Subgroups — C₁₃×#34969 #15721308

Order 3328.

1962 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2530	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2527	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2492	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2477	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2470	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2427	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2422	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2401	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2398	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
18	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
20	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
21	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#123	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
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×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
40	C₁₃×#401	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×#400	C₂²	1	2	yes	—
46	C₁₃×#397	C₂²	1	2	yes	—
47	C₁₃×#397	C₂²	1	2	yes	—
48	C₁₃×#397	C₂²	1	2	yes	—
49	C₁₃×#397	C₂²	1	2	yes	—
50	C₁₃×#397	C₂²	1	2	yes	—
51	C₁₃×#396	C₂²	1	2	yes	—
52	C₁₃×#394	C₂²	1	2	yes	—
53	C₁₃×#394	C₂²	1	2	yes	—
54	C₁₃×#393	C₂²	1	2	yes	—
55	C₁₃×#393	C₂²	1	2	yes	—
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×#391	C₂²	1	2	yes	—
60	C₁₃×#391	C₂²	1	2	yes	—
61	C₁₃×#391	C₂²	1	1	yes	characteristic
62	C₁₃×#390	C₂²	1	1	yes	characteristic
63	C₁₃×#390	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	1	yes	characteristic
67	C₁₃×#389	C₂²	1	1	yes	characteristic
68	C₁₃×#389	C₂²	1	1	yes	characteristic
69	C₁₃×#389	C₂²	1	2	yes	—
70	C₁₃×#389	C₂²	1	1	yes	characteristic
71	C₁₃×#389	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×#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×#386	C₂²	1	2	yes	—
85	C₁₃×#386	C₂²	1	2	yes	—
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#385	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#384	C₂²	1	1	yes	characteristic
91	C₁₃×#382	C₂²	1	1	yes	characteristic
92	C₁₃×#381	C₂²	1	2	yes	—
93	C₁₃×#380	C₂²	1	1	yes	characteristic
94	C₁₃×#380	C₂²	1	1	yes	characteristic
95	C₁₃×#380	C₂²	1	2	yes	—
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	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	2	yes	—
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₁₃×C₂²⋊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	1	yes	characteristic
119	C₁₃×#376	C₂²	1	1	yes	characteristic
120	C₁₃×#376	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×D₄×C₁₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
133	C₁₃×C₄⋊Q₈	—	2	4	no	—
134	C₁₃×#124	—	2	4	no	—
135	C₁₃×#123	—	2	8	no	—
136	C₁₃×C₂²⋊Q₈	—	2	8	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×#121	—	2	4	no	—
139	C₄×Q₈×C₁₃	—	2	4	no	—
140	C₄×Q₈×C₁₃	—	4	4	no	—
141	C₄×D₄×C₁₃	—	2	4	no	—
142	C₄×D₄×C₁₃	—	2	4	no	—
143	C₄×D₄×C₁₃	—	2	4	no	—
144	C₄×D₄×C₁₃	—	4	4	no	—
145	C₁₃×#117	—	2	4	no	—
146	C₁₃×#117	—	2	4	no	—
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	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	—	2	4	no	—
186	C₂×C₄²×C₁₃	—	4	4	no	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
194	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
212	C₁₃×#95	C₂³	1	1	yes	characteristic
213	C₁₃×#95	C₂³	1	1	yes	characteristic
214	C₁₃×#95	C₂³	1	1	yes	characteristic
215	C₁₃×#95	C₂³	1	1	yes	characteristic
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	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	C₁₃×#95	C₂³	1	2	yes	—
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	2	yes	—
238	#34969	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	—	2	4	no	—
246	C₂×Q₈×C₁₃	—	4	2	no	—
247	C₂×D₄×C₁₃	—	2	4	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	4	2	no	—
252	C₂×D₄×C₁₃	#41	1	4	yes	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	4	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	4	no	—
