Subgroups — C₁₃×#61895 #15748234

Order 3328.

1794 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3371	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3117	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3105	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#559	—	2	2	no	—
18	C₁₃×#559	C₂²	1	4	yes	—
19	C₁₃×#559	C₂²	1	4	yes	—
20	C₁₃×#559	C₂²	1	2	yes	complemented
21	C₁₃×#557	C₂²	1	2	yes	complemented
22	C₁₃×#556	—	2	2	no	—
23	C₁₃×#556	C₂²	1	2	yes	complemented
24	C₁₃×#554	C₂²	1	2	yes	complemented
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#539	—	2	1	no	—
27	C₁₃×#539	—	2	1	no	—
28	C₁₃×#536	—	2	1	no	—
29	C₁₃×#533	C₂²	1	1	yes	characteristic
30	C₁₃×#532	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₁₃×#529	C₂²	1	2	yes	—
33	C₁₃×#529	C₂²	1	2	yes	—
34	C₂×C₁₃×#124	—	2	1	no	—
35	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#123	—	2	1	no	—
38	C₂×C₁₃×#123	—	2	1	no	—
39	C₁₃×#520	—	2	1	no	—
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	—	2	1	no	—
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#497	C₂²	1	2	yes	complemented
46	C₁₃×#496	C₂²	1	4	yes	—
47	C₁₃×#496	C₂²	1	2	yes	complemented
48	C₁₃×#495	C₂²	1	4	yes	complemented
49	C₁₃×#490	C₂²	1	4	yes	—
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#489	C₂²	1	2	yes	complemented
52	C₁₃×#488	C₂²	1	4	yes	complemented
53	C₁₃×#484	C₂²	1	2	yes	—
54	C₁₃×#481	C₂²	1	2	yes	—
55	C₁₃×#479	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	complemented
57	C₁₃×#476	C₂²	1	2	yes	complemented
58	C₁₃×#474	C₂²	1	2	yes	complemented
59	C₁₃×#464	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	complemented
63	C₁₃×#463	C₂²	1	4	yes	complemented
64	C₁₃×#463	C₂²	1	4	yes	complemented
65	C₁₃×#461	C₂²	1	2	yes	complemented
66	C₁₃×#460	C₂²	1	4	yes	—
67	C₁₃×#459	C₂²	1	4	yes	—
68	C₁₃×#459	C₂²	1	2	yes	complemented
69	C₁₃×#451	C₂²	1	2	yes	—
70	C₁₃×#450	C₂²	1	2	yes	—
71	C₁₃×#450	C₂²	1	2	yes	—
72	C₁₃×#448	C₂²	1	2	yes	—
73	C₁₃×#447	C₂²	1	2	yes	—
74	C₁₃×#447	C₂²	1	2	yes	—
75	C₁₃×#446	C₂²	1	4	yes	complemented
76	C₁₃×#446	C₂²	1	4	yes	complemented
77	C₁₃×#442	C₂²	1	4	yes	complemented
78	C₁₃×#441	C₂²	1	4	yes	complemented
79	C₁₃×#440	C₂²	1	4	yes	complemented
80	C₁₃×#440	C₂²	1	4	yes	complemented
81	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
82	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
83	C₁₃×#432	C₂²	1	1	yes	characteristic
84	C₁₃×#432	C₂²	1	1	yes	characteristic
85	C₁₃×#432	C₂²	1	2	yes	—
86	C₁₃×#431	C₂²	1	2	yes	—
87	C₂×C₁₃×#41	—	2	1	no	—
88	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	—	2	1	no	—
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	—	2	1	no	—
95	C₂³×C₄×C₁₃	—	2	1	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×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×D₈	C₂³	1	4	yes	—
101	C₂×C₁₃×D₈	C₂³	1	4	yes	—
102	C₁₃×C₄⋊Q₈	—	2	2	no	—
103	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₁₃×#127	—	2	2	no	—
107	C₁₃×#127	C₂³	1	4	yes	—
