Subgroups — C₁₃×#61845 #15748184

Order 3328.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3233	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic
20	C₁₃×#3111	C₂	1	2	yes	maximal, complemented
21	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3102	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#559	C₂²	1	1	yes	characteristic
25	C₁₃×#559	C₂²	1	1	yes	characteristic
26	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#557	C₂²	1	1	yes	characteristic
28	C₁₃×#557	C₂²	1	2	yes	—
29	C₁₃×#557	C₂²	1	1	yes	characteristic
30	C₁₃×#557	C₂²	1	1	yes	characteristic
31	C₁₃×#556	—	2	1	no	—
32	C₁₃×#556	—	2	1	no	—
33	C₁₃×#556	C₂²	1	2	yes	—
34	C₁₃×#554	—	2	1	no	—
35	C₁₃×#554	—	2	2	no	—
36	C₁₃×#554	C₂²	1	1	yes	characteristic
37	C₁₃×#554	C₂²	1	2	yes	—
38	C₁₃×#554	C₂²	1	2	yes	—
39	C₁₃×#552	—	2	2	no	—
40	D₄×Q₈×C₁₃	—	2	1	no	—
41	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#539	—	2	2	no	—
43	C₁₃×#536	—	2	1	no	—
44	C₁₃×#533	—	2	2	no	—
45	C₁₃×#533	—	2	1	no	—
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₁₃×#533	C₂²	1	1	yes	characteristic
48	C₁₃×#533	C₂²	1	2	yes	—
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#529	C₂²	1	2	yes	—
51	C₁₃×#529	C₂²	1	2	yes	—
52	C₁₃×#520	—	2	1	no	—
53	C₄×C₁₃×#41	C₂²	1	2	yes	—
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	2	yes	—
58	C₁₃×#501	C₂²	1	2	yes	—
59	C₁₃×#501	C₂²	1	2	yes	—
60	C₁₃×#500	C₂²	1	1	yes	characteristic
61	C₁₃×#499	C₂²	1	2	yes	—
62	C₁₃×#499	C₂²	1	2	yes	—
63	C₁₃×#498	C₂²	1	1	yes	characteristic
64	C₁₃×#491	C₂²	1	2	yes	—
65	C₁₃×#489	C₂²	1	2	yes	—
66	C₁₃×#489	C₂²	1	2	yes	—
67	C₁₃×#488	C₂²	1	2	yes	—
68	C₁₃×#488	C₂²	1	2	yes	—
69	C₁₃×#486	C₂²	1	1	yes	characteristic
70	C₁₃×#486	C₂²	1	1	yes	characteristic
71	C₁₃×#485	C₂²	1	2	yes	—
72	C₁₃×#485	C₂²	1	1	yes	characteristic
73	C₁₃×#485	C₂²	1	1	yes	characteristic
74	C₁₃×#485	C₂²	1	2	yes	—
75	C₁₃×#482	C₂²	1	2	yes	—
76	C₁₃×#482	C₂²	1	2	yes	—
77	C₁₃×#482	C₂²	1	2	yes	—
78	C₁₃×#479	C₂²	1	2	yes	—
79	C₁₃×#479	C₂²	1	2	yes	—
80	C₁₃×#479	C₂²	1	2	yes	—
81	C₁₃×#479	C₂²	1	2	yes	—
82	C₁₃×#478	C₂²	1	2	yes	—
83	C₁₃×#478	C₂²	1	2	yes	—
84	C₁₃×#478	C₂²	1	2	yes	—
85	C₁₃×#478	C₂²	1	2	yes	—
86	C₁₃×#478	C₂²	1	2	yes	—
87	C₁₃×#478	C₂²	1	2	yes	—
88	C₁₃×#477	C₂²	1	1	yes	characteristic
89	C₁₃×#477	C₂²	1	1	yes	characteristic
90	C₁₃×#477	C₂²	1	2	yes	—
91	C₁₃×#476	C₂²	1	2	yes	—
92	C₁₃×#475	C₂²	1	1	yes	characteristic
93	C₁₃×#475	C₂²	1	1	yes	characteristic
94	C₁₃×#475	C₂²	1	1	yes	characteristic
95	C₁₃×#475	C₂²	1	1	yes	characteristic
96	C₁₃×#475	C₂²	1	2	yes	—
97	C₁₃×#474	C₂²	1	1	yes	characteristic
98	C₁₃×#474	C₂²	1	1	yes	characteristic
99	C₁₃×#474	C₂²	1	2	yes	—
100	C₁₃×#464	C₂²	1	2	yes	—
101	C₁₃×#464	C₂²	1	2	yes	—
102	C₁₃×#463	C₂²	1	2	yes	—
103	C₁₃×#463	C₂²	1	2	yes	—
104	C₁₃×#462	C₂²	1	1	yes	characteristic
105	C₁₃×#461	C₂²	1	1	yes	characteristic
106	C₁₃×#460	C₂²	1	1	yes	characteristic
107	C₁₃×#459	C₂²	1	1	yes	characteristic
108	C₁₃×#452	C₂²	1	1	yes	characteristic
109	C₁₃×#452	C₂²	1	1	yes	characteristic
110	C₁₃×#449	C₂²	1	2	yes	—
111	C₁₃×#446	C₂²	1	1	yes	characteristic
112	C₁₃×#446	C₂²	1	1	yes	characteristic
113	C₁₃×#446	C₂²	1	2	yes	—
114	C₁₃×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
117	C₁₃×#442	C₂²	1	2	yes	—
118	C₁₃×#442	C₂²	1	2	yes	—
119	C₁₃×#441	C₂²	1	2	yes	—
120	C₁₃×#440	C₂²	1	2	yes	—
121	C₁₃×#440	C₂²	1	2	yes	—
122	C₁₃×#440	C₂²	1	2	yes	—
123	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
124	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
125	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
126	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
