Subgroups — C₁₃×#60891 #15747230

Order 3328.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3244	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3236	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3232	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3231	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3099	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#3098	C₂	1	1	yes	maximal, characteristic
17	C₁₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#557	—	2	1	no	—
25	C₁₃×#557	—	2	1	no	—
26	C₁₃×#554	—	2	2	no	—
27	C₁₃×#554	—	2	1	no	—
28	C₁₃×#554	—	2	2	no	—
29	C₁₃×#554	—	2	1	no	—
30	C₁₃×#544	C₂²	1	1	yes	characteristic
31	C₁₃×#544	C₂²	1	1	yes	characteristic
32	C₁₃×#544	C₂²	1	1	yes	characteristic
33	C₁₃×#544	C₂²	1	2	yes	—
34	C₁₃×#544	C₂²	1	2	yes	—
35	C₁₃×#542	—	2	1	no	—
36	C₁₃×#542	C₂²	1	2	yes	—
37	C₁₃×#541	—	2	1	no	—
38	C₁₃×#541	C₂²	1	2	yes	—
39	C₁₃×#539	—	2	2	no	—
40	C₁₃×#537	C₂²	1	1	yes	characteristic
41	C₁₃×#536	C₂²	1	1	yes	characteristic
42	C₁₃×#536	C₂²	1	1	yes	characteristic
43	C₁₃×#533	—	2	1	no	—
44	C₁₃×#533	C₂²	1	2	yes	—
45	C₁₃×#533	C₂²	1	1	yes	characteristic
46	C₁₃×#533	C₂²	1	2	yes	—
47	C₁₃×#529	—	2	2	no	—
48	C₁₃×#529	—	2	1	no	—
49	C₁₃×#529	C₂²	1	2	yes	—
50	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#125	C₂²	1	2	yes	—
52	C₁₃×#520	C₂²	1	1	yes	characteristic
53	C₁₃×#520	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	2	yes	—
58	C₁₃×#501	C₂²	1	2	yes	—
59	C₁₃×#501	C₂²	1	2	yes	—
60	C₁₃×#501	C₂²	1	2	yes	—
61	C₁₃×#500	C₂²	1	2	yes	—
62	C₁₃×#499	C₂²	1	2	yes	—
63	C₁₃×#499	C₂²	1	2	yes	—
64	C₁₃×#498	C₂²	1	2	yes	—
65	C₁₃×#491	C₂²	1	2	yes	—
66	C₁₃×#491	C₂²	1	2	yes	—
67	C₁₃×#489	C₂²	1	2	yes	—
68	C₁₃×#489	C₂²	1	2	yes	—
69	C₁₃×#488	C₂²	1	2	yes	—
70	C₁₃×#488	C₂²	1	2	yes	—
71	C₁₃×#487	C₂²	1	2	yes	—
72	C₁₃×#487	C₂²	1	2	yes	—
73	C₁₃×#485	C₂²	1	2	yes	—
74	C₁₃×#485	C₂²	1	2	yes	—
75	C₁₃×#485	C₂²	1	2	yes	—
76	C₁₃×#485	C₂²	1	2	yes	—
77	C₁₃×#485	C₂²	1	2	yes	—
78	C₁₃×#485	C₂²	1	2	yes	—
79	C₁₃×#484	C₂²	1	2	yes	—
80	C₁₃×#484	C₂²	1	2	yes	—
81	C₁₃×#484	C₂²	1	2	yes	—
82	C₁₃×#483	C₂²	1	2	yes	—
83	C₁₃×#483	C₂²	1	2	yes	—
84	C₁₃×#483	C₂²	1	2	yes	—
85	C₁₃×#482	C₂²	1	2	yes	—
86	C₁₃×#482	C₂²	1	2	yes	—
87	C₁₃×#481	C₂²	1	2	yes	—
88	C₁₃×#480	C₂²	1	2	yes	—
89	C₁₃×#479	C₂²	1	2	yes	—
90	C₁₃×#479	C₂²	1	2	yes	—
91	C₁₃×#479	C₂²	1	2	yes	—
92	C₁₃×#479	C₂²	1	2	yes	—
93	C₁₃×#479	C₂²	1	1	yes	characteristic
94	C₁₃×#479	C₂²	1	1	yes	characteristic
95	C₁₃×#479	C₂²	1	2	yes	—
96	C₁₃×#479	C₂²	1	2	yes	—
97	C₁₃×#479	C₂²	1	2	yes	—
98	C₁₃×#479	C₂²	1	2	yes	—
99	C₁₃×#478	C₂²	1	1	yes	characteristic
100	C₁₃×#478	C₂²	1	1	yes	characteristic
101	C₁₃×#478	C₂²	1	2	yes	—
102	C₁₃×#478	C₂²	1	2	yes	—
103	C₁₃×#477	C₂²	1	1	yes	characteristic
104	C₁₃×#477	C₂²	1	2	yes	—
105	C₁₃×#476	C₂²	1	1	yes	characteristic
106	C₁₃×#475	C₂²	1	1	yes	characteristic
107	C₁₃×#475	C₂²	1	2	yes	—
108	C₁₃×#474	C₂²	1	1	yes	characteristic
109	C₁₃×#433	C₂²	1	2	yes	—
110	C₁₃×#433	C₂²	1	2	yes	—
111	C₁₃×#432	C₂²	1	2	yes	—
112	C₁₃×#431	C₂²	1	2	yes	—
113	C₁₃×#428	C₂²	1	1	yes	characteristic
114	C₁₃×#428	C₂²	1	1	yes	characteristic
115	C₁₃×#428	C₂²	1	1	yes	characteristic
116	C₁₃×#428	C₂²	1	1	yes	characteristic
117	C₁₃×#427	C₂²	1	1	yes	characteristic
118	C₁₃×#427	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
120	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
121	C₁₃×#423	C₂²	1	1	yes	characteristic
122	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
123	C₁₃×#419	C₂²	1	1	yes	characteristic
124	C₁₃×#419	C₂²	1	1	yes	characteristic
125	C₁₃×#417	C₂²	1	1	yes	characteristic
126	C₁₃×#417	C₂²	1	1	yes	characteristic
