Subgroups — C₁₃×#61421 #15747760

Order 3328.

1964 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3400	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3397	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3396	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3392	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3042	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	2	yes	—
22	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₁₃×#559	C₂²	1	2	yes	—
24	C₁₃×#559	C₂²	1	2	yes	—
25	C₁₃×#559	C₂²	1	2	yes	complemented
26	C₁₃×#557	C₂²	1	2	yes	complemented
27	C₁₃×#556	—	2	1	no	—
28	C₁₃×#556	C₂²	1	4	yes	complemented
29	C₁₃×#554	—	2	1	no	—
30	C₁₃×#552	—	2	2	no	—
31	C₁₃×#550	C₂²	1	2	yes	—
32	C₁₃×#550	C₂²	1	2	yes	—
33	C₁₃×#546	—	2	2	no	—
34	C₁₃×#546	—	2	2	no	—
35	C₁₃×#540	—	2	2	no	—
36	C₁₃×#539	—	2	2	no	—
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#535	C₂²	1	2	yes	—
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₁₃×#532	—	2	1	no	—
41	C₁₃×#532	—	2	1	no	—
42	C₁₃×#532	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	2	no	—
45	C₁₃×#520	C₂²	1	2	yes	—
46	C₁₃×#518	C₂²	1	2	yes	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#497	C₂²	1	4	yes	complemented
50	C₁₃×#496	C₂²	1	4	yes	—
51	C₁₃×#496	C₂²	1	4	yes	complemented
52	C₁₃×#495	C₂²	1	4	yes	complemented
53	C₁₃×#493	C₂²	1	2	yes	—
54	C₁₃×#492	C₂²	1	2	yes	—
55	C₁₃×#492	C₂²	1	4	yes	complemented
56	C₁₃×#464	C₂²	1	2	yes	complemented
57	C₁₃×#464	C₂²	1	4	yes	complemented
58	C₁₃×#463	C₂²	1	2	yes	complemented
59	C₁₃×#463	C₂²	1	4	yes	complemented
60	C₁₃×#463	C₂²	1	4	yes	complemented
61	C₁₃×#463	C₂²	1	4	yes	complemented
62	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#461	C₂²	1	4	yes	complemented
65	C₁₃×#461	C₂²	1	4	yes	complemented
66	C₁₃×#460	C₂²	1	2	yes	—
67	C₁₃×#460	C₂²	1	4	yes	—
68	C₁₃×#460	C₂²	1	2	yes	—
69	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#460	C₂²	1	4	yes	complemented
71	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#459	C₂²	1	4	yes	complemented
73	C₁₃×#446	C₂²	1	4	yes	complemented
74	C₁₃×#446	C₂²	1	2	yes	complemented
75	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
76	C₁₃×#442	C₂²	1	4	yes	complemented
77	C₁₃×#441	C₂²	1	2	yes	complemented
78	C₁₃×#440	C₂²	1	2	yes	complemented
79	C₁₃×#440	C₂²	1	4	yes	complemented
80	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
81	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
82	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
83	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
84	C₁₃×#428	C₂²	1	1	yes	characteristic
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₁₃×#419	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#102	C₂²	1	2	yes	—
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	—	2	2	no	—
95	C₂×C₁₃×#41	C₂³	1	2	yes	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₁₃×#137	—	2	4	no	—
102	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
103	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
104	C₁₃×#135	—	4	4	no	—
105	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×SD₁₆	—	4	4	no	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
115	C₂×C₁₃×D₈	C₂³	1	4	yes	—
116	C₂×C₁₃×D₈	C₂³	1	2	yes	—
117	C₂×C₁₃×D₈	C₂³	1	4	yes	—
118	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
