Subgroups — C₁₃×#62006 #15748345

Order 3328.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3514	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×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3326	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3322	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3277	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×#3256	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3102	C₂	1	2	yes	maximal, complemented
21	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
27	C₁₃×#559	—	2	1	no	—
28	C₁₃×#559	C₂²	1	1	yes	characteristic
29	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#556	—	2	1	no	—
32	C₁₃×#556	C₂²	1	1	yes	characteristic
33	C₁₃×#556	C₂²	1	1	yes	characteristic
34	C₁₃×#555	—	2	1	no	—
35	C₁₃×#553	—	2	2	no	—
36	C₁₃×#553	C₂²	1	2	yes	complemented
37	C₁₃×#551	—	2	2	no	—
38	C₁₃×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#548	C₂²	1	2	yes	—
41	C₁₃×#548	C₂²	1	2	yes	complemented
42	C₁₃×#546	—	2	1	no	—
43	C₁₃×#546	C₂²	1	2	yes	—
44	D₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#542	—	2	1	no	—
46	C₁₃×#538	—	2	2	no	—
47	C₁₃×#532	—	2	1	no	—
48	C₁₃×#532	C₂²	1	1	yes	characteristic
49	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#529	—	2	2	no	—
51	C₁₃×#529	C₂²	1	2	yes	—
52	C₁₃×#529	C₂²	1	1	yes	characteristic
53	C₁₃×#529	C₂²	1	2	yes	complemented
54	C₂×C₁₃×#124	C₂²	1	2	yes	—
55	C₁₃×#518	—	2	1	no	—
56	C₄×C₁₃×#41	—	2	1	no	—
57	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#495	C₂²	1	2	yes	—
61	C₁₃×#495	C₂²	1	2	yes	complemented
62	C₁₃×#493	C₂²	1	1	yes	characteristic
63	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#488	C₂²	1	2	yes	—
65	C₁₃×#488	C₂²	1	2	yes	complemented
66	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#486	C₂²	1	1	yes	characteristic
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#483	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#482	C₂²	1	2	yes	—
71	C₁₃×#480	C₂²	1	1	yes	characteristic
72	C₁₃×#479	C₂²	1	2	yes	complemented
73	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#478	C₂²	1	2	yes	complemented
76	C₁₃×#478	C₂²	1	2	yes	complemented
77	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#474	C₂²	1	1	yes	characteristic
79	C₁₃×#470	C₂²	1	2	yes	complemented
80	C₁₃×#469	C₂²	1	2	yes	—
81	C₁₃×#469	C₂²	1	2	yes	—
82	C₁₃×#468	C₂²	1	2	yes	—
83	C₁₃×#468	C₂²	1	2	yes	complemented
84	C₁₃×#468	C₂²	1	2	yes	complemented
85	C₁₃×#464	C₂²	1	2	yes	—
86	C₁₃×#464	C₂²	1	1	yes	characteristic
87	C₁₃×#464	C₂²	1	1	yes	characteristic
88	C₁₃×#464	C₂²	1	2	yes	complemented
89	C₁₃×#464	C₂²	1	2	yes	complemented
90	C₁₃×#464	C₂²	1	2	yes	complemented
91	C₁₃×#464	C₂²	1	2	yes	complemented
92	C₁₃×#463	C₂²	1	2	yes	—
93	C₁₃×#463	C₂²	1	2	yes	—
94	C₁₃×#463	C₂²	1	2	yes	complemented
95	C₁₃×#463	C₂²	1	2	yes	complemented
96	C₁₃×#463	C₂²	1	2	yes	complemented
97	C₁₃×#463	C₂²	1	2	yes	complemented
98	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
99	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#460	C₂²	1	1	yes	characteristic
101	C₁₃×#460	C₂²	1	1	yes	characteristic
102	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#459	C₂²	1	1	yes	characteristic
104	C₁₃×#452	C₂²	1	2	yes	complemented
105	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
106	C₁₃×#451	C₂²	1	2	yes	complemented
107	C₁₃×#450	C₂²	1	2	yes	—
108	C₁₃×#449	C₂²	1	2	yes	—
109	C₁₃×#449	C₂²	1	2	yes	complemented
110	C₁₃×#449	C₂²	1	2	yes	complemented
111	C₁₃×#448	C₂²	1	1	yes	characteristic
112	C₁₃×#448	C₂²	1	2	yes	complemented
113	C₁₃×#447	C₂²	1	2	yes	—
114	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
117	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
121	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
