Subgroups — C₁₃×#34902 #15721241

Order 3328.

1768 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2596	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2594	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2592	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2570	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2545	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2525	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2512	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2469	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2448	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2401	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2396	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#126	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
18	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
19	C₁₃×#2298	C₂	1	2	yes	maximal, complemented
20	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
22	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#126	C₂²	1	2	yes	—
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#124	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	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
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×#399	C₂²	1	2	yes	—
43	C₁₃×#398	C₂²	1	2	yes	—
44	C₁₃×#398	C₂²	1	2	yes	—
45	C₁₃×#397	C₂²	1	2	yes	—
46	C₁₃×#397	C₂²	1	2	yes	—
47	C₁₃×#397	C₂²	1	2	yes	—
48	C₁₃×#396	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#396	C₂²	1	2	yes	—
51	C₁₃×#395	C₂²	1	2	yes	—
52	C₁₃×#393	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×#390	C₂²	1	1	yes	characteristic
60	C₁₃×#390	C₂²	1	1	yes	characteristic
61	C₁₃×#390	C₂²	1	1	yes	characteristic
62	C₁₃×#390	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	1	yes	characteristic
67	C₁₃×#389	C₂²	1	1	yes	characteristic
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×#388	C₂²	1	2	yes	—
73	C₁₃×#388	C₂²	1	2	yes	—
74	C₁₃×#388	C₂²	1	2	yes	—
75	C₁₃×#388	C₂²	1	2	yes	—
76	C₁₃×#388	C₂²	1	2	yes	—
77	C₁₃×#388	C₂²	1	2	yes	—
78	C₁₃×#388	C₂²	1	2	yes	—
79	C₁₃×#388	C₂²	1	2	yes	—
80	C₁₃×#388	C₂²	1	2	yes	—
81	C₁₃×#388	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×#387	C₂²	1	2	yes	—
90	C₁₃×#387	C₂²	1	2	yes	—
91	C₁₃×#384	C₂²	1	1	yes	characteristic
92	C₁₃×#383	C₂²	1	2	yes	—
93	C₁₃×#382	C₂²	1	1	yes	characteristic
94	C₁₃×#382	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	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	1	yes	characteristic
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	2	yes	—
111	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
113	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₁₃×#376	C₂²	1	2	yes	—
119	C₄³×C₁₃	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₁₃×C₄⋊Q₈	—	2	4	no	—
129	C₁₃×#126	—	2	8	no	—
130	C₁₃×#124	—	2	4	no	—
131	C₁₃×#124	—	2	4	no	—
132	C₄×Q₈×C₁₃	—	2	4	no	—
133	C₄×Q₈×C₁₃	—	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	C₄×Q₈×C₁₃	—	2	4	no	—
139	C₄×D₄×C₁₃	—	2	4	no	—
140	C₁₃×#117	—	2	8	no	—
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	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	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
217	C₁₃×#95	C₂³	1	1	yes	characteristic
218	C₁₃×#95	C₂³	1	1	yes	characteristic
219	C₁₃×#95	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	1	yes	characteristic
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	2	yes	—
223	C₁₃×#95	C₂³	1	1	yes	characteristic
224	C₁₃×#95	C₂³	1	1	yes	characteristic
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	#34902	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	#41	1	4	yes	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	4	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	4	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	4	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	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	4	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	4	2	no	—
298	C₁₃×C₄⋊C₄	—	4	2	no	—
299	C₁₃×C₄⋊C₄	#41	1	4	yes	—
300	C₁₃×C₂²⋊C₄	—	2	4	no	—
301	C₁₃×C₂²⋊C₄	—	2	4	no	—
302	C₁₃×C₂²⋊C₄	—	2	4	no	—
303	C₁₃×C₂²⋊C₄	—	2	4	no	—
304	C₁₃×C₂²⋊C₄	—	2	4	no	—
305	C₁₃×C₂²⋊C₄	—	2	4	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	4	2	no	—
