Subgroups — C₁₃×#34490 #15720829

Order 3328.

1840 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2382	C₂	1	2	yes	maximal
3	C₁₃×#2381	C₂	1	2	yes	maximal
4	C₁₃×#2371	C₂	1	2	yes	maximal
5	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2369	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2356	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2356	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2356	C₂	1	2	yes	maximal
11	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2336	C₂	1	2	yes	maximal
14	C₁₃×#2336	C₂	1	2	yes	maximal
15	C₁₃×#2331	C₂	1	2	yes	maximal
16	C₁₃×#2331	C₂	1	1	yes	maximal, characteristic
17	C₁₃×#2330	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#2320	C₂	1	2	yes	maximal
19	C₁₃×#2320	C₂	1	1	yes	maximal, characteristic
20	C₁₃×#2320	C₂	1	1	yes	maximal, characteristic
21	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
22	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
23	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
24	C₁₃×#557	C₄	1	16	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#125	C₂²	1	2	yes	—
30	C₂×C₁₃×#125	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#391	C₂²	1	1	yes	characteristic
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#391	C₂²	1	2	yes	—
44	C₁₃×#391	C₂²	1	2	yes	—
45	C₁₃×#391	C₂²	1	2	yes	—
46	C₁₃×#391	C₂²	1	2	yes	—
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic
51	C₁₃×#389	C₂²	1	1	yes	characteristic
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	2	yes	—
54	C₁₃×#389	C₂²	1	1	yes	characteristic
55	C₁₃×#389	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	1	yes	characteristic
61	C₁₃×#387	C₂²	1	2	yes	—
62	C₁₃×#387	C₂²	1	1	yes	characteristic
63	C₁₃×#387	C₂²	1	1	yes	characteristic
64	C₁₃×#387	C₂²	1	1	yes	characteristic
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×#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×#387	C₂²	1	2	yes	—
86	C₁₃×#387	C₂²	1	2	yes	—
87	C₁₃×#387	C₂²	1	2	yes	—
88	C₁₃×#384	C₂²	1	1	yes	characteristic
89	C₁₃×#383	C₂²	1	2	yes	—
90	C₁₃×#383	C₂²	1	2	yes	—
91	C₁₃×#383	C₂²	1	2	yes	—
92	C₁₃×#383	C₂²	1	2	yes	—
93	C₁₃×#382	C₂²	1	1	yes	characteristic
94	C₁₃×#382	C₂²	1	2	yes	—
95	C₁₃×#382	C₂²	1	2	yes	—
96	C₁₃×#382	C₂²	1	2	yes	—
97	C₁₃×#382	C₂²	1	1	yes	characteristic
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
118	C₁₃×#376	C₂²	1	1	yes	characteristic
119	C₁₃×#376	C₂²	1	1	yes	characteristic
120	C₁₃×#376	C₂²	1	2	yes	—
121	C₁₃×#376	C₂²	1	2	yes	—
122	C₁₃×#376	C₂²	1	2	yes	—
123	C₄³×C₁₃	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
127	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
128	C₁₃×C₄⋊Q₈	C₂×C₄	1	16	yes	—
129	C₁₃×#125	C₂×C₄	1	8	yes	—
130	C₁₃×#125	C₂×C₄	1	8	yes	—
131	C₁₃×#125	C₂×C₄	1	16	yes	—
132	C₁₃×#125	C₂×C₄	1	16	yes	—
133	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
134	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
135	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
136	C₄×Q₈×C₁₃	C₂×C₄	1	16	yes	—
137	C₄×Q₈×C₁₃	C₂×C₄	1	8	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	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	2	yes	—
183	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	1	yes	characteristic
194	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	C₁₃×#95	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	C₁₃×#95	C₂³	1	1	yes	characteristic
216	C₁₃×#95	C₂³	1	2	yes	—
217	C₁₃×#95	C₂³	1	1	yes	characteristic
218	C₁₃×#95	C₂³	1	2	yes	—
219	C₁₃×#95	C₂³	1	1	yes	characteristic
220	C₁₃×#95	C₂³	1	1	yes	characteristic
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	1	yes	characteristic
223	C₁₃×#95	C₂³	1	2	yes	—
224	C₁₃×#95	C₂³	1	2	yes	—
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	1	yes	characteristic
228	C₁₃×#95	C₂³	1	1	yes	characteristic
