Subgroups — C₁₃×#62561 #15748900

Order 3328.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3319	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3309	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3305	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3179	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#562	—	2	2	no	—
25	C₁₃×#560	—	2	2	no	—
26	C₁₃×#556	C₂²	1	1	yes	characteristic
27	C₁₃×#555	C₂²	1	1	yes	characteristic
28	C₁₃×#555	C₂²	1	2	yes	complemented
29	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#553	—	2	1	no	—
31	C₁₃×#553	C₂²	1	2	yes	complemented
32	C₁₃×#552	—	2	1	no	—
33	C₁₃×#550	C₂²	1	2	yes	—
34	C₁₃×#550	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#548	—	2	1	no	—
37	C₁₃×#547	C₂²	1	1	yes	characteristic
38	C₁₃×#547	C₂²	1	1	yes	characteristic
39	C₁₃×#546	—	2	1	no	—
40	C₁₃×#546	C₂²	1	2	yes	—
41	D₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#544	C₂²	1	2	yes	complemented
43	C₁₃×#542	—	2	2	no	—
44	C₁₃×#542	C₂²	1	2	yes	—
45	C₁₃×#540	C₂²	1	2	yes	complemented
46	C₁₃×#538	—	2	2	no	—
47	C₁₃×#537	—	2	1	no	—
48	C₁₃×#537	—	2	1	no	—
49	C₁₃×#536	—	2	1	no	—
50	C₁₃×#535	—	2	1	no	—
51	C₁₃×#535	C₂²	1	2	yes	—
52	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#532	C₂²	1	1	yes	characteristic
54	C₁₃×#532	C₂²	1	1	yes	characteristic
55	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#529	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	2	yes	complemented
58	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#496	C₂²	1	2	yes	complemented
60	C₁₃×#493	C₂²	1	1	yes	characteristic
61	C₁₃×#490	C₂²	1	2	yes	—
62	C₁₃×#490	C₂²	1	2	yes	complemented
63	C₁₃×#489	C₂²	1	2	yes	—
64	C₁₃×#489	C₂²	1	2	yes	complemented
65	C₁₃×#488	C₂²	1	2	yes	—
66	C₁₃×#488	C₂²	1	2	yes	complemented
67	C₁₃×#488	C₂²	1	2	yes	complemented
68	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#486	C₂²	1	1	yes	characteristic
71	C₁₃×#486	C₂²	1	1	yes	characteristic
72	C₁₃×#486	C₂²	1	1	yes	characteristic
73	C₁₃×#486	C₂²	1	2	yes	complemented
74	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#485	C₂²	1	2	yes	complemented
76	C₁₃×#484	C₂²	1	2	yes	complemented
77	C₁₃×#482	C₂²	1	2	yes	—
78	C₁₃×#482	C₂²	1	2	yes	—
79	C₁₃×#482	C₂²	1	2	yes	complemented
80	C₁₃×#480	C₂²	1	2	yes	—
81	C₁₃×#479	C₂²	1	2	yes	complemented
82	C₁₃×#478	C₂²	1	2	yes	complemented
83	C₁₃×#477	C₂²	1	2	yes	complemented
84	C₁₃×#476	C₂²	1	1	yes	characteristic
85	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#474	C₂²	1	1	yes	characteristic
87	C₁₃×#474	C₂²	1	2	yes	complemented
88	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#469	C₂²	1	2	yes	—
90	C₁₃×#468	C₂²	1	2	yes	complemented
91	C₁₃×#466	C₂²	1	2	yes	—
92	C₁₃×#466	C₂²	1	1	yes	characteristic
93	C₁₃×#466	C₂²	1	1	yes	characteristic
94	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#465	C₂²	1	2	yes	complemented
97	C₁₃×#463	C₂²	1	2	yes	—
98	C₁₃×#463	C₂²	1	2	yes	—
99	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
101	C₁₃×#459	C₂²	1	1	yes	characteristic
102	C₁₃×#459	C₂²	1	1	yes	characteristic
103	C₁₃×#459	C₂²	1	2	yes	complemented
104	C₁₃×#459	C₂²	1	2	yes	complemented
105	C₁₃×#449	C₂²	1	2	yes	complemented
106	C₁₃×#449	C₂²	1	2	yes	complemented
107	C₁₃×#449	C₂²	1	2	yes	complemented
108	C₁₃×#449	C₂²	1	2	yes	complemented
109	C₁₃×#447	C₂²	1	2	yes	—
110	C₁₃×#447	C₂²	1	2	yes	—
111	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
113	C₁₃×#442	C₂²	1	2	yes	complemented
114	C₁₃×#440	C₂²	1	2	yes	complemented
115	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
117	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
118	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₁₃×#436	C₂²	1	1	yes	characteristic
122	C₁₃×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
125	C₁₃×#433	C₂²	1	2	yes	complemented
126	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#418	C₂²	1	2	yes	—
