Subgroups — C₁₃×#61281 #15747620

Order 3328.

1796 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3356	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3353	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3348	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3344	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3342	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3335	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3063	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2912	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#131	C₂²	1	2	yes	—
20	C₁₃×#559	—	2	1	no	—
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#556	—	2	2	no	—
23	C₁₃×#556	C₂²	1	2	yes	—
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#555	C₂²	1	2	yes	—
26	C₁₃×#554	C₂²	1	2	yes	—
27	C₁₃×#554	C₂²	1	2	yes	—
28	C₁₃×#553	—	2	2	no	—
29	C₁₃×#552	C₂²	1	4	yes	—
30	C₁₃×#548	—	2	2	no	—
31	C₁₃×#547	C₂²	1	2	yes	—
32	C₁₃×#542	—	2	2	no	—
33	C₁₃×#539	—	2	2	no	—
34	C₁₃×#537	C₂²	1	2	yes	—
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	—	2	1	no	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₃×#529	—	2	2	no	—
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₁₃×#520	C₂²	1	2	yes	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#501	C₂²	1	4	yes	—
47	C₁₃×#500	C₂²	1	2	yes	—
48	C₁₃×#498	C₂²	1	2	yes	—
49	C₁₃×#485	C₂²	1	4	yes	—
50	C₁₃×#485	C₂²	1	4	yes	—
51	C₁₃×#485	C₂²	1	4	yes	—
52	C₁₃×#484	C₂²	1	4	yes	—
53	C₁₃×#483	C₂²	1	4	yes	—
54	C₁₃×#483	C₂²	1	4	yes	—
55	C₁₃×#482	C₂²	1	4	yes	—
56	C₁₃×#481	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	2	yes	—
58	C₁₃×#478	C₂²	1	2	yes	—
59	C₁₃×#477	C₂²	1	1	yes	characteristic
60	C₁₃×#476	C₂²	1	1	yes	characteristic
61	C₁₃×#475	C₂²	1	2	yes	—
62	C₁₃×#475	C₂²	1	4	yes	—
63	C₁₃×#475	C₂²	1	2	yes	—
64	C₁₃×#475	C₂²	1	1	yes	characteristic
65	C₁₃×#474	C₂²	1	1	yes	characteristic
66	C₁₃×#470	C₂²	1	4	yes	—
67	C₁₃×#468	C₂²	1	4	yes	—
68	C₁₃×#467	C₂²	1	4	yes	—
69	C₁₃×#465	C₂²	1	4	yes	—
70	C₁₃×#441	C₂²	1	2	yes	—
71	C₁₃×#440	C₂²	1	2	yes	—
72	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
73	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
74	C₁₃×#436	C₂²	1	2	yes	—
75	C₁₃×#435	C₂²	1	4	yes	—
76	C₈×D₄×C₁₃	C₂²	1	2	yes	—
77	C₁₃×#428	C₂²	1	2	yes	—
78	C₁₃×#428	C₂²	1	4	yes	—
79	C₁₃×#428	C₂²	1	4	yes	—
80	C₁₃×#428	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₁₃×#427	C₂²	1	2	yes	—
83	C₁₃×#427	C₂²	1	4	yes	—
84	C₂×C₁₃×#106	C₂²	1	2	yes	—
85	C₂×C₁₃×#106	C₂²	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₁₃×#419	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#103	C₂²	1	2	yes	—
91	C₁₃×#408	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×#41	C₂³	1	2	yes	—
96	C₂²×Q₈×C₁₃	—	2	1	no	—
97	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#137	—	2	4	no	—
99	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
101	C₁₃×#131	—	2	8	no	—
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	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	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×#127	D₄	1	1	yes	characteristic
116	C₁₃×#126	—	2	4	no	—
117	C₁₃×#126	—	2	4	no	—
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#125	—	2	2	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	4	no	—
