Subgroups — C₁₃×#61878 #15748217

Order 3328.

1656 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3384	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3370	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3125	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3124	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic
19	C₁₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	1	no	—
21	C₁₃×#563	—	2	1	no	—
22	C₁₃×#559	C₂²	1	2	yes	—
23	Q₈²×C₁₃	C₂²	1	2	yes	—
24	C₁₃×#557	C₂²	1	2	yes	—
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#556	—	2	1	no	—
27	C₁₃×#556	C₂²	1	2	yes	—
28	C₁₃×#554	—	2	2	no	—
29	C₁₃×#554	—	2	2	no	—
30	C₁₃×#554	C₂²	1	2	yes	—
31	C₁₃×#554	C₂²	1	2	yes	—
32	D₄×Q₈×C₁₃	—	2	1	no	—
33	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₁₃×#544	—	2	1	no	—
35	C₁₃×#544	—	2	1	no	—
36	C₁₃×#544	C₂²	1	1	yes	characteristic
37	C₁₃×#544	C₂²	1	1	yes	characteristic
38	C₁₃×#542	—	2	2	no	—
39	C₁₃×#542	C₂²	1	2	yes	—
40	C₁₃×#542	C₂²	1	2	yes	—
41	C₁₃×#536	—	2	2	no	—
42	C₁₃×#533	—	2	1	no	—
43	C₁₃×#533	C₂²	1	1	yes	characteristic
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#532	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#125	—	2	1	no	—
47	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
48	C₁₃×#520	C₂²	1	1	yes	characteristic
49	C₁₃×#520	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	2	yes	—
52	C₁₃×#501	C₂²	1	2	yes	—
53	C₁₃×#501	C₂²	1	2	yes	—
54	C₁₃×#501	C₂²	1	2	yes	—
55	C₁₃×#500	C₂²	1	2	yes	—
56	C₁₃×#498	C₂²	1	2	yes	—
57	C₁₃×#491	C₂²	1	2	yes	—
58	C₁₃×#490	C₂²	1	2	yes	—
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#489	C₂²	1	2	yes	—
61	C₁₃×#488	C₂²	1	2	yes	—
62	C₁₃×#488	C₂²	1	2	yes	—
63	C₁₃×#485	C₂²	1	2	yes	—
64	C₁₃×#484	C₂²	1	2	yes	—
65	C₁₃×#483	C₂²	1	2	yes	—
66	C₁₃×#482	C₂²	1	2	yes	—
67	C₁₃×#481	C₂²	1	2	yes	—
68	C₁₃×#480	C₂²	1	2	yes	—
69	C₁₃×#479	C₂²	1	2	yes	—
70	C₁₃×#479	C₂²	1	2	yes	—
71	C₁₃×#479	C₂²	1	2	yes	—
72	C₁₃×#479	C₂²	1	2	yes	—
73	C₁₃×#478	C₂²	1	2	yes	—
74	C₁₃×#478	C₂²	1	2	yes	—
75	C₁₃×#478	C₂²	1	2	yes	—
76	C₁₃×#478	C₂²	1	2	yes	—
77	C₁₃×#477	C₂²	1	1	yes	characteristic
78	C₁₃×#477	C₂²	1	2	yes	—
79	C₁₃×#477	C₂²	1	2	yes	—
80	C₁₃×#476	C₂²	1	2	yes	—
81	C₁₃×#476	C₂²	1	1	yes	characteristic
82	C₁₃×#476	C₂²	1	2	yes	—
83	C₁₃×#475	C₂²	1	1	yes	characteristic
84	C₁₃×#475	C₂²	1	2	yes	—
85	C₁₃×#475	C₂²	1	2	yes	—
86	C₁₃×#474	C₂²	1	2	yes	—
87	C₁₃×#474	C₂²	1	1	yes	characteristic
88	C₁₃×#474	C₂²	1	2	yes	—
89	C₁₃×#464	C₂²	1	2	yes	—
90	C₁₃×#464	C₂²	1	2	yes	—
91	C₁₃×#463	C₂²	1	2	yes	—
92	C₁₃×#463	C₂²	1	2	yes	—
93	C₁₃×#462	C₂²	1	1	yes	characteristic
94	C₁₃×#461	C₂²	1	1	yes	characteristic
95	C₁₃×#460	C₂²	1	1	yes	characteristic
96	C₁₃×#459	C₂²	1	1	yes	characteristic
97	C₁₃×#452	C₂²	1	2	yes	—
98	C₁₃×#449	C₂²	1	2	yes	—
99	C₁₃×#446	C₂²	1	2	yes	—
100	C₁₃×#446	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	2	yes	—
102	C₁₃×#446	C₂²	1	2	yes	—
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#442	C₂²	1	2	yes	—
105	C₁₃×#441	C₂²	1	2	yes	—
106	C₁₃×#441	C₂²	1	2	yes	—
107	C₁₃×#440	C₂²	1	2	yes	—
108	C₁₃×#440	C₂²	1	2	yes	—
109	C₁₃×#440	C₂²	1	2	yes	—
110	C₁₃×#440	C₂²	1	2	yes	—
111	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
112	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
114	C₄×C₁₃×D₈	C₂²	1	2	yes	—
115	C₁₃×#433	C₂²	1	2	yes	—