128	C₁₃×#417	C₂²	1	2	yes	complemented
129	C₁₃×#416	C₂²	1	2	yes	complemented
130	C₁₃×#416	C₂²	1	2	yes	complemented
131	C₁₃×#416	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	—
133	C₁₃×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	1	no	—
137	C₂×C₁₃×#41	—	2	1	no	—
138	C₂×C₁₃×#41	—	2	1	no	—
139	C₂×C₁₃×#41	C₂³	1	2	yes	—
140	C₂×C₁₃×#41	C₂³	1	2	yes	—
141	C₂²×Q₈×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	—	2	1	no	—
143	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
144	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×D₈	C₂³	1	2	yes	—
149	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×D₈	C₂³	1	2	yes	—
152	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
153	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
156	C₁₃×C₄⋊Q₈	—	2	2	no	—
157	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×#127	—	2	2	no	—
164	C₁₃×#127	C₂³	1	1	yes	characteristic
165	C₁₃×#127	C₂³	1	2	yes	—
166	C₁₃×#127	C₂³	1	1	yes	characteristic
167	C₁₃×#127	C₂³	1	1	yes	characteristic
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	D₄	1	2	yes	—
172	C₁₃×#125	—	2	2	no	—
173	C₁₃×#125	D₄	1	1	yes	characteristic
174	C₁₃×#125	C₂³	1	2	yes	—
175	C₁₃×#125	C₂³	1	2	yes	—
176	C₁₃×#124	—	2	2	no	—
177	C₁₃×#124	—	2	2	no	—
178	C₁₃×#124	—	2	2	no	—
179	C₁₃×#124	—	2	2	no	—
180	C₁₃×#124	—	2	1	no	—
181	C₁₃×#124	—	2	1	no	—
182	C₁₃×#124	D₄	1	1	yes	characteristic
183	C₁₃×#124	C₂³	1	2	yes	—
184	C₁₃×#124	C₂³	1	2	yes	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	—	2	2	no	—
188	C₁₃×#123	—	2	2	no	—
189	C₁₃×#123	—	2	2	no	—
190	C₁₃×#123	—	2	2	no	—
191	C₁₃×#123	—	2	2	no	—
192	C₁₃×#123	D₄	1	2	yes	—
193	C₁₃×C₂²⋊Q₈	—	2	1	no	—
194	C₁₃×C₂²⋊Q₈	—	2	1	no	—
195	C₁₃×C₂²⋊Q₈	—	2	1	no	—
196	C₁₃×C₂²⋊Q₈	—	2	1	no	—
197	C₁₃×C₂²⋊Q₈	—	2	1	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	—	2	1	no	—
200	C₁₃×C₂²⋊Q₈	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	—	2	2	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
205	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₁₃×#121	—	2	1	no	—
207	C₁₃×#121	—	2	1	no	—
208	C₁₃×#121	—	2	2	no	—
209	C₁₃×#121	—	2	2	no	—
210	C₁₃×#121	—	2	1	no	—
211	C₁₃×#121	—	2	1	no	—
212	C₁₃×#121	—	2	1	no	—
213	C₁₃×#121	—	2	1	no	—
214	C₁₃×#121	—	2	1	no	—
215	C₁₃×#121	—	2	2	no	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	—	2	1	no	—
218	C₁₃×#121	—	2	2	no	—
219	C₁₃×#121	—	2	2	no	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	—	2	2	no	—
223	C₁₃×#121	—	2	2	no	—
224	C₁₃×#121	D₄	1	1	yes	characteristic
225	C₁₃×#121	C₂³	1	2	yes	—
226	C₁₃×#121	C₂³	1	2	yes	—
227	C₁₃×#121	C₂³	1	1	yes	characteristic
228	C₁₃×#121	C₂³	1	1	yes	characteristic
229	C₁₃×#121	C₂³	1	1	yes	characteristic
230	C₁₃×#121	C₂³	1	2	yes	—
231	C₁₃×#121	C₂³	1	1	yes	characteristic
232	C₁₃×#120	—	2	2	no	—
233	C₁₃×#120	—	2	2	no	—
234	C₁₃×#120	—	2	2	no	—
235	C₁₃×#120	—	2	2	no	—
236	C₄×Q₈×C₁₃	—	2	1	no	—
237	C₄×Q₈×C₁₃	—	2	1	no	—
238	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₃	—	2	2	no	—
241	C₄×D₄×C₁₃	—	2	2	no	—
242	C₄×D₄×C₁₃	—	2	1	no	—
243	C₄×D₄×C₁₃	—	2	1	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	—	2	1	no	—
246	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₁₃	C₂³	1	2	yes	—
251	C₄×D₄×C₁₃	C₂³	1	2	yes	—
252	C₄×D₄×C₁₃	C₂³	1	2	yes	—
253	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	—	2	1	no	—
257	C₁₃×#117	—	2	2	no	—
258	C₁₃×#117	C₂³	1	2	yes	—
259	C₁₃×#117	C₂³	1	2	yes	—
260	C₁₃×#117	C₂³	1	2	yes	—
261	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
266	C₁₃×#107	C₂³	1	1	yes	characteristic
267	C₁₃×#107	C₂³	1	1	yes	characteristic
268	C₁₃×#107	C₂³	1	1	yes	characteristic
269	C₁₃×#107	C₂³	1	1	yes	characteristic
270	C₁₃×#107	C₂³	1	2	yes	—
271	C₁₃×#107	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
277	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₁₃×#103	C₂³	1	2	yes	—
279	C₁₃×#103	C₂³	1	2	yes	—
