Subgroups — C₁₃×#36750 #15723089

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2807	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2788	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2768	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2763	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2729	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2720	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2704	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2704	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2646	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2549	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2442	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2437	C₂	1	2	yes	maximal
16	C₁₃×#2437	C₂	1	2	yes	maximal
17	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#2312	C₂	1	1	yes	maximal, characteristic
19	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#400	C₂²	1	2	yes	complemented
34	C₁₃×#400	C₂²	1	2	yes	complemented
35	C₁₃×#400	C₂²	1	2	yes	complemented
36	C₁₃×#400	C₂²	1	2	yes	complemented
37	C₁₃×#399	C₂²	1	2	yes	—
38	C₁₃×#399	C₂²	1	2	yes	—
39	C₁₃×#398	C₂²	1	2	yes	complemented
40	C₁₃×#398	C₂²	1	2	yes	complemented
41	C₁₃×#398	C₂²	1	2	yes	complemented
42	C₁₃×#398	C₂²	1	2	yes	complemented
43	C₁₃×#398	C₂²	1	2	yes	complemented
44	C₁₃×#398	C₂²	1	2	yes	complemented
45	C₁₃×#398	C₂²	1	2	yes	complemented
46	C₁₃×#398	C₂²	1	2	yes	complemented
47	C₁₃×#396	C₂²	1	2	yes	—
48	C₁₃×#396	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#396	C₂²	1	2	yes	—
51	C₁₃×#395	C₂²	1	2	yes	complemented
52	C₁₃×#395	C₂²	1	2	yes	complemented
53	C₁₃×#395	C₂²	1	2	yes	complemented
54	C₁₃×#395	C₂²	1	2	yes	complemented
55	C₁₃×#393	C₂²	1	2	yes	—
56	C₁₃×#393	C₂²	1	2	yes	—
57	C₁₃×#391	C₂²	1	2	yes	complemented
58	C₁₃×#391	C₂²	1	2	yes	complemented
59	C₁₃×#391	C₂²	1	2	yes	complemented
60	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#389	C₂²	1	2	yes	complemented
62	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#389	C₂²	1	2	yes	complemented
64	C₁₃×#389	C₂²	1	2	yes	complemented
65	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#389	C₂²	1	2	yes	complemented
67	C₁₃×#389	C₂²	1	2	yes	complemented
68	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#388	C₂²	1	2	yes	—
74	C₁₃×#388	C₂²	1	2	yes	—
75	C₁₃×#388	C₂²	1	2	yes	—
76	C₁₃×#388	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	complemented
78	C₁₃×#387	C₂²	1	2	yes	complemented
79	C₁₃×#385	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#385	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#385	C₂²	1	2	yes	—
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#385	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	—
91	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#382	C₂²	1	2	yes	complemented
94	C₁₃×#380	C₂²	1	2	yes	—
95	C₁₃×#380	C₂²	1	2	yes	—
96	C₁₃×#380	C₂²	1	2	yes	—
97	C₁₃×#380	C₂²	1	1	yes	characteristic
98	C₁₃×#380	C₂²	1	1	yes	characteristic
99	C₁₃×#380	C₂²	1	1	yes	characteristic
100	C₁₃×#380	C₂²	1	1	yes	characteristic
101	C₁₃×#380	C₂²	1	2	yes	—
102	C₁₃×#380	C₂²	1	2	yes	—
103	C₁₃×#379	C₂²	1	2	yes	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	—	4	2	no	—
119	C₁₃×#125	—	4	2	no	—
120	C₁₃×#125	—	4	4	no	—
121	C₁₃×C₂²⋊Q₈	—	4	4	no	—
122	C₁₃×C₂²⋊Q₈	—	4	4	no	—
