Subgroups — C₁₃×#61280 #15747619

Order 3328.

1760 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3352	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3351	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3350	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3349	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3346	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3344	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3337	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3336	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3098	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2912	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
27	C₁₃×#559	—	2	1	no	—
28	C₁₃×#557	—	2	1	no	—
29	C₁₃×#556	—	2	1	no	—
30	C₁₃×#556	—	2	1	no	—
31	C₁₃×#556	C₂²	1	2	yes	—
32	C₁₃×#554	C₂²	1	2	yes	—
33	C₁₃×#553	—	2	2	no	—
34	C₁₃×#553	—	2	2	no	—
35	C₁₃×#553	C₂²	1	2	yes	—
36	C₁₃×#553	C₂²	1	2	yes	—
37	C₁₃×#552	C₂²	1	2	yes	—
38	C₁₃×#552	C₂²	1	2	yes	—
39	C₁₃×#552	C₂²	1	2	yes	—
40	C₁₃×#552	C₂²	1	2	yes	—
41	C₁₃×#541	—	2	1	no	—
42	C₁₃×#540	—	2	1	no	—
43	C₁₃×#539	—	2	2	no	—
44	C₁₃×#537	C₂²	1	1	yes	characteristic
45	C₁₃×#537	C₂²	1	1	yes	characteristic
46	C₁₃×#536	C₂²	1	1	yes	characteristic
47	C₁₃×#536	C₂²	1	1	yes	characteristic
48	C₁₃×#533	C₂²	1	1	yes	characteristic
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#529	—	2	1	no	—
51	C₁₃×#529	—	2	1	no	—
52	C₁₃×#529	—	2	2	no	—
53	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
54	C₁₃×#520	C₂²	1	1	yes	characteristic
55	C₁₃×#520	C₂²	1	1	yes	characteristic
56	C₁₃×#520	C₂²	1	1	yes	characteristic
57	C₁₃×#520	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
59	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
60	C₁₃×#501	C₂²	1	2	yes	—
61	C₁₃×#501	C₂²	1	2	yes	—
62	C₁₃×#499	C₂²	1	2	yes	—
63	C₁₃×#499	C₂²	1	2	yes	—
64	C₁₃×#485	C₂²	1	2	yes	—
65	C₁₃×#485	C₂²	1	2	yes	—
66	C₁₃×#485	C₂²	1	2	yes	—
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#485	C₂²	1	2	yes	—
69	C₁₃×#485	C₂²	1	2	yes	—
70	C₁₃×#484	C₂²	1	2	yes	—
71	C₁₃×#484	C₂²	1	2	yes	—
72	C₁₃×#484	C₂²	1	2	yes	—
73	C₁₃×#483	C₂²	1	2	yes	—
74	C₁₃×#483	C₂²	1	2	yes	—
75	C₁₃×#483	C₂²	1	2	yes	—
76	C₁₃×#482	C₂²	1	2	yes	—
77	C₁₃×#482	C₂²	1	2	yes	—
78	C₁₃×#481	C₂²	1	2	yes	—
79	C₁₃×#480	C₂²	1	2	yes	—
80	C₁₃×#479	C₂²	1	2	yes	—
81	C₁₃×#479	C₂²	1	2	yes	—
82	C₁₃×#479	C₂²	1	2	yes	—
83	C₁₃×#479	C₂²	1	2	yes	—
84	C₁₃×#479	C₂²	1	1	yes	characteristic
85	C₁₃×#479	C₂²	1	1	yes	characteristic
86	C₁₃×#478	C₂²	1	1	yes	characteristic
87	C₁₃×#478	C₂²	1	1	yes	characteristic
88	C₁₃×#477	C₂²	1	1	yes	characteristic
89	C₁₃×#476	C₂²	1	1	yes	characteristic
90	C₁₃×#475	C₂²	1	1	yes	characteristic
91	C₁₃×#474	C₂²	1	1	yes	characteristic
92	C₁₃×#470	C₂²	1	2	yes	—
93	C₁₃×#470	C₂²	1	2	yes	—
94	C₁₃×#468	C₂²	1	2	yes	—
95	C₁₃×#468	C₂²	1	2	yes	—
96	C₁₃×#467	C₂²	1	2	yes	—
97	C₁₃×#467	C₂²	1	2	yes	—
98	C₁₃×#465	C₂²	1	2	yes	—
99	C₁₃×#465	C₂²	1	2	yes	—
100	C₁₃×#441	C₂²	1	2	yes	—
101	C₁₃×#440	C₂²	1	2	yes	—
102	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
103	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
104	C₁₃×#436	C₂²	1	2	yes	—
105	C₁₃×#435	C₂²	1	2	yes	—
106	C₁₃×#435	C₂²	1	2	yes	—
107	C₈×D₄×C₁₃	C₂²	1	2	yes	—
108	C₁₃×#428	C₂²	1	1	yes	characteristic
109	C₁₃×#428	C₂²	1	1	yes	characteristic
110	C₁₃×#428	C₂²	1	2	yes	—
111	C₁₃×#428	C₂²	1	2	yes	—
112	C₁₃×#428	C₂²	1	2	yes	—
113	C₁₃×#428	C₂²	1	2	yes	—
114	C₁₃×#428	C₂²	1	1	yes	characteristic
115	C₁₃×#428	C₂²	1	1	yes	characteristic
