Subgroups — C₁₃×#61279 #15747618

Order 3328.

1860 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3357	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3354	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3350	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3345	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3341	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3335	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3096	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3062	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2912	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#131	C₂²	1	2	yes	—
20	C₁₃×#559	—	2	2	no	—
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	2	yes	complemented
23	C₁₃×#555	C₂²	1	2	yes	—
24	C₁₃×#555	C₂²	1	2	yes	complemented
25	C₁₃×#554	C₂²	1	2	yes	complemented
26	C₁₃×#553	—	2	2	no	—
27	C₁₃×#553	C₂²	1	4	yes	—
28	C₁₃×#550	—	2	1	no	—
29	C₁₃×#548	—	2	2	no	—
30	C₁₃×#547	C₂²	1	2	yes	—
31	C₁₃×#547	C₂²	1	2	yes	complemented
32	C₁₃×#542	—	2	2	no	—
33	C₁₃×#538	—	2	2	no	—
34	C₁₃×#537	C₂²	1	2	yes	—
35	C₁₃×#535	C₂²	1	2	yes	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	—	2	1	no	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₃×#525	—	2	2	no	—
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₁₃×#520	C₂²	1	2	yes	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#501	C₂²	1	4	yes	complemented
47	C₁₃×#500	C₂²	1	2	yes	complemented
48	C₁₃×#498	C₂²	1	2	yes	complemented
49	C₁₃×#485	C₂²	1	4	yes	complemented
50	C₁₃×#483	C₂²	1	4	yes	complemented
51	C₁₃×#482	C₂²	1	4	yes	—
52	C₁₃×#482	C₂²	1	4	yes	—
53	C₁₃×#482	C₂²	1	4	yes	complemented
54	C₁₃×#481	C₂²	1	4	yes	—
55	C₁₃×#481	C₂²	1	4	yes	complemented
56	C₁₃×#480	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	2	yes	complemented
58	C₁₃×#478	C₂²	1	2	yes	complemented
59	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#476	C₂²	1	2	yes	—
61	C₁₃×#476	C₂²	1	4	yes	—
62	C₁₃×#476	C₂²	1	2	yes	—
63	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#469	C₂²	1	4	yes	—
67	C₁₃×#468	C₂²	1	4	yes	—
68	C₁₃×#466	C₂²	1	4	yes	—
69	C₁₃×#465	C₂²	1	4	yes	—
70	C₁₃×#442	C₂²	1	2	yes	—
71	C₁₃×#440	C₂²	1	2	yes	—
72	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
73	C₄×C₁₃×D₈	C₂²	1	2	yes	—
74	C₁₃×#436	C₂²	1	2	yes	complemented
75	C₁₃×#435	C₂²	1	4	yes	complemented
76	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
77	C₁₃×#428	C₂²	1	2	yes	—
78	C₁₃×#428	C₂²	1	2	yes	—
79	C₁₃×#428	C₂²	1	1	yes	characteristic
80	C₁₃×#428	C₂²	1	4	yes	complemented
81	C₁₃×#428	C₂²	1	4	yes	complemented
82	C₁₃×#427	C₂²	1	2	yes	—
83	C₁₃×#427	C₂²	1	4	yes	complemented
84	C₂×C₁₃×#106	C₂²	1	2	yes	—
85	C₂×C₁₃×#106	C₂²	1	4	yes	complemented
86	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₁₃×#418	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×#408	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	1	yes	characteristic
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	—	2	1	no	—
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	—	2	1	no	—
100	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
101	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×D₈	C₂³	1	2	yes	—
103	C₁₃×#131	—	2	8	no	—