123	C₁₃×C₂²⋊Q₈	—	4	4	no	—
124	C₁₃×C₂²⋊Q₈	—	4	4	no	—
125	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
157	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
159	C₂×C₁₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	—	4	2	no	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	#36750	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂⁴×C₁₃	—	2	2	no	—
209	C₂⁴×C₁₃	—	2	2	no	—
210	C₂⁴×C₁₃	—	4	1	no	—
211	C₂⁴×C₁₃	—	4	1	no	—
212	C₂⁴×C₁₃	—	4	1	no	—
213	C₂⁴×C₁₃	—	4	1	no	—
214	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
215	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
216	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂×Q₈×C₁₃	—	2	4	no	—
218	C₂×Q₈×C₁₃	—	4	2	no	—
219	C₂×Q₈×C₁₃	—	4	2	no	—
220	C₂×Q₈×C₁₃	—	4	2	no	—
221	C₂×Q₈×C₁₃	—	4	2	no	—
222	C₂×Q₈×C₁₃	—	4	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	2	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	4	1	no	—
230	C₂²×C₄×C₁₃	—	4	1	no	—
231	C₂²×C₄×C₁₃	—	4	1	no	—
232	C₂²×C₄×C₁₃	—	4	1	no	—
233	C₂²×C₄×C₁₃	—	4	1	no	—
234	C₂²×C₄×C₁₃	—	4	1	no	—
235	C₂²×C₄×C₁₃	—	4	1	no	—
236	C₂²×C₄×C₁₃	—	4	2	no	—
237	C₂²×C₄×C₁₃	—	4	2	no	—
238	C₂²×C₄×C₁₃	—	4	1	no	—
239	C₂²×C₄×C₁₃	—	4	1	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	4	2	no	—
244	C₂²×C₄×C₁₃	—	4	1	no	—
245	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
246	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	4	2	no	—
269	C₁₃×C₄⋊C₄	—	4	2	no	—
270	C₁₃×C₄⋊C₄	—	4	1	no	—
271	C₁₃×C₄⋊C₄	—	4	1	no	—
272	C₁₃×C₄⋊C₄	—	4	1	no	—
273	C₁₃×C₄⋊C₄	—	4	1	no	—
274	C₁₃×C₄⋊C₄	—	4	2	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	4	2	no	—
277	C₁₃×C₄⋊C₄	—	4	2	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	2	no	—
280	C₁₃×C₄⋊C₄	—	4	2	no	—
281	C₁₃×C₄⋊C₄	—	4	2	no	—
282	C₁₃×C₄⋊C₄	—	4	2	no	—
283	C₁₃×C₄⋊C₄	—	4	2	no	—
284	C₁₃×C₄⋊C₄	—	4	2	no	—
285	C₁₃×C₄⋊C₄	—	4	1	no	—
286	C₁₃×C₄⋊C₄	—	4	1	no	—
287	C₁₃×C₄⋊C₄	—	4	2	no	—
288	C₁₃×C₄⋊C₄	—	4	2	no	—
289	C₁₃×C₄⋊C₄	—	4	2	no	—
290	C₁₃×C₄⋊C₄	—	4	2	no	—
291	C₁₃×C₄⋊C₄	—	4	1	no	—
292	C₁₃×C₄⋊C₄	—	4	2	no	—
293	C₁₃×C₄⋊C₄	—	4	1	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	2	4	no	—
299	C₁₃×C₂²⋊C₄	—	2	4	no	—
300	C₁₃×C₂²⋊C₄	—	4	2	no	—
301	C₁₃×C₂²⋊C₄	—	4	2	no	—
302	C₁₃×C₂²⋊C₄	—	4	2	no	—
303	C₁₃×C₂²⋊C₄	—	4	2	no	—
304	C₁₃×C₂²⋊C₄	—	4	2	no	—
305	C₁₃×C₂²⋊C₄	—	4	2	no	—
306	C₁₃×C₂²⋊C₄	—	4	2	no	—
307	C₁₃×C₂²⋊C₄	—	4	2	no	—
308	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
309	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
310	C₄²×C₁₃	—	2	2	no	—
311	C₄²×C₁₃	—	2	2	no	—
312	C₄²×C₁₃	—	4	1	no	—
313	C₄²×C₁₃	—	4	1	no	—
314	C₄²×C₁₃	—	4	2	no	—
315	C₄²×C₁₃	—	4	2	no	—
316	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#2851	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#2807	C₂×C₁₃	1	2	yes	complemented
319	#2788	C₂×C₁₃	1	2	yes	complemented
320	#2768	C₂×C₁₃	1	2	yes	complemented
321	#2763	C₂×C₁₃	1	2	yes	complemented
322	#2729	C₂×C₁₃	1	2	yes	complemented
323	#2720	C₂×C₁₃	1	2	yes	complemented
324	#2704	C₂×C₁₃	1	2	yes	complemented
325	#2704	C₂×C₁₃	1	2	yes	complemented
326	#2659	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#2646	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#2549	C₂×C₁₃	1	2	yes	complemented
329	#2442	C₂×C₁₃	1	2	yes	complemented
330	#2437	C₂×C₁₃	1	2	yes	—
331	#2437	C₂×C₁₃	1	2	yes	—
