Subgroups — C₁₃×#24367 #15710706

Order 3328.

1604 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
19	C₂×C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
20	C₂×C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×C₂²⋊Q₈	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	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
34	C₁₃×#463	—	2	4	no	—
35	C₁₃×#461	—	2	4	no	—
36	C₁₃×#450	—	2	4	no	—
37	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₁₃×#394	—	2	1	no	—
49	C₁₃×#394	—	2	1	no	—
50	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
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×#386	—	2	1	no	—
55	C₁₃×#386	—	2	1	no	—
56	C₁₃×#385	—	2	1	no	—
57	C₁₃×#385	—	2	1	no	—
58	C₁₃×#380	C₂²	1	1	yes	characteristic
59	C₁₃×#379	—	2	1	no	—
60	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
61	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₁₃	—	2	1	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	4	1	no	—
71	C₂×C₁₃×#41	—	4	1	no	—
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	—	2	2	no	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	—	2	2	no	—
79	C₂²×D₄×C₁₃	—	4	1	no	—
80	C₂²×D₄×C₁₃	—	4	1	no	—
81	C₂²×D₄×C₁₃	D₄	1	4	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	—	2	1	no	—
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×AGL(1,ℤ/8)	—	2	32	no	—
90	C₂×C₁₃×SD₁₆	—	2	2	no	—
91	C₂×C₁₃×SD₁₆	—	2	2	no	—
92	C₂×C₁₃×SD₁₆	—	2	2	no	—
93	C₂×C₁₃×SD₁₆	—	2	2	no	—
94	C₂×C₁₃×SD₁₆	—	2	2	no	—
95	C₂×C₁₃×SD₁₆	—	2	2	no	—
96	C₂×C₁₃×SD₁₆	—	2	2	no	—
97	C₂×C₁₃×SD₁₆	—	2	2	no	—
98	C₂×C₁₃×SD₁₆	—	2	2	no	—
99	C₂×C₁₃×SD₁₆	—	4	1	no	—
100	C₂×C₁₃×SD₁₆	—	4	1	no	—
101	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
102	C₂×C₁₃×D₈	—	2	2	no	—
103	C₂×C₁₃×D₈	—	2	2	no	—
104	C₂×C₁₃×D₈	—	2	2	no	—
105	C₂×C₁₃×D₈	—	2	2	no	—
106	C₂×C₁₃×D₈	—	2	2	no	—
107	C₂×C₁₃×D₈	D₄	1	4	yes	—
108	C₂×C₁₃×M₁₆	—	2	2	no	—
109	C₂×C₁₃×M₁₆	—	2	2	no	—
110	C₂×C₁₃×M₁₆	—	2	2	no	—
111	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	—	2	2	no	—
116	C₁₃×C₄⋊Q₈	—	4	1	no	—
117	C₁₃×#124	—	2	2	no	—
118	C₁₃×#124	—	4	1	no	—
119	C₁₃×C₂²⋊Q₈	—	2	2	no	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₄×D₄×C₁₃	—	2	2	no	—
122	C₄×D₄×C₁₃	—	2	2	no	—
123	C₄×D₄×C₁₃	—	4	1	no	—
124	C₄×D₄×C₁₃	—	4	1	no	—
125	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
144	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
145	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
146	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
148	C₁₃×C₄⋊C₈	—	2	2	no	—
149	C₁₃×C₄⋊C₈	—	2	2	no	—
150	C₁₃×#103	—	2	2	no	—
151	C₁₃×#103	—	2	2	no	—
152	C₁₃×#103	—	2	2	no	—
153	C₁₃×#103	—	4	1	no	—
154	C₁₃×#102	—	2	2	no	—
155	C₁₃×#102	—	2	2	no	—
156	C₁₃×#102	—	2	2	no	—
157	C₁₃×#102	—	4	1	no	—
158	C₁₃×C₂²⋊C₈	—	2	2	no	—
159	C₁₃×#95	—	2	1	no	—
160	C₁₃×#95	—	2	1	no	—
161	C₁₃×#95	—	2	1	no	—
