Subgroups — C₁₃×#62569 #15748908

Order 3328.

1712 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3322	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3321	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3319	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3308	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3221	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3179	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	1	no	—
21	C₁₃×#562	—	2	1	no	—
22	C₁₃×#562	—	2	2	no	—
23	C₁₃×#556	C₂²	1	2	yes	—
24	C₁₃×#555	C₂²	1	2	yes	—
25	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#553	C₂²	1	2	yes	—
28	C₁₃×#552	—	2	1	no	—
29	C₁₃×#551	—	2	2	no	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#548	—	2	1	no	—
33	C₁₃×#548	C₂²	1	2	yes	—
34	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#546	C₂²	1	2	yes	—
36	C₁₃×#544	C₂²	1	2	yes	complemented
37	C₁₃×#543	—	2	1	no	—
38	C₁₃×#542	—	2	2	no	—
39	C₁₃×#542	—	2	2	no	—
40	C₁₃×#542	C₂²	1	2	yes	—
41	C₁₃×#540	C₂²	1	2	yes	complemented
42	C₁₃×#538	—	2	1	no	—
43	C₁₃×#537	—	2	1	no	—
44	C₁₃×#536	—	2	1	no	—
45	C₁₃×#536	C₂²	1	2	yes	—
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₁₃×#533	C₂²	1	1	yes	characteristic
48	C₁₃×#532	C₂²	1	1	yes	characteristic
49	C₁₃×#529	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	2	yes	complemented
52	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#496	C₂²	1	2	yes	—
54	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#491	C₂²	1	2	yes	complemented
56	C₁₃×#491	C₂²	1	2	yes	complemented
57	C₁₃×#489	C₂²	1	2	yes	—
58	C₁₃×#489	C₂²	1	2	yes	—
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#489	C₂²	1	2	yes	—
61	C₁₃×#488	C₂²	1	2	yes	—
62	C₁₃×#488	C₂²	1	2	yes	—
63	C₁₃×#488	C₂²	1	2	yes	—
64	C₁₃×#487	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#485	C₂²	1	2	yes	—
69	C₁₃×#485	C₂²	1	2	yes	complemented
70	C₁₃×#484	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	2	yes	—
72	C₁₃×#480	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	—
75	C₁₃×#477	C₂²	1	2	yes	complemented
76	C₁₃×#477	C₂²	1	2	yes	complemented
77	C₁₃×#475	C₂²	1	2	yes	complemented
78	C₁₃×#474	C₂²	1	2	yes	—
79	C₁₃×#469	C₂²	1	2	yes	—
80	C₁₃×#468	C₂²	1	2	yes	—
81	C₁₃×#468	C₂²	1	2	yes	—
82	C₁₃×#468	C₂²	1	2	yes	complemented
83	C₁₃×#466	C₂²	1	2	yes	—
84	C₁₃×#465	C₂²	1	2	yes	complemented
85	C₁₃×#463	C₂²	1	2	yes	—
86	C₁₃×#463	C₂²	1	2	yes	—
87	C₁₃×#463	C₂²	1	2	yes	—
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#461	C₂²	1	2	yes	complemented
90	C₁₃×#461	C₂²	1	2	yes	complemented
91	C₁₃×#449	C₂²	1	2	yes	—
92	C₁₃×#449	C₂²	1	2	yes	—
93	C₁₃×#448	C₂²	1	1	yes	characteristic
94	C₁₃×#448	C₂²	1	1	yes	characteristic
95	C₁₃×#448	C₂²	1	2	yes	complemented
96	C₁₃×#448	C₂²	1	2	yes	complemented
97	C₁₃×#447	C₂²	1	1	yes	characteristic
98	C₁₃×#447	C₂²	1	1	yes	characteristic
99	C₁₃×#446	C₂²	1	2	yes	complemented
100	C₁₃×#442	C₂²	1	2	yes	—
101	C₁₃×#440	C₂²	1	2	yes	complemented
102	C₁₃×#440	C₂²	1	2	yes	complemented
103	C₁₃×#440	C₂²	1	2	yes	complemented
104	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
105	C₄×C₁₃×D₈	C₂²	1	2	yes	—
106	C₁₃×#436	C₂²	1	2	yes	—
107	C₁₃×#435	C₂²	1	2	yes	—
108	C₁₃×#435	C₂²	1	2	yes	complemented
109	C₁₃×#433	C₂²	1	2	yes	complemented
110	C₁₃×#432	C₂²	1	1	yes	characteristic
111	C₁₃×#419	C₂²	1	2	yes	—
112	C₁₃×#419	C₂²	1	2	yes	complemented
113	C₁₃×#418	C₂²	1	2	yes	—
114	C₁₃×#417	C₂²	1	2	yes	—
115	C₁₃×#416	C₂²	1	2	yes	—
116	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
117	C₁₃×#405	C₂²	1	2	yes	complemented