229	C₁₃×#95	C₂³	1	1	yes	characteristic
230	C₁₃×#95	C₂³	1	1	yes	characteristic
231	C₁₃×#95	C₂³	1	1	yes	characteristic
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	1	yes	characteristic
234	#34490	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	4	1	no	—
238	C₂×Q₈×C₁₃	—	4	2	no	—
239	C₂×Q₈×C₁₃	—	4	2	no	—
240	C₂×Q₈×C₁₃	—	4	1	no	—
241	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
242	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
243	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
277	C₁₃×C₄⋊C₄	—	4	1	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	1	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	C₂²×C₄	1	4	yes	—
286	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
287	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
288	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
289	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
290	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
291	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
292	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
293	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
294	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
295	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
296	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
297	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
298	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	—	2	2	no	—
301	C₄²×C₁₃	—	2	2	no	—
302	C₄²×C₁₃	—	2	2	no	—
303	C₄²×C₁₃	—	2	2	no	—
304	C₄²×C₁₃	—	2	2	no	—
305	C₄²×C₁₃	—	4	2	no	—
306	C₄²×C₁₃	—	4	1	no	—
307	C₄²×C₁₃	—	4	2	no	—
308	C₄²×C₁₃	—	4	1	no	—
309	C₄²×C₁₃	—	4	2	no	—
310	C₄²×C₁₃	—	4	2	no	—
311	C₄²×C₁₃	—	4	2	no	—
312	C₄²×C₁₃	—	4	2	no	—
313	C₄²×C₁₃	—	4	2	no	—
314	C₄²×C₁₃	—	4	2	no	—
315	C₄²×C₁₃	—	4	1	no	—
316	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
317	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
318	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
319	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
320	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
321	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
322	C₂×#557	C₂×C₁₃	1	1	yes	characteristic
323	#2382	C₂×C₁₃	1	2	yes	—
324	#2381	C₂×C₁₃	1	2	yes	—
325	#2371	C₂×C₁₃	1	2	yes	—
326	#2370	C₂×C₁₃	1	1	yes	characteristic
327	#2370	C₂×C₁₃	1	1	yes	characteristic
328	#2369	C₂×C₁₃	1	1	yes	characteristic
329	#2356	C₂×C₁₃	1	1	yes	characteristic
330	#2356	C₂×C₁₃	1	2	yes	—
331	#2356	C₂×C₁₃	1	1	yes	characteristic
332	#2355	C₂×C₁₃	1	1	yes	characteristic
333	#2355	C₂×C₁₃	1	1	yes	characteristic
334	#2336	C₂×C₁₃	1	2	yes	—
335	#2336	C₂×C₁₃	1	2	yes	—
336	#2331	C₂×C₁₃	1	1	yes	characteristic
337	#2331	C₂×C₁₃	1	2	yes	—
338	#2330	C₂×C₁₃	1	1	yes	characteristic
339	#2320	C₂×C₁₃	1	1	yes	characteristic
340	#2320	C₂×C₁₃	1	1	yes	characteristic
341	#2320	C₂×C₁₃	1	2	yes	—
342	C₄×#125	C₂×C₁₃	1	1	yes	characteristic
343	#2295	C₂×C₁₃	1	1	yes	characteristic
344	#2295	C₂×C₁₃	1	1	yes	characteristic
345	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
346	Q₈×C₁₃	—	2	8	no	—
347	Q₈×C₁₃	—	4	4	no	—
348	Q₈×C₁₃	—	4	8	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	1	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	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	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	2	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	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	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	1	no	—
384	C₂×C₄×C₁₃	—	2	1	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	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	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	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
406	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
