Subgroups — C₁₃×#62165 #15748504

Order 3328.

1694 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3344	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3343	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3338	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3315	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3314	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3258	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#564	—	2	1	no	—
21	C₁₃×#563	—	2	1	no	—
22	C₁₃×#557	C₂²	1	2	yes	complemented
23	C₁₃×#556	C₂²	1	1	yes	characteristic
24	C₁₃×#554	C₂²	1	2	yes	—
25	C₁₃×#554	C₂²	1	2	yes	—
26	C₁₃×#552	—	2	1	no	—
27	C₁₃×#552	—	2	2	no	—
28	C₁₃×#552	C₂²	1	2	yes	—
29	C₁₃×#552	C₂²	1	2	yes	complemented
30	C₁₃×#551	—	2	2	no	—
31	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#548	—	2	1	no	—
33	C₁₃×#547	C₂²	1	1	yes	characteristic
34	C₁₃×#547	C₂²	1	1	yes	characteristic
35	C₁₃×#546	C₂²	1	2	yes	—
36	C₁₃×#544	—	2	1	no	—
37	C₁₃×#544	C₂²	1	2	yes	complemented
38	C₁₃×#542	C₂²	1	2	yes	—
39	C₁₃×#541	—	2	2	no	—
40	C₁₃×#541	C₂²	1	2	yes	complemented
41	C₁₃×#539	—	2	2	no	—
42	C₁₃×#539	—	2	1	no	—
43	C₁₃×#533	C₂²	1	1	yes	characteristic
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#529	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
47	C₁₃×#525	—	2	1	no	—
48	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
49	C₁₃×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	2	yes	complemented
52	C₁₃×#501	C₂²	1	2	yes	complemented
53	C₁₃×#500	C₂²	1	2	yes	complemented
54	C₁₃×#491	C₂²	1	2	yes	complemented
55	C₁₃×#489	C₂²	1	2	yes	—
56	C₁₃×#488	C₂²	1	2	yes	—
57	C₁₃×#485	C₂²	1	2	yes	complemented
58	C₁₃×#484	C₂²	1	2	yes	—
59	C₁₃×#484	C₂²	1	2	yes	—
60	C₁₃×#484	C₂²	1	2	yes	complemented
61	C₁₃×#484	C₂²	1	2	yes	complemented
62	C₁₃×#483	C₂²	1	2	yes	—
63	C₁₃×#483	C₂²	1	2	yes	complemented
64	C₁₃×#482	C₂²	1	2	yes	—
65	C₁₃×#480	C₂²	1	2	yes	—
66	C₁₃×#479	C₂²	1	2	yes	complemented
67	C₁₃×#479	C₂²	1	2	yes	complemented
68	C₁₃×#479	C₂²	1	2	yes	complemented
69	C₁₃×#478	C₂²	1	2	yes	—
70	C₁₃×#478	C₂²	1	2	yes	—
71	C₁₃×#478	C₂²	1	2	yes	—
72	C₁₃×#478	C₂²	1	2	yes	—
73	C₁₃×#478	C₂²	1	2	yes	—
74	C₁₃×#477	C₂²	1	2	yes	complemented
75	C₁₃×#477	C₂²	1	2	yes	complemented
76	C₁₃×#477	C₂²	1	2	yes	complemented
77	C₁₃×#477	C₂²	1	2	yes	complemented
78	C₁₃×#475	C₂²	1	2	yes	complemented
79	C₁₃×#474	C₂²	1	2	yes	—
80	C₁₃×#474	C₂²	1	1	yes	characteristic
81	C₁₃×#474	C₂²	1	1	yes	characteristic
82	C₁₃×#470	C₂²	1	2	yes	complemented
83	C₁₃×#468	C₂²	1	2	yes	—
84	C₁₃×#467	C₂²	1	2	yes	—
85	C₁₃×#467	C₂²	1	2	yes	—
86	C₁₃×#467	C₂²	1	2	yes	complemented
87	C₁₃×#465	C₂²	1	2	yes	—
88	C₁₃×#464	C₂²	1	2	yes	—
89	C₁₃×#464	C₂²	1	2	yes	—
90	C₁₃×#462	C₂²	1	2	yes	complemented
91	C₁₃×#462	C₂²	1	2	yes	complemented
92	C₁₃×#461	C₂²	1	1	yes	characteristic
93	C₁₃×#461	C₂²	1	1	yes	characteristic
94	C₁₃×#452	C₂²	1	2	yes	—
95	C₁₃×#452	C₂²	1	2	yes	—
96	C₁₃×#450	C₂²	1	2	yes	—
97	C₁₃×#446	C₂²	1	2	yes	complemented
98	C₁₃×#441	C₂²	1	2	yes	complemented
99	C₁₃×#440	C₂²	1	2	yes	—
100	C₁₃×#440	C₂²	1	2	yes	—
101	C₁₃×#440	C₂²	1	2	yes	—
102	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
103	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
104	C₁₃×#435	C₂²	1	2	yes	—
105	C₁₃×#435	C₂²	1	2	yes	complemented
106	C₈×D₄×C₁₃	C₂²	1	2	yes	—
107	C₁₃×#433	C₂²	1	2	yes	complemented
108	C₁₃×#432	C₂²	1	1	yes	characteristic
109	C₁₃×#428	C₂²	1	2	yes	complemented
110	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
