Subgroups — C₁₃×#62590 #15748929

Order 3328.

1790 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3333	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3332	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3323	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3322	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3234	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3219	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3171	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3142	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	—	2	1	no	—
19	C₁₃×#559	C₂²	1	2	yes	—
20	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#553	C₂²	1	2	yes	—
24	C₁₃×#552	—	2	2	no	—
25	C₁₃×#552	—	2	1	no	—
26	C₁₃×#552	C₂²	1	2	yes	—
27	C₁₃×#550	—	2	1	no	—
28	C₁₃×#550	C₂²	1	2	yes	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#546	—	2	2	no	—
32	C₁₃×#546	C₂²	1	4	yes	—
33	C₁₃×#541	—	2	1	no	—
34	C₁₃×#540	—	2	2	no	—
35	C₁₃×#539	—	2	2	no	—
36	C₁₃×#535	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	2	yes	—
40	C₁₃×#532	C₂²	1	2	yes	—
41	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
42	C₁₃×#529	C₂²	1	1	yes	characteristic
43	C₁₃×#529	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
45	C₁₃×#520	—	2	1	no	—
46	C₁₃×#518	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	2	yes	complemented
49	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#497	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#496	C₂²	1	2	yes	—
52	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#491	C₂²	1	2	yes	complemented
54	C₁₃×#490	C₂²	1	2	yes	—
55	C₁₃×#490	C₂²	1	2	yes	—
56	C₁₃×#490	C₂²	1	2	yes	—
57	C₁₃×#489	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#488	C₂²	1	4	yes	complemented
59	C₁₃×#488	C₂²	1	4	yes	complemented
60	C₁₃×#486	C₂²	1	2	yes	—
61	C₁₃×#486	C₂²	1	2	yes	—
62	C₁₃×#485	C₂²	1	4	yes	—
63	C₁₃×#481	C₂²	1	4	yes	complemented
64	C₁₃×#480	C₂²	1	4	yes	complemented
65	C₁₃×#478	C₂²	1	4	yes	complemented
66	C₁₃×#478	C₂²	1	4	yes	complemented
67	C₁₃×#477	C₂²	1	2	yes	complemented
68	C₁₃×#475	C₂²	1	2	yes	complemented
69	C₁₃×#470	C₂²	1	2	yes	—
70	C₁₃×#469	C₂²	1	4	yes	complemented
71	C₁₃×#468	C₂²	1	2	yes	—
72	C₁₃×#468	C₂²	1	4	yes	complemented
73	C₁₃×#464	C₂²	1	4	yes	complemented
74	C₁₃×#463	C₂²	1	4	yes	complemented
75	C₁₃×#460	C₂²	1	2	yes	—
76	C₁₃×#459	C₂²	1	2	yes	—
77	C₁₃×#452	C₂²	1	4	yes	complemented
78	C₁₃×#450	C₂²	1	2	yes	—
79	C₁₃×#449	C₂²	1	4	yes	complemented
80	C₁₃×#447	C₂²	1	2	yes	—
81	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
82	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
83	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
85	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
86	C₁₃×#436	C₂²	1	4	yes	—
87	C₁₃×#436	C₂²	1	2	yes	complemented
88	C₁₃×#432	C₂²	1	1	yes	characteristic
89	C₁₃×#432	C₂²	1	2	yes	complemented
90	C₁₃×#418	C₂²	1	4	yes	—
91	C₁₃×#417	C₂²	1	4	yes	complemented
92	C₁₃×#417	C₂²	1	4	yes	complemented
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
98	C₂×C₁₃×#41	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
102	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×D₈	C₂³	1	4	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×#127	—	2	2	no	—
114	C₁₃×#127	—	2	1	no	—
115	C₁₃×#127	—	2	1	no	—
116	C₁₃×#127	C₂³	1	2	yes	—
117	C₁₃×#127	C₂³	1	2	yes	—
118	C₁₃×#126	—	2	2	no	—
119	C₁₃×#126	—	2	2	no	—
120	C₁₃×#126	—	2	1	no	—
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#125	—	2	2	no	—