116	C₁₃×#433	C₂²	1	2	yes	—
117	C₁₃×#432	C₂²	1	1	yes	characteristic
118	C₁₃×#432	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	1	no	—
120	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₁₃	—	2	2	no	—
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×D₈	C₂³	1	2	yes	—
126	C₁₃×C₄⋊Q₈	—	2	2	no	—
127	C₁₃×C₄⋊Q₈	—	2	2	no	—
128	C₁₃×C₄⋊Q₈	—	2	1	no	—
129	C₁₃×C₄⋊Q₈	—	2	1	no	—
130	C₁₃×C₄⋊Q₈	—	2	2	no	—
131	C₁₃×C₄⋊Q₈	—	2	2	no	—
132	C₁₃×C₄⋊Q₈	—	2	2	no	—
133	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
134	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₁₃×#127	C₂³	1	1	yes	characteristic
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#126	—	2	2	no	—
147	C₁₃×#125	—	2	1	no	—
148	C₁₃×#125	—	2	1	no	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	2	no	—
152	C₁₃×#125	—	2	2	no	—
153	C₁₃×#125	—	2	1	no	—
154	C₁₃×#125	—	2	1	no	—
155	C₁₃×#125	—	2	1	no	—
156	C₁₃×#125	D₄	1	1	yes	characteristic
157	C₁₃×#125	D₄	1	1	yes	characteristic
158	C₁₃×#125	C₂³	1	2	yes	—
159	C₁₃×#125	C₂³	1	2	yes	—
160	C₁₃×#125	C₂³	1	2	yes	—
161	C₁₃×#125	C₂³	1	2	yes	—
162	C₁₃×#124	—	2	2	no	—
163	C₁₃×#124	—	2	2	no	—
164	C₁₃×#124	—	2	2	no	—
165	C₁₃×#124	—	2	1	no	—
166	C₁₃×#124	C₂³	1	2	yes	—
167	C₁₃×#124	C₂³	1	2	yes	—
168	C₁₃×#123	—	2	2	no	—
169	C₁₃×#123	—	2	2	no	—
170	C₁₃×#123	—	2	2	no	—
171	C₁₃×#123	—	2	2	no	—
172	C₁₃×C₂²⋊Q₈	—	2	2	no	—
173	C₁₃×C₂²⋊Q₈	—	2	2	no	—
174	C₁₃×C₂²⋊Q₈	—	2	2	no	—
175	C₁₃×C₂²⋊Q₈	—	2	1	no	—
176	C₁₃×C₂²⋊Q₈	—	2	2	no	—
177	C₁₃×C₂²⋊Q₈	—	2	2	no	—
178	C₁₃×C₂²⋊Q₈	—	2	2	no	—
179	C₁₃×C₂²⋊Q₈	—	2	2	no	—
180	C₁₃×C₂²⋊Q₈	—	2	2	no	—
181	C₁₃×C₂²⋊Q₈	—	2	2	no	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
188	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₁₃×#121	—	2	1	no	—
191	C₁₃×#121	C₂³	1	2	yes	—
192	C₄×Q₈×C₁₃	—	2	2	no	—
193	C₄×Q₈×C₁₃	—	2	2	no	—
194	C₄×Q₈×C₁₃	—	2	2	no	—
195	C₄×Q₈×C₁₃	—	2	1	no	—
196	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
197	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
198	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
199	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
200	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
202	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
204	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
205	C₄×D₄×C₁₃	—	2	1	no	—
206	C₄×D₄×C₁₃	—	2	1	no	—
207	C₄×D₄×C₁₃	—	2	2	no	—
208	C₄×D₄×C₁₃	—	2	2	no	—
209	C₄×D₄×C₁₃	—	2	2	no	—
210	C₄×D₄×C₁₃	—	2	1	no	—
211	C₄×D₄×C₁₃	C₂³	1	2	yes	—
212	C₄×D₄×C₁₃	C₂³	1	2	yes	—
213	C₄×D₄×C₁₃	C₂³	1	2	yes	—
214	C₄×D₄×C₁₃	C₂³	1	2	yes	—
215	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₁₃	C₂³	1	2	yes	—
217	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
218	C₁₃×#117	—	2	1	no	—
219	C₁₃×#117	—	2	1	no	—
220	C₁₃×#117	—	2	1	no	—
221	C₁₃×#117	—	2	2	no	—
222	C₁₃×#117	—	2	1	no	—
223	C₁₃×#117	C₂³	1	1	yes	characteristic
224	C₁₃×#117	C₂³	1	1	yes	characteristic
225	C₁₃×#117	C₂³	1	1	yes	characteristic
226	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
232	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃	—	2	1	no	—
235	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
236	C₁₃×#107	C₂³	1	2	yes	—
237	C₁₃×#107	C₂³	1	2	yes	—
238	C₁₃×#107	C₂³	1	2	yes	—
239	C₁₃×#107	C₂³	1	2	yes	—
240	C₁₃×#107	C₂³	1	2	yes	—
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#106	C₂³	1	2	yes	—
