Subgroups — C₁₃×#61006 #15747345

Order 3328.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3257	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3198	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3119	C₂	1	4	yes	maximal, complemented
18	C₁₃×#3118	C₂	1	4	yes	maximal, complemented
19	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#559	—	2	1	no	—
21	C₁₃×#559	—	2	1	no	—
22	C₁₃×#556	—	2	1	no	—
23	C₁₃×#555	—	2	1	no	—
24	C₁₃×#554	—	2	1	no	—
25	C₁₃×#553	—	2	1	no	—
26	C₁₃×#553	—	2	1	no	—
27	C₁₃×#550	—	2	1	no	—
28	C₁₃×#550	—	2	1	no	—
29	C₁₃×#548	—	2	1	no	—
30	C₁₃×#548	—	2	1	no	—
31	C₁₃×#547	—	2	1	no	—
32	C₁₃×#546	—	2	1	no	—
33	C₁₃×#546	—	2	1	no	—
34	C₁₃×#546	—	2	1	no	—
35	C₁₃×#546	—	2	1	no	—
36	C₁₃×#542	C₂²	1	2	yes	—
37	C₁₃×#542	C₂²	1	2	yes	complemented
38	C₁₃×#540	C₂²	1	2	yes	—
39	C₁₃×#540	C₂²	1	2	yes	—
40	C₁₃×#537	C₂²	1	2	yes	—
41	C₁₃×#535	C₂²	1	2	yes	—
42	C₁₃×#533	C₂²	1	1	yes	characteristic
43	C₁₃×#533	C₂²	1	1	yes	characteristic
44	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#532	C₂²	1	1	yes	characteristic
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₁₃×#532	C₂²	1	1	yes	characteristic
48	C₁₃×#532	C₂²	1	1	yes	characteristic
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
54	C₁₃×#520	C₂²	1	2	yes	complemented
55	C₁₃×#518	C₂²	1	2	yes	—
56	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
57	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#493	C₂²	1	1	yes	characteristic
62	C₁₃×#493	C₂²	1	1	yes	characteristic
63	C₁₃×#492	C₂²	1	1	yes	characteristic
64	C₁₃×#492	C₂²	1	1	yes	characteristic
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#486	C₂²	1	1	yes	characteristic
68	C₁₃×#486	C₂²	1	1	yes	characteristic
69	C₁₃×#486	C₂²	1	1	yes	characteristic
70	C₁₃×#486	C₂²	1	1	yes	characteristic
71	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#485	C₂²	1	4	yes	—
74	C₁₃×#482	C₂²	1	4	yes	—
75	C₁₃×#481	C₂²	1	4	yes	complemented
76	C₁₃×#480	C₂²	1	4	yes	complemented
77	C₁₃×#479	C₂²	1	4	yes	complemented
78	C₁₃×#478	C₂²	1	4	yes	complemented
79	C₁₃×#476	C₂²	1	4	yes	complemented
80	C₁₃×#474	C₂²	1	4	yes	complemented
81	C₁₃×#469	C₂²	1	4	yes	complemented
82	C₁₃×#468	C₂²	1	4	yes	complemented
83	C₁₃×#466	C₂²	1	4	yes	complemented
84	C₁₃×#465	C₂²	1	4	yes	complemented
85	C₁₃×#463	C₂²	1	4	yes	complemented
86	C₁₃×#463	C₂²	1	4	yes	complemented
87	C₁₃×#460	C₂²	1	4	yes	—
88	C₁₃×#459	C₂²	1	4	yes	—
89	C₁₃×#450	C₂²	1	4	yes	—
90	C₁₃×#449	C₂²	1	4	yes	complemented
91	C₁₃×#449	C₂²	1	4	yes	complemented
92	C₁₃×#447	C₂²	1	4	yes	—
93	C₁₃×#442	C₂²	1	4	yes	complemented
94	C₁₃×#440	C₂²	1	4	yes	complemented
95	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
96	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
97	C₁₃×#433	C₂²	1	2	yes	—
98	C₁₃×#433	C₂²	1	2	yes	complemented
99	C₁₃×#431	C₂²	1	1	yes	characteristic
100	C₁₃×#431	C₂²	1	1	yes	characteristic
101	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#424	C₂²	1	2	yes	complemented
104	C₁₃×#408	C₂²	1	2	yes	—
105	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₁₃×#41	—	2	1	no	—
108	C₂×C₁₃×#41	—	2	1	no	—
109	C₂×C₁₃×#41	—	2	1	no	—
110	C₂×C₁₃×#41	—	2	1	no	—
111	C₂×C₁₃×#41	—	2	1	no	—
112	C₂×C₁₃×#41	—	2	1	no	—
113	C₂×C₁₃×#41	C₂³	1	2	yes	—
114	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
115	C₂²×Q₈×C₁₃	—	2	1	no	—
116	C₂²×D₄×C₁₃	—	2	1	no	—
117	C₂²×D₄×C₁₃	—	2	1	no	—
118	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₁₃×D₈	C₂³	1	4	yes	—
122	C₂×C₁₃×D₈	C₂³	1	4	yes	—
123	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
124	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
125	C₁₃×C₄⋊Q₈	—	2	1	no	—
126	C₁₃×C₄⋊Q₈	—	2	1	no	—
127	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₁₃×#127	—	2	2	no	—
134	C₁₃×#127	—	2	1	no	—
135	C₁₃×#127	—	2	1	no	—
136	C₁₃×#127	C₂³	1	2	yes	—
137	C₁₃×#127	C₂³	1	1	yes	characteristic
138	C₁₃×#127	C₂³	1	1	yes	characteristic
