Subgroups — C₁₃×#36760 #15723099

Order 3328.

1662 conjugacy classes of subgroups.

The subgroup lattice has 876 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×#2798	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2783	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2772	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2754	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2725	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2725	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2721	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2716	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2626	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2626	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2505	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2480	C₂	1	2	yes	maximal
15	C₁₃×#2480	C₂	1	2	yes	maximal
16	C₁₃×#2473	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₁₃×#388	C₂	1	1	yes	maximal, characteristic
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#126	C₂²	1	2	yes	—
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#400	C₂²	1	2	yes	complemented
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×#399	C₂²	1	2	yes	—
37	C₁₃×#399	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	2	yes	complemented
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×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	2	yes	—
44	C₁₃×#397	C₂²	1	2	yes	—
45	C₁₃×#397	C₂²	1	2	yes	—
46	C₁₃×#397	C₂²	1	2	yes	—
47	C₁₃×#397	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×#396	C₂²	1	2	yes	—
52	C₁₃×#396	C₂²	1	2	yes	—
53	C₁₃×#396	C₂²	1	2	yes	—
54	C₁₃×#393	C₂²	1	2	yes	—
55	C₁₃×#393	C₂²	1	2	yes	—
56	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#391	C₂²	1	2	yes	complemented
58	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#391	C₂²	1	2	yes	complemented
60	C₁₃×#389	C₂²	1	2	yes	complemented
61	C₁₃×#389	C₂²	1	2	yes	complemented
62	C₁₃×#389	C₂²	1	2	yes	complemented
63	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#389	C₂²	1	2	yes	complemented
65	C₁₃×#389	C₂²	1	2	yes	complemented
66	C₁₃×#389	C₂²	1	2	yes	complemented
67	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
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×#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×#388	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	complemented
79	C₁₃×#387	C₂²	1	2	yes	complemented
80	C₁₃×#387	C₂²	1	2	yes	complemented
81	C₁₃×#387	C₂²	1	2	yes	complemented
82	C₁₃×#387	C₂²	1	2	yes	complemented
83	C₁₃×#387	C₂²	1	2	yes	complemented
84	C₁₃×#387	C₂²	1	2	yes	complemented
85	C₁₃×#387	C₂²	1	2	yes	complemented
86	C₁₃×#387	C₂²	1	2	yes	complemented
87	C₁₃×#387	C₂²	1	2	yes	complemented
88	C₁₃×#385	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	—
91	C₁₃×#385	C₂²	1	2	yes	—
92	C₁₃×#385	C₂²	1	2	yes	—
93	C₁₃×#385	C₂²	1	2	yes	—
94	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#382	C₂²	1	2	yes	complemented
96	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#380	C₂²	1	2	yes	—
98	C₁₃×#380	C₂²	1	1	yes	characteristic
99	C₁₃×#380	C₂²	1	1	yes	characteristic
100	C₁₃×#380	C₂²	1	2	yes	—
101	C₁₃×#379	C₂²	1	2	yes	—
102	C₁₃×#379	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	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	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	—	4	2	no	—
117	C₁₃×#126	—	4	4	no	—
118	C₁₃×#126	—	4	4	no	—
119	C₁₃×#125	—	4	2	no	—
120	C₁₃×#125	—	4	4	no	—
121	C₁₃×C₂²⋊Q₈	—	2	4	no	—
122	C₁₃×C₂²⋊Q₈	—	2	4	no	—
123	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