243	C₁₃×#106	C₂³	1	2	yes	—
244	C₁₃×#106	C₂³	1	2	yes	—
245	C₁₃×#106	C₂³	1	2	yes	—
246	C₁₃×#106	C₂³	1	2	yes	—
247	C₁₃×#106	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
255	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₁₃×#103	C₂³	1	2	yes	—
257	C₁₃×#103	C₂³	1	2	yes	—
258	C₁₃×#103	C₂³	1	2	yes	—
259	C₁₃×#103	C₂³	1	2	yes	—
260	C₁₃×#103	C₂³	1	2	yes	—
261	C₁₃×#103	C₂³	1	2	yes	—
262	C₁₃×#103	C₂³	1	2	yes	—
263	C₁₃×#103	C₂³	1	2	yes	—
264	C₁₃×#102	C₂³	1	2	yes	—
265	C₁₃×#102	C₂³	1	2	yes	—
266	C₁₃×#102	C₂³	1	2	yes	—
267	C₁₃×#102	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×#102	C₂³	1	2	yes	—
271	C₁₃×#102	C₂³	1	2	yes	—
272	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₁₃×#97	C₂³	1	2	yes	—
275	C₁₃×#97	C₂³	1	2	yes	—
276	C₁₃×#97	C₂³	1	2	yes	—
277	C₁₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₁₃	C₂³	1	2	yes	—
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#61878	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₁₃×#41	—	2	2	no	—
282	C₁₃×#41	—	2	2	no	—
283	C₁₃×#41	—	8	2	no	—
284	C₂×Q₈×C₁₃	—	2	1	no	—
285	C₂×Q₈×C₁₃	—	2	2	no	—
286	C₂×Q₈×C₁₃	—	2	2	no	—
287	C₂×Q₈×C₁₃	—	2	2	no	—
288	C₂×Q₈×C₁₃	—	2	2	no	—
289	C₂×Q₈×C₁₃	—	2	1	no	—
290	C₂×Q₈×C₁₃	—	8	4	no	—
291	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
292	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
293	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₁₃	—	2	1	no	—
296	C₂×D₄×C₁₃	—	2	2	no	—
297	C₂×D₄×C₁₃	—	2	1	no	—
298	C₂×D₄×C₁₃	—	2	1	no	—
299	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
300	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	—	2	1	no	—
302	C₂²×C₄×C₁₃	—	2	1	no	—
303	C₂²×C₄×C₁₃	—	2	1	no	—
304	C₂²×C₄×C₁₃	—	2	2	no	—
305	C₂²×C₄×C₁₃	—	2	1	no	—
306	C₂²×C₄×C₁₃	—	2	1	no	—
307	C₂²×C₄×C₁₃	—	2	2	no	—
308	C₂²×C₄×C₁₃	—	2	2	no	—
309	C₂²×C₄×C₁₃	—	2	2	no	—
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₁₃×Q₁₆	—	2	4	no	—
315	C₁₃×SD₁₆	—	2	4	no	—
316	C₁₃×SD₁₆	—	2	4	no	—
317	C₁₃×D₈	—	2	4	no	—
318	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
320	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
321	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	1	no	—
325	C₁₃×C₄⋊C₄	—	2	1	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	1	no	—
335	C₁₃×C₄⋊C₄	—	2	1	no	—
336	C₁₃×C₄⋊C₄	—	2	1	no	—
337	C₁₃×C₄⋊C₄	—	2	1	no	—
338	C₁₃×C₄⋊C₄	—	2	1	no	—
339	C₁₃×C₄⋊C₄	—	2	1	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	—	2	2	no	—
345	C₁₃×C₄⋊C₄	—	2	2	no	—
346	C₁₃×C₄⋊C₄	—	2	2	no	—
347	C₁₃×C₄⋊C₄	—	2	2	no	—
348	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
349	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
350	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
351	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	2	yes	—
355	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
356	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
357	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
358	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
359	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
360	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
362	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₁₃×C₂²⋊C₄	—	2	2	no	—
365	C₁₃×C₂²⋊C₄	—	2	1	no	—
366	C₁₃×C₂²⋊C₄	—	2	1	no	—
367	C₁₃×C₂²⋊C₄	—	2	1	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	—	2	2	no	—
