Subgroups — C₁₃×#34499 #15720838

Order 3328.

2032 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2383	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2378	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2343	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2334	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2334	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic
20	C₁₃×#2314	C₂	1	2	yes	maximal, complemented
21	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
22	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#556	C₄	1	16	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#126	C₂²	1	2	yes	—
27	C₂×C₁₃×#126	C₂²	1	2	yes	—
28	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊Q₈	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	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#117	C₂²	1	2	yes	—
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#391	C₂²	1	1	yes	characteristic
44	C₁₃×#391	C₂²	1	1	yes	characteristic
45	C₁₃×#391	C₂²	1	1	yes	characteristic
46	C₁₃×#391	C₂²	1	1	yes	characteristic
47	C₁₃×#391	C₂²	1	1	yes	characteristic
48	C₁₃×#391	C₂²	1	2	yes	—
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#390	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	1	yes	characteristic
54	C₁₃×#389	C₂²	1	1	yes	characteristic
55	C₁₃×#389	C₂²	1	1	yes	characteristic
56	C₁₃×#389	C₂²	1	1	yes	characteristic
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#389	C₂²	1	2	yes	—
60	C₁₃×#389	C₂²	1	2	yes	—
61	C₁₃×#389	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	1	yes	characteristic
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	1	yes	characteristic
75	C₁₃×#387	C₂²	1	1	yes	characteristic
76	C₁₃×#387	C₂²	1	1	yes	characteristic
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×#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	2	yes	—
95	C₁₃×#384	C₂²	1	1	yes	characteristic
96	C₁₃×#383	C₂²	1	2	yes	—
97	C₁₃×#382	C₂²	1	1	yes	characteristic
98	C₁₃×#382	C₂²	1	2	yes	—
99	C₁₃×#382	C₂²	1	1	yes	characteristic
100	C₁₃×#382	C₂²	1	2	yes	—
101	C₁₃×#381	C₂²	1	2	yes	—
102	C₁₃×#380	C₂²	1	2	yes	—
103	C₁₃×#380	C₂²	1	2	yes	—
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
113	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₁₃×#376	C₂²	1	1	yes	characteristic
120	C₁₃×#376	C₂²	1	1	yes	characteristic
121	C₁₃×#376	C₂²	1	2	yes	—
122	C₂×C₁₃×#95	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	1	yes	characteristic
127	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
131	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
132	C₁₃×#126	C₂×C₄	1	16	yes	complemented
133	C₁₃×#126	C₂×C₄	1	16	yes	complemented
134	C₁₃×#124	C₂×C₄	1	8	yes	—
135	C₁₃×#124	C₂×C₄	1	8	yes	—
136	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
137	C₄×Q₈×C₁₃	—	4	2	no	—
138	C₄×Q₈×C₁₃	—	4	2	no	—
139	C₄×Q₈×C₁₃	—	4	2	no	—
140	C₄×Q₈×C₁₃	—	4	2	no	—
141	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
142	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
143	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
144	C₄×D₄×C₁₃	—	4	2	no	—
145	C₄×D₄×C₁₃	—	4	2	no	—
146	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
147	C₁₃×#117	C₂×C₄	1	16	yes	complemented
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	1	yes	characteristic
208	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
217	C₁₃×#95	C₂³	1	2	yes	—
218	C₁₃×#95	C₂³	1	2	yes	—
219	C₁₃×#95	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	2	yes	—
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	2	yes	—