111	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
112	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
113	C₁₃×#424	C₂²	1	2	yes	complemented
114	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₁₃×#417	C₂²	1	2	yes	—
116	C₁₃×#416	C₂²	1	2	yes	—
117	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
118	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	1	no	—
120	C₂×C₁₃×#41	C₂³	1	2	yes	—
121	C₂²×Q₈×C₁₃	—	2	1	no	—
122	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	—	2	1	no	—
124	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
129	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
132	C₁₃×C₄⋊Q₈	—	2	2	no	—
133	C₁₃×C₄⋊Q₈	—	2	2	no	—
134	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#126	D₄	1	2	yes	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	—	2	2	no	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	2	no	—
152	C₁₃×#125	—	2	2	no	—
153	C₁₃×#125	—	2	2	no	—
154	C₁₃×#125	—	2	2	no	—
155	C₁₃×#125	—	2	2	no	—
156	C₁₃×#125	—	2	1	no	—
157	C₁₃×#125	—	2	1	no	—
158	C₁₃×#125	—	2	1	no	—
159	C₁₃×#125	—	2	1	no	—
160	C₁₃×#125	D₄	1	1	yes	characteristic
161	C₁₃×#125	C₂³	1	2	yes	—
162	C₁₃×#125	C₂³	1	2	yes	—
163	C₁₃×#125	C₂³	1	2	yes	—
164	C₁₃×#124	—	2	2	no	—
165	C₁₃×#124	D₄	1	1	yes	characteristic
166	C₁₃×#124	C₂³	1	2	yes	—
167	C₁₃×#123	—	2	2	no	—
168	C₁₃×#123	—	2	2	no	—
169	C₁₃×#123	—	2	2	no	—
170	C₁₃×#123	—	2	2	no	—
171	C₁₃×#123	—	2	2	no	—
172	C₁₃×#123	—	2	2	no	—
173	C₁₃×#123	D₄	1	2	yes	—
174	C₁₃×C₂²⋊Q₈	—	2	1	no	—
175	C₁₃×C₂²⋊Q₈	—	2	1	no	—
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	2	no	—
181	C₁₃×C₂²⋊Q₈	—	2	2	no	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₁₃×#121	—	2	1	no	—
194	C₁₃×#121	—	2	2	no	—
195	C₁₃×#121	D₄	1	1	yes	characteristic
196	C₁₃×#121	C₂³	1	2	yes	—
197	C₁₃×#120	—	2	2	no	—
198	C₄×Q₈×C₁₃	—	2	2	no	—
199	C₄×Q₈×C₁₃	—	2	1	no	—
200	C₄×Q₈×C₁₃	—	2	1	no	—
201	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
202	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
203	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
204	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
205	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
206	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₁₃	—	2	2	no	—
208	C₄×D₄×C₁₃	—	2	2	no	—
209	C₄×D₄×C₁₃	—	2	2	no	—
210	C₄×D₄×C₁₃	—	2	2	no	—
211	C₄×D₄×C₁₃	—	2	1	no	—
212	C₄×D₄×C₁₃	—	2	1	no	—
213	C₄×D₄×C₁₃	C₂³	1	2	yes	—
214	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
215	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₁₃	C₂³	1	2	yes	—
219	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
220	C₁₃×#117	—	2	1	no	—
221	C₁₃×#117	—	2	1	no	—
222	C₁₃×#117	—	2	2	no	—
223	C₁₃×#117	—	2	1	no	—
224	C₁₃×#117	—	2	2	no	—
225	C₁₃×#117	—	2	2	no	—
226	C₁₃×#117	C₂³	1	2	yes	—
227	C₁₃×#117	C₂³	1	2	yes	—
228	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
235	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
240	C₁₃×#107	C₂³	1	2	yes	—
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×#107	C₂³	1	2	yes	—
246	C₁₃×#107	C₂³	1	2	yes	—
247	C₁₃×#107	C₂³	1	2	yes	—
248	C₁₃×#106	C₂³	1	2	yes	—
249	C₁₃×#106	C₂³	1	2	yes	—
250	C₁₃×#106	C₂³	1	2	yes	—
251	C₁₃×#106	C₂³	1	2	yes	—
252	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	2	yes	—
263	C₁₃×#103	C₂³	1	2	yes	—
264	C₁₃×#103	C₂³	1	2	yes	—
265	C₁₃×#103	C₂³	1	2	yes	—
266	C₁₃×#103	C₂³	1	2	yes	—
267	C₁₃×#103	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×#102	C₂³	1	2	yes	—
271	C₁₃×#102	C₂³	1	2	yes	—
272	C₁₃×#102	C₂³	1	2	yes	—
