Subgroups — C₁₃×#61930 #15748269

Order 3328.

1678 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3403	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3393	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×#3365	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3223	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3221	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3123	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3122	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3121	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3102	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	2	no	—
21	C₁₃×#559	C₂²	1	2	yes	—
22	C₁₃×#559	C₂²	1	2	yes	—
23	C₁₃×#559	C₂²	1	2	yes	complemented
24	C₁₃×#557	C₂²	1	2	yes	complemented
25	C₁₃×#556	C₂²	1	2	yes	—
26	C₁₃×#556	C₂²	1	2	yes	—
27	C₁₃×#556	C₂²	1	2	yes	complemented
28	C₁₃×#554	C₂²	1	2	yes	complemented
29	C₁₃×#552	—	2	2	no	—
30	C₁₃×#551	—	2	2	no	—
31	C₁₃×#551	—	2	2	no	—
32	C₁₃×#542	—	2	2	no	—
33	C₁₃×#542	—	2	2	no	—
34	C₁₃×#542	C₂²	1	2	yes	—
35	C₁₃×#541	C₂²	1	1	yes	characteristic
36	C₁₃×#540	C₂²	1	1	yes	characteristic
37	C₁₃×#539	—	2	2	no	—
38	C₁₃×#536	C₂²	1	1	yes	characteristic
39	C₁₃×#535	C₂²	1	1	yes	characteristic
40	C₁₃×#533	C₂²	1	1	yes	characteristic
41	C₁₃×#529	—	2	2	no	—
42	C₁₃×#529	C₂²	1	2	yes	—
43	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
44	C₁₃×#519	C₂²	1	1	yes	characteristic
45	C₁₃×#518	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₁₃×#497	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#496	C₂²	1	2	yes	—
49	C₁₃×#496	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#495	C₂²	1	2	yes	—
51	C₁₃×#495	C₂²	1	2	yes	—
52	C₁₃×#495	C₂²	1	2	yes	—
53	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#489	C₂²	1	2	yes	—
58	C₁₃×#488	C₂²	1	2	yes	—
59	C₁₃×#488	C₂²	1	2	yes	—
60	C₁₃×#488	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#488	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#486	C₂²	1	2	yes	—
63	C₁₃×#485	C₂²	1	2	yes	—
64	C₁₃×#482	C₂²	1	2	yes	—
65	C₁₃×#479	C₂²	1	2	yes	complemented
66	C₁₃×#478	C₂²	1	2	yes	—
67	C₁₃×#478	C₂²	1	2	yes	—
68	C₁₃×#478	C₂²	1	2	yes	complemented
69	C₁₃×#477	C₂²	1	2	yes	complemented
70	C₁₃×#475	C₂²	1	2	yes	complemented
71	C₁₃×#464	C₂²	1	2	yes	—
72	C₁₃×#464	C₂²	1	2	yes	—
73	C₁₃×#464	C₂²	1	2	yes	—
74	C₁₃×#464	C₂²	1	2	yes	complemented
75	C₁₃×#464	C₂²	1	2	yes	complemented
76	C₁₃×#464	C₂²	1	2	yes	complemented
77	C₁₃×#464	C₂²	1	2	yes	complemented
78	C₁₃×#463	C₂²	1	2	yes	—
79	C₁₃×#463	C₂²	1	2	yes	—
80	C₁₃×#463	C₂²	1	2	yes	—
81	C₁₃×#463	C₂²	1	2	yes	complemented
82	C₁₃×#463	C₂²	1	2	yes	complemented
83	C₁₃×#462	C₂²	1	2	yes	complemented
84	C₁₃×#461	C₂²	1	2	yes	—
85	C₁₃×#461	C₂²	1	2	yes	complemented
86	C₁₃×#460	C₂²	1	2	yes	—
87	C₁₃×#459	C₂²	1	2	yes	—
88	C₁₃×#459	C₂²	1	2	yes	—
89	C₁₃×#452	C₂²	1	2	yes	—
90	C₁₃×#451	C₂²	1	2	yes	—
91	C₁₃×#450	C₂²	1	2	yes	—
92	C₁₃×#449	C₂²	1	2	yes	—
93	C₁₃×#448	C₂²	1	2	yes	—
94	C₁₃×#447	C₂²	1	2	yes	—
95	C₁₃×#446	C₂²	1	2	yes	complemented
96	C₁₃×#446	C₂²	1	2	yes	complemented
97	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
98	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
99	C₁₃×#442	C₂²	1	2	yes	—