378	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
379	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
380	C₄²×C₁₃	—	2	1	no	—
381	C₄²×C₁₃	—	2	1	no	—
382	C₄²×C₁₃	—	2	1	no	—
383	C₄²×C₁₃	—	2	2	no	—
384	C₄²×C₁₃	—	2	2	no	—
385	C₄²×C₁₃	—	2	2	no	—
386	C₄²×C₁₃	—	2	2	no	—
387	C₄²×C₁₃	—	2	2	no	—
388	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₁₃	C₂⁴	1	2	yes	—
391	C₄²×C₁₃	C₂⁴	1	2	yes	—
392	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
394	#3550	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
396	#3387	C₂×C₁₃	1	2	yes	complemented
397	#3386	C₂×C₁₃	1	2	yes	complemented
398	#3385	C₂×C₁₃	1	2	yes	complemented
399	#3384	C₂×C₁₃	1	2	yes	complemented
400	#3377	C₂×C₁₃	1	2	yes	complemented
401	#3376	C₂×C₁₃	1	2	yes	complemented
402	#3371	C₂×C₁₃	1	2	yes	complemented
403	#3370	C₂×C₁₃	1	2	yes	complemented
404	#3244	C₂×C₁₃	1	2	yes	complemented
405	#3243	C₂×C₁₃	1	2	yes	complemented
406	#3236	C₂×C₁₃	1	1	yes	characteristic, complemented
407	#3234	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3125	C₂×C₁₃	1	2	yes	complemented
409	#3124	C₂×C₁₃	1	2	yes	complemented
410	#3116	C₂×C₁₃	1	1	yes	characteristic, complemented
411	#3115	C₂×C₁₃	1	1	yes	characteristic
412	#2987	C₂×C₁₃	1	1	yes	characteristic, complemented
413	C₂³×C₁₃	—	2	1	no	—
414	C₂³×C₁₃	—	2	2	no	—
415	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	Q₈×C₁₃	—	2	1	no	—
417	Q₈×C₁₃	—	2	2	no	—
418	Q₈×C₁₃	—	2	2	no	—
419	Q₈×C₁₃	—	4	2	no	—
420	Q₈×C₁₃	—	4	2	no	—
421	Q₈×C₁₃	—	4	2	no	—
422	Q₈×C₁₃	—	8	2	no	—
423	Q₈×C₁₃	—	8	2	no	—
424	Q₈×C₁₃	—	8	2	no	—
425	Q₈×C₁₃	—	8	2	no	—
426	Q₈×C₁₃	—	8	1	no	—
427	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
428	D₄×C₁₃	—	2	4	no	—
429	D₄×C₁₃	—	2	1	no	—
430	D₄×C₁₃	—	2	2	no	—
431	D₄×C₁₃	—	2	2	no	—
432	D₄×C₁₃	—	4	2	no	—
433	D₄×C₁₃	—	8	1	no	—
434	D₄×C₁₃	—	8	2	no	—
435	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
436	C₂×C₄×C₁₃	—	2	4	no	—
437	C₂×C₄×C₁₃	—	2	1	no	—
438	C₂×C₄×C₁₃	—	2	1	no	—
439	C₂×C₄×C₁₃	—	2	1	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	1	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	4	1	no	—
448	C₂×C₄×C₁₃	—	4	1	no	—
449	C₂×C₄×C₁₃	—	4	4	no	—
450	C₂×C₄×C₁₃	—	8	1	no	—
451	C₂×C₄×C₁₃	—	8	2	no	—
452	C₂×C₄×C₁₃	—	8	1	no	—
453	C₂×C₄×C₁₃	—	8	2	no	—
454	C₂×C₄×C₁₃	—	8	2	no	—
455	C₂×C₄×C₁₃	—	8	2	no	—
456	C₂×C₄×C₁₃	—	8	1	no	—
457	C₂×C₄×C₁₃	—	8	1	no	—
458	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
468	C₈×C₁₃	—	2	2	no	—
469	C₈×C₁₃	—	2	2	no	—
470	C₈×C₁₃	—	2	2	no	—
471	C₈×C₁₃	—	2	2	no	—
472	#563	—	2	1	no	—
473	#563	—	2	1	no	—
474	#559	C₂²×C₁₃	1	2	yes	—
475	Q₈²	C₂²×C₁₃	1	2	yes	—
476	#557	C₂²×C₁₃	1	2	yes	—
477	#557	C₂²×C₁₃	1	2	yes	—
478	#556	—	2	1	no	—
479	#556	C₂²×C₁₃	1	2	yes	—
480	#554	—	2	2	no	—
481	#554	—	2	2	no	—
482	#554	C₂²×C₁₃	1	2	yes	—
483	#554	C₂²×C₁₃	1	2	yes	—
484	D₄×Q₈	—	2	1	no	—
485	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
486	#544	—	2	1	no	—
487	#544	—	2	1	no	—
488	#544	C₂²×C₁₃	1	1	yes	characteristic
489	#544	C₂²×C₁₃	1	1	yes	characteristic
490	#542	—	2	2	no	—
491	#542	C₂²×C₁₃	1	2	yes	—
492	#542	C₂²×C₁₃	1	2	yes	—
493	#536	—	2	2	no	—
494	#533	—	2	1	no	—
495	#533	C₂²×C₁₃	1	1	yes	characteristic
496	#533	C₂²×C₁₃	1	1	yes	characteristic
497	#532	C₂²×C₁₃	1	1	yes	characteristic
498	C₂×#125	—	2	1	no	—