162	C₁₃×#95	D₄	1	1	yes	characteristic
163	C₁₃×#95	D₄	1	1	yes	characteristic
164	#24367	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂⁴×C₁₃	—	2	1	no	—
166	C₂⁴×C₁₃	—	2	1	no	—
167	C₂⁴×C₁₃	—	2	1	no	—
168	C₂⁴×C₁₃	—	2	4	no	—
169	C₂⁴×C₁₃	—	4	2	no	—
170	C₂⁴×C₁₃	—	4	2	no	—
171	C₂⁴×C₁₃	—	4	2	no	—
172	C₂⁴×C₁₃	—	4	2	no	—
173	C₂⁴×C₁₃	—	8	1	no	—
174	C₂⁴×C₁₃	—	8	1	no	—
175	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₁₃×#41	—	2	8	no	—
177	C₁₃×#41	—	4	4	no	—
178	C₁₃×#41	—	4	4	no	—
179	C₁₃×#41	—	4	4	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
192	C₂×D₄×C₁₃	—	2	8	no	—
193	C₂×D₄×C₁₃	—	2	4	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	1	no	—
196	C₂×D₄×C₁₃	—	2	1	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	1	no	—
207	C₂×D₄×C₁₃	—	4	4	no	—
208	C₂×D₄×C₁₃	—	4	4	no	—
209	C₂×D₄×C₁₃	—	4	4	no	—
210	C₂×D₄×C₁₃	—	4	2	no	—
211	C₂×D₄×C₁₃	—	4	2	no	—
212	C₂×D₄×C₁₃	—	4	2	no	—
213	C₂×D₄×C₁₃	—	4	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	4	2	no	—
230	C₂²×C₄×C₁₃	—	4	2	no	—
231	C₂²×C₄×C₁₃	—	4	2	no	—
232	C₂²×C₄×C₁₃	—	4	2	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	8	1	no	—
237	C₂²×C₄×C₁₃	—	8	1	no	—
238	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	#41	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₁₃×SD₁₆	—	2	8	no	—
247	C₁₃×SD₁₆	—	2	8	no	—
248	C₁₃×SD₁₆	—	4	4	no	—
249	C₁₃×SD₁₆	—	4	4	no	—
250	C₁₃×D₈	—	2	8	no	—
251	C₁₃×D₈	—	2	8	no	—
252	C₁₃×M₁₆	—	2	8	no	—
253	C₂×C₈×C₁₃	—	2	1	no	—
254	C₂×C₈×C₁₃	—	2	1	no	—
255	C₂×C₈×C₁₃	—	2	1	no	—
256	C₂×C₈×C₁₃	—	2	1	no	—
257	C₂×C₈×C₁₃	—	2	1	no	—
258	C₂×C₈×C₁₃	—	2	1	no	—
259	C₂×C₈×C₁₃	—	2	1	no	—
260	C₂×C₈×C₁₃	—	2	1	no	—
261	C₂×C₈×C₁₃	—	2	1	no	—
262	C₂×C₈×C₁₃	—	2	1	no	—
263	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
264	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	—	4	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₁₃×C₂²⋊C₄	—	4	1	no	—
276	C₁₃×C₂²⋊C₄	—	4	2	no	—
277	C₁₃×C₂²⋊C₄	—	4	2	no	—
278	C₁₃×C₂²⋊C₄	—	4	2	no	—
279	C₁₃×C₂²⋊C₄	—	4	2	no	—
280	C₁₃×C₂²⋊C₄	—	4	2	no	—
281	C₁₃×C₂²⋊C₄	—	4	2	no	—
282	C₁₃×C₂²⋊C₄	—	4	2	no	—
283	C₁₃×C₂²⋊C₄	—	4	2	no	—
284	C₁₃×C₂²⋊C₄	—	4	2	no	—
285	C₁₃×C₂²⋊C₄	—	4	2	no	—
286	C₁₃×C₂²⋊C₄	—	8	1	no	—
287	C₁₃×C₂²⋊C₄	—	8	1	no	—
288	C₄²×C₁₃	—	2	1	no	—
289	C₄²×C₁₃	—	2	1	no	—
290	C₄²×C₁₃	—	2	1	no	—
291	C₄²×C₁₃	—	2	1	no	—
292	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
293	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#2432	C₂×C₁₃	1	1	yes	characteristic, complemented
297	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2054	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2013	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2012	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	2	1	no	—
312	C₂³×C₁₃	—	2	1	no	—
313	C₂³×C₁₃	—	2	1	no	—
314	C₂³×C₁₃	—	2	1	no	—
