Subgroups — C₁₃×#25124 #15711463

Order 3328.

1362 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2416	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#121	—	2	1	no	—
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₃×#120	—	2	1	no	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#469	—	2	4	no	—
30	C₁₃×#447	—	2	4	no	—
31	C₁₃×#435	—	2	4	no	—
32	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#102	—	2	4	no	—
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#396	—	2	1	no	—
48	C₁₃×#394	—	2	1	no	—
49	C₁₃×#394	—	2	1	no	—
50	C₁₃×#392	—	2	1	no	—
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#386	—	2	1	no	—
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#379	—	2	1	no	—
59	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₁₃	—	2	1	no	—
64	C₂²×D₄×C₁₃	—	2	2	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	—	2	2	no	—
71	C₂²×D₄×C₁₃	—	2	1	no	—
72	C₂²×D₄×C₁₃	—	2	2	no	—
73	C₂²×D₄×C₁₃	—	4	1	no	—
74	C₂²×D₄×C₁₃	—	4	1	no	—
75	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	—	2	1	no	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×D₈	—	2	2	no	—
83	C₂×C₁₃×D₈	—	2	2	no	—
84	C₂×C₁₃×D₈	—	2	2	no	—
85	C₂×C₁₃×D₈	—	2	2	no	—
86	C₂×C₁₃×D₈	—	4	1	no	—
87	C₂×C₁₃×D₈	—	4	1	no	—
88	C₂×C₁₃×M₁₆	—	2	2	no	—
89	C₂×C₁₃×M₁₆	—	2	2	no	—
90	C₂×C₁₃×M₁₆	—	4	1	no	—
91	C₂²×C₈×C₁₃	—	2	2	no	—
92	C₂²×C₈×C₁₃	—	2	2	no	—
93	C₂²×C₈×C₁₃	—	4	1	no	—
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#121	—	2	2	no	—
99	C₁₃×#121	—	2	2	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	2	no	—
103	C₁₃×#121	—	4	1	no	—
104	C₁₃×#121	—	4	1	no	—
105	C₁₃×#121	—	4	1	no	—
106	C₁₃×#121	—	4	4	no	—
107	C₁₃×#120	—	4	4	no	—
108	C₄×D₄×C₁₃	—	2	2	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
114	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
133	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₁₃×#106	—	2	2	no	—
136	C₁₃×#106	—	4	1	no	—
137	C₁₃×C₄⋊C₈	—	2	2	no	—
138	C₁₃×#102	—	2	2	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×#102	—	2	2	no	—
143	C₁₃×#102	—	2	2	no	—
144	C₁₃×#102	—	4	1	no	—
145	C₁₃×#102	D₄	1	4	yes	complemented
146	C₁₃×C₂²⋊C₈	—	2	2	no	—
147	C₁₃×C₂²⋊C₈	D₄	1	4	yes	complemented
148	C₁₃×#97	—	2	2	no	—
149	C₁₃×#95	—	2	1	no	—
150	C₁₃×#95	—	2	1	no	—
151	C₁₃×#95	—	2	1	no	—
152	#25124	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂⁴×C₁₃	—	2	1	no	—
154	C₂⁴×C₁₃	—	2	1	no	—
155	C₂⁴×C₁₃	—	2	1	no	—
156	C₂⁴×C₁₃	—	4	2	no	—
157	C₂⁴×C₁₃	—	4	2	no	—
158	C₂⁴×C₁₃	—	4	2	no	—
159	C₂⁴×C₁₃	—	4	2	no	—
160	C₂⁴×C₁₃	—	4	2	no	—
161	C₂⁴×C₁₃	—	8	1	no	—
162	C₂⁴×C₁₃	—	8	1	no	—
163	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂×D₄×C₁₃	—	2	8	no	—
166	C₂×D₄×C₁₃	—	2	2	no	—
167	C₂×D₄×C₁₃	—	2	2	no	—
168	C₂×D₄×C₁₃	—	2	2	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	2	1	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	4	4	no	—
186	C₂×D₄×C₁₃	—	4	4	no	—
187	C₂×D₄×C₁₃	—	4	2	no	—
188	C₂×D₄×C₁₃	—	4	2	no	—
189	C₂×D₄×C₁₃	—	4	4	no	—
190	C₂×D₄×C₁₃	—	4	2	no	—
191	C₂×D₄×C₁₃	—	4	2	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	4	2	no	—
