Subgroups — C₁₃×#34500 #15720839

Order 3328.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2379	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2376	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2366	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2359	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2335	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2322	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
21	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#559	C₄	1	16	yes	complemented
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#124	C₂²	1	2	yes	—
29	C₂×C₁₃×#123	C₂²	1	2	yes	—
30	C₂×C₁₃×#123	C₂²	1	2	yes	—
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×C₄×D₄×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#117	C₂²	1	2	yes	—
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
45	C₁₃×#391	C₂²	1	1	yes	characteristic
46	C₁₃×#391	C₂²	1	1	yes	characteristic
47	C₁₃×#391	C₂²	1	1	yes	characteristic
48	C₁₃×#391	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	2	yes	—
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#390	C₂²	1	1	yes	characteristic
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#390	C₂²	1	1	yes	characteristic
54	C₁₃×#390	C₂²	1	2	yes	—
55	C₁₃×#389	C₂²	1	1	yes	characteristic
56	C₁₃×#389	C₂²	1	1	yes	characteristic
57	C₁₃×#389	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	2	yes	—
62	C₁₃×#389	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#388	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×#387	C₂²	1	1	yes	characteristic
76	C₁₃×#387	C₂²	1	1	yes	characteristic
77	C₁₃×#387	C₂²	1	1	yes	characteristic
78	C₁₃×#387	C₂²	1	1	yes	characteristic
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×#386	C₂²	1	2	yes	—
84	C₁₃×#386	C₂²	1	2	yes	—
85	C₁₃×#386	C₂²	1	2	yes	—
86	C₁₃×#386	C₂²	1	2	yes	—
87	C₁₃×#386	C₂²	1	2	yes	—
88	C₁₃×#386	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#385	C₂²	1	2	yes	—
91	C₁₃×#385	C₂²	1	2	yes	—
92	C₁₃×#385	C₂²	1	2	yes	—
93	C₁₃×#385	C₂²	1	2	yes	—
94	C₁₃×#385	C₂²	1	2	yes	—
95	C₁₃×#385	C₂²	1	2	yes	—
96	C₁₃×#385	C₂²	1	2	yes	—
97	C₁₃×#384	C₂²	1	1	yes	characteristic
98	C₁₃×#383	C₂²	1	2	yes	—
99	C₁₃×#382	C₂²	1	1	yes	characteristic
100	C₁₃×#382	C₂²	1	2	yes	—
101	C₁₃×#382	C₂²	1	2	yes	—
102	C₁₃×#382	C₂²	1	1	yes	characteristic
103	C₁₃×#381	C₂²	1	2	yes	—
104	C₁₃×#380	C₂²	1	2	yes	—
105	C₁₃×#380	C₂²	1	2	yes	—
106	C₁₃×#380	C₂²	1	2	yes	—
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
112	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₄⋊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	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₁₃×#376	C₂²	1	1	yes	characteristic
121	C₁₃×#376	C₂²	1	1	yes	characteristic
122	C₂×C₁₃×#95	C₂²	1	2	yes	—
123	C₄³×C₁₃	C₂²	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	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
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	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
136	C₁₃×#127	C₂×C₄	1	8	yes	—
137	C₁₃×#124	C₂×C₄	1	8	yes	complemented
138	C₁₃×#124	C₂×C₄	1	8	yes	complemented
139	C₁₃×#124	C₂×C₄	1	16	yes	complemented
140	C₁₃×#123	C₂×C₄	1	16	yes	complemented
141	C₁₃×#123	C₂×C₄	1	16	yes	complemented
142	C₄×Q₈×C₁₃	—	4	2	no	—
143	C₄×Q₈×C₁₃	—	4	2	no	—
144	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
145	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
146	C₄×D₄×C₁₃	—	4	2	no	—
147	C₄×D₄×C₁₃	—	4	2	no	—
148	C₄×D₄×C₁₃	—	4	2	no	—
149	C₄×D₄×C₁₃	—	4	2	no	—
150	C₄×D₄×C₁₃	—	4	4	no	—