260	C₂²×C₄×C₁₃	—	2	4	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	4	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	2	4	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	4	2	no	—
270	C₂²×C₄×C₁₃	—	4	2	no	—
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	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	4	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	—	2	4	no	—
304	C₁₃×C₄⋊C₄	—	2	4	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	4	2	no	—
308	C₁₃×C₄⋊C₄	—	4	2	no	—
309	C₁₃×C₄⋊C₄	—	4	2	no	—
310	C₁₃×C₄⋊C₄	—	4	2	no	—
311	C₁₃×C₄⋊C₄	#41	1	4	yes	—
312	C₁₃×C₄⋊C₄	#41	1	4	yes	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	4	no	—
323	C₁₃×C₂²⋊C₄	—	2	4	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	4	2	no	—
328	C₁₃×C₂²⋊C₄	—	4	2	no	—
329	C₁₃×C₂²⋊C₄	#41	1	4	yes	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	2	no	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	—	2	2	no	—
338	C₄²×C₁₃	—	2	2	no	—
339	C₄²×C₁₃	—	2	4	no	—
340	C₄²×C₁₃	—	2	2	no	—
341	C₄²×C₁₃	—	2	2	no	—
342	C₄²×C₁₃	—	2	2	no	—
343	C₄²×C₁₃	—	2	4	no	—
344	C₄²×C₁₃	—	2	4	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	2	2	no	—
347	C₄²×C₁₃	—	2	2	no	—
348	C₄²×C₁₃	—	4	2	no	—
349	C₄²×C₁₃	—	4	2	no	—
350	C₄²×C₁₃	#41	1	4	yes	—
351	#2530	C₂×C₁₃	1	2	yes	complemented
352	#2527	C₂×C₁₃	1	2	yes	complemented
353	#2511	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2509	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#2494	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#2492	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#2477	C₂×C₁₃	1	2	yes	complemented
358	#2470	C₂×C₁₃	1	2	yes	complemented
359	#2452	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#2447	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#2427	C₂×C₁₃	1	1	yes	characteristic
362	#2422	C₂×C₁₃	1	1	yes	characteristic
363	#2401	C₂×C₁₃	1	2	yes	complemented
364	#2398	C₂×C₁₃	1	2	yes	complemented
365	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
366	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
367	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
369	C₄×#123	C₂×C₁₃	1	2	yes	complemented
370	C₄×#121	C₂×C₁₃	1	1	yes	characteristic
371	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
372	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
373	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
374	C₂³×C₁₃	—	2	1	no	—
375	C₂³×C₁₃	—	2	1	no	—
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	2	2	no	—
378	C₂³×C₁₃	—	2	2	no	—
379	C₂³×C₁₃	—	2	2	no	—
380	C₂³×C₁₃	—	2	1	no	—
381	C₂³×C₁₃	—	2	1	no	—
382	C₂³×C₁₃	—	2	1	no	—
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	2	1	no	—
385	C₂³×C₁₃	—	2	2	no	—
386	C₂³×C₁₃	C₂×#41	1	4	yes	—
387	C₂³×C₁₃	C₂×#41	1	2	yes	—
388	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
389	Q₈×C₁₃	—	4	8	no	—
390	Q₈×C₁₃	—	4	4	no	—
391	D₄×C₁₃	—	2	8	no	—
392	D₄×C₁₃	—	4	8	no	—
393	C₂×C₄×C₁₃	—	2	8	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	1	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	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	1	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	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	1	no	—
439	C₂×C₄×C₁₃	—	2	1	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	1	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	4	8	no	—
445	C₂×C₄×C₁₃	—	4	8	no	—
446	C₂×C₄×C₁₃	—	4	4	no	—
447	C₂×C₄×C₁₃	—	4	4	no	—
448	C₂×C₄×C₁₃	—	4	8	no	—
449	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
450	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
451	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
452	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
453	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
454	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
455	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
456	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
