Subgroups — C₁₃×#62559 #15748898

Order 3328.

1666 conjugacy classes of subgroups.

The subgroup lattice has 980 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×#3561	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3327	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3314	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3178	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#564	—	2	1	no	—
21	C₁₃×#563	—	2	1	no	—
22	C₁₃×#563	—	2	1	no	—
23	C₁₃×#562	—	2	1	no	—
24	C₁₃×#557	C₂²	1	2	yes	complemented
25	C₁₃×#556	C₂²	1	2	yes	—
26	C₁₃×#554	C₂²	1	2	yes	—
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	2	yes	—
32	C₁₃×#548	C₂²	1	2	yes	—
33	C₁₃×#546	C₂²	1	2	yes	—
34	C₁₃×#544	—	2	1	no	—
35	C₁₃×#544	C₂²	1	2	yes	complemented
36	C₁₃×#543	—	2	1	no	—
37	C₁₃×#542	—	2	2	no	—
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	1	no	—
42	C₁₃×#538	—	2	1	no	—
43	C₁₃×#536	C₂²	1	2	yes	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#533	C₂²	1	1	yes	characteristic
46	C₁₃×#529	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
49	C₁₃×#501	C₂²	1	2	yes	complemented
50	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#497	C₂²	1	2	yes	—
52	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#491	C₂²	1	2	yes	complemented
54	C₁₃×#491	C₂²	1	2	yes	complemented
55	C₁₃×#489	C₂²	1	2	yes	—
56	C₁₃×#489	C₂²	1	2	yes	—
57	C₁₃×#488	C₂²	1	2	yes	—
58	C₁₃×#488	C₂²	1	2	yes	—
59	C₁₃×#488	C₂²	1	2	yes	—
60	C₁₃×#488	C₂²	1	2	yes	—
61	C₁₃×#488	C₂²	1	2	yes	—
62	C₁₃×#487	C₂²	1	2	yes	complemented
63	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#485	C₂²	1	2	yes	complemented
66	C₁₃×#484	C₂²	1	2	yes	—
67	C₁₃×#484	C₂²	1	2	yes	complemented
68	C₁₃×#483	C₂²	1	2	yes	—
69	C₁₃×#482	C₂²	1	2	yes	—
70	C₁₃×#480	C₂²	1	2	yes	—
71	C₁₃×#479	C₂²	1	2	yes	complemented
72	C₁₃×#479	C₂²	1	2	yes	complemented
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	—
75	C₁₃×#477	C₂²	1	2	yes	complemented
76	C₁₃×#474	C₂²	1	2	yes	—
77	C₁₃×#470	C₂²	1	2	yes	complemented
78	C₁₃×#468	C₂²	1	2	yes	—
79	C₁₃×#467	C₂²	1	2	yes	—
80	C₁₃×#467	C₂²	1	2	yes	—
81	C₁₃×#467	C₂²	1	2	yes	complemented
82	C₁₃×#465	C₂²	1	2	yes	—
83	C₁₃×#464	C₂²	1	2	yes	—
84	C₁₃×#464	C₂²	1	2	yes	—
85	C₁₃×#464	C₂²	1	2	yes	—
86	C₁₃×#464	C₂²	1	2	yes	—
87	C₁₃×#462	C₂²	1	2	yes	complemented
88	C₁₃×#462	C₂²	1	2	yes	complemented
89	C₁₃×#452	C₂²	1	2	yes	—
90	C₁₃×#452	C₂²	1	2	yes	—
91	C₁₃×#451	C₂²	1	2	yes	—
92	C₁₃×#451	C₂²	1	2	yes	complemented
93	C₁₃×#451	C₂²	1	2	yes	complemented
94	C₁₃×#450	C₂²	1	2	yes	—
95	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
96	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#441	C₂²	1	2	yes	complemented
98	C₁₃×#440	C₂²	1	2	yes	—
99	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
100	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
101	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
102	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
103	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
104	C₁₃×#435	C₂²	1	2	yes	—
105	C₈×D₄×C₁₃	C₂²	1	2	yes	—
106	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#433	C₂²	1	2	yes	complemented
108	C₁₃×#432	C₂²	1	1	yes	characteristic
109	C₁₃×#419	C₂²	1	2	yes	complemented
110	C₁₃×#417	C₂²	1	2	yes	—
111	C₁₃×#416	C₂²	1	2	yes	—
112	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
113	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
114	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
115	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
