₄	1	2	yes	—
35	#11719364	C₄	1	2	yes	—
36	#11719344	C₄	1	1	yes	characteristic
37	#11719336	C₄	1	1	yes	characteristic
38	#11719321	C₄	1	1	yes	characteristic
39	#11719317	C₄	1	1	yes	characteristic
40	#11719283	C₂²	1	1	yes	characteristic
41	C₄×#6131	C₂²	1	1	yes	characteristic
42	#11719262	C₂²	1	2	yes	—
43	#11719262	C₂²	1	1	yes	characteristic
44	#11719252	C₂²	1	2	yes	—
45	C₄×D₄×D₁₃	C₂²	1	1	yes	characteristic
46	#11719233	C₂²	1	2	yes	—
47	D₁₃×#117	C₂²	1	2	yes	—
48	C₄×#6127	C₂²	1	1	yes	characteristic
49	C₄×#6127	C₂²	1	1	yes	characteristic
50	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
51	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#436	C₂²	1	1	yes	characteristic
53	C₁₃×#435	C₂²	1	2	yes	complemented
54	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
56	C₁₃×#433	C₂²	1	2	yes	complemented
57	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#424	C₂²	1	2	yes	complemented
59	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	#11718789	C₂²	1	2	yes	complemented
61	#11718788	C₂²	1	2	yes	—
62	#11718780	C₂²	1	2	yes	complemented
63	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	—
64	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
65	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
66	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
67	#11718763	C₂²	1	2	yes	complemented
68	#11718763	C₂²	1	2	yes	complemented
69	#11718685	C₂²	1	1	yes	characteristic, complemented
70	Q₈×#1055	C₂²	1	1	yes	characteristic, complemented
71	#11718673	C₂²	1	1	yes	characteristic
72	#11718673	C₂²	1	2	yes	complemented
73	#11718672	C₂²	1	2	yes	complemented
74	D₄×#1055	C₂²	1	1	yes	characteristic
75	#11718661	C₂²	1	2	yes	complemented
76	#11718660	C₂²	1	2	yes	complemented
77	#11718586	C₂²	1	1	yes	characteristic, complemented
78	#11718585	C₂²	1	1	yes	characteristic, complemented
79	#11718501	C₂²	1	1	yes	characteristic, complemented
80	#11718501	C₂²	1	1	yes	characteristic, complemented
81	#11718500	C₂²	1	1	yes	characteristic
82	#11718500	C₂²	1	2	yes	—
83	#11718500	C₂²	1	2	yes	—
84	#11718500	C₂²	1	2	yes	—
85	#11718500	C₂²	1	1	yes	characteristic
86	#11718500	C₂²	1	2	yes	complemented
87	#11718498	C₂²	1	1	yes	characteristic
88	#11718498	C₂²	1	1	yes	characteristic, complemented
89	#11718497	C₂²	1	2	yes	complemented
90	#11718496	C₂²	1	2	yes	complemented
91	#11718495	C₂²	1	1	yes	characteristic
92	#11718495	C₂²	1	1	yes	characteristic
93	#11718495	C₂²	1	2	yes	complemented
94	#11718494	C₂²	1	2	yes	complemented
95	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
96	D₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
97	D₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
98	D₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
99	D₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
100	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
101	#11718491	C₂²	1	1	yes	characteristic, complemented
102	#11718491	C₂²	1	1	yes	characteristic, complemented
103	#11718491	C₂²	1	2	yes	complemented
104	#11718489	C₂²	1	2	yes	complemented
105	#11718391	C₂²	1	2	yes	complemented
106	#11718389	C₂²	1	2	yes	—
107	#11718389	C₂²	1	2	yes	complemented
108	#11718389	C₂²	1	2	yes	complemented
109	#11718389	C₂²	1	2	yes	complemented
110	#11718388	C₂²	1	1	yes	characteristic
111	#11718388	C₂²	1	1	yes	characteristic
112	#11718387	C₂²	1	2	yes	—
113	#11718386	C₂²	1	2	yes	—
114	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
115	#11718381	C₂²	1	1	yes	characteristic, complemented
116	#11718381	C₂²	1	2	yes	complemented
117	#11718381	C₂²	1	2	yes	complemented
118	#11718381	C₂²	1	1	yes	characteristic, complemented
119	#11718369	C₂²	1	2	yes	—
120	#11718367	C₂²	1	2	yes	complemented
121	#11718366	C₂²	1	2	yes	complemented
122	#11718362	C₂²	1	2	yes	complemented
123	#11718350	C₂²	1	2	yes	—
124	C₄×#6094	C₂²	1	1	yes	characteristic
125	C₈×D₅₂	C₂²	1	1	yes	characteristic
126	C₈×D₅₂	C₂²	1	1	yes	characteristic
127	C₈×D₅₂	C₂²	1	2	yes	complemented
128	#11718346	C₂²	1	1	yes	characteristic, complemented
129	#11718346	C₂²	1	2	yes	complemented
130	#11718346	C₂²	1	1	yes	characteristic, complemented
131	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
132	#11718340	C₂²	1	1	yes	characteristic, complemented
133	#11718340	C₂²	1	1	yes	characteristic, complemented
134	#11718340	C₂²	1	2	yes	complemented
135	C₂×#6131	C₂×C₄	1	1	yes	characteristic
136	C₂×D₄×D₁₃	C₂×C₄	1	1	yes	characteristic
137	C₂×#6127	C₂×C₄	1	1	yes	characteristic
138	C₂×#6127	C₂³	1	1	yes	characteristic
139	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
140	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
141	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
142	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
