Subgroups — C₁₃×#61468 #15747807

Order 3328.

1908 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3355	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3326	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3322	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3275	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3183	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3114	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3111	C₂	1	2	yes	maximal, complemented
21	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
24	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₁₃×#559	—	2	1	no	—
27	C₁₃×#559	C₂²	1	1	yes	characteristic
28	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#556	—	2	1	no	—
31	C₁₃×#556	C₂²	1	1	yes	characteristic
32	C₁₃×#554	C₂²	1	1	yes	characteristic
33	C₁₃×#554	C₂²	1	1	yes	characteristic
34	C₁₃×#553	—	2	2	no	—
35	C₁₃×#553	—	2	1	no	—
36	C₁₃×#553	C₂²	1	2	yes	—
37	C₁₃×#553	C₂²	1	2	yes	complemented
38	C₁₃×#551	—	2	2	no	—
39	C₁₃×#550	C₂²	1	1	yes	characteristic
40	C₁₃×#548	C₂²	1	2	yes	complemented
41	C₁₃×#546	—	2	1	no	—
42	C₁₃×#546	C₂²	1	2	yes	—
43	D₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#532	—	2	1	no	—
45	C₁₃×#532	C₂²	1	1	yes	characteristic
46	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#529	—	2	1	no	—
48	C₁₃×#529	—	2	2	no	—
49	C₁₃×#529	C₂²	1	2	yes	—
50	C₁₃×#529	C₂²	1	2	yes	complemented
51	C₁₃×#525	—	2	2	no	—
52	C₄×C₁₃×#41	—	2	1	no	—
53	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₁₃	—	2	1	no	—
58	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
59	C₁₃×#499	C₂²	1	2	yes	complemented
60	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#495	C₂²	1	2	yes	complemented
62	C₁₃×#493	C₂²	1	1	yes	characteristic
63	C₁₃×#488	C₂²	1	2	yes	complemented
64	C₁₃×#488	C₂²	1	2	yes	complemented
65	C₁₃×#486	C₂²	1	1	yes	characteristic
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#483	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	—
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#480	C₂²	1	2	yes	complemented
72	C₁₃×#480	C₂²	1	2	yes	complemented
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	—
75	C₁₃×#478	C₂²	1	2	yes	complemented
76	C₁₃×#478	C₂²	1	2	yes	complemented
77	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#474	C₂²	1	1	yes	characteristic
81	C₁₃×#470	C₂²	1	2	yes	complemented
82	C₁₃×#469	C₂²	1	2	yes	—
83	C₁₃×#469	C₂²	1	2	yes	complemented
84	C₁₃×#469	C₂²	1	2	yes	complemented
85	C₁₃×#468	C₂²	1	2	yes	—
86	C₁₃×#468	C₂²	1	2	yes	complemented
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#463	C₂²	1	2	yes	complemented
90	C₁₃×#463	C₂²	1	2	yes	complemented
91	C₁₃×#460	C₂²	1	1	yes	characteristic
92	C₁₃×#460	C₂²	1	1	yes	characteristic
93	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#459	C₂²	1	1	yes	characteristic
95	C₁₃×#452	C₂²	1	2	yes	complemented
96	C₁₃×#450	C₂²	1	2	yes	—
97	C₁₃×#449	C₂²	1	2	yes	—
98	C₁₃×#449	C₂²	1	2	yes	—
99	C₁₃×#448	C₂²	1	2	yes	complemented
100	C₁₃×#447	C₂²	1	2	yes	—
101	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#442	C₂²	1	2	yes	complemented
105	C₁₃×#442	C₂²	1	2	yes	complemented
106	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
108	C₁₃×#440	C₂²	1	1	yes	characteristic
109	C₁₃×#440	C₂²	1	1	yes	characteristic
110	C₁₃×#440	C₂²	1	2	yes	complemented
111	C₁₃×#440	C₂²	1	2	yes	complemented
112	C₁₃×#440	C₂²	1	2	yes	complemented
113	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
116	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
117	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
118	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
119	C₄×C₁₃×D₈	C₂²	1	2	yes	—
120	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
121	C₁₃×#436	C₂²	1	1	yes	characteristic
122	C₁₃×#436	C₂²	1	1	yes	characteristic
123	C₁₃×#436	C₂²	1	2	yes	complemented
124	C₁₃×#436	C₂²	1	2	yes	complemented
125	C₁₃×#432	C₂²	1	2	yes	complemented
