Subgroups — C₁₃×#34917 #15721256

Order 3328.

2028 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2578	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2576	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2570	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2566	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2562	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2535	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2515	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2497	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2494	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2457	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2401	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2392	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
20	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	C₂²	1	2	yes	—
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
40	C₁₃×#401	C₂²	1	2	yes	—
41	C₁₃×#400	C₂²	1	2	yes	—
42	C₁₃×#400	C₂²	1	2	yes	—
43	C₁₃×#400	C₂²	1	2	yes	—
44	C₁₃×#398	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×#397	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×#394	C₂²	1	2	yes	—
53	C₁₃×#394	C₂²	1	2	yes	—
54	C₁₃×#394	C₂²	1	2	yes	—
55	C₁₃×#392	C₂²	1	2	yes	—
56	C₁₃×#390	C₂²	1	1	yes	characteristic
57	C₁₃×#390	C₂²	1	1	yes	characteristic
58	C₁₃×#389	C₂²	1	1	yes	characteristic
59	C₁₃×#389	C₂²	1	1	yes	characteristic
60	C₁₃×#389	C₂²	1	1	yes	characteristic
61	C₁₃×#389	C₂²	1	1	yes	characteristic
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×#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×#386	C₂²	1	2	yes	—
75	C₁₃×#386	C₂²	1	2	yes	—
76	C₁₃×#386	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	2	yes	—
78	C₁₃×#386	C₂²	1	2	yes	—
79	C₁₃×#385	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#384	C₂²	1	1	yes	characteristic
83	C₁₃×#384	C₂²	1	1	yes	characteristic
84	C₁₃×#383	C₂²	1	2	yes	—
85	C₁₃×#382	C₂²	1	1	yes	characteristic
86	C₁₃×#382	C₂²	1	2	yes	—
87	C₁₃×#382	C₂²	1	1	yes	characteristic
88	C₁₃×#382	C₂²	1	1	yes	characteristic
89	C₁₃×#381	C₂²	1	2	yes	—
90	C₁₃×#381	C₂²	1	2	yes	—
91	C₁₃×#380	C₂²	1	1	yes	characteristic
92	C₁₃×#380	C₂²	1	1	yes	characteristic
93	C₁₃×#380	C₂²	1	1	yes	characteristic
94	C₁₃×#380	C₂²	1	1	yes	characteristic
95	C₁₃×#380	C₂²	1	1	yes	characteristic
96	C₁₃×#380	C₂²	1	1	yes	characteristic
97	C₁₃×#380	C₂²	1	2	yes	—
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₁₃×#376	C₂²	1	2	yes	—
122	C₄³×C₁₃	C₂²	1	1	yes	characteristic
123	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
136	C₁₃×#125	—	2	4	no	—
137	C₁₃×#123	—	2	8	no	—
138	C₁₃×#121	—	2	4	no	—
139	C₁₃×#121	—	2	4	no	—
140	C₄×D₄×C₁₃	—	2	4	no	—
141	C₄×D₄×C₁₃	—	2	4	no	—
142	C₄×D₄×C₁₃	—	2	8	no	—
143	C₄×D₄×C₁₃	—	2	4	no	—
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	—	2	4	no	—
146	C₄×D₄×C₁₃	—	2	4	no	—
147	C₄×D₄×C₁₃	—	4	4	no	—
148	C₁₃×#117	—	4	4	no	—
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	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	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	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₂²⋊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×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	—	2	4	no	—