122	C₁₃×#125	C₂³	1	2	yes	—
123	C₁₃×#124	—	2	2	no	—
124	C₁₃×#124	—	2	2	no	—
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	—	2	4	no	—
127	C₁₃×#124	D₄	1	2	yes	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×#123	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	1	no	—
133	C₁₃×C₂²⋊Q₈	—	2	1	no	—
134	C₁₃×C₂²⋊Q₈	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₁₃×#121	—	2	2	no	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	—	2	4	no	—
143	C₁₃×#121	D₄	1	2	yes	—
144	C₁₃×#121	D₄	1	2	yes	—
145	C₁₃×#121	C₂³	1	4	yes	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₁₃	—	2	4	no	—
159	C₄×D₄×C₁₃	—	2	2	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	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	1	yes	characteristic
168	C₄×D₄×C₁₃	C₂³	1	2	yes	—
169	C₄×D₄×C₁₃	C₂³	1	2	yes	—
170	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	4	no	—
172	C₁₃×#117	—	2	1	no	—
173	C₁₃×#117	C₂³	1	2	yes	—
174	C₁₃×#117	C₂³	1	1	yes	characteristic
175	C₁₃×#117	C₂³	1	4	yes	—
176	C₁₃×#117	C₂³	1	4	yes	—
177	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₄²×C₁₃	—	2	1	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	4	yes	—
188	C₁₃×#107	C₂³	1	2	yes	—
189	C₁₃×#107	C₂³	1	2	yes	—
190	C₁₃×#107	C₂³	1	4	yes	—
191	C₁₃×#106	C₂³	1	4	yes	—
192	C₁₃×#106	C₂³	1	2	yes	—
193	C₁₃×#106	C₂³	1	2	yes	—
194	C₁₃×#106	C₂³	1	4	yes	—
195	C₁₃×#106	C₂³	1	4	yes	—
196	C₁₃×#106	C₂³	1	2	yes	—
197	C₁₃×#106	C₂³	1	4	yes	—
198	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
200	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	2	yes	—
204	C₁₃×#103	C₂³	1	2	yes	—
205	C₁₃×#103	C₂³	1	2	yes	—
206	C₁₃×#103	C₂³	1	2	yes	—
207	C₁₃×#103	C₂³	1	2	yes	—
208	C₁₃×#102	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	2	yes	—
210	C₁₃×#102	C₂³	1	2	yes	—
211	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₁₃×#97	C₂³	1	2	yes	—
214	C₄×C₈×C₁₃	C₂³	1	2	yes	—
215	#61281	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₃×#41	—	2	4	no	—
217	C₁₃×#41	—	2	4	no	—
218	C₁₃×#41	—	2	2	no	—
219	C₁₃×#41	—	2	2	no	—
220	C₁₃×#41	—	8	4	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	2	1	no	—
225	C₂×Q₈×C₁₃	—	2	2	no	—
226	C₂×Q₈×C₁₃	—	2	2	no	—
227	C₂×Q₈×C₁₃	—	2	2	no	—
228	C₂×Q₈×C₁₃	—	8	2	no	—
229	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	—	2	4	no	—
234	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
235	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	4	no	—
243	C₂²×C₄×C₁₃	—	2	4	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₁₃×Q₁₆	—	2	4	no	—
252	C₁₃×SD₁₆	—	2	4	no	—
253	C₁₃×M₁₆	—	2	2	no	—
254	C₁₃×M₁₆	—	2	8	no	—
255	C₁₃×M₁₆	#41	1	4	yes	complemented
256	C₂×C₈×C₁₃	—	2	4	no	—
257	C₂×C₈×C₁₃	—	2	8	no	—
258	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
259	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
260	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	2	no	—
264	C₁₃×C₄⋊C₄	—	2	2	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
285	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	1	no	—
295	C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
298	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
299	C₄²×C₁₃	—	2	2	no	—
