Subgroups — C₁₃×#34432 #15720771

Order 3328.

2010 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2382	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2381	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2371	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2368	C₂	1	2	yes	maximal
6	C₁₃×#2365	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2360	C₂	1	2	yes	maximal
8	C₁₃×#2343	C₂	1	2	yes	maximal
9	C₁₃×#2343	C₂	1	2	yes	maximal
10	C₁₃×#2336	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2336	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2331	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2329	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#2329	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2327	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2313	C₂	1	1	yes	maximal, characteristic
17	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
18	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
19	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic
20	C₁₃×#544	C₄	1	16	yes	complemented
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#125	C₂²	1	2	yes	—
24	C₂×C₁₃×#125	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#391	C₂²	1	1	yes	characteristic
36	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#391	C₂²	1	2	yes	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#391	C₂²	1	2	yes	—
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	2	yes	—
45	C₁₃×#389	C₂²	1	2	yes	—
46	C₁₃×#389	C₂²	1	2	yes	—
47	C₁₃×#389	C₂²	1	2	yes	—
48	C₁₃×#389	C₂²	1	2	yes	—
49	C₁₃×#387	C₂²	1	2	yes	—
50	C₁₃×#387	C₂²	1	2	yes	—
51	C₁₃×#387	C₂²	1	2	yes	—
52	C₁₃×#387	C₂²	1	2	yes	—
53	C₁₃×#387	C₂²	1	2	yes	—
54	C₁₃×#387	C₂²	1	2	yes	—
55	C₁₃×#387	C₂²	1	2	yes	—
56	C₁₃×#387	C₂²	1	2	yes	—
57	C₁₃×#387	C₂²	1	2	yes	—
58	C₁₃×#387	C₂²	1	2	yes	—
59	C₁₃×#387	C₂²	1	2	yes	—
60	C₁₃×#387	C₂²	1	2	yes	—
61	C₁₃×#387	C₂²	1	2	yes	—
62	C₁₃×#387	C₂²	1	2	yes	—
63	C₁₃×#387	C₂²	1	2	yes	—
64	C₁₃×#387	C₂²	1	2	yes	—
65	C₁₃×#387	C₂²	1	2	yes	—
66	C₁₃×#387	C₂²	1	2	yes	—
67	C₁₃×#387	C₂²	1	2	yes	—
68	C₁₃×#387	C₂²	1	2	yes	—
69	C₁₃×#387	C₂²	1	2	yes	—
70	C₁₃×#387	C₂²	1	2	yes	—
71	C₁₃×#387	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×#385	C₂²	1	2	yes	—
78	C₁₃×#385	C₂²	1	2	yes	—
79	C₁₃×#385	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#383	C₂²	1	2	yes	—
82	C₁₃×#383	C₂²	1	2	yes	—
83	C₁₃×#382	C₂²	1	2	yes	—
84	C₁₃×#382	C₂²	1	2	yes	—
85	C₁₃×#381	C₂²	1	2	yes	—
86	C₁₃×#380	C₂²	1	1	yes	characteristic
87	C₁₃×#380	C₂²	1	1	yes	characteristic
88	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
89	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
90	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
97	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₁₃×#376	C₂²	1	2	yes	—
103	C₁₃×#376	C₂²	1	2	yes	—
104	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
105	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
107	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
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	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
119	C₁₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
120	C₁₃×#125	C₂×C₄	1	16	yes	complemented
121	C₁₃×#125	C₂×C₄	1	16	yes	complemented
122	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
123	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
124	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
125	C₄×Q₈×C₁₃	—	4	2	no	—
126	C₄×Q₈×C₁₃	—	4	2	no	—
127	C₄×Q₈×C₁₃	—	4	4	no	—
128	C₁₃×#117	C₂×C₄	1	16	yes	—
129	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	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	1	yes	characteristic
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	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×C₄²×C₁₃	—	4	2	no	—
161	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₁₃×#95	C₂³	1	2	yes	—
178	C₁₃×#95	C₂³	1	2	yes	—
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	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	#34432	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₂×Q₈×C₁₃	—	4	1	no	—
212	C₂×Q₈×C₁₃	—	4	1	no	—
213	C₂×Q₈×C₁₃	—	4	2	no	—
214	C₂×Q₈×C₁₃	—	4	2	no	—
215	C₂×Q₈×C₁₃	—	4	1	no	—
216	C₂×Q₈×C₁₃	—	4	1	no	—
217	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
218	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
219	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	2	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	—	4	1	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	C₂²×C₄	1	4	yes	—
239	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
240	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
263	C₁₃×C₄⋊C₄	—	4	2	no	—