118	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	1	no	—
120	C₂×C₁₃×#41	—	2	1	no	—
121	C₂×C₁₃×#41	C₂³	1	2	yes	—
122	C₂²×Q₈×C₁₃	—	2	1	no	—
123	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
124	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
130	C₂×C₁₃×D₈	C₂³	1	2	yes	—
131	C₂×C₁₃×D₈	C₂³	1	2	yes	—
132	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
133	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
134	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	—	2	2	no	—
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₁₃×#127	C₂³	1	1	yes	characteristic
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#126	—	2	2	no	—
147	C₁₃×#126	—	2	2	no	—
148	C₁₃×#126	—	2	2	no	—
149	C₁₃×#126	D₄	1	2	yes	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	1	no	—
152	C₁₃×#125	D₄	1	1	yes	characteristic
153	C₁₃×#125	C₂³	1	2	yes	—
154	C₁₃×#125	C₂³	1	2	yes	—
155	C₁₃×#124	—	2	2	no	—
156	C₁₃×#124	—	2	2	no	—
157	C₁₃×#124	—	2	2	no	—
158	C₁₃×#124	—	2	2	no	—
159	C₁₃×#124	—	2	2	no	—
160	C₁₃×#124	—	2	1	no	—
161	C₁₃×#124	—	2	1	no	—
162	C₁₃×#124	—	2	1	no	—
163	C₁₃×#124	D₄	1	1	yes	characteristic
164	C₁₃×#124	C₂³	1	2	yes	—
165	C₁₃×#124	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
176	C₁₃×C₂²⋊Q₈	—	2	1	no	—
177	C₁₃×C₂²⋊Q₈	—	2	2	no	—
178	C₁₃×C₂²⋊Q₈	—	2	1	no	—
179	C₁₃×C₂²⋊Q₈	—	2	1	no	—
180	C₁₃×C₂²⋊Q₈	—	2	1	no	—
181	C₁₃×C₂²⋊Q₈	—	2	1	no	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	1	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×#121	—	2	1	no	—
197	C₁₃×#121	—	2	2	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	2	no	—
200	C₁₃×#121	—	2	1	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	D₄	1	1	yes	characteristic
205	C₁₃×#121	C₂³	1	1	yes	characteristic
206	C₁₃×#121	C₂³	1	1	yes	characteristic
207	C₁₃×#121	C₂³	1	2	yes	—
208	C₁₃×#121	C₂³	1	2	yes	—
209	C₁₃×#121	C₂³	1	2	yes	—
210	C₁₃×#120	—	2	2	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₁₃	—	2	2	no	—
218	C₄×D₄×C₁₃	—	2	2	no	—
219	C₄×D₄×C₁₃	—	2	2	no	—
220	C₄×D₄×C₁₃	—	2	1	no	—
221	C₄×D₄×C₁₃	C₂³	1	2	yes	—
222	C₄×D₄×C₁₃	C₂³	1	2	yes	—
223	C₄×D₄×C₁₃	C₂³	1	2	yes	—
224	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₁₃	C₂³	1	2	yes	—
227	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
228	C₁₃×#117	—	2	1	no	—
229	C₁₃×#117	—	2	1	no	—
230	C₁₃×#117	—	2	2	no	—
231	C₁₃×#117	—	2	2	no	—
232	C₁₃×#117	C₂³	1	2	yes	—
233	C₁₃×#117	C₂³	1	2	yes	—
234	C₁₃×#117	C₂³	1	2	yes	—
235	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
239	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#107	C₂³	1	2	yes	—
243	C₁₃×#107	C₂³	1	2	yes	—
244	C₁₃×#107	C₂³	1	2	yes	—
245	C₁₃×#106	C₂³	1	2	yes	—
246	C₁₃×#106	C₂³	1	2	yes	—
247	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#103	C₂³	1	2	yes	—
253	C₁₃×#103	C₂³	1	2	yes	—
254	C₁₃×#103	C₂³	1	2	yes	—
255	C₁₃×#103	C₂³	1	2	yes	—
256	C₁₃×#103	C₂³	1	2	yes	—
257	C₁₃×#103	C₂³	1	2	yes	—
258	C₁₃×#103	C₂³	1	2	yes	—
259	C₁₃×#103	C₂³	1	2	yes	—
260	C₁₃×#103	C₂³	1	2	yes	—
261	C₁₃×#103	C₂³	1	2	yes	—
262	C₁₃×#102	C₂³	1	2	yes	—
263	C₁₃×#102	C₂³	1	2	yes	—
264	C₁₃×#102	C₂³	1	2	yes	—
265	C₁₃×#102	C₂³	1	2	yes	—
266	C₁₃×#102	C₂³	1	2	yes	—
267	C₁₃×#102	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₁₃×#97	C₂³	1	2	yes	—
275	C₁₃×#97	C₂³	1	2	yes	—
276	C₁₃×#97	C₂³	1	2	yes	—
277	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#62569	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂⁴×C₁₃	—	2	1	no	—
282	C₁₃×#41	—	4	2	no	—
283	C₁₃×#41	—	4	2	no	—
284	C₁₃×#41	—	8	2	no	—
285	C₁₃×#41	—	8	2	no	—
286	C₂×Q₈×C₁₃	—	2	1	no	—
287	C₂×Q₈×C₁₃	—	2	1	no	—
288	C₂×Q₈×C₁₃	—	2	1	no	—
