Subgroups — #16727586

Order 3328.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128400	C₂	1	1	yes	maximal, characteristic
2	#13123847	C₂	1	2	yes	maximal, complemented
3	#13123836	C₂	1	2	yes	maximal, complemented
4	#13123830	C₂	1	2	yes	maximal, complemented
5	#13123826	C₂	1	2	yes	maximal, complemented
6	#13123821	C₂	1	2	yes	maximal, complemented
7	#13123817	C₂	1	2	yes	maximal, complemented
8	#13123807	C₂	1	2	yes	maximal, complemented
9	#13123798	C₂	1	2	yes	maximal, complemented
10	#13123783	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123776	C₂	1	1	yes	maximal, characteristic, complemented
12	M₁₆×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
13	#13123558	C₂	1	1	yes	maximal, characteristic, complemented
14	#13123558	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123537	C₂	1	1	yes	maximal, characteristic, complemented
16	#13123528	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#11718367	C₂	1	1	yes	maximal, characteristic, complemented
18	#13123502	C₂	1	1	yes	maximal, characteristic, complemented
19	#13123491	C₂	1	1	yes	maximal, characteristic, complemented
20	#13123491	C₂	1	1	yes	maximal, characteristic, complemented
21	#13123252	C₂	1	1	yes	maximal, characteristic, complemented
22	D₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
27	#11719533	C₂²	1	1	yes	characteristic
28	#11719533	C₂²	1	1	yes	characteristic
29	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
30	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
31	C₂²×#6094	C₂²	1	1	yes	characteristic
32	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
33	#11719289	C₄	1	1	yes	characteristic
34	#11719286	C₄	1	1	yes	characteristic
35	#11719286	C₄	1	1	yes	characteristic
36	#11719284	C₄	1	1	yes	characteristic
37	#11719268	C₄	1	1	yes	characteristic
38	#11719263	C₄	1	1	yes	characteristic
39	#11719263	C₄	1	1	yes	characteristic
40	#11719261	C₄	1	2	yes	—
41	#11719261	C₄	1	2	yes	—
42	#11719256	C₄	1	1	yes	characteristic
43	#11719255	C₄	1	2	yes	—
44	#11719246	C₄	1	2	yes	—
45	#11719233	C₂²	1	2	yes	—
46	#11719233	C₂²	1	2	yes	—
47	D₁₃×#117	C₂²	1	1	yes	characteristic
48	D₁₃×#117	C₂²	1	1	yes	characteristic
49	#11719184	C₂²	1	2	yes	—
50	C₄×#6127	C₂²	1	2	yes	—
51	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
52	#11719175	C₂²	1	1	yes	characteristic
53	C₁₃×#405	C₂²	1	1	yes	characteristic
54	C₁₃×#405	C₂²	1	1	yes	characteristic
55	C₁₃×#405	C₂²	1	2	yes	complemented
56	C₁₃×#405	C₂²	1	2	yes	complemented
57	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
59	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
61	#11718895	C₂²	1	1	yes	characteristic
62	#11718895	C₂²	1	1	yes	characteristic
63	#11718789	C₂²	1	2	yes	complemented
64	#11718789	C₂²	1	2	yes	complemented
65	#11718789	C₂²	1	2	yes	complemented
66	#11718789	C₂²	1	2	yes	complemented
67	#11718788	C₂²	1	2	yes	complemented
68	#11718788	C₂²	1	2	yes	complemented
69	#11718788	C₂²	1	2	yes	complemented
70	#11718788	C₂²	1	2	yes	complemented
71	#11718787	C₂²	1	1	yes	characteristic
72	#11718787	C₂²	1	1	yes	characteristic
73	#11718783	C₂²	1	1	yes	characteristic
74	#11718783	C₂²	1	1	yes	characteristic
75	#11718780	C₂²	1	1	yes	characteristic
76	#11718780	C₂²	1	1	yes	characteristic
77	#11718772	C₂²	1	2	yes	complemented
78	#11718772	C₂²	1	2	yes	complemented
79	#11718772	C₂²	1	2	yes	complemented
80	#11718772	C₂²	1	2	yes	complemented
81	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
82	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
83	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
84	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
85	C₂×#88060	C₂²	1	1	yes	characteristic
86	C₂×#88060	C₂²	1	1	yes	characteristic
87	#11718763	C₂²	1	1	yes	characteristic
88	#11718763	C₂²	1	1	yes	characteristic
89	#11718762	C₂²	1	1	yes	characteristic
90	#11718762	C₂²	1	1	yes	characteristic
91	#11718661	C₂²	1	2	yes	complemented
92	#11718661	C₂²	1	2	yes	complemented
93	#11718658	C₂²	1	1	yes	characteristic
94	#11718658	C₂²	1	1	yes	characteristic
95	#11718587	C₂²	1	2	yes	complemented
96	#11718586	C₂²	1	2	yes	complemented
97	#11718585	C₂²	1	1	yes	characteristic
98	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
99	#11718370	C₂²	1	2	yes	complemented
100	#11718370	C₂²	1	2	yes	complemented
101	#11718369	C₂²	1	2	yes	complemented
102	#11718369	C₂²	1	2	yes	complemented
103	#11718368	C₂²	1	2	yes	complemented
104	#11718367	C₂²	1	1	yes	characteristic
105	#11718367	C₂²	1	2	yes	—
106	#11718367	C₂²	1	1	yes	characteristic
107	#11718367	C₂²	1	1	yes	characteristic
108	#11718367	C₂²	1	1	yes	characteristic
109	#11718367	C₂²	1	1	yes	characteristic
110	#11718367	C₂²	1	1	yes	characteristic
111	#11718367	C₂²	1	1	yes	characteristic
112	#11718367	C₂²	1	1	yes	characteristic
113	#11718367	C₂²	1	2	yes	—
114	#11718366	C₂²	1	2	yes	complemented
115	#11718366	C₂²	1	2	yes	complemented
116	D₁₃×#97	C₂²	1	2	yes	complemented