116	C₁₃×#428	C₂²	1	1	yes	characteristic
117	C₁₃×#427	C₂²	1	1	yes	characteristic
118	C₁₃×#427	C₂²	1	1	yes	characteristic
119	C₁₃×#427	C₂²	1	2	yes	—
120	C₁₃×#427	C₂²	1	2	yes	—
121	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
122	C₂×C₁₃×#107	C₂²	1	2	yes	—
123	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
124	C₂×C₁₃×#106	C₂²	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₁₃×#419	C₂²	1	1	yes	characteristic
127	C₁₃×#417	C₂²	1	1	yes	characteristic
128	C₁₃×#416	C₂²	1	1	yes	characteristic
129	C₁₃×#416	C₂²	1	1	yes	characteristic
130	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
132	C₁₃×#408	C₂²	1	1	yes	characteristic
133	C₁₃×#408	C₂²	1	1	yes	characteristic
134	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₁₃×#137	—	2	4	no	—
140	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
142	C₁₃×#131	—	2	4	no	—
143	C₁₃×#131	—	2	4	no	—
144	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
152	C₁₃×C₄⋊Q₈	—	2	1	no	—
153	C₁₃×C₄⋊Q₈	—	2	1	no	—
154	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₁₃×#127	D₄	1	1	yes	characteristic
158	C₁₃×#126	—	2	2	no	—
159	C₁₃×#126	—	2	2	no	—
160	C₁₃×#126	—	2	2	no	—
161	C₁₃×#126	—	2	2	no	—
162	C₁₃×#126	—	2	2	no	—
163	C₁₃×#126	—	2	2	no	—
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	2	no	—
166	C₁₃×#125	—	2	2	no	—
167	C₁₃×#125	—	2	2	no	—
168	C₁₃×#125	—	2	2	no	—
169	C₁₃×#125	—	2	2	no	—
170	C₁₃×#125	—	2	2	no	—
171	C₁₃×#125	—	2	1	no	—
172	C₁₃×#125	—	2	1	no	—
173	C₁₃×#125	C₂³	1	1	yes	characteristic
174	C₁₃×#125	C₂³	1	1	yes	characteristic
175	C₁₃×#125	C₂³	1	2	yes	—
176	C₁₃×#125	C₂³	1	2	yes	—
177	C₁₃×#124	—	2	2	no	—
178	C₁₃×#124	—	2	1	no	—
179	C₁₃×#124	—	2	1	no	—
180	C₁₃×#124	D₄	1	1	yes	characteristic
181	C₁₃×#124	D₄	1	1	yes	characteristic
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	—	2	2	no	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	—	2	2	no	—
188	C₁₃×#123	—	2	2	no	—
189	C₁₃×#123	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	1	no	—
191	C₁₃×C₂²⋊Q₈	—	2	1	no	—
192	C₁₃×C₂²⋊Q₈	—	2	1	no	—
193	C₁₃×C₂²⋊Q₈	—	2	1	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×#121	—	2	1	no	—
203	C₁₃×#121	—	2	1	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	—	2	2	no	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	D₄	1	2	yes	—
209	C₁₃×#121	D₄	1	2	yes	—
210	C₁₃×#121	C₂³	1	2	yes	—
211	C₁₃×#121	C₂³	1	2	yes	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	2	no	—
217	C₄×Q₈×C₁₃	—	2	1	no	—
218	C₄×Q₈×C₁₃	—	2	1	no	—
219	C₄×Q₈×C₁₃	—	2	1	no	—
220	C₄×Q₈×C₁₃	—	2	1	no	—
221	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₁₃	—	2	2	no	—
226	C₄×D₄×C₁₃	—	2	2	no	—
227	C₄×D₄×C₁₃	—	2	1	no	—
228	C₄×D₄×C₁₃	—	2	1	no	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	—	2	2	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	1	no	—
233	C₄×D₄×C₁₃	—	2	2	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	1	no	—
236	C₄×D₄×C₁₃	—	2	2	no	—
237	C₄×D₄×C₁₃	—	2	2	no	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₃	C₂³	1	2	yes	—
241	C₄×D₄×C₁₃	C₂³	1	2	yes	—
242	C₁₃×#117	—	2	2	no	—
243	C₁₃×#117	—	2	2	no	—
244	C₁₃×#117	—	2	2	no	—
245	C₁₃×#117	—	2	2	no	—
246	C₁₃×#117	—	2	1	no	—
247	C₁₃×#117	C₂³	1	1	yes	characteristic
248	C₁₃×#117	C₂³	1	1	yes	characteristic
249	C₁₃×#117	C₂³	1	1	yes	characteristic
250	C₁₃×#117	C₂³	1	2	yes	—
251	C₁₃×#117	C₂³	1	2	yes	—
252	C₁₃×#117	C₂³	1	2	yes	—
253	C₁₃×#117	C₂³	1	2	yes	—
254	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₄²×C₁₃	—	2	1	no	—