499	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
500	#520	C₂²×C₁₃	1	1	yes	characteristic
501	#520	C₂²×C₁₃	1	1	yes	characteristic
502	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
503	#501	C₂²×C₁₃	1	2	yes	—
504	#501	C₂²×C₁₃	1	2	yes	—
505	#501	C₂²×C₁₃	1	2	yes	—
506	#501	C₂²×C₁₃	1	2	yes	—
507	#500	C₂²×C₁₃	1	2	yes	—
508	#498	C₂²×C₁₃	1	2	yes	—
509	#491	C₂²×C₁₃	1	2	yes	—
510	#490	C₂²×C₁₃	1	2	yes	—
511	#489	C₂²×C₁₃	1	2	yes	—
512	#489	C₂²×C₁₃	1	2	yes	—
513	#488	C₂²×C₁₃	1	2	yes	—
514	#488	C₂²×C₁₃	1	2	yes	—
515	#485	C₂²×C₁₃	1	2	yes	—
516	#484	C₂²×C₁₃	1	2	yes	—
517	#483	C₂²×C₁₃	1	2	yes	—
518	#482	C₂²×C₁₃	1	2	yes	—
519	#481	C₂²×C₁₃	1	2	yes	—
520	#480	C₂²×C₁₃	1	2	yes	—
521	#479	C₂²×C₁₃	1	2	yes	—
522	#479	C₂²×C₁₃	1	2	yes	—
523	#479	C₂²×C₁₃	1	2	yes	—
524	#479	C₂²×C₁₃	1	2	yes	—
525	#478	C₂²×C₁₃	1	2	yes	—
526	#478	C₂²×C₁₃	1	2	yes	—
527	#478	C₂²×C₁₃	1	2	yes	—
528	#478	C₂²×C₁₃	1	2	yes	—
529	#477	C₂²×C₁₃	1	1	yes	characteristic
530	#477	C₂²×C₁₃	1	2	yes	—
531	#477	C₂²×C₁₃	1	2	yes	—
532	#476	C₂²×C₁₃	1	2	yes	—
533	#476	C₂²×C₁₃	1	1	yes	characteristic
534	#476	C₂²×C₁₃	1	2	yes	—
535	#475	C₂²×C₁₃	1	1	yes	characteristic
536	#475	C₂²×C₁₃	1	2	yes	—
537	#475	C₂²×C₁₃	1	2	yes	—
538	#474	C₂²×C₁₃	1	2	yes	—
539	#474	C₂²×C₁₃	1	1	yes	characteristic
540	#474	C₂²×C₁₃	1	2	yes	—
541	#464	C₂²×C₁₃	1	2	yes	—
542	#464	C₂²×C₁₃	1	2	yes	—
543	#463	C₂²×C₁₃	1	2	yes	—
544	#463	C₂²×C₁₃	1	2	yes	—
545	#462	C₂²×C₁₃	1	1	yes	characteristic
546	#461	C₂²×C₁₃	1	1	yes	characteristic
547	#460	C₂²×C₁₃	1	1	yes	characteristic
548	#459	C₂²×C₁₃	1	1	yes	characteristic
549	#452	C₂²×C₁₃	1	2	yes	—
550	#449	C₂²×C₁₃	1	2	yes	—
551	#446	C₂²×C₁₃	1	2	yes	—
552	#446	C₂²×C₁₃	1	2	yes	—
553	#446	C₂²×C₁₃	1	2	yes	—
554	#446	C₂²×C₁₃	1	2	yes	—
555	#442	C₂²×C₁₃	1	2	yes	—
556	#442	C₂²×C₁₃	1	2	yes	—
557	#441	C₂²×C₁₃	1	2	yes	—
558	#441	C₂²×C₁₃	1	2	yes	—
559	#440	C₂²×C₁₃	1	2	yes	—
560	#440	C₂²×C₁₃	1	2	yes	—
561	#440	C₂²×C₁₃	1	2	yes	—
562	#440	C₂²×C₁₃	1	2	yes	—
563	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
564	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
565	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
566	C₄×D₈	C₂²×C₁₃	1	2	yes	—
567	#433	C₂²×C₁₃	1	2	yes	—
568	#433	C₂²×C₁₃	1	2	yes	—
569	#432	C₂²×C₁₃	1	1	yes	characteristic
570	#432	C₂²×C₁₃	1	1	yes	characteristic
571	C₂²×C₁₃	—	2	1	no	—
572	C₂²×C₁₃	—	2	1	no	—
573	C₂²×C₁₃	—	2	1	no	—
574	C₂²×C₁₃	—	2	2	no	—
575	C₂²×C₁₃	—	4	1	no	—
576	C₂²×C₁₃	—	4	1	no	—
577	C₂²×C₁₃	—	4	2	no	—
578	C₂²×C₁₃	—	4	2	no	—
579	C₂²×C₁₃	—	4	2	no	—
580	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
581	C₄×C₁₃	—	2	1	no	—
582	C₄×C₁₃	—	2	1	no	—
583	C₄×C₁₃	—	2	2	no	—
584	C₄×C₁₃	—	2	2	no	—
585	C₄×C₁₃	—	2	1	no	—
586	C₄×C₁₃	—	2	1	no	—
587	C₄×C₁₃	—	2	2	no	—
588	C₄×C₁₃	—	2	2	no	—
589	C₄×C₁₃	—	2	1	no	—
590	C₄×C₁₃	—	2	2	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	2	no	—
593	C₄×C₁₃	—	4	2	no	—
594	C₄×C₁₃	—	4	1	no	—
595	C₄×C₁₃	—	4	2	no	—
596	C₄×C₁₃	—	4	1	no	—
597	C₄×C₁₃	—	4	2	no	—
598	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
599	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
600	C₂×#41	—	2	1	no	—
601	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
602	C₂²×Q₈	—	2	2	no	—
603	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
604	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
