Subgroups — C₁₃×#34528 #15720867

Order 3328.

2008 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#563	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2382	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2379	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2365	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2362	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2359	C₂	1	2	yes	maximal
11	C₁₃×#2335	C₂	1	2	yes	maximal
12	C₁₃×#2334	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2334	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2331	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
20	C₁₃×#563	C₄	1	16	yes	complemented
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#126	C₂²	1	2	yes	—
23	C₂×C₁₃×#126	C₂²	1	2	yes	—
24	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#123	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₁₃×#391	C₂²	1	1	yes	characteristic
35	C₁₃×#391	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#391	C₂²	1	2	yes	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#390	C₂²	1	1	yes	characteristic
40	C₁₃×#389	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	2	yes	—
45	C₁₃×#389	C₂²	1	2	yes	—
46	C₁₃×#389	C₂²	1	2	yes	—
47	C₁₃×#389	C₂²	1	2	yes	—
48	C₁₃×#389	C₂²	1	2	yes	—
49	C₁₃×#389	C₂²	1	2	yes	—
50	C₁₃×#388	C₂²	1	2	yes	—
51	C₁₃×#388	C₂²	1	2	yes	—
52	C₁₃×#388	C₂²	1	2	yes	—
53	C₁₃×#388	C₂²	1	2	yes	—
54	C₁₃×#388	C₂²	1	2	yes	—
55	C₁₃×#388	C₂²	1	2	yes	—
56	C₁₃×#388	C₂²	1	2	yes	—
57	C₁₃×#388	C₂²	1	2	yes	—
58	C₁₃×#388	C₂²	1	2	yes	—
59	C₁₃×#388	C₂²	1	2	yes	—
60	C₁₃×#387	C₂²	1	2	yes	—
61	C₁₃×#387	C₂²	1	2	yes	—
62	C₁₃×#387	C₂²	1	2	yes	—
63	C₁₃×#387	C₂²	1	2	yes	—
64	C₁₃×#387	C₂²	1	2	yes	—
65	C₁₃×#387	C₂²	1	2	yes	—
66	C₁₃×#387	C₂²	1	2	yes	—
67	C₁₃×#387	C₂²	1	2	yes	—
68	C₁₃×#387	C₂²	1	2	yes	—
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×#386	C₂²	1	2	yes	—
77	C₁₃×#385	C₂²	1	2	yes	—
78	C₁₃×#385	C₂²	1	2	yes	—
79	C₁₃×#385	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#382	C₂²	1	1	yes	characteristic
83	C₁₃×#382	C₂²	1	1	yes	characteristic
84	C₁₃×#382	C₂²	1	1	yes	characteristic
85	C₁₃×#382	C₂²	1	2	yes	—
86	C₁₃×#380	C₂²	1	2	yes	—
87	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
88	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
89	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₁₃×#376	C₂²	1	2	yes	—
106	C₂×C₁₃×#95	C₂²	1	2	yes	—
107	C₄³×C₁₃	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
115	C₁₃×#126	C₂×C₄	1	16	yes	complemented
116	C₁₃×#126	C₂×C₄	1	16	yes	complemented
117	C₁₃×#125	C₂×C₄	1	8	yes	complemented
118	C₁₃×#125	C₂×C₄	1	8	yes	complemented
119	C₁₃×#124	C₂×C₄	1	8	yes	—
120	C₁₃×#123	C₂×C₄	1	16	yes	—
121	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
122	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
123	C₄×Q₈×C₁₃	—	4	4	no	—
124	C₄×Q₈×C₁₃	—	4	2	no	—
125	C₄×D₄×C₁₃	—	4	2	no	—
126	C₁₃×#117	—	4	4	no	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#95	C₂³	1	2	yes	—
208	#34528	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₁₃	—	4	2	no	—
211	C₂×Q₈×C₁₃	—	4	1	no	—
212	C₂×Q₈×C₁₃	—	4	2	no	—
213	C₂×Q₈×C₁₃	—	4	1	no	—
214	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
215	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
216	C₂×D₄×C₁₃	—	4	1	no	—
217	C₂×D₄×C₁₃	—	4	1	no	—
218	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	4	2	no	—
221	C₂²×C₄×C₁₃	—	4	2	no	—
222	C₂²×C₄×C₁₃	—	4	2	no	—
223	C₂²×C₄×C₁₃	—	4	2	no	—
224	C₂²×C₄×C₁₃	—	4	2	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	4	2	no	—
227	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	4	2	no	—
250	C₁₃×C₄⋊C₄	—	4	2	no	—
251	C₁₃×C₄⋊C₄	—	4	1	no	—
252	C₁₃×C₄⋊C₄	—	4	1	no	—
253	C₁₃×C₄⋊C₄	—	4	2	no	—
254	C₁₃×C₄⋊C₄	—	4	1	no	—
255	C₁₃×C₄⋊C₄	—	4	1	no	—
256	C₁₃×C₄⋊C₄	—	4	2	no	—
257	C₁₃×C₄⋊C₄	—	4	2	no	—
258	C₁₃×C₄⋊C₄	—	4	2	no	—
259	C₁₃×C₄⋊C₄	—	4	1	no	—
260	C₁₃×C₄⋊C₄	—	4	2	no	—
261	C₁₃×C₄⋊C₄	—	4	1	no	—
262	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
263	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
264	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
265	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
266	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
267	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
268	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
269	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
270	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
271	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	4	2	no	—
