Subgroups — C₁₃×#34975 #15721314

Order 3328.

1738 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2533	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2528	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2506	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2496	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2489	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2478	C₂	1	2	yes	maximal
8	C₁₃×#2475	C₂	1	2	yes	maximal
9	C₁₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2429	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2421	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2402	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2401	C₂	1	2	yes	maximal
15	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#125	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#126	C₂	1	2	yes	maximal
19	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
20	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
21	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#126	C₂²	1	2	yes	—
26	C₂×C₁₃×#125	C₂²	1	2	yes	—
27	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊Q₈	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	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#401	C₂²	1	2	yes	—
38	C₁₃×#400	C₂²	1	2	yes	—
39	C₁₃×#400	C₂²	1	2	yes	—
40	C₁₃×#400	C₂²	1	2	yes	—
41	C₁₃×#400	C₂²	1	2	yes	—
42	C₁₃×#400	C₂²	1	2	yes	—
43	C₁₃×#400	C₂²	1	2	yes	—
44	C₁₃×#400	C₂²	1	2	yes	—
45	C₁₃×#398	C₂²	1	2	yes	—
46	C₁₃×#398	C₂²	1	2	yes	—
47	C₁₃×#398	C₂²	1	2	yes	—
48	C₁₃×#398	C₂²	1	2	yes	—
49	C₁₃×#397	C₂²	1	2	yes	—
50	C₁₃×#397	C₂²	1	2	yes	—
51	C₁₃×#397	C₂²	1	2	yes	—
52	C₁₃×#396	C₂²	1	2	yes	—
53	C₁₃×#391	C₂²	1	1	yes	characteristic
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×#391	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	2	yes	—
66	C₁₃×#389	C₂²	1	2	yes	—
67	C₁₃×#389	C₂²	1	2	yes	—
68	C₁₃×#389	C₂²	1	2	yes	—
69	C₁₃×#388	C₂²	1	2	yes	—
70	C₁₃×#388	C₂²	1	2	yes	—
71	C₁₃×#388	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×#385	C₂²	1	2	yes	—
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#384	C₂²	1	1	yes	characteristic
88	C₁₃×#383	C₂²	1	2	yes	—
89	C₁₃×#382	C₂²	1	1	yes	characteristic
90	C₁₃×#382	C₂²	1	2	yes	—
91	C₁₃×#380	C₂²	1	1	yes	characteristic
92	C₁₃×#380	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	1	yes	characteristic
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
110	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₁₃×#376	C₂²	1	1	yes	characteristic
118	C₁₃×#376	C₂²	1	1	yes	characteristic
119	C₁₃×#376	C₂²	1	2	yes	—
120	C₄³×C₁₃	C₂²	1	1	yes	characteristic
121	C₄³×C₁₃	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃	C₂²	1	2	yes	—
123	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×C₄⋊Q₈	—	2	4	no	—
129	C₁₃×#126	—	2	8	no	—
130	C₁₃×#125	—	2	8	no	—
131	C₁₃×#125	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	2	4	no	—
133	C₁₃×C₂²⋊Q₈	—	2	4	no	—
134	C₄×Q₈×C₁₃	—	2	4	no	—
135	C₄×Q₈×C₁₃	—	2	4	no	—
136	C₄×Q₈×C₁₃	—	2	4	no	—
137	C₄×Q₈×C₁₃	—	2	4	no	—
138	C₁₃×#117	—	2	4	no	—
139	C₁₃×#117	—	2	4	no	—
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	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	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	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×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	1	yes	characteristic
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₁₃	—	2	4	no	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
194	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₁₃×#95	C₂³	1	1	yes	characteristic
202	C₁₃×#95	C₂³	1	1	yes	characteristic
203	C₁₃×#95	C₂³	1	1	yes	characteristic
204	C₁₃×#95	C₂³	1	1	yes	characteristic
205	C₁₃×#95	C₂³	1	1	yes	characteristic
206	C₁₃×#95	C₂³	1	1	yes	characteristic
207	C₁₃×#95	C₂³	1	1	yes	characteristic
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	C₁₃×#95	C₂³	1	2	yes	—
234	C₁₃×#95	C₂³	1	2	yes	—
235	#34975	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	#41	1	4	yes	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	4	no	—
284	C₁₃×C₄⋊C₄	—	2	2	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	4	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	—	2	4	no	—
300	C₁₃×C₄⋊C₄	#41	1	4	yes	—
301	C₁₃×C₄⋊C₄	#41	1	4	yes	—
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
303	C₁₃×C₂²⋊C₄	—	2	4	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	#41	1	4	yes	—