273	C₁₃×#102	C₂³	1	2	yes	—
274	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₁₃×#97	C₂³	1	2	yes	—
278	C₁₃×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#62165	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂⁴×C₁₃	—	2	1	no	—
282	C₁₃×#41	—	2	4	no	—
283	C₁₃×#41	—	4	2	no	—
284	C₁₃×#41	—	8	2	no	—
285	C₂×Q₈×C₁₃	—	2	1	no	—
286	C₂×Q₈×C₁₃	—	2	1	no	—
287	C₂×Q₈×C₁₃	—	2	2	no	—
288	C₂×Q₈×C₁₃	—	2	2	no	—
289	C₂×Q₈×C₁₃	—	8	2	no	—
290	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
293	C₂×D₄×C₁₃	—	2	2	no	—
294	C₂×D₄×C₁₃	—	2	2	no	—
295	C₂×D₄×C₁₃	—	2	2	no	—
296	C₂×D₄×C₁₃	—	2	1	no	—
297	C₂×D₄×C₁₃	—	4	1	no	—
298	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
299	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	—	2	1	no	—
303	C₂²×C₄×C₁₃	—	2	1	no	—
304	C₂²×C₄×C₁₃	—	2	1	no	—
305	C₂²×C₄×C₁₃	—	2	2	no	—
306	C₂²×C₄×C₁₃	—	2	2	no	—
307	C₂²×C₄×C₁₃	—	2	2	no	—
308	C₂²×C₄×C₁₃	—	2	1	no	—
309	C₂²×C₄×C₁₃	—	2	1	no	—
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	—	2	1	no	—
312	C₂²×C₄×C₁₃	—	2	1	no	—
313	C₂²×C₄×C₁₃	—	8	2	no	—
314	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
318	C₁₃×Q₁₆	—	4	2	no	—
319	C₁₃×Q₁₆	—	4	2	no	—
320	C₁₃×SD₁₆	—	2	4	no	—
321	C₁₃×SD₁₆	—	4	2	no	—
322	C₁₃×M₁₆	—	4	2	no	—
323	C₂×C₈×C₁₃	—	4	1	no	—
324	C₂×C₈×C₁₃	—	4	2	no	—
325	C₂×C₈×C₁₃	—	4	1	no	—
326	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
327	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
328	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	1	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	1	no	—
340	C₁₃×C₄⋊C₄	—	2	1	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	1	no	—
343	C₁₃×C₄⋊C₄	—	2	1	no	—
344	C₁₃×C₄⋊C₄	—	2	1	no	—
345	C₁₃×C₄⋊C₄	—	2	2	no	—
346	C₁₃×C₄⋊C₄	—	2	2	no	—
347	C₁₃×C₄⋊C₄	—	2	2	no	—
348	C₁₃×C₄⋊C₄	—	2	1	no	—
349	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
357	C₁₃×C₄⋊C₄	—	2	2	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
369	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
370	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	1	no	—
378	C₁₃×C₂²⋊C₄	—	2	1	no	—
379	C₁₃×C₂²⋊C₄	—	2	1	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	2	no	—
385	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
386	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
387	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
388	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
389	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
390	C₄²×C₁₃	—	2	2	no	—
391	C₄²×C₁₃	—	2	2	no	—
392	C₄²×C₁₃	—	2	2	no	—
393	C₄²×C₁₃	—	2	2	no	—
394	C₄²×C₁₃	—	2	2	no	—
395	C₄²×C₁₃	—	2	2	no	—
396	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₁₃	C₂⁴	1	2	yes	—
399	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
400	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
401	#3563	C₂×C₁₃	1	1	yes	characteristic, complemented
402	#3520	C₂×C₁₃	1	1	yes	characteristic
403	#3386	C₂×C₁₃	1	2	yes	complemented
404	#3377	C₂×C₁₃	1	2	yes	complemented
405	#3344	C₂×C₁₃	1	2	yes	complemented
406	#3343	C₂×C₁₃	1	2	yes	complemented
407	#3338	C₂×C₁₃	1	2	yes	complemented
408	#3315	C₂×C₁₃	1	2	yes	complemented
409	#3314	C₂×C₁₃	1	2	yes	complemented
410	#3296	C₂×C₁₃	1	2	yes	complemented
411	#3258	C₂×C₁₃	1	2	yes	complemented
412	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
413	#3243	C₂×C₁₃	1	2	yes	complemented
414	#3236	C₂×C₁₃	1	1	yes	characteristic, complemented
415	#3120	C₂×C₁₃	1	2	yes	complemented
416	#3110	C₂×C₁₃	1	1	yes	characteristic, complemented