265	C₂×C₄²×C₁₃	—	2	1	no	—
266	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
267	C₁₃×#107	C₂³	1	1	yes	characteristic
268	C₁₃×#107	C₂³	1	2	yes	—
269	C₁₃×#107	C₂³	1	2	yes	—
270	C₁₃×#107	C₂³	1	2	yes	—
271	C₁₃×#107	C₂³	1	2	yes	—
272	C₁₃×#107	C₂³	1	1	yes	characteristic
273	C₁₃×#107	C₂³	1	2	yes	—
274	C₁₃×#107	C₂³	1	1	yes	characteristic
275	C₁₃×#107	C₂³	1	1	yes	characteristic
276	C₁₃×#107	C₂³	1	2	yes	—
277	C₁₃×#107	C₂³	1	2	yes	—
278	C₁₃×#106	C₂³	1	1	yes	characteristic
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×#106	C₂³	1	2	yes	—
281	C₁₃×#106	C₂³	1	2	yes	—
282	C₁₃×#106	C₂³	1	2	yes	—
283	C₁₃×#106	C₂³	1	1	yes	characteristic
284	C₁₃×#106	C₂³	1	2	yes	—
285	C₁₃×#106	C₂³	1	1	yes	characteristic
286	C₁₃×#106	C₂³	1	1	yes	characteristic
287	C₁₃×#106	C₂³	1	2	yes	—
288	C₁₃×#106	C₂³	1	2	yes	—
289	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	1	yes	characteristic
298	C₁₃×#103	C₂³	1	1	yes	characteristic
299	C₁₃×#103	C₂³	1	1	yes	characteristic
300	C₁₃×#103	C₂³	1	1	yes	characteristic
301	C₁₃×#103	C₂³	1	2	yes	—
302	C₁₃×#103	C₂³	1	2	yes	—
303	C₁₃×#103	C₂³	1	2	yes	—
304	C₁₃×#102	C₂³	1	1	yes	characteristic
305	C₁₃×#102	C₂³	1	1	yes	characteristic
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×#102	C₂³	1	1	yes	characteristic
308	C₁₃×#102	C₂³	1	2	yes	—
309	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₁₃×#97	C₂³	1	2	yes	—
314	C₄×C₈×C₁₃	C₂³	1	2	yes	—
315	#61280	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₁₃×#41	—	2	2	no	—
317	C₁₃×#41	—	2	2	no	—
318	C₁₃×#41	—	2	2	no	—
319	C₁₃×#41	—	2	2	no	—
320	C₁₃×#41	—	2	2	no	—
321	C₁₃×#41	—	2	2	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	1	no	—
325	C₂×Q₈×C₁₃	—	2	2	no	—
326	C₂×Q₈×C₁₃	—	2	2	no	—
327	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₃	—	2	1	no	—
342	C₂²×C₄×C₁₃	—	2	1	no	—
343	C₂²×C₄×C₁₃	—	2	1	no	—
344	C₂²×C₄×C₁₃	—	2	1	no	—
345	C₂²×C₄×C₁₃	—	2	2	no	—
346	C₂²×C₄×C₁₃	—	2	2	no	—
347	C₂²×C₄×C₁₃	—	2	2	no	—
348	C₂²×C₄×C₁₃	—	2	2	no	—
349	C₂²×C₄×C₁₃	—	2	1	no	—
350	C₂²×C₄×C₁₃	—	2	1	no	—
351	C₂²×C₄×C₁₃	—	2	1	no	—
352	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₁₃×Q₁₆	—	2	4	no	—
358	C₁₃×SD₁₆	—	2	4	no	—
359	C₁₃×M₁₆	—	2	2	no	—
360	C₁₃×M₁₆	—	2	4	no	—
361	C₁₃×M₁₆	—	2	4	no	—
362	C₁₃×M₁₆	#41	1	4	yes	—
363	C₂×C₈×C₁₃	—	2	2	no	—
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	C₂⁴	1	2	yes	—
368	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	2	no	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	2	no	—
378	C₁₃×C₄⋊C₄	—	2	2	no	—
379	C₁₃×C₄⋊C₄	—	2	1	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	1	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	1	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	—	2	2	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	1	no	—
397	C₁₃×C₄⋊C₄	—	2	1	no	—
398	C₁₃×C₄⋊C₄	—	2	2	no	—
399	C₁₃×C₄⋊C₄	—	2	2	no	—
400	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
409	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
411	C₁₃×C₂²⋊C₄	—	2	2	no	—
412	C₁₃×C₂²⋊C₄	—	2	2	no	—
413	C₁₃×C₂²⋊C₄	—	2	2	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
415	C₁₃×C₂²⋊C₄	—	2	1	no	—
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	1	no	—
419	C₁₃×C₂²⋊C₄	—	2	1	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	—	2	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
429	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₄²×C₁₃	—	2	1	no	—
433	C₄²×C₁₃	—	2	1	no	—
434	C₄²×C₁₃	—	2	2	no	—
435	C₄²×C₁₃	—	2	1	no	—
436	C₄²×C₁₃	—	2	2	no	—