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	1	yes	characteristic
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	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	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	—	2	4	no	—
151	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
152	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
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×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×C₄²×C₁₃	—	4	2	no	—
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	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#95	C₂³	1	2	yes	—
206	#36760	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂⁴×C₁₃	—	2	2	no	—
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	C₂⁴	1	2	yes	—
215	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂×Q₈×C₁₃	—	2	2	no	—
217	C₂×Q₈×C₁₃	—	2	2	no	—
218	C₂×Q₈×C₁₃	—	4	1	no	—
219	C₂×Q₈×C₁₃	—	4	1	no	—
220	C₂×Q₈×C₁₃	—	4	1	no	—
221	C₂×Q₈×C₁₃	—	4	1	no	—
222	C₂²×C₄×C₁₃	—	2	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	1	no	—
237	C₂²×C₄×C₁₃	—	4	1	no	—
238	C₂²×C₄×C₁₃	—	4	1	no	—
239	C₂²×C₄×C₁₃	#41	1	4	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	4	2	no	—
267	C₁₃×C₄⋊C₄	—	4	1	no	—
268	C₁₃×C₄⋊C₄	—	4	1	no	—
269	C₁₃×C₄⋊C₄	—	4	2	no	—
270	C₁₃×C₄⋊C₄	—	4	2	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	—	4	2	no	—
274	C₁₃×C₄⋊C₄	—	4	1	no	—
275	C₁₃×C₄⋊C₄	—	4	1	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×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	4	2	no	—
292	C₁₃×C₂²⋊C₄	—	4	2	no	—
293	C₁₃×C₂²⋊C₄	—	4	2	no	—
294	C₁₃×C₂²⋊C₄	—	4	2	no	—
295	C₁₃×C₂²⋊C₄	—	4	2	no	—
296	C₁₃×C₂²⋊C₄	—	4	2	no	—
297	C₁₃×C₂²⋊C₄	—	4	2	no	—
298	C₁₃×C₂²⋊C₄	—	4	2	no	—
299	C₁₃×C₂²⋊C₄	—	4	2	no	—
300	C₁₃×C₂²⋊C₄	—	4	2	no	—
301	C₄²×C₁₃	—	2	2	no	—
302	C₄²×C₁₃	—	2	2	no	—
303	C₄²×C₁₃	—	4	1	no	—
304	C₄²×C₁₃	—	4	1	no	—
305	C₄²×C₁₃	—	4	2	no	—
306	C₄²×C₁₃	—	4	2	no	—
307	C₄²×C₁₃	—	4	2	no	—
308	C₄²×C₁₃	—	4	2	no	—
309	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#2851	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#2798	C₂×C₁₃	1	2	yes	complemented
312	#2783	C₂×C₁₃	1	2	yes	complemented
313	#2772	C₂×C₁₃	1	2	yes	complemented
314	#2754	C₂×C₁₃	1	2	yes	complemented
315	#2725	C₂×C₁₃	1	2	yes	complemented
316	#2725	C₂×C₁₃	1	2	yes	complemented
317	#2721	C₂×C₁₃	1	2	yes	complemented
318	#2716	C₂×C₁₃	1	2	yes	complemented
319	#2626	C₂×C₁₃	1	1	yes	characteristic
320	#2626	C₂×C₁₃	1	1	yes	characteristic
321	#2505	C₂×C₁₃	1	2	yes	complemented
322	#2480	C₂×C₁₃	1	2	yes	—
323	#2480	C₂×C₁₃	1	2	yes	—
324	#2473	C₂×C₁₃	1	2	yes	complemented
325	#2329	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#2329	C₂×C₁₃	1	1	yes	characteristic, complemented
327	C₂×#388	C₂×C₁₃	1	1	yes	characteristic
328	C₂³×C₁₃	—	2	1	no	—
329	C₂³×C₁₃	—	2	1	no	—
330	C₂³×C₁₃	—	2	1	no	—
331	C₂³×C₁₃	—	2	1	no	—
332	C₂³×C₁₃	—	2	2	no	—
333	C₂³×C₁₃	—	2	2	no	—
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	2	no	—
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	2	2	no	—
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	4	4	no	—
340	C₂³×C₁₃	—	4	4	no	—
341	C₂³×C₁₃	—	4	4	no	—
342	C₂³×C₁₃	—	8	2	no	—
343	C₂³×C₁₃	—	8	2	no	—
344	C₂³×C₁₃	—	8	2	no	—
345	C₂³×C₁₃	—	8	2	no	—
346	C₂³×C₁₃	C₂×#41	1	2	yes	—
347	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
348	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
349	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
350	Q₈×C₁₃	—	8	2	no	—