407	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
408	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
409	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
410	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
411	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
412	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
413	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
414	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
416	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
417	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
418	#557	C₄×C₁₃	1	16	yes	complemented
419	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
421	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#125	C₂²×C₁₃	1	2	yes	—
424	C₂×#125	C₂²×C₁₃	1	2	yes	—
425	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
427	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
430	#391	C₂²×C₁₃	1	1	yes	characteristic
431	#391	C₂²×C₁₃	1	2	yes	—
432	#391	C₂²×C₁₃	1	1	yes	characteristic
433	#391	C₂²×C₁₃	1	1	yes	characteristic
434	#391	C₂²×C₁₃	1	2	yes	—
435	#391	C₂²×C₁₃	1	1	yes	characteristic
436	#391	C₂²×C₁₃	1	2	yes	—
437	#391	C₂²×C₁₃	1	2	yes	—
438	#391	C₂²×C₁₃	1	2	yes	—
439	#391	C₂²×C₁₃	1	1	yes	characteristic
440	#391	C₂²×C₁₃	1	1	yes	characteristic
441	#389	C₂²×C₁₃	1	1	yes	characteristic
442	#389	C₂²×C₁₃	1	1	yes	characteristic
443	#389	C₂²×C₁₃	1	2	yes	—
444	#389	C₂²×C₁₃	1	1	yes	characteristic
445	#389	C₂²×C₁₃	1	1	yes	characteristic
446	#389	C₂²×C₁₃	1	2	yes	—
447	#389	C₂²×C₁₃	1	2	yes	—
448	#389	C₂²×C₁₃	1	1	yes	characteristic
449	#389	C₂²×C₁₃	1	2	yes	—
450	#389	C₂²×C₁₃	1	1	yes	characteristic
451	#389	C₂²×C₁₃	1	2	yes	—
452	#389	C₂²×C₁₃	1	1	yes	characteristic
453	#389	C₂²×C₁₃	1	1	yes	characteristic
454	#387	C₂²×C₁₃	1	2	yes	—
455	#387	C₂²×C₁₃	1	2	yes	—
456	#387	C₂²×C₁₃	1	1	yes	characteristic
457	#387	C₂²×C₁₃	1	2	yes	—
458	#387	C₂²×C₁₃	1	2	yes	—
459	#387	C₂²×C₁₃	1	2	yes	—
460	#387	C₂²×C₁₃	1	2	yes	—
461	#387	C₂²×C₁₃	1	2	yes	—
462	#387	C₂²×C₁₃	1	2	yes	—
463	#387	C₂²×C₁₃	1	2	yes	—
464	#387	C₂²×C₁₃	1	2	yes	—
465	#387	C₂²×C₁₃	1	2	yes	—
466	#387	C₂²×C₁₃	1	2	yes	—
467	#387	C₂²×C₁₃	1	2	yes	—
468	#387	C₂²×C₁₃	1	2	yes	—
469	#387	C₂²×C₁₃	1	2	yes	—
470	#387	C₂²×C₁₃	1	1	yes	characteristic
471	#387	C₂²×C₁₃	1	2	yes	—
472	#387	C₂²×C₁₃	1	2	yes	—
473	#387	C₂²×C₁₃	1	2	yes	—
474	#387	C₂²×C₁₃	1	2	yes	—
475	#387	C₂²×C₁₃	1	2	yes	—
476	#387	C₂²×C₁₃	1	2	yes	—
477	#387	C₂²×C₁₃	1	2	yes	—
478	#387	C₂²×C₁₃	1	2	yes	—
479	#387	C₂²×C₁₃	1	1	yes	characteristic
480	#387	C₂²×C₁₃	1	1	yes	characteristic
481	#387	C₂²×C₁₃	1	2	yes	—
482	#384	C₂²×C₁₃	1	1	yes	characteristic
483	#383	C₂²×C₁₃	1	2	yes	—
484	#383	C₂²×C₁₃	1	2	yes	—
485	#383	C₂²×C₁₃	1	2	yes	—
486	#383	C₂²×C₁₃	1	2	yes	—
487	#382	C₂²×C₁₃	1	1	yes	characteristic
488	#382	C₂²×C₁₃	1	2	yes	—
489	#382	C₂²×C₁₃	1	2	yes	—
490	#382	C₂²×C₁₃	1	2	yes	—
491	#382	C₂²×C₁₃	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
493	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
494	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
499	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
500	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
501	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
502	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
503	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
504	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
505	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
506	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
507	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
508	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
509	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
510	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
511	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