117	#11718362	C₂²	1	2	yes	complemented
118	#11718362	C₂²	1	2	yes	complemented
119	#11718362	C₂²	1	2	yes	complemented
120	#11718362	C₂²	1	2	yes	complemented
121	#11718362	C₂²	1	2	yes	complemented
122	#11718362	C₂²	1	2	yes	complemented
123	#11718351	C₂²	1	2	yes	complemented
124	#11718351	C₂²	1	2	yes	complemented
125	#11718350	C₂²	1	2	yes	complemented
126	#11718350	C₂²	1	2	yes	complemented
127	#11718349	C₂²	1	2	yes	—
128	C₄×#6094	C₂²	1	2	yes	complemented
129	C₈×D₅₂	C₂²	1	2	yes	—
130	#11718346	C₂²	1	2	yes	complemented
131	#11718346	C₂²	1	2	yes	complemented
132	C₄×C₈×D₁₃	C₂²	1	2	yes	complemented
133	#11718340	C₂²	1	2	yes	complemented
134	C₈×Dic₂₆	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
136	C₂×#6127	C₂×C₄	1	2	yes	—
137	C₂²×D₅₂	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
140	C₁₃×#131	—	2	4	no	—
141	C₁₃×#131	—	2	4	no	—
142	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
148	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
149	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
151	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
153	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
154	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
155	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
156	C₁₃×#117	C₂³	1	1	yes	characteristic
157	C₁₃×#117	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
160	#88200	C₂×C₄	1	1	yes	characteristic
161	#88200	C₂×C₄	1	1	yes	characteristic
162	#88200	C₂×C₄	1	1	yes	characteristic
163	#88200	C₂×C₄	1	1	yes	characteristic
164	#88192	C₂×C₄	1	1	yes	characteristic
165	#88192	C₂×C₄	1	1	yes	characteristic
166	#88192	C₂×C₄	1	1	yes	characteristic
167	#88192	C₂×C₄	1	1	yes	characteristic
168	#88191	C₂×C₄	1	2	yes	—
169	#88191	C₂×C₄	1	2	yes	—
170	#88189	C₂×C₄	1	2	yes	—
171	#88189	C₂×C₄	1	2	yes	—
172	#88184	C₂×C₄	1	2	yes	—
173	#88183	C₂×C₄	1	2	yes	—
174	#88183	C₂×C₄	1	2	yes	—
175	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
176	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
177	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
178	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
179	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
180	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
181	C₂×#6103	C₂×C₄	1	1	yes	characteristic
182	C₂×#6103	C₂×C₄	1	1	yes	characteristic
183	#88180	C₂×C₄	1	2	yes	—
184	#88180	C₂³	1	1	yes	characteristic
185	#88180	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
187	#88178	C₂×C₄	1	2	yes	—
188	#88178	C₂×C₄	1	2	yes	—
189	#88178	C₂×C₄	1	2	yes	—
190	C₂×#6099	C₂³	1	1	yes	characteristic
191	C₂×#6099	C₂³	1	1	yes	characteristic
192	C₂²×#1055	C₂³	1	1	yes	characteristic
193	C₂²×#1055	C₂³	1	1	yes	characteristic
194	M₁₆×D₁₃	—	2	4	no	—
195	M₁₆×D₁₃	—	2	4	no	—
196	C₂×#6094	—	2	4	no	—
197	C₂×#6094	C₂³	1	1	yes	characteristic
198	C₂×#6094	C₂³	1	1	yes	characteristic
199	C₂×#6094	C₂³	1	1	yes	characteristic
200	C₂×#6094	C₂³	1	1	yes	characteristic
201	C₂×#6094	C₂³	1	2	yes	—
202	C₂×#6094	C₂³	1	2	yes	—
203	C₂×C₈×D₁₃	—	2	4	no	—
204	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₈×D₁₃	C₂³	1	2	yes	—
209	C₂×C₈×D₁₃	C₂³	1	2	yes	—
210	#88152	C₂×C₄	1	2	yes	—
211	#88152	C₂×C₄	1	2	yes	—
212	#88150	C₂×C₄	1	2	yes	—
213	#88150	C₂×C₄	1	2	yes	—
214	#88148	C₂×C₄	1	2	yes	—
215	#88148	C₂×C₄	1	2	yes	—
216	#88146	C₂×C₄	1	1	yes	characteristic
217	#88146	C₂×C₄	1	1	yes	characteristic
218	#88146	C₂×C₄	1	1	yes	characteristic
219	#88146	C₂×C₄	1	1	yes	characteristic
220	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
221	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
222	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
223	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
224	#88143	C₂×C₄	1	2	yes	—
225	#88143	C₂×C₄	1	2	yes	—
226	#88139	C₂×C₄	1	2	yes	—
227	#88139	C₂×C₄	1	2	yes	—
228	#88138	C₂×C₄	1	2	yes	—
229	#88138	C₂×C₄	1	2	yes	—
230	#88137	C₂×C₄	1	2	yes	—
231	#88137	C₂×C₄	1	2	yes	—
232	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
233	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
234	#88133	C₂×C₄	1	2	yes	—
235	#88133	C₂×C₄	1	2	yes	—
236	#88131	C₂×C₄	1	2	yes	—
237	#88131	C₂×C₄	1	2	yes	—
238	#88130	C₂×C₄	1	2	yes	—
239	#88130	C₂×C₄	1	2	yes	—
240	#88129	C₂×C₄	1	2	yes	—
241	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
242	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
243	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
244	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
245	C₄×D₅₂	C₂×C₄	1	2	yes	—
246	C₄×D₅₂	C₂³	1	1	yes	characteristic
247	C₄×D₅₂	C₂³	1	1	yes	characteristic
248	C₄×D₅₂	C₂³	1	1	yes	characteristic
249	C₄×D₅₂	C₂³	1	1	yes	characteristic
250	#88126	C₂×C₄	1	2	yes	—
251	#88126	C₂×C₄	1	2	yes	—
252	#88126	C₂³	1	2	yes	—
253	#88126	C₂³	1	2	yes	—
254	C₄²×D₁₃	C₂³	1	2	yes	—
255	C₄²×D₁₃	C₂³	1	2	yes	—
256	#88124	C₂×C₄	1	1	yes	characteristic
257	#88124	C₂×C₄	1	1	yes	characteristic