605	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
606	C₂×D₈	C₂³×C₁₃	1	2	yes	—
607	C₄⋊Q₈	—	2	2	no	—
608	C₄⋊Q₈	—	2	2	no	—
609	C₄⋊Q₈	—	2	1	no	—
610	C₄⋊Q₈	—	2	1	no	—
611	C₄⋊Q₈	—	2	2	no	—
612	C₄⋊Q₈	—	2	2	no	—
613	C₄⋊Q₈	—	2	2	no	—
614	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
615	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
616	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
617	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
618	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
619	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
620	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
621	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
622	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
623	#127	C₂³×C₁₃	1	1	yes	characteristic
624	#126	—	2	2	no	—
625	#126	—	2	2	no	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#125	—	2	1	no	—
629	#125	—	2	1	no	—
630	#125	—	2	2	no	—
631	#125	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	—	2	1	no	—
635	#125	—	2	1	no	—
636	#125	—	2	1	no	—
637	#125	D₄×C₁₃	1	1	yes	characteristic
638	#125	D₄×C₁₃	1	1	yes	characteristic
639	#125	C₂³×C₁₃	1	2	yes	—
640	#125	C₂³×C₁₃	1	2	yes	—
641	#125	C₂³×C₁₃	1	2	yes	—
642	#125	C₂³×C₁₃	1	2	yes	—
643	#124	—	2	2	no	—
644	#124	—	2	2	no	—
645	#124	—	2	2	no	—
646	#124	—	2	1	no	—
647	#124	C₂³×C₁₃	1	2	yes	—
648	#124	C₂³×C₁₃	1	2	yes	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	2	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
669	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
670	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
671	#121	—	2	1	no	—
672	#121	C₂³×C₁₃	1	2	yes	—
673	C₄×Q₈	—	2	2	no	—
674	C₄×Q₈	—	2	2	no	—
675	C₄×Q₈	—	2	2	no	—
676	C₄×Q₈	—	2	1	no	—
677	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
678	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
679	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
680	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
681	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
682	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
683	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
684	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
685	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
686	C₄×D₄	—	2	1	no	—
687	C₄×D₄	—	2	1	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	1	no	—
692	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
693	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
694	C₄×D₄	C₂³×C₁₃	1	2	yes	—
695	C₄×D₄	C₂³×C₁₃	1	2	yes	—
696	C₄×D₄	C₂³×C₁₃	1	2	yes	—
697	C₄×D₄	C₂³×C₁₃	1	2	yes	—
698	C₄×D₄	C₂³×C₁₃	1	2	yes	—
699	#117	—	2	1	no	—
700	#117	—	2	1	no	—
701	#117	—	2	1	no	—
702	#117	—	2	2	no	—
703	#117	—	2	1	no	—
704	#117	C₂³×C₁₃	1	1	yes	characteristic
705	#117	C₂³×C₁₃	1	1	yes	characteristic
706	#117	C₂³×C₁₃	1	1	yes	characteristic
707	C₂×C₄⋊C₄	—	2	1	no	—
708	C₂×C₄⋊C₄	—	2	1	no	—
709	C₂×C₄⋊C₄	—	2	1	no	—
710	C₂×C₄⋊C₄	—	2	1	no	—
711	C₂×C₄⋊C₄	—	2	2	no	—
712	C₂×C₄⋊C₄	—	2	2	no	—
713	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×C₄²	—	2	1	no	—
716	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
717	#107	C₂³×C₁₃	1	2	yes	—
718	#107	C₂³×C₁₃	1	2	yes	—
719	#107	C₂³×C₁₃	1	2	yes	—
720	#107	C₂³×C₁₃	1	2	yes	—
721	#107	C₂³×C₁₃	1	2	yes	—
722	#107	C₂³×C₁₃	1	2	yes	—