191	C₂×C₄²×C₁₃	—	2	4	no	—
192	C₂×C₄²×C₁₃	—	4	4	no	—
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
205	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	1	yes	characteristic
213	C₁₃×#95	C₂³	1	1	yes	characteristic
214	C₁₃×#95	C₂³	1	1	yes	characteristic
215	C₁₃×#95	C₂³	1	1	yes	characteristic
216	C₁₃×#95	C₂³	1	2	yes	—
217	C₁₃×#95	C₂³	1	2	yes	—
218	C₁₃×#95	C₂³	1	1	yes	characteristic
219	C₁₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	2	yes	—
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	2	yes	—
230	C₁₃×#95	C₂³	1	2	yes	—
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	2	yes	—
234	C₁₃×#95	C₂³	1	2	yes	—
235	C₁₃×#95	C₂³	1	2	yes	—
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	2	yes	—
238	#34917	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
240	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	4	no	—
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	4	2	no	—
252	C₂×D₄×C₁₃	—	4	2	no	—
253	C₂×D₄×C₁₃	#41	1	4	yes	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	4	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	2	4	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	—	4	2	no	—
277	C₂²×C₄×C₁₃	—	4	1	no	—
278	C₂²×C₄×C₁₃	—	4	1	no	—
279	C₂²×C₄×C₁₃	—	4	2	no	—
280	C₂²×C₄×C₁₃	#41	1	4	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	4	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	4	no	—
311	C₁₃×C₄⋊C₄	—	2	4	no	—
312	C₁₃×C₄⋊C₄	—	2	4	no	—
313	C₁₃×C₄⋊C₄	—	2	4	no	—
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	4	2	no	—
317	C₁₃×C₄⋊C₄	—	4	2	no	—
318	C₁₃×C₄⋊C₄	—	4	2	no	—
319	C₁₃×C₄⋊C₄	—	4	2	no	—
320	C₁₃×C₄⋊C₄	—	4	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	4	no	—
329	C₁₃×C₂²⋊C₄	—	2	4	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	4	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	4	no	—
335	C₁₃×C₂²⋊C₄	—	4	2	no	—
336	C₁₃×C₂²⋊C₄	—	4	2	no	—
337	C₁₃×C₂²⋊C₄	—	4	2	no	—
338	C₁₃×C₂²⋊C₄	—	4	2	no	—
339	C₁₃×C₂²⋊C₄	—	4	2	no	—
340	C₁₃×C₂²⋊C₄	—	4	2	no	—
341	C₁₃×C₂²⋊C₄	#41	1	4	yes	—
342	C₄²×C₁₃	—	2	2	no	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	2	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	2	2	no	—
347	C₄²×C₁₃	—	2	2	no	—
348	C₄²×C₁₃	—	2	2	no	—
349	C₄²×C₁₃	—	2	2	no	—
350	C₄²×C₁₃	—	2	2	no	—
351	C₄²×C₁₃	—	2	4	no	—
352	C₄²×C₁₃	—	2	2	no	—
353	C₄²×C₁₃	—	2	4	no	—
354	C₄²×C₁₃	—	2	4	no	—
355	C₄²×C₁₃	—	4	2	no	—
356	C₄²×C₁₃	—	4	2	no	—
357	C₄²×C₁₃	—	4	1	no	—
358	C₄²×C₁₃	#41	1	4	yes	—
359	C₄²×C₁₃	#41	1	4	yes	—
360	#2578	C₂×C₁₃	1	2	yes	complemented
361	#2576	C₂×C₁₃	1	2	yes	complemented
362	#2570	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#2566	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#2562	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#2535	C₂×C₁₃	1	1	yes	characteristic
366	#2515	C₂×C₁₃	1	2	yes	complemented
367	#2497	C₂×C₁₃	1	1	yes	characteristic, complemented
368	#2494	C₂×C₁₃	1	1	yes	characteristic, complemented
369	#2457	C₂×C₁₃	1	2	yes	complemented
370	#2422	C₂×C₁₃	1	1	yes	characteristic, complemented
371	#2420	C₂×C₁₃	1	1	yes	characteristic, complemented
372	#2401	C₂×C₁₃	1	2	yes	complemented
373	#2392	C₂×C₁₃	1	2	yes	complemented
374	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