351	Q₈×C₁₃	—	8	2	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	2	1	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	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	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	1	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	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	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	2	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	1	no	—
399	C₂×C₄×C₁₃	—	4	4	no	—
400	C₂×C₄×C₁₃	—	4	4	no	—
401	C₂×C₄×C₁₃	—	4	4	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	8	2	no	—
404	C₂×C₄×C₁₃	—	8	2	no	—
405	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
406	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
407	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
408	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
409	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	C₂×#126	C₂²×C₁₃	1	2	yes	—
411	C₂×#126	C₂²×C₁₃	1	2	yes	—
412	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
414	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
417	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
418	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
421	#400	C₂²×C₁₃	1	2	yes	complemented
422	#400	C₂²×C₁₃	1	2	yes	complemented
423	#400	C₂²×C₁₃	1	2	yes	complemented
424	#400	C₂²×C₁₃	1	2	yes	complemented
425	#399	C₂²×C₁₃	1	2	yes	—
426	#399	C₂²×C₁₃	1	2	yes	—
427	#398	C₂²×C₁₃	1	2	yes	complemented
428	#398	C₂²×C₁₃	1	2	yes	complemented
429	#398	C₂²×C₁₃	1	2	yes	complemented
430	#398	C₂²×C₁₃	1	2	yes	complemented
431	#397	C₂²×C₁₃	1	2	yes	—
432	#397	C₂²×C₁₃	1	2	yes	—
433	#397	C₂²×C₁₃	1	2	yes	—
434	#397	C₂²×C₁₃	1	2	yes	—
435	#397	C₂²×C₁₃	1	2	yes	—
436	#397	C₂²×C₁₃	1	2	yes	—
437	#396	C₂²×C₁₃	1	2	yes	—
438	#396	C₂²×C₁₃	1	2	yes	—
439	#396	C₂²×C₁₃	1	2	yes	—
440	#396	C₂²×C₁₃	1	2	yes	—
441	#396	C₂²×C₁₃	1	2	yes	—
442	#396	C₂²×C₁₃	1	2	yes	—
443	#393	C₂²×C₁₃	1	2	yes	—
444	#393	C₂²×C₁₃	1	2	yes	—
445	#391	C₂²×C₁₃	1	2	yes	complemented
446	#391	C₂²×C₁₃	1	2	yes	complemented
447	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	#389	C₂²×C₁₃	1	2	yes	complemented
450	#389	C₂²×C₁₃	1	2	yes	complemented
451	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	#389	C₂²×C₁₃	1	2	yes	complemented
454	#389	C₂²×C₁₃	1	2	yes	complemented
455	#389	C₂²×C₁₃	1	2	yes	complemented
456	#389	C₂²×C₁₃	1	2	yes	complemented
457	#388	C₂²×C₁₃	1	2	yes	—
458	#388	C₂²×C₁₃	1	2	yes	—
459	#388	C₂²×C₁₃	1	2	yes	—
460	#388	C₂²×C₁₃	1	2	yes	—
461	#388	C₂²×C₁₃	1	2	yes	—
462	#388	C₂²×C₁₃	1	2	yes	—
463	#388	C₂²×C₁₃	1	2	yes	—
464	#388	C₂²×C₁₃	1	2	yes	—
465	#388	C₂²×C₁₃	1	2	yes	—
466	#388	C₂²×C₁₃	1	2	yes	—
467	#387	C₂²×C₁₃	1	2	yes	complemented
468	#387	C₂²×C₁₃	1	2	yes	complemented
469	#387	C₂²×C₁₃	1	2	yes	complemented
470	#387	C₂²×C₁₃	1	2	yes	complemented
471	#387	C₂²×C₁₃	1	2	yes	complemented
472	#387	C₂²×C₁₃	1	2	yes	complemented
473	#387	C₂²×C₁₃	1	2	yes	complemented
474	#387	C₂²×C₁₃	1	2	yes	complemented
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	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
485	#382	C₂²×C₁₃	1	2	yes	complemented
486	#380	C₂²×C₁₃	1	1	yes	characteristic
487	#380	C₂²×C₁₃	1	1	yes	characteristic
488	#380	C₂²×C₁₃	1	2	yes	—
489	#380	C₂²×C₁₃	1	2	yes	—
490	#379	C₂²×C₁₃	1	2	yes	—
491	#379	C₂²×C₁₃	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
493	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
494	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
495	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
496	C₂²×C₁₃	—	2	2	no	—
497	C₂²×C₁₃	—	2	2	no	—
498	C₂²×C₁₃	—	2	2	no	—
499	C₂²×C₁₃	—	2	2	no	—
500	C₂²×C₁₃	—	2	2	no	—
501	C₂²×C₁₃	—	2	2	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	4	2	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	8	8	no	—
