Subgroups — C₁₃×#62560 #15748899

Order 3328.

1660 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3554	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3315	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3313	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3302	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3300	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3178	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3137	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×#563	—	2	2	no	—
25	C₁₃×#562	—	2	2	no	—
26	C₁₃×#559	—	2	1	no	—
27	C₁₃×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#557	—	2	1	no	—
30	C₁₃×#557	C₂²	1	1	yes	characteristic
31	C₁₃×#557	C₂²	1	1	yes	characteristic
32	C₁₃×#556	—	2	1	no	—
33	C₁₃×#556	C₂²	1	2	yes	—
34	C₁₃×#556	C₂²	1	1	yes	characteristic
35	C₁₃×#554	—	2	1	no	—
36	C₁₃×#554	C₂²	1	1	yes	characteristic
37	C₁₃×#552	C₂²	1	2	yes	—
38	C₁₃×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#548	C₂²	1	2	yes	—
41	C₁₃×#547	C₂²	1	2	yes	—
42	C₁₃×#544	C₂²	1	2	yes	—
43	C₁₃×#542	—	2	1	no	—
44	C₁₃×#542	—	2	1	no	—
45	C₁₃×#542	C₂²	1	2	yes	—
46	C₁₃×#541	—	2	2	no	—
47	C₁₃×#541	—	2	1	no	—
48	C₁₃×#541	C₂²	1	2	yes	—
49	C₁₃×#540	—	2	1	no	—
50	C₁₃×#539	—	2	2	no	—
51	C₁₃×#536	C₂²	1	2	yes	—
52	C₁₃×#533	C₂²	1	1	yes	characteristic
53	C₁₃×#533	C₂²	1	1	yes	characteristic
54	C₁₃×#533	C₂²	1	1	yes	characteristic
55	C₁₃×#532	C₂²	1	1	yes	characteristic
56	C₁₃×#529	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	2	yes	—
58	C₁₃×#500	C₂²	1	1	yes	characteristic
59	C₁₃×#497	C₂²	1	2	yes	—
60	C₁₃×#494	C₂²	1	1	yes	characteristic
61	C₁₃×#491	C₂²	1	2	yes	—
62	C₁₃×#491	C₂²	1	2	yes	—
63	C₁₃×#489	C₂²	1	2	yes	—
64	C₁₃×#489	C₂²	1	2	yes	—
65	C₁₃×#488	C₂²	1	2	yes	—
66	C₁₃×#488	C₂²	1	2	yes	—
67	C₁₃×#488	C₂²	1	2	yes	—
68	C₁₃×#487	C₂²	1	1	yes	characteristic
69	C₁₃×#487	C₂²	1	2	yes	—
70	C₁₃×#487	C₂²	1	1	yes	characteristic
71	C₁₃×#487	C₂²	1	1	yes	characteristic
72	C₁₃×#487	C₂²	1	1	yes	characteristic
73	C₁₃×#486	C₂²	1	1	yes	characteristic
74	C₁₃×#486	C₂²	1	1	yes	characteristic
75	C₁₃×#485	C₂²	1	2	yes	—
76	C₁₃×#485	C₂²	1	2	yes	—
77	C₁₃×#485	C₂²	1	2	yes	—
78	C₁₃×#484	C₂²	1	2	yes	—
79	C₁₃×#482	C₂²	1	2	yes	—
80	C₁₃×#480	C₂²	1	2	yes	—
81	C₁₃×#479	C₂²	1	2	yes	—
82	C₁₃×#478	C₂²	1	2	yes	—
83	C₁₃×#477	C₂²	1	1	yes	characteristic
84	C₁₃×#477	C₂²	1	2	yes	—
85	C₁₃×#477	C₂²	1	1	yes	characteristic
86	C₁₃×#475	C₂²	1	1	yes	characteristic
87	C₁₃×#475	C₂²	1	1	yes	characteristic
88	C₁₃×#474	C₂²	1	2	yes	—
89	C₁₃×#470	C₂²	1	2	yes	—
90	C₁₃×#468	C₂²	1	2	yes	—
91	C₁₃×#467	C₂²	1	2	yes	—
92	C₁₃×#467	C₂²	1	1	yes	characteristic
93	C₁₃×#467	C₂²	1	1	yes	characteristic
94	C₁₃×#467	C₂²	1	1	yes	characteristic
95	C₁₃×#467	C₂²	1	1	yes	characteristic
96	C₁₃×#465	C₂²	1	2	yes	—
97	C₁₃×#464	C₂²	1	2	yes	—
98	C₁₃×#464	C₂²	1	2	yes	—
99	C₁₃×#462	C₂²	1	1	yes	characteristic
100	C₁₃×#462	C₂²	1	2	yes	—
101	C₁₃×#462	C₂²	1	2	yes	—
102	C₁₃×#462	C₂²	1	1	yes	characteristic
103	C₁₃×#460	C₂²	1	1	yes	characteristic
104	C₁₃×#460	C₂²	1	1	yes	characteristic
105	C₁₃×#452	C₂²	1	2	yes	—
106	C₁₃×#452	C₂²	1	2	yes	—
107	C₁₃×#452	C₂²	1	2	yes	—
108	C₁₃×#452	C₂²	1	2	yes	—
109	C₁₃×#451	C₂²	1	2	yes	—
