Subgroups — C₁₃×#36752 #15723091

Order 3328.

1570 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2851	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2805	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2802	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2792	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2791	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2791	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2755	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2734	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2713	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2646	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2569	C₂	1	2	yes	maximal
14	C₁₃×#2440	C₂	1	2	yes	maximal
15	C₁₃×#2438	C₂	1	2	yes	maximal
16	C₁₃×#2438	C₂	1	2	yes	maximal
17	C₁₃×#2316	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#2313	C₂	1	1	yes	maximal, characteristic
19	C₂×C₁₃×#387	C₂	1	1	yes	maximal, characteristic
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#117	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#400	C₂²	1	2	yes	—
30	C₁₃×#400	C₂²	1	2	yes	—
31	C₁₃×#400	C₂²	1	2	yes	—
32	C₁₃×#400	C₂²	1	2	yes	—
33	C₁₃×#400	C₂²	1	2	yes	—
34	C₁₃×#400	C₂²	1	2	yes	—
35	C₁₃×#398	C₂²	1	2	yes	—
36	C₁₃×#398	C₂²	1	2	yes	—
37	C₁₃×#398	C₂²	1	2	yes	—
38	C₁₃×#398	C₂²	1	2	yes	—
39	C₁₃×#398	C₂²	1	2	yes	—
40	C₁₃×#398	C₂²	1	2	yes	—
41	C₁₃×#398	C₂²	1	2	yes	—
42	C₁₃×#398	C₂²	1	2	yes	—
43	C₁₃×#398	C₂²	1	2	yes	—
44	C₁₃×#398	C₂²	1	2	yes	—
45	C₁₃×#398	C₂²	1	2	yes	—
46	C₁₃×#398	C₂²	1	2	yes	—
47	C₁₃×#395	C₂²	1	2	yes	—
48	C₁₃×#395	C₂²	1	2	yes	—
49	C₁₃×#395	C₂²	1	2	yes	—
50	C₁₃×#395	C₂²	1	2	yes	—
51	C₁₃×#395	C₂²	1	2	yes	—
52	C₁₃×#395	C₂²	1	2	yes	—
53	C₁₃×#391	C₂²	1	2	yes	—
54	C₁₃×#391	C₂²	1	2	yes	—
55	C₁₃×#391	C₂²	1	2	yes	—
56	C₁₃×#389	C₂²	1	2	yes	—
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	1	yes	characteristic
59	C₁₃×#389	C₂²	1	2	yes	—
60	C₁₃×#389	C₂²	1	2	yes	—
61	C₁₃×#389	C₂²	1	1	yes	characteristic
62	C₁₃×#389	C₂²	1	2	yes	—
63	C₁₃×#389	C₂²	1	2	yes	—
64	C₁₃×#389	C₂²	1	2	yes	—
65	C₁₃×#389	C₂²	1	1	yes	characteristic
66	C₁₃×#389	C₂²	1	2	yes	—
67	C₁₃×#389	C₂²	1	2	yes	—
68	C₁₃×#389	C₂²	1	1	yes	characteristic
69	C₁₃×#387	C₂²	1	2	yes	—
70	C₁₃×#387	C₂²	1	2	yes	—
71	C₁₃×#387	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#387	C₂²	1	2	yes	—
86	C₁₃×#387	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#385	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	—
91	C₁₃×#384	C₂²	1	1	yes	characteristic
92	C₁₃×#384	C₂²	1	2	yes	—
93	C₁₃×#382	C₂²	1	1	yes	characteristic
94	C₁₃×#381	C₂²	1	2	yes	—
95	C₁₃×#380	C₂²	1	1	yes	characteristic
96	C₁₃×#380	C₂²	1	1	yes	characteristic