139	C₁₃×#127	C₂³	1	1	yes	characteristic
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#125	—	2	1	no	—
143	C₁₃×#125	—	2	1	no	—
144	C₁₃×#125	C₂³	1	2	yes	—
145	C₁₃×#124	—	2	2	no	—
146	C₁₃×#124	—	2	2	no	—
147	C₁₃×#124	—	2	2	no	—
148	C₁₃×#124	—	2	1	no	—
149	C₁₃×#124	—	2	1	no	—
150	C₁₃×#124	—	2	1	no	—
151	C₁₃×#124	—	2	1	no	—
152	C₁₃×#124	—	2	1	no	—
153	C₁₃×#124	—	2	1	no	—
154	C₁₃×#124	C₂³	1	2	yes	—
155	C₁₃×#123	—	2	2	no	—
156	C₁₃×#123	—	2	2	no	—
157	C₁₃×#123	—	2	2	no	—
158	C₁₃×#123	—	2	2	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×C₂²⋊Q₈	—	2	2	no	—
162	C₁₃×C₂²⋊Q₈	—	2	1	no	—
163	C₁₃×C₂²⋊Q₈	—	2	1	no	—
164	C₁₃×C₂²⋊Q₈	—	2	1	no	—
165	C₁₃×C₂²⋊Q₈	—	2	1	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	1	no	—
174	C₁₃×#121	—	2	1	no	—
175	C₁₃×#121	—	2	1	no	—
176	C₁₃×#121	—	2	1	no	—
177	C₁₃×#121	—	2	1	no	—
178	C₁₃×#121	—	2	1	no	—
179	C₁₃×#121	—	2	1	no	—
180	C₁₃×#121	—	2	1	no	—
181	C₁₃×#121	—	2	2	no	—
182	C₁₃×#121	—	2	2	no	—
183	C₁₃×#121	—	2	2	no	—
184	C₁₃×#121	—	2	2	no	—
185	C₁₃×#121	C₂³	1	2	yes	—
186	C₁₃×#121	C₂³	1	2	yes	—
187	C₁₃×#121	C₂³	1	2	yes	—
188	C₁₃×#121	C₂³	1	2	yes	—
189	C₁₃×#121	C₂³	1	2	yes	—
190	C₁₃×#121	C₂³	1	2	yes	—
191	C₁₃×#120	—	2	2	no	—
192	C₁₃×#120	—	2	2	no	—
193	C₄×Q₈×C₁₃	—	2	1	no	—
194	C₄×Q₈×C₁₃	—	2	1	no	—
195	C₄×Q₈×C₁₃	—	2	1	no	—
196	C₄×Q₈×C₁₃	—	2	1	no	—
197	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
198	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
199	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
200	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	—	2	2	no	—
202	C₄×D₄×C₁₃	—	2	2	no	—
203	C₄×D₄×C₁₃	—	2	2	no	—
204	C₄×D₄×C₁₃	—	2	2	no	—
205	C₄×D₄×C₁₃	—	2	1	no	—
206	C₄×D₄×C₁₃	—	2	1	no	—
207	C₄×D₄×C₁₃	—	2	1	no	—
208	C₄×D₄×C₁₃	—	2	1	no	—
209	C₄×D₄×C₁₃	—	2	1	no	—
210	C₄×D₄×C₁₃	—	2	1	no	—
211	C₄×D₄×C₁₃	—	2	1	no	—
212	C₄×D₄×C₁₃	—	2	1	no	—
213	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
214	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
215	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
216	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
217	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
218	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
219	C₄×D₄×C₁₃	C₂³	1	2	yes	—
220	C₄×D₄×C₁₃	C₂³	1	2	yes	—
221	C₄×D₄×C₁₃	C₂³	1	2	yes	—
222	C₄×D₄×C₁₃	C₂³	1	2	yes	—
223	C₄×D₄×C₁₃	C₂³	1	2	yes	—
224	C₄×D₄×C₁₃	C₂³	1	2	yes	—
225	C₁₃×#117	—	2	1	no	—
226	C₁₃×#117	—	2	1	no	—
227	C₁₃×#117	—	2	2	no	—
228	C₁₃×#117	C₂³	1	2	yes	—
229	C₁₃×#117	C₂³	1	1	yes	characteristic
230	C₁₃×#117	C₂³	1	1	yes	characteristic
231	C₁₃×#117	C₂³	1	1	yes	characteristic
232	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
235	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
240	C₁₃×#107	C₂³	1	4	yes	—
241	C₁₃×#107	C₂³	1	4	yes	—
242	C₁₃×#106	C₂³	1	4	yes	—
243	C₁₃×#106	C₂³	1	4	yes	—
244	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
245	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
246	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
247	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₁₃×#103	C₂³	1	4	yes	—
249	C₁₃×#103	C₂³	1	4	yes	—
250	C₁₃×#102	C₂³	1	4	yes	—
251	C₁₃×#102	C₂³	1	4	yes	—
252	C₁₃×#102	C₂³	1	4	yes	—
253	C₁₃×#102	C₂³	1	4	yes	—
254	C₁₃×#102	C₂³	1	4	yes	—
255	C₁₃×#102	C₂³	1	4	yes	—
256	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₁₃×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₃	C₂³	1	2	yes	—
264	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
266	#61006	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂⁴×C₁₃	—	2	2	no	—
268	C₁₃×#41	—	4	2	no	—
269	C₁₃×#41	—	4	4	no	—
270	C₁₃×#41	—	8	2	no	—
271	C₁₃×#41	—	8	2	no	—
272	C₁₃×#41	—	8	2	no	—
273	C₁₃×#41	—	8	2	no	—
274	C₁₃×#41	—	8	2	no	—
275	C₁₃×#41	—	8	2	no	—
276	C₂×Q₈×C₁₃	—	2	1	no	—
277	C₂×Q₈×C₁₃	—	2	1	no	—
278	C₂×Q₈×C₁₃	—	2	1	no	—
279	C₂×Q₈×C₁₃	—	2	1	no	—
280	C₂×Q₈×C₁₃	—	2	2	no	—