116	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
117	C₁₃×#405	C₂²	1	2	yes	complemented
118	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	C₂³	1	2	yes	—
120	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
130	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
133	C₁₃×C₄⋊Q₈	—	2	2	no	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₁₃×#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	—	2	2	no	—
147	C₁₃×#126	—	2	2	no	—
148	C₁₃×#126	—	2	2	no	—
149	C₁₃×#126	D₄	1	2	yes	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	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	2	no	—
157	C₁₃×#125	—	2	2	no	—
158	C₁₃×#125	—	2	1	no	—
159	C₁₃×#125	—	2	1	no	—
160	C₁₃×#125	—	2	1	no	—
161	C₁₃×#125	—	2	1	no	—
162	C₁₃×#125	D₄	1	1	yes	characteristic
163	C₁₃×#125	C₂³	1	2	yes	—
164	C₁₃×#125	C₂³	1	2	yes	—
165	C₁₃×#125	C₂³	1	2	yes	—
166	C₁₃×#124	—	2	2	no	—
167	C₁₃×#124	—	2	2	no	—
168	C₁₃×#124	—	2	1	no	—
169	C₁₃×#124	—	2	1	no	—
170	C₁₃×#124	D₄	1	1	yes	characteristic
171	C₁₃×#124	C₂³	1	2	yes	—
172	C₁₃×#124	C₂³	1	2	yes	—
173	C₁₃×#124	C₂³	1	2	yes	—
174	C₁₃×#123	—	2	2	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×#123	—	2	2	no	—
177	C₁₃×#123	—	2	2	no	—
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	D₄	1	2	yes	—
181	C₁₃×C₂²⋊Q₈	—	2	2	no	—
182	C₁₃×C₂²⋊Q₈	—	2	1	no	—
183	C₁₃×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	D₄	1	1	yes	characteristic
203	C₁₃×#121	C₂³	1	2	yes	—
204	C₁₃×#120	—	2	2	no	—
205	C₄×Q₈×C₁₃	—	2	2	no	—
206	C₄×Q₈×C₁₃	—	2	1	no	—
207	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₁₃	—	2	2	no	—
215	C₄×D₄×C₁₃	—	2	2	no	—
216	C₄×D₄×C₁₃	—	2	2	no	—
217	C₄×D₄×C₁₃	C₂³	1	2	yes	—
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	2	no	—
224	C₁₃×#117	—	2	2	no	—
225	C₁₃×#117	C₂³	1	2	yes	—
226	C₁₃×#117	C₂³	1	2	yes	—
227	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
232	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
233	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
234	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
236	C₁₃×#107	C₂³	1	2	yes	—
237	C₁₃×#107	C₂³	1	2	yes	—
238	C₁₃×#107	C₂³	1	2	yes	—
239	C₁₃×#107	C₂³	1	2	yes	—
240	C₁₃×#106	C₂³	1	2	yes	—
241	C₁₃×#106	C₂³	1	2	yes	—
242	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
243	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
244	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
245	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
246	C₁₃×#103	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	2	yes	—
248	C₁₃×#103	C₂³	1	2	yes	—
249	C₁₃×#103	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#103	C₂³	1	2	yes	—
253	C₁₃×#103	C₂³	1	2	yes	—
254	C₁₃×#103	C₂³	1	2	yes	—
255	C₁₃×#103	C₂³	1	2	yes	—
256	C₁₃×#103	C₂³	1	2	yes	—
257	C₁₃×#103	C₂³	1	2	yes	—
258	C₁₃×#103	C₂³	1	2	yes	—
259	C₁₃×#103	C₂³	1	2	yes	—
260	C₁₃×#102	C₂³	1	2	yes	—
261	C₁₃×#102	C₂³	1	2	yes	—
262	C₁₃×#102	C₂³	1	2	yes	—
263	C₁₃×#102	C₂³	1	2	yes	—
264	C₁₃×#102	C₂³	1	2	yes	—
265	C₁₃×#102	C₂³	1	2	yes	—
266	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
269	C₁₃×#97	C₂³	1	2	yes	—
270	C₁₃×#97	C₂³	1	2	yes	—
271	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
272	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
273	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
274	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
275	C₄×C₈×C₁₃	C₂³	1	2	yes	—
276	#62559	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂⁴×C₁₃	—	2	1	no	—
278	C₁₃×#41	—	4	2	no	—
279	C₁₃×#41	—	4	2	no	—
