Subgroups — C₁₃×#60042 #15746381

Order 3328.

1648 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2734	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2731	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2721	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2612	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2604	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2574	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2545	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2529	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2521	C₂	1	2	yes	maximal
11	C₁₃×#2519	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2479	C₂	1	2	yes	maximal
13	C₁₃×#2441	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2372	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#2371	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2298	C₂	1	2	yes	maximal, complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#126	C₂²	1	2	yes	—
24	C₂×C₁₃×#125	C₂²	1	2	yes	—
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₁₃×#400	C₂²	1	2	yes	—
32	C₁₃×#399	C₂²	1	2	yes	—
33	C₁₃×#399	C₂²	1	2	yes	—
34	C₁₃×#399	C₂²	1	2	yes	—
35	C₁₃×#398	C₂²	1	2	yes	—
36	C₁₃×#398	C₂²	1	2	yes	—
37	C₁₃×#398	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	2	yes	—
39	C₁₃×#397	C₂²	1	2	yes	—
40	C₁₃×#396	C₂²	1	2	yes	—
41	C₁₃×#396	C₂²	1	2	yes	—
42	C₁₃×#396	C₂²	1	2	yes	—
43	C₁₃×#395	C₂²	1	2	yes	—
44	C₁₃×#395	C₂²	1	2	yes	—
45	C₁₃×#394	C₂²	1	2	yes	—
46	C₁₃×#393	C₂²	1	2	yes	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#391	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#391	C₂²	1	1	yes	characteristic
51	C₁₃×#391	C₂²	1	1	yes	characteristic
52	C₁₃×#391	C₂²	1	1	yes	characteristic
53	C₁₃×#390	C₂²	1	1	yes	characteristic
54	C₁₃×#389	C₂²	1	2	yes	—
55	C₁₃×#389	C₂²	1	2	yes	—
56	C₁₃×#389	C₂²	1	2	yes	—
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#389	C₂²	1	2	yes	—
60	C₁₃×#388	C₂²	1	2	yes	—
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#386	C₂²	1	2	yes	—
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#384	C₂²	1	1	yes	characteristic
88	C₁₃×#384	C₂²	1	1	yes	characteristic
89	C₁₃×#382	C₂²	1	2	yes	—
90	C₁₃×#382	C₂²	1	1	yes	characteristic
91	C₁₃×#380	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₁₃×#376	C₂²	1	2	yes	—
104	C₁₃×#376	C₂²	1	2	yes	—
105	C₁₃×#376	C₂²	1	2	yes	—
106	C₄³×C₁₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	—	2	4	no	—
113	C₁₃×C₄⋊Q₈	—	2	4	no	—
114	C₁₃×#126	—	2	8	no	—
115	C₁₃×#126	—	4	4	no	—
116	C₁₃×#125	—	2	8	no	—
117	C₁₃×#125	—	4	2	no	—
118	C₁₃×#124	—	2	4	no	—
119	C₁₃×#124	—	4	2	no	—
120	C₄×Q₈×C₁₃	—	4	2	no	—
121	C₄×Q₈×C₁₃	—	4	2	no	—
122	C₁₃×#117	—	2	8	no	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₁₃×#95	C₂³	1	2	yes	—