510	C₂²×C₁₃	#541	1	4	yes	—
511	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
512	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
515	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
516	C₂²×C₁₃	#585	1	1	yes	characteristic
517	C₂²×C₁₃	#585	1	1	yes	characteristic
518	C₄×C₁₃	—	2	2	no	—
519	C₄×C₁₃	—	2	2	no	—
520	C₄×C₁₃	—	2	2	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	4	2	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	1	no	—
529	C₄×C₁₃	—	4	2	no	—
530	C₄×C₁₃	—	4	1	no	—
531	C₄×C₁₃	—	4	2	no	—
532	C₄×C₁₃	—	4	2	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
536	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₄⋊Q₈	—	4	2	no	—
545	#126	—	4	4	no	—
546	#126	—	4	4	no	—
547	#125	—	4	2	no	—
548	#125	—	4	4	no	—
549	C₂²⋊Q₈	—	2	4	no	—
550	C₂²⋊Q₈	—	2	4	no	—
551	C₂×C₄⋊C₄	—	4	2	no	—
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	4	no	—
579	C₂×C₂²⋊C₄	—	4	2	no	—
580	C₂×C₂²⋊C₄	—	4	2	no	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄²	—	4	2	no	—
600	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
608	#95	C₂³×C₁₃	1	2	yes	—
609	#95	C₂³×C₁₃	1	2	yes	—
610	#95	C₂³×C₁₃	1	2	yes	—
611	#95	C₂³×C₁₃	1	2	yes	—
612	#95	C₂³×C₁₃	1	2	yes	—
613	#95	C₂³×C₁₃	1	2	yes	—
614	#95	C₂³×C₁₃	1	2	yes	—
615	#95	C₂³×C₁₃	1	2	yes	—
616	#95	C₂³×C₁₃	1	2	yes	—
617	#95	C₂³×C₁₃	1	2	yes	—
618	#95	C₂³×C₁₃	1	2	yes	—
619	#95	C₂³×C₁₃	1	2	yes	—
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	C₂×C₁₃	—	2	4	no	—
635	C₂×C₁₃	—	8	2	no	—
636	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
637	C₂×C₁₃	#3505	1	1	yes	characteristic
638	C₂×C₁₃	#3506	1	1	yes	characteristic
639	C₂×C₁₃	#3535	1	1	yes	characteristic
640	C₂×C₁₃	#3536	1	1	yes	characteristic
641	C₂×C₁₃	#3561	1	1	yes	characteristic
642	C₂×C₁₃	#3564	1	1	yes	characteristic
643	C₂⁴	—	2	2	no	—
644	C₂⁴	—	2	2	no	—
645	C₂⁴	—	2	2	no	—
646	C₂⁴	—	4	1	no	—
647	C₂⁴	—	4	1	no	—
648	C₂⁴	—	4	1	no	—
649	C₂⁴	—	4	1	no	—
650	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
651	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	4	1	no	—
655	C₂×Q₈	—	4	1	no	—
656	C₂×Q₈	—	4	1	no	—
657	C₂×Q₈	—	4	1	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	—	4	1	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	C₁₃×#41	1	4	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	1	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	1	no	—
713	C₄⋊C₄	—	4	1	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	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	4	1	no	—
740	C₄²	—	4	1	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₁₃	#36760	1	1	yes	characteristic, direct product factor, Sylow
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	4	no	—
760	C₂³	—	8	2	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	2	no	—
763	C₂³	—	8	2	no	—
764	C₂³	C₂×C₁₃×#41	1	2	yes	—
765	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
766	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
767	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
768	Q₈	—	8	2	no	—
769	Q₈	—	8	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	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	1	no	—
803	C₂×C₄	—	2	1	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	2	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	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
824	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
825	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
826	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	8	8	no	—
841	C₂²	C₁₃×#541	1	4	yes	—
842	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