122	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
123	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
124	C₁₃×#436	C₂²	1	1	yes	characteristic
125	C₁₃×#436	C₂²	1	1	yes	characteristic
126	C₁₃×#436	C₂²	1	2	yes	complemented
127	C₁₃×#436	C₂²	1	2	yes	complemented
128	C₁₃×#431	C₂²	1	2	yes	complemented
129	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
131	C₁₃×#423	C₂²	1	2	yes	complemented
132	C₁₃×#419	C₂²	1	2	yes	complemented
133	C₁₃×#418	C₂²	1	2	yes	—
134	C₁₃×#417	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂×C₁₃×#41	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₁₃×#137	—	4	4	no	—
144	C₁₃×#137	—	4	4	no	—
145	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
146	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×D₈	C₂³	1	2	yes	—
158	C₂×C₁₃×D₈	C₂³	1	2	yes	—
159	C₂×C₁₃×D₈	C₂³	1	2	yes	—
160	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
162	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	—	2	1	no	—
164	C₁₃×C₄⋊Q₈	—	2	1	no	—
165	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₃×#127	—	2	1	no	—
168	C₁₃×#127	C₂³	1	1	yes	characteristic
169	C₁₃×#127	C₂³	1	1	yes	characteristic
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#126	—	2	2	no	—
173	C₁₃×#126	—	2	2	no	—
174	C₁₃×#126	—	2	1	no	—
175	C₁₃×#126	—	2	2	no	—
176	C₁₃×#125	—	2	2	no	—
177	C₁₃×#125	C₂³	1	1	yes	characteristic
178	C₁₃×#125	C₂³	1	2	yes	—
179	C₁₃×#124	—	2	1	no	—
180	C₁₃×#124	—	2	1	no	—
181	C₁₃×#124	—	2	1	no	—
182	C₁₃×#124	—	2	2	no	—
183	C₁₃×#124	—	2	2	no	—
184	C₁₃×#124	—	2	2	no	—
185	C₁₃×#124	—	2	2	no	—
186	C₁₃×#124	—	2	1	no	—
187	C₁₃×#124	C₂³	1	1	yes	characteristic
188	C₁₃×#124	C₂³	1	2	yes	—
189	C₁₃×#124	C₂³	1	2	yes	—
190	C₁₃×#124	C₂³	1	2	yes	—
191	C₁₃×#124	C₂³	1	2	yes	—
192	C₁₃×#123	—	2	1	no	—
193	C₁₃×#123	—	2	2	no	—
194	C₁₃×#123	—	2	2	no	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	—	2	1	no	—
200	C₁₃×C₂²⋊Q₈	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	—	2	2	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	—	2	2	no	—
209	C₁₃×#121	—	2	1	no	—
210	C₁₃×#121	—	2	1	no	—
211	C₁₃×#121	—	2	1	no	—
212	C₁₃×#121	—	2	1	no	—
213	C₁₃×#121	—	2	2	no	—
214	C₁₃×#121	—	2	2	no	—
215	C₁₃×#121	C₂³	1	2	yes	—
216	C₁₃×#121	C₂³	1	1	yes	characteristic
217	C₁₃×#121	C₂³	1	2	yes	—
218	C₁₃×#121	C₂³	1	2	yes	—
219	C₁₃×#120	—	2	2	no	—
220	C₁₃×#120	—	2	2	no	—
221	C₄×Q₈×C₁₃	—	2	1	no	—
222	C₄×Q₈×C₁₃	—	2	1	no	—
223	C₄×Q₈×C₁₃	—	2	1	no	—
224	C₄×Q₈×C₁₃	—	2	1	no	—
225	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
226	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	—	2	2	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	—	2	1	no	—
241	C₄×D₄×C₁₃	—	2	1	no	—
242	C₄×D₄×C₁₃	—	2	1	no	—
243	C₄×D₄×C₁₃	—	2	2	no	—
244	C₄×D₄×C₁₃	—	2	2	no	—
245	C₄×D₄×C₁₃	—	2	2	no	—
246	C₄×D₄×C₁₃	—	2	1	no	—
247	C₄×D₄×C₁₃	—	2	1	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
250	C₄×D₄×C₁₃	D₄	1	2	yes	—
251	C₄×D₄×C₁₃	C₂³	1	2	yes	—
252	C₄×D₄×C₁₃	C₂³	1	2	yes	—
253	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₁₃	C₂³	1	2	yes	—
257	C₁₃×#117	—	2	1	no	—
258	C₁₃×#117	—	2	2	no	—
259	C₁₃×#117	—	2	2	no	—
260	C₁₃×#117	—	2	1	no	—
261	C₁₃×#117	—	2	2	no	—
262	C₁₃×#117	D₄	1	1	yes	characteristic
263	C₁₃×#117	D₄	1	2	yes	—
264	C₁₃×#117	C₂³	1	2	yes	—
265	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²×C₁₃	—	2	1	no	—
271	C₂×C₄²×C₁₃	—	2	2	no	—
272	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
274	C₁₃×#107	C₂³	1	1	yes	characteristic
275	C₁₃×#107	C₂³	1	2	yes	—
276	C₁₃×#107	C₂³	1	1	yes	characteristic
277	C₁₃×#106	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	1	yes	characteristic
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
285	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	1	yes	characteristic
295	C₁₃×#103	C₂³	1	1	yes	characteristic