194	C₂×D₄×C₁₃	—	4	2	no	—
195	C₂×D₄×C₁₃	—	4	2	no	—
196	C₂×D₄×C₁₃	—	4	2	no	—
197	C₂×D₄×C₁₃	—	4	2	no	—
198	C₂×D₄×C₁₃	—	4	2	no	—
199	C₂×D₄×C₁₃	—	4	2	no	—
200	C₂×D₄×C₁₃	—	8	1	no	—
201	C₂×D₄×C₁₃	—	8	1	no	—
202	C₂×D₄×C₁₃	—	8	1	no	—
203	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₁₃	#41	1	2	yes	—
205	C₂²×C₄×C₁₃	—	2	1	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	2	1	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	4	2	no	—
221	C₂²×C₄×C₁₃	—	4	2	no	—
222	C₂²×C₄×C₁₃	—	8	1	no	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₁₃	#41	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₁₃×D₈	—	4	4	no	—
231	C₁₃×D₈	—	4	4	no	—
232	C₁₃×M₁₆	—	4	4	no	—
233	C₂×C₈×C₁₃	—	2	1	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	no	—
238	C₂×C₈×C₁₃	—	2	1	no	—
239	C₂×C₈×C₁₃	—	2	1	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	2	1	no	—
242	C₂×C₈×C₁₃	—	4	4	no	—
243	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
244	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
245	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	4	2	no	—
257	C₁₃×C₄⋊C₄	—	4	2	no	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₂²⋊C₄	—	2	2	no	—
260	C₁₃×C₂²⋊C₄	—	2	2	no	—
261	C₁₃×C₂²⋊C₄	—	4	2	no	—
262	C₁₃×C₂²⋊C₄	—	4	2	no	—
263	C₁₃×C₂²⋊C₄	—	4	2	no	—
264	C₁₃×C₂²⋊C₄	—	4	2	no	—
265	C₁₃×C₂²⋊C₄	—	4	2	no	—
266	C₁₃×C₂²⋊C₄	—	4	2	no	—
267	C₁₃×C₂²⋊C₄	—	4	2	no	—
268	C₁₃×C₂²⋊C₄	—	4	2	no	—
269	C₁₃×C₂²⋊C₄	—	4	2	no	—
270	C₁₃×C₂²⋊C₄	—	8	1	no	—
271	C₁₃×C₂²⋊C₄	—	8	1	no	—
272	C₁₃×C₂²⋊C₄	—	8	1	no	—
273	C₄²×C₁₃	—	2	1	no	—
274	C₄²×C₁₃	—	2	1	no	—
275	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂×#435	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2416	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2408	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#2065	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#2054	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1999	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1972	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1936	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1895	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#1893	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂³×C₁₃	—	2	1	no	—
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	2	1	no	—
293	C₂³×C₁₃	—	2	1	no	—
294	C₂³×C₁₃	—	2	1	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	1	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	1	no	—
299	C₂³×C₁₃	—	2	1	no	—
300	C₂³×C₁₃	—	2	1	no	—
301	C₂³×C₁₃	—	2	1	no	—
302	C₂³×C₁₃	—	2	1	no	—
303	C₂³×C₁₃	—	4	8	no	—
304	C₂³×C₁₃	—	4	1	no	—
305	C₂³×C₁₃	—	4	1	no	—
306	C₂³×C₁₃	—	4	1	no	—
307	C₂³×C₁₃	—	4	1	no	—
308	C₂³×C₁₃	—	4	1	no	—
309	C₂³×C₁₃	—	4	1	no	—
310	C₂³×C₁₃	—	4	1	no	—
311	C₂³×C₁₃	—	4	1	no	—
312	C₂³×C₁₃	—	4	1	no	—
313	C₂³×C₁₃	—	4	1	no	—
314	C₂³×C₁₃	—	4	1	no	—
315	C₂³×C₁₃	—	4	1	no	—
316	C₂³×C₁₃	—	4	1	no	—
317	C₂³×C₁₃	—	4	1	no	—
318	C₂³×C₁₃	—	4	1	no	—
319	C₂³×C₁₃	—	4	1	no	—
320	C₂³×C₁₃	—	4	1	no	—
321	C₂³×C₁₃	—	4	1	no	—