417	#3083	C₂×C₁₃	1	2	yes	complemented
418	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
419	#2992	C₂×C₁₃	1	1	yes	characteristic, complemented
420	C₂³×C₁₃	—	2	1	no	—
421	C₂³×C₁₃	—	2	1	no	—
422	C₂³×C₁₃	—	4	2	no	—
423	C₂³×C₁₃	—	4	2	no	—
424	C₂³×C₁₃	—	8	1	no	—
425	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
426	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
427	Q₈×C₁₃	—	2	2	no	—
428	Q₈×C₁₃	—	2	2	no	—
429	Q₈×C₁₃	—	2	2	no	—
430	Q₈×C₁₃	—	2	2	no	—
431	Q₈×C₁₃	—	4	1	no	—
432	Q₈×C₁₃	—	4	2	no	—
433	Q₈×C₁₃	—	8	1	no	—
434	Q₈×C₁₃	—	8	2	no	—
435	Q₈×C₁₃	—	8	2	no	—
436	D₄×C₁₃	—	2	4	no	—
437	D₄×C₁₃	—	2	1	no	—
438	D₄×C₁₃	—	2	1	no	—
439	D₄×C₁₃	—	2	1	no	—
440	D₄×C₁₃	—	4	1	no	—
441	D₄×C₁₃	—	4	2	no	—
442	D₄×C₁₃	—	4	4	no	—
443	D₄×C₁₃	—	8	2	no	—
444	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	2	1	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	2	no	—
451	C₂×C₄×C₁₃	—	2	2	no	—
452	C₂×C₄×C₁₃	—	2	2	no	—
453	C₂×C₄×C₁₃	—	2	2	no	—
454	C₂×C₄×C₁₃	—	2	1	no	—
455	C₂×C₄×C₁₃	—	2	2	no	—
456	C₂×C₄×C₁₃	—	2	2	no	—
457	C₂×C₄×C₁₃	—	2	1	no	—
458	C₂×C₄×C₁₃	—	4	1	no	—
459	C₂×C₄×C₁₃	—	4	4	no	—
460	C₂×C₄×C₁₃	—	4	2	no	—
461	C₂×C₄×C₁₃	—	4	2	no	—
462	C₂×C₄×C₁₃	—	4	2	no	—
463	C₂×C₄×C₁₃	—	8	1	no	—
464	C₂×C₄×C₁₃	—	8	1	no	—
465	C₂×C₄×C₁₃	—	8	2	no	—
466	C₂×C₄×C₁₃	—	8	1	no	—
467	C₂×C₄×C₁₃	—	8	2	no	—
468	C₂×C₄×C₁₃	—	8	1	no	—
469	C₂×C₄×C₁₃	—	8	2	no	—
470	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
479	C₈×C₁₃	—	2	2	no	—
480	C₈×C₁₃	—	2	2	no	—
481	C₈×C₁₃	—	2	2	no	—
482	C₈×C₁₃	—	2	2	no	—
483	#564	—	2	1	no	—
484	#563	—	2	1	no	—
485	#557	C₂²×C₁₃	1	2	yes	complemented
486	#556	C₂²×C₁₃	1	1	yes	characteristic
487	#554	C₂²×C₁₃	1	2	yes	—
488	#554	C₂²×C₁₃	1	2	yes	—
489	#552	—	2	1	no	—
490	#552	—	2	2	no	—
491	#552	C₂²×C₁₃	1	2	yes	—
492	#552	C₂²×C₁₃	1	2	yes	complemented
493	#551	—	2	2	no	—
494	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
495	#548	—	2	1	no	—
496	#547	C₂²×C₁₃	1	1	yes	characteristic
497	#547	C₂²×C₁₃	1	1	yes	characteristic
498	#546	C₂²×C₁₃	1	2	yes	—
499	#544	—	2	1	no	—
500	#544	C₂²×C₁₃	1	2	yes	complemented
501	#542	C₂²×C₁₃	1	2	yes	—
502	#541	—	2	2	no	—
503	#541	C₂²×C₁₃	1	2	yes	complemented
504	#539	—	2	2	no	—
505	#539	—	2	1	no	—
506	#533	C₂²×C₁₃	1	1	yes	characteristic
507	#533	C₂²×C₁₃	1	1	yes	characteristic
508	#529	C₂²×C₁₃	1	1	yes	characteristic
509	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
510	#525	—	2	1	no	—
511	C₂×C₂²⋊Q₈	—	2	1	no	—
512	#520	C₂²×C₁₃	1	2	yes	—
513	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
514	#501	C₂²×C₁₃	1	2	yes	complemented
515	#501	C₂²×C₁₃	1	2	yes	complemented
516	#500	C₂²×C₁₃	1	2	yes	complemented
517	#491	C₂²×C₁₃	1	2	yes	complemented
518	#489	C₂²×C₁₃	1	2	yes	—
519	#488	C₂²×C₁₃	1	2	yes	—
520	#485	C₂²×C₁₃	1	2	yes	complemented
521	#484	C₂²×C₁₃	1	2	yes	—
522	#484	C₂²×C₁₃	1	2	yes	—
523	#484	C₂²×C₁₃	1	2	yes	complemented
524	#484	C₂²×C₁₃	1	2	yes	complemented
525	#483	C₂²×C₁₃	1	2	yes	—
526	#483	C₂²×C₁₃	1	2	yes	complemented
527	#482	C₂²×C₁₃	1	2	yes	—
528	#480	C₂²×C₁₃	1	2	yes	—
529	#479	C₂²×C₁₃	1	2	yes	complemented
530	#479	C₂²×C₁₃	1	2	yes	complemented
531	#479	C₂²×C₁₃	1	2	yes	complemented
532	#478	C₂²×C₁₃	1	2	yes	—
533	#478	C₂²×C₁₃	1	2	yes	—
534	#478	C₂²×C₁₃	1	2	yes	—
535	#478	C₂²×C₁₃	1	2	yes	—
536	#478	C₂²×C₁₃	1	2	yes	—
537	#477	C₂²×C₁₃	1	2	yes	complemented
538	#477	C₂²×C₁₃	1	2	yes	complemented
539	#477	C₂²×C₁₃	1	2	yes	complemented
540	#477	C₂²×C₁₃	1	2	yes	complemented
541	#475	C₂²×C₁₃	1	2	yes	complemented
