Subgroups — C₁₃×#62568 #15748907

Order 3328.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3558	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3327	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3324	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3314	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3313	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3311	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3310	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3222	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3178	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	2	no	—
21	C₁₃×#562	—	2	1	no	—
22	C₁₃×H(3,𝔽₄)	—	2	1	no	—
23	C₁₃×#559	C₂²	1	2	yes	—
24	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#557	—	2	1	no	—
26	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#556	—	2	1	no	—
28	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#556	C₂²	1	2	yes	complemented
30	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#552	C₂²	1	2	yes	complemented
32	C₁₃×#548	C₂²	1	2	yes	—
33	C₁₃×#546	—	2	2	no	—
34	C₁₃×#546	C₂²	1	2	yes	—
35	D₄²×C₁₃	C₂²	1	2	yes	—
36	C₁₃×#544	C₂²	1	2	yes	complemented
37	C₁₃×#542	—	2	1	no	—
38	C₁₃×#542	C₂²	1	2	yes	—
39	C₁₃×#541	—	2	2	no	—
40	C₁₃×#541	—	2	1	no	—
41	C₁₃×#541	C₂²	1	2	yes	complemented
42	C₁₃×#538	—	2	2	no	—
43	C₁₃×#538	—	2	1	no	—
44	C₁₃×#535	C₂²	1	2	yes	—
45	C₁₃×#534	—	2	1	no	—
46	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#532	C₂²	1	1	yes	characteristic
49	C₁₃×#529	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	2	yes	complemented
52	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#497	C₂²	1	2	yes	complemented
54	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#490	C₂²	1	2	yes	—
56	C₁₃×#490	C₂²	1	2	yes	complemented
57	C₁₃×#489	C₂²	1	2	yes	complemented
58	C₁₃×#489	C₂²	1	2	yes	complemented
59	C₁₃×#489	C₂²	1	2	yes	complemented
60	C₁₃×#489	C₂²	1	2	yes	complemented
61	C₁₃×#488	C₂²	1	2	yes	complemented
62	C₁₃×#488	C₂²	1	2	yes	complemented
63	C₁₃×#488	C₂²	1	2	yes	complemented
64	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#486	C₂²	1	2	yes	—
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#484	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	2	yes	—
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#480	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	complemented
75	C₁₃×#477	C₂²	1	2	yes	complemented
76	C₁₃×#476	C₂²	1	2	yes	complemented
77	C₁₃×#474	C₂²	1	2	yes	complemented
78	C₁₃×#474	C₂²	1	2	yes	complemented
79	C₁₃×#470	C₂²	1	2	yes	complemented
80	C₁₃×#468	C₂²	1	2	yes	—
81	C₁₃×#468	C₂²	1	2	yes	complemented
82	C₁₃×#468	C₂²	1	2	yes	complemented
83	C₁₃×#467	C₂²	1	2	yes	complemented
84	C₁₃×#465	C₂²	1	2	yes	—
85	C₁₃×#464	C₂²	1	2	yes	complemented
86	C₁₃×#464	C₂²	1	2	yes	complemented
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#464	C₂²	1	2	yes	complemented
89	C₁₃×#460	C₂²	1	2	yes	—
90	C₁₃×#460	C₂²	1	2	yes	—
91	C₁₃×#452	C₂²	1	2	yes	complemented
92	C₁₃×#452	C₂²	1	2	yes	complemented
93	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#450	C₂²	1	1	yes	characteristic
96	C₁₃×#450	C₂²	1	1	yes	characteristic
97	C₁₃×#450	C₂²	1	2	yes	complemented
98	C₁₃×#450	C₂²	1	2	yes	complemented
99	C₁₃×#446	C₂²	1	2	yes	complemented
100	C₁₃×#441	C₂²	1	2	yes	complemented
101	C₁₃×#440	C₂²	1	2	yes	complemented
102	C₁₃×#440	C₂²	1	2	yes	complemented
103	C₁₃×#440	C₂²	1	2	yes	complemented
104	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
106	C₁₃×#436	C₂²	1	2	yes	complemented
107	C₁₃×#435	C₂²	1	2	yes	complemented
108	C₁₃×#435	C₂²	1	2	yes	complemented
109	C₁₃×#433	C₂²	1	2	yes	complemented
110	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#419	C₂²	1	2	yes	complemented
112	C₁₃×#418	C₂²	1	2	yes	—
113	C₁₃×#418	C₂²	1	2	yes	complemented
114	C₁₃×#417	C₂²	1	2	yes	complemented
115	C₁₃×#416	C₂²	1	2	yes	complemented
