Subgroups — C₁₃×#36819 #15723158

Order 3328.

1680 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2851	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2786	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2761	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2755	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2750	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2715	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2713	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2707	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2695	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2652	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2608	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2587	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2583	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2478	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2432	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#2406	C₂	1	1	yes	maximal, characteristic
17	C₁₃×#2332	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#125	C₂²	1	2	yes	—
24	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
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×#397	C₂²	1	2	yes	—
41	C₁₃×#397	C₂²	1	2	yes	—
42	C₁₃×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	2	yes	—
44	C₁₃×#397	C₂²	1	2	yes	—
45	C₁₃×#396	C₂²	1	2	yes	—
46	C₁₃×#396	C₂²	1	2	yes	—
47	C₁₃×#396	C₂²	1	2	yes	—
48	C₁₃×#396	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#395	C₂²	1	2	yes	—
51	C₁₃×#395	C₂²	1	2	yes	—
52	C₁₃×#394	C₂²	1	2	yes	—
53	C₁₃×#394	C₂²	1	2	yes	—
54	C₁₃×#394	C₂²	1	2	yes	—
55	C₁₃×#391	C₂²	1	1	yes	characteristic
56	C₁₃×#391	C₂²	1	2	yes	—
57	C₁₃×#391	C₂²	1	2	yes	—
58	C₁₃×#390	C₂²	1	2	yes	—
59	C₁₃×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#389	C₂²	1	2	yes	—
61	C₁₃×#389	C₂²	1	2	yes	—
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	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	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×#386	C₂²	1	1	yes	characteristic
84	C₁₃×#386	C₂²	1	2	yes	—
85	C₁₃×#386	C₂²	1	1	yes	characteristic
86	C₁₃×#386	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×#385	C₂²	1	2	yes	—
92	C₁₃×#385	C₂²	1	2	yes	—
93	C₁₃×#385	C₂²	1	2	yes	—
94	C₁₃×#385	C₂²	1	2	yes	—
95	C₁₃×#382	C₂²	1	2	yes	—
96	C₁₃×#381	C₂²	1	2	yes	—
97	C₁₃×#381	C₂²	1	1	yes	characteristic
98	C₁₃×#380	C₂²	1	2	yes	—
99	C₁₃×#380	C₂²	1	2	yes	—
100	C₁₃×#380	C₂²	1	2	yes	—
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
107	C₂×C₁₃×#41	—	2	4	no	—
108	C₂×C₁₃×#41	—	4	2	no	—
109	C₂×C₁₃×#41	—	4	2	no	—
110	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	—	4	2	no	—
122	C₁₃×#126	—	4	4	no	—
123	C₁₃×#125	—	4	4	no	—
124	C₁₃×#124	—	4	2	no	—
125	C₁₃×#123	—	4	2	no	—
126	C₁₃×#123	—	4	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	4	no	—
128	C₁₃×#117	—	4	2	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊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×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	—	4	2	no	—