542	#474	C₂²×C₁₃	1	1	yes	characteristic
543	#474	C₂²×C₁₃	1	2	yes	—
544	#474	C₂²×C₁₃	1	1	yes	characteristic
545	#470	C₂²×C₁₃	1	2	yes	complemented
546	#468	C₂²×C₁₃	1	2	yes	—
547	#467	C₂²×C₁₃	1	2	yes	—
548	#467	C₂²×C₁₃	1	2	yes	—
549	#467	C₂²×C₁₃	1	2	yes	complemented
550	#465	C₂²×C₁₃	1	2	yes	—
551	#464	C₂²×C₁₃	1	2	yes	—
552	#464	C₂²×C₁₃	1	2	yes	—
553	#462	C₂²×C₁₃	1	2	yes	complemented
554	#462	C₂²×C₁₃	1	2	yes	complemented
555	#461	C₂²×C₁₃	1	1	yes	characteristic
556	#461	C₂²×C₁₃	1	1	yes	characteristic
557	#452	C₂²×C₁₃	1	2	yes	—
558	#452	C₂²×C₁₃	1	2	yes	—
559	#450	C₂²×C₁₃	1	2	yes	—
560	#446	C₂²×C₁₃	1	2	yes	complemented
561	#441	C₂²×C₁₃	1	2	yes	complemented
562	#440	C₂²×C₁₃	1	2	yes	—
563	#440	C₂²×C₁₃	1	2	yes	—
564	#440	C₂²×C₁₃	1	2	yes	—
565	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
566	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
567	#435	C₂²×C₁₃	1	2	yes	—
568	#435	C₂²×C₁₃	1	2	yes	complemented
569	C₈×D₄	C₂²×C₁₃	1	2	yes	—
570	#433	C₂²×C₁₃	1	2	yes	complemented
571	#432	C₂²×C₁₃	1	1	yes	characteristic
572	#428	C₂²×C₁₃	1	2	yes	complemented
573	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
574	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
575	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
576	#424	C₂²×C₁₃	1	2	yes	complemented
577	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
578	#417	C₂²×C₁₃	1	2	yes	—
579	#416	C₂²×C₁₃	1	2	yes	—
580	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
581	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
582	C₂²×C₁₃	—	2	1	no	—
583	C₂²×C₁₃	—	2	1	no	—
584	C₂²×C₁₃	—	2	2	no	—
585	C₂²×C₁₃	—	2	2	no	—
586	C₂²×C₁₃	—	2	2	no	—
587	C₂²×C₁₃	—	2	2	no	—
588	C₂²×C₁₃	—	4	1	no	—
589	C₂²×C₁₃	—	4	1	no	—
590	C₂²×C₁₃	—	4	1	no	—
591	C₂²×C₁₃	—	4	1	no	—
592	C₂²×C₁₃	—	4	1	no	—
593	C₂²×C₁₃	—	8	4	no	—
594	C₂²×C₁₃	#578	1	2	yes	—
595	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
596	C₄×C₁₃	—	2	1	no	—
597	C₄×C₁₃	—	2	1	no	—
598	C₄×C₁₃	—	2	2	no	—
599	C₄×C₁₃	—	2	2	no	—
600	C₄×C₁₃	—	2	1	no	—
601	C₄×C₁₃	—	2	1	no	—
602	C₄×C₁₃	—	2	1	no	—
603	C₄×C₁₃	—	2	2	no	—
604	C₄×C₁₃	—	4	1	no	—
605	C₄×C₁₃	—	4	1	no	—
606	C₄×C₁₃	—	4	2	no	—
607	C₄×C₁₃	—	4	2	no	—
608	C₄×C₁₃	—	4	2	no	—
609	C₄×C₁₃	—	4	2	no	—
610	C₄×C₁₃	—	4	2	no	—
611	C₄×C₁₃	—	4	2	no	—
612	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
613	C₄×C₁₃	#585	1	1	yes	characteristic
614	C₂×#41	—	2	1	no	—
615	C₂×#41	C₂³×C₁₃	1	2	yes	—
616	C₂²×Q₈	—	2	1	no	—
617	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂³×C₄	—	2	1	no	—
619	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
620	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
622	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
623	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
624	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
625	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
626	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
627	C₄⋊Q₈	—	2	2	no	—
628	C₄⋊Q₈	—	2	2	no	—
629	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
630	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
633	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
634	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	D₄×C₁₃	1	2	yes	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	2	no	—
649	#125	—	2	2	no	—
650	#125	—	2	2	no	—
651	#125	—	2	1	no	—
652	#125	—	2	1	no	—
653	#125	—	2	1	no	—
654	#125	—	2	1	no	—
655	#125	D₄×C₁₃	1	1	yes	characteristic
656	#125	C₂³×C₁₃	1	2	yes	—
657	#125	C₂³×C₁₃	1	2	yes	—