180	C₁₃×#95	C₂³	1	2	yes	—
181	C₁₃×#95	C₂³	1	2	yes	—
182	C₁₃×#95	C₂³	1	2	yes	—
183	C₁₃×#95	C₂³	1	2	yes	—
184	C₁₃×#95	C₂³	1	2	yes	—
185	C₁₃×#95	C₂³	1	2	yes	—
186	C₁₃×#95	C₂³	1	2	yes	—
187	C₁₃×#95	C₂³	1	2	yes	—
188	C₁₃×#95	C₂³	1	2	yes	—
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	#60042	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₁₃	—	2	2	no	—
208	C₂×Q₈×C₁₃	—	2	2	no	—
209	C₂×Q₈×C₁₃	—	4	1	no	—
210	C₂×Q₈×C₁₃	—	4	1	no	—
211	C₂×Q₈×C₁₃	—	4	1	no	—
212	C₂×Q₈×C₁₃	—	4	1	no	—
213	C₂×Q₈×C₁₃	—	4	1	no	—
214	C₂×Q₈×C₁₃	—	4	1	no	—
215	C₂×Q₈×C₁₃	#41	1	4	yes	—
216	C₂×D₄×C₁₃	—	2	2	no	—
217	C₂×D₄×C₁₃	—	4	1	no	—
218	C₂×D₄×C₁₃	—	4	1	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	4	2	no	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	4	2	no	—
255	C₁₃×C₄⋊C₄	—	4	1	no	—
256	C₁₃×C₄⋊C₄	—	4	1	no	—
257	C₁₃×C₄⋊C₄	—	4	1	no	—
258	C₁₃×C₄⋊C₄	—	4	1	no	—
259	C₁₃×C₄⋊C₄	—	4	2	no	—
260	C₁₃×C₄⋊C₄	—	4	1	no	—
261	C₁₃×C₄⋊C₄	—	4	1	no	—
262	C₁₃×C₄⋊C₄	—	4	2	no	—
263	C₁₃×C₄⋊C₄	—	4	2	no	—
264	C₁₃×C₄⋊C₄	—	4	2	no	—
265	C₁₃×C₄⋊C₄	#41	1	8	yes	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	4	2	no	—
276	C₁₃×C₂²⋊C₄	—	4	2	no	—
277	C₁₃×C₂²⋊C₄	—	4	2	no	—
278	C₁₃×C₂²⋊C₄	—	4	2	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	—	2	4	no	—
281	C₄²×C₁₃	—	2	2	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	2	4	no	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	—	2	2	no	—
286	C₄²×C₁₃	—	2	2	no	—
287	C₄²×C₁₃	—	2	2	no	—
288	C₄²×C₁₃	—	2	2	no	—
289	C₄²×C₁₃	—	2	4	no	—
290	C₄²×C₁₃	—	2	4	no	—
291	C₄²×C₁₃	—	2	4	no	—
292	C₄²×C₁₃	—	4	1	no	—
293	C₄²×C₁₃	—	4	2	no	—
294	C₄²×C₁₃	—	4	1	no	—
295	C₄²×C₁₃	—	4	1	no	—
296	#2734	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2731	C₂×C₁₃	1	1	yes	characteristic
298	#2721	C₂×C₁₃	1	2	yes	complemented
299	#2612	C₂×C₁₃	1	2	yes	complemented
300	#2604	C₂×C₁₃	1	2	yes	complemented
301	#2574	C₂×C₁₃	1	2	yes	complemented
302	#2565	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2545	C₂×C₁₃	1	1	yes	characteristic
304	#2529	C₂×C₁₃	1	2	yes	complemented
305	#2521	C₂×C₁₃	1	2	yes	—
306	#2519	C₂×C₁₃	1	2	yes	complemented
307	#2479	C₂×C₁₃	1	2	yes	—
308	#2441	C₂×C₁₃	1	2	yes	complemented
309	#2373	C₂×C₁₃	1	2	yes	complemented
310	#2372	C₂×C₁₃	1	1	yes	characteristic
311	#2371	C₂×C₁₃	1	2	yes	complemented
312	#2369	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#2298	C₂×C₁₃	1	2	yes	complemented
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
323	Q₈×C₁₃	—	4	4	no	—
324	Q₈×C₁₃	—	4	4	no	—
325	Q₈×C₁₃	—	8	2	no	—
326	D₄×C₁₃	—	8	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	4	8	no	—
370	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
371	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
372	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