127	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
128	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
129	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
130	C₄×C₁₃×D₈	C₂²	1	2	yes	—
131	C₁₃×#432	C₂²	1	2	yes	—
132	C₁₃×#432	C₂²	1	1	yes	characteristic
133	C₁₃×#431	C₂²	1	2	yes	—
134	C₁₃×#431	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₁₃	—	2	1	no	—
138	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
139	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
143	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×D₈	C₂³	1	2	yes	—
145	C₁₃×C₄⋊Q₈	—	2	1	no	—
146	C₁₃×C₄⋊Q₈	—	2	2	no	—
147	C₁₃×C₄⋊Q₈	—	2	1	no	—
148	C₁₃×C₄⋊Q₈	—	2	1	no	—
149	C₁₃×C₄⋊Q₈	—	2	1	no	—
150	C₁₃×C₄⋊Q₈	—	2	2	no	—
151	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₁₃×#127	C₂³	1	1	yes	characteristic
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×#125	—	2	2	no	—
164	C₁₃×#125	—	2	2	no	—
165	C₁₃×#125	—	2	2	no	—
166	C₁₃×#125	—	2	2	no	—
167	C₁₃×#125	—	2	2	no	—
168	C₁₃×#125	—	2	1	no	—
169	C₁₃×#125	C₂³	1	2	yes	—
170	C₁₃×#125	C₂³	1	2	yes	—
171	C₁₃×#125	C₂³	1	2	yes	—
172	C₁₃×#125	C₂³	1	2	yes	—
173	C₁₃×#125	C₂³	1	2	yes	—
174	C₁₃×#124	—	2	1	no	—
175	C₁₃×#124	—	2	1	no	—
176	C₁₃×#124	—	2	1	no	—
177	C₁₃×#124	C₂³	1	2	yes	—
178	C₁₃×#124	C₂³	1	2	yes	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	—	2	2	no	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	1	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	1	no	—
188	C₁₃×C₂²⋊Q₈	—	2	1	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	1	no	—
192	C₁₃×C₂²⋊Q₈	—	2	1	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
200	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₁₃×#121	—	2	1	no	—
202	C₁₃×#121	C₂³	1	2	yes	—
203	C₄×Q₈×C₁₃	—	2	1	no	—
204	C₄×Q₈×C₁₃	—	2	1	no	—
205	C₄×Q₈×C₁₃	—	2	2	no	—
206	C₄×Q₈×C₁₃	—	2	1	no	—
207	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	—	2	2	no	—
209	C₄×Q₈×C₁₃	—	2	1	no	—
210	C₄×Q₈×C₁₃	—	2	2	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₁₃	D₄	1	2	yes	—
215	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
227	C₄×D₄×C₁₃	—	2	1	no	—
228	C₄×D₄×C₁₃	—	2	2	no	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	—	2	1	no	—
231	C₄×D₄×C₁₃	—	2	2	no	—
232	C₄×D₄×C₁₃	—	2	2	no	—
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	1	no	—
236	C₄×D₄×C₁₃	C₂³	1	2	yes	—
237	C₄×D₄×C₁₃	C₂³	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	2	yes	—
240	C₄×D₄×C₁₃	C₂³	1	2	yes	—
241	C₄×D₄×C₁₃	C₂³	1	2	yes	—
242	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
243	C₁₃×#117	—	2	1	no	—
244	C₁₃×#117	—	2	2	no	—
245	C₁₃×#117	—	2	2	no	—
246	C₁₃×#117	—	2	1	no	—
247	C₁₃×#117	—	2	2	no	—
248	C₁₃×#117	—	2	2	no	—
249	C₁₃×#117	C₂³	1	2	yes	—
250	C₁₃×#117	C₂³	1	1	yes	characteristic
251	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
255	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
256	C₂×C₄²×C₁₃	—	2	2	no	—
257	C₂×C₄²×C₁₃	—	2	1	no	—
258	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
259	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
260	C₁₃×#107	C₂³	1	2	yes	—
261	C₁₃×#107	C₂³	1	1	yes	characteristic
262	C₁₃×#107	C₂³	1	1	yes	characteristic
263	C₁₃×#107	C₂³	1	2	yes	—
264	C₁₃×#107	C₂³	1	2	yes	—
265	C₁₃×#107	C₂³	1	2	yes	—
266	C₁₃×#107	C₂³	1	2	yes	—
267	C₁₃×#106	C₂³	1	1	yes	characteristic
268	C₁₃×#106	C₂³	1	2	yes	—
269	C₁₃×#106	C₂³	1	1	yes	characteristic
270	C₁₃×#106	C₂³	1	2	yes	—
271	C₁₃×#106	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
277	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₃×#103	C₂³	1	1	yes	characteristic