122	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₁₃×#127	—	2	1	no	—
126	C₁₃×#127	—	2	1	no	—
127	C₁₃×#127	C₂³	1	4	yes	—
128	C₁₃×#127	C₂³	1	1	yes	characteristic
129	C₁₃×#127	C₂³	1	2	yes	—
130	C₁₃×#127	C₂³	1	2	yes	—
131	C₁₃×#126	—	2	4	no	—
132	C₁₃×#126	—	2	4	no	—
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#125	—	2	4	no	—
135	C₁₃×#125	D₄	1	2	yes	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#124	—	2	2	no	—
139	C₁₃×#124	C₂³	1	4	yes	—
140	C₁₃×#124	C₂³	1	4	yes	—
141	C₁₃×#124	C₂³	1	2	yes	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×#123	—	2	4	no	—
144	C₁₃×#123	—	2	4	no	—
145	C₁₃×#123	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	—	2	4	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
150	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#120	—	2	4	no	—
160	C₄×Q₈×C₁₃	—	2	2	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	1	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	4	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	C₂³	1	4	yes	—
181	C₄×D₄×C₁₃	C₂³	1	4	yes	—
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	4	yes	—
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	4	no	—
187	C₁₃×#117	—	2	1	no	—
188	C₁₃×#117	C₂³	1	1	yes	characteristic
189	C₁₃×#117	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₂×C₄²×C₁₃	—	2	1	no	—
195	C₂×C₄²×C₁₃	—	2	1	no	—
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₁₃×#107	C₂³	1	2	yes	—
198	C₁₃×#106	C₂³	1	2	yes	—
199	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	2	yes	—
205	C₁₃×#103	C₂³	1	2	yes	—
206	C₁₃×#103	C₂³	1	2	yes	—
207	C₁₃×#103	C₂³	1	2	yes	—
208	C₁₃×#103	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	4	yes	—
210	C₁₃×#102	C₂³	1	4	yes	—
211	C₁₃×#102	C₂³	1	2	yes	—
212	C₁₃×#102	C₂³	1	2	yes	—
213	C₁₃×#102	C₂³	1	2	yes	—
214	C₁₃×#97	C₂³	1	2	yes	—
215	C₁₃×#97	C₂³	1	4	yes	—
216	C₄×C₈×C₁₃	C₂³	1	2	yes	—
217	C₄×C₈×C₁₃	C₂³	1	4	yes	—
218	#61421	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂⁴×C₁₃	—	2	2	no	—
220	C₁₃×#41	—	2	4	no	—
221	C₁₃×#41	—	2	2	no	—
222	C₁₃×#41	—	2	2	no	—
223	C₁₃×#41	—	2	4	no	—
224	C₁₃×#41	—	8	4	no	—
225	C₁₃×#41	—	8	4	no	—
226	C₂×Q₈×C₁₃	—	2	1	no	—
227	C₂×Q₈×C₁₃	—	2	2	no	—
228	C₂×Q₈×C₁₃	—	2	2	no	—
229	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
231	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	—	2	1	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	2	2	no	—
239	C₂×D₄×C₁₃	—	2	2	no	—
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	—	2	4	no	—
242	C₂×D₄×C₁₃	—	2	4	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	8	2	no	—
248	C₂×D₄×C₁₃	—	8	2	no	—
249	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
251	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	1	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	4	no	—
259	C₂²×C₄×C₁₃	—	2	4	no	—
260	C₂²×C₄×C₁₃	—	2	4	no	—
261	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₁₃×Q₁₆	—	2	4	no	—
265	C₁₃×Q₁₆	—	4	2	no	—
266	C₁₃×SD₁₆	—	2	8	no	—
267	C₁₃×SD₁₆	—	2	4	no	—
268	C₁₃×SD₁₆	—	4	4	no	—
269	C₁₃×SD₁₆	—	4	4	no	—
270	C₁₃×SD₁₆	—	4	2	no	—
271	C₁₃×SD₁₆	—	4	2	no	—
272	C₁₃×SD₁₆	—	4	4	no	—
273	C₁₃×D₈	—	2	8	no	—
274	C₁₃×D₈	—	4	2	no	—
275	C₁₃×D₈	—	4	4	no	—
276	C₁₃×M₁₆	—	2	2	no	—
277	C₁₃×M₁₆	#41	1	4	yes	complemented
278	C₂×C₈×C₁₃	—	2	4	no	—
279	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
280	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