375	C₄×#123	C₂×C₁₃	1	2	yes	complemented
376	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
377	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
378	#2290	C₂×C₁₃	1	2	yes	complemented
379	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
380	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
381	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
382	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	2	2	no	—
385	C₂³×C₁₃	—	2	1	no	—
386	C₂³×C₁₃	—	2	1	no	—
387	C₂³×C₁₃	—	2	1	no	—
388	C₂³×C₁₃	—	2	1	no	—
389	C₂³×C₁₃	—	2	2	no	—
390	C₂³×C₁₃	—	2	2	no	—
391	C₂³×C₁₃	—	2	1	no	—
392	C₂³×C₁₃	—	2	1	no	—
393	C₂³×C₁₃	—	2	1	no	—
394	C₂³×C₁₃	—	2	1	no	—
395	C₂³×C₁₃	—	2	1	no	—
396	C₂³×C₁₃	—	2	1	no	—
397	C₂³×C₁₃	—	2	2	no	—
398	C₂³×C₁₃	—	2	1	no	—
399	C₂³×C₁₃	—	2	2	no	—
400	C₂³×C₁₃	—	2	1	no	—
401	C₂³×C₁₃	C₂×#41	1	4	yes	—
402	C₂³×C₁₃	C₂×#41	1	2	yes	—
403	C₂³×C₁₃	C₂×#41	1	2	yes	—
404	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
405	D₄×C₁₃	—	2	8	no	—
406	D₄×C₁₃	—	2	8	no	—
407	D₄×C₁₃	—	4	8	no	—
408	D₄×C₁₃	—	4	8	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	1	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	1	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	8	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	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	2	no	—
431	C₂×C₄×C₁₃	—	2	1	no	—
432	C₂×C₄×C₁₃	—	2	1	no	—
433	C₂×C₄×C₁₃	—	2	1	no	—
434	C₂×C₄×C₁₃	—	2	1	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	1	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	1	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	2	no	—
451	C₂×C₄×C₁₃	—	2	2	no	—
452	C₂×C₄×C₁₃	—	2	1	no	—
453	C₂×C₄×C₁₃	—	2	1	no	—
454	C₂×C₄×C₁₃	—	2	1	no	—
455	C₂×C₄×C₁₃	—	2	2	no	—
456	C₂×C₄×C₁₃	—	2	2	no	—
457	C₂×C₄×C₁₃	—	2	2	no	—
458	C₂×C₄×C₁₃	—	4	4	no	—
459	C₂×C₄×C₁₃	—	4	4	no	—
460	C₂×C₄×C₁₃	—	4	8	no	—
461	C₂×C₄×C₁₃	—	4	8	no	—
462	C₂×C₄×C₁₃	—	4	4	no	—
463	C₂×C₄×C₁₃	—	4	4	no	—
464	C₂×C₄×C₁₃	—	4	4	no	—
465	C₂×C₄×C₁₃	—	4	8	no	—
466	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
467	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
468	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
469	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
470	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
471	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
472	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
473	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
474	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
475	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
476	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
477	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
478	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×#123	C₂²×C₁₃	1	2	yes	—
480	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
482	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
485	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
486	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
488	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
490	C₂×#117	C₂²×C₁₃	1	2	yes	—
491	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
492	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