281	C₂×Q₈×C₁₃	—	8	2	no	—
282	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
284	C₂×D₄×C₁₃	—	2	2	no	—
285	C₂×D₄×C₁₃	—	2	2	no	—
286	C₂×D₄×C₁₃	—	2	2	no	—
287	C₂×D₄×C₁₃	—	2	2	no	—
288	C₂×D₄×C₁₃	—	2	2	no	—
289	C₂×D₄×C₁₃	—	2	2	no	—
290	C₂×D₄×C₁₃	—	2	2	no	—
291	C₂×D₄×C₁₃	—	2	1	no	—
292	C₂×D₄×C₁₃	—	2	2	no	—
293	C₂×D₄×C₁₃	—	2	1	no	—
294	C₂×D₄×C₁₃	—	2	1	no	—
295	C₂×D₄×C₁₃	—	2	1	no	—
296	C₂×D₄×C₁₃	—	2	1	no	—
297	C₂×D₄×C₁₃	—	2	1	no	—
298	C₂×D₄×C₁₃	—	2	2	no	—
299	C₂×D₄×C₁₃	—	2	2	no	—
300	C₂×D₄×C₁₃	—	4	4	no	—
301	C₂×D₄×C₁₃	—	8	2	no	—
302	C₂×D₄×C₁₃	—	8	2	no	—
303	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
307	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
308	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₃	—	2	2	no	—
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	—	2	2	no	—
312	C₂²×C₄×C₁₃	—	2	2	no	—
313	C₂²×C₄×C₁₃	—	2	2	no	—
314	C₂²×C₄×C₁₃	—	2	2	no	—
315	C₂²×C₄×C₁₃	—	2	2	no	—
316	C₂²×C₄×C₁₃	—	2	2	no	—
317	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₁₃×SD₁₆	—	4	4	no	—
327	C₁₃×SD₁₆	—	4	4	no	—
328	C₁₃×D₈	—	4	4	no	—
329	C₁₃×D₈	—	4	4	no	—
330	C₁₃×M₁₆	—	4	2	no	—
331	C₂×C₈×C₁₃	—	4	2	no	—
332	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
334	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
335	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	1	no	—
338	C₁₃×C₄⋊C₄	—	2	1	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	1	no	—
343	C₁₃×C₄⋊C₄	—	2	1	no	—
344	C₁₃×C₄⋊C₄	—	2	1	no	—
345	C₁₃×C₄⋊C₄	—	2	1	no	—
346	C₁₃×C₄⋊C₄	—	2	2	no	—
347	C₁₃×C₄⋊C₄	—	2	2	no	—
348	C₁₃×C₄⋊C₄	—	2	2	no	—
349	C₁₃×C₄⋊C₄	—	2	2	no	—
350	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
351	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
352	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
353	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
354	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
355	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
356	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
357	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
358	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
359	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	—	2	2	no	—
365	C₁₃×C₂²⋊C₄	—	2	2	no	—
366	C₁₃×C₂²⋊C₄	—	2	2	no	—
367	C₁₃×C₂²⋊C₄	—	2	2	no	—
368	C₁₃×C₂²⋊C₄	—	2	2	no	—
369	C₁₃×C₂²⋊C₄	—	2	2	no	—
370	C₁₃×C₂²⋊C₄	—	2	2	no	—
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	2	no	—
377	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
378	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
380	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
381	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
382	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₁₃	—	2	2	no	—
384	C₄²×C₁₃	—	2	2	no	—
385	C₄²×C₁₃	—	2	2	no	—
386	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
387	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
394	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
395	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
396	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
398	#3257	C₂×C₁₃	1	4	yes	complemented
399	#3231	C₂×C₁₃	1	1	yes	characteristic, complemented
400	#3228	C₂×C₁₃	1	1	yes	characteristic, complemented
401	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
402	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
403	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3207	C₂×C₁₃	1	1	yes	characteristic, complemented
406	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
407	#3198	C₂×C₁₃	1	4	yes	complemented
408	#3184	C₂×C₁₃	1	1	yes	characteristic, complemented
409	#3182	C₂×C₁₃	1	1	yes	characteristic, complemented
410	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
411	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
412	#3119	C₂×C₁₃	1	4	yes	complemented
413	#3118	C₂×C₁₃	1	4	yes	complemented
