Subgroups — C₁₃×#61010 #15747349

Order 3328.

1700 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3258	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3257	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3233	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3232	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3212	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3201	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3198	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3183	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3168	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3127	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3126	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×#3123	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3122	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#559	—	2	2	no	—
21	C₁₃×#556	—	2	2	no	—
22	C₁₃×#553	—	2	2	no	—
23	C₁₃×#553	—	2	2	no	—
24	C₁₃×#553	—	2	2	no	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#551	—	2	2	no	—
27	C₁₃×#551	—	2	2	no	—
28	C₁₃×#542	C₂²	1	2	yes	—
29	C₁₃×#542	C₂²	1	2	yes	—
30	C₁₃×#541	C₂²	1	1	yes	characteristic
31	C₁₃×#541	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#540	C₂²	1	1	yes	characteristic
33	C₁₃×#540	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#537	C₂²	1	2	yes	—
35	C₁₃×#536	C₂²	1	1	yes	characteristic
36	C₁₃×#535	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#529	C₂²	1	2	yes	—
40	C₁₃×#529	C₂²	1	2	yes	—
41	C₁₃×#529	C₂²	1	2	yes	—
42	C₁₃×#529	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
45	C₁₃×#520	C₂²	1	2	yes	complemented
46	C₁₃×#519	C₂²	1	1	yes	characteristic
47	C₁₃×#518	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₁₃×#499	C₂²	1	2	yes	complemented
50	C₁₃×#499	C₂²	1	2	yes	complemented
51	C₁₃×#495	C₂²	1	2	yes	—
52	C₁₃×#495	C₂²	1	2	yes	—
53	C₁₃×#488	C₂²	1	2	yes	—
54	C₁₃×#488	C₂²	1	2	yes	—
55	C₁₃×#488	C₂²	1	2	yes	complemented
56	C₁₃×#488	C₂²	1	2	yes	complemented
57	C₁₃×#485	C₂²	1	2	yes	—
58	C₁₃×#485	C₂²	1	2	yes	—
59	C₁₃×#484	C₂²	1	2	yes	complemented
60	C₁₃×#483	C₂²	1	2	yes	complemented
61	C₁₃×#482	C₂²	1	2	yes	—
62	C₁₃×#482	C₂²	1	2	yes	—
63	C₁₃×#481	C₂²	1	2	yes	—
64	C₁₃×#480	C₂²	1	2	yes	—
65	C₁₃×#479	C₂²	1	2	yes	complemented
66	C₁₃×#479	C₂²	1	2	yes	complemented
67	C₁₃×#478	C₂²	1	2	yes	—
68	C₁₃×#478	C₂²	1	2	yes	—
69	C₁₃×#477	C₂²	1	2	yes	complemented
70	C₁₃×#476	C₂²	1	2	yes	complemented
71	C₁₃×#475	C₂²	1	2	yes	complemented
72	C₁₃×#474	C₂²	1	2	yes	complemented
73	C₁₃×#470	C₂²	1	2	yes	complemented
74	C₁₃×#469	C₂²	1	2	yes	—
75	C₁₃×#468	C₂²	1	2	yes	—
76	C₁₃×#468	C₂²	1	2	yes	complemented
77	C₁₃×#467	C₂²	1	2	yes	complemented
78	C₁₃×#466	C₂²	1	2	yes	—
79	C₁₃×#465	C₂²	1	2	yes	—
80	C₁₃×#465	C₂²	1	2	yes	complemented
81	C₁₃×#464	C₂²	1	2	yes	—
82	C₁₃×#464	C₂²	1	2	yes	—
83	C₁₃×#463	C₂²	1	2	yes	—
84	C₁₃×#463	C₂²	1	2	yes	—
85	C₁₃×#462	C₂²	1	2	yes	complemented
86	C₁₃×#461	C₂²	1	2	yes	—
87	C₁₃×#460	C₂²	1	2	yes	complemented
88	C₁₃×#459	C₂²	1	2	yes	—
89	C₁₃×#452	C₂²	1	2	yes	complemented
90	C₁₃×#452	C₂²	1	2	yes	complemented
91	C₁₃×#451	C₂²	1	2	yes	—
92	C₁₃×#450	C₂²	1	2	yes	—
93	C₁₃×#449	C₂²	1	2	yes	—
94	C₁₃×#449	C₂²	1	2	yes	—
95	C₁₃×#448	C₂²	1	2	yes	—
96	C₁₃×#447	C₂²	1	2	yes	—
97	C₁₃×#442	C₂²	1	2	yes	—
98	C₁₃×#441	C₂²	1	2	yes	complemented
99	C₁₃×#440	C₂²	1	2	yes	—
100	C₁₃×#440	C₂²	1	2	yes	complemented