658	#125	C₂³×C₁₃	1	2	yes	—
659	#124	—	2	2	no	—
660	#124	D₄×C₁₃	1	1	yes	characteristic
661	#124	C₂³×C₁₃	1	2	yes	—
662	#123	—	2	2	no	—
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	D₄×C₁₃	1	2	yes	—
669	C₂²⋊Q₈	—	2	1	no	—
670	C₂²⋊Q₈	—	2	1	no	—
671	C₂²⋊Q₈	—	2	1	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	1	no	—
674	C₂²⋊Q₈	—	2	1	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
683	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
684	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
685	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
688	#121	—	2	1	no	—
689	#121	—	2	2	no	—
690	#121	D₄×C₁₃	1	1	yes	characteristic
691	#121	C₂³×C₁₃	1	2	yes	—
692	#120	—	2	2	no	—
693	C₄×Q₈	—	2	2	no	—
694	C₄×Q₈	—	2	1	no	—
695	C₄×Q₈	—	2	1	no	—
696	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
697	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
698	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
699	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
700	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
701	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
702	C₄×D₄	—	2	2	no	—
703	C₄×D₄	—	2	2	no	—
704	C₄×D₄	—	2	2	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	1	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
709	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
710	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
711	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
712	C₄×D₄	C₂³×C₁₃	1	2	yes	—
713	C₄×D₄	C₂³×C₁₃	1	2	yes	—
714	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
715	#117	—	2	1	no	—
716	#117	—	2	1	no	—
717	#117	—	2	2	no	—
718	#117	—	2	1	no	—
719	#117	—	2	2	no	—
720	#117	—	2	2	no	—
721	#117	C₂³×C₁₃	1	2	yes	—
722	#117	C₂³×C₁₃	1	2	yes	—
723	C₂×C₄⋊C₄	—	2	1	no	—
724	C₂×C₄⋊C₄	—	2	1	no	—
725	C₂×C₄⋊C₄	—	2	2	no	—
726	C₂×C₄⋊C₄	—	2	1	no	—
727	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
732	C₂×C₂²⋊C₄	—	2	1	no	—
733	C₂×C₂²⋊C₄	—	2	2	no	—
734	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
735	#107	C₂³×C₁₃	1	2	yes	—
736	#107	C₂³×C₁₃	1	2	yes	—
737	#107	C₂³×C₁₃	1	2	yes	—
738	#107	C₂³×C₁₃	1	2	yes	—
739	#107	C₂³×C₁₃	1	2	yes	—
740	#107	C₂³×C₁₃	1	2	yes	—
741	#107	C₂³×C₁₃	1	2	yes	—
742	#107	C₂³×C₁₃	1	2	yes	—
743	#106	C₂³×C₁₃	1	2	yes	—
744	#106	C₂³×C₁₃	1	2	yes	—
745	#106	C₂³×C₁₃	1	2	yes	—
746	#106	C₂³×C₁₃	1	2	yes	—
747	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
748	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
749	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
750	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
751	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
753	#103	C₂³×C₁₃	1	2	yes	—
754	#103	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	#102	C₂³×C₁₃	1	2	yes	—
764	#102	C₂³×C₁₃	1	2	yes	—
765	#102	C₂³×C₁₃	1	2	yes	—
766	#102	C₂³×C₁₃	1	2	yes	—
767	#102	C₂³×C₁₃	1	2	yes	—
768	#102	C₂³×C₁₃	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
772	#97	C₂³×C₁₃	1	2	yes	—
773	#97	C₂³×C₁₃	1	2	yes	—
774	C₄×C₈	C₂³×C₁₃	1	2	yes	—
775	C₂×C₁₃	—	2	2	no	—
776	C₂×C₁₃	—	4	2	no	—
777	C₂×C₁₃	—	4	2	no	—
778	C₂×C₁₃	—	8	1	no	—
779	C₂×C₁₃	#3489	1	1	yes	characteristic
780	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
781	C₂×C₁₃	#3585	1	1	yes	characteristic
782	C₂⁴	—	2	1	no	—
783	#41	—	2	4	no	—
784	#41	—	4	2	no	—
785	#41	—	8	2	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	2	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	—	8	2	no	—