281	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
282	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
294	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
295	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
296	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
297	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
298	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
302	C₁₃×C₂²⋊C₄	—	2	1	no	—
303	C₁₃×C₂²⋊C₄	—	2	4	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	1	no	—
307	C₁₃×C₂²⋊C₄	—	2	1	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
315	C₄²×C₁₃	—	2	2	no	—
316	C₄²×C₁₃	—	2	1	no	—
317	C₄²×C₁₃	—	2	1	no	—
318	C₄²×C₁₃	—	2	1	no	—
319	C₄²×C₁₃	—	2	2	no	—
320	C₄²×C₁₃	—	2	4	no	—
321	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₄²×C₁₃	C₂⁴	1	4	yes	—
325	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
326	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#3401	C₂×C₁₃	1	4	yes	complemented
329	#3400	C₂×C₁₃	1	2	yes	complemented
330	#3399	C₂×C₁₃	1	2	yes	complemented
331	#3397	C₂×C₁₃	1	4	yes	complemented
332	#3396	C₂×C₁₃	1	2	yes	complemented
333	#3392	C₂×C₁₃	1	2	yes	complemented
334	#3154	C₂×C₁₃	1	2	yes	complemented
335	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3045	C₂×C₁₃	1	2	yes	complemented
337	#3042	C₂×C₁₃	1	2	yes	complemented
338	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#2946	C₂×C₁₃	1	2	yes	complemented
342	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	2	4	no	—
345	C₂³×C₁₃	—	2	1	no	—
346	C₂³×C₁₃	—	4	4	no	—
347	C₂³×C₁₃	—	8	2	no	—
348	C₂³×C₁₃	—	8	2	no	—
349	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	Q₈×C₁₃	—	2	4	no	—
351	Q₈×C₁₃	—	2	2	no	—
352	Q₈×C₁₃	—	2	2	no	—
353	Q₈×C₁₃	—	2	1	no	—
354	Q₈×C₁₃	—	2	2	no	—
355	Q₈×C₁₃	—	2	2	no	—
356	Q₈×C₁₃	—	2	1	no	—
357	Q₈×C₁₃	—	4	2	no	—
358	Q₈×C₁₃	—	4	2	no	—
359	D₄×C₁₃	—	2	2	no	—
360	D₄×C₁₃	—	2	4	no	—
361	D₄×C₁₃	—	2	1	no	—
362	D₄×C₁₃	—	2	2	no	—
363	D₄×C₁₃	—	2	1	no	—
364	D₄×C₁₃	—	2	4	no	—
365	D₄×C₁₃	—	4	4	no	—
366	D₄×C₁₃	—	4	2	no	—
367	D₄×C₁₃	—	4	4	no	—
368	D₄×C₁₃	—	4	4	no	—
369	D₄×C₁₃	—	4	2	no	—
370	D₄×C₁₃	—	4	4	no	—
371	D₄×C₁₃	—	8	1	no	—
372	D₄×C₁₃	—	8	2	no	—
373	D₄×C₁₃	—	8	2	no	—
374	D₄×C₁₃	—	8	4	no	—
375	D₄×C₁₃	—	8	4	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	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	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	2	no	—
385	C₂×C₄×C₁₃	—	4	2	no	—
386	C₂×C₄×C₁₃	—	4	2	no	—
387	C₂×C₄×C₁₃	—	4	4	no	—
388	C₂×C₄×C₁₃	—	4	2	no	—
389	C₂×C₄×C₁₃	—	8	4	no	—
390	C₂×C₄×C₁₃	—	8	4	no	—
391	C₂×C₄×C₁₃	—	8	4	no	—
392	C₂×C₄×C₁₃	—	8	1	no	—
393	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
396	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
401	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
403	C₈×C₁₃	—	2	2	no	—
404	C₈×C₁₃	—	2	2	no	—
405	C₈×C₁₃	—	2	2	no	—
406	C₈×C₁₃	C₂×#41	1	4	yes	—
407	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
409	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
410	C₂×#135	C₂²×C₁₃	1	2	yes	—
411	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
412	#559	C₂²×C₁₃	1	2	yes	—
413	#559	C₂²×C₁₃	1	2	yes	—
414	#559	C₂²×C₁₃	1	2	yes	complemented
415	#557	C₂²×C₁₃	1	2	yes	complemented
416	#556	—	2	1	no	—
417	#556	C₂²×C₁₃	1	4	yes	complemented
418	#554	—	2	1	no	—
419	#552	—	2	2	no	—