373	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
374	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
375	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
376	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
377	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
378	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#126	C₂²×C₁₃	1	2	yes	—
381	C₂×#126	C₂²×C₁₃	1	2	yes	—
382	C₂×#125	C₂²×C₁₃	1	2	yes	—
383	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#117	C₂²×C₁₃	1	2	yes	—
389	#400	C₂²×C₁₃	1	2	yes	—
390	#399	C₂²×C₁₃	1	2	yes	—
391	#399	C₂²×C₁₃	1	2	yes	—
392	#399	C₂²×C₁₃	1	2	yes	—
393	#398	C₂²×C₁₃	1	2	yes	—
394	#398	C₂²×C₁₃	1	2	yes	—
395	#398	C₂²×C₁₃	1	2	yes	—
396	#398	C₂²×C₁₃	1	2	yes	—
397	#397	C₂²×C₁₃	1	2	yes	—
398	#396	C₂²×C₁₃	1	2	yes	—
399	#396	C₂²×C₁₃	1	2	yes	—
400	#396	C₂²×C₁₃	1	2	yes	—
401	#395	C₂²×C₁₃	1	2	yes	—
402	#395	C₂²×C₁₃	1	2	yes	—
403	#394	C₂²×C₁₃	1	2	yes	—
404	#393	C₂²×C₁₃	1	2	yes	—
405	#391	C₂²×C₁₃	1	1	yes	characteristic
406	#391	C₂²×C₁₃	1	1	yes	characteristic
407	#391	C₂²×C₁₃	1	1	yes	characteristic
408	#391	C₂²×C₁₃	1	1	yes	characteristic
409	#391	C₂²×C₁₃	1	1	yes	characteristic
410	#391	C₂²×C₁₃	1	2	yes	—
411	#390	C₂²×C₁₃	1	1	yes	characteristic
412	#389	C₂²×C₁₃	1	2	yes	—
413	#389	C₂²×C₁₃	1	2	yes	—
414	#389	C₂²×C₁₃	1	2	yes	—
415	#389	C₂²×C₁₃	1	2	yes	—
416	#389	C₂²×C₁₃	1	2	yes	—
417	#389	C₂²×C₁₃	1	2	yes	—
418	#388	C₂²×C₁₃	1	2	yes	—
419	#388	C₂²×C₁₃	1	2	yes	—
420	#388	C₂²×C₁₃	1	2	yes	—
421	#388	C₂²×C₁₃	1	2	yes	—
422	#388	C₂²×C₁₃	1	2	yes	—
423	#388	C₂²×C₁₃	1	2	yes	—
424	#388	C₂²×C₁₃	1	2	yes	—
425	#388	C₂²×C₁₃	1	2	yes	—
426	#388	C₂²×C₁₃	1	2	yes	—
427	#388	C₂²×C₁₃	1	2	yes	—
428	#388	C₂²×C₁₃	1	2	yes	—
429	#388	C₂²×C₁₃	1	2	yes	—
430	#387	C₂²×C₁₃	1	2	yes	—
431	#387	C₂²×C₁₃	1	2	yes	—
432	#387	C₂²×C₁₃	1	2	yes	—
433	#387	C₂²×C₁₃	1	2	yes	—
434	#387	C₂²×C₁₃	1	2	yes	—
435	#387	C₂²×C₁₃	1	2	yes	—
436	#387	C₂²×C₁₃	1	2	yes	—
437	#387	C₂²×C₁₃	1	2	yes	—
438	#387	C₂²×C₁₃	1	2	yes	—
439	#387	C₂²×C₁₃	1	2	yes	—
440	#387	C₂²×C₁₃	1	2	yes	—
441	#387	C₂²×C₁₃	1	2	yes	—
442	#387	C₂²×C₁₃	1	2	yes	—
443	#386	C₂²×C₁₃	1	2	yes	—
444	#385	C₂²×C₁₃	1	2	yes	—
445	#384	C₂²×C₁₃	1	1	yes	characteristic
446	#384	C₂²×C₁₃	1	1	yes	characteristic
447	#382	C₂²×C₁₃	1	1	yes	characteristic
448	#382	C₂²×C₁₃	1	2	yes	—
449	#380	C₂²×C₁₃	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
451	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
460	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
461	#376	C₂²×C₁₃	1	2	yes	—
462	#376	C₂²×C₁₃	1	2	yes	—
463	#376	C₂²×C₁₃	1	2	yes	—
464	C₄³	C₂²×C₁₃	1	1	yes	characteristic
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
473	C₂²×C₁₃	C₂²×#41	1	2	yes	—
474	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