322	C₂³×C₁₃	—	4	1	no	—
323	C₂³×C₁₃	—	8	4	no	—
324	C₂³×C₁₃	—	8	4	no	—
325	C₂³×C₁₃	—	8	4	no	—
326	C₂³×C₁₃	—	8	4	no	—
327	C₂³×C₁₃	—	8	4	no	—
328	C₂³×C₁₃	—	8	4	no	—
329	C₂³×C₁₃	#121	1	2	yes	—
330	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
331	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
332	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
333	D₄×C₁₃	—	2	2	no	—
334	D₄×C₁₃	—	2	2	no	—
335	D₄×C₁₃	—	2	2	no	—
336	D₄×C₁₃	—	2	2	no	—
337	D₄×C₁₃	—	4	8	no	—
338	D₄×C₁₃	—	4	4	no	—
339	D₄×C₁₃	—	4	1	no	—
340	D₄×C₁₃	—	4	1	no	—
341	D₄×C₁₃	—	4	1	no	—
342	D₄×C₁₃	—	4	1	no	—
343	D₄×C₁₃	—	4	1	no	—
344	D₄×C₁₃	—	4	1	no	—
345	D₄×C₁₃	—	4	1	no	—
346	D₄×C₁₃	—	4	1	no	—
347	D₄×C₁₃	—	8	4	no	—
348	D₄×C₁₃	—	8	4	no	—
349	D₄×C₁₃	—	8	4	no	—
350	D₄×C₁₃	—	8	4	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	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	1	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	1	no	—
376	C₂×C₄×C₁₃	—	4	1	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	—	8	4	no	—
386	C₂×C₄×C₁₃	#121	1	2	yes	—
387	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
391	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
392	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
393	C₈×C₁₃	—	2	2	no	—
394	C₈×C₁₃	—	2	2	no	—
395	C₈×C₁₃	—	2	2	no	—
396	C₈×C₁₃	—	4	1	no	—
397	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
398	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
401	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#121	—	2	1	no	—
403	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
407	C₂×#120	—	2	1	no	—
408	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
410	#469	—	2	4	no	—
411	#447	—	2	4	no	—
412	#435	—	2	4	no	—
413	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₂×#102	—	2	4	no	—
417	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
424	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#396	—	2	1	no	—
429	#394	—	2	1	no	—
430	#394	—	2	1	no	—
431	#392	—	2	1	no	—
432	#390	C₂²×C₁₃	1	1	yes	characteristic
433	#390	C₂²×C₁₃	1	1	yes	characteristic
434	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#386	—	2	1	no	—
437	#380	C₂²×C₁₃	1	1	yes	characteristic
438	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#379	—	2	1	no	—
440	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	2	2	no	—
446	C₂²×C₁₃	—	2	2	no	—
447	C₂²×C₁₃	—	2	2	no	—
448	C₂²×C₁₃	—	2	2	no	—
449	C₂²×C₁₃	—	2	2	no	—
450	C₂²×C₁₃	—	4	1	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	4	2	no	—
453	C₂²×C₁₃	—	4	1	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	1	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	1	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	1	no	—
460	C₂²×C₁₃	—	4	1	no	—
461	C₂²×C₁₃	—	4	1	no	—
462	C₂²×C₁₃	—	4	2	no	—
463	C₂²×C₁₃	—	8	16	no	—
464	C₂²×C₁₃	—	8	1	no	—
465	C₂²×C₁₃	—	8	1	no	—
466	C₂²×C₁₃	—	8	1	no	—
467	C₂²×C₁₃	—	8	1	no	—
468	C₂²×C₁₃	—	8	1	no	—
469	C₂²×C₁₃	—	8	1	no	—
470	C₂²×C₁₃	—	8	1	no	—
471	C₂²×C₁₃	—	8	1	no	—
472	C₂²×C₁₃	—	8	1	no	—
473	C₂²×C₁₃	—	8	1	no	—