127	C₁₃×#416	C₂²	1	1	yes	characteristic
128	C₁₃×#416	C₂²	1	1	yes	characteristic
129	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
130	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
131	C₁₃×#408	C₂²	1	1	yes	characteristic
132	C₁₃×#408	C₂²	1	1	yes	characteristic
133	C₁₃×#405	C₂²	1	1	yes	characteristic
134	C₁₃×#405	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	—	2	1	no	—
143	C₁₃×C₄⋊Q₈	—	2	1	no	—
144	C₁₃×C₄⋊Q₈	—	2	1	no	—
145	C₁₃×C₄⋊Q₈	—	2	2	no	—
146	C₁₃×C₄⋊Q₈	—	2	1	no	—
147	C₁₃×C₄⋊Q₈	—	2	2	no	—
148	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
150	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₁₃×#126	—	2	2	no	—
155	C₁₃×#126	—	2	2	no	—
156	C₁₃×#126	—	2	2	no	—
157	C₁₃×#126	—	2	2	no	—
158	C₁₃×#125	—	2	2	no	—
159	C₁₃×#125	—	2	1	no	—
160	C₁₃×#125	—	2	2	no	—
161	C₁₃×#125	—	2	1	no	—
162	C₁₃×#125	—	2	2	no	—
163	C₁₃×#125	—	2	1	no	—
164	C₁₃×#125	—	2	2	no	—
165	C₁₃×#125	—	2	1	no	—
166	C₁₃×#125	—	2	1	no	—
167	C₁₃×#125	—	2	2	no	—
168	C₁₃×#125	—	2	2	no	—
169	C₁₃×#125	—	2	2	no	—
170	C₁₃×#125	C₂³	1	1	yes	characteristic
171	C₁₃×#125	C₂³	1	2	yes	—
172	C₁₃×#125	C₂³	1	2	yes	—
173	C₁₃×#125	C₂³	1	1	yes	characteristic
174	C₁₃×#125	C₂³	1	2	yes	—
175	C₁₃×#125	C₂³	1	2	yes	—
176	C₁₃×#125	C₂³	1	2	yes	—
177	C₁₃×#124	—	2	1	no	—
178	C₁₃×#124	—	2	2	no	—
179	C₁₃×#124	C₂³	1	2	yes	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	—	2	2	no	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	1	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	1	no	—
187	C₁₃×C₂²⋊Q₈	—	2	1	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	1	no	—
191	C₁₃×C₂²⋊Q₈	—	2	1	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	—	2	2	no	—
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	—	2	1	no	—
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₄×Q₈×C₁₃	—	2	1	no	—
207	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	—	2	1	no	—
209	C₄×Q₈×C₁₃	—	2	1	no	—
210	C₄×Q₈×C₁₃	—	2	2	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	2	no	—
214	C₄×Q₈×C₁₃	—	2	2	no	—
215	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
217	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₁₃	—	2	2	no	—
222	C₄×D₄×C₁₃	—	2	2	no	—
223	C₄×D₄×C₁₃	—	2	1	no	—
224	C₄×D₄×C₁₃	—	2	1	no	—
225	C₄×D₄×C₁₃	—	2	1	no	—
226	C₄×D₄×C₁₃	—	2	1	no	—
227	C₄×D₄×C₁₃	—	2	2	no	—
228	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
229	C₄×D₄×C₁₃	D₄	1	2	yes	—
230	C₄×D₄×C₁₃	D₄	1	2	yes	—
231	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
232	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
234	C₁₃×#117	—	2	2	no	—
235	C₁₃×#117	—	2	1	no	—
236	C₁₃×#117	—	2	2	no	—
237	C₁₃×#117	C₂³	1	1	yes	characteristic
238	C₁₃×#117	C₂³	1	1	yes	characteristic
239	C₁₃×#117	C₂³	1	1	yes	characteristic
240	C₁₃×#117	C₂³	1	2	yes	—
241	C₁₃×#117	C₂³	1	2	yes	—
242	C₁₃×#117	C₂³	1	1	yes	characteristic
243	C₁₃×#117	C₂³	1	2	yes	—
244	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
253	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
254	C₂×C₄²×C₁₃	—	2	1	no	—
255	C₂×C₄²×C₁₃	—	2	1	no	—
256	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
258	C₁₃×#107	C₂³	1	2	yes	—
259	C₁₃×#107	C₂³	1	2	yes	—
260	C₁₃×#107	C₂³	1	1	yes	characteristic
261	C₁₃×#107	C₂³	1	1	yes	characteristic
262	C₁₃×#107	C₂³	1	1	yes	characteristic
263	C₁₃×#107	C₂³	1	1	yes	characteristic
264	C₁₃×#107	C₂³	1	2	yes	—
265	C₁₃×#107	C₂³	1	2	yes	—
266	C₁₃×#107	C₂³	1	2	yes	—
267	C₁₃×#107	C₂³	1	2	yes	—
268	C₁₃×#106	C₂³	1	2	yes	—
269	C₁₃×#106	C₂³	1	2	yes	—
270	C₁₃×#106	C₂³	1	1	yes	characteristic
271	C₁₃×#106	C₂³	1	1	yes	characteristic