280	C₁₃×#103	C₂³	1	2	yes	—
281	C₁₃×#103	C₂³	1	2	yes	—
282	C₁₃×#103	C₂³	1	2	yes	—
283	C₁₃×#103	C₂³	1	2	yes	—
284	C₁₃×#102	C₂³	1	1	yes	characteristic
285	C₁₃×#102	C₂³	1	2	yes	—
286	C₁₃×#102	C₂³	1	2	yes	—
287	C₁₃×#102	C₂³	1	2	yes	—
288	C₁₃×#102	C₂³	1	1	yes	characteristic
289	C₁₃×#102	C₂³	1	2	yes	—
290	C₁₃×#102	C₂³	1	2	yes	—
291	C₁₃×#102	C₂³	1	2	yes	—
292	C₁₃×#102	C₂³	1	2	yes	—
293	C₁₃×#102	C₂³	1	1	yes	characteristic
294	C₁₃×#102	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	1	yes	characteristic
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×#97	C₂³	1	2	yes	—
306	C₁₃×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	#62561	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂⁴×C₁₃	—	2	2	no	—
314	C₁₃×#41	—	4	2	no	—
315	C₁₃×#41	—	4	2	no	—
316	C₁₃×#41	—	4	2	no	—
317	C₁₃×#41	—	4	2	no	—
318	C₁₃×#41	—	8	2	no	—
319	C₁₃×#41	—	8	2	no	—
320	C₁₃×#41	—	8	2	no	—
321	C₁₃×#41	—	8	2	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	1	no	—
325	C₂×Q₈×C₁₃	—	2	2	no	—
326	C₂×Q₈×C₁₃	—	2	1	no	—
327	C₂×Q₈×C₁₃	—	8	2	no	—
328	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
330	C₂×D₄×C₁₃	—	2	2	no	—
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	1	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	1	no	—
339	C₂×D₄×C₁₃	—	2	1	no	—
340	C₂×D₄×C₁₃	—	2	1	no	—
341	C₂×D₄×C₁₃	—	2	1	no	—
342	C₂×D₄×C₁₃	—	2	2	no	—
343	C₂×D₄×C₁₃	—	2	1	no	—
344	C₂×D₄×C₁₃	—	2	1	no	—
345	C₂×D₄×C₁₃	—	2	2	no	—
346	C₂×D₄×C₁₃	—	2	2	no	—
347	C₂×D₄×C₁₃	—	2	1	no	—
348	C₂×D₄×C₁₃	—	4	2	no	—
349	C₂×D₄×C₁₃	—	4	2	no	—
350	C₂×D₄×C₁₃	—	8	2	no	—
351	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
355	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₁₃	—	2	2	no	—
359	C₂²×C₄×C₁₃	—	2	1	no	—
360	C₂²×C₄×C₁₃	—	2	1	no	—
361	C₂²×C₄×C₁₃	—	2	1	no	—
362	C₂²×C₄×C₁₃	—	2	1	no	—
363	C₂²×C₄×C₁₃	—	2	2	no	—
364	C₂²×C₄×C₁₃	—	2	2	no	—
365	C₂²×C₄×C₁₃	—	2	2	no	—
366	C₂²×C₄×C₁₃	—	2	2	no	—
367	C₂²×C₄×C₁₃	—	2	2	no	—
368	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
372	C₁₃×SD₁₆	—	4	2	no	—
373	C₁₃×SD₁₆	—	4	2	no	—
374	C₁₃×D₈	—	4	1	no	—
375	C₁₃×D₈	—	4	1	no	—
376	C₁₃×D₈	—	4	1	no	—
377	C₁₃×D₈	—	4	1	no	—
378	C₁₃×D₈	—	4	2	no	—
379	C₁₃×D₈	—	4	2	no	—
380	C₁₃×M₁₆	—	4	2	no	—
381	C₂×C₈×C₁₃	—	4	1	no	—
382	C₂×C₈×C₁₃	—	4	2	no	—
383	C₂×C₈×C₁₃	—	4	1	no	—
384	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
389	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	2	no	—
396	C₁₃×C₄⋊C₄	—	2	1	no	—
397	C₁₃×C₄⋊C₄	—	2	1	no	—
398	C₁₃×C₄⋊C₄	—	2	1	no	—
399	C₁₃×C₄⋊C₄	—	2	2	no	—
400	C₁₃×C₄⋊C₄	—	2	2	no	—
401	C₁₃×C₄⋊C₄	—	2	2	no	—
402	C₁₃×C₄⋊C₄	—	2	1	no	—
403	C₁₃×C₄⋊C₄	—	2	2	no	—
404	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
407	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
411	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
413	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	1	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	1	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	1	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	1	no	—
433	C₁₃×C₂²⋊C₄	—	2	2	no	—
434	C₁₃×C₂²⋊C₄	—	2	1	no	—
435	C₁₃×C₂²⋊C₄	—	2	2	no	—
436	C₁₃×C₂²⋊C₄	—	2	1	no	—
437	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
441	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₄²×C₁₃	—	2	2	no	—
443	C₄²×C₁₃	—	2	2	no	—
444	C₄²×C₁₃	—	2	2	no	—
445	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
448	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
449	C₄²×C₁₃	C₂⁴	1	2	yes	—
450	#3547	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3546	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3367	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#3366	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3330	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3325	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3319	C₂×C₁₃	1	2	yes	complemented