151	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
152	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
153	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
154	C₁₃×#117	—	4	4	no	—
155	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₂²⋊C₄	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	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	1	yes	characteristic
215	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	1	yes	characteristic
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	2	yes	—
230	C₁₃×#95	C₂³	1	1	yes	characteristic
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	1	yes	characteristic
233	C₁₃×#95	C₂³	1	1	yes	characteristic
234	C₁₃×#95	C₂³	1	2	yes	—
235	C₁₃×#95	C₂³	1	1	yes	characteristic
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	1	yes	characteristic
238	C₁₃×#95	C₂³	1	1	yes	characteristic
239	C₁₃×#95	C₂³	1	1	yes	characteristic
240	C₁₃×#95	C₂³	1	1	yes	characteristic
241	C₁₃×#95	C₂³	1	1	yes	characteristic
242	C₁₃×#95	C₂³	1	1	yes	characteristic
243	#34500	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
245	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₁₃	—	2	2	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	4	1	no	—
249	C₂×Q₈×C₁₃	—	4	1	no	—
250	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
251	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	4	2	no	—
257	C₂×D₄×C₁₃	—	4	2	no	—
258	C₂×D₄×C₁₃	—	4	2	no	—
259	C₂×D₄×C₁₃	—	4	2	no	—
260	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
261	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
262	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
263	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	4	2	no	—
266	C₂²×C₄×C₁₃	—	4	2	no	—
267	C₂²×C₄×C₁₃	—	4	2	no	—
268	C₂²×C₄×C₁₃	—	4	2	no	—
269	C₂²×C₄×C₁₃	—	4	2	no	—
270	C₂²×C₄×C₁₃	—	4	2	no	—
271	C₂²×C₄×C₁₃	—	4	2	no	—
272	C₂²×C₄×C₁₃	—	4	2	no	—
273	C₂²×C₄×C₁₃	—	4	2	no	—
274	C₂²×C₄×C₁₃	—	4	2	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	—	4	2	no	—
277	C₂²×C₄×C₁₃	—	4	2	no	—
278	C₂²×C₄×C₁₃	—	4	2	no	—
279	C₂²×C₄×C₁₃	—	4	2	no	—
280	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
281	C₂²×C₄×C₁₃	C₂²×C₄	1	8	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	2	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	4	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	4	2	no	—
311	C₁₃×C₄⋊C₄	—	4	2	no	—
312	C₁₃×C₄⋊C₄	—	4	1	no	—
313	C₁₃×C₄⋊C₄	—	4	1	no	—
314	C₁₃×C₄⋊C₄	—	4	2	no	—
315	C₁₃×C₄⋊C₄	—	4	1	no	—
316	C₁₃×C₄⋊C₄	—	4	2	no	—
317	C₁₃×C₄⋊C₄	—	4	1	no	—
318	C₁₃×C₄⋊C₄	—	4	2	no	—
319	C₁₃×C₄⋊C₄	—	4	2	no	—
320	C₁₃×C₄⋊C₄	—	4	2	no	—
321	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
322	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
323	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
324	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
325	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
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	—	4	2	no	—
330	C₁₃×C₂²⋊C₄	—	4	2	no	—
331	C₁₃×C₂²⋊C₄	—	4	2	no	—
332	C₁₃×C₂²⋊C₄	—	4	2	no	—
333	C₁₃×C₂²⋊C₄	—	4	2	no	—
334	C₁₃×C₂²⋊C₄	—	4	2	no	—
335	C₁₃×C₂²⋊C₄	—	4	2	no	—
336	C₁₃×C₂²⋊C₄	—	4	2	no	—
337	C₁₃×C₂²⋊C₄	—	4	2	no	—
338	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
339	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
340	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
341	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
342	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
343	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
344	C₄²×C₁₃	—	2	2	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	2	2	no	—