272	C₁₃×#106	C₂³	1	1	yes	characteristic
273	C₁₃×#106	C₂³	1	1	yes	characteristic
274	C₁₃×#106	C₂³	1	2	yes	—
275	C₁₃×#106	C₂³	1	2	yes	—
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×#106	C₂³	1	2	yes	—
278	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	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	2	yes	—
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	1	yes	characteristic
291	C₁₃×#103	C₂³	1	1	yes	characteristic
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	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×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	2	yes	—
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	#60891	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	2	2	no	—
314	C₁₃×#41	—	2	2	no	—
315	C₁₃×#41	—	2	2	no	—
316	C₁₃×#41	—	2	2	no	—
317	C₂×Q₈×C₁₃	—	2	1	no	—
318	C₂×Q₈×C₁₃	—	2	2	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	—	2	2	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₁₃	—	2	1	no	—
329	C₂×D₄×C₁₃	—	2	2	no	—
330	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
331	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₁₃	—	2	1	no	—
334	C₂²×C₄×C₁₃	—	2	1	no	—
335	C₂²×C₄×C₁₃	—	2	2	no	—
336	C₂²×C₄×C₁₃	—	2	2	no	—
337	C₂²×C₄×C₁₃	—	2	1	no	—
338	C₂²×C₄×C₁₃	—	2	1	no	—
339	C₂²×C₄×C₁₃	—	2	1	no	—
340	C₂²×C₄×C₁₃	—	2	1	no	—
341	C₂²×C₄×C₁₃	—	2	1	no	—
342	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
345	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
346	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₁₃×M₁₆	—	2	2	no	—
349	C₁₃×M₁₆	—	2	2	no	—
350	C₂×C₈×C₁₃	—	2	2	no	—
351	C₂×C₈×C₁₃	—	2	2	no	—
352	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
355	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
356	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	1	no	—
360	C₁₃×C₄⋊C₄	—	2	2	no	—
361	C₁₃×C₄⋊C₄	—	2	1	no	—
362	C₁₃×C₄⋊C₄	—	2	2	no	—
363	C₁₃×C₄⋊C₄	—	2	2	no	—
364	C₁₃×C₄⋊C₄	—	2	2	no	—
365	C₁₃×C₄⋊C₄	—	2	2	no	—
366	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
371	C₁₃×C₄⋊C₄	—	2	2	no	—
372	C₁₃×C₄⋊C₄	—	2	1	no	—
373	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
378	C₁₃×C₄⋊C₄	—	2	2	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	2	no	—
381	C₁₃×C₄⋊C₄	—	2	2	no	—
382	C₁₃×C₄⋊C₄	—	2	1	no	—
383	C₁₃×C₄⋊C₄	—	2	1	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	1	no	—
386	C₁₃×C₄⋊C₄	—	2	1	no	—
387	C₁₃×C₄⋊C₄	—	2	2	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
396	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
397	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
398	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
399	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
400	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
402	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₁₃×C₂²⋊C₄	—	2	2	no	—
405	C₁₃×C₂²⋊C₄	—	2	2	no	—
406	C₁₃×C₂²⋊C₄	—	2	2	no	—
407	C₁₃×C₂²⋊C₄	—	2	2	no	—
408	C₁₃×C₂²⋊C₄	—	2	1	no	—
409	C₁₃×C₂²⋊C₄	—	2	1	no	—
410	C₁₃×C₂²⋊C₄	—	2	1	no	—
411	C₁₃×C₂²⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
418	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
419	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
420	C₄²×C₁₃	—	2	2	no	—
421	C₄²×C₁₃	—	2	1	no	—
422	C₄²×C₁₃	—	2	1	no	—
423	C₄²×C₁₃	—	2	1	no	—
424	C₄²×C₁₃	—	2	2	no	—
425	C₄²×C₁₃	—	2	2	no	—
426	C₄²×C₁₃	—	2	2	no	—
427	C₄²×C₁₃	—	2	1	no	—
428	C₄²×C₁₃	—	2	1	no	—
429	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
430	C₄²×C₁₃	C₂×D₄	1	2	yes	—
431	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₁₃	C₂×D₄	1	2	yes	—
433	C₄²×C₁₃	C₂⁴	1	2	yes	—