310	C₄²×C₁₃	—	2	2	no	—
311	C₄²×C₁₃	—	2	2	no	—
312	C₄²×C₁₃	—	2	2	no	—
313	C₄²×C₁₃	—	2	2	no	—
314	C₄²×C₁₃	—	2	2	no	—
315	C₄²×C₁₃	—	2	2	no	—
316	C₄²×C₁₃	—	2	2	no	—
317	C₄²×C₁₃	—	2	4	no	—
318	C₄²×C₁₃	—	2	4	no	—
319	C₄²×C₁₃	—	2	2	no	—
320	C₄²×C₁₃	—	2	2	no	—
321	C₄²×C₁₃	—	2	4	no	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	4	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	2	no	—
330	C₄²×C₁₃	—	2	4	no	—
331	C₄²×C₁₃	—	2	4	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	#41	1	4	yes	—
334	#2533	C₂×C₁₃	1	2	yes	complemented
335	#2528	C₂×C₁₃	1	2	yes	complemented
336	#2514	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#2506	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#2496	C₂×C₁₃	1	1	yes	characteristic
339	#2489	C₂×C₁₃	1	1	yes	characteristic
340	#2478	C₂×C₁₃	1	2	yes	—
341	#2475	C₂×C₁₃	1	2	yes	—
342	#2453	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#2446	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#2429	C₂×C₁₃	1	1	yes	characteristic
345	#2421	C₂×C₁₃	1	1	yes	characteristic
346	#2402	C₂×C₁₃	1	2	yes	complemented
347	#2401	C₂×C₁₃	1	2	yes	—
348	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
349	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₄×#125	C₂×C₁₃	1	2	yes	complemented
351	C₄×#126	C₂×C₁₃	1	2	yes	—
352	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
353	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
354	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
356	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
357	C₂³×C₁₃	—	2	1	no	—
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	—	2	1	no	—
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	C₂×#41	1	2	yes	—
364	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
365	Q₈×C₁₃	—	2	8	no	—
366	Q₈×C₁₃	—	4	4	no	—
367	C₂×C₄×C₁₃	—	2	8	no	—
368	C₂×C₄×C₁₃	—	2	1	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	2	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	2	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	2	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	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	1	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	1	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	1	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	4	4	no	—
421	C₂×C₄×C₁₃	—	4	4	no	—
422	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
423	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
424	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
425	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
426	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
427	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
428	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
429	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
430	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
431	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
432	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
433	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
434	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
435	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
436	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#126	C₂²×C₁₃	1	2	yes	—
438	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#125	C₂²×C₁₃	1	2	yes	—
440	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
448	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
449	#401	C₂²×C₁₃	1	2	yes	—
450	#400	C₂²×C₁₃	1	2	yes	—
451	#400	C₂²×C₁₃	1	2	yes	—
452	#400	C₂²×C₁₃	1	2	yes	—
453	#400	C₂²×C₁₃	1	2	yes	—
454	#400	C₂²×C₁₃	1	2	yes	—
455	#400	C₂²×C₁₃	1	2	yes	—
456	#400	C₂²×C₁₃	1	2	yes	—
457	#398	C₂²×C₁₃	1	2	yes	—
458	#398	C₂²×C₁₃	1	2	yes	—
459	#398	C₂²×C₁₃	1	2	yes	—
460	#398	C₂²×C₁₃	1	2	yes	—
461	#397	C₂²×C₁₃	1	2	yes	—
462	#397	C₂²×C₁₃	1	2	yes	—
463	#397	C₂²×C₁₃	1	2	yes	—
464	#396	C₂²×C₁₃	1	2	yes	—
465	#391	C₂²×C₁₃	1	1	yes	characteristic
466	#391	C₂²×C₁₃	1	1	yes	characteristic
467	#391	C₂²×C₁₃	1	1	yes	characteristic
468	#391	C₂²×C₁₃	1	1	yes	characteristic
469	#391	C₂²×C₁₃	1	1	yes	characteristic
470	#391	C₂²×C₁₃	1	1	yes	characteristic
471	#389	C₂²×C₁₃	1	1	yes	characteristic
472	#389	C₂²×C₁₃	1	2	yes	—
473	#389	C₂²×C₁₃	1	1	yes	characteristic
474	#389	C₂²×C₁₃	1	2	yes	—
475	#389	C₂²×C₁₃	1	2	yes	—
476	#389	C₂²×C₁₃	1	2	yes	—
477	#389	C₂²×C₁₃	1	1	yes	characteristic
478	#389	C₂²×C₁₃	1	1	yes	characteristic