100	C₁₃×#441	C₂²	1	2	yes	complemented
101	C₁₃×#440	C₂²	1	2	yes	—
102	C₁₃×#440	C₂²	1	2	yes	complemented
103	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
104	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
106	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
107	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
108	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
109	C₄×C₁₃×D₈	C₂²	1	2	yes	—
110	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
111	C₁₃×#433	C₂²	1	2	yes	—
112	C₁₃×#433	C₂²	1	1	yes	characteristic
113	C₁₃×#433	C₂²	1	1	yes	characteristic
114	C₁₃×#431	C₂²	1	2	yes	—
115	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
116	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
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×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×D₈	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	2	yes	—
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₁₃×C₄⋊Q₈	—	2	2	no	—
131	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
134	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₃×#127	C₂³	1	1	yes	characteristic
137	C₁₃×#127	C₂³	1	2	yes	—
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×#126	—	2	2	no	—
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	2	no	—
148	C₁₃×#125	—	2	2	no	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	D₄	1	2	yes	—
151	C₁₃×#125	C₂³	1	1	yes	characteristic
152	C₁₃×#125	C₂³	1	1	yes	characteristic
153	C₁₃×#125	C₂³	1	2	yes	—
154	C₁₃×#124	—	2	2	no	—
155	C₁₃×#124	—	2	2	no	—
156	C₁₃×#124	—	2	2	no	—
157	C₁₃×#124	—	2	2	no	—
158	C₁₃×#124	—	2	1	no	—
159	C₁₃×#124	—	2	1	no	—
160	C₁₃×#124	C₂³	1	2	yes	—
161	C₁₃×#124	C₂³	1	2	yes	—
162	C₁₃×#124	C₂³	1	2	yes	—
163	C₁₃×#124	C₂³	1	1	yes	characteristic
164	C₁₃×#124	C₂³	1	2	yes	—
165	C₁₃×#124	C₂³	1	1	yes	characteristic
166	C₁₃×#124	C₂³	1	2	yes	—
167	C₁₃×#123	—	2	2	no	—
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×#123	—	2	2	no	—
173	C₁₃×#123	—	2	2	no	—
174	C₁₃×#123	—	2	2	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×#123	—	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	D₄	1	2	yes	—
186	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₁₃×#121	—	2	2	no	—
189	C₁₃×#121	—	2	2	no	—
190	C₁₃×#121	C₂³	1	2	yes	—
191	C₁₃×#120	—	2	1	no	—
192	C₁₃×#120	—	2	1	no	—
193	C₄×Q₈×C₁₃	—	2	2	no	—
194	C₄×Q₈×C₁₃	—	2	2	no	—
195	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	2	yes	—
201	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
202	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
203	C₄×D₄×C₁₃	—	2	2	no	—
204	C₄×D₄×C₁₃	—	2	2	no	—
205	C₄×D₄×C₁₃	—	2	2	no	—
206	C₄×D₄×C₁₃	—	2	2	no	—
207	C₄×D₄×C₁₃	—	2	2	no	—
208	C₄×D₄×C₁₃	—	2	2	no	—
209	C₄×D₄×C₁₃	C₂³	1	2	yes	—
210	C₄×D₄×C₁₃	C₂³	1	2	yes	—
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	C₁₃×#117	—	2	2	no	—
216	C₁₃×#117	—	2	2	no	—
217	C₁₃×#117	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
223	C₁₃×#117	C₂³	1	1	yes	characteristic
224	C₁₃×#117	C₂³	1	1	yes	characteristic
225	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₄²×C₁₃	—	2	1	no	—
229	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₃×C₄⋊C₈	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×#97	C₂³	1	1	yes	characteristic