126	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
128	C₁₃×#428	C₂²	1	2	yes	complemented
129	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
130	C₁₃×#418	C₂²	1	2	yes	—
131	C₁₃×#417	C₂²	1	1	yes	characteristic
132	C₁₃×#417	C₂²	1	2	yes	complemented
133	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
134	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	1	no	—
137	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
138	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×#41	C₂³	1	2	yes	—
140	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₃	—	2	2	no	—
144	C₁₃×#137	—	2	4	no	—
145	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
146	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×D₈	C₂³	1	2	yes	—
154	C₂×C₁₃×D₈	C₂³	1	2	yes	—
155	C₂×C₁₃×D₈	C₂³	1	2	yes	—
156	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
160	C₁₃×C₄⋊Q₈	—	2	1	no	—
161	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×#127	—	2	1	no	—
164	C₁₃×#127	C₂³	1	1	yes	characteristic
165	C₁₃×#127	C₂³	1	1	yes	characteristic
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#125	—	2	1	no	—
172	C₁₃×#125	—	2	2	no	—
173	C₁₃×#125	C₂³	1	2	yes	—
174	C₁₃×#125	C₂³	1	2	yes	—
175	C₁₃×#124	—	2	1	no	—
176	C₁₃×#124	—	2	1	no	—
177	C₁₃×#124	—	2	1	no	—
178	C₁₃×#124	—	2	2	no	—
179	C₁₃×#124	—	2	1	no	—
180	C₁₃×#124	—	2	1	no	—
181	C₁₃×#124	C₂³	1	2	yes	—
182	C₁₃×#124	C₂³	1	2	yes	—
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	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×#121	—	2	2	no	—
197	C₁₃×#121	—	2	2	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	1	no	—
200	C₁₃×#121	—	2	1	no	—
201	C₁₃×#121	—	2	1	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	C₂³	1	2	yes	—
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₁₃×#121	C₂³	1	2	yes	—
208	C₁₃×#120	—	2	2	no	—
209	C₁₃×#120	—	2	2	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₁₃	—	2	1	no	—
224	C₄×D₄×C₁₃	—	2	2	no	—
225	C₄×D₄×C₁₃	—	2	1	no	—
226	C₄×D₄×C₁₃	—	2	1	no	—
227	C₄×D₄×C₁₃	—	2	2	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	1	no	—
232	C₄×D₄×C₁₃	—	2	1	no	—
233	C₄×D₄×C₁₃	—	2	2	no	—
234	C₄×D₄×C₁₃	—	2	2	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	—	2	1	no	—
237	C₄×D₄×C₁₃	—	2	2	no	—
238	C₄×D₄×C₁₃	—	2	2	no	—
239	C₄×D₄×C₁₃	—	2	1	no	—
240	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
241	C₄×D₄×C₁₃	D₄	1	2	yes	—
242	C₄×D₄×C₁₃	C₂³	1	2	yes	—
243	C₄×D₄×C₁₃	C₂³	1	2	yes	—
244	C₄×D₄×C₁₃	C₂³	1	2	yes	—
245	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₁₃	C₂³	1	2	yes	—
248	C₄×D₄×C₁₃	C₂³	1	2	yes	—
249	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₁₃	C₂³	1	2	yes	—
251	C₁₃×#117	—	2	2	no	—
252	C₁₃×#117	—	2	1	no	—
253	C₁₃×#117	—	2	2	no	—
254	C₁₃×#117	—	2	2	no	—
255	C₁₃×#117	D₄	1	1	yes	characteristic
256	C₁₃×#117	D₄	1	2	yes	—
257	C₁₃×#117	C₂³	1	2	yes	—
258	C₁₃×#117	C₂³	1	1	yes	characteristic
259	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²×C₁₃	—	2	1	no	—
266	C₂×C₄²×C₁₃	—	2	1	no	—
267	C₂×C₄²×C₁₃	—	2	2	no	—
268	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
269	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
270	C₁₃×#107	C₂³	1	1	yes	characteristic
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	2	yes	—
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	1	yes	characteristic
277	C₁₃×#106	C₂³	1	2	yes	—
278	C₁₃×#106	C₂³	1	2	yes	—
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	2	yes	—
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×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	1	yes	characteristic
308	C₁₃×#97	C₂³	1	1	yes	characteristic
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₁₃	C₂³	1	2	yes	—
313	C₄×C₈×C₁₃	C₂³	1	2	yes	—
314	#61468	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂⁴×C₁₃	—	2	2	no	—
316	C₁₃×#41	—	2	4	no	—
317	C₁₃×#41	—	2	2	no	—
318	C₁₃×#41	—	4	2	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	4	1	no	—
321	C₁₃×#41	—	4	4	no	—