493	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
494	#401	C₂²×C₁₃	1	2	yes	—
495	#400	C₂²×C₁₃	1	2	yes	—
496	#400	C₂²×C₁₃	1	2	yes	—
497	#400	C₂²×C₁₃	1	2	yes	—
498	#398	C₂²×C₁₃	1	2	yes	—
499	#397	C₂²×C₁₃	1	2	yes	—
500	#397	C₂²×C₁₃	1	2	yes	—
501	#397	C₂²×C₁₃	1	2	yes	—
502	#397	C₂²×C₁₃	1	2	yes	—
503	#396	C₂²×C₁₃	1	2	yes	—
504	#396	C₂²×C₁₃	1	2	yes	—
505	#396	C₂²×C₁₃	1	2	yes	—
506	#394	C₂²×C₁₃	1	2	yes	—
507	#394	C₂²×C₁₃	1	2	yes	—
508	#394	C₂²×C₁₃	1	2	yes	—
509	#392	C₂²×C₁₃	1	2	yes	—
510	#390	C₂²×C₁₃	1	1	yes	characteristic
511	#390	C₂²×C₁₃	1	1	yes	characteristic
512	#389	C₂²×C₁₃	1	1	yes	characteristic
513	#389	C₂²×C₁₃	1	1	yes	characteristic
514	#389	C₂²×C₁₃	1	1	yes	characteristic
515	#389	C₂²×C₁₃	1	1	yes	characteristic
516	#388	C₂²×C₁₃	1	2	yes	—
517	#388	C₂²×C₁₃	1	2	yes	—
518	#388	C₂²×C₁₃	1	2	yes	—
519	#388	C₂²×C₁₃	1	2	yes	—
520	#388	C₂²×C₁₃	1	2	yes	—
521	#388	C₂²×C₁₃	1	2	yes	—
522	#387	C₂²×C₁₃	1	2	yes	—
523	#387	C₂²×C₁₃	1	2	yes	—
524	#387	C₂²×C₁₃	1	2	yes	—
525	#387	C₂²×C₁₃	1	2	yes	—
526	#387	C₂²×C₁₃	1	2	yes	—
527	#387	C₂²×C₁₃	1	2	yes	—
528	#386	C₂²×C₁₃	1	2	yes	—
529	#386	C₂²×C₁₃	1	2	yes	—
530	#386	C₂²×C₁₃	1	2	yes	—
531	#386	C₂²×C₁₃	1	2	yes	—
532	#386	C₂²×C₁₃	1	2	yes	—
533	#385	C₂²×C₁₃	1	2	yes	—
534	#385	C₂²×C₁₃	1	2	yes	—
535	#385	C₂²×C₁₃	1	2	yes	—
536	#384	C₂²×C₁₃	1	1	yes	characteristic
537	#384	C₂²×C₁₃	1	1	yes	characteristic
538	#383	C₂²×C₁₃	1	2	yes	—
539	#382	C₂²×C₁₃	1	1	yes	characteristic
540	#382	C₂²×C₁₃	1	1	yes	characteristic
541	#382	C₂²×C₁₃	1	1	yes	characteristic
542	#382	C₂²×C₁₃	1	2	yes	—
543	#381	C₂²×C₁₃	1	2	yes	—
544	#381	C₂²×C₁₃	1	2	yes	—
545	#380	C₂²×C₁₃	1	1	yes	characteristic
546	#380	C₂²×C₁₃	1	1	yes	characteristic
547	#380	C₂²×C₁₃	1	1	yes	characteristic
548	#380	C₂²×C₁₃	1	1	yes	characteristic
549	#380	C₂²×C₁₃	1	2	yes	—
550	#380	C₂²×C₁₃	1	1	yes	characteristic
551	#380	C₂²×C₁₃	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
555	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
556	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
563	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
564	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
565	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
566	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
567	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
568	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
569	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
571	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
572	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
574	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
575	#376	C₂²×C₁₃	1	2	yes	—
576	C₄³	C₂²×C₁₃	1	1	yes	characteristic
577	C₂²×C₁₃	—	2	4	no	—
578	C₂²×C₁₃	—	2	2	no	—
579	C₂²×C₁₃	—	2	2	no	—
580	C₂²×C₁₃	—	2	2	no	—
581	C₂²×C₁₃	—	2	2	no	—
582	C₂²×C₁₃	—	2	2	no	—
583	C₂²×C₁₃	—	2	4	no	—
584	C₂²×C₁₃	—	2	4	no	—
585	C₂²×C₁₃	—	2	2	no	—
586	C₂²×C₁₃	—	4	1	no	—
587	C₂²×C₁₃	—	4	1	no	—
588	C₂²×C₁₃	—	4	2	no	—
589	C₂²×C₁₃	—	4	2	no	—
590	C₂²×C₁₃	—	4	1	no	—
591	C₂²×C₁₃	—	4	1	no	—
592	C₂²×C₁₃	—	4	2	no	—
593	C₂²×C₁₃	—	4	1	no	—
594	C₂²×C₁₃	—	4	1	no	—
595	C₂²×C₁₃	—	4	2	no	—
596	C₂²×C₁₃	—	4	1	no	—
597	C₂²×C₁₃	—	4	1	no	—
598	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