459	#3309	C₂×C₁₃	1	2	yes	complemented
460	#3305	C₂×C₁₃	1	2	yes	complemented
461	#3303	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3297	C₂×C₁₃	1	2	yes	complemented
463	#3294	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3243	C₂×C₁₃	1	2	yes	complemented
465	#3235	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3220	C₂×C₁₃	1	2	yes	complemented
467	#3214	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3179	C₂×C₁₃	1	2	yes	complemented
469	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3136	C₂×C₁₃	1	2	yes	complemented
471	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
473	C₂³×C₁₃	—	2	1	no	—
474	C₂³×C₁₃	—	2	1	no	—
475	C₂³×C₁₃	—	2	1	no	—
476	C₂³×C₁₃	—	2	2	no	—
477	C₂³×C₁₃	—	2	1	no	—
478	C₂³×C₁₃	—	8	2	no	—
479	C₂³×C₁₃	—	8	2	no	—
480	C₂³×C₁₃	—	8	2	no	—
481	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
482	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
483	Q₈×C₁₃	—	2	2	no	—
484	Q₈×C₁₃	—	2	2	no	—
485	Q₈×C₁₃	—	2	2	no	—
486	Q₈×C₁₃	—	4	2	no	—
487	Q₈×C₁₃	—	8	1	no	—
488	Q₈×C₁₃	—	8	2	no	—
489	Q₈×C₁₃	—	8	1	no	—
490	Q₈×C₁₃	—	8	1	no	—
491	D₄×C₁₃	—	2	2	no	—
492	D₄×C₁₃	—	2	1	no	—
493	D₄×C₁₃	—	2	1	no	—
494	D₄×C₁₃	—	2	1	no	—
495	D₄×C₁₃	—	2	1	no	—
496	D₄×C₁₃	—	2	1	no	—
497	D₄×C₁₃	—	2	1	no	—
498	D₄×C₁₃	—	2	2	no	—
499	D₄×C₁₃	—	2	2	no	—
500	D₄×C₁₃	—	2	1	no	—
501	D₄×C₁₃	—	2	1	no	—
502	D₄×C₁₃	—	4	2	no	—
503	D₄×C₁₃	—	4	2	no	—
504	D₄×C₁₃	—	8	1	no	—
505	D₄×C₁₃	—	8	1	no	—
506	D₄×C₁₃	—	8	1	no	—
507	D₄×C₁₃	—	8	2	no	—
508	D₄×C₁₃	—	8	2	no	—
509	D₄×C₁₃	—	8	1	no	—
510	D₄×C₁₃	—	8	1	no	—
511	D₄×C₁₃	—	8	2	no	—
512	D₄×C₁₃	—	8	2	no	—
513	D₄×C₁₃	—	8	2	no	—
514	D₄×C₁₃	—	8	2	no	—
515	D₄×C₁₃	—	8	2	no	—
516	D₄×C₁₃	—	8	1	no	—
517	D₄×C₁₃	—	8	1	no	—
518	D₄×C₁₃	—	8	1	no	—
519	D₄×C₁₃	—	8	1	no	—
520	D₄×C₁₃	—	8	2	no	—
521	C₂×C₄×C₁₃	—	2	2	no	—
522	C₂×C₄×C₁₃	—	2	2	no	—
523	C₂×C₄×C₁₃	—	2	1	no	—
524	C₂×C₄×C₁₃	—	2	1	no	—
525	C₂×C₄×C₁₃	—	2	2	no	—
526	C₂×C₄×C₁₃	—	2	2	no	—
527	C₂×C₄×C₁₃	—	2	1	no	—
528	C₂×C₄×C₁₃	—	2	1	no	—
529	C₂×C₄×C₁₃	—	2	2	no	—
530	C₂×C₄×C₁₃	—	2	2	no	—
531	C₂×C₄×C₁₃	—	2	1	no	—
532	C₂×C₄×C₁₃	—	2	1	no	—
533	C₂×C₄×C₁₃	—	4	1	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	4	2	no	—
536	C₂×C₄×C₁₃	—	4	2	no	—
537	C₂×C₄×C₁₃	—	4	2	no	—
538	C₂×C₄×C₁₃	—	8	2	no	—
539	C₂×C₄×C₁₃	—	8	2	no	—
540	C₂×C₄×C₁₃	—	8	2	no	—
541	C₂×C₄×C₁₃	—	8	2	no	—
542	C₂×C₄×C₁₃	—	8	2	no	—
543	C₂×C₄×C₁₃	—	8	2	no	—
544	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
553	C₈×C₁₃	—	2	1	no	—
554	C₈×C₁₃	—	2	1	no	—
555	C₈×C₁₃	—	2	1	no	—
556	C₈×C₁₃	—	2	1	no	—
557	C₈×C₁₃	—	2	2	no	—
558	C₈×C₁₃	—	2	2	no	—
559	#562	—	2	2	no	—
560	#560	—	2	2	no	—
561	#556	C₂²×C₁₃	1	1	yes	characteristic
562	#555	C₂²×C₁₃	1	1	yes	characteristic
563	#555	C₂²×C₁₃	1	2	yes	complemented
564	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
565	#553	—	2	1	no	—
566	#553	C₂²×C₁₃	1	2	yes	complemented
567	#552	—	2	1	no	—
568	#550	C₂²×C₁₃	1	2	yes	—
569	#550	C₂²×C₁₃	1	1	yes	characteristic
570	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
571	#548	—	2	1	no	—
572	#547	C₂²×C₁₃	1	1	yes	characteristic
573	#547	C₂²×C₁₃	1	1	yes	characteristic
574	#546	—	2	1	no	—
575	#546	C₂²×C₁₃	1	2	yes	—
576	D₄²	C₂²×C₁₃	1	1	yes	characteristic
577	#544	C₂²×C₁₃	1	2	yes	complemented
578	#542	—	2	2	no	—
579	#542	C₂²×C₁₃	1	2	yes	—
580	#540	C₂²×C₁₃	1	2	yes	complemented
581	#538	—	2	2	no	—
582	#537	—	2	1	no	—
583	#537	—	2	1	no	—
584	#536	—	2	1	no	—
585	#535	—	2	1	no	—
586	#535	C₂²×C₁₃	1	2	yes	—
587	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
588	#532	C₂²×C₁₃	1	1	yes	characteristic
589	#532	C₂²×C₁₃	1	1	yes	characteristic
590	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
591	#529	C₂²×C₁₃	1	1	yes	characteristic
592	#501	C₂²×C₁₃	1	2	yes	complemented
593	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
594	#496	C₂²×C₁₃	1	2	yes	complemented
