Subgroups — C₁₃×#62587 #15748926

Order 3328.

1726 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×#3517	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3317	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3315	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3304	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3302	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3240	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3216	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3181	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3135	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#557	—	2	1	no	—
19	C₁₃×#557	C₂²	1	1	yes	characteristic
20	C₁₃×#557	C₂²	1	2	yes	—
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	2	yes	—
23	C₁₃×#553	—	2	1	no	—
24	C₁₃×#553	—	2	2	no	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#552	C₂²	1	4	yes	—
27	C₁₃×#550	—	2	1	no	—
28	C₁₃×#550	C₂²	1	1	yes	characteristic
29	C₁₃×#550	C₂²	1	2	yes	—
30	C₁₃×#550	C₂²	1	1	yes	characteristic
31	C₁₃×#547	C₂²	1	1	yes	characteristic
32	C₁₃×#547	C₂²	1	2	yes	—
33	C₁₃×#541	—	2	2	no	—
34	C₁₃×#540	—	2	2	no	—
35	C₁₃×#540	—	2	1	no	—
36	C₁₃×#536	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	2	yes	—
39	C₁₃×#533	C₂²	1	2	yes	—
40	C₁₃×#532	C₂²	1	2	yes	—
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₁₃×#529	C₂²	1	1	yes	characteristic
44	C₁₃×#529	C₂²	1	2	yes	—
45	C₁₃×#520	—	2	1	no	—
46	C₁₃×#519	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	1	yes	characteristic
49	C₁₃×#501	C₂²	1	2	yes	—
50	C₁₃×#497	C₂²	1	1	yes	characteristic
51	C₁₃×#497	C₂²	1	2	yes	—
52	C₁₃×#491	C₂²	1	4	yes	—
53	C₁₃×#491	C₂²	1	1	yes	characteristic
54	C₁₃×#490	C₂²	1	4	yes	—
55	C₁₃×#489	C₂²	1	1	yes	characteristic
56	C₁₃×#489	C₂²	1	2	yes	—
57	C₁₃×#489	C₂²	1	2	yes	—
58	C₁₃×#489	C₂²	1	2	yes	—
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#487	C₂²	1	2	yes	—
61	C₁₃×#486	C₂²	1	2	yes	—
62	C₁₃×#485	C₂²	1	4	yes	—
63	C₁₃×#484	C₂²	1	2	yes	—
64	C₁₃×#482	C₂²	1	4	yes	—
65	C₁₃×#481	C₂²	1	2	yes	—
66	C₁₃×#479	C₂²	1	4	yes	—
67	C₁₃×#478	C₂²	1	4	yes	—
68	C₁₃×#475	C₂²	1	2	yes	—
69	C₁₃×#474	C₂²	1	2	yes	—
70	C₁₃×#470	C₂²	1	2	yes	—
71	C₁₃×#468	C₂²	1	2	yes	—
72	C₁₃×#467	C₂²	1	4	yes	—
73	C₁₃×#465	C₂²	1	4	yes	—
74	C₁₃×#462	C₂²	1	2	yes	—
75	C₁₃×#462	C₂²	1	4	yes	—
76	C₁₃×#460	C₂²	1	2	yes	—
77	C₁₃×#460	C₂²	1	4	yes	—
78	C₁₃×#452	C₂²	1	4	yes	—
79	C₁₃×#452	C₂²	1	4	yes	—
80	C₁₃×#452	C₂²	1	4	yes	—
81	C₁₃×#446	C₂²	1	2	yes	—
82	C₁₃×#441	C₂²	1	4	yes	—
83	C₁₃×#440	C₂²	1	4	yes	—
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
86	C₁₃×#435	C₂²	1	4	yes	—
87	C₈×D₄×C₁₃	C₂²	1	2	yes	—
88	C₁₃×#432	C₂²	1	1	yes	characteristic
89	C₁₃×#432	C₂²	1	2	yes	—
90	C₁₃×#417	C₂²	1	4	yes	—
91	C₁₃×#416	C₂²	1	4	yes	—
92	C₁₃×#416	C₂²	1	4	yes	—
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₂×C₁₃×#97	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂×C₁₃×#41	C₂³	1	2	yes	—
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂²×Q₈×C₁₃	—	2	1	no	—
101	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
106	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