599	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
600	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
601	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
602	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
603	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	C₂²×C₁₃	#585	1	1	yes	characteristic
605	C₄×C₁₃	—	2	2	no	—
606	C₄×C₁₃	—	2	2	no	—
607	C₄×C₁₃	—	2	2	no	—
608	C₄×C₁₃	—	2	2	no	—
609	C₄×C₁₃	—	2	2	no	—
610	C₄×C₁₃	—	2	2	no	—
611	C₄×C₁₃	—	4	1	no	—
612	C₄×C₁₃	—	4	1	no	—
613	C₄×C₁₃	—	4	2	no	—
614	C₄×C₁₃	—	4	2	no	—
615	C₄×C₁₃	—	4	2	no	—
616	C₄×C₁₃	—	4	1	no	—
617	C₄×C₁₃	—	4	2	no	—
618	C₄×C₁₃	—	4	1	no	—
619	C₄×C₁₃	—	4	1	no	—
620	C₄×C₁₃	—	4	2	no	—
621	C₄×C₁₃	—	4	2	no	—
622	C₄×C₁₃	—	4	2	no	—
623	C₄×C₁₃	#529	1	4	yes	—
624	C₄×C₁₃	#553	1	4	yes	—
625	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
627	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
628	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
631	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
633	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
634	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
636	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
638	#125	—	2	4	no	—
639	#123	—	2	8	no	—
640	#121	—	2	4	no	—
641	#121	—	2	4	no	—
642	C₄×D₄	—	2	4	no	—
643	C₄×D₄	—	2	4	no	—
644	C₄×D₄	—	2	8	no	—
645	C₄×D₄	—	2	4	no	—
646	C₄×D₄	—	2	4	no	—
647	C₄×D₄	—	2	4	no	—
648	C₄×D₄	—	2	4	no	—
649	C₄×D₄	—	4	4	no	—
650	#117	—	4	4	no	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
692	C₂×C₄²	—	2	4	no	—
693	C₂×C₄²	—	2	4	no	—
694	C₂×C₄²	—	4	4	no	—
695	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
696	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
697	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
701	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
705	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
708	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
709	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
710	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
711	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
713	#95	C₂³×C₁₃	1	2	yes	—
714	#95	C₂³×C₁₃	1	2	yes	—
715	#95	C₂³×C₁₃	1	2	yes	—
716	#95	C₂³×C₁₃	1	2	yes	—
717	#95	C₂³×C₁₃	1	2	yes	—
718	#95	C₂³×C₁₃	1	1	yes	characteristic
719	#95	C₂³×C₁₃	1	1	yes	characteristic
720	#95	C₂³×C₁₃	1	1	yes	characteristic
721	#95	C₂³×C₁₃	1	1	yes	characteristic
722	#95	C₂³×C₁₃	1	2	yes	—
723	#95	C₂³×C₁₃	1	2	yes	—
724	#95	C₂³×C₁₃	1	1	yes	characteristic
725	#95	C₂³×C₁₃	1	1	yes	characteristic
726	#95	C₂³×C₁₃	1	2	yes	—
727	#95	C₂³×C₁₃	1	2	yes	—
728	#95	C₂³×C₁₃	1	2	yes	—
729	#95	C₂³×C₁₃	1	2	yes	—
730	#95	C₂³×C₁₃	1	2	yes	—
731	#95	C₂³×C₁₃	1	2	yes	—
732	#95	C₂³×C₁₃	1	2	yes	—
733	#95	C₂³×C₁₃	1	2	yes	—
734	#95	C₂³×C₁₃	1	2	yes	—
735	#95	C₂³×C₁₃	1	2	yes	—
736	#95	C₂³×C₁₃	1	2	yes	—
737	#95	C₂³×C₁₃	1	2	yes	—
738	#95	C₂³×C₁₃	1	2	yes	—
739	#95	C₂³×C₁₃	1	2	yes	—
740	C₂×C₁₃	—	4	4	no	—
741	C₂×C₁₃	—	4	2	no	—
742	C₂×C₁₃	—	4	2	no	—
743	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
744	C₂×C₁₃	#3444	1	1	yes	characteristic
745	C₂×C₁₃	#3460	1	1	yes	characteristic
746	C₂×C₁₃	C₂×#553	1	1	yes	characteristic
747	C₂×C₁₃	#3475	1	1	yes	characteristic
748	C₂×C₁₃	#3475	1	1	yes	characteristic