457	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
458	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
459	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
460	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
461	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
462	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×#123	C₂²×C₁₃	1	2	yes	—
465	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
467	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
470	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
474	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
476	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
477	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
478	#401	C₂²×C₁₃	1	2	yes	—
479	#400	C₂²×C₁₃	1	2	yes	—
480	#400	C₂²×C₁₃	1	2	yes	—
481	#400	C₂²×C₁₃	1	2	yes	—
482	#400	C₂²×C₁₃	1	2	yes	—
483	#400	C₂²×C₁₃	1	2	yes	—
484	#397	C₂²×C₁₃	1	2	yes	—
485	#397	C₂²×C₁₃	1	2	yes	—
486	#397	C₂²×C₁₃	1	2	yes	—
487	#397	C₂²×C₁₃	1	2	yes	—
488	#397	C₂²×C₁₃	1	2	yes	—
489	#396	C₂²×C₁₃	1	2	yes	—
490	#394	C₂²×C₁₃	1	2	yes	—
491	#394	C₂²×C₁₃	1	2	yes	—
492	#393	C₂²×C₁₃	1	2	yes	—
493	#393	C₂²×C₁₃	1	2	yes	—
494	#391	C₂²×C₁₃	1	2	yes	—
495	#391	C₂²×C₁₃	1	1	yes	characteristic
496	#391	C₂²×C₁₃	1	1	yes	characteristic
497	#391	C₂²×C₁₃	1	1	yes	characteristic
498	#391	C₂²×C₁₃	1	1	yes	characteristic
499	#391	C₂²×C₁₃	1	2	yes	—
500	#390	C₂²×C₁₃	1	1	yes	characteristic
501	#390	C₂²×C₁₃	1	1	yes	characteristic
502	#389	C₂²×C₁₃	1	1	yes	characteristic
503	#389	C₂²×C₁₃	1	1	yes	characteristic
504	#389	C₂²×C₁₃	1	2	yes	—
505	#389	C₂²×C₁₃	1	1	yes	characteristic
506	#389	C₂²×C₁₃	1	1	yes	characteristic
507	#389	C₂²×C₁₃	1	1	yes	characteristic
508	#389	C₂²×C₁₃	1	2	yes	—
509	#389	C₂²×C₁₃	1	1	yes	characteristic
510	#388	C₂²×C₁₃	1	2	yes	—
511	#388	C₂²×C₁₃	1	2	yes	—
512	#388	C₂²×C₁₃	1	2	yes	—
513	#388	C₂²×C₁₃	1	2	yes	—
514	#388	C₂²×C₁₃	1	2	yes	—
515	#387	C₂²×C₁₃	1	2	yes	—
516	#387	C₂²×C₁₃	1	2	yes	—
517	#387	C₂²×C₁₃	1	2	yes	—
518	#387	C₂²×C₁₃	1	2	yes	—
519	#387	C₂²×C₁₃	1	2	yes	—
520	#387	C₂²×C₁₃	1	2	yes	—
521	#387	C₂²×C₁₃	1	2	yes	—
522	#386	C₂²×C₁₃	1	2	yes	—
523	#386	C₂²×C₁₃	1	2	yes	—
524	#385	C₂²×C₁₃	1	2	yes	—
525	#385	C₂²×C₁₃	1	2	yes	—
526	#385	C₂²×C₁₃	1	2	yes	—
527	#385	C₂²×C₁₃	1	2	yes	—
528	#384	C₂²×C₁₃	1	1	yes	characteristic
529	#382	C₂²×C₁₃	1	1	yes	characteristic
530	#381	C₂²×C₁₃	1	2	yes	—
531	#380	C₂²×C₁₃	1	1	yes	characteristic
532	#380	C₂²×C₁₃	1	2	yes	—
533	#380	C₂²×C₁₃	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
535	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
536	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
537	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
539	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
540	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
541	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
542	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
543	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
546	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
548	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
549	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
551	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
552	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
553	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
554	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
555	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
556	#376	C₂²×C₁₃	1	2	yes	—
557	#376	C₂²×C₁₃	1	1	yes	characteristic
558	#376	C₂²×C₁₃	1	1	yes	characteristic
559	C₄³	C₂²×C₁₃	1	1	yes	characteristic
560	C₄³	C₂²×C₁₃	1	1	yes	characteristic
561	C₂²×C₁₃	—	2	4	no	—
562	C₂²×C₁₃	—	2	2	no	—
563	C₂²×C₁₃	—	2	4	no	—
564	C₂²×C₁₃	—	2	2	no	—
565	C₂²×C₁₃	—	2	2	no	—
566	C₂²×C₁₃	—	2	4	no	—
567	C₂²×C₁₃	—	4	1	no	—
568	C₂²×C₁₃	—	4	2	no	—
569	C₂²×C₁₃	—	4	2	no	—
570	C₂²×C₁₃	—	4	1	no	—
571	C₂²×C₁₃	—	4	2	no	—
572	C₂²×C₁₃	—	4	1	no	—
573	C₂²×C₁₃	—	4	2	no	—
574	C₂²×C₁₃	—	4	1	no	—