437	C₄²×C₁₃	—	2	2	no	—
438	C₄²×C₁₃	—	2	2	no	—
439	C₄²×C₁₃	—	2	2	no	—
440	C₄²×C₁₃	—	2	2	no	—
441	C₄²×C₁₃	—	2	1	no	—
442	C₄²×C₁₃	—	2	1	no	—
443	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
446	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
447	#3512	C₂×C₁₃	1	1	yes	characteristic
448	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3352	C₂×C₁₃	1	2	yes	complemented
450	#3351	C₂×C₁₃	1	2	yes	complemented
451	#3350	C₂×C₁₃	1	2	yes	complemented
452	#3349	C₂×C₁₃	1	2	yes	complemented
453	#3346	C₂×C₁₃	1	2	yes	complemented
454	#3344	C₂×C₁₃	1	2	yes	complemented
455	#3337	C₂×C₁₃	1	2	yes	complemented
456	#3336	C₂×C₁₃	1	2	yes	complemented
457	#3166	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3099	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3098	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3097	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3097	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
463	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
466	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#2935	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#2912	C₂×C₁₃	1	1	yes	characteristic, complemented
470	C₂³×C₁₃	—	2	1	no	—
471	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
472	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
473	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
474	Q₈×C₁₃	—	2	2	no	—
475	Q₈×C₁₃	—	2	2	no	—
476	Q₈×C₁₃	—	2	2	no	—
477	Q₈×C₁₃	—	2	1	no	—
478	Q₈×C₁₃	—	2	2	no	—
479	Q₈×C₁₃	—	2	1	no	—
480	Q₈×C₁₃	—	4	2	no	—
481	Q₈×C₁₃	—	4	2	no	—
482	Q₈×C₁₃	—	8	1	no	—
483	D₄×C₁₃	—	2	4	no	—
484	D₄×C₁₃	—	2	4	no	—
485	D₄×C₁₃	—	2	2	no	—
486	D₄×C₁₃	—	2	2	no	—
487	D₄×C₁₃	—	2	1	no	—
488	D₄×C₁₃	—	2	1	no	—
489	D₄×C₁₃	—	4	2	no	—
490	D₄×C₁₃	—	4	2	no	—
491	D₄×C₁₃	—	4	2	no	—
492	D₄×C₁₃	—	8	2	no	—
493	D₄×C₁₃	—	8	2	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	—	2	2	no	—
496	C₂×C₄×C₁₃	—	2	2	no	—
497	C₂×C₄×C₁₃	—	2	2	no	—
498	C₂×C₄×C₁₃	—	2	1	no	—
499	C₂×C₄×C₁₃	—	2	1	no	—
500	C₂×C₄×C₁₃	—	2	2	no	—
501	C₂×C₄×C₁₃	—	2	1	no	—
502	C₂×C₄×C₁₃	—	2	1	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	2	2	no	—
505	C₂×C₄×C₁₃	—	2	2	no	—
506	C₂×C₄×C₁₃	—	2	2	no	—
507	C₂×C₄×C₁₃	—	2	1	no	—
508	C₂×C₄×C₁₃	—	2	1	no	—
509	C₂×C₄×C₁₃	—	4	1	no	—
510	C₂×C₄×C₁₃	—	4	1	no	—
511	C₂×C₄×C₁₃	—	4	2	no	—
512	C₂×C₄×C₁₃	—	4	2	no	—
513	C₂×C₄×C₁₃	—	8	1	no	—
514	C₂×C₄×C₁₃	—	8	1	no	—
515	C₂×C₄×C₁₃	—	8	1	no	—
516	C₂×C₄×C₁₃	—	8	2	no	—
517	C₂×C₄×C₁₃	—	8	2	no	—
518	C₂×C₄×C₁₃	—	8	2	no	—
519	C₂×C₄×C₁₃	—	8	1	no	—
520	C₂×C₄×C₁₃	—	8	2	no	—
521	C₂×C₄×C₁₃	—	8	1	no	—
522	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
530	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
531	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
532	C₈×C₁₃	—	2	1	no	—
533	C₈×C₁₃	—	2	1	no	—
534	C₈×C₁₃	—	2	1	no	—
535	C₈×C₁₃	—	2	1	no	—
536	C₈×C₁₃	—	2	2	no	—
537	C₈×C₁₃	C₂×#41	1	4	yes	—
538	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
539	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
540	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
541	#559	—	2	1	no	—
542	#557	—	2	1	no	—
543	#556	—	2	1	no	—
544	#556	—	2	1	no	—
545	#556	C₂²×C₁₃	1	2	yes	—
546	#554	C₂²×C₁₃	1	2	yes	—
547	#553	—	2	2	no	—
548	#553	—	2	2	no	—
549	#553	C₂²×C₁₃	1	2	yes	—
550	#553	C₂²×C₁₃	1	2	yes	—
551	#552	C₂²×C₁₃	1	2	yes	—
552	#552	C₂²×C₁₃	1	2	yes	—
553	#552	C₂²×C₁₃	1	2	yes	—
554	#552	C₂²×C₁₃	1	2	yes	—
555	#541	—	2	1	no	—
556	#540	—	2	1	no	—
557	#539	—	2	2	no	—