311	C₁₃×C₂²⋊C₄	—	4	2	no	—
312	C₁₃×C₂²⋊C₄	—	4	2	no	—
313	C₄²×C₁₃	—	2	4	no	—
314	C₄²×C₁₃	—	2	2	no	—
315	C₄²×C₁₃	—	2	2	no	—
316	C₄²×C₁₃	—	2	4	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	—	2	2	no	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	—	2	2	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	4	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	4	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	2	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	—	4	1	no	—
333	C₄²×C₁₃	—	4	1	no	—
334	C₄²×C₁₃	—	4	1	no	—
335	C₄²×C₁₃	—	4	2	no	—
336	C₄²×C₁₃	#41	1	4	yes	—
337	C₄²×C₁₃	#41	1	4	yes	—
338	C₄²×C₁₃	#41	1	4	yes	—
339	#2596	C₂×C₁₃	1	2	yes	complemented
340	#2594	C₂×C₁₃	1	2	yes	complemented
341	#2592	C₂×C₁₃	1	1	yes	characteristic
342	#2581	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#2570	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#2545	C₂×C₁₃	1	1	yes	characteristic
345	#2525	C₂×C₁₃	1	2	yes	complemented
346	#2514	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#2512	C₂×C₁₃	1	1	yes	characteristic
348	#2469	C₂×C₁₃	1	2	yes	complemented
349	#2448	C₂×C₁₃	1	1	yes	characteristic
350	#2446	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#2401	C₂×C₁₃	1	2	yes	complemented
352	#2396	C₂×C₁₃	1	2	yes	complemented
353	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
354	C₄×#126	C₂×C₁₃	1	2	yes	complemented
355	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
356	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
357	#2298	C₂×C₁₃	1	2	yes	complemented
358	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#2293	C₂×C₁₃	1	1	yes	characteristic
360	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
361	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
370	Q₈×C₁₃	—	2	8	no	—
371	Q₈×C₁₃	—	2	8	no	—
372	Q₈×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	4	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	1	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	1	no	—
381	C₂×C₄×C₁₃	—	2	1	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	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	1	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	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	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	1	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	1	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	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	4	8	no	—
426	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
427	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
428	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
429	C₂×C₄×C₁₃	C₂×#41	1	4	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	C₂×#41	1	2	yes	—
435	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
436	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
437	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
438	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
439	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
440	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
441	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#126	C₂²×C₁₃	1	2	yes	—
443	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×#117	C₂²×C₁₃	1	2	yes	—
454	#401	C₂²×C₁₃	1	2	yes	—
455	#400	C₂²×C₁₃	1	2	yes	—
456	#400	C₂²×C₁₃	1	2	yes	—
457	#400	C₂²×C₁₃	1	2	yes	—
458	#400	C₂²×C₁₃	1	2	yes	—
459	#399	C₂²×C₁₃	1	2	yes	—
460	#398	C₂²×C₁₃	1	2	yes	—
461	#398	C₂²×C₁₃	1	2	yes	—
462	#397	C₂²×C₁₃	1	2	yes	—
463	#397	C₂²×C₁₃	1	2	yes	—
464	#397	C₂²×C₁₃	1	2	yes	—
465	#396	C₂²×C₁₃	1	2	yes	—
466	#396	C₂²×C₁₃	1	2	yes	—
467	#396	C₂²×C₁₃	1	2	yes	—
468	#395	C₂²×C₁₃	1	2	yes	—
469	#393	C₂²×C₁₃	1	2	yes	—
470	#391	C₂²×C₁₃	1	1	yes	characteristic
471	#391	C₂²×C₁₃	1	1	yes	characteristic
472	#391	C₂²×C₁₃	1	1	yes	characteristic
473	#391	C₂²×C₁₃	1	1	yes	characteristic
474	#391	C₂²×C₁₃	1	1	yes	characteristic
475	#391	C₂²×C₁₃	1	1	yes	characteristic
476	#390	C₂²×C₁₃	1	1	yes	characteristic
477	#390	C₂²×C₁₃	1	1	yes	characteristic
478	#390	C₂²×C₁₃	1	1	yes	characteristic
479	#390	C₂²×C₁₃	1	1	yes	characteristic
480	#389	C₂²×C₁₃	1	2	yes	—
481	#389	C₂²×C₁₃	1	2	yes	—
482	#389	C₂²×C₁₃	1	1	yes	characteristic