575	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
576	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
577	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
578	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
579	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
580	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
582	C₄×C₁₃	—	2	2	no	—
583	C₄×C₁₃	—	2	2	no	—
584	C₄×C₁₃	—	2	2	no	—
585	C₄×C₁₃	—	2	2	no	—
586	C₄×C₁₃	—	2	4	no	—
587	C₄×C₁₃	—	2	2	no	—
588	C₄×C₁₃	—	2	2	no	—
589	C₄×C₁₃	—	4	1	no	—
590	C₄×C₁₃	—	4	2	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	1	no	—
593	C₄×C₁₃	—	4	2	no	—
594	C₄×C₁₃	—	4	1	no	—
595	C₄×C₁₃	—	4	2	no	—
596	C₄×C₁₃	—	4	2	no	—
597	C₄×C₁₃	—	4	2	no	—
598	C₄×C₁₃	—	4	1	no	—
599	C₄×C₁₃	—	4	1	no	—
600	C₄×C₁₃	—	4	1	no	—
601	C₄×C₁₃	#529	1	4	yes	—
602	C₄×C₁₃	#542	1	4	yes	—
603	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
605	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
606	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
610	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
612	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
613	C₄⋊Q₈	—	2	4	no	—
614	#124	—	2	4	no	—
615	#123	—	2	8	no	—
616	C₂²⋊Q₈	—	2	8	no	—
617	C₂²⋊Q₈	—	2	4	no	—
618	#121	—	2	4	no	—
619	C₄×Q₈	—	2	4	no	—
620	C₄×Q₈	—	4	4	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	4	no	—
623	C₄×D₄	—	2	4	no	—
624	C₄×D₄	—	4	4	no	—
625	#117	—	2	4	no	—
626	#117	—	2	4	no	—
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₄²	—	2	4	no	—
666	C₂×C₄²	—	4	4	no	—
667	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
672	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
676	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
677	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
686	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
687	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
688	#95	C₂³×C₁₃	1	1	yes	characteristic
689	#95	C₂³×C₁₃	1	1	yes	characteristic
690	#95	C₂³×C₁₃	1	1	yes	characteristic
691	#95	C₂³×C₁₃	1	1	yes	characteristic
692	#95	C₂³×C₁₃	1	1	yes	characteristic
693	#95	C₂³×C₁₃	1	1	yes	characteristic
694	#95	C₂³×C₁₃	1	1	yes	characteristic
695	#95	C₂³×C₁₃	1	1	yes	characteristic
696	#95	C₂³×C₁₃	1	2	yes	—
697	#95	C₂³×C₁₃	1	2	yes	—
698	#95	C₂³×C₁₃	1	2	yes	—
699	#95	C₂³×C₁₃	1	2	yes	—
700	#95	C₂³×C₁₃	1	2	yes	—
701	#95	C₂³×C₁₃	1	2	yes	—
702	#95	C₂³×C₁₃	1	2	yes	—
703	#95	C₂³×C₁₃	1	2	yes	—
704	#95	C₂³×C₁₃	1	2	yes	—
705	#95	C₂³×C₁₃	1	2	yes	—
706	#95	C₂³×C₁₃	1	2	yes	—
707	#95	C₂³×C₁₃	1	2	yes	—
708	#95	C₂³×C₁₃	1	2	yes	—
709	#95	C₂³×C₁₃	1	2	yes	—
710	#95	C₂³×C₁₃	1	2	yes	—
711	#95	C₂³×C₁₃	1	2	yes	—
712	#95	C₂³×C₁₃	1	2	yes	—
713	#95	C₂³×C₁₃	1	2	yes	—
714	#95	C₂³×C₁₃	1	2	yes	—
715	#95	C₂³×C₁₃	1	2	yes	—
716	#95	C₂³×C₁₃	1	2	yes	—
717	#95	C₂³×C₁₃	1	2	yes	—
718	C₂×C₁₃	—	4	4	no	—
719	C₂×C₁₃	—	4	2	no	—
720	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
721	C₂×C₁₃	#3444	1	1	yes	characteristic
722	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
723	C₂×C₁₃	#3481	1	1	yes	characteristic
724	C₂×C₁₃	#3481	1	1	yes	characteristic
725	C₂×C₁₃	#3482	1	1	yes	characteristic
726	C₂×C₁₃	#3482	1	1	yes	characteristic
727	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
728	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	4	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	4	no	—
734	C₂×Q₈	—	4	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	C₁₃×#41	1	4	yes	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	4	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	C₁₃×#41	1	4	yes	—
800	C₄⋊C₄	C₁₃×#41	1	4	yes	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	C₁₃×#41	1	4	yes	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	4	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	4	no	—
832	C₄²	—	2	4	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	4	2	no	—
837	C₄²	—	4	2	no	—
838	C₄²	C₁₃×#41	1	4	yes	—
839	C₁₃	#34969	1	1	yes	characteristic, direct product factor, Sylow