474	C₂²×C₁₃	—	8	1	no	—
475	C₂²×C₁₃	—	8	1	no	—
476	C₂²×C₁₃	—	8	1	no	—
477	C₂²×C₁₃	—	8	1	no	—
478	C₂²×C₁₃	—	8	1	no	—
479	C₂²×C₁₃	#469	1	4	yes	complemented
480	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
481	C₂²×C₁₃	D₄²	1	1	yes	characteristic
482	C₂²×C₁₃	#546	1	1	yes	characteristic
483	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
484	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
485	C₂²×C₁₃	#576	1	1	yes	characteristic
486	C₂²×C₁₃	#577	1	1	yes	characteristic
487	C₄×C₁₃	—	2	2	no	—
488	C₄×C₁₃	—	4	1	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	1	no	—
491	C₄×C₁₃	—	4	1	no	—
492	C₄×C₁₃	—	8	1	no	—
493	C₄×C₁₃	—	8	1	no	—
494	C₄×C₁₃	—	8	1	no	—
495	C₄×C₁₃	—	8	1	no	—
496	C₄×C₁₃	#525	1	1	yes	characteristic
497	C₄×C₁₃	#538	1	1	yes	characteristic
498	C₄×C₁₃	D₄²	1	1	yes	characteristic
499	C₄×C₁₃	#546	1	1	yes	characteristic
500	C₂⁵	—	2	1	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	2	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	2	no	—
510	C₂²×D₄	—	4	1	no	—
511	C₂²×D₄	—	4	1	no	—
512	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂×D₈	—	2	2	no	—
520	C₂×D₈	—	2	2	no	—
521	C₂×D₈	—	2	2	no	—
522	C₂×D₈	—	2	2	no	—
523	C₂×D₈	—	4	1	no	—
524	C₂×D₈	—	4	1	no	—
525	C₂×M₁₆	—	2	2	no	—
526	C₂×M₁₆	—	2	2	no	—
527	C₂×M₁₆	—	4	1	no	—
528	C₂²×C₈	—	2	2	no	—
529	C₂²×C₈	—	2	2	no	—
530	C₂²×C₈	—	4	1	no	—
531	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#121	—	2	2	no	—
539	#121	—	2	2	no	—
540	#121	—	4	1	no	—
541	#121	—	4	1	no	—
542	#121	—	4	1	no	—
543	#121	—	4	4	no	—
544	#120	—	4	4	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	4	1	no	—
551	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	1	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
572	#106	—	2	2	no	—
573	#106	—	4	1	no	—
574	C₄⋊C₈	—	2	2	no	—
575	#102	—	2	2	no	—
576	#102	—	2	2	no	—
577	#102	—	2	2	no	—
578	#102	—	2	2	no	—
579	#102	—	2	2	no	—
580	#102	—	2	2	no	—
581	#102	—	4	1	no	—
582	#102	D₄×C₁₃	1	4	yes	complemented
583	C₂²⋊C₈	—	2	2	no	—
584	C₂²⋊C₈	D₄×C₁₃	1	4	yes	complemented
585	#97	—	2	2	no	—
586	#95	—	2	1	no	—
587	#95	—	2	1	no	—
588	#95	—	2	1	no	—
589	C₂×C₁₃	—	2	4	no	—
590	C₂×C₁₃	—	8	1	no	—
591	C₂×C₁₃	—	8	2	no	—
592	C₂×C₁₃	—	8	2	no	—
593	C₂×C₁₃	—	16	1	no	—
594	C₂×C₁₃	#2424	1	1	yes	characteristic
595	C₂×C₁₃	C₂×#469	1	1	yes	characteristic
596	C₂×C₁₃	#3062	1	1	yes	characteristic
597	C₂×C₁₃	#3264	1	1	yes	characteristic
598	C₂×C₁₃	#3265	1	1	yes	characteristic
599	C₂×C₁₃	#3306	1	1	yes	characteristic
600	C₂×C₁₃	#3318	1	1	yes	characteristic
601	C₂⁴	—	2	1	no	—
602	C₂⁴	—	2	1	no	—
603	C₂⁴	—	2	1	no	—
604	C₂⁴	—	4	2	no	—
605	C₂⁴	—	4	2	no	—
606	C₂⁴	—	4	2	no	—
607	C₂⁴	—	4	2	no	—
608	C₂⁴	—	4	2	no	—
609	C₂⁴	—	8	1	no	—
610	C₂⁴	—	8	1	no	—
611	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
612	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂×D₄	—	2	8	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	4	4	no	—
634	C₂×D₄	—	4	4	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	4	no	—
