Subgroups — C₁₃×#61339 #15747678

Order 3328.

1912 conjugacy classes of subgroups.

The subgroup lattice has 832 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×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3366	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3081	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2948	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
20	C₁₃×#559	C₂²	1	2	yes	complemented
21	C₁₃×#559	C₂²	1	2	yes	complemented
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#554	—	2	2	no	—
24	C₁₃×#554	C₂²	1	2	yes	complemented
25	C₁₃×#554	C₂²	1	4	yes	complemented
26	C₁₃×#550	C₂²	1	2	yes	complemented
27	C₁₃×#550	C₂²	1	2	yes	complemented
28	D₄×Q₈×C₁₃	—	2	1	no	—
29	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
30	C₁₃×#546	—	2	2	no	—
31	C₁₃×#546	—	2	2	no	—
32	C₁₃×#544	C₂²	1	2	yes	—
33	C₁₃×#543	—	2	2	no	—
34	C₁₃×#540	—	2	2	no	—
35	C₁₃×#535	C₂²	1	2	yes	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	—	2	1	no	—
39	C₁₃×#532	—	2	1	no	—
40	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
42	C₁₃×#518	C₂²	1	2	yes	—
43	C₁₃×#518	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×#490	C₂²	1	4	yes	complemented
47	C₁₃×#490	C₂²	1	4	yes	complemented
48	C₁₃×#489	C₂²	1	4	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#486	C₂²	1	4	yes	complemented
51	C₁₃×#486	C₂²	1	2	yes	complemented
52	C₁₃×#486	C₂²	1	2	yes	complemented
53	C₁₃×#479	C₂²	1	2	yes	complemented
54	C₁₃×#478	C₂²	1	2	yes	complemented
55	C₁₃×#478	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	complemented
57	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#476	C₂²	1	4	yes	complemented
60	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#474	C₂²	1	4	yes	complemented
63	C₁₃×#463	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#459	C₂²	1	2	yes	—
66	C₁₃×#459	C₂²	1	4	yes	—
67	C₁₃×#459	C₂²	1	2	yes	—
68	C₁₃×#459	C₂²	1	4	yes	complemented
69	C₁₃×#459	C₂²	1	4	yes	complemented
70	C₁₃×#446	C₂²	1	4	yes	complemented
71	C₁₃×#446	C₂²	1	2	yes	complemented
72	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
73	C₁₃×#442	C₂²	1	2	yes	complemented
74	C₁₃×#442	C₂²	1	4	yes	complemented
75	C₁₃×#442	C₂²	1	4	yes	complemented
76	C₁₃×#440	C₂²	1	2	yes	complemented
77	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
78	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
79	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
80	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₁₃×#427	C₂²	1	2	yes	—
83	C₁₃×#424	C₂²	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₁₃×#418	C₂²	1	2	yes	—
86	C₁₃×#418	C₂²	1	2	yes	—
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×#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	1	yes	characteristic
96	C₂²×Q₈×C₁₃	—	2	2	no	—
97	C₂²×D₄×C₁₃	—	2	1	no	—
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	—	2	1	no	—
102	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×D₈	—	2	8	no	—
105	C₂×C₁₃×D₈	C₂³	1	4	yes	—
106	C₂×C₁₃×D₈	C₂³	1	2	yes	—
107	C₂×C₁₃×D₈	C₂³	1	4	yes	—
108	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#127	—	2	1	no	—
118	C₁₃×#127	—	2	1	no	—
119	C₁₃×#127	C₂³	1	2	yes	—
120	C₁₃×#127	C₂³	1	2	yes	—
121	C₁₃×#127	C₂³	1	4	yes	—
122	C₁₃×#125	—	2	2	no	—
123	C₁₃×#125	D₄	1	2	yes	—
124	C₁₃×#125	C₂³	1	4	yes	—