296	C₁₃×#103	C₂³	1	1	yes	characteristic
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×#102	C₂³	1	1	yes	characteristic
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₃	C₂³	1	2	yes	—
314	C₄×C₈×C₁₃	C₂³	1	2	yes	—
315	#62006	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	2	no	—
317	C₁₃×#41	—	2	4	no	—
318	C₁₃×#41	—	4	2	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	4	4	no	—
321	C₁₃×#41	—	4	2	no	—
322	C₁₃×#41	—	4	2	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	—	4	1	no	—
328	C₂×Q₈×C₁₃	—	4	2	no	—
329	C₂×Q₈×C₁₃	—	4	2	no	—
330	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
339	C₂×D₄×C₁₃	—	2	2	no	—
340	C₂×D₄×C₁₃	—	2	2	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	—	2	1	no	—
345	C₂×D₄×C₁₃	—	2	2	no	—
346	C₂×D₄×C₁₃	—	4	2	no	—
347	C₂×D₄×C₁₃	—	4	2	no	—
348	C₂×D₄×C₁₃	—	4	4	no	—
349	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
353	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	2	no	—
359	C₂²×C₄×C₁₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
366	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
369	C₁₃×Q₁₆	—	2	2	no	—
370	C₁₃×Q₁₆	—	2	4	no	—
371	C₁₃×Q₁₆	—	4	1	no	—
372	C₁₃×Q₁₆	—	4	2	no	—
373	C₁₃×SD₁₆	—	2	2	no	—
374	C₁₃×SD₁₆	—	2	4	no	—
375	C₁₃×SD₁₆	—	4	2	no	—
376	C₁₃×SD₁₆	—	4	1	no	—
377	C₁₃×SD₁₆	—	4	2	no	—
378	C₁₃×SD₁₆	—	4	2	no	—
379	C₁₃×SD₁₆	—	4	2	no	—
380	C₁₃×D₈	—	4	2	no	—
381	C₁₃×D₈	—	4	2	no	—
382	C₁₃×D₈	—	4	2	no	—
383	C₁₃×M₁₆	—	4	2	no	—
384	C₁₃×M₁₆	—	4	2	no	—
385	C₁₃×M₁₆	—	4	2	no	—
386	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
390	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
391	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
392	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
397	C₁₃×C₄⋊C₄	—	2	1	no	—
398	C₁₃×C₄⋊C₄	—	2	1	no	—
399	C₁₃×C₄⋊C₄	—	2	1	no	—
400	C₁₃×C₄⋊C₄	—	2	1	no	—
401	C₁₃×C₄⋊C₄	—	2	2	no	—
402	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
407	C₁₃×C₄⋊C₄	—	2	2	no	—
408	C₁₃×C₄⋊C₄	—	2	2	no	—
409	C₁₃×C₄⋊C₄	—	2	1	no	—
410	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
417	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	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	—	2	2	no	—
437	C₁₃×C₂²⋊C₄	—	2	2	no	—
438	C₁₃×C₂²⋊C₄	—	2	2	no	—
439	C₁₃×C₂²⋊C₄	—	2	1	no	—
440	C₁₃×C₂²⋊C₄	—	2	2	no	—
441	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₄²×C₁₃	—	2	1	no	—
445	C₄²×C₁₃	—	2	1	no	—
446	C₄²×C₁₃	—	2	2	no	—
447	C₄²×C₁₃	—	2	2	no	—
448	C₄²×C₁₃	—	2	1	no	—
449	C₄²×C₁₃	—	2	1	no	—
450	C₄²×C₁₃	—	2	2	no	—
451	C₄²×C₁₃	—	2	1	no	—
452	C₄²×C₁₃	C₂×D₄	1	2	yes	—
453	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₁₃	C₂×D₄	1	2	yes	—
455	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₁₃	C₂⁴	1	2	yes	—
457	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
458	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
459	#3514	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3396	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3394	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3365	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3364	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3328	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3326	C₂×C₁₃	1	2	yes	complemented
467	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3322	C₂×C₁₃	1	2	yes	complemented
469	#3278	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3277	C₂×C₁₃	1	2	yes	complemented
471	#3275	C₂×C₁₃	1	2	yes	complemented
472	#3274	C₂×C₁₃	1	1	yes	characteristic, complemented
473	#3256	C₂×C₁₃	1	2	yes	complemented
474	#3251	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#3211	C₂×C₁₃	1	2	yes	complemented
476	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
478	#3102	C₂×C₁₃	1	2	yes	complemented