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	2	no	—
852	C₂³	C₂×C₁₃×#41	1	4	yes	—
853	C₂³	C₂×C₁₃×#41	1	2	yes	—
854	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
855	Q₈	—	4	8	no	—
856	Q₈	—	4	4	no	—
857	D₄	—	2	8	no	—
858	D₄	—	4	8	no	—
859	C₂×C₄	—	2	8	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	4	8	no	—
911	C₂×C₄	—	4	8	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
916	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
917	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
918	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
919	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
920	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
921	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
922	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
923	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
924	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
925	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
926	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
927	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	1	no	—
942	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
943	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
944	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
945	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
946	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
947	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
948	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	4	1	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	C₁₃×#529	1	4	yes	—
969	C₄	C₁₃×#542	1	4	yes	—
970	C₂	—	4	4	no	—
971	C₂	—	4	2	no	—
972	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
973	C₂	C₁₃×#3444	1	1	yes	characteristic
974	C₂	C₂×C₁₃×#542	1	1	yes	characteristic
975	C₂	C₁₃×#3481	1	1	yes	characteristic
976	C₂	C₁₃×#3481	1	1	yes	characteristic
977	C₂	C₁₃×#3482	1	1	yes	characteristic
978	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	C₂×C₁₃×#121	C₂²
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×#2530	C₂	semidirect
2. C₁₃×#2527	C₂	semidirect
3. C₁₃×#2511	C₂	semidirect
4. C₁₃×#2509	C₂	semidirect
5. C₁₃×#2494	C₂	semidirect
6. C₁₃×#2492	C₂	semidirect
7. C₁₃×#2477	C₂	semidirect
8. C₁₃×#2470	C₂	semidirect
9. C₁₃×#2452	C₂	semidirect
10. C₁₃×#2447	C₂	semidirect
13. C₁₃×#2401	C₂	semidirect
14. C₁₃×#2398	C₂	semidirect
15. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
16. C₄×C₁₃×#124	C₂	semidirect
17. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
18. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
19. C₄×C₁₃×#123	C₂	semidirect
21. C₁₃×#2295	C₂	semidirect
22. C₄²×D₄×C₁₃	C₂	semidirect
23. C₄×C₁₃×#117	C₂	semidirect
238. #34969	C₁₃	direct (N × H)
351. #2530	C₂×C₁₃	semidirect
352. #2527	C₂×C₁₃	semidirect
353. #2511	C₂×C₁₃	semidirect
354. #2509	C₂×C₁₃	semidirect
355. #2494	C₂×C₁₃	semidirect
356. #2492	C₂×C₁₃	semidirect
357. #2477	C₂×C₁₃	semidirect
358. #2470	C₂×C₁₃	semidirect
359. #2452	C₂×C₁₃	semidirect
360. #2447	C₂×C₁₃	semidirect
363. #2401	C₂×C₁₃	semidirect
364. #2398	C₂×C₁₃	semidirect
365. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
366. C₄×#124	C₂×C₁₃	semidirect
367. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
368. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
369. C₄×#123	C₂×C₁₃	semidirect
371. #2295	C₂×C₁₃	semidirect
372. C₄²×D₄	C₂×C₁₃	semidirect
373. C₄×#117	C₂×C₁₃	semidirect
839. C₁₃	#34969	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×#2530	2
C₁₃×#2527	2
C₁₃×#2511	2
C₁₃×#2509	2
C₁₃×#2494	2
C₁₃×#2492	2
C₁₃×#2477	2
C₁₃×#2470	2
C₁₃×#2452	2
C₁₃×#2447	2
C₁₃×#2427	2
C₁₃×#2422	2
C₁₃×#2401	2
C₁₃×#2398	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#124	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
C₁₃×#2295	2
C₄²×D₄×C₁₃	2
C₄×C₁₃×#117	2
#34969	13

Subgroups — C13×#34969 #15721308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34969 #15721308