125	C₁₃×#125	C₂³	1	2	yes	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	C₂³	1	4	yes	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×#123	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	4	no	—
133	C₁₃×C₂²⋊Q₈	—	2	1	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	4	no	—
139	C₁₃×C₂²⋊Q₈	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	2	no	—
145	C₁₃×#121	—	2	2	no	—
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	—	2	4	no	—
148	C₁₃×#121	—	2	4	no	—
149	C₁₃×#120	—	2	4	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×D₄×C₁₃	—	2	1	no	—
157	C₄×D₄×C₁₃	—	2	1	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₁₃	C₂³	1	2	yes	—
168	C₄×D₄×C₁₃	C₂³	1	4	yes	—
169	C₄×D₄×C₁₃	C₂³	1	4	yes	—
170	C₄×D₄×C₁₃	C₂³	1	4	yes	—
171	C₄×D₄×C₁₃	C₂³	1	4	yes	—
172	C₄×D₄×C₁₃	C₂³	1	2	yes	—
173	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
174	C₁₃×#117	—	2	1	no	—
175	C₁₃×#117	C₂³	1	2	yes	—
176	C₁₃×#117	C₂³	1	1	yes	characteristic
177	C₁₃×#117	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₂×C₁₃×C₂²⋊C₄	—	2	4	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×#106	C₂³	1	2	yes	—
190	C₁₃×#106	C₂³	1	2	yes	—
191	C₁₃×#106	C₂³	1	2	yes	—
192	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
196	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
197	C₁₃×#103	C₂³	1	2	yes	—
198	C₁₃×#103	C₂³	1	2	yes	—
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#102	C₂³	1	4	yes	—
201	C₁₃×#102	C₂³	1	4	yes	—
202	C₁₃×#102	C₂³	1	2	yes	—
203	C₁₃×#102	C₂³	1	2	yes	—
204	C₁₃×#102	C₂³	1	2	yes	—
205	C₁₃×#102	C₂³	1	2	yes	—
206	C₁₃×#102	C₂³	1	2	yes	—
207	C₁₃×#102	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	4	yes	—
209	C₁₃×#102	C₂³	1	4	yes	—
210	C₁₃×#102	C₂³	1	4	yes	—
211	C₁₃×#97	C₂³	1	2	yes	—
212	C₁₃×#97	C₂³	1	4	yes	—
213	C₄×C₈×C₁₃	C₂³	1	2	yes	—
214	C₄×C₈×C₁₃	C₂³	1	4	yes	—
215	#61339	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂⁴×C₁₃	—	2	1	no	—
217	C₂⁴×C₁₃	—	2	2	no	—
218	C₁₃×#41	—	2	2	no	—
219	C₁₃×#41	—	2	2	no	—
220	C₁₃×#41	—	8	4	no	—
221	C₁₃×#41	—	8	4	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	4	no	—
225	C₂×Q₈×C₁₃	—	8	4	no	—
226	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	2	4	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	2	4	no	—
239	C₂×D₄×C₁₃	—	2	2	no	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	8	2	no	—
242	C₂×D₄×C₁₃	—	8	2	no	—
243	C₂×D₄×C₁₃	#41	1	4	yes	complemented
244	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
245	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
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	1	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	2	4	no	—
254	C₂²×C₄×C₁₃	—	2	4	no	—
255	C₂²×C₄×C₁₃	—	2	4	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	8	2	no	—
258	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₁₃×SD₁₆	—	2	4	no	—
262	C₁₃×D₈	—	2	8	no	—
263	C₁₃×D₈	—	2	8	no	—
264	C₁₃×D₈	—	2	4	no	—
265	C₁₃×M₁₆	—	2	2	no	—
266	C₁₃×M₁₆	—	2	2	no	—
267	C₂×C₈×C₁₃	—	2	4	no	—
268	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
269	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
271	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	4	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	C₂×D₄	1	4	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
292	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
293	C₁₃×C₂²⋊C₄	—	2	1	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	4	no	—