315	C₂³×C₁₃	—	2	1	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	4	8	no	—
319	C₂³×C₁₃	—	4	8	no	—
320	C₂³×C₁₃	—	4	1	no	—
321	C₂³×C₁₃	—	4	1	no	—
322	C₂³×C₁₃	—	4	1	no	—
323	C₂³×C₁₃	—	4	1	no	—
324	C₂³×C₁₃	—	4	1	no	—
325	C₂³×C₁₃	—	4	1	no	—
326	C₂³×C₁₃	—	4	1	no	—
327	C₂³×C₁₃	—	4	1	no	—
328	C₂³×C₁₃	—	4	1	no	—
329	C₂³×C₁₃	—	4	1	no	—
330	C₂³×C₁₃	—	4	1	no	—
331	C₂³×C₁₃	—	4	1	no	—
332	C₂³×C₁₃	—	4	1	no	—
333	C₂³×C₁₃	—	4	1	no	—
334	C₂³×C₁₃	—	4	1	no	—
335	C₂³×C₁₃	—	4	1	no	—
336	C₂³×C₁₃	—	8	4	no	—
337	C₂³×C₁₃	—	8	4	no	—
338	C₂³×C₁₃	—	8	4	no	—
339	C₂³×C₁₃	—	8	4	no	—
340	C₂³×C₁₃	—	8	4	no	—
341	C₂³×C₁₃	#121	1	2	yes	—
342	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₁₃	—	2	2	no	—
344	Q₈×C₁₃	—	2	2	no	—
345	Q₈×C₁₃	—	4	1	no	—
346	Q₈×C₁₃	—	4	1	no	—
347	Q₈×C₁₃	—	4	1	no	—
348	Q₈×C₁₃	—	4	1	no	—
349	Q₈×C₁₃	—	4	1	no	—
350	Q₈×C₁₃	—	4	1	no	—
351	D₄×C₁₃	—	2	2	no	—
352	D₄×C₁₃	—	2	2	no	—
353	D₄×C₁₃	—	2	2	no	—
354	D₄×C₁₃	—	2	2	no	—
355	D₄×C₁₃	—	2	2	no	—
356	D₄×C₁₃	—	2	2	no	—
357	D₄×C₁₃	—	2	2	no	—
358	D₄×C₁₃	—	4	8	no	—
359	D₄×C₁₃	—	4	8	no	—
360	D₄×C₁₃	—	4	1	no	—
361	D₄×C₁₃	—	4	1	no	—
362	D₄×C₁₃	—	4	1	no	—
363	D₄×C₁₃	—	4	1	no	—
364	D₄×C₁₃	#120	1	4	yes	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	4	8	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	—	4	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	4	1	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	1	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	1	no	—
393	C₂×C₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	4	1	no	—
395	C₂×C₄×C₁₃	—	4	1	no	—
396	C₂×C₄×C₁₃	—	4	1	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	8	4	no	—
399	C₂×C₄×C₁₃	—	8	4	no	—
400	C₂×C₄×C₁₃	#121	1	2	yes	—
401	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	complemented
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
406	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
407	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
408	C₈×C₁₃	—	2	2	no	—
409	C₈×C₁₃	—	2	2	no	—
410	C₈×C₁₃	—	4	1	no	—
411	C₈×C₁₃	—	4	1	no	—
412	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
413	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×AGL(1,ℤ/8)	—	2	4	no	—
415	C₂×AGL(1,ℤ/8)	—	2	4	no	—
416	C₂×AGL(1,ℤ/8)	—	2	4	no	—
417	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
418	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
419	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
421	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
422	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
423	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
429	C₂²×C₂²⋊C₄	—	2	1	no	—
430	#463	—	2	4	no	—
431	#461	—	2	4	no	—
432	#450	—	2	4	no	—
433	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
444	#394	—	2	1	no	—
445	#394	—	2	1	no	—
446	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#390	C₂²×C₁₃	1	1	yes	characteristic