116	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
117	C₁₃×#405	C₂²	1	2	yes	complemented
118	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₁₃×#41	—	2	1	no	—
120	C₂×C₁₃×#41	C₂³	1	2	yes	—
121	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₁₃	—	2	2	no	—
123	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
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×SD₁₆	C₂³	1	2	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
133	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	—	2	1	no	—
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	—	2	1	no	—
137	C₁₃×C₄⋊Q₈	—	2	2	no	—
138	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₁₃×#127	C₂³	1	2	yes	—
145	C₁₃×#127	C₂³	1	1	yes	characteristic
146	C₁₃×#126	—	2	2	no	—
147	C₁₃×#126	—	2	2	no	—
148	C₁₃×#126	—	2	2	no	—
149	C₁₃×#126	—	2	2	no	—
150	C₁₃×#126	—	2	2	no	—
151	C₁₃×#126	—	2	2	no	—
152	C₁₃×#126	—	2	2	no	—
153	C₁₃×#126	D₄	1	2	yes	—
154	C₁₃×#125	—	2	2	no	—
155	C₁₃×#125	—	2	2	no	—
156	C₁₃×#125	—	2	2	no	—
157	C₁₃×#125	—	2	1	no	—
158	C₁₃×#125	—	2	2	no	—
159	C₁₃×#125	—	2	2	no	—
160	C₁₃×#125	—	2	1	no	—
161	C₁₃×#125	D₄	1	1	yes	characteristic
162	C₁₃×#125	C₂³	1	2	yes	—
163	C₁₃×#125	C₂³	1	2	yes	—
164	C₁₃×#124	—	2	2	no	—
165	C₁₃×#124	—	2	1	no	—
166	C₁₃×#124	—	2	2	no	—
167	C₁₃×#124	—	2	2	no	—
168	C₁₃×#124	—	2	2	no	—
169	C₁₃×#124	—	2	1	no	—
170	C₁₃×#124	—	2	1	no	—
171	C₁₃×#124	—	2	1	no	—
172	C₁₃×#124	D₄	1	1	yes	characteristic
173	C₁₃×#124	C₂³	1	2	yes	—
174	C₁₃×#124	C₂³	1	2	yes	—
175	C₁₃×#124	C₂³	1	2	yes	—
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	—	2	2	no	—
181	C₁₃×#123	D₄	1	2	yes	—
182	C₁₃×C₂²⋊Q₈	—	2	1	no	—
183	C₁₃×C₂²⋊Q₈	—	2	1	no	—
184	C₁₃×C₂²⋊Q₈	—	2	1	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
191	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
192	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×#121	—	2	2	no	—
197	C₁₃×#121	—	2	1	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	2	no	—
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×#121	C₂³	1	2	yes	—
205	C₁₃×#120	—	2	2	no	—
206	C₁₃×#120	—	2	2	no	—
207	C₁₃×#120	—	2	2	no	—
208	C₁₃×#120	—	2	2	no	—
209	C₁₃×#120	—	2	2	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	2	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	1	no	—
217	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₁₃	—	2	1	no	—
224	C₄×D₄×C₁₃	—	2	2	no	—
225	C₄×D₄×C₁₃	—	2	2	no	—
226	C₄×D₄×C₁₃	—	2	1	no	—
227	C₄×D₄×C₁₃	C₂³	1	2	yes	—
228	C₄×D₄×C₁₃	C₂³	1	2	yes	—
229	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₁₃	C₂³	1	2	yes	—
231	C₁₃×#117	—	2	1	no	—
232	C₁₃×#117	—	2	2	no	—
233	C₁₃×#117	C₂³	1	2	yes	—
234	C₁₃×#117	C₂³	1	2	yes	—
235	C₁₃×#117	C₂³	1	2	yes	—
236	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
239	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#107	C₂³	1	2	yes	—
243	C₁₃×#107	C₂³	1	2	yes	—
244	C₁₃×#107	C₂³	1	2	yes	—
245	C₁₃×#106	C₂³	1	2	yes	—
246	C₁₃×#106	C₂³	1	2	yes	—
247	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#103	C₂³	1	2	yes	—
253	C₁₃×#103	C₂³	1	2	yes	—
254	C₁₃×#103	C₂³	1	2	yes	—
255	C₁₃×#103	C₂³	1	2	yes	—
256	C₁₃×#103	C₂³	1	2	yes	—
257	C₁₃×#103	C₂³	1	2	yes	—
258	C₁₃×#102	C₂³	1	2	yes	—
259	C₁₃×#102	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×#102	C₂³	1	2	yes	—
267	C₁₃×#102	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₁₃×#97	C₂³	1	2	yes	—
275	C₁₃×#97	C₂³	1	2	yes	—
276	C₁₃×#97	C₂³	1	2	yes	—
277	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#62568	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂⁴×C₁₃	—	2	1	no	—
282	C₂⁴×C₁₃	—	2	2	no	—
283	C₁₃×#41	—	4	2	no	—
284	C₁₃×#41	—	4	2	no	—
285	C₁₃×#41	—	8	2	no	—
286	C₂×Q₈×C₁₃	—	2	1	no	—
287	C₂×Q₈×C₁₃	—	2	1	no	—
288	C₂×Q₈×C₁₃	—	2	1	no	—
289	C₂×Q₈×C₁₃	—	2	2	no	—
290	C₂×Q₈×C₁₃	—	2	1	no	—
291	C₂×Q₈×C₁₃	—	2	1	no	—
292	C₂×Q₈×C₁₃	—	4	2	no	—
