Subgroups — C₁₃×#34920 #15721259

Order 3328.

1692 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2590	C₂	1	2	yes	maximal
2	C₁₃×#2588	C₂	1	2	yes	maximal
3	C₁₃×#2584	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2581	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2565	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2550	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2520	C₂	1	2	yes	maximal
8	C₁₃×#2508	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2506	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2462	C₂	1	2	yes	maximal
11	C₁₃×#2453	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2451	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2402	C₂	1	2	yes	maximal
14	C₁₃×#2399	C₂	1	2	yes	maximal
15	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
16	C₄×C₁₃×#125	C₂	1	2	yes	maximal
17	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
18	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
19	C₁₃×#2295	C₂	1	2	yes	maximal
20	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
21	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
22	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
23	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#125	C₂²	1	2	yes	—
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#400	C₂²	1	2	yes	—
36	C₁₃×#400	C₂²	1	2	yes	—
37	C₁₃×#400	C₂²	1	2	yes	—
38	C₁₃×#400	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×#391	C₂²	1	2	yes	—
52	C₁₃×#391	C₂²	1	2	yes	—
53	C₁₃×#391	C₂²	1	2	yes	—
54	C₁₃×#391	C₂²	1	1	yes	characteristic
55	C₁₃×#391	C₂²	1	1	yes	characteristic
56	C₁₃×#391	C₂²	1	1	yes	characteristic
57	C₁₃×#391	C₂²	1	1	yes	characteristic
58	C₁₃×#389	C₂²	1	1	yes	characteristic
59	C₁₃×#389	C₂²	1	1	yes	characteristic
60	C₁₃×#389	C₂²	1	1	yes	characteristic
61	C₁₃×#389	C₂²	1	1	yes	characteristic
62	C₁₃×#389	C₂²	1	1	yes	characteristic
63	C₁₃×#389	C₂²	1	1	yes	characteristic
64	C₁₃×#389	C₂²	1	1	yes	characteristic
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	2	yes	—
69	C₁₃×#389	C₂²	1	2	yes	—
70	C₁₃×#389	C₂²	1	1	yes	characteristic
71	C₁₃×#389	C₂²	1	1	yes	characteristic
72	C₁₃×#389	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×#387	C₂²	1	2	yes	—
88	C₁₃×#387	C₂²	1	2	yes	—
89	C₁₃×#384	C₂²	1	1	yes	characteristic
90	C₁₃×#382	C₂²	1	2	yes	—
91	C₁₃×#382	C₂²	1	1	yes	characteristic
92	C₁₃×#382	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	1	yes	characteristic
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
117	C₁₃×#376	C₂²	1	2	yes	—
118	C₁₃×#376	C₂²	1	2	yes	—
119	C₄³×C₁₃	C₂²	1	1	yes	characteristic
120	C₄³×C₁₃	C₂²	1	2	yes	—
121	C₄³×C₁₃	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
125	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₁₃×C₄⋊Q₈	—	2	4	no	—
127	C₁₃×#125	—	2	8	no	—
128	C₁₃×#125	—	2	4	no	—
129	C₁₃×#125	—	2	4	no	—
130	C₄×Q₈×C₁₃	—	2	4	no	—
131	C₄×Q₈×C₁₃	—	2	4	no	—
132	C₄×Q₈×C₁₃	—	2	4	no	—
133	C₄×Q₈×C₁₃	—	2	8	no	—
134	C₄×Q₈×C₁₃	—	2	4	no	—
135	C₄×Q₈×C₁₃	—	2	4	no	—
136	C₄×Q₈×C₁₃	Q₈	1	8	yes	complemented
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×C₄⋊C₄	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	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₁₃×#95	C₂³	1	1	yes	characteristic
201	C₁₃×#95	C₂³	1	1	yes	characteristic
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	1	yes	characteristic
204	C₁₃×#95	C₂³	1	1	yes	characteristic
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	1	yes	characteristic