300	C₄²×C₁₃	—	2	1	no	—
301	C₄²×C₁₃	—	2	1	no	—
302	C₄²×C₁₃	—	2	1	no	—
303	C₄²×C₁₃	—	2	2	no	—
304	C₄²×C₁₃	—	2	4	no	—
305	C₄²×C₁₃	—	2	4	no	—
306	C₄²×C₁₃	—	2	2	no	—
307	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
311	#3511	C₂×C₁₃	1	1	yes	characteristic
312	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#3356	C₂×C₁₃	1	2	yes	complemented
314	#3353	C₂×C₁₃	1	2	yes	complemented
315	#3348	C₂×C₁₃	1	4	yes	complemented
316	#3344	C₂×C₁₃	1	4	yes	complemented
317	#3342	C₂×C₁₃	1	2	yes	complemented
318	#3335	C₂×C₁₃	1	2	yes	complemented
319	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#3099	C₂×C₁₃	1	2	yes	complemented
321	#3097	C₂×C₁₃	1	2	yes	complemented
322	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
323	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#3063	C₂×C₁₃	1	2	yes	complemented
325	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#2935	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#2912	C₂×C₁₃	1	2	yes	complemented
328	C₂³×C₁₃	—	2	1	no	—
329	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
330	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₁₃	—	2	4	no	—
332	Q₈×C₁₃	—	2	2	no	—
333	Q₈×C₁₃	—	2	1	no	—
334	Q₈×C₁₃	—	2	2	no	—
335	Q₈×C₁₃	—	2	1	no	—
336	Q₈×C₁₃	—	4	2	no	—
337	Q₈×C₁₃	—	4	2	no	—
338	Q₈×C₁₃	—	4	4	no	—
339	Q₈×C₁₃	—	8	1	no	—
340	Q₈×C₁₃	—	8	2	no	—
341	D₄×C₁₃	—	2	8	no	—
342	D₄×C₁₃	—	2	4	no	—
343	D₄×C₁₃	—	2	4	no	—
344	D₄×C₁₃	—	2	1	no	—
345	D₄×C₁₃	—	2	1	no	—
346	D₄×C₁₃	—	4	2	no	—
347	D₄×C₁₃	—	4	2	no	—
348	D₄×C₁₃	—	8	4	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	4	no	—
351	C₂×C₄×C₁₃	—	2	4	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	2	no	—
362	C₂×C₄×C₁₃	—	4	2	no	—
363	C₂×C₄×C₁₃	—	4	2	no	—
364	C₂×C₄×C₁₃	—	4	2	no	—
365	C₂×C₄×C₁₃	—	8	1	no	—
366	C₂×C₄×C₁₃	—	8	4	no	—
367	C₂×C₄×C₁₃	—	8	2	no	—
368	C₂×C₄×C₁₃	—	8	4	no	—
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
376	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
377	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
378	C₈×C₁₃	—	2	2	no	—
379	C₈×C₁₃	—	2	2	no	—
380	C₈×C₁₃	—	2	2	no	—
381	C₈×C₁₃	C₂×#41	1	4	yes	—
382	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#131	C₂²×C₁₃	1	2	yes	—
384	#559	—	2	1	no	—
385	#557	—	2	1	no	—
386	#556	—	2	2	no	—
387	#556	C₂²×C₁₃	1	2	yes	—
388	#556	C₂²×C₁₃	1	2	yes	—
389	#555	C₂²×C₁₃	1	2	yes	—
390	#554	C₂²×C₁₃	1	2	yes	—
391	#554	C₂²×C₁₃	1	2	yes	—
392	#553	—	2	2	no	—
393	#552	C₂²×C₁₃	1	4	yes	—
394	#548	—	2	2	no	—
395	#547	C₂²×C₁₃	1	2	yes	—
396	#542	—	2	2	no	—
397	#539	—	2	2	no	—
398	#537	C₂²×C₁₃	1	2	yes	—
399	#536	C₂²×C₁₃	1	2	yes	—
400	#533	—	2	1	no	—
401	#533	C₂²×C₁₃	1	1	yes	characteristic
402	#532	—	2	1	no	—
403	#532	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
405	#529	—	2	2	no	—
406	#520	C₂²×C₁₃	1	2	yes	—
407	#520	C₂²×C₁₃	1	2	yes	—
408	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
410	#501	C₂²×C₁₃	1	4	yes	—
411	#500	C₂²×C₁₃	1	2	yes	—
412	#498	C₂²×C₁₃	1	2	yes	—
413	#485	C₂²×C₁₃	1	4	yes	—
414	#485	C₂²×C₁₃	1	4	yes	—
415	#485	C₂²×C₁₃	1	4	yes	—
416	#484	C₂²×C₁₃	1	4	yes	—
417	#483	C₂²×C₁₃	1	4	yes	—
418	#483	C₂²×C₁₃	1	4	yes	—
419	#482	C₂²×C₁₃	1	4	yes	—
420	#481	C₂²×C₁₃	1	4	yes	—
421	#479	C₂²×C₁₃	1	2	yes	—