293	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
295	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂×D₄×C₁₃	—	2	2	no	—
298	C₂×D₄×C₁₃	—	2	2	no	—
299	C₂×D₄×C₁₃	—	2	2	no	—
300	C₂×D₄×C₁₃	—	2	2	no	—
301	C₂×D₄×C₁₃	—	2	1	no	—
302	C₂×D₄×C₁₃	—	2	1	no	—
303	C₂×D₄×C₁₃	—	2	1	no	—
304	C₂×D₄×C₁₃	—	2	2	no	—
305	C₂×D₄×C₁₃	—	2	2	no	—
306	C₂×D₄×C₁₃	—	4	2	no	—
307	C₂×D₄×C₁₃	—	4	2	no	—
308	C₂×D₄×C₁₃	—	4	2	no	—
309	C₂×D₄×C₁₃	—	8	4	no	—
310	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
312	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
313	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₃	—	2	1	no	—
315	C₂²×C₄×C₁₃	—	2	2	no	—
316	C₂²×C₄×C₁₃	—	2	2	no	—
317	C₂²×C₄×C₁₃	—	2	2	no	—
318	C₂²×C₄×C₁₃	—	2	2	no	—
319	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
323	C₁₃×Q₁₆	—	4	2	no	—
324	C₁₃×Q₁₆	—	4	2	no	—
325	C₁₃×SD₁₆	—	4	2	no	—
326	C₁₃×SD₁₆	—	4	2	no	—
327	C₁₃×SD₁₆	—	4	2	no	—
328	C₁₃×SD₁₆	—	4	2	no	—
329	C₁₃×M₁₆	—	4	2	no	—
330	C₁₃×M₁₆	—	4	2	no	—
331	C₂×C₈×C₁₃	—	4	2	no	—
332	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
334	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
335	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	1	no	—
338	C₁₃×C₄⋊C₄	—	2	1	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	1	no	—
341	C₁₃×C₄⋊C₄	—	2	1	no	—
342	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
349	C₁₃×C₄⋊C₄	—	2	1	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	1	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	C₂×D₄	1	2	yes	—
359	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
360	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
364	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
366	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
368	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
369	C₁₃×C₂²⋊C₄	—	2	2	no	—
370	C₁₃×C₂²⋊C₄	—	2	1	no	—
371	C₁₃×C₂²⋊C₄	—	2	1	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	2	no	—
377	C₁₃×C₂²⋊C₄	—	2	2	no	—
378	C₁₃×C₂²⋊C₄	—	2	2	no	—
379	C₁₃×C₂²⋊C₄	—	2	2	no	—
380	C₁₃×C₂²⋊C₄	—	2	2	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	—	2	2	no	—
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	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
391	C₄²×C₁₃	—	2	2	no	—
392	C₄²×C₁₃	—	2	1	no	—
393	C₄²×C₁₃	—	2	1	no	—
394	C₄²×C₁₃	—	2	2	no	—
395	C₄²×C₁₃	—	2	2	no	—
396	C₄²×C₁₃	—	2	2	no	—
397	C₄²×C₁₃	—	2	2	no	—
398	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₁₃	C₂⁴	1	2	yes	—
402	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
403	#3558	C₂×C₁₃	1	1	yes	characteristic
404	#3555	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3375	C₂×C₁₃	1	2	yes	complemented
406	#3371	C₂×C₁₃	1	2	yes	complemented
407	#3327	C₂×C₁₃	1	2	yes	complemented
408	#3324	C₂×C₁₃	1	2	yes	complemented
409	#3314	C₂×C₁₃	1	2	yes	complemented
410	#3313	C₂×C₁₃	1	2	yes	complemented
411	#3311	C₂×C₁₃	1	2	yes	complemented
412	#3310	C₂×C₁₃	1	2	yes	complemented
413	#3243	C₂×C₁₃	1	2	yes	complemented
414	#3235	C₂×C₁₃	1	1	yes	characteristic, complemented
415	#3222	C₂×C₁₃	1	2	yes	complemented
416	#3215	C₂×C₁₃	1	1	yes	characteristic, complemented
417	#3182	C₂×C₁₃	1	1	yes	characteristic, complemented
418	#3178	C₂×C₁₃	1	2	yes	complemented
419	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
420	#3136	C₂×C₁₃	1	2	yes	complemented
421	#2967	C₂×C₁₃	1	1	yes	characteristic, complemented
422	C₂³×C₁₃	—	2	2	no	—
423	C₂³×C₁₃	—	2	2	no	—
424	C₂³×C₁₃	—	4	2	no	—
425	C₂³×C₁₃	—	8	1	no	—
426	C₂³×C₁₃	—	8	2	no	—
427	C₂³×C₁₃	—	8	2	no	—
428	C₂³×C₁₃	—	8	1	no	—
429	C₂³×C₁₃	—	8	2	no	—
430	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
431	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	Q₈×C₁₃	—	2	2	no	—
433	Q₈×C₁₃	—	2	2	no	—
434	Q₈×C₁₃	—	2	2	no	—
435	Q₈×C₁₃	—	2	2	no	—
436	Q₈×C₁₃	—	4	1	no	—
437	Q₈×C₁₃	—	4	2	no	—
438	Q₈×C₁₃	—	8	1	no	—
439	Q₈×C₁₃	—	8	1	no	—
440	Q₈×C₁₃	—	8	2	no	—