347	C₄²×C₁₃	—	2	2	no	—
348	C₄²×C₁₃	—	2	2	no	—
349	C₄²×C₁₃	—	4	2	no	—
350	C₄²×C₁₃	—	4	1	no	—
351	C₄²×C₁₃	—	4	1	no	—
352	C₄²×C₁₃	—	4	1	no	—
353	C₄²×C₁₃	—	4	2	no	—
354	C₄²×C₁₃	—	4	2	no	—
355	C₄²×C₁₃	—	4	2	no	—
356	C₄²×C₁₃	—	4	2	no	—
357	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
358	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
359	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
360	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
361	C₂×#559	C₂×C₁₃	1	1	yes	characteristic
362	#2379	C₂×C₁₃	1	2	yes	complemented
363	#2376	C₂×C₁₃	1	2	yes	complemented
364	#2367	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#2367	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#2366	C₂×C₁₃	1	1	yes	characteristic
367	#2359	C₂×C₁₃	1	2	yes	complemented
368	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
369	#2352	C₂×C₁₃	1	2	yes	complemented
370	#2351	C₂×C₁₃	1	1	yes	characteristic, complemented
371	#2349	C₂×C₁₃	1	1	yes	characteristic, complemented
372	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#2337	C₂×C₁₃	1	2	yes	complemented
374	#2335	C₂×C₁₃	1	2	yes	complemented
375	#2328	C₂×C₁₃	1	1	yes	characteristic
376	#2326	C₂×C₁₃	1	1	yes	characteristic, complemented
377	#2322	C₂×C₁₃	1	2	yes	complemented
378	#2320	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#2319	C₂×C₁₃	1	1	yes	characteristic, complemented
380	#2318	C₂×C₁₃	1	2	yes	complemented
381	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
382	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
384	C₂³×C₁₃	—	2	2	no	—
385	C₂³×C₁₃	—	2	2	no	—
386	C₂³×C₁₃	—	2	2	no	—
387	C₂³×C₁₃	—	2	2	no	—
388	C₂³×C₁₃	—	2	2	no	—
389	C₂³×C₁₃	—	2	2	no	—
390	C₂³×C₁₃	—	2	2	no	—
391	C₂³×C₁₃	—	2	2	no	—
392	C₂³×C₁₃	—	2	2	no	—
393	C₂³×C₁₃	—	2	2	no	—
394	C₂³×C₁₃	—	2	2	no	—
395	C₂³×C₁₃	—	2	2	no	—
396	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
397	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
398	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
399	Q₈×C₁₃	—	2	8	no	—
400	Q₈×C₁₃	—	4	4	no	—
401	D₄×C₁₃	—	2	8	no	—
402	D₄×C₁₃	—	2	8	no	—
403	D₄×C₁₃	—	4	8	no	—
404	D₄×C₁₃	—	4	8	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	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	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	1	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	1	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	1	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	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	1	no	—
437	C₂×C₄×C₁₃	—	2	1	no	—
438	C₂×C₄×C₁₃	—	2	1	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	1	no	—
443	C₂×C₄×C₁₃	—	2	1	no	—
444	C₂×C₄×C₁₃	—	2	1	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	1	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	1	no	—
451	C₂×C₄×C₁₃	—	2	1	no	—
452	C₂×C₄×C₁₃	—	2	1	no	—
453	C₂×C₄×C₁₃	—	2	2	no	—
454	C₂×C₄×C₁₃	—	2	1	no	—
455	C₂×C₄×C₁₃	—	2	1	no	—
456	C₂×C₄×C₁₃	—	4	8	no	—
457	C₂×C₄×C₁₃	—	4	8	no	—
458	C₂×C₄×C₁₃	—	8	4	no	—
459	C₂×C₄×C₁₃	—	8	4	no	—
460	C₂×C₄×C₁₃	—	8	4	no	—
461	C₂×C₄×C₁₃	—	8	4	no	—
462	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
464	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
467	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
468	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
469	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
470	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
471	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
472	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