332	#2315	C₂×C₁₃	1	1	yes	characteristic
333	#2312	C₂×C₁₃	1	1	yes	characteristic
334	C₂×#388	C₂×C₁₃	1	1	yes	characteristic
335	C₂³×C₁₃	—	2	1	no	—
336	C₂³×C₁₃	—	2	1	no	—
337	C₂³×C₁₃	—	2	1	no	—
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	8	no	—
346	C₂³×C₁₃	—	4	4	no	—
347	C₂³×C₁₃	—	4	4	no	—
348	C₂³×C₁₃	—	8	2	no	—
349	C₂³×C₁₃	—	8	2	no	—
350	C₂³×C₁₃	—	8	2	no	—
351	C₂³×C₁₃	—	8	2	no	—
352	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
353	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
354	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
355	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
356	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
357	Q₈×C₁₃	—	8	4	no	—
358	Q₈×C₁₃	—	8	4	no	—
359	C₂×C₄×C₁₃	—	2	1	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	—	4	4	no	—
407	C₂×C₄×C₁₃	—	4	4	no	—
408	C₂×C₄×C₁₃	—	4	4	no	—
409	C₂×C₄×C₁₃	—	8	2	no	—
410	C₂×C₄×C₁₃	—	8	2	no	—
411	C₂×C₄×C₁₃	—	8	4	no	—
412	C₂×C₄×C₁₃	—	8	4	no	—
413	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
414	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
415	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
416	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
421	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
422	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
423	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
424	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
425	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
426	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
427	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
429	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
430	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
431	#400	C₂²×C₁₃	1	2	yes	complemented
432	#400	C₂²×C₁₃	1	2	yes	complemented
433	#400	C₂²×C₁₃	1	2	yes	complemented
434	#400	C₂²×C₁₃	1	2	yes	complemented
435	#399	C₂²×C₁₃	1	2	yes	—
436	#399	C₂²×C₁₃	1	2	yes	—
437	#398	C₂²×C₁₃	1	2	yes	complemented
438	#398	C₂²×C₁₃	1	2	yes	complemented
439	#398	C₂²×C₁₃	1	2	yes	complemented
440	#398	C₂²×C₁₃	1	2	yes	complemented
441	#398	C₂²×C₁₃	1	2	yes	complemented
442	#398	C₂²×C₁₃	1	2	yes	complemented
443	#398	C₂²×C₁₃	1	2	yes	complemented
444	#398	C₂²×C₁₃	1	2	yes	complemented
445	#396	C₂²×C₁₃	1	2	yes	—
446	#396	C₂²×C₁₃	1	2	yes	—
447	#396	C₂²×C₁₃	1	2	yes	—
448	#396	C₂²×C₁₃	1	2	yes	—
449	#395	C₂²×C₁₃	1	2	yes	complemented
450	#395	C₂²×C₁₃	1	2	yes	complemented
451	#395	C₂²×C₁₃	1	2	yes	complemented
452	#395	C₂²×C₁₃	1	2	yes	complemented
453	#393	C₂²×C₁₃	1	2	yes	—
454	#393	C₂²×C₁₃	1	2	yes	—
455	#391	C₂²×C₁₃	1	2	yes	complemented
456	#391	C₂²×C₁₃	1	2	yes	complemented
457	#391	C₂²×C₁₃	1	2	yes	complemented
458	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#389	C₂²×C₁₃	1	2	yes	complemented
461	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	#389	C₂²×C₁₃	1	2	yes	complemented
464	#389	C₂²×C₁₃	1	2	yes	complemented
465	#389	C₂²×C₁₃	1	2	yes	complemented
466	#389	C₂²×C₁₃	1	2	yes	complemented
467	#388	C₂²×C₁₃	1	2	yes	—
468	#388	C₂²×C₁₃	1	2	yes	—
469	#388	C₂²×C₁₃	1	2	yes	—
470	#388	C₂²×C₁₃	1	2	yes	—
471	#388	C₂²×C₁₃	1	2	yes	—
472	#388	C₂²×C₁₃	1	2	yes	—
473	#388	C₂²×C₁₃	1	2	yes	—
474	#388	C₂²×C₁₃	1	2	yes	—
475	#387	C₂²×C₁₃	1	2	yes	complemented
476	#387	C₂²×C₁₃	1	2	yes	complemented