280	C₂×Q₈×C₁₃	—	2	1	no	—
281	C₂×Q₈×C₁₃	—	2	1	no	—
282	C₂×Q₈×C₁₃	—	2	2	no	—
283	C₂×Q₈×C₁₃	—	2	2	no	—
284	C₂×Q₈×C₁₃	—	2	1	no	—
285	C₂×Q₈×C₁₃	—	4	1	no	—
286	C₂×Q₈×C₁₃	—	4	1	no	—
287	C₂×Q₈×C₁₃	—	4	2	no	—
288	C₂×Q₈×C₁₃	—	4	2	no	—
289	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
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	1	no	—
296	C₂×D₄×C₁₃	—	4	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	2	yes	—
301	C₂²×C₄×C₁₃	—	2	1	no	—
302	C₂²×C₄×C₁₃	—	2	1	no	—
303	C₂²×C₄×C₁₃	—	2	1	no	—
304	C₂²×C₄×C₁₃	—	2	2	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	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
312	C₁₃×Q₁₆	—	4	2	no	—
313	C₁₃×Q₁₆	—	4	2	no	—
314	C₁₃×Q₁₆	—	4	2	no	—
315	C₁₃×Q₁₆	—	4	2	no	—
316	C₁₃×SD₁₆	—	4	2	no	—
317	C₁₃×SD₁₆	—	4	2	no	—
318	C₁₃×M₁₆	—	4	2	no	—
319	C₂×C₈×C₁₃	—	4	2	no	—
320	C₂×C₈×C₁₃	—	4	1	no	—
321	C₂×C₈×C₁₃	—	4	1	no	—
322	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
327	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	1	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	1	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	1	no	—
337	C₁₃×C₄⋊C₄	—	2	1	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	1	no	—
342	C₁₃×C₄⋊C₄	—	2	1	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	—	2	2	no	—
345	C₁₃×C₄⋊C₄	—	2	2	no	—
346	C₁₃×C₄⋊C₄	—	2	2	no	—
347	C₁₃×C₄⋊C₄	—	2	1	no	—
348	C₁₃×C₄⋊C₄	—	2	2	no	—
349	C₁₃×C₄⋊C₄	—	2	2	no	—
350	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
356	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
357	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
358	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
359	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
360	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
361	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
362	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
366	C₁₃×C₂²⋊C₄	—	2	2	no	—
367	C₁₃×C₂²⋊C₄	—	2	2	no	—
368	C₁₃×C₂²⋊C₄	—	2	2	no	—
369	C₁₃×C₂²⋊C₄	—	2	2	no	—
370	C₁₃×C₂²⋊C₄	—	2	2	no	—
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	2	no	—
377	C₁₃×C₂²⋊C₄	—	2	2	no	—
378	C₁₃×C₂²⋊C₄	—	2	2	no	—
379	C₁₃×C₂²⋊C₄	—	2	2	no	—
380	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
381	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
382	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
383	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
384	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
385	C₄²×C₁₃	—	2	2	no	—
386	C₄²×C₁₃	—	2	2	no	—
387	C₄²×C₁₃	—	2	2	no	—
388	C₄²×C₁₃	—	2	2	no	—
389	C₄²×C₁₃	—	2	2	no	—
390	C₄²×C₁₃	—	2	2	no	—
391	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
394	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
395	C₄²×C₁₃	C₂⁴	1	2	yes	—
396	#3563	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#3561	C₂×C₁₃	1	1	yes	characteristic
398	#3377	C₂×C₁₃	1	2	yes	complemented
399	#3364	C₂×C₁₃	1	2	yes	complemented
400	#3327	C₂×C₁₃	1	2	yes	complemented
401	#3314	C₂×C₁₃	1	2	yes	complemented
402	#3312	C₂×C₁₃	1	2	yes	complemented
403	#3300	C₂×C₁₃	1	2	yes	complemented
404	#3299	C₂×C₁₃	1	2	yes	complemented
405	#3296	C₂×C₁₃	1	2	yes	complemented
406	#3243	C₂×C₁₃	1	2	yes	complemented
407	#3236	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3223	C₂×C₁₃	1	2	yes	complemented
409	#3215	C₂×C₁₃	1	1	yes	characteristic, complemented
410	#3178	C₂×C₁₃	1	2	yes	complemented
411	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
412	#3137	C₂×C₁₃	1	2	yes	complemented