264	C₁₃×C₄⋊C₄	—	4	2	no	—
265	C₁₃×C₄⋊C₄	—	4	2	no	—
266	C₁₃×C₄⋊C₄	—	4	1	no	—
267	C₁₃×C₄⋊C₄	—	4	1	no	—
268	C₁₃×C₄⋊C₄	—	4	2	no	—
269	C₁₃×C₄⋊C₄	—	4	1	no	—
270	C₁₃×C₄⋊C₄	—	4	1	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
274	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
275	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
276	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
277	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
278	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
279	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
280	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
281	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
282	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
283	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
287	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
288	C₄²×C₁₃	—	2	2	no	—
289	C₄²×C₁₃	—	2	2	no	—
290	C₄²×C₁₃	—	2	4	no	—
291	C₄²×C₁₃	—	2	4	no	—
292	C₄²×C₁₃	—	4	1	no	—
293	C₄²×C₁₃	—	4	1	no	—
294	C₄²×C₁₃	—	4	2	no	—
295	C₄²×C₁₃	—	4	2	no	—
296	C₄²×C₁₃	—	4	2	no	—
297	C₄²×C₁₃	—	4	2	no	—
298	C₄²×C₁₃	—	4	2	no	—
299	C₄²×C₁₃	—	4	2	no	—
300	C₄²×C₁₃	—	4	2	no	—
301	C₄²×C₁₃	—	4	2	no	—
302	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
303	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
304	C₂×#544	C₂×C₁₃	1	1	yes	characteristic
305	#2382	C₂×C₁₃	1	2	yes	complemented
306	#2381	C₂×C₁₃	1	2	yes	complemented
307	#2371	C₂×C₁₃	1	2	yes	complemented
308	#2368	C₂×C₁₃	1	2	yes	—
309	#2365	C₂×C₁₃	1	2	yes	complemented
310	#2360	C₂×C₁₃	1	2	yes	—
311	#2343	C₂×C₁₃	1	2	yes	—
312	#2343	C₂×C₁₃	1	2	yes	—
313	#2336	C₂×C₁₃	1	2	yes	complemented
314	#2336	C₂×C₁₃	1	2	yes	complemented
315	#2331	C₂×C₁₃	1	2	yes	complemented
316	#2329	C₂×C₁₃	1	1	yes	characteristic
317	#2329	C₂×C₁₃	1	1	yes	characteristic
318	#2327	C₂×C₁₃	1	2	yes	complemented
319	#2313	C₂×C₁₃	1	1	yes	characteristic
320	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
321	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
322	C₂×#387	C₂×C₁₃	1	1	yes	characteristic
323	C₂³×C₁₃	—	2	1	no	—
324	C₂³×C₁₃	—	2	1	no	—
325	C₂³×C₁₃	—	2	1	no	—
326	C₂³×C₁₃	—	2	1	no	—
327	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
328	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
329	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
330	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
331	Q₈×C₁₃	—	4	4	no	—
332	Q₈×C₁₃	—	4	4	no	—
333	Q₈×C₁₃	—	4	8	no	—
334	C₂×C₄×C₁₃	—	2	8	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	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	1	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	1	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	1	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	2	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	1	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	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	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	4	4	no	—
380	C₂×C₄×C₁₃	—	4	4	no	—
381	C₂×C₄×C₁₃	—	4	4	no	—
382	C₂×C₄×C₁₃	—	4	4	no	—
383	C₂×C₄×C₁₃	—	8	2	no	—
384	C₂×C₄×C₁₃	—	8	2	no	—
385	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
386	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
387	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
388	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
389	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
390	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
391	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
392	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
393	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
394	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
395	#544	C₄×C₁₃	1	16	yes	complemented
396	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
397	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
398	C₂×#125	C₂²×C₁₃	1	2	yes	—
399	C₂×#125	C₂²×C₁₃	1	2	yes	—
400	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
403	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
405	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#117	C₂²×C₁₃	1	2	yes	—
407	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
410	#391	C₂²×C₁₃	1	2	yes	—
411	#391	C₂²×C₁₃	1	2	yes	—
412	#391	C₂²×C₁₃	1	2	yes	—
413	#391	C₂²×C₁₃	1	1	yes	characteristic
414	#391	C₂²×C₁₃	1	2	yes	—
415	#391	C₂²×C₁₃	1	2	yes	—
416	#391	C₂²×C₁₃	1	1	yes	characteristic
417	#389	C₂²×C₁₃	1	2	yes	—
418	#389	C₂²×C₁₃	1	2	yes	—
419	#389	C₂²×C₁₃	1	2	yes	—
420	#389	C₂²×C₁₃	1	1	yes	characteristic
421	#389	C₂²×C₁₃	1	2	yes	—
422	#389	C₂²×C₁₃	1	2	yes	—
423	#389	C₂²×C₁₃	1	1	yes	characteristic
424	#387	C₂²×C₁₃	1	2	yes	—