473	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
474	#559	C₄×C₁₃	1	16	yes	complemented
475	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
476	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
477	C₂×#124	C₂²×C₁₃	1	2	yes	—
478	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×#123	C₂²×C₁₃	1	2	yes	—
480	C₂×#123	C₂²×C₁₃	1	2	yes	—
481	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
482	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
485	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
486	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
488	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
490	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
491	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
492	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
493	C₂×#117	C₂²×C₁₃	1	2	yes	—
494	C₂²×C₄⋊C₄	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	2	yes	—
499	#391	C₂²×C₁₃	1	1	yes	characteristic
500	#390	C₂²×C₁₃	1	1	yes	characteristic
501	#390	C₂²×C₁₃	1	1	yes	characteristic
502	#390	C₂²×C₁₃	1	1	yes	characteristic
503	#390	C₂²×C₁₃	1	2	yes	—
504	#390	C₂²×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
509	#389	C₂²×C₁₃	1	2	yes	—
510	#389	C₂²×C₁₃	1	2	yes	—
511	#389	C₂²×C₁₃	1	1	yes	characteristic
512	#389	C₂²×C₁₃	1	1	yes	characteristic
513	#388	C₂²×C₁₃	1	2	yes	—
514	#388	C₂²×C₁₃	1	2	yes	—
515	#388	C₂²×C₁₃	1	2	yes	—
516	#388	C₂²×C₁₃	1	2	yes	—
517	#388	C₂²×C₁₃	1	2	yes	—
518	#388	C₂²×C₁₃	1	2	yes	—
519	#388	C₂²×C₁₃	1	2	yes	—
520	#388	C₂²×C₁₃	1	2	yes	—
521	#388	C₂²×C₁₃	1	2	yes	—
522	#388	C₂²×C₁₃	1	2	yes	—
523	#388	C₂²×C₁₃	1	2	yes	—
524	#388	C₂²×C₁₃	1	2	yes	—
525	#387	C₂²×C₁₃	1	1	yes	characteristic
526	#387	C₂²×C₁₃	1	2	yes	—
527	#387	C₂²×C₁₃	1	2	yes	—
528	#387	C₂²×C₁₃	1	2	yes	—
529	#387	C₂²×C₁₃	1	2	yes	—
530	#387	C₂²×C₁₃	1	1	yes	characteristic
531	#387	C₂²×C₁₃	1	1	yes	characteristic
532	#387	C₂²×C₁₃	1	1	yes	characteristic
533	#386	C₂²×C₁₃	1	2	yes	—
534	#386	C₂²×C₁₃	1	2	yes	—
535	#386	C₂²×C₁₃	1	2	yes	—
536	#386	C₂²×C₁₃	1	2	yes	—
537	#386	C₂²×C₁₃	1	2	yes	—
538	#386	C₂²×C₁₃	1	2	yes	—
539	#385	C₂²×C₁₃	1	2	yes	—
540	#385	C₂²×C₁₃	1	2	yes	—
541	#385	C₂²×C₁₃	1	2	yes	—
542	#385	C₂²×C₁₃	1	2	yes	—
543	#385	C₂²×C₁₃	1	2	yes	—
544	#385	C₂²×C₁₃	1	2	yes	—
545	#385	C₂²×C₁₃	1	2	yes	—
546	#385	C₂²×C₁₃	1	2	yes	—
547	#384	C₂²×C₁₃	1	1	yes	characteristic
548	#383	C₂²×C₁₃	1	2	yes	—
549	#382	C₂²×C₁₃	1	2	yes	—
550	#382	C₂²×C₁₃	1	2	yes	—
551	#382	C₂²×C₁₃	1	1	yes	characteristic
552	#382	C₂²×C₁₃	1	1	yes	characteristic
553	#381	C₂²×C₁₃	1	2	yes	—
554	#380	C₂²×C₁₃	1	2	yes	—
555	#380	C₂²×C₁₃	1	2	yes	—
556	#380	C₂²×C₁₃	1	2	yes	—
557	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
561	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
563	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
565	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
566	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
567	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
568	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
569	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
570	#376	C₂²×C₁₃	1	1	yes	characteristic
571	#376	C₂²×C₁₃	1	1	yes	characteristic
572	C₂×#95	C₂²×C₁₃	1	2	yes	—
573	C₄³	C₂²×C₁₃	1	1	yes	characteristic
574	C₂²×C₁₃	—	2	4	no	—
575	C₂²×C₁₃	—	2	4	no	—
576	C₂²×C₁₃	—	2	4	no	—
577	C₂²×C₁₃	—	2	4	no	—
578	C₂²×C₁₃	—	2	4	no	—
579	C₂²×C₁₃	—	2	4	no	—
580	C₂²×C₁₃	—	4	2	no	—
581	C₂²×C₁₃	—	4	2	no	—
582	C₂²×C₁₃	—	4	2	no	—
583	C₂²×C₁₃	—	4	2	no	—
584	C₂²×C₁₃	—	4	2	no	—