322	C₁₃×#41	—	8	2	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	1	no	—
325	C₂×Q₈×C₁₃	—	2	1	no	—
326	C₂×Q₈×C₁₃	—	2	2	no	—
327	C₂×Q₈×C₁₃	—	4	1	no	—
328	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₁₃	—	2	4	no	—
333	C₂×D₄×C₁₃	—	2	1	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	2	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	2	no	—
340	C₂×D₄×C₁₃	—	2	1	no	—
341	C₂×D₄×C₁₃	—	2	1	no	—
342	C₂×D₄×C₁₃	—	2	1	no	—
343	C₂×D₄×C₁₃	—	2	1	no	—
344	C₂×D₄×C₁₃	—	4	2	no	—
345	C₂×D₄×C₁₃	—	4	4	no	—
346	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
349	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
350	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₁₃	—	2	1	no	—
352	C₂²×C₄×C₁₃	—	2	1	no	—
353	C₂²×C₄×C₁₃	—	2	2	no	—
354	C₂²×C₄×C₁₃	—	2	1	no	—
355	C₂²×C₄×C₁₃	—	2	1	no	—
356	C₂²×C₄×C₁₃	—	2	2	no	—
357	C₂²×C₄×C₁₃	—	2	2	no	—
358	C₂²×C₄×C₁₃	—	2	1	no	—
359	C₂²×C₄×C₁₃	—	2	2	no	—
360	C₂²×C₄×C₁₃	—	2	2	no	—
361	C₂²×C₄×C₁₃	—	2	2	no	—
362	C₂²×C₄×C₁₃	—	2	2	no	—
363	C₂²×C₄×C₁₃	—	8	4	no	—
364	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
366	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
370	C₁₃×Q₁₆	—	2	2	no	—
371	C₁₃×Q₁₆	—	2	2	no	—
372	C₁₃×SD₁₆	—	2	4	no	—
373	C₁₃×SD₁₆	—	2	2	no	—
374	C₁₃×SD₁₆	—	4	2	no	—
375	C₁₃×SD₁₆	—	4	2	no	—
376	C₁₃×SD₁₆	#41	1	4	yes	complemented
377	C₁₃×D₈	—	2	4	no	—
378	C₁₃×D₈	—	2	4	no	—
379	C₁₃×D₈	—	4	2	no	—
380	C₁₃×M₁₆	—	2	4	no	—
381	C₁₃×M₁₆	—	2	2	no	—
382	C₁₃×M₁₆	—	4	1	no	—
383	C₁₃×M₁₆	—	4	2	no	—
384	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
387	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
388	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	1	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	2	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	—	2	2	no	—
401	C₁₃×C₄⋊C₄	—	2	1	no	—
402	C₁₃×C₄⋊C₄	—	2	1	no	—
403	C₁₃×C₄⋊C₄	—	2	2	no	—
404	C₁₃×C₄⋊C₄	—	2	2	no	—
405	C₁₃×C₄⋊C₄	—	2	1	no	—
406	C₁₃×C₄⋊C₄	—	2	2	no	—
407	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
412	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
416	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	1	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	1	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	1	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	—	2	2	no	—
434	C₁₃×C₂²⋊C₄	—	2	2	no	—
435	C₁₃×C₂²⋊C₄	—	2	2	no	—
436	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₄²×C₁₃	—	2	1	no	—
440	C₄²×C₁₃	—	2	1	no	—
441	C₄²×C₁₃	—	2	1	no	—
442	C₄²×C₁₃	—	2	1	no	—
443	C₄²×C₁₃	—	2	2	no	—
444	C₄²×C₁₃	—	2	1	no	—
445	C₄²×C₁₃	—	2	2	no	—
446	C₄²×C₁₃	—	2	1	no	—
447	C₄²×C₁₃	—	2	1	no	—
448	C₄²×C₁₃	C₂×D₄	1	2	yes	—
449	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₁₃	C₂×D₄	1	2	yes	—
451	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₁₃	C₂⁴	1	2	yes	—
453	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
454	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
455	#3481	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3396	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3381	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3365	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3361	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3356	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3355	C₂×C₁₃	1	2	yes	complemented
463	#3333	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3326	C₂×C₁₃	1	2	yes	complemented
465	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3322	C₂×C₁₃	1	2	yes	complemented
467	#3275	C₂×C₁₃	1	2	yes	complemented
468	#3274	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3184	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3183	C₂×C₁₃	1	2	yes	complemented
471	#3115	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#3114	C₂×C₁₃	1	2	yes	complemented
473	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
474	#3111	C₂×C₁₃	1	2	yes	complemented