413	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
414	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
415	C₂³×C₁₃	—	2	2	no	—
416	C₂³×C₁₃	—	4	2	no	—
417	C₂³×C₁₃	—	8	1	no	—
418	C₂³×C₁₃	—	8	1	no	—
419	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
420	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
421	Q₈×C₁₃	—	2	2	no	—
422	Q₈×C₁₃	—	2	2	no	—
423	Q₈×C₁₃	—	2	2	no	—
424	Q₈×C₁₃	—	2	2	no	—
425	Q₈×C₁₃	—	2	2	no	—
426	Q₈×C₁₃	—	2	2	no	—
427	Q₈×C₁₃	—	4	1	no	—
428	Q₈×C₁₃	—	8	1	no	—
429	Q₈×C₁₃	—	8	1	no	—
430	Q₈×C₁₃	—	8	2	no	—
431	Q₈×C₁₃	—	8	2	no	—
432	Q₈×C₁₃	—	8	1	no	—
433	D₄×C₁₃	—	2	4	no	—
434	D₄×C₁₃	—	2	2	no	—
435	D₄×C₁₃	—	2	2	no	—
436	D₄×C₁₃	—	4	1	no	—
437	D₄×C₁₃	—	8	1	no	—
438	D₄×C₁₃	—	8	2	no	—
439	D₄×C₁₃	—	8	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	1	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
453	C₂×C₄×C₁₃	—	4	2	no	—
454	C₂×C₄×C₁₃	—	8	2	no	—
455	C₂×C₄×C₁₃	—	8	2	no	—
456	C₂×C₄×C₁₃	—	8	1	no	—
457	C₂×C₄×C₁₃	—	8	2	no	—
458	C₂×C₄×C₁₃	—	8	2	no	—
459	C₂×C₄×C₁₃	—	8	1	no	—
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
469	C₈×C₁₃	—	2	1	no	—
470	C₈×C₁₃	—	2	1	no	—
471	C₈×C₁₃	—	2	2	no	—
472	C₈×C₁₃	—	2	1	no	—
473	C₈×C₁₃	—	2	1	no	—
474	C₈×C₁₃	—	2	2	no	—
475	#564	—	2	1	no	—
476	#563	—	2	1	no	—
477	#563	—	2	1	no	—
478	#562	—	2	1	no	—
479	#557	C₂²×C₁₃	1	2	yes	complemented
480	#556	C₂²×C₁₃	1	2	yes	—
481	#554	C₂²×C₁₃	1	2	yes	—
482	#552	—	2	2	no	—
483	#552	C₂²×C₁₃	1	2	yes	—
484	#552	C₂²×C₁₃	1	2	yes	complemented
485	#551	—	2	2	no	—
486	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
487	#548	C₂²×C₁₃	1	2	yes	—
488	#546	C₂²×C₁₃	1	2	yes	—
489	#544	—	2	1	no	—
490	#544	C₂²×C₁₃	1	2	yes	complemented
491	#543	—	2	1	no	—
492	#542	—	2	2	no	—
493	#542	C₂²×C₁₃	1	2	yes	—
494	#541	—	2	2	no	—
495	#541	C₂²×C₁₃	1	2	yes	complemented
496	#539	—	2	1	no	—
497	#538	—	2	1	no	—
498	#536	C₂²×C₁₃	1	2	yes	—
499	#533	C₂²×C₁₃	1	1	yes	characteristic
500	#533	C₂²×C₁₃	1	1	yes	characteristic
501	#529	C₂²×C₁₃	1	1	yes	characteristic
502	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
503	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
504	#501	C₂²×C₁₃	1	2	yes	complemented
505	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
506	#497	C₂²×C₁₃	1	2	yes	—
507	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
508	#491	C₂²×C₁₃	1	2	yes	complemented
509	#491	C₂²×C₁₃	1	2	yes	complemented
510	#489	C₂²×C₁₃	1	2	yes	—
511	#489	C₂²×C₁₃	1	2	yes	—
512	#488	C₂²×C₁₃	1	2	yes	—
513	#488	C₂²×C₁₃	1	2	yes	—
514	#488	C₂²×C₁₃	1	2	yes	—
515	#488	C₂²×C₁₃	1	2	yes	—
516	#488	C₂²×C₁₃	1	2	yes	—
517	#487	C₂²×C₁₃	1	2	yes	complemented
518	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
519	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
520	#485	C₂²×C₁₃	1	2	yes	complemented
521	#484	C₂²×C₁₃	1	2	yes	—
522	#484	C₂²×C₁₃	1	2	yes	complemented
523	#483	C₂²×C₁₃	1	2	yes	—
524	#482	C₂²×C₁₃	1	2	yes	—
525	#480	C₂²×C₁₃	1	2	yes	—
526	#479	C₂²×C₁₃	1	2	yes	complemented
527	#479	C₂²×C₁₃	1	2	yes	complemented
528	#479	C₂²×C₁₃	1	2	yes	complemented
529	#478	C₂²×C₁₃	1	2	yes	—
530	#477	C₂²×C₁₃	1	2	yes	complemented
531	#474	C₂²×C₁₃	1	2	yes	—
532	#470	C₂²×C₁₃	1	2	yes	complemented
533	#468	C₂²×C₁₃	1	2	yes	—
534	#467	C₂²×C₁₃	1	2	yes	—
535	#467	C₂²×C₁₃	1	2	yes	—
536	#467	C₂²×C₁₃	1	2	yes	complemented
537	#465	C₂²×C₁₃	1	2	yes	—
538	#464	C₂²×C₁₃	1	2	yes	—
539	#464	C₂²×C₁₃	1	2	yes	—
540	#464	C₂²×C₁₃	1	2	yes	—
541	#464	C₂²×C₁₃	1	2	yes	—
542	#462	C₂²×C₁₃	1	2	yes	complemented
543	#462	C₂²×C₁₃	1	2	yes	complemented