791	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
792	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
793	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	4	1	no	—
799	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
800	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
801	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
802	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	8	2	no	—
815	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
816	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
819	Q₁₆	—	4	2	no	—
820	Q₁₆	—	4	2	no	—
821	SD₁₆	—	2	4	no	—
822	SD₁₆	—	4	2	no	—
823	M₁₆	—	4	2	no	—
824	C₂×C₈	—	4	1	no	—
825	C₂×C₈	—	4	2	no	—
826	C₂×C₈	—	4	1	no	—
827	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
828	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
829	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
830	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
861	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
862	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
863	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
864	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
866	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
870	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	1	no	—
881	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₁₃	1	2	yes	—
887	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
888	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
889	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
890	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	—	2	2	no	—
897	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
898	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
899	C₄²	C₂⁴×C₁₃	1	2	yes	—
900	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
901	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
902	C₁₃	#62165	1	1	yes	characteristic, direct product factor, Sylow
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	4	2	no	—
906	C₂³	—	4	2	no	—
907	C₂³	—	8	1	no	—
908	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
909	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
910	Q₈	—	2	2	no	—
911	Q₈	—	2	2	no	—
912	Q₈	—	2	2	no	—
913	Q₈	—	2	2	no	—
914	Q₈	—	4	1	no	—
915	Q₈	—	4	2	no	—
916	Q₈	—	8	2	no	—
917	Q₈	—	8	1	no	—
918	Q₈	—	8	2	no	—
919	D₄	—	2	4	no	—
920	D₄	—	2	1	no	—
921	D₄	—	2	1	no	—
922	D₄	—	2	1	no	—
923	D₄	—	4	1	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	4	no	—
926	D₄	—	8	2	no	—
927	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	4	1	no	—
942	C₂×C₄	—	4	4	no	—
943	C₂×C₄	—	4	2	no	—
944	C₂×C₄	—	4	2	no	—
945	C₂×C₄	—	4	2	no	—
946	C₂×C₄	—	8	1	no	—
947	C₂×C₄	—	8	1	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	1	no	—
950	C₂×C₄	—	8	1	no	—
951	C₂×C₄	—	8	2	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
955	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
956	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
958	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
961	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
962	C₈	—	2	2	no	—
963	C₈	—	2	2	no	—
964	C₈	—	2	2	no	—
965	C₈	—	2	2	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	8	4	no	—
978	C₂²	C₁₃×#578	1	2	yes	—
979	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
997	C₄	C₁₃×#585	1	1	yes	characteristic
998	C₂	—	2	2	no	—
999	C₂	—	4	2	no	—
1000	C₂	—	4	2	no	—
1001	C₂	—	8	1	no	—
1002	C₂	C₁₃×#3489	1	1	yes	characteristic