448	#390	C₂²×C₁₃	1	1	yes	characteristic
449	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	#386	—	2	1	no	—
451	#386	—	2	1	no	—
452	#385	—	2	1	no	—
453	#385	—	2	1	no	—
454	#380	C₂²×C₁₃	1	1	yes	characteristic
455	#379	—	2	1	no	—
456	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
457	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	C₂²×C₁₃	—	2	2	no	—
462	C₂²×C₁₃	—	2	4	no	—
463	C₂²×C₁₃	—	2	2	no	—
464	C₂²×C₁₃	—	2	2	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	1	no	—
467	C₂²×C₁₃	—	4	1	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	1	no	—
471	C₂²×C₁₃	—	4	1	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	—	4	2	no	—
478	C₂²×C₁₃	—	4	2	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	2	no	—
481	C₂²×C₁₃	—	8	16	no	—
482	C₂²×C₁₃	—	8	1	no	—
483	C₂²×C₁₃	—	8	1	no	—
484	C₂²×C₁₃	—	8	1	no	—
485	C₂²×C₁₃	—	8	1	no	—
486	C₂²×C₁₃	—	8	1	no	—
487	C₂²×C₁₃	—	8	1	no	—
488	C₂²×C₁₃	—	8	1	no	—
489	C₂²×C₁₃	—	8	1	no	—
490	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
491	C₂²×C₁₃	D₄²	1	1	yes	characteristic
492	C₂²×C₁₃	D₄²	1	1	yes	characteristic
493	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
494	C₂²×C₁₃	#575	1	1	yes	characteristic
495	C₂²×C₁₃	#577	1	1	yes	characteristic
496	C₂²×C₁₃	#577	1	1	yes	characteristic
497	C₄×C₁₃	—	2	2	no	—
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	4	2	no	—
500	C₄×C₁₃	—	4	1	no	—
501	C₄×C₁₃	—	4	1	no	—
502	C₄×C₁₃	—	4	1	no	—
503	C₄×C₁₃	—	8	1	no	—
504	C₄×C₁₃	—	8	1	no	—
505	C₄×C₁₃	—	8	1	no	—
506	C₄×C₁₃	—	8	1	no	—
507	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
508	C₄×C₁₃	#534	1	1	yes	characteristic
509	C₄×C₁₃	#546	1	1	yes	characteristic
510	C₄×C₁₃	#546	1	1	yes	characteristic
511	C₂⁵	—	2	1	no	—
512	C₂×#41	—	2	2	no	—
513	C₂×#41	—	2	2	no	—
514	C₂×#41	—	2	2	no	—
515	C₂×#41	—	2	2	no	—
516	C₂×#41	—	4	1	no	—
517	C₂×#41	—	4	1	no	—
518	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
519	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
520	C₂²×D₄	—	2	2	no	—
521	C₂²×D₄	—	2	2	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	2	no	—
525	C₂²×D₄	—	4	1	no	—
526	C₂²×D₄	—	4	1	no	—
527	C₂²×D₄	D₄×C₁₃	1	4	yes	—
528	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
530	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	1	no	—
533	C₂³×C₄	—	2	1	no	—
534	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
535	AGL(1,ℤ/8)	—	2	32	no	—
536	C₂×SD₁₆	—	2	2	no	—
537	C₂×SD₁₆	—	2	2	no	—
538	C₂×SD₁₆	—	2	2	no	—
539	C₂×SD₁₆	—	2	2	no	—
540	C₂×SD₁₆	—	2	2	no	—
541	C₂×SD₁₆	—	2	2	no	—
542	C₂×SD₁₆	—	2	2	no	—
543	C₂×SD₁₆	—	2	2	no	—
544	C₂×SD₁₆	—	2	2	no	—
545	C₂×SD₁₆	—	4	1	no	—
546	C₂×SD₁₆	—	4	1	no	—
547	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
548	C₂×D₈	—	2	2	no	—
549	C₂×D₈	—	2	2	no	—
550	C₂×D₈	—	2	2	no	—
551	C₂×D₈	—	2	2	no	—