479	#3040	C₂×C₁₃	1	2	yes	complemented
480	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
482	C₂³×C₁₃	—	2	1	no	—
483	C₂³×C₁₃	—	2	2	no	—
484	C₂³×C₁₃	—	2	2	no	—
485	C₂³×C₁₃	—	4	4	no	—
486	C₂³×C₁₃	—	8	2	no	—
487	C₂³×C₁₃	—	8	2	no	—
488	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
489	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
490	Q₈×C₁₃	—	2	2	no	—
491	Q₈×C₁₃	—	2	1	no	—
492	Q₈×C₁₃	—	2	1	no	—
493	Q₈×C₁₃	—	2	1	no	—
494	Q₈×C₁₃	—	2	2	no	—
495	Q₈×C₁₃	—	2	1	no	—
496	Q₈×C₁₃	—	2	2	no	—
497	Q₈×C₁₃	—	2	1	no	—
498	Q₈×C₁₃	—	4	2	no	—
499	Q₈×C₁₃	—	4	2	no	—
500	Q₈×C₁₃	—	8	2	no	—
501	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
502	D₄×C₁₃	—	2	2	no	—
503	D₄×C₁₃	—	2	1	no	—
504	D₄×C₁₃	—	2	2	no	—
505	D₄×C₁₃	—	2	2	no	—
506	D₄×C₁₃	—	2	2	no	—
507	D₄×C₁₃	—	2	2	no	—
508	D₄×C₁₃	—	2	1	no	—
509	D₄×C₁₃	—	4	2	no	—
510	D₄×C₁₃	—	4	4	no	—
511	D₄×C₁₃	—	4	4	no	—
512	D₄×C₁₃	—	4	4	no	—
513	D₄×C₁₃	—	4	2	no	—
514	D₄×C₁₃	—	4	2	no	—
515	D₄×C₁₃	—	8	1	no	—
516	D₄×C₁₃	—	8	1	no	—
517	D₄×C₁₃	—	8	2	no	—
518	D₄×C₁₃	—	8	1	no	—
519	D₄×C₁₃	—	8	2	no	—
520	D₄×C₁₃	—	8	2	no	—
521	C₂×C₄×C₁₃	—	2	1	no	—
522	C₂×C₄×C₁₃	—	2	2	no	—
523	C₂×C₄×C₁₃	—	2	2	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	1	no	—
529	C₂×C₄×C₁₃	—	2	1	no	—
530	C₂×C₄×C₁₃	—	2	2	no	—
531	C₂×C₄×C₁₃	—	2	1	no	—
532	C₂×C₄×C₁₃	—	2	1	no	—
533	C₂×C₄×C₁₃	—	2	1	no	—
534	C₂×C₄×C₁₃	—	2	2	no	—
535	C₂×C₄×C₁₃	—	4	2	no	—
536	C₂×C₄×C₁₃	—	4	1	no	—
537	C₂×C₄×C₁₃	—	4	2	no	—
538	C₂×C₄×C₁₃	—	4	4	no	—
539	C₂×C₄×C₁₃	—	4	2	no	—
540	C₂×C₄×C₁₃	—	4	4	no	—
541	C₂×C₄×C₁₃	—	4	2	no	—
542	C₂×C₄×C₁₃	—	8	2	no	—
543	C₂×C₄×C₁₃	—	8	2	no	—
544	C₂×C₄×C₁₃	—	8	2	no	—
545	C₂×C₄×C₁₃	—	8	1	no	—
546	C₂×C₄×C₁₃	—	8	2	no	—
547	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
556	C₈×C₁₃	—	2	1	no	—
557	C₈×C₁₃	—	2	2	no	—
558	C₈×C₁₃	—	2	1	no	—
559	C₈×C₁₃	—	2	2	no	—
560	C₈×C₁₃	—	2	1	no	—
561	C₈×C₁₃	—	2	1	no	—
562	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
563	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
564	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
565	#559	—	2	1	no	—
566	#559	C₂²×C₁₃	1	1	yes	characteristic
567	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
568	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
569	#556	—	2	1	no	—
570	#556	C₂²×C₁₃	1	1	yes	characteristic
571	#556	C₂²×C₁₃	1	1	yes	characteristic
572	#555	—	2	1	no	—
573	#553	—	2	2	no	—
574	#553	C₂²×C₁₃	1	2	yes	complemented
575	#551	—	2	2	no	—
576	#550	C₂²×C₁₃	1	1	yes	characteristic
577	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
578	#548	C₂²×C₁₃	1	2	yes	—
579	#548	C₂²×C₁₃	1	2	yes	complemented
580	#546	—	2	1	no	—
581	#546	C₂²×C₁₃	1	2	yes	—
582	D₄²	C₂²×C₁₃	1	1	yes	characteristic
583	#542	—	2	1	no	—
584	#538	—	2	2	no	—
585	#532	—	2	1	no	—
586	#532	C₂²×C₁₃	1	1	yes	characteristic
587	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
588	#529	—	2	2	no	—
589	#529	C₂²×C₁₃	1	2	yes	—
590	#529	C₂²×C₁₃	1	1	yes	characteristic
591	#529	C₂²×C₁₃	1	2	yes	complemented
592	C₂×#124	C₂²×C₁₃	1	2	yes	—
593	#518	—	2	1	no	—
594	C₄×#41	—	2	1	no	—
595	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
596	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
597	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	#495	C₂²×C₁₃	1	2	yes	—
599	#495	C₂²×C₁₃	1	2	yes	complemented
600	#493	C₂²×C₁₃	1	1	yes	characteristic
601	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
602	#488	C₂²×C₁₃	1	2	yes	—
603	#488	C₂²×C₁₃	1	2	yes	complemented
604	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	#486	C₂²×C₁₃	1	1	yes	characteristic
606	#485	C₂²×C₁₃	1	2	yes	complemented
607	#483	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#482	C₂²×C₁₃	1	2	yes	—
609	#480	C₂²×C₁₃	1	1	yes	characteristic
610	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