298	C₁₃×C₂²⋊C₄	—	2	4	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₁₃×C₂²⋊C₄	—	2	2	no	—
301	C₁₃×C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄	1	4	yes	—
306	C₄²×C₁₃	—	2	1	no	—
307	C₄²×C₁₃	—	2	1	no	—
308	C₄²×C₁₃	—	2	1	no	—
309	C₄²×C₁₃	—	2	2	no	—
310	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₄²×C₁₃	C₂⁴	1	4	yes	—
314	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
315	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#3373	C₂×C₁₃	1	2	yes	complemented
318	#3370	C₂×C₁₃	1	4	yes	complemented
319	#3366	C₂×C₁₃	1	2	yes	complemented
320	#3366	C₂×C₁₃	1	4	yes	complemented
321	#3361	C₂×C₁₃	1	2	yes	complemented
322	#3358	C₂×C₁₃	1	2	yes	complemented
323	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#3136	C₂×C₁₃	1	2	yes	complemented
325	#3081	C₂×C₁₃	1	2	yes	complemented
326	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#3041	C₂×C₁₃	1	2	yes	complemented
328	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#2948	C₂×C₁₃	1	2	yes	complemented
331	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
332	C₂³×C₁₃	—	2	2	no	—
333	C₂³×C₁₃	—	2	4	no	—
334	C₂³×C₁₃	—	2	4	no	—
335	C₂³×C₁₃	—	2	1	no	—
336	C₂³×C₁₃	—	4	4	no	—
337	C₂³×C₁₃	—	8	1	no	—
338	C₂³×C₁₃	—	8	1	no	—
339	C₂³×C₁₃	—	8	2	no	—
340	C₂³×C₁₃	—	8	2	no	—
341	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₁₃	—	2	4	no	—
343	Q₈×C₁₃	—	2	1	no	—
344	Q₈×C₁₃	—	2	1	no	—
345	Q₈×C₁₃	—	4	2	no	—
346	Q₈×C₁₃	—	4	2	no	—
347	Q₈×C₁₃	—	8	1	no	—
348	Q₈×C₁₃	—	8	4	no	—
349	D₄×C₁₃	—	2	4	no	—
350	D₄×C₁₃	—	2	4	no	—
351	D₄×C₁₃	—	2	1	no	—
352	D₄×C₁₃	—	2	2	no	—
353	D₄×C₁₃	—	2	4	no	—
354	D₄×C₁₃	—	2	1	no	—
355	D₄×C₁₃	—	4	4	no	—
356	D₄×C₁₃	—	4	2	no	—
357	D₄×C₁₃	—	4	4	no	—
358	D₄×C₁₃	—	4	4	no	—
359	D₄×C₁₃	—	8	2	no	—
360	D₄×C₁₃	—	8	2	no	—
361	D₄×C₁₃	—	8	4	no	—
362	D₄×C₁₃	—	8	4	no	—
363	D₄×C₁₃	C₂×#41	1	4	yes	—
364	C₂×C₄×C₁₃	—	2	2	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	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	2	no	—
373	C₂×C₄×C₁₃	—	4	2	no	—
374	C₂×C₄×C₁₃	—	4	4	no	—
375	C₂×C₄×C₁₃	—	4	2	no	—
376	C₂×C₄×C₁₃	—	8	4	no	—
377	C₂×C₄×C₁₃	—	8	2	no	—
378	C₂×C₄×C₁₃	—	8	4	no	—
379	C₂×C₄×C₁₃	—	8	4	no	—
380	C₂×C₄×C₁₃	—	8	4	no	—
381	C₂×C₄×C₁₃	—	8	1	no	—
382	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
386	C₂×C₄×C₁₃	C₂²×D₄	1	4	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	C₂×#41	1	2	yes	—
390	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
391	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
392	C₈×C₁₃	—	2	2	no	—
393	C₈×C₁₃	—	2	2	no	—
394	C₈×C₁₃	—	2	2	no	—
395	C₈×C₁₃	—	2	2	no	—
396	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
397	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
398	#559	C₂²×C₁₃	1	2	yes	complemented
399	#559	C₂²×C₁₃	1	2	yes	complemented
400	#554	—	2	1	no	—
401	#554	—	2	2	no	—
402	#554	C₂²×C₁₃	1	2	yes	complemented
403	#554	C₂²×C₁₃	1	4	yes	complemented
404	#550	C₂²×C₁₃	1	2	yes	complemented
405	#550	C₂²×C₁₃	1	2	yes	complemented
406	D₄×Q₈	—	2	1	no	—
407	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
408	#546	—	2	2	no	—
409	#546	—	2	2	no	—
410	#544	C₂²×C₁₃	1	2	yes	—
411	#543	—	2	2	no	—
412	#540	—	2	2	no	—
413	#535	C₂²×C₁₃	1	2	yes	—
414	#533	C₂²×C₁₃	1	1	yes	characteristic
415	#533	C₂²×C₁₃	1	1	yes	characteristic
416	#532	—	2	1	no	—
417	#532	—	2	1	no	—
418	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₂²⋊Q₈	—	2	2	no	—
420	#518	C₂²×C₁₃	1	2	yes	—
421	#518	C₂²×C₁₃	1	2	yes	—