552	C₂×D₈	—	2	2	no	—
553	C₂×D₈	D₄×C₁₃	1	4	yes	—
554	C₂×M₁₆	—	2	2	no	—
555	C₂×M₁₆	—	2	2	no	—
556	C₂×M₁₆	—	2	2	no	—
557	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
559	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
560	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₄⋊Q₈	—	2	2	no	—
562	C₄⋊Q₈	—	4	1	no	—
563	#124	—	2	2	no	—
564	#124	—	4	1	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	4	1	no	—
570	C₄×D₄	—	4	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	4	4	no	—
590	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
594	C₄⋊C₈	—	2	2	no	—
595	C₄⋊C₈	—	2	2	no	—
596	#103	—	2	2	no	—
597	#103	—	2	2	no	—
598	#103	—	2	2	no	—
599	#103	—	4	1	no	—
600	#102	—	2	2	no	—
601	#102	—	2	2	no	—
602	#102	—	2	2	no	—
603	#102	—	4	1	no	—
604	C₂²⋊C₈	—	2	2	no	—
605	#95	—	2	1	no	—
606	#95	—	2	1	no	—
607	#95	—	2	1	no	—
608	#95	D₄×C₁₃	1	1	yes	characteristic
609	#95	D₄×C₁₃	1	1	yes	characteristic
610	C₂×C₁₃	—	4	2	no	—
611	C₂×C₁₃	—	4	4	no	—
612	C₂×C₁₃	—	8	2	no	—
613	C₂×C₁₃	—	8	2	no	—
614	C₂×C₁₃	#2410	1	1	yes	characteristic
615	C₂×C₁₃	#3036	1	1	yes	characteristic
616	C₂×C₁₃	#3042	1	1	yes	characteristic
617	C₂×C₁₃	#3265	1	1	yes	characteristic
618	C₂×C₁₃	#3267	1	1	yes	characteristic
619	C₂×C₁₃	#3272	1	1	yes	characteristic
620	C₂×C₁₃	#3275	1	1	yes	characteristic
621	C₂⁴	—	2	1	no	—
622	C₂⁴	—	2	1	no	—
623	C₂⁴	—	2	1	no	—
624	C₂⁴	—	2	4	no	—
625	C₂⁴	—	4	2	no	—
626	C₂⁴	—	4	2	no	—
627	C₂⁴	—	4	2	no	—
628	C₂⁴	—	4	2	no	—
629	C₂⁴	—	8	1	no	—
630	C₂⁴	—	8	1	no	—
631	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
632	#41	—	2	8	no	—
633	#41	—	4	4	no	—
634	#41	—	4	4	no	—
635	#41	—	4	4	no	—
636	C₂×Q₈	—	2	1	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
648	C₂×D₄	—	2	8	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	4	4	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
672	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
673	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
674	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
675	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	8	1	no	—
693	C₂²×C₄	—	8	1	no	—
694	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
699	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₁₃×#41	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
702	SD₁₆	—	2	8	no	—
703	SD₁₆	—	2	8	no	—
704	SD₁₆	—	4	4	no	—
705	SD₁₆	—	4	4	no	—
706	D₈	—	2	8	no	—
707	D₈	—	2	8	no	—
708	M₁₆	—	2	8	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	2	1	no	—
711	C₂×C₈	—	2	1	no	—
712	C₂×C₈	—	2	1	no	—
713	C₂×C₈	—	2	1	no	—
714	C₂×C₈	—	2	1	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	—	2	1	no	—
717	C₂×C₈	—	2	1	no	—
718	C₂×C₈	—	2	1	no	—
719	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
720	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	4	1	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	8	1	no	—