283	C₁₃×#103	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	2	yes	—
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#102	C₂³	1	1	yes	characteristic
294	C₁₃×#102	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	1	yes	characteristic
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₁₃×#97	C₂³	1	2	yes	—
306	C₁₃×#97	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₁₃	C₂³	1	2	yes	—
309	C₄×C₈×C₁₃	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	#61845	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	2	2	no	—
314	C₁₃×#41	—	2	2	no	—
315	C₁₃×#41	—	4	4	no	—
316	C₂×Q₈×C₁₃	—	2	2	no	—
317	C₂×Q₈×C₁₃	—	2	1	no	—
318	C₂×Q₈×C₁₃	—	2	1	no	—
319	C₂×Q₈×C₁₃	—	2	1	no	—
320	C₂×Q₈×C₁₃	—	2	2	no	—
321	C₂×Q₈×C₁₃	—	2	1	no	—
322	C₂×Q₈×C₁₃	—	4	2	no	—
323	C₂×Q₈×C₁₃	—	4	4	no	—
324	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₁₃	—	2	1	no	—
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	1	no	—
333	C₂×D₄×C₁₃	—	2	1	no	—
334	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
335	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃	—	2	1	no	—
337	C₂²×C₄×C₁₃	—	2	2	no	—
338	C₂²×C₄×C₁₃	—	2	1	no	—
339	C₂²×C₄×C₁₃	—	2	2	no	—
340	C₂²×C₄×C₁₃	—	2	2	no	—
341	C₂²×C₄×C₁₃	—	2	1	no	—
342	C₂²×C₄×C₁₃	—	2	2	no	—
343	C₂²×C₄×C₁₃	—	2	2	no	—
344	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
346	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
348	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₁₃×Q₁₆	—	2	2	no	—
350	C₁₃×Q₁₆	—	2	2	no	—
351	C₁₃×SD₁₆	—	2	4	no	—
352	C₁₃×SD₁₆	—	2	2	no	—
353	C₁₃×SD₁₆	—	2	2	no	—
354	C₁₃×D₈	—	2	4	no	—
355	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
359	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
361	C₁₃×C₄⋊C₄	—	2	1	no	—
362	C₁₃×C₄⋊C₄	—	2	2	no	—
363	C₁₃×C₄⋊C₄	—	2	2	no	—
364	C₁₃×C₄⋊C₄	—	2	2	no	—
365	C₁₃×C₄⋊C₄	—	2	2	no	—
366	C₁₃×C₄⋊C₄	—	2	2	no	—
367	C₁₃×C₄⋊C₄	—	2	2	no	—
368	C₁₃×C₄⋊C₄	—	2	1	no	—
369	C₁₃×C₄⋊C₄	—	2	1	no	—
370	C₁₃×C₄⋊C₄	—	2	1	no	—
371	C₁₃×C₄⋊C₄	—	2	1	no	—
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
374	C₁₃×C₄⋊C₄	—	2	1	no	—
375	C₁₃×C₄⋊C₄	—	2	1	no	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	2	no	—
378	C₁₃×C₄⋊C₄	—	2	1	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	2	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	1	no	—
385	C₁₃×C₄⋊C₄	—	2	1	no	—
386	C₁₃×C₄⋊C₄	—	2	1	no	—
387	C₁₃×C₄⋊C₄	—	2	2	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
390	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
397	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
398	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
399	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
400	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₁₃×C₂²⋊C₄	—	2	1	no	—
404	C₁₃×C₂²⋊C₄	—	2	1	no	—
405	C₁₃×C₂²⋊C₄	—	2	2	no	—
406	C₁₃×C₂²⋊C₄	—	2	1	no	—
407	C₁₃×C₂²⋊C₄	—	2	2	no	—
408	C₁₃×C₂²⋊C₄	—	2	2	no	—
409	C₁₃×C₂²⋊C₄	—	2	2	no	—
410	C₁₃×C₂²⋊C₄	—	2	2	no	—
411	C₁₃×C₂²⋊C₄	—	2	2	no	—
412	C₁₃×C₂²⋊C₄	—	2	1	no	—
413	C₁₃×C₂²⋊C₄	—	2	1	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
415	C₁₃×C₂²⋊C₄	—	2	2	no	—
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₄²×C₁₃	—	2	2	no	—
420	C₄²×C₁₃	—	2	1	no	—
421	C₄²×C₁₃	—	2	2	no	—
422	C₄²×C₁₃	—	2	1	no	—
423	C₄²×C₁₃	—	2	2	no	—
424	C₄²×C₁₃	—	2	1	no	—
425	C₄²×C₁₃	—	2	2	no	—
426	C₄²×C₁₃	—	2	2	no	—
427	C₄²×C₁₃	—	2	1	no	—
428	C₄²×C₁₃	—	2	1	no	—
429	C₄²×C₁₃	C₂×D₄	1	2	yes	—
430	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₁₃	C₂×D₄	1	2	yes	—
432	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₁₃	C₂⁴	1	2	yes	—
434	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