723	#106	C₂³×C₁₃	1	2	yes	—
724	#106	C₂³×C₁₃	1	2	yes	—
725	#106	C₂³×C₁₃	1	2	yes	—
726	#106	C₂³×C₁₃	1	2	yes	—
727	#106	C₂³×C₁₃	1	2	yes	—
728	#106	C₂³×C₁₃	1	2	yes	—
729	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
730	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
731	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
732	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
733	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
734	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
735	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
736	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
737	#103	C₂³×C₁₃	1	2	yes	—
738	#103	C₂³×C₁₃	1	2	yes	—
739	#103	C₂³×C₁₃	1	2	yes	—
740	#103	C₂³×C₁₃	1	2	yes	—
741	#103	C₂³×C₁₃	1	2	yes	—
742	#103	C₂³×C₁₃	1	2	yes	—
743	#103	C₂³×C₁₃	1	2	yes	—
744	#103	C₂³×C₁₃	1	2	yes	—
745	#102	C₂³×C₁₃	1	2	yes	—
746	#102	C₂³×C₁₃	1	2	yes	—
747	#102	C₂³×C₁₃	1	2	yes	—
748	#102	C₂³×C₁₃	1	2	yes	—
749	#102	C₂³×C₁₃	1	2	yes	—
750	#102	C₂³×C₁₃	1	2	yes	—
751	#102	C₂³×C₁₃	1	2	yes	—
752	#102	C₂³×C₁₃	1	2	yes	—
753	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
754	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
755	#97	C₂³×C₁₃	1	2	yes	—
756	#97	C₂³×C₁₃	1	2	yes	—
757	#97	C₂³×C₁₃	1	2	yes	—
758	#97	C₂³×C₁₃	1	2	yes	—
759	C₄×C₈	C₂³×C₁₃	1	2	yes	—
760	C₄×C₈	C₂³×C₁₃	1	2	yes	—
761	C₂×C₁₃	—	4	1	no	—
762	C₂×C₁₃	—	4	2	no	—
763	C₂×C₁₃	—	8	2	no	—
764	C₂×C₁₃	#3486	1	1	yes	characteristic
765	C₂×C₁₃	#3585	1	1	yes	characteristic
766	C₂×C₁₃	#3586	1	1	yes	characteristic
767	#41	—	2	2	no	—
768	#41	—	2	2	no	—
769	#41	—	8	2	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	8	4	no	—
777	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
778	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
779	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
780	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
786	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	—	2	1	no	—
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
800	Q₁₆	—	2	4	no	—
801	SD₁₆	—	2	4	no	—
802	SD₁₆	—	2	4	no	—
803	D₈	—	2	4	no	—
804	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
805	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
806	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
807	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
835	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
837	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
838	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
839	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
840	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
841	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
842	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
843	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
844	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
846	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
847	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
848	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
849	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	1	no	—
852	C₂²⋊C₄	—	2	1	no	—
853	C₂²⋊C₄	—	2	1	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
865	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
866	C₄²	—	2	1	no	—
867	C₄²	—	2	1	no	—