223	C₁₃×#95	C₂³	1	2	yes	—
224	C₁₃×#95	C₂³	1	2	yes	—
225	C₁₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
230	C₁₃×#95	C₂³	1	1	yes	characteristic
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	1	yes	characteristic
233	C₁₃×#95	C₂³	1	2	yes	—
234	C₁₃×#95	C₂³	1	1	yes	characteristic
235	C₁₃×#95	C₂³	1	1	yes	characteristic
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	1	yes	characteristic
238	C₁₃×#95	C₂³	1	1	yes	characteristic
239	C₁₃×#95	C₂³	1	1	yes	characteristic
240	#34499	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₁₃	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	—	2	2	no	—
246	C₂×Q₈×C₁₃	—	4	1	no	—
247	C₂×Q₈×C₁₃	—	4	1	no	—
248	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
249	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
250	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
254	C₂²×C₄×C₁₃	—	2	4	no	—
255	C₂²×C₄×C₁₃	—	4	2	no	—
256	C₂²×C₄×C₁₃	—	4	2	no	—
257	C₂²×C₄×C₁₃	—	4	2	no	—
258	C₂²×C₄×C₁₃	—	4	2	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	2	no	—
262	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	4	1	no	—
292	C₁₃×C₄⋊C₄	—	4	1	no	—
293	C₁₃×C₄⋊C₄	—	4	1	no	—
294	C₁₃×C₄⋊C₄	—	4	2	no	—
295	C₁₃×C₄⋊C₄	—	4	1	no	—
296	C₁₃×C₄⋊C₄	—	4	2	no	—
297	C₁₃×C₄⋊C₄	—	4	2	no	—
298	C₁₃×C₄⋊C₄	—	4	2	no	—
299	C₁₃×C₄⋊C₄	—	4	2	no	—
300	C₁₃×C₄⋊C₄	—	4	2	no	—
301	C₁₃×C₄⋊C₄	—	4	2	no	—
302	C₁₃×C₄⋊C₄	—	4	2	no	—
303	C₁₃×C₄⋊C₄	—	4	2	no	—
304	C₁₃×C₄⋊C₄	—	4	2	no	—
305	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
306	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
307	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
308	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
309	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
310	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
311	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
312	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
313	C₁₃×C₂²⋊C₄	—	4	2	no	—
314	C₁₃×C₂²⋊C₄	—	4	2	no	—
315	C₁₃×C₂²⋊C₄	—	4	2	no	—
316	C₁₃×C₂²⋊C₄	—	4	2	no	—
317	C₁₃×C₂²⋊C₄	—	4	2	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
320	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
321	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
322	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
323	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	4	2	no	—
330	C₄²×C₁₃	—	4	1	no	—
331	C₄²×C₁₃	—	4	2	no	—
332	C₄²×C₁₃	—	4	2	no	—
333	C₄²×C₁₃	—	4	1	no	—
334	C₄²×C₁₃	—	4	1	no	—
335	C₄²×C₁₃	—	4	2	no	—
336	C₄²×C₁₃	—	4	2	no	—
337	C₄²×C₁₃	—	4	2	no	—
338	C₄²×C₁₃	—	4	2	no	—
339	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
340	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
341	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
342	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
343	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
344	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
345	#2383	C₂×C₁₃	1	2	yes	complemented
346	#2378	C₂×C₁₃	1	2	yes	complemented
347	#2373	C₂×C₁₃	1	2	yes	complemented
348	#2367	C₂×C₁₃	1	1	yes	characteristic
349	#2367	C₂×C₁₃	1	1	yes	characteristic
350	#2365	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2351	C₂×C₁₃	1	1	yes	characteristic, complemented
353	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2349	C₂×C₁₃	1	1	yes	characteristic
355	#2343	C₂×C₁₃	1	2	yes	complemented
356	#2334	C₂×C₁₃	1	2	yes	complemented
357	#2334	C₂×C₁₃	1	2	yes	complemented
358	#2329	C₂×C₁₃	1	2	yes	complemented
359	#2327	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#2326	C₂×C₁₃	1	1	yes	characteristic