843	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
845	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
846	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
847	C₂²	C₁₃×#585	1	1	yes	characteristic
848	C₂²	C₁₃×#585	1	1	yes	characteristic
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₂	—	2	4	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
869	C₂	C₁₃×#3505	1	1	yes	characteristic
870	C₂	C₁₃×#3506	1	1	yes	characteristic
871	C₂	C₁₃×#3535	1	1	yes	characteristic
872	C₂	C₁₃×#3536	1	1	yes	characteristic
873	C₂	C₁₃×#3561	1	1	yes	characteristic
874	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×#2798	C₂	semidirect
4. C₁₃×#2783	C₂	semidirect
5. C₁₃×#2772	C₂	semidirect
6. C₁₃×#2754	C₂	semidirect
7. C₁₃×#2725	C₂	semidirect
8. C₁₃×#2725	C₂	semidirect
9. C₁₃×#2721	C₂	semidirect
10. C₁₃×#2716	C₂	semidirect
13. C₁₃×#2505	C₂	semidirect
16. C₁₃×#2473	C₂	semidirect
17. C₁₃×#2329	C₂	semidirect
18. C₁₃×#2329	C₂	semidirect
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×#125	C₂²	semidirect
24. C₂×C₁₃×#125	C₂²	semidirect
32. C₁₃×#400	C₂²	semidirect
33. C₁₃×#400	C₂²	semidirect
34. C₁₃×#400	C₂²	semidirect
35. C₁₃×#400	C₂²	semidirect
38. C₁₃×#398	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
40. C₁₃×#398	C₂²	semidirect
41. C₁₃×#398	C₂²	semidirect
56. C₁₃×#391	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
78. C₁₃×#387	C₂²	semidirect
79. C₁₃×#387	C₂²	semidirect
80. C₁₃×#387	C₂²	semidirect
81. C₁₃×#387	C₂²	semidirect
82. C₁₃×#387	C₂²	semidirect
83. C₁₃×#387	C₂²	semidirect
84. C₁₃×#387	C₂²	semidirect
85. C₁₃×#387	C₂²	semidirect
86. C₁₃×#387	C₂²	semidirect
87. C₁₃×#387	C₂²	semidirect
94. C₁₃×#384	C₂²	semidirect
95. C₁₃×#382	C₂²	semidirect
96. C₁₃×#382	C₂²	semidirect
206. #36760	C₁₃	direct (N × H)
309. #2857	C₂×C₁₃	semidirect
310. #2851	C₂×C₁₃	semidirect
311. #2798	C₂×C₁₃	semidirect
312. #2783	C₂×C₁₃	semidirect
313. #2772	C₂×C₁₃	semidirect
314. #2754	C₂×C₁₃	semidirect
315. #2725	C₂×C₁₃	semidirect
316. #2725	C₂×C₁₃	semidirect
317. #2721	C₂×C₁₃	semidirect
318. #2716	C₂×C₁₃	semidirect
321. #2505	C₂×C₁₃	semidirect
324. #2473	C₂×C₁₃	semidirect
325. #2329	C₂×C₁₃	semidirect
326. #2329	C₂×C₁₃	semidirect
409. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
412. C₂×#125	C₂²×C₁₃	semidirect
413. C₂×#125	C₂²×C₁₃	semidirect
421. #400	C₂²×C₁₃	semidirect
422. #400	C₂²×C₁₃	semidirect
423. #400	C₂²×C₁₃	semidirect
424. #400	C₂²×C₁₃	semidirect
427. #398	C₂²×C₁₃	semidirect
428. #398	C₂²×C₁₃	semidirect
429. #398	C₂²×C₁₃	semidirect
430. #398	C₂²×C₁₃	semidirect
445. #391	C₂²×C₁₃	semidirect
446. #391	C₂²×C₁₃	semidirect
447. #391	C₂²×C₁₃	semidirect
448. #391	C₂²×C₁₃	semidirect
449. #389	C₂²×C₁₃	semidirect
450. #389	C₂²×C₁₃	semidirect
451. #389	C₂²×C₁₃	semidirect
452. #389	C₂²×C₁₃	semidirect
453. #389	C₂²×C₁₃	semidirect
454. #389	C₂²×C₁₃	semidirect
455. #389	C₂²×C₁₃	semidirect
456. #389	C₂²×C₁₃	semidirect
467. #387	C₂²×C₁₃	semidirect
468. #387	C₂²×C₁₃	semidirect
469. #387	C₂²×C₁₃	semidirect
470. #387	C₂²×C₁₃	semidirect
471. #387	C₂²×C₁₃	semidirect
472. #387	C₂²×C₁₃	semidirect
473. #387	C₂²×C₁₃	semidirect
474. #387	C₂²×C₁₃	semidirect
475. #387	C₂²×C₁₃	semidirect
476. #387	C₂²×C₁₃	semidirect
483. #384	C₂²×C₁₃	semidirect
484. #382	C₂²×C₁₃	semidirect
485. #382	C₂²×C₁₃	semidirect
745. C₁₃	#36760	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×#2798	2
C₁₃×#2783	2
C₁₃×#2772	2
C₁₃×#2754	2
C₁₃×#2725	2
C₁₃×#2721	2
C₁₃×#2716	2
C₁₃×#2626	2
C₁₃×#2505	2
C₁₃×#2480	2
C₁₃×#2473	2
C₁₃×#2329	2
C₂×C₁₃×#388	2
#36760	13

Subgroups — C13×#36760 #15723099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36760 #15723099