97	C₁₃×#380	C₂²	1	2	yes	—
98	C₁₃×#380	C₂²	1	2	yes	—
99	C₁₃×#380	C₂²	1	2	yes	—
100	C₁₃×#380	C₂²	1	1	yes	characteristic
101	C₁₃×#380	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
104	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
105	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	—	4	2	no	—
117	C₁₃×C₄⋊Q₈	—	4	4	no	—
118	C₁₃×#125	—	4	2	no	—
119	C₁₃×C₂²⋊Q₈	—	4	4	no	—
120	C₁₃×C₂²⋊Q₈	—	4	4	no	—
121	C₁₃×#117	—	4	4	no	—
122	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
123	C₂×C₁₃×C₄⋊C₄	Q₈	1	8	yes	complemented
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃	—	4	2	no	—
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₁₃×#95	C₂³	1	2	yes	—
172	C₁₃×#95	C₂³	1	2	yes	—
173	C₁₃×#95	C₂³	1	2	yes	—
174	C₁₃×#95	C₂³	1	2	yes	—
175	C₁₃×#95	C₂³	1	2	yes	—
176	C₁₃×#95	C₂³	1	2	yes	—
177	C₁₃×#95	C₂³	1	2	yes	—
178	C₁₃×#95	C₂³	1	2	yes	—
179	C₁₃×#95	C₂³	1	2	yes	—
180	C₁₃×#95	C₂³	1	2	yes	—
181	C₁₃×#95	C₂³	1	2	yes	—
182	C₁₃×#95	C₂³	1	2	yes	—
183	C₁₃×#95	C₂³	1	2	yes	—
184	C₁₃×#95	C₂³	1	2	yes	—
185	C₁₃×#95	C₂³	1	2	yes	—
186	C₁₃×#95	C₂³	1	2	yes	—
187	C₁₃×#95	C₂³	1	2	yes	—
188	C₁₃×#95	C₂³	1	2	yes	—
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	#36752	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂×Q₈×C₁₃	—	2	4	no	—
206	C₂×Q₈×C₁₃	—	4	2	no	—
207	C₂×Q₈×C₁₃	—	4	2	no	—
208	C₂×Q₈×C₁₃	—	4	2	no	—
209	C₂×Q₈×C₁₃	—	4	2	no	—
210	C₂×Q₈×C₁₃	—	4	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	4	1	no	—
220	C₂²×C₄×C₁₃	—	4	1	no	—
221	C₂²×C₄×C₁₃	—	4	1	no	—
222	C₂²×C₄×C₁₃	—	4	1	no	—
223	C₂²×C₄×C₁₃	—	4	1	no	—
224	C₂²×C₄×C₁₃	—	4	1	no	—
225	C₂²×C₄×C₁₃	—	4	1	no	—
226	C₂²×C₄×C₁₃	—	4	1	no	—
227	C₂²×C₄×C₁₃	—	4	1	no	—
228	C₂²×C₄×C₁₃	—	4	1	no	—
229	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
230	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
231	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
232	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	4	2	no	—
255	C₁₃×C₄⋊C₄	—	4	2	no	—
256	C₁₃×C₄⋊C₄	—	4	1	no	—
257	C₁₃×C₄⋊C₄	—	4	1	no	—
258	C₁₃×C₄⋊C₄	—	4	1	no	—
259	C₁₃×C₄⋊C₄	—	4	1	no	—
260	C₁₃×C₄⋊C₄	—	4	2	no	—
261	C₁₃×C₄⋊C₄	—	4	2	no	—
262	C₁₃×C₄⋊C₄	—	4	2	no	—
263	C₁₃×C₄⋊C₄	—	4	2	no	—
264	C₁₃×C₄⋊C₄	—	4	2	no	—
265	C₁₃×C₄⋊C₄	—	4	2	no	—
266	C₁₃×C₄⋊C₄	—	4	2	no	—
267	C₁₃×C₄⋊C₄	—	4	2	no	—
268	C₁₃×C₄⋊C₄	—	4	2	no	—
269	C₁₃×C₄⋊C₄	—	4	2	no	—
270	C₁₃×C₄⋊C₄	—	4	2	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	—	4	2	no	—
274	C₁₃×C₄⋊C₄	—	4	1	no	—
275	C₁₃×C₄⋊C₄	—	4	1	no	—
276	C₁₃×C₄⋊C₄	—	4	2	no	—
277	C₁₃×C₄⋊C₄	—	4	1	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	1	no	—
280	C₁₃×C₄⋊C₄	—	4	2	no	—
281	C₁₃×C₄⋊C₄	—	4	2	no	—
282	C₁₃×C₄⋊C₄	C₂×Q₈	1	8	yes	—
283	C₁₃×C₄⋊C₄	C₂×Q₈	1	8	yes	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₄²×C₁₃	—	2	2	no	—