361	#2320	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#2319	C₂×C₁₃	1	1	yes	characteristic
363	#2314	C₂×C₁₃	1	2	yes	complemented
364	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
365	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	2	2	no	—
373	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
374	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
375	Q₈×C₁₃	—	2	8	no	—
376	Q₈×C₁₃	—	2	8	no	—
377	Q₈×C₁₃	—	4	4	no	—
378	D₄×C₁₃	—	2	8	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	1	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	1	no	—
388	C₂×C₄×C₁₃	—	2	1	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	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	1	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	1	no	—
432	C₂×C₄×C₁₃	—	4	8	no	—
433	C₂×C₄×C₁₃	—	8	4	no	—
434	C₂×C₄×C₁₃	—	8	4	no	—
435	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
436	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
437	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
438	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
439	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
440	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
441	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
442	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
443	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
444	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
445	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
446	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
447	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
448	#556	C₄×C₁₃	1	16	yes	complemented
449	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#126	C₂²×C₁₃	1	2	yes	—
451	C₂×#126	C₂²×C₁₃	1	2	yes	—
452	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
455	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
461	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
465	C₂×#117	C₂²×C₁₃	1	2	yes	—
466	#391	C₂²×C₁₃	1	1	yes	characteristic
467	#391	C₂²×C₁₃	1	1	yes	characteristic
468	#391	C₂²×C₁₃	1	1	yes	characteristic
469	#391	C₂²×C₁₃	1	1	yes	characteristic
470	#391	C₂²×C₁₃	1	2	yes	—
471	#391	C₂²×C₁₃	1	1	yes	characteristic
472	#391	C₂²×C₁₃	1	1	yes	characteristic
473	#390	C₂²×C₁₃	1	1	yes	characteristic
474	#390	C₂²×C₁₃	1	1	yes	characteristic
475	#389	C₂²×C₁₃	1	1	yes	characteristic
476	#389	C₂²×C₁₃	1	1	yes	characteristic
477	#389	C₂²×C₁₃	1	1	yes	characteristic
478	#389	C₂²×C₁₃	1	2	yes	—
479	#389	C₂²×C₁₃	1	2	yes	—
480	#389	C₂²×C₁₃	1	1	yes	characteristic
481	#389	C₂²×C₁₃	1	2	yes	—
482	#389	C₂²×C₁₃	1	2	yes	—
483	#389	C₂²×C₁₃	1	2	yes	—
484	#389	C₂²×C₁₃	1	1	yes	characteristic
485	#389	C₂²×C₁₃	1	1	yes	characteristic
486	#388	C₂²×C₁₃	1	2	yes	—
487	#388	C₂²×C₁₃	1	2	yes	—
488	#388	C₂²×C₁₃	1	2	yes	—
489	#388	C₂²×C₁₃	1	2	yes	—
490	#388	C₂²×C₁₃	1	2	yes	—
491	#388	C₂²×C₁₃	1	2	yes	—
492	#388	C₂²×C₁₃	1	2	yes	—
493	#388	C₂²×C₁₃	1	2	yes	—
494	#388	C₂²×C₁₃	1	2	yes	—
495	#388	C₂²×C₁₃	1	2	yes	—
496	#387	C₂²×C₁₃	1	1	yes	characteristic
497	#387	C₂²×C₁₃	1	2	yes	—
498	#387	C₂²×C₁₃	1	2	yes	—
499	#387	C₂²×C₁₃	1	2	yes	—
500	#387	C₂²×C₁₃	1	2	yes	—
501	#387	C₂²×C₁₃	1	2	yes	—
502	#387	C₂²×C₁₃	1	2	yes	—
503	#387	C₂²×C₁₃	1	2	yes	—
504	#387	C₂²×C₁₃	1	2	yes	—
505	#387	C₂²×C₁₃	1	2	yes	—
506	#387	C₂²×C₁₃	1	2	yes	—
507	#387	C₂²×C₁₃	1	1	yes	characteristic
508	#387	C₂²×C₁₃	1	2	yes	—
509	#387	C₂²×C₁₃	1	1	yes	characteristic
510	#387	C₂²×C₁₃	1	1	yes	characteristic
511	#387	C₂²×C₁₃	1	2	yes	—
512	#385	C₂²×C₁₃	1	2	yes	—