422	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
424	#490	C₂²×C₁₃	1	4	yes	complemented
425	#490	C₂²×C₁₃	1	4	yes	complemented
426	#489	C₂²×C₁₃	1	4	yes	complemented
427	#488	C₂²×C₁₃	1	4	yes	complemented
428	#486	C₂²×C₁₃	1	4	yes	complemented
429	#486	C₂²×C₁₃	1	2	yes	complemented
430	#486	C₂²×C₁₃	1	2	yes	complemented
431	#479	C₂²×C₁₃	1	2	yes	complemented
432	#478	C₂²×C₁₃	1	2	yes	complemented
433	#478	C₂²×C₁₃	1	4	yes	complemented
434	#478	C₂²×C₁₃	1	4	yes	complemented
435	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#476	C₂²×C₁₃	1	4	yes	complemented
438	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
440	#474	C₂²×C₁₃	1	4	yes	complemented
441	#463	C₂²×C₁₃	1	4	yes	complemented
442	#463	C₂²×C₁₃	1	4	yes	complemented
443	#459	C₂²×C₁₃	1	2	yes	—
444	#459	C₂²×C₁₃	1	4	yes	—
445	#459	C₂²×C₁₃	1	2	yes	—
446	#459	C₂²×C₁₃	1	4	yes	complemented
447	#459	C₂²×C₁₃	1	4	yes	complemented
448	#446	C₂²×C₁₃	1	4	yes	complemented
449	#446	C₂²×C₁₃	1	2	yes	complemented
450	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
451	#442	C₂²×C₁₃	1	2	yes	complemented
452	#442	C₂²×C₁₃	1	4	yes	complemented
453	#442	C₂²×C₁₃	1	4	yes	complemented
454	#440	C₂²×C₁₃	1	2	yes	complemented
455	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
456	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
457	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
458	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
459	#428	C₂²×C₁₃	1	1	yes	characteristic
460	#427	C₂²×C₁₃	1	2	yes	—
461	#424	C₂²×C₁₃	1	2	yes	—
462	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
463	#418	C₂²×C₁₃	1	2	yes	—
464	#418	C₂²×C₁₃	1	2	yes	—
465	#418	C₂²×C₁₃	1	1	yes	characteristic
466	#417	C₂²×C₁₃	1	1	yes	characteristic
467	#416	C₂²×C₁₃	1	2	yes	—
468	C₂×#102	C₂²×C₁₃	1	2	yes	—
469	#405	C₂²×C₁₃	1	2	yes	—
470	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
471	C₂²×C₁₃	—	2	1	no	—
472	C₂²×C₁₃	—	2	1	no	—
473	C₂²×C₁₃	—	2	4	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	—	4	1	no	—
477	C₂²×C₁₃	—	4	4	no	—
478	C₂²×C₁₃	—	4	1	no	—
479	C₂²×C₁₃	—	4	4	no	—
480	C₂²×C₁₃	—	4	1	no	—
481	C₂²×C₁₃	—	4	4	no	—
482	C₂²×C₁₃	—	8	4	no	—
483	C₂²×C₁₃	—	16	4	no	—
484	C₂²×C₁₃	#548	1	2	yes	—
485	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
486	C₄×C₁₃	—	2	1	no	—
487	C₄×C₁₃	—	2	1	no	—
488	C₄×C₁₃	—	2	4	no	—
489	C₄×C₁₃	—	2	1	no	—
490	C₄×C₁₃	—	2	4	no	—
491	C₄×C₁₃	—	4	1	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	4	1	no	—
494	C₄×C₁₃	—	4	1	no	—
495	C₄×C₁₃	—	4	2	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	#548	1	2	yes	—
498	C₄×C₁₃	#576	1	2	yes	—
499	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
500	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
504	C₂²×Q₈	—	2	2	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
508	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂³×C₄	—	2	1	no	—
510	AGL(1,ℤ/8)	—	2	4	no	—
511	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
512	C₂×D₈	—	2	8	no	—
513	C₂×D₈	C₂³×C₁₃	1	4	yes	—
514	C₂×D₈	C₂³×C₁₃	1	4	yes	—
515	C₂×D₈	C₂³×C₁₃	1	2	yes	—
516	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
519	C₄⋊Q₈	—	2	2	no	—
520	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
521	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
522	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
525	#127	—	2	1	no	—
526	#127	—	2	1	no	—