101	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
102	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
103	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
104	C₄×C₁₃×D₈	C₂²	1	2	yes	—
105	C₁₃×#433	C₂²	1	1	yes	characteristic
106	C₁₃×#433	C₂²	1	1	yes	characteristic
107	C₁₃×#433	C₂²	1	1	yes	characteristic, complemented
108	C₁₃×#433	C₂²	1	1	yes	characteristic, complemented
109	C₁₃×#431	C₂²	1	2	yes	—
110	C₁₃×#431	C₂²	1	2	yes	complemented
111	C₁₃×#424	C₂²	1	2	yes	complemented
112	C₁₃×#408	C₂²	1	2	yes	—
113	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₁₃×#41	C₂³	1	2	yes	—
116	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
121	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×SD₁₆	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	C₂×C₁₃×D₈	C₂³	1	2	yes	—
127	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
128	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	—	2	1	no	—
130	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×#127	—	2	1	no	—
133	C₁₃×#127	C₂³	1	1	yes	characteristic
134	C₁₃×#126	—	2	2	no	—
135	C₁₃×#126	—	2	2	no	—
136	C₁₃×#126	—	2	2	no	—
137	C₁₃×#126	—	2	2	no	—
138	C₁₃×#126	—	2	2	no	—
139	C₁₃×#126	—	2	2	no	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#125	—	2	2	no	—
143	C₁₃×#125	—	2	2	no	—
144	C₁₃×#125	—	2	2	no	—
145	C₁₃×#125	C₂³	1	1	yes	characteristic
146	C₁₃×#125	C₂³	1	1	yes	characteristic
147	C₁₃×#125	C₂³	1	2	yes	—
148	C₁₃×#125	C₂³	1	2	yes	—
149	C₁₃×#124	—	2	1	no	—
150	C₁₃×#124	—	2	1	no	—
151	C₁₃×#124	—	2	2	no	—
152	C₁₃×#124	—	2	2	no	—
153	C₁₃×#124	—	2	2	no	—
154	C₁₃×#124	C₂³	1	2	yes	—
155	C₁₃×#124	C₂³	1	2	yes	—
156	C₁₃×#124	C₂³	1	2	yes	—
157	C₁₃×#123	—	2	1	no	—
158	C₁₃×#123	—	2	1	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×#123	—	2	2	no	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×#123	—	2	2	no	—
164	C₁₃×#123	—	2	2	no	—
165	C₁₃×#123	—	2	2	no	—
166	C₁₃×#123	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	—	2	2	no	—
169	C₁₃×C₂²⋊Q₈	—	2	2	no	—
170	C₁₃×C₂²⋊Q₈	—	2	2	no	—
171	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	2	no	—
177	C₁₃×#121	—	2	2	no	—
178	C₁₃×#121	—	2	2	no	—
179	C₁₃×#121	—	2	2	no	—
180	C₁₃×#121	—	2	2	no	—
181	C₁₃×#121	C₂³	1	2	yes	—
182	C₁₃×#121	C₂³	1	2	yes	—
183	C₁₃×#121	C₂³	1	2	yes	—
184	C₁₃×#121	C₂³	1	2	yes	—
185	C₁₃×#120	—	2	1	no	—
186	C₁₃×#120	—	2	1	no	—
187	C₄×Q₈×C₁₃	—	2	2	no	—
188	C₄×Q₈×C₁₃	—	2	2	no	—
189	C₄×Q₈×C₁₃	D₄	1	2	yes	—
190	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
191	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
192	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
193	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
194	C₄×D₄×C₁₃	—	2	2	no	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₄×D₄×C₁₃	—	2	2	no	—
197	C₄×D₄×C₁₃	—	2	2	no	—
198	C₄×D₄×C₁₃	—	2	2	no	—
199	C₄×D₄×C₁₃	—	2	2	no	—
200	C₄×D₄×C₁₃	—	2	2	no	—
201	C₄×D₄×C₁₃	—	2	2	no	—
202	C₄×D₄×C₁₃	D₄	1	2	yes	—
203	C₄×D₄×C₁₃	D₄	1	2	yes	—
204	C₄×D₄×C₁₃	D₄	1	2	yes	—
205	C₄×D₄×C₁₃	C₂³	1	2	yes	—
206	C₄×D₄×C₁₃	C₂³	1	2	yes	—
207	C₄×D₄×C₁₃	C₂³	1	2	yes	—
208	C₄×D₄×C₁₃	C₂³	1	2	yes	—
209	C₁₃×#117	—	2	2	no	—
210	C₁₃×#117	—	2	2	no	—
211	C₁₃×#117	—	2	2	no	—
212	C₁₃×#117	—	2	2	no	—
213	C₁₃×#117	—	2	2	no	—
214	C₁₃×#117	—	2	2	no	—
215	C₁₃×#117	C₂³	1	1	yes	characteristic
216	C₁₃×#117	C₂³	1	1	yes	characteristic
217	C₁₃×#117	C₂³	1	1	yes	characteristic