275	C₁₃×C₂²⋊C₄	—	4	2	no	—
276	C₁₃×C₂²⋊C₄	—	4	2	no	—
277	C₁₃×C₂²⋊C₄	—	4	2	no	—
278	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
279	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
280	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
281	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
282	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
283	C₄²×C₁₃	—	2	4	no	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	—	2	2	no	—
286	C₄²×C₁₃	—	2	2	no	—
287	C₄²×C₁₃	—	2	4	no	—
288	C₄²×C₁₃	—	4	2	no	—
289	C₄²×C₁₃	—	4	1	no	—
290	C₄²×C₁₃	—	4	2	no	—
291	C₄²×C₁₃	—	4	1	no	—
292	C₄²×C₁₃	—	4	2	no	—
293	C₄²×C₁₃	—	4	1	no	—
294	C₄²×C₁₃	—	4	2	no	—
295	C₄²×C₁₃	—	4	2	no	—
296	C₄²×C₁₃	—	4	2	no	—
297	C₄²×C₁₃	—	4	2	no	—
298	C₄²×C₁₃	—	4	2	no	—
299	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
300	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
301	C₂×#563	C₂×C₁₃	1	1	yes	characteristic
302	#2382	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2382	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2379	C₂×C₁₃	1	1	yes	characteristic
305	#2373	C₂×C₁₃	1	2	yes	complemented
306	#2373	C₂×C₁₃	1	2	yes	complemented
307	#2368	C₂×C₁₃	1	2	yes	complemented
308	#2365	C₂×C₁₃	1	2	yes	complemented
309	#2362	C₂×C₁₃	1	2	yes	complemented
310	#2359	C₂×C₁₃	1	2	yes	—
311	#2335	C₂×C₁₃	1	2	yes	—
312	#2334	C₂×C₁₃	1	2	yes	complemented
313	#2334	C₂×C₁₃	1	2	yes	complemented
314	#2331	C₂×C₁₃	1	2	yes	complemented
315	#2329	C₂×C₁₃	1	2	yes	complemented
316	#2323	C₂×C₁₃	1	2	yes	complemented
317	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
318	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
319	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
327	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
328	Q₈×C₁₃	—	4	8	no	—
329	Q₈×C₁₃	—	4	4	no	—
330	D₄×C₁₃	—	4	4	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	2	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	1	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	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	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	—	4	8	no	—
375	C₂×C₄×C₁₃	—	8	4	no	—
376	C₂×C₄×C₁₃	—	8	4	no	—
377	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
378	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
379	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
380	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
381	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
382	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
383	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
384	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
385	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
386	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
387	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
388	#563	C₄×C₁₃	1	16	yes	complemented
389	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
390	C₂×#126	C₂²×C₁₃	1	2	yes	—
391	C₂×#126	C₂²×C₁₃	1	2	yes	—
392	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#123	C₂²×C₁₃	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
397	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
398	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
399	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#117	C₂²×C₁₃	1	2	yes	—
402	#391	C₂²×C₁₃	1	2	yes	—
403	#391	C₂²×C₁₃	1	2	yes	—
404	#391	C₂²×C₁₃	1	1	yes	characteristic
405	#391	C₂²×C₁₃	1	2	yes	—
406	#391	C₂²×C₁₃	1	2	yes	—
407	#390	C₂²×C₁₃	1	1	yes	characteristic
408	#389	C₂²×C₁₃	1	1	yes	characteristic
409	#389	C₂²×C₁₃	1	1	yes	characteristic
410	#389	C₂²×C₁₃	1	1	yes	characteristic
411	#389	C₂²×C₁₃	1	1	yes	characteristic
412	#389	C₂²×C₁₃	1	2	yes	—
413	#389	C₂²×C₁₃	1	2	yes	—
414	#389	C₂²×C₁₃	1	2	yes	—
415	#389	C₂²×C₁₃	1	2	yes	—
416	#389	C₂²×C₁₃	1	2	yes	—
417	#389	C₂²×C₁₃	1	2	yes	—
418	#388	C₂²×C₁₃	1	2	yes	—
419	#388	C₂²×C₁₃	1	2	yes	—
420	#388	C₂²×C₁₃	1	2	yes	—
421	#388	C₂²×C₁₃	1	2	yes	—
422	#388	C₂²×C₁₃	1	2	yes	—
423	#388	C₂²×C₁₃	1	2	yes	—
424	#388	C₂²×C₁₃	1	2	yes	—
425	#388	C₂²×C₁₃	1	2	yes	—
426	#388	C₂²×C₁₃	1	2	yes	—
427	#388	C₂²×C₁₃	1	2	yes	—
428	#387	C₂²×C₁₃	1	2	yes	—
429	#387	C₂²×C₁₃	1	2	yes	—
430	#387	C₂²×C₁₃	1	2	yes	—
431	#387	C₂²×C₁₃	1	2	yes	—
432	#387	C₂²×C₁₃	1	2	yes	—
433	#387	C₂²×C₁₃	1	2	yes	—
434	#387	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	#386	C₂²×C₁₃	1	2	yes	—
445	#385	C₂²×C₁₃	1	2	yes	—
446	#385	C₂²×C₁₃	1	2	yes	—
447	#385	C₂²×C₁₃	1	2	yes	—
448	#385	C₂²×C₁₃	1	2	yes	—
449	#385	C₂²×C₁₃	1	2	yes	—
