Subgroups — C₁₃×#60703 #15747042

Order 3328.

1910 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3179	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3178	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3175	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3173	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
19	C₁₃×#542	—	2	2	no	—
20	C₁₃×#542	—	2	2	no	—
21	C₁₃×#542	C₂²	1	4	yes	—
22	C₁₃×#542	C₂²	1	4	yes	—
23	C₁₃×#542	C₂²	1	2	yes	complemented
24	C₁₃×#542	C₂²	1	2	yes	complemented
25	C₁₃×#541	C₂²	1	2	yes	complemented
26	C₁₃×#540	C₂²	1	2	yes	complemented
27	C₁₃×#539	—	2	1	no	—
28	C₁₃×#539	—	2	1	no	—
29	C₁₃×#538	—	2	1	no	—
30	C₁₃×#538	—	2	1	no	—
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₁₃×#532	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₃×#529	—	2	2	no	—
35	C₁₃×#529	—	2	2	no	—
36	C₂×C₁₃×#126	—	2	1	no	—
37	C₂×C₁₃×#124	—	2	1	no	—
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
39	C₁₃×#525	C₂²	1	2	yes	—
40	C₂×C₁₃×#123	—	2	1	no	—
41	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×#41	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	4	yes	complemented
49	C₁₃×#500	C₂²	1	2	yes	complemented
50	C₁₃×#498	C₂²	1	2	yes	complemented
51	C₁₃×#497	C₂²	1	2	yes	complemented
52	C₁₃×#496	C₂²	1	2	yes	complemented
53	C₁₃×#495	C₂²	1	4	yes	complemented
54	C₁₃×#489	C₂²	1	2	yes	complemented
55	C₁₃×#489	C₂²	1	2	yes	complemented
56	C₁₃×#489	C₂²	1	4	yes	complemented
57	C₁₃×#488	C₂²	1	4	yes	complemented
58	C₁₃×#487	C₂²	1	2	yes	complemented
59	C₁₃×#486	C₂²	1	2	yes	complemented
60	C₁₃×#470	C₂²	1	4	yes	complemented
61	C₁₃×#469	C₂²	1	4	yes	—
62	C₁₃×#468	C₂²	1	4	yes	—
63	C₁₃×#468	C₂²	1	4	yes	complemented
64	C₁₃×#467	C₂²	1	4	yes	complemented
65	C₁₃×#466	C₂²	1	4	yes	—
66	C₁₃×#465	C₂²	1	4	yes	—
67	C₁₃×#465	C₂²	1	4	yes	complemented
68	C₁₃×#442	C₂²	1	4	yes	complemented
69	C₁₃×#441	C₂²	1	4	yes	complemented
70	C₁₃×#440	C₂²	1	4	yes	complemented
71	C₁₃×#440	C₂²	1	4	yes	complemented
72	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
73	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
74	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
75	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
76	C₁₃×#428	C₂²	1	2	yes	—
77	C₁₃×#428	C₂²	1	2	yes	—
78	C₁₃×#419	C₂²	1	2	yes	—
79	C₁₃×#418	C₂²	1	2	yes	—
80	C₁₃×#417	C₂²	1	2	yes	—
81	C₁₃×#417	C₂²	1	2	yes	—
82	C₁₃×#405	C₂²	1	4	yes	complemented
83	C₁₃×#405	C₂²	1	4	yes	complemented
84	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
85	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
86	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
87	C₂×C₁₃×#41	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₃	—	2	1	no	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	—	2	1	no	—
91	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	—	2	1	no	—
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×#137	—	2	8	no	—
95	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
96	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
97	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×D₈	C₂³	1	4	yes	—
100	C₂×C₁₃×M₁₆	—	2	8	no	—