258	#88124	C₂×C₄	1	2	yes	—
259	#88123	C₂×C₄	1	1	yes	characteristic
260	#88123	C₂×C₄	1	1	yes	characteristic
261	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
262	C₄×Dic₂₆	C₂³	1	2	yes	—
263	C₄×Dic₂₆	C₂³	1	2	yes	—
264	C₁₃×#97	C₂³	1	1	yes	characteristic
265	C₁₃×#97	C₂³	1	1	yes	characteristic
266	C₁₃×#97	C₂³	1	1	yes	characteristic
267	C₁₃×#97	C₂³	1	1	yes	characteristic
268	C₁₃×#97	C₂³	1	2	yes	—
269	C₁₃×#97	C₂³	1	2	yes	—
270	C₁₃×#97	C₂³	1	2	yes	—
271	C₄×C₈×C₁₃	C₂³	1	2	yes	—
272	C₄×C₈×C₁₃	C₂³	1	2	yes	—
273	C₄×C₈×C₁₃	C₂³	1	2	yes	—
274	C₂²⋊#1055	C₂³	1	2	yes	—
275	C₂²⋊#1055	C₂³	1	2	yes	—
276	C₂²⋊#1055	C₂³	1	2	yes	—
277	C₂²⋊#1055	C₂³	1	2	yes	—
278	#88060	C₂³	1	1	yes	characteristic
279	#88060	C₂³	1	1	yes	characteristic
280	#88060	C₂³	1	1	yes	characteristic
281	#88060	C₂³	1	1	yes	characteristic
282	#88060	C₂³	1	1	yes	characteristic
283	#88060	C₂³	1	1	yes	characteristic
284	#88060	C₂³	1	1	yes	characteristic
285	#88060	C₂³	1	1	yes	characteristic
286	#88060	C₂³	1	2	yes	—
287	#88060	C₂³	1	2	yes	—
288	#88060	C₂³	1	2	yes	—
289	#88060	C₂³	1	2	yes	—
290	#88055	C₂³	1	2	yes	—
291	#88055	C₂³	1	2	yes	—
292	#88055	C₂³	1	2	yes	—
293	#88055	C₂³	1	2	yes	—
294	#88054	C₂³	1	2	yes	—
295	#88054	C₂³	1	2	yes	—
296	#88054	C₂³	1	2	yes	—
297	#88054	C₂³	1	2	yes	—
298	#88054	C₂³	1	2	yes	—
299	#88054	C₂³	1	2	yes	—
300	#88054	C₂³	1	2	yes	—
301	#88054	C₂³	1	2	yes	—
302	C₈×Dic₁₃	C₂³	1	2	yes	—
303	C₈×Dic₁₃	C₂³	1	2	yes	—
304	C₈×Dic₁₃	C₂³	1	2	yes	—
305	C₈×Dic₁₃	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	2	yes	—
309	C₄⋊#1055	C₂³	1	1	yes	characteristic
310	C₄⋊#1055	C₂³	1	1	yes	characteristic
311	C₄⋊#1055	C₂³	1	2	yes	—
312	#88043	C₂³	1	2	yes	—
313	#88043	C₂³	1	2	yes	—
314	C₄×#1055	C₂³	1	2	yes	—
315	C₄×#1055	C₂³	1	2	yes	—
316	#60216	—	13	1	no	maximal, Sylow
317	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
318	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
319	C₁₃×#41	—	2	2	no	—
320	C₁₃×#41	—	2	2	no	—
321	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
322	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
323	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
324	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
325	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
327	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
328	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
331	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
332	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
333	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
334	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
335	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
336	#6127	—	4	4	no	—
337	C₂×D₅₂	—	4	2	no	—
338	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
339	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
340	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
341	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₄×D₁₃	—	2	2	no	—
343	C₂×C₄×D₁₃	—	2	2	no	—
344	C₂×C₄×D₁₃	—	2	2	no	—
345	C₂×C₄×D₁₃	—	2	2	no	—
346	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
347	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
351	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
352	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
353	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
354	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
358	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
359	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
360	C₁₃×M₁₆	—	2	2	no	—
361	C₁₃×M₁₆	—	2	4	no	—
362	C₁₃×M₁₆	—	2	4	no	—
363	C₁₃×M₁₆	#41	1	4	yes	complemented
364	C₂×C₈×C₁₃	—	2	2	no	—
365	C₂×C₈×C₁₃	—	2	4	no	—
366	C₂×C₈×C₁₃	—	2	4	no	—
367	C₂×C₈×C₁₃	#41	1	4	yes	complemented
368	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
369	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
372	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
375	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
376	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
377	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
378	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
379	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
380	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
381	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
382	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
383	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
384	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
385	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₄²×C₁₃	C₂⁴	1	2	yes	—
387	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
389	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
390	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
391	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
392	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
393	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