143	C₁₃×#126	C₂×C₄	1	2	yes	—
144	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
145	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
146	C₁₃×#123	C₂×C₄	1	2	yes	—
147	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
148	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
149	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
151	C₄×D₄×C₁₃	C₂³	1	2	yes	—
152	C₁₃×#117	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
154	#88200	C₂×C₄	1	1	yes	characteristic
155	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
156	#88198	C₂×C₄	1	1	yes	characteristic
157	#88193	C₂×C₄	1	2	yes	—
158	#88192	C₂×C₄	1	2	yes	—
159	#88192	C₂×C₄	1	1	yes	characteristic
160	#88191	C₂×C₄	1	2	yes	—
161	#88190	C₂×C₄	1	1	yes	characteristic
162	#88190	C₂×C₄	1	2	yes	—
163	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
164	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
165	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
166	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
167	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
168	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
169	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
170	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
171	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
172	#88180	C₂×C₄	1	1	yes	characteristic
173	#88180	C₂³	1	1	yes	characteristic
174	#88180	C₂³	1	2	yes	—
175	C₂×#6099	C₂³	1	2	yes	—
176	C₂×#6099	C₂³	1	2	yes	—
177	C₂²×#1055	C₂³	1	2	yes	—
178	M₁₆×D₁₃	—	4	4	no	—
179	#88155	—	4	4	no	—
180	C₂×#6094	C₂³	1	2	yes	—
181	C₂×#6094	C₂³	1	1	yes	characteristic
182	C₂×#6094	C₂³	1	1	yes	characteristic
183	C₂×#6094	C₂³	1	2	yes	—
184	C₂×C₈×D₁₃	—	4	4	no	—
185	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
186	C₂×C₈×D₁₃	C₂³	1	2	yes	—
187	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₈×D₁₃	C₂³	1	2	yes	—
189	C₂×C₈×D₁₃	C₂³	1	2	yes	—
190	C₂×C₈×D₁₃	C₂³	1	2	yes	—
191	C₂×C₈×D₁₃	C₂³	1	2	yes	—
192	C₂×C₈×D₁₃	C₂³	1	2	yes	—
193	#88152	C₂×C₄	1	2	yes	—
194	#88151	C₂×C₄	1	1	yes	characteristic
195	#88151	C₂×C₄	1	2	yes	—
196	#88151	C₂×C₄	1	1	yes	characteristic
197	#88150	C₂×C₄	1	2	yes	—
198	#88150	C₂×C₄	1	2	yes	—
199	#88150	C₂×C₄	1	2	yes	—
200	#88148	C₂×C₄	1	2	yes	—
201	#88148	C₂×C₄	1	2	yes	—
202	#88147	C₂×C₄	1	1	yes	characteristic
203	#88147	C₂×C₄	1	1	yes	characteristic
204	#88147	C₂×C₄	1	2	yes	—
205	#88146	C₂×C₄	1	2	yes	—
206	#88146	C₂×C₄	1	2	yes	—
207	#88146	C₂×C₄	1	1	yes	characteristic
208	#88146	C₂×C₄	1	2	yes	—
209	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
210	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
211	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
212	#88144	C₂×C₄	1	1	yes	characteristic
213	#88144	C₂×C₄	1	2	yes	—
214	#88143	C₂×C₄	1	2	yes	—
215	#88143	C₂×C₄	1	2	yes	—
216	#88142	C₂×C₄	1	1	yes	characteristic
217	#88139	C₂×C₄	1	2	yes	—
218	#88138	C₂×C₄	1	2	yes	—
219	#88138	C₂×C₄	1	2	yes	—
220	#88137	C₂×C₄	1	2	yes	—
221	#88137	C₂×C₄	1	2	yes	—
222	#88137	C₂×C₄	1	2	yes	—
223	#88137	C₂×C₄	1	2	yes	—
224	#88137	C₂×C₄	1	2	yes	—
225	#88136	C₂×C₄	1	2	yes	—
226	#88135	C₂×C₄	1	2	yes	—
227	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
228	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
229	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
230	#88133	C₂×C₄	1	2	yes	—
231	#88133	C₂×C₄	1	2	yes	—
232	#88133	C₂×C₄	1	2	yes	—
233	#88133	C₂×C₄	1	2	yes	—
234	#88132	C₂×C₄	1	2	yes	—
235	#88131	C₂×C₄	1	2	yes	—
236	#88131	C₂×C₄	1	2	yes	—
237	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
238	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
239	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
240	C₄×D₅₂	C₂³	1	1	yes	characteristic
241	C₄×D₅₂	C₂³	1	2	yes	—
242	#88126	C₂×C₄	1	2	yes	—
243	#88126	C₂³	1	1	yes	characteristic
244	#88126	C₂³	1	1	yes	characteristic
245	#88126	C₂³	1	2	yes	—
246	C₄²×D₁₃	C₂³	1	2	yes	—
247	C₄²×D₁₃	C₂³	1	1	yes	characteristic
248	C₄²×D₁₃	C₂³	1	1	yes	characteristic
249	C₄²×D₁₃	C₂³	1	2	yes	—
250	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
251	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
252	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
253	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
254	C₄×Dic₂₆	C₂³	1	2	yes	—
255	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
260	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
261	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
263	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
264	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₁₃×#97	C₂³	1	2	yes	—
267	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
268	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
269	C₄×C₈×C₁₃	C₂³	1	2	yes	—
270	C₂²⋊#1055	C₂³	1	2	yes	—