544	#452	C₂²×C₁₃	1	2	yes	—
545	#452	C₂²×C₁₃	1	2	yes	—
546	#451	C₂²×C₁₃	1	2	yes	—
547	#451	C₂²×C₁₃	1	2	yes	complemented
548	#451	C₂²×C₁₃	1	2	yes	complemented
549	#450	C₂²×C₁₃	1	2	yes	—
550	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
551	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
552	#441	C₂²×C₁₃	1	2	yes	complemented
553	#440	C₂²×C₁₃	1	2	yes	—
554	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
555	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
556	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
557	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
558	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
559	#435	C₂²×C₁₃	1	2	yes	—
560	C₈×D₄	C₂²×C₁₃	1	2	yes	—
561	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
562	#433	C₂²×C₁₃	1	2	yes	complemented
563	#432	C₂²×C₁₃	1	1	yes	characteristic
564	#419	C₂²×C₁₃	1	2	yes	complemented
565	#417	C₂²×C₁₃	1	2	yes	—
566	#416	C₂²×C₁₃	1	2	yes	—
567	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
568	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
569	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
570	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
571	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
572	#405	C₂²×C₁₃	1	2	yes	complemented
573	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
574	C₂²×C₁₃	—	2	1	no	—
575	C₂²×C₁₃	—	2	1	no	—
576	C₂²×C₁₃	—	2	2	no	—
577	C₂²×C₁₃	—	2	2	no	—
578	C₂²×C₁₃	—	2	2	no	—
579	C₂²×C₁₃	—	4	2	no	—
580	C₂²×C₁₃	—	4	2	no	—
581	C₂²×C₁₃	—	4	2	no	—
582	C₂²×C₁₃	—	16	2	no	—
583	C₂²×C₁₃	#578	1	2	yes	—
584	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
585	C₄×C₁₃	—	2	1	no	—
586	C₄×C₁₃	—	2	1	no	—
587	C₄×C₁₃	—	2	2	no	—
588	C₄×C₁₃	—	2	2	no	—
589	C₄×C₁₃	—	2	1	no	—
590	C₄×C₁₃	—	2	1	no	—
591	C₄×C₁₃	—	2	1	no	—
592	C₄×C₁₃	—	2	2	no	—
593	C₄×C₁₃	—	4	2	no	—
594	C₄×C₁₃	—	4	2	no	—
595	C₄×C₁₃	—	4	2	no	—
596	C₄×C₁₃	—	4	2	no	—
597	C₄×C₁₃	—	4	2	no	—
598	C₄×C₁₃	—	4	2	no	—
599	C₄×C₁₃	—	4	2	no	—
600	C₄×C₁₃	#585	1	1	yes	characteristic
601	C₄×C₁₃	#585	1	1	yes	characteristic
602	C₂×#41	C₂³×C₁₃	1	2	yes	—
603	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
605	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
607	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
608	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
609	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
610	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
612	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
613	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
614	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
615	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
616	C₄⋊Q₈	—	2	2	no	—
617	C₄⋊Q₈	—	2	2	no	—
618	C₄⋊Q₈	—	2	2	no	—
619	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
620	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
622	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
625	#126	—	2	2	no	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	D₄×C₁₃	1	2	yes	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	2	no	—
641	#125	—	2	1	no	—
642	#125	—	2	1	no	—
643	#125	—	2	1	no	—
644	#125	—	2	1	no	—
645	#125	D₄×C₁₃	1	1	yes	characteristic
646	#125	C₂³×C₁₃	1	2	yes	—
647	#125	C₂³×C₁₃	1	2	yes	—
648	#125	C₂³×C₁₃	1	2	yes	—
649	#124	—	2	2	no	—
650	#124	—	2	2	no	—
651	#124	—	2	1	no	—
652	#124	—	2	1	no	—
653	#124	D₄×C₁₃	1	1	yes	characteristic
654	#124	C₂³×C₁₃	1	2	yes	—
655	#124	C₂³×C₁₃	1	2	yes	—
656	#124	C₂³×C₁₃	1	2	yes	—