476	C₂²×C₁₃	#585	1	1	yes	characteristic
477	C₄×C₁₃	—	2	4	no	—
478	C₄×C₁₃	—	2	4	no	—
479	C₄×C₁₃	—	2	4	no	—
480	C₄×C₁₃	—	2	4	no	—
481	C₄×C₁₃	—	2	2	no	—
482	C₄×C₁₃	—	2	2	no	—
483	C₄×C₁₃	—	2	2	no	—
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	4	2	no	—
486	C₄×C₁₃	—	4	1	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	1	no	—
490	C₄×C₁₃	—	4	1	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	4	2	no	—
494	C₄×C₁₃	—	4	2	no	—
495	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
500	C₄⋊Q₈	—	2	4	no	—
501	C₄⋊Q₈	—	2	4	no	—
502	#126	—	2	8	no	—
503	#126	—	4	4	no	—
504	#125	—	2	8	no	—
505	#125	—	4	2	no	—
506	#124	—	2	4	no	—
507	#124	—	4	2	no	—
508	C₄×Q₈	—	4	2	no	—
509	C₄×Q₈	—	4	2	no	—
510	#117	—	2	8	no	—
511	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
551	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
552	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
556	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
559	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
562	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
563	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
567	#95	C₂³×C₁₃	1	2	yes	—
568	#95	C₂³×C₁₃	1	2	yes	—
569	#95	C₂³×C₁₃	1	2	yes	—
570	#95	C₂³×C₁₃	1	2	yes	—
571	#95	C₂³×C₁₃	1	2	yes	—
572	#95	C₂³×C₁₃	1	2	yes	—
573	#95	C₂³×C₁₃	1	2	yes	—
574	#95	C₂³×C₁₃	1	2	yes	—
575	#95	C₂³×C₁₃	1	2	yes	—
576	#95	C₂³×C₁₃	1	2	yes	—
577	#95	C₂³×C₁₃	1	2	yes	—
578	#95	C₂³×C₁₃	1	2	yes	—
579	#95	C₂³×C₁₃	1	2	yes	—
580	#95	C₂³×C₁₃	1	2	yes	—
581	#95	C₂³×C₁₃	1	2	yes	—
582	#95	C₂³×C₁₃	1	2	yes	—
583	#95	C₂³×C₁₃	1	2	yes	—
584	#95	C₂³×C₁₃	1	2	yes	—
585	#95	C₂³×C₁₃	1	2	yes	—
586	#95	C₂³×C₁₃	1	2	yes	—
587	#95	C₂³×C₁₃	1	2	yes	—
588	#95	C₂³×C₁₃	1	2	yes	—
589	#95	C₂³×C₁₃	1	2	yes	—
590	#95	C₂³×C₁₃	1	2	yes	—
591	#95	C₂³×C₁₃	1	2	yes	—
592	#95	C₂³×C₁₃	1	2	yes	—
593	C₂×C₁₃	—	8	2	no	—
594	C₂×C₁₃	#3482	1	2	yes	—
595	C₂×C₁₃	#3483	1	1	yes	characteristic
596	C₂×C₁₃	#3495	1	2	yes	—
597	C₂×C₁₃	#3505	1	1	yes	characteristic
598	C₂×C₁₃	#3544	1	1	yes	characteristic
599	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	4	1	no	—
603	C₂×Q₈	—	4	1	no	—
604	C₂×Q₈	—	4	1	no	—
605	C₂×Q₈	—	4	1	no	—
606	C₂×Q₈	—	4	1	no	—
607	C₂×Q₈	—	4	1	no	—
608	C₂×Q₈	C₁₃×#41	1	4	yes	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	4	1	no	—
611	C₂×D₄	—	4	1	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	4	1	no	—
648	C₄⋊C₄	—	4	1	no	—
649	C₄⋊C₄	—	4	1	no	—
650	C₄⋊C₄	—	4	1	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	1	no	—
653	C₄⋊C₄	—	4	1	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	C₁₃×#41	1	8	yes	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	4	no	—
677	C₄²	—	2	2	no	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	4	1	no	—