414	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
415	C₂³×C₁₃	—	2	2	no	—
416	C₂³×C₁₃	—	2	2	no	—
417	C₂³×C₁₃	—	2	2	no	—
418	C₂³×C₁₃	—	4	4	no	—
419	C₂³×C₁₃	—	8	2	no	—
420	C₂³×C₁₃	—	8	2	no	—
421	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
422	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
423	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	Q₈×C₁₃	—	2	4	no	—
425	Q₈×C₁₃	—	4	1	no	—
426	Q₈×C₁₃	—	4	2	no	—
427	Q₈×C₁₃	—	4	2	no	—
428	Q₈×C₁₃	—	4	2	no	—
429	Q₈×C₁₃	—	4	2	no	—
430	Q₈×C₁₃	—	8	2	no	—
431	D₄×C₁₃	—	2	4	no	—
432	D₄×C₁₃	—	2	4	no	—
433	D₄×C₁₃	—	2	4	no	—
434	D₄×C₁₃	—	4	1	no	—
435	D₄×C₁₃	—	4	1	no	—
436	D₄×C₁₃	—	4	1	no	—
437	D₄×C₁₃	—	4	4	no	—
438	D₄×C₁₃	—	4	4	no	—
439	D₄×C₁₃	—	4	2	no	—
440	D₄×C₁₃	—	4	2	no	—
441	D₄×C₁₃	—	4	2	no	—
442	D₄×C₁₃	—	4	2	no	—
443	D₄×C₁₃	—	4	2	no	—
444	D₄×C₁₃	—	4	2	no	—
445	D₄×C₁₃	—	8	2	no	—
446	D₄×C₁₃	—	8	2	no	—
447	D₄×C₁₃	—	8	2	no	—
448	D₄×C₁₃	—	8	2	no	—
449	D₄×C₁₃	—	8	2	no	—
450	D₄×C₁₃	—	8	2	no	—
451	D₄×C₁₃	—	8	2	no	—
452	D₄×C₁₃	—	8	2	no	—
453	C₂×C₄×C₁₃	—	2	2	no	—
454	C₂×C₄×C₁₃	—	2	2	no	—
455	C₂×C₄×C₁₃	—	2	2	no	—
456	C₂×C₄×C₁₃	—	2	2	no	—
457	C₂×C₄×C₁₃	—	2	2	no	—
458	C₂×C₄×C₁₃	—	2	2	no	—
459	C₂×C₄×C₁₃	—	2	2	no	—
460	C₂×C₄×C₁₃	—	2	2	no	—
461	C₂×C₄×C₁₃	—	2	2	no	—
462	C₂×C₄×C₁₃	—	2	2	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	2	2	no	—
465	C₂×C₄×C₁₃	—	2	2	no	—
466	C₂×C₄×C₁₃	—	2	2	no	—
467	C₂×C₄×C₁₃	—	4	4	no	—
468	C₂×C₄×C₁₃	—	8	2	no	—
469	C₂×C₄×C₁₃	—	8	2	no	—
470	C₂×C₄×C₁₃	—	8	2	no	—
471	C₂×C₄×C₁₃	—	8	2	no	—
472	C₂×C₄×C₁₃	—	8	2	no	—
473	C₂×C₄×C₁₃	—	8	2	no	—
474	C₂×C₄×C₁₃	—	8	2	no	—
475	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
487	C₈×C₁₃	—	2	2	no	—
488	C₈×C₁₃	—	2	2	no	—
489	C₈×C₁₃	—	2	2	no	—
490	C₈×C₁₃	—	2	2	no	—
491	#559	—	2	1	no	—
492	#559	—	2	1	no	—
493	#556	—	2	1	no	—
494	#555	—	2	1	no	—
495	#554	—	2	1	no	—
496	#553	—	2	1	no	—
497	#553	—	2	1	no	—
498	#550	—	2	1	no	—
499	#550	—	2	1	no	—
500	#548	—	2	1	no	—
501	#548	—	2	1	no	—
502	#547	—	2	1	no	—
503	#546	—	2	1	no	—
504	#546	—	2	1	no	—
505	#546	—	2	1	no	—
506	#546	—	2	1	no	—
507	#542	C₂²×C₁₃	1	2	yes	—
508	#542	C₂²×C₁₃	1	2	yes	complemented
509	#540	C₂²×C₁₃	1	2	yes	—
510	#540	C₂²×C₁₃	1	2	yes	—
511	#537	C₂²×C₁₃	1	2	yes	—
512	#535	C₂²×C₁₃	1	2	yes	—
513	#533	C₂²×C₁₃	1	1	yes	characteristic
514	#533	C₂²×C₁₃	1	1	yes	characteristic
515	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	#532	C₂²×C₁₃	1	1	yes	characteristic
517	#532	C₂²×C₁₃	1	1	yes	characteristic
518	#532	C₂²×C₁₃	1	1	yes	characteristic
519	#532	C₂²×C₁₃	1	1	yes	characteristic
520	#532	C₂²×C₁₃	1	1	yes	characteristic
521	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
522	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
525	#520	C₂²×C₁₃	1	2	yes	complemented
526	#518	C₂²×C₁₃	1	2	yes	—
527	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
528	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
529	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
530	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
531	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
532	#493	C₂²×C₁₃	1	1	yes	characteristic
533	#493	C₂²×C₁₃	1	1	yes	characteristic
534	#492	C₂²×C₁₃	1	1	yes	characteristic
535	#492	C₂²×C₁₃	1	1	yes	characteristic
536	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
537	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
538	#486	C₂²×C₁₃	1	1	yes	characteristic
539	#486	C₂²×C₁₃	1	1	yes	characteristic
540	#486	C₂²×C₁₃	1	1	yes	characteristic
541	#486	C₂²×C₁₃	1	1	yes	characteristic
542	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
543	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
544	#485	C₂²×C₁₃	1	4	yes	—
545	#482	C₂²×C₁₃	1	4	yes	—
546	#481	C₂²×C₁₃	1	4	yes	complemented
547	#480	C₂²×C₁₃	1	4	yes	complemented
548	#479	C₂²×C₁₃	1	4	yes	complemented
549	#478	C₂²×C₁₃	1	4	yes	complemented
550	#476	C₂²×C₁₃	1	4	yes	complemented