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	#123	D₄×C₁₃	1	2	yes	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	—	2	1	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
678	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
679	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
680	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
681	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
682	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
683	#121	—	2	2	no	—
684	#121	—	2	2	no	—
685	#121	D₄×C₁₃	1	1	yes	characteristic
686	#121	C₂³×C₁₃	1	2	yes	—
687	#120	—	2	2	no	—
688	C₄×Q₈	—	2	2	no	—
689	C₄×Q₈	—	2	1	no	—
690	C₄×Q₈	—	2	1	no	—
691	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
692	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
693	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
694	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
695	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
696	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
697	C₄×D₄	—	2	2	no	—
698	C₄×D₄	—	2	2	no	—
699	C₄×D₄	—	2	2	no	—
700	C₄×D₄	C₂³×C₁₃	1	2	yes	—
701	C₄×D₄	C₂³×C₁₃	1	2	yes	—
702	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
703	#117	—	2	1	no	—
704	#117	—	2	1	no	—
705	#117	—	2	2	no	—
706	#117	—	2	2	no	—
707	#117	—	2	2	no	—
708	#117	C₂³×C₁₃	1	2	yes	—
709	#117	C₂³×C₁₃	1	2	yes	—
710	C₂×C₄⋊C₄	—	2	1	no	—
711	C₂×C₄⋊C₄	—	2	1	no	—
712	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
715	C₂×C₂²⋊C₄	—	2	1	no	—
716	C₂×C₂²⋊C₄	—	2	1	no	—
717	C₂×C₂²⋊C₄	—	2	2	no	—
718	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
719	#107	C₂³×C₁₃	1	2	yes	—
720	#107	C₂³×C₁₃	1	2	yes	—
721	#107	C₂³×C₁₃	1	2	yes	—
722	#107	C₂³×C₁₃	1	2	yes	—
723	#106	C₂³×C₁₃	1	2	yes	—
724	#106	C₂³×C₁₃	1	2	yes	—
725	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
726	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
727	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
728	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
729	#103	C₂³×C₁₃	1	2	yes	—
730	#103	C₂³×C₁₃	1	2	yes	—
731	#103	C₂³×C₁₃	1	2	yes	—
732	#103	C₂³×C₁₃	1	2	yes	—
733	#103	C₂³×C₁₃	1	2	yes	—
734	#103	C₂³×C₁₃	1	2	yes	—
735	#103	C₂³×C₁₃	1	2	yes	—
736	#103	C₂³×C₁₃	1	2	yes	—
737	#103	C₂³×C₁₃	1	2	yes	—
738	#103	C₂³×C₁₃	1	2	yes	—
739	#103	C₂³×C₁₃	1	2	yes	—
740	#103	C₂³×C₁₃	1	2	yes	—
741	#103	C₂³×C₁₃	1	2	yes	—
742	#103	C₂³×C₁₃	1	2	yes	—
743	#102	C₂³×C₁₃	1	2	yes	—
744	#102	C₂³×C₁₃	1	2	yes	—
745	#102	C₂³×C₁₃	1	2	yes	—
746	#102	C₂³×C₁₃	1	2	yes	—
747	#102	C₂³×C₁₃	1	2	yes	—
748	#102	C₂³×C₁₃	1	2	yes	—
749	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
750	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
751	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
752	#97	C₂³×C₁₃	1	2	yes	—
753	#97	C₂³×C₁₃	1	2	yes	—
754	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
755	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
756	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
757	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
758	C₄×C₈	C₂³×C₁₃	1	2	yes	—
759	C₂×C₁₃	—	2	2	no	—
760	C₂×C₁₃	—	4	2	no	—
761	C₂×C₁₃	—	8	2	no	—
762	C₂×C₁₃	#3500	1	1	yes	characteristic
763	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
764	C₂×C₁₃	#3584	1	1	yes	characteristic
765	C₂⁴	—	2	1	no	—
766	#41	—	4	2	no	—
767	#41	—	4	2	no	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	2	2	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	4	1	no	—
774	C₂×Q₈	—	4	1	no	—
775	C₂×Q₈	—	4	2	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