595	#493	C₂²×C₁₃	1	1	yes	characteristic
596	#490	C₂²×C₁₃	1	2	yes	—
597	#490	C₂²×C₁₃	1	2	yes	complemented
598	#489	C₂²×C₁₃	1	2	yes	—
599	#489	C₂²×C₁₃	1	2	yes	complemented
600	#488	C₂²×C₁₃	1	2	yes	—
601	#488	C₂²×C₁₃	1	2	yes	complemented
602	#488	C₂²×C₁₃	1	2	yes	complemented
603	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
604	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	#486	C₂²×C₁₃	1	1	yes	characteristic
606	#486	C₂²×C₁₃	1	1	yes	characteristic
607	#486	C₂²×C₁₃	1	1	yes	characteristic
608	#486	C₂²×C₁₃	1	2	yes	complemented
609	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	#485	C₂²×C₁₃	1	2	yes	complemented
611	#484	C₂²×C₁₃	1	2	yes	complemented
612	#482	C₂²×C₁₃	1	2	yes	—
613	#482	C₂²×C₁₃	1	2	yes	—
614	#482	C₂²×C₁₃	1	2	yes	complemented
615	#480	C₂²×C₁₃	1	2	yes	—
616	#479	C₂²×C₁₃	1	2	yes	complemented
617	#478	C₂²×C₁₃	1	2	yes	complemented
618	#477	C₂²×C₁₃	1	2	yes	complemented
619	#476	C₂²×C₁₃	1	1	yes	characteristic
620	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
621	#474	C₂²×C₁₃	1	1	yes	characteristic
622	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
623	#474	C₂²×C₁₃	1	2	yes	complemented
624	#469	C₂²×C₁₃	1	2	yes	—
625	#468	C₂²×C₁₃	1	2	yes	complemented
626	#466	C₂²×C₁₃	1	1	yes	characteristic
627	#466	C₂²×C₁₃	1	1	yes	characteristic
628	#466	C₂²×C₁₃	1	2	yes	—
629	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#465	C₂²×C₁₃	1	2	yes	complemented
632	#463	C₂²×C₁₃	1	2	yes	—
633	#463	C₂²×C₁₃	1	2	yes	—
634	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#459	C₂²×C₁₃	1	1	yes	characteristic
637	#459	C₂²×C₁₃	1	1	yes	characteristic
638	#459	C₂²×C₁₃	1	2	yes	complemented
639	#459	C₂²×C₁₃	1	2	yes	complemented
640	#449	C₂²×C₁₃	1	2	yes	complemented
641	#449	C₂²×C₁₃	1	2	yes	complemented
642	#449	C₂²×C₁₃	1	2	yes	complemented
643	#449	C₂²×C₁₃	1	2	yes	complemented
644	#447	C₂²×C₁₃	1	2	yes	—
645	#447	C₂²×C₁₃	1	2	yes	—
646	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
647	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	#442	C₂²×C₁₃	1	2	yes	complemented
649	#440	C₂²×C₁₃	1	2	yes	complemented
650	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
651	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
652	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
653	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
656	#436	C₂²×C₁₃	1	1	yes	characteristic
657	#435	C₂²×C₁₃	1	2	yes	complemented
658	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
659	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
660	#433	C₂²×C₁₃	1	2	yes	complemented
661	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#418	C₂²×C₁₃	1	2	yes	—
663	#417	C₂²×C₁₃	1	2	yes	complemented
664	#416	C₂²×C₁₃	1	2	yes	complemented
665	#416	C₂²×C₁₃	1	2	yes	complemented
666	#416	C₂²×C₁₃	1	2	yes	complemented
667	C₂×#102	C₂²×C₁₃	1	2	yes	—
668	#405	C₂²×C₁₃	1	2	yes	complemented
669	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
670	C₂²×C₁₃	—	2	1	no	—
671	C₂²×C₁₃	—	2	2	no	—
672	C₂²×C₁₃	—	2	1	no	—
673	C₂²×C₁₃	—	2	2	no	—
674	C₂²×C₁₃	—	2	1	no	—
675	C₂²×C₁₃	—	2	2	no	—
676	C₂²×C₁₃	—	4	1	no	—
677	C₂²×C₁₃	—	4	1	no	—
678	C₂²×C₁₃	—	4	1	no	—
679	C₂²×C₁₃	—	4	2	no	—
680	C₂²×C₁₃	—	4	1	no	—
681	C₂²×C₁₃	—	4	1	no	—
682	C₂²×C₁₃	—	4	2	no	—
683	C₂²×C₁₃	—	4	1	no	—
684	C₂²×C₁₃	—	4	1	no	—
685	C₂²×C₁₃	—	4	1	no	—
686	C₂²×C₁₃	—	4	1	no	—
687	C₂²×C₁₃	—	4	1	no	—
688	C₂²×C₁₃	—	4	1	no	—
689	C₂²×C₁₃	—	4	1	no	—
690	C₂²×C₁₃	—	4	2	no	—
691	C₂²×C₁₃	—	16	4	no	—
692	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
693	C₄×C₁₃	—	2	1	no	—
694	C₄×C₁₃	—	2	1	no	—
695	C₄×C₁₃	—	2	2	no	—
696	C₄×C₁₃	—	2	1	no	—
697	C₄×C₁₃	—	2	2	no	—
698	C₄×C₁₃	—	2	1	no	—
699	C₄×C₁₃	—	2	2	no	—
700	C₄×C₁₃	—	4	2	no	—
701	C₄×C₁₃	—	4	2	no	—
702	C₄×C₁₃	—	4	1	no	—
703	C₄×C₁₃	—	4	1	no	—
704	C₄×C₁₃	—	4	1	no	—
705	C₄×C₁₃	—	4	1	no	—
706	C₄×C₁₃	—	4	2	no	—
707	C₄×C₁₃	#576	1	2	yes	—