743	C₂²⋊C₄	—	8	1	no	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	1	no	—
746	C₄²	—	2	1	no	—
747	C₄²	—	2	1	no	—
748	C₁₃	#24367	1	1	yes	characteristic, direct product factor, Sylow
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	4	8	no	—
761	C₂³	—	4	8	no	—
762	C₂³	—	4	1	no	—
763	C₂³	—	4	1	no	—
764	C₂³	—	4	1	no	—
765	C₂³	—	4	1	no	—
766	C₂³	—	4	1	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	4	1	no	—
770	C₂³	—	4	1	no	—
771	C₂³	—	4	1	no	—
772	C₂³	—	4	1	no	—
773	C₂³	—	4	1	no	—
774	C₂³	—	4	1	no	—
775	C₂³	—	4	1	no	—
776	C₂³	—	4	1	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	8	4	no	—
779	C₂³	—	8	4	no	—
780	C₂³	—	8	4	no	—
781	C₂³	—	8	4	no	—
782	C₂³	—	8	4	no	—
783	C₂³	C₁₃×#121	1	2	yes	—
784	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
785	Q₈	—	2	2	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	4	1	no	—
788	Q₈	—	4	1	no	—
789	Q₈	—	4	1	no	—
790	Q₈	—	4	1	no	—
791	Q₈	—	4	1	no	—
792	Q₈	—	4	1	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	2	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	no	—
800	D₄	—	4	8	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	1	no	—
803	D₄	—	4	1	no	—
804	D₄	—	4	1	no	—
805	D₄	—	4	1	no	—
806	D₄	C₁₃×#120	1	4	yes	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	4	8	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	8	4	no	—
841	C₂×C₄	—	8	4	no	—
842	C₂×C₄	C₁₃×#121	1	2	yes	—
843	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	complemented
844	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
847	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
848	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
849	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
850	C₈	—	2	2	no	—
851	C₈	—	2	2	no	—
852	C₈	—	4	1	no	—
853	C₈	—	4	1	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	4	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	8	16	no	—
875	C₂²	—	8	1	no	—
876	C₂²	—	8	1	no	—
877	C₂²	—	8	1	no	—
878	C₂²	—	8	1	no	—
879	C₂²	—	8	1	no	—
880	C₂²	—	8	1	no	—
881	C₂²	—	8	1	no	—
882	C₂²	—	8	1	no	—
883	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
884	C₂²	D₄²×C₁₃	1	1	yes	characteristic
885	C₂²	D₄²×C₁₃	1	1	yes	characteristic
886	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
887	C₂²	C₁₃×#575	1	1	yes	characteristic
888	C₂²	C₁₃×#577	1	1	yes	characteristic
889	C₂²	C₁₃×#577	1	1	yes	characteristic
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	2	no	—
896	C₄	—	8	1	no	—
897	C₄	—	8	1	no	—
898	C₄	—	8	1	no	—
899	C₄	—	8	1	no	—
900	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
901	C₄	C₁₃×#534	1	1	yes	characteristic
902	C₄	C₁₃×#546	1	1	yes	characteristic
903	C₄	C₁₃×#546	1	1	yes	characteristic
904	C₂	—	4	2	no	—
905	C₂	—	4	4	no	—
906	C₂	—	8	2	no	—
907	C₂	—	8	2	no	—
908	C₂	C₁₃×#2410	1	1	yes	characteristic