394	#6103	C₂²×C₄	1	1	yes	characteristic
395	#6103	C₂²×C₄	1	1	yes	characteristic
396	#6103	C₂²×C₄	1	2	yes	—
397	#6103	C₂²×C₄	1	2	yes	—
398	#6103	C₂²×C₄	1	2	yes	—
399	#6103	C₂²×C₄	1	2	yes	—
400	#6103	C₂²×C₄	1	2	yes	—
401	#6103	C₂²×C₄	1	2	yes	—
402	#6103	C₂²×C₄	1	1	yes	characteristic
403	#6103	C₂²×C₄	1	1	yes	characteristic
404	#6103	C₂²×C₄	1	1	yes	characteristic
405	#6103	C₂²×C₄	1	1	yes	characteristic
406	#6103	C₂²×C₄	1	1	yes	characteristic
407	#6103	C₂²×C₄	1	1	yes	characteristic
408	#6103	C₂²×C₄	1	2	yes	—
409	#6103	C₂²×C₄	1	2	yes	—
410	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
411	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
412	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
413	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
414	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
415	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
416	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
417	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
418	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
419	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
420	#6101	C₂²×C₄	1	2	yes	—
421	#6101	C₂²×C₄	1	2	yes	—
422	#6101	C₂²×C₄	1	2	yes	—
423	#6101	C₂²×C₄	1	2	yes	—
424	#6101	C₂²×C₄	1	2	yes	—
425	#6101	C₂²×C₄	1	2	yes	—
426	#6101	C₂²×C₄	1	2	yes	—
427	#6101	C₂²×C₄	1	2	yes	—
428	#6101	C₂²×C₄	1	2	yes	—
429	#6101	C₂²×C₄	1	2	yes	—
430	#6101	C₂²×C₄	1	2	yes	—
431	#6101	C₂²×C₄	1	2	yes	—
432	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
433	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
434	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
435	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
436	C₄×Dic₁₃	C₂⁴	1	2	yes	—
437	C₄×Dic₁₃	C₂⁴	1	2	yes	—
438	#6099	—	2	2	no	—
439	#6099	—	2	2	no	—
440	C₂×#1055	—	2	2	no	—
441	C₂×#1055	—	2	2	no	—
442	C₂×#1055	C₂⁴	1	1	yes	characteristic
443	C₂×#1055	C₂⁴	1	1	yes	characteristic
444	C₂×#1055	C₂⁴	1	2	yes	—
445	C₂×#1055	C₂⁴	1	2	yes	—
446	C₂×#1055	C₂⁴	1	1	yes	characteristic
447	C₂×#1055	C₂⁴	1	1	yes	characteristic
448	#6094	—	2	2	no	—
449	#6094	—	2	2	no	—
450	#6094	—	2	2	no	—
451	#6094	—	2	2	no	—
452	#6094	—	2	4	no	—
453	#6094	—	2	4	no	—
454	C₈×D₁₃	—	2	2	no	—
455	C₈×D₁₃	—	2	2	no	—
456	C₈×D₁₃	—	2	2	no	—
457	C₈×D₁₃	—	2	2	no	—
458	C₈×D₁₃	—	2	4	no	—
459	C₈×D₁₃	—	2	4	no	—
460	#3475	—	13	1	no	—
461	#2970	—	13	2	no	—
462	#2969	—	13	2	no	—
463	#2968	—	13	2	no	—
464	#2968	—	13	2	no	—
465	#2967	—	13	2	no	—
466	#2967	—	13	2	no	—
467	#2966	—	13	2	no	—
468	#2965	—	13	2	no	—
469	#2962	—	13	1	no	—
470	#2961	—	13	1	no	—
471	D₄×M₁₆	—	13	1	no	—
472	#2933	—	13	1	no	—
473	#2933	—	13	1	no	—
474	#2930	—	13	1	no	—
475	#2929	—	13	1	no	—
476	C₂×#435	—	13	1	no	—
477	#2925	—	13	1	no	—
478	#2924	—	13	1	no	—
479	#2924	—	13	1	no	—
480	#2875	D₁₃	1	1	yes	characteristic, complemented
481	#2873	—	13	1	no	—
482	C₂×#405	—	13	1	no	—
483	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
484	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
485	C₂²×D₁₃	—	2	2	no	—
486	C₂²×D₁₃	—	2	2	no	—
487	C₂²×D₁₃	—	2	2	no	—
488	C₂²×D₁₃	—	4	1	no	—
489	C₂²×D₁₃	—	4	1	no	—
490	C₂²×D₁₃	—	4	1	no	—
491	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
492	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
493	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
494	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
495	Q₈×C₁₃	—	2	2	no	—
496	D₄×C₁₃	—	2	4	no	—
497	D₄×C₁₃	—	2	2	no	—
498	C₂×C₄×C₁₃	—	2	2	no	—
499	C₂×C₄×C₁₃	—	2	2	no	—
500	C₂×C₄×C₁₃	—	4	1	no	—
501	C₂×C₄×C₁₃	—	4	2	no	—
502	C₂×C₄×C₁₃	—	4	1	no	—
503	C₂×C₄×C₁₃	—	4	2	no	—
504	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
505	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
506	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
507	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
508	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
509	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
510	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
511	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
512	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
513	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
514	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
515	C₂²⋊D₁₃	—	2	4	no	—
516	C₂²⋊D₁₃	—	4	2	no	—
517	C₂²⋊D₁₃	—	4	2	no	—
518	C₂²⋊D₁₃	—	4	2	no	—
519	C₂×Dic₁₃	—	2	2	no	—
520	C₂×Dic₁₃	—	2	2	no	—
521	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
522	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
523	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
524	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
525	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
526	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
527	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
528	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
529	D₅₂	—	2	2	no	—