108	C₁₃×#127	C₂³	1	1	yes	characteristic
109	C₁₃×#126	—	2	2	no	—
110	C₁₃×#126	—	2	2	no	—
111	C₁₃×#126	—	2	2	no	—
112	C₁₃×#126	—	2	2	no	—
113	C₁₃×#125	—	2	2	no	—
114	C₁₃×#125	—	2	2	no	—
115	C₁₃×#125	—	2	1	no	—
116	C₁₃×#125	C₂³	1	2	yes	—
117	C₁₃×#125	C₂³	1	2	yes	—
118	C₁₃×#124	—	2	4	no	—
119	C₁₃×#124	—	2	4	no	—
120	C₁₃×#124	—	2	2	no	—
121	C₁₃×#124	—	2	2	no	—
122	C₁₃×#124	—	2	1	no	—
123	C₁₃×#124	—	2	1	no	—
124	C₁₃×#124	—	2	1	no	—
125	C₁₃×#124	C₂³	1	2	yes	—
126	C₁₃×#124	C₂³	1	2	yes	—
127	C₁₃×#124	C₂³	1	4	yes	—
128	C₁₃×#124	C₂³	1	2	yes	—
129	C₁₃×#124	C₂³	1	2	yes	—
130	C₁₃×#123	—	2	2	no	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×#123	—	2	4	no	—
133	C₁₃×#123	—	2	4	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	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₁₃×#121	—	2	1	no	—
145	C₁₃×#121	C₂³	1	2	yes	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	—	2	1	no	—
149	C₄×Q₈×C₁₃	D₄	1	2	yes	—
150	C₄×Q₈×C₁₃	D₄	1	2	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×D₄×C₁₃	—	2	2	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	4	no	—
160	C₄×D₄×C₁₃	—	2	4	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	C₂³	1	4	yes	—
168	C₄×D₄×C₁₃	C₂³	1	2	yes	—
169	C₄×D₄×C₁₃	C₂³	1	2	yes	—
170	C₄×D₄×C₁₃	C₂³	1	2	yes	—
171	C₄×D₄×C₁₃	C₂³	1	2	yes	—
172	C₁₃×#117	—	2	1	no	—
173	C₁₃×#117	—	2	2	no	—
174	C₁₃×#117	—	2	2	no	—
175	C₁₃×#117	—	2	2	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
180	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
188	C₂×C₄²×C₁₃	—	2	1	no	—
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₁₃×#107	C₂³	1	4	yes	—
193	C₁₃×#106	C₂³	1	4	yes	—
194	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
196	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
197	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
198	C₁₃×#103	C₂³	1	4	yes	—
199	C₁₃×#103	C₂³	1	4	yes	—
200	C₁₃×#103	C₂³	1	4	yes	—
201	C₁₃×#102	C₂³	1	4	yes	—
202	C₁₃×#102	C₂³	1	4	yes	—
203	C₁₃×#102	C₂³	1	4	yes	—
204	C₁₃×#102	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₃×#97	C₂³	1	2	yes	—
209	C₁₃×#97	C₂³	1	4	yes	—
210	C₁₃×#97	C₂³	1	2	yes	—
211	C₄×C₈×C₁₃	C₂³	1	4	yes	—
212	#61895	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂⁴×C₁₃	—	2	1	no	—
214	C₂⁴×C₁₃	—	2	1	no	—
215	C₁₃×#41	—	4	4	no	—
216	C₂×Q₈×C₁₃	—	2	1	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	4	2	no	—
220	C₂×Q₈×C₁₃	—	4	2	no	—
221	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
224	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
225	C₂×D₄×C₁₃	—	2	2	no	—
226	C₂×D₄×C₁₃	—	2	1	no	—
227	C₂×D₄×C₁₃	—	2	1	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	4	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	4	no	—
232	C₂×D₄×C₁₃	—	4	2	no	—
233	C₂×D₄×C₁₃	—	4	2	no	—
234	C₂×D₄×C₁₃	—	4	4	no	—
235	C₂×D₄×C₁₃	—	8	2	no	—
236	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	2	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	4	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	8	2	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	1	yes	characteristic