749	C₂×C₁₃	#3481	1	1	yes	characteristic
750	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
751	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	4	no	—
756	C₂×D₄	—	2	4	no	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	C₁₃×#41	1	4	yes	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	4	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	4	no	—
784	C₂²×C₄	—	2	4	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	—	4	2	no	—
788	C₂²×C₄	—	4	1	no	—
789	C₂²×C₄	—	4	1	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	C₁₃×#41	1	4	yes	—
792	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
799	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
802	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
803	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	4	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	4	no	—
822	C₄⋊C₄	—	2	4	no	—
823	C₄⋊C₄	—	2	4	no	—
824	C₄⋊C₄	—	2	4	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	4	2	no	—
828	C₄⋊C₄	—	4	2	no	—
829	C₄⋊C₄	—	4	2	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	2	4	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	4	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	4	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	—	4	2	no	—
851	C₂²⋊C₄	—	4	2	no	—
852	C₂²⋊C₄	C₁₃×#41	1	4	yes	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	2	no	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	4	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	4	no	—
865	C₄²	—	2	4	no	—
866	C₄²	—	4	2	no	—
867	C₄²	—	4	2	no	—
868	C₄²	—	4	1	no	—
869	C₄²	C₁₃×#41	1	4	yes	—
870	C₄²	C₁₃×#41	1	4	yes	—
871	C₁₃	#34917	1	1	yes	characteristic, direct product factor, Sylow
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	1	no	—
876	C₂³	—	2	1	no	—
877	C₂³	—	2	1	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	2	2	no	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	1	no	—
890	C₂³	C₂×C₁₃×#41	1	4	yes	—
891	C₂³	C₂×C₁₃×#41	1	2	yes	—
892	C₂³	C₂×C₁₃×#41	1	2	yes	—
893	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
894	D₄	—	2	8	no	—
895	D₄	—	2	8	no	—
896	D₄	—	4	8	no	—
897	D₄	—	4	8	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	8	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	4	4	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	8	no	—
950	C₂×C₄	—	4	8	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	4	no	—
954	C₂×C₄	—	4	8	no	—
955	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
956	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
957	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
958	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
959	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
960	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
961	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
962	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
963	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
964	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
965	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
966	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
967	C₂²	—	2	4	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	2	4	no	—