558	#537	C₂²×C₁₃	1	1	yes	characteristic
559	#537	C₂²×C₁₃	1	1	yes	characteristic
560	#536	C₂²×C₁₃	1	1	yes	characteristic
561	#536	C₂²×C₁₃	1	1	yes	characteristic
562	#533	C₂²×C₁₃	1	1	yes	characteristic
563	#532	C₂²×C₁₃	1	1	yes	characteristic
564	#529	—	2	1	no	—
565	#529	—	2	1	no	—
566	#529	—	2	2	no	—
567	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
568	#520	C₂²×C₁₃	1	1	yes	characteristic
569	#520	C₂²×C₁₃	1	1	yes	characteristic
570	#520	C₂²×C₁₃	1	1	yes	characteristic
571	#520	C₂²×C₁₃	1	1	yes	characteristic
572	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
573	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
574	#501	C₂²×C₁₃	1	2	yes	—
575	#501	C₂²×C₁₃	1	2	yes	—
576	#499	C₂²×C₁₃	1	2	yes	—
577	#499	C₂²×C₁₃	1	2	yes	—
578	#485	C₂²×C₁₃	1	2	yes	—
579	#485	C₂²×C₁₃	1	2	yes	—
580	#485	C₂²×C₁₃	1	2	yes	—
581	#485	C₂²×C₁₃	1	2	yes	—
582	#485	C₂²×C₁₃	1	2	yes	—
583	#485	C₂²×C₁₃	1	2	yes	—
584	#484	C₂²×C₁₃	1	2	yes	—
585	#484	C₂²×C₁₃	1	2	yes	—
586	#484	C₂²×C₁₃	1	2	yes	—
587	#483	C₂²×C₁₃	1	2	yes	—
588	#483	C₂²×C₁₃	1	2	yes	—
589	#483	C₂²×C₁₃	1	2	yes	—
590	#482	C₂²×C₁₃	1	2	yes	—
591	#482	C₂²×C₁₃	1	2	yes	—
592	#481	C₂²×C₁₃	1	2	yes	—
593	#480	C₂²×C₁₃	1	2	yes	—
594	#479	C₂²×C₁₃	1	2	yes	—
595	#479	C₂²×C₁₃	1	2	yes	—
596	#479	C₂²×C₁₃	1	2	yes	—
597	#479	C₂²×C₁₃	1	2	yes	—
598	#479	C₂²×C₁₃	1	1	yes	characteristic
599	#479	C₂²×C₁₃	1	1	yes	characteristic
600	#478	C₂²×C₁₃	1	1	yes	characteristic
601	#478	C₂²×C₁₃	1	1	yes	characteristic
602	#477	C₂²×C₁₃	1	1	yes	characteristic
603	#476	C₂²×C₁₃	1	1	yes	characteristic
604	#475	C₂²×C₁₃	1	1	yes	characteristic
605	#474	C₂²×C₁₃	1	1	yes	characteristic
606	#470	C₂²×C₁₃	1	2	yes	—
607	#470	C₂²×C₁₃	1	2	yes	—
608	#468	C₂²×C₁₃	1	2	yes	—
609	#468	C₂²×C₁₃	1	2	yes	—
610	#467	C₂²×C₁₃	1	2	yes	—
611	#467	C₂²×C₁₃	1	2	yes	—
612	#465	C₂²×C₁₃	1	2	yes	—
613	#465	C₂²×C₁₃	1	2	yes	—
614	#441	C₂²×C₁₃	1	2	yes	—
615	#440	C₂²×C₁₃	1	2	yes	—
616	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
617	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
618	#436	C₂²×C₁₃	1	2	yes	—
619	#435	C₂²×C₁₃	1	2	yes	—
620	#435	C₂²×C₁₃	1	2	yes	—
621	C₈×D₄	C₂²×C₁₃	1	2	yes	—
622	#428	C₂²×C₁₃	1	2	yes	—
623	#428	C₂²×C₁₃	1	2	yes	—
624	#428	C₂²×C₁₃	1	2	yes	—
625	#428	C₂²×C₁₃	1	2	yes	—
626	#428	C₂²×C₁₃	1	1	yes	characteristic
627	#428	C₂²×C₁₃	1	1	yes	characteristic
628	#428	C₂²×C₁₃	1	1	yes	characteristic
629	#428	C₂²×C₁₃	1	1	yes	characteristic
630	#428	C₂²×C₁₃	1	1	yes	characteristic
631	#427	C₂²×C₁₃	1	1	yes	characteristic
632	#427	C₂²×C₁₃	1	1	yes	characteristic
633	#427	C₂²×C₁₃	1	2	yes	—
634	#427	C₂²×C₁₃	1	2	yes	—
635	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
636	C₂×#107	C₂²×C₁₃	1	2	yes	—
637	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
638	C₂×#106	C₂²×C₁₃	1	2	yes	—
639	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
640	#419	C₂²×C₁₃	1	1	yes	characteristic
641	#417	C₂²×C₁₃	1	1	yes	characteristic
642	#416	C₂²×C₁₃	1	1	yes	characteristic
643	#416	C₂²×C₁₃	1	1	yes	characteristic
644	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
645	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
646	#408	C₂²×C₁₃	1	1	yes	characteristic
647	#408	C₂²×C₁₃	1	1	yes	characteristic
648	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
649	C₂²×C₁₃	—	2	1	no	—
650	C₂²×C₁₃	—	2	1	no	—
651	C₂²×C₁₃	—	2	2	no	—
652	C₂²×C₁₃	—	2	2	no	—
653	C₂²×C₁₃	—	2	2	no	—
654	C₂²×C₁₃	—	2	2	no	—
655	C₂²×C₁₃	—	2	2	no	—
656	C₂²×C₁₃	—	2	2	no	—
657	C₂²×C₁₃	—	4	1	no	—
658	C₂²×C₁₃	—	4	1	no	—
