Subgroups — C₁₃×#22443 #15708782

Order 3328.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 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×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1753	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)	C₄	1	8	yes	complemented
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
31	C₁₃×#440	—	2	4	no	—
32	C₄×C₁₃×SD₁₆	—	2	4	no	—
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
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, complemented
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#390	—	2	1	no	—
47	C₁₃×#390	—	2	1	no	—
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#386	—	2	1	no	—
53	C₁₃×#386	—	2	1	no	—
54	C₁₃×#380	—	2	1	no	—
55	C₁₃×#380	C₂²	1	1	yes	characteristic
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₁₃×#379	—	2	1	no	—
58	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
59	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
64	C₂⁵×C₁₃	—	2	1	no	—
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	4	1	no	—
69	C₂×C₁₃×#41	—	4	1	no	—
70	C₂×C₁₃×#41	C₂×C₄	1	4	yes	complemented
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	—	2	2	no	—
73	C₂²×D₄×C₁₃	—	2	2	no	—
74	C₂²×D₄×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	—	2	1	no	—
76	C₂²×D₄×C₁₃	—	2	2	no	—
77	C₂²×D₄×C₁₃	—	4	1	no	—
78	C₂²×D₄×C₁₃	—	4	1	no	—
79	C₂²×D₄×C₁₃	C₂×C₄	1	4	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×AGL(1,ℤ/8)	—	2	32	no	—
88	C₂×C₁₃×SD₁₆	—	2	2	no	—
89	C₂×C₁₃×SD₁₆	—	2	2	no	—
90	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
91	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	complemented
92	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
93	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
94	C₂×C₁₃×D₈	—	2	2	no	—
95	C₂×C₁₃×D₈	—	2	2	no	—
96	C₂×C₁₃×D₈	—	2	2	no	—
97	C₂×C₁₃×D₈	—	2	2	no	—
98	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	—
99	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	complemented
100	C₂×C₁₃×M₁₆	—	2	2	no	—
101	C₂×C₁₃×M₁₆	—	2	2	no	—
102	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	complemented
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	—	2	2	no	—
109	C₄×Q₈×C₁₃	—	4	1	no	—
110	C₄×Q₈×C₁₃	—	4	1	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	—	2	2	no	—
113	C₄×D₄×C₁₃	—	4	1	no	—
114	C₄×D₄×C₁₃	—	4	1	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
134	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
135	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	—	2	1	no	—
137	C₂×C₄²×C₁₃	—	2	1	no	—
138	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₁₃×#107	—	2	2	no	—
141	C₁₃×#106	—	2	2	no	—
142	C₁₃×#103	—	2	2	no	—
143	C₁₃×#103	—	2	2	no	—
144	C₁₃×#102	—	2	2	no	—
145	C₁₃×#102	—	2	2	no	—
146	C₁₃×#102	—	4	1	no	—
147	C₁₃×#102	—	4	1	no	—
148	C₁₃×#102	—	4	1	no	—
149	C₁₃×#102	—	4	1	no	—
150	C₁₃×C₂²⋊C₈	—	2	2	no	—
151	C₁₃×#97	—	2	2	no	—
152	C₄×C₈×C₁₃	—	2	2	no	—
153	C₁₃×#95	—	2	1	no	—
154	C₁₃×#95	—	2	1	no	—
155	C₁₃×#95	D₄	1	1	yes	characteristic
156	C₁₃×#95	D₄	1	1	yes	characteristic
157	#22443	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂⁴×C₁₃	—	2	1	no	—
159	C₂⁴×C₁₃	—	2	1	no	—
160	C₂⁴×C₁₃	—	2	1	no	—
161	C₂⁴×C₁₃	—	2	4	no	—
162	C₂⁴×C₁₃	—	4	2	no	—
163	C₂⁴×C₁₃	—	4	2	no	—
164	C₂⁴×C₁₃	—	4	2	no	—
165	C₂⁴×C₁₃	—	4	2	no	—
166	C₂⁴×C₁₃	—	8	1	no	—
167	C₂⁴×C₁₃	—	8	1	no	—
168	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₁₃×#41	—	2	8	no	—
170	C₁₃×#41	—	4	4	no	—
171	C₁₃×#41	—	4	4	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
177	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
178	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₁₃	—	2	8	no	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	2	4	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	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	1	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	4	4	no	—
196	C₂×D₄×C₁₃	—	4	4	no	—
197	C₂×D₄×C₁₃	—	4	4	no	—
198	C₂×D₄×C₁₃	—	4	2	no	—
199	C₂×D₄×C₁₃	—	4	2	no	—
200	C₂×D₄×C₁₃	—	4	2	no	—
201	C₂×D₄×C₁₃	—	4	2	no	—
202	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