110	C₁₃×#451	C₂²	1	2	yes	—
111	C₁₃×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
113	C₁₃×#441	C₂²	1	2	yes	—
114	C₁₃×#440	C₂²	1	2	yes	—
115	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
116	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
117	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
118	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
121	C₁₃×#436	C₂²	1	1	yes	characteristic
122	C₁₃×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₁₃	C₂²	1	2	yes	—
125	C₁₃×#433	C₂²	1	2	yes	—
126	C₁₃×#432	C₂²	1	1	yes	characteristic
127	C₁₃×#419	C₂²	1	2	yes	—
128	C₁₃×#417	C₂²	1	2	yes	—
129	C₁₃×#416	C₂²	1	2	yes	—
130	C₁₃×#416	C₂²	1	2	yes	—
131	C₁₃×#416	C₂²	1	2	yes	—
132	C₂×C₁₃×#103	C₂²	1	2	yes	—
133	C₁₃×#405	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	C₂³	1	2	yes	—
136	C₂×C₁₃×#41	C₂³	1	2	yes	—
137	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
138	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
147	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
150	C₁₃×C₄⋊Q₈	—	2	1	no	—
151	C₁₃×C₄⋊Q₈	—	2	2	no	—
152	C₁₃×C₄⋊Q₈	—	2	1	no	—
153	C₁₃×C₄⋊Q₈	—	2	1	no	—
154	C₁₃×C₄⋊Q₈	—	2	2	no	—
155	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×#127	—	2	1	no	—
165	C₁₃×#127	C₂³	1	1	yes	characteristic
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#126	—	2	2	no	—
173	C₁₃×#126	D₄	1	2	yes	—
174	C₁₃×#125	—	2	2	no	—
175	C₁₃×#125	—	2	1	no	—
176	C₁₃×#125	—	2	2	no	—
177	C₁₃×#125	—	2	2	no	—
178	C₁₃×#125	—	2	2	no	—
179	C₁₃×#125	—	2	1	no	—
180	C₁₃×#125	—	2	2	no	—
181	C₁₃×#125	—	2	2	no	—
182	C₁₃×#125	—	2	1	no	—
183	C₁₃×#125	—	2	1	no	—
184	C₁₃×#125	D₄	1	1	yes	characteristic
185	C₁₃×#125	C₂³	1	2	yes	—
186	C₁₃×#125	C₂³	1	2	yes	—
187	C₁₃×#124	—	2	1	no	—
188	C₁₃×#124	—	2	1	no	—
189	C₁₃×#124	—	2	2	no	—
190	C₁₃×#124	—	2	2	no	—
191	C₁₃×#124	—	2	2	no	—
192	C₁₃×#124	D₄	1	1	yes	characteristic
193	C₁₃×#124	C₂³	1	2	yes	—
194	C₁₃×#124	C₂³	1	2	yes	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	D₄	1	2	yes	—
203	C₁₃×C₂²⋊Q₈	—	2	1	no	—
204	C₁₃×C₂²⋊Q₈	—	2	1	no	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	—	2	2	no	—
209	C₁₃×C₂²⋊Q₈	—	2	2	no	—
210	C₁₃×C₂²⋊Q₈	—	2	2	no	—
211	C₁₃×C₂²⋊Q₈	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	2	no	—
213	C₁₃×C₂²⋊Q₈	—	2	2	no	—
214	C₁₃×C₂²⋊Q₈	—	2	2	no	—
215	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
216	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₃×#121	—	2	2	no	—
224	C₁₃×#121	—	2	2	no	—
225	C₁₃×#121	—	2	1	no	—
226	C₁₃×#121	—	2	1	no	—
227	C₁₃×#121	—	2	2	no	—
228	C₁₃×#121	D₄	1	1	yes	characteristic
229	C₁₃×#121	C₂³	1	2	yes	—
230	C₄×Q₈×C₁₃	—	2	1	no	—
231	C₄×Q₈×C₁₃	—	2	1	no	—
232	C₄×Q₈×C₁₃	—	2	2	no	—
233	C₄×Q₈×C₁₃	—	2	1	no	—
234	C₄×Q₈×C₁₃	—	2	1	no	—
235	C₄×Q₈×C₁₃	—	2	1	no	—
236	C₄×Q₈×C₁₃	—	2	1	no	—
237	C₄×Q₈×C₁₃	—	2	1	no	—
238	C₄×Q₈×C₁₃	—	2	1	no	—
239	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
240	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₁₃	—	2	1	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	1	no	—
250	C₄×D₄×C₁₃	—	2	1	no	—
251	C₄×D₄×C₁₃	—	2	2	no	—
252	C₄×D₄×C₁₃	—	2	1	no	—
253	C₄×D₄×C₁₃	—	2	1	no	—
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₄×D₄×C₁₃	C₂³	1	2	yes	—