434	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
435	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
436	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
437	#3461	C₂×C₁₃	1	1	yes	characteristic
438	#3244	C₂×C₁₃	1	2	yes	complemented
439	#3243	C₂×C₁₃	1	2	yes	complemented
440	#3242	C₂×C₁₃	1	2	yes	complemented
441	#3242	C₂×C₁₃	1	2	yes	complemented
442	#3240	C₂×C₁₃	1	2	yes	complemented
443	#3236	C₂×C₁₃	1	2	yes	complemented
444	#3232	C₂×C₁₃	1	2	yes	complemented
445	#3231	C₂×C₁₃	1	2	yes	complemented
446	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
447	#3163	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3137	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3137	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3099	C₂×C₁₃	1	1	yes	characteristic
451	#3098	C₂×C₁₃	1	1	yes	characteristic
452	#3097	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#3097	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3080	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
457	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
459	C₂³×C₁₃	—	2	1	no	—
460	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
461	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₁₃	—	2	2	no	—
463	Q₈×C₁₃	—	2	2	no	—
464	Q₈×C₁₃	—	2	2	no	—
465	Q₈×C₁₃	—	2	1	no	—
466	Q₈×C₁₃	—	2	1	no	—
467	Q₈×C₁₃	—	4	2	no	—
468	Q₈×C₁₃	—	8	1	no	—
469	Q₈×C₁₃	—	8	2	no	—
470	Q₈×C₁₃	—	8	2	no	—
471	Q₈×C₁₃	—	8	1	no	—
472	Q₈×C₁₃	—	8	2	no	—
473	D₄×C₁₃	—	2	4	no	—
474	D₄×C₁₃	—	2	2	no	—
475	D₄×C₁₃	—	2	1	no	—
476	D₄×C₁₃	—	2	1	no	—
477	D₄×C₁₃	—	4	2	no	—
478	D₄×C₁₃	—	8	2	no	—
479	C₂×C₄×C₁₃	—	2	2	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	1	no	—
482	C₂×C₄×C₁₃	—	2	1	no	—
483	C₂×C₄×C₁₃	—	2	1	no	—
484	C₂×C₄×C₁₃	—	2	2	no	—
485	C₂×C₄×C₁₃	—	2	1	no	—
486	C₂×C₄×C₁₃	—	2	1	no	—
487	C₂×C₄×C₁₃	—	2	2	no	—
488	C₂×C₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	1	no	—
490	C₂×C₄×C₁₃	—	2	2	no	—
491	C₂×C₄×C₁₃	—	2	1	no	—
492	C₂×C₄×C₁₃	—	4	1	no	—
493	C₂×C₄×C₁₃	—	4	2	no	—
494	C₂×C₄×C₁₃	—	4	1	no	—
495	C₂×C₄×C₁₃	—	4	2	no	—
496	C₂×C₄×C₁₃	—	4	2	no	—
497	C₂×C₄×C₁₃	—	4	2	no	—
498	C₂×C₄×C₁₃	—	4	2	no	—
499	C₂×C₄×C₁₃	—	8	1	no	—
500	C₂×C₄×C₁₃	—	8	1	no	—
501	C₂×C₄×C₁₃	—	8	2	no	—
502	C₂×C₄×C₁₃	—	8	1	no	—
503	C₂×C₄×C₁₃	—	8	1	no	—
504	C₂×C₄×C₁₃	—	8	2	no	—
505	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
514	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
515	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
516	C₈×C₁₃	—	2	1	no	—
517	C₈×C₁₃	—	2	1	no	—
518	C₈×C₁₃	—	2	1	no	—
519	C₈×C₁₃	—	2	1	no	—
520	C₈×C₁₃	—	2	2	no	—
521	C₈×C₁₃	—	2	2	no	—
522	#557	—	2	1	no	—
523	#557	—	2	1	no	—
524	#554	—	2	2	no	—
525	#554	—	2	1	no	—
526	#554	—	2	2	no	—
527	#554	—	2	1	no	—
528	#544	C₂²×C₁₃	1	1	yes	characteristic
529	#544	C₂²×C₁₃	1	1	yes	characteristic
530	#544	C₂²×C₁₃	1	1	yes	characteristic
531	#544	C₂²×C₁₃	1	2	yes	—
532	#544	C₂²×C₁₃	1	2	yes	—
533	#542	—	2	1	no	—
534	#542	C₂²×C₁₃	1	2	yes	—
535	#541	—	2	1	no	—
536	#541	C₂²×C₁₃	1	2	yes	—
537	#539	—	2	2	no	—
538	#537	C₂²×C₁₃	1	1	yes	characteristic
539	#536	C₂²×C₁₃	1	1	yes	characteristic
540	#536	C₂²×C₁₃	1	1	yes	characteristic
541	#533	—	2	1	no	—
542	#533	C₂²×C₁₃	1	2	yes	—
543	#533	C₂²×C₁₃	1	1	yes	characteristic
544	#533	C₂²×C₁₃	1	2	yes	—
545	#529	—	2	2	no	—
546	#529	—	2	1	no	—
547	#529	C₂²×C₁₃	1	2	yes	—
548	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
549	C₂×#125	C₂²×C₁₃	1	2	yes	—
550	#520	C₂²×C₁₃	1	1	yes	characteristic
551	#520	C₂²×C₁₃	1	1	yes	characteristic
552	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
553	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