271	C₂²⋊#1055	C₂³	1	2	yes	—
272	C₂²⋊#1055	C₂³	1	1	yes	characteristic
273	C₂²⋊#1055	C₂³	1	1	yes	characteristic
274	#88060	C₂³	1	2	yes	—
275	#88060	C₂³	1	2	yes	—
276	#88060	C₂³	1	1	yes	characteristic
277	#88060	C₂³	1	2	yes	—
278	#88060	C₂³	1	2	yes	—
279	#88060	C₂³	1	1	yes	characteristic
280	#88060	C₂³	1	1	yes	characteristic
281	#88060	C₂³	1	1	yes	characteristic
282	#88055	C₂³	1	1	yes	characteristic
283	#88055	C₂³	1	2	yes	—
284	#88055	C₂³	1	2	yes	—
285	#88055	C₂³	1	1	yes	characteristic
286	#88054	C₂³	1	2	yes	—
287	#88054	C₂³	1	2	yes	—
288	#88054	C₂³	1	2	yes	—
289	#88054	C₂³	1	2	yes	—
290	#88054	C₂³	1	2	yes	—
291	#88054	C₂³	1	2	yes	—
292	#88054	C₂³	1	2	yes	—
293	#88054	C₂³	1	1	yes	characteristic
294	#88054	C₂³	1	1	yes	characteristic
295	#88054	C₂³	1	2	yes	—
296	#88054	C₂³	1	1	yes	characteristic
297	#88054	C₂³	1	1	yes	characteristic
298	C₈×Dic₁₃	C₂³	1	2	yes	—
299	C₈×Dic₁₃	C₂³	1	2	yes	—
300	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
301	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
302	C₄⋊#1055	C₂³	1	1	yes	characteristic
303	C₄⋊#1055	C₂³	1	2	yes	—
304	C₄⋊#1055	C₂³	1	2	yes	—
305	C₄⋊#1055	C₂³	1	2	yes	—
306	C₄⋊#1055	C₂³	1	1	yes	characteristic
307	C₄⋊#1055	C₂³	1	1	yes	characteristic
308	C₄⋊#1055	C₂³	1	1	yes	characteristic
309	#88043	C₂³	1	2	yes	—
310	C₄×#1055	C₂³	1	2	yes	—
311	C₄×#1055	C₂³	1	1	yes	characteristic
312	C₄×#1055	C₂³	1	1	yes	characteristic
313	#60271	—	13	1	no	maximal, Sylow
314	C₂³×D₁₃	C₂²×C₄	1	2	yes	—
315	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
316	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
317	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
318	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
319	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
323	C₂×C₂²⋊D₁₃	C₂²×C₄	1	1	yes	characteristic
324	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
325	C₂×C₂²⋊D₁₃	C₂²×C₄	1	1	yes	characteristic
326	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
327	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
328	#6131	—	2	4	no	—
329	D₄×D₁₃	—	2	4	no	—
330	#6127	—	2	4	no	—
331	#6127	—	2	2	no	—
332	#6127	—	2	2	no	—
333	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
334	C₂×D₅₂	C₂²×C₄	1	2	yes	—
335	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
336	C₂×C₄×D₁₃	—	2	4	no	—
337	C₂×C₄×D₁₃	—	2	4	no	—
338	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
339	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
342	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
343	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
344	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
346	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
347	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
348	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
349	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
351	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
352	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
353	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
354	C₁₃×M₁₆	—	4	2	no	—
355	C₂×C₈×C₁₃	—	4	2	no	—
356	C₂×C₈×C₁₃	—	4	2	no	—
357	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
361	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
364	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
366	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
367	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
368	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
369	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
370	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
371	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
372	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
373	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
374	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
375	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
376	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₄²×C₁₃	C₂⁴	1	2	yes	—
378	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
380	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
381	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
382	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
383	C₂²⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
384	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
385	C₂²⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
386	#6103	C₂²×C₄	1	2	yes	—
387	#6103	C₂²×C₄	1	2	yes	—
388	#6103	C₂²×C₄	1	1	yes	characteristic
389	#6103	C₂²×C₄	1	1	yes	characteristic
390	#6103	C₂²×C₄	1	1	yes	characteristic
391	#6103	C₂²×C₄	1	1	yes	characteristic
392	#6103	C₂²×C₄	1	2	yes	—
393	#6103	C₂²×C₄	1	2	yes	—
394	#6103	C₂²×C₄	1	2	yes	—
395	#6103	C₂²×C₄	1	2	yes	—