256	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
257	C₁₃×#117	—	2	1	no	—
258	C₁₃×#117	—	2	1	no	—
259	C₁₃×#117	—	2	2	no	—
260	C₁₃×#117	C₂³	1	2	yes	—
261	C₁₃×#117	C₂³	1	2	yes	—
262	C₁₃×#117	C₂³	1	2	yes	—
263	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
264	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
283	C₁₃×#103	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	2	yes	—
285	C₁₃×#103	C₂³	1	2	yes	—
286	C₁₃×#103	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	1	yes	characteristic
295	C₁₃×#103	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
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	#62560	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	4	2	no	—
314	C₁₃×#41	—	4	2	no	—
315	C₁₃×#41	—	4	2	no	—
316	C₁₃×#41	—	4	2	no	—
317	C₂×Q₈×C₁₃	—	2	1	no	—
318	C₂×Q₈×C₁₃	—	2	1	no	—
319	C₂×Q₈×C₁₃	—	2	1	no	—
320	C₂×Q₈×C₁₃	—	2	1	no	—
321	C₂×Q₈×C₁₃	—	2	2	no	—
322	C₂×Q₈×C₁₃	—	2	2	no	—
323	C₂×Q₈×C₁₃	—	4	2	no	—
324	C₂×Q₈×C₁₃	—	4	2	no	—
325	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	1	no	—
335	C₂×D₄×C₁₃	—	2	1	no	—
336	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
338	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₁₃	—	2	2	no	—
340	C₂²×C₄×C₁₃	—	2	2	no	—
341	C₂²×C₄×C₁₃	—	2	2	no	—
342	C₂²×C₄×C₁₃	—	2	2	no	—
343	C₂²×C₄×C₁₃	—	2	2	no	—
344	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
348	C₁₃×Q₁₆	—	4	2	no	—
349	C₁₃×Q₁₆	—	4	1	no	—
350	C₁₃×Q₁₆	—	4	1	no	—
351	C₁₃×Q₁₆	—	4	1	no	—
352	C₁₃×Q₁₆	—	4	1	no	—
353	C₁₃×Q₁₆	—	4	2	no	—
354	C₁₃×SD₁₆	—	4	2	no	—
355	C₁₃×SD₁₆	—	4	2	no	—
356	C₁₃×M₁₆	—	4	2	no	—
357	C₂×C₈×C₁₃	—	4	2	no	—
358	C₂×C₈×C₁₃	—	4	1	no	—
359	C₂×C₈×C₁₃	—	4	1	no	—
360	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
365	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
366	C₁₃×C₄⋊C₄	—	2	1	no	—
367	C₁₃×C₄⋊C₄	—	2	2	no	—
368	C₁₃×C₄⋊C₄	—	2	2	no	—
369	C₁₃×C₄⋊C₄	—	2	2	no	—
370	C₁₃×C₄⋊C₄	—	2	1	no	—
371	C₁₃×C₄⋊C₄	—	2	1	no	—
372	C₁₃×C₄⋊C₄	—	2	1	no	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
374	C₁₃×C₄⋊C₄	—	2	1	no	—
375	C₁₃×C₄⋊C₄	—	2	1	no	—
376	C₁₃×C₄⋊C₄	—	2	1	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	1	no	—
379	C₁₃×C₄⋊C₄	—	2	1	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	2	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	1	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	2	2	no	—
398	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₂²⋊C₄	—	2	1	no	—
411	C₁₃×C₂²⋊C₄	—	2	1	no	—
412	C₁₃×C₂²⋊C₄	—	2	1	no	—
413	C₁₃×C₂²⋊C₄	—	2	1	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
415	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
426	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
429	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₄²×C₁₃	—	2	2	no	—
431	C₄²×C₁₃	—	2	1	no	—
432	C₄²×C₁₃	—	2	1	no	—
433	C₄²×C₁₃	—	2	1	no	—
434	C₄²×C₁₃	—	2	1	no	—
435	C₄²×C₁₃	—	2	2	no	—
436	C₄²×C₁₃	—	2	2	no	—
437	C₄²×C₁₃	—	2	2	no	—
438	C₄²×C₁₃	—	2	2	no	—
439	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
443	C₄²×C₁₃	C₂⁴	1	2	yes	—
444	#3555	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3554	C₂×C₁₃	1	1	yes	characteristic