104	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×#127	—	2	2	no	—
117	C₁₃×#127	D₄	1	1	yes	characteristic
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	C₂³	1	2	yes	—
122	C₁₃×#124	—	2	2	no	—
123	C₁₃×#124	—	2	2	no	—
124	C₁₃×#124	—	2	4	no	—
125	C₁₃×#124	—	2	4	no	—
126	C₁₃×#124	D₄	1	2	yes	—
127	C₁₃×#123	—	2	4	no	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	2	no	—
131	C₁₃×C₂²⋊Q₈	—	2	1	no	—
132	C₁₃×C₂²⋊Q₈	—	2	1	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	—	2	2	no	—
139	C₁₃×#121	—	2	2	no	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	—	2	4	no	—
142	C₁₃×#121	D₄	1	2	yes	—
143	C₁₃×#121	D₄	1	2	yes	—
144	C₁₃×#121	C₂³	1	4	yes	—
145	C₁₃×#121	C₂³	1	4	yes	—
146	C₁₃×#121	C₂³	1	4	yes	—
147	C₁₃×#120	—	2	4	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	2	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
155	C₄×D₄×C₁₃	—	2	4	no	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	4	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	1	no	—
161	C₄×D₄×C₁₃	—	2	1	no	—
162	C₄×D₄×C₁₃	—	2	4	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	C₂³	1	2	yes	—
168	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₁₃	C₂³	1	2	yes	—
170	C₄×D₄×C₁₃	C₂³	1	2	yes	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	—	2	2	no	—
173	C₁₃×#117	—	2	1	no	—
174	C₁₃×#117	C₂³	1	2	yes	—
175	C₁₃×#117	C₂³	1	1	yes	characteristic
176	C₁₃×#117	C₂³	1	4	yes	—
177	C₁₃×#117	C₂³	1	4	yes	—
178	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₄²×C₁₃	—	2	1	no	—
185	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₁₃×#107	C₂³	1	2	yes	—
187	C₁₃×#107	C₂³	1	2	yes	—
188	C₁₃×#107	C₂³	1	2	yes	—
189	C₁₃×#107	C₂³	1	4	yes	—
190	C₁₃×#107	C₂³	1	4	yes	—
191	C₁₃×#106	C₂³	1	4	yes	—
192	C₁₃×#106	C₂³	1	4	yes	—
193	C₁₃×#106	C₂³	1	2	yes	—
194	C₁₃×#106	C₂³	1	2	yes	—
195	C₁₃×#106	C₂³	1	4	yes	—
196	C₁₃×#106	C₂³	1	2	yes	—
197	C₁₃×#106	C₂³	1	4	yes	—
198	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
200	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₁₃×#103	C₂³	1	2	yes	—
202	C₁₃×#103	C₂³	1	2	yes	—
203	C₁₃×#103	C₂³	1	2	yes	—
204	C₁₃×#102	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	2	yes	—
207	C₁₃×#102	C₂³	1	2	yes	—
208	C₁₃×#102	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	2	yes	—
210	C₁₃×#102	C₂³	1	2	yes	—
211	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₁₃×#97	C₂³	1	2	yes	—
214	C₄×C₈×C₁₃	C₂³	1	2	yes	—
215	#61279	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂⁴×C₁₃	—	2	1	no	—
217	C₁₃×#41	—	2	4	no	—
218	C₁₃×#41	—	2	4	no	—
219	C₁₃×#41	—	2	2	no	—
220	C₁₃×#41	—	2	2	no	—
221	C₁₃×#41	—	8	4	no	—
222	C₁₃×#41	—	8	4	no	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	2	1	no	—
226	C₂×Q₈×C₁₃	—	2	2	no	—
227	C₂×Q₈×C₁₃	—	8	2	no	—
228	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	4	no	—
232	C₂×D₄×C₁₃	—	2	4	no	—
233	C₂×D₄×C₁₃	—	2	4	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	2	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
238	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
240	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	4	no	—
246	C₂²×C₄×C₁₃	—	2	4	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	1	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	—	8	2	no	—