778	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
779	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
780	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	4	1	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
787	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
788	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
800	Q₁₆	—	4	2	no	—
801	Q₁₆	—	4	2	no	—
802	Q₁₆	—	4	2	no	—
803	Q₁₆	—	4	2	no	—
804	SD₁₆	—	4	2	no	—
805	SD₁₆	—	4	2	no	—
806	M₁₆	—	4	2	no	—
807	C₂×C₈	—	4	2	no	—
808	C₂×C₈	—	4	1	no	—
809	C₂×C₈	—	4	1	no	—
810	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
812	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
813	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
814	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
815	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
845	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
846	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
847	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
848	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
849	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
850	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
851	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
869	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
870	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
871	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
872	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
880	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
881	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
882	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
883	C₄²	C₂⁴×C₁₃	1	2	yes	—
884	C₁₃	#62559	1	1	yes	characteristic, direct product factor, Sylow
885	C₂³	—	2	2	no	—
886	C₂³	—	4	2	no	—
887	C₂³	—	8	1	no	—
888	C₂³	—	8	1	no	—
889	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
890	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
891	Q₈	—	2	2	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	2	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	2	2	no	—
896	Q₈	—	2	2	no	—
897	Q₈	—	4	1	no	—
898	Q₈	—	8	2	no	—
899	Q₈	—	8	1	no	—
900	Q₈	—	8	1	no	—
901	Q₈	—	8	1	no	—
902	Q₈	—	8	2	no	—
903	D₄	—	2	4	no	—
904	D₄	—	2	2	no	—
905	D₄	—	2	2	no	—
906	D₄	—	4	1	no	—
907	D₄	—	8	1	no	—
908	D₄	—	8	2	no	—
909	D₄	—	8	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	8	2	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	1	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	1	no	—
930	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
933	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
934	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
938	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
939	C₈	—	2	1	no	—
940	C₈	—	2	1	no	—
941	C₈	—	2	2	no	—
942	C₈	—	2	1	no	—
943	C₈	—	2	1	no	—
944	C₈	—	2	2	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	16	2	no	—
954	C₂²	C₁₃×#578	1	2	yes	—
955	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	1	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	C₁₃×#585	1	1	yes	characteristic
972	C₄	C₁₃×#585	1	1	yes	characteristic
973	C₂	—	2	2	no	—
974	C₂	—	4	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₁₃×#3500	1	1	yes	characteristic
977	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
978	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×#3561	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×#3377	C₂	semidirect