611	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#479	C₂²×C₁₃	1	2	yes	complemented
613	#478	C₂²×C₁₃	1	2	yes	complemented
614	#478	C₂²×C₁₃	1	2	yes	complemented
615	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	#474	C₂²×C₁₃	1	1	yes	characteristic
617	#470	C₂²×C₁₃	1	2	yes	complemented
618	#469	C₂²×C₁₃	1	2	yes	—
619	#469	C₂²×C₁₃	1	2	yes	—
620	#468	C₂²×C₁₃	1	2	yes	—
621	#468	C₂²×C₁₃	1	2	yes	complemented
622	#468	C₂²×C₁₃	1	2	yes	complemented
623	#464	C₂²×C₁₃	1	1	yes	characteristic
624	#464	C₂²×C₁₃	1	1	yes	characteristic
625	#464	C₂²×C₁₃	1	2	yes	—
626	#464	C₂²×C₁₃	1	2	yes	complemented
627	#464	C₂²×C₁₃	1	2	yes	complemented
628	#464	C₂²×C₁₃	1	2	yes	complemented
629	#464	C₂²×C₁₃	1	2	yes	complemented
630	#463	C₂²×C₁₃	1	2	yes	—
631	#463	C₂²×C₁₃	1	2	yes	—
632	#463	C₂²×C₁₃	1	2	yes	complemented
633	#463	C₂²×C₁₃	1	2	yes	complemented
634	#463	C₂²×C₁₃	1	2	yes	complemented
635	#463	C₂²×C₁₃	1	2	yes	complemented
636	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
638	#460	C₂²×C₁₃	1	1	yes	characteristic
639	#460	C₂²×C₁₃	1	1	yes	characteristic
640	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
641	#459	C₂²×C₁₃	1	1	yes	characteristic
642	#452	C₂²×C₁₃	1	2	yes	complemented
643	#451	C₂²×C₁₃	1	2	yes	complemented
644	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
645	#450	C₂²×C₁₃	1	2	yes	—
646	#449	C₂²×C₁₃	1	2	yes	—
647	#449	C₂²×C₁₃	1	2	yes	complemented
648	#449	C₂²×C₁₃	1	2	yes	complemented
649	#448	C₂²×C₁₃	1	1	yes	characteristic
650	#448	C₂²×C₁₃	1	2	yes	complemented
651	#447	C₂²×C₁₃	1	2	yes	—
652	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
656	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
658	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
659	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
660	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
661	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
662	#436	C₂²×C₁₃	1	1	yes	characteristic
663	#436	C₂²×C₁₃	1	1	yes	characteristic
664	#436	C₂²×C₁₃	1	2	yes	complemented
665	#436	C₂²×C₁₃	1	2	yes	complemented
666	#431	C₂²×C₁₃	1	2	yes	complemented
667	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
668	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
669	#423	C₂²×C₁₃	1	2	yes	complemented
670	#419	C₂²×C₁₃	1	2	yes	complemented
671	#418	C₂²×C₁₃	1	2	yes	—
672	#417	C₂²×C₁₃	1	2	yes	complemented
673	C₂²×C₁₃	—	2	1	no	—
674	C₂²×C₁₃	—	2	2	no	—
675	C₂²×C₁₃	—	2	1	no	—
676	C₂²×C₁₃	—	2	2	no	—
677	C₂²×C₁₃	—	2	1	no	—
678	C₂²×C₁₃	—	2	2	no	—
679	C₂²×C₁₃	—	4	2	no	—
680	C₂²×C₁₃	—	4	2	no	—
681	C₂²×C₁₃	—	4	1	no	—
682	C₂²×C₁₃	—	4	2	no	—
683	C₂²×C₁₃	—	4	2	no	—
684	C₂²×C₁₃	—	4	1	no	—
685	C₂²×C₁₃	—	4	2	no	—
686	C₂²×C₁₃	—	4	1	no	—
687	C₂²×C₁₃	—	4	2	no	—
688	C₂²×C₁₃	—	16	4	no	—
689	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
690	C₄×C₁₃	—	2	1	no	—
691	C₄×C₁₃	—	2	2	no	—
692	C₄×C₁₃	—	2	1	no	—
693	C₄×C₁₃	—	2	2	no	—
694	C₄×C₁₃	—	2	1	no	—
695	C₄×C₁₃	—	2	2	no	—
696	C₄×C₁₃	—	2	1	no	—
697	C₄×C₁₃	—	2	2	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	—	4	1	no	—
704	C₄×C₁₃	—	4	1	no	—
705	C₄×C₁₃	—	4	2	no	—
706	C₄×C₁₃	#575	1	2	yes	—
707	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
708	C₄×C₁₃	#585	1	1	yes	characteristic
709	C₂×#41	—	2	1	no	—
710	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
711	C₂×#41	C₂³×C₁₃	1	2	yes	—
712	C₂×#41	C₂³×C₁₃	1	2	yes	—
713	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
714	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
715	C₂²×D₄	—	2	1	no	—
716	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
717	#137	—	4	4	no	—
718	#137	—	4	4	no	—
719	AGL(1,ℤ/8)	—	4	4	no	—
720	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
721	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