527	#127	C₂³×C₁₃	1	2	yes	—
528	#127	C₂³×C₁₃	1	2	yes	—
529	#127	C₂³×C₁₃	1	4	yes	—
530	#125	—	2	2	no	—
531	#125	D₄×C₁₃	1	2	yes	—
532	#125	C₂³×C₁₃	1	2	yes	—
533	#125	C₂³×C₁₃	1	4	yes	—
534	#124	—	2	2	no	—
535	#124	—	2	2	no	—
536	#124	C₂³×C₁₃	1	4	yes	—
537	#123	—	2	4	no	—
538	#123	—	2	4	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	—	2	4	no	—
546	C₂²⋊Q₈	—	2	4	no	—
547	C₂²⋊Q₈	—	2	4	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
550	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	2	no	—
554	#121	—	2	2	no	—
555	#121	—	2	4	no	—
556	#121	—	2	4	no	—
557	#120	—	2	4	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
562	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
563	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	C₂³×C₁₃	1	2	yes	—
575	C₄×D₄	C₂³×C₁₃	1	2	yes	—
576	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
577	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
578	C₄×D₄	C₂³×C₁₃	1	4	yes	—
579	C₄×D₄	C₂³×C₁₃	1	4	yes	—
580	C₄×D₄	C₂³×C₁₃	1	4	yes	—
581	C₄×D₄	C₂³×C₁₃	1	4	yes	—
582	#117	—	2	1	no	—
583	#117	C₂³×C₁₃	1	1	yes	characteristic
584	#117	C₂³×C₁₃	1	2	yes	—
585	#117	C₂³×C₁₃	1	2	yes	—
586	C₂×C₄⋊C₄	—	2	4	no	—
587	C₂×C₄⋊C₄	—	2	2	no	—
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	4	no	—
591	C₂×C₂²⋊C₄	—	2	4	no	—
592	C₂×C₄²	—	2	1	no	—
593	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
594	#107	C₂³×C₁₃	1	2	yes	—
595	#107	C₂³×C₁₃	1	2	yes	—
596	#107	C₂³×C₁₃	1	2	yes	—
597	#106	C₂³×C₁₃	1	2	yes	—
598	#106	C₂³×C₁₃	1	2	yes	—
599	#106	C₂³×C₁₃	1	2	yes	—
600	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
603	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
604	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
605	#103	C₂³×C₁₃	1	2	yes	—
606	#103	C₂³×C₁₃	1	2	yes	—
607	#103	C₂³×C₁₃	1	2	yes	—
608	#102	C₂³×C₁₃	1	4	yes	—
609	#102	C₂³×C₁₃	1	4	yes	—
610	#102	C₂³×C₁₃	1	2	yes	—
611	#102	C₂³×C₁₃	1	2	yes	—
612	#102	C₂³×C₁₃	1	2	yes	—
613	#102	C₂³×C₁₃	1	2	yes	—
614	#102	C₂³×C₁₃	1	2	yes	—
615	#102	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	#97	C₂³×C₁₃	1	2	yes	—
620	#97	C₂³×C₁₃	1	4	yes	—
621	C₄×C₈	C₂³×C₁₃	1	2	yes	—
622	C₄×C₈	C₂³×C₁₃	1	4	yes	—
623	C₂×C₁₃	—	2	2	no	—
624	C₂×C₁₃	—	4	4	no	—
625	C₂×C₁₃	—	8	1	no	—
626	C₂×C₁₃	—	8	4	no	—
627	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
628	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
629	C₂×C₁₃	#3585	1	1	yes	characteristic
630	C₂⁴	—	2	1	no	—
631	C₂⁴	—	2	2	no	—
632	#41	—	2	2	no	—
633	#41	—	2	2	no	—
634	#41	—	8	4	no	—
635	#41	—	8	4	no	—
636	C₂×Q₈	—	2	1	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	4	no	—
639	C₂×Q₈	—	8	4	no	—
640	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
641	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
642	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	4	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	8	2	no	—
656	C₂×D₄	—	8	2	no	—
657	C₂×D₄	C₁₃×#41	1	4	yes	complemented
658	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
659	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
660	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	8	2	no	—
672	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
675	SD₁₆	—	2	4	no	—
676	D₈	—	2	8	no	—
677	D₈	—	2	8	no	—
678	D₈	—	2	4	no	—
679	M₁₆	—	2	2	no	—
680	M₁₆	—	2	2	no	—
681	C₂×C₈	—	2	4	no	—
682	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