659	C₂²×C₁₃	—	4	1	no	—
660	C₂²×C₁₃	#547	1	2	yes	—
661	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
662	C₄×C₁₃	—	2	1	no	—
663	C₄×C₁₃	—	2	1	no	—
664	C₄×C₁₃	—	2	1	no	—
665	C₄×C₁₃	—	2	1	no	—
666	C₄×C₁₃	—	2	2	no	—
667	C₄×C₁₃	—	2	2	no	—
668	C₄×C₁₃	—	4	1	no	—
669	C₄×C₁₃	—	4	2	no	—
670	C₄×C₁₃	—	4	2	no	—
671	C₄×C₁₃	—	4	1	no	—
672	C₄×C₁₃	—	4	1	no	—
673	C₄×C₁₃	—	4	1	no	—
674	C₄×C₁₃	—	4	2	no	—
675	C₄×C₁₃	—	4	1	no	—
676	C₄×C₁₃	—	4	1	no	—
677	C₄×C₁₃	—	4	1	no	—
678	C₄×C₁₃	—	4	2	no	—
679	C₄×C₁₃	#547	1	2	yes	—
680	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
681	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
682	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
685	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
686	#137	—	2	4	no	—
687	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
689	#131	—	2	4	no	—
690	#131	—	2	4	no	—
691	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
692	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
693	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
694	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
695	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
696	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
697	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
698	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
699	C₄⋊Q₈	—	2	1	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
704	#127	D₄×C₁₃	1	1	yes	characteristic
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	1	no	—
719	#125	—	2	1	no	—
720	#125	C₂³×C₁₃	1	2	yes	—
721	#125	C₂³×C₁₃	1	2	yes	—
722	#125	C₂³×C₁₃	1	1	yes	characteristic
723	#125	C₂³×C₁₃	1	1	yes	characteristic
724	#124	—	2	2	no	—
725	#124	—	2	1	no	—
726	#124	—	2	1	no	—
727	#124	D₄×C₁₃	1	1	yes	characteristic
728	#124	D₄×C₁₃	1	1	yes	characteristic
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
744	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
745	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
746	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
747	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
749	#121	—	2	1	no	—
750	#121	—	2	1	no	—
751	#121	—	2	2	no	—
752	#121	—	2	2	no	—
753	#121	—	2	2	no	—
754	#121	—	2	2	no	—
755	#121	D₄×C₁₃	1	2	yes	—
756	#121	D₄×C₁₃	1	2	yes	—
757	#121	C₂³×C₁₃	1	2	yes	—
758	#121	C₂³×C₁₃	1	2	yes	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
769	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
770	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₁₃	1	2	yes	—
788	C₄×D₄	C₂³×C₁₃	1	2	yes	—
789	#117	—	2	2	no	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	—	2	2	no	—
793	#117	—	2	1	no	—
794	#117	C₂³×C₁₃	1	1	yes	characteristic
795	#117	C₂³×C₁₃	1	1	yes	characteristic
796	#117	C₂³×C₁₃	1	1	yes	characteristic
797	#117	C₂³×C₁₃	1	2	yes	—
798	#117	C₂³×C₁₃	1	2	yes	—
799	#117	C₂³×C₁₃	1	2	yes	—
800	#117	C₂³×C₁₃	1	2	yes	—
801	C₂×C₄⋊C₄	—	2	1	no	—
802	C₂×C₄⋊C₄	—	2	1	no	—
803	C₂×C₄⋊C₄	—	2	1	no	—
804	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
805	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
806	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
807	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
808	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
809	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
810	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
811	C₂×C₄²	—	2	1	no	—
812	C₂×C₄²	—	2	1	no	—
813	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