868	C₄²	—	2	1	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
875	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
876	C₄²	C₂⁴×C₁₃	1	2	yes	—
877	C₄²	C₂⁴×C₁₃	1	2	yes	—
878	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
879	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
880	C₁₃	#61878	1	1	yes	characteristic, direct product factor, Sylow
881	C₂³	—	2	1	no	—
882	C₂³	—	2	2	no	—
883	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
884	Q₈	—	2	1	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	2	2	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	4	2	no	—
890	Q₈	—	8	2	no	—
891	Q₈	—	8	2	no	—
892	Q₈	—	8	1	no	—
893	Q₈	—	8	2	no	—
894	Q₈	—	8	2	no	—
895	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
896	D₄	—	2	4	no	—
897	D₄	—	2	1	no	—
898	D₄	—	2	2	no	—
899	D₄	—	2	2	no	—
900	D₄	—	4	2	no	—
901	D₄	—	8	1	no	—
902	D₄	—	8	2	no	—
903	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	8	1	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	1	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	—	8	1	no	—
925	C₂×C₄	—	8	1	no	—
926	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
928	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
933	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
935	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
936	C₈	—	2	2	no	—
937	C₈	—	2	2	no	—
938	C₈	—	2	2	no	—
939	C₈	—	2	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	2	no	—
967	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
968	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
969	C₂	—	4	1	no	—
970	C₂	—	4	2	no	—
971	C₂	—	8	2	no	—
972	C₂	C₁₃×#3486	1	1	yes	characteristic
973	C₂	C₁₃×#3585	1	1	yes	characteristic
974	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3115	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3550	C₂	semidirect
2. C₁₃×#3504	C₂	semidirect
3. C₁₃×#3387	C₂	semidirect
4. C₁₃×#3386	C₂	semidirect
5. C₁₃×#3385	C₂	semidirect
6. C₁₃×#3384	C₂	semidirect
7. C₁₃×#3377	C₂	semidirect
8. C₁₃×#3376	C₂	semidirect
9. C₁₃×#3371	C₂	semidirect
10. C₁₃×#3370	C₂	semidirect
11. C₁₃×#3244	C₂	semidirect
12. C₁₃×#3243	C₂	semidirect
13. C₁₃×#3236	C₂	semidirect
14. C₁₃×#3234	C₂	semidirect
15. C₁₃×#3125	C₂	semidirect
16. C₁₃×#3124	C₂	semidirect
17. C₁₃×#3116	C₂	semidirect
19. C₁₃×#2987	C₂	semidirect
280. #61878	C₁₃	direct (N × H)
394. #3550	C₂×C₁₃	semidirect
395. #3504	C₂×C₁₃	semidirect
396. #3387	C₂×C₁₃	semidirect
397. #3386	C₂×C₁₃	semidirect
398. #3385	C₂×C₁₃	semidirect
399. #3384	C₂×C₁₃	semidirect
400. #3377	C₂×C₁₃	semidirect
401. #3376	C₂×C₁₃	semidirect
402. #3371	C₂×C₁₃	semidirect
403. #3370	C₂×C₁₃	semidirect
404. #3244	C₂×C₁₃	semidirect
405. #3243	C₂×C₁₃	semidirect
406. #3236	C₂×C₁₃	semidirect
407. #3234	C₂×C₁₃	semidirect
408. #3125	C₂×C₁₃	semidirect
409. #3124	C₂×C₁₃	semidirect
410. #3116	C₂×C₁₃	semidirect
412. #2987	C₂×C₁₃	semidirect
880. C₁₃	#61878	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×#3550	2
C₁₃×#3504	2
C₁₃×#3387	2
C₁₃×#3386	2
C₁₃×#3385	2
C₁₃×#3384	2
C₁₃×#3377	2
C₁₃×#3376	2
C₁₃×#3371	2
C₁₃×#3370	2
C₁₃×#3244	2
C₁₃×#3243	2
C₁₃×#3236	2
C₁₃×#3234	2
C₁₃×#3125	2
C₁₃×#3124	2
C₁₃×#3116	2
C₁₃×#3115	2
C₁₃×#2987	2
#61878	13

Subgroups — C13×#61878 #15748217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61878 #15748217