708	C₄×C₁₃	#585	1	1	yes	characteristic
709	C₄×C₁₃	#585	1	1	yes	characteristic
710	C₂×#41	—	2	1	no	—
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	1	no	—
713	C₂×#41	—	2	1	no	—
714	C₂×#41	C₂³×C₁₃	1	2	yes	—
715	C₂×#41	C₂³×C₁₃	1	2	yes	—
716	C₂²×Q₈	—	2	1	no	—
717	C₂²×D₄	—	2	1	no	—
718	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
721	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
722	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
723	C₂×D₈	C₂³×C₁₃	1	2	yes	—
724	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
726	C₂×D₈	C₂³×C₁₃	1	2	yes	—
727	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
728	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
730	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
731	C₄⋊Q₈	—	2	2	no	—
732	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
738	#127	—	2	2	no	—
739	#127	C₂³×C₁₃	1	1	yes	characteristic
740	#127	C₂³×C₁₃	1	1	yes	characteristic
741	#127	C₂³×C₁₃	1	1	yes	characteristic
742	#127	C₂³×C₁₃	1	2	yes	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	D₄×C₁₃	1	2	yes	—
747	#125	—	2	2	no	—
748	#125	D₄×C₁₃	1	1	yes	characteristic
749	#125	C₂³×C₁₃	1	2	yes	—
750	#125	C₂³×C₁₃	1	2	yes	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	—	2	1	no	—
756	#124	—	2	1	no	—
757	#124	D₄×C₁₃	1	1	yes	characteristic
758	#124	C₂³×C₁₃	1	2	yes	—
759	#124	C₂³×C₁₃	1	2	yes	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	D₄×C₁₃	1	2	yes	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
780	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	D₄×C₁₃	1	1	yes	characteristic
800	#121	C₂³×C₁₃	1	1	yes	characteristic
801	#121	C₂³×C₁₃	1	1	yes	characteristic
802	#121	C₂³×C₁₃	1	1	yes	characteristic
803	#121	C₂³×C₁₃	1	1	yes	characteristic
804	#121	C₂³×C₁₃	1	2	yes	—
805	#121	C₂³×C₁₃	1	2	yes	—
806	#121	C₂³×C₁₃	1	2	yes	—
807	#120	—	2	2	no	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	C₄×Q₈	—	2	1	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
814	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₁₃	1	2	yes	—
826	C₄×D₄	C₂³×C₁₃	1	2	yes	—
827	C₄×D₄	C₂³×C₁₃	1	2	yes	—
828	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₁₃	1	2	yes	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	—	2	2	no	—
833	#117	C₂³×C₁₃	1	2	yes	—
834	#117	C₂³×C₁₃	1	2	yes	—
835	#117	C₂³×C₁₃	1	2	yes	—
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
839	C₂×C₂²⋊C₄	—	2	2	no	—
840	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
841	#107	C₂³×C₁₃	1	1	yes	characteristic
842	#107	C₂³×C₁₃	1	1	yes	characteristic
843	#107	C₂³×C₁₃	1	1	yes	characteristic
844	#107	C₂³×C₁₃	1	1	yes	characteristic
845	#107	C₂³×C₁₃	1	2	yes	—
846	#107	C₂³×C₁₃	1	2	yes	—
847	#106	C₂³×C₁₃	1	2	yes	—
848	#106	C₂³×C₁₃	1	2	yes	—
849	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
852	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
853	#103	C₂³×C₁₃	1	2	yes	—
854	#103	C₂³×C₁₃	1	2	yes	—
855	#103	C₂³×C₁₃	1	2	yes	—
856	#103	C₂³×C₁₃	1	2	yes	—
857	#103	C₂³×C₁₃	1	2	yes	—
858	#103	C₂³×C₁₃	1	2	yes	—
859	#102	C₂³×C₁₃	1	1	yes	characteristic
860	#102	C₂³×C₁₃	1	2	yes	—
861	#102	C₂³×C₁₃	1	2	yes	—
862	#102	C₂³×C₁₃	1	2	yes	—
863	#102	C₂³×C₁₃	1	1	yes	characteristic
864	#102	C₂³×C₁₃	1	2	yes	—
865	#102	C₂³×C₁₃	1	2	yes	—
866	#102	C₂³×C₁₃	1	2	yes	—
867	#102	C₂³×C₁₃	1	2	yes	—
868	#102	C₂³×C₁₃	1	1	yes	characteristic
869	#102	C₂³×C₁₃	1	2	yes	—
870	#102	C₂³×C₁₃	1	1	yes	characteristic
871	#102	C₂³×C₁₃	1	2	yes	—
872	#102	C₂³×C₁₃	1	2	yes	—
873	#102	C₂³×C₁₃	1	1	yes	characteristic
874	#102	C₂³×C₁₃	1	1	yes	characteristic
875	#102	C₂³×C₁₃	1	1	yes	characteristic
876	#102	C₂³×C₁₃	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
880	#97	C₂³×C₁₃	1	2	yes	—
881	#97	C₂³×C₁₃	1	2	yes	—
882	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₁₃	1	2	yes	—
887	C₂×C₁₃	—	4	1	no	—
888	C₂×C₁₃	—	4	2	no	—
889	C₂×C₁₃	—	8	1	no	—
890	C₂×C₁₃	—	8	1	no	—