551	#474	C₂²×C₁₃	1	4	yes	complemented
552	#469	C₂²×C₁₃	1	4	yes	complemented
553	#468	C₂²×C₁₃	1	4	yes	complemented
554	#466	C₂²×C₁₃	1	4	yes	complemented
555	#465	C₂²×C₁₃	1	4	yes	complemented
556	#463	C₂²×C₁₃	1	4	yes	complemented
557	#463	C₂²×C₁₃	1	4	yes	complemented
558	#460	C₂²×C₁₃	1	4	yes	—
559	#459	C₂²×C₁₃	1	4	yes	—
560	#450	C₂²×C₁₃	1	4	yes	—
561	#449	C₂²×C₁₃	1	4	yes	complemented
562	#449	C₂²×C₁₃	1	4	yes	complemented
563	#447	C₂²×C₁₃	1	4	yes	—
564	#442	C₂²×C₁₃	1	4	yes	complemented
565	#440	C₂²×C₁₃	1	4	yes	complemented
566	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
567	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
568	#433	C₂²×C₁₃	1	2	yes	—
569	#433	C₂²×C₁₃	1	2	yes	complemented
570	#431	C₂²×C₁₃	1	1	yes	characteristic
571	#431	C₂²×C₁₃	1	1	yes	characteristic
572	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
573	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
574	#424	C₂²×C₁₃	1	2	yes	complemented
575	#408	C₂²×C₁₃	1	2	yes	—
576	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
577	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
578	C₂²×C₁₃	—	2	1	no	—
579	C₂²×C₁₃	—	2	1	no	—
580	C₂²×C₁₃	—	2	1	no	—
581	C₂²×C₁₃	—	2	1	no	—
582	C₂²×C₁₃	—	2	1	no	—
583	C₂²×C₁₃	—	2	1	no	—
584	C₂²×C₁₃	—	2	1	no	—
585	C₂²×C₁₃	—	2	1	no	—
586	C₂²×C₁₃	—	2	1	no	—
587	C₂²×C₁₃	—	4	2	no	—
588	C₂²×C₁₃	—	4	2	no	—
589	C₂²×C₁₃	—	4	2	no	—
590	C₂²×C₁₃	—	4	2	no	—
591	C₂²×C₁₃	—	4	2	no	—
592	C₂²×C₁₃	—	4	2	no	—
593	C₂²×C₁₃	—	4	2	no	—
594	C₂²×C₁₃	—	4	2	no	—
595	C₂²×C₁₃	—	4	2	no	—
596	C₂²×C₁₃	—	16	4	no	—
597	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
598	C₄×C₁₃	—	2	1	no	—
599	C₄×C₁₃	—	2	1	no	—
600	C₄×C₁₃	—	2	1	no	—
601	C₄×C₁₃	—	2	1	no	—
602	C₄×C₁₃	—	2	1	no	—
603	C₄×C₁₃	—	2	1	no	—
604	C₄×C₁₃	—	2	1	no	—
605	C₄×C₁₃	—	2	1	no	—
606	C₄×C₁₃	—	2	1	no	—
607	C₄×C₁₃	—	4	2	no	—
608	C₄×C₁₃	—	4	2	no	—
609	C₄×C₁₃	—	4	2	no	—
610	C₄×C₁₃	—	4	2	no	—
611	C₄×C₁₃	—	4	2	no	—
612	C₄×C₁₃	#576	1	2	yes	—
613	C₄×C₁₃	#577	1	2	yes	—
614	C₄×C₁₃	#585	1	2	yes	—
615	C₂×#41	—	2	1	no	—
616	C₂×#41	—	2	1	no	—
617	C₂×#41	—	2	1	no	—
618	C₂×#41	—	2	1	no	—
619	C₂×#41	—	2	1	no	—
620	C₂×#41	—	2	1	no	—
621	C₂×#41	C₂³×C₁₃	1	2	yes	—
622	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
623	C₂²×Q₈	—	2	1	no	—
624	C₂²×D₄	—	2	1	no	—
625	C₂²×D₄	—	2	1	no	—
626	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
627	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
628	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
629	C₂×D₈	C₂³×C₁₃	1	4	yes	—
630	C₂×D₈	C₂³×C₁₃	1	4	yes	—
631	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
632	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
633	C₄⋊Q₈	—	2	1	no	—
634	C₄⋊Q₈	—	2	1	no	—
635	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
636	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
637	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
638	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
639	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
640	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
641	#127	—	2	2	no	—
642	#127	—	2	1	no	—
643	#127	—	2	1	no	—
644	#127	C₂³×C₁₃	1	1	yes	characteristic
645	#127	C₂³×C₁₃	1	1	yes	characteristic
646	#127	C₂³×C₁₃	1	2	yes	—
647	#127	C₂³×C₁₃	1	1	yes	characteristic
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#125	—	2	1	no	—
651	#125	—	2	1	no	—
652	#125	C₂³×C₁₃	1	2	yes	—
653	#124	—	2	2	no	—
654	#124	—	2	2	no	—
655	#124	—	2	2	no	—
656	#124	—	2	1	no	—
657	#124	—	2	1	no	—
658	#124	—	2	1	no	—
659	#124	—	2	1	no	—
660	#124	—	2	1	no	—
661	#124	—	2	1	no	—
662	#124	C₂³×C₁₃	1	2	yes	—
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	1	no	—
671	C₂²⋊Q₈	—	2	1	no	—
672	C₂²⋊Q₈	—	2	1	no	—
673	C₂²⋊Q₈	—	2	1	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
677	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
678	#121	—	2	2	no	—
679	#121	—	2	2	no	—