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₁₃×SD₁₆	—	2	4	no	—
258	C₁₃×D₈	—	2	4	no	—
259	C₁₃×M₁₆	—	2	2	no	—
260	C₁₃×M₁₆	—	2	8	no	—
261	C₁₃×M₁₆	#41	1	4	yes	complemented
262	C₂×C₈×C₁₃	—	2	4	no	—
263	C₂×C₈×C₁₃	—	2	8	no	—
264	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
265	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
266	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
284	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	2	no	—
296	C₁₃×C₂²⋊C₄	—	2	1	no	—
297	C₁₃×C₂²⋊C₄	—	2	1	no	—
298	C₁₃×C₂²⋊C₄	—	2	4	no	—
299	C₁₃×C₂²⋊C₄	—	2	4	no	—
300	C₁₃×C₂²⋊C₄	—	2	4	no	—
301	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
302	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
303	C₄²×C₁₃	—	2	1	no	—
304	C₄²×C₁₃	—	2	1	no	—
305	C₄²×C₁₃	—	2	1	no	—
306	C₄²×C₁₃	—	2	4	no	—
307	C₄²×C₁₃	—	2	4	no	—
308	C₄²×C₁₃	—	2	2	no	—
309	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
312	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
313	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#3357	C₂×C₁₃	1	2	yes	complemented
316	#3354	C₂×C₁₃	1	2	yes	complemented
317	#3350	C₂×C₁₃	1	4	yes	complemented
318	#3345	C₂×C₁₃	1	4	yes	complemented
319	#3341	C₂×C₁₃	1	2	yes	complemented
320	#3335	C₂×C₁₃	1	2	yes	complemented
321	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#3099	C₂×C₁₃	1	2	yes	complemented
323	#3096	C₂×C₁₃	1	2	yes	complemented
324	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
325	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#3062	C₂×C₁₃	1	2	yes	complemented
327	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#2935	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#2912	C₂×C₁₃	1	2	yes	complemented
330	C₂³×C₁₃	—	2	1	no	—
331	C₂³×C₁₃	—	2	2	no	—
332	C₂³×C₁₃	—	4	2	no	—
333	C₂³×C₁₃	—	8	1	no	—
334	C₂³×C₁₃	—	8	1	no	—
335	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
336	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
337	Q₈×C₁₃	—	2	4	no	—
338	Q₈×C₁₃	—	2	1	no	—
339	Q₈×C₁₃	—	2	1	no	—
340	Q₈×C₁₃	—	4	4	no	—
341	Q₈×C₁₃	—	4	2	no	—
342	Q₈×C₁₃	—	8	1	no	—
343	Q₈×C₁₃	—	8	2	no	—
344	D₄×C₁₃	—	2	8	no	—
345	D₄×C₁₃	—	2	4	no	—
346	D₄×C₁₃	—	2	4	no	—
347	D₄×C₁₃	—	2	1	no	—
348	D₄×C₁₃	—	2	2	no	—
349	D₄×C₁₃	—	2	2	no	—
350	D₄×C₁₃	—	2	1	no	—
351	D₄×C₁₃	—	4	2	no	—
352	D₄×C₁₃	—	4	2	no	—
353	D₄×C₁₃	—	4	2	no	—
354	D₄×C₁₃	—	8	4	no	—
355	D₄×C₁₃	—	8	4	no	—
356	D₄×C₁₃	—	8	4	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	4	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	2	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	4	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	2	no	—
369	C₂×C₄×C₁₃	—	4	2	no	—
370	C₂×C₄×C₁₃	—	4	2	no	—
371	C₂×C₄×C₁₃	—	4	4	no	—
372	C₂×C₄×C₁₃	—	8	2	no	—
373	C₂×C₄×C₁₃	—	8	1	no	—
374	C₂×C₄×C₁₃	—	8	2	no	—
375	C₂×C₄×C₁₃	—	8	4	no	—
376	C₂×C₄×C₁₃	—	8	4	no	—
377	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
378	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
384	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
385	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
386	C₈×C₁₃	—	2	2	no	—
387	C₈×C₁₃	—	2	2	no	—
388	C₈×C₁₃	—	2	2	no	—
389	C₈×C₁₃	C₂×#41	1	4	yes	—