554	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
555	#501	C₂²×C₁₃	1	2	yes	—
556	#501	C₂²×C₁₃	1	2	yes	—
557	#501	C₂²×C₁₃	1	2	yes	—
558	#501	C₂²×C₁₃	1	2	yes	—
559	#500	C₂²×C₁₃	1	2	yes	—
560	#499	C₂²×C₁₃	1	2	yes	—
561	#499	C₂²×C₁₃	1	2	yes	—
562	#498	C₂²×C₁₃	1	2	yes	—
563	#491	C₂²×C₁₃	1	2	yes	—
564	#491	C₂²×C₁₃	1	2	yes	—
565	#489	C₂²×C₁₃	1	2	yes	—
566	#489	C₂²×C₁₃	1	2	yes	—
567	#488	C₂²×C₁₃	1	2	yes	—
568	#488	C₂²×C₁₃	1	2	yes	—
569	#487	C₂²×C₁₃	1	2	yes	—
570	#487	C₂²×C₁₃	1	2	yes	—
571	#485	C₂²×C₁₃	1	2	yes	—
572	#485	C₂²×C₁₃	1	2	yes	—
573	#485	C₂²×C₁₃	1	2	yes	—
574	#485	C₂²×C₁₃	1	2	yes	—
575	#485	C₂²×C₁₃	1	2	yes	—
576	#485	C₂²×C₁₃	1	2	yes	—
577	#484	C₂²×C₁₃	1	2	yes	—
578	#484	C₂²×C₁₃	1	2	yes	—
579	#484	C₂²×C₁₃	1	2	yes	—
580	#483	C₂²×C₁₃	1	2	yes	—
581	#483	C₂²×C₁₃	1	2	yes	—
582	#483	C₂²×C₁₃	1	2	yes	—
583	#482	C₂²×C₁₃	1	2	yes	—
584	#482	C₂²×C₁₃	1	2	yes	—
585	#481	C₂²×C₁₃	1	2	yes	—
586	#480	C₂²×C₁₃	1	2	yes	—
587	#479	C₂²×C₁₃	1	2	yes	—
588	#479	C₂²×C₁₃	1	2	yes	—
589	#479	C₂²×C₁₃	1	2	yes	—
590	#479	C₂²×C₁₃	1	2	yes	—
591	#479	C₂²×C₁₃	1	1	yes	characteristic
592	#479	C₂²×C₁₃	1	1	yes	characteristic
593	#479	C₂²×C₁₃	1	2	yes	—
594	#479	C₂²×C₁₃	1	2	yes	—
595	#479	C₂²×C₁₃	1	2	yes	—
596	#479	C₂²×C₁₃	1	2	yes	—
597	#478	C₂²×C₁₃	1	1	yes	characteristic
598	#478	C₂²×C₁₃	1	1	yes	characteristic
599	#478	C₂²×C₁₃	1	2	yes	—
600	#478	C₂²×C₁₃	1	2	yes	—
601	#477	C₂²×C₁₃	1	1	yes	characteristic
602	#477	C₂²×C₁₃	1	2	yes	—
603	#476	C₂²×C₁₃	1	1	yes	characteristic
604	#475	C₂²×C₁₃	1	1	yes	characteristic
605	#475	C₂²×C₁₃	1	2	yes	—
606	#474	C₂²×C₁₃	1	1	yes	characteristic
607	#433	C₂²×C₁₃	1	2	yes	—
608	#433	C₂²×C₁₃	1	2	yes	—
609	#432	C₂²×C₁₃	1	2	yes	—
610	#431	C₂²×C₁₃	1	2	yes	—
611	#428	C₂²×C₁₃	1	1	yes	characteristic
612	#428	C₂²×C₁₃	1	1	yes	characteristic
613	#428	C₂²×C₁₃	1	1	yes	characteristic
614	#428	C₂²×C₁₃	1	1	yes	characteristic
615	#427	C₂²×C₁₃	1	1	yes	characteristic
616	#427	C₂²×C₁₃	1	1	yes	characteristic
617	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
618	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
619	#423	C₂²×C₁₃	1	1	yes	characteristic
620	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
621	#419	C₂²×C₁₃	1	1	yes	characteristic
622	#419	C₂²×C₁₃	1	1	yes	characteristic
623	#417	C₂²×C₁₃	1	1	yes	characteristic
624	#417	C₂²×C₁₃	1	1	yes	characteristic
625	#416	C₂²×C₁₃	1	1	yes	characteristic
626	#416	C₂²×C₁₃	1	1	yes	characteristic
627	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
628	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
629	#408	C₂²×C₁₃	1	1	yes	characteristic
630	#408	C₂²×C₁₃	1	1	yes	characteristic
631	#405	C₂²×C₁₃	1	1	yes	characteristic
632	#405	C₂²×C₁₃	1	1	yes	characteristic
633	C₂²×C₁₃	—	2	1	no	—
634	C₂²×C₁₃	—	2	1	no	—
635	C₂²×C₁₃	—	2	2	no	—
636	C₂²×C₁₃	—	2	2	no	—
637	C₂²×C₁₃	—	2	2	no	—
638	C₂²×C₁₃	—	4	1	no	—
639	C₂²×C₁₃	—	4	1	no	—
640	C₂²×C₁₃	—	4	1	no	—
641	C₂²×C₁₃	#536	1	2	yes	—
642	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
643	C₄×C₁₃	—	2	1	no	—
644	C₄×C₁₃	—	2	1	no	—
645	C₄×C₁₃	—	2	2	no	—
646	C₄×C₁₃	—	2	1	no	—
647	C₄×C₁₃	—	2	1	no	—
648	C₄×C₁₃	—	2	2	no	—
649	C₄×C₁₃	—	2	2	no	—
650	C₄×C₁₃	—	4	2	no	—
651	C₄×C₁₃	—	4	1	no	—
652	C₄×C₁₃	—	4	2	no	—
653	C₄×C₁₃	—	4	1	no	—
654	C₄×C₁₃	—	4	1	no	—
655	C₄×C₁₃	—	4	1	no	—
656	C₄×C₁₃	—	4	2	no	—
657	C₄×C₁₃	—	4	1	no	—
658	C₄×C₁₃	—	4	1	no	—
659	C₄×C₁₃	—	4	1	no	—
660	C₄×C₁₃	—	4	2	no	—
661	C₄×C₁₃	#536	1	2	yes	—
662	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
663	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
664	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