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	1	no	—
117	C₁₃×#127	—	2	2	no	—
118	C₁₃×#127	C₂³	1	1	yes	characteristic
119	C₁₃×#127	C₂³	1	2	yes	—
120	C₁₃×#126	—	2	4	no	—
121	C₁₃×#126	—	2	4	no	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	1	no	—
124	C₁₃×#125	—	2	1	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	4	no	—
127	C₁₃×#125	—	2	4	no	—
128	C₁₃×#125	—	2	1	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	C₂³	1	4	yes	—
131	C₁₃×#125	C₂³	1	1	yes	characteristic
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	C₂³	1	1	yes	characteristic
134	C₁₃×#124	C₂³	1	2	yes	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×#123	—	2	1	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#121	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	—	2	2	no	—
166	C₄×Q₈×C₁₃	—	2	2	no	—
167	C₄×Q₈×C₁₃	—	2	2	no	—
168	C₄×Q₈×C₁₃	—	2	1	no	—
169	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
170	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	D₄	1	2	yes	—
184	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	2	yes	—
187	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	4	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	1	no	—
194	C₁₃×#117	D₄	1	1	yes	characteristic
195	C₁₃×#117	D₄	1	2	yes	—
196	C₁₃×#117	C₂³	1	4	yes	—
197	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₁₃×#107	C₂³	1	2	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#106	C₂³	1	2	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	2	yes	—
210	C₁₃×#103	C₂³	1	4	yes	—
211	C₁₃×#103	C₂³	1	4	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	2	yes	—
216	C₁₃×#102	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
222	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₁₃×#97	C₂³	1	1	yes	characteristic
224	C₁₃×#97	C₂³	1	2	yes	—
225	C₁₃×#97	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#62587	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₁₃×#41	—	4	2	no	—
230	C₁₃×#41	—	4	4	no	—
231	C₁₃×#41	—	4	4	no	—
232	C₁₃×#41	—	4	4	no	—
233	C₁₃×#41	—	4	4	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	4	4	no	—
238	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	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	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₁₃×Q₁₆	—	4	4	no	—
268	C₁₃×Q₁₆	—	4	2	no	—
269	C₁₃×SD₁₆	—	4	4	no	—
270	C₁₃×SD₁₆	—	4	2	no	—
271	C₁₃×M₁₆	—	4	2	no	—
272	C₂×C₈×C₁₃	—	4	4	no	—
273	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	4	no	—
288	C₁₃×C₄⋊C₄	—	2	4	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	1	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	1	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
320	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	C₂×D₄	1	2	yes	—
328	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₁₃	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	#3517	C₂×C₁₃	1	1	yes	characteristic
335	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3374	C₂×C₁₃	1	2	yes	complemented
337	#3368	C₂×C₁₃	1	2	yes	complemented
338	#3317	C₂×C₁₃	1	4	yes	complemented
339	#3315	C₂×C₁₃	1	4	yes	complemented