435	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
436	C₄²×C₁₃	C₂⁴	1	2	yes	—
437	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
438	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
439	#3389	C₂×C₁₃	1	2	yes	complemented
440	#3388	C₂×C₁₃	1	2	yes	complemented
441	#3387	C₂×C₁₃	1	1	yes	characteristic, complemented
442	#3386	C₂×C₁₃	1	1	yes	characteristic, complemented
443	#3383	C₂×C₁₃	1	1	yes	characteristic, complemented
444	#3381	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3377	C₂×C₁₃	1	2	yes	complemented
446	#3376	C₂×C₁₃	1	2	yes	complemented
447	#3375	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3373	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3365	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3361	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3240	C₂×C₁₃	1	2	yes	complemented
452	#3237	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#3233	C₂×C₁₃	1	2	yes	complemented
454	#3228	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3115	C₂×C₁₃	1	1	yes	characteristic
456	#3111	C₂×C₁₃	1	2	yes	complemented
457	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3102	C₂×C₁₃	1	2	yes	complemented
459	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
460	C₂³×C₁₃	—	2	1	no	—
461	C₂³×C₁₃	—	2	2	no	—
462	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
463	Q₈×C₁₃	—	2	2	no	—
464	Q₈×C₁₃	—	2	2	no	—
465	Q₈×C₁₃	—	2	1	no	—
466	Q₈×C₁₃	—	2	1	no	—
467	Q₈×C₁₃	—	2	1	no	—
468	Q₈×C₁₃	—	2	1	no	—
469	Q₈×C₁₃	—	2	1	no	—
470	Q₈×C₁₃	—	4	2	no	—
471	Q₈×C₁₃	—	4	4	no	—
472	Q₈×C₁₃	—	4	2	no	—
473	Q₈×C₁₃	—	4	2	no	—
474	Q₈×C₁₃	—	8	1	no	—
475	Q₈×C₁₃	—	8	2	no	—
476	Q₈×C₁₃	—	8	1	no	—
477	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
478	D₄×C₁₃	—	2	4	no	—
479	D₄×C₁₃	—	2	1	no	—
480	D₄×C₁₃	—	2	2	no	—
481	D₄×C₁₃	—	2	2	no	—
482	D₄×C₁₃	—	4	4	no	—
483	D₄×C₁₃	—	4	2	no	—
484	D₄×C₁₃	—	8	1	no	—
485	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
486	C₂×C₄×C₁₃	—	2	4	no	—
487	C₂×C₄×C₁₃	—	2	1	no	—
488	C₂×C₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	1	no	—
490	C₂×C₄×C₁₃	—	2	1	no	—
491	C₂×C₄×C₁₃	—	2	1	no	—
492	C₂×C₄×C₁₃	—	2	1	no	—
493	C₂×C₄×C₁₃	—	2	2	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	2	no	—
497	C₂×C₄×C₁₃	—	2	1	no	—
498	C₂×C₄×C₁₃	—	2	1	no	—
499	C₂×C₄×C₁₃	—	2	1	no	—
500	C₂×C₄×C₁₃	—	4	2	no	—
501	C₂×C₄×C₁₃	—	4	1	no	—
502	C₂×C₄×C₁₃	—	4	2	no	—
503	C₂×C₄×C₁₃	—	4	4	no	—
504	C₂×C₄×C₁₃	—	4	4	no	—
505	C₂×C₄×C₁₃	—	4	2	no	—
506	C₂×C₄×C₁₃	—	8	2	no	—
507	C₂×C₄×C₁₃	—	8	2	no	—
508	C₂×C₄×C₁₃	—	8	2	no	—
509	C₂×C₄×C₁₃	—	8	1	no	—
510	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
520	C₈×C₁₃	—	2	2	no	—
521	C₈×C₁₃	—	2	2	no	—
522	C₈×C₁₃	—	2	1	no	—
523	C₈×C₁₃	—	2	1	no	—
524	C₈×C₁₃	—	2	1	no	—
525	C₈×C₁₃	—	2	1	no	—
526	#559	C₂²×C₁₃	1	1	yes	characteristic
527	#559	C₂²×C₁₃	1	1	yes	characteristic
528	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
529	#557	C₂²×C₁₃	1	1	yes	characteristic
530	#557	C₂²×C₁₃	1	2	yes	—
531	#557	C₂²×C₁₃	1	1	yes	characteristic
532	#557	C₂²×C₁₃	1	1	yes	characteristic
533	#556	—	2	1	no	—
534	#556	—	2	1	no	—
535	#556	C₂²×C₁₃	1	2	yes	—
536	#554	—	2	1	no	—
537	#554	—	2	2	no	—
538	#554	C₂²×C₁₃	1	1	yes	characteristic
539	#554	C₂²×C₁₃	1	2	yes	—
540	#554	C₂²×C₁₃	1	2	yes	—
541	#552	—	2	2	no	—
542	D₄×Q₈	—	2	1	no	—
543	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
544	#539	—	2	2	no	—
545	#536	—	2	1	no	—
546	#533	—	2	2	no	—
547	#533	—	2	1	no	—
548	#533	C₂²×C₁₃	1	1	yes	characteristic
549	#533	C₂²×C₁₃	1	1	yes	characteristic
550	#533	C₂²×C₁₃	1	2	yes	—
551	#532	C₂²×C₁₃	1	1	yes	characteristic