513	#385	C₂²×C₁₃	1	2	yes	—
514	#385	C₂²×C₁₃	1	2	yes	—
515	#385	C₂²×C₁₃	1	2	yes	—
516	#385	C₂²×C₁₃	1	2	yes	—
517	#385	C₂²×C₁₃	1	2	yes	—
518	#384	C₂²×C₁₃	1	2	yes	—
519	#384	C₂²×C₁₃	1	1	yes	characteristic
520	#383	C₂²×C₁₃	1	2	yes	—
521	#382	C₂²×C₁₃	1	2	yes	—
522	#382	C₂²×C₁₃	1	1	yes	characteristic
523	#382	C₂²×C₁₃	1	2	yes	—
524	#382	C₂²×C₁₃	1	1	yes	characteristic
525	#381	C₂²×C₁₃	1	2	yes	—
526	#380	C₂²×C₁₃	1	2	yes	—
527	#380	C₂²×C₁₃	1	2	yes	—
528	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
530	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
531	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
532	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
533	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
534	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
535	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
536	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
537	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
539	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
540	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
541	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
542	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
543	#376	C₂²×C₁₃	1	1	yes	characteristic
544	#376	C₂²×C₁₃	1	1	yes	characteristic
545	#376	C₂²×C₁₃	1	2	yes	—
546	C₂×#95	C₂²×C₁₃	1	2	yes	—
547	C₄³	C₂²×C₁₃	1	1	yes	characteristic
548	C₂²×C₁₃	—	2	4	no	—
549	C₂²×C₁₃	—	2	4	no	—
550	C₂²×C₁₃	—	2	4	no	—
551	C₂²×C₁₃	—	4	2	no	—
552	C₂²×C₁₃	—	4	2	no	—
553	C₂²×C₁₃	—	4	2	no	—
554	C₂²×C₁₃	—	4	2	no	—
555	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
556	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
558	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
559	C₂²×C₁₃	#585	1	1	yes	characteristic
560	C₂²×C₁₃	#585	1	1	yes	characteristic
561	C₂²×C₁₃	#585	1	1	yes	characteristic
562	C₄×C₁₃	—	2	4	no	—
563	C₄×C₁₃	—	2	4	no	—
564	C₄×C₁₃	—	2	2	no	—
565	C₄×C₁₃	—	2	4	no	—
566	C₄×C₁₃	—	2	2	no	—
567	C₄×C₁₃	—	2	2	no	—
568	C₄×C₁₃	—	2	2	no	—
569	C₄×C₁₃	—	2	2	no	—
570	C₄×C₁₃	—	2	2	no	—
571	C₄×C₁₃	—	2	2	no	—
572	C₄×C₁₃	—	4	1	no	—
573	C₄×C₁₃	—	4	1	no	—
574	C₄×C₁₃	—	4	2	no	—
575	C₄×C₁₃	—	4	1	no	—
576	C₄×C₁₃	—	4	1	no	—
577	C₄×C₁₃	—	4	2	no	—
578	C₄×C₁₃	—	4	1	no	—
579	C₄×C₁₃	—	4	1	no	—
580	C₄×C₁₃	—	4	2	no	—
581	C₄×C₁₃	—	4	2	no	—
582	C₄×C₁₃	—	4	1	no	—
583	C₄×C₁₃	#520	1	4	yes	—
584	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
587	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
589	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
590	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
591	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
592	#126	C₂×C₄×C₁₃	1	16	yes	complemented
593	#126	C₂×C₄×C₁₃	1	16	yes	complemented
594	#124	C₂×C₄×C₁₃	1	8	yes	—
595	#124	C₂×C₄×C₁₃	1	8	yes	—
596	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
597	C₄×Q₈	—	4	2	no	—
598	C₄×Q₈	—	4	2	no	—
599	C₄×Q₈	—	4	2	no	—
600	C₄×Q₈	—	4	2	no	—
601	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
602	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
603	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
604	C₄×D₄	—	4	2	no	—
605	C₄×D₄	—	4	2	no	—
606	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
607	#117	C₂×C₄×C₁₃	1	16	yes	complemented
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
660	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
663	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
664	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
667	#95	C₂³×C₁₃	1	1	yes	characteristic