203	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
204	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
205	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
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	4	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	—	4	2	no	—
218	C₂²×C₄×C₁₃	—	4	2	no	—
219	C₂²×C₄×C₁₃	—	4	2	no	—
220	C₂²×C₄×C₁₃	—	4	2	no	—
221	C₂²×C₄×C₁₃	—	4	2	no	—
222	C₂²×C₄×C₁₃	—	4	2	no	—
223	C₂²×C₄×C₁₃	—	8	1	no	—
224	C₂²×C₄×C₁₃	—	8	1	no	—
225	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	#41	1	2	yes	—
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₁₃×SD₁₆	—	2	8	no	—
234	C₁₃×SD₁₆	C₂²⋊C₄	1	16	yes	complemented
235	C₁₃×D₈	—	2	8	no	—
236	C₁₃×D₈	—	2	8	no	—
237	C₁₃×M₁₆	—	2	8	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	—	2	1	no	—
243	C₂×C₈×C₁₃	—	2	1	no	—
244	C₂×C₈×C₁₃	—	2	1	no	—
245	C₂×C₈×C₁₃	—	2	1	no	—
246	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
247	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
248	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
249	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	4	2	no	—
259	C₁₃×C₄⋊C₄	—	4	2	no	—
260	C₁₃×C₂²⋊C₄	—	2	2	no	—
261	C₁₃×C₂²⋊C₄	—	4	1	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	—	8	1	no	—
270	C₁₃×C₂²⋊C₄	—	8	1	no	—
271	C₁₃×C₂²⋊C₄	—	8	1	no	—
272	C₁₃×C₂²⋊C₄	—	8	1	no	—
273	C₁₃×C₂²⋊C₄	—	8	1	no	—
274	C₄²×C₁₃	—	2	1	no	—
275	C₄²×C₁₃	—	2	1	no	—
276	C₄²×C₁₃	—	2	1	no	—
277	C₄²×C₁₃	—	2	1	no	—
278	C₄²×C₁₃	—	4	2	no	—
279	C₄²×C₁₃	—	4	2	no	—
280	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic
281	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#2341	C₂×C₁₃	1	1	yes	characteristic, complemented
284	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1972	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#1879	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#1786	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	2	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	—	2	1	no	—
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	4	8	no	—
307	C₂³×C₁₃	—	4	8	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	—	4	1	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	C₄×D₄	1	2	yes	—
330	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₁₃	—	2	2	no	—
332	Q₈×C₁₃	—	2	2	no	—
333	Q₈×C₁₃	—	2	2	no	—
334	Q₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	complemented
335	D₄×C₁₃	—	2	2	no	—
336	D₄×C₁₃	—	2	2	no	—
337	D₄×C₁₃	—	2	2	no	—
338	D₄×C₁₃	—	2	2	no	—
339	D₄×C₁₃	—	2	2	no	—
340	D₄×C₁₃	—	2	2	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	4	8	no	—
343	D₄×C₁₃	—	4	8	no	—
344	D₄×C₁₃	—	4	1	no	—
345	D₄×C₁₃	—	4	1	no	—
346	D₄×C₁₃	—	4	1	no	—
347	D₄×C₁₃	—	4	1	no	—
348	D₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	1	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	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	4	8	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	—	8	4	no	—
383	C₂×C₄×C₁₃	—	8	4	no	—
384	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
385	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	complemented
386	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
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	H(5,𝔽₂)	1	1	yes	characteristic
391	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
392	C₈×C₁₃	—	2	2	no	—
393	C₈×C₁₃	—	4	1	no	—
394	C₈×C₁₃	—	4	1	no	—
395	C₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	complemented
396	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
397	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×AGL(1,ℤ/8)	—	2	4	no	—
399	C₂×AGL(1,ℤ/8)	—	2	4	no	—
400	C₂×AGL(1,ℤ/8)	C₄×C₁₃	1	8	yes	complemented
401	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
402	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
403	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
404	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
407	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	—	2	1	no	—
411	#440	—	2	4	no	—
412	C₄×SD₁₆	—	2	4	no	—
413	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