396	#6103	C₂²×C₄	1	2	yes	—
397	#6103	C₂²×C₄	1	2	yes	—
398	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
403	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
404	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
405	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
406	#6101	C₂²×C₄	1	2	yes	—
407	#6101	C₂²×C₄	1	1	yes	characteristic
408	#6101	C₂²×C₄	1	1	yes	characteristic
409	#6101	C₂²×C₄	1	1	yes	characteristic
410	#6101	C₂²×C₄	1	1	yes	characteristic
411	#6101	C₂²×C₄	1	2	yes	—
412	#6101	C₂²×C₄	1	2	yes	—
413	#6101	C₂²×C₄	1	2	yes	—
414	#6101	C₂²×C₄	1	2	yes	—
415	#6101	C₂²×C₄	1	2	yes	—
416	#6101	C₂²×C₄	1	2	yes	—
417	#6101	C₂²×C₄	1	2	yes	—
418	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
419	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
420	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
421	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
422	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
423	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
424	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
425	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
426	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
427	C₄×Dic₁₃	C₂⁴	1	2	yes	—
428	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
429	#6099	—	4	2	no	—
430	#6099	—	4	2	no	—
431	C₂×#1055	—	4	2	no	—
432	C₂×#1055	C₂⁴	1	1	yes	characteristic
433	C₂×#1055	C₂⁴	1	1	yes	characteristic
434	C₂×#1055	C₂⁴	1	1	yes	characteristic
435	C₂×#1055	C₂⁴	1	2	yes	—
436	C₂×#1055	C₂⁴	1	2	yes	—
437	C₂×#1055	C₂⁴	1	1	yes	characteristic
438	#6094	—	2	4	no	—
439	#6094	—	2	2	no	—
440	#6094	—	2	2	no	—
441	#6094	—	4	2	no	—
442	C₈×D₁₃	—	2	2	no	—
443	C₈×D₁₃	—	2	4	no	—
444	C₈×D₁₃	—	2	2	no	—
445	C₈×D₁₃	—	4	2	no	—
446	C₈×D₁₃	—	4	2	no	—
447	C₈×D₁₃	—	4	2	no	—
448	C₈×D₁₃	—	4	2	no	—
449	C₈×D₁₃	—	4	2	no	—
450	#3475	—	13	1	no	—
451	#2994	—	13	1	no	—
452	#2994	—	13	2	no	—
453	#2994	—	13	2	no	—
454	#2994	D₁₃	1	1	yes	characteristic, complemented
455	#2993	—	13	1	no	—
456	#2993	—	13	1	no	—
457	#2992	—	13	2	no	—
458	#2992	—	13	2	no	—
459	#2990	—	13	1	no	—
460	#2990	—	13	1	no	—
461	#2988	—	13	1	no	—
462	#2988	—	13	1	no	—
463	#2962	—	13	1	no	—
464	#2960	—	13	1	no	—
465	D₄×M₁₆	—	13	1	no	—
466	#2933	—	13	2	no	—
467	#2929	—	13	2	no	—
468	C₂×C₈×D₄	—	13	1	no	—
469	#2924	—	13	2	no	—
470	#2922	—	13	1	no	—
471	#2906	—	13	1	no	—
472	C₂×#424	—	13	2	no	—
473	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
474	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
475	C₂²×D₁₃	—	2	4	no	—
476	C₂²×D₁₃	—	2	4	no	—
477	C₂²×D₁₃	—	4	2	no	—
478	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
479	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
480	C₂²×D₁₃	C₂³×C₄	1	2	yes	—
481	Q₈×C₁₃	—	2	2	no	—
482	D₄×C₁₃	—	2	2	no	—
483	D₄×C₁₃	—	4	2	no	—
484	C₂×C₄×C₁₃	—	2	2	no	—
485	C₂×C₄×C₁₃	—	2	2	no	—
486	C₂×C₄×C₁₃	—	2	1	no	—
487	C₂×C₄×C₁₃	—	2	2	no	—
488	C₂×C₄×C₁₃	—	2	1	no	—
489	C₂×C₄×C₁₃	—	4	1	no	—
490	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
494	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
495	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
497	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
498	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
499	C₂²⋊D₁₃	—	2	2	no	—
500	C₂²⋊D₁₃	—	2	4	no	—
501	C₂²⋊D₁₃	—	2	4	no	—
502	C₂²⋊D₁₃	—	2	2	no	—
503	C₂²⋊D₁₃	—	4	2	no	—
504	C₂×Dic₁₃	—	2	4	no	—
505	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
506	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
507	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
508	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
509	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
510	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
511	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
512	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
513	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
514	D₅₂	—	2	2	no	—
515	D₅₂	—	2	4	no	—
516	D₅₂	#131	1	4	yes	complemented
517	C₄×D₁₃	—	2	4	no	—
518	C₄×D₁₃	—	2	4	no	—
519	C₄×D₁₃	—	2	4	no	—
520	C₄×D₁₃	—	2	2	no	—
521	C₄×D₁₃	—	2	2	no	—
522	C₄×D₁₃	—	2	2	no	—
523	C₄×D₁₃	—	2	1	no	—
524	C₄×D₁₃	—	2	2	no	—
525	C₄×D₁₃	—	2	1	no	—
526	C₄×D₁₃	—	2	4	no	—
527	C₄×D₁₃	—	4	1	no	—
528	C₄×D₁₃	—	4	2	no	—
529	C₄×D₁₃	—	4	2	no	—
530	C₄×D₁₃	—	4	1	no	—
531	C₄×D₁₃	H(5,𝔽₂)	1	2	yes	—
532	C₄×D₁₃	2₋¹⁺⁴	1	2	yes	—
533	Dic₂₆	—	2	2	no	—
534	Dic₂₆	—	2	2	no	—
535	Dic₂₆	—	4	2	no	—
536	C₈×C₁₃	—	2	1	no	—
537	C₈×C₁₃	—	2	2	no	—
538	C₈×C₁₃	—	2	1	no	—
539	C₈×C₁₃	—	2	2	no	—
540	C₈×C₁₃	—	2	1	no	—
541	C₈×C₁₃	—	2	1	no	—
542	#1055	—	2	1	no	—
543	#1055	—	2	2	no	—
544	#1055	—	2	2	no	—
545	#1055	—	2	1	no	—
546	#1055	—	2	1	no	—
547	#1055	—	2	1	no	—
548	C₂×#131	—	13	2	no	—