101	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
104	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
105	C₁₃×C₄⋊Q₈	—	2	1	no	—
106	C₁₃×C₄⋊Q₈	—	2	1	no	—
107	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×#127	C₂³	1	1	yes	characteristic
113	C₁₃×#126	—	2	4	no	—
114	C₁₃×#126	—	2	4	no	—
115	C₁₃×#126	—	2	2	no	—
116	C₁₃×#126	—	2	2	no	—
117	C₁₃×#126	—	2	2	no	—
118	C₁₃×#126	—	2	2	no	—
119	C₁₃×#125	—	2	2	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	C₂³	1	2	yes	—
122	C₁₃×#124	—	2	4	no	—
123	C₁₃×#124	—	2	4	no	—
124	C₁₃×#124	—	2	2	no	—
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	—	2	1	no	—
127	C₁₃×#124	—	2	1	no	—
128	C₁₃×#124	C₂³	1	2	yes	—
129	C₁₃×#124	C₂³	1	2	yes	—
130	C₁₃×#124	C₂³	1	2	yes	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	4	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	1	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	—	2	1	no	—
151	C₁₃×#121	—	2	2	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	C₂³	1	4	yes	—
154	C₁₃×#121	C₂³	1	2	yes	—
155	C₁₃×#121	C₂³	1	2	yes	—
156	C₁₃×#120	—	2	2	no	—
157	C₄×Q₈×C₁₃	—	2	2	no	—
158	C₄×Q₈×C₁₃	—	2	1	no	—
159	C₄×Q₈×C₁₃	—	2	1	no	—
160	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	2	no	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	C₂³	1	2	yes	—
171	C₄×D₄×C₁₃	C₂³	1	4	yes	—
172	C₄×D₄×C₁₃	C₂³	1	2	yes	—
173	C₁₃×#117	—	2	2	no	—
174	C₁₃×#117	D₄	1	2	yes	—
175	C₁₃×#117	D₄	1	2	yes	—
176	C₁₃×#117	C₂³	1	2	yes	—
177	C₁₃×#117	C₂³	1	2	yes	—
178	C₁₃×#117	C₂³	1	2	yes	—
179	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
183	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
188	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
189	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
192	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	—	2	1	no	—
194	C₂×C₄²×C₁₃	—	2	2	no	—
195	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₁₃×#107	C₂³	1	4	yes	—
198	C₁₃×#107	C₂³	1	4	yes	—
199	C₁₃×#106	C₂³	1	4	yes	—
200	C₁₃×#106	C₂³	1	4	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×#102	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	4	yes	—
209	C₁₃×#97	C₂³	1	4	yes	—
210	C₁₃×#97	C₂³	1	2	yes	—
211	C₁₃×#97	C₂³	1	2	yes	—
212	C₄×C₈×C₁₃	C₂³	1	4	yes	—
213	C₄×C₈×C₁₃	C₂³	1	2	yes	—
214	C₄×C₈×C₁₃	C₂³	1	2	yes	—
215	#60703	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂⁴×C₁₃	—	2	1	no	—
217	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₁₃×#41	—	2	4	no	—
219	C₁₃×#41	—	2	4	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	2	4	no	—
226	C₂×Q₈×C₁₃	—	8	2	no	—
227	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	4	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	1	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	8	2	no	—
238	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	1	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	4	no	—
248	C₂²×C₄×C₁₃	—	8	2	no	—
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₁₃×Q₁₆	—	2	8	no	—
258	C₁₃×SD₁₆	—	2	8	no	—
259	C₁₃×SD₁₆	—	2	8	no	—
260	C₁₃×D₈	—	2	8	no	—
261	C₁₃×M₁₆	—	2	4	no	—
262	C₁₃×M₁₆	—	2	8	no	—
263	C₁₃×M₁₆	#41	1	8	yes	—