891	C₂×C₁₃	—	8	1	no	—
892	C₂×C₁₃	—	8	2	no	—
893	C₂×C₁₃	—	8	1	no	—
894	C₂×C₁₃	#3500	1	1	yes	characteristic
895	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
896	C₂×C₁₃	#3584	1	1	yes	characteristic
897	C₂⁴	—	2	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	8	2	no	—
903	#41	—	8	2	no	—
904	#41	—	8	2	no	—
905	#41	—	8	2	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	2	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	8	2	no	—
912	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	4	2	no	—
933	C₂×D₄	—	4	2	no	—
934	C₂×D₄	—	8	2	no	—
935	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
936	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
937	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
939	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
940	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
941	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	2	no	—
958	D₈	—	4	1	no	—
959	D₈	—	4	1	no	—
960	D₈	—	4	1	no	—
961	D₈	—	4	1	no	—
962	D₈	—	4	2	no	—
963	D₈	—	4	2	no	—
964	M₁₆	—	4	2	no	—
965	C₂×C₈	—	4	1	no	—
966	C₂×C₈	—	4	2	no	—
967	C₂×C₈	—	4	1	no	—
968	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
973	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1030	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₁₃	1	2	yes	—
1034	C₁₃	#62561	1	1	yes	characteristic, direct product factor, Sylow
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	8	2	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1044	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	8	2	no	—
1050	Q₈	—	8	1	no	—
1051	Q₈	—	8	1	no	—
1052	Q₈	—	8	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	1	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	1	no	—
1081	D₄	—	8	1	no	—
1082	D₄	—	8	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1114	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₈	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	16	4	no	—
1143	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	2	no	—
1158	C₄	C₁₃×#576	1	2	yes	—
1159	C₄	C₁₃×#585	1	1	yes	characteristic
1160	C₄	C₁₃×#585	1	1	yes	characteristic
1161	C₂	—	4	2	no	—
1162	C₂	—	4	1	no	—
1163	C₂	—	8	1	no	—
1164	C₂	—	8	2	no	—
1165	C₂	—	8	1	no	—
1166	C₂	—	8	1	no	—
1167	C₂	—	8	1	no	—
1168	C₂	C₁₃×#3500	1	1	yes	characteristic
1169	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1170	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3547	C₂	semidirect
2. C₁₃×#3546	C₂	semidirect
3. C₁₃×#3367	C₂	semidirect
4. C₁₃×#3366	C₂	semidirect
5. C₁₃×#3360	C₂	semidirect
6. C₁₃×#3358	C₂	semidirect
7. C₁₃×#3330	C₂	semidirect
8. C₁₃×#3325	C₂	semidirect
9. C₁₃×#3319	C₂	semidirect
10. C₁₃×#3309	C₂	semidirect
11. C₁₃×#3305	C₂	semidirect
12. C₁₃×#3303	C₂	semidirect
13. C₁₃×#3297	C₂	semidirect
14. C₁₃×#3294	C₂	semidirect
15. C₁₃×#3243	C₂	semidirect
16. C₁₃×#3235	C₂	semidirect
17. C₁₃×#3220	C₂	semidirect
18. C₁₃×#3214	C₂	semidirect
19. C₁₃×#3179	C₂	semidirect
20. C₁₃×#3169	C₂	semidirect
21. C₁₃×#3136	C₂	semidirect
22. C₁₃×#3131	C₂	semidirect
23. C₁₃×#2966	C₂	semidirect
28. C₁₃×#555	C₂²	semidirect
29. C₁₃×#554	C₂²	semidirect
31. C₁₃×#553	C₂²	semidirect
35. D₄×Q₈×C₁₃	C₂²	semidirect
42. C₁₃×#544	C₂²	semidirect
45. C₁₃×#540	C₂²	semidirect
52. C₁₃×#533	C₂²	semidirect
55. C₁₃×#532	C₂²	semidirect
57. C₁₃×#501	C₂²	semidirect
58. C₁₃×#500	C₂²	semidirect
59. C₁₃×#496	C₂²	semidirect
62. C₁₃×#490	C₂²	semidirect
64. C₁₃×#489	C₂²	semidirect
66. C₁₃×#488	C₂²	semidirect
67. C₁₃×#488	C₂²	semidirect
68. C₁₃×#487	C₂²	semidirect
69. C₁₃×#487	C₂²	semidirect
73. C₁₃×#486	C₂²	semidirect
74. C₁₃×#486	C₂²	semidirect
75. C₁₃×#485	C₂²	semidirect
76. C₁₃×#484	C₂²	semidirect
79. C₁₃×#482	C₂²	semidirect
81. C₁₃×#479	C₂²	semidirect
82. C₁₃×#478	C₂²	semidirect
83. C₁₃×#477	C₂²	semidirect
85. C₁₃×#476	C₂²	semidirect
87. C₁₃×#474	C₂²	semidirect