680	#121	—	2	2	no	—
681	#121	—	2	1	no	—
682	#121	—	2	1	no	—
683	#121	—	2	1	no	—
684	#121	—	2	1	no	—
685	#121	—	2	1	no	—
686	#121	—	2	1	no	—
687	#121	—	2	1	no	—
688	#121	—	2	1	no	—
689	#121	—	2	2	no	—
690	#121	—	2	2	no	—
691	#121	—	2	2	no	—
692	#121	—	2	2	no	—
693	#121	C₂³×C₁₃	1	2	yes	—
694	#121	C₂³×C₁₃	1	2	yes	—
695	#121	C₂³×C₁₃	1	2	yes	—
696	#121	C₂³×C₁₃	1	2	yes	—
697	#121	C₂³×C₁₃	1	2	yes	—
698	#121	C₂³×C₁₃	1	2	yes	—
699	#120	—	2	2	no	—
700	#120	—	2	2	no	—
701	C₄×Q₈	—	2	1	no	—
702	C₄×Q₈	—	2	1	no	—
703	C₄×Q₈	—	2	1	no	—
704	C₄×Q₈	—	2	1	no	—
705	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
706	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
707	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
708	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
709	C₄×D₄	—	2	2	no	—
710	C₄×D₄	—	2	2	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	1	no	—
714	C₄×D₄	—	2	1	no	—
715	C₄×D₄	—	2	1	no	—
716	C₄×D₄	—	2	1	no	—
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	—	2	1	no	—
720	C₄×D₄	—	2	1	no	—
721	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
722	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
723	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
724	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
725	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
726	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
727	C₄×D₄	C₂³×C₁₃	1	2	yes	—
728	C₄×D₄	C₂³×C₁₃	1	2	yes	—
729	C₄×D₄	C₂³×C₁₃	1	2	yes	—
730	C₄×D₄	C₂³×C₁₃	1	2	yes	—
731	C₄×D₄	C₂³×C₁₃	1	2	yes	—
732	C₄×D₄	C₂³×C₁₃	1	2	yes	—
733	#117	—	2	1	no	—
734	#117	—	2	1	no	—
735	#117	—	2	2	no	—
736	#117	C₂³×C₁₃	1	2	yes	—
737	#117	C₂³×C₁₃	1	1	yes	characteristic
738	#117	C₂³×C₁₃	1	1	yes	characteristic
739	#117	C₂³×C₁₃	1	1	yes	characteristic
740	C₂×C₄⋊C₄	—	2	1	no	—
741	C₂×C₄⋊C₄	—	2	2	no	—
742	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
743	C₂×C₂²⋊C₄	—	2	2	no	—
744	C₂×C₂²⋊C₄	—	2	2	no	—
745	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
746	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
748	#107	C₂³×C₁₃	1	4	yes	—
749	#107	C₂³×C₁₃	1	4	yes	—
750	#106	C₂³×C₁₃	1	4	yes	—
751	#106	C₂³×C₁₃	1	4	yes	—
752	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
753	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
754	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
755	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
756	#103	C₂³×C₁₃	1	4	yes	—
757	#103	C₂³×C₁₃	1	4	yes	—
758	#102	C₂³×C₁₃	1	4	yes	—
759	#102	C₂³×C₁₃	1	4	yes	—
760	#102	C₂³×C₁₃	1	4	yes	—
761	#102	C₂³×C₁₃	1	4	yes	—
762	#102	C₂³×C₁₃	1	4	yes	—
763	#102	C₂³×C₁₃	1	4	yes	—
764	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
765	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
766	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
768	#97	C₂³×C₁₃	1	2	yes	—
769	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
770	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
771	C₄×C₈	C₂³×C₁₃	1	2	yes	—
772	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
773	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
774	C₂×C₁₃	—	4	1	no	—
775	C₂×C₁₃	—	4	1	no	—
776	C₂×C₁₃	—	4	1	no	—
777	C₂×C₁₃	—	8	2	no	—
778	C₂×C₁₃	—	8	2	no	—
779	C₂×C₁₃	—	8	2	no	—
780	C₂×C₁₃	#3449	1	1	yes	characteristic
781	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
782	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
783	C₂⁴	—	2	2	no	—
784	#41	—	4	2	no	—
785	#41	—	4	4	no	—
786	#41	—	8	2	no	—
787	#41	—	8	2	no	—
788	#41	—	8	2	no	—
789	#41	—	8	2	no	—
790	#41	—	8	2	no	—
791	#41	—	8	2	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	8	2	no	—
798	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
799	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	1	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	4	4	no	—
817	C₂×D₄	—	8	2	no	—
818	C₂×D₄	—	8	2	no	—