475	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
476	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
477	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
478	C₂³×C₁₃	—	2	1	no	—
479	C₂³×C₁₃	—	2	2	no	—
480	C₂³×C₁₃	—	2	2	no	—
481	C₂³×C₁₃	—	4	4	no	—
482	C₂³×C₁₃	—	4	4	no	—
483	C₂³×C₁₃	—	8	2	no	—
484	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
485	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
486	Q₈×C₁₃	—	2	2	no	—
487	Q₈×C₁₃	—	2	1	no	—
488	Q₈×C₁₃	—	2	1	no	—
489	Q₈×C₁₃	—	2	1	no	—
490	Q₈×C₁₃	—	2	1	no	—
491	Q₈×C₁₃	—	2	1	no	—
492	Q₈×C₁₃	—	4	2	no	—
493	Q₈×C₁₃	—	4	2	no	—
494	Q₈×C₁₃	—	8	1	no	—
495	Q₈×C₁₃	C₂×#41	1	2	yes	—
496	D₄×C₁₃	—	2	2	no	—
497	D₄×C₁₃	—	2	2	no	—
498	D₄×C₁₃	—	2	2	no	—
499	D₄×C₁₃	—	2	1	no	—
500	D₄×C₁₃	—	2	2	no	—
501	D₄×C₁₃	—	2	2	no	—
502	D₄×C₁₃	—	4	2	no	—
503	D₄×C₁₃	—	4	4	no	—
504	D₄×C₁₃	—	4	4	no	—
505	D₄×C₁₃	—	4	2	no	—
506	D₄×C₁₃	—	4	4	no	—
507	D₄×C₁₃	—	4	4	no	—
508	D₄×C₁₃	—	4	2	no	—
509	D₄×C₁₃	—	4	2	no	—
510	D₄×C₁₃	—	8	1	no	—
511	D₄×C₁₃	—	8	1	no	—
512	D₄×C₁₃	—	8	2	no	—
513	D₄×C₁₃	—	8	2	no	—
514	D₄×C₁₃	C₂×#41	1	2	yes	—
515	C₂×C₄×C₁₃	—	2	1	no	—
516	C₂×C₄×C₁₃	—	2	2	no	—
517	C₂×C₄×C₁₃	—	2	2	no	—
518	C₂×C₄×C₁₃	—	2	1	no	—
519	C₂×C₄×C₁₃	—	2	2	no	—
520	C₂×C₄×C₁₃	—	2	1	no	—
521	C₂×C₄×C₁₃	—	2	1	no	—
522	C₂×C₄×C₁₃	—	2	1	no	—
523	C₂×C₄×C₁₃	—	2	1	no	—
524	C₂×C₄×C₁₃	—	2	1	no	—
525	C₂×C₄×C₁₃	—	2	2	no	—
526	C₂×C₄×C₁₃	—	2	1	no	—
527	C₂×C₄×C₁₃	—	2	1	no	—
528	C₂×C₄×C₁₃	—	2	2	no	—
529	C₂×C₄×C₁₃	—	4	2	no	—
530	C₂×C₄×C₁₃	—	4	2	no	—
531	C₂×C₄×C₁₃	—	4	1	no	—
532	C₂×C₄×C₁₃	—	4	4	no	—
533	C₂×C₄×C₁₃	—	4	2	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	4	2	no	—
536	C₂×C₄×C₁₃	—	4	4	no	—
537	C₂×C₄×C₁₃	—	4	4	no	—
538	C₂×C₄×C₁₃	—	4	2	no	—
539	C₂×C₄×C₁₃	—	8	2	no	—
540	C₂×C₄×C₁₃	—	8	2	no	—
541	C₂×C₄×C₁₃	—	8	2	no	—
542	C₂×C₄×C₁₃	—	8	1	no	—
543	C₂×C₄×C₁₃	—	8	2	no	—
544	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
553	C₈×C₁₃	—	2	2	no	—
554	C₈×C₁₃	—	2	1	no	—
555	C₈×C₁₃	—	2	1	no	—
556	C₈×C₁₃	—	2	1	no	—
557	C₈×C₁₃	—	2	2	no	—
558	C₈×C₁₃	C₂×#41	1	2	yes	—
559	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
560	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
561	#559	—	2	1	no	—
562	#559	C₂²×C₁₃	1	1	yes	characteristic
563	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
564	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
565	#556	—	2	1	no	—
566	#556	C₂²×C₁₃	1	1	yes	characteristic
567	#554	C₂²×C₁₃	1	1	yes	characteristic
568	#554	C₂²×C₁₃	1	1	yes	characteristic
569	#553	—	2	2	no	—
570	#553	—	2	1	no	—
571	#553	C₂²×C₁₃	1	2	yes	—
572	#553	C₂²×C₁₃	1	2	yes	complemented
573	#551	—	2	2	no	—
574	#550	C₂²×C₁₃	1	1	yes	characteristic
575	#548	C₂²×C₁₃	1	2	yes	complemented
576	#546	—	2	1	no	—
577	#546	C₂²×C₁₃	1	2	yes	—
578	D₄²	C₂²×C₁₃	1	1	yes	characteristic
579	#532	—	2	1	no	—
580	#532	C₂²×C₁₃	1	1	yes	characteristic
581	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
582	#529	—	2	1	no	—
583	#529	—	2	2	no	—
584	#529	C₂²×C₁₃	1	2	yes	—
585	#529	C₂²×C₁₃	1	2	yes	complemented
586	#525	—	2	2	no	—
587	C₄×#41	—	2	1	no	—
588	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
589	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
590	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
591	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
592	C₂×C₄×D₄	—	2	1	no	—
593	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
594	#499	C₂²×C₁₃	1	2	yes	complemented
595	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	#495	C₂²×C₁₃	1	2	yes	complemented
597	#493	C₂²×C₁₃	1	1	yes	characteristic
598	#488	C₂²×C₁₃	1	2	yes	complemented
599	#488	C₂²×C₁₃	1	2	yes	complemented
600	#486	C₂²×C₁₃	1	1	yes	characteristic
601	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
602	#485	C₂²×C₁₃	1	2	yes	complemented
603	#483	C₂²×C₁₃	1	2	yes	complemented
604	#482	C₂²×C₁₃	1	2	yes	—
605	#482	C₂²×C₁₃	1	2	yes	complemented
606	#480	C₂²×C₁₃	1	2	yes	complemented
607	#480	C₂²×C₁₃	1	2	yes	complemented