446	#3375	C₂×C₁₃	1	1	yes	characteristic, complemented
447	#3374	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3365	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3333	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3328	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3315	C₂×C₁₃	1	2	yes	complemented
453	#3313	C₂×C₁₃	1	2	yes	complemented
454	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3302	C₂×C₁₃	1	2	yes	complemented
456	#3300	C₂×C₁₃	1	2	yes	complemented
457	#3299	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3243	C₂×C₁₃	1	2	yes	complemented
459	#3237	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3223	C₂×C₁₃	1	2	yes	complemented
461	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3178	C₂×C₁₃	1	2	yes	complemented
463	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3137	C₂×C₁₃	1	2	yes	complemented
465	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
467	C₂³×C₁₃	—	2	2	no	—
468	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
469	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
470	Q₈×C₁₃	—	2	2	no	—
471	Q₈×C₁₃	—	2	1	no	—
472	Q₈×C₁₃	—	2	1	no	—
473	Q₈×C₁₃	—	2	1	no	—
474	Q₈×C₁₃	—	2	1	no	—
475	Q₈×C₁₃	—	2	1	no	—
476	Q₈×C₁₃	—	2	1	no	—
477	Q₈×C₁₃	—	2	2	no	—
478	Q₈×C₁₃	—	2	2	no	—
479	Q₈×C₁₃	—	2	1	no	—
480	Q₈×C₁₃	—	2	1	no	—
481	Q₈×C₁₃	—	4	2	no	—
482	Q₈×C₁₃	—	8	1	no	—
483	Q₈×C₁₃	—	8	1	no	—
484	Q₈×C₁₃	—	8	1	no	—
485	Q₈×C₁₃	—	8	2	no	—
486	Q₈×C₁₃	—	8	2	no	—
487	D₄×C₁₃	—	2	2	no	—
488	D₄×C₁₃	—	2	2	no	—
489	D₄×C₁₃	—	2	2	no	—
490	D₄×C₁₃	—	4	2	no	—
491	D₄×C₁₃	—	4	2	no	—
492	D₄×C₁₃	—	8	1	no	—
493	D₄×C₁₃	—	8	2	no	—
494	D₄×C₁₃	—	8	2	no	—
495	D₄×C₁₃	—	8	2	no	—
496	C₂×C₄×C₁₃	—	2	2	no	—
497	C₂×C₄×C₁₃	—	2	2	no	—
498	C₂×C₄×C₁₃	—	2	1	no	—
499	C₂×C₄×C₁₃	—	2	1	no	—
500	C₂×C₄×C₁₃	—	2	2	no	—
501	C₂×C₄×C₁₃	—	2	1	no	—
502	C₂×C₄×C₁₃	—	2	1	no	—
503	C₂×C₄×C₁₃	—	2	2	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	2	1	no	—
506	C₂×C₄×C₁₃	—	2	2	no	—
507	C₂×C₄×C₁₃	—	2	1	no	—
508	C₂×C₄×C₁₃	—	2	1	no	—
509	C₂×C₄×C₁₃	—	2	2	no	—
510	C₂×C₄×C₁₃	—	2	1	no	—
511	C₂×C₄×C₁₃	—	2	1	no	—
512	C₂×C₄×C₁₃	—	4	1	no	—
513	C₂×C₄×C₁₃	—	8	2	no	—
514	C₂×C₄×C₁₃	—	8	2	no	—
515	C₂×C₄×C₁₃	—	8	2	no	—
516	C₂×C₄×C₁₃	—	8	2	no	—
517	C₂×C₄×C₁₃	—	8	2	no	—
518	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
527	C₈×C₁₃	—	2	1	no	—
528	C₈×C₁₃	—	2	1	no	—
529	C₈×C₁₃	—	2	2	no	—
530	C₈×C₁₃	—	2	1	no	—
531	C₈×C₁₃	—	2	1	no	—
532	C₈×C₁₃	—	2	2	no	—
533	#563	—	2	2	no	—
534	#562	—	2	2	no	—
535	#559	—	2	1	no	—
536	#559	C₂²×C₁₃	1	1	yes	characteristic
537	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
538	#557	—	2	1	no	—
539	#557	C₂²×C₁₃	1	1	yes	characteristic
540	#557	C₂²×C₁₃	1	1	yes	characteristic
541	#556	—	2	1	no	—
542	#556	C₂²×C₁₃	1	1	yes	characteristic
543	#556	C₂²×C₁₃	1	2	yes	—
544	#554	—	2	1	no	—
545	#554	C₂²×C₁₃	1	1	yes	characteristic
546	#552	C₂²×C₁₃	1	2	yes	—
547	#550	C₂²×C₁₃	1	1	yes	characteristic
548	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
549	#548	C₂²×C₁₃	1	2	yes	—
550	#547	C₂²×C₁₃	1	2	yes	—
551	#544	C₂²×C₁₃	1	2	yes	—
552	#542	—	2	1	no	—
553	#542	—	2	1	no	—
554	#542	C₂²×C₁₃	1	2	yes	—
555	#541	—	2	2	no	—
556	#541	—	2	1	no	—