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	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	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	#36819	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₁₃×#41	—	4	16	no	—
212	C₂×Q₈×C₁₃	—	2	2	no	—
213	C₂×Q₈×C₁₃	—	2	2	no	—
214	C₂×Q₈×C₁₃	—	2	2	no	—
215	C₂×Q₈×C₁₃	—	4	1	no	—
216	C₂×Q₈×C₁₃	—	4	1	no	—
217	C₂×Q₈×C₁₃	—	4	1	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	2	2	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	2	2	no	—
222	C₂×D₄×C₁₃	—	2	2	no	—
223	C₂×D₄×C₁₃	—	2	2	no	—
224	C₂×D₄×C₁₃	—	4	1	no	—
225	C₂×D₄×C₁₃	—	4	1	no	—
226	C₂×D₄×C₁₃	—	4	1	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	4	2	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	2	no	—
237	C₂²×C₄×C₁₃	—	4	1	no	—
238	C₂²×C₄×C₁₃	—	4	1	no	—
239	C₂²×C₄×C₁₃	—	4	1	no	—
240	C₂²×C₄×C₁₃	—	4	1	no	—
241	C₂²×C₄×C₁₃	—	4	1	no	—
242	C₂²×C₄×C₁₃	—	4	1	no	—
243	C₂²×C₄×C₁₃	#41	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	4	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	2	no	—
275	C₁₃×C₄⋊C₄	—	4	2	no	—
276	C₁₃×C₄⋊C₄	—	4	2	no	—
277	C₁₃×C₄⋊C₄	—	4	2	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	2	no	—
280	C₁₃×C₄⋊C₄	—	4	2	no	—
281	C₁₃×C₄⋊C₄	—	4	2	no	—
282	C₁₃×C₄⋊C₄	—	4	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
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	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	4	2	no	—
290	C₁₃×C₂²⋊C₄	—	4	2	no	—
291	C₁₃×C₂²⋊C₄	—	4	2	no	—
292	C₁₃×C₂²⋊C₄	—	4	2	no	—
293	C₁₃×C₂²⋊C₄	—	4	2	no	—
294	C₁₃×C₂²⋊C₄	—	4	2	no	—
295	C₁₃×C₂²⋊C₄	—	4	2	no	—
296	C₁₃×C₂²⋊C₄	—	4	1	no	—
297	C₁₃×C₂²⋊C₄	—	4	1	no	—
298	C₁₃×C₂²⋊C₄	—	4	2	no	—
299	C₁₃×C₂²⋊C₄	—	4	2	no	—
300	C₄²×C₁₃	—	2	4	no	—
301	C₄²×C₁₃	—	4	1	no	—
302	C₄²×C₁₃	—	4	1	no	—
303	C₄²×C₁₃	—	4	2	no	—
304	C₄²×C₁₃	—	4	1	no	—
305	C₄²×C₁₃	—	4	1	no	—
306	C₄²×C₁₃	—	4	1	no	—
307	C₄²×C₁₃	—	4	2	no	—
308	C₄²×C₁₃	—	4	1	no	—
309	#2851	C₂×C₁₃	1	2	yes	complemented
310	#2786	C₂×C₁₃	1	2	yes	complemented
311	#2761	C₂×C₁₃	1	2	yes	complemented
312	#2755	C₂×C₁₃	1	2	yes	complemented
313	#2750	C₂×C₁₃	1	2	yes	complemented
314	#2715	C₂×C₁₃	1	2	yes	complemented
315	#2713	C₂×C₁₃	1	2	yes	complemented
316	#2707	C₂×C₁₃	1	2	yes	complemented
317	#2695	C₂×C₁₃	1	2	yes	complemented
318	#2652	C₂×C₁₃	1	2	yes	complemented
319	#2608	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#2587	C₂×C₁₃	1	2	yes	complemented
321	#2583	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#2478	C₂×C₁₃	1	2	yes	complemented
323	#2432	C₂×C₁₃	1	1	yes	characteristic
324	#2406	C₂×C₁₃	1	1	yes	characteristic
325	#2332	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#2313	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#2297	C₂×C₁₃	1	1	yes	characteristic
328	C₂³×C₁₃	—	2	1	no	—
329	C₂³×C₁₃	—	2	1	no	—
330	C₂³×C₁₃	—	2	1	no	—
331	C₂³×C₁₃	—	2	1	no	—
332	C₂³×C₁₃	—	2	2	no	—
333	C₂³×C₁₃	—	2	2	no	—
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	2	no	—
336	C₂³×C₁₃	—	2	1	no	—
337	C₂³×C₁₃	—	2	1	no	—
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	C₂×#41	1	2	yes	—
342	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