259	C₁₃×#97	C₂³	1	2	yes	—
260	C₁₃×#97	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₁₃	C₂³	1	2	yes	—
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	#61930	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂⁴×C₁₃	—	2	1	no	—
268	C₁₃×#41	—	4	2	no	—
269	C₂×Q₈×C₁₃	—	2	1	no	—
270	C₂×Q₈×C₁₃	—	2	2	no	—
271	C₂×Q₈×C₁₃	—	4	2	no	—
272	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
273	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
274	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
278	C₂×D₄×C₁₃	—	2	1	no	—
279	C₂×D₄×C₁₃	—	2	2	no	—
280	C₂×D₄×C₁₃	—	2	1	no	—
281	C₂×D₄×C₁₃	—	2	2	no	—
282	C₂×D₄×C₁₃	—	2	2	no	—
283	C₂×D₄×C₁₃	—	2	2	no	—
284	C₂×D₄×C₁₃	—	4	2	no	—
285	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	—	2	1	no	—
289	C₂²×C₄×C₁₃	—	2	1	no	—
290	C₂²×C₄×C₁₃	—	2	2	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	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₁₃×Q₁₆	—	4	2	no	—
299	C₁₃×Q₁₆	—	4	2	no	—
300	C₁₃×Q₁₆	—	4	2	no	—
301	C₁₃×SD₁₆	—	4	2	no	—
302	C₁₃×SD₁₆	—	4	2	no	—
303	C₁₃×SD₁₆	—	4	2	no	—
304	C₁₃×SD₁₆	—	4	2	no	—
305	C₁₃×SD₁₆	—	4	2	no	—
306	C₁₃×SD₁₆	—	4	2	no	—
307	C₁₃×D₈	—	4	2	no	—
308	C₁₃×D₈	—	4	2	no	—
309	C₁₃×D₈	—	4	2	no	—
310	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
311	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
312	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
313	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
330	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
331	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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×C₂²⋊C₄	—	2	1	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	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	1	yes	characteristic
363	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₁₃	—	2	2	no	—
365	C₄²×C₁₃	—	2	1	no	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	2	no	—
368	C₄²×C₁₃	—	2	2	no	—
369	C₄²×C₁₃	—	2	2	no	—
370	C₄²×C₁₃	—	2	2	no	—
371	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₁₃	C₂⁴	1	2	yes	—
374	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₄²×C₁₃	C₂⁴	1	2	yes	—
377	#3557	C₂×C₁₃	1	1	yes	characteristic, complemented
378	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#3403	C₂×C₁₃	1	2	yes	complemented
380	#3401	C₂×C₁₃	1	2	yes	complemented
381	#3394	C₂×C₁₃	1	2	yes	complemented
382	#3393	C₂×C₁₃	1	2	yes	complemented
383	#3377	C₂×C₁₃	1	2	yes	complemented
384	#3376	C₂×C₁₃	1	2	yes	complemented
385	#3365	C₂×C₁₃	1	2	yes	complemented
386	#3361	C₂×C₁₃	1	2	yes	complemented
387	#3224	C₂×C₁₃	1	2	yes	complemented
388	#3223	C₂×C₁₃	1	1	yes	characteristic, complemented
389	#3221	C₂×C₁₃	1	1	yes	characteristic, complemented
390	#3211	C₂×C₁₃	1	2	yes	complemented
391	#3123	C₂×C₁₃	1	1	yes	characteristic, complemented
392	#3122	C₂×C₁₃	1	1	yes	characteristic, complemented
393	#3121	C₂×C₁₃	1	2	yes	complemented
394	#3102	C₂×C₁₃	1	2	yes	complemented
395	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
396	C₂³×C₁₃	—	2	2	no	—
397	C₂³×C₁₃	—	2	2	no	—
398	C₂³×C₁₃	—	2	1	no	—
399	C₂³×C₁₃	—	4	2	no	—
400	C₂³×C₁₃	—	8	2	no	—