557	#541	C₂²×C₁₃	1	2	yes	—
558	#540	—	2	1	no	—
559	#539	—	2	2	no	—
560	#536	C₂²×C₁₃	1	2	yes	—
561	#533	C₂²×C₁₃	1	1	yes	characteristic
562	#533	C₂²×C₁₃	1	1	yes	characteristic
563	#533	C₂²×C₁₃	1	1	yes	characteristic
564	#532	C₂²×C₁₃	1	1	yes	characteristic
565	#529	C₂²×C₁₃	1	1	yes	characteristic
566	#501	C₂²×C₁₃	1	2	yes	—
567	#500	C₂²×C₁₃	1	1	yes	characteristic
568	#497	C₂²×C₁₃	1	2	yes	—
569	#494	C₂²×C₁₃	1	1	yes	characteristic
570	#491	C₂²×C₁₃	1	2	yes	—
571	#491	C₂²×C₁₃	1	2	yes	—
572	#489	C₂²×C₁₃	1	2	yes	—
573	#489	C₂²×C₁₃	1	2	yes	—
574	#488	C₂²×C₁₃	1	2	yes	—
575	#488	C₂²×C₁₃	1	2	yes	—
576	#488	C₂²×C₁₃	1	2	yes	—
577	#487	C₂²×C₁₃	1	1	yes	characteristic
578	#487	C₂²×C₁₃	1	1	yes	characteristic
579	#487	C₂²×C₁₃	1	2	yes	—
580	#487	C₂²×C₁₃	1	1	yes	characteristic
581	#487	C₂²×C₁₃	1	1	yes	characteristic
582	#486	C₂²×C₁₃	1	1	yes	characteristic
583	#486	C₂²×C₁₃	1	1	yes	characteristic
584	#485	C₂²×C₁₃	1	2	yes	—
585	#485	C₂²×C₁₃	1	2	yes	—
586	#485	C₂²×C₁₃	1	2	yes	—
587	#484	C₂²×C₁₃	1	2	yes	—
588	#482	C₂²×C₁₃	1	2	yes	—
589	#480	C₂²×C₁₃	1	2	yes	—
590	#479	C₂²×C₁₃	1	2	yes	—
591	#478	C₂²×C₁₃	1	2	yes	—
592	#477	C₂²×C₁₃	1	1	yes	characteristic
593	#477	C₂²×C₁₃	1	2	yes	—
594	#477	C₂²×C₁₃	1	1	yes	characteristic
595	#475	C₂²×C₁₃	1	1	yes	characteristic
596	#475	C₂²×C₁₃	1	1	yes	characteristic
597	#474	C₂²×C₁₃	1	2	yes	—
598	#470	C₂²×C₁₃	1	2	yes	—
599	#468	C₂²×C₁₃	1	2	yes	—
600	#467	C₂²×C₁₃	1	1	yes	characteristic
601	#467	C₂²×C₁₃	1	1	yes	characteristic
602	#467	C₂²×C₁₃	1	1	yes	characteristic
603	#467	C₂²×C₁₃	1	1	yes	characteristic
604	#467	C₂²×C₁₃	1	2	yes	—
605	#465	C₂²×C₁₃	1	2	yes	—
606	#464	C₂²×C₁₃	1	2	yes	—
607	#464	C₂²×C₁₃	1	2	yes	—
608	#462	C₂²×C₁₃	1	1	yes	characteristic
609	#462	C₂²×C₁₃	1	2	yes	—
610	#462	C₂²×C₁₃	1	1	yes	characteristic
611	#462	C₂²×C₁₃	1	2	yes	—
612	#460	C₂²×C₁₃	1	1	yes	characteristic
613	#460	C₂²×C₁₃	1	1	yes	characteristic
614	#452	C₂²×C₁₃	1	2	yes	—
615	#452	C₂²×C₁₃	1	2	yes	—
616	#452	C₂²×C₁₃	1	2	yes	—
617	#452	C₂²×C₁₃	1	2	yes	—
618	#451	C₂²×C₁₃	1	2	yes	—
619	#451	C₂²×C₁₃	1	2	yes	—
620	#446	C₂²×C₁₃	1	1	yes	characteristic
621	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
622	#441	C₂²×C₁₃	1	2	yes	—
623	#440	C₂²×C₁₃	1	2	yes	—
624	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
625	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
626	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
627	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
628	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
629	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
630	#436	C₂²×C₁₃	1	1	yes	characteristic
631	#435	C₂²×C₁₃	1	2	yes	—
632	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
633	C₈×D₄	C₂²×C₁₃	1	2	yes	—
634	#433	C₂²×C₁₃	1	2	yes	—
635	#432	C₂²×C₁₃	1	1	yes	characteristic
636	#419	C₂²×C₁₃	1	2	yes	—
637	#417	C₂²×C₁₃	1	2	yes	—
638	#416	C₂²×C₁₃	1	2	yes	—
639	#416	C₂²×C₁₃	1	2	yes	—
640	#416	C₂²×C₁₃	1	2	yes	—
641	C₂×#103	C₂²×C₁₃	1	2	yes	—
642	#405	C₂²×C₁₃	1	2	yes	—
643	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
644	C₂²×C₁₃	—	2	1	no	—
645	C₂²×C₁₃	—	2	2	no	—
646	C₂²×C₁₃	—	2	2	no	—
647	C₂²×C₁₃	—	2	1	no	—
648	C₂²×C₁₃	—	2	1	no	—
649	C₂²×C₁₃	—	2	2	no	—