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	1	yes	characteristic
256	C₁₃×Q₁₆	—	4	4	no	—
257	C₁₃×SD₁₆	—	4	4	no	—
258	C₁₃×SD₁₆	—	4	4	no	—
259	C₁₃×SD₁₆	—	4	4	no	—
260	C₁₃×D₈	—	4	4	no	—
261	C₁₃×D₈	—	4	4	no	—
262	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
263	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₂²⋊C₄	—	2	2	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	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	2	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	C₄²×C₁₃	—	2	4	no	—
306	C₄²×C₁₃	—	2	2	no	—
307	C₄²×C₁₃	—	2	2	no	—
308	C₄²×C₁₃	—	2	2	no	—
309	C₄²×C₁₃	C₂×D₄	1	2	yes	—
310	C₄²×C₁₃	C₂×D₄	1	2	yes	—
311	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₁₃	C₂⁴	1	2	yes	—
314	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₄²×C₁₃	C₂⁴	1	2	yes	—
317	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
318	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#3403	C₂×C₁₃	1	4	yes	complemented
320	#3401	C₂×C₁₃	1	4	yes	complemented
321	#3371	C₂×C₁₃	1	4	yes	complemented
322	#3370	C₂×C₁₃	1	4	yes	complemented
323	#3217	C₂×C₁₃	1	2	yes	complemented
324	#3215	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#3213	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#3211	C₂×C₁₃	1	2	yes	complemented
327	#3117	C₂×C₁₃	1	2	yes	complemented
328	#3110	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#3109	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#3105	C₂×C₁₃	1	2	yes	complemented
331	#2983	C₂×C₁₃	1	1	yes	characteristic, complemented
332	C₂³×C₁₃	—	2	2	no	—
333	C₂³×C₁₃	—	2	2	no	—
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	4	2	no	—
336	C₂³×C₁₃	—	4	2	no	—
337	C₂³×C₁₃	—	4	2	no	—
338	C₂³×C₁₃	—	4	2	no	—
339	C₂³×C₁₃	—	4	2	no	—
340	C₂³×C₁₃	—	4	2	no	—
341	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₁₃	—	2	4	no	—
343	Q₈×C₁₃	—	2	4	no	—
344	Q₈×C₁₃	—	4	2	no	—
345	Q₈×C₁₃	—	4	2	no	—
346	Q₈×C₁₃	—	4	2	no	—
347	Q₈×C₁₃	—	4	2	no	—
348	Q₈×C₁₃	—	8	1	no	—
349	D₄×C₁₃	—	2	4	no	—
350	D₄×C₁₃	—	2	2	no	—
351	D₄×C₁₃	—	2	4	no	—
352	D₄×C₁₃	—	2	2	no	—
353	D₄×C₁₃	—	4	2	no	—
354	D₄×C₁₃	—	4	2	no	—
355	D₄×C₁₃	—	4	8	no	—
356	D₄×C₁₃	—	4	2	no	—
357	D₄×C₁₃	—	4	4	no	—
358	D₄×C₁₃	—	8	1	no	—
359	D₄×C₁₃	—	8	4	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	4	no	—
373	C₂×C₄×C₁₃	—	4	2	no	—
374	C₂×C₄×C₁₃	—	4	2	no	—
375	C₂×C₄×C₁₃	—	8	2	no	—
376	C₂×C₄×C₁₃	—	8	2	no	—
377	C₂×C₄×C₁₃	—	8	4	no	—
378	C₂×C₄×C₁₃	—	8	2	no	—
379	C₂×C₄×C₁₃	—	8	2	no	—
380	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
390	C₈×C₁₃	—	2	4	no	—
391	C₈×C₁₃	—	2	4	no	—
392	#559	—	2	2	no	—
393	#559	—	2	2	no	—
394	#559	C₂²×C₁₃	1	4	yes	—
395	#559	C₂²×C₁₃	1	4	yes	—
396	#559	C₂²×C₁₃	1	2	yes	complemented
397	#557	C₂²×C₁₃	1	2	yes	complemented
398	#556	—	2	2	no	—
399	#556	C₂²×C₁₃	1	2	yes	complemented
400	#554	C₂²×C₁₃	1	2	yes	complemented
401	#552	—	2	2	no	—
402	#539	—	2	1	no	—
403	#539	—	2	1	no	—