549	C₂²×M₁₆	—	13	2	no	—
550	C₂³×C₈	—	13	2	no	—
551	#556	—	13	1	no	—
552	#555	—	13	1	no	—
553	#554	—	13	1	no	—
554	#553	—	13	2	no	—
555	#552	—	13	2	no	—
556	#552	—	13	1	no	—
557	#552	—	13	1	no	—
558	#551	—	13	2	no	—
559	#551	—	13	2	no	—
560	#547	—	13	1	no	—
561	#546	—	13	1	no	—
562	#546	—	13	1	no	—
563	#533	—	13	1	no	—
564	#529	—	13	2	no	—
565	#529	—	13	1	no	—
566	#529	—	13	2	no	—
567	#529	C₂×D₁₃	1	1	yes	characteristic
568	#525	—	13	2	no	—
569	C₄×#41	—	13	1	no	—
570	C₄×#41	—	13	1	no	—
571	C₄×#41	—	13	1	no	—
572	C₂×C₄×D₄	—	13	1	no	—
573	C₂×#117	—	13	2	no	—
574	#446	—	13	1	no	—
575	#446	—	13	2	no	—
576	#446	—	13	2	no	—
577	#446	—	13	1	no	—
578	#446	—	13	1	no	—
579	#446	—	13	2	no	—
580	#446	C₂×D₁₃	1	1	yes	characteristic, complemented
581	C₈×Q₈	—	13	1	no	—
582	C₈×Q₈	—	13	1	no	—
583	C₈×Q₈	—	13	2	no	—
584	C₈×Q₈	—	13	1	no	—
585	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
586	#436	—	13	2	no	—
587	#436	—	13	1	no	—
588	#436	—	13	2	no	—
589	#436	C₂×D₁₃	1	1	yes	characteristic
590	#435	—	13	2	no	—
591	#435	—	13	2	no	—
592	#435	—	13	2	no	—
593	#435	—	13	2	no	—
594	#435	—	13	2	no	—
595	#435	—	13	2	no	—
596	#435	—	13	2	no	—
597	#435	—	13	2	no	—
598	#435	—	13	2	no	—
599	#435	C₂×D₁₃	1	2	yes	complemented
600	C₈×D₄	—	13	2	no	—
601	C₈×D₄	—	13	2	no	—
602	C₈×D₄	—	13	2	no	—
603	C₈×D₄	—	13	2	no	—
604	C₈×D₄	—	13	1	no	—
605	C₈×D₄	—	13	1	no	—
606	C₈×D₄	—	13	1	no	—
607	C₈×D₄	—	13	2	no	—
608	C₈×D₄	—	13	2	no	—
609	C₈×D₄	—	13	1	no	—
610	C₈×D₄	—	13	2	no	—
611	C₈×D₄	—	13	1	no	—
612	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
613	C₈×D₄	C₂×D₁₃	1	2	yes	complemented
614	#433	—	13	2	no	—
615	#433	—	13	1	no	—
616	#433	—	13	1	no	—
617	#433	—	13	1	no	—
618	#433	—	13	1	no	—
619	#433	—	13	2	no	—
620	#433	—	13	2	no	—
621	#433	C₂×D₁₃	1	2	yes	complemented
622	#432	—	13	2	no	—
623	#432	—	13	2	no	—
624	#431	—	13	1	no	—
625	#431	—	13	2	no	—
626	#431	—	13	1	no	—
627	#431	—	13	1	no	—
628	#431	—	13	2	no	—
629	#431	C₂×D₁₃	1	1	yes	characteristic, complemented
630	#424	—	13	2	no	—
631	#424	—	13	2	no	—
632	#424	—	13	2	no	—
633	#424	—	13	2	no	—
634	#424	—	13	1	no	—
635	#424	—	13	2	no	—
636	#424	—	13	2	no	—
637	#424	—	13	2	no	—
638	#424	—	13	2	no	—
639	#424	—	13	1	no	—
640	#424	C₂×D₁₃	1	2	yes	complemented
641	#423	—	13	1	no	—
642	#423	—	13	1	no	—
643	#423	—	13	1	no	—
644	C₂×C₄⋊C₈	—	13	2	no	—
645	C₂×C₄⋊C₈	—	13	2	no	—
646	C₂×C₄⋊C₈	—	13	2	no	—
647	C₂×C₄⋊C₈	—	13	2	no	—
648	C₂×C₄⋊C₈	—	13	1	no	—
649	C₂×C₄⋊C₈	—	13	1	no	—
650	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
651	#408	—	13	1	no	—
652	#408	—	13	1	no	—
653	#407	—	13	2	no	—
654	C₂×C₂²⋊C₈	—	13	2	no	—
655	#405	—	13	2	no	—
656	#405	—	13	2	no	—
657	C₄×M₁₆	—	13	1	no	—
658	C₂×C₄×C₈	—	13	1	no	—
659	C₂²×C₁₃	—	2	2	no	—
660	C₂²×C₁₃	—	2	1	no	—
661	C₂²×C₁₃	—	2	1	no	—
662	C₂²×C₁₃	—	2	2	no	—
663	C₂²×C₁₃	—	2	2	no	—
664	C₂²×C₁₃	—	2	1	no	—
665	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
666	C₂×D₁₃	—	2	2	no	—
667	C₂×D₁₃	—	2	1	no	—
668	C₂×D₁₃	—	2	2	no	—
669	C₂×D₁₃	—	2	1	no	—
670	C₂×D₁₃	—	2	1	no	—
671	C₂×D₁₃	—	2	1	no	—
672	C₂×D₁₃	—	2	1	no	—
673	C₂×D₁₃	—	4	8	no	—
674	C₂×D₁₃	#520	1	2	yes	—
675	C₂×D₁₃	C₂×#131	1	4	yes	—
676	C₄×C₁₃	—	2	1	no	—
677	C₄×C₁₃	—	2	2	no	—
678	C₄×C₁₃	—	2	1	no	—
679	C₄×C₁₃	—	2	2	no	—
680	C₄×C₁₃	—	2	2	no	—
681	C₄×C₁₃	—	2	1	no	—
682	C₄×C₁₃	—	2	1	no	—
683	C₄×C₁₃	C₂×#131	1	2	yes	—
684	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
685	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
686	Dic₁₃	—	2	1	no	—
687	Dic₁₃	—	2	2	no	—
688	Dic₁₃	—	2	2	no	—
689	Dic₁₃	—	2	1	no	—
690	Dic₁₃	—	2	1	no	—
691	Dic₁₃	—	2	1	no	—
692	Dic₁₃	—	2	2	no	—
693	Dic₁₃	—	2	1	no	—
694	Dic₁₃	#520	1	2	yes	—
695	C₂×#41	—	13	1	no	—
696	C₂×#41	—	13	1	no	—
697	C₂×#41	—	13	1	no	—
698	C₂²×D₄	—	13	1	no	—
699	C₂³×C₄	—	13	2	no	—
700	#131	—	52	4	no	—
701	C₂×M₁₆	—	13	2	no	—
702	C₂×M₁₆	—	13	2	no	—
703	C₂×M₁₆	—	13	1	no	—
704	C₂×M₁₆	—	13	2	no	—
705	C₂×M₁₆	—	13	1	no	—
706	C₂×M₁₆	—	13	2	no	—
707	C₂×M₁₆	—	52	4	no	—
708	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
709	C₂²×C₈	—	13	2	no	—
710	C₂²×C₈	—	13	1	no	—
711	C₂²×C₈	—	13	2	no	—
712	C₂²×C₈	—	13	1	no	—
713	C₂²×C₈	—	13	2	no	—
714	C₂²×C₈	—	13	2	no	—
715	C₂²×C₈	—	13	2	no	—
716	C₂²×C₈	—	13	2	no	—
717	C₂²×C₈	—	13	2	no	—
718	C₂²×C₈	—	52	4	no	—
719	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
720	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
721	C₄⋊Q₈	—	13	1	no	—
722	C₄⋊Q₈	—	13	1	no	—
723	#126	—	13	2	no	—
724	#126	—	13	2	no	—
725	#126	—	13	2	no	—
726	#126	—	13	2	no	—
727	#126	—	13	2	no	—
728	#126	C₄×D₁₃	1	2	yes	—
729	#125	—	13	2	no	—
730	#125	—	13	2	no	—
731	#125	—	13	1	no	—
732	#125	—	13	2	no	—
733	#125	C₄×D₁₃	1	1	yes	characteristic
734	#124	—	13	1	no	—
735	#124	—	13	2	no	—
736	#124	—	13	2	no	—