390	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#131	C₂²×C₁₃	1	2	yes	—
392	#559	—	2	2	no	—
393	#556	—	2	1	no	—
394	#556	C₂²×C₁₃	1	2	yes	complemented
395	#555	C₂²×C₁₃	1	2	yes	—
396	#555	C₂²×C₁₃	1	2	yes	complemented
397	#554	C₂²×C₁₃	1	2	yes	complemented
398	#553	—	2	2	no	—
399	#553	C₂²×C₁₃	1	4	yes	—
400	#550	—	2	1	no	—
401	#548	—	2	2	no	—
402	#547	C₂²×C₁₃	1	2	yes	—
403	#547	C₂²×C₁₃	1	2	yes	complemented
404	#542	—	2	2	no	—
405	#538	—	2	2	no	—
406	#537	C₂²×C₁₃	1	2	yes	—
407	#535	C₂²×C₁₃	1	2	yes	—
408	#533	—	2	1	no	—
409	#533	C₂²×C₁₃	1	1	yes	characteristic
410	#532	—	2	1	no	—
411	#532	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
413	#525	—	2	2	no	—
414	#520	C₂²×C₁₃	1	2	yes	—
415	#520	C₂²×C₁₃	1	2	yes	—
416	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
418	#501	C₂²×C₁₃	1	4	yes	complemented
419	#500	C₂²×C₁₃	1	2	yes	complemented
420	#498	C₂²×C₁₃	1	2	yes	complemented
421	#485	C₂²×C₁₃	1	4	yes	complemented
422	#483	C₂²×C₁₃	1	4	yes	complemented
423	#482	C₂²×C₁₃	1	4	yes	—
424	#482	C₂²×C₁₃	1	4	yes	—
425	#482	C₂²×C₁₃	1	4	yes	complemented
426	#481	C₂²×C₁₃	1	4	yes	—
427	#481	C₂²×C₁₃	1	4	yes	complemented
428	#480	C₂²×C₁₃	1	4	yes	—
429	#479	C₂²×C₁₃	1	2	yes	complemented
430	#478	C₂²×C₁₃	1	2	yes	complemented
431	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#476	C₂²×C₁₃	1	2	yes	—
433	#476	C₂²×C₁₃	1	4	yes	—
434	#476	C₂²×C₁₃	1	2	yes	—
435	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	#469	C₂²×C₁₃	1	4	yes	—
439	#468	C₂²×C₁₃	1	4	yes	—
440	#466	C₂²×C₁₃	1	4	yes	—
441	#465	C₂²×C₁₃	1	4	yes	—
442	#442	C₂²×C₁₃	1	2	yes	—
443	#440	C₂²×C₁₃	1	2	yes	—
444	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
445	C₄×D₈	C₂²×C₁₃	1	2	yes	—
446	#436	C₂²×C₁₃	1	2	yes	complemented
447	#435	C₂²×C₁₃	1	4	yes	complemented
448	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
449	#428	C₂²×C₁₃	1	2	yes	—
450	#428	C₂²×C₁₃	1	2	yes	—
451	#428	C₂²×C₁₃	1	1	yes	characteristic
452	#428	C₂²×C₁₃	1	4	yes	complemented
453	#428	C₂²×C₁₃	1	4	yes	complemented
454	#427	C₂²×C₁₃	1	2	yes	—
455	#427	C₂²×C₁₃	1	4	yes	complemented
456	C₂×#106	C₂²×C₁₃	1	2	yes	—
457	C₂×#106	C₂²×C₁₃	1	4	yes	complemented
458	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
459	#418	C₂²×C₁₃	1	1	yes	characteristic
460	#417	C₂²×C₁₃	1	1	yes	characteristic
461	#416	C₂²×C₁₃	1	2	yes	—
462	C₂×#102	C₂²×C₁₃	1	2	yes	—
463	#408	C₂²×C₁₃	1	2	yes	—
464	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
465	C₂²×C₁₃	—	2	1	no	—
466	C₂²×C₁₃	—	2	1	no	—
467	C₂²×C₁₃	—	2	4	no	—
468	C₂²×C₁₃	—	2	4	no	—
469	C₂²×C₁₃	—	2	4	no	—
470	C₂²×C₁₃	—	4	1	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	1	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	1	no	—
476	C₂²×C₁₃	—	8	4	no	—
477	C₂²×C₁₃	#547	1	2	yes	—
478	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
479	C₄×C₁₃	—	2	1	no	—
480	C₄×C₁₃	—	2	1	no	—
481	C₄×C₁₃	—	2	4	no	—
482	C₄×C₁₃	—	2	1	no	—
483	C₄×C₁₃	—	4	1	no	—
484	C₄×C₁₃	—	4	4	no	—
485	C₄×C₁₃	—	4	2	no	—
486	C₄×C₁₃	—	4	1	no	—
487	C₄×C₁₃	—	4	1	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	#547	1	2	yes	—
491	C₄×C₁₃	#577	1	2	yes	—
492	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
493	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×#41	C₂³×C₁₃	1	2	yes	—