401	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	Q₈×C₁₃	—	2	2	no	—
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	2	no	—
408	Q₈×C₁₃	—	4	2	no	—
409	Q₈×C₁₃	—	4	2	no	—
410	Q₈×C₁₃	—	8	2	no	—
411	D₄×C₁₃	—	2	2	no	—
412	D₄×C₁₃	—	2	2	no	—
413	D₄×C₁₃	—	2	2	no	—
414	D₄×C₁₃	—	2	2	no	—
415	D₄×C₁₃	—	2	2	no	—
416	D₄×C₁₃	—	4	2	no	—
417	D₄×C₁₃	—	4	2	no	—
418	D₄×C₁₃	—	8	2	no	—
419	D₄×C₁₃	—	8	2	no	—
420	D₄×C₁₃	—	8	2	no	—
421	D₄×C₁₃	—	8	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	1	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	4	2	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	—	4	2	no	—
433	C₂×C₄×C₁₃	—	8	2	no	—
434	C₂×C₄×C₁₃	—	8	2	no	—
435	C₂×C₄×C₁₃	—	8	2	no	—
436	C₂×C₄×C₁₃	—	8	2	no	—
437	C₂×C₄×C₁₃	—	8	2	no	—
438	C₂×C₄×C₁₃	—	8	2	no	—
439	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
447	C₈×C₁₃	—	2	2	no	—
448	C₈×C₁₃	—	2	2	no	—
449	C₈×C₁₃	—	2	2	no	—
450	C₈×C₁₃	—	2	2	no	—
451	#563	—	2	2	no	—
452	#559	C₂²×C₁₃	1	2	yes	—
453	#559	C₂²×C₁₃	1	2	yes	—
454	#559	C₂²×C₁₃	1	2	yes	complemented
455	#557	C₂²×C₁₃	1	2	yes	complemented
456	#556	C₂²×C₁₃	1	2	yes	—
457	#556	C₂²×C₁₃	1	2	yes	—
458	#556	C₂²×C₁₃	1	2	yes	complemented
459	#554	C₂²×C₁₃	1	2	yes	complemented
460	#552	—	2	2	no	—
461	#551	—	2	2	no	—
462	#551	—	2	2	no	—
463	#542	—	2	2	no	—
464	#542	—	2	2	no	—
465	#542	C₂²×C₁₃	1	2	yes	—
466	#541	C₂²×C₁₃	1	1	yes	characteristic
467	#540	C₂²×C₁₃	1	1	yes	characteristic
468	#539	—	2	2	no	—
469	#536	C₂²×C₁₃	1	1	yes	characteristic
470	#535	C₂²×C₁₃	1	1	yes	characteristic
471	#533	C₂²×C₁₃	1	1	yes	characteristic
472	#529	—	2	2	no	—
473	#529	C₂²×C₁₃	1	2	yes	—
474	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
475	#519	C₂²×C₁₃	1	1	yes	characteristic
476	#518	C₂²×C₁₃	1	1	yes	characteristic
477	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
478	#497	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	#496	C₂²×C₁₃	1	2	yes	—
480	#496	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#495	C₂²×C₁₃	1	2	yes	—
482	#495	C₂²×C₁₃	1	2	yes	—
483	#495	C₂²×C₁₃	1	2	yes	—
484	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
485	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	#489	C₂²×C₁₃	1	2	yes	—
489	#488	C₂²×C₁₃	1	2	yes	—
490	#488	C₂²×C₁₃	1	2	yes	—
491	#488	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	#488	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	#486	C₂²×C₁₃	1	2	yes	—
494	#485	C₂²×C₁₃	1	2	yes	—
495	#482	C₂²×C₁₃	1	2	yes	—
496	#479	C₂²×C₁₃	1	2	yes	complemented
497	#478	C₂²×C₁₃	1	2	yes	—
498	#478	C₂²×C₁₃	1	2	yes	—
499	#478	C₂²×C₁₃	1	2	yes	complemented
500	#477	C₂²×C₁₃	1	2	yes	complemented
501	#475	C₂²×C₁₃	1	2	yes	complemented
502	#464	C₂²×C₁₃	1	2	yes	—
503	#464	C₂²×C₁₃	1	2	yes	—
504	#464	C₂²×C₁₃	1	2	yes	—
505	#464	C₂²×C₁₃	1	2	yes	complemented
506	#464	C₂²×C₁₃	1	2	yes	complemented
507	#464	C₂²×C₁₃	1	2	yes	complemented
508	#464	C₂²×C₁₃	1	2	yes	complemented
509	#463	C₂²×C₁₃	1	2	yes	—
510	#463	C₂²×C₁₃	1	2	yes	—
511	#463	C₂²×C₁₃	1	2	yes	—
512	#463	C₂²×C₁₃	1	2	yes	complemented
513	#463	C₂²×C₁₃	1	2	yes	complemented
514	#462	C₂²×C₁₃	1	2	yes	complemented
515	#461	C₂²×C₁₃	1	2	yes	—
516	#461	C₂²×C₁₃	1	2	yes	complemented
517	#460	C₂²×C₁₃	1	2	yes	—
518	#459	C₂²×C₁₃	1	2	yes	—
519	#459	C₂²×C₁₃	1	2	yes	—