479	#389	C₂²×C₁₃	1	1	yes	characteristic
480	#389	C₂²×C₁₃	1	1	yes	characteristic
481	#388	C₂²×C₁₃	1	2	yes	—
482	#388	C₂²×C₁₃	1	2	yes	—
483	#388	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	#387	C₂²×C₁₃	1	2	yes	—
491	#387	C₂²×C₁₃	1	2	yes	—
492	#387	C₂²×C₁₃	1	2	yes	—
493	#387	C₂²×C₁₃	1	2	yes	—
494	#387	C₂²×C₁₃	1	2	yes	—
495	#387	C₂²×C₁₃	1	2	yes	—
496	#387	C₂²×C₁₃	1	2	yes	—
497	#385	C₂²×C₁₃	1	2	yes	—
498	#385	C₂²×C₁₃	1	2	yes	—
499	#384	C₂²×C₁₃	1	1	yes	characteristic
500	#383	C₂²×C₁₃	1	2	yes	—
501	#382	C₂²×C₁₃	1	1	yes	characteristic
502	#382	C₂²×C₁₃	1	2	yes	—
503	#380	C₂²×C₁₃	1	1	yes	characteristic
504	#380	C₂²×C₁₃	1	1	yes	characteristic
505	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
506	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
507	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
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	2	yes	—
512	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
513	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
514	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
515	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
516	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
517	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
518	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
519	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
520	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
521	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
522	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
523	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
524	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
525	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
526	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
527	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
528	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
529	#376	C₂²×C₁₃	1	2	yes	—
530	#376	C₂²×C₁₃	1	1	yes	characteristic
531	#376	C₂²×C₁₃	1	1	yes	characteristic
532	C₄³	C₂²×C₁₃	1	2	yes	—
533	C₄³	C₂²×C₁₃	1	1	yes	characteristic
534	C₄³	C₂²×C₁₃	1	1	yes	characteristic
535	C₂²×C₁₃	—	2	2	no	—
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	2	no	—
538	C₂²×C₁₃	—	4	1	no	—
539	C₂²×C₁₃	—	4	1	no	—
540	C₂²×C₁₃	—	4	1	no	—
541	C₂²×C₁₃	—	4	1	no	—
542	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
543	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
544	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
545	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
546	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
547	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
549	C₄×C₁₃	—	2	4	no	—
550	C₄×C₁₃	—	2	2	no	—
551	C₄×C₁₃	—	2	2	no	—
552	C₄×C₁₃	—	2	2	no	—
553	C₄×C₁₃	—	2	2	no	—
554	C₄×C₁₃	—	2	4	no	—
555	C₄×C₁₃	—	2	2	no	—
556	C₄×C₁₃	—	2	2	no	—
557	C₄×C₁₃	—	4	1	no	—
558	C₄×C₁₃	—	4	2	no	—
559	C₄×C₁₃	—	4	2	no	—
560	C₄×C₁₃	—	4	2	no	—
561	C₄×C₁₃	—	4	1	no	—
562	C₄×C₁₃	—	4	1	no	—
563	C₄×C₁₃	—	4	1	no	—
564	C₄×C₁₃	—	4	2	no	—
565	C₄×C₁₃	—	4	1	no	—
566	C₄×C₁₃	—	4	1	no	—
567	C₄×C₁₃	—	4	2	no	—
568	C₄×C₁₃	—	4	2	no	—
569	C₄×C₁₃	#529	1	4	yes	—
570	C₄×C₁₃	#541	1	4	yes	—
571	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₄⋊Q₈	—	2	4	no	—
577	#126	—	2	8	no	—
578	#125	—	2	8	no	—
579	#125	—	2	4	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₄×Q₈	—	2	4	no	—
583	C₄×Q₈	—	2	4	no	—
584	C₄×Q₈	—	2	4	no	—
585	C₄×Q₈	—	2	4	no	—
586	#117	—	2	4	no	—
587	#117	—	2	4	no	—
588	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄²	—	2	4	no	—
625	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
635	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	#95	C₂³×C₁₃	1	1	yes	characteristic
650	#95	C₂³×C₁₃	1	1	yes	characteristic
651	#95	C₂³×C₁₃	1	1	yes	characteristic
652	#95	C₂³×C₁₃	1	1	yes	characteristic
653	#95	C₂³×C₁₃	1	1	yes	characteristic
654	#95	C₂³×C₁₃	1	1	yes	characteristic
655	#95	C₂³×C₁₃	1	1	yes	characteristic
656	#95	C₂³×C₁₃	1	1	yes	characteristic
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	#95	C₂³×C₁₃	1	2	yes	—
665	#95	C₂³×C₁₃	1	2	yes	—
666	#95	C₂³×C₁₃	1	2	yes	—
667	#95	C₂³×C₁₃	1	2	yes	—
668	#95	C₂³×C₁₃	1	2	yes	—
669	#95	C₂³×C₁₃	1	2	yes	—
670	#95	C₂³×C₁₃	1	2	yes	—
671	#95	C₂³×C₁₃	1	2	yes	—
672	#95	C₂³×C₁₃	1	2	yes	—
673	#95	C₂³×C₁₃	1	2	yes	—
674	#95	C₂³×C₁₃	1	2	yes	—
675	#95	C₂³×C₁₃	1	2	yes	—
676	#95	C₂³×C₁₃	1	2	yes	—
677	#95	C₂³×C₁₃	1	2	yes	—