552	#529	C₂²×C₁₃	1	2	yes	—
553	#529	C₂²×C₁₃	1	2	yes	—
554	#520	—	2	1	no	—
555	C₄×#41	C₂²×C₁₃	1	2	yes	—
556	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
557	C₂×C₄×Q₈	—	2	1	no	—
558	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
559	#501	C₂²×C₁₃	1	2	yes	—
560	#501	C₂²×C₁₃	1	2	yes	—
561	#501	C₂²×C₁₃	1	2	yes	—
562	#500	C₂²×C₁₃	1	1	yes	characteristic
563	#499	C₂²×C₁₃	1	2	yes	—
564	#499	C₂²×C₁₃	1	2	yes	—
565	#498	C₂²×C₁₃	1	1	yes	characteristic
566	#491	C₂²×C₁₃	1	2	yes	—
567	#489	C₂²×C₁₃	1	2	yes	—
568	#489	C₂²×C₁₃	1	2	yes	—
569	#488	C₂²×C₁₃	1	2	yes	—
570	#488	C₂²×C₁₃	1	2	yes	—
571	#486	C₂²×C₁₃	1	1	yes	characteristic
572	#486	C₂²×C₁₃	1	1	yes	characteristic
573	#485	C₂²×C₁₃	1	2	yes	—
574	#485	C₂²×C₁₃	1	1	yes	characteristic
575	#485	C₂²×C₁₃	1	1	yes	characteristic
576	#485	C₂²×C₁₃	1	2	yes	—
577	#482	C₂²×C₁₃	1	2	yes	—
578	#482	C₂²×C₁₃	1	2	yes	—
579	#482	C₂²×C₁₃	1	2	yes	—
580	#479	C₂²×C₁₃	1	2	yes	—
581	#479	C₂²×C₁₃	1	2	yes	—
582	#479	C₂²×C₁₃	1	2	yes	—
583	#479	C₂²×C₁₃	1	2	yes	—
584	#478	C₂²×C₁₃	1	2	yes	—
585	#478	C₂²×C₁₃	1	2	yes	—
586	#478	C₂²×C₁₃	1	2	yes	—
587	#478	C₂²×C₁₃	1	2	yes	—
588	#478	C₂²×C₁₃	1	2	yes	—
589	#478	C₂²×C₁₃	1	2	yes	—
590	#477	C₂²×C₁₃	1	1	yes	characteristic
591	#477	C₂²×C₁₃	1	1	yes	characteristic
592	#477	C₂²×C₁₃	1	2	yes	—
593	#476	C₂²×C₁₃	1	2	yes	—
594	#475	C₂²×C₁₃	1	1	yes	characteristic
595	#475	C₂²×C₁₃	1	1	yes	characteristic
596	#475	C₂²×C₁₃	1	1	yes	characteristic
597	#475	C₂²×C₁₃	1	1	yes	characteristic
598	#475	C₂²×C₁₃	1	2	yes	—
599	#474	C₂²×C₁₃	1	1	yes	characteristic
600	#474	C₂²×C₁₃	1	1	yes	characteristic
601	#474	C₂²×C₁₃	1	2	yes	—
602	#464	C₂²×C₁₃	1	2	yes	—
603	#464	C₂²×C₁₃	1	2	yes	—
604	#463	C₂²×C₁₃	1	2	yes	—
605	#463	C₂²×C₁₃	1	2	yes	—
606	#462	C₂²×C₁₃	1	1	yes	characteristic
607	#461	C₂²×C₁₃	1	1	yes	characteristic
608	#460	C₂²×C₁₃	1	1	yes	characteristic
609	#459	C₂²×C₁₃	1	1	yes	characteristic
610	#452	C₂²×C₁₃	1	1	yes	characteristic
611	#452	C₂²×C₁₃	1	1	yes	characteristic
612	#449	C₂²×C₁₃	1	2	yes	—
613	#446	C₂²×C₁₃	1	1	yes	characteristic
614	#446	C₂²×C₁₃	1	1	yes	characteristic
615	#446	C₂²×C₁₃	1	2	yes	—
616	#446	C₂²×C₁₃	1	2	yes	—
617	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
618	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
619	#442	C₂²×C₁₃	1	2	yes	—
620	#442	C₂²×C₁₃	1	2	yes	—
621	#441	C₂²×C₁₃	1	2	yes	—
622	#440	C₂²×C₁₃	1	2	yes	—
623	#440	C₂²×C₁₃	1	2	yes	—
624	#440	C₂²×C₁₃	1	2	yes	—
625	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
626	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
627	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
628	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
629	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
630	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
631	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
632	C₄×D₈	C₂²×C₁₃	1	2	yes	—
633	#432	C₂²×C₁₃	1	2	yes	—
634	#432	C₂²×C₁₃	1	1	yes	characteristic
635	#431	C₂²×C₁₃	1	2	yes	—
636	#431	C₂²×C₁₃	1	1	yes	characteristic
637	C₂²×C₁₃	—	2	1	no	—
638	C₂²×C₁₃	—	2	1	no	—
639	C₂²×C₁₃	—	2	2	no	—
640	C₂²×C₁₃	—	2	1	no	—
641	C₂²×C₁₃	—	4	1	no	—
642	C₂²×C₁₃	—	4	1	no	—
643	C₂²×C₁₃	—	4	2	no	—
644	C₂²×C₁₃	—	4	2	no	—
645	C₂²×C₁₃	—	4	2	no	—
646	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
647	C₄×C₁₃	—	2	2	no	—
648	C₄×C₁₃	—	2	2	no	—
649	C₄×C₁₃	—	2	1	no	—
650	C₄×C₁₃	—	2	1	no	—
651	C₄×C₁₃	—	2	1	no	—
652	C₄×C₁₃	—	2	2	no	—
653	C₄×C₁₃	—	2	1	no	—
654	C₄×C₁₃	—	2	2	no	—
655	C₄×C₁₃	—	2	2	no	—
656	C₄×C₁₃	—	4	1	no	—
657	C₄×C₁₃	—	4	1	no	—
658	C₄×C₁₃	—	4	2	no	—
659	C₄×C₁₃	—	4	1	no	—
660	C₄×C₁₃	—	4	1	no	—
661	C₄×C₁₃	—	4	1	no	—