909	C₂	C₁₃×#3036	1	1	yes	characteristic
910	C₂	C₁₃×#3042	1	1	yes	characteristic
911	C₂	C₁₃×#3265	1	1	yes	characteristic
912	C₂	C₁₃×#3267	1	1	yes	characteristic
913	C₂	C₁₃×#3272	1	1	yes	characteristic
914	C₂	C₁₃×#3275	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#463	C₂	semidirect
3. C₂×C₁₃×#461	C₂	semidirect
4. C₂×C₁₃×#450	C₂	semidirect
5. C₁₃×#2432	C₂	semidirect
6. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
7. C₁₃×#2055	C₂	semidirect
8. C₁₃×#2054	C₂	semidirect
9. C₁₃×#2013	C₂	semidirect
10. C₁₃×#2012	C₂	semidirect
11. C₁₃×#1894	C₂	semidirect
12. C₁₃×#1879	C₂	semidirect
13. C₁₃×#1877	C₂	semidirect
14. C₁₃×#1851	C₂	semidirect
15. C₁₃×#1788	C₂	semidirect
28. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₁₃×#124	C₂²	semidirect
37. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
38. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
39. C₂×C₁₃×#103	C₂²	semidirect
40. C₂×C₁₃×#103	C₂²	semidirect
41. C₂×C₁₃×#103	C₂²	semidirect
42. C₂×C₁₃×#103	C₂²	semidirect
45. C₂×C₁₃×#102	C₂²	semidirect
46. C₂×C₁₃×#102	C₂²	semidirect
50. C₁₃×#391	C₂²	semidirect
53. C₁₃×#390	C₂²	semidirect
61. C₁₃×#340	C₂²	semidirect
62. C₁₃×#340	C₂²	semidirect
63. C₁₃×#336	C₂²	semidirect
64. C₁₃×#336	C₂²	semidirect
164. #24367	C₁₃	direct (N × H)
293. C₂×#463	C₂×C₁₃	semidirect
294. C₂×#461	C₂×C₁₃	semidirect
295. C₂×#450	C₂×C₁₃	semidirect
296. #2432	C₂×C₁₃	semidirect
297. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
298. #2055	C₂×C₁₃	semidirect
299. #2054	C₂×C₁₃	semidirect
300. #2013	C₂×C₁₃	semidirect
301. #2012	C₂×C₁₃	semidirect
302. #1894	C₂×C₁₃	semidirect
303. #1879	C₂×C₁₃	semidirect
304. #1877	C₂×C₁₃	semidirect
305. #1851	C₂×C₁₃	semidirect
306. #1788	C₂×C₁₃	semidirect
401. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
424. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
425. C₂×#124	C₂²×C₁₃	semidirect
433. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
434. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
435. C₂×#103	C₂²×C₁₃	semidirect
436. C₂×#103	C₂²×C₁₃	semidirect
437. C₂×#103	C₂²×C₁₃	semidirect
438. C₂×#103	C₂²×C₁₃	semidirect
441. C₂×#102	C₂²×C₁₃	semidirect
442. C₂×#102	C₂²×C₁₃	semidirect
446. #391	C₂²×C₁₃	semidirect
449. #390	C₂²×C₁₃	semidirect
457. #340	C₂²×C₁₃	semidirect
458. #340	C₂²×C₁₃	semidirect
459. #336	C₂²×C₁₃	semidirect
460. #336	C₂²×C₁₃	semidirect
748. C₁₃	#24367	direct (N × H)
843. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×AGL(1,ℤ/8)	2
C₂×C₁₃×#463	2
C₂×C₁₃×#461	2
C₂×C₁₃×#450	2
C₁₃×#2432	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2055	2
C₁₃×#2054	2
C₁₃×#2013	2
C₁₃×#2012	2
C₁₃×#1894	2
C₁₃×#1879	2
C₁₃×#1877	2
C₁₃×#1851	2
C₁₃×#1788	2
#24367	13

Subgroups — C13×#24367 #15710706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24367 #15710706