608	#479	C₂²×C₁₃	1	2	yes	complemented
609	#478	C₂²×C₁₃	1	2	yes	—
610	#478	C₂²×C₁₃	1	2	yes	complemented
611	#478	C₂²×C₁₃	1	2	yes	complemented
612	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#474	C₂²×C₁₃	1	1	yes	characteristic
616	#470	C₂²×C₁₃	1	2	yes	complemented
617	#469	C₂²×C₁₃	1	2	yes	—
618	#469	C₂²×C₁₃	1	2	yes	complemented
619	#469	C₂²×C₁₃	1	2	yes	complemented
620	#468	C₂²×C₁₃	1	2	yes	—
621	#468	C₂²×C₁₃	1	2	yes	complemented
622	#464	C₂²×C₁₃	1	2	yes	complemented
623	#463	C₂²×C₁₃	1	2	yes	—
624	#463	C₂²×C₁₃	1	2	yes	complemented
625	#463	C₂²×C₁₃	1	2	yes	complemented
626	#460	C₂²×C₁₃	1	1	yes	characteristic
627	#460	C₂²×C₁₃	1	1	yes	characteristic
628	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	#459	C₂²×C₁₃	1	1	yes	characteristic
630	#452	C₂²×C₁₃	1	2	yes	complemented
631	#450	C₂²×C₁₃	1	2	yes	—
632	#449	C₂²×C₁₃	1	2	yes	—
633	#449	C₂²×C₁₃	1	2	yes	—
634	#448	C₂²×C₁₃	1	2	yes	complemented
635	#447	C₂²×C₁₃	1	2	yes	—
636	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
638	#442	C₂²×C₁₃	1	2	yes	—
639	#442	C₂²×C₁₃	1	2	yes	complemented
640	#442	C₂²×C₁₃	1	2	yes	complemented
641	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	#440	C₂²×C₁₃	1	1	yes	characteristic
644	#440	C₂²×C₁₃	1	1	yes	characteristic
645	#440	C₂²×C₁₃	1	2	yes	complemented
646	#440	C₂²×C₁₃	1	2	yes	complemented
647	#440	C₂²×C₁₃	1	2	yes	complemented
648	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
651	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
652	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
653	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
654	C₄×D₈	C₂²×C₁₃	1	2	yes	—
655	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
656	#436	C₂²×C₁₃	1	1	yes	characteristic
657	#436	C₂²×C₁₃	1	1	yes	characteristic
658	#436	C₂²×C₁₃	1	2	yes	complemented
659	#436	C₂²×C₁₃	1	2	yes	complemented
660	#432	C₂²×C₁₃	1	2	yes	complemented
661	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
663	#428	C₂²×C₁₃	1	2	yes	complemented
664	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	#418	C₂²×C₁₃	1	2	yes	—
666	#417	C₂²×C₁₃	1	1	yes	characteristic
667	#417	C₂²×C₁₃	1	2	yes	complemented
668	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
669	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	C₂²×C₁₃	—	2	1	no	—
671	C₂²×C₁₃	—	2	2	no	—
672	C₂²×C₁₃	—	2	1	no	—
673	C₂²×C₁₃	—	2	2	no	—
674	C₂²×C₁₃	—	2	2	no	—
675	C₂²×C₁₃	—	2	1	no	—
676	C₂²×C₁₃	—	2	2	no	—
677	C₂²×C₁₃	—	4	1	no	—
678	C₂²×C₁₃	—	4	1	no	—
679	C₂²×C₁₃	—	4	2	no	—
680	C₂²×C₁₃	—	4	2	no	—
681	C₂²×C₁₃	—	4	2	no	—
682	C₂²×C₁₃	—	4	2	no	—
683	C₂²×C₁₃	—	4	2	no	—
684	C₂²×C₁₃	—	4	2	no	—
685	C₂²×C₁₃	—	8	8	no	—
686	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
687	C₄×C₁₃	—	2	1	no	—
688	C₄×C₁₃	—	2	2	no	—
689	C₄×C₁₃	—	2	1	no	—
690	C₄×C₁₃	—	2	2	no	—
691	C₄×C₁₃	—	2	1	no	—
692	C₄×C₁₃	—	2	2	no	—
693	C₄×C₁₃	—	2	1	no	—
694	C₄×C₁₃	—	2	2	no	—
695	C₄×C₁₃	—	4	1	no	—
696	C₄×C₁₃	—	4	2	no	—
697	C₄×C₁₃	—	4	1	no	—
698	C₄×C₁₃	—	4	1	no	—
699	C₄×C₁₃	—	4	1	no	—
700	C₄×C₁₃	—	4	1	no	—
701	C₄×C₁₃	—	4	1	no	—
702	C₄×C₁₃	—	4	2	no	—
703	C₄×C₁₃	#575	1	2	yes	—
704	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
705	C₄×C₁₃	#585	1	1	yes	characteristic
706	C₂×#41	—	2	1	no	—
707	C₂×#41	—	2	1	no	—
708	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
709	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
710	C₂×#41	C₂³×C₁₃	1	2	yes	—
711	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
712	C₂²×D₄	—	2	1	no	—
713	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
714	C₂³×C₄	—	2	2	no	—
715	#137	—	2	4	no	—
716	AGL(1,ℤ/8)	—	2	8	no	—
717	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
718	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
721	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₁₃	1	2	yes	—
725	C₂×D₈	C₂³×C₁₃	1	2	yes	—
726	C₂×D₈	C₂³×C₁₃	1	2	yes	—
727	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