289	C₄²×C₁₃	—	2	2	no	—
290	C₄²×C₁₃	—	4	1	no	—
291	C₄²×C₁₃	—	4	1	no	—
292	C₄²×C₁₃	—	4	2	no	—
293	C₄²×C₁₃	—	4	2	no	—
294	C₄²×C₁₃	—	4	2	no	—
295	C₄²×C₁₃	—	4	2	no	—
296	#2857	C₂×C₁₃	1	1	yes	characteristic
297	#2851	C₂×C₁₃	1	1	yes	characteristic
298	#2805	C₂×C₁₃	1	2	yes	complemented
299	#2802	C₂×C₁₃	1	2	yes	complemented
300	#2792	C₂×C₁₃	1	2	yes	complemented
301	#2791	C₂×C₁₃	1	2	yes	complemented
302	#2791	C₂×C₁₃	1	2	yes	complemented
303	#2755	C₂×C₁₃	1	2	yes	complemented
304	#2734	C₂×C₁₃	1	2	yes	complemented
305	#2713	C₂×C₁₃	1	2	yes	complemented
306	#2659	C₂×C₁₃	1	1	yes	characteristic
307	#2646	C₂×C₁₃	1	1	yes	characteristic
308	#2569	C₂×C₁₃	1	2	yes	—
309	#2440	C₂×C₁₃	1	2	yes	—
310	#2438	C₂×C₁₃	1	2	yes	—
311	#2438	C₂×C₁₃	1	2	yes	—
312	#2316	C₂×C₁₃	1	1	yes	characteristic
313	#2313	C₂×C₁₃	1	1	yes	characteristic
314	C₂×#387	C₂×C₁₃	1	1	yes	characteristic
315	C₂³×C₁₃	—	2	1	no	—
316	C₂³×C₁₃	—	2	1	no	—
317	C₂³×C₁₃	—	2	1	no	—
318	C₂³×C₁₃	—	2	1	no	—
319	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
320	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
321	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
322	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
323	Q₈×C₁₃	—	8	4	no	—
324	Q₈×C₁₃	—	8	4	no	—
325	C₂×C₄×C₁₃	—	2	8	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	1	no	—
360	C₂×C₄×C₁₃	—	2	1	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	1	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	4	4	no	—
375	C₂×C₄×C₁₃	—	4	4	no	—
376	C₂×C₄×C₁₃	—	4	4	no	—
377	C₂×C₄×C₁₃	—	4	4	no	—
378	C₂×C₄×C₁₃	—	8	2	no	—
379	C₂×C₄×C₁₃	—	8	2	no	—
380	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
381	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
382	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
383	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
384	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
385	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
386	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
388	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
390	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
391	C₂×#117	C₂²×C₁₃	1	2	yes	—
392	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
394	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
395	#400	C₂²×C₁₃	1	2	yes	—
396	#400	C₂²×C₁₃	1	2	yes	—
397	#400	C₂²×C₁₃	1	2	yes	—
398	#400	C₂²×C₁₃	1	2	yes	—
399	#400	C₂²×C₁₃	1	2	yes	—
400	#400	C₂²×C₁₃	1	2	yes	—
401	#398	C₂²×C₁₃	1	2	yes	—
402	#398	C₂²×C₁₃	1	2	yes	—
403	#398	C₂²×C₁₃	1	2	yes	—
404	#398	C₂²×C₁₃	1	2	yes	—
405	#398	C₂²×C₁₃	1	2	yes	—
406	#398	C₂²×C₁₃	1	2	yes	—
407	#398	C₂²×C₁₃	1	2	yes	—