585	C₂²×C₁₃	—	4	2	no	—
586	C₂²×C₁₃	—	4	2	no	—
587	C₂²×C₁₃	—	4	2	no	—
588	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
589	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
592	C₂²×C₁₃	#585	1	1	yes	characteristic
593	C₂²×C₁₃	#585	1	1	yes	characteristic
594	C₂²×C₁₃	#585	1	1	yes	characteristic
595	C₄×C₁₃	—	2	4	no	—
596	C₄×C₁₃	—	2	2	no	—
597	C₄×C₁₃	—	2	2	no	—
598	C₄×C₁₃	—	2	2	no	—
599	C₄×C₁₃	—	2	2	no	—
600	C₄×C₁₃	—	2	2	no	—
601	C₄×C₁₃	—	2	4	no	—
602	C₄×C₁₃	—	2	2	no	—
603	C₄×C₁₃	—	2	2	no	—
604	C₄×C₁₃	—	4	1	no	—
605	C₄×C₁₃	—	4	2	no	—
606	C₄×C₁₃	—	4	1	no	—
607	C₄×C₁₃	—	4	2	no	—
608	C₄×C₁₃	—	4	1	no	—
609	C₄×C₁₃	—	4	1	no	—
610	C₄×C₁₃	—	4	2	no	—
611	C₄×C₁₃	—	4	1	no	—
612	C₄×C₁₃	—	4	1	no	—
613	C₄×C₁₃	—	4	2	no	—
614	C₄×C₁₃	—	4	1	no	—
615	C₄×C₁₃	#520	1	4	yes	—
616	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
617	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
621	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
622	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
623	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
624	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
625	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
626	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
627	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
628	#127	C₂×C₄×C₁₃	1	8	yes	—
629	#124	C₂×C₄×C₁₃	1	8	yes	complemented
630	#124	C₂×C₄×C₁₃	1	8	yes	complemented
631	#124	C₂×C₄×C₁₃	1	16	yes	complemented
632	#123	C₂×C₄×C₁₃	1	16	yes	complemented
633	#123	C₂×C₄×C₁₃	1	16	yes	complemented
634	C₄×Q₈	—	4	2	no	—
635	C₄×Q₈	—	4	2	no	—
636	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
637	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
638	C₄×D₄	—	4	2	no	—
639	C₄×D₄	—	4	2	no	—
640	C₄×D₄	—	4	2	no	—
641	C₄×D₄	—	4	2	no	—
642	C₄×D₄	—	4	4	no	—
643	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
644	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
645	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
646	#117	—	4	4	no	—
647	C₂×C₄⋊C₄	—	4	4	no	—
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
689	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
695	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
696	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
697	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
698	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
702	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
704	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
705	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
706	#95	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
711	#95	C₂³×C₁₃	1	1	yes	characteristic
712	#95	C₂³×C₁₃	1	1	yes	characteristic
713	#95	C₂³×C₁₃	1	1	yes	characteristic
714	#95	C₂³×C₁₃	1	1	yes	characteristic
715	#95	C₂³×C₁₃	1	1	yes	characteristic
716	#95	C₂³×C₁₃	1	1	yes	characteristic
717	#95	C₂³×C₁₃	1	1	yes	characteristic
718	#95	C₂³×C₁₃	1	1	yes	characteristic
719	#95	C₂³×C₁₃	1	1	yes	characteristic
720	#95	C₂³×C₁₃	1	2	yes	—
721	#95	C₂³×C₁₃	1	2	yes	—
722	#95	C₂³×C₁₃	1	2	yes	—
723	#95	C₂³×C₁₃	1	2	yes	—
724	#95	C₂³×C₁₃	1	2	yes	—
725	#95	C₂³×C₁₃	1	2	yes	—
726	#95	C₂³×C₁₃	1	2	yes	—
727	#95	C₂³×C₁₃	1	1	yes	characteristic
728	#95	C₂³×C₁₃	1	2	yes	—
729	#95	C₂³×C₁₃	1	2	yes	—
730	#95	C₂³×C₁₃	1	1	yes	characteristic
731	#95	C₂³×C₁₃	1	2	yes	—
732	#95	C₂³×C₁₃	1	2	yes	—
733	#95	C₂³×C₁₃	1	1	yes	characteristic
734	#95	C₂³×C₁₃	1	2	yes	—
735	C₂×C₁₃	—	4	4	no	—
736	C₂×C₁₃	—	4	4	no	—
737	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
738	C₂×C₁₃	#3428	1	1	yes	characteristic