289	C₂×Q₈×C₁₃	—	2	2	no	—
290	C₂×Q₈×C₁₃	—	2	1	no	—
291	C₂×Q₈×C₁₃	—	2	2	no	—
292	C₂×Q₈×C₁₃	—	2	1	no	—
293	C₂×Q₈×C₁₃	—	4	2	no	—
294	C₂×Q₈×C₁₃	—	4	2	no	—
295	C₂×Q₈×C₁₃	—	4	2	no	—
296	C₂×Q₈×C₁₃	—	8	2	no	—
297	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
300	C₂×D₄×C₁₃	—	2	2	no	—
301	C₂×D₄×C₁₃	—	2	2	no	—
302	C₂×D₄×C₁₃	—	2	2	no	—
303	C₂×D₄×C₁₃	—	2	1	no	—
304	C₂×D₄×C₁₃	—	2	2	no	—
305	C₂×D₄×C₁₃	—	2	1	no	—
306	C₂×D₄×C₁₃	—	2	1	no	—
307	C₂×D₄×C₁₃	—	2	1	no	—
308	C₂×D₄×C₁₃	—	2	1	no	—
309	C₂×D₄×C₁₃	—	4	2	no	—
310	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
311	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
313	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	—	2	1	no	—
316	C₂²×C₄×C₁₃	—	2	2	no	—
317	C₂²×C₄×C₁₃	—	2	2	no	—
318	C₂²×C₄×C₁₃	—	2	1	no	—
319	C₂²×C₄×C₁₃	—	2	1	no	—
320	C₂²×C₄×C₁₃	—	2	2	no	—
321	C₂²×C₄×C₁₃	—	2	2	no	—
322	C₂²×C₄×C₁₃	—	2	2	no	—
323	C₂²×C₄×C₁₃	—	2	2	no	—
324	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
328	C₁₃×SD₁₆	—	4	2	no	—
329	C₁₃×SD₁₆	—	4	2	no	—
330	C₁₃×SD₁₆	—	4	2	no	—
331	C₁₃×SD₁₆	—	4	2	no	—
332	C₁₃×D₈	—	4	2	no	—
333	C₁₃×D₈	—	4	2	no	—
334	C₁₃×M₁₆	—	4	2	no	—
335	C₁₃×M₁₆	—	4	2	no	—
336	C₂×C₈×C₁₃	—	4	2	no	—
337	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
338	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
339	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
340	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
341	C₁₃×C₄⋊C₄	—	2	1	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	—	2	2	no	—
345	C₁₃×C₄⋊C₄	—	2	2	no	—
346	C₁₃×C₄⋊C₄	—	2	1	no	—
347	C₁₃×C₄⋊C₄	—	2	1	no	—
348	C₁₃×C₄⋊C₄	—	2	1	no	—
349	C₁₃×C₄⋊C₄	—	2	2	no	—
350	C₁₃×C₄⋊C₄	—	2	2	no	—
351	C₁₃×C₄⋊C₄	—	2	2	no	—
352	C₁₃×C₄⋊C₄	—	2	2	no	—
353	C₁₃×C₄⋊C₄	—	2	2	no	—
354	C₁₃×C₄⋊C₄	—	2	2	no	—
355	C₁₃×C₄⋊C₄	—	2	1	no	—
356	C₁₃×C₄⋊C₄	—	2	1	no	—
357	C₁₃×C₄⋊C₄	—	2	2	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
360	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
361	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
364	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
367	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
369	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
370	C₁₃×C₂²⋊C₄	—	2	2	no	—
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	2	no	—
377	C₁₃×C₂²⋊C₄	—	2	2	no	—
378	C₁₃×C₂²⋊C₄	—	2	2	no	—
379	C₁₃×C₂²⋊C₄	—	2	2	no	—
380	C₁₃×C₂²⋊C₄	—	2	1	no	—
381	C₁₃×C₂²⋊C₄	—	2	2	no	—
382	C₁₃×C₂²⋊C₄	—	2	2	no	—
383	C₁₃×C₂²⋊C₄	—	2	2	no	—
384	C₁₃×C₂²⋊C₄	—	2	1	no	—
385	C₁₃×C₂²⋊C₄	—	2	2	no	—
386	C₁₃×C₂²⋊C₄	—	2	2	no	—
387	C₁₃×C₂²⋊C₄	—	2	1	no	—
388	C₁₃×C₂²⋊C₄	—	2	2	no	—
389	C₁₃×C₂²⋊C₄	—	2	1	no	—
390	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
391	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
392	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
393	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
394	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
395	C₄²×C₁₃	—	2	2	no	—
396	C₄²×C₁₃	—	2	2	no	—
397	C₄²×C₁₃	—	2	2	no	—
398	C₄²×C₁₃	—	2	2	no	—
399	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
402	C₄²×C₁₃	C₂⁴	1	2	yes	—
403	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
404	#3561	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3547	C₂×C₁₃	1	1	yes	characteristic, complemented
406	#3376	C₂×C₁₃	1	2	yes	complemented
407	#3367	C₂×C₁₃	1	2	yes	complemented
408	#3329	C₂×C₁₃	1	2	yes	complemented
409	#3322	C₂×C₁₃	1	2	yes	complemented
410	#3321	C₂×C₁₃	1	2	yes	complemented
411	#3320	C₂×C₁₃	1	2	yes	complemented
412	#3319	C₂×C₁₃	1	2	yes	complemented