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, complemented
422	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	#390	—	2	1	no	—
427	#390	—	2	1	no	—
428	#390	C₂²×C₁₃	1	1	yes	characteristic
429	#390	C₂²×C₁₃	1	1	yes	characteristic
430	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#386	—	2	1	no	—
433	#386	—	2	1	no	—
434	#380	—	2	1	no	—
435	#380	C₂²×C₁₃	1	1	yes	characteristic
436	#380	C₂²×C₁₃	1	1	yes	characteristic
437	#379	—	2	1	no	—
438	C₄×C₂²⋊C₄	—	2	1	no	—
439	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
440	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	2	4	no	—
446	C₂²×C₁₃	—	2	2	no	—
447	C₂²×C₁₃	—	2	2	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	4	1	no	—
452	C₂²×C₁₃	—	4	1	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	1	no	—
456	C₂²×C₁₃	—	4	1	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	2	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	8	16	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	C₂×C₄×D₄	1	1	yes	characteristic
474	C₂²×C₁₃	D₄²	1	1	yes	characteristic
475	C₂²×C₁₃	D₄²	1	1	yes	characteristic
476	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
477	C₂²×C₁₃	#575	1	1	yes	characteristic
478	C₂²×C₁₃	#576	1	1	yes	characteristic
479	C₂²×C₁₃	#577	1	1	yes	characteristic
480	C₄×C₁₃	—	2	2	no	—
481	C₄×C₁₃	—	2	4	no	—
482	C₄×C₁₃	—	2	2	no	—
483	C₄×C₁₃	—	4	1	no	—
484	C₄×C₁₃	—	4	1	no	—
485	C₄×C₁₃	—	4	1	no	—
486	C₄×C₁₃	—	8	1	no	—
487	C₄×C₁₃	—	8	1	no	—
488	C₄×C₁₃	—	8	1	no	—
489	C₄×C₁₃	—	8	1	no	—
490	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
491	C₄×C₁₃	#518	1	1	yes	characteristic
492	C₄×C₁₃	#546	1	1	yes	characteristic
493	C₄×C₁₃	#546	1	1	yes	characteristic
494	C₂⁵	—	2	1	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	4	1	no	—
499	C₂×#41	—	4	1	no	—
500	C₂×#41	C₂×C₄×C₁₃	1	4	yes	complemented
501	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	—	2	2	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	2	no	—
507	C₂²×D₄	—	4	1	no	—
508	C₂²×D₄	—	4	1	no	—
509	C₂²×D₄	C₂×C₄×C₁₃	1	4	yes	—
510	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
517	AGL(1,ℤ/8)	—	2	32	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
521	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
522	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
523	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
524	C₂×D₈	—	2	2	no	—
525	C₂×D₈	—	2	2	no	—
526	C₂×D₈	—	2	2	no	—
527	C₂×D₈	—	2	2	no	—
528	C₂×D₈	C₂×C₄×C₁₃	1	4	yes	—
529	C₂×D₈	C₂×C₄×C₁₃	1	4	yes	complemented
530	C₂×M₁₆	—	2	2	no	—
531	C₂×M₁₆	—	2	2	no	—
532	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
533	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
536	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	4	1	no	—
540	C₄×Q₈	—	4	1	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	4	1	no	—
544	C₄×D₄	—	4	1	no	—
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	4	4	no	—
564	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
566	C₂×C₄²	—	2	1	no	—
567	C₂×C₄²	—	2	1	no	—
568	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
570	#107	—	2	2	no	—
571	#106	—	2	2	no	—
572	#103	—	2	2	no	—
573	#103	—	2	2	no	—
574	#102	—	2	2	no	—
575	#102	—	2	2	no	—
576	#102	—	4	1	no	—
577	#102	—	4	1	no	—
578	#102	—	4	1	no	—
579	#102	—	4	1	no	—
580	C₂²⋊C₈	—	2	2	no	—
581	#97	—	2	2	no	—
582	C₄×C₈	—	2	2	no	—
583	#95	—	2	1	no	—
584	#95	—	2	1	no	—
585	#95	D₄×C₁₃	1	1	yes	characteristic
586	#95	D₄×C₁₃	1	1	yes	characteristic
587	C₂×C₁₃	—	4	2	no	—
588	C₂×C₁₃	—	4	4	no	—
589	C₂×C₁₃	—	8	2	no	—
590	C₂×C₁₃	—	8	2	no	—
591	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
592	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
593	C₂×C₁₃	#2946	1	1	yes	characteristic
594	C₂×C₁₃	#3265	1	1	yes	characteristic
595	C₂×C₁₃	#3268	1	1	yes	characteristic
596	C₂×C₁₃	#3274	1	1	yes	characteristic
597	C₂×C₁₃	#3275	1	1	yes	characteristic
598	C₂⁴	—	2	1	no	—
599	C₂⁴	—	2	1	no	—
600	C₂⁴	—	2	1	no	—
601	C₂⁴	—	2	4	no	—
602	C₂⁴	—	4	2	no	—
603	C₂⁴	—	4	2	no	—
604	C₂⁴	—	4	2	no	—
605	C₂⁴	—	4	2	no	—
606	C₂⁴	—	8	1	no	—