483	#389	C₂²×C₁₃	1	1	yes	characteristic
484	#389	C₂²×C₁₃	1	1	yes	characteristic
485	#389	C₂²×C₁₃	1	1	yes	characteristic
486	#388	C₂²×C₁₃	1	2	yes	—
487	#388	C₂²×C₁₃	1	2	yes	—
488	#388	C₂²×C₁₃	1	2	yes	—
489	#388	C₂²×C₁₃	1	2	yes	—
490	#388	C₂²×C₁₃	1	2	yes	—
491	#388	C₂²×C₁₃	1	2	yes	—
492	#388	C₂²×C₁₃	1	2	yes	—
493	#388	C₂²×C₁₃	1	2	yes	—
494	#388	C₂²×C₁₃	1	2	yes	—
495	#388	C₂²×C₁₃	1	2	yes	—
496	#388	C₂²×C₁₃	1	2	yes	—
497	#388	C₂²×C₁₃	1	2	yes	—
498	#388	C₂²×C₁₃	1	2	yes	—
499	#387	C₂²×C₁₃	1	2	yes	—
500	#387	C₂²×C₁₃	1	2	yes	—
501	#387	C₂²×C₁₃	1	2	yes	—
502	#387	C₂²×C₁₃	1	2	yes	—
503	#387	C₂²×C₁₃	1	2	yes	—
504	#387	C₂²×C₁₃	1	2	yes	—
505	#387	C₂²×C₁₃	1	2	yes	—
506	#387	C₂²×C₁₃	1	2	yes	—
507	#387	C₂²×C₁₃	1	2	yes	—
508	#384	C₂²×C₁₃	1	1	yes	characteristic
509	#383	C₂²×C₁₃	1	2	yes	—
510	#382	C₂²×C₁₃	1	1	yes	characteristic
511	#382	C₂²×C₁₃	1	1	yes	characteristic
512	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
513	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
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	1	yes	characteristic
521	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
523	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
524	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
525	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
526	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
527	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
528	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
529	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
530	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
532	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
533	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
534	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
535	#376	C₂²×C₁₃	1	2	yes	—
536	C₄³	C₂²×C₁₃	1	2	yes	—
537	C₄³	C₂²×C₁₃	1	1	yes	characteristic
538	C₄³	C₂²×C₁₃	1	1	yes	characteristic
539	C₄³	C₂²×C₁₃	1	1	yes	characteristic
540	C₂²×C₁₃	—	4	2	no	—
541	C₂²×C₁₃	—	4	2	no	—
542	C₂²×C₁₃	—	4	2	no	—
543	C₂²×C₁₃	—	4	2	no	—
544	C₂²×C₁₃	—	4	2	no	—
545	C₂²×C₁₃	—	4	2	no	—
546	C₂²×C₁₃	—	4	2	no	—
547	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
548	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
549	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
550	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
551	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
552	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₂²×C₁₃	#585	1	1	yes	characteristic
554	C₄×C₁₃	—	2	4	no	—
555	C₄×C₁₃	—	2	2	no	—
556	C₄×C₁₃	—	2	2	no	—
557	C₄×C₁₃	—	2	2	no	—
558	C₄×C₁₃	—	2	2	no	—
559	C₄×C₁₃	—	2	2	no	—
560	C₄×C₁₃	—	2	2	no	—
561	C₄×C₁₃	—	2	2	no	—
562	C₄×C₁₃	—	2	2	no	—
563	C₄×C₁₃	—	4	2	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	1	no	—
569	C₄×C₁₃	—	4	2	no	—
570	C₄×C₁₃	—	4	2	no	—
571	C₄×C₁₃	—	4	1	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	1	no	—
574	C₄×C₁₃	#529	1	4	yes	—
575	C₄×C₁₃	#556	1	4	yes	—
576	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
577	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
578	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
581	C₄⋊Q₈	—	2	4	no	—
582	#126	—	2	8	no	—
583	#124	—	2	4	no	—
584	#124	—	2	4	no	—
585	C₄×Q₈	—	2	4	no	—
586	C₄×Q₈	—	2	4	no	—
587	C₄×Q₈	—	2	4	no	—
588	C₄×Q₈	—	2	4	no	—
589	C₄×Q₈	—	2	4	no	—
590	C₄×Q₈	—	2	4	no	—
591	C₄×Q₈	—	2	4	no	—
592	C₄×D₄	—	2	4	no	—
593	#117	—	2	8	no	—
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	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₂²⋊C₄	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	1	yes	characteristic
637	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
674	#95	C₂³×C₁₃	1	1	yes	characteristic
675	#95	C₂³×C₁₃	1	1	yes	characteristic
676	#95	C₂³×C₁₃	1	2	yes	—
677	#95	C₂³×C₁₃	1	1	yes	characteristic
678	#95	C₂³×C₁₃	1	2	yes	—
679	#95	C₂³×C₁₃	1	2	yes	—
680	#95	C₂³×C₁₃	1	1	yes	characteristic
681	#95	C₂³×C₁₃	1	1	yes	characteristic
682	#95	C₂³×C₁₃	1	2	yes	—
683	#95	C₂³×C₁₃	1	2	yes	—
684	#95	C₂³×C₁₃	1	2	yes	—
685	#95	C₂³×C₁₃	1	2	yes	—
686	#95	C₂³×C₁₃	1	2	yes	—
687	#95	C₂³×C₁₃	1	2	yes	—
688	C₂×C₁₃	—	8	2	no	—
689	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