477	#385	C₂²×C₁₃	1	2	yes	—
478	#385	C₂²×C₁₃	1	2	yes	—
479	#385	C₂²×C₁₃	1	2	yes	—
480	#385	C₂²×C₁₃	1	2	yes	—
481	#385	C₂²×C₁₃	1	2	yes	—
482	#385	C₂²×C₁₃	1	2	yes	—
483	#385	C₂²×C₁₃	1	2	yes	—
484	#385	C₂²×C₁₃	1	2	yes	—
485	#385	C₂²×C₁₃	1	2	yes	—
486	#385	C₂²×C₁₃	1	2	yes	—
487	#385	C₂²×C₁₃	1	2	yes	—
488	#385	C₂²×C₁₃	1	2	yes	—
489	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	#382	C₂²×C₁₃	1	2	yes	complemented
492	#380	C₂²×C₁₃	1	1	yes	characteristic
493	#380	C₂²×C₁₃	1	1	yes	characteristic
494	#380	C₂²×C₁₃	1	1	yes	characteristic
495	#380	C₂²×C₁₃	1	1	yes	characteristic
496	#380	C₂²×C₁₃	1	2	yes	—
497	#380	C₂²×C₁₃	1	2	yes	—
498	#380	C₂²×C₁₃	1	2	yes	—
499	#380	C₂²×C₁₃	1	2	yes	—
500	#380	C₂²×C₁₃	1	2	yes	—
501	#379	C₂²×C₁₃	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
503	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
504	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	2	2	no	—
509	C₂²×C₁₃	—	2	2	no	—
510	C₂²×C₁₃	—	2	2	no	—
511	C₂²×C₁₃	—	2	4	no	—
512	C₂²×C₁₃	—	2	4	no	—
513	C₂²×C₁₃	—	2	4	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	2	no	—
518	C₂²×C₁₃	—	8	8	no	—
519	C₂²×C₁₃	#544	1	4	yes	—
520	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
521	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
525	C₂²×C₁₃	#585	1	1	yes	characteristic
526	C₂²×C₁₃	#585	1	1	yes	characteristic
527	C₄×C₁₃	—	2	2	no	—
528	C₄×C₁₃	—	2	2	no	—
529	C₄×C₁₃	—	2	4	no	—
530	C₄×C₁₃	—	2	2	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	4	1	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	2	no	—
537	C₄×C₁₃	—	4	1	no	—
538	C₄×C₁₃	—	4	2	no	—
539	C₄×C₁₃	—	4	2	no	—
540	C₄×C₁₃	—	4	2	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	—	4	2	no	—
543	C₄×C₁₃	—	4	2	no	—
544	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
545	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
546	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
547	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
552	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
553	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₄⋊Q₈	—	4	2	no	—
556	#125	—	4	2	no	—
557	#125	—	4	4	no	—
558	C₂²⋊Q₈	—	4	4	no	—
559	C₂²⋊Q₈	—	4	4	no	—
560	C₂²⋊Q₈	—	4	4	no	—
561	C₂²⋊Q₈	—	4	4	no	—
562	C₂×C₄⋊C₄	—	4	2	no	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
593	C₂×C₂²⋊C₄	—	4	2	no	—
594	C₂×C₂²⋊C₄	—	4	2	no	—
595	C₂×C₂²⋊C₄	—	4	4	no	—
596	C₂×C₂²⋊C₄	Q₈×C₁₃	1	8	yes	complemented
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄²	—	4	2	no	—
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
620	#95	C₂³×C₁₃	1	2	yes	—
621	#95	C₂³×C₁₃	1	2	yes	—
622	#95	C₂³×C₁₃	1	2	yes	—
623	#95	C₂³×C₁₃	1	2	yes	—
624	#95	C₂³×C₁₃	1	2	yes	—
625	#95	C₂³×C₁₃	1	2	yes	—
626	#95	C₂³×C₁₃	1	2	yes	—
627	#95	C₂³×C₁₃	1	2	yes	—
628	#95	C₂³×C₁₃	1	2	yes	—
629	#95	C₂³×C₁₃	1	2	yes	—
630	#95	C₂³×C₁₃	1	2	yes	—
631	#95	C₂³×C₁₃	1	2	yes	—
632	#95	C₂³×C₁₃	1	2	yes	—
633	#95	C₂³×C₁₃	1	2	yes	—
634	#95	C₂³×C₁₃	1	2	yes	—
635	#95	C₂³×C₁₃	1	2	yes	—
636	#95	C₂³×C₁₃	1	2	yes	—
637	#95	C₂³×C₁₃	1	2	yes	—
638	#95	C₂³×C₁₃	1	2	yes	—
639	#95	C₂³×C₁₃	1	2	yes	—
640	#95	C₂³×C₁₃	1	2	yes	—
641	#95	C₂³×C₁₃	1	2	yes	—
642	#95	C₂³×C₁₃	1	2	yes	—
643	#95	C₂³×C₁₃	1	2	yes	—
644	C₂×C₁₃	—	2	4	no	—
645	C₂×C₁₃	—	4	4	no	—
646	C₂×C₁₃	C₂×#544	1	1	yes	characteristic
647	C₂×C₁₃	#3501	1	1	yes	characteristic