662	C₄×C₁₃	—	4	2	no	—
663	C₄×C₁₃	—	4	2	no	—
664	C₄×C₁₃	—	4	1	no	—
665	C₄×C₁₃	#575	1	2	yes	—
666	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
667	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
668	C₂×#41	—	2	1	no	—
669	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
670	C₂²×Q₈	—	2	1	no	—
671	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
672	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
673	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
674	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×D₈	C₂³×C₁₃	1	2	yes	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	2	no	—
680	C₄⋊Q₈	—	2	1	no	—
681	C₄⋊Q₈	—	2	1	no	—
682	C₄⋊Q₈	—	2	1	no	—
683	C₄⋊Q₈	—	2	2	no	—
684	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
685	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
688	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
690	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
691	#127	C₂³×C₁₃	1	1	yes	characteristic
692	#126	—	2	2	no	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	2	no	—
700	#125	—	2	2	no	—
701	#125	—	2	1	no	—
702	#125	C₂³×C₁₃	1	2	yes	—
703	#125	C₂³×C₁₃	1	2	yes	—
704	#125	C₂³×C₁₃	1	2	yes	—
705	#125	C₂³×C₁₃	1	2	yes	—
706	#125	C₂³×C₁₃	1	2	yes	—
707	#124	—	2	1	no	—
708	#124	—	2	1	no	—
709	#124	—	2	1	no	—
710	#124	C₂³×C₁₃	1	2	yes	—
711	#124	C₂³×C₁₃	1	2	yes	—
712	#123	—	2	2	no	—
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
733	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
734	#121	—	2	1	no	—
735	#121	C₂³×C₁₃	1	2	yes	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	2	no	—
742	C₄×Q₈	—	2	1	no	—
743	C₄×Q₈	—	2	2	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
747	C₄×Q₈	D₄×C₁₃	1	2	yes	—
748	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
749	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
750	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
751	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
752	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
753	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
754	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
755	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
759	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	—	2	1	no	—
769	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
770	C₄×D₄	C₂³×C₁₃	1	2	yes	—
771	C₄×D₄	C₂³×C₁₃	1	2	yes	—
772	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₁₃	1	2	yes	—
774	C₄×D₄	C₂³×C₁₃	1	2	yes	—
775	C₄×D₄	C₂³×C₁₃	1	2	yes	—
776	#117	—	2	1	no	—
777	#117	—	2	2	no	—
778	#117	—	2	2	no	—
779	#117	—	2	1	no	—
780	#117	—	2	2	no	—
781	#117	—	2	2	no	—
782	#117	C₂³×C₁₃	1	2	yes	—
783	#117	C₂³×C₁₃	1	1	yes	characteristic
784	C₂×C₄⋊C₄	—	2	1	no	—
785	C₂×C₄⋊C₄	—	2	2	no	—
786	C₂×C₄⋊C₄	—	2	2	no	—
787	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
788	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
789	C₂×C₄²	—	2	2	no	—
790	C₂×C₄²	—	2	1	no	—
791	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
792	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
793	#107	C₂³×C₁₃	1	2	yes	—
794	#107	C₂³×C₁₃	1	1	yes	characteristic
795	#107	C₂³×C₁₃	1	1	yes	characteristic
796	#107	C₂³×C₁₃	1	2	yes	—
797	#107	C₂³×C₁₃	1	2	yes	—
798	#107	C₂³×C₁₃	1	2	yes	—
799	#107	C₂³×C₁₃	1	2	yes	—
800	#106	C₂³×C₁₃	1	1	yes	characteristic
801	#106	C₂³×C₁₃	1	2	yes	—
802	#106	C₂³×C₁₃	1	1	yes	characteristic
803	#106	C₂³×C₁₃	1	2	yes	—
804	#106	C₂³×C₁₃	1	2	yes	—
805	#106	C₂³×C₁₃	1	2	yes	—
806	#106	C₂³×C₁₃	1	2	yes	—
807	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