668	#95	C₂³×C₁₃	1	2	yes	—
669	#95	C₂³×C₁₃	1	2	yes	—
670	#95	C₂³×C₁₃	1	2	yes	—
671	#95	C₂³×C₁₃	1	2	yes	—
672	#95	C₂³×C₁₃	1	1	yes	characteristic
673	#95	C₂³×C₁₃	1	1	yes	characteristic
674	#95	C₂³×C₁₃	1	2	yes	—
675	#95	C₂³×C₁₃	1	1	yes	characteristic
676	#95	C₂³×C₁₃	1	1	yes	characteristic
677	#95	C₂³×C₁₃	1	1	yes	characteristic
678	#95	C₂³×C₁₃	1	2	yes	—
679	#95	C₂³×C₁₃	1	1	yes	characteristic
680	#95	C₂³×C₁₃	1	1	yes	characteristic
681	#95	C₂³×C₁₃	1	1	yes	characteristic
682	#95	C₂³×C₁₃	1	1	yes	characteristic
683	#95	C₂³×C₁₃	1	1	yes	characteristic
684	#95	C₂³×C₁₃	1	2	yes	—
685	#95	C₂³×C₁₃	1	2	yes	—
686	#95	C₂³×C₁₃	1	2	yes	—
687	#95	C₂³×C₁₃	1	2	yes	—
688	#95	C₂³×C₁₃	1	2	yes	—
689	#95	C₂³×C₁₃	1	1	yes	characteristic
690	#95	C₂³×C₁₃	1	1	yes	characteristic
691	#95	C₂³×C₁₃	1	2	yes	—
692	#95	C₂³×C₁₃	1	2	yes	—
693	#95	C₂³×C₁₃	1	2	yes	—
694	#95	C₂³×C₁₃	1	2	yes	—
695	#95	C₂³×C₁₃	1	2	yes	—
696	#95	C₂³×C₁₃	1	2	yes	—
697	#95	C₂³×C₁₃	1	2	yes	—
698	#95	C₂³×C₁₃	1	2	yes	—
699	#95	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×C₁₃	—	4	4	no	—
701	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
702	C₂×C₁₃	#3428	1	1	yes	characteristic
703	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
704	C₂×C₁₃	#3555	1	1	yes	characteristic
705	C₂×C₁₃	#3557	1	1	yes	characteristic
706	C₂×C₁₃	#3561	1	1	yes	characteristic
707	C₂×C₁₃	#3562	1	1	yes	characteristic
708	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	4	1	no	—
714	C₂×Q₈	—	4	1	no	—
715	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
716	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
717	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
730	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	1	no	—
763	C₄⋊C₄	—	4	1	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
773	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
774	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
775	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
776	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
777	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
778	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
779	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
787	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
788	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
789	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
790	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	4	2	no	—
797	C₄²	—	4	2	no	—
798	C₄²	—	4	2	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₄²	—	4	1	no	—
802	C₄²	—	4	2	no	—
803	C₄²	—	4	2	no	—
804	C₄²	—	4	1	no	—
805	C₄²	—	4	1	no	—
806	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
807	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
808	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
809	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
810	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
811	C₁₃	#34499	1	1	yes	characteristic, direct product factor, Sylow
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
819	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
820	Q₈	—	2	8	no	—
821	Q₈	—	2	8	no	—
822	Q₈	—	4	4	no	—
823	D₄	—	2	8	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	4	8	no	—
878	C₂×C₄	—	8	4	no	—
879	C₂×C₄	—	8	4	no	—
880	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
881	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
882	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
883	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