218	C₁₃×#117	C₂³	1	1	yes	characteristic
219	C₁₃×#117	C₂³	1	1	yes	characteristic
220	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
223	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
224	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
225	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
228	C₁₃×#107	C₂³	1	2	yes	—
229	C₁₃×#107	C₂³	1	2	yes	—
230	C₁₃×#107	C₂³	1	2	yes	—
231	C₁₃×#107	C₂³	1	2	yes	—
232	C₁₃×#106	C₂³	1	2	yes	—
233	C₁₃×#106	C₂³	1	2	yes	—
234	C₁₃×#106	C₂³	1	2	yes	—
235	C₁₃×#106	C₂³	1	2	yes	—
236	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
239	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
240	C₁₃×#103	C₂³	1	2	yes	—
241	C₁₃×#103	C₂³	1	2	yes	—
242	C₁₃×#103	C₂³	1	2	yes	—
243	C₁₃×#103	C₂³	1	2	yes	—
244	C₁₃×#103	C₂³	1	2	yes	—
245	C₁₃×#103	C₂³	1	2	yes	—
246	C₁₃×#103	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	2	yes	—
248	C₁₃×#102	C₂³	1	2	yes	—
249	C₁₃×#102	C₂³	1	2	yes	—
250	C₁₃×#102	C₂³	1	2	yes	—
251	C₁₃×#102	C₂³	1	2	yes	—
252	C₁₃×#102	C₂³	1	2	yes	—
253	C₁₃×#102	C₂³	1	2	yes	—
254	C₁₃×#102	C₂³	1	2	yes	—
255	C₁₃×#102	C₂³	1	2	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	1	yes	characteristic
261	C₁₃×#97	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₃	C₂³	1	2	yes	—
263	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₃	C₂³	1	2	yes	—
266	#61010	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂⁴×C₁₃	—	2	1	no	—
268	C₁₃×#41	—	4	2	no	—
269	C₁₃×#41	—	4	2	no	—
270	C₁₃×#41	—	4	2	no	—
271	C₂×Q₈×C₁₃	—	2	1	no	—
272	C₂×Q₈×C₁₃	—	2	2	no	—
273	C₂×Q₈×C₁₃	—	4	2	no	—
274	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
277	C₂×D₄×C₁₃	—	2	2	no	—
278	C₂×D₄×C₁₃	—	2	2	no	—
279	C₂×D₄×C₁₃	—	2	2	no	—
280	C₂×D₄×C₁₃	—	2	2	no	—
281	C₂×D₄×C₁₃	—	2	2	no	—
282	C₂×D₄×C₁₃	—	2	1	no	—
283	C₂×D₄×C₁₃	—	2	2	no	—
284	C₂×D₄×C₁₃	—	4	2	no	—
285	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
288	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	—	2	1	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	2	no	—
294	C₂²×C₄×C₁₃	—	2	2	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₁₃×Q₁₆	—	4	2	no	—
304	C₁₃×Q₁₆	—	4	2	no	—
305	C₁₃×SD₁₆	—	4	2	no	—
306	C₁₃×SD₁₆	—	4	2	no	—
307	C₁₃×SD₁₆	—	4	2	no	—
308	C₁₃×SD₁₆	—	4	2	no	—
309	C₁₃×D₈	—	4	2	no	—
310	C₁₃×D₈	—	4	2	no	—
311	C₁₃×M₁₆	—	4	2	no	—
312	C₂×C₈×C₁₃	—	4	2	no	—
313	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
316	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
335	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
336	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
337	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
340	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
341	C₁₃×C₂²⋊C₄	—	2	1	no	—
342	C₁₃×C₂²⋊C₄	—	2	1	no	—
343	C₁₃×C₂²⋊C₄	—	2	2	no	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
363	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
364	C₄²×C₁₃	—	2	2	no	—
365	C₄²×C₁₃	—	2	2	no	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	2	no	—
368	C₄²×C₁₃	—	2	1	no	—
369	C₄²×C₁₃	—	2	1	no	—
370	C₄²×C₁₃	C₂×D₄	1	2	yes	—
371	C₄²×C₁₃	C₂×D₄	1	2	yes	—
372	C₄²×C₁₃	C₂×D₄	1	2	yes	—
373	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
377	#3512	C₂×C₁₃	1	1	yes	characteristic, complemented
378	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#3258	C₂×C₁₃	1	2	yes	complemented
380	#3257	C₂×C₁₃	1	2	yes	complemented