123	C₁₃×#125	—	2	2	no	—
124	C₁₃×#125	—	2	1	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	—	2	1	no	—
128	C₁₃×#125	C₂³	1	2	yes	—
129	C₁₃×#125	C₂³	1	2	yes	—
130	C₁₃×#125	C₂³	1	1	yes	characteristic
131	C₁₃×#125	C₂³	1	2	yes	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	C₂³	1	4	yes	—
135	C₁₃×#124	C₂³	1	1	yes	characteristic
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	1	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	4	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#121	C₂³	1	1	yes	characteristic
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#121	C₂³	1	4	yes	—
162	C₁₃×#120	—	2	4	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	—	2	1	no	—
166	C₄×Q₈×C₁₃	—	2	1	no	—
167	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	2	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
182	C₄×D₄×C₁₃	D₄	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	4	yes	—
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	C₁₃×#117	—	2	1	no	—
189	C₁₃×#117	—	2	2	no	—
190	C₁₃×#117	—	2	1	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	D₄	1	1	yes	characteristic
193	C₁₃×#117	D₄	1	2	yes	—
194	C₁₃×#117	C₂³	1	2	yes	—
195	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	2	yes	—
205	C₁₃×#106	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	2	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	2	yes	—
211	C₁₃×#103	C₂³	1	4	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	2	yes	—
214	C₁₃×#102	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	4	yes	—
216	C₁₃×#102	C₂³	1	4	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	2	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
222	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
223	C₁₃×#97	C₂³	1	1	yes	characteristic
224	C₁₃×#97	C₂³	1	1	yes	characteristic
225	C₁₃×#97	C₂³	1	2	yes	—
226	C₄×C₈×C₁₃	C₂³	1	2	yes	—
227	C₄×C₈×C₁₃	C₂³	1	4	yes	—
228	#62590	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	2	no	—
230	C₁₃×#41	—	4	2	no	—
231	C₁₃×#41	—	4	4	no	—
232	C₁₃×#41	—	4	4	no	—
233	C₁₃×#41	—	4	4	no	—
234	C₁₃×#41	—	8	4	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
240	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	4	no	—
244	C₂×D₄×C₁₃	—	2	4	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	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	4	4	no	—
251	C₂×D₄×C₁₃	—	4	4	no	—
252	C₂×D₄×C₁₃	—	8	2	no	—
253	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	4	no	—
261	C₂²×C₄×C₁₃	—	2	4	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₁₃×Q₁₆	—	4	2	no	—
270	C₁₃×SD₁₆	—	4	4	no	—
271	C₁₃×SD₁₆	—	4	2	no	—
272	C₁₃×D₈	—	4	4	no	—
273	C₁₃×M₁₆	—	4	4	no	—
274	C₁₃×M₁₆	—	4	2	no	—
275	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
277	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	1	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	1	no	—
322	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
323	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	—	2	1	no	—
329	C₄²×C₁₃	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂×D₄	1	2	yes	—
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	#3515	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3365	C₂×C₁₃	1	2	yes	complemented
339	#3361	C₂×C₁₃	1	2	yes	complemented
340	#3333	C₂×C₁₃	1	2	yes	complemented
341	#3332	C₂×C₁₃	1	2	yes	complemented
342	#3323	C₂×C₁₃	1	4	yes	complemented
343	#3322	C₂×C₁₃	1	4	yes	complemented
344	#3237	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3234	C₂×C₁₃	1	2	yes	complemented