340	#3304	C₂×C₁₃	1	2	yes	complemented
341	#3302	C₂×C₁₃	1	2	yes	complemented
342	#3240	C₂×C₁₃	1	2	yes	complemented
343	#3239	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3216	C₂×C₁₃	1	2	yes	complemented
345	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3181	C₂×C₁₃	1	2	yes	complemented
347	#3172	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3135	C₂×C₁₃	1	2	yes	complemented
350	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
354	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
355	Q₈×C₁₃	—	2	2	no	—
356	Q₈×C₁₃	—	2	2	no	—
357	Q₈×C₁₃	—	2	2	no	—
358	Q₈×C₁₃	—	2	4	no	—
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	4	2	no	—
361	Q₈×C₁₃	—	4	4	no	—
362	Q₈×C₁₃	—	4	4	no	—
363	D₄×C₁₃	—	2	2	no	—
364	D₄×C₁₃	—	2	4	no	—
365	D₄×C₁₃	—	2	2	no	—
366	D₄×C₁₃	—	4	2	no	—
367	D₄×C₁₃	—	4	4	no	—
368	D₄×C₁₃	—	4	2	no	—
369	D₄×C₁₃	—	8	2	no	—
370	D₄×C₁₃	—	8	1	no	—
371	D₄×C₁₃	—	8	2	no	—
372	D₄×C₁₃	—	8	1	no	—
373	D₄×C₁₃	—	8	2	no	—
374	D₄×C₁₃	—	8	2	no	—
375	D₄×C₁₃	—	8	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	4	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	4	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	2	no	—
388	C₂×C₄×C₁₃	—	4	2	no	—
389	C₂×C₄×C₁₃	—	4	4	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	2	no	—
392	C₂×C₄×C₁₃	—	8	2	no	—
393	C₂×C₄×C₁₃	—	8	2	no	—
394	C₂×C₄×C₁₃	—	8	2	no	—
395	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	2	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	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
404	C₈×C₁₃	—	2	2	no	—
405	C₈×C₁₃	—	2	4	no	—
406	C₈×C₁₃	—	2	2	no	—
407	#557	—	2	1	no	—
408	#557	C₂²×C₁₃	1	1	yes	characteristic
409	#557	C₂²×C₁₃	1	2	yes	—
410	#556	—	2	1	no	—
411	#556	C₂²×C₁₃	1	2	yes	—
412	#553	—	2	1	no	—
413	#553	—	2	2	no	—
414	#552	—	2	2	no	—
415	#552	C₂²×C₁₃	1	4	yes	—
416	#550	—	2	1	no	—
417	#550	C₂²×C₁₃	1	1	yes	characteristic
418	#550	C₂²×C₁₃	1	2	yes	—
419	#550	C₂²×C₁₃	1	1	yes	characteristic
420	#547	C₂²×C₁₃	1	1	yes	characteristic
421	#547	C₂²×C₁₃	1	2	yes	—
422	#541	—	2	2	no	—
423	#540	—	2	2	no	—
424	#540	—	2	1	no	—
425	#536	—	2	1	no	—
426	#533	C₂²×C₁₃	1	1	yes	characteristic
427	#533	C₂²×C₁₃	1	2	yes	—
428	#533	C₂²×C₁₃	1	2	yes	—
429	#532	C₂²×C₁₃	1	2	yes	—
430	#532	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
432	#529	C₂²×C₁₃	1	1	yes	characteristic
433	#529	C₂²×C₁₃	1	2	yes	—
434	#520	—	2	1	no	—
435	#519	—	2	1	no	—
436	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
437	#501	C₂²×C₁₃	1	1	yes	characteristic
438	#501	C₂²×C₁₃	1	2	yes	—
439	#497	C₂²×C₁₃	1	1	yes	characteristic
440	#497	C₂²×C₁₃	1	2	yes	—
441	#491	C₂²×C₁₃	1	4	yes	—
442	#491	C₂²×C₁₃	1	1	yes	characteristic
443	#490	C₂²×C₁₃	1	4	yes	—
444	#489	C₂²×C₁₃	1	1	yes	characteristic
445	#489	C₂²×C₁₃	1	2	yes	—
446	#489	C₂²×C₁₃	1	2	yes	—
447	#489	C₂²×C₁₃	1	2	yes	—
448	#489	C₂²×C₁₃	1	2	yes	—
449	#487	C₂²×C₁₃	1	2	yes	—
450	#486	C₂²×C₁₃	1	2	yes	—
451	#485	C₂²×C₁₃	1	4	yes	—
452	#484	C₂²×C₁₃	1	2	yes	—
453	#482	C₂²×C₁₃	1	4	yes	—
454	#481	C₂²×C₁₃	1	2	yes	—
455	#479	C₂²×C₁₃	1	4	yes	—
456	#478	C₂²×C₁₃	1	4	yes	—
457	#475	C₂²×C₁₃	1	2	yes	—
458	#474	C₂²×C₁₃	1	2	yes	—