690	C₂×C₁₃	#3444	1	1	yes	characteristic
691	C₂×C₁₃	#3461	1	1	yes	characteristic
692	C₂×C₁₃	C₂×#556	1	1	yes	characteristic
693	C₂×C₁₃	#3480	1	1	yes	characteristic
694	C₂×C₁₃	#3480	1	1	yes	characteristic
695	C₂×C₁₃	#3482	1	1	yes	characteristic
696	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	C₁₃×#41	1	4	yes	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	C₁₃×#41	1	4	yes	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	4	no	—
780	C₄²	—	2	2	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	4	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	4	no	—
788	C₄²	—	2	2	no	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	4	1	no	—
793	C₄²	—	4	1	no	—
794	C₄²	—	4	1	no	—
795	C₄²	—	4	2	no	—
796	C₄²	C₁₃×#41	1	4	yes	—
797	C₄²	C₁₃×#41	1	4	yes	—
798	C₄²	C₁₃×#41	1	4	yes	—
799	C₁₃	#34902	1	1	yes	characteristic, direct product factor, Sylow
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
808	Q₈	—	2	8	no	—
809	Q₈	—	2	8	no	—
810	Q₈	—	4	4	no	—
811	D₄	—	4	4	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	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	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	4	8	no	—
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	C₂×C₁₃×#41	1	4	yes	—
868	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
869	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
870	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
871	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
872	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
873	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
874	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
875	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
876	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
877	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
878	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
887	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
888	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
889	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
890	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
891	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
892	C₂²	C₁₃×#585	1	1	yes	characteristic
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	C₁₃×#529	1	4	yes	—
914	C₄	C₁₃×#556	1	4	yes	—
915	C₂	—	8	2	no	—
916	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
917	C₂	C₁₃×#3444	1	1	yes	characteristic
918	C₂	C₁₃×#3461	1	1	yes	characteristic
919	C₂	C₂×C₁₃×#556	1	1	yes	characteristic
920	C₂	C₁₃×#3480	1	1	yes	characteristic
921	C₂	C₁₃×#3480	1	1	yes	characteristic
922	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	C₂²×D₄×C₁₃	C₂³
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×#2596	C₂	semidirect
2. C₁₃×#2594	C₂	semidirect
4. C₁₃×#2581	C₂	semidirect
5. C₁₃×#2570	C₂	semidirect
7. C₁₃×#2525	C₂	semidirect
8. C₁₃×#2514	C₂	semidirect
10. C₁₃×#2469	C₂	semidirect
12. C₁₃×#2446	C₂	semidirect
13. C₁₃×#2401	C₂	semidirect
14. C₁₃×#2396	C₂	semidirect
15. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
16. C₄×C₁₃×#126	C₂	semidirect
19. C₁₃×#2298	C₂	semidirect
20. C₁₃×#2295	C₂	semidirect
22. C₄²×Q₈×C₁₃	C₂	semidirect
23. C₄²×Q₈×C₁₃	C₂	semidirect
235. #34902	C₁₃	direct (N × H)
339. #2596	C₂×C₁₃	semidirect
340. #2594	C₂×C₁₃	semidirect
342. #2581	C₂×C₁₃	semidirect
343. #2570	C₂×C₁₃	semidirect
345. #2525	C₂×C₁₃	semidirect
346. #2514	C₂×C₁₃	semidirect
348. #2469	C₂×C₁₃	semidirect
350. #2446	C₂×C₁₃	semidirect
351. #2401	C₂×C₁₃	semidirect
352. #2396	C₂×C₁₃	semidirect
353. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
354. C₄×#126	C₂×C₁₃	semidirect
357. #2298	C₂×C₁₃	semidirect
358. #2295	C₂×C₁₃	semidirect
360. C₄²×Q₈	C₂×C₁₃	semidirect
361. C₄²×Q₈	C₂×C₁₃	semidirect
799. C₁₃	#34902	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×#2596	2
C₁₃×#2594	2
C₁₃×#2592	2
C₁₃×#2581	2
C₁₃×#2570	2
C₁₃×#2545	2
C₁₃×#2525	2
C₁₃×#2514	2
C₁₃×#2512	2
C₁₃×#2469	2
C₁₃×#2448	2
C₁₃×#2446	2
C₁₃×#2401	2
C₁₃×#2396	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#126	2
C₄×C₁₃×#124	2
C₁₃×#2298	2
C₁₃×#2295	2
C₁₃×#2293	2
C₄²×Q₈×C₁₃	2
#34902	13

Subgroups — C13×#34902 #15721241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34902 #15721241