413	#3308	C₂×C₁₃	1	2	yes	complemented
414	#3243	C₂×C₁₃	1	2	yes	complemented
415	#3237	C₂×C₁₃	1	1	yes	characteristic, complemented
416	#3221	C₂×C₁₃	1	2	yes	complemented
417	#3213	C₂×C₁₃	1	1	yes	characteristic, complemented
418	#3182	C₂×C₁₃	1	1	yes	characteristic, complemented
419	#3179	C₂×C₁₃	1	2	yes	complemented
420	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
421	#3137	C₂×C₁₃	1	2	yes	complemented
422	#2967	C₂×C₁₃	1	1	yes	characteristic, complemented
423	C₂³×C₁₃	—	2	2	no	—
424	C₂³×C₁₃	—	2	1	no	—
425	C₂³×C₁₃	—	2	1	no	—
426	C₂³×C₁₃	—	4	2	no	—
427	C₂³×C₁₃	—	8	1	no	—
428	C₂³×C₁₃	—	8	1	no	—
429	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
430	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
431	Q₈×C₁₃	—	2	2	no	—
432	Q₈×C₁₃	—	2	2	no	—
433	Q₈×C₁₃	—	2	2	no	—
434	Q₈×C₁₃	—	2	2	no	—
435	Q₈×C₁₃	—	4	1	no	—
436	Q₈×C₁₃	—	4	2	no	—
437	Q₈×C₁₃	—	8	1	no	—
438	Q₈×C₁₃	—	8	1	no	—
439	Q₈×C₁₃	—	8	2	no	—
440	Q₈×C₁₃	—	8	1	no	—
441	Q₈×C₁₃	—	8	2	no	—
442	Q₈×C₁₃	—	8	1	no	—
443	D₄×C₁₃	—	2	2	no	—
444	D₄×C₁₃	—	2	2	no	—
445	D₄×C₁₃	—	2	2	no	—
446	D₄×C₁₃	—	2	2	no	—
447	D₄×C₁₃	—	4	2	no	—
448	D₄×C₁₃	—	4	1	no	—
449	D₄×C₁₃	—	8	1	no	—
450	D₄×C₁₃	—	8	1	no	—
451	D₄×C₁₃	—	8	1	no	—
452	D₄×C₁₃	—	8	2	no	—
453	D₄×C₁₃	—	8	2	no	—
454	D₄×C₁₃	—	8	2	no	—
455	D₄×C₁₃	—	8	1	no	—
456	D₄×C₁₃	—	8	1	no	—
457	D₄×C₁₃	—	8	2	no	—
458	C₂×C₄×C₁₃	—	2	2	no	—
459	C₂×C₄×C₁₃	—	2	2	no	—
460	C₂×C₄×C₁₃	—	2	2	no	—
461	C₂×C₄×C₁₃	—	2	2	no	—
462	C₂×C₄×C₁₃	—	2	2	no	—
463	C₂×C₄×C₁₃	—	2	1	no	—
464	C₂×C₄×C₁₃	—	2	2	no	—
465	C₂×C₄×C₁₃	—	2	2	no	—
466	C₂×C₄×C₁₃	—	2	2	no	—
467	C₂×C₄×C₁₃	—	2	1	no	—
468	C₂×C₄×C₁₃	—	4	1	no	—
469	C₂×C₄×C₁₃	—	4	1	no	—
470	C₂×C₄×C₁₃	—	4	2	no	—
471	C₂×C₄×C₁₃	—	4	2	no	—
472	C₂×C₄×C₁₃	—	8	2	no	—
473	C₂×C₄×C₁₃	—	8	2	no	—
474	C₂×C₄×C₁₃	—	8	2	no	—
475	C₂×C₄×C₁₃	—	8	2	no	—
476	C₂×C₄×C₁₃	—	8	2	no	—
477	C₂×C₄×C₁₃	—	8	1	no	—
478	C₂×C₄×C₁₃	—	8	2	no	—
479	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
488	C₈×C₁₃	—	2	2	no	—
489	C₈×C₁₃	—	2	2	no	—
490	C₈×C₁₃	—	2	2	no	—
491	C₈×C₁₃	—	2	2	no	—
492	#563	—	2	1	no	—
493	#562	—	2	1	no	—
494	#562	—	2	2	no	—
495	#556	C₂²×C₁₃	1	2	yes	—
496	#555	C₂²×C₁₃	1	2	yes	—
497	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	#553	C₂²×C₁₃	1	2	yes	—
500	#552	—	2	1	no	—
501	#551	—	2	2	no	—
502	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
503	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	#548	—	2	1	no	—
505	#548	C₂²×C₁₃	1	2	yes	—
506	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
507	#546	C₂²×C₁₃	1	2	yes	—
508	#544	C₂²×C₁₃	1	2	yes	complemented
509	#543	—	2	1	no	—
510	#542	—	2	2	no	—
511	#542	—	2	2	no	—
512	#542	C₂²×C₁₃	1	2	yes	—
513	#540	C₂²×C₁₃	1	2	yes	complemented
514	#538	—	2	1	no	—
515	#537	—	2	1	no	—
516	#536	—	2	1	no	—
517	#536	C₂²×C₁₃	1	2	yes	—
518	#533	C₂²×C₁₃	1	1	yes	characteristic
519	#533	C₂²×C₁₃	1	1	yes	characteristic
520	#532	C₂²×C₁₃	1	1	yes	characteristic
521	#529	C₂²×C₁₃	1	1	yes	characteristic
522	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
523	#501	C₂²×C₁₃	1	2	yes	complemented
524	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
525	#496	C₂²×C₁₃	1	2	yes	—
526	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
527	#491	C₂²×C₁₃	1	2	yes	complemented
528	#491	C₂²×C₁₃	1	2	yes	complemented
529	#489	C₂²×C₁₃	1	2	yes	—
530	#489	C₂²×C₁₃	1	2	yes	—
531	#489	C₂²×C₁₃	1	2	yes	—
532	#489	C₂²×C₁₃	1	2	yes	—
533	#488	C₂²×C₁₃	1	2	yes	—
534	#488	C₂²×C₁₃	1	2	yes	—
535	#488	C₂²×C₁₃	1	2	yes	—
536	#487	C₂²×C₁₃	1	2	yes	complemented
537	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