638	C₂×D₄	—	4	2	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	2	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	8	1	no	—
649	C₂×D₄	—	8	1	no	—
650	C₂×D₄	—	8	1	no	—
651	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
652	C₂×D₄	C₁₃×#41	1	2	yes	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	8	1	no	—
671	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
676	C₂²×C₄	C₁₃×#41	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
678	D₈	—	4	4	no	—
679	D₈	—	4	4	no	—
680	M₁₆	—	4	4	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	4	4	no	—
691	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
692	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
693	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	8	1	no	—
719	C₂²⋊C₄	—	8	1	no	—
720	C₂²⋊C₄	—	8	1	no	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	1	no	—
723	C₁₃	#25124	1	1	yes	characteristic, direct product factor, Sylow
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	4	8	no	—
738	C₂³	—	4	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	8	4	no	—
758	C₂³	—	8	4	no	—
759	C₂³	—	8	4	no	—
760	C₂³	—	8	4	no	—
761	C₂³	—	8	4	no	—
762	C₂³	—	8	4	no	—
763	C₂³	C₁₃×#121	1	2	yes	—
764	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
765	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
766	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	4	8	no	—
772	D₄	—	4	4	no	—
773	D₄	—	4	1	no	—
774	D₄	—	4	1	no	—
775	D₄	—	4	1	no	—
776	D₄	—	4	1	no	—
777	D₄	—	4	1	no	—
778	D₄	—	4	1	no	—
779	D₄	—	4	1	no	—
780	D₄	—	4	1	no	—
781	D₄	—	8	4	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	4	no	—
784	D₄	—	8	4	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	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	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	8	4	no	—
820	C₂×C₄	C₁₃×#121	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
823	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
824	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
825	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
827	C₈	—	2	2	no	—
828	C₈	—	2	2	no	—
829	C₈	—	2	2	no	—
830	C₈	—	4	1	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	8	16	no	—
851	C₂²	—	8	1	no	—
852	C₂²	—	8	1	no	—
853	C₂²	—	8	1	no	—
854	C₂²	—	8	1	no	—
855	C₂²	—	8	1	no	—
856	C₂²	—	8	1	no	—
857	C₂²	—	8	1	no	—
858	C₂²	—	8	1	no	—
859	C₂²	—	8	1	no	—
860	C₂²	—	8	1	no	—
861	C₂²	—	8	1	no	—
862	C₂²	—	8	1	no	—
863	C₂²	—	8	1	no	—
864	C₂²	—	8	1	no	—
865	C₂²	—	8	1	no	—
866	C₂²	C₁₃×#469	1	4	yes	complemented
867	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
868	C₂²	D₄²×C₁₃	1	1	yes	characteristic
869	C₂²	C₁₃×#546	1	1	yes	characteristic
870	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
871	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
872	C₂²	C₁₃×#576	1	1	yes	characteristic
873	C₂²	C₁₃×#577	1	1	yes	characteristic
874	C₄	—	2	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	8	1	no	—
880	C₄	—	8	1	no	—
881	C₄	—	8	1	no	—
882	C₄	—	8	1	no	—
883	C₄	C₁₃×#525	1	1	yes	characteristic
884	C₄	C₁₃×#538	1	1	yes	characteristic