814	#107	C₂³×C₁₃	1	1	yes	characteristic
815	#107	C₂³×C₁₃	1	2	yes	—
816	#107	C₂³×C₁₃	1	2	yes	—
817	#107	C₂³×C₁₃	1	2	yes	—
818	#107	C₂³×C₁₃	1	2	yes	—
819	#107	C₂³×C₁₃	1	1	yes	characteristic
820	#107	C₂³×C₁₃	1	2	yes	—
821	#107	C₂³×C₁₃	1	1	yes	characteristic
822	#107	C₂³×C₁₃	1	1	yes	characteristic
823	#107	C₂³×C₁₃	1	2	yes	—
824	#107	C₂³×C₁₃	1	2	yes	—
825	#106	C₂³×C₁₃	1	1	yes	characteristic
826	#106	C₂³×C₁₃	1	2	yes	—
827	#106	C₂³×C₁₃	1	2	yes	—
828	#106	C₂³×C₁₃	1	2	yes	—
829	#106	C₂³×C₁₃	1	2	yes	—
830	#106	C₂³×C₁₃	1	1	yes	characteristic
831	#106	C₂³×C₁₃	1	2	yes	—
832	#106	C₂³×C₁₃	1	1	yes	characteristic
833	#106	C₂³×C₁₃	1	1	yes	characteristic
834	#106	C₂³×C₁₃	1	2	yes	—
835	#106	C₂³×C₁₃	1	2	yes	—
836	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
840	#103	C₂³×C₁₃	1	2	yes	—
841	#103	C₂³×C₁₃	1	2	yes	—
842	#103	C₂³×C₁₃	1	2	yes	—
843	#103	C₂³×C₁₃	1	2	yes	—
844	#103	C₂³×C₁₃	1	1	yes	characteristic
845	#103	C₂³×C₁₃	1	1	yes	characteristic
846	#103	C₂³×C₁₃	1	1	yes	characteristic
847	#103	C₂³×C₁₃	1	1	yes	characteristic
848	#103	C₂³×C₁₃	1	2	yes	—
849	#103	C₂³×C₁₃	1	2	yes	—
850	#103	C₂³×C₁₃	1	2	yes	—
851	#102	C₂³×C₁₃	1	1	yes	characteristic
852	#102	C₂³×C₁₃	1	1	yes	characteristic
853	#102	C₂³×C₁₃	1	1	yes	characteristic
854	#102	C₂³×C₁₃	1	1	yes	characteristic
855	#102	C₂³×C₁₃	1	2	yes	—
856	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
860	#97	C₂³×C₁₃	1	2	yes	—
861	C₄×C₈	C₂³×C₁₃	1	2	yes	—
862	C₂×C₁₃	—	2	2	no	—
863	C₂×C₁₃	—	4	2	no	—
864	C₂×C₁₃	—	4	2	no	—
865	C₂×C₁₃	—	8	1	no	—
866	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
867	C₂×C₁₃	#3584	1	1	yes	characteristic
868	C₂×C₁₃	#3586	1	1	yes	characteristic
869	#41	—	2	2	no	—
870	#41	—	2	2	no	—
871	#41	—	2	2	no	—
872	#41	—	2	2	no	—
873	#41	—	2	2	no	—
874	#41	—	2	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
881	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
882	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
883	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
888	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
889	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
890	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
891	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
892	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
893	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
906	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
907	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
910	Q₁₆	—	2	4	no	—
911	SD₁₆	—	2	4	no	—
912	M₁₆	—	2	2	no	—
913	M₁₆	—	2	4	no	—
914	M₁₆	—	2	4	no	—
915	M₁₆	C₁₃×#41	1	4	yes	—
916	C₂×C₈	—	2	2	no	—
917	C₂×C₈	—	2	2	no	—
918	C₂×C₈	—	2	4	no	—
919	C₂×C₈	—	2	4	no	—
920	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
921	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
925	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
954	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
955	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
962	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
984	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
997	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
998	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
999	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1000	C₁₃	#61280	1	1	yes	characteristic, direct product factor, Sylow
1001	C₂³	—	2	1	no	—
1002	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1003	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1004	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	4	2	no	—