381	#3233	C₂×C₁₃	1	2	yes	complemented
382	#3232	C₂×C₁₃	1	2	yes	complemented
383	#3212	C₂×C₁₃	1	2	yes	complemented
384	#3211	C₂×C₁₃	1	2	yes	complemented
385	#3201	C₂×C₁₃	1	2	yes	complemented
386	#3198	C₂×C₁₃	1	2	yes	complemented
387	#3183	C₂×C₁₃	1	2	yes	complemented
388	#3168	C₂×C₁₃	1	2	yes	complemented
389	#3127	C₂×C₁₃	1	1	yes	characteristic, complemented
390	#3126	C₂×C₁₃	1	1	yes	characteristic, complemented
391	#3125	C₂×C₁₃	1	2	yes	complemented
392	#3124	C₂×C₁₃	1	2	yes	complemented
393	#3123	C₂×C₁₃	1	1	yes	characteristic, complemented
394	#3122	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
396	C₂³×C₁₃	—	2	2	no	—
397	C₂³×C₁₃	—	2	2	no	—
398	C₂³×C₁₃	—	4	2	no	—
399	C₂³×C₁₃	—	8	2	no	—
400	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	Q₈×C₁₃	—	2	2	no	—
404	Q₈×C₁₃	—	2	2	no	—
405	Q₈×C₁₃	—	2	2	no	—
406	Q₈×C₁₃	—	2	2	no	—
407	Q₈×C₁₃	—	4	1	no	—
408	Q₈×C₁₃	—	4	2	no	—
409	Q₈×C₁₃	—	8	2	no	—
410	D₄×C₁₃	—	2	2	no	—
411	D₄×C₁₃	—	2	2	no	—
412	D₄×C₁₃	—	2	2	no	—
413	D₄×C₁₃	—	2	2	no	—
414	D₄×C₁₃	—	4	1	no	—
415	D₄×C₁₃	—	4	1	no	—
416	D₄×C₁₃	—	4	1	no	—
417	D₄×C₁₃	—	4	2	no	—
418	D₄×C₁₃	—	4	4	no	—
419	D₄×C₁₃	—	8	2	no	—
420	D₄×C₁₃	—	8	2	no	—
421	D₄×C₁₃	—	8	2	no	—
422	D₄×C₁₃	—	8	2	no	—
423	D₄×C₁₃	—	8	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	4	2	no	—
434	C₂×C₄×C₁₃	—	4	2	no	—
435	C₂×C₄×C₁₃	—	4	2	no	—
436	C₂×C₄×C₁₃	—	4	4	no	—
437	C₂×C₄×C₁₃	—	4	2	no	—
438	C₂×C₄×C₁₃	—	8	2	no	—
439	C₂×C₄×C₁₃	—	8	2	no	—
440	C₂×C₄×C₁₃	—	8	2	no	—
441	C₂×C₄×C₁₃	—	8	2	no	—
442	C₂×C₄×C₁₃	—	8	2	no	—
443	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
451	C₈×C₁₃	—	2	2	no	—
452	C₈×C₁₃	—	2	2	no	—
453	C₈×C₁₃	—	2	2	no	—
454	C₈×C₁₃	—	2	2	no	—
455	#559	—	2	2	no	—
456	#556	—	2	2	no	—
457	#553	—	2	2	no	—
458	#553	—	2	2	no	—
459	#553	—	2	2	no	—
460	#552	—	2	2	no	—
461	#551	—	2	2	no	—
462	#551	—	2	2	no	—
463	#542	C₂²×C₁₃	1	2	yes	—
464	#542	C₂²×C₁₃	1	2	yes	—
465	#541	C₂²×C₁₃	1	1	yes	characteristic
466	#541	C₂²×C₁₃	1	1	yes	characteristic, complemented
467	#540	C₂²×C₁₃	1	1	yes	characteristic
468	#540	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#537	C₂²×C₁₃	1	2	yes	—
470	#536	C₂²×C₁₃	1	1	yes	characteristic
471	#535	C₂²×C₁₃	1	1	yes	characteristic
472	#533	C₂²×C₁₃	1	1	yes	characteristic
473	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#529	C₂²×C₁₃	1	2	yes	—
475	#529	C₂²×C₁₃	1	2	yes	—
476	#529	C₂²×C₁₃	1	2	yes	—
477	#529	C₂²×C₁₃	1	2	yes	complemented
478	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
480	#520	C₂²×C₁₃	1	2	yes	complemented
481	#519	C₂²×C₁₃	1	1	yes	characteristic
482	#518	C₂²×C₁₃	1	1	yes	characteristic
483	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
484	#499	C₂²×C₁₃	1	2	yes	complemented
485	#499	C₂²×C₁₃	1	2	yes	complemented
486	#495	C₂²×C₁₃	1	2	yes	—
487	#495	C₂²×C₁₃	1	2	yes	—
488	#488	C₂²×C₁₃	1	2	yes	—
489	#488	C₂²×C₁₃	1	2	yes	—
490	#488	C₂²×C₁₃	1	2	yes	complemented
491	#488	C₂²×C₁₃	1	2	yes	complemented
492	#485	C₂²×C₁₃	1	2	yes	—
493	#485	C₂²×C₁₃	1	2	yes	—
494	#484	C₂²×C₁₃	1	2	yes	complemented
495	#483	C₂²×C₁₃	1	2	yes	complemented
496	#482	C₂²×C₁₃	1	2	yes	—
497	#482	C₂²×C₁₃	1	2	yes	—
498	#481	C₂²×C₁₃	1	2	yes	—
499	#480	C₂²×C₁₃	1	2	yes	—
500	#479	C₂²×C₁₃	1	2	yes	complemented
501	#479	C₂²×C₁₃	1	2	yes	complemented
502	#478	C₂²×C₁₃	1	2	yes	—
503	#478	C₂²×C₁₃	1	2	yes	—
504	#477	C₂²×C₁₃	1	2	yes	complemented
505	#476	C₂²×C₁₃	1	2	yes	complemented