408	#398	C₂²×C₁₃	1	2	yes	—
409	#398	C₂²×C₁₃	1	2	yes	—
410	#398	C₂²×C₁₃	1	2	yes	—
411	#398	C₂²×C₁₃	1	2	yes	—
412	#398	C₂²×C₁₃	1	2	yes	—
413	#395	C₂²×C₁₃	1	2	yes	—
414	#395	C₂²×C₁₃	1	2	yes	—
415	#395	C₂²×C₁₃	1	2	yes	—
416	#395	C₂²×C₁₃	1	2	yes	—
417	#395	C₂²×C₁₃	1	2	yes	—
418	#395	C₂²×C₁₃	1	2	yes	—
419	#391	C₂²×C₁₃	1	2	yes	—
420	#391	C₂²×C₁₃	1	2	yes	—
421	#391	C₂²×C₁₃	1	2	yes	—
422	#389	C₂²×C₁₃	1	2	yes	—
423	#389	C₂²×C₁₃	1	2	yes	—
424	#389	C₂²×C₁₃	1	2	yes	—
425	#389	C₂²×C₁₃	1	2	yes	—
426	#389	C₂²×C₁₃	1	1	yes	characteristic
427	#389	C₂²×C₁₃	1	1	yes	characteristic
428	#389	C₂²×C₁₃	1	1	yes	characteristic
429	#389	C₂²×C₁₃	1	2	yes	—
430	#389	C₂²×C₁₃	1	1	yes	characteristic
431	#389	C₂²×C₁₃	1	2	yes	—
432	#389	C₂²×C₁₃	1	2	yes	—
433	#389	C₂²×C₁₃	1	2	yes	—
434	#389	C₂²×C₁₃	1	2	yes	—
435	#387	C₂²×C₁₃	1	2	yes	—
436	#387	C₂²×C₁₃	1	2	yes	—
437	#387	C₂²×C₁₃	1	2	yes	—
438	#387	C₂²×C₁₃	1	2	yes	—
439	#387	C₂²×C₁₃	1	2	yes	—
440	#387	C₂²×C₁₃	1	2	yes	—
441	#387	C₂²×C₁₃	1	2	yes	—
442	#387	C₂²×C₁₃	1	2	yes	—
443	#387	C₂²×C₁₃	1	2	yes	—
444	#387	C₂²×C₁₃	1	2	yes	—
445	#387	C₂²×C₁₃	1	2	yes	—
446	#387	C₂²×C₁₃	1	2	yes	—
447	#387	C₂²×C₁₃	1	2	yes	—
448	#387	C₂²×C₁₃	1	2	yes	—
449	#387	C₂²×C₁₃	1	2	yes	—
450	#387	C₂²×C₁₃	1	2	yes	—
451	#387	C₂²×C₁₃	1	2	yes	—
452	#387	C₂²×C₁₃	1	2	yes	—
453	#385	C₂²×C₁₃	1	2	yes	—
454	#385	C₂²×C₁₃	1	2	yes	—
455	#385	C₂²×C₁₃	1	2	yes	—
456	#385	C₂²×C₁₃	1	2	yes	—
457	#384	C₂²×C₁₃	1	1	yes	characteristic
458	#384	C₂²×C₁₃	1	2	yes	—
459	#382	C₂²×C₁₃	1	1	yes	characteristic
460	#381	C₂²×C₁₃	1	2	yes	—
461	#380	C₂²×C₁₃	1	1	yes	characteristic
462	#380	C₂²×C₁₃	1	1	yes	characteristic
463	#380	C₂²×C₁₃	1	2	yes	—
464	#380	C₂²×C₁₃	1	2	yes	—
465	#380	C₂²×C₁₃	1	2	yes	—
466	#380	C₂²×C₁₃	1	1	yes	characteristic
467	#380	C₂²×C₁₃	1	1	yes	characteristic
468	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
469	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
470	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
473	C₂²×C₁₃	—	2	2	no	—
474	C₂²×C₁₃	—	2	2	no	—
475	C₂²×C₁₃	—	2	2	no	—
476	C₂²×C₁₃	—	2	2	no	—
477	C₂²×C₁₃	—	2	2	no	—
478	C₂²×C₁₃	—	2	2	no	—
479	C₂²×C₁₃	#544	1	4	yes	—
480	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
481	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
485	C₂²×C₁₃	#585	1	1	yes	characteristic
486	C₂²×C₁₃	#585	1	1	yes	characteristic
487	C₄×C₁₃	—	2	4	no	—
488	C₄×C₁₃	—	2	2	no	—
489	C₄×C₁₃	—	2	2	no	—
490	C₄×C₁₃	—	2	4	no	—
491	C₄×C₁₃	—	2	2	no	—
492	C₄×C₁₃	—	2	2	no	—
493	C₄×C₁₃	—	4	1	no	—
494	C₄×C₁₃	—	4	2	no	—
495	C₄×C₁₃	—	4	2	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	—	4	2	no	—
498	C₄×C₁₃	—	4	2	no	—
499	C₄×C₁₃	—	4	1	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	—	4	2	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	—	4	2	no	—