404	#536	—	2	1	no	—
405	#533	C₂²×C₁₃	1	1	yes	characteristic
406	#532	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
408	#529	C₂²×C₁₃	1	2	yes	—
409	#529	C₂²×C₁₃	1	2	yes	—
410	C₂×#124	—	2	1	no	—
411	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#123	—	2	1	no	—
414	C₂×#123	—	2	1	no	—
415	#520	—	2	1	no	—
416	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×C₄×D₄	—	2	1	no	—
419	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
421	#497	C₂²×C₁₃	1	2	yes	complemented
422	#496	C₂²×C₁₃	1	4	yes	—
423	#496	C₂²×C₁₃	1	2	yes	complemented
424	#495	C₂²×C₁₃	1	4	yes	complemented
425	#490	C₂²×C₁₃	1	4	yes	—
426	#489	C₂²×C₁₃	1	2	yes	complemented
427	#489	C₂²×C₁₃	1	2	yes	complemented
428	#488	C₂²×C₁₃	1	4	yes	complemented
429	#484	C₂²×C₁₃	1	2	yes	—
430	#481	C₂²×C₁₃	1	2	yes	—
431	#479	C₂²×C₁₃	1	4	yes	complemented
432	#478	C₂²×C₁₃	1	4	yes	complemented
433	#476	C₂²×C₁₃	1	2	yes	complemented
434	#474	C₂²×C₁₃	1	2	yes	complemented
435	#464	C₂²×C₁₃	1	4	yes	complemented
436	#464	C₂²×C₁₃	1	4	yes	complemented
437	#464	C₂²×C₁₃	1	4	yes	complemented
438	#463	C₂²×C₁₃	1	4	yes	complemented
439	#463	C₂²×C₁₃	1	4	yes	complemented
440	#463	C₂²×C₁₃	1	4	yes	complemented
441	#461	C₂²×C₁₃	1	2	yes	complemented
442	#460	C₂²×C₁₃	1	4	yes	—
443	#459	C₂²×C₁₃	1	4	yes	—
444	#459	C₂²×C₁₃	1	2	yes	complemented
445	#451	C₂²×C₁₃	1	2	yes	—
446	#450	C₂²×C₁₃	1	2	yes	—
447	#450	C₂²×C₁₃	1	2	yes	—
448	#448	C₂²×C₁₃	1	2	yes	—
449	#447	C₂²×C₁₃	1	2	yes	—
450	#447	C₂²×C₁₃	1	2	yes	—
451	#446	C₂²×C₁₃	1	4	yes	complemented
452	#446	C₂²×C₁₃	1	4	yes	complemented
453	#442	C₂²×C₁₃	1	4	yes	complemented
454	#441	C₂²×C₁₃	1	4	yes	complemented
455	#440	C₂²×C₁₃	1	4	yes	complemented
456	#440	C₂²×C₁₃	1	4	yes	complemented
457	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
458	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
459	#432	C₂²×C₁₃	1	1	yes	characteristic
460	#432	C₂²×C₁₃	1	1	yes	characteristic
461	#432	C₂²×C₁₃	1	2	yes	—
462	#431	C₂²×C₁₃	1	2	yes	—
463	C₂²×C₁₃	—	2	1	no	—
464	C₂²×C₁₃	—	2	1	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	8	4	no	—
475	C₂²×C₁₃	—	8	4	no	—
476	C₂²×C₁₃	#575	1	2	yes	—
477	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
478	C₄×C₁₃	—	2	2	no	—
479	C₄×C₁₃	—	2	1	no	—
480	C₄×C₁₃	—	2	1	no	—
481	C₄×C₁₃	—	2	2	no	—
482	C₄×C₁₃	—	2	1	no	—
483	C₄×C₁₃	—	2	1	no	—
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	2	1	no	—
486	C₄×C₁₃	—	2	2	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	2	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	#585	1	2	yes	—
493	C₂×#41	—	2	1	no	—
494	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
504	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
505	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
506	C₂×D₈	C₂³×C₁₃	1	4	yes	—
507	C₂×D₈	C₂³×C₁₃	1	4	yes	—
508	C₄⋊Q₈	—	2	2	no	—
509	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
512	#127	—	2	2	no	—
513	#127	C₂³×C₁₃	1	4	yes	—
514	#127	C₂³×C₁₃	1	1	yes	characteristic