520	#452	C₂²×C₁₃	1	2	yes	—
521	#451	C₂²×C₁₃	1	2	yes	—
522	#450	C₂²×C₁₃	1	2	yes	—
523	#449	C₂²×C₁₃	1	2	yes	—
524	#448	C₂²×C₁₃	1	2	yes	—
525	#447	C₂²×C₁₃	1	2	yes	—
526	#446	C₂²×C₁₃	1	2	yes	complemented
527	#446	C₂²×C₁₃	1	2	yes	complemented
528	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
529	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
530	#442	C₂²×C₁₃	1	2	yes	—
531	#441	C₂²×C₁₃	1	2	yes	complemented
532	#440	C₂²×C₁₃	1	2	yes	—
533	#440	C₂²×C₁₃	1	2	yes	complemented
534	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
535	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
536	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
537	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
538	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
539	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
540	C₄×D₈	C₂²×C₁₃	1	2	yes	—
541	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
542	#433	C₂²×C₁₃	1	2	yes	—
543	#433	C₂²×C₁₃	1	1	yes	characteristic
544	#433	C₂²×C₁₃	1	1	yes	characteristic
545	#431	C₂²×C₁₃	1	2	yes	—
546	C₂²×C₁₃	—	2	2	no	—
547	C₂²×C₁₃	—	2	1	no	—
548	C₂²×C₁₃	—	4	2	no	—
549	C₂²×C₁₃	—	4	2	no	—
550	C₂²×C₁₃	—	4	2	no	—
551	C₂²×C₁₃	—	4	2	no	—
552	C₂²×C₁₃	—	4	2	no	—
553	C₂²×C₁₃	—	4	1	no	—
554	C₂²×C₁₃	—	4	2	no	—
555	C₂²×C₁₃	—	4	2	no	—
556	C₂²×C₁₃	—	16	2	no	—
557	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₁₃	—	2	2	no	—
559	C₄×C₁₃	—	2	2	no	—
560	C₄×C₁₃	—	2	2	no	—
561	C₄×C₁₃	—	2	2	no	—
562	C₄×C₁₃	—	2	2	no	—
563	C₄×C₁₃	—	2	2	no	—
564	C₄×C₁₃	—	2	1	no	—
565	C₄×C₁₃	—	4	2	no	—
566	C₄×C₁₃	—	4	2	no	—
567	C₄×C₁₃	—	4	2	no	—
568	C₄×C₁₃	—	4	1	no	—
569	C₄×C₁₃	—	4	1	no	—
570	C₄×C₁₃	—	4	1	no	—
571	C₄×C₁₃	—	4	2	no	—
572	C₄×C₁₃	#585	1	2	yes	—
573	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
574	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
577	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
578	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
579	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
584	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
585	C₂×D₈	C₂³×C₁₃	1	2	yes	—
586	C₂×D₈	C₂³×C₁₃	1	2	yes	—
587	C₂×D₈	C₂³×C₁₃	1	2	yes	—
588	C₄⋊Q₈	—	2	2	no	—
589	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
592	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
594	#127	C₂³×C₁₃	1	2	yes	—
595	#127	C₂³×C₁₃	1	1	yes	characteristic
596	#126	—	2	2	no	—
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	D₄×C₁₃	1	2	yes	—
609	#125	C₂³×C₁₃	1	2	yes	—
610	#125	C₂³×C₁₃	1	1	yes	characteristic
611	#125	C₂³×C₁₃	1	1	yes	characteristic
612	#124	—	2	2	no	—
613	#124	—	2	2	no	—
614	#124	—	2	2	no	—
615	#124	—	2	2	no	—
616	#124	—	2	1	no	—
617	#124	—	2	1	no	—
618	#124	C₂³×C₁₃	1	2	yes	—
619	#124	C₂³×C₁₃	1	2	yes	—
620	#124	C₂³×C₁₃	1	2	yes	—
621	#124	C₂³×C₁₃	1	2	yes	—
622	#124	C₂³×C₁₃	1	1	yes	characteristic
623	#124	C₂³×C₁₃	1	1	yes	characteristic
624	#124	C₂³×C₁₃	1	2	yes	—
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	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
644	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	C₂³×C₁₃	1	2	yes	—
649	#120	—	2	1	no	—
650	#120	—	2	1	no	—
651	C₄×Q₈	—	2	2	no	—
652	C₄×Q₈	—	2	2	no	—