512	#376	C₂²×C₁₃	1	1	yes	characteristic
513	#376	C₂²×C₁₃	1	1	yes	characteristic
514	#376	C₂²×C₁₃	1	2	yes	—
515	#376	C₂²×C₁₃	1	2	yes	—
516	#376	C₂²×C₁₃	1	2	yes	—
517	C₄³	C₂²×C₁₃	1	1	yes	characteristic
518	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
519	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
521	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
522	C₂²×C₁₃	#585	1	1	yes	characteristic
523	C₂²×C₁₃	#585	1	1	yes	characteristic
524	C₂²×C₁₃	#585	1	1	yes	characteristic
525	C₄×C₁₃	—	2	4	no	—
526	C₄×C₁₃	—	2	2	no	—
527	C₄×C₁₃	—	2	4	no	—
528	C₄×C₁₃	—	2	4	no	—
529	C₄×C₁₃	—	2	2	no	—
530	C₄×C₁₃	—	2	2	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	2	4	no	—
533	C₄×C₁₃	—	2	2	no	—
534	C₄×C₁₃	—	2	2	no	—
535	C₄×C₁₃	—	2	2	no	—
536	C₄×C₁₃	—	4	1	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	4	1	no	—
539	C₄×C₁₃	—	4	2	no	—
540	C₄×C₁₃	—	4	2	no	—
541	C₄×C₁₃	—	4	1	no	—
542	C₄×C₁₃	—	4	1	no	—
543	C₄×C₁₃	—	4	1	no	—
544	C₄×C₁₃	—	4	1	no	—
545	C₄×C₁₃	—	4	1	no	—
546	C₄×C₁₃	—	4	2	no	—
547	C₄×C₁₃	#519	1	4	yes	—
548	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
550	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
552	C₄⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
553	#125	C₂×C₄×C₁₃	1	8	yes	—
554	#125	C₂×C₄×C₁₃	1	8	yes	—
555	#125	C₂×C₄×C₁₃	1	16	yes	—
556	#125	C₂×C₄×C₁₃	1	16	yes	—
557	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
558	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
559	C₄×Q₈	C₂×C₄×C₁₃	1	16	yes	—
560	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
561	C₄×Q₈	C₂×C₄×C₁₃	1	8	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	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
594	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
607	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
615	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
617	#95	C₂³×C₁₃	1	1	yes	characteristic
618	#95	C₂³×C₁₃	1	2	yes	—
619	#95	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	1	yes	characteristic
623	#95	C₂³×C₁₃	1	2	yes	—
624	#95	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
630	#95	C₂³×C₁₃	1	1	yes	characteristic
631	#95	C₂³×C₁₃	1	1	yes	characteristic
632	#95	C₂³×C₁₃	1	1	yes	characteristic
633	#95	C₂³×C₁₃	1	1	yes	characteristic
634	#95	C₂³×C₁₃	1	2	yes	—
635	#95	C₂³×C₁₃	1	1	yes	characteristic
636	#95	C₂³×C₁₃	1	1	yes	characteristic
637	#95	C₂³×C₁₃	1	1	yes	characteristic
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	#95	C₂³×C₁₃	1	2	yes	—
645	#95	C₂³×C₁₃	1	2	yes	—
646	#95	C₂³×C₁₃	1	2	yes	—
647	#95	C₂³×C₁₃	1	1	yes	characteristic
648	#95	C₂³×C₁₃	1	2	yes	—
649	#95	C₂³×C₁₃	1	2	yes	—
650	#95	C₂³×C₁₃	1	2	yes	—
651	#95	C₂³×C₁₃	1	2	yes	—
652	#95	C₂³×C₁₃	1	2	yes	—
653	#95	C₂³×C₁₃	1	2	yes	—
654	#95	C₂³×C₁₃	1	2	yes	—
655	#95	C₂³×C₁₃	1	2	yes	—
656	#95	C₂³×C₁₃	1	1	yes	characteristic
657	#95	C₂³×C₁₃	1	2	yes	—
658	C₂×C₁₃	C₂×#519	1	1	yes	characteristic
659	C₂×C₁₃	#3428	1	1	yes	characteristic
660	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
661	C₂×C₁₃	#3555	1	1	yes	characteristic
662	C₂×C₁₃	#3557	1	1	yes	characteristic
663	C₂×C₁₃	#3563	1	1	yes	characteristic
664	C₂×C₁₃	#3565	1	1	yes	characteristic
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	4	1	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	—	4	1	no	—
671	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
672	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
673	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
674	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	4	1	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	1	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	1	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
716	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
717	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