1012	Q₈	—	4	2	no	—
1013	Q₈	—	8	1	no	—
1014	D₄	—	2	4	no	—
1015	D₄	—	2	4	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	2	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	8	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	4	1	no	—
1041	C₂×C₄	—	4	1	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	8	1	no	—
1045	C₂×C₄	—	8	1	no	—
1046	C₂×C₄	—	8	1	no	—
1047	C₂×C₄	—	8	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	1	no	—
1051	C₂×C₄	—	8	2	no	—
1052	C₂×C₄	—	8	1	no	—
1053	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1054	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1055	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1056	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1059	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1060	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1061	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1062	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	2	no	—
1068	C₈	C₂×C₁₃×#41	1	4	yes	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	2	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	C₁₃×#547	1	2	yes	—
1081	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1082	C₄	—	2	1	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	C₁₃×#547	1	2	yes	—
1100	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1101	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	4	2	no	—
1105	C₂	—	8	1	no	—
1106	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
1107	C₂	C₁₃×#3584	1	1	yes	characteristic
1108	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3512	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3507	C₂	semidirect
3. C₁₃×#3352	C₂	semidirect
4. C₁₃×#3351	C₂	semidirect
5. C₁₃×#3350	C₂	semidirect
6. C₁₃×#3349	C₂	semidirect
7. C₁₃×#3346	C₂	semidirect
8. C₁₃×#3344	C₂	semidirect
9. C₁₃×#3337	C₂	semidirect
10. C₁₃×#3336	C₂	semidirect
11. C₁₃×#3166	C₂	semidirect
12. C₁₃×#3099	C₂	semidirect
13. C₁₃×#3098	C₂	semidirect
14. C₁₃×#3097	C₂	semidirect
15. C₁₃×#3097	C₂	semidirect
16. C₁₃×#3076	C₂	semidirect
17. C₂×C₁₃×#479	C₂	semidirect
18. C₁₃×#3063	C₂	semidirect
19. C₁₃×#3063	C₂	semidirect
20. C₄×C₁₃×#137	C₂	semidirect
21. C₁₃×#2935	C₂	semidirect
22. C₁₃×#2913	C₂	semidirect
23. C₁₃×#2912	C₂	semidirect
315. #61280	C₁₃	direct (N × H)
448. #3507	C₂×C₁₃	semidirect
449. #3352	C₂×C₁₃	semidirect
450. #3351	C₂×C₁₃	semidirect
451. #3350	C₂×C₁₃	semidirect
452. #3349	C₂×C₁₃	semidirect
453. #3346	C₂×C₁₃	semidirect
454. #3344	C₂×C₁₃	semidirect
455. #3337	C₂×C₁₃	semidirect
456. #3336	C₂×C₁₃	semidirect
457. #3166	C₂×C₁₃	semidirect
458. #3099	C₂×C₁₃	semidirect
459. #3098	C₂×C₁₃	semidirect
460. #3097	C₂×C₁₃	semidirect
461. #3097	C₂×C₁₃	semidirect
462. #3076	C₂×C₁₃	semidirect
463. C₂×#479	C₂×C₁₃	semidirect
464. #3063	C₂×C₁₃	semidirect
465. #3063	C₂×C₁₃	semidirect
466. C₄×#137	C₂×C₁₃	semidirect
467. #2935	C₂×C₁₃	semidirect
468. #2913	C₂×C₁₃	semidirect
469. #2912	C₂×C₁₃	semidirect
1000. C₁₃	#61280	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3512	2
C₁₃×#3507	2
C₁₃×#3352	2
C₁₃×#3351	2
C₁₃×#3350	2
C₁₃×#3349	2
C₁₃×#3346	2
C₁₃×#3344	2
C₁₃×#3337	2
C₁₃×#3336	2
C₁₃×#3166	2
C₁₃×#3099	2
C₁₃×#3098	2
C₁₃×#3097	2
C₁₃×#3076	2
C₂×C₁₃×#479	2
C₁₃×#3063	2
C₄×C₁₃×#137	2
C₁₃×#2935	2
C₁₃×#2913	2
C₁₃×#2912	2
#61280	13

Subgroups — C13×#61280 #15747619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61280 #15747619