607	C₂⁴	—	8	1	no	—
608	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
609	#41	—	2	8	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
617	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
618	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
619	C₂×D₄	—	2	8	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	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	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	4	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	C₂²×C₄×C₁₃	1	2	yes	—
643	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
644	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
645	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
646	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	4	no	—
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	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	4	2	no	—
663	C₂²×C₄	—	8	1	no	—
664	C₂²×C₄	—	8	1	no	—
665	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
666	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₁₃×#41	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
673	SD₁₆	—	2	8	no	—
674	SD₁₆	C₁₃×C₂²⋊C₄	1	16	yes	complemented
675	D₈	—	2	8	no	—
676	D₈	—	2	8	no	—
677	M₁₆	—	2	8	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	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	C₂²×C₄×C₁₃	1	2	yes	—
687	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
688	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
689	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	4	1	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	8	1	no	—
710	C₂²⋊C₄	—	8	1	no	—
711	C₂²⋊C₄	—	8	1	no	—
712	C₂²⋊C₄	—	8	1	no	—
713	C₂²⋊C₄	—	8	1	no	—
714	C₄²	—	2	1	no	—
715	C₄²	—	2	1	no	—
716	C₄²	—	2	1	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	4	2	no	—
719	C₄²	—	4	2	no	—
720	C₁₃	#22443	1	1	yes	characteristic, direct product factor, Sylow
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
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	1	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	4	8	no	—
733	C₂³	—	4	8	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	4	1	no	—
736	C₂³	—	4	1	no	—
737	C₂³	—	4	1	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	—	8	4	no	—
751	C₂³	—	8	4	no	—
752	C₂³	—	8	4	no	—
753	C₂³	—	8	4	no	—
754	C₂³	—	8	4	no	—
755	C₂³	C₄×D₄×C₁₃	1	2	yes	—
756	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
757	Q₈	—	2	2	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	2	no	—
760	Q₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	complemented
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	2	no	—
764	D₄	—	2	2	no	—
765	D₄	—	2	2	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	4	8	no	—
769	D₄	—	4	8	no	—
770	D₄	—	4	1	no	—
771	D₄	—	4	1	no	—
772	D₄	—	4	1	no	—
773	D₄	—	4	1	no	—
774	D₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	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	—	4	8	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	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	—	8	4	no	—
809	C₂×C₄	—	8	4	no	—
810	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
811	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	complemented
812	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
815	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
816	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
817	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
818	C₈	—	2	2	no	—
819	C₈	—	4	1	no	—
820	C₈	—	4	1	no	—
821	C₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	complemented
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	8	16	no	—
843	C₂²	—	8	1	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	8	1	no	—
847	C₂²	—	8	1	no	—
848	C₂²	—	8	1	no	—
849	C₂²	—	8	1	no	—
850	C₂²	—	8	1	no	—
851	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
852	C₂²	D₄²×C₁₃	1	1	yes	characteristic
853	C₂²	D₄²×C₁₃	1	1	yes	characteristic
854	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
855	C₂²	C₁₃×#575	1	1	yes	characteristic
856	C₂²	C₁₃×#576	1	1	yes	characteristic