441	Q₈×C₁₃	—	8	1	no	—
442	Q₈×C₁₃	—	8	1	no	—
443	D₄×C₁₃	—	2	2	no	—
444	D₄×C₁₃	—	2	2	no	—
445	D₄×C₁₃	—	2	2	no	—
446	D₄×C₁₃	—	2	2	no	—
447	D₄×C₁₃	—	4	2	no	—
448	D₄×C₁₃	—	4	1	no	—
449	D₄×C₁₃	—	4	4	no	—
450	D₄×C₁₃	—	8	1	no	—
451	D₄×C₁₃	—	8	2	no	—
452	D₄×C₁₃	—	8	2	no	—
453	D₄×C₁₃	—	8	1	no	—
454	D₄×C₁₃	—	8	2	no	—
455	D₄×C₁₃	—	8	1	no	—
456	D₄×C₁₃	—	8	2	no	—
457	D₄×C₁₃	—	8	2	no	—
458	C₂×C₄×C₁₃	—	2	2	no	—
459	C₂×C₄×C₁₃	—	2	2	no	—
460	C₂×C₄×C₁₃	—	2	2	no	—
461	C₂×C₄×C₁₃	—	2	1	no	—
462	C₂×C₄×C₁₃	—	2	1	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	2	1	no	—
465	C₂×C₄×C₁₃	—	2	2	no	—
466	C₂×C₄×C₁₃	—	2	2	no	—
467	C₂×C₄×C₁₃	—	2	2	no	—
468	C₂×C₄×C₁₃	—	2	1	no	—
469	C₂×C₄×C₁₃	—	4	1	no	—
470	C₂×C₄×C₁₃	—	4	1	no	—
471	C₂×C₄×C₁₃	—	8	2	no	—
472	C₂×C₄×C₁₃	—	8	2	no	—
473	C₂×C₄×C₁₃	—	8	2	no	—
474	C₂×C₄×C₁₃	—	8	2	no	—
475	C₂×C₄×C₁₃	—	8	1	no	—
476	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
485	C₈×C₁₃	—	2	2	no	—
486	C₈×C₁₃	—	2	2	no	—
487	C₈×C₁₃	—	2	2	no	—
488	C₈×C₁₃	—	2	2	no	—
489	#563	—	2	2	no	—
490	#562	—	2	1	no	—
491	H(3,𝔽₄)	—	2	1	no	—
492	#559	C₂²×C₁₃	1	2	yes	—
493	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	#557	—	2	1	no	—
495	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	#556	—	2	1	no	—
497	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	#556	C₂²×C₁₃	1	2	yes	complemented
499	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
500	#552	C₂²×C₁₃	1	2	yes	complemented
501	#548	C₂²×C₁₃	1	2	yes	—
502	#546	—	2	2	no	—
503	#546	C₂²×C₁₃	1	2	yes	—
504	D₄²	C₂²×C₁₃	1	2	yes	—
505	#544	C₂²×C₁₃	1	2	yes	complemented
506	#542	—	2	1	no	—
507	#542	C₂²×C₁₃	1	2	yes	—
508	#541	—	2	2	no	—
509	#541	—	2	1	no	—
510	#541	C₂²×C₁₃	1	2	yes	complemented
511	#538	—	2	2	no	—
512	#538	—	2	1	no	—
513	#535	C₂²×C₁₃	1	2	yes	—
514	#534	—	2	1	no	—
515	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	#532	C₂²×C₁₃	1	1	yes	characteristic
518	#529	C₂²×C₁₃	1	1	yes	characteristic
519	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
520	#501	C₂²×C₁₃	1	2	yes	complemented
521	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
522	#497	C₂²×C₁₃	1	2	yes	complemented
523	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	#490	C₂²×C₁₃	1	2	yes	—
525	#490	C₂²×C₁₃	1	2	yes	complemented
526	#489	C₂²×C₁₃	1	2	yes	complemented
527	#489	C₂²×C₁₃	1	2	yes	complemented
528	#489	C₂²×C₁₃	1	2	yes	complemented
529	#489	C₂²×C₁₃	1	2	yes	complemented
530	#488	C₂²×C₁₃	1	2	yes	complemented
531	#488	C₂²×C₁₃	1	2	yes	complemented
532	#488	C₂²×C₁₃	1	2	yes	complemented
533	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
534	#486	C₂²×C₁₃	1	2	yes	—
535	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
536	#485	C₂²×C₁₃	1	2	yes	complemented
537	#484	C₂²×C₁₃	1	2	yes	complemented
538	#482	C₂²×C₁₃	1	2	yes	—
539	#482	C₂²×C₁₃	1	2	yes	complemented
540	#482	C₂²×C₁₃	1	2	yes	complemented
541	#480	C₂²×C₁₃	1	2	yes	—
542	#479	C₂²×C₁₃	1	2	yes	complemented
543	#478	C₂²×C₁₃	1	2	yes	complemented
544	#477	C₂²×C₁₃	1	2	yes	complemented
545	#476	C₂²×C₁₃	1	2	yes	complemented
546	#474	C₂²×C₁₃	1	2	yes	complemented
547	#474	C₂²×C₁₃	1	2	yes	complemented
548	#470	C₂²×C₁₃	1	2	yes	complemented
549	#468	C₂²×C₁₃	1	2	yes	—
550	#468	C₂²×C₁₃	1	2	yes	complemented
551	#468	C₂²×C₁₃	1	2	yes	complemented
552	#467	C₂²×C₁₃	1	2	yes	complemented
553	#465	C₂²×C₁₃	1	2	yes	—
554	#464	C₂²×C₁₃	1	2	yes	complemented
555	#464	C₂²×C₁₃	1	2	yes	complemented
556	#464	C₂²×C₁₃	1	2	yes	complemented
557	#464	C₂²×C₁₃	1	2	yes	complemented
558	#460	C₂²×C₁₃	1	2	yes	—
559	#460	C₂²×C₁₃	1	2	yes	—
560	#452	C₂²×C₁₃	1	2	yes	complemented
561	#452	C₂²×C₁₃	1	2	yes	complemented
562	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
563	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
564	#450	C₂²×C₁₃	1	1	yes	characteristic
565	#450	C₂²×C₁₃	1	1	yes	characteristic
566	#450	C₂²×C₁₃	1	2	yes	complemented
567	#450	C₂²×C₁₃	1	2	yes	complemented