420	#550	C₂²×C₁₃	1	2	yes	—
421	#550	C₂²×C₁₃	1	2	yes	—
422	#546	—	2	2	no	—
423	#546	—	2	2	no	—
424	#540	—	2	2	no	—
425	#539	—	2	2	no	—
426	#536	C₂²×C₁₃	1	2	yes	—
427	#535	C₂²×C₁₃	1	2	yes	—
428	#533	C₂²×C₁₃	1	1	yes	characteristic
429	#532	—	2	1	no	—
430	#532	—	2	1	no	—
431	#532	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
433	#529	—	2	2	no	—
434	#520	C₂²×C₁₃	1	2	yes	—
435	#518	C₂²×C₁₃	1	2	yes	—
436	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
438	#497	C₂²×C₁₃	1	4	yes	complemented
439	#496	C₂²×C₁₃	1	4	yes	—
440	#496	C₂²×C₁₃	1	4	yes	complemented
441	#495	C₂²×C₁₃	1	4	yes	complemented
442	#493	C₂²×C₁₃	1	2	yes	—
443	#492	C₂²×C₁₃	1	2	yes	—
444	#492	C₂²×C₁₃	1	4	yes	complemented
445	#464	C₂²×C₁₃	1	4	yes	complemented
446	#464	C₂²×C₁₃	1	2	yes	complemented
447	#463	C₂²×C₁₃	1	4	yes	complemented
448	#463	C₂²×C₁₃	1	4	yes	complemented
449	#463	C₂²×C₁₃	1	2	yes	complemented
450	#463	C₂²×C₁₃	1	4	yes	complemented
451	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
453	#461	C₂²×C₁₃	1	4	yes	complemented
454	#461	C₂²×C₁₃	1	4	yes	complemented
455	#460	C₂²×C₁₃	1	2	yes	—
456	#460	C₂²×C₁₃	1	4	yes	—
457	#460	C₂²×C₁₃	1	2	yes	—
458	#460	C₂²×C₁₃	1	4	yes	complemented
459	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#459	C₂²×C₁₃	1	4	yes	complemented
461	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	#446	C₂²×C₁₃	1	4	yes	complemented
463	#446	C₂²×C₁₃	1	2	yes	complemented
464	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
465	#442	C₂²×C₁₃	1	4	yes	complemented
466	#441	C₂²×C₁₃	1	2	yes	complemented
467	#440	C₂²×C₁₃	1	2	yes	complemented
468	#440	C₂²×C₁₃	1	4	yes	complemented
469	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
470	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
471	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
472	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
473	#428	C₂²×C₁₃	1	1	yes	characteristic
474	#424	C₂²×C₁₃	1	2	yes	—
475	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
476	#419	C₂²×C₁₃	1	1	yes	characteristic
477	#417	C₂²×C₁₃	1	1	yes	characteristic
478	#416	C₂²×C₁₃	1	2	yes	—
479	C₂×#102	C₂²×C₁₃	1	2	yes	—
480	#405	C₂²×C₁₃	1	2	yes	—
481	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
482	C₂²×C₁₃	—	2	1	no	—
483	C₂²×C₁₃	—	2	1	no	—
484	C₂²×C₁₃	—	4	1	no	—
485	C₂²×C₁₃	—	4	2	no	—
486	C₂²×C₁₃	—	4	4	no	—
487	C₂²×C₁₃	—	4	2	no	—
488	C₂²×C₁₃	—	4	1	no	—
489	C₂²×C₁₃	—	4	4	no	—
490	C₂²×C₁₃	—	4	1	no	—
491	C₂²×C₁₃	—	4	4	no	—
492	C₂²×C₁₃	—	4	2	no	—
493	C₂²×C₁₃	—	16	4	no	—
494	C₂²×C₁₃	#550	1	2	yes	—
495	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
496	C₄×C₁₃	—	2	1	no	—
497	C₄×C₁₃	—	2	1	no	—
498	C₄×C₁₃	—	2	4	no	—
499	C₄×C₁₃	—	2	1	no	—
500	C₄×C₁₃	—	2	4	no	—
501	C₄×C₁₃	—	4	1	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	1	no	—
504	C₄×C₁₃	—	4	2	no	—
505	C₄×C₁₃	—	4	2	no	—
506	C₄×C₁₃	—	4	1	no	—
507	C₄×C₁₃	#550	1	2	yes	—
508	C₄×C₁₃	#577	1	2	yes	—
509	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
510	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂×#41	—	2	2	no	—
512	C₂×#41	—	2	2	no	—
513	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×#41	C₂³×C₁₃	1	2	yes	—
515	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
519	#137	—	2	4	no	—
520	AGL(1,ℤ/8)	—	2	8	no	—
521	AGL(1,ℤ/8)	—	4	4	no	—
522	#135	—	4	4	no	—
523	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