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	1	yes	characteristic
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	C₁₃×#95	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	C₁₃×#95	C₂³	1	2	yes	—
216	C₁₃×#95	C₂³	1	2	yes	—
217	C₁₃×#95	C₂³	1	2	yes	—
218	C₁₃×#95	C₂³	1	2	yes	—
219	C₁₃×#95	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	2	yes	—
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	2	yes	—
223	C₁₃×#95	C₂³	1	2	yes	—
224	C₁₃×#95	C₂³	1	2	yes	—
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	2	yes	—
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	2	yes	—
230	C₁₃×#95	C₂³	1	2	yes	—
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	2	yes	—
233	#34920	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	4	no	—
240	C₂×Q₈×C₁₃	—	2	4	no	—
241	C₂×Q₈×C₁₃	—	4	2	no	—
242	C₂×Q₈×C₁₃	C₂×Q₈	1	4	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	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	4	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	4	no	—
288	C₁₃×C₄⋊C₄	—	2	4	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	4	2	no	—
295	C₁₃×C₄⋊C₄	—	4	2	no	—
296	C₁₃×C₄⋊C₄	—	4	2	no	—
297	C₁₃×C₄⋊C₄	—	4	2	no	—
298	C₁₃×C₄⋊C₄	C₂×Q₈	1	8	yes	—
299	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
300	C₁₃×C₄⋊C₄	#41	1	4	yes	—
301	C₁₃×C₄⋊C₄	#41	1	4	yes	—
302	C₄²×C₁₃	—	2	2	no	—
303	C₄²×C₁₃	—	2	2	no	—
304	C₄²×C₁₃	—	2	4	no	—
305	C₄²×C₁₃	—	2	2	no	—
306	C₄²×C₁₃	—	2	2	no	—
307	C₄²×C₁₃	—	2	4	no	—
308	C₄²×C₁₃	—	2	2	no	—
309	C₄²×C₁₃	—	2	2	no	—
310	C₄²×C₁₃	—	2	2	no	—
311	C₄²×C₁₃	—	2	2	no	—
312	C₄²×C₁₃	—	2	4	no	—
313	C₄²×C₁₃	—	2	4	no	—
314	C₄²×C₁₃	—	2	4	no	—
315	C₄²×C₁₃	—	2	2	no	—
316	C₄²×C₁₃	—	2	2	no	—
317	C₄²×C₁₃	—	2	2	no	—
318	C₄²×C₁₃	—	2	2	no	—
319	C₄²×C₁₃	—	2	4	no	—
320	C₄²×C₁₃	—	2	2	no	—
321	C₄²×C₁₃	—	4	1	no	—
322	C₄²×C₁₃	—	4	2	no	—
323	C₄²×C₁₃	—	4	1	no	—
324	C₄²×C₁₃	—	4	1	no	—
325	C₄²×C₁₃	C₂×Q₈	1	8	yes	—
326	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
327	C₄²×C₁₃	#41	1	4	yes	—
328	C₄²×C₁₃	#41	1	4	yes	—
329	#2590	C₂×C₁₃	1	2	yes	—
330	#2588	C₂×C₁₃	1	2	yes	—
331	#2584	C₂×C₁₃	1	1	yes	characteristic
332	#2581	C₂×C₁₃	1	1	yes	characteristic
333	#2565	C₂×C₁₃	1	1	yes	characteristic
334	#2550	C₂×C₁₃	1	1	yes	characteristic
335	#2520	C₂×C₁₃	1	2	yes	—
336	#2508	C₂×C₁₃	1	1	yes	characteristic
337	#2506	C₂×C₁₃	1	1	yes	characteristic
338	#2462	C₂×C₁₃	1	2	yes	—
339	#2453	C₂×C₁₃	1	1	yes	characteristic
340	#2451	C₂×C₁₃	1	1	yes	characteristic
341	#2402	C₂×C₁₃	1	2	yes	—
342	#2399	C₂×C₁₃	1	2	yes	—
343	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
344	C₄×#125	C₂×C₁₃	1	1	yes	characteristic
345	C₄×#125	C₂×C₁₃	1	1	yes	characteristic
346	C₄×#125	C₂×C₁₃	1	2	yes	—
347	#2295	C₂×C₁₃	1	2	yes	—
348	#2295	C₂×C₁₃	1	1	yes	characteristic
349	#2295	C₂×C₁₃	1	1	yes	characteristic
350	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic
351	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic
352	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
353	Q₈×C₁₃	—	2	8	no	—
354	Q₈×C₁₃	—	2	8	no	—
355	Q₈×C₁₃	—	4	8	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	1	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	1	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	1	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	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
409	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
410	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
411	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