498	C₂²×Q₈	—	2	1	no	—
499	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂³×C₄	—	2	1	no	—
501	AGL(1,ℤ/8)	—	2	4	no	—
502	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
503	C₂×D₈	C₂³×C₁₃	1	2	yes	—
504	#131	—	2	8	no	—
505	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
506	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
507	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
508	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
509	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
517	#127	—	2	2	no	—
518	#127	D₄×C₁₃	1	1	yes	characteristic
519	#126	—	2	4	no	—
520	#126	—	2	4	no	—
521	#125	—	2	2	no	—
522	#125	C₂³×C₁₃	1	2	yes	—
523	#124	—	2	2	no	—
524	#124	—	2	2	no	—
525	#124	—	2	4	no	—
526	#124	—	2	4	no	—
527	#124	D₄×C₁₃	1	2	yes	—
528	#123	—	2	4	no	—
529	#123	—	2	4	no	—
530	#123	—	2	4	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
538	#121	—	2	2	no	—
539	#121	—	2	2	no	—
540	#121	—	2	2	no	—
541	#121	—	2	4	no	—
542	#121	—	2	4	no	—
543	#121	D₄×C₁₃	1	2	yes	—
544	#121	D₄×C₁₃	1	2	yes	—
545	#121	C₂³×C₁₃	1	4	yes	—
546	#121	C₂³×C₁₃	1	4	yes	—
547	#121	C₂³×C₁₃	1	4	yes	—
548	#120	—	2	4	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₄×D₄	—	2	4	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	4	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	C₂³×C₁₃	1	2	yes	—
567	C₄×D₄	C₂³×C₁₃	1	2	yes	—
568	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
570	C₄×D₄	C₂³×C₁₃	1	2	yes	—
571	C₄×D₄	C₂³×C₁₃	1	2	yes	—
572	#117	—	2	2	no	—
573	#117	—	2	2	no	—
574	#117	—	2	1	no	—
575	#117	C₂³×C₁₃	1	1	yes	characteristic
576	#117	C₂³×C₁₃	1	2	yes	—
577	#117	C₂³×C₁₃	1	4	yes	—
578	#117	C₂³×C₁₃	1	4	yes	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
587	#107	C₂³×C₁₃	1	2	yes	—
588	#107	C₂³×C₁₃	1	2	yes	—
589	#107	C₂³×C₁₃	1	2	yes	—
590	#107	C₂³×C₁₃	1	4	yes	—
591	#107	C₂³×C₁₃	1	4	yes	—
592	#106	C₂³×C₁₃	1	4	yes	—
593	#106	C₂³×C₁₃	1	4	yes	—
594	#106	C₂³×C₁₃	1	2	yes	—
595	#106	C₂³×C₁₃	1	2	yes	—
596	#106	C₂³×C₁₃	1	4	yes	—
597	#106	C₂³×C₁₃	1	2	yes	—
598	#106	C₂³×C₁₃	1	4	yes	—
599	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
601	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
602	#103	C₂³×C₁₃	1	2	yes	—
603	#103	C₂³×C₁₃	1	2	yes	—
604	#103	C₂³×C₁₃	1	2	yes	—
605	#102	C₂³×C₁₃	1	4	yes	—
606	#102	C₂³×C₁₃	1	4	yes	—
607	#102	C₂³×C₁₃	1	2	yes	—
608	#102	C₂³×C₁₃	1	2	yes	—
609	#102	C₂³×C₁₃	1	2	yes	—
610	#102	C₂³×C₁₃	1	2	yes	—
611	#102	C₂³×C₁₃	1	2	yes	—
612	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
613	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
614	#97	C₂³×C₁₃	1	2	yes	—
615	C₄×C₈	C₂³×C₁₃	1	2	yes	—
616	C₂×C₁₃	—	2	2	no	—
617	C₂×C₁₃	—	4	4	no	—
618	C₂×C₁₃	—	8	1	no	—
619	C₂×C₁₃	—	8	2	no	—
620	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
621	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
622	C₂×C₁₃	#3585	1	1	yes	characteristic
623	C₂⁴	—	2	1	no	—
624	#41	—	2	4	no	—
625	#41	—	2	4	no	—
626	#41	—	2	2	no	—
627	#41	—	2	2	no	—
628	#41	—	8	4	no	—
629	#41	—	8	4	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	2	1	no	—
633	C₂×Q₈	—	2	2	no	—
634	C₂×Q₈	—	8	2	no	—
635	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
636	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