538	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
539	#485	C₂²×C₁₃	1	2	yes	—
540	#485	C₂²×C₁₃	1	2	yes	—
541	#485	C₂²×C₁₃	1	2	yes	complemented
542	#484	C₂²×C₁₃	1	2	yes	complemented
543	#482	C₂²×C₁₃	1	2	yes	—
544	#480	C₂²×C₁₃	1	2	yes	—
545	#479	C₂²×C₁₃	1	2	yes	complemented
546	#478	C₂²×C₁₃	1	2	yes	—
547	#477	C₂²×C₁₃	1	2	yes	complemented
548	#477	C₂²×C₁₃	1	2	yes	complemented
549	#475	C₂²×C₁₃	1	2	yes	complemented
550	#474	C₂²×C₁₃	1	2	yes	—
551	#469	C₂²×C₁₃	1	2	yes	—
552	#468	C₂²×C₁₃	1	2	yes	—
553	#468	C₂²×C₁₃	1	2	yes	—
554	#468	C₂²×C₁₃	1	2	yes	complemented
555	#466	C₂²×C₁₃	1	2	yes	—
556	#465	C₂²×C₁₃	1	2	yes	complemented
557	#463	C₂²×C₁₃	1	2	yes	—
558	#463	C₂²×C₁₃	1	2	yes	—
559	#463	C₂²×C₁₃	1	2	yes	—
560	#463	C₂²×C₁₃	1	2	yes	—
561	#461	C₂²×C₁₃	1	2	yes	complemented
562	#461	C₂²×C₁₃	1	2	yes	complemented
563	#449	C₂²×C₁₃	1	2	yes	—
564	#449	C₂²×C₁₃	1	2	yes	—
565	#448	C₂²×C₁₃	1	1	yes	characteristic
566	#448	C₂²×C₁₃	1	1	yes	characteristic
567	#448	C₂²×C₁₃	1	2	yes	complemented
568	#448	C₂²×C₁₃	1	2	yes	complemented
569	#447	C₂²×C₁₃	1	1	yes	characteristic
570	#447	C₂²×C₁₃	1	1	yes	characteristic
571	#446	C₂²×C₁₃	1	2	yes	complemented
572	#442	C₂²×C₁₃	1	2	yes	—
573	#440	C₂²×C₁₃	1	2	yes	complemented
574	#440	C₂²×C₁₃	1	2	yes	complemented
575	#440	C₂²×C₁₃	1	2	yes	complemented
576	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
577	C₄×D₈	C₂²×C₁₃	1	2	yes	—
578	#436	C₂²×C₁₃	1	2	yes	—
579	#435	C₂²×C₁₃	1	2	yes	—
580	#435	C₂²×C₁₃	1	2	yes	complemented
581	#433	C₂²×C₁₃	1	2	yes	complemented
582	#432	C₂²×C₁₃	1	1	yes	characteristic
583	#419	C₂²×C₁₃	1	2	yes	—
584	#419	C₂²×C₁₃	1	2	yes	complemented
585	#418	C₂²×C₁₃	1	2	yes	—
586	#417	C₂²×C₁₃	1	2	yes	—
587	#416	C₂²×C₁₃	1	2	yes	—
588	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
589	#405	C₂²×C₁₃	1	2	yes	complemented
590	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
591	C₂²×C₁₃	—	2	1	no	—
592	C₂²×C₁₃	—	2	2	no	—
593	C₂²×C₁₃	—	2	1	no	—
594	C₂²×C₁₃	—	2	2	no	—
595	C₂²×C₁₃	—	2	2	no	—
596	C₂²×C₁₃	—	2	1	no	—
597	C₂²×C₁₃	—	4	1	no	—
598	C₂²×C₁₃	—	4	1	no	—
599	C₂²×C₁₃	—	4	2	no	—
600	C₂²×C₁₃	—	4	1	no	—
601	C₂²×C₁₃	—	4	1	no	—
602	C₂²×C₁₃	—	4	2	no	—
603	C₂²×C₁₃	—	4	2	no	—
604	C₂²×C₁₃	—	4	1	no	—
605	C₂²×C₁₃	—	4	1	no	—
606	C₂²×C₁₃	—	16	2	no	—
607	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
608	C₄×C₁₃	—	2	1	no	—
609	C₄×C₁₃	—	2	1	no	—
610	C₄×C₁₃	—	2	2	no	—
611	C₄×C₁₃	—	2	1	no	—
612	C₄×C₁₃	—	2	1	no	—
613	C₄×C₁₃	—	2	2	no	—
614	C₄×C₁₃	—	2	2	no	—
615	C₄×C₁₃	—	2	1	no	—
616	C₄×C₁₃	—	4	1	no	—
617	C₄×C₁₃	—	4	1	no	—
618	C₄×C₁₃	—	4	2	no	—
619	C₄×C₁₃	—	4	2	no	—
620	C₄×C₁₃	—	4	2	no	—
621	C₄×C₁₃	—	4	2	no	—
622	C₄×C₁₃	—	4	2	no	—
623	C₄×C₁₃	#585	1	2	yes	—
624	C₂×#41	—	2	1	no	—
625	C₂×#41	—	2	1	no	—
626	C₂×#41	C₂³×C₁₃	1	2	yes	—
627	C₂²×Q₈	—	2	1	no	—
628	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
629	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
630	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
635	C₂×D₈	C₂³×C₁₃	1	2	yes	—
636	C₂×D₈	C₂³×C₁₃	1	2	yes	—
637	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
638	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
639	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
644	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
647	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
648	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
649	#127	C₂³×C₁₃	1	1	yes	characteristic
650	#126	—	2	2	no	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	D₄×C₁₃	1	2	yes	—
655	#125	—	2	2	no	—
656	#125	—	2	1	no	—
657	#125	D₄×C₁₃	1	1	yes	characteristic