678	#95	C₂³×C₁₃	1	2	yes	—
679	#95	C₂³×C₁₃	1	2	yes	—
680	#95	C₂³×C₁₃	1	2	yes	—
681	#95	C₂³×C₁₃	1	2	yes	—
682	#95	C₂³×C₁₃	1	2	yes	—
683	C₂×C₁₃	—	4	2	no	—
684	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
685	C₂×C₁₃	#3444	1	1	yes	characteristic
686	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
687	C₂×C₁₃	#3482	1	1	yes	characteristic
688	C₂×C₁₃	#3482	1	1	yes	characteristic
689	C₂×C₁₃	#3482	1	1	yes	characteristic
690	C₂×C₁₃	#3482	1	1	yes	characteristic
691	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂×Q₈	—	2	2	no	—
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	C₁₃×#41	1	4	yes	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	C₁₃×#41	1	4	yes	—
756	C₄⋊C₄	C₁₃×#41	1	4	yes	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	C₁₃×#41	1	4	yes	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	4	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	4	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	4	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	4	no	—
788	C₄²	C₁₃×#41	1	4	yes	—
789	C₁₃	#34975	1	1	yes	characteristic, direct product factor, Sylow
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	C₂×C₁₃×#41	1	2	yes	—
797	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
798	Q₈	—	2	8	no	—
799	Q₈	—	4	4	no	—
800	C₂×C₄	—	2	8	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	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
856	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
857	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
858	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
859	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
860	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
861	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
862	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
863	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
864	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
865	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
866	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
867	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
868	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
877	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
878	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
879	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
880	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
881	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
882	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
883	C₄	—	2	4	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	C₁₃×#529	1	4	yes	—
904	C₄	C₁₃×#541	1	4	yes	—
905	C₂	—	4	2	no	—
906	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
907	C₂	C₁₃×#3444	1	1	yes	characteristic
908	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
909	C₂	C₁₃×#3482	1	1	yes	characteristic
910	C₂	C₁₃×#3482	1	1	yes	characteristic
911	C₂	C₁₃×#3482	1	1	yes	characteristic
912	C₂	C₁₃×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁴×C₁₃	C₂⁴
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
1. C₁₃×#2533	C₂	semidirect
2. C₁₃×#2528	C₂	semidirect
3. C₁₃×#2514	C₂	semidirect
4. C₁₃×#2506	C₂	semidirect
9. C₁₃×#2453	C₂	semidirect
10. C₁₃×#2446	C₂	semidirect
13. C₁₃×#2402	C₂	semidirect
15. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
16. C₄×C₁₃×#125	C₂	semidirect
17. C₄×C₁₃×#125	C₂	semidirect
21. C₁₃×#2295	C₂	semidirect
22. C₄²×Q₈×C₁₃	C₂	semidirect
235. #34975	C₁₃	direct (N × H)
334. #2533	C₂×C₁₃	semidirect
335. #2528	C₂×C₁₃	semidirect
336. #2514	C₂×C₁₃	semidirect
337. #2506	C₂×C₁₃	semidirect
342. #2453	C₂×C₁₃	semidirect
343. #2446	C₂×C₁₃	semidirect
346. #2402	C₂×C₁₃	semidirect
348. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
349. C₄×#125	C₂×C₁₃	semidirect
350. C₄×#125	C₂×C₁₃	semidirect
354. #2295	C₂×C₁₃	semidirect
355. C₄²×Q₈	C₂×C₁₃	semidirect
789. C₁₃	#34975	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×#2533	2
C₁₃×#2528	2
C₁₃×#2514	2
C₁₃×#2506	2
C₁₃×#2496	2
C₁₃×#2489	2
C₁₃×#2478	2
C₁₃×#2475	2
C₁₃×#2453	2
C₁₃×#2446	2
C₁₃×#2429	2
C₁₃×#2421	2
C₁₃×#2402	2
C₁₃×#2401	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#125	2
C₄×C₁₃×#126	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2295	2
C₄²×Q₈×C₁₃	2
C₄×C₁₃×#117	2
#34975	13

Subgroups — C13×#34975 #15721314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34975 #15721314