425	#387	C₂²×C₁₃	1	2	yes	—
426	#387	C₂²×C₁₃	1	2	yes	—
427	#387	C₂²×C₁₃	1	2	yes	—
428	#387	C₂²×C₁₃	1	2	yes	—
429	#387	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	#387	C₂²×C₁₃	1	2	yes	—
444	#387	C₂²×C₁₃	1	2	yes	—
445	#387	C₂²×C₁₃	1	2	yes	—
446	#387	C₂²×C₁₃	1	2	yes	—
447	#387	C₂²×C₁₃	1	2	yes	—
448	#387	C₂²×C₁₃	1	2	yes	—
449	#387	C₂²×C₁₃	1	2	yes	—
450	#387	C₂²×C₁₃	1	2	yes	—
451	#387	C₂²×C₁₃	1	2	yes	—
452	#385	C₂²×C₁₃	1	2	yes	—
453	#385	C₂²×C₁₃	1	2	yes	—
454	#385	C₂²×C₁₃	1	2	yes	—
455	#385	C₂²×C₁₃	1	2	yes	—
456	#383	C₂²×C₁₃	1	2	yes	—
457	#383	C₂²×C₁₃	1	2	yes	—
458	#382	C₂²×C₁₃	1	2	yes	—
459	#382	C₂²×C₁₃	1	2	yes	—
460	#381	C₂²×C₁₃	1	2	yes	—
461	#380	C₂²×C₁₃	1	1	yes	characteristic
462	#380	C₂²×C₁₃	1	1	yes	characteristic
463	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
468	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
469	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
471	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
472	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
474	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
475	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
476	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
477	#376	C₂²×C₁₃	1	2	yes	—
478	#376	C₂²×C₁₃	1	2	yes	—
479	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
480	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
482	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
483	C₂²×C₁₃	—	2	2	no	—
484	C₂²×C₁₃	—	2	2	no	—
485	C₂²×C₁₃	—	2	2	no	—
486	C₂²×C₁₃	—	2	2	no	—
487	C₂²×C₁₃	—	2	2	no	—
488	C₂²×C₁₃	—	2	2	no	—
489	C₂²×C₁₃	#519	1	4	yes	—
490	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
491	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
493	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
494	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
495	C₂²×C₁₃	#585	1	1	yes	characteristic
496	C₂²×C₁₃	#585	1	1	yes	characteristic
497	C₄×C₁₃	—	2	4	no	—
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	2	2	no	—
500	C₄×C₁₃	—	2	4	no	—
501	C₄×C₁₃	—	2	4	no	—
502	C₄×C₁₃	—	2	4	no	—
503	C₄×C₁₃	—	2	4	no	—
504	C₄×C₁₃	—	2	4	no	—
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	2	2	no	—
507	C₄×C₁₃	—	4	2	no	—
508	C₄×C₁₃	—	4	1	no	—
509	C₄×C₁₃	—	4	2	no	—
510	C₄×C₁₃	—	4	2	no	—
511	C₄×C₁₃	—	4	1	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₄×C₁₃	—	4	2	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
517	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
525	C₄⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
526	C₄⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
527	#125	C₂×C₄×C₁₃	1	16	yes	complemented
528	#125	C₂×C₄×C₁₃	1	16	yes	complemented
529	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
530	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
531	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
532	C₄×Q₈	—	4	2	no	—
533	C₄×Q₈	—	4	2	no	—
534	C₄×Q₈	—	4	4	no	—
535	#117	C₂×C₄×C₁₃	1	16	yes	—
536	C₂×C₄⋊C₄	—	4	2	no	—
537	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄²	—	4	2	no	—
568	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
572	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
574	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
576	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
583	C₂×C₄²	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	#95	C₂³×C₁₃	1	2	yes	—
594	#95	C₂³×C₁₃	1	2	yes	—
595	#95	C₂³×C₁₃	1	2	yes	—
596	#95	C₂³×C₁₃	1	2	yes	—
597	#95	C₂³×C₁₃	1	2	yes	—
598	#95	C₂³×C₁₃	1	2	yes	—
599	#95	C₂³×C₁₃	1	2	yes	—
600	#95	C₂³×C₁₃	1	2	yes	—
601	#95	C₂³×C₁₃	1	2	yes	—
602	#95	C₂³×C₁₃	1	2	yes	—
603	#95	C₂³×C₁₃	1	2	yes	—
604	#95	C₂³×C₁₃	1	2	yes	—
605	#95	C₂³×C₁₃	1	2	yes	—
606	#95	C₂³×C₁₃	1	2	yes	—
607	#95	C₂³×C₁₃	1	2	yes	—
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	C₂×C₁₃	—	2	4	no	—
617	C₂×C₁₃	C₂×#519	1	1	yes	characteristic
618	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
620	C₂×C₁₃	#3535	1	1	yes	characteristic
621	C₂×C₁₃	#3538	1	1	yes	characteristic
622	C₂×C₁₃	#3563	1	1	yes	characteristic
623	C₂×C₁₃	#3564	1	1	yes	characteristic
624	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
625	C₂×Q₈	—	4	1	no	—
626	C₂×Q₈	—	4	1	no	—
627	C₂×Q₈	—	4	2	no	—
628	C₂×Q₈	—	4	2	no	—
629	C₂×Q₈	—	4	1	no	—
630	C₂×Q₈	—	4	1	no	—
631	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
632	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
633	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	4	1	no	—
643	C₂²×C₄	—	4	1	no	—
644	C₂²×C₄	—	4	1	no	—
645	C₂²×C₄	—	4	1	no	—
646	C₂²×C₄	—	4	1	no	—
647	C₂²×C₄	—	4	1	no	—
648	C₂²×C₄	—	4	1	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	—	4	1	no	—