264	C₂×C₈×C₁₃	—	2	8	no	—
265	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
266	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
284	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
285	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
286	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
289	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
290	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	2	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₁₃×C₂²⋊C₄	—	2	2	no	—
301	C₁₃×C₂²⋊C₄	—	2	2	no	—
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
308	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
309	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
311	C₄²×C₁₃	—	2	2	no	—
312	C₄²×C₁₃	—	2	2	no	—
313	C₄²×C₁₃	—	2	2	no	—
314	C₄²×C₁₃	—	2	4	no	—
315	C₄²×C₁₃	C₂×D₄	1	2	yes	—
316	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₃	C₂⁴	1	2	yes	—
319	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
320	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
321	#3455	C₂×C₁₃	1	1	yes	characteristic, complemented
322	C₂×#542	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#3179	C₂×C₁₃	1	4	yes	complemented
324	#3178	C₂×C₁₃	1	4	yes	complemented
325	#3175	C₂×C₁₃	1	4	yes	complemented
326	#3173	C₂×C₁₃	1	4	yes	complemented
327	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#3153	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#3056	C₂×C₁₃	1	2	yes	complemented
332	#3055	C₂×C₁₃	1	2	yes	complemented
333	C₄×#137	C₂×C₁₃	1	2	yes	complemented
334	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
335	#2873	C₂×C₁₃	1	1	yes	characteristic, complemented
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	2	2	no	—
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	4	1	no	—
340	C₂³×C₁₃	—	4	1	no	—
341	C₂³×C₁₃	—	4	2	no	—
342	C₂³×C₁₃	—	4	2	no	—
343	C₂³×C₁₃	—	4	2	no	—
344	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
345	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₁₃	—	2	2	no	—
347	Q₈×C₁₃	—	2	4	no	—
348	Q₈×C₁₃	—	2	2	no	—
349	Q₈×C₁₃	—	4	2	no	—
350	Q₈×C₁₃	—	8	1	no	—
351	Q₈×C₁₃	—	8	1	no	—
352	Q₈×C₁₃	—	8	2	no	—
353	Q₈×C₁₃	—	8	2	no	—
354	D₄×C₁₃	—	2	2	no	—
355	D₄×C₁₃	—	2	4	no	—
356	D₄×C₁₃	—	2	2	no	—
357	D₄×C₁₃	—	4	4	no	—
358	D₄×C₁₃	—	4	2	no	—
359	D₄×C₁₃	—	8	1	no	—
360	D₄×C₁₃	—	8	1	no	—
361	D₄×C₁₃	—	8	2	no	—
362	D₄×C₁₃	—	8	2	no	—
363	D₄×C₁₃	—	8	4	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	4	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	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	2	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	2	no	—
379	C₂×C₄×C₁₃	—	4	2	no	—
380	C₂×C₄×C₁₃	—	4	2	no	—
381	C₂×C₄×C₁₃	—	4	4	no	—
382	C₂×C₄×C₁₃	—	8	2	no	—
383	C₂×C₄×C₁₃	—	8	2	no	—
384	C₂×C₄×C₁₃	—	8	4	no	—
385	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
394	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
395	C₈×C₁₃	—	2	4	no	—
396	C₈×C₁₃	C₂×#41	1	8	yes	—
397	C₂×#137	C₂²×C₁₃	1	2	yes	—
398	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
399	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
400	#542	—	2	2	no	—