343	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
344	Q₈×C₁₃	—	4	4	no	—
345	Q₈×C₁₃	—	8	2	no	—
346	D₄×C₁₃	—	4	4	no	—
347	D₄×C₁₃	—	4	4	no	—
348	D₄×C₁₃	—	4	4	no	—
349	C₂×C₄×C₁₃	—	2	8	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	1	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	—	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	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	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	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	8	no	—
396	C₂×C₄×C₁₃	—	4	4	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	8	2	no	—
399	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
400	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
401	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
403	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#126	C₂²×C₁₃	1	2	yes	—
406	C₂×#125	C₂²×C₁₃	1	2	yes	—
407	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
412	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
413	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
414	#400	C₂²×C₁₃	1	2	yes	—
415	#400	C₂²×C₁₃	1	2	yes	—
416	#400	C₂²×C₁₃	1	2	yes	—
417	#400	C₂²×C₁₃	1	2	yes	—
418	#398	C₂²×C₁₃	1	2	yes	—
419	#398	C₂²×C₁₃	1	2	yes	—
420	#398	C₂²×C₁₃	1	2	yes	—
421	#398	C₂²×C₁₃	1	2	yes	—
422	#398	C₂²×C₁₃	1	2	yes	—
423	#397	C₂²×C₁₃	1	2	yes	—
424	#397	C₂²×C₁₃	1	2	yes	—
425	#397	C₂²×C₁₃	1	2	yes	—
426	#397	C₂²×C₁₃	1	2	yes	—
427	#397	C₂²×C₁₃	1	2	yes	—
428	#396	C₂²×C₁₃	1	2	yes	—
429	#396	C₂²×C₁₃	1	2	yes	—
430	#396	C₂²×C₁₃	1	2	yes	—
431	#396	C₂²×C₁₃	1	2	yes	—
432	#396	C₂²×C₁₃	1	2	yes	—
433	#395	C₂²×C₁₃	1	2	yes	—
434	#395	C₂²×C₁₃	1	2	yes	—
435	#394	C₂²×C₁₃	1	2	yes	—
436	#394	C₂²×C₁₃	1	2	yes	—
437	#394	C₂²×C₁₃	1	2	yes	—
438	#391	C₂²×C₁₃	1	2	yes	—
439	#391	C₂²×C₁₃	1	1	yes	characteristic
440	#391	C₂²×C₁₃	1	2	yes	—
441	#390	C₂²×C₁₃	1	1	yes	characteristic
442	#390	C₂²×C₁₃	1	2	yes	—
443	#389	C₂²×C₁₃	1	2	yes	—
444	#389	C₂²×C₁₃	1	2	yes	—
445	#389	C₂²×C₁₃	1	2	yes	—
446	#389	C₂²×C₁₃	1	2	yes	—
447	#389	C₂²×C₁₃	1	2	yes	—
448	#389	C₂²×C₁₃	1	2	yes	—
449	#388	C₂²×C₁₃	1	2	yes	—
450	#388	C₂²×C₁₃	1	2	yes	—
451	#388	C₂²×C₁₃	1	2	yes	—
452	#388	C₂²×C₁₃	1	2	yes	—
453	#388	C₂²×C₁₃	1	2	yes	—
454	#387	C₂²×C₁₃	1	2	yes	—
455	#387	C₂²×C₁₃	1	2	yes	—
456	#387	C₂²×C₁₃	1	2	yes	—
457	#387	C₂²×C₁₃	1	2	yes	—
458	#387	C₂²×C₁₃	1	2	yes	—
459	#387	C₂²×C₁₃	1	2	yes	—
460	#387	C₂²×C₁₃	1	2	yes	—
461	#387	C₂²×C₁₃	1	2	yes	—
462	#387	C₂²×C₁₃	1	2	yes	—
463	#387	C₂²×C₁₃	1	2	yes	—
464	#387	C₂²×C₁₃	1	2	yes	—
465	#387	C₂²×C₁₃	1	2	yes	—
466	#386	C₂²×C₁₃	1	1	yes	characteristic
467	#386	C₂²×C₁₃	1	1	yes	characteristic
468	#386	C₂²×C₁₃	1	2	yes	—
469	#386	C₂²×C₁₃	1	2	yes	—
470	#385	C₂²×C₁₃	1	2	yes	—
471	#385	C₂²×C₁₃	1	2	yes	—
472	#385	C₂²×C₁₃	1	2	yes	—
473	#385	C₂²×C₁₃	1	2	yes	—
474	#385	C₂²×C₁₃	1	2	yes	—
475	#385	C₂²×C₁₃	1	2	yes	—
476	#385	C₂²×C₁₃	1	2	yes	—
477	#385	C₂²×C₁₃	1	2	yes	—
478	#382	C₂²×C₁₃	1	2	yes	—
479	#381	C₂²×C₁₃	1	2	yes	—
480	#381	C₂²×C₁₃	1	1	yes	characteristic
481	#380	C₂²×C₁₃	1	2	yes	—
482	#380	C₂²×C₁₃	1	2	yes	—