568	#446	C₂²×C₁₃	1	2	yes	complemented
569	#441	C₂²×C₁₃	1	2	yes	complemented
570	#440	C₂²×C₁₃	1	2	yes	complemented
571	#440	C₂²×C₁₃	1	2	yes	complemented
572	#440	C₂²×C₁₃	1	2	yes	complemented
573	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
574	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
575	#436	C₂²×C₁₃	1	2	yes	complemented
576	#435	C₂²×C₁₃	1	2	yes	complemented
577	#435	C₂²×C₁₃	1	2	yes	complemented
578	#433	C₂²×C₁₃	1	2	yes	complemented
579	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
580	#419	C₂²×C₁₃	1	2	yes	complemented
581	#418	C₂²×C₁₃	1	2	yes	—
582	#418	C₂²×C₁₃	1	2	yes	complemented
583	#417	C₂²×C₁₃	1	2	yes	complemented
584	#416	C₂²×C₁₃	1	2	yes	complemented
585	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
586	#405	C₂²×C₁₃	1	2	yes	complemented
587	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
588	C₂²×C₁₃	—	2	1	no	—
589	C₂²×C₁₃	—	2	2	no	—
590	C₂²×C₁₃	—	2	1	no	—
591	C₂²×C₁₃	—	2	2	no	—
592	C₂²×C₁₃	—	2	1	no	—
593	C₂²×C₁₃	—	2	2	no	—
594	C₂²×C₁₃	—	4	2	no	—
595	C₂²×C₁₃	—	4	2	no	—
596	C₂²×C₁₃	—	4	2	no	—
597	C₂²×C₁₃	—	4	2	no	—
598	C₂²×C₁₃	—	4	2	no	—
599	C₂²×C₁₃	—	4	2	no	—
600	C₂²×C₁₃	—	16	2	no	—
601	C₂²×C₁₃	—	16	4	no	—
602	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
603	C₄×C₁₃	—	2	1	no	—
604	C₄×C₁₃	—	2	1	no	—
605	C₄×C₁₃	—	2	2	no	—
606	C₄×C₁₃	—	2	1	no	—
607	C₄×C₁₃	—	2	1	no	—
608	C₄×C₁₃	—	2	2	no	—
609	C₄×C₁₃	—	2	2	no	—
610	C₄×C₁₃	—	2	1	no	—
611	C₄×C₁₃	—	4	2	no	—
612	C₄×C₁₃	—	4	1	no	—
613	C₄×C₁₃	—	4	2	no	—
614	C₄×C₁₃	—	4	1	no	—
615	C₄×C₁₃	—	4	2	no	—
616	C₄×C₁₃	—	4	2	no	—
617	C₄×C₁₃	—	4	1	no	—
618	C₄×C₁₃	—	4	1	no	—
619	C₄×C₁₃	#585	1	2	yes	—
620	C₂×#41	—	2	1	no	—
621	C₂×#41	C₂³×C₁₃	1	2	yes	—
622	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
623	C₂²×D₄	—	2	2	no	—
624	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
625	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
626	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
627	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
628	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
629	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
632	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
633	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
634	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
635	C₄⋊Q₈	—	2	1	no	—
636	C₄⋊Q₈	—	2	2	no	—
637	C₄⋊Q₈	—	2	1	no	—
638	C₄⋊Q₈	—	2	2	no	—
639	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
640	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
641	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
642	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
644	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
645	#127	C₂³×C₁₃	1	1	yes	characteristic
646	#127	C₂³×C₁₃	1	2	yes	—
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	D₄×C₁₃	1	2	yes	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	2	no	—
658	#125	—	2	1	no	—
659	#125	—	2	2	no	—
660	#125	—	2	2	no	—
661	#125	—	2	1	no	—
662	#125	D₄×C₁₃	1	1	yes	characteristic
663	#125	C₂³×C₁₃	1	2	yes	—
664	#125	C₂³×C₁₃	1	2	yes	—
665	#124	—	2	2	no	—
666	#124	—	2	1	no	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	1	no	—
671	#124	—	2	1	no	—
672	#124	—	2	1	no	—
673	#124	D₄×C₁₃	1	1	yes	characteristic
674	#124	C₂³×C₁₃	1	2	yes	—
675	#124	C₂³×C₁₃	1	2	yes	—
676	#124	C₂³×C₁₃	1	2	yes	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	D₄×C₁₃	1	2	yes	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
692	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
693	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
694	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
696	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
697	#121	—	2	2	no	—
698	#121	—	2	1	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	D₄×C₁₃	1	1	yes	characteristic
704	#121	C₂³×C₁₃	1	2	yes	—