459	#470	C₂²×C₁₃	1	2	yes	—
460	#468	C₂²×C₁₃	1	2	yes	—
461	#467	C₂²×C₁₃	1	4	yes	—
462	#465	C₂²×C₁₃	1	4	yes	—
463	#462	C₂²×C₁₃	1	2	yes	—
464	#462	C₂²×C₁₃	1	4	yes	—
465	#460	C₂²×C₁₃	1	2	yes	—
466	#460	C₂²×C₁₃	1	4	yes	—
467	#452	C₂²×C₁₃	1	4	yes	—
468	#452	C₂²×C₁₃	1	4	yes	—
469	#452	C₂²×C₁₃	1	4	yes	—
470	#446	C₂²×C₁₃	1	2	yes	—
471	#441	C₂²×C₁₃	1	4	yes	—
472	#440	C₂²×C₁₃	1	4	yes	—
473	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
474	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
475	#435	C₂²×C₁₃	1	4	yes	—
476	C₈×D₄	C₂²×C₁₃	1	2	yes	—
477	#432	C₂²×C₁₃	1	1	yes	characteristic
478	#432	C₂²×C₁₃	1	2	yes	—
479	#417	C₂²×C₁₃	1	4	yes	—
480	#416	C₂²×C₁₃	1	4	yes	—
481	#416	C₂²×C₁₃	1	4	yes	—
482	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×#97	C₂²×C₁₃	1	2	yes	—
484	C₂²×C₁₃	—	2	2	no	—
485	C₂²×C₁₃	—	2	1	no	—
486	C₂²×C₁₃	—	2	2	no	—
487	C₂²×C₁₃	—	2	1	no	—
488	C₂²×C₁₃	—	2	1	no	—
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	4	2	no	—
491	C₂²×C₁₃	—	4	1	no	—
492	C₂²×C₁₃	—	4	2	no	—
493	C₂²×C₁₃	—	4	1	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₁₃	—	2	1	no	—
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	2	1	no	—
500	C₄×C₁₃	—	2	2	no	—
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	2	1	no	—
503	C₄×C₁₃	—	2	2	no	—
504	C₄×C₁₃	—	4	1	no	—
505	C₄×C₁₃	—	4	2	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	1	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	1	no	—
510	C₄×C₁₃	—	4	4	no	—
511	C₄×C₁₃	#575	1	2	yes	—
512	C₄×C₁₃	#585	1	2	yes	—
513	C₂×#41	—	2	1	no	—
514	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
515	C₂×#41	C₂³×C₁₃	1	2	yes	—
516	C₂×#41	C₂³×C₁₃	1	2	yes	—
517	C₂×#41	C₂³×C₁₃	1	2	yes	—
518	C₂²×Q₈	—	2	1	no	—
519	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
520	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
521	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
522	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
523	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
524	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
530	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
534	#127	—	2	1	no	—
535	#127	—	2	2	no	—
536	#127	C₂³×C₁₃	1	1	yes	characteristic
537	#127	C₂³×C₁₃	1	2	yes	—
538	#126	—	2	4	no	—
539	#126	—	2	4	no	—
540	#126	—	2	2	no	—
541	#126	—	2	1	no	—
542	#125	—	2	1	no	—
543	#125	—	2	2	no	—
544	#125	—	2	4	no	—
545	#125	—	2	4	no	—
546	#125	—	2	1	no	—
547	#125	—	2	2	no	—
548	#125	C₂³×C₁₃	1	1	yes	characteristic
549	#125	C₂³×C₁₃	1	4	yes	—
550	#124	—	2	2	no	—
551	#124	C₂³×C₁₃	1	1	yes	characteristic
552	#124	C₂³×C₁₃	1	2	yes	—
553	#123	—	2	4	no	—
554	#123	—	2	1	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	#123	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
564	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
565	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
566	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
567	#121	—	2	1	no	—
568	#121	—	2	2	no	—
569	#121	—	2	1	no	—
570	#121	—	2	2	no	—
571	#121	—	2	1	no	—
572	#121	—	2	2	no	—
573	#121	—	2	1	no	—
574	#121	—	2	2	no	—
575	#121	—	2	2	no	—
576	#121	—	2	2	no	—