658	#125	C₂³×C₁₃	1	2	yes	—
659	#125	C₂³×C₁₃	1	2	yes	—
660	#124	—	2	2	no	—
661	#124	—	2	2	no	—
662	#124	—	2	2	no	—
663	#124	—	2	2	no	—
664	#124	—	2	2	no	—
665	#124	—	2	1	no	—
666	#124	—	2	1	no	—
667	#124	—	2	1	no	—
668	#124	D₄×C₁₃	1	1	yes	characteristic
669	#124	C₂³×C₁₃	1	2	yes	—
670	#124	C₂³×C₁₃	1	2	yes	—
671	#124	C₂³×C₁₃	1	2	yes	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	D₄×C₁₃	1	2	yes	—
681	C₂²⋊Q₈	—	2	1	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
699	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
700	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
701	#121	—	2	1	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	—	2	1	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	D₄×C₁₃	1	1	yes	characteristic
710	#121	C₂³×C₁₃	1	1	yes	characteristic
711	#121	C₂³×C₁₃	1	1	yes	characteristic
712	#121	C₂³×C₁₃	1	2	yes	—
713	#121	C₂³×C₁₃	1	2	yes	—
714	#121	C₂³×C₁₃	1	2	yes	—
715	#120	—	2	2	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
720	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
721	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
727	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
728	C₄×D₄	C₂³×C₁₃	1	2	yes	—
729	C₄×D₄	C₂³×C₁₃	1	2	yes	—
730	C₄×D₄	C₂³×C₁₃	1	2	yes	—
731	C₄×D₄	C₂³×C₁₃	1	2	yes	—
732	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
733	#117	—	2	1	no	—
734	#117	—	2	1	no	—
735	#117	—	2	2	no	—
736	#117	—	2	2	no	—
737	#117	C₂³×C₁₃	1	2	yes	—
738	#117	C₂³×C₁₃	1	2	yes	—
739	#117	C₂³×C₁₃	1	2	yes	—
740	C₂×C₄⋊C₄	—	2	1	no	—
741	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
742	C₂×C₂²⋊C₄	—	2	1	no	—
743	C₂×C₂²⋊C₄	—	2	1	no	—
744	C₂×C₂²⋊C₄	—	2	2	no	—
745	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
746	#107	C₂³×C₁₃	1	2	yes	—
747	#107	C₂³×C₁₃	1	2	yes	—
748	#107	C₂³×C₁₃	1	2	yes	—
749	#107	C₂³×C₁₃	1	2	yes	—
750	#106	C₂³×C₁₃	1	2	yes	—
751	#106	C₂³×C₁₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
753	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
754	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
755	#103	C₂³×C₁₃	1	2	yes	—
756	#103	C₂³×C₁₃	1	2	yes	—
757	#103	C₂³×C₁₃	1	2	yes	—
758	#103	C₂³×C₁₃	1	2	yes	—
759	#103	C₂³×C₁₃	1	2	yes	—
760	#103	C₂³×C₁₃	1	2	yes	—
761	#103	C₂³×C₁₃	1	2	yes	—
762	#103	C₂³×C₁₃	1	2	yes	—
763	#103	C₂³×C₁₃	1	2	yes	—
764	#103	C₂³×C₁₃	1	2	yes	—
765	#103	C₂³×C₁₃	1	2	yes	—
766	#103	C₂³×C₁₃	1	2	yes	—
767	#102	C₂³×C₁₃	1	2	yes	—
768	#102	C₂³×C₁₃	1	2	yes	—
769	#102	C₂³×C₁₃	1	2	yes	—
770	#102	C₂³×C₁₃	1	2	yes	—
771	#102	C₂³×C₁₃	1	2	yes	—
772	#102	C₂³×C₁₃	1	2	yes	—
773	#102	C₂³×C₁₃	1	2	yes	—
774	#102	C₂³×C₁₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
776	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
777	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
779	#97	C₂³×C₁₃	1	2	yes	—
780	#97	C₂³×C₁₃	1	2	yes	—
781	#97	C₂³×C₁₃	1	2	yes	—
782	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
784	C₄×C₈	C₂³×C₁₃	1	2	yes	—
785	C₂×C₁₃	—	4	2	no	—
786	C₂×C₁₃	—	4	1	no	—
787	C₂×C₁₃	—	8	1	no	—
788	C₂×C₁₃	—	8	1	no	—
789	C₂×C₁₃	—	8	2	no	—
790	C₂×C₁₃	#3500	1	1	yes	characteristic
791	C₂×C₁₃	#3585	1	1	yes	characteristic
792	C₂×C₁₃	#3586	1	1	yes	characteristic
793	C₂⁴	—	2	1	no	—
794	#41	—	4	2	no	—
795	#41	—	4	2	no	—
796	#41	—	8	2	no	—
797	#41	—	8	2	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	2	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	4	2	no	—
806	C₂×Q₈	—	4	2	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	8	2	no	—
809	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
810	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