705	#121	C₂³×C₁₃	1	2	yes	—
706	#120	—	2	2	no	—
707	#120	—	2	2	no	—
708	#120	—	2	2	no	—
709	#120	—	2	2	no	—
710	#120	—	2	2	no	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	—	2	2	no	—
713	C₄×Q₈	—	2	1	no	—
714	C₄×Q₈	—	2	1	no	—
715	C₄×Q₈	—	2	1	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
720	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
721	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
722	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
723	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	C₂³×C₁₃	1	2	yes	—
729	C₄×D₄	C₂³×C₁₃	1	2	yes	—
730	C₄×D₄	C₂³×C₁₃	1	2	yes	—
731	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
732	#117	—	2	1	no	—
733	#117	—	2	2	no	—
734	#117	C₂³×C₁₃	1	2	yes	—
735	#117	C₂³×C₁₃	1	2	yes	—
736	#117	C₂³×C₁₃	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
738	C₂×C₂²⋊C₄	—	2	1	no	—
739	C₂×C₂²⋊C₄	—	2	1	no	—
740	C₂×C₂²⋊C₄	—	2	2	no	—
741	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
742	#107	C₂³×C₁₃	1	2	yes	—
743	#107	C₂³×C₁₃	1	2	yes	—
744	#107	C₂³×C₁₃	1	2	yes	—
745	#107	C₂³×C₁₃	1	2	yes	—
746	#106	C₂³×C₁₃	1	2	yes	—
747	#106	C₂³×C₁₃	1	2	yes	—
748	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
749	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
750	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
751	#103	C₂³×C₁₃	1	2	yes	—
752	#103	C₂³×C₁₃	1	2	yes	—
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	#102	C₂³×C₁₃	1	2	yes	—
760	#102	C₂³×C₁₃	1	2	yes	—
761	#102	C₂³×C₁₃	1	2	yes	—
762	#102	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	#102	C₂³×C₁₃	1	2	yes	—
770	#102	C₂³×C₁₃	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
772	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
773	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
775	#97	C₂³×C₁₃	1	2	yes	—
776	#97	C₂³×C₁₃	1	2	yes	—
777	#97	C₂³×C₁₃	1	2	yes	—
778	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
779	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
780	C₄×C₈	C₂³×C₁₃	1	2	yes	—
781	C₂×C₁₃	—	4	1	no	—
782	C₂×C₁₃	—	4	2	no	—
783	C₂×C₁₃	—	8	2	no	—
784	C₂×C₁₃	—	8	2	no	—
785	C₂×C₁₃	#3500	1	1	yes	characteristic
786	C₂×C₁₃	#3585	1	1	yes	characteristic
787	C₂×C₁₃	#3586	1	1	yes	characteristic
788	C₂⁴	—	2	1	no	—
789	C₂⁴	—	2	2	no	—
790	#41	—	4	2	no	—
791	#41	—	4	2	no	—
792	#41	—	8	2	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	4	2	no	—
800	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
801	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
802	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	4	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	8	4	no	—
817	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
818	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
819	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
820	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
827	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
830	Q₁₆	—	4	2	no	—
831	Q₁₆	—	4	2	no	—
832	SD₁₆	—	4	2	no	—
833	SD₁₆	—	4	2	no	—
834	SD₁₆	—	4	2	no	—
835	SD₁₆	—	4	2	no	—
836	M₁₆	—	4	2	no	—
837	M₁₆	—	4	2	no	—
838	C₂×C₈	—	4	2	no	—
839	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
840	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
841	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
842	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	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	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
868	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
869	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
870	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
872	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
873	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
875	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	1	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