422	#478	C₂²×C₁₃	1	2	yes	—
423	#477	C₂²×C₁₃	1	1	yes	characteristic
424	#476	C₂²×C₁₃	1	1	yes	characteristic
425	#475	C₂²×C₁₃	1	2	yes	—
426	#475	C₂²×C₁₃	1	4	yes	—
427	#475	C₂²×C₁₃	1	2	yes	—
428	#475	C₂²×C₁₃	1	1	yes	characteristic
429	#474	C₂²×C₁₃	1	1	yes	characteristic
430	#470	C₂²×C₁₃	1	4	yes	—
431	#468	C₂²×C₁₃	1	4	yes	—
432	#467	C₂²×C₁₃	1	4	yes	—
433	#465	C₂²×C₁₃	1	4	yes	—
434	#441	C₂²×C₁₃	1	2	yes	—
435	#440	C₂²×C₁₃	1	2	yes	—
436	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
437	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
438	#436	C₂²×C₁₃	1	2	yes	—
439	#435	C₂²×C₁₃	1	4	yes	—
440	C₈×D₄	C₂²×C₁₃	1	2	yes	—
441	#428	C₂²×C₁₃	1	4	yes	—
442	#428	C₂²×C₁₃	1	4	yes	—
443	#428	C₂²×C₁₃	1	2	yes	—
444	#428	C₂²×C₁₃	1	2	yes	—
445	#428	C₂²×C₁₃	1	1	yes	characteristic
446	#427	C₂²×C₁₃	1	2	yes	—
447	#427	C₂²×C₁₃	1	4	yes	—
448	C₂×#106	C₂²×C₁₃	1	2	yes	—
449	C₂×#106	C₂²×C₁₃	1	4	yes	—
450	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
451	#419	C₂²×C₁₃	1	1	yes	characteristic
452	#417	C₂²×C₁₃	1	1	yes	characteristic
453	#416	C₂²×C₁₃	1	2	yes	—
454	C₂×#103	C₂²×C₁₃	1	2	yes	—
455	#408	C₂²×C₁₃	1	2	yes	—
456	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
457	C₂²×C₁₃	—	2	1	no	—
458	C₂²×C₁₃	—	2	1	no	—
459	C₂²×C₁₃	—	2	4	no	—
460	C₂²×C₁₃	—	2	4	no	—
461	C₂²×C₁₃	—	2	4	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	1	no	—
464	C₂²×C₁₃	—	4	1	no	—
465	C₂²×C₁₃	#547	1	2	yes	—
466	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	4	no	—
470	C₄×C₁₃	—	2	1	no	—
471	C₄×C₁₃	—	4	1	no	—
472	C₄×C₁₃	—	4	2	no	—
473	C₄×C₁₃	—	4	2	no	—
474	C₄×C₁₃	—	4	1	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	—	4	1	no	—
477	C₄×C₁₃	—	4	4	no	—
478	C₄×C₁₃	—	4	2	no	—
479	C₄×C₁₃	#547	1	2	yes	—
480	C₄×C₁₃	#577	1	2	yes	—
481	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
482	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂×#41	—	2	2	no	—
484	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
485	C₂×#41	C₂³×C₁₃	1	2	yes	—
486	C₂²×Q₈	—	2	1	no	—
487	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
488	#137	—	2	4	no	—
489	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
490	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
491	#131	—	2	8	no	—
492	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
493	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
496	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	—	2	1	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
501	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
502	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
503	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
505	#127	D₄×C₁₃	1	1	yes	characteristic
506	#126	—	2	4	no	—
507	#126	—	2	4	no	—
508	#126	—	2	4	no	—
509	#125	—	2	2	no	—
510	#125	—	2	2	no	—
511	#125	—	2	4	no	—
512	#125	C₂³×C₁₃	1	2	yes	—
513	#124	—	2	2	no	—
514	#124	—	2	2	no	—
515	#124	—	2	2	no	—
516	#124	—	2	4	no	—
517	#124	D₄×C₁₃	1	2	yes	—
518	#123	—	2	4	no	—
519	#123	—	2	4	no	—
520	#123	—	2	4	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	1	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
528	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
529	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