811	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
823	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
824	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
825	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
826	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
837	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
840	SD₁₆	—	4	2	no	—
841	SD₁₆	—	4	2	no	—
842	SD₁₆	—	4	2	no	—
843	SD₁₆	—	4	2	no	—
844	D₈	—	4	2	no	—
845	D₈	—	4	2	no	—
846	M₁₆	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	C₂×C₈	—	4	2	no	—
849	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
850	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
851	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
852	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
872	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
873	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
874	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
875	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
876	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
877	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
878	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
879	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
880	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
881	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	1	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	1	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	1	no	—
902	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
903	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
904	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
912	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
913	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
914	C₄²	C₂⁴×C₁₃	1	2	yes	—
915	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
916	C₁₃	#62569	1	1	yes	characteristic, direct product factor, Sylow
917	C₂³	—	2	2	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	4	2	no	—
921	C₂³	—	8	1	no	—
922	C₂³	—	8	1	no	—
923	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
924	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
925	Q₈	—	2	2	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	4	1	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	8	2	no	—
932	Q₈	—	8	1	no	—
933	Q₈	—	8	2	no	—
934	Q₈	—	8	1	no	—
935	Q₈	—	8	1	no	—
936	Q₈	—	8	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	2	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	2	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	1	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	1	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	2	no	—
949	D₄	—	8	1	no	—
950	D₄	—	8	1	no	—
951	D₄	—	8	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	4	1	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	8	2	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	1	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
976	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
979	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
981	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₈	—	2	2	no	—
985	C₈	—	2	2	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	16	2	no	—
1002	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	C₁₃×#585	1	2	yes	—
1019	C₂	—	4	1	no	—
1020	C₂	—	4	2	no	—
1021	C₂	—	8	2	no	—
1022	C₂	—	8	1	no	—
1023	C₂	—	8	1	no	—
1024	C₂	C₁₃×#3500	1	1	yes	characteristic
1025	C₂	C₁₃×#3585	1	1	yes	characteristic