648	C₂×C₁₃	#3501	1	1	yes	characteristic
649	C₂×C₁₃	#3534	1	1	yes	characteristic
650	C₂×C₁₃	#3536	1	1	yes	characteristic
651	C₂×C₁₃	#3558	1	1	yes	characteristic
652	C₂×C₁₃	#3564	1	1	yes	characteristic
653	C₂⁴	—	2	2	no	—
654	C₂⁴	—	2	2	no	—
655	C₂⁴	—	4	1	no	—
656	C₂⁴	—	4	1	no	—
657	C₂⁴	—	4	1	no	—
658	C₂⁴	—	4	1	no	—
659	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
660	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
661	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
662	C₂×Q₈	—	2	4	no	—
663	C₂×Q₈	—	4	2	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×Q₈	—	4	2	no	—
666	C₂×Q₈	—	4	2	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	—	4	1	no	—
678	C₂²×C₄	—	4	1	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	1	no	—
684	C₂²×C₄	—	4	1	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	1	no	—
690	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
691	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
692	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	1	no	—
724	C₄⋊C₄	—	4	1	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	1	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	1	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	1	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
754	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	4	1	no	—
758	C₄²	—	4	1	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	2	no	—
761	C₁₃	#36750	1	1	yes	characteristic, direct product factor, Sylow
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	8	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	8	2	no	—
776	C₂³	—	8	2	no	—
777	C₂³	—	8	2	no	—
778	C₂³	—	8	2	no	—
779	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
780	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
781	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
782	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
783	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
784	Q₈	—	8	4	no	—
785	Q₈	—	8	4	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
841	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
842	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
843	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
844	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	8	no	—
859	C₂²	C₁₃×#544	1	4	yes	—
860	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
861	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
862	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
863	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
864	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
865	C₂²	C₁₃×#585	1	1	yes	characteristic
866	C₂²	C₁₃×#585	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	4	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₂	—	2	4	no	—
885	C₂	—	4	4	no	—
886	C₂	C₂×C₁₃×#544	1	1	yes	characteristic
887	C₂	C₁₃×#3501	1	1	yes	characteristic
888	C₂	C₁₃×#3501	1	1	yes	characteristic
889	C₂	C₁₃×#3534	1	1	yes	characteristic
890	C₂	C₁₃×#3536	1	1	yes	characteristic
891	C₂	C₁₃×#3558	1	1	yes	characteristic
892	C₂	C₁₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×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×#2857	C₂	semidirect
2. C₁₃×#2851	C₂	semidirect
3. C₁₃×#2807	C₂	semidirect
4. C₁₃×#2788	C₂	semidirect
5. C₁₃×#2768	C₂	semidirect