737	#124	C₄×D₁₃	1	1	yes	characteristic
738	#123	—	13	2	no	—
739	#123	—	13	2	no	—
740	#123	—	13	2	no	—
741	#123	—	13	2	no	—
742	#123	—	13	2	no	—
743	#123	—	13	2	no	—
744	#123	—	13	2	no	—
745	#123	C₄×D₁₃	1	2	yes	—
746	C₂²⋊Q₈	—	13	1	no	—
747	C₂²⋊Q₈	—	13	2	no	—
748	C₂²⋊Q₈	—	13	1	no	—
749	C₂²⋊Q₈	—	13	2	no	—
750	C₂²⋊Q₈	—	13	2	no	—
751	C₂²⋊Q₈	—	13	1	no	—
752	C₂²⋊Q₈	—	13	2	no	—
753	C₂²⋊Q₈	—	13	2	no	—
754	C₂²⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
755	#121	—	13	2	no	—
756	#121	—	13	2	no	—
757	#121	—	13	1	no	—
758	#121	—	13	2	no	—
759	#121	—	13	2	no	—
760	#121	C₄×D₁₃	1	1	yes	characteristic
761	#120	—	13	2	no	—
762	#120	—	13	2	no	—
763	C₄×Q₈	—	13	1	no	—
764	C₄×Q₈	—	13	1	no	—
765	C₄×Q₈	—	13	1	no	—
766	C₄×Q₈	—	13	1	no	—
767	C₄×Q₈	—	13	1	no	—
768	C₄×Q₈	—	13	2	no	—
769	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
770	C₄×D₄	—	13	1	no	—
771	C₄×D₄	—	13	1	no	—
772	C₄×D₄	—	13	1	no	—
773	C₄×D₄	—	13	1	no	—
774	C₄×D₄	—	13	2	no	—
775	C₄×D₄	—	13	1	no	—
776	C₄×D₄	—	13	2	no	—
777	C₄×D₄	—	13	2	no	—
778	C₄×D₄	—	13	2	no	—
779	C₄×D₄	—	13	1	no	—
780	C₄×D₄	—	13	1	no	—
781	C₄×D₄	—	13	2	no	—
782	C₄×D₄	—	13	2	no	—
783	C₄×D₄	—	13	1	no	—
784	C₄×D₄	—	13	1	no	—
785	C₄×D₄	—	13	1	no	—
786	C₄×D₄	—	13	1	no	—
787	C₄×D₄	—	13	2	no	—
788	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
789	C₄×D₄	C₂²×D₁₃	1	2	yes	—
790	#117	—	13	1	no	—
791	#117	—	13	2	no	—
792	#117	—	13	1	no	—
793	#117	—	13	2	no	—
794	#117	—	13	2	no	—
795	#117	—	13	2	no	—
796	#117	—	13	1	no	—
797	#117	—	13	2	no	—
798	#117	—	13	2	no	—
799	#117	—	13	2	no	—
800	#117	—	13	1	no	—
801	#117	—	13	2	no	—
802	#117	—	13	1	no	—
803	#117	C₂²×D₁₃	1	2	yes	—
804	C₂×C₄⋊C₄	—	13	2	no	—
805	C₂×C₄⋊C₄	—	13	2	no	—
806	C₂×C₄⋊C₄	—	13	1	no	—
807	C₂×C₂²⋊C₄	—	13	2	no	—
808	C₂×C₂²⋊C₄	—	13	2	no	—
809	C₂×C₂²⋊C₄	—	13	2	no	—
810	C₂×C₄²	—	13	2	no	—
811	C₂×C₄²	—	13	2	no	—
812	C₂×C₄²	—	13	1	no	—
813	C₂×C₄²	—	13	1	no	—
814	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
815	C₄⋊C₈	—	13	1	no	—
816	C₄⋊C₈	—	13	2	no	—
817	C₄⋊C₈	—	13	1	no	—
818	C₄⋊C₈	—	13	2	no	—
819	C₄⋊C₈	—	13	2	no	—
820	C₄⋊C₈	—	13	2	no	—
821	C₄⋊C₈	—	13	2	no	—
822	C₄⋊C₈	—	13	2	no	—
823	C₄⋊C₈	—	13	2	no	—
824	C₄⋊C₈	—	13	2	no	—
825	C₄⋊C₈	—	13	1	no	—
826	C₄⋊C₈	—	13	1	no	—
827	C₄⋊C₈	—	13	1	no	—
828	C₄⋊C₈	—	13	1	no	—
829	C₄⋊C₈	—	13	1	no	—
830	C₄⋊C₈	—	13	2	no	—
831	C₄⋊C₈	—	13	2	no	—
832	C₄⋊C₈	—	13	2	no	—
833	C₄⋊C₈	—	13	1	no	—
834	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
835	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
836	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
837	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
838	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
839	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
840	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
841	C₂²⋊C₈	—	13	2	no	—
842	C₂²⋊C₈	—	13	2	no	—
843	C₂²⋊C₈	—	13	1	no	—
844	C₂²⋊C₈	—	13	1	no	—
845	C₂²⋊C₈	—	13	2	no	—
846	C₂²⋊C₈	—	13	2	no	—
847	C₂²⋊C₈	—	13	2	no	—
848	C₂²⋊C₈	—	13	2	no	—
849	C₂²⋊C₈	—	13	1	no	—
850	C₂²⋊C₈	—	13	1	no	—
851	C₂²⋊C₈	—	13	1	no	—
852	C₂²⋊C₈	—	13	1	no	—
853	C₂²⋊C₈	C₂²×D₁₃	1	2	yes	—
854	C₂²⋊C₈	C₂²×D₁₃	1	2	yes	—
855	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
856	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
857	#97	—	13	1	no	—
858	#97	—	13	1	no	—
859	#97	—	13	2	no	—
860	#97	—	13	2	no	—
861	#97	—	13	2	no	—
862	#97	C₂²×D₁₃	1	2	yes	—
863	C₄×C₈	—	13	1	no	—
864	C₄×C₈	—	13	1	no	—
865	C₄×C₈	—	13	2	no	—
866	C₄×C₈	—	13	2	no	—
867	C₄×C₈	—	13	1	no	—
868	C₄×C₈	—	13	1	no	—
869	C₄×C₈	—	13	2	no	—
870	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
871	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
872	C₄×C₈	C₂²×D₁₃	1	2	yes	—
873	C₂×C₁₃	—	4	2	no	—
874	C₂×C₁₃	—	4	1	no	—
875	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
876	C₂×C₁₃	C₂²×#131	1	1	yes	characteristic
877	C₂×C₁₃	#3573	1	1	yes	characteristic
878	D₁₃	—	2	2	no	—
879	D₁₃	—	2	4	no	—
880	D₁₃	—	4	1	no	—
881	C₂⁴	—	13	2	no	—
882	#41	—	26	2	no	—
883	#41	—	26	2	no	—
884	#41	—	26	4	no	—
885	#41	—	26	4	no	—
886	C₂×Q₈	—	13	1	no	—
887	C₂×Q₈	—	13	1	no	—
888	C₂×Q₈	—	13	2	no	—
889	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
890	C₂×D₄	—	13	1	no	—
891	C₂×D₄	—	13	2	no	—
892	C₂×D₄	—	13	1	no	—
893	C₂×D₄	—	13	2	no	—
894	C₂×D₄	—	13	2	no	—
895	C₂×D₄	—	13	1	no	—
896	C₂×D₄	—	13	1	no	—
897	C₂×D₄	—	13	2	no	—
898	C₂×D₄	—	26	4	no	—
899	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
900	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
901	C₂²×C₄	—	13	1	no	—
902	C₂²×C₄	—	13	2	no	—
903	C₂²×C₄	—	13	2	no	—
904	C₂²×C₄	—	13	2	no	—
905	C₂²×C₄	—	13	1	no	—
906	C₂²×C₄	—	13	1	no	—
907	C₂²×C₄	—	13	2	no	—
908	C₂²×C₄	—	13	2	no	—
909	C₂²×C₄	—	13	2	no	—
910	C₂²×C₄	—	13	1	no	—
911	C₂²×C₄	—	13	1	no	—