530	D₅₂	—	2	2	no	—
531	D₅₂	—	4	1	no	—
532	D₅₂	—	4	1	no	—
533	C₄×D₁₃	—	2	4	no	—
534	C₄×D₁₃	—	2	2	no	—
535	C₄×D₁₃	—	2	2	no	—
536	C₄×D₁₃	—	2	2	no	—
537	C₄×D₁₃	—	2	2	no	—
538	C₄×D₁₃	—	2	1	no	—
539	C₄×D₁₃	—	2	1	no	—
540	C₄×D₁₃	—	2	1	no	—
541	C₄×D₁₃	—	2	1	no	—
542	C₄×D₁₃	—	2	1	no	—
543	C₄×D₁₃	—	2	1	no	—
544	C₄×D₁₃	—	2	1	no	—
545	C₄×D₁₃	—	2	1	no	—
546	C₄×D₁₃	—	4	2	no	—
547	C₄×D₁₃	—	4	2	no	—
548	C₄×D₁₃	—	4	2	no	—
549	Dic₂₆	—	4	2	no	—
550	Dic₂₆	—	4	2	no	—
551	C₈×C₁₃	—	2	1	no	—
552	C₈×C₁₃	—	2	1	no	—
553	C₈×C₁₃	—	2	2	no	—
554	C₈×C₁₃	C₂×#41	1	2	yes	—
555	C₈×C₁₃	C₂×#41	1	4	yes	—
556	C₈×C₁₃	C₂×#41	1	2	yes	—
557	#1055	—	2	1	no	—
558	#1055	—	2	1	no	—
559	#1055	—	2	2	no	—
560	#1055	—	2	2	no	—
561	#1055	—	2	1	no	—
562	#1055	—	2	1	no	—
563	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
564	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
565	C₂²×M₁₆	—	13	1	no	—
566	C₂²×M₁₆	—	13	1	no	—
567	C₂²×M₁₆	—	13	1	no	—
568	C₂³×C₈	—	13	1	no	—
569	#556	—	13	1	no	—
570	#555	—	13	1	no	—
571	#554	—	13	1	no	—
572	#553	—	13	1	no	—
573	#553	—	13	1	no	—
574	#552	—	13	1	no	—
575	#552	—	13	1	no	—
576	#552	—	13	2	no	—
577	#551	—	13	2	no	—
578	#551	—	13	2	no	—
579	#547	—	13	1	no	—
580	#546	—	13	2	no	—
581	#533	—	13	1	no	—
582	#529	—	13	2	no	—
583	#529	—	13	2	no	—
584	#529	—	13	2	no	—
585	#525	—	13	1	no	—
586	#525	—	13	1	no	—
587	C₄×#41	—	13	2	no	—
588	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
589	C₂×C₄×D₄	—	13	1	no	—
590	C₂×#117	—	13	1	no	—
591	C₂×#117	—	13	1	no	—
592	#446	—	13	2	no	—
593	#446	—	13	2	no	—
594	#446	—	13	2	no	—
595	#446	—	13	2	no	—
596	#446	—	13	2	no	—
597	#446	—	13	2	no	—
598	#446	—	13	2	no	—
599	C₈×Q₈	—	13	2	no	—
600	#436	—	13	2	no	—
601	#436	—	13	2	no	—
602	#436	—	13	2	no	—
603	#436	—	13	2	no	—
604	#436	—	13	2	no	—
605	#435	—	13	2	no	—
606	#435	—	13	2	no	—
607	#435	—	13	2	no	—
608	#435	—	13	2	no	—
609	#435	—	13	2	no	—
610	#435	—	13	2	no	—
611	#435	—	13	2	no	—
612	#435	—	13	2	no	—
613	#435	—	13	1	no	—
614	#435	—	13	1	no	—
615	#435	—	13	1	no	—
616	#435	—	13	1	no	—
617	#435	—	13	1	no	—
618	#435	—	13	1	no	—
619	#435	—	13	1	no	—
620	#435	—	13	1	no	—
621	#435	—	13	2	no	—
622	#435	—	13	2	no	—
623	C₈×D₄	—	13	2	no	—
624	C₈×D₄	—	13	2	no	—
625	C₈×D₄	—	13	2	no	—
626	C₈×D₄	—	13	2	no	—
627	C₈×D₄	—	13	2	no	—
628	#433	—	13	2	no	—
629	#433	—	13	2	no	—
630	#433	—	13	2	no	—
631	#433	—	13	2	no	—
632	#433	—	13	2	no	—
633	#433	—	13	2	no	—
634	#432	—	13	2	no	—
635	#432	—	13	2	no	—
636	#432	—	13	2	no	—
637	#431	—	13	2	no	—
638	#431	—	13	2	no	—
639	#431	—	13	2	no	—
640	#424	—	13	1	no	—
641	#424	—	13	1	no	—
642	#424	—	13	1	no	—
643	#424	—	13	1	no	—
644	#423	—	13	1	no	—
645	C₂×C₄⋊C₈	—	13	1	no	—
646	#408	—	13	1	no	—
647	#408	—	13	1	no	—
648	#407	—	13	1	no	—
649	#407	—	13	1	no	—
650	C₂×C₂²⋊C₈	—	13	1	no	—
651	C₂×C₂²⋊C₈	—	13	1	no	—
652	#405	—	13	1	no	—
653	#405	—	13	1	no	—
654	#405	—	13	1	no	—
655	#405	—	13	1	no	—
656	#405	—	13	1	no	—
657	#405	—	13	1	no	—
658	#405	—	13	2	no	—
659	#405	—	13	2	no	—
660	#405	—	13	2	no	—
661	#405	—	13	2	no	—
662	#405	C₂×D₁₃	1	1	yes	characteristic
663	#405	C₂×D₁₃	1	1	yes	characteristic
664	#405	C₂×D₁₃	1	2	yes	complemented
665	#405	C₂×D₁₃	1	2	yes	complemented
666	C₄×M₁₆	—	13	2	no	—
667	C₄×M₁₆	—	13	2	no	—
668	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
669	C₄×M₁₆	C₂×D₁₃	1	2	yes	complemented
670	C₂×#97	—	13	2	no	—
671	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
672	C₂×#97	C₂×D₁₃	1	2	yes	complemented
673	C₂×C₄×C₈	—	13	2	no	—
674	C₂²×C₁₃	—	2	1	no	—
675	C₂²×C₁₃	—	2	1	no	—
676	C₂²×C₁₃	—	2	2	no	—
677	C₂²×C₁₃	—	2	2	no	—
678	C₂²×C₁₃	—	2	2	no	—
679	C₂²×C₁₃	C₄×#41	1	2	yes	—
680	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
681	C₂×D₁₃	—	2	1	no	—
682	C₂×D₁₃	—	2	1	no	—
683	C₂×D₁₃	—	2	1	no	—
684	C₂×D₁₃	—	2	1	no	—
685	C₂×D₁₃	—	2	1	no	—
686	C₂×D₁₃	—	2	1	no	—
687	C₂×D₁₃	—	2	1	no	—
688	C₂×D₁₃	—	2	1	no	—
689	C₂×D₁₃	—	2	1	no	—
690	C₂×D₁₃	—	2	1	no	—
691	C₂×D₁₃	—	2	1	no	—
692	C₂×D₁₃	—	4	4	no	—
693	C₂×D₁₃	—	8	2	no	—
694	C₂×D₁₃	#568	1	2	yes	—
695	C₄×C₁₃	—	2	2	no	—
696	C₄×C₁₃	—	2	1	no	—
697	C₄×C₁₃	—	2	2	no	—
698	C₄×C₁₃	—	2	1	no	—
699	C₄×C₁₃	—	2	1	no	—
700	C₄×C₁₃	—	2	2	no	—
701	C₄×C₁₃	—	2	1	no	—
702	C₄×C₁₃	C₄×#41	1	2	yes	—
703	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
704	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
705	Dic₁₃	—	2	1	no	—
706	Dic₁₃	—	2	1	no	—
707	Dic₁₃	—	2	1	no	—
708	Dic₁₃	—	2	1	no	—
709	Dic₁₃	—	2	2	no	—
710	Dic₁₃	—	2	2	no	—
711	Dic₁₃	—	2	2	no	—
712	Dic₁₃	—	2	2	no	—
713	C₂×#41	—	13	2	no	—
714	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
715	C₂²×D₄	—	13	1	no	—
716	C₂³×C₄	—	13	1	no	—
717	C₂³×C₄	—	13	1	no	—
718	#131	—	2	4	no	—
719	#131	—	2	4	no	—
720	C₂×M₁₆	—	13	1	no	—
721	C₂×M₁₆	—	13	1	no	—
722	C₂×M₁₆	—	13	1	no	—
723	C₂×M₁₆	—	13	2	no	—
724	C₂×M₁₆	—	13	1	no	—
725	C₂×M₁₆	—	13	1	no	—
726	C₂×M₁₆	—	13	2	no	—
727	C₂×M₁₆	—	13	1	no	—
728	C₂×M₁₆	—	26	4	no	—
729	C₂×M₁₆	—	26	4	no	—