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×Q₈	C₂³×C₁₃	1	2	yes	—
658	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
659	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
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	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	C₂³×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	C₄×D₄	C₂³×C₁₃	1	2	yes	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	—	2	2	no	—
676	#117	—	2	1	no	—
677	#117	—	2	1	no	—
678	#117	—	2	1	no	—
679	#117	—	2	2	no	—
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×C₂²⋊C₄	—	2	2	no	—
685	C₂×C₂²⋊C₄	—	2	2	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
688	#107	C₂³×C₁₃	1	2	yes	—
689	#107	C₂³×C₁₃	1	2	yes	—
690	#106	C₂³×C₁₃	1	2	yes	—
691	#106	C₂³×C₁₃	1	2	yes	—
692	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
693	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
694	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
695	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
696	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
697	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
698	#103	C₂³×C₁₃	1	2	yes	—
699	#103	C₂³×C₁₃	1	2	yes	—
700	#103	C₂³×C₁₃	1	2	yes	—
701	#103	C₂³×C₁₃	1	2	yes	—
702	#103	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	#102	C₂³×C₁₃	1	2	yes	—
707	#102	C₂³×C₁₃	1	2	yes	—
708	#102	C₂³×C₁₃	1	2	yes	—
709	#102	C₂³×C₁₃	1	2	yes	—
710	#102	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	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
715	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
716	#97	C₂³×C₁₃	1	1	yes	characteristic
717	#97	C₂³×C₁₃	1	2	yes	—
718	#97	C₂³×C₁₃	1	1	yes	characteristic
719	C₄×C₈	C₂³×C₁₃	1	2	yes	—
720	C₄×C₈	C₂³×C₁₃	1	2	yes	—
721	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
722	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
723	C₄×C₈	C₂³×C₁₃	1	2	yes	—
724	C₂×C₁₃	—	4	1	no	—
725	C₂×C₁₃	—	8	2	no	—
726	C₂×C₁₃	—	8	1	no	—
727	C₂×C₁₃	—	8	2	no	—
728	C₂×C₁₃	#3487	1	1	yes	characteristic
729	C₂×C₁₃	#3584	1	2	yes	—
730	C₂⁴	—	2	1	no	—
731	#41	—	4	2	no	—
732	C₂×Q₈	—	2	1	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	4	2	no	—
735	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
736	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
737	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
741	C₂×D₄	—	2	1	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	1	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
749	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
750	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
761	Q₁₆	—	4	2	no	—
762	Q₁₆	—	4	2	no	—
763	Q₁₆	—	4	2	no	—
764	SD₁₆	—	4	2	no	—
765	SD₁₆	—	4	2	no	—
766	SD₁₆	—	4	2	no	—
767	SD₁₆	—	4	2	no	—
768	SD₁₆	—	4	2	no	—
769	SD₁₆	—	4	2	no	—
770	D₈	—	4	2	no	—
771	D₈	—	4	2	no	—
772	D₈	—	4	2	no	—
773	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
774	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
775	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
776	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
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	C₂×D₄×C₁₃	1	2	yes	—