577	#121	—	2	2	no	—
578	#121	C₂³×C₁₃	1	2	yes	—
579	#121	C₂³×C₁₃	1	1	yes	characteristic
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
588	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
591	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	D₄×C₁₃	1	2	yes	—
602	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₁₃	1	2	yes	—
605	C₄×D₄	C₂³×C₁₃	1	2	yes	—
606	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
607	#117	—	2	1	no	—
608	#117	—	2	2	no	—
609	#117	—	2	4	no	—
610	#117	—	2	2	no	—
611	#117	—	2	1	no	—
612	#117	D₄×C₁₃	1	1	yes	characteristic
613	#117	D₄×C₁₃	1	2	yes	—
614	#117	C₂³×C₁₃	1	4	yes	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	2	no	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
621	#107	C₂³×C₁₃	1	2	yes	—
622	#107	C₂³×C₁₃	1	4	yes	—
623	#106	C₂³×C₁₃	1	2	yes	—
624	#106	C₂³×C₁₃	1	4	yes	—
625	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
626	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
627	#103	C₂³×C₁₃	1	2	yes	—
628	#103	C₂³×C₁₃	1	4	yes	—
629	#103	C₂³×C₁₃	1	4	yes	—
630	#103	C₂³×C₁₃	1	4	yes	—
631	#103	C₂³×C₁₃	1	4	yes	—
632	#103	C₂³×C₁₃	1	2	yes	—
633	#103	C₂³×C₁₃	1	2	yes	—
634	#102	C₂³×C₁₃	1	2	yes	—
635	#102	C₂³×C₁₃	1	4	yes	—
636	#102	C₂³×C₁₃	1	4	yes	—
637	#102	C₂³×C₁₃	1	4	yes	—
638	#102	C₂³×C₁₃	1	4	yes	—
639	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
641	#97	C₂³×C₁₃	1	1	yes	characteristic
642	#97	C₂³×C₁₃	1	2	yes	—
643	#97	C₂³×C₁₃	1	4	yes	—
644	#97	C₂³×C₁₃	1	1	yes	characteristic
645	C₄×C₈	C₂³×C₁₃	1	2	yes	—
646	C₂×C₁₃	—	4	1	no	—
647	C₂×C₁₃	—	4	2	no	—
648	C₂×C₁₃	—	8	2	no	—
649	C₂×C₁₃	—	8	1	no	—
650	C₂×C₁₃	#3500	1	1	yes	characteristic
651	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
652	C₂×C₁₃	#3586	1	1	yes	characteristic
653	#41	—	4	2	no	—
654	#41	—	4	4	no	—
655	#41	—	4	4	no	—
656	#41	—	4	4	no	—
657	#41	—	4	4	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	4	4	no	—
662	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
664	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
665	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
677	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
688	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
691	Q₁₆	—	4	4	no	—
692	Q₁₆	—	4	2	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	—	4	2	no	—
695	M₁₆	—	4	2	no	—
696	C₂×C₈	—	4	4	no	—
697	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
698	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
699	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
724	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
725	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
727	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
744	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
745	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₄²	—	2	4	no	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	1	no	—
750	C₄²	—	2	2	no	—
751	C₄²	C₂×D₄×C₁₃	1	2	yes	—
752	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₄²	C₂×D₄×C₁₃	1	2	yes	—
754	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