515	#126	—	2	2	no	—
516	#126	—	2	2	no	—
517	#126	—	2	2	no	—
518	#126	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	2	2	no	—
521	#125	—	2	1	no	—
522	#125	C₂³×C₁₃	1	2	yes	—
523	#125	C₂³×C₁₃	1	2	yes	—
524	#124	—	2	4	no	—
525	#124	—	2	4	no	—
526	#124	—	2	2	no	—
527	#124	—	2	2	no	—
528	#124	—	2	1	no	—
529	#124	—	2	1	no	—
530	#124	—	2	1	no	—
531	#124	C₂³×C₁₃	1	2	yes	—
532	#124	C₂³×C₁₃	1	4	yes	—
533	#124	C₂³×C₁₃	1	2	yes	—
534	#124	C₂³×C₁₃	1	2	yes	—
535	#124	C₂³×C₁₃	1	2	yes	—
536	#123	—	2	2	no	—
537	#123	—	2	2	no	—
538	#123	—	2	4	no	—
539	#123	—	2	4	no	—
540	#123	—	2	4	no	—
541	#123	—	2	4	no	—
542	#123	—	2	2	no	—
543	#123	—	2	2	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
550	#121	—	2	1	no	—
551	#121	C₂³×C₁₃	1	2	yes	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	D₄×C₁₃	1	2	yes	—
556	C₄×Q₈	D₄×C₁₃	1	2	yes	—
557	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
558	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
559	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
560	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
561	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
562	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	4	no	—
566	C₄×D₄	—	2	4	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	C₂³×C₁₃	1	4	yes	—
573	C₄×D₄	C₂³×C₁₃	1	2	yes	—
574	C₄×D₄	C₂³×C₁₃	1	2	yes	—
575	C₄×D₄	C₂³×C₁₃	1	2	yes	—
576	C₄×D₄	C₂³×C₁₃	1	2	yes	—
577	C₄×D₄	C₂³×C₁₃	1	2	yes	—
578	#117	—	2	1	no	—
579	#117	—	2	2	no	—
580	#117	—	2	2	no	—
581	#117	—	2	2	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	2	no	—
584	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₄²	—	2	1	no	—
595	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
598	#107	C₂³×C₁₃	1	4	yes	—
599	#106	C₂³×C₁₃	1	4	yes	—
600	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
601	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
602	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
603	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
604	#103	C₂³×C₁₃	1	4	yes	—
605	#103	C₂³×C₁₃	1	4	yes	—
606	#103	C₂³×C₁₃	1	4	yes	—
607	#102	C₂³×C₁₃	1	4	yes	—
608	#102	C₂³×C₁₃	1	4	yes	—
609	#102	C₂³×C₁₃	1	4	yes	—
610	#102	C₂³×C₁₃	1	4	yes	—
611	#102	C₂³×C₁₃	1	4	yes	—
612	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
613	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
614	#97	C₂³×C₁₃	1	2	yes	—
615	#97	C₂³×C₁₃	1	4	yes	—
616	#97	C₂³×C₁₃	1	2	yes	—
617	C₄×C₈	C₂³×C₁₃	1	4	yes	—
618	C₂×C₁₃	—	2	2	no	—
619	C₂×C₁₃	—	8	2	no	—
620	C₂×C₁₃	—	8	2	no	—
621	C₂×C₁₃	—	8	2	no	—
622	C₂×C₁₃	#3487	1	1	yes	characteristic
623	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
624	C₂×C₁₃	#3585	1	1	yes	characteristic
625	C₂⁴	—	2	1	no	—
626	C₂⁴	—	2	1	no	—
627	#41	—	4	4	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	4	2	no	—
632	C₂×Q₈	—	4	2	no	—
633	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
634	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
635	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