401	#542	—	2	2	no	—
402	#542	C₂²×C₁₃	1	4	yes	—
403	#542	C₂²×C₁₃	1	4	yes	—
404	#542	C₂²×C₁₃	1	2	yes	complemented
405	#542	C₂²×C₁₃	1	2	yes	complemented
406	#541	C₂²×C₁₃	1	2	yes	complemented
407	#540	C₂²×C₁₃	1	2	yes	complemented
408	#539	—	2	1	no	—
409	#539	—	2	1	no	—
410	#538	—	2	1	no	—
411	#538	—	2	1	no	—
412	#533	C₂²×C₁₃	1	1	yes	characteristic
413	#532	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
415	#529	—	2	2	no	—
416	#529	—	2	2	no	—
417	C₂×#126	—	2	1	no	—
418	C₂×#124	—	2	1	no	—
419	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
420	#525	C₂²×C₁₃	1	2	yes	—
421	C₂×#123	—	2	1	no	—
422	C₂×C₂²⋊Q₈	—	2	1	no	—
423	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
425	C₄×#41	C₂²×C₁₃	1	2	yes	—
426	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
429	#501	C₂²×C₁₃	1	4	yes	complemented
430	#500	C₂²×C₁₃	1	2	yes	complemented
431	#498	C₂²×C₁₃	1	2	yes	complemented
432	#497	C₂²×C₁₃	1	2	yes	complemented
433	#496	C₂²×C₁₃	1	2	yes	complemented
434	#495	C₂²×C₁₃	1	4	yes	complemented
435	#489	C₂²×C₁₃	1	2	yes	complemented
436	#489	C₂²×C₁₃	1	2	yes	complemented
437	#489	C₂²×C₁₃	1	4	yes	complemented
438	#488	C₂²×C₁₃	1	4	yes	complemented
439	#487	C₂²×C₁₃	1	2	yes	complemented
440	#486	C₂²×C₁₃	1	2	yes	complemented
441	#470	C₂²×C₁₃	1	4	yes	complemented
442	#469	C₂²×C₁₃	1	4	yes	—
443	#468	C₂²×C₁₃	1	4	yes	—
444	#468	C₂²×C₁₃	1	4	yes	complemented
445	#467	C₂²×C₁₃	1	4	yes	complemented
446	#466	C₂²×C₁₃	1	4	yes	—
447	#465	C₂²×C₁₃	1	4	yes	—
448	#465	C₂²×C₁₃	1	4	yes	complemented
449	#442	C₂²×C₁₃	1	4	yes	complemented
450	#441	C₂²×C₁₃	1	4	yes	complemented
451	#440	C₂²×C₁₃	1	4	yes	complemented
452	#440	C₂²×C₁₃	1	4	yes	complemented
453	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
454	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
455	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
456	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
457	#428	C₂²×C₁₃	1	2	yes	—
458	#428	C₂²×C₁₃	1	2	yes	—
459	#419	C₂²×C₁₃	1	2	yes	—
460	#418	C₂²×C₁₃	1	2	yes	—
461	#417	C₂²×C₁₃	1	2	yes	—
462	#417	C₂²×C₁₃	1	2	yes	—
463	#405	C₂²×C₁₃	1	4	yes	complemented
464	#405	C₂²×C₁₃	1	4	yes	complemented
465	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
466	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
467	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
468	C₂²×C₁₃	—	2	1	no	—
469	C₂²×C₁₃	—	2	1	no	—
470	C₂²×C₁₃	—	2	2	no	—
471	C₂²×C₁₃	—	2	2	no	—
472	C₂²×C₁₃	—	2	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	—	8	2	no	—
480	C₂²×C₁₃	—	8	4	no	—
481	C₂²×C₁₃	#532	1	2	yes	—
482	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
483	C₄×C₁₃	—	2	2	no	—
484	C₄×C₁₃	—	2	1	no	—
485	C₄×C₁₃	—	2	1	no	—
486	C₄×C₁₃	—	2	2	no	—
487	C₄×C₁₃	—	2	1	no	—
488	C₄×C₁₃	—	2	1	no	—
489	C₄×C₁₃	—	2	2	no	—
490	C₄×C₁₃	—	4	2	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	4	2	no	—
494	C₄×C₁₃	—	4	2	no	—
495	C₄×C₁₃	—	4	2	no	—
496	C₄×C₁₃	#532	1	2	yes	—
497	C₄×C₁₃	C₂²×#41	1	2	yes	—
498	C₂×#41	C₂³×C₁₃	1	2	yes	—
499	C₂²×Q₈	—	2	1	no	—
500	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
505	#137	—	2	8	no	—
506	AGL(1,ℤ/8)	—	2	8	no	—