666	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
667	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
668	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
669	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
670	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
671	C₄⋊Q₈	—	2	1	no	—
672	C₄⋊Q₈	—	2	1	no	—
673	C₄⋊Q₈	—	2	1	no	—
674	C₄⋊Q₈	—	2	2	no	—
675	C₄⋊Q₈	—	2	1	no	—
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
678	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
679	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
680	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
681	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
682	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
683	#126	—	2	2	no	—
684	#126	—	2	2	no	—
685	#126	—	2	2	no	—
686	#126	—	2	2	no	—
687	#125	—	2	2	no	—
688	#125	—	2	1	no	—
689	#125	—	2	2	no	—
690	#125	—	2	1	no	—
691	#125	—	2	2	no	—
692	#125	—	2	1	no	—
693	#125	—	2	2	no	—
694	#125	—	2	1	no	—
695	#125	—	2	1	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	C₂³×C₁₃	1	2	yes	—
700	#125	C₂³×C₁₃	1	1	yes	characteristic
701	#125	C₂³×C₁₃	1	2	yes	—
702	#125	C₂³×C₁₃	1	2	yes	—
703	#125	C₂³×C₁₃	1	2	yes	—
704	#125	C₂³×C₁₃	1	2	yes	—
705	#125	C₂³×C₁₃	1	1	yes	characteristic
706	#124	—	2	1	no	—
707	#124	—	2	2	no	—
708	#124	C₂³×C₁₃	1	2	yes	—
709	#123	—	2	2	no	—
710	#123	—	2	2	no	—
711	#123	—	2	2	no	—
712	#123	—	2	2	no	—
713	C₂²⋊Q₈	—	2	1	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	1	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	1	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
730	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
732	#121	—	2	2	no	—
733	#121	—	2	1	no	—
734	#121	C₂³×C₁₃	1	2	yes	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	—	2	2	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	—	2	2	no	—
743	C₄×Q₈	—	2	2	no	—
744	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
745	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
746	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
747	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
748	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
749	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	—	2	1	no	—
753	C₄×D₄	—	2	1	no	—
754	C₄×D₄	—	2	1	no	—
755	C₄×D₄	—	2	1	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
758	C₄×D₄	D₄×C₁₃	1	2	yes	—
759	C₄×D₄	D₄×C₁₃	1	2	yes	—
760	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
761	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
762	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
763	#117	—	2	2	no	—
764	#117	—	2	1	no	—
765	#117	—	2	2	no	—
766	#117	C₂³×C₁₃	1	1	yes	characteristic
767	#117	C₂³×C₁₃	1	1	yes	characteristic
768	#117	C₂³×C₁₃	1	1	yes	characteristic
769	#117	C₂³×C₁₃	1	2	yes	—
770	#117	C₂³×C₁₃	1	2	yes	—
771	#117	C₂³×C₁₃	1	1	yes	characteristic
772	#117	C₂³×C₁₃	1	2	yes	—
773	C₂×C₄⋊C₄	—	2	1	no	—
774	C₂×C₄⋊C₄	—	2	1	no	—
775	C₂×C₄⋊C₄	—	2	1	no	—
776	C₂×C₄⋊C₄	—	2	2	no	—
777	C₂×C₄⋊C₄	—	2	2	no	—
778	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
779	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
780	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
781	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
783	C₂×C₄²	—	2	1	no	—
784	C₂×C₄²	—	2	1	no	—
785	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
786	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
787	#107	C₂³×C₁₃	1	2	yes	—
788	#107	C₂³×C₁₃	1	2	yes	—
789	#107	C₂³×C₁₃	1	1	yes	characteristic
790	#107	C₂³×C₁₃	1	1	yes	characteristic