730	C₂×M₁₆	—	26	4	no	—
731	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
732	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
733	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
734	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
735	C₂²×C₈	—	13	1	no	—
736	C₂²×C₈	—	13	1	no	—
737	C₂²×C₈	—	13	1	no	—
738	C₂²×C₈	—	13	1	no	—
739	C₂²×C₈	—	13	1	no	—
740	C₂²×C₈	—	13	1	no	—
741	C₂²×C₈	—	13	2	no	—
742	C₂²×C₈	—	13	2	no	—
743	C₂²×C₈	—	26	4	no	—
744	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
745	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
746	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
747	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
748	C₄⋊Q₈	—	13	1	no	—
749	C₄⋊Q₈	—	13	1	no	—
750	#126	—	13	2	no	—
751	#126	—	13	2	no	—
752	#126	—	13	2	no	—
753	#126	—	13	2	no	—
754	#126	—	13	2	no	—
755	#126	—	13	2	no	—
756	#125	—	13	2	no	—
757	#125	—	13	2	no	—
758	#125	—	13	2	no	—
759	#125	—	13	1	no	—
760	#125	—	13	1	no	—
761	#124	—	13	2	no	—
762	#124	—	13	2	no	—
763	#124	—	13	2	no	—
764	#123	—	13	2	no	—
765	#123	—	13	2	no	—
766	#123	—	13	2	no	—
767	#123	—	13	2	no	—
768	#123	—	13	2	no	—
769	#123	—	13	2	no	—
770	#123	—	13	2	no	—
771	#123	—	13	2	no	—
772	C₂²⋊Q₈	—	13	1	no	—
773	C₂²⋊Q₈	—	13	1	no	—
774	C₂²⋊Q₈	—	13	1	no	—
775	C₂²⋊Q₈	—	13	1	no	—
776	C₂²⋊Q₈	—	13	2	no	—
777	C₂²⋊Q₈	—	13	2	no	—
778	C₂²⋊Q₈	—	13	2	no	—
779	C₂²⋊Q₈	—	13	2	no	—
780	C₂²⋊Q₈	—	13	2	no	—
781	#121	—	13	1	no	—
782	#121	—	13	1	no	—
783	#121	—	13	1	no	—
784	#121	—	13	1	no	—
785	#121	—	13	2	no	—
786	#121	—	13	2	no	—
787	#121	—	13	2	no	—
788	#120	—	13	2	no	—
789	#120	—	13	2	no	—
790	C₄×Q₈	—	13	2	no	—
791	C₄×Q₈	—	13	2	no	—
792	C₄×Q₈	—	13	2	no	—
793	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
794	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
795	C₄×D₄	—	13	2	no	—
796	C₄×D₄	—	13	2	no	—
797	C₄×D₄	—	13	2	no	—
798	C₄×D₄	—	13	2	no	—
799	C₄×D₄	—	13	2	no	—
800	C₄×D₄	—	13	2	no	—
801	C₄×D₄	—	13	1	no	—
802	C₄×D₄	—	13	1	no	—
803	C₄×D₄	—	13	1	no	—
804	C₄×D₄	—	13	1	no	—
805	C₄×D₄	—	13	2	no	—
806	C₄×D₄	—	13	1	no	—
807	C₄×D₄	—	13	1	no	—
808	C₄×D₄	—	13	1	no	—
809	C₄×D₄	—	13	1	no	—
810	C₄×D₄	C₄×D₁₃	1	2	yes	—
811	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
812	C₄×D₄	C₄×D₁₃	1	2	yes	—
813	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
814	#117	—	13	2	no	—
815	#117	—	13	1	no	—
816	#117	—	13	1	no	—
817	#117	—	13	1	no	—
818	#117	—	13	1	no	—
819	#117	—	13	1	no	—
820	#117	—	13	1	no	—
821	#117	—	13	2	no	—
822	#117	—	13	2	no	—
823	#117	—	13	2	no	—
824	#117	—	13	2	no	—
825	#117	—	13	2	no	—
826	#117	—	13	2	no	—
827	#117	C₂²×D₁₃	1	1	yes	characteristic
828	#117	C₂²×D₁₃	1	2	yes	—
829	C₂×C₄⋊C₄	—	13	1	no	—
830	C₂×C₄⋊C₄	—	13	1	no	—
831	C₂×C₄⋊C₄	—	13	1	no	—
832	C₂×C₄⋊C₄	—	13	1	no	—
833	C₂×C₄⋊C₄	—	13	1	no	—
834	C₂×C₂²⋊C₄	—	13	1	no	—
835	C₂×C₂²⋊C₄	—	13	1	no	—
836	C₂×C₂²⋊C₄	—	13	2	no	—
837	C₂×C₂²⋊C₄	—	13	2	no	—
838	C₂×C₄²	—	13	2	no	—
839	C₂×C₄²	—	13	2	no	—
840	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
841	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
842	C₄⋊C₈	—	13	2	no	—
843	C₄⋊C₈	—	13	2	no	—
844	C₄⋊C₈	—	13	2	no	—
845	C₄⋊C₈	—	13	2	no	—
846	C₄⋊C₈	—	13	2	no	—
847	C₄⋊C₈	—	13	2	no	—
848	C₄⋊C₈	—	13	2	no	—
849	C₄⋊C₈	—	13	2	no	—
850	C₄⋊C₈	—	13	1	no	—
851	C₄⋊C₈	—	13	1	no	—
852	C₄⋊C₈	—	13	1	no	—
853	C₄⋊C₈	—	13	1	no	—
854	C₄⋊C₈	—	13	2	no	—
855	C₄⋊C₈	—	13	2	no	—
856	C₂²⋊C₈	—	13	2	no	—
857	C₂²⋊C₈	—	13	2	no	—
858	C₂²⋊C₈	—	13	2	no	—
859	C₂²⋊C₈	—	13	2	no	—
860	C₂²⋊C₈	—	13	1	no	—
861	C₂²⋊C₈	—	13	1	no	—
862	C₂²⋊C₈	—	13	1	no	—
863	C₂²⋊C₈	—	13	1	no	—
864	C₂²⋊C₈	—	13	1	no	—
865	C₂²⋊C₈	—	13	1	no	—
866	C₂²⋊C₈	—	13	1	no	—
867	C₂²⋊C₈	—	13	1	no	—
868	C₂²⋊C₈	—	13	2	no	—
869	C₂²⋊C₈	—	13	2	no	—
870	C₂²⋊C₈	—	13	2	no	—
871	C₂²⋊C₈	—	13	2	no	—
872	#97	—	13	2	no	—
873	#97	—	13	2	no	—
874	#97	—	13	2	no	—
875	#97	—	13	2	no	—
876	#97	—	13	2	no	—
877	#97	—	13	2	no	—
878	#97	C₂²×D₁₃	1	2	yes	—
879	#97	C₂²×D₁₃	1	1	yes	characteristic
880	#97	C₂²×D₁₃	1	1	yes	characteristic
881	#97	C₂²×D₁₃	1	1	yes	characteristic
882	#97	C₂²×D₁₃	1	1	yes	characteristic
883	#97	C₂²×D₁₃	1	2	yes	—
884	#97	C₂²×D₁₃	1	2	yes	—
885	C₄×C₈	—	13	2	no	—
886	C₄×C₈	—	13	2	no	—
887	C₄×C₈	—	13	2	no	—
888	C₄×C₈	—	13	2	no	—
889	C₄×C₈	—	13	2	no	—
890	C₄×C₈	—	13	2	no	—
891	C₄×C₈	C₂²×D₁₃	1	2	yes	—
892	C₄×C₈	C₂²×D₁₃	1	2	yes	—
893	C₄×C₈	C₂²×D₁₃	1	2	yes	—
894	C₂×C₁₃	—	2	2	no	—
895	C₂×C₁₃	—	4	2	no	—
896	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
897	C₂×C₁₃	C₂×#568	1	1	yes	characteristic
898	C₂×C₁₃	#3573	1	1	yes	characteristic
899	D₁₃	—	2	2	no	—
900	D₁₃	—	4	1	no	—
901	D₁₃	—	4	1	no	—
902	D₁₃	—	4	1	no	—
903	C₂⁴	—	13	1	no	—
904	C₂⁴	—	13	1	no	—
905	#41	—	2	2	no	—
906	#41	—	2	2	no	—
907	#41	—	52	4	no	—
908	C₂×Q₈	—	13	2	no	—
909	C₂×Q₈	—	13	2	no	—
910	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
911	C₂×D₄	—	13	2	no	—
912	C₂×D₄	—	13	2	no	—
913	C₂×D₄	—	13	2	no	—
914	C₂×D₄	—	13	2	no	—
915	C₂×D₄	—	13	1	no	—