683	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
684	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
685	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
697	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
698	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
699	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
700	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
702	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
703	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
705	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
720	C₄²	—	2	1	no	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	2	2	no	—
724	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
725	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₄²	C₂⁴×C₁₃	1	4	yes	—
728	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₁₃	#61339	1	1	yes	characteristic, direct product factor, Sylow
730	C₂³	—	2	2	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	4	4	no	—
735	C₂³	—	8	1	no	—
736	C₂³	—	8	1	no	—
737	C₂³	—	8	2	no	—
738	C₂³	—	8	2	no	—
739	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
740	Q₈	—	2	4	no	—
741	Q₈	—	2	1	no	—
742	Q₈	—	2	1	no	—
743	Q₈	—	4	2	no	—
744	Q₈	—	4	2	no	—
745	Q₈	—	8	4	no	—
746	Q₈	—	8	1	no	—
747	D₄	—	2	4	no	—
748	D₄	—	2	4	no	—
749	D₄	—	2	1	no	—
750	D₄	—	2	2	no	—
751	D₄	—	2	4	no	—
752	D₄	—	2	1	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	4	no	—
756	D₄	—	4	4	no	—
757	D₄	—	8	2	no	—
758	D₄	—	8	2	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	C₂×C₁₃×#41	1	4	yes	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	8	2	no	—
775	C₂×C₄	—	8	4	no	—
776	C₂×C₄	—	8	4	no	—
777	C₂×C₄	—	8	4	no	—
778	C₂×C₄	—	8	4	no	—
779	C₂×C₄	—	8	1	no	—
780	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
784	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
785	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
787	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
788	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
789	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
790	C₈	—	2	2	no	—
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₈	—	2	2	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	4	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	4	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	4	no	—
805	C₂²	—	8	4	no	—
806	C₂²	—	16	4	no	—
807	C₂²	C₁₃×#548	1	2	yes	—
808	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
809	C₄	—	2	1	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	4	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	1	no	—
820	C₄	C₁₃×#548	1	2	yes	—
821	C₄	C₁₃×#576	1	2	yes	—
822	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
823	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
824	C₂	—	2	2	no	—
825	C₂	—	4	4	no	—
826	C₂	—	8	4	no	—
827	C₂	—	8	1	no	—
828	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
829	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
830	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×#3501	C₂	semidirect
3. C₁₃×#3373	C₂	semidirect
4. C₁₃×#3370	C₂	semidirect
5. C₁₃×#3366	C₂	semidirect
6. C₁₃×#3366	C₂	semidirect
7. C₁₃×#3361	C₂	semidirect
8. C₁₃×#3358	C₂	semidirect
9. C₁₃×#3138	C₂	semidirect
10. C₁₃×#3136	C₂	semidirect
11. C₁₃×#3081	C₂	semidirect
12. C₁₃×#3076	C₂	semidirect
13. C₁₃×#3041	C₂	semidirect