636	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	4	no	—
647	C₂×D₄	—	8	2	no	—
648	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
649	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	8	2	no	—
660	C₂²×C₄	—	8	2	no	—
661	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
665	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
668	Q₁₆	—	4	4	no	—
669	SD₁₆	—	4	4	no	—
670	SD₁₆	—	4	4	no	—
671	SD₁₆	—	4	4	no	—
672	D₈	—	4	4	no	—
673	D₈	—	4	4	no	—
674	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
675	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
691	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
692	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
693	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
694	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
695	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	2	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	C₂×D₄×C₁₃	1	2	yes	—
722	C₄²	C₂×D₄×C₁₃	1	2	yes	—
723	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
724	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
725	C₄²	C₂⁴×C₁₃	1	2	yes	—
726	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
728	C₄²	C₂⁴×C₁₃	1	2	yes	—
729	C₁₃	#61895	1	1	yes	characteristic, direct product factor, Sylow
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	4	2	no	—
738	C₂³	—	4	2	no	—
739	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
740	Q₈	—	2	4	no	—
741	Q₈	—	2	4	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	2	no	—
744	Q₈	—	4	2	no	—
745	Q₈	—	4	2	no	—
746	Q₈	—	8	1	no	—
747	D₄	—	2	4	no	—
748	D₄	—	2	2	no	—
749	D₄	—	2	4	no	—
750	D₄	—	2	2	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	2	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	4	no	—
756	D₄	—	8	4	no	—
757	D₄	—	8	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	8	4	no	—
774	C₂×C₄	—	8	2	no	—
775	C₂×C₄	—	8	2	no	—
776	C₂×C₄	—	8	2	no	—
777	C₂×C₄	—	8	2	no	—
778	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
780	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
781	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
784	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
787	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
788	C₈	—	2	4	no	—
789	C₈	—	2	4	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	2	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	8	4	no	—
802	C₂²	—	8	4	no	—
803	C₂²	C₁₃×#575	1	2	yes	—
804	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
805	C₄	—	2	1	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	1	no	—
808	C₄	—	2	2	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	1	no	—
814	C₄	—	4	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	C₁₃×#585	1	2	yes	—
820	C₂	—	2	2	no	—
821	C₂	—	8	2	no	—
822	C₂	—	8	2	no	—
823	C₂	—	8	2	no	—
824	C₂	C₁₃×#3487	1	1	yes	characteristic
825	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