506	#475	C₂²×C₁₃	1	2	yes	complemented
507	#474	C₂²×C₁₃	1	2	yes	complemented
508	#470	C₂²×C₁₃	1	2	yes	complemented
509	#469	C₂²×C₁₃	1	2	yes	—
510	#468	C₂²×C₁₃	1	2	yes	—
511	#468	C₂²×C₁₃	1	2	yes	complemented
512	#467	C₂²×C₁₃	1	2	yes	complemented
513	#466	C₂²×C₁₃	1	2	yes	—
514	#465	C₂²×C₁₃	1	2	yes	—
515	#465	C₂²×C₁₃	1	2	yes	complemented
516	#464	C₂²×C₁₃	1	2	yes	—
517	#464	C₂²×C₁₃	1	2	yes	—
518	#463	C₂²×C₁₃	1	2	yes	—
519	#463	C₂²×C₁₃	1	2	yes	—
520	#462	C₂²×C₁₃	1	2	yes	complemented
521	#461	C₂²×C₁₃	1	2	yes	—
522	#460	C₂²×C₁₃	1	2	yes	complemented
523	#459	C₂²×C₁₃	1	2	yes	—
524	#452	C₂²×C₁₃	1	2	yes	complemented
525	#452	C₂²×C₁₃	1	2	yes	complemented
526	#451	C₂²×C₁₃	1	2	yes	—
527	#450	C₂²×C₁₃	1	2	yes	—
528	#449	C₂²×C₁₃	1	2	yes	—
529	#449	C₂²×C₁₃	1	2	yes	—
530	#448	C₂²×C₁₃	1	2	yes	—
531	#447	C₂²×C₁₃	1	2	yes	—
532	#442	C₂²×C₁₃	1	2	yes	—
533	#441	C₂²×C₁₃	1	2	yes	complemented
534	#440	C₂²×C₁₃	1	2	yes	—
535	#440	C₂²×C₁₃	1	2	yes	complemented
536	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
537	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
538	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
539	C₄×D₈	C₂²×C₁₃	1	2	yes	—
540	#433	C₂²×C₁₃	1	1	yes	characteristic
541	#433	C₂²×C₁₃	1	1	yes	characteristic
542	#433	C₂²×C₁₃	1	1	yes	characteristic, complemented
543	#433	C₂²×C₁₃	1	1	yes	characteristic, complemented
544	#431	C₂²×C₁₃	1	2	yes	—
545	#431	C₂²×C₁₃	1	2	yes	complemented
546	#424	C₂²×C₁₃	1	2	yes	complemented
547	#408	C₂²×C₁₃	1	2	yes	—
548	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
549	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
550	C₂²×C₁₃	—	2	2	no	—
551	C₂²×C₁₃	—	2	2	no	—
552	C₂²×C₁₃	—	2	2	no	—
553	C₂²×C₁₃	—	2	1	no	—
554	C₂²×C₁₃	—	2	1	no	—
555	C₂²×C₁₃	—	2	1	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	—	4	2	no	—
558	C₂²×C₁₃	—	4	2	no	—
559	C₂²×C₁₃	—	4	2	no	—
560	C₂²×C₁₃	—	4	2	no	—
561	C₂²×C₁₃	—	4	2	no	—
562	C₂²×C₁₃	—	16	2	no	—
563	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
564	C₄×C₁₃	—	2	2	no	—
565	C₄×C₁₃	—	2	2	no	—
566	C₄×C₁₃	—	2	2	no	—
567	C₄×C₁₃	—	2	2	no	—
568	C₄×C₁₃	—	2	1	no	—
569	C₄×C₁₃	—	2	1	no	—
570	C₄×C₁₃	—	2	1	no	—
571	C₄×C₁₃	—	4	2	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	2	no	—
574	C₄×C₁₃	—	4	2	no	—
575	C₄×C₁₃	—	4	2	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	#585	1	2	yes	—
578	C₂×#41	C₂³×C₁₃	1	2	yes	—
579	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
580	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
583	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
584	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
585	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
586	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
587	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
588	C₂×D₈	C₂³×C₁₃	1	2	yes	—
589	C₂×D₈	C₂³×C₁₃	1	2	yes	—
590	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
591	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
592	C₄⋊Q₈	—	2	1	no	—
593	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
595	#127	—	2	1	no	—
596	#127	C₂³×C₁₃	1	1	yes	characteristic
597	#126	—	2	2	no	—
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#126	—	2	2	no	—
604	#126	—	2	2	no	—
605	#125	—	2	2	no	—
606	#125	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	C₂³×C₁₃	1	2	yes	—
609	#125	C₂³×C₁₃	1	1	yes	characteristic