483	#380	C₂²×C₁₃	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
486	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
487	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
489	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
490	C₂²×C₁₃	—	2	2	no	—
491	C₂²×C₁₃	—	2	2	no	—
492	C₂²×C₁₃	—	2	2	no	—
493	C₂²×C₁₃	—	2	2	no	—
494	C₂²×C₁₃	—	2	4	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	—	4	1	no	—
497	C₂²×C₁₃	—	4	2	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	1	no	—
501	C₂²×C₁₃	—	4	1	no	—
502	C₂²×C₁₃	—	4	1	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
506	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
509	C₂²×C₁₃	#585	1	2	yes	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	2	2	no	—
513	C₄×C₁₃	—	2	4	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	2	no	—
516	C₄×C₁₃	—	4	1	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	2	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	2	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₂×#41	—	2	4	no	—
527	C₂×#41	—	4	2	no	—
528	C₂×#41	—	4	2	no	—
529	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
530	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
539	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₄⋊Q₈	—	4	2	no	—
541	#126	—	4	4	no	—
542	#125	—	4	4	no	—
543	#124	—	4	2	no	—
544	#123	—	4	2	no	—
545	#123	—	4	2	no	—
546	C₂²⋊Q₈	—	2	4	no	—
547	#117	—	4	2	no	—
548	C₂×C₄⋊C₄	—	2	4	no	—
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	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₄²	—	4	2	no	—
590	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
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	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
599	#95	C₂³×C₁₃	1	2	yes	—
600	#95	C₂³×C₁₃	1	2	yes	—
601	#95	C₂³×C₁₃	1	2	yes	—
602	#95	C₂³×C₁₃	1	2	yes	—
603	#95	C₂³×C₁₃	1	2	yes	—
604	#95	C₂³×C₁₃	1	2	yes	—
605	#95	C₂³×C₁₃	1	2	yes	—
606	#95	C₂³×C₁₃	1	2	yes	—
607	#95	C₂³×C₁₃	1	2	yes	—
608	#95	C₂³×C₁₃	1	2	yes	—
609	#95	C₂³×C₁₃	1	2	yes	—
610	#95	C₂³×C₁₃	1	2	yes	—
611	#95	C₂³×C₁₃	1	2	yes	—
612	#95	C₂³×C₁₃	1	2	yes	—
613	#95	C₂³×C₁₃	1	2	yes	—
614	#95	C₂³×C₁₃	1	2	yes	—
615	#95	C₂³×C₁₃	1	2	yes	—
616	#95	C₂³×C₁₃	1	2	yes	—
617	#95	C₂³×C₁₃	1	2	yes	—
618	#95	C₂³×C₁₃	1	2	yes	—
619	#95	C₂³×C₁₃	1	2	yes	—
620	#95	C₂³×C₁₃	1	2	yes	—
621	#95	C₂³×C₁₃	1	2	yes	—
622	#95	C₂³×C₁₃	1	2	yes	—
623	#95	C₂³×C₁₃	1	2	yes	—
624	#95	C₂³×C₁₃	1	2	yes	—
625	#95	C₂³×C₁₃	1	2	yes	—
626	C₂×C₁₃	—	4	2	no	—
627	C₂×C₁₃	—	4	2	no	—
628	C₂×C₁₃	—	8	1	no	—
629	C₂×C₁₃	#3455	1	1	yes	characteristic
630	C₂×C₁₃	#3490	1	1	yes	characteristic
631	C₂×C₁₃	#3509	1	1	yes	characteristic
632	C₂×C₁₃	#3541	1	2	yes	—
633	C₂×C₁₃	#3559	1	2	yes	—
634	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
636	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
637	#41	—	4	16	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	2	2	no	—
641	C₂×Q₈	—	4	1	no	—
642	C₂×Q₈	—	4	1	no	—
643	C₂×Q₈	—	4	1	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	4	1	no	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	1	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	—	4	1	no	—