728	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
734	#127	—	2	1	no	—
735	#127	C₂³×C₁₃	1	1	yes	characteristic
736	#127	C₂³×C₁₃	1	1	yes	characteristic
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#125	—	2	1	no	—
743	#125	—	2	2	no	—
744	#125	C₂³×C₁₃	1	2	yes	—
745	#125	C₂³×C₁₃	1	2	yes	—
746	#124	—	2	1	no	—
747	#124	—	2	1	no	—
748	#124	—	2	1	no	—
749	#124	—	2	2	no	—
750	#124	—	2	1	no	—
751	#124	—	2	1	no	—
752	#124	C₂³×C₁₃	1	2	yes	—
753	#124	C₂³×C₁₃	1	2	yes	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
766	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
767	#121	—	2	2	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	—	2	1	no	—
771	#121	—	2	1	no	—
772	#121	—	2	1	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	C₂³×C₁₃	1	2	yes	—
776	#121	C₂³×C₁₃	1	2	yes	—
777	#121	C₂³×C₁₃	1	2	yes	—
778	#121	C₂³×C₁₃	1	2	yes	—
779	#120	—	2	2	no	—
780	#120	—	2	2	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
793	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
812	C₄×D₄	D₄×C₁₃	1	2	yes	—
813	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₁₃	1	2	yes	—
815	C₄×D₄	C₂³×C₁₃	1	2	yes	—
816	C₄×D₄	C₂³×C₁₃	1	2	yes	—
817	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₁₃	1	2	yes	—
819	C₄×D₄	C₂³×C₁₃	1	2	yes	—
820	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₁₃	1	2	yes	—
822	#117	—	2	2	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	D₄×C₁₃	1	1	yes	characteristic
827	#117	D₄×C₁₃	1	2	yes	—
828	#117	C₂³×C₁₃	1	1	yes	characteristic
829	#117	C₂³×C₁₃	1	2	yes	—
830	C₂×C₄⋊C₄	—	2	1	no	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
833	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
834	C₂×C₂²⋊C₄	—	2	2	no	—
835	C₂×C₂²⋊C₄	—	2	2	no	—
836	C₂×C₄²	—	2	1	no	—
837	C₂×C₄²	—	2	1	no	—
838	C₂×C₄²	—	2	2	no	—
839	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
840	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
841	#107	C₂³×C₁₃	1	1	yes	characteristic
842	#107	C₂³×C₁₃	1	2	yes	—
843	#107	C₂³×C₁₃	1	1	yes	characteristic
844	#107	C₂³×C₁₃	1	2	yes	—
845	#107	C₂³×C₁₃	1	2	yes	—
846	#106	C₂³×C₁₃	1	1	yes	characteristic
847	#106	C₂³×C₁₃	1	1	yes	characteristic
848	#106	C₂³×C₁₃	1	2	yes	—
849	#106	C₂³×C₁₃	1	2	yes	—
850	#106	C₂³×C₁₃	1	2	yes	—
851	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
855	#103	C₂³×C₁₃	1	1	yes	characteristic
856	#103	C₂³×C₁₃	1	1	yes	characteristic
857	#103	C₂³×C₁₃	1	1	yes	characteristic
858	#103	C₂³×C₁₃	1	2	yes	—
859	#103	C₂³×C₁₃	1	1	yes	characteristic
860	#103	C₂³×C₁₃	1	1	yes	characteristic
861	#103	C₂³×C₁₃	1	1	yes	characteristic
862	#103	C₂³×C₁₃	1	2	yes	—
863	#103	C₂³×C₁₃	1	2	yes	—
864	#102	C₂³×C₁₃	1	1	yes	characteristic
865	#102	C₂³×C₁₃	1	1	yes	characteristic
866	#102	C₂³×C₁₃	1	2	yes	—
867	#102	C₂³×C₁₃	1	2	yes	—
868	#102	C₂³×C₁₃	1	2	yes	—
869	#102	C₂³×C₁₃	1	2	yes	—
870	#102	C₂³×C₁₃	1	2	yes	—
871	#102	C₂³×C₁₃	1	2	yes	—
872	#102	C₂³×C₁₃	1	2	yes	—
873	#102	C₂³×C₁₃	1	2	yes	—
874	#102	C₂³×C₁₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
878	#97	C₂³×C₁₃	1	1	yes	characteristic
879	#97	C₂³×C₁₃	1	1	yes	characteristic
880	#97	C₂³×C₁₃	1	2	yes	—
881	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₁₃	1	2	yes	—
884	C₄×C₈	C₂³×C₁₃	1	2	yes	—
885	C₂×C₁₃	—	4	1	no	—
886	C₂×C₁₃	—	4	2	no	—
887	C₂×C₁₃	—	4	2	no	—
888	C₂×C₁₃	—	8	2	no	—
889	C₂×C₁₃	—	8	2	no	—
890	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
891	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
892	C₂×C₁₃	#3585	1	1	yes	characteristic
893	C₂⁴	—	2	2	no	—
894	#41	—	2	4	no	—
895	#41	—	2	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	1	no	—
899	#41	—	4	4	no	—
900	#41	—	8	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	4	1	no	—
906	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
910	C₂×D₄	—	2	4	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	4	no	—
924	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
925	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