826	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3507	C₂	semidirect
2. C₂×C₁₃×#559	C₂	semidirect
3. C₁₃×#3403	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3371	C₂	semidirect
6. C₁₃×#3370	C₂	semidirect
7. C₁₃×#3217	C₂	semidirect
8. C₁₃×#3215	C₂	semidirect
9. C₁₃×#3213	C₂	semidirect
10. C₁₃×#3211	C₂	semidirect
11. C₁₃×#3117	C₂	semidirect
12. C₁₃×#3110	C₂	semidirect
13. C₁₃×#3109	C₂	semidirect
14. C₁₃×#3105	C₂	semidirect
15. C₁₃×#2983	C₂	semidirect
20. C₁₃×#559	C₂²	semidirect
21. C₁₃×#557	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
45. C₁₃×#497	C₂²	semidirect
47. C₁₃×#496	C₂²	semidirect
48. C₁₃×#495	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#489	C₂²	semidirect
52. C₁₃×#488	C₂²	semidirect
55. C₁₃×#479	C₂²	semidirect
56. C₁₃×#478	C₂²	semidirect
57. C₁₃×#476	C₂²	semidirect
58. C₁₃×#474	C₂²	semidirect
59. C₁₃×#464	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#463	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
68. C₁₃×#459	C₂²	semidirect
75. C₁₃×#446	C₂²	semidirect
76. C₁₃×#446	C₂²	semidirect
77. C₁₃×#442	C₂²	semidirect
78. C₁₃×#441	C₂²	semidirect
79. C₁₃×#440	C₂²	semidirect
80. C₁₃×#440	C₂²	semidirect
81. C₄×C₁₃×SD₁₆	C₂²	semidirect
82. C₄×C₁₃×D₈	C₂²	semidirect
212. #61895	C₁₃	direct (N × H)
317. #3507	C₂×C₁₃	semidirect
318. C₂×#559	C₂×C₁₃	semidirect
319. #3403	C₂×C₁₃	semidirect
320. #3401	C₂×C₁₃	semidirect
321. #3371	C₂×C₁₃	semidirect
322. #3370	C₂×C₁₃	semidirect
323. #3217	C₂×C₁₃	semidirect
324. #3215	C₂×C₁₃	semidirect
325. #3213	C₂×C₁₃	semidirect
326. #3211	C₂×C₁₃	semidirect
327. #3117	C₂×C₁₃	semidirect
328. #3110	C₂×C₁₃	semidirect
329. #3109	C₂×C₁₃	semidirect
330. #3105	C₂×C₁₃	semidirect
331. #2983	C₂×C₁₃	semidirect
396. #559	C₂²×C₁₃	semidirect
397. #557	C₂²×C₁₃	semidirect
399. #556	C₂²×C₁₃	semidirect
400. #554	C₂²×C₁₃	semidirect
421. #497	C₂²×C₁₃	semidirect
423. #496	C₂²×C₁₃	semidirect
424. #495	C₂²×C₁₃	semidirect
426. #489	C₂²×C₁₃	semidirect
427. #489	C₂²×C₁₃	semidirect
428. #488	C₂²×C₁₃	semidirect
431. #479	C₂²×C₁₃	semidirect
432. #478	C₂²×C₁₃	semidirect
433. #476	C₂²×C₁₃	semidirect
434. #474	C₂²×C₁₃	semidirect
435. #464	C₂²×C₁₃	semidirect
436. #464	C₂²×C₁₃	semidirect
437. #464	C₂²×C₁₃	semidirect
438. #463	C₂²×C₁₃	semidirect
439. #463	C₂²×C₁₃	semidirect
440. #463	C₂²×C₁₃	semidirect
441. #461	C₂²×C₁₃	semidirect
444. #459	C₂²×C₁₃	semidirect
451. #446	C₂²×C₁₃	semidirect
452. #446	C₂²×C₁₃	semidirect
453. #442	C₂²×C₁₃	semidirect
454. #441	C₂²×C₁₃	semidirect
455. #440	C₂²×C₁₃	semidirect
456. #440	C₂²×C₁₃	semidirect
457. C₄×SD₁₆	C₂²×C₁₃	semidirect
458. C₄×D₈	C₂²×C₁₃	semidirect
729. C₁₃	#61895	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×#3507	2
C₂×C₁₃×#559	2
C₁₃×#3403	2
C₁₃×#3401	2
C₁₃×#3371	2
C₁₃×#3370	2
C₁₃×#3217	2
C₁₃×#3215	2
C₁₃×#3213	2
C₁₃×#3211	2
C₁₃×#3117	2
C₁₃×#3110	2
C₁₃×#3109	2
C₁₃×#3105	2
C₁₃×#2983	2
#61895	13

Subgroups — C13×#61895 #15748234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61895 #15748234