524	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
525	C₂×SD₁₆	—	4	4	no	—
526	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
527	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
528	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
529	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
530	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
531	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
532	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
533	C₂×D₈	C₂³×C₁₃	1	4	yes	—
534	C₂×D₈	C₂³×C₁₃	1	2	yes	—
535	C₂×D₈	C₂³×C₁₃	1	4	yes	—
536	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
539	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
540	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
543	#127	—	2	1	no	—
544	#127	—	2	1	no	—
545	#127	C₂³×C₁₃	1	2	yes	—
546	#127	C₂³×C₁₃	1	2	yes	—
547	#127	C₂³×C₁₃	1	1	yes	characteristic
548	#127	C₂³×C₁₃	1	4	yes	—
549	#126	—	2	4	no	—
550	#126	—	2	4	no	—
551	#125	—	2	2	no	—
552	#125	—	2	4	no	—
553	#125	D₄×C₁₃	1	2	yes	—
554	#124	—	2	2	no	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	C₂³×C₁₃	1	2	yes	—
558	#124	C₂³×C₁₃	1	4	yes	—
559	#124	C₂³×C₁₃	1	4	yes	—
560	#123	—	2	4	no	—
561	#123	—	2	4	no	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
568	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	#121	—	2	4	no	—
576	#121	—	2	4	no	—
577	#120	—	2	4	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
582	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
583	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
586	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
587	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	4	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
599	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₄×D₄	C₂³×C₁₃	1	4	yes	—
601	C₄×D₄	C₂³×C₁₃	1	4	yes	—
602	C₄×D₄	C₂³×C₁₃	1	4	yes	—
603	#117	—	2	2	no	—
604	#117	—	2	4	no	—
605	#117	—	2	1	no	—
606	#117	C₂³×C₁₃	1	1	yes	characteristic
607	#117	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	2	no	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	—	2	4	no	—
612	C₂×C₄²	—	2	1	no	—
613	C₂×C₄²	—	2	1	no	—
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	#107	C₂³×C₁₃	1	2	yes	—
616	#106	C₂³×C₁₃	1	2	yes	—
617	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
618	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
619	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
620	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
621	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
622	#103	C₂³×C₁₃	1	2	yes	—
623	#103	C₂³×C₁₃	1	2	yes	—
624	#103	C₂³×C₁₃	1	2	yes	—
625	#103	C₂³×C₁₃	1	2	yes	—
626	#103	C₂³×C₁₃	1	2	yes	—
627	#102	C₂³×C₁₃	1	4	yes	—
628	#102	C₂³×C₁₃	1	4	yes	—
629	#102	C₂³×C₁₃	1	2	yes	—
630	#102	C₂³×C₁₃	1	2	yes	—
631	#102	C₂³×C₁₃	1	2	yes	—
632	#97	C₂³×C₁₃	1	2	yes	—
633	#97	C₂³×C₁₃	1	4	yes	—
634	C₄×C₈	C₂³×C₁₃	1	2	yes	—
635	C₄×C₈	C₂³×C₁₃	1	4	yes	—
636	C₂×C₁₃	—	2	2	no	—
637	C₂×C₁₃	—	8	1	no	—
638	C₂×C₁₃	—	8	2	no	—
639	C₂×C₁₃	—	8	4	no	—
640	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
641	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
642	C₂×C₁₃	#3585	1	1	yes	characteristic
643	C₂⁴	—	2	2	no	—
644	#41	—	2	4	no	—
645	#41	—	2	2	no	—
646	#41	—	2	2	no	—
647	#41	—	2	4	no	—
648	#41	—	8	4	no	—