722	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
723	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
725	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
731	C₂×D₈	C₂³×C₁₃	1	2	yes	—
732	C₂×D₈	C₂³×C₁₃	1	2	yes	—
733	C₂×D₈	C₂³×C₁₃	1	2	yes	—
734	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
735	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
736	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
737	C₄⋊Q₈	—	2	1	no	—
738	C₄⋊Q₈	—	2	1	no	—
739	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
741	#127	—	2	1	no	—
742	#127	C₂³×C₁₃	1	1	yes	characteristic
743	#127	C₂³×C₁₃	1	1	yes	characteristic
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	1	no	—
749	#126	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	C₂³×C₁₃	1	1	yes	characteristic
752	#125	C₂³×C₁₃	1	2	yes	—
753	#124	—	2	1	no	—
754	#124	—	2	1	no	—
755	#124	—	2	1	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	1	no	—
761	#124	C₂³×C₁₃	1	1	yes	characteristic
762	#124	C₂³×C₁₃	1	2	yes	—
763	#124	C₂³×C₁₃	1	2	yes	—
764	#124	C₂³×C₁₃	1	2	yes	—
765	#124	C₂³×C₁₃	1	2	yes	—
766	#123	—	2	1	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
779	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	C₂³×C₁₃	1	2	yes	—
790	#121	C₂³×C₁₃	1	1	yes	characteristic
791	#121	C₂³×C₁₃	1	2	yes	—
792	#121	C₂³×C₁₃	1	2	yes	—
793	#120	—	2	2	no	—
794	#120	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
805	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
806	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
824	C₄×D₄	D₄×C₁₃	1	2	yes	—
825	C₄×D₄	C₂³×C₁₃	1	2	yes	—
826	C₄×D₄	C₂³×C₁₃	1	2	yes	—
827	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₁₃	1	2	yes	—
829	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₁₃	1	2	yes	—
831	#117	—	2	1	no	—
832	#117	—	2	2	no	—
833	#117	—	2	2	no	—
834	#117	—	2	1	no	—
835	#117	—	2	2	no	—
836	#117	D₄×C₁₃	1	1	yes	characteristic
837	#117	D₄×C₁₃	1	2	yes	—
838	#117	C₂³×C₁₃	1	2	yes	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₄²	—	2	1	no	—
845	C₂×C₄²	—	2	2	no	—
846	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
847	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
848	#107	C₂³×C₁₃	1	1	yes	characteristic
849	#107	C₂³×C₁₃	1	2	yes	—
850	#107	C₂³×C₁₃	1	1	yes	characteristic
851	#106	C₂³×C₁₃	1	1	yes	characteristic
852	#106	C₂³×C₁₃	1	1	yes	characteristic
853	#106	C₂³×C₁₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
855	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
859	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
860	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
861	#103	C₂³×C₁₃	1	2	yes	—
862	#103	C₂³×C₁₃	1	2	yes	—
863	#103	C₂³×C₁₃	1	1	yes	characteristic
864	#103	C₂³×C₁₃	1	2	yes	—
865	#103	C₂³×C₁₃	1	2	yes	—
866	#103	C₂³×C₁₃	1	1	yes	characteristic
867	#103	C₂³×C₁₃	1	1	yes	characteristic
868	#103	C₂³×C₁₃	1	1	yes	characteristic
869	#103	C₂³×C₁₃	1	1	yes	characteristic
870	#103	C₂³×C₁₃	1	1	yes	characteristic
871	#103	C₂³×C₁₃	1	2	yes	—
872	#102	C₂³×C₁₃	1	2	yes	—
873	#102	C₂³×C₁₃	1	2	yes	—
874	#102	C₂³×C₁₃	1	1	yes	characteristic
875	#102	C₂³×C₁₃	1	2	yes	—
876	#102	C₂³×C₁₃	1	2	yes	—
877	#102	C₂³×C₁₃	1	2	yes	—
878	#102	C₂³×C₁₃	1	1	yes	characteristic
879	#102	C₂³×C₁₃	1	2	yes	—
880	#102	C₂³×C₁₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₁₃	1	2	yes	—
888	C₄×C₈	C₂³×C₁₃	1	2	yes	—
889	C₂×C₁₃	—	4	1	no	—
890	C₂×C₁₃	—	4	2	no	—
891	C₂×C₁₃	—	8	2	no	—
892	C₂×C₁₃	—	8	2	no	—
893	C₂×C₁₃	—	8	1	no	—
894	C₂×C₁₃	#3488	1	1	yes	characteristic
895	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
896	C₂×C₁₃	#3584	1	1	yes	characteristic
897	C₂⁴	—	2	2	no	—
898	#41	—	2	4	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	4	no	—
902	#41	—	4	2	no	—