662	C₂²×C₄	—	4	1	no	—
663	C₂²×C₄	—	4	1	no	—
664	C₂²×C₄	—	4	1	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	C₁₃×#41	1	4	yes	—
670	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	4	1	no	—
716	C₂²⋊C₄	—	4	1	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	4	1	no	—
728	C₄²	—	4	1	no	—
729	C₄²	—	4	1	no	—
730	C₄²	—	4	1	no	—
731	C₄²	—	4	1	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	1	no	—
734	C₄²	—	4	2	no	—
735	C₁₃	#36819	1	1	yes	characteristic, direct product factor, Sylow
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	C₂×C₁₃×#41	1	2	yes	—
750	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
751	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
752	Q₈	—	4	4	no	—
753	Q₈	—	8	2	no	—
754	D₄	—	4	4	no	—
755	D₄	—	4	4	no	—
756	D₄	—	4	4	no	—
757	C₂×C₄	—	2	8	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	8	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
808	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
809	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
810	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
827	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
828	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
829	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
830	C₂²	C₁₃×#585	1	2	yes	—
831	C₄	—	2	4	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₂	—	4	2	no	—
848	C₂	—	4	2	no	—
849	C₂	—	8	1	no	—
850	C₂	C₁₃×#3455	1	1	yes	characteristic
851	C₂	C₁₃×#3490	1	1	yes	characteristic
852	C₂	C₁₃×#3509	1	1	yes	characteristic
853	C₂	C₁₃×#3541	1	2	yes	—
854	C₂	C₁₃×#3559	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
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
1. C₁₃×#2851	C₂	semidirect
2. C₁₃×#2786	C₂	semidirect
3. C₁₃×#2761	C₂	semidirect
4. C₁₃×#2755	C₂	semidirect
5. C₁₃×#2750	C₂	semidirect
6. C₁₃×#2715	C₂	semidirect
7. C₁₃×#2713	C₂	semidirect
8. C₁₃×#2707	C₂	semidirect
9. C₁₃×#2695	C₂	semidirect
10. C₁₃×#2652	C₂	semidirect
11. C₁₃×#2608	C₂	semidirect
12. C₁₃×#2587	C₂	semidirect
13. C₁₃×#2583	C₂	semidirect
14. C₁₃×#2478	C₂	semidirect
17. C₁₃×#2332	C₂	semidirect
18. C₁₃×#2313	C₂	semidirect
207. #36819	C₁₃	direct (N × H)
309. #2851	C₂×C₁₃	semidirect
310. #2786	C₂×C₁₃	semidirect
311. #2761	C₂×C₁₃	semidirect
312. #2755	C₂×C₁₃	semidirect
313. #2750	C₂×C₁₃	semidirect
314. #2715	C₂×C₁₃	semidirect
315. #2713	C₂×C₁₃	semidirect
316. #2707	C₂×C₁₃	semidirect
317. #2695	C₂×C₁₃	semidirect
318. #2652	C₂×C₁₃	semidirect
319. #2608	C₂×C₁₃	semidirect
320. #2587	C₂×C₁₃	semidirect
321. #2583	C₂×C₁₃	semidirect
322. #2478	C₂×C₁₃	semidirect
325. #2332	C₂×C₁₃	semidirect
326. #2313	C₂×C₁₃	semidirect
735. C₁₃	#36819	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×#2851	2
C₁₃×#2786	2
C₁₃×#2761	2
C₁₃×#2755	2
C₁₃×#2750	2
C₁₃×#2715	2
C₁₃×#2713	2
C₁₃×#2707	2
C₁₃×#2695	2
C₁₃×#2652	2
C₁₃×#2608	2
C₁₃×#2587	2
C₁₃×#2583	2
C₁₃×#2478	2
C₁₃×#2432	2
C₁₃×#2406	2
C₁₃×#2332	2
C₁₃×#2313	2
C₁₃×#2297	2
#36819	13

Subgroups — C13×#36819 #15723158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36819 #15723158