412	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
413	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
414	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
415	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
416	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
417	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
418	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
419	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
420	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
421	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
422	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
423	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
424	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
425	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#125	C₂²×C₁₃	1	2	yes	—
429	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
430	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
436	#400	C₂²×C₁₃	1	2	yes	—
437	#400	C₂²×C₁₃	1	2	yes	—
438	#400	C₂²×C₁₃	1	2	yes	—
439	#400	C₂²×C₁₃	1	2	yes	—
440	#398	C₂²×C₁₃	1	2	yes	—
441	#398	C₂²×C₁₃	1	2	yes	—
442	#398	C₂²×C₁₃	1	2	yes	—
443	#398	C₂²×C₁₃	1	2	yes	—
444	#398	C₂²×C₁₃	1	2	yes	—
445	#398	C₂²×C₁₃	1	2	yes	—
446	#398	C₂²×C₁₃	1	2	yes	—
447	#398	C₂²×C₁₃	1	2	yes	—
448	#395	C₂²×C₁₃	1	2	yes	—
449	#395	C₂²×C₁₃	1	2	yes	—
450	#395	C₂²×C₁₃	1	2	yes	—
451	#395	C₂²×C₁₃	1	2	yes	—
452	#391	C₂²×C₁₃	1	2	yes	—
453	#391	C₂²×C₁₃	1	1	yes	characteristic
454	#391	C₂²×C₁₃	1	1	yes	characteristic
455	#391	C₂²×C₁₃	1	1	yes	characteristic
456	#391	C₂²×C₁₃	1	1	yes	characteristic
457	#391	C₂²×C₁₃	1	2	yes	—
458	#391	C₂²×C₁₃	1	2	yes	—
459	#389	C₂²×C₁₃	1	1	yes	characteristic
460	#389	C₂²×C₁₃	1	2	yes	—
461	#389	C₂²×C₁₃	1	1	yes	characteristic
462	#389	C₂²×C₁₃	1	2	yes	—
463	#389	C₂²×C₁₃	1	1	yes	characteristic
464	#389	C₂²×C₁₃	1	1	yes	characteristic
465	#389	C₂²×C₁₃	1	1	yes	characteristic
466	#389	C₂²×C₁₃	1	1	yes	characteristic
467	#389	C₂²×C₁₃	1	2	yes	—
468	#389	C₂²×C₁₃	1	2	yes	—
469	#389	C₂²×C₁₃	1	1	yes	characteristic
470	#389	C₂²×C₁₃	1	1	yes	characteristic
471	#389	C₂²×C₁₃	1	2	yes	—
472	#389	C₂²×C₁₃	1	1	yes	characteristic
473	#389	C₂²×C₁₃	1	1	yes	characteristic
474	#387	C₂²×C₁₃	1	2	yes	—
475	#387	C₂²×C₁₃	1	2	yes	—
476	#387	C₂²×C₁₃	1	2	yes	—
477	#387	C₂²×C₁₃	1	2	yes	—
478	#387	C₂²×C₁₃	1	2	yes	—
479	#387	C₂²×C₁₃	1	2	yes	—
480	#387	C₂²×C₁₃	1	2	yes	—
481	#387	C₂²×C₁₃	1	2	yes	—
482	#387	C₂²×C₁₃	1	2	yes	—
483	#387	C₂²×C₁₃	1	2	yes	—
484	#387	C₂²×C₁₃	1	2	yes	—
485	#387	C₂²×C₁₃	1	2	yes	—
486	#387	C₂²×C₁₃	1	2	yes	—
487	#387	C₂²×C₁₃	1	2	yes	—
488	#387	C₂²×C₁₃	1	2	yes	—
489	#387	C₂²×C₁₃	1	2	yes	—
490	#384	C₂²×C₁₃	1	1	yes	characteristic
491	#382	C₂²×C₁₃	1	1	yes	characteristic
492	#382	C₂²×C₁₃	1	1	yes	characteristic
493	#382	C₂²×C₁₃	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
495	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
496	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
499	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
500	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
501	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
502	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
503	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
504	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
505	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
506	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
507	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