645	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
646	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
647	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
648	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
649	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	8	2	no	—
660	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
663	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
664	SD₁₆	—	2	4	no	—
665	D₈	—	2	4	no	—
666	M₁₆	—	2	2	no	—
667	M₁₆	—	2	8	no	—
668	M₁₆	C₁₃×#41	1	4	yes	complemented
669	C₂×C₈	—	2	4	no	—
670	C₂×C₈	—	2	8	no	—
671	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
672	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
673	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
674	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	4	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
689	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
690	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
691	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
692	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
694	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
695	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
709	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	1	no	—
712	C₄²	—	2	1	no	—
713	C₄²	—	2	4	no	—
714	C₄²	—	2	4	no	—
715	C₄²	—	2	2	no	—
716	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
718	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₁₃	#61279	1	1	yes	characteristic, direct product factor, Sylow
721	C₂³	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	2	no	—
724	C₂³	—	8	1	no	—
725	C₂³	—	8	1	no	—
726	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
727	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
728	Q₈	—	2	4	no	—
729	Q₈	—	2	1	no	—
730	Q₈	—	2	1	no	—
731	Q₈	—	4	4	no	—
732	Q₈	—	4	2	no	—
733	Q₈	—	8	2	no	—
734	Q₈	—	8	1	no	—
735	D₄	—	2	8	no	—
736	D₄	—	2	4	no	—
737	D₄	—	2	4	no	—
738	D₄	—	2	1	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	1	no	—
742	D₄	—	4	2	no	—
743	D₄	—	4	2	no	—
744	D₄	—	4	2	no	—
745	D₄	—	8	4	no	—
746	D₄	—	8	4	no	—
747	D₄	—	8	4	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	2	no	—
763	C₂×C₄	—	8	2	no	—
764	C₂×C₄	—	8	1	no	—
765	C₂×C₄	—	8	2	no	—
766	C₂×C₄	—	8	4	no	—
767	C₂×C₄	—	8	4	no	—
768	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
769	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
774	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
775	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
776	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
777	C₈	—	2	2	no	—
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	C₂×C₁₃×#41	1	4	yes	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	4	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	4	no	—
793	C₂²	C₁₃×#547	1	2	yes	—
794	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	4	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	4	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	1	no	—
806	C₄	C₁₃×#547	1	2	yes	—
807	C₄	C₁₃×#577	1	2	yes	—
808	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
809	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