649	#41	—	8	4	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
654	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
655	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
656	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
657	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	8	2	no	—
672	C₂×D₄	—	8	2	no	—
673	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
674	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
675	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	2	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
688	Q₁₆	—	2	4	no	—
689	Q₁₆	—	4	2	no	—
690	SD₁₆	—	2	8	no	—
691	SD₁₆	—	2	4	no	—
692	SD₁₆	—	4	4	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	—	4	2	no	—
695	SD₁₆	—	4	2	no	—
696	SD₁₆	—	4	4	no	—
697	D₈	—	2	8	no	—
698	D₈	—	4	2	no	—
699	D₈	—	4	4	no	—
700	M₁₆	—	2	2	no	—
701	M₁₆	C₁₃×#41	1	4	yes	complemented
702	C₂×C₈	—	2	4	no	—
703	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
704	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
705	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
706	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
720	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
723	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	4	no	—
745	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₄²	C₂⁴×C₁₃	1	4	yes	—
749	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
750	C₁₃	#61421	1	1	yes	characteristic, direct product factor, Sylow
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	4	4	no	—
755	C₂³	—	8	2	no	—
756	C₂³	—	8	2	no	—
757	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
758	Q₈	—	2	4	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	1	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	1	no	—
765	Q₈	—	4	2	no	—
766	Q₈	—	4	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	1	no	—
772	D₄	—	2	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	4	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	2	no	—
779	D₄	—	8	2	no	—
780	D₄	—	8	2	no	—
781	D₄	—	8	1	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	4	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	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	1	no	—
801	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
804	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
806	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
808	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
809	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
810	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
811	C₈	—	2	2	no	—
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	C₂×C₁₃×#41	1	4	yes	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	4	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	16	4	no	—
827	C₂²	C₁₃×#550	1	2	yes	—
828	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
829	C₄	—	2	1	no	—
830	C₄	—	2	4	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	4	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	C₁₃×#550	1	2	yes	—
841	C₄	C₁₃×#577	1	2	yes	—
842	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
843	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	8	4	no	—
846	C₂	—	8	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
849	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