530	#121	—	2	2	no	—
531	#121	—	2	2	no	—
532	#121	—	2	4	no	—
533	#121	D₄×C₁₃	1	2	yes	—
534	#121	D₄×C₁₃	1	2	yes	—
535	#121	C₂³×C₁₃	1	4	yes	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
545	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
546	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
547	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₄×D₄	C₂³×C₁₃	1	2	yes	—
559	C₄×D₄	C₂³×C₁₃	1	2	yes	—
560	#117	—	2	2	no	—
561	#117	—	2	4	no	—
562	#117	—	2	1	no	—
563	#117	C₂³×C₁₃	1	1	yes	characteristic
564	#117	C₂³×C₁₃	1	2	yes	—
565	#117	C₂³×C₁₃	1	4	yes	—
566	#117	C₂³×C₁₃	1	4	yes	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
573	C₂×C₄²	—	2	1	no	—
574	C₂×C₄²	—	2	1	no	—
575	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
576	#107	C₂³×C₁₃	1	2	yes	—
577	#107	C₂³×C₁₃	1	4	yes	—
578	#107	C₂³×C₁₃	1	2	yes	—
579	#107	C₂³×C₁₃	1	2	yes	—
580	#107	C₂³×C₁₃	1	4	yes	—
581	#106	C₂³×C₁₃	1	4	yes	—
582	#106	C₂³×C₁₃	1	2	yes	—
583	#106	C₂³×C₁₃	1	2	yes	—
584	#106	C₂³×C₁₃	1	4	yes	—
585	#106	C₂³×C₁₃	1	4	yes	—
586	#106	C₂³×C₁₃	1	2	yes	—
587	#106	C₂³×C₁₃	1	4	yes	—
588	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
589	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
590	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
591	#103	C₂³×C₁₃	1	4	yes	—
592	#103	C₂³×C₁₃	1	4	yes	—
593	#103	C₂³×C₁₃	1	2	yes	—
594	#103	C₂³×C₁₃	1	2	yes	—
595	#103	C₂³×C₁₃	1	2	yes	—
596	#103	C₂³×C₁₃	1	2	yes	—
597	#103	C₂³×C₁₃	1	2	yes	—
598	#102	C₂³×C₁₃	1	2	yes	—
599	#102	C₂³×C₁₃	1	2	yes	—
600	#102	C₂³×C₁₃	1	2	yes	—
601	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
602	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
603	#97	C₂³×C₁₃	1	2	yes	—
604	C₄×C₈	C₂³×C₁₃	1	2	yes	—
605	C₂×C₁₃	—	2	2	no	—
606	C₂×C₁₃	—	4	4	no	—
607	C₂×C₁₃	—	8	1	no	—
608	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
609	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
610	C₂×C₁₃	#3586	1	1	yes	characteristic
611	#41	—	2	4	no	—
612	#41	—	2	4	no	—
613	#41	—	2	2	no	—
614	#41	—	2	2	no	—
615	#41	—	8	4	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	2	no	—
621	C₂×Q₈	—	2	2	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	8	2	no	—
624	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
630	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
631	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
632	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
633	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
645	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
646	Q₁₆	—	2	4	no	—
647	SD₁₆	—	2	4	no	—
648	M₁₆	—	2	2	no	—
649	M₁₆	—	2	8	no	—
650	M₁₆	C₁₃×#41	1	4	yes	complemented
651	C₂×C₈	—	2	4	no	—
652	C₂×C₈	—	2	8	no	—
653	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
654	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
655	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
656	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
678	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	1	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
693	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	1	no	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