650	C₂²×C₁₃	—	4	2	no	—
651	C₂²×C₁₃	—	4	2	no	—
652	C₂²×C₁₃	—	4	2	no	—
653	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
654	C₄×C₁₃	—	2	1	no	—
655	C₄×C₁₃	—	2	1	no	—
656	C₄×C₁₃	—	2	2	no	—
657	C₄×C₁₃	—	2	1	no	—
658	C₄×C₁₃	—	2	2	no	—
659	C₄×C₁₃	—	2	1	no	—
660	C₄×C₁₃	—	2	2	no	—
661	C₄×C₁₃	—	4	1	no	—
662	C₄×C₁₃	—	4	1	no	—
663	C₄×C₁₃	—	4	2	no	—
664	C₄×C₁₃	—	4	1	no	—
665	C₄×C₁₃	—	4	1	no	—
666	C₄×C₁₃	—	4	1	no	—
667	C₄×C₁₃	—	4	2	no	—
668	C₄×C₁₃	—	4	1	no	—
669	C₄×C₁₃	—	4	1	no	—
670	C₄×C₁₃	—	4	1	no	—
671	C₄×C₁₃	—	4	2	no	—
672	C₄×C₁₃	#578	1	2	yes	—
673	C₄×C₁₃	#585	1	1	yes	characteristic
674	C₄×C₁₃	#585	1	1	yes	characteristic
675	C₂×#41	C₂³×C₁₃	1	2	yes	—
676	C₂×#41	C₂³×C₁₃	1	2	yes	—
677	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
678	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
679	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
680	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
681	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
682	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
686	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
687	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
688	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
689	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
696	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
699	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
704	#127	—	2	1	no	—
705	#127	C₂³×C₁₃	1	1	yes	characteristic
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	D₄×C₁₃	1	2	yes	—
714	#125	—	2	2	no	—
715	#125	—	2	1	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	1	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	1	no	—
723	#125	—	2	1	no	—
724	#125	D₄×C₁₃	1	1	yes	characteristic
725	#125	C₂³×C₁₃	1	2	yes	—
726	#125	C₂³×C₁₃	1	2	yes	—
727	#124	—	2	1	no	—
728	#124	—	2	1	no	—
729	#124	—	2	2	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	D₄×C₁₃	1	1	yes	characteristic
733	#124	C₂³×C₁₃	1	2	yes	—
734	#124	C₂³×C₁₃	1	2	yes	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	D₄×C₁₃	1	2	yes	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
756	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
763	#121	—	2	2	no	—
764	#121	—	2	2	no	—
765	#121	—	2	1	no	—
766	#121	—	2	1	no	—
767	#121	—	2	2	no	—
768	#121	D₄×C₁₃	1	1	yes	characteristic
769	#121	C₂³×C₁₃	1	2	yes	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
784	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	C₂³×C₁₃	1	2	yes	—
795	C₄×D₄	C₂³×C₁₃	1	2	yes	—
796	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	C₂³×C₁₃	1	2	yes	—
801	#117	C₂³×C₁₃	1	2	yes	—
802	#117	C₂³×C₁₃	1	2	yes	—
803	C₂×C₄⋊C₄	—	2	2	no	—
804	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
805	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
806	#107	C₂³×C₁₃	1	1	yes	characteristic
807	#107	C₂³×C₁₃	1	1	yes	characteristic
808	#107	C₂³×C₁₃	1	1	yes	characteristic
809	#107	C₂³×C₁₃	1	1	yes	characteristic
810	#107	C₂³×C₁₃	1	2	yes	—
811	#107	C₂³×C₁₃	1	2	yes	—
812	#106	C₂³×C₁₃	1	2	yes	—
813	#106	C₂³×C₁₃	1	2	yes	—
814	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