850	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3507	C₂	semidirect
3. C₁₃×#3401	C₂	semidirect
4. C₁₃×#3400	C₂	semidirect
5. C₁₃×#3399	C₂	semidirect
6. C₁₃×#3397	C₂	semidirect
7. C₁₃×#3396	C₂	semidirect
8. C₁₃×#3392	C₂	semidirect
9. C₁₃×#3154	C₂	semidirect
10. C₁₃×#3151	C₂	semidirect
11. C₁₃×#3045	C₂	semidirect
12. C₁₃×#3042	C₂	semidirect
13. C₁₃×#3035	C₂	semidirect
14. C₂×C₁₃×#460	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
16. C₁₃×#2946	C₂	semidirect
17. C₄×C₁₃×#137	C₂	semidirect
25. C₁₃×#559	C₂²	semidirect
26. C₁₃×#557	C₂²	semidirect
28. C₁₃×#556	C₂²	semidirect
49. C₁₃×#497	C₂²	semidirect
51. C₁₃×#496	C₂²	semidirect
52. C₁₃×#495	C₂²	semidirect
55. C₁₃×#492	C₂²	semidirect
56. C₁₃×#464	C₂²	semidirect
57. C₁₃×#464	C₂²	semidirect
58. C₁₃×#463	C₂²	semidirect
59. C₁₃×#463	C₂²	semidirect
60. C₁₃×#463	C₂²	semidirect
61. C₁₃×#463	C₂²	semidirect
62. C₁₃×#462	C₂²	semidirect
63. C₁₃×#461	C₂²	semidirect
64. C₁₃×#461	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
70. C₁₃×#460	C₂²	semidirect
71. C₁₃×#459	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#446	C₂²	semidirect
74. C₁₃×#446	C₂²	semidirect
75. C₈×Q₈×C₁₃	C₂²	semidirect
76. C₁₃×#442	C₂²	semidirect
77. C₁₃×#441	C₂²	semidirect
78. C₁₃×#440	C₂²	semidirect
79. C₁₃×#440	C₂²	semidirect
80. C₄×C₁₃×Q₁₆	C₂²	semidirect
81. C₄×C₁₃×SD₁₆	C₂²	semidirect
82. C₄×C₁₃×SD₁₆	C₂²	semidirect
83. C₄×C₁₃×D₈	C₂²	semidirect
218. #61421	C₁₃	direct (N × H)
277. C₁₃×M₁₆	#41	semidirect
326. #3508	C₂×C₁₃	semidirect
327. #3507	C₂×C₁₃	semidirect
328. #3401	C₂×C₁₃	semidirect
329. #3400	C₂×C₁₃	semidirect
330. #3399	C₂×C₁₃	semidirect
331. #3397	C₂×C₁₃	semidirect
332. #3396	C₂×C₁₃	semidirect
333. #3392	C₂×C₁₃	semidirect
334. #3154	C₂×C₁₃	semidirect
335. #3151	C₂×C₁₃	semidirect
336. #3045	C₂×C₁₃	semidirect
337. #3042	C₂×C₁₃	semidirect
338. #3035	C₂×C₁₃	semidirect
339. C₂×#460	C₂×C₁₃	semidirect
340. #2962	C₂×C₁₃	semidirect
341. #2946	C₂×C₁₃	semidirect
342. C₄×#137	C₂×C₁₃	semidirect
414. #559	C₂²×C₁₃	semidirect
415. #557	C₂²×C₁₃	semidirect
417. #556	C₂²×C₁₃	semidirect
438. #497	C₂²×C₁₃	semidirect
440. #496	C₂²×C₁₃	semidirect
441. #495	C₂²×C₁₃	semidirect
444. #492	C₂²×C₁₃	semidirect
445. #464	C₂²×C₁₃	semidirect
446. #464	C₂²×C₁₃	semidirect
447. #463	C₂²×C₁₃	semidirect
448. #463	C₂²×C₁₃	semidirect
449. #463	C₂²×C₁₃	semidirect
450. #463	C₂²×C₁₃	semidirect
451. #462	C₂²×C₁₃	semidirect
452. #461	C₂²×C₁₃	semidirect
453. #461	C₂²×C₁₃	semidirect
454. #461	C₂²×C₁₃	semidirect
458. #460	C₂²×C₁₃	semidirect
459. #460	C₂²×C₁₃	semidirect
460. #459	C₂²×C₁₃	semidirect
461. #459	C₂²×C₁₃	semidirect
462. #446	C₂²×C₁₃	semidirect
463. #446	C₂²×C₁₃	semidirect
464. C₈×Q₈	C₂²×C₁₃	semidirect
465. #442	C₂²×C₁₃	semidirect
466. #441	C₂²×C₁₃	semidirect
467. #440	C₂²×C₁₃	semidirect
468. #440	C₂²×C₁₃	semidirect
469. C₄×Q₁₆	C₂²×C₁₃	semidirect
470. C₄×SD₁₆	C₂²×C₁₃	semidirect
471. C₄×SD₁₆	C₂²×C₁₃	semidirect
472. C₄×D₈	C₂²×C₁₃	semidirect
701. M₁₆	C₁₃×#41	semidirect
750. C₁₃	#61421	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×#3508	2
C₁₃×#3507	2
C₁₃×#3401	2
C₁₃×#3400	2
C₁₃×#3399	2
C₁₃×#3397	2
C₁₃×#3396	2
C₁₃×#3392	2
C₁₃×#3154	2
C₁₃×#3151	2
C₁₃×#3045	2
C₁₃×#3042	2
C₁₃×#3035	2
C₂×C₁₃×#460	2
C₁₃×#2962	2
C₁₃×#2946	2
C₄×C₁₃×#137	2
#61421	13

Subgroups — C13×#61421 #15747760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61421 #15747760