14. C₂×C₁₃×#459	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
16. C₁₃×#2948	C₂	semidirect
17. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
20. C₁₃×#559	C₂²	semidirect
21. C₁₃×#559	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
26. C₁₃×#550	C₂²	semidirect
27. C₁₃×#550	C₂²	semidirect
29. D₄×Q₈×C₁₃	C₂²	semidirect
46. C₁₃×#490	C₂²	semidirect
47. C₁₃×#490	C₂²	semidirect
48. C₁₃×#489	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#486	C₂²	semidirect
51. C₁₃×#486	C₂²	semidirect
52. C₁₃×#486	C₂²	semidirect
53. C₁₃×#479	C₂²	semidirect
54. C₁₃×#478	C₂²	semidirect
55. C₁₃×#478	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#476	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#474	C₂²	semidirect
62. C₁₃×#474	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
68. C₁₃×#459	C₂²	semidirect
69. C₁₃×#459	C₂²	semidirect
70. C₁₃×#446	C₂²	semidirect
71. C₁₃×#446	C₂²	semidirect
72. C₈×Q₈×C₁₃	C₂²	semidirect
73. C₁₃×#442	C₂²	semidirect
74. C₁₃×#442	C₂²	semidirect
75. C₁₃×#442	C₂²	semidirect
76. C₁₃×#440	C₂²	semidirect
77. C₄×C₁₃×SD₁₆	C₂²	semidirect
78. C₄×C₁₃×D₈	C₂²	semidirect
79. C₄×C₁₃×D₈	C₂²	semidirect
80. C₄×C₁₃×D₈	C₂²	semidirect
215. #61339	C₁₃	direct (N × H)
243. C₂×D₄×C₁₃	#41	semidirect
315. #3508	C₂×C₁₃	semidirect
316. #3501	C₂×C₁₃	semidirect
317. #3373	C₂×C₁₃	semidirect
318. #3370	C₂×C₁₃	semidirect
319. #3366	C₂×C₁₃	semidirect
320. #3366	C₂×C₁₃	semidirect
321. #3361	C₂×C₁₃	semidirect
322. #3358	C₂×C₁₃	semidirect
323. #3138	C₂×C₁₃	semidirect
324. #3136	C₂×C₁₃	semidirect
325. #3081	C₂×C₁₃	semidirect
326. #3076	C₂×C₁₃	semidirect
327. #3041	C₂×C₁₃	semidirect
328. C₂×#459	C₂×C₁₃	semidirect
329. #2962	C₂×C₁₃	semidirect
330. #2948	C₂×C₁₃	semidirect
331. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
398. #559	C₂²×C₁₃	semidirect
399. #559	C₂²×C₁₃	semidirect
402. #554	C₂²×C₁₃	semidirect
403. #554	C₂²×C₁₃	semidirect
404. #550	C₂²×C₁₃	semidirect
405. #550	C₂²×C₁₃	semidirect
407. D₄×Q₈	C₂²×C₁₃	semidirect
424. #490	C₂²×C₁₃	semidirect
425. #490	C₂²×C₁₃	semidirect
426. #489	C₂²×C₁₃	semidirect
427. #488	C₂²×C₁₃	semidirect
428. #486	C₂²×C₁₃	semidirect
429. #486	C₂²×C₁₃	semidirect
430. #486	C₂²×C₁₃	semidirect
431. #479	C₂²×C₁₃	semidirect
432. #478	C₂²×C₁₃	semidirect
433. #478	C₂²×C₁₃	semidirect
434. #478	C₂²×C₁₃	semidirect
435. #477	C₂²×C₁₃	semidirect
436. #476	C₂²×C₁₃	semidirect
437. #476	C₂²×C₁₃	semidirect
438. #475	C₂²×C₁₃	semidirect
439. #474	C₂²×C₁₃	semidirect
440. #474	C₂²×C₁₃	semidirect
441. #463	C₂²×C₁₃	semidirect
442. #463	C₂²×C₁₃	semidirect
446. #459	C₂²×C₁₃	semidirect
447. #459	C₂²×C₁₃	semidirect
448. #446	C₂²×C₁₃	semidirect
449. #446	C₂²×C₁₃	semidirect
450. C₈×Q₈	C₂²×C₁₃	semidirect
451. #442	C₂²×C₁₃	semidirect
452. #442	C₂²×C₁₃	semidirect
453. #442	C₂²×C₁₃	semidirect
454. #440	C₂²×C₁₃	semidirect
455. C₄×SD₁₆	C₂²×C₁₃	semidirect
456. C₄×D₈	C₂²×C₁₃	semidirect
457. C₄×D₈	C₂²×C₁₃	semidirect
458. C₄×D₈	C₂²×C₁₃	semidirect
657. C₂×D₄	C₁₃×#41	semidirect
729. C₁₃	#61339	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×#3501	2
C₁₃×#3373	2
C₁₃×#3370	2
C₁₃×#3366	2
C₁₃×#3361	2
C₁₃×#3358	2
C₁₃×#3138	2
C₁₃×#3136	2
C₁₃×#3081	2
C₁₃×#3076	2
C₁₃×#3041	2
C₂×C₁₃×#459	2
C₁₃×#2962	2
C₁₃×#2948	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61339	13

Subgroups — C13×#61339 #15747678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61339 #15747678