793	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
794	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
795	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
796	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
797	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
798	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
799	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
800	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
802	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
803	C₂²⋊C₄	—	2	1	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₁₃	1	2	yes	—
825	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
826	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
827	C₄²	—	2	2	no	—
828	C₄²	—	2	1	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
835	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
836	C₄²	C₂⁴×C₁₃	1	2	yes	—
837	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
838	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
839	C₄²	C₂⁴×C₁₃	1	2	yes	—
840	C₁₃	#61930	1	1	yes	characteristic, direct product factor, Sylow
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	4	2	no	—
845	C₂³	—	8	2	no	—
846	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
847	Q₈	—	2	2	no	—
848	Q₈	—	2	2	no	—
849	Q₈	—	2	2	no	—
850	Q₈	—	2	2	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	4	2	no	—
853	Q₈	—	4	2	no	—
854	Q₈	—	4	2	no	—
855	Q₈	—	8	2	no	—
856	D₄	—	2	2	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	2	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	4	2	no	—
862	D₄	—	4	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	2	no	—
866	D₄	—	8	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	8	2	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	—	8	2	no	—
881	C₂×C₄	—	8	2	no	—
882	C₂×C₄	—	8	2	no	—
883	C₂×C₄	—	8	2	no	—
884	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
888	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
889	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
890	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
891	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
892	C₈	—	2	2	no	—
893	C₈	—	2	2	no	—
894	C₈	—	2	2	no	—
895	C₈	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	16	2	no	—
907	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
908	C₄	—	2	2	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	1	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	2	no	—
922	C₄	C₁₃×#585	1	2	yes	—
923	C₂	—	4	1	no	—
924	C₂	—	8	2	no	—
925	C₂	—	8	2	no	—
926	C₂	—	8	1	no	—
927	C₂	C₁₃×#3487	1	1	yes	characteristic
928	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 ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3557	C₂	semidirect
2. C₁₃×#3510	C₂	semidirect
3. C₁₃×#3403	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3394	C₂	semidirect
6. C₁₃×#3393	C₂	semidirect
7. C₁₃×#3377	C₂	semidirect
8. C₁₃×#3376	C₂	semidirect
9. C₁₃×#3365	C₂	semidirect
10. C₁₃×#3361	C₂	semidirect
11. C₁₃×#3224	C₂	semidirect
12. C₁₃×#3223	C₂	semidirect
13. C₁₃×#3221	C₂	semidirect
14. C₁₃×#3211	C₂	semidirect
15. C₁₃×#3123	C₂	semidirect
16. C₁₃×#3122	C₂	semidirect
17. C₁₃×#3121	C₂	semidirect