1003	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1004	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3520	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×#3563	C₂	semidirect
3. C₁₃×#3386	C₂	semidirect
4. C₁₃×#3377	C₂	semidirect
5. C₁₃×#3344	C₂	semidirect
6. C₁₃×#3343	C₂	semidirect
7. C₁₃×#3338	C₂	semidirect
8. C₁₃×#3315	C₂	semidirect
9. C₁₃×#3314	C₂	semidirect
10. C₁₃×#3296	C₂	semidirect
11. C₁₃×#3258	C₂	semidirect
12. C₁₃×#3249	C₂	semidirect
13. C₁₃×#3243	C₂	semidirect
14. C₁₃×#3236	C₂	semidirect
15. C₁₃×#3120	C₂	semidirect
16. C₁₃×#3110	C₂	semidirect
17. C₁₃×#3083	C₂	semidirect
18. C₂×C₁₃×#478	C₂	semidirect
19. C₁₃×#2992	C₂	semidirect
22. C₁₃×#557	C₂²	semidirect
29. C₁₃×#552	C₂²	semidirect
37. C₁₃×#544	C₂²	semidirect
40. C₁₃×#541	C₂²	semidirect
51. C₁₃×#501	C₂²	semidirect
52. C₁₃×#501	C₂²	semidirect
53. C₁₃×#500	C₂²	semidirect
54. C₁₃×#491	C₂²	semidirect
57. C₁₃×#485	C₂²	semidirect
60. C₁₃×#484	C₂²	semidirect
61. C₁₃×#484	C₂²	semidirect
63. C₁₃×#483	C₂²	semidirect
66. C₁₃×#479	C₂²	semidirect
67. C₁₃×#479	C₂²	semidirect
68. C₁₃×#479	C₂²	semidirect
74. C₁₃×#477	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#477	C₂²	semidirect
78. C₁₃×#475	C₂²	semidirect
82. C₁₃×#470	C₂²	semidirect
86. C₁₃×#467	C₂²	semidirect
90. C₁₃×#462	C₂²	semidirect
91. C₁₃×#462	C₂²	semidirect
97. C₁₃×#446	C₂²	semidirect
98. C₁₃×#441	C₂²	semidirect
102. C₄×C₁₃×Q₁₆	C₂²	semidirect
105. C₁₃×#435	C₂²	semidirect
107. C₁₃×#433	C₂²	semidirect
109. C₁₃×#428	C₂²	semidirect
111. C₂×C₁₃×#107	C₂²	semidirect
113. C₁₃×#424	C₂²	semidirect
280. #62165	C₁₃	direct (N × H)
401. #3563	C₂×C₁₃	semidirect
403. #3386	C₂×C₁₃	semidirect
404. #3377	C₂×C₁₃	semidirect
405. #3344	C₂×C₁₃	semidirect
406. #3343	C₂×C₁₃	semidirect
407. #3338	C₂×C₁₃	semidirect
408. #3315	C₂×C₁₃	semidirect
409. #3314	C₂×C₁₃	semidirect
410. #3296	C₂×C₁₃	semidirect
411. #3258	C₂×C₁₃	semidirect
412. #3249	C₂×C₁₃	semidirect
413. #3243	C₂×C₁₃	semidirect
414. #3236	C₂×C₁₃	semidirect
415. #3120	C₂×C₁₃	semidirect
416. #3110	C₂×C₁₃	semidirect
417. #3083	C₂×C₁₃	semidirect
418. C₂×#478	C₂×C₁₃	semidirect
419. #2992	C₂×C₁₃	semidirect
485. #557	C₂²×C₁₃	semidirect
492. #552	C₂²×C₁₃	semidirect
500. #544	C₂²×C₁₃	semidirect
503. #541	C₂²×C₁₃	semidirect
514. #501	C₂²×C₁₃	semidirect
515. #501	C₂²×C₁₃	semidirect
516. #500	C₂²×C₁₃	semidirect
517. #491	C₂²×C₁₃	semidirect
520. #485	C₂²×C₁₃	semidirect
523. #484	C₂²×C₁₃	semidirect
524. #484	C₂²×C₁₃	semidirect
526. #483	C₂²×C₁₃	semidirect
529. #479	C₂²×C₁₃	semidirect
530. #479	C₂²×C₁₃	semidirect
531. #479	C₂²×C₁₃	semidirect
537. #477	C₂²×C₁₃	semidirect
538. #477	C₂²×C₁₃	semidirect
539. #477	C₂²×C₁₃	semidirect
540. #477	C₂²×C₁₃	semidirect
541. #475	C₂²×C₁₃	semidirect
545. #470	C₂²×C₁₃	semidirect
549. #467	C₂²×C₁₃	semidirect
553. #462	C₂²×C₁₃	semidirect
554. #462	C₂²×C₁₃	semidirect
560. #446	C₂²×C₁₃	semidirect
561. #441	C₂²×C₁₃	semidirect
565. C₄×Q₁₆	C₂²×C₁₃	semidirect
568. #435	C₂²×C₁₃	semidirect
570. #433	C₂²×C₁₃	semidirect
572. #428	C₂²×C₁₃	semidirect
574. C₂×#107	C₂²×C₁₃	semidirect
576. #424	C₂²×C₁₃	semidirect
902. C₁₃	#62165	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×#3563	2
C₁₃×#3520	2
C₁₃×#3386	2
C₁₃×#3377	2
C₁₃×#3344	2
C₁₃×#3343	2
C₁₃×#3338	2
C₁₃×#3315	2
C₁₃×#3314	2
C₁₃×#3296	2
C₁₃×#3258	2
C₁₃×#3249	2
C₁₃×#3243	2
C₁₃×#3236	2
C₁₃×#3120	2
C₁₃×#3110	2
C₁₃×#3083	2
C₂×C₁₃×#478	2
C₁₃×#2992	2
#62165	13

Subgroups — C13×#62165 #15748504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62165 #15748504