808	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
809	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
810	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
811	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
814	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
815	#103	C₂³×C₁₃	1	1	yes	characteristic
816	#103	C₂³×C₁₃	1	1	yes	characteristic
817	#103	C₂³×C₁₃	1	1	yes	characteristic
818	#103	C₂³×C₁₃	1	2	yes	—
819	#103	C₂³×C₁₃	1	1	yes	characteristic
820	#103	C₂³×C₁₃	1	2	yes	—
821	#103	C₂³×C₁₃	1	1	yes	characteristic
822	#103	C₂³×C₁₃	1	1	yes	characteristic
823	#103	C₂³×C₁₃	1	2	yes	—
824	#103	C₂³×C₁₃	1	2	yes	—
825	#103	C₂³×C₁₃	1	2	yes	—
826	#102	C₂³×C₁₃	1	1	yes	characteristic
827	#102	C₂³×C₁₃	1	2	yes	—
828	#102	C₂³×C₁₃	1	2	yes	—
829	#102	C₂³×C₁₃	1	1	yes	characteristic
830	#102	C₂³×C₁₃	1	2	yes	—
831	#102	C₂³×C₁₃	1	2	yes	—
832	#102	C₂³×C₁₃	1	2	yes	—
833	#102	C₂³×C₁₃	1	2	yes	—
834	#102	C₂³×C₁₃	1	2	yes	—
835	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
836	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
837	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
838	#97	C₂³×C₁₃	1	2	yes	—
839	#97	C₂³×C₁₃	1	2	yes	—
840	#97	C₂³×C₁₃	1	2	yes	—
841	C₄×C₈	C₂³×C₁₃	1	2	yes	—
842	C₄×C₈	C₂³×C₁₃	1	2	yes	—
843	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
844	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
845	C₂×C₁₃	—	4	1	no	—
846	C₂×C₁₃	—	4	2	no	—
847	C₂×C₁₃	—	8	2	no	—
848	C₂×C₁₃	#3486	1	1	yes	characteristic
849	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
850	C₂×C₁₃	#3584	1	1	yes	characteristic
851	#41	—	2	2	no	—
852	#41	—	2	2	no	—
853	#41	—	4	4	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	4	2	no	—
861	C₂×Q₈	—	4	4	no	—
862	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
863	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
864	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
865	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
866	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
867	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	—	2	1	no	—
872	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
873	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
883	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
884	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
885	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
887	Q₁₆	—	2	2	no	—
888	Q₁₆	—	2	2	no	—
889	SD₁₆	—	2	4	no	—
890	SD₁₆	—	2	2	no	—
891	SD₁₆	—	2	2	no	—
892	D₈	—	2	4	no	—
893	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
894	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
896	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
897	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
898	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
928	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
929	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
930	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
931	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
932	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
933	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
938	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	C₂×D₄×C₁₃	1	2	yes	—
968	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
969	C₄²	C₂×D₄×C₁₃	1	2	yes	—
970	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
971	C₄²	C₂⁴×C₁₃	1	2	yes	—
972	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
973	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
974	C₄²	C₂⁴×C₁₃	1	2	yes	—