18. C₁₃×#3102	C₂	semidirect
19. C₁₃×#2986	C₂	semidirect
23. C₁₃×#559	C₂²	semidirect
24. C₁₃×#557	C₂²	semidirect
27. C₁₃×#556	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
47. C₁₃×#497	C₂²	semidirect
49. C₁₃×#496	C₂²	semidirect
53. C₁₃×#494	C₂²	semidirect
54. C₁₃×#492	C₂²	semidirect
55. C₁₃×#491	C₂²	semidirect
56. C₁₃×#491	C₂²	semidirect
60. C₁₃×#488	C₂²	semidirect
61. C₁₃×#488	C₂²	semidirect
65. C₁₃×#479	C₂²	semidirect
68. C₁₃×#478	C₂²	semidirect
69. C₁₃×#477	C₂²	semidirect
70. C₁₃×#475	C₂²	semidirect
74. C₁₃×#464	C₂²	semidirect
75. C₁₃×#464	C₂²	semidirect
76. C₁₃×#464	C₂²	semidirect
77. C₁₃×#464	C₂²	semidirect
81. C₁₃×#463	C₂²	semidirect
82. C₁₃×#463	C₂²	semidirect
83. C₁₃×#462	C₂²	semidirect
85. C₁₃×#461	C₂²	semidirect
95. C₁₃×#446	C₂²	semidirect
96. C₁₃×#446	C₂²	semidirect
97. C₈×Q₈×C₁₃	C₂²	semidirect
98. C₈×Q₈×C₁₃	C₂²	semidirect
100. C₁₃×#441	C₂²	semidirect
102. C₁₃×#440	C₂²	semidirect
103. C₄×C₁₃×Q₁₆	C₂²	semidirect
104. C₄×C₁₃×Q₁₆	C₂²	semidirect
106. C₄×C₁₃×SD₁₆	C₂²	semidirect
107. C₄×C₁₃×SD₁₆	C₂²	semidirect
108. C₄×C₁₃×SD₁₆	C₂²	semidirect
110. C₄×C₁₃×D₈	C₂²	semidirect
266. #61930	C₁₃	direct (N × H)
377. #3557	C₂×C₁₃	semidirect
378. #3510	C₂×C₁₃	semidirect
379. #3403	C₂×C₁₃	semidirect
380. #3401	C₂×C₁₃	semidirect
381. #3394	C₂×C₁₃	semidirect
382. #3393	C₂×C₁₃	semidirect
383. #3377	C₂×C₁₃	semidirect
384. #3376	C₂×C₁₃	semidirect
385. #3365	C₂×C₁₃	semidirect
386. #3361	C₂×C₁₃	semidirect
387. #3224	C₂×C₁₃	semidirect
388. #3223	C₂×C₁₃	semidirect
389. #3221	C₂×C₁₃	semidirect
390. #3211	C₂×C₁₃	semidirect
391. #3123	C₂×C₁₃	semidirect
392. #3122	C₂×C₁₃	semidirect
393. #3121	C₂×C₁₃	semidirect
394. #3102	C₂×C₁₃	semidirect
395. #2986	C₂×C₁₃	semidirect
454. #559	C₂²×C₁₃	semidirect
455. #557	C₂²×C₁₃	semidirect
458. #556	C₂²×C₁₃	semidirect
459. #554	C₂²×C₁₃	semidirect
478. #497	C₂²×C₁₃	semidirect
480. #496	C₂²×C₁₃	semidirect
484. #494	C₂²×C₁₃	semidirect
485. #492	C₂²×C₁₃	semidirect
486. #491	C₂²×C₁₃	semidirect
487. #491	C₂²×C₁₃	semidirect
491. #488	C₂²×C₁₃	semidirect
492. #488	C₂²×C₁₃	semidirect
496. #479	C₂²×C₁₃	semidirect
499. #478	C₂²×C₁₃	semidirect
500. #477	C₂²×C₁₃	semidirect
501. #475	C₂²×C₁₃	semidirect
505. #464	C₂²×C₁₃	semidirect
506. #464	C₂²×C₁₃	semidirect
507. #464	C₂²×C₁₃	semidirect
508. #464	C₂²×C₁₃	semidirect
512. #463	C₂²×C₁₃	semidirect
513. #463	C₂²×C₁₃	semidirect
514. #462	C₂²×C₁₃	semidirect
516. #461	C₂²×C₁₃	semidirect
526. #446	C₂²×C₁₃	semidirect
527. #446	C₂²×C₁₃	semidirect
528. C₈×Q₈	C₂²×C₁₃	semidirect
529. C₈×Q₈	C₂²×C₁₃	semidirect
531. #441	C₂²×C₁₃	semidirect
533. #440	C₂²×C₁₃	semidirect
534. C₄×Q₁₆	C₂²×C₁₃	semidirect
535. C₄×Q₁₆	C₂²×C₁₃	semidirect
537. C₄×SD₁₆	C₂²×C₁₃	semidirect
538. C₄×SD₁₆	C₂²×C₁₃	semidirect
539. C₄×SD₁₆	C₂²×C₁₃	semidirect
541. C₄×D₈	C₂²×C₁₃	semidirect
840. C₁₃	#61930	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×#3557	2
C₁₃×#3510	2
C₁₃×#3403	2
C₁₃×#3401	2
C₁₃×#3394	2
C₁₃×#3393	2
C₁₃×#3377	2
C₁₃×#3376	2
C₁₃×#3365	2
C₁₃×#3361	2
C₁₃×#3224	2
C₁₃×#3223	2
C₁₃×#3221	2
C₁₃×#3211	2
C₁₃×#3123	2
C₁₃×#3122	2
C₁₃×#3121	2
C₁₃×#3102	2
C₁₃×#2986	2
#61930	13

Subgroups — C13×#61930 #15748269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61930 #15748269