705	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₁₃	#61281	1	1	yes	characteristic, direct product factor, Sylow
707	C₂³	—	2	1	no	—
708	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
709	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
710	Q₈	—	2	4	no	—
711	Q₈	—	2	2	no	—
712	Q₈	—	2	1	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	2	1	no	—
715	Q₈	—	4	2	no	—
716	Q₈	—	4	4	no	—
717	Q₈	—	4	2	no	—
718	Q₈	—	8	2	no	—
719	Q₈	—	8	1	no	—
720	D₄	—	2	8	no	—
721	D₄	—	2	4	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	1	no	—
724	D₄	—	2	1	no	—
725	D₄	—	4	2	no	—
726	D₄	—	4	2	no	—
727	D₄	—	8	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	8	1	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	—	8	2	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
750	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
754	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
755	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
756	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	2	2	no	—
759	C₈	—	2	2	no	—
760	C₈	C₂×C₁₃×#41	1	4	yes	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	C₁₃×#547	1	2	yes	—
770	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	4	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	4	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	2	no	—
783	C₄	C₁₃×#547	1	2	yes	—
784	C₄	C₁₃×#577	1	2	yes	—
785	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
786	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
787	C₂	—	2	2	no	—
788	C₂	—	4	4	no	—
789	C₂	—	8	1	no	—
790	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
791	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
792	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×#3511	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3507	C₂	semidirect
3. C₁₃×#3356	C₂	semidirect
4. C₁₃×#3353	C₂	semidirect
5. C₁₃×#3348	C₂	semidirect
6. C₁₃×#3344	C₂	semidirect
7. C₁₃×#3342	C₂	semidirect
8. C₁₃×#3335	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₁₃×#3099	C₂	semidirect
11. C₁₃×#3097	C₂	semidirect
12. C₁₃×#3076	C₂	semidirect
13. C₂×C₁₃×#475	C₂	semidirect
14. C₁₃×#3063	C₂	semidirect
15. C₄×C₁₃×#137	C₂	semidirect
16. C₁₃×#2935	C₂	semidirect
17. C₁₃×#2912	C₂	semidirect
215. #61281	C₁₃	direct (N × H)
255. C₁₃×M₁₆	#41	semidirect
312. #3507	C₂×C₁₃	semidirect
313. #3356	C₂×C₁₃	semidirect
314. #3353	C₂×C₁₃	semidirect
315. #3348	C₂×C₁₃	semidirect
316. #3344	C₂×C₁₃	semidirect
317. #3342	C₂×C₁₃	semidirect
318. #3335	C₂×C₁₃	semidirect
319. #3165	C₂×C₁₃	semidirect
320. #3099	C₂×C₁₃	semidirect
321. #3097	C₂×C₁₃	semidirect
322. #3076	C₂×C₁₃	semidirect
323. C₂×#475	C₂×C₁₃	semidirect
324. #3063	C₂×C₁₃	semidirect
325. C₄×#137	C₂×C₁₃	semidirect
326. #2935	C₂×C₁₃	semidirect
327. #2912	C₂×C₁₃	semidirect
650. M₁₆	C₁₃×#41	semidirect
706. C₁₃	#61281	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×#3511	2
C₁₃×#3507	2
C₁₃×#3356	2
C₁₃×#3353	2
C₁₃×#3348	2
C₁₃×#3344	2
C₁₃×#3342	2
C₁₃×#3335	2
C₁₃×#3165	2
C₁₃×#3099	2
C₁₃×#3097	2
C₁₃×#3076	2
C₂×C₁₃×#475	2
C₁₃×#3063	2
C₄×C₁₃×#137	2
C₁₃×#2935	2
C₁₃×#2912	2
#61281	13

Subgroups — C13×#61281 #15747620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61281 #15747620