916	C₂×D₄	—	13	1	no	—
917	C₂×D₄	—	13	1	no	—
918	C₂×D₄	—	13	1	no	—
919	C₂×D₄	—	52	2	no	—
920	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
921	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
922	C₂²×C₄	—	13	1	no	—
923	C₂²×C₄	—	13	1	no	—
924	C₂²×C₄	—	13	2	no	—
925	C₂²×C₄	—	13	1	no	—
926	C₂²×C₄	—	13	1	no	—
927	C₂²×C₄	—	13	1	no	—
928	C₂²×C₄	—	13	1	no	—
929	C₂²×C₄	—	13	1	no	—
930	C₂²×C₄	—	13	1	no	—
931	C₂²×C₄	—	13	1	no	—
932	C₂²×C₄	—	13	1	no	—
933	C₂²×C₄	—	13	2	no	—
934	C₂²×C₄	—	13	2	no	—
935	C₂²×C₄	—	13	2	no	—
936	C₂²×C₄	—	26	2	no	—
937	C₂²×C₄	—	26	2	no	—
938	C₂²×C₄	—	26	2	no	—
939	C₂²×C₄	—	26	2	no	—
940	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
941	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
942	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
943	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
944	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
945	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
946	M₁₆	—	2	2	no	—
947	M₁₆	—	2	4	no	—
948	M₁₆	—	2	4	no	—
949	M₁₆	—	26	2	no	—
950	M₁₆	—	26	2	no	—
951	M₁₆	—	26	2	no	—
952	M₁₆	—	26	2	no	—
953	M₁₆	—	26	4	no	—
954	M₁₆	—	26	4	no	—
955	M₁₆	—	26	2	no	—
956	M₁₆	—	26	2	no	—
957	M₁₆	#6127	1	4	yes	complemented
958	C₂×C₈	—	2	2	no	—
959	C₂×C₈	—	2	4	no	—
960	C₂×C₈	—	2	4	no	—
961	C₂×C₈	—	13	1	no	—
962	C₂×C₈	—	13	2	no	—
963	C₂×C₈	—	13	2	no	—
964	C₂×C₈	—	13	1	no	—
965	C₂×C₈	—	13	1	no	—
966	C₂×C₈	—	13	1	no	—
967	C₂×C₈	—	26	2	no	—
968	C₂×C₈	—	26	2	no	—
969	C₂×C₈	—	26	2	no	—
970	C₂×C₈	—	26	2	no	—
971	C₂×C₈	—	26	2	no	—
972	C₂×C₈	—	26	2	no	—
973	C₂×C₈	—	26	4	no	—
974	C₂×C₈	—	26	4	no	—
975	C₂×C₈	#6127	1	4	yes	complemented
976	C₂×C₈	C₂³×D₁₃	1	2	yes	—
977	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
978	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
979	C₂×C₈	C₂³×D₁₃	1	2	yes	—
980	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
981	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
982	C₄⋊C₄	—	13	1	no	—
983	C₄⋊C₄	—	13	1	no	—
984	C₄⋊C₄	—	13	1	no	—
985	C₄⋊C₄	—	13	1	no	—
986	C₄⋊C₄	—	13	1	no	—
987	C₄⋊C₄	—	13	2	no	—
988	C₄⋊C₄	—	13	2	no	—
989	C₄⋊C₄	—	13	2	no	—
990	C₄⋊C₄	—	13	2	no	—
991	C₄⋊C₄	—	13	1	no	—
992	C₄⋊C₄	—	13	1	no	—
993	C₄⋊C₄	—	13	1	no	—
994	C₄⋊C₄	—	13	2	no	—
995	C₄⋊C₄	—	13	2	no	—
996	C₄⋊C₄	—	13	2	no	—
997	C₄⋊C₄	—	13	2	no	—
998	C₄⋊C₄	—	13	2	no	—
999	C₄⋊C₄	—	13	2	no	—
1000	C₄⋊C₄	—	13	2	no	—
1001	C₄⋊C₄	—	13	2	no	—
1002	C₄⋊C₄	—	13	2	no	—
1003	C₄⋊C₄	—	13	2	no	—
1004	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1007	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1008	C₂²⋊C₄	—	13	2	no	—
1009	C₂²⋊C₄	—	13	2	no	—
1010	C₂²⋊C₄	—	13	2	no	—
1011	C₂²⋊C₄	—	13	2	no	—
1012	C₂²⋊C₄	—	13	2	no	—
1013	C₂²⋊C₄	—	13	2	no	—
1014	C₂²⋊C₄	—	13	1	no	—
1015	C₂²⋊C₄	—	13	1	no	—
1016	C₂²⋊C₄	—	13	2	no	—
1017	C₂²⋊C₄	—	13	2	no	—
1018	C₂²⋊C₄	—	13	2	no	—
1019	C₂²⋊C₄	—	13	2	no	—
1020	C₂²⋊C₄	—	13	1	no	—
1021	C₂²⋊C₄	—	13	1	no	—
1022	C₂²⋊C₄	—	13	1	no	—
1023	C₂²⋊C₄	—	13	1	no	—
1024	C₂²⋊C₄	—	13	1	no	—
1025	C₂²⋊C₄	—	13	1	no	—
1026	C₂²⋊C₄	—	13	2	no	—
1027	C₂²⋊C₄	—	13	2	no	—
1028	C₂²⋊C₄	—	13	2	no	—
1029	C₂²⋊C₄	—	13	2	no	—
1030	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1031	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1032	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1033	C₄²	—	13	2	no	—
1034	C₄²	—	13	2	no	—
1035	C₄²	—	13	2	no	—
1036	C₄²	—	13	2	no	—
1037	C₄²	—	13	2	no	—
1038	C₄²	—	13	2	no	—
1039	C₄²	C₂×C₄×D₁₃	1	2	yes	—
1040	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
1041	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
1042	C₄²	C₂×C₄×D₁₃	1	2	yes	—
1043	C₄²	C₂³×D₁₃	1	2	yes	—
1044	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1045	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1046	C₁₃	#60216	1	1	yes	characteristic, complemented, Sylow
1047	C₂³	—	13	1	no	—
1048	C₂³	—	13	1	no	—
1049	C₂³	—	13	1	no	—
1050	C₂³	—	13	1	no	—
1051	C₂³	—	26	2	no	—
1052	C₂³	—	26	2	no	—
1053	C₂³	—	26	2	no	—
1054	C₂³	—	52	1	no	—
1055	C₂³	—	52	1	no	—
1056	C₂³	—	52	1	no	—
1057	C₂³	C₂²×C₄×D₁₃	1	2	yes	—
1058	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	52	2	no	—
1061	Q₈	—	52	2	no	—
1062	D₄	—	2	4	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	26	2	no	—
1065	D₄	—	26	2	no	—
1066	D₄	—	26	4	no	—
1067	D₄	—	52	1	no	—
1068	D₄	—	52	1	no	—
1069	D₄	—	52	2	no	—
1070	D₄	—	52	2	no	—
1071	D₄	—	52	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	4	1	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	13	1	no	—
1079	C₂×C₄	—	13	1	no	—
1080	C₂×C₄	—	13	2	no	—
1081	C₂×C₄	—	13	2	no	—
1082	C₂×C₄	—	13	2	no	—
1083	C₂×C₄	—	13	2	no	—
1084	C₂×C₄	—	13	1	no	—
1085	C₂×C₄	—	13	1	no	—
1086	C₂×C₄	—	26	4	no	—
1087	C₂×C₄	—	26	2	no	—
1088	C₂×C₄	—	26	2	no	—
1089	C₂×C₄	—	26	2	no	—
1090	C₂×C₄	—	26	2	no	—
1091	C₂×C₄	—	26	2	no	—
1092	C₂×C₄	—	26	2	no	—
1093	C₂×C₄	—	26	1	no	—
1094	C₂×C₄	—	26	1	no	—
1095	C₂×C₄	—	26	1	no	—
1096	C₂×C₄	—	26	1	no	—