610	#125	C₂³×C₁₃	1	1	yes	characteristic
611	#125	C₂³×C₁₃	1	2	yes	—
612	#124	—	2	1	no	—
613	#124	—	2	1	no	—
614	#124	—	2	2	no	—
615	#124	—	2	2	no	—
616	#124	—	2	2	no	—
617	#124	C₂³×C₁₃	1	2	yes	—
618	#124	C₂³×C₁₃	1	2	yes	—
619	#124	C₂³×C₁₃	1	2	yes	—
620	#123	—	2	1	no	—
621	#123	—	2	1	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
635	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
636	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
637	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
638	#121	—	2	2	no	—
639	#121	—	2	2	no	—
640	#121	—	2	2	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	2	no	—
644	#121	C₂³×C₁₃	1	2	yes	—
645	#121	C₂³×C₁₃	1	2	yes	—
646	#121	C₂³×C₁₃	1	2	yes	—
647	#121	C₂³×C₁₃	1	2	yes	—
648	#120	—	2	1	no	—
649	#120	—	2	1	no	—
650	C₄×Q₈	—	2	2	no	—
651	C₄×Q₈	—	2	2	no	—
652	C₄×Q₈	D₄×C₁₃	1	2	yes	—
653	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
654	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
655	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
656	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
657	C₄×D₄	—	2	2	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	2	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	D₄×C₁₃	1	2	yes	—
666	C₄×D₄	D₄×C₁₃	1	2	yes	—
667	C₄×D₄	D₄×C₁₃	1	2	yes	—
668	C₄×D₄	C₂³×C₁₃	1	2	yes	—
669	C₄×D₄	C₂³×C₁₃	1	2	yes	—
670	C₄×D₄	C₂³×C₁₃	1	2	yes	—
671	C₄×D₄	C₂³×C₁₃	1	2	yes	—
672	#117	—	2	2	no	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	—	2	2	no	—
676	#117	—	2	2	no	—
677	#117	—	2	2	no	—
678	#117	C₂³×C₁₃	1	1	yes	characteristic
679	#117	C₂³×C₁₃	1	1	yes	characteristic
680	#117	C₂³×C₁₃	1	1	yes	characteristic
681	#117	C₂³×C₁₃	1	1	yes	characteristic
682	#117	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄⋊C₄	—	2	2	no	—
684	C₂×C₄⋊C₄	—	2	2	no	—
685	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
686	C₂×C₂²⋊C₄	—	2	2	no	—
687	C₂×C₂²⋊C₄	—	2	2	no	—
688	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
691	#107	C₂³×C₁₃	1	2	yes	—
692	#107	C₂³×C₁₃	1	2	yes	—
693	#107	C₂³×C₁₃	1	2	yes	—
694	#107	C₂³×C₁₃	1	2	yes	—
695	#106	C₂³×C₁₃	1	2	yes	—
696	#106	C₂³×C₁₃	1	2	yes	—
697	#106	C₂³×C₁₃	1	2	yes	—
698	#106	C₂³×C₁₃	1	2	yes	—
699	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
700	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
701	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
702	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
703	#103	C₂³×C₁₃	1	2	yes	—
704	#103	C₂³×C₁₃	1	2	yes	—
705	#103	C₂³×C₁₃	1	2	yes	—
706	#103	C₂³×C₁₃	1	2	yes	—
707	#103	C₂³×C₁₃	1	2	yes	—
708	#103	C₂³×C₁₃	1	2	yes	—
709	#103	C₂³×C₁₃	1	2	yes	—
710	#103	C₂³×C₁₃	1	2	yes	—
711	#102	C₂³×C₁₃	1	2	yes	—
712	#102	C₂³×C₁₃	1	2	yes	—
713	#102	C₂³×C₁₃	1	2	yes	—
714	#102	C₂³×C₁₃	1	2	yes	—
715	#102	C₂³×C₁₃	1	2	yes	—
716	#102	C₂³×C₁₃	1	2	yes	—
717	#102	C₂³×C₁₃	1	2	yes	—
718	#102	C₂³×C₁₃	1	2	yes	—
719	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
722	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
723	#97	C₂³×C₁₃	1	1	yes	characteristic
724	#97	C₂³×C₁₃	1	1	yes	characteristic
725	C₄×C₈	C₂³×C₁₃	1	2	yes	—
726	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
727	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
728	C₄×C₈	C₂³×C₁₃	1	2	yes	—
729	C₂×C₁₃	—	4	1	no	—
730	C₂×C₁₃	—	4	1	no	—
731	C₂×C₁₃	—	4	1	no	—
732	C₂×C₁₃	—	8	2	no	—
733	C₂×C₁₃	—	8	2	no	—