817	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
818	#103	C₂³×C₁₃	1	1	yes	characteristic
819	#103	C₂³×C₁₃	1	2	yes	—
820	#103	C₂³×C₁₃	1	2	yes	—
821	#103	C₂³×C₁₃	1	2	yes	—
822	#103	C₂³×C₁₃	1	1	yes	characteristic
823	#103	C₂³×C₁₃	1	2	yes	—
824	#103	C₂³×C₁₃	1	2	yes	—
825	#103	C₂³×C₁₃	1	2	yes	—
826	#103	C₂³×C₁₃	1	2	yes	—
827	#103	C₂³×C₁₃	1	1	yes	characteristic
828	#103	C₂³×C₁₃	1	2	yes	—
829	#103	C₂³×C₁₃	1	1	yes	characteristic
830	#103	C₂³×C₁₃	1	2	yes	—
831	#103	C₂³×C₁₃	1	2	yes	—
832	#103	C₂³×C₁₃	1	1	yes	characteristic
833	#103	C₂³×C₁₃	1	1	yes	characteristic
834	#103	C₂³×C₁₃	1	1	yes	characteristic
835	#103	C₂³×C₁₃	1	1	yes	characteristic
836	#102	C₂³×C₁₃	1	2	yes	—
837	#102	C₂³×C₁₃	1	2	yes	—
838	#102	C₂³×C₁₃	1	2	yes	—
839	#102	C₂³×C₁₃	1	2	yes	—
840	#102	C₂³×C₁₃	1	2	yes	—
841	#102	C₂³×C₁₃	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
843	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
845	#97	C₂³×C₁₃	1	2	yes	—
846	#97	C₂³×C₁₃	1	2	yes	—
847	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
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	C₂×C₁₃	—	4	1	no	—
853	C₂×C₁₃	—	4	2	no	—
854	C₂×C₁₃	—	8	2	no	—
855	C₂×C₁₃	#3500	1	1	yes	characteristic
856	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
857	C₂×C₁₃	#3584	1	1	yes	characteristic
858	#41	—	4	2	no	—
859	#41	—	4	2	no	—
860	#41	—	4	2	no	—
861	#41	—	4	2	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	1	no	—
864	C₂×Q₈	—	2	1	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	2	2	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	4	2	no	—
869	C₂×Q₈	—	4	2	no	—
870	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
871	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
872	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
873	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
874	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
875	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
882	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
883	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
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	C₂×D₄×C₁₃	1	1	yes	characteristic
890	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
893	Q₁₆	—	4	2	no	—
894	Q₁₆	—	4	1	no	—
895	Q₁₆	—	4	1	no	—
896	Q₁₆	—	4	1	no	—
897	Q₁₆	—	4	1	no	—
898	Q₁₆	—	4	2	no	—
899	SD₁₆	—	4	2	no	—
900	SD₁₆	—	4	2	no	—
901	M₁₆	—	4	2	no	—
902	C₂×C₈	—	4	2	no	—
903	C₂×C₈	—	4	1	no	—
904	C₂×C₈	—	4	1	no	—
905	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
908	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
910	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
952	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
971	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
974	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
985	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
986	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
987	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
988	C₄²	C₂⁴×C₁₃	1	2	yes	—
989	C₁₃	#62560	1	1	yes	characteristic, direct product factor, Sylow
990	C₂³	—	2	2	no	—
991	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