810	C₂	—	2	2	no	—
811	C₂	—	4	4	no	—
812	C₂	—	8	2	no	—
813	C₂	—	8	1	no	—
814	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
815	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
816	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3506	C₂	semidirect
3. C₁₃×#3357	C₂	semidirect
4. C₁₃×#3354	C₂	semidirect
5. C₁₃×#3350	C₂	semidirect
6. C₁₃×#3345	C₂	semidirect
7. C₁₃×#3341	C₂	semidirect
8. C₁₃×#3335	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₁₃×#3099	C₂	semidirect
11. C₁₃×#3096	C₂	semidirect
12. C₁₃×#3076	C₂	semidirect
13. C₂×C₁₃×#476	C₂	semidirect
14. C₁₃×#3062	C₂	semidirect
15. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
16. C₁₃×#2935	C₂	semidirect
17. C₁₃×#2912	C₂	semidirect
22. C₁₃×#556	C₂²	semidirect
24. C₁₃×#555	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
31. C₁₃×#547	C₂²	semidirect
46. C₁₃×#501	C₂²	semidirect
47. C₁₃×#500	C₂²	semidirect
48. C₁₃×#498	C₂²	semidirect
49. C₁₃×#485	C₂²	semidirect
50. C₁₃×#483	C₂²	semidirect
53. C₁₃×#482	C₂²	semidirect
55. C₁₃×#481	C₂²	semidirect
57. C₁₃×#479	C₂²	semidirect
58. C₁₃×#478	C₂²	semidirect
59. C₁₃×#477	C₂²	semidirect
63. C₁₃×#476	C₂²	semidirect
64. C₁₃×#475	C₂²	semidirect
65. C₁₃×#474	C₂²	semidirect
74. C₁₃×#436	C₂²	semidirect
75. C₁₃×#435	C₂²	semidirect
76. C₈×D₄×C₁₃	C₂²	semidirect
80. C₁₃×#428	C₂²	semidirect
81. C₁₃×#428	C₂²	semidirect
83. C₁₃×#427	C₂²	semidirect
85. C₂×C₁₃×#106	C₂²	semidirect
215. #61279	C₁₃	direct (N × H)
261. C₁₃×M₁₆	#41	semidirect
313. #3511	C₂×C₁₃	semidirect
314. #3506	C₂×C₁₃	semidirect
315. #3357	C₂×C₁₃	semidirect
316. #3354	C₂×C₁₃	semidirect
317. #3350	C₂×C₁₃	semidirect
318. #3345	C₂×C₁₃	semidirect
319. #3341	C₂×C₁₃	semidirect
320. #3335	C₂×C₁₃	semidirect
321. #3165	C₂×C₁₃	semidirect
322. #3099	C₂×C₁₃	semidirect
323. #3096	C₂×C₁₃	semidirect
324. #3076	C₂×C₁₃	semidirect
325. C₂×#476	C₂×C₁₃	semidirect
326. #3062	C₂×C₁₃	semidirect
327. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
328. #2935	C₂×C₁₃	semidirect
329. #2912	C₂×C₁₃	semidirect
394. #556	C₂²×C₁₃	semidirect
396. #555	C₂²×C₁₃	semidirect
397. #554	C₂²×C₁₃	semidirect
403. #547	C₂²×C₁₃	semidirect
418. #501	C₂²×C₁₃	semidirect
419. #500	C₂²×C₁₃	semidirect
420. #498	C₂²×C₁₃	semidirect
421. #485	C₂²×C₁₃	semidirect
422. #483	C₂²×C₁₃	semidirect
425. #482	C₂²×C₁₃	semidirect
427. #481	C₂²×C₁₃	semidirect
429. #479	C₂²×C₁₃	semidirect
430. #478	C₂²×C₁₃	semidirect
431. #477	C₂²×C₁₃	semidirect
435. #476	C₂²×C₁₃	semidirect
436. #475	C₂²×C₁₃	semidirect
437. #474	C₂²×C₁₃	semidirect
446. #436	C₂²×C₁₃	semidirect
447. #435	C₂²×C₁₃	semidirect
448. C₈×D₄	C₂²×C₁₃	semidirect
452. #428	C₂²×C₁₃	semidirect
453. #428	C₂²×C₁₃	semidirect
455. #427	C₂²×C₁₃	semidirect
457. C₂×#106	C₂²×C₁₃	semidirect
668. M₁₆	C₁₃×#41	semidirect
720. C₁₃	#61279	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×#3511	2
C₁₃×#3506	2
C₁₃×#3357	2
C₁₃×#3354	2
C₁₃×#3350	2
C₁₃×#3345	2
C₁₃×#3341	2
C₁₃×#3335	2
C₁₃×#3165	2
C₁₃×#3099	2
C₁₃×#3096	2
C₁₃×#3076	2
C₂×C₁₃×#476	2
C₁₃×#3062	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2935	2
C₁₃×#2912	2
#61279	13

Subgroups — C13×#61279 #15747618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61279 #15747618