912	C₂²×C₄	—	13	2	no	—
913	C₂²×C₄	—	13	2	no	—
914	C₂²×C₄	—	13	1	no	—
915	C₂²×C₄	—	26	4	no	—
916	C₂²×C₄	—	26	4	no	—
917	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
918	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
919	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
920	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
921	M₁₆	—	4	2	no	—
922	M₁₆	—	26	2	no	—
923	M₁₆	—	26	4	no	—
924	M₁₆	—	26	2	no	—
925	M₁₆	—	52	2	no	—
926	M₁₆	—	52	2	no	—
927	M₁₆	—	52	2	no	—
928	C₂×C₈	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	—	13	1	no	—
931	C₂×C₈	—	13	1	no	—
932	C₂×C₈	—	13	1	no	—
933	C₂×C₈	—	13	1	no	—
934	C₂×C₈	—	13	2	no	—
935	C₂×C₈	—	13	2	no	—
936	C₂×C₈	—	26	2	no	—
937	C₂×C₈	—	26	4	no	—
938	C₂×C₈	—	26	2	no	—
939	C₂×C₈	—	52	2	no	—
940	C₂×C₈	—	52	2	no	—
941	C₂×C₈	—	52	2	no	—
942	C₂×C₈	—	52	2	no	—
943	C₂×C₈	—	52	2	no	—
944	C₂×C₈	—	52	2	no	—
945	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
946	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
947	C₂×C₈	C₂³×D₁₃	1	2	yes	—
948	C₂×C₈	C₂³×D₁₃	1	2	yes	—
949	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
950	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
951	C₄⋊C₄	—	13	1	no	—
952	C₄⋊C₄	—	13	1	no	—
953	C₄⋊C₄	—	13	1	no	—
954	C₄⋊C₄	—	13	2	no	—
955	C₄⋊C₄	—	13	2	no	—
956	C₄⋊C₄	—	13	2	no	—
957	C₄⋊C₄	—	13	2	no	—
958	C₄⋊C₄	—	13	2	no	—
959	C₄⋊C₄	—	13	1	no	—
960	C₄⋊C₄	—	13	1	no	—
961	C₄⋊C₄	—	13	1	no	—
962	C₄⋊C₄	—	13	2	no	—
963	C₄⋊C₄	—	13	2	no	—
964	C₄⋊C₄	—	13	2	no	—
965	C₄⋊C₄	—	13	1	no	—
966	C₄⋊C₄	—	13	1	no	—
967	C₄⋊C₄	—	13	2	no	—
968	C₄⋊C₄	—	13	2	no	—
969	C₄⋊C₄	—	13	2	no	—
970	C₄⋊C₄	—	13	2	no	—
971	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
972	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
973	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
976	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
977	C₂²⋊C₄	—	13	2	no	—
978	C₂²⋊C₄	—	13	2	no	—
979	C₂²⋊C₄	—	13	2	no	—
980	C₂²⋊C₄	—	13	1	no	—
981	C₂²⋊C₄	—	13	2	no	—
982	C₂²⋊C₄	—	13	1	no	—
983	C₂²⋊C₄	—	13	2	no	—
984	C₂²⋊C₄	—	13	1	no	—
985	C₂²⋊C₄	—	13	1	no	—
986	C₂²⋊C₄	—	13	2	no	—
987	C₂²⋊C₄	—	13	2	no	—
988	C₂²⋊C₄	—	13	2	no	—
989	C₂²⋊C₄	—	13	2	no	—
990	C₂²⋊C₄	—	13	2	no	—
991	C₂²⋊C₄	—	13	2	no	—
992	C₂²⋊C₄	—	13	1	no	—
993	C₂²⋊C₄	—	13	2	no	—
994	C₂²⋊C₄	—	13	1	no	—
995	C₂²⋊C₄	—	13	2	no	—
996	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
997	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
998	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
999	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1000	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1001	C₄²	—	13	2	no	—
1002	C₄²	—	13	2	no	—
1003	C₄²	—	13	2	no	—
1004	C₄²	—	13	2	no	—
1005	C₄²	—	13	1	no	—
1006	C₄²	—	13	1	no	—
1007	C₄²	—	13	1	no	—
1008	C₄²	—	13	1	no	—
1009	C₄²	—	13	1	no	—
1010	C₄²	—	13	2	no	—
1011	C₄²	—	13	1	no	—
1012	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
1013	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
1014	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1015	C₄²	C₂³×D₁₃	1	2	yes	—
1016	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1017	C₁₃	#60271	1	1	yes	characteristic, complemented, Sylow
1018	C₂³	—	13	1	no	—
1019	C₂³	—	13	2	no	—
1020	C₂³	—	13	1	no	—
1021	C₂³	—	26	4	no	—
1022	C₂³	—	26	4	no	—
1023	C₂³	—	52	2	no	—
1024	C₂³	C₂²×C₄×D₁₃	1	2	yes	—
1025	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
1026	Q₈	—	2	2	no	—
1027	Q₈	—	26	2	no	—
1028	Q₈	—	26	2	no	—
1029	Q₈	—	52	2	no	—
1030	D₄	—	2	2	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	13	4	no	—
1033	D₄	—	26	4	no	—
1034	D₄	—	26	2	no	—
1035	D₄	—	26	2	no	—
1036	D₄	—	26	4	no	—
1037	D₄	—	26	4	no	—
1038	D₄	—	26	2	no	—
1039	D₄	—	52	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	4	1	no	—
1046	C₂×C₄	—	13	1	no	—
1047	C₂×C₄	—	13	2	no	—
1048	C₂×C₄	—	13	2	no	—
1049	C₂×C₄	—	13	1	no	—
1050	C₂×C₄	—	13	1	no	—
1051	C₂×C₄	—	13	2	no	—
1052	C₂×C₄	—	13	1	no	—
1053	C₂×C₄	—	13	2	no	—
1054	C₂×C₄	—	13	2	no	—
1055	C₂×C₄	—	13	1	no	—
1056	C₂×C₄	—	13	1	no	—
1057	C₂×C₄	—	26	4	no	—
1058	C₂×C₄	—	26	4	no	—
1059	C₂×C₄	—	26	4	no	—
1060	C₂×C₄	—	26	4	no	—
1061	C₂×C₄	—	26	4	no	—
1062	C₂×C₄	—	26	2	no	—
1063	C₂×C₄	—	26	2	no	—
1064	C₂×C₄	—	26	2	no	—
1065	C₂×C₄	—	26	1	no	—
1066	C₂×C₄	—	26	2	no	—
1067	C₂×C₄	—	26	1	no	—
1068	C₂×C₄	—	52	1	no	—
1069	C₂×C₄	—	52	2	no	—
1070	C₂×C₄	—	52	1	no	—
1071	C₂×C₄	—	52	2	no	—
1072	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1073	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1074	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1075	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1076	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1077	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1078	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1079	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1080	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₈	—	2	2	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	2	1	no	—