652	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
653	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
654	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
655	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	—	4	1	no	—
679	C₄⋊C₄	—	4	2	no	—
680	C₄⋊C₄	—	4	2	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	—	4	1	no	—
685	C₄⋊C₄	—	4	1	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
688	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
689	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
690	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
691	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
692	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
693	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
694	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
695	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
696	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
697	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
701	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	4	1	no	—
707	C₄²	—	4	1	no	—
708	C₄²	—	4	2	no	—
709	C₄²	—	4	2	no	—
710	C₄²	—	4	2	no	—
711	C₄²	—	4	2	no	—
712	C₄²	—	4	2	no	—
713	C₄²	—	4	2	no	—
714	C₄²	—	4	2	no	—
715	C₄²	—	4	2	no	—
716	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
717	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
718	C₁₃	#34432	1	1	yes	characteristic, direct product factor, Sylow
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
724	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
725	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
726	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
727	Q₈	—	4	4	no	—
728	Q₈	—	4	4	no	—
729	Q₈	—	4	8	no	—
730	C₂×C₄	—	2	8	no	—
731	C₂×C₄	—	2	1	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	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	8	2	no	—
780	C₂×C₄	—	8	2	no	—
781	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
782	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
783	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
784	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
785	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
786	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
787	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
788	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
789	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
790	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	C₁₃×#519	1	4	yes	—
798	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
799	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
800	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
801	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
802	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
803	C₂²	C₁₃×#585	1	1	yes	characteristic
804	C₂²	C₁₃×#585	1	1	yes	characteristic
805	C₄	—	2	2	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	4	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	4	no	—
812	C₄	—	2	4	no	—
813	C₄	—	2	4	no	—
814	C₄	—	2	4	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₂	—	2	4	no	—
824	C₂	C₂×C₁₃×#519	1	1	yes	characteristic
825	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
827	C₂	C₁₃×#3535	1	1	yes	characteristic
828	C₂	C₁₃×#3538	1	1	yes	characteristic
829	C₂	C₁₃×#3563	1	1	yes	characteristic
830	C₂	C₁₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2382	C₂	semidirect
3. C₁₃×#2381	C₂	semidirect
4. C₁₃×#2371	C₂	semidirect
6. C₁₃×#2365	C₂	semidirect
10. C₁₃×#2336	C₂	semidirect
11. C₁₃×#2336	C₂	semidirect
12. C₁₃×#2331	C₂	semidirect
15. C₁₃×#2327	C₂	semidirect
20. C₁₃×#544	C₄	semidirect
118. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
119. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
120. C₁₃×#125	C₂×C₄	semidirect
121. C₁₃×#125	C₂×C₄	semidirect
209. #34432	C₁₃	direct (N × H)
305. #2382	C₂×C₁₃	semidirect
306. #2381	C₂×C₁₃	semidirect
307. #2371	C₂×C₁₃	semidirect
309. #2365	C₂×C₁₃	semidirect
313. #2336	C₂×C₁₃	semidirect
314. #2336	C₂×C₁₃	semidirect
315. #2331	C₂×C₁₃	semidirect
318. #2327	C₂×C₁₃	semidirect
395. #544	C₄×C₁₃	semidirect
525. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
526. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
527. #125	C₂×C₄×C₁₃	semidirect
528. #125	C₂×C₄×C₁₃	semidirect
718. C₁₃	#34432	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#544	2
C₁₃×#2382	2
C₁₃×#2381	2
C₁₃×#2371	2
C₁₃×#2368	2
C₁₃×#2365	2
C₁₃×#2360	2
C₁₃×#2343	2
C₁₃×#2336	2
C₁₃×#2331	2
C₁₃×#2329	2
C₁₃×#2327	2
C₁₃×#2313	2
C₄×C₁₃×C₂²⋊Q₈	2
C₂×C₁₃×#387	2
#34432	13

Subgroups — C13×#34432 #15720771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34432 #15720771