450	#382	C₂²×C₁₃	1	1	yes	characteristic
451	#382	C₂²×C₁₃	1	1	yes	characteristic
452	#382	C₂²×C₁₃	1	2	yes	—
453	#382	C₂²×C₁₃	1	1	yes	characteristic
454	#380	C₂²×C₁₃	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
461	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
463	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
467	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
473	#376	C₂²×C₁₃	1	2	yes	—
474	C₂×#95	C₂²×C₁₃	1	2	yes	—
475	C₄³	C₂²×C₁₃	1	1	yes	characteristic
476	C₂²×C₁₃	—	2	4	no	—
477	C₂²×C₁₃	—	2	4	no	—
478	C₂²×C₁₃	—	2	4	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	2	no	—
481	C₂²×C₁₃	—	4	2	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
484	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
485	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
486	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
487	C₂²×C₁₃	#585	1	1	yes	characteristic
488	C₂²×C₁₃	#585	1	1	yes	characteristic
489	C₂²×C₁₃	#585	1	1	yes	characteristic
490	C₄×C₁₃	—	2	4	no	—
491	C₄×C₁₃	—	2	4	no	—
492	C₄×C₁₃	—	2	2	no	—
493	C₄×C₁₃	—	2	4	no	—
494	C₄×C₁₃	—	2	2	no	—
495	C₄×C₁₃	—	2	4	no	—
496	C₄×C₁₃	—	2	2	no	—
497	C₄×C₁₃	—	2	4	no	—
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	2	2	no	—
500	C₄×C₁₃	—	2	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	C₄×C₁₃	—	4	1	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	2	no	—
508	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
509	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
512	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
513	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
514	C₄⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
515	#126	C₂×C₄×C₁₃	1	16	yes	complemented
516	#126	C₂×C₄×C₁₃	1	16	yes	complemented
517	#125	C₂×C₄×C₁₃	1	8	yes	complemented
518	#125	C₂×C₄×C₁₃	1	8	yes	complemented
519	#124	C₂×C₄×C₁₃	1	8	yes	—
520	#123	C₂×C₄×C₁₃	1	16	yes	—
521	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
522	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
523	C₄×Q₈	—	4	4	no	—
524	C₄×Q₈	—	4	2	no	—
525	C₄×D₄	—	4	2	no	—
526	#117	—	4	4	no	—
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	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂×C₂²⋊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×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
572	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
579	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₄²	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	#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	C₂×C₁₃	—	4	4	no	—
609	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
611	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
612	C₂×C₁₃	#3559	1	1	yes	characteristic
613	C₂×C₁₃	#3561	1	1	yes	characteristic
614	C₂×C₁₃	#3563	1	1	yes	characteristic
615	C₂×C₁₃	#3568	1	1	yes	characteristic
616	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
617	C₂×Q₈	—	4	2	no	—
618	C₂×Q₈	—	4	1	no	—
619	C₂×Q₈	—	4	2	no	—
620	C₂×Q₈	—	4	1	no	—
621	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
622	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
623	C₂×D₄	—	4	1	no	—
624	C₂×D₄	—	4	1	no	—
625	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	2	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
635	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
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	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	1	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	1	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	1	no	—
663	C₄⋊C₄	—	4	1	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	1	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
670	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
671	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
672	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
673	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
674	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
675	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
676	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
677	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
678	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	2	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	2	no	—
685	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
686	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
687	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