819	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
820	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
821	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
822	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
823	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
824	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
834	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
835	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
836	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
837	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
842	SD₁₆	—	4	4	no	—
843	SD₁₆	—	4	4	no	—
844	D₈	—	4	4	no	—
845	D₈	—	4	4	no	—
846	M₁₆	—	4	2	no	—
847	C₂×C₈	—	4	2	no	—
848	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
849	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
850	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
851	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	1	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
867	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
868	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
869	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
870	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
872	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
894	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
895	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
896	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
897	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
898	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
899	C₄²	—	2	2	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
903	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
904	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
905	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
906	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
907	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
908	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
909	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
910	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
911	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
912	C₁₃	#61006	1	1	yes	characteristic, direct product factor, Sylow
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	4	4	no	—
917	C₂³	—	8	2	no	—
918	C₂³	—	8	2	no	—
919	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
920	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
921	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
922	Q₈	—	2	4	no	—
923	Q₈	—	4	1	no	—
924	Q₈	—	4	2	no	—
925	Q₈	—	4	2	no	—
926	Q₈	—	4	2	no	—
927	Q₈	—	4	2	no	—
928	Q₈	—	8	2	no	—
929	D₄	—	2	4	no	—
930	D₄	—	2	4	no	—
931	D₄	—	2	4	no	—
932	D₄	—	4	1	no	—
933	D₄	—	4	1	no	—
934	D₄	—	4	1	no	—
935	D₄	—	4	4	no	—
936	D₄	—	4	4	no	—
937	D₄	—	4	2	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	2	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	2	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	2	no	—
949	D₄	—	8	2	no	—
950	D₄	—	8	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
976	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
977	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
979	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
984	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	1	no	—
993	C₂²	—	2	1	no	—
994	C₂²	—	2	1	no	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	16	4	no	—
1008	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	1	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₄	C₁₃×#576	1	2	yes	—
1024	C₄	C₁₃×#577	1	2	yes	—
1025	C₄	C₁₃×#585	1	2	yes	—
1026	C₂	—	4	1	no	—
1027	C₂	—	4	1	no	—
1028	C₂	—	4	1	no	—
1029	C₂	—	8	2	no	—
1030	C₂	—	8	2	no	—
1031	C₂	—	8	2	no	—
1032	C₂	C₁₃×#3449	1	1	yes	characteristic
1033	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1034	C₂	C₂×C₁₃×#577	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×#3511	C₂	semidirect