975	C₁₃	#61845	1	1	yes	characteristic, direct product factor, Sylow
976	C₂³	—	2	1	no	—
977	C₂³	—	2	2	no	—
978	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
979	Q₈	—	2	2	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	1	no	—
983	Q₈	—	2	1	no	—
984	Q₈	—	2	1	no	—
985	Q₈	—	2	1	no	—
986	Q₈	—	4	2	no	—
987	Q₈	—	4	4	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	8	1	no	—
991	Q₈	—	8	2	no	—
992	Q₈	—	8	1	no	—
993	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
994	D₄	—	2	4	no	—
995	D₄	—	2	1	no	—
996	D₄	—	2	2	no	—
997	D₄	—	2	2	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	2	no	—
1000	D₄	—	8	1	no	—
1001	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1002	C₂×C₄	—	2	4	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	—	4	1	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	—	8	2	no	—
1024	C₂×C₄	—	8	2	no	—
1025	C₂×C₄	—	8	1	no	—
1026	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1029	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1030	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1031	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1033	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1035	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1036	C₈	—	2	2	no	—
1037	C₈	—	2	2	no	—
1038	C₈	—	2	1	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	2	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	1	no	—
1070	C₄	C₁₃×#575	1	2	yes	—
1071	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1072	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1073	C₂	—	4	1	no	—
1074	C₂	—	4	2	no	—
1075	C₂	—	8	2	no	—
1076	C₂	C₁₃×#3486	1	1	yes	characteristic
1077	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1078	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3115	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3507	C₂	semidirect
2. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3389	C₂	semidirect
4. C₁₃×#3388	C₂	semidirect
5. C₁₃×#3387	C₂	semidirect
6. C₁₃×#3386	C₂	semidirect
7. C₁₃×#3383	C₂	semidirect
8. C₁₃×#3381	C₂	semidirect
9. C₁₃×#3377	C₂	semidirect
10. C₁₃×#3376	C₂	semidirect
11. C₁₃×#3375	C₂	semidirect
12. C₁₃×#3373	C₂	semidirect
13. C₁₃×#3365	C₂	semidirect
14. C₁₃×#3361	C₂	semidirect
15. C₁₃×#3240	C₂	semidirect
16. C₁₃×#3237	C₂	semidirect
17. C₁₃×#3233	C₂	semidirect
18. C₁₃×#3228	C₂	semidirect
20. C₁₃×#3111	C₂	semidirect
21. C₁₃×#3107	C₂	semidirect
22. C₁₃×#3102	C₂	semidirect
23. C₁₃×#2984	C₂	semidirect
312. #61845	C₁₃	direct (N × H)
437. #3507	C₂×C₁₃	semidirect
438. Q₈×#41	C₂×C₁₃	semidirect
439. #3389	C₂×C₁₃	semidirect
440. #3388	C₂×C₁₃	semidirect
441. #3387	C₂×C₁₃	semidirect
442. #3386	C₂×C₁₃	semidirect
443. #3383	C₂×C₁₃	semidirect
444. #3381	C₂×C₁₃	semidirect
445. #3377	C₂×C₁₃	semidirect
446. #3376	C₂×C₁₃	semidirect
447. #3375	C₂×C₁₃	semidirect
448. #3373	C₂×C₁₃	semidirect
449. #3365	C₂×C₁₃	semidirect
450. #3361	C₂×C₁₃	semidirect
451. #3240	C₂×C₁₃	semidirect
452. #3237	C₂×C₁₃	semidirect
453. #3233	C₂×C₁₃	semidirect
454. #3228	C₂×C₁₃	semidirect
456. #3111	C₂×C₁₃	semidirect
457. #3107	C₂×C₁₃	semidirect
458. #3102	C₂×C₁₃	semidirect
459. #2984	C₂×C₁₃	semidirect
975. C₁₃	#61845	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×#3507	2
Q₈×C₁₃×#41	2
C₁₃×#3389	2
C₁₃×#3388	2
C₁₃×#3387	2
C₁₃×#3386	2
C₁₃×#3383	2
C₁₃×#3381	2
C₁₃×#3377	2
C₁₃×#3376	2
C₁₃×#3375	2
C₁₃×#3373	2
C₁₃×#3365	2
C₁₃×#3361	2
C₁₃×#3240	2
C₁₃×#3237	2
C₁₃×#3233	2
C₁₃×#3228	2
C₁₃×#3115	2
C₁₃×#3111	2
C₁₃×#3107	2
C₁₃×#3102	2
C₁₃×#2984	2
#61845	13

Subgroups — C13×#61845 #15748184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61845 #15748184