504	C₄×C₁₃	—	4	2	no	—
505	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
506	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
507	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₄⋊Q₈	—	4	2	no	—
515	C₄⋊Q₈	—	4	4	no	—
516	#125	—	4	2	no	—
517	C₂²⋊Q₈	—	4	4	no	—
518	C₂²⋊Q₈	—	4	4	no	—
519	#117	—	4	4	no	—
520	C₂×C₄⋊C₄	—	4	2	no	—
521	C₂×C₄⋊C₄	Q₈×C₁₃	1	8	yes	complemented
522	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₄²	—	4	2	no	—
561	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
566	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
569	#95	C₂³×C₁₃	1	2	yes	—
570	#95	C₂³×C₁₃	1	2	yes	—
571	#95	C₂³×C₁₃	1	2	yes	—
572	#95	C₂³×C₁₃	1	2	yes	—
573	#95	C₂³×C₁₃	1	2	yes	—
574	#95	C₂³×C₁₃	1	2	yes	—
575	#95	C₂³×C₁₃	1	2	yes	—
576	#95	C₂³×C₁₃	1	2	yes	—
577	#95	C₂³×C₁₃	1	2	yes	—
578	#95	C₂³×C₁₃	1	2	yes	—
579	#95	C₂³×C₁₃	1	2	yes	—
580	#95	C₂³×C₁₃	1	2	yes	—
581	#95	C₂³×C₁₃	1	2	yes	—
582	#95	C₂³×C₁₃	1	2	yes	—
583	#95	C₂³×C₁₃	1	2	yes	—
584	#95	C₂³×C₁₃	1	2	yes	—
585	#95	C₂³×C₁₃	1	2	yes	—
586	#95	C₂³×C₁₃	1	2	yes	—
587	#95	C₂³×C₁₃	1	2	yes	—
588	#95	C₂³×C₁₃	1	2	yes	—
589	#95	C₂³×C₁₃	1	2	yes	—
590	#95	C₂³×C₁₃	1	2	yes	—
591	#95	C₂³×C₁₃	1	2	yes	—
592	#95	C₂³×C₁₃	1	2	yes	—
593	#95	C₂³×C₁₃	1	2	yes	—
594	#95	C₂³×C₁₃	1	2	yes	—
595	#95	C₂³×C₁₃	1	2	yes	—
596	#95	C₂³×C₁₃	1	2	yes	—
597	#95	C₂³×C₁₃	1	2	yes	—
598	#95	C₂³×C₁₃	1	2	yes	—
599	#95	C₂³×C₁₃	1	2	yes	—
600	#95	C₂³×C₁₃	1	2	yes	—
601	C₂×C₁₃	—	2	4	no	—
602	C₂×C₁₃	C₂×#544	1	1	yes	characteristic
603	C₂×C₁₃	#3501	1	1	yes	characteristic
604	C₂×C₁₃	#3502	1	1	yes	characteristic
605	C₂×C₁₃	#3534	1	1	yes	characteristic
606	C₂×C₁₃	#3538	1	1	yes	characteristic
607	C₂×C₁₃	#3559	1	1	yes	characteristic
608	C₂×C₁₃	#3564	1	1	yes	characteristic
609	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	4	1	no	—
625	C₂²×C₄	—	4	1	no	—
626	C₂²×C₄	—	4	1	no	—
627	C₂²×C₄	—	4	1	no	—
628	C₂²×C₄	—	4	1	no	—
629	C₂²×C₄	—	4	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	no	—
633	C₂²×C₄	—	4	1	no	—
634	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
635	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
636	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
637	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	1	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	—	4	2	no	—
671	C₄⋊C₄	—	4	1	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	1	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	—	4	1	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	—	4	1	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
688	C₄⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	4	1	no	—
696	C₄²	—	4	1	no	—
697	C₄²	—	4	2	no	—