2. C₁₃×#3508	C₂	semidirect
3. C₁₃×#3257	C₂	semidirect
4. C₁₃×#3231	C₂	semidirect
5. C₁₃×#3228	C₂	semidirect
6. C₁₃×#3227	C₂	semidirect
7. C₁₃×#3226	C₂	semidirect
8. C₁₃×#3208	C₂	semidirect
9. C₁₃×#3207	C₂	semidirect
10. C₁₃×#3207	C₂	semidirect
11. C₁₃×#3205	C₂	semidirect
12. C₁₃×#3198	C₂	semidirect
13. C₁₃×#3184	C₂	semidirect
14. C₁₃×#3182	C₂	semidirect
15. C₁₃×#3169	C₂	semidirect
16. C₁₃×#3167	C₂	semidirect
17. C₁₃×#3119	C₂	semidirect
18. C₁₃×#3118	C₂	semidirect
19. C₁₃×#2922	C₂	semidirect
37. C₁₃×#542	C₂²	semidirect
44. C₁₃×#533	C₂²	semidirect
50. C₁₃×#532	C₂²	semidirect
51. C₁₃×#532	C₂²	semidirect
52. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
54. C₁₃×#520	C₂²	semidirect
57. C₁₃×#500	C₂²	semidirect
58. C₁₃×#500	C₂²	semidirect
59. C₁₃×#498	C₂²	semidirect
60. C₁₃×#498	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#487	C₂²	semidirect
71. C₁₃×#486	C₂²	semidirect
72. C₁₃×#486	C₂²	semidirect
75. C₁₃×#481	C₂²	semidirect
76. C₁₃×#480	C₂²	semidirect
77. C₁₃×#479	C₂²	semidirect
78. C₁₃×#478	C₂²	semidirect
79. C₁₃×#476	C₂²	semidirect
80. C₁₃×#474	C₂²	semidirect
81. C₁₃×#469	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#466	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#463	C₂²	semidirect
86. C₁₃×#463	C₂²	semidirect
90. C₁₃×#449	C₂²	semidirect
91. C₁₃×#449	C₂²	semidirect
93. C₁₃×#442	C₂²	semidirect
94. C₁₃×#440	C₂²	semidirect
95. C₄×C₁₃×SD₁₆	C₂²	semidirect
96. C₄×C₁₃×D₈	C₂²	semidirect
98. C₁₃×#433	C₂²	semidirect
101. C₁₃×#431	C₂²	semidirect
102. C₁₃×#431	C₂²	semidirect
103. C₁₃×#424	C₂²	semidirect
105. C₄×C₁₃×M₁₆	C₂²	semidirect
106. C₂×C₄×C₈×C₁₃	C₂²	semidirect
266. #61006	C₁₃	direct (N × H)
396. #3511	C₂×C₁₃	semidirect
397. #3508	C₂×C₁₃	semidirect
398. #3257	C₂×C₁₃	semidirect
399. #3231	C₂×C₁₃	semidirect
400. #3228	C₂×C₁₃	semidirect
401. #3227	C₂×C₁₃	semidirect
402. #3226	C₂×C₁₃	semidirect
403. #3208	C₂×C₁₃	semidirect
404. #3207	C₂×C₁₃	semidirect
405. #3207	C₂×C₁₃	semidirect
406. #3205	C₂×C₁₃	semidirect
407. #3198	C₂×C₁₃	semidirect
408. #3184	C₂×C₁₃	semidirect
409. #3182	C₂×C₁₃	semidirect
410. #3169	C₂×C₁₃	semidirect
411. #3167	C₂×C₁₃	semidirect
412. #3119	C₂×C₁₃	semidirect
413. #3118	C₂×C₁₃	semidirect
414. #2922	C₂×C₁₃	semidirect
508. #542	C₂²×C₁₃	semidirect
515. #533	C₂²×C₁₃	semidirect
521. #532	C₂²×C₁₃	semidirect
522. #532	C₂²×C₁₃	semidirect
523. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
525. #520	C₂²×C₁₃	semidirect
528. #500	C₂²×C₁₃	semidirect
529. #500	C₂²×C₁₃	semidirect
530. #498	C₂²×C₁₃	semidirect
531. #498	C₂²×C₁₃	semidirect
536. #487	C₂²×C₁₃	semidirect
537. #487	C₂²×C₁₃	semidirect
542. #486	C₂²×C₁₃	semidirect
543. #486	C₂²×C₁₃	semidirect
546. #481	C₂²×C₁₃	semidirect
547. #480	C₂²×C₁₃	semidirect
548. #479	C₂²×C₁₃	semidirect
549. #478	C₂²×C₁₃	semidirect
550. #476	C₂²×C₁₃	semidirect
551. #474	C₂²×C₁₃	semidirect
552. #469	C₂²×C₁₃	semidirect
553. #468	C₂²×C₁₃	semidirect
554. #466	C₂²×C₁₃	semidirect
555. #465	C₂²×C₁₃	semidirect
556. #463	C₂²×C₁₃	semidirect
557. #463	C₂²×C₁₃	semidirect
561. #449	C₂²×C₁₃	semidirect
562. #449	C₂²×C₁₃	semidirect
564. #442	C₂²×C₁₃	semidirect
565. #440	C₂²×C₁₃	semidirect
566. C₄×SD₁₆	C₂²×C₁₃	semidirect
567. C₄×D₈	C₂²×C₁₃	semidirect
569. #433	C₂²×C₁₃	semidirect
572. #431	C₂²×C₁₃	semidirect
573. #431	C₂²×C₁₃	semidirect
574. #424	C₂²×C₁₃	semidirect
576. C₄×M₁₆	C₂²×C₁₃	semidirect
577. C₂×C₄×C₈	C₂²×C₁₃	semidirect
912. C₁₃	#61006	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×#3511	2
C₁₃×#3508	2
C₁₃×#3257	2
C₁₃×#3231	2
C₁₃×#3228	2
C₁₃×#3227	2
C₁₃×#3226	2
C₁₃×#3208	2
C₁₃×#3207	2
C₁₃×#3205	2
C₁₃×#3198	2
C₁₃×#3184	2
C₁₃×#3182	2
C₁₃×#3169	2
C₁₃×#3167	2
C₁₃×#3119	2
C₁₃×#3118	2
C₁₃×#2922	2
#61006	13

Subgroups — C13×#61006 #15747345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61006 #15747345