857	C₂²	C₁₃×#577	1	1	yes	characteristic
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	4	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	8	1	no	—
865	C₄	—	8	1	no	—
866	C₄	—	8	1	no	—
867	C₄	—	8	1	no	—
868	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
869	C₄	C₁₃×#518	1	1	yes	characteristic
870	C₄	C₁₃×#546	1	1	yes	characteristic
871	C₄	C₁₃×#546	1	1	yes	characteristic
872	C₂	—	4	2	no	—
873	C₂	—	4	4	no	—
874	C₂	—	8	2	no	—
875	C₂	—	8	2	no	—
876	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
877	C₂	C₄×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
878	C₂	C₁₃×#2946	1	1	yes	characteristic
879	C₂	C₁₃×#3265	1	1	yes	characteristic
880	C₂	C₁₃×#3268	1	1	yes	characteristic
881	C₂	C₁₃×#3274	1	1	yes	characteristic
882	C₂	C₁₃×#3275	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂×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×#440	C₂	semidirect
3. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
4. C₁₃×#2341	C₂	semidirect
5. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
6. C₁₃×#1972	C₂	semidirect
7. C₁₃×#1970	C₂	semidirect
8. C₁₃×#1880	C₂	semidirect
9. C₁₃×#1880	C₂	semidirect
10. C₁₃×#1879	C₂	semidirect
11. C₁₃×#1879	C₂	semidirect
12. C₁₃×#1809	C₂	semidirect
13. C₁₃×#1788	C₂	semidirect
14. C₁₃×#1786	C₂	semidirect
15. C₁₃×#1753	C₂	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₄	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
27. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
33. C₂×C₁₃×#107	C₂²	semidirect
34. C₂×C₁₃×#106	C₂²	semidirect
35. C₂×C₁₃×#103	C₂²	semidirect
36. C₂×C₁₃×#103	C₂²	semidirect
41. C₂×C₁₃×#102	C₂²	semidirect
42. C₂×C₁₃×#102	C₂²	semidirect
44. C₂×C₁₃×#97	C₂²	semidirect
45. C₂×C₄×C₈×C₁₃	C₂²	semidirect
50. C₁₃×#390	C₂²	semidirect
51. C₁₃×#390	C₂²	semidirect
60. C₁₃×#340	C₂²	semidirect
61. C₁₃×#340	C₂²	semidirect
62. C₁₃×#336	C₂²	semidirect
63. C₁₃×#336	C₂²	semidirect
70. C₂×C₁₃×#41	C₂×C₄	semidirect
91. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
99. C₂×C₁₃×D₈	C₂×C₄	semidirect
102. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
157. #22443	C₁₃	direct (N × H)
234. C₁₃×SD₁₆	C₂²⋊C₄	semidirect
281. C₂×#440	C₂×C₁₃	semidirect
282. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
283. #2341	C₂×C₁₃	semidirect
284. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
285. #1972	C₂×C₁₃	semidirect
286. #1970	C₂×C₁₃	semidirect
287. #1880	C₂×C₁₃	semidirect
288. #1880	C₂×C₁₃	semidirect
289. #1879	C₂×C₁₃	semidirect
290. #1879	C₂×C₁₃	semidirect
291. #1809	C₂×C₁₃	semidirect
292. #1788	C₂×C₁₃	semidirect
293. #1786	C₂×C₁₃	semidirect
294. #1753	C₂×C₁₃	semidirect
334. Q₈×C₁₃	C₂×C₂²⋊C₄	semidirect
385. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
395. C₈×C₁₃	C₂×C₂²⋊C₄	semidirect
400. C₂×AGL(1,ℤ/8)	C₄×C₁₃	semidirect
406. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
407. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
413. C₂×#107	C₂²×C₁₃	semidirect
414. C₂×#106	C₂²×C₁₃	semidirect
415. C₂×#103	C₂²×C₁₃	semidirect
416. C₂×#103	C₂²×C₁₃	semidirect
421. C₂×#102	C₂²×C₁₃	semidirect
422. C₂×#102	C₂²×C₁₃	semidirect
424. C₂×#97	C₂²×C₁₃	semidirect
425. C₂×C₄×C₈	C₂²×C₁₃	semidirect
430. #390	C₂²×C₁₃	semidirect
431. #390	C₂²×C₁₃	semidirect
440. #340	C₂²×C₁₃	semidirect
441. #340	C₂²×C₁₃	semidirect
442. #336	C₂²×C₁₃	semidirect
443. #336	C₂²×C₁₃	semidirect
500. C₂×#41	C₂×C₄×C₁₃	semidirect
521. C₂×SD₁₆	C₂×C₄×C₁₃	semidirect
529. C₂×D₈	C₂×C₄×C₁₃	semidirect
532. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
674. SD₁₆	C₁₃×C₂²⋊C₄	semidirect
720. C₁₃	#22443	direct (N × H)
760. Q₈	C₂×C₁₃×C₂²⋊C₄	semidirect
811. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect
821. C₈	C₂×C₁₃×C₂²⋊C₄	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×#440	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2341	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#1972	2
C₁₃×#1970	2
C₁₃×#1880	2
C₁₃×#1879	2
C₁₃×#1809	2
C₁₃×#1788	2
C₁₃×#1786	2
C₁₃×#1753	2
#22443	13

Subgroups — C13×#22443 #15708782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22443 #15708782