88. C₁₃×#474	C₂²	semidirect
90. C₁₃×#468	C₂²	semidirect
94. C₁₃×#466	C₂²	semidirect
95. C₁₃×#466	C₂²	semidirect
96. C₁₃×#465	C₂²	semidirect
99. C₁₃×#461	C₂²	semidirect
100. C₁₃×#461	C₂²	semidirect
103. C₁₃×#459	C₂²	semidirect
104. C₁₃×#459	C₂²	semidirect
105. C₁₃×#449	C₂²	semidirect
106. C₁₃×#449	C₂²	semidirect
107. C₁₃×#449	C₂²	semidirect
108. C₁₃×#449	C₂²	semidirect
111. C₁₃×#446	C₂²	semidirect
112. C₈×Q₈×C₁₃	C₂²	semidirect
113. C₁₃×#442	C₂²	semidirect
114. C₁₃×#440	C₂²	semidirect
115. C₄×C₁₃×SD₁₆	C₂²	semidirect
118. C₄×C₁₃×D₈	C₂²	semidirect
119. C₄×C₁₃×D₈	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
122. C₁₃×#435	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₁₃×#433	C₂²	semidirect
126. C₁₃×#432	C₂²	semidirect
128. C₁₃×#417	C₂²	semidirect
129. C₁₃×#416	C₂²	semidirect
130. C₁₃×#416	C₂²	semidirect
131. C₁₃×#416	C₂²	semidirect
133. C₁₃×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₁₃	C₂²	semidirect
312. #62561	C₁₃	direct (N × H)
450. #3547	C₂×C₁₃	semidirect
451. #3546	C₂×C₁₃	semidirect
452. #3367	C₂×C₁₃	semidirect
453. #3366	C₂×C₁₃	semidirect
454. #3360	C₂×C₁₃	semidirect
455. #3358	C₂×C₁₃	semidirect
456. #3330	C₂×C₁₃	semidirect
457. #3325	C₂×C₁₃	semidirect
458. #3319	C₂×C₁₃	semidirect
459. #3309	C₂×C₁₃	semidirect
460. #3305	C₂×C₁₃	semidirect
461. #3303	C₂×C₁₃	semidirect
462. #3297	C₂×C₁₃	semidirect
463. #3294	C₂×C₁₃	semidirect
464. #3243	C₂×C₁₃	semidirect
465. #3235	C₂×C₁₃	semidirect
466. #3220	C₂×C₁₃	semidirect
467. #3214	C₂×C₁₃	semidirect
468. #3179	C₂×C₁₃	semidirect
469. #3169	C₂×C₁₃	semidirect
470. #3136	C₂×C₁₃	semidirect
471. #3131	C₂×C₁₃	semidirect
472. #2966	C₂×C₁₃	semidirect
563. #555	C₂²×C₁₃	semidirect
564. #554	C₂²×C₁₃	semidirect
566. #553	C₂²×C₁₃	semidirect
570. D₄×Q₈	C₂²×C₁₃	semidirect
577. #544	C₂²×C₁₃	semidirect
580. #540	C₂²×C₁₃	semidirect
587. #533	C₂²×C₁₃	semidirect
590. #532	C₂²×C₁₃	semidirect
592. #501	C₂²×C₁₃	semidirect
593. #500	C₂²×C₁₃	semidirect
594. #496	C₂²×C₁₃	semidirect
597. #490	C₂²×C₁₃	semidirect
599. #489	C₂²×C₁₃	semidirect
601. #488	C₂²×C₁₃	semidirect
602. #488	C₂²×C₁₃	semidirect
603. #487	C₂²×C₁₃	semidirect
604. #487	C₂²×C₁₃	semidirect
608. #486	C₂²×C₁₃	semidirect
609. #486	C₂²×C₁₃	semidirect
610. #485	C₂²×C₁₃	semidirect
611. #484	C₂²×C₁₃	semidirect
614. #482	C₂²×C₁₃	semidirect
616. #479	C₂²×C₁₃	semidirect
617. #478	C₂²×C₁₃	semidirect
618. #477	C₂²×C₁₃	semidirect
620. #476	C₂²×C₁₃	semidirect
622. #474	C₂²×C₁₃	semidirect
623. #474	C₂²×C₁₃	semidirect
625. #468	C₂²×C₁₃	semidirect
629. #466	C₂²×C₁₃	semidirect
630. #466	C₂²×C₁₃	semidirect
631. #465	C₂²×C₁₃	semidirect
634. #461	C₂²×C₁₃	semidirect
635. #461	C₂²×C₁₃	semidirect
638. #459	C₂²×C₁₃	semidirect
639. #459	C₂²×C₁₃	semidirect
640. #449	C₂²×C₁₃	semidirect
641. #449	C₂²×C₁₃	semidirect
642. #449	C₂²×C₁₃	semidirect
643. #449	C₂²×C₁₃	semidirect
646. #446	C₂²×C₁₃	semidirect
647. C₈×Q₈	C₂²×C₁₃	semidirect
648. #442	C₂²×C₁₃	semidirect
649. #440	C₂²×C₁₃	semidirect
650. C₄×SD₁₆	C₂²×C₁₃	semidirect
653. C₄×D₈	C₂²×C₁₃	semidirect
654. C₄×D₈	C₂²×C₁₃	semidirect
655. C₄×D₈	C₂²×C₁₃	semidirect
657. #435	C₂²×C₁₃	semidirect
659. C₈×D₄	C₂²×C₁₃	semidirect
660. #433	C₂²×C₁₃	semidirect
661. #432	C₂²×C₁₃	semidirect
663. #417	C₂²×C₁₃	semidirect
664. #416	C₂²×C₁₃	semidirect
665. #416	C₂²×C₁₃	semidirect
666. #416	C₂²×C₁₃	semidirect
668. #405	C₂²×C₁₃	semidirect
669. C₂×C₄×C₈	C₂²×C₁₃	semidirect
1034. C₁₃	#62561	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×#3547	2
C₁₃×#3546	2
C₁₃×#3367	2
C₁₃×#3366	2
C₁₃×#3360	2
C₁₃×#3358	2
C₁₃×#3330	2
C₁₃×#3325	2
C₁₃×#3319	2
C₁₃×#3309	2
C₁₃×#3305	2
C₁₃×#3303	2
C₁₃×#3297	2
C₁₃×#3294	2
C₁₃×#3243	2
C₁₃×#3235	2
C₁₃×#3220	2
C₁₃×#3214	2
C₁₃×#3179	2
C₁₃×#3169	2
C₁₃×#3136	2
C₁₃×#3131	2
C₁₃×#2966	2
#62561	13

Subgroups — C13×#62561 #15748900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62561 #15748900