755	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
756	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
757	C₄²	C₂⁴×C₁₃	1	2	yes	—
758	C₁₃	#62587	1	1	yes	characteristic, direct product factor, Sylow
759	C₂³	—	2	2	no	—
760	C₂³	—	2	1	no	—
761	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
762	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
763	Q₈	—	2	2	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	4	no	—
767	Q₈	—	2	2	no	—
768	Q₈	—	4	4	no	—
769	Q₈	—	4	2	no	—
770	Q₈	—	4	4	no	—
771	D₄	—	2	2	no	—
772	D₄	—	2	4	no	—
773	D₄	—	2	2	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	4	no	—
776	D₄	—	4	2	no	—
777	D₄	—	8	2	no	—
778	D₄	—	8	1	no	—
779	D₄	—	8	2	no	—
780	D₄	—	8	1	no	—
781	D₄	—	8	2	no	—
782	D₄	—	8	2	no	—
783	D₄	—	8	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	4	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	8	2	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	—	8	2	no	—
803	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
804	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
810	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
811	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
812	C₈	—	2	2	no	—
813	C₈	—	2	4	no	—
814	C₈	—	2	2	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	1	no	—
827	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
828	C₄	—	2	1	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	4	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	2	no	—
842	C₄	C₁₃×#575	1	2	yes	—
843	C₄	C₁₃×#585	1	2	yes	—
844	C₂	—	4	1	no	—
845	C₂	—	4	2	no	—
846	C₂	—	8	2	no	—
847	C₂	—	8	1	no	—
848	C₂	C₁₃×#3500	1	1	yes	characteristic
849	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
850	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3517	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3374	C₂	semidirect
4. C₁₃×#3368	C₂	semidirect
5. C₁₃×#3317	C₂	semidirect
6. C₁₃×#3315	C₂	semidirect
7. C₁₃×#3304	C₂	semidirect
8. C₁₃×#3302	C₂	semidirect
9. C₁₃×#3240	C₂	semidirect
10. C₁₃×#3239	C₂	semidirect
11. C₁₃×#3216	C₂	semidirect
12. C₁₃×#3216	C₂	semidirect
13. C₁₃×#3181	C₂	semidirect
14. C₁₃×#3172	C₂	semidirect
15. C₁₃×#3141	C₂	semidirect
16. C₁₃×#3135	C₂	semidirect
17. C₁₃×#2970	C₂	semidirect
228. #62587	C₁₃	direct (N × H)
335. #3509	C₂×C₁₃	semidirect
336. #3374	C₂×C₁₃	semidirect
337. #3368	C₂×C₁₃	semidirect
338. #3317	C₂×C₁₃	semidirect
339. #3315	C₂×C₁₃	semidirect
340. #3304	C₂×C₁₃	semidirect
341. #3302	C₂×C₁₃	semidirect
342. #3240	C₂×C₁₃	semidirect
343. #3239	C₂×C₁₃	semidirect
344. #3216	C₂×C₁₃	semidirect
345. #3216	C₂×C₁₃	semidirect
346. #3181	C₂×C₁₃	semidirect
347. #3172	C₂×C₁₃	semidirect
348. #3141	C₂×C₁₃	semidirect
349. #3135	C₂×C₁₃	semidirect
350. #2970	C₂×C₁₃	semidirect
758. C₁₃	#62587	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×#3517	2
C₁₃×#3509	2
C₁₃×#3374	2
C₁₃×#3368	2
C₁₃×#3317	2
C₁₃×#3315	2
C₁₃×#3304	2
C₁₃×#3302	2
C₁₃×#3240	2
C₁₃×#3239	2
C₁₃×#3216	2
C₁₃×#3181	2
C₁₃×#3172	2
C₁₃×#3141	2
C₁₃×#3135	2
C₁₃×#2970	2
#62587	13

Subgroups — C13×#62587 #15748926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62587 #15748926