718	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
719	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
720	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
721	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
722	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
723	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
724	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
725	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
726	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
727	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
728	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	4	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	4	2	no	—
736	C₄²	—	4	1	no	—
737	C₄²	—	4	2	no	—
738	C₄²	—	4	1	no	—
739	C₄²	—	4	2	no	—
740	C₄²	—	4	2	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	2	no	—
745	C₄²	—	4	1	no	—
746	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
747	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
748	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
749	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
750	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
751	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
752	C₁₃	#34490	1	1	yes	characteristic, direct product factor, Sylow
753	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
754	Q₈	—	2	8	no	—
755	Q₈	—	4	4	no	—
756	Q₈	—	4	8	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	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	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
813	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
814	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
815	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
816	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
817	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
818	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
819	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
820	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
821	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
822	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
823	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
824	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
825	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
826	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
827	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
828	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
829	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
830	C₂²	C₁₃×#585	1	1	yes	characteristic
831	C₂²	C₁₃×#585	1	1	yes	characteristic
832	C₂²	C₁₃×#585	1	1	yes	characteristic
833	C₄	—	2	2	no	—
834	C₄	—	2	4	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	4	no	—
837	C₄	—	2	4	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	4	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	C₁₃×#519	1	4	yes	—
856	C₂	C₂×C₁₃×#519	1	1	yes	characteristic
857	C₂	C₁₃×#3428	1	1	yes	characteristic
858	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
859	C₂	C₁₃×#3555	1	1	yes	characteristic
860	C₂	C₁₃×#3557	1	1	yes	characteristic
861	C₂	C₁₃×#3563	1	1	yes	characteristic
862	C₂	C₁₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
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
24. C₁₃×#557	C₄	semidirect
234. #34490	C₁₃	direct (N × H)
418. #557	C₄×C₁₃	semidirect
752. C₁₃	#34490	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×#557	2
C₁₃×#2382	2
C₁₃×#2381	2
C₁₃×#2371	2
C₁₃×#2370	2
C₁₃×#2369	2
C₁₃×#2356	2
C₁₃×#2355	2
C₁₃×#2336	2
C₁₃×#2331	2
C₁₃×#2330	2
C₁₃×#2320	2
C₄×C₁₃×#125	2
C₁₃×#2295	2
#34490	13

Subgroups — C13×#34490 #15720829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34490 #15720829