1026	C₂	C₁₃×#3586	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×#3561	C₂	semidirect
2. C₁₃×#3547	C₂	semidirect
3. C₁₃×#3376	C₂	semidirect
4. C₁₃×#3367	C₂	semidirect
5. C₁₃×#3329	C₂	semidirect
6. C₁₃×#3322	C₂	semidirect
7. C₁₃×#3321	C₂	semidirect
8. C₁₃×#3320	C₂	semidirect
9. C₁₃×#3319	C₂	semidirect
10. C₁₃×#3308	C₂	semidirect
11. C₁₃×#3243	C₂	semidirect
12. C₁₃×#3237	C₂	semidirect
13. C₁₃×#3221	C₂	semidirect
14. C₁₃×#3213	C₂	semidirect
15. C₁₃×#3182	C₂	semidirect
16. C₁₃×#3179	C₂	semidirect
17. C₁₃×#3140	C₂	semidirect
18. C₁₃×#3137	C₂	semidirect
19. C₁₃×#2967	C₂	semidirect
25. C₁₃×#555	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
31. D₄×Q₈×C₁₃	C₂²	semidirect
34. C₁₃×#547	C₂²	semidirect
36. C₁₃×#544	C₂²	semidirect
41. C₁₃×#540	C₂²	semidirect
51. C₁₃×#501	C₂²	semidirect
52. C₁₃×#500	C₂²	semidirect
54. C₁₃×#492	C₂²	semidirect
55. C₁₃×#491	C₂²	semidirect
56. C₁₃×#491	C₂²	semidirect
64. C₁₃×#487	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
69. C₁₃×#485	C₂²	semidirect
70. C₁₃×#484	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
89. C₁₃×#461	C₂²	semidirect
90. C₁₃×#461	C₂²	semidirect
95. C₁₃×#448	C₂²	semidirect
96. C₁₃×#448	C₂²	semidirect
99. C₁₃×#446	C₂²	semidirect
101. C₁₃×#440	C₂²	semidirect
102. C₁₃×#440	C₂²	semidirect
103. C₁₃×#440	C₂²	semidirect
104. C₄×C₁₃×SD₁₆	C₂²	semidirect
108. C₁₃×#435	C₂²	semidirect
109. C₁₃×#433	C₂²	semidirect
112. C₁₃×#419	C₂²	semidirect
116. C₂×C₁₃×#103	C₂²	semidirect
117. C₁₃×#405	C₂²	semidirect
280. #62569	C₁₃	direct (N × H)
404. #3561	C₂×C₁₃	semidirect
405. #3547	C₂×C₁₃	semidirect
406. #3376	C₂×C₁₃	semidirect
407. #3367	C₂×C₁₃	semidirect
408. #3329	C₂×C₁₃	semidirect
409. #3322	C₂×C₁₃	semidirect
410. #3321	C₂×C₁₃	semidirect
411. #3320	C₂×C₁₃	semidirect
412. #3319	C₂×C₁₃	semidirect
413. #3308	C₂×C₁₃	semidirect
414. #3243	C₂×C₁₃	semidirect
415. #3237	C₂×C₁₃	semidirect
416. #3221	C₂×C₁₃	semidirect
417. #3213	C₂×C₁₃	semidirect
418. #3182	C₂×C₁₃	semidirect
419. #3179	C₂×C₁₃	semidirect
420. #3140	C₂×C₁₃	semidirect
421. #3137	C₂×C₁₃	semidirect
422. #2967	C₂×C₁₃	semidirect
497. #555	C₂²×C₁₃	semidirect
498. #554	C₂²×C₁₃	semidirect
503. D₄×Q₈	C₂²×C₁₃	semidirect
506. #547	C₂²×C₁₃	semidirect
508. #544	C₂²×C₁₃	semidirect
513. #540	C₂²×C₁₃	semidirect
523. #501	C₂²×C₁₃	semidirect
524. #500	C₂²×C₁₃	semidirect
526. #492	C₂²×C₁₃	semidirect
527. #491	C₂²×C₁₃	semidirect
528. #491	C₂²×C₁₃	semidirect
536. #487	C₂²×C₁₃	semidirect
537. #487	C₂²×C₁₃	semidirect
538. #486	C₂²×C₁₃	semidirect
541. #485	C₂²×C₁₃	semidirect
542. #484	C₂²×C₁₃	semidirect
545. #479	C₂²×C₁₃	semidirect
547. #477	C₂²×C₁₃	semidirect
548. #477	C₂²×C₁₃	semidirect
549. #475	C₂²×C₁₃	semidirect
554. #468	C₂²×C₁₃	semidirect
556. #465	C₂²×C₁₃	semidirect
561. #461	C₂²×C₁₃	semidirect
562. #461	C₂²×C₁₃	semidirect
567. #448	C₂²×C₁₃	semidirect
568. #448	C₂²×C₁₃	semidirect
571. #446	C₂²×C₁₃	semidirect
573. #440	C₂²×C₁₃	semidirect
574. #440	C₂²×C₁₃	semidirect
575. #440	C₂²×C₁₃	semidirect
576. C₄×SD₁₆	C₂²×C₁₃	semidirect
580. #435	C₂²×C₁₃	semidirect
581. #433	C₂²×C₁₃	semidirect
584. #419	C₂²×C₁₃	semidirect
588. C₂×#103	C₂²×C₁₃	semidirect
589. #405	C₂²×C₁₃	semidirect
916. C₁₃	#62569	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×#3561	2
C₁₃×#3547	2
C₁₃×#3376	2
C₁₃×#3367	2
C₁₃×#3329	2
C₁₃×#3322	2
C₁₃×#3321	2
C₁₃×#3320	2
C₁₃×#3319	2
C₁₃×#3308	2
C₁₃×#3243	2
C₁₃×#3237	2
C₁₃×#3221	2
C₁₃×#3213	2
C₁₃×#3182	2
C₁₃×#3179	2
C₁₃×#3140	2
C₁₃×#3137	2
C₁₃×#2967	2
#62569	13

Subgroups — C13×#62569 #15748908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62569 #15748908