903	#41	—	4	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	4	1	no	—
909	C₂×Q₈	—	4	2	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
915	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	4	no	—
930	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
931	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
932	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
933	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
934	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
935	C₂²×C₄	—	2	1	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	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
945	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
946	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
947	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
950	Q₁₆	—	2	2	no	—
951	Q₁₆	—	2	4	no	—
952	Q₁₆	—	4	2	no	—
953	Q₁₆	—	4	1	no	—
954	SD₁₆	—	2	2	no	—
955	SD₁₆	—	2	4	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	1	no	—
961	D₈	—	4	2	no	—
962	D₈	—	4	2	no	—
963	D₈	—	4	2	no	—
964	M₁₆	—	4	2	no	—
965	M₁₆	—	4	2	no	—
966	M₁₆	—	4	2	no	—
967	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
971	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
972	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1034	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1036	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₁₃	1	2	yes	—
1038	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1040	C₁₃	#62006	1	1	yes	characteristic, direct product factor, Sylow
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1048	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	4	2	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	1	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1114	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	16	4	no	—
1137	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	C₁₃×#575	1	2	yes	—
1155	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1156	C₄	C₁₃×#585	1	1	yes	characteristic
1157	C₂	—	4	2	no	—
1158	C₂	—	4	1	no	—
1159	C₂	—	8	1	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	8	2	no	—
1162	C₂	C₁₃×#3488	1	1	yes	characteristic
1163	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1164	C₂	C₁₃×#3584	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×#3514	C₂	semidirect
2. C₁₃×#3480	C₂	semidirect
3. C₁₃×#3396	C₂	semidirect
4. C₁₃×#3394	C₂	semidirect
5. C₁₃×#3365	C₂	semidirect
6. C₁₃×#3364	C₂	semidirect
7. C₁₃×#3328	C₂	semidirect
8. C₁₃×#3326	C₂	semidirect
9. C₁₃×#3324	C₂	semidirect
10. C₁₃×#3322	C₂	semidirect
11. C₁₃×#3278	C₂	semidirect
12. C₁₃×#3277	C₂	semidirect
13. C₁₃×#3275	C₂	semidirect
14. C₁₃×#3274	C₂	semidirect
15. C₁₃×#3256	C₂	semidirect
16. C₁₃×#3251	C₂	semidirect
17. C₁₃×#3211	C₂	semidirect
18. C₁₃×#3207	C₂	semidirect
19. C₁₃×#3108	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3040	C₂	semidirect
22. C₁₃×#3037	C₂	semidirect
23. C₁₃×#2991	C₂	semidirect
24. C₂×C₁₃×#137	C₂²	semidirect
25. C₂×C₁₃×#137	C₂²	semidirect
29. C₁₃×#559	C₂²	semidirect
30. C₁₃×#557	C₂²	semidirect
36. C₁₃×#553	C₂²	semidirect
41. C₁₃×#548	C₂²	semidirect
49. C₁₃×#532	C₂²	semidirect
53. C₁₃×#529	C₂²	semidirect
58. C₄×C₁₃×#41	C₂²	semidirect
59. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
61. C₁₃×#495	C₂²	semidirect
63. C₁₃×#492	C₂²	semidirect
65. C₁₃×#488	C₂²	semidirect
66. C₁₃×#487	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#483	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#478	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
83. C₁₃×#468	C₂²	semidirect
84. C₁₃×#468	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
89. C₁₃×#464	C₂²	semidirect
90. C₁₃×#464	C₂²	semidirect
91. C₁₃×#464	C₂²	semidirect
94. C₁₃×#463	C₂²	semidirect
95. C₁₃×#463	C₂²	semidirect