884	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
885	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
886	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
887	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
888	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
889	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
890	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
891	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
892	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
901	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
903	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
904	C₂²	C₁₃×#585	1	1	yes	characteristic
905	C₂²	C₁₃×#585	1	1	yes	characteristic
906	C₂²	C₁₃×#585	1	1	yes	characteristic
907	C₄	—	2	2	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	4	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	1	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	1	no	—
928	C₄	C₁₃×#520	1	4	yes	—
929	C₂	—	4	4	no	—
930	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
931	C₂	C₁₃×#3428	1	1	yes	characteristic
932	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
933	C₂	C₁₃×#3555	1	1	yes	characteristic
934	C₂	C₁₃×#3557	1	1	yes	characteristic
935	C₂	C₁₃×#3561	1	1	yes	characteristic
936	C₂	C₁₃×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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×#2383	C₂	semidirect
3. C₁₃×#2378	C₂	semidirect
4. C₁₃×#2373	C₂	semidirect
7. C₁₃×#2365	C₂	semidirect
8. C₁₃×#2355	C₂	semidirect
9. C₁₃×#2351	C₂	semidirect
10. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
12. C₁₃×#2343	C₂	semidirect
13. C₁₃×#2334	C₂	semidirect
14. C₁₃×#2334	C₂	semidirect
15. C₁₃×#2329	C₂	semidirect
16. C₁₃×#2327	C₂	semidirect
18. C₁₃×#2320	C₂	semidirect
20. C₁₃×#2314	C₂	semidirect
22. C₁₃×#2295	C₂	semidirect
23. C₁₃×#2295	C₂	semidirect
24. C₁₃×#556	C₄	semidirect
131. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
132. C₁₃×#126	C₂×C₄	semidirect
133. C₁₃×#126	C₂×C₄	semidirect
136. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
141. C₄×Q₈×C₁₃	C₂×C₄	semidirect
142. C₄×Q₈×C₁₃	C₂×C₄	semidirect
143. C₄×Q₈×C₁₃	C₂×C₄	semidirect
147. C₁₃×#117	C₂×C₄	semidirect
240. #34499	C₁₃	direct (N × H)
345. #2383	C₂×C₁₃	semidirect
346. #2378	C₂×C₁₃	semidirect
347. #2373	C₂×C₁₃	semidirect
350. #2365	C₂×C₁₃	semidirect
351. #2355	C₂×C₁₃	semidirect
352. #2351	C₂×C₁₃	semidirect
353. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
355. #2343	C₂×C₁₃	semidirect
356. #2334	C₂×C₁₃	semidirect
357. #2334	C₂×C₁₃	semidirect
358. #2329	C₂×C₁₃	semidirect
359. #2327	C₂×C₁₃	semidirect
361. #2320	C₂×C₁₃	semidirect
363. #2314	C₂×C₁₃	semidirect
365. #2295	C₂×C₁₃	semidirect
366. #2295	C₂×C₁₃	semidirect
448. #556	C₄×C₁₃	semidirect
591. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
592. #126	C₂×C₄×C₁₃	semidirect
593. #126	C₂×C₄×C₁₃	semidirect
596. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
601. C₄×Q₈	C₂×C₄×C₁₃	semidirect
602. C₄×Q₈	C₂×C₄×C₁₃	semidirect
603. C₄×Q₈	C₂×C₄×C₁₃	semidirect
607. #117	C₂×C₄×C₁₃	semidirect
811. C₁₃	#34499	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×#556	2
C₁₃×#2383	2
C₁₃×#2378	2
C₁₃×#2373	2
C₁₃×#2367	2
C₁₃×#2365	2
C₁₃×#2355	2
C₁₃×#2351	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#2349	2
C₁₃×#2343	2
C₁₃×#2334	2
C₁₃×#2329	2
C₁₃×#2327	2
C₁₃×#2326	2
C₁₃×#2320	2
C₁₃×#2319	2
C₁₃×#2314	2
C₄×C₁₃×#124	2
C₁₃×#2295	2
#34499	13

Subgroups — C13×#34499 #15720838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34499 #15720838