974	C₂²	—	2	4	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	1	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	1	no	—
984	C₂²	—	4	1	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	1	no	—
987	C₂²	—	4	1	no	—
988	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
989	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
990	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
991	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
992	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
993	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
994	C₂²	C₁₃×#585	1	1	yes	characteristic
995	C₄	—	2	2	no	—
996	C₄	—	2	2	no	—
997	C₄	—	2	2	no	—
998	C₄	—	2	2	no	—
999	C₄	—	2	2	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	4	1	no	—
1002	C₄	—	4	1	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	1	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	1	no	—
1010	C₄	—	4	2	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	C₁₃×#529	1	4	yes	—
1014	C₄	C₁₃×#553	1	4	yes	—
1015	C₂	—	4	4	no	—
1016	C₂	—	4	2	no	—
1017	C₂	—	4	2	no	—
1018	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
1019	C₂	C₁₃×#3444	1	1	yes	characteristic
1020	C₂	C₁₃×#3460	1	1	yes	characteristic
1021	C₂	C₂×C₁₃×#553	1	1	yes	characteristic
1022	C₂	C₁₃×#3475	1	1	yes	characteristic
1023	C₂	C₁₃×#3475	1	1	yes	characteristic
1024	C₂	C₁₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₁₃×#2535	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2578	C₂	semidirect
2. C₁₃×#2576	C₂	semidirect
3. C₁₃×#2570	C₂	semidirect
4. C₁₃×#2566	C₂	semidirect
5. C₁₃×#2562	C₂	semidirect
7. C₁₃×#2515	C₂	semidirect
8. C₁₃×#2497	C₂	semidirect
9. C₁₃×#2494	C₂	semidirect
10. C₁₃×#2457	C₂	semidirect
11. C₁₃×#2422	C₂	semidirect
12. C₁₃×#2420	C₂	semidirect
13. C₁₃×#2401	C₂	semidirect
14. C₁₃×#2392	C₂	semidirect
15. C₄×C₁₃×#125	C₂	semidirect
16. C₄×C₁₃×#123	C₂	semidirect
17. C₄×C₁₃×#121	C₂	semidirect
18. C₄×C₁₃×#121	C₂	semidirect
19. C₁₃×#2290	C₂	semidirect
20. C₁₃×#2285	C₂	semidirect
21. C₁₃×#2283	C₂	semidirect
22. C₄²×D₄×C₁₃	C₂	semidirect
23. C₄²×D₄×C₁₃	C₂	semidirect
238. #34917	C₁₃	direct (N × H)
360. #2578	C₂×C₁₃	semidirect
361. #2576	C₂×C₁₃	semidirect
362. #2570	C₂×C₁₃	semidirect
363. #2566	C₂×C₁₃	semidirect
364. #2562	C₂×C₁₃	semidirect
366. #2515	C₂×C₁₃	semidirect
367. #2497	C₂×C₁₃	semidirect
368. #2494	C₂×C₁₃	semidirect
369. #2457	C₂×C₁₃	semidirect
370. #2422	C₂×C₁₃	semidirect
371. #2420	C₂×C₁₃	semidirect
372. #2401	C₂×C₁₃	semidirect
373. #2392	C₂×C₁₃	semidirect
374. C₄×#125	C₂×C₁₃	semidirect
375. C₄×#123	C₂×C₁₃	semidirect
376. C₄×#121	C₂×C₁₃	semidirect
377. C₄×#121	C₂×C₁₃	semidirect
378. #2290	C₂×C₁₃	semidirect
379. #2285	C₂×C₁₃	semidirect
380. #2283	C₂×C₁₃	semidirect
381. C₄²×D₄	C₂×C₁₃	semidirect
382. C₄²×D₄	C₂×C₁₃	semidirect
871. C₁₃	#34917	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×#2578	2
C₁₃×#2576	2
C₁₃×#2570	2
C₁₃×#2566	2
C₁₃×#2562	2
C₁₃×#2535	2
C₁₃×#2515	2
C₁₃×#2497	2
C₁₃×#2494	2
C₁₃×#2457	2
C₁₃×#2422	2
C₁₃×#2420	2
C₁₃×#2401	2
C₁₃×#2392	2
C₄×C₁₃×#125	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
C₁₃×#2290	2
C₁₃×#2285	2
C₁₃×#2283	2
C₄²×D₄×C₁₃	2
#34917	13

Subgroups — C13×#34917 #15721256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34917 #15721256