734	C₂×C₁₃	#3449	1	1	yes	characteristic
735	C₂×C₁₃	#3584	1	2	yes	—
736	C₂⁴	—	2	1	no	—
737	#41	—	4	2	no	—
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	C₂×Q₈	—	2	1	no	—
741	C₂×Q₈	—	2	2	no	—
742	C₂×Q₈	—	4	2	no	—
743	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
745	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
755	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
757	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
772	Q₁₆	—	4	2	no	—
773	Q₁₆	—	4	2	no	—
774	SD₁₆	—	4	2	no	—
775	SD₁₆	—	4	2	no	—
776	SD₁₆	—	4	2	no	—
777	SD₁₆	—	4	2	no	—
778	D₈	—	4	2	no	—
779	D₈	—	4	2	no	—
780	M₁₆	—	4	2	no	—
781	C₂×C₈	—	4	2	no	—
782	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
783	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
784	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
785	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
804	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
805	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
806	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
807	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
808	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	2	1	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄×C₁₃	1	2	yes	—
831	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
832	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	1	no	—
838	C₄²	—	2	1	no	—
839	C₄²	C₂×D₄×C₁₃	1	2	yes	—
840	C₄²	C₂×D₄×C₁₃	1	2	yes	—
841	C₄²	C₂×D₄×C₁₃	1	2	yes	—
842	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
843	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
844	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
845	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
846	C₁₃	#61010	1	1	yes	characteristic, direct product factor, Sylow
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	4	2	no	—
850	C₂³	—	8	2	no	—
851	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
852	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
853	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	1	no	—
859	Q₈	—	4	2	no	—
860	Q₈	—	8	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	2	no	—
865	D₄	—	4	1	no	—
866	D₄	—	4	1	no	—
867	D₄	—	4	1	no	—
868	D₄	—	4	2	no	—
869	D₄	—	4	4	no	—
870	D₄	—	8	2	no	—
871	D₄	—	8	2	no	—
872	D₄	—	8	2	no	—
873	D₄	—	8	2	no	—
874	D₄	—	8	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	4	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	8	2	no	—
890	C₂×C₄	—	8	2	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	—	8	2	no	—
894	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
896	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
897	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
901	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	16	2	no	—
919	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	C₁₃×#585	1	2	yes	—
934	C₂	—	4	1	no	—
935	C₂	—	4	1	no	—
936	C₂	—	4	1	no	—
937	C₂	—	8	2	no	—
938	C₂	—	8	2	no	—
939	C₂	C₁₃×#3449	1	1	yes	characteristic
940	C₂	C₁₃×#3584	1	2	yes	—

	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×#3512	C₂	semidirect
2. C₁₃×#3510	C₂	semidirect
3. C₁₃×#3258	C₂	semidirect
4. C₁₃×#3257	C₂	semidirect
5. C₁₃×#3233	C₂	semidirect
6. C₁₃×#3232	C₂	semidirect
7. C₁₃×#3212	C₂	semidirect
8. C₁₃×#3211	C₂	semidirect
9. C₁₃×#3201	C₂	semidirect
10. C₁₃×#3198	C₂	semidirect
11. C₁₃×#3183	C₂	semidirect