791	#107	C₂³×C₁₃	1	1	yes	characteristic
792	#107	C₂³×C₁₃	1	1	yes	characteristic
793	#107	C₂³×C₁₃	1	2	yes	—
794	#107	C₂³×C₁₃	1	2	yes	—
795	#107	C₂³×C₁₃	1	2	yes	—
796	#107	C₂³×C₁₃	1	2	yes	—
797	#106	C₂³×C₁₃	1	2	yes	—
798	#106	C₂³×C₁₃	1	2	yes	—
799	#106	C₂³×C₁₃	1	1	yes	characteristic
800	#106	C₂³×C₁₃	1	1	yes	characteristic
801	#106	C₂³×C₁₃	1	1	yes	characteristic
802	#106	C₂³×C₁₃	1	1	yes	characteristic
803	#106	C₂³×C₁₃	1	2	yes	—
804	#106	C₂³×C₁₃	1	2	yes	—
805	#106	C₂³×C₁₃	1	2	yes	—
806	#106	C₂³×C₁₃	1	2	yes	—
807	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
808	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
809	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
812	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
813	#103	C₂³×C₁₃	1	2	yes	—
814	#103	C₂³×C₁₃	1	2	yes	—
815	#103	C₂³×C₁₃	1	2	yes	—
816	#103	C₂³×C₁₃	1	2	yes	—
817	#103	C₂³×C₁₃	1	1	yes	characteristic
818	#103	C₂³×C₁₃	1	1	yes	characteristic
819	#103	C₂³×C₁₃	1	1	yes	characteristic
820	#103	C₂³×C₁₃	1	1	yes	characteristic
821	#103	C₂³×C₁₃	1	2	yes	—
822	#103	C₂³×C₁₃	1	2	yes	—
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	#102	C₂³×C₁₃	1	1	yes	characteristic
828	#102	C₂³×C₁₃	1	1	yes	characteristic
829	#102	C₂³×C₁₃	1	1	yes	characteristic
830	#102	C₂³×C₁₃	1	1	yes	characteristic
831	#102	C₂³×C₁₃	1	2	yes	—
832	#102	C₂³×C₁₃	1	2	yes	—
833	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
834	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
835	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
836	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
837	#97	C₂³×C₁₃	1	2	yes	—
838	#97	C₂³×C₁₃	1	2	yes	—
839	C₄×C₈	C₂³×C₁₃	1	2	yes	—
840	C₄×C₈	C₂³×C₁₃	1	2	yes	—
841	C₂×C₁₃	—	2	2	no	—
842	C₂×C₁₃	—	4	2	no	—
843	C₂×C₁₃	—	8	1	no	—
844	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
845	C₂×C₁₃	#3584	1	1	yes	characteristic
846	C₂×C₁₃	#3586	1	1	yes	characteristic
847	#41	—	2	2	no	—
848	#41	—	2	2	no	—
849	#41	—	2	2	no	—
850	#41	—	2	2	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	2	no	—
853	C₂×Q₈	—	2	1	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
860	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
861	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
862	C₂×D₄	—	2	1	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
865	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
866	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
877	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
878	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
879	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
880	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
881	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
882	M₁₆	—	2	2	no	—
883	M₁₆	—	2	2	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
887	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
888	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
889	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
890	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	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	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
927	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
928	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
931	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
935	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
936	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
952	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
953	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	1	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	2	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