1087	C₈	—	26	1	no	—
1088	C₈	—	26	2	no	—
1089	C₈	—	26	1	no	—
1090	C₈	—	26	2	no	—
1091	C₈	—	26	1	no	—
1092	C₈	—	26	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	1	no	—
1099	C₂²	—	13	4	no	—
1100	C₂²	—	13	2	no	—
1101	C₂²	—	26	1	no	—
1102	C₂²	—	26	2	no	—
1103	C₂²	—	26	1	no	—
1104	C₂²	—	26	2	no	—
1105	C₂²	—	26	1	no	—
1106	C₂²	—	26	1	no	—
1107	C₂²	—	26	1	no	—
1108	C₂²	—	52	8	no	—
1109	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
1110	C₄	—	2	1	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	1	no	—
1117	C₄	—	13	2	no	—
1118	C₄	—	26	1	no	—
1119	C₄	—	26	1	no	—
1120	C₄	—	26	2	no	—
1121	C₄	—	26	1	no	—
1122	C₄	—	26	2	no	—
1123	C₄	—	26	1	no	—
1124	C₄	—	26	2	no	—
1125	C₄	—	26	1	no	—
1126	C₄	D₁₃×#131	1	2	yes	—
1127	C₄	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1128	C₄	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1129	C₂	—	4	2	no	—
1130	C₂	—	4	1	no	—
1131	C₂	—	26	2	no	—
1132	C₂	—	26	4	no	—
1133	C₂	—	52	1	no	—
1134	C₂	D₁₃×#520	1	1	yes	characteristic
1135	C₂	C₂×D₁₃×#131	1	1	yes	characteristic
1136	C₂	#13129547	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₁₃
commutator, socle	C₂²×C₁₃	C₂⁴×C₄
Fitting	C₁₃×#2994	C₂
prime radical	#13128392	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	#2994	D₁₃
hypocenter	C₁₃	#60271
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #2994

Complements

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

N	H ≅ G/N	type
2. #13123994	C₂	semidirect
3. #13123991	C₂	semidirect
4. #13123991	C₂	semidirect
5. #13123985	C₂	semidirect
6. #13123980	C₂	semidirect
7. #13123971	C₂	semidirect
8. #13123970	C₂	semidirect
9. #13123960	C₂	semidirect
10. #13123957	C₂	semidirect
11. #13123946	C₂	semidirect
12. #13123945	C₂	semidirect
13. #13123778	C₂	semidirect
14. #13123767	C₂	semidirect
15. #13123572	C₂	semidirect
16. #13123559	C₂	semidirect
17. #13123525	C₂	semidirect
18. C₈×D₄×D₁₃	C₂	semidirect
19. #13123492	C₂	semidirect
20. #13123475	C₂	semidirect
21. #13123401	C₂	semidirect
22. D₁₃×#424	C₂	semidirect
23. C₁₃×#2994	C₂	semidirect
50. C₁₃×#446	C₂²	semidirect
51. C₈×Q₈×C₁₃	C₂²	semidirect
53. C₁₃×#435	C₂²	semidirect
55. C₈×D₄×C₁₃	C₂²	semidirect
56. C₁₃×#433	C₂²	semidirect
57. C₁₃×#431	C₂²	semidirect
58. C₁₃×#424	C₂²	semidirect
59. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
60. #11718789	C₂²	semidirect
62. #11718780	C₂²	semidirect
64. C₈×C₂²⋊D₁₃	C₂²	semidirect
65. C₈×C₂²⋊D₁₃	C₂²	semidirect
66. C₈×C₂²⋊D₁₃	C₂²	semidirect
67. #11718763	C₂²	semidirect
68. #11718763	C₂²	semidirect
69. #11718685	C₂²	semidirect
70. Q₈×#1055	C₂²	semidirect
72. #11718673	C₂²	semidirect
73. #11718672	C₂²	semidirect
75. #11718661	C₂²	semidirect
76. #11718660	C₂²	semidirect
77. #11718586	C₂²	semidirect
78. #11718585	C₂²	semidirect
79. #11718501	C₂²	semidirect
80. #11718501	C₂²	semidirect
86. #11718500	C₂²	semidirect
88. #11718498	C₂²	semidirect
89. #11718497	C₂²	semidirect
90. #11718496	C₂²	semidirect
93. #11718495	C₂²	semidirect
94. #11718494	C₂²	semidirect
96. D₁₃×C₄⋊C₈	C₂²	semidirect
97. D₁₃×C₄⋊C₈	C₂²	semidirect
98. D₁₃×C₄⋊C₈	C₂²	semidirect
99. D₁₃×C₄⋊C₈	C₂²	semidirect
100. D₁₃×C₄⋊C₈	C₂²	semidirect
101. #11718491	C₂²	semidirect
102. #11718491	C₂²	semidirect
103. #11718491	C₂²	semidirect
104. #11718489	C₂²	semidirect
105. #11718391	C₂²	semidirect
107. #11718389	C₂²	semidirect
108. #11718389	C₂²	semidirect
109. #11718389	C₂²	semidirect
115. #11718381	C₂²	semidirect
116. #11718381	C₂²	semidirect
117. #11718381	C₂²	semidirect
118. #11718381	C₂²	semidirect
120. #11718367	C₂²	semidirect
121. #11718366	C₂²	semidirect
122. #11718362	C₂²	semidirect
127. C₈×D₅₂	C₂²	semidirect
128. #11718346	C₂²	semidirect
129. #11718346	C₂²	semidirect
130. #11718346	C₂²	semidirect
132. #11718340	C₂²	semidirect
133. #11718340	C₂²	semidirect
134. #11718340	C₂²	semidirect
454. #2994	D₁₃	semidirect
516. D₅₂	#131	semidirect
580. #446	C₂×D₁₃	semidirect
585. C₈×Q₈	C₂×D₁₃	semidirect
599. #435	C₂×D₁₃	semidirect
613. C₈×D₄	C₂×D₁₃	semidirect
621. #433	C₂×D₁₃	semidirect
629. #431	C₂×D₁₃	semidirect
640. #424	C₂×D₁₃	semidirect
650. C₂×C₄⋊C₈	C₂×D₁₃	semidirect
1017. C₁₃	#60271	semidirect

Maximal subgroups

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

subgroup	index
#13128392	2
#13123994	2
#13123991	2
#13123985	2
#13123980	2
#13123971	2
#13123970	2
#13123960	2
#13123957	2
#13123946	2
#13123945	2
#13123778	2
#13123767	2
#13123572	2
#13123559	2
#13123525	2
C₈×D₄×D₁₃	2
#13123492	2
#13123475	2
#13123401	2
D₁₃×#424	2
C₁₃×#2994	2
#60271	13