4. C₁₃×#3364	C₂	semidirect
5. C₁₃×#3327	C₂	semidirect
6. C₁₃×#3314	C₂	semidirect
7. C₁₃×#3312	C₂	semidirect
8. C₁₃×#3300	C₂	semidirect
9. C₁₃×#3299	C₂	semidirect
10. C₁₃×#3296	C₂	semidirect
11. C₁₃×#3243	C₂	semidirect
12. C₁₃×#3236	C₂	semidirect
13. C₁₃×#3223	C₂	semidirect
14. C₁₃×#3215	C₂	semidirect
15. C₁₃×#3178	C₂	semidirect
16. C₁₃×#3170	C₂	semidirect
17. C₁₃×#3137	C₂	semidirect
18. C₂×C₁₃×#488	C₂	semidirect
19. C₁₃×#2966	C₂	semidirect
24. C₁₃×#557	C₂²	semidirect
29. C₁₃×#552	C₂²	semidirect
35. C₁₃×#544	C₂²	semidirect
40. C₁₃×#541	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
50. C₁₃×#500	C₂²	semidirect
52. C₁₃×#494	C₂²	semidirect
53. C₁₃×#491	C₂²	semidirect
54. C₁₃×#491	C₂²	semidirect
62. C₁₃×#487	C₂²	semidirect
63. C₁₃×#487	C₂²	semidirect
64. C₁₃×#487	C₂²	semidirect
65. C₁₃×#485	C₂²	semidirect
67. C₁₃×#484	C₂²	semidirect
71. C₁₃×#479	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
77. C₁₃×#470	C₂²	semidirect
81. C₁₃×#467	C₂²	semidirect
87. C₁₃×#462	C₂²	semidirect
88. C₁₃×#462	C₂²	semidirect
92. C₁₃×#451	C₂²	semidirect
93. C₁₃×#451	C₂²	semidirect
95. C₁₃×#446	C₂²	semidirect
96. C₈×Q₈×C₁₃	C₂²	semidirect
97. C₁₃×#441	C₂²	semidirect
99. C₄×C₁₃×Q₁₆	C₂²	semidirect
100. C₄×C₁₃×Q₁₆	C₂²	semidirect
101. C₄×C₁₃×Q₁₆	C₂²	semidirect
103. C₁₃×#436	C₂²	semidirect
106. C₈×D₄×C₁₃	C₂²	semidirect
107. C₁₃×#433	C₂²	semidirect
109. C₁₃×#419	C₂²	semidirect
114. C₂×C₁₃×#103	C₂²	semidirect
117. C₁₃×#405	C₂²	semidirect
276. #62559	C₁₃	direct (N × H)
396. #3563	C₂×C₁₃	semidirect
398. #3377	C₂×C₁₃	semidirect
399. #3364	C₂×C₁₃	semidirect
400. #3327	C₂×C₁₃	semidirect
401. #3314	C₂×C₁₃	semidirect
402. #3312	C₂×C₁₃	semidirect
403. #3300	C₂×C₁₃	semidirect
404. #3299	C₂×C₁₃	semidirect
405. #3296	C₂×C₁₃	semidirect
406. #3243	C₂×C₁₃	semidirect
407. #3236	C₂×C₁₃	semidirect
408. #3223	C₂×C₁₃	semidirect
409. #3215	C₂×C₁₃	semidirect
410. #3178	C₂×C₁₃	semidirect
411. #3170	C₂×C₁₃	semidirect
412. #3137	C₂×C₁₃	semidirect
413. C₂×#488	C₂×C₁₃	semidirect
414. #2966	C₂×C₁₃	semidirect
479. #557	C₂²×C₁₃	semidirect
484. #552	C₂²×C₁₃	semidirect
490. #544	C₂²×C₁₃	semidirect
495. #541	C₂²×C₁₃	semidirect
504. #501	C₂²×C₁₃	semidirect
505. #500	C₂²×C₁₃	semidirect
507. #494	C₂²×C₁₃	semidirect
508. #491	C₂²×C₁₃	semidirect
509. #491	C₂²×C₁₃	semidirect
517. #487	C₂²×C₁₃	semidirect
518. #487	C₂²×C₁₃	semidirect
519. #487	C₂²×C₁₃	semidirect
520. #485	C₂²×C₁₃	semidirect
522. #484	C₂²×C₁₃	semidirect
526. #479	C₂²×C₁₃	semidirect
527. #479	C₂²×C₁₃	semidirect
528. #479	C₂²×C₁₃	semidirect
530. #477	C₂²×C₁₃	semidirect
532. #470	C₂²×C₁₃	semidirect
536. #467	C₂²×C₁₃	semidirect
542. #462	C₂²×C₁₃	semidirect
543. #462	C₂²×C₁₃	semidirect
547. #451	C₂²×C₁₃	semidirect
548. #451	C₂²×C₁₃	semidirect
550. #446	C₂²×C₁₃	semidirect
551. C₈×Q₈	C₂²×C₁₃	semidirect
552. #441	C₂²×C₁₃	semidirect
554. C₄×Q₁₆	C₂²×C₁₃	semidirect
555. C₄×Q₁₆	C₂²×C₁₃	semidirect
556. C₄×Q₁₆	C₂²×C₁₃	semidirect
558. #436	C₂²×C₁₃	semidirect
561. C₈×D₄	C₂²×C₁₃	semidirect
562. #433	C₂²×C₁₃	semidirect
564. #419	C₂²×C₁₃	semidirect
569. C₂×#103	C₂²×C₁₃	semidirect
572. #405	C₂²×C₁₃	semidirect
884. C₁₃	#62559	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×#3561	2
C₁₃×#3377	2
C₁₃×#3364	2
C₁₃×#3327	2
C₁₃×#3314	2
C₁₃×#3312	2
C₁₃×#3300	2
C₁₃×#3299	2
C₁₃×#3296	2
C₁₃×#3243	2
C₁₃×#3236	2
C₁₃×#3223	2
C₁₃×#3215	2
C₁₃×#3178	2
C₁₃×#3170	2
C₁₃×#3137	2
C₂×C₁₃×#488	2
C₁₃×#2966	2
#62559	13

Subgroups — C13×#62559 #15748898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62559 #15748898