508	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
509	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
510	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
511	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
512	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
513	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
514	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
515	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
516	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
517	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
518	#376	C₂²×C₁₃	1	2	yes	—
519	#376	C₂²×C₁₃	1	2	yes	—
520	C₄³	C₂²×C₁₃	1	1	yes	characteristic
521	C₄³	C₂²×C₁₃	1	2	yes	—
522	C₄³	C₂²×C₁₃	1	1	yes	characteristic
523	C₄³	C₂²×C₁₃	1	1	yes	characteristic
524	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
525	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
526	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
527	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
528	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
529	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	C₂²×C₁₃	#585	1	1	yes	characteristic
531	C₄×C₁₃	—	2	4	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	2	no	—
534	C₄×C₁₃	—	2	2	no	—
535	C₄×C₁₃	—	2	2	no	—
536	C₄×C₁₃	—	2	4	no	—
537	C₄×C₁₃	—	2	2	no	—
538	C₄×C₁₃	—	2	2	no	—
539	C₄×C₁₃	—	2	4	no	—
540	C₄×C₁₃	—	2	2	no	—
541	C₄×C₁₃	—	2	2	no	—
542	C₄×C₁₃	—	4	2	no	—
543	C₄×C₁₃	—	4	2	no	—
544	C₄×C₁₃	—	4	1	no	—
545	C₄×C₁₃	—	4	1	no	—
546	C₄×C₁₃	—	4	2	no	—
547	C₄×C₁₃	—	4	1	no	—
548	C₄×C₁₃	—	4	1	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	1	no	—
551	C₄×C₁₃	—	4	2	no	—
552	C₄×C₁₃	#533	1	4	yes	—
553	C₄×C₁₃	#557	1	4	yes	—
554	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
556	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₄⋊Q₈	—	2	4	no	—
558	#125	—	2	8	no	—
559	#125	—	2	4	no	—
560	#125	—	2	4	no	—
561	C₄×Q₈	—	2	4	no	—
562	C₄×Q₈	—	2	4	no	—
563	C₄×Q₈	—	2	4	no	—
564	C₄×Q₈	—	2	8	no	—
565	C₄×Q₈	—	2	4	no	—
566	C₄×Q₈	—	2	4	no	—
567	C₄×Q₈	Q₈×C₁₃	1	8	yes	complemented
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
631	#95	C₂³×C₁₃	1	2	yes	—
632	#95	C₂³×C₁₃	1	2	yes	—
633	#95	C₂³×C₁₃	1	2	yes	—
634	#95	C₂³×C₁₃	1	2	yes	—
635	#95	C₂³×C₁₃	1	2	yes	—
636	#95	C₂³×C₁₃	1	2	yes	—
637	#95	C₂³×C₁₃	1	2	yes	—
638	#95	C₂³×C₁₃	1	2	yes	—
639	#95	C₂³×C₁₃	1	1	yes	characteristic
640	#95	C₂³×C₁₃	1	1	yes	characteristic
641	#95	C₂³×C₁₃	1	2	yes	—
642	#95	C₂³×C₁₃	1	1	yes	characteristic
643	#95	C₂³×C₁₃	1	1	yes	characteristic
644	#95	C₂³×C₁₃	1	2	yes	—
645	#95	C₂³×C₁₃	1	1	yes	characteristic
646	#95	C₂³×C₁₃	1	2	yes	—
647	#95	C₂³×C₁₃	1	1	yes	characteristic
648	#95	C₂³×C₁₃	1	2	yes	—
649	#95	C₂³×C₁₃	1	2	yes	—
650	#95	C₂³×C₁₃	1	2	yes	—
651	#95	C₂³×C₁₃	1	2	yes	—
652	#95	C₂³×C₁₃	1	2	yes	—
653	#95	C₂³×C₁₃	1	2	yes	—
654	#95	C₂³×C₁₃	1	2	yes	—
655	#95	C₂³×C₁₃	1	2	yes	—
656	#95	C₂³×C₁₃	1	2	yes	—
657	#95	C₂³×C₁₃	1	2	yes	—
658	#95	C₂³×C₁₃	1	2	yes	—
659	#95	C₂³×C₁₃	1	2	yes	—
660	#95	C₂³×C₁₃	1	2	yes	—
661	#95	C₂³×C₁₃	1	2	yes	—
662	#95	C₂³×C₁₃	1	2	yes	—
663	#95	C₂³×C₁₃	1	2	yes	—
664	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
665	C₂×C₁₃	#3444	1	1	yes	characteristic
666	C₂×C₁₃	#3461	1	1	yes	characteristic
667	C₂×C₁₃	#3475	1	1	yes	characteristic
668	C₂×C₁₃	C₂×#557	1	1	yes	characteristic
669	C₂×C₁₃	Q₈×#41	1	1	yes	characteristic
670	C₂×C₁₃	#3482	1	1	yes	characteristic
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	2	no	—