507	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
508	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
509	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
510	C₂×D₈	C₂³×C₁₃	1	4	yes	—
511	C₂×M₁₆	—	2	8	no	—
512	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
513	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
514	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
515	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
516	C₄⋊Q₈	—	2	1	no	—
517	C₄⋊Q₈	—	2	1	no	—
518	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
520	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
521	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	#127	C₂³×C₁₃	1	1	yes	characteristic
524	#126	—	2	4	no	—
525	#126	—	2	4	no	—
526	#126	—	2	2	no	—
527	#126	—	2	2	no	—
528	#126	—	2	2	no	—
529	#126	—	2	2	no	—
530	#125	—	2	2	no	—
531	#125	—	2	2	no	—
532	#125	C₂³×C₁₃	1	2	yes	—
533	#124	—	2	4	no	—
534	#124	—	2	4	no	—
535	#124	—	2	2	no	—
536	#124	—	2	2	no	—
537	#124	—	2	1	no	—
538	#124	—	2	1	no	—
539	#124	C₂³×C₁₃	1	2	yes	—
540	#124	C₂³×C₁₃	1	2	yes	—
541	#124	C₂³×C₁₃	1	2	yes	—
542	#123	—	2	2	no	—
543	#123	—	2	2	no	—
544	#123	—	2	2	no	—
545	#123	—	2	4	no	—
546	#123	—	2	4	no	—
547	#123	—	2	2	no	—
548	#123	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	4	no	—
553	C₂²⋊Q₈	—	2	4	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
557	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
558	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
559	#121	—	2	2	no	—
560	#121	—	2	1	no	—
561	#121	—	2	1	no	—
562	#121	—	2	2	no	—
563	#121	—	2	2	no	—
564	#121	C₂³×C₁₃	1	4	yes	—
565	#121	C₂³×C₁₃	1	2	yes	—
566	#121	C₂³×C₁₃	1	2	yes	—
567	#120	—	2	2	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	—	2	1	no	—
571	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
572	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
573	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	C₂³×C₁₃	1	4	yes	—
582	C₄×D₄	C₂³×C₁₃	1	2	yes	—
583	C₄×D₄	C₂³×C₁₃	1	2	yes	—
584	#117	—	2	2	no	—
585	#117	D₄×C₁₃	1	2	yes	—
586	#117	D₄×C₁₃	1	2	yes	—
587	#117	C₂³×C₁₃	1	2	yes	—
588	#117	C₂³×C₁₃	1	2	yes	—
589	#117	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
603	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
604	C₂×C₄²	—	2	1	no	—
605	C₂×C₄²	—	2	2	no	—
606	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
608	#107	C₂³×C₁₃	1	4	yes	—
609	#107	C₂³×C₁₃	1	4	yes	—
610	#106	C₂³×C₁₃	1	4	yes	—
611	#106	C₂³×C₁₃	1	4	yes	—
612	#103	C₂³×C₁₃	1	4	yes	—
613	#103	C₂³×C₁₃	1	4	yes	—
614	#103	C₂³×C₁₃	1	4	yes	—
615	#103	C₂³×C₁₃	1	4	yes	—
616	#102	C₂³×C₁₃	1	4	yes	—
617	#102	C₂³×C₁₃	1	4	yes	—
618	#102	C₂³×C₁₃	1	4	yes	—
619	#102	C₂³×C₁₃	1	4	yes	—
620	#97	C₂³×C₁₃	1	4	yes	—
621	#97	C₂³×C₁₃	1	2	yes	—
622	#97	C₂³×C₁₃	1	2	yes	—
623	C₄×C₈	C₂³×C₁₃	1	4	yes	—
624	C₄×C₈	C₂³×C₁₃	1	2	yes	—
625	C₄×C₈	C₂³×C₁₃	1	2	yes	—
626	C₂×C₁₃	—	2	2	no	—
627	C₂×C₁₃	—	4	2	no	—
628	C₂×C₁₃	—	8	2	no	—
629	C₂×C₁₃	—	8	2	no	—
630	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
631	C₂×C₁₃	#3585	1	1	yes	characteristic
632	C₂×C₁₃	#3586	1	1	yes	characteristic
633	C₂⁴	—	2	1	no	—