346	#3219	C₂×C₁₃	1	2	yes	complemented
347	#3217	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3172	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3171	C₂×C₁₃	1	2	yes	complemented
350	#3142	C₂×C₁₃	1	2	yes	complemented
351	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	—	2	4	no	—
355	C₂³×C₁₃	—	4	4	no	—
356	C₂³×C₁₃	—	8	2	no	—
357	C₂³×C₁₃	—	8	2	no	—
358	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	4	2	no	—
365	Q₈×C₁₃	—	4	2	no	—
366	Q₈×C₁₃	—	8	1	no	—
367	D₄×C₁₃	—	2	2	no	—
368	D₄×C₁₃	—	2	2	no	—
369	D₄×C₁₃	—	2	4	no	—
370	D₄×C₁₃	—	2	4	no	—
371	D₄×C₁₃	—	4	2	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	4	no	—
374	D₄×C₁₃	—	4	4	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	8	2	no	—
377	D₄×C₁₃	—	8	2	no	—
378	D₄×C₁₃	—	8	1	no	—
379	D₄×C₁₃	—	8	4	no	—
380	D₄×C₁₃	—	8	4	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	8	2	no	—
397	C₂×C₄×C₁₃	—	8	4	no	—
398	C₂×C₄×C₁₃	—	8	4	no	—
399	C₂×C₄×C₁₃	—	8	2	no	—
400	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
409	C₈×C₁₃	—	2	2	no	—
410	C₈×C₁₃	—	2	4	no	—
411	C₈×C₁₃	—	2	2	no	—
412	#559	—	2	1	no	—
413	#559	C₂²×C₁₃	1	2	yes	—
414	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	#553	C₂²×C₁₃	1	2	yes	—
418	#552	—	2	2	no	—
419	#552	—	2	1	no	—
420	#552	C₂²×C₁₃	1	2	yes	—
421	#550	—	2	1	no	—
422	#550	C₂²×C₁₃	1	2	yes	—
423	#547	—	2	1	no	—
424	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	#546	—	2	2	no	—
426	#546	C₂²×C₁₃	1	4	yes	—
427	#541	—	2	1	no	—
428	#540	—	2	2	no	—
429	#539	—	2	2	no	—
430	#535	—	2	1	no	—
431	#533	C₂²×C₁₃	1	1	yes	characteristic
432	#533	C₂²×C₁₃	1	1	yes	characteristic
433	#532	C₂²×C₁₃	1	2	yes	—
434	#532	C₂²×C₁₃	1	2	yes	—
435	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
436	#529	C₂²×C₁₃	1	1	yes	characteristic
437	#529	C₂²×C₁₃	1	2	yes	complemented
438	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
439	#520	—	2	1	no	—
440	#518	—	2	1	no	—
441	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
442	#501	C₂²×C₁₃	1	2	yes	complemented
443	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	#497	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	#496	C₂²×C₁₃	1	2	yes	—
446	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#491	C₂²×C₁₃	1	2	yes	complemented
448	#490	C₂²×C₁₃	1	2	yes	—
449	#490	C₂²×C₁₃	1	2	yes	—
450	#490	C₂²×C₁₃	1	2	yes	—
451	#489	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#488	C₂²×C₁₃	1	4	yes	complemented
453	#488	C₂²×C₁₃	1	4	yes	complemented
454	#486	C₂²×C₁₃	1	2	yes	—
455	#486	C₂²×C₁₃	1	2	yes	—
456	#485	C₂²×C₁₃	1	4	yes	—
457	#481	C₂²×C₁₃	1	4	yes	complemented
458	#480	C₂²×C₁₃	1	4	yes	complemented
459	#478	C₂²×C₁₃	1	4	yes	complemented
460	#478	C₂²×C₁₃	1	4	yes	complemented
461	#477	C₂²×C₁₃	1	2	yes	complemented
462	#475	C₂²×C₁₃	1	2	yes	complemented
463	#470	C₂²×C₁₃	1	2	yes	—
464	#469	C₂²×C₁₃	1	4	yes	complemented
465	#468	C₂²×C₁₃	1	2	yes	—
466	#468	C₂²×C₁₃	1	4	yes	complemented
467	#464	C₂²×C₁₃	1	4	yes	complemented
468	#463	C₂²×C₁₃	1	4	yes	complemented
469	#460	C₂²×C₁₃	1	2	yes	—
470	#459	C₂²×C₁₃	1	2	yes	—
471	#452	C₂²×C₁₃	1	4	yes	complemented
472	#450	C₂²×C₁₃	1	2	yes	—
473	#449	C₂²×C₁₃	1	4	yes	complemented
474	#447	C₂²×C₁₃	1	2	yes	—
475	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
476	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
477	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
478	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
479	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