686	C₄²	—	4	2	no	—
687	C₄²	—	4	1	no	—
688	C₄²	—	4	1	no	—
689	C₁₃	#60042	1	1	yes	characteristic, direct product factor, Sylow
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
698	Q₈	—	4	4	no	—
699	Q₈	—	4	4	no	—
700	Q₈	—	8	2	no	—
701	D₄	—	8	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	8	no	—
745	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
746	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
747	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
748	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
749	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
750	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
751	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
752	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
761	C₂²	C₂²×C₁₃×#41	1	2	yes	—
762	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
763	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
764	C₂²	C₁₃×#585	1	1	yes	characteristic
765	C₄	—	2	2	no	—
766	C₄	—	2	4	no	—
767	C₄	—	2	4	no	—
768	C₄	—	2	4	no	—
769	C₄	—	2	4	no	—
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	2	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₂	—	8	2	no	—
784	C₂	C₁₃×#3482	1	2	yes	—
785	C₂	C₁₃×#3483	1	1	yes	characteristic
786	C₂	C₁₃×#3495	1	2	yes	—
787	C₂	C₁₃×#3505	1	1	yes	characteristic
788	C₂	C₁₃×#3544	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2734	C₂	semidirect
3. C₁₃×#2721	C₂	semidirect
4. C₁₃×#2612	C₂	semidirect
5. C₁₃×#2604	C₂	semidirect
6. C₁₃×#2574	C₂	semidirect
7. C₁₃×#2565	C₂	semidirect
9. C₁₃×#2529	C₂	semidirect
11. C₁₃×#2519	C₂	semidirect
13. C₁₃×#2441	C₂	semidirect
14. C₁₃×#2373	C₂	semidirect
16. C₁₃×#2371	C₂	semidirect
17. C₁₃×#2369	C₂	semidirect
18. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
19. C₁₃×#2298	C₂	semidirect
205. #60042	C₁₃	direct (N × H)
296. #2734	C₂×C₁₃	semidirect
298. #2721	C₂×C₁₃	semidirect
299. #2612	C₂×C₁₃	semidirect
300. #2604	C₂×C₁₃	semidirect
301. #2574	C₂×C₁₃	semidirect
302. #2565	C₂×C₁₃	semidirect
304. #2529	C₂×C₁₃	semidirect
306. #2519	C₂×C₁₃	semidirect
308. #2441	C₂×C₁₃	semidirect
309. #2373	C₂×C₁₃	semidirect
311. #2371	C₂×C₁₃	semidirect
312. #2369	C₂×C₁₃	semidirect
313. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
314. #2298	C₂×C₁₃	semidirect
689. C₁₃	#60042	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×#2734	2
C₁₃×#2731	2
C₁₃×#2721	2
C₁₃×#2612	2
C₁₃×#2604	2
C₁₃×#2574	2
C₁₃×#2565	2
C₁₃×#2545	2
C₁₃×#2529	2
C₁₃×#2521	2
C₁₃×#2519	2
C₁₃×#2479	2
C₁₃×#2441	2
C₁₃×#2373	2
C₁₃×#2372	2
C₁₃×#2371	2
C₁₃×#2369	2
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2298	2
#60042	13

Subgroups — C13×#60042 #15746381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60042 #15746381