964	C₄²	C₂×D₄×C₁₃	1	2	yes	—
965	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
966	C₄²	C₂×D₄×C₁₃	1	2	yes	—
967	C₄²	C₂⁴×C₁₃	1	2	yes	—
968	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
969	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
970	C₁₃	#60891	1	1	yes	characteristic, direct product factor, Sylow
971	C₂³	—	2	1	no	—
972	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
973	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	2	1	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	4	2	no	—
980	Q₈	—	8	1	no	—
981	Q₈	—	8	2	no	—
982	Q₈	—	8	2	no	—
983	Q₈	—	8	1	no	—
984	Q₈	—	8	2	no	—
985	D₄	—	2	4	no	—
986	D₄	—	2	2	no	—
987	D₄	—	2	1	no	—
988	D₄	—	2	1	no	—
989	D₄	—	4	2	no	—
990	D₄	—	8	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	1	no	—
1007	C₂×C₄	—	4	2	no	—
1008	C₂×C₄	—	4	2	no	—
1009	C₂×C₄	—	4	2	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	8	1	no	—
1012	C₂×C₄	—	8	1	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	—	8	1	no	—
1015	C₂×C₄	—	8	1	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1023	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1025	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1026	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1027	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	C₁₃×#536	1	2	yes	—
1043	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1044	C₄	—	2	1	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	2	no	—
1062	C₄	C₁₃×#536	1	2	yes	—
1063	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1064	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1065	C₂	—	2	2	no	—
1066	C₂	—	4	2	no	—
1067	C₂	—	8	1	no	—
1068	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
1069	C₂	C₁₃×#3584	1	1	yes	characteristic
1070	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#537	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3504	C₂	semidirect
3. C₁₃×#3244	C₂	semidirect
4. C₁₃×#3243	C₂	semidirect
5. C₁₃×#3242	C₂	semidirect
6. C₁₃×#3242	C₂	semidirect
7. C₁₃×#3240	C₂	semidirect
8. C₁₃×#3236	C₂	semidirect
9. C₁₃×#3232	C₂	semidirect
10. C₁₃×#3231	C₂	semidirect
11. C₁₃×#3164	C₂	semidirect
12. C₁₃×#3163	C₂	semidirect
13. C₁₃×#3137	C₂	semidirect
14. C₁₃×#3137	C₂	semidirect
17. C₁₃×#3097	C₂	semidirect
18. C₁₃×#3097	C₂	semidirect
19. C₁₃×#3080	C₂	semidirect
20. C₁₃×#3078	C₂	semidirect
21. C₁₃×#3076	C₂	semidirect
22. C₂×C₁₃×#479	C₂	semidirect
23. C₁₃×#2925	C₂	semidirect
312. #60891	C₁₃	direct (N × H)
436. #3504	C₂×C₁₃	semidirect
438. #3244	C₂×C₁₃	semidirect
439. #3243	C₂×C₁₃	semidirect
440. #3242	C₂×C₁₃	semidirect
441. #3242	C₂×C₁₃	semidirect
442. #3240	C₂×C₁₃	semidirect
443. #3236	C₂×C₁₃	semidirect
444. #3232	C₂×C₁₃	semidirect
445. #3231	C₂×C₁₃	semidirect
446. #3164	C₂×C₁₃	semidirect
447. #3163	C₂×C₁₃	semidirect
448. #3137	C₂×C₁₃	semidirect
449. #3137	C₂×C₁₃	semidirect
452. #3097	C₂×C₁₃	semidirect
453. #3097	C₂×C₁₃	semidirect
454. #3080	C₂×C₁₃	semidirect
455. #3078	C₂×C₁₃	semidirect
456. #3076	C₂×C₁₃	semidirect
457. C₂×#479	C₂×C₁₃	semidirect
458. #2925	C₂×C₁₃	semidirect
970. C₁₃	#60891	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×#3504	2
C₁₃×#3461	2
C₁₃×#3244	2
C₁₃×#3243	2
C₁₃×#3242	2
C₁₃×#3240	2
C₁₃×#3236	2
C₁₃×#3232	2
C₁₃×#3231	2
C₁₃×#3164	2
C₁₃×#3163	2
C₁₃×#3137	2
C₁₃×#3099	2
C₁₃×#3098	2
C₁₃×#3097	2
C₁₃×#3080	2
C₁₃×#3078	2
C₁₃×#3076	2
C₂×C₁₃×#479	2
C₁₃×#2925	2
#60891	13

Subgroups — C13×#60891 #15747230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60891 #15747230