926	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
927	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
928	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	8	4	no	—
942	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
943	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
944	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
945	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
946	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
948	Q₁₆	—	2	2	no	—
949	Q₁₆	—	2	2	no	—
950	SD₁₆	—	2	4	no	—
951	SD₁₆	—	2	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	C₁₃×#41	1	4	yes	complemented
955	D₈	—	2	4	no	—
956	D₈	—	2	4	no	—
957	D₈	—	4	2	no	—
958	M₁₆	—	2	4	no	—
959	M₁₆	—	2	2	no	—
960	M₁₆	—	4	1	no	—
961	M₁₆	—	4	2	no	—
962	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
965	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
966	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
989	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1027	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1028	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1029	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₁₃	1	2	yes	—
1031	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1033	C₁₃	#61468	1	1	yes	characteristic, direct product factor, Sylow
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	4	4	no	—
1038	C₂³	—	4	4	no	—
1039	C₂³	—	8	2	no	—
1040	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1041	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	4	2	no	—
1050	Q₈	—	8	1	no	—
1051	Q₈	C₂×C₁₃×#41	1	2	yes	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	4	2	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	8	1	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	C₂×C₁₃×#41	1	2	yes	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	1	no	—
1100	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	2	no	—
1114	C₈	C₂×C₁₃×#41	1	2	yes	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	8	8	no	—
1131	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	C₁₃×#575	1	2	yes	—
1149	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1150	C₄	C₁₃×#585	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	2	no	—
1156	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1157	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1158	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3481	C₂	semidirect
2. C₁₃×#3480	C₂	semidirect
3. C₁₃×#3396	C₂	semidirect
4. C₁₃×#3381	C₂	semidirect
5. C₁₃×#3365	C₂	semidirect
6. C₁₃×#3361	C₂	semidirect
7. C₁₃×#3356	C₂	semidirect
8. C₁₃×#3355	C₂	semidirect
9. C₁₃×#3333	C₂	semidirect
10. C₁₃×#3326	C₂	semidirect
11. C₁₃×#3324	C₂	semidirect
12. C₁₃×#3322	C₂	semidirect
13. C₁₃×#3275	C₂	semidirect
14. C₁₃×#3274	C₂	semidirect
15. C₁₃×#3184	C₂	semidirect
16. C₁₃×#3183	C₂	semidirect
17. C₁₃×#3115	C₂	semidirect
18. C₁₃×#3114	C₂	semidirect
19. C₁₃×#3112	C₂	semidirect
20. C₁₃×#3111	C₂	semidirect
21. C₁₃×#2971	C₂	semidirect
22. C₄×C₁₃×#137	C₂	semidirect
23. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
28. C₁₃×#559	C₂²	semidirect
29. C₁₃×#557	C₂²	semidirect
37. C₁₃×#553	C₂²	semidirect
40. C₁₃×#548	C₂²	semidirect
46. C₁₃×#532	C₂²	semidirect
50. C₁₃×#529	C₂²	semidirect
55. C₄×C₁₃×#41	C₂²	semidirect
56. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
59. C₁₃×#499	C₂²	semidirect
60. C₁₃×#498	C₂²	semidirect
61. C₁₃×#495	C₂²	semidirect
63. C₁₃×#488	C₂²	semidirect
64. C₁₃×#488	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#483	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#480	C₂²	semidirect
72. C₁₃×#480	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#478	C₂²	semidirect
77. C₁₃×#477	C₂²	semidirect
78. C₁₃×#477	C₂²	semidirect
79. C₁₃×#475	C₂²	semidirect
81. C₁₃×#470	C₂²	semidirect
83. C₁₃×#469	C₂²	semidirect
84. C₁₃×#469	C₂²	semidirect