634	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	2	no	—
641	C₂×Q₈	—	2	2	no	—
642	C₂×Q₈	—	2	4	no	—
643	C₂×Q₈	—	8	2	no	—
644	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
645	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	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	4	no	—
654	C₂×D₄	—	8	2	no	—
655	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
656	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	8	2	no	—
666	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
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	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
674	Q₁₆	—	2	8	no	—
675	SD₁₆	—	2	8	no	—
676	SD₁₆	—	2	8	no	—
677	D₈	—	2	8	no	—
678	M₁₆	—	2	4	no	—
679	M₁₆	—	2	8	no	—
680	M₁₆	C₁₃×#41	1	8	yes	—
681	C₂×C₈	—	2	8	no	—
682	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
683	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
702	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
703	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
705	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
706	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
726	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
727	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	4	no	—
732	C₄²	C₂×D₄×C₁₃	1	2	yes	—
733	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
735	C₄²	C₂⁴×C₁₃	1	2	yes	—
736	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₁₃	#60703	1	1	yes	characteristic, direct product factor, Sylow
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
748	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
749	Q₈	—	2	2	no	—
750	Q₈	—	2	4	no	—
751	Q₈	—	2	2	no	—
752	Q₈	—	4	2	no	—
753	Q₈	—	8	2	no	—
754	Q₈	—	8	2	no	—
755	Q₈	—	8	1	no	—
756	Q₈	—	8	1	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	4	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	4	no	—
761	D₄	—	4	2	no	—
762	D₄	—	8	1	no	—
763	D₄	—	8	1	no	—
764	D₄	—	8	4	no	—
765	D₄	—	8	2	no	—
766	D₄	—	8	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	4	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	8	4	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	2	no	—
788	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
789	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
796	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
797	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
798	C₈	—	2	4	no	—
799	C₈	C₂×C₁₃×#41	1	8	yes	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	2	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	8	2	no	—
812	C₂²	—	8	4	no	—
813	C₂²	C₁₃×#532	1	2	yes	—
814	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
815	C₄	—	2	2	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	C₁₃×#532	1	2	yes	—
829	C₄	C₂²×C₁₃×#41	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	8	2	no	—
833	C₂	—	8	2	no	—
834	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
835	C₂	C₁₃×#3585	1	1	yes	characteristic
836	C₂	C₁₃×#3586	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 ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3455	C₂	semidirect