688	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
689	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	4	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₄²	—	4	2	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	1	no	—
701	C₄²	—	4	2	no	—
702	C₄²	—	4	1	no	—
703	C₄²	—	4	2	no	—
704	C₄²	—	4	1	no	—
705	C₄²	—	4	2	no	—
706	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
707	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
708	C₁₃	#34528	1	1	yes	characteristic, direct product factor, Sylow
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
716	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
717	Q₈	—	4	8	no	—
718	Q₈	—	4	4	no	—
719	D₄	—	4	4	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	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	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	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	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	—	8	4	no	—
765	C₂×C₄	—	8	4	no	—
766	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
767	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
768	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
769	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
770	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
771	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
772	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
773	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
774	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
775	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
776	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
777	C₂²	—	2	4	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
785	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
786	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
787	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
788	C₂²	C₁₃×#585	1	1	yes	characteristic
789	C₂²	C₁₃×#585	1	1	yes	characteristic
790	C₂²	C₁₃×#585	1	1	yes	characteristic
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	4	no	—
795	C₄	—	2	4	no	—
796	C₄	—	2	2	no	—
797	C₄	—	2	4	no	—
798	C₄	—	2	2	no	—
799	C₄	—	2	4	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	4	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₂	—	4	4	no	—
810	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
811	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
812	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
813	C₂	C₁₃×#3559	1	1	yes	characteristic
814	C₂	C₁₃×#3561	1	1	yes	characteristic
815	C₂	C₁₃×#3563	1	1	yes	characteristic
816	C₂	C₁₃×#3568	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2382	C₂	semidirect
3. C₁₃×#2382	C₂	semidirect
5. C₁₃×#2373	C₂	semidirect
6. C₁₃×#2373	C₂	semidirect
7. C₁₃×#2368	C₂	semidirect
8. C₁₃×#2365	C₂	semidirect
9. C₁₃×#2362	C₂	semidirect
12. C₁₃×#2334	C₂	semidirect
13. C₁₃×#2334	C₂	semidirect
14. C₁₃×#2331	C₂	semidirect
15. C₁₃×#2329	C₂	semidirect
16. C₁₃×#2323	C₂	semidirect
17. C₄×C₁₃×#125	C₂	semidirect
18. C₄×C₁₃×#125	C₂	semidirect
20. C₁₃×#563	C₄	semidirect
114. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
115. C₁₃×#126	C₂×C₄	semidirect
116. C₁₃×#126	C₂×C₄	semidirect
117. C₁₃×#125	C₂×C₄	semidirect
118. C₁₃×#125	C₂×C₄	semidirect
121. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
122. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
208. #34528	C₁₃	direct (N × H)
302. #2382	C₂×C₁₃	semidirect
303. #2382	C₂×C₁₃	semidirect
305. #2373	C₂×C₁₃	semidirect
306. #2373	C₂×C₁₃	semidirect
307. #2368	C₂×C₁₃	semidirect
308. #2365	C₂×C₁₃	semidirect
309. #2362	C₂×C₁₃	semidirect
312. #2334	C₂×C₁₃	semidirect
313. #2334	C₂×C₁₃	semidirect
314. #2331	C₂×C₁₃	semidirect
315. #2329	C₂×C₁₃	semidirect
316. #2323	C₂×C₁₃	semidirect
317. C₄×#125	C₂×C₁₃	semidirect
318. C₄×#125	C₂×C₁₃	semidirect
388. #563	C₄×C₁₃	semidirect
514. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
515. #126	C₂×C₄×C₁₃	semidirect
516. #126	C₂×C₄×C₁₃	semidirect
517. #125	C₂×C₄×C₁₃	semidirect
518. #125	C₂×C₄×C₁₃	semidirect
521. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
522. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
708. C₁₃	#34528	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#563	2
C₁₃×#2382	2
C₁₃×#2379	2
C₁₃×#2373	2
C₁₃×#2368	2
C₁₃×#2365	2
C₁₃×#2362	2
C₁₃×#2359	2
C₁₃×#2335	2
C₁₃×#2334	2
C₁₃×#2331	2
C₁₃×#2329	2
C₁₃×#2323	2
C₄×C₁₃×#125	2
C₄×C₁₃×#124	2
#34528	13

Subgroups — C13×#34528 #15720867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34528 #15720867