12. C₁₃×#3168	C₂	semidirect
13. C₁₃×#3127	C₂	semidirect
14. C₁₃×#3126	C₂	semidirect
15. C₁₃×#3125	C₂	semidirect
16. C₁₃×#3124	C₂	semidirect
17. C₁₃×#3123	C₂	semidirect
18. C₁₃×#3122	C₂	semidirect
19. C₁₃×#2922	C₂	semidirect
31. C₁₃×#541	C₂²	semidirect
33. C₁₃×#540	C₂²	semidirect
38. C₁₃×#532	C₂²	semidirect
42. C₁₃×#529	C₂²	semidirect
43. C₂×C₁₃×#125	C₂²	semidirect
45. C₁₃×#520	C₂²	semidirect
49. C₁₃×#499	C₂²	semidirect
50. C₁₃×#499	C₂²	semidirect
55. C₁₃×#488	C₂²	semidirect
56. C₁₃×#488	C₂²	semidirect
59. C₁₃×#484	C₂²	semidirect
60. C₁₃×#483	C₂²	semidirect
65. C₁₃×#479	C₂²	semidirect
66. C₁₃×#479	C₂²	semidirect
69. C₁₃×#477	C₂²	semidirect
70. C₁₃×#476	C₂²	semidirect
71. C₁₃×#475	C₂²	semidirect
72. C₁₃×#474	C₂²	semidirect
73. C₁₃×#470	C₂²	semidirect
76. C₁₃×#468	C₂²	semidirect
77. C₁₃×#467	C₂²	semidirect
80. C₁₃×#465	C₂²	semidirect
85. C₁₃×#462	C₂²	semidirect
87. C₁₃×#460	C₂²	semidirect
89. C₁₃×#452	C₂²	semidirect
90. C₁₃×#452	C₂²	semidirect
98. C₁₃×#441	C₂²	semidirect
100. C₁₃×#440	C₂²	semidirect
101. C₄×C₁₃×Q₁₆	C₂²	semidirect
103. C₄×C₁₃×SD₁₆	C₂²	semidirect
107. C₁₃×#433	C₂²	semidirect
108. C₁₃×#433	C₂²	semidirect
110. C₁₃×#431	C₂²	semidirect
111. C₁₃×#424	C₂²	semidirect
113. C₄×C₁₃×M₁₆	C₂²	semidirect
114. C₂×C₄×C₈×C₁₃	C₂²	semidirect
266. #61010	C₁₃	direct (N × H)
377. #3512	C₂×C₁₃	semidirect
378. #3510	C₂×C₁₃	semidirect
379. #3258	C₂×C₁₃	semidirect
380. #3257	C₂×C₁₃	semidirect
381. #3233	C₂×C₁₃	semidirect
382. #3232	C₂×C₁₃	semidirect
383. #3212	C₂×C₁₃	semidirect
384. #3211	C₂×C₁₃	semidirect
385. #3201	C₂×C₁₃	semidirect
386. #3198	C₂×C₁₃	semidirect
387. #3183	C₂×C₁₃	semidirect
388. #3168	C₂×C₁₃	semidirect
389. #3127	C₂×C₁₃	semidirect
390. #3126	C₂×C₁₃	semidirect
391. #3125	C₂×C₁₃	semidirect
392. #3124	C₂×C₁₃	semidirect
393. #3123	C₂×C₁₃	semidirect
394. #3122	C₂×C₁₃	semidirect
395. #2922	C₂×C₁₃	semidirect
466. #541	C₂²×C₁₃	semidirect
468. #540	C₂²×C₁₃	semidirect
473. #532	C₂²×C₁₃	semidirect
477. #529	C₂²×C₁₃	semidirect
478. C₂×#125	C₂²×C₁₃	semidirect
480. #520	C₂²×C₁₃	semidirect
484. #499	C₂²×C₁₃	semidirect
485. #499	C₂²×C₁₃	semidirect
490. #488	C₂²×C₁₃	semidirect
491. #488	C₂²×C₁₃	semidirect
494. #484	C₂²×C₁₃	semidirect
495. #483	C₂²×C₁₃	semidirect
500. #479	C₂²×C₁₃	semidirect
501. #479	C₂²×C₁₃	semidirect
504. #477	C₂²×C₁₃	semidirect
505. #476	C₂²×C₁₃	semidirect
506. #475	C₂²×C₁₃	semidirect
507. #474	C₂²×C₁₃	semidirect
508. #470	C₂²×C₁₃	semidirect
511. #468	C₂²×C₁₃	semidirect
512. #467	C₂²×C₁₃	semidirect
515. #465	C₂²×C₁₃	semidirect
520. #462	C₂²×C₁₃	semidirect
522. #460	C₂²×C₁₃	semidirect
524. #452	C₂²×C₁₃	semidirect
525. #452	C₂²×C₁₃	semidirect
533. #441	C₂²×C₁₃	semidirect
535. #440	C₂²×C₁₃	semidirect
536. C₄×Q₁₆	C₂²×C₁₃	semidirect
538. C₄×SD₁₆	C₂²×C₁₃	semidirect
542. #433	C₂²×C₁₃	semidirect
543. #433	C₂²×C₁₃	semidirect
545. #431	C₂²×C₁₃	semidirect
546. #424	C₂²×C₁₃	semidirect
548. C₄×M₁₆	C₂²×C₁₃	semidirect
549. C₂×C₄×C₈	C₂²×C₁₃	semidirect
846. C₁₃	#61010	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×#3512	2
C₁₃×#3510	2
C₁₃×#3258	2
C₁₃×#3257	2
C₁₃×#3233	2
C₁₃×#3232	2
C₁₃×#3212	2
C₁₃×#3211	2
C₁₃×#3201	2
C₁₃×#3198	2
C₁₃×#3183	2
C₁₃×#3168	2
C₁₃×#3127	2
C₁₃×#3126	2
C₁₃×#3125	2
C₁₃×#3124	2
C₁₃×#3123	2
C₁₃×#3122	2
C₁₃×#2922	2
#61010	13

Subgroups — C13×#61010 #15747349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61010 #15747349