2. C₂×C₁₃×#542	C₂	semidirect
3. C₁₃×#3179	C₂	semidirect
4. C₁₃×#3178	C₂	semidirect
5. C₁₃×#3175	C₂	semidirect
6. C₁₃×#3173	C₂	semidirect
7. C₁₃×#3165	C₂	semidirect
8. C₁₃×#3153	C₂	semidirect
9. C₁₃×#3141	C₂	semidirect
10. C₁₃×#3140	C₂	semidirect
11. C₁₃×#3056	C₂	semidirect
12. C₁₃×#3055	C₂	semidirect
13. C₄×C₁₃×#137	C₂	semidirect
14. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
15. C₁₃×#2873	C₂	semidirect
23. C₁₃×#542	C₂²	semidirect
24. C₁₃×#542	C₂²	semidirect
25. C₁₃×#541	C₂²	semidirect
26. C₁₃×#540	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#500	C₂²	semidirect
50. C₁₃×#498	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
52. C₁₃×#496	C₂²	semidirect
53. C₁₃×#495	C₂²	semidirect
54. C₁₃×#489	C₂²	semidirect
55. C₁₃×#489	C₂²	semidirect
56. C₁₃×#489	C₂²	semidirect
57. C₁₃×#488	C₂²	semidirect
58. C₁₃×#487	C₂²	semidirect
59. C₁₃×#486	C₂²	semidirect
60. C₁₃×#470	C₂²	semidirect
63. C₁₃×#468	C₂²	semidirect
64. C₁₃×#467	C₂²	semidirect
67. C₁₃×#465	C₂²	semidirect
68. C₁₃×#442	C₂²	semidirect
69. C₁₃×#441	C₂²	semidirect
70. C₁₃×#440	C₂²	semidirect
71. C₁₃×#440	C₂²	semidirect
72. C₄×C₁₃×Q₁₆	C₂²	semidirect
73. C₄×C₁₃×SD₁₆	C₂²	semidirect
74. C₄×C₁₃×SD₁₆	C₂²	semidirect
75. C₄×C₁₃×D₈	C₂²	semidirect
82. C₁₃×#405	C₂²	semidirect
83. C₁₃×#405	C₂²	semidirect
215. #60703	C₁₃	direct (N × H)
321. #3455	C₂×C₁₃	semidirect
322. C₂×#542	C₂×C₁₃	semidirect
323. #3179	C₂×C₁₃	semidirect
324. #3178	C₂×C₁₃	semidirect
325. #3175	C₂×C₁₃	semidirect
326. #3173	C₂×C₁₃	semidirect
327. #3165	C₂×C₁₃	semidirect
328. #3153	C₂×C₁₃	semidirect
329. #3141	C₂×C₁₃	semidirect
330. #3140	C₂×C₁₃	semidirect
331. #3056	C₂×C₁₃	semidirect
332. #3055	C₂×C₁₃	semidirect
333. C₄×#137	C₂×C₁₃	semidirect
334. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
335. #2873	C₂×C₁₃	semidirect
404. #542	C₂²×C₁₃	semidirect
405. #542	C₂²×C₁₃	semidirect
406. #541	C₂²×C₁₃	semidirect
407. #540	C₂²×C₁₃	semidirect
429. #501	C₂²×C₁₃	semidirect
430. #500	C₂²×C₁₃	semidirect
431. #498	C₂²×C₁₃	semidirect
432. #497	C₂²×C₁₃	semidirect
433. #496	C₂²×C₁₃	semidirect
434. #495	C₂²×C₁₃	semidirect
435. #489	C₂²×C₁₃	semidirect
436. #489	C₂²×C₁₃	semidirect
437. #489	C₂²×C₁₃	semidirect
438. #488	C₂²×C₁₃	semidirect
439. #487	C₂²×C₁₃	semidirect
440. #486	C₂²×C₁₃	semidirect
441. #470	C₂²×C₁₃	semidirect
444. #468	C₂²×C₁₃	semidirect
445. #467	C₂²×C₁₃	semidirect
448. #465	C₂²×C₁₃	semidirect
449. #442	C₂²×C₁₃	semidirect
450. #441	C₂²×C₁₃	semidirect
451. #440	C₂²×C₁₃	semidirect
452. #440	C₂²×C₁₃	semidirect
453. C₄×Q₁₆	C₂²×C₁₃	semidirect
454. C₄×SD₁₆	C₂²×C₁₃	semidirect
455. C₄×SD₁₆	C₂²×C₁₃	semidirect
456. C₄×D₈	C₂²×C₁₃	semidirect
463. #405	C₂²×C₁₃	semidirect
464. #405	C₂²×C₁₃	semidirect
738. C₁₃	#60703	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×#3455	2
C₂×C₁₃×#542	2
C₁₃×#3179	2
C₁₃×#3178	2
C₁₃×#3175	2
C₁₃×#3173	2
C₁₃×#3165	2
C₁₃×#3153	2
C₁₃×#3141	2
C₁₃×#3140	2
C₁₃×#3056	2
C₁₃×#3055	2
C₄×C₁₃×#137	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2873	2
#60703	13

Subgroups — C13×#60703 #15747042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60703 #15747042