992	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	2	2	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	2	1	no	—
1004	Q₈	—	4	2	no	—
1005	Q₈	—	8	2	no	—
1006	Q₈	—	8	1	no	—
1007	Q₈	—	8	1	no	—
1008	Q₈	—	8	1	no	—
1009	Q₈	—	8	2	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	2	2	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	2	no	—
1015	D₄	—	8	1	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	2	no	—
1018	D₄	—	8	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	4	1	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1043	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1044	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1045	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1049	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1050	C₈	—	2	1	no	—
1051	C₈	—	2	1	no	—
1052	C₈	—	2	2	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	2	no	—
1056	C₂²	—	2	1	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1066	C₄	—	2	1	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	C₁₃×#578	1	2	yes	—
1085	C₄	C₁₃×#585	1	1	yes	characteristic
1086	C₄	C₁₃×#585	1	1	yes	characteristic
1087	C₂	—	4	1	no	—
1088	C₂	—	4	2	no	—
1089	C₂	—	8	2	no	—
1090	C₂	C₁₃×#3500	1	1	yes	characteristic
1091	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1092	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3554	C₂
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×#3555	C₂	semidirect
3. C₁₃×#3375	C₂	semidirect
4. C₁₃×#3374	C₂	semidirect
5. C₁₃×#3365	C₂	semidirect
6. C₁₃×#3363	C₂	semidirect
7. C₁₃×#3333	C₂	semidirect
8. C₁₃×#3328	C₂	semidirect
9. C₁₃×#3315	C₂	semidirect
10. C₁₃×#3313	C₂	semidirect
11. C₁₃×#3304	C₂	semidirect
12. C₁₃×#3302	C₂	semidirect
13. C₁₃×#3300	C₂	semidirect
14. C₁₃×#3299	C₂	semidirect
15. C₁₃×#3243	C₂	semidirect
16. C₁₃×#3237	C₂	semidirect
17. C₁₃×#3223	C₂	semidirect
18. C₁₃×#3216	C₂	semidirect
19. C₁₃×#3178	C₂	semidirect
20. C₁₃×#3170	C₂	semidirect
21. C₁₃×#3137	C₂	semidirect
22. C₁₃×#3131	C₂	semidirect
23. C₁₃×#2966	C₂	semidirect
312. #62560	C₁₃	direct (N × H)
444. #3555	C₂×C₁₃	semidirect
446. #3375	C₂×C₁₃	semidirect
447. #3374	C₂×C₁₃	semidirect
448. #3365	C₂×C₁₃	semidirect
449. #3363	C₂×C₁₃	semidirect
450. #3333	C₂×C₁₃	semidirect
451. #3328	C₂×C₁₃	semidirect
452. #3315	C₂×C₁₃	semidirect
453. #3313	C₂×C₁₃	semidirect
454. #3304	C₂×C₁₃	semidirect
455. #3302	C₂×C₁₃	semidirect
456. #3300	C₂×C₁₃	semidirect
457. #3299	C₂×C₁₃	semidirect
458. #3243	C₂×C₁₃	semidirect
459. #3237	C₂×C₁₃	semidirect
460. #3223	C₂×C₁₃	semidirect
461. #3216	C₂×C₁₃	semidirect
462. #3178	C₂×C₁₃	semidirect
463. #3170	C₂×C₁₃	semidirect
464. #3137	C₂×C₁₃	semidirect
465. #3131	C₂×C₁₃	semidirect
466. #2966	C₂×C₁₃	semidirect
989. C₁₃	#62560	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×#3555	2
C₁₃×#3554	2
C₁₃×#3375	2
C₁₃×#3374	2
C₁₃×#3365	2
C₁₃×#3363	2
C₁₃×#3333	2
C₁₃×#3328	2
C₁₃×#3315	2
C₁₃×#3313	2
C₁₃×#3304	2
C₁₃×#3302	2
C₁₃×#3300	2
C₁₃×#3299	2
C₁₃×#3243	2
C₁₃×#3237	2
C₁₃×#3223	2
C₁₃×#3216	2
C₁₃×#3178	2
C₁₃×#3170	2
C₁₃×#3137	2
C₁₃×#3131	2
C₁₃×#2966	2
#62560	13

Subgroups — C13×#62560 #15748899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62560 #15748899