96. C₁₃×#463	C₂²	semidirect
97. C₁₃×#463	C₂²	semidirect
98. C₁₃×#462	C₂²	semidirect
99. C₁₃×#462	C₂²	semidirect
102. C₁₃×#460	C₂²	semidirect
104. C₁₃×#452	C₂²	semidirect
105. C₁₃×#451	C₂²	semidirect
106. C₁₃×#451	C₂²	semidirect
109. C₁₃×#449	C₂²	semidirect
110. C₁₃×#449	C₂²	semidirect
112. C₁₃×#448	C₂²	semidirect
114. C₈×Q₈×C₁₃	C₂²	semidirect
115. C₈×Q₈×C₁₃	C₂²	semidirect
116. C₄×C₁₃×Q₁₆	C₂²	semidirect
117. C₄×C₁₃×Q₁₆	C₂²	semidirect
118. C₄×C₁₃×Q₁₆	C₂²	semidirect
121. C₄×C₁₃×SD₁₆	C₂²	semidirect
122. C₄×C₁₃×SD₁₆	C₂²	semidirect
123. C₄×C₁₃×D₈	C₂²	semidirect
126. C₁₃×#436	C₂²	semidirect
127. C₁₃×#436	C₂²	semidirect
128. C₁₃×#431	C₂²	semidirect
129. C₁₃×#431	C₂²	semidirect
130. C₁₃×#423	C₂²	semidirect
131. C₁₃×#423	C₂²	semidirect
132. C₁₃×#419	C₂²	semidirect
134. C₁₃×#417	C₂²	semidirect
315. #62006	C₁₃	direct (N × H)
459. #3514	C₂×C₁₃	semidirect
460. #3480	C₂×C₁₃	semidirect
461. #3396	C₂×C₁₃	semidirect
462. #3394	C₂×C₁₃	semidirect
463. #3365	C₂×C₁₃	semidirect
464. #3364	C₂×C₁₃	semidirect
465. #3328	C₂×C₁₃	semidirect
466. #3326	C₂×C₁₃	semidirect
467. #3324	C₂×C₁₃	semidirect
468. #3322	C₂×C₁₃	semidirect
469. #3278	C₂×C₁₃	semidirect
470. #3277	C₂×C₁₃	semidirect
471. #3275	C₂×C₁₃	semidirect
472. #3274	C₂×C₁₃	semidirect
473. #3256	C₂×C₁₃	semidirect
474. #3251	C₂×C₁₃	semidirect
475. #3211	C₂×C₁₃	semidirect
476. #3207	C₂×C₁₃	semidirect
477. #3108	C₂×C₁₃	semidirect
478. #3102	C₂×C₁₃	semidirect
479. #3040	C₂×C₁₃	semidirect
480. #3037	C₂×C₁₃	semidirect
481. #2991	C₂×C₁₃	semidirect
562. C₂×#137	C₂²×C₁₃	semidirect
563. C₂×#137	C₂²×C₁₃	semidirect
567. #559	C₂²×C₁₃	semidirect
568. #557	C₂²×C₁₃	semidirect
574. #553	C₂²×C₁₃	semidirect
579. #548	C₂²×C₁₃	semidirect
587. #532	C₂²×C₁₃	semidirect
591. #529	C₂²×C₁₃	semidirect
596. C₄×#41	C₂²×C₁₃	semidirect
597. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
599. #495	C₂²×C₁₃	semidirect
601. #492	C₂²×C₁₃	semidirect
603. #488	C₂²×C₁₃	semidirect
604. #487	C₂²×C₁₃	semidirect
606. #485	C₂²×C₁₃	semidirect
607. #483	C₂²×C₁₃	semidirect
610. #479	C₂²×C₁₃	semidirect
611. #479	C₂²×C₁₃	semidirect
612. #479	C₂²×C₁₃	semidirect
613. #478	C₂²×C₁₃	semidirect
614. #478	C₂²×C₁₃	semidirect
615. #475	C₂²×C₁₃	semidirect
617. #470	C₂²×C₁₃	semidirect
621. #468	C₂²×C₁₃	semidirect
622. #468	C₂²×C₁₃	semidirect
626. #464	C₂²×C₁₃	semidirect
627. #464	C₂²×C₁₃	semidirect
628. #464	C₂²×C₁₃	semidirect
629. #464	C₂²×C₁₃	semidirect
632. #463	C₂²×C₁₃	semidirect
633. #463	C₂²×C₁₃	semidirect
634. #463	C₂²×C₁₃	semidirect
635. #463	C₂²×C₁₃	semidirect
636. #462	C₂²×C₁₃	semidirect
637. #462	C₂²×C₁₃	semidirect
640. #460	C₂²×C₁₃	semidirect
642. #452	C₂²×C₁₃	semidirect
643. #451	C₂²×C₁₃	semidirect
644. #451	C₂²×C₁₃	semidirect
647. #449	C₂²×C₁₃	semidirect
648. #449	C₂²×C₁₃	semidirect
650. #448	C₂²×C₁₃	semidirect
652. C₈×Q₈	C₂²×C₁₃	semidirect
653. C₈×Q₈	C₂²×C₁₃	semidirect
654. C₄×Q₁₆	C₂²×C₁₃	semidirect
655. C₄×Q₁₆	C₂²×C₁₃	semidirect
656. C₄×Q₁₆	C₂²×C₁₃	semidirect
659. C₄×SD₁₆	C₂²×C₁₃	semidirect
660. C₄×SD₁₆	C₂²×C₁₃	semidirect
661. C₄×D₈	C₂²×C₁₃	semidirect
664. #436	C₂²×C₁₃	semidirect
665. #436	C₂²×C₁₃	semidirect
666. #431	C₂²×C₁₃	semidirect
667. #431	C₂²×C₁₃	semidirect
668. #423	C₂²×C₁₃	semidirect
669. #423	C₂²×C₁₃	semidirect
670. #419	C₂²×C₁₃	semidirect
672. #417	C₂²×C₁₃	semidirect
1040. C₁₃	#62006	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×#3514	2
C₁₃×#3480	2
C₁₃×#3396	2
C₁₃×#3394	2
C₁₃×#3365	2
C₁₃×#3364	2
C₁₃×#3328	2
C₁₃×#3326	2
C₁₃×#3324	2
C₁₃×#3322	2
C₁₃×#3278	2
C₁₃×#3277	2
C₁₃×#3275	2
C₁₃×#3274	2
C₁₃×#3256	2
C₁₃×#3251	2
C₁₃×#3211	2
C₁₃×#3207	2
C₁₃×#3108	2
C₁₃×#3102	2
C₁₃×#3040	2
C₁₃×#3037	2
C₁₃×#2991	2
#62006	13

Subgroups — C13×#62006 #15748345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62006 #15748345