894	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	1	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
906	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
907	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
908	C₄²	C₂⁴×C₁₃	1	2	yes	—
909	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
910	C₁₃	#62568	1	1	yes	characteristic, direct product factor, Sylow
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	4	2	no	—
914	C₂³	—	8	1	no	—
915	C₂³	—	8	2	no	—
916	C₂³	—	8	2	no	—
917	C₂³	—	8	1	no	—
918	C₂³	—	8	2	no	—
919	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
920	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
921	Q₈	—	2	2	no	—
922	Q₈	—	2	2	no	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	2	no	—
925	Q₈	—	4	1	no	—
926	Q₈	—	4	2	no	—
927	Q₈	—	8	1	no	—
928	Q₈	—	8	1	no	—
929	Q₈	—	8	1	no	—
930	Q₈	—	8	1	no	—
931	Q₈	—	8	2	no	—
932	D₄	—	2	2	no	—
933	D₄	—	2	2	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	2	no	—
936	D₄	—	4	2	no	—
937	D₄	—	4	1	no	—
938	D₄	—	4	4	no	—
939	D₄	—	8	2	no	—
940	D₄	—	8	1	no	—
941	D₄	—	8	2	no	—
942	D₄	—	8	1	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	4	1	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	8	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	—	8	2	no	—
964	C₂×C₄	—	8	1	no	—
965	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
968	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
969	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
970	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
972	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
973	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
974	C₈	—	2	2	no	—
975	C₈	—	2	2	no	—
976	C₈	—	2	2	no	—
977	C₈	—	2	2	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	2	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	16	2	no	—
991	C₂²	—	16	4	no	—
992	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
993	C₄	—	2	1	no	—
994	C₄	—	2	1	no	—
995	C₄	—	2	2	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	2	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	1	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	1	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	1	no	—
1008	C₄	—	4	1	no	—
1009	C₄	C₁₃×#585	1	2	yes	—
1010	C₂	—	4	1	no	—
1011	C₂	—	4	2	no	—
1012	C₂	—	8	2	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₁₃×#3500	1	1	yes	characteristic
1015	C₂	C₁₃×#3585	1	1	yes	characteristic
1016	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×#3558	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
2. C₁₃×#3555	C₂	semidirect
3. C₁₃×#3375	C₂	semidirect
4. C₁₃×#3371	C₂	semidirect
5. C₁₃×#3327	C₂	semidirect
6. C₁₃×#3324	C₂	semidirect
7. C₁₃×#3314	C₂	semidirect
8. C₁₃×#3313	C₂	semidirect
9. C₁₃×#3311	C₂	semidirect
10. C₁₃×#3310	C₂	semidirect
11. C₁₃×#3243	C₂	semidirect
12. C₁₃×#3235	C₂	semidirect
13. C₁₃×#3222	C₂	semidirect
14. C₁₃×#3215	C₂	semidirect
15. C₁₃×#3182	C₂	semidirect
16. C₁₃×#3178	C₂	semidirect
17. C₁₃×#3140	C₂	semidirect
18. C₁₃×#3136	C₂	semidirect
19. C₁₃×#2967	C₂	semidirect
24. Q₈²×C₁₃	C₂²	semidirect
26. C₁₃×#557	C₂²	semidirect
28. C₁₃×#556	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
30. C₁₃×#554	C₂²	semidirect
31. C₁₃×#552	C₂²	semidirect
36. C₁₃×#544	C₂²	semidirect
41. C₁₃×#541	C₂²	semidirect
46. C₁₃×#533	C₂²	semidirect
47. C₁₃×#533	C₂²	semidirect
51. C₁₃×#501	C₂²	semidirect
52. C₁₃×#500	C₂²	semidirect
53. C₁₃×#497	C₂²	semidirect
54. C₁₃×#492	C₂²	semidirect
56. C₁₃×#490	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#489	C₂²	semidirect
59. C₁₃×#489	C₂²	semidirect
60. C₁₃×#489	C₂²	semidirect
61. C₁₃×#488	C₂²	semidirect
62. C₁₃×#488	C₂²	semidirect
63. C₁₃×#488	C₂²	semidirect
64. C₁₃×#487	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#484	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#474	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#467	C₂²	semidirect