86. C₁₃×#468	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
89. C₁₃×#463	C₂²	semidirect
90. C₁₃×#463	C₂²	semidirect
93. C₁₃×#460	C₂²	semidirect
95. C₁₃×#452	C₂²	semidirect
99. C₁₃×#448	C₂²	semidirect
101. C₈×Q₈×C₁₃	C₂²	semidirect
102. C₈×Q₈×C₁₃	C₂²	semidirect
104. C₁₃×#442	C₂²	semidirect
105. C₁₃×#442	C₂²	semidirect
106. C₁₃×#441	C₂²	semidirect
107. C₁₃×#441	C₂²	semidirect
110. C₁₃×#440	C₂²	semidirect
111. C₁₃×#440	C₂²	semidirect
112. C₁₃×#440	C₂²	semidirect
113. C₄×C₁₃×Q₁₆	C₂²	semidirect
114. C₄×C₁₃×Q₁₆	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
123. C₁₃×#436	C₂²	semidirect
124. C₁₃×#436	C₂²	semidirect
125. C₁₃×#432	C₂²	semidirect
126. C₁₃×#432	C₂²	semidirect
127. C₁₃×#428	C₂²	semidirect
128. C₁₃×#428	C₂²	semidirect
129. C₁₃×#419	C₂²	semidirect
132. C₁₃×#417	C₂²	semidirect
133. C₄×C₁₃×M₁₆	C₂²	semidirect
134. C₄×C₁₃×M₁₆	C₂²	semidirect
314. #61468	C₁₃	direct (N × H)
376. C₁₃×SD₁₆	#41	semidirect
455. #3481	C₂×C₁₃	semidirect
456. #3480	C₂×C₁₃	semidirect
457. #3396	C₂×C₁₃	semidirect
458. #3381	C₂×C₁₃	semidirect
459. #3365	C₂×C₁₃	semidirect
460. #3361	C₂×C₁₃	semidirect
461. #3356	C₂×C₁₃	semidirect
462. #3355	C₂×C₁₃	semidirect
463. #3333	C₂×C₁₃	semidirect
464. #3326	C₂×C₁₃	semidirect
465. #3324	C₂×C₁₃	semidirect
466. #3322	C₂×C₁₃	semidirect
467. #3275	C₂×C₁₃	semidirect
468. #3274	C₂×C₁₃	semidirect
469. #3184	C₂×C₁₃	semidirect
470. #3183	C₂×C₁₃	semidirect
471. #3115	C₂×C₁₃	semidirect
472. #3114	C₂×C₁₃	semidirect
473. #3112	C₂×C₁₃	semidirect
474. #3111	C₂×C₁₃	semidirect
475. #2971	C₂×C₁₃	semidirect
476. C₄×#137	C₂×C₁₃	semidirect
477. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
563. #559	C₂²×C₁₃	semidirect
564. #557	C₂²×C₁₃	semidirect
572. #553	C₂²×C₁₃	semidirect
575. #548	C₂²×C₁₃	semidirect
581. #532	C₂²×C₁₃	semidirect
585. #529	C₂²×C₁₃	semidirect
590. C₄×#41	C₂²×C₁₃	semidirect
591. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
594. #499	C₂²×C₁₃	semidirect
595. #498	C₂²×C₁₃	semidirect
596. #495	C₂²×C₁₃	semidirect
598. #488	C₂²×C₁₃	semidirect
599. #488	C₂²×C₁₃	semidirect
601. #486	C₂²×C₁₃	semidirect
602. #485	C₂²×C₁₃	semidirect
603. #483	C₂²×C₁₃	semidirect
605. #482	C₂²×C₁₃	semidirect
606. #480	C₂²×C₁₃	semidirect
607. #480	C₂²×C₁₃	semidirect
608. #479	C₂²×C₁₃	semidirect
610. #478	C₂²×C₁₃	semidirect
611. #478	C₂²×C₁₃	semidirect
612. #477	C₂²×C₁₃	semidirect
613. #477	C₂²×C₁₃	semidirect
614. #475	C₂²×C₁₃	semidirect
616. #470	C₂²×C₁₃	semidirect
618. #469	C₂²×C₁₃	semidirect
619. #469	C₂²×C₁₃	semidirect
621. #468	C₂²×C₁₃	semidirect
622. #464	C₂²×C₁₃	semidirect
624. #463	C₂²×C₁₃	semidirect
625. #463	C₂²×C₁₃	semidirect
628. #460	C₂²×C₁₃	semidirect
630. #452	C₂²×C₁₃	semidirect
634. #448	C₂²×C₁₃	semidirect
636. C₈×Q₈	C₂²×C₁₃	semidirect
637. C₈×Q₈	C₂²×C₁₃	semidirect
639. #442	C₂²×C₁₃	semidirect
640. #442	C₂²×C₁₃	semidirect
641. #441	C₂²×C₁₃	semidirect
642. #441	C₂²×C₁₃	semidirect
645. #440	C₂²×C₁₃	semidirect
646. #440	C₂²×C₁₃	semidirect
647. #440	C₂²×C₁₃	semidirect
648. C₄×Q₁₆	C₂²×C₁₃	semidirect
649. C₄×Q₁₆	C₂²×C₁₃	semidirect
653. C₄×SD₁₆	C₂²×C₁₃	semidirect
655. C₄×D₈	C₂²×C₁₃	semidirect
658. #436	C₂²×C₁₃	semidirect
659. #436	C₂²×C₁₃	semidirect
660. #432	C₂²×C₁₃	semidirect
661. #432	C₂²×C₁₃	semidirect
662. #428	C₂²×C₁₃	semidirect
663. #428	C₂²×C₁₃	semidirect
664. #419	C₂²×C₁₃	semidirect
667. #417	C₂²×C₁₃	semidirect
668. C₄×M₁₆	C₂²×C₁₃	semidirect
669. C₄×M₁₆	C₂²×C₁₃	semidirect
954. SD₁₆	C₁₃×#41	semidirect
1033. C₁₃	#61468	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×#3481	2
C₁₃×#3480	2
C₁₃×#3396	2
C₁₃×#3381	2
C₁₃×#3365	2
C₁₃×#3361	2
C₁₃×#3356	2
C₁₃×#3355	2
C₁₃×#3333	2
C₁₃×#3326	2
C₁₃×#3324	2
C₁₃×#3322	2
C₁₃×#3275	2
C₁₃×#3274	2
C₁₃×#3184	2
C₁₃×#3183	2
C₁₃×#3115	2
C₁₃×#3114	2
C₁₃×#3112	2
C₁₃×#3111	2
C₁₃×#2971	2
C₄×C₁₃×#137	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61468	13

Subgroups — C13×#61468 #15747807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61468 #15747807