698	C₄²	—	4	2	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	2	no	—
701	C₁₃	#36752	1	1	yes	characteristic, direct product factor, Sylow
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
707	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
708	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
709	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
710	Q₈	—	8	4	no	—
711	Q₈	—	8	4	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	8	2	no	—
766	C₂×C₄	—	8	2	no	—
767	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
768	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
769	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
770	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
771	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
772	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	C₁₃×#544	1	4	yes	—
780	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
781	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
782	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
783	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
784	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
785	C₂²	C₁₃×#585	1	1	yes	characteristic
786	C₂²	C₁₃×#585	1	1	yes	characteristic
787	C₄	—	2	2	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	4	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	4	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₂	—	2	4	no	—
806	C₂	C₂×C₁₃×#544	1	1	yes	characteristic
807	C₂	C₁₃×#3501	1	1	yes	characteristic
808	C₂	C₁₃×#3502	1	1	yes	characteristic
809	C₂	C₁₃×#3534	1	1	yes	characteristic
810	C₂	C₁₃×#3538	1	1	yes	characteristic
811	C₂	C₁₃×#3559	1	1	yes	characteristic
812	C₂	C₁₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2805	C₂	semidirect
4. C₁₃×#2802	C₂	semidirect
5. C₁₃×#2792	C₂	semidirect
6. C₁₃×#2791	C₂	semidirect
7. C₁₃×#2791	C₂	semidirect
8. C₁₃×#2755	C₂	semidirect
9. C₁₃×#2734	C₂	semidirect
10. C₁₃×#2713	C₂	semidirect
123. C₂×C₁₃×C₄⋊C₄	Q₈	semidirect
203. #36752	C₁₃	direct (N × H)
298. #2805	C₂×C₁₃	semidirect
299. #2802	C₂×C₁₃	semidirect
300. #2792	C₂×C₁₃	semidirect
301. #2791	C₂×C₁₃	semidirect
302. #2791	C₂×C₁₃	semidirect
303. #2755	C₂×C₁₃	semidirect
304. #2734	C₂×C₁₃	semidirect
305. #2713	C₂×C₁₃	semidirect
521. C₂×C₄⋊C₄	Q₈×C₁₃	semidirect
701. C₁₃	#36752	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×#2857	2
C₁₃×#2851	2
C₁₃×#2805	2
C₁₃×#2802	2
C₁₃×#2792	2
C₁₃×#2791	2
C₁₃×#2755	2
C₁₃×#2734	2
C₁₃×#2713	2
C₁₃×#2659	2
C₁₃×#2646	2
C₁₃×#2569	2
C₁₃×#2440	2
C₁₃×#2438	2
C₁₃×#2316	2
C₁₃×#2313	2
C₂×C₁₃×#387	2
#36752	13

Subgroups — C13×#36752 #15723091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36752 #15723091