480	#436	C₂²×C₁₃	1	4	yes	—
481	#436	C₂²×C₁₃	1	2	yes	complemented
482	#432	C₂²×C₁₃	1	1	yes	characteristic
483	#432	C₂²×C₁₃	1	2	yes	complemented
484	#418	C₂²×C₁₃	1	4	yes	—
485	#417	C₂²×C₁₃	1	4	yes	complemented
486	#417	C₂²×C₁₃	1	4	yes	complemented
487	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
488	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	2	no	—
492	C₂²×C₁₃	—	2	1	no	—
493	C₂²×C₁₃	—	2	1	no	—
494	C₂²×C₁₃	—	2	2	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	—	4	4	no	—
497	C₂²×C₁₃	—	4	4	no	—
498	C₂²×C₁₃	—	4	1	no	—
499	C₂²×C₁₃	—	4	1	no	—
500	C₂²×C₁₃	—	4	4	no	—
501	C₂²×C₁₃	—	16	4	no	—
502	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
503	C₄×C₁₃	—	2	1	no	—
504	C₄×C₁₃	—	2	2	no	—
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	2	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	1	no	—
509	C₄×C₁₃	—	2	2	no	—
510	C₄×C₁₃	—	4	1	no	—
511	C₄×C₁₃	—	4	2	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₄×C₁₃	—	4	2	no	—
514	C₄×C₁₃	—	4	1	no	—
515	C₄×C₁₃	—	4	1	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	#575	1	2	yes	—
518	C₄×C₁₃	#585	1	2	yes	—
519	C₂×#41	—	2	1	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
522	C₂×#41	C₂³×C₁₃	1	4	yes	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
526	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
527	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
528	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
529	C₂×D₈	C₂³×C₁₃	1	4	yes	—
530	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
531	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
536	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
537	#127	—	2	2	no	—
538	#127	—	2	1	no	—
539	#127	—	2	1	no	—
540	#127	C₂³×C₁₃	1	2	yes	—
541	#127	C₂³×C₁₃	1	2	yes	—
542	#126	—	2	2	no	—
543	#126	—	2	2	no	—
544	#126	—	2	1	no	—
545	#126	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	2	1	no	—
549	#125	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	1	no	—
552	#125	C₂³×C₁₃	1	1	yes	characteristic
553	#125	C₂³×C₁₃	1	2	yes	—
554	#125	C₂³×C₁₃	1	2	yes	—
555	#125	C₂³×C₁₃	1	2	yes	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	C₂³×C₁₃	1	1	yes	characteristic
559	#124	C₂³×C₁₃	1	4	yes	—
560	#123	—	2	2	no	—
561	#123	—	2	1	no	—
562	#123	—	2	2	no	—
563	#123	—	2	4	no	—
564	#123	—	2	4	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
576	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
577	#121	—	2	2	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	4	no	—
582	#121	—	2	4	no	—
583	#121	C₂³×C₁₃	1	1	yes	characteristic
584	#121	C₂³×C₁₃	1	2	yes	—
585	#121	C₂³×C₁₃	1	4	yes	—
586	#120	—	2	4	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
594	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
606	C₄×D₄	D₄×C₁₃	1	2	yes	—
607	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₁₃	1	2	yes	—
609	C₄×D₄	C₂³×C₁₃	1	4	yes	—
610	C₄×D₄	C₂³×C₁₃	1	2	yes	—
611	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
612	#117	—	2	1	no	—
613	#117	—	2	2	no	—
614	#117	—	2	1	no	—
615	#117	—	2	2	no	—
616	#117	D₄×C₁₃	1	1	yes	characteristic
617	#117	D₄×C₁₃	1	2	yes	—
618	#117	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄⋊C₄	—	2	2	no	—
620	C₂×C₄⋊C₄	—	2	2	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₂²⋊C₄	—	2	4	no	—
625	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
626	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
627	#107	C₂³×C₁₃	1	4	yes	—
628	#107	C₂³×C₁₃	1	2	yes	—
629	#106	C₂³×C₁₃	1	4	yes	—
630	#106	C₂³×C₁₃	1	2	yes	—