885	C₄	D₄²×C₁₃	1	1	yes	characteristic
886	C₄	C₁₃×#546	1	1	yes	characteristic
887	C₂	—	2	4	no	—
888	C₂	—	8	1	no	—
889	C₂	—	8	2	no	—
890	C₂	—	8	2	no	—
891	C₂	—	16	1	no	—
892	C₂	C₁₃×#2424	1	1	yes	characteristic
893	C₂	C₂×C₁₃×#469	1	1	yes	characteristic
894	C₂	C₁₃×#3062	1	1	yes	characteristic
895	C₂	C₁₃×#3264	1	1	yes	characteristic
896	C₂	C₁₃×#3265	1	1	yes	characteristic
897	C₂	C₁₃×#3306	1	1	yes	characteristic
898	C₂	C₁₃×#3318	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#469	C₂	semidirect
2. C₂×C₁₃×#447	C₂	semidirect
3. C₂×C₁₃×#435	C₂	semidirect
4. C₂²×C₁₃×#102	C₂	semidirect
5. C₁₃×#2416	C₂	semidirect
6. C₁₃×#2408	C₂	semidirect
7. C₁₃×#2065	C₂	semidirect
8. C₁₃×#2054	C₂	semidirect
9. C₁₃×#2034	C₂	semidirect
10. C₁₃×#1999	C₂	semidirect
11. C₁₃×#1972	C₂	semidirect
12. C₁₃×#1936	C₂	semidirect
13. C₁₃×#1895	C₂	semidirect
14. C₁₃×#1893	C₂	semidirect
15. C₁₃×#1853	C₂	semidirect
19. C₂²×C₁₃×M₁₆	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
32. C₂×C₁₃×#106	C₂²	semidirect
33. C₂×C₁₃×#106	C₂²	semidirect
34. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
42. C₂×C₁₃×#102	C₂²	semidirect
43. C₂×C₁₃×#102	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
46. C₂×C₁₃×#97	C₂²	semidirect
53. C₁₃×#390	C₂²	semidirect
54. C₁₃×#389	C₂²	semidirect
57. C₁₃×#380	C₂²	semidirect
59. C₁₃×#340	C₂²	semidirect
60. C₁₃×#340	C₂²	semidirect
61. C₁₃×#340	C₂²	semidirect
62. C₁₃×#340	C₂²	semidirect
145. C₁₃×#102	D₄	semidirect
147. C₁₃×C₂²⋊C₈	D₄	semidirect
152. #25124	C₁₃	direct (N × H)
275. C₂×#469	C₂×C₁₃	semidirect
276. C₂×#447	C₂×C₁₃	semidirect
277. C₂×#435	C₂×C₁₃	semidirect
278. C₂²×#102	C₂×C₁₃	semidirect
279. #2416	C₂×C₁₃	semidirect
280. #2408	C₂×C₁₃	semidirect
281. #2065	C₂×C₁₃	semidirect
282. #2054	C₂×C₁₃	semidirect
283. #2034	C₂×C₁₃	semidirect
284. #1999	C₂×C₁₃	semidirect
285. #1972	C₂×C₁₃	semidirect
286. #1936	C₂×C₁₃	semidirect
287. #1895	C₂×C₁₃	semidirect
288. #1893	C₂×C₁₃	semidirect
289. #1853	C₂×C₁₃	semidirect
400. C₂²×M₁₆	C₂²×C₁₃	semidirect
406. C₂×#121	C₂²×C₁₃	semidirect
413. C₂×#106	C₂²×C₁₃	semidirect
414. C₂×#106	C₂²×C₁₃	semidirect
415. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
423. C₂×#102	C₂²×C₁₃	semidirect
424. C₂×#102	C₂²×C₁₃	semidirect
426. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
427. C₂×#97	C₂²×C₁₃	semidirect
434. #390	C₂²×C₁₃	semidirect
435. #389	C₂²×C₁₃	semidirect
438. #380	C₂²×C₁₃	semidirect
440. #340	C₂²×C₁₃	semidirect
441. #340	C₂²×C₁₃	semidirect
442. #340	C₂²×C₁₃	semidirect
443. #340	C₂²×C₁₃	semidirect
479. C₂²×C₁₃	#469	semidirect
582. #102	D₄×C₁₃	semidirect
584. C₂²⋊C₈	D₄×C₁₃	semidirect
723. C₁₃	#25124	direct (N × H)
866. C₂²	C₁₃×#469	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#469	2
C₂×C₁₃×#447	2
C₂×C₁₃×#435	2
C₂²×C₁₃×#102	2
C₁₃×#2416	2
C₁₃×#2408	2
C₁₃×#2065	2
C₁₃×#2054	2
C₁₃×#2034	2
C₁₃×#1999	2
C₁₃×#1972	2
C₁₃×#1936	2
C₁₃×#1895	2
C₁₃×#1893	2
C₁₃×#1853	2
#25124	13

Subgroups — C13×#25124 #15711463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25124 #15711463