85. C₁₃×#464	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
91. C₁₃×#452	C₂²	semidirect
92. C₁₃×#452	C₂²	semidirect
93. C₁₃×#451	C₂²	semidirect
94. C₁₃×#451	C₂²	semidirect
97. C₁₃×#450	C₂²	semidirect
98. C₁₃×#450	C₂²	semidirect
99. C₁₃×#446	C₂²	semidirect
100. C₁₃×#441	C₂²	semidirect
101. C₁₃×#440	C₂²	semidirect
102. C₁₃×#440	C₂²	semidirect
103. C₁₃×#440	C₂²	semidirect
104. C₄×C₁₃×Q₁₆	C₂²	semidirect
105. C₄×C₁₃×SD₁₆	C₂²	semidirect
106. C₁₃×#436	C₂²	semidirect
107. C₁₃×#435	C₂²	semidirect
108. C₁₃×#435	C₂²	semidirect
109. C₁₃×#433	C₂²	semidirect
110. C₁₃×#432	C₂²	semidirect
111. C₁₃×#419	C₂²	semidirect
113. C₁₃×#418	C₂²	semidirect
114. C₁₃×#417	C₂²	semidirect
115. C₁₃×#416	C₂²	semidirect
116. C₂×C₁₃×#102	C₂²	semidirect
117. C₁₃×#405	C₂²	semidirect
118. C₄×C₁₃×M₁₆	C₂²	semidirect
280. #62568	C₁₃	direct (N × H)
404. #3555	C₂×C₁₃	semidirect
405. #3375	C₂×C₁₃	semidirect
406. #3371	C₂×C₁₃	semidirect
407. #3327	C₂×C₁₃	semidirect
408. #3324	C₂×C₁₃	semidirect
409. #3314	C₂×C₁₃	semidirect
410. #3313	C₂×C₁₃	semidirect
411. #3311	C₂×C₁₃	semidirect
412. #3310	C₂×C₁₃	semidirect
413. #3243	C₂×C₁₃	semidirect
414. #3235	C₂×C₁₃	semidirect
415. #3222	C₂×C₁₃	semidirect
416. #3215	C₂×C₁₃	semidirect
417. #3182	C₂×C₁₃	semidirect
418. #3178	C₂×C₁₃	semidirect
419. #3140	C₂×C₁₃	semidirect
420. #3136	C₂×C₁₃	semidirect
421. #2967	C₂×C₁₃	semidirect
493. Q₈²	C₂²×C₁₃	semidirect
495. #557	C₂²×C₁₃	semidirect
497. #556	C₂²×C₁₃	semidirect
498. #556	C₂²×C₁₃	semidirect
499. #554	C₂²×C₁₃	semidirect
500. #552	C₂²×C₁₃	semidirect
505. #544	C₂²×C₁₃	semidirect
510. #541	C₂²×C₁₃	semidirect
515. #533	C₂²×C₁₃	semidirect
516. #533	C₂²×C₁₃	semidirect
520. #501	C₂²×C₁₃	semidirect
521. #500	C₂²×C₁₃	semidirect
522. #497	C₂²×C₁₃	semidirect
523. #492	C₂²×C₁₃	semidirect
525. #490	C₂²×C₁₃	semidirect
526. #489	C₂²×C₁₃	semidirect
527. #489	C₂²×C₁₃	semidirect
528. #489	C₂²×C₁₃	semidirect
529. #489	C₂²×C₁₃	semidirect
530. #488	C₂²×C₁₃	semidirect
531. #488	C₂²×C₁₃	semidirect
532. #488	C₂²×C₁₃	semidirect
533. #487	C₂²×C₁₃	semidirect
535. #486	C₂²×C₁₃	semidirect
536. #485	C₂²×C₁₃	semidirect
537. #484	C₂²×C₁₃	semidirect
539. #482	C₂²×C₁₃	semidirect
540. #482	C₂²×C₁₃	semidirect
542. #479	C₂²×C₁₃	semidirect
543. #478	C₂²×C₁₃	semidirect
544. #477	C₂²×C₁₃	semidirect
545. #476	C₂²×C₁₃	semidirect
546. #474	C₂²×C₁₃	semidirect
547. #474	C₂²×C₁₃	semidirect
548. #470	C₂²×C₁₃	semidirect
550. #468	C₂²×C₁₃	semidirect
551. #468	C₂²×C₁₃	semidirect
552. #467	C₂²×C₁₃	semidirect
554. #464	C₂²×C₁₃	semidirect
555. #464	C₂²×C₁₃	semidirect
556. #464	C₂²×C₁₃	semidirect
557. #464	C₂²×C₁₃	semidirect
560. #452	C₂²×C₁₃	semidirect
561. #452	C₂²×C₁₃	semidirect
562. #451	C₂²×C₁₃	semidirect
563. #451	C₂²×C₁₃	semidirect
566. #450	C₂²×C₁₃	semidirect
567. #450	C₂²×C₁₃	semidirect
568. #446	C₂²×C₁₃	semidirect
569. #441	C₂²×C₁₃	semidirect
570. #440	C₂²×C₁₃	semidirect
571. #440	C₂²×C₁₃	semidirect
572. #440	C₂²×C₁₃	semidirect
573. C₄×Q₁₆	C₂²×C₁₃	semidirect
574. C₄×SD₁₆	C₂²×C₁₃	semidirect
575. #436	C₂²×C₁₃	semidirect
576. #435	C₂²×C₁₃	semidirect
577. #435	C₂²×C₁₃	semidirect
578. #433	C₂²×C₁₃	semidirect
579. #432	C₂²×C₁₃	semidirect
580. #419	C₂²×C₁₃	semidirect
582. #418	C₂²×C₁₃	semidirect
583. #417	C₂²×C₁₃	semidirect
584. #416	C₂²×C₁₃	semidirect
585. C₂×#102	C₂²×C₁₃	semidirect
586. #405	C₂²×C₁₃	semidirect
587. C₄×M₁₆	C₂²×C₁₃	semidirect
910. C₁₃	#62568	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×#3558	2
C₁₃×#3555	2
C₁₃×#3375	2
C₁₃×#3371	2
C₁₃×#3327	2
C₁₃×#3324	2
C₁₃×#3314	2
C₁₃×#3313	2
C₁₃×#3311	2
C₁₃×#3310	2
C₁₃×#3243	2
C₁₃×#3235	2
C₁₃×#3222	2
C₁₃×#3215	2
C₁₃×#3182	2
C₁₃×#3178	2
C₁₃×#3140	2
C₁₃×#3136	2
C₁₃×#2967	2
#62568	13

Subgroups — C13×#62568 #15748907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62568 #15748907