631	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
632	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
633	#103	C₂³×C₁₃	1	2	yes	—
634	#103	C₂³×C₁₃	1	2	yes	—
635	#103	C₂³×C₁₃	1	4	yes	—
636	#103	C₂³×C₁₃	1	4	yes	—
637	#103	C₂³×C₁₃	1	2	yes	—
638	#102	C₂³×C₁₃	1	4	yes	—
639	#102	C₂³×C₁₃	1	4	yes	—
640	#102	C₂³×C₁₃	1	4	yes	—
641	#102	C₂³×C₁₃	1	4	yes	—
642	#102	C₂³×C₁₃	1	4	yes	—
643	#102	C₂³×C₁₃	1	4	yes	—
644	#102	C₂³×C₁₃	1	2	yes	—
645	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
646	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
647	#97	C₂³×C₁₃	1	1	yes	characteristic
648	#97	C₂³×C₁₃	1	1	yes	characteristic
649	#97	C₂³×C₁₃	1	2	yes	—
650	C₄×C₈	C₂³×C₁₃	1	2	yes	—
651	C₄×C₈	C₂³×C₁₃	1	4	yes	—
652	C₂×C₁₃	—	4	2	no	—
653	C₂×C₁₃	—	4	1	no	—
654	C₂×C₁₃	—	8	1	no	—
655	C₂×C₁₃	—	8	4	no	—
656	C₂×C₁₃	#3500	1	1	yes	characteristic
657	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
658	C₂×C₁₃	#3585	1	1	yes	characteristic
659	C₂⁴	—	2	2	no	—
660	#41	—	4	2	no	—
661	#41	—	4	4	no	—
662	#41	—	4	4	no	—
663	#41	—	4	4	no	—
664	#41	—	8	4	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
669	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
670	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	4	4	no	—
681	C₂×D₄	—	4	4	no	—
682	C₂×D₄	—	8	2	no	—
683	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
684	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
685	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
686	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
695	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
699	Q₁₆	—	4	2	no	—
700	SD₁₆	—	4	4	no	—
701	SD₁₆	—	4	2	no	—
702	D₈	—	4	4	no	—
703	M₁₆	—	4	4	no	—
704	M₁₆	—	4	2	no	—
705	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
706	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
707	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
731	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
732	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	1	no	—
759	C₄²	C₂×D₄×C₁₃	1	2	yes	—
760	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₁₃	1	2	yes	—
763	C₄²	C₂⁴×C₁₃	1	2	yes	—
764	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
765	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
766	C₁₃	#62590	1	1	yes	characteristic, direct product factor, Sylow
767	C₂³	—	2	1	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	8	2	no	—
771	C₂³	—	8	2	no	—
772	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	4	2	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	8	1	no	—
781	D₄	—	2	2	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	4	no	—
784	D₄	—	2	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	4	no	—
790	D₄	—	8	2	no	—
791	D₄	—	8	2	no	—
792	D₄	—	8	1	no	—
793	D₄	—	8	4	no	—
794	D₄	—	8	4	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	8	2	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
822	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₈	—	2	2	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	16	4	no	—
839	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
840	C₄	—	2	1	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	C₁₃×#575	1	2	yes	—
855	C₄	C₁₃×#585	1	2	yes	—
856	C₂	—	4	1	no	—
857	C₂	—	4	2	no	—
858	C₂	—	8	4	no	—
859	C₂	—	8	1	no	—
860	C₂	C₁₃×#3500	1	1	yes	characteristic
861	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
862	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3515	C₂	semidirect
2. C₁₃×#3508	C₂	semidirect