739	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂×C₁₃	#3554	1	1	yes	characteristic
741	C₂×C₁₃	#3557	1	1	yes	characteristic
742	C₂×C₁₃	#3558	1	1	yes	characteristic
743	C₂×C₁₃	#3562	1	1	yes	characteristic
744	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
745	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	4	1	no	—
749	C₂×Q₈	—	4	1	no	—
750	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
751	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	—	4	2	no	—
760	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
761	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
762	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
763	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	4	2	no	—
766	C₂²×C₄	—	4	2	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
781	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
782	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
796	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
801	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	2	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	1	no	—
816	C₄⋊C₄	—	4	1	no	—
817	C₄⋊C₄	—	4	2	no	—
818	C₄⋊C₄	—	4	1	no	—
819	C₄⋊C₄	—	4	2	no	—
820	C₄⋊C₄	—	4	1	no	—
821	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
822	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
823	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
824	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
825	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
839	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
840	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
841	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
842	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
843	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	4	2	no	—
850	C₄²	—	4	2	no	—
851	C₄²	—	4	2	no	—
852	C₄²	—	4	2	no	—
853	C₄²	—	4	2	no	—
854	C₄²	—	4	1	no	—
855	C₄²	—	4	1	no	—
856	C₄²	—	4	1	no	—
857	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
858	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
859	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
860	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
861	C₁₃	#34500	1	1	yes	characteristic, direct product factor, Sylow
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
875	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
876	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
877	Q₈	—	2	8	no	—
878	Q₈	—	4	4	no	—
879	D₄	—	2	8	no	—
880	D₄	—	2	8	no	—
881	D₄	—	4	8	no	—
882	D₄	—	4	8	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	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	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	4	8	no	—
935	C₂×C₄	—	4	8	no	—
936	C₂×C₄	—	8	4	no	—
937	C₂×C₄	—	8	4	no	—
938	C₂×C₄	—	8	4	no	—
939	C₂×C₄	—	8	4	no	—
940	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
941	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
942	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
943	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
944	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
945	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
946	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
947	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
948	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
949	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
950	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
951	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
952	C₂²	—	2	4	no	—