676	C₂×Q₈	—	2	4	no	—
677	C₂×Q₈	—	2	4	no	—
678	C₂×Q₈	—	4	2	no	—
679	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
680	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
736	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
737	C₄⋊C₄	C₁₃×#41	1	4	yes	—
738	C₄⋊C₄	C₁₃×#41	1	4	yes	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	4	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	4	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	4	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	4	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	4	1	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	1	no	—
761	C₄²	—	4	1	no	—
762	C₄²	C₂×Q₈×C₁₃	1	8	yes	—
763	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
764	C₄²	C₁₃×#41	1	4	yes	—
765	C₄²	C₁₃×#41	1	4	yes	—
766	C₁₃	#34920	1	1	yes	characteristic, direct product factor, Sylow
767	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
768	Q₈	—	2	8	no	—
769	Q₈	—	2	8	no	—
770	Q₈	—	4	8	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	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	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
824	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
825	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
826	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
827	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
828	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
829	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
830	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
831	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
832	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
833	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
834	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
835	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
836	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
837	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
838	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
839	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
840	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
841	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
842	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
843	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
844	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
845	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
846	C₂²	C₁₃×#585	1	1	yes	characteristic
847	C₄	—	2	4	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	C₁₃×#533	1	4	yes	—
869	C₄	C₁₃×#557	1	4	yes	—
870	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
871	C₂	C₁₃×#3444	1	1	yes	characteristic
872	C₂	C₁₃×#3461	1	1	yes	characteristic
873	C₂	C₁₃×#3475	1	1	yes	characteristic
874	C₂	C₂×C₁₃×#557	1	1	yes	characteristic
875	C₂	Q₈×C₁₃×#41	1	1	yes	characteristic
876	C₂	C₁₃×#3482	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
136. C₄×Q₈×C₁₃	Q₈	semidirect
233. #34920	C₁₃	direct (N × H)
567. C₄×Q₈	Q₈×C₁₃	semidirect
766. C₁₃	#34920	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×#2590	2
C₁₃×#2588	2
C₁₃×#2584	2
C₁₃×#2581	2
C₁₃×#2565	2
C₁₃×#2550	2
C₁₃×#2520	2
C₁₃×#2508	2
C₁₃×#2506	2
C₁₃×#2462	2
C₁₃×#2453	2
C₁₃×#2451	2
C₁₃×#2402	2
C₁₃×#2399	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#125	2
C₁₃×#2295	2
C₄²×Q₈×C₁₃	2
#34920	13

Subgroups — C13×#34920 #15721259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34920 #15721259