3. C₁₃×#3365	C₂	semidirect
4. C₁₃×#3361	C₂	semidirect
5. C₁₃×#3333	C₂	semidirect
6. C₁₃×#3332	C₂	semidirect
7. C₁₃×#3323	C₂	semidirect
8. C₁₃×#3322	C₂	semidirect
9. C₁₃×#3237	C₂	semidirect
10. C₁₃×#3234	C₂	semidirect
11. C₁₃×#3219	C₂	semidirect
12. C₁₃×#3217	C₂	semidirect
13. C₁₃×#3172	C₂	semidirect
14. C₁₃×#3171	C₂	semidirect
15. C₁₃×#3142	C₂	semidirect
16. C₁₃×#3138	C₂	semidirect
17. C₁₃×#2971	C₂	semidirect
20. C₁₃×#557	C₂²	semidirect
21. C₁₃×#554	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
30. C₁₃×#547	C₂²	semidirect
43. C₁₃×#529	C₂²	semidirect
44. C₂×C₁₃×#125	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
50. C₁₃×#497	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
53. C₁₃×#491	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#488	C₂²	semidirect
59. C₁₃×#488	C₂²	semidirect
63. C₁₃×#481	C₂²	semidirect
64. C₁₃×#480	C₂²	semidirect
65. C₁₃×#478	C₂²	semidirect
66. C₁₃×#478	C₂²	semidirect
67. C₁₃×#477	C₂²	semidirect
68. C₁₃×#475	C₂²	semidirect
70. C₁₃×#469	C₂²	semidirect
72. C₁₃×#468	C₂²	semidirect
73. C₁₃×#464	C₂²	semidirect
74. C₁₃×#463	C₂²	semidirect
77. C₁₃×#452	C₂²	semidirect
79. C₁₃×#449	C₂²	semidirect
81. C₈×Q₈×C₁₃	C₂²	semidirect
82. C₄×C₁₃×Q₁₆	C₂²	semidirect
83. C₄×C₁₃×SD₁₆	C₂²	semidirect
84. C₄×C₁₃×SD₁₆	C₂²	semidirect
85. C₄×C₁₃×D₈	C₂²	semidirect
87. C₁₃×#436	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
91. C₁₃×#417	C₂²	semidirect
92. C₁₃×#417	C₂²	semidirect
94. C₄×C₁₃×M₁₆	C₂²	semidirect
228. #62590	C₁₃	direct (N × H)
336. #3515	C₂×C₁₃	semidirect
337. #3508	C₂×C₁₃	semidirect
338. #3365	C₂×C₁₃	semidirect
339. #3361	C₂×C₁₃	semidirect
340. #3333	C₂×C₁₃	semidirect
341. #3332	C₂×C₁₃	semidirect
342. #3323	C₂×C₁₃	semidirect
343. #3322	C₂×C₁₃	semidirect
344. #3237	C₂×C₁₃	semidirect
345. #3234	C₂×C₁₃	semidirect
346. #3219	C₂×C₁₃	semidirect
347. #3217	C₂×C₁₃	semidirect
348. #3172	C₂×C₁₃	semidirect
349. #3171	C₂×C₁₃	semidirect
350. #3142	C₂×C₁₃	semidirect
351. #3138	C₂×C₁₃	semidirect
352. #2971	C₂×C₁₃	semidirect
414. #557	C₂²×C₁₃	semidirect
415. #554	C₂²×C₁₃	semidirect
416. #554	C₂²×C₁₃	semidirect
424. #547	C₂²×C₁₃	semidirect
437. #529	C₂²×C₁₃	semidirect
438. C₂×#125	C₂²×C₁₃	semidirect
442. #501	C₂²×C₁₃	semidirect
443. #501	C₂²×C₁₃	semidirect
444. #497	C₂²×C₁₃	semidirect
446. #491	C₂²×C₁₃	semidirect
447. #491	C₂²×C₁₃	semidirect
451. #489	C₂²×C₁₃	semidirect
452. #488	C₂²×C₁₃	semidirect
453. #488	C₂²×C₁₃	semidirect
457. #481	C₂²×C₁₃	semidirect
458. #480	C₂²×C₁₃	semidirect
459. #478	C₂²×C₁₃	semidirect
460. #478	C₂²×C₁₃	semidirect
461. #477	C₂²×C₁₃	semidirect
462. #475	C₂²×C₁₃	semidirect
464. #469	C₂²×C₁₃	semidirect
466. #468	C₂²×C₁₃	semidirect
467. #464	C₂²×C₁₃	semidirect
468. #463	C₂²×C₁₃	semidirect
471. #452	C₂²×C₁₃	semidirect
473. #449	C₂²×C₁₃	semidirect
475. C₈×Q₈	C₂²×C₁₃	semidirect
476. C₄×Q₁₆	C₂²×C₁₃	semidirect
477. C₄×SD₁₆	C₂²×C₁₃	semidirect
478. C₄×SD₁₆	C₂²×C₁₃	semidirect
479. C₄×D₈	C₂²×C₁₃	semidirect
481. #436	C₂²×C₁₃	semidirect
483. #432	C₂²×C₁₃	semidirect
485. #417	C₂²×C₁₃	semidirect
486. #417	C₂²×C₁₃	semidirect
488. C₄×M₁₆	C₂²×C₁₃	semidirect
766. C₁₃	#62590	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×#3515	2
C₁₃×#3508	2
C₁₃×#3365	2
C₁₃×#3361	2
C₁₃×#3333	2
C₁₃×#3332	2
C₁₃×#3323	2
C₁₃×#3322	2
C₁₃×#3237	2
C₁₃×#3234	2
C₁₃×#3219	2
C₁₃×#3217	2
C₁₃×#3172	2
C₁₃×#3171	2
C₁₃×#3142	2
C₁₃×#3138	2
C₁₃×#2971	2
#62590	13

Subgroups — C13×#62590 #15748929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62590 #15748929