6. C₁₃×#2763	C₂	semidirect
7. C₁₃×#2729	C₂	semidirect
8. C₁₃×#2720	C₂	semidirect
9. C₁₃×#2704	C₂	semidirect
10. C₁₃×#2704	C₂	semidirect
11. C₁₃×#2659	C₂	semidirect
12. C₁₃×#2646	C₂	semidirect
13. C₁₃×#2549	C₂	semidirect
14. C₁₃×#2442	C₂	semidirect
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
22. C₂×C₁₃×#125	C₂²	semidirect
33. C₁₃×#400	C₂²	semidirect
34. C₁₃×#400	C₂²	semidirect
35. C₁₃×#400	C₂²	semidirect
36. C₁₃×#400	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
40. C₁₃×#398	C₂²	semidirect
41. C₁₃×#398	C₂²	semidirect
42. C₁₃×#398	C₂²	semidirect
43. C₁₃×#398	C₂²	semidirect
44. C₁₃×#398	C₂²	semidirect
45. C₁₃×#398	C₂²	semidirect
46. C₁₃×#398	C₂²	semidirect
51. C₁₃×#395	C₂²	semidirect
52. C₁₃×#395	C₂²	semidirect
53. C₁₃×#395	C₂²	semidirect
54. C₁₃×#395	C₂²	semidirect
57. C₁₃×#391	C₂²	semidirect
58. C₁₃×#391	C₂²	semidirect
59. C₁₃×#391	C₂²	semidirect
60. C₁₃×#389	C₂²	semidirect
61. C₁₃×#389	C₂²	semidirect
62. C₁₃×#389	C₂²	semidirect
63. C₁₃×#389	C₂²	semidirect
64. C₁₃×#389	C₂²	semidirect
65. C₁₃×#389	C₂²	semidirect
66. C₁₃×#389	C₂²	semidirect
67. C₁₃×#389	C₂²	semidirect
68. C₁₃×#389	C₂²	semidirect
77. C₁₃×#387	C₂²	semidirect
78. C₁₃×#387	C₂²	semidirect
91. C₁₃×#384	C₂²	semidirect
92. C₁₃×#382	C₂²	semidirect
93. C₁₃×#382	C₂²	semidirect
159. C₂×C₁₃×C₂²⋊C₄	Q₈	semidirect
207. #36750	C₁₃	direct (N × H)
316. #2857	C₂×C₁₃	semidirect
317. #2851	C₂×C₁₃	semidirect
318. #2807	C₂×C₁₃	semidirect
319. #2788	C₂×C₁₃	semidirect
320. #2768	C₂×C₁₃	semidirect
321. #2763	C₂×C₁₃	semidirect
322. #2729	C₂×C₁₃	semidirect
323. #2720	C₂×C₁₃	semidirect
324. #2704	C₂×C₁₃	semidirect
325. #2704	C₂×C₁₃	semidirect
326. #2659	C₂×C₁₃	semidirect
327. #2646	C₂×C₁₃	semidirect
328. #2549	C₂×C₁₃	semidirect
329. #2442	C₂×C₁₃	semidirect
418. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
419. C₂×#125	C₂²×C₁₃	semidirect
420. C₂×#125	C₂²×C₁₃	semidirect
431. #400	C₂²×C₁₃	semidirect
432. #400	C₂²×C₁₃	semidirect
433. #400	C₂²×C₁₃	semidirect
434. #400	C₂²×C₁₃	semidirect
437. #398	C₂²×C₁₃	semidirect
438. #398	C₂²×C₁₃	semidirect
439. #398	C₂²×C₁₃	semidirect
440. #398	C₂²×C₁₃	semidirect
441. #398	C₂²×C₁₃	semidirect
442. #398	C₂²×C₁₃	semidirect
443. #398	C₂²×C₁₃	semidirect
444. #398	C₂²×C₁₃	semidirect
449. #395	C₂²×C₁₃	semidirect
450. #395	C₂²×C₁₃	semidirect
451. #395	C₂²×C₁₃	semidirect
452. #395	C₂²×C₁₃	semidirect
455. #391	C₂²×C₁₃	semidirect
456. #391	C₂²×C₁₃	semidirect
457. #391	C₂²×C₁₃	semidirect
458. #389	C₂²×C₁₃	semidirect
459. #389	C₂²×C₁₃	semidirect
460. #389	C₂²×C₁₃	semidirect
461. #389	C₂²×C₁₃	semidirect
462. #389	C₂²×C₁₃	semidirect
463. #389	C₂²×C₁₃	semidirect
464. #389	C₂²×C₁₃	semidirect
465. #389	C₂²×C₁₃	semidirect
466. #389	C₂²×C₁₃	semidirect
475. #387	C₂²×C₁₃	semidirect
476. #387	C₂²×C₁₃	semidirect
489. #384	C₂²×C₁₃	semidirect
490. #382	C₂²×C₁₃	semidirect
491. #382	C₂²×C₁₃	semidirect
596. C₂×C₂²⋊C₄	Q₈×C₁₃	semidirect
761. C₁₃	#36750	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×#2857	2
C₁₃×#2851	2
C₁₃×#2807	2
C₁₃×#2788	2
C₁₃×#2768	2
C₁₃×#2763	2
C₁₃×#2729	2
C₁₃×#2720	2
C₁₃×#2704	2
C₁₃×#2659	2
C₁₃×#2646	2
C₁₃×#2549	2
C₁₃×#2442	2
C₁₃×#2437	2
C₁₃×#2315	2
C₁₃×#2312	2
C₂×C₁₃×#388	2
#36750	13

Subgroups — C13×#36750 #15723089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36750 #15723089