953	C₂²	—	2	4	no	—
954	C₂²	—	2	4	no	—
955	C₂²	—	2	4	no	—
956	C₂²	—	2	4	no	—
957	C₂²	—	2	4	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	2	no	—
966	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
967	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
968	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
969	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
970	C₂²	C₁₃×#585	1	1	yes	characteristic
971	C₂²	C₁₃×#585	1	1	yes	characteristic
972	C₂²	C₁₃×#585	1	1	yes	characteristic
973	C₄	—	2	2	no	—
974	C₄	—	2	4	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	4	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	1	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	1	no	—
993	C₄	C₁₃×#520	1	4	yes	—
994	C₂	—	4	4	no	—
995	C₂	—	4	4	no	—
996	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
997	C₂	C₁₃×#3428	1	1	yes	characteristic
998	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
999	C₂	C₁₃×#3554	1	1	yes	characteristic
1000	C₂	C₁₃×#3557	1	1	yes	characteristic
1001	C₂	C₁₃×#3558	1	1	yes	characteristic
1002	C₂	C₁₃×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2379	C₂	semidirect
3. C₁₃×#2376	C₂	semidirect
4. C₁₃×#2367	C₂	semidirect
5. C₁₃×#2367	C₂	semidirect
7. C₁₃×#2359	C₂	semidirect
8. C₁₃×#2355	C₂	semidirect
9. C₁₃×#2352	C₂	semidirect
10. C₁₃×#2351	C₂	semidirect
11. C₁₃×#2349	C₂	semidirect
12. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
13. C₁₃×#2337	C₂	semidirect
14. C₁₃×#2335	C₂	semidirect
16. C₁₃×#2326	C₂	semidirect
17. C₁₃×#2322	C₂	semidirect
18. C₁₃×#2320	C₂	semidirect
19. C₁₃×#2319	C₂	semidirect
20. C₁₃×#2318	C₂	semidirect
21. C₄×C₁₃×#124	C₂	semidirect
22. C₁₃×#2295	C₂	semidirect
23. C₁₃×#2293	C₂	semidirect
24. C₁₃×#559	C₄	semidirect
137. C₁₃×#124	C₂×C₄	semidirect
138. C₁₃×#124	C₂×C₄	semidirect
139. C₁₃×#124	C₂×C₄	semidirect
140. C₁₃×#123	C₂×C₄	semidirect
141. C₁₃×#123	C₂×C₄	semidirect
144. C₄×Q₈×C₁₃	C₂×C₄	semidirect
145. C₄×Q₈×C₁₃	C₂×C₄	semidirect
151. C₄×D₄×C₁₃	C₂×C₄	semidirect
152. C₄×D₄×C₁₃	C₂×C₄	semidirect
153. C₄×D₄×C₁₃	C₂×C₄	semidirect
243. #34500	C₁₃	direct (N × H)
362. #2379	C₂×C₁₃	semidirect
363. #2376	C₂×C₁₃	semidirect
364. #2367	C₂×C₁₃	semidirect
365. #2367	C₂×C₁₃	semidirect
367. #2359	C₂×C₁₃	semidirect
368. #2355	C₂×C₁₃	semidirect
369. #2352	C₂×C₁₃	semidirect
370. #2351	C₂×C₁₃	semidirect
371. #2349	C₂×C₁₃	semidirect
372. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
373. #2337	C₂×C₁₃	semidirect
374. #2335	C₂×C₁₃	semidirect
376. #2326	C₂×C₁₃	semidirect
377. #2322	C₂×C₁₃	semidirect
378. #2320	C₂×C₁₃	semidirect
379. #2319	C₂×C₁₃	semidirect
380. #2318	C₂×C₁₃	semidirect
381. C₄×#124	C₂×C₁₃	semidirect
382. #2295	C₂×C₁₃	semidirect
383. #2293	C₂×C₁₃	semidirect
474. #559	C₄×C₁₃	semidirect
629. #124	C₂×C₄×C₁₃	semidirect
630. #124	C₂×C₄×C₁₃	semidirect
631. #124	C₂×C₄×C₁₃	semidirect
632. #123	C₂×C₄×C₁₃	semidirect
633. #123	C₂×C₄×C₁₃	semidirect
636. C₄×Q₈	C₂×C₄×C₁₃	semidirect
637. C₄×Q₈	C₂×C₄×C₁₃	semidirect
643. C₄×D₄	C₂×C₄×C₁₃	semidirect
644. C₄×D₄	C₂×C₄×C₁₃	semidirect
645. C₄×D₄	C₂×C₄×C₁₃	semidirect
861. C₁₃	#34500	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#559	2
C₁₃×#2379	2
C₁₃×#2376	2
C₁₃×#2367	2
C₁₃×#2366	2
C₁₃×#2359	2
C₁₃×#2355	2
C₁₃×#2352	2
C₁₃×#2351	2
C₁₃×#2349	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2337	2
C₁₃×#2335	2
C₁₃×#2328	2
C₁₃×#2326	2
C₁₃×#2322	2
C₁₃×#2320	2
C₁₃×#2319	2
C₁₃×#2318	2
C₄×C₁₃×#124	2
C₁₃×#2295	2
C₁₃×#2293	2
#34500	13

Subgroups — C13×#34500 #15720839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34500 #15720839