1097	C₂×C₄	—	26	1	no	—
1098	C₂×C₄	—	26	1	no	—
1099	C₂×C₄	—	26	1	no	—
1100	C₂×C₄	—	26	1	no	—
1101	C₂×C₄	—	52	2	no	—
1102	C₂×C₄	—	52	2	no	—
1103	C₂×C₄	—	52	2	no	—
1104	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1105	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1106	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1108	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1109	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1110	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1111	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1112	C₂×C₄	C₂×#6127	1	2	yes	—
1113	C₂×C₄	C₂×#6127	1	2	yes	—
1114	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	26	1	no	—
1119	C₈	—	26	1	no	—
1120	C₈	—	26	2	no	—
1121	C₈	—	26	2	no	—
1122	C₈	—	26	1	no	—
1123	C₈	—	26	1	no	—
1124	C₈	C₂×#6127	1	2	yes	—
1125	C₈	C₂×#6127	1	4	yes	—
1126	C₈	C₂×#6127	1	2	yes	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	13	2	no	—
1133	C₂²	—	26	1	no	—
1134	C₂²	—	26	1	no	—
1135	C₂²	—	26	1	no	—
1136	C₂²	—	26	1	no	—
1137	C₂²	—	26	1	no	—
1138	C₂²	—	26	1	no	—
1139	C₂²	—	26	1	no	—
1140	C₂²	—	26	1	no	—
1141	C₂²	—	26	1	no	—
1142	C₂²	—	26	1	no	—
1143	C₂²	—	26	1	no	—
1144	C₂²	—	52	4	no	—
1145	C₂²	—	104	2	no	—
1146	C₂²	C₄×#6127	1	2	yes	—
1147	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	26	2	no	—
1156	C₄	—	26	2	no	—
1157	C₄	—	26	2	no	—
1158	C₄	—	26	2	no	—
1159	C₄	—	26	1	no	—
1160	C₄	—	26	1	no	—
1161	C₄	—	26	1	no	—
1162	C₄	—	26	1	no	—
1163	C₄	C₄×#6127	1	2	yes	—
1164	C₄	C₂²×#6127	1	1	yes	characteristic
1165	C₄	C₂²×#6127	1	1	yes	characteristic
1166	C₂	—	2	2	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	26	2	no	—
1169	C₂	—	52	1	no	—
1170	C₂	—	52	1	no	—
1171	C₂	—	52	1	no	—
1172	C₂	C₂×C₄×#6127	1	1	yes	characteristic
1173	C₂	D₁₃×#568	1	1	yes	characteristic
1174	C₂	#13129549	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₁₃
commutator, socle	C₂²×C₁₃	C₂⁴×C₄
Fitting	C₁₃×#2875	C₂
prime radical	#13128400	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	#2875	D₁₃
hypocenter	C₁₃	#60216
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #2875

Complements

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

N	H ≅ G/N	type
2. #13123847	C₂	semidirect
3. #13123836	C₂	semidirect
4. #13123830	C₂	semidirect
5. #13123826	C₂	semidirect
6. #13123821	C₂	semidirect
7. #13123817	C₂	semidirect
8. #13123807	C₂	semidirect
9. #13123798	C₂	semidirect
10. #13123783	C₂	semidirect
11. #13123776	C₂	semidirect
12. M₁₆×D₅₂	C₂	semidirect
13. #13123558	C₂	semidirect
14. #13123558	C₂	semidirect
15. #13123537	C₂	semidirect
16. #13123528	C₂	semidirect
17. C₂×#11718367	C₂	semidirect
18. #13123502	C₂	semidirect
19. #13123491	C₂	semidirect
20. #13123491	C₂	semidirect
21. #13123252	C₂	semidirect
22. D₁₃×#405	C₂	semidirect
23. C₁₃×#2875	C₂	semidirect
55. C₁₃×#405	C₂²	semidirect
56. C₁₃×#405	C₂²	semidirect
58. C₄×C₁₃×M₁₆	C₂²	semidirect
60. C₂×C₁₃×#97	C₂²	semidirect
63. #11718789	C₂²	semidirect
64. #11718789	C₂²	semidirect
65. #11718789	C₂²	semidirect
66. #11718789	C₂²	semidirect
67. #11718788	C₂²	semidirect
68. #11718788	C₂²	semidirect
69. #11718788	C₂²	semidirect
70. #11718788	C₂²	semidirect
77. #11718772	C₂²	semidirect
78. #11718772	C₂²	semidirect
79. #11718772	C₂²	semidirect
80. #11718772	C₂²	semidirect
81. C₈×C₂²⋊D₁₃	C₂²	semidirect
82. C₈×C₂²⋊D₁₃	C₂²	semidirect
83. C₈×C₂²⋊D₁₃	C₂²	semidirect
84. C₈×C₂²⋊D₁₃	C₂²	semidirect
91. #11718661	C₂²	semidirect
92. #11718661	C₂²	semidirect
95. #11718587	C₂²	semidirect
96. #11718586	C₂²	semidirect
99. #11718370	C₂²	semidirect
100. #11718370	C₂²	semidirect
101. #11718369	C₂²	semidirect
102. #11718369	C₂²	semidirect
103. #11718368	C₂²	semidirect
114. #11718366	C₂²	semidirect
115. #11718366	C₂²	semidirect
116. D₁₃×#97	C₂²	semidirect
117. #11718362	C₂²	semidirect
118. #11718362	C₂²	semidirect
119. #11718362	C₂²	semidirect
120. #11718362	C₂²	semidirect
121. #11718362	C₂²	semidirect
122. #11718362	C₂²	semidirect
123. #11718351	C₂²	semidirect
124. #11718351	C₂²	semidirect
125. #11718350	C₂²	semidirect
126. #11718350	C₂²	semidirect
128. C₄×#6094	C₂²	semidirect
130. #11718346	C₂²	semidirect
131. #11718346	C₂²	semidirect
132. C₄×C₈×D₁₃	C₂²	semidirect
133. #11718340	C₂²	semidirect
134. C₈×Dic₂₆	C₂²	semidirect
363. C₁₃×M₁₆	#41	semidirect
367. C₂×C₈×C₁₃	#41	semidirect
480. #2875	D₁₃	semidirect
664. #405	C₂×D₁₃	semidirect
665. #405	C₂×D₁₃	semidirect
669. C₄×M₁₆	C₂×D₁₃	semidirect
672. C₂×#97	C₂×D₁₃	semidirect
957. M₁₆	#6127	semidirect
975. C₂×C₈	#6127	semidirect
1046. C₁₃	#60216	semidirect

Maximal subgroups

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

subgroup	index
#13128400	2
#13123847	2
#13123836	2
#13123830	2
#13123826	2
#13123821	2
#13123817	2
#13123807	2
#13123798	2
#13123783	2
#13123776	2
M₁₆×D₅₂	2
#13123558	2
#13123537	2
#13123528	2
C₂×#11718367	2
#13123502	2
#13123491	2
#13123252	2
D₁₃×#405	2
C₁₃×#2875	2
#60216	13