Subgroups — C₁₃×#34510 #15720849

Order 3328.

2148 conjugacy classes of subgroups.

The subgroup lattice has 872 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×#2380	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2379	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2372	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2359	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2356	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2335	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2320	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
18	C₄×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
20	C₁₃×#559	C₄	1	16	yes	complemented
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#123	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#391	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#391	C₂²	1	2	yes	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#390	C₂²	1	1	yes	characteristic
40	C₁₃×#390	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	2	yes	—
42	C₁₃×#389	C₂²	1	2	yes	—
43	C₁₃×#388	C₂²	1	2	yes	—
44	C₁₃×#388	C₂²	1	2	yes	—
45	C₁₃×#388	C₂²	1	2	yes	—
46	C₁₃×#388	C₂²	1	2	yes	—
47	C₁₃×#388	C₂²	1	2	yes	—
48	C₁₃×#388	C₂²	1	2	yes	—
49	C₁₃×#388	C₂²	1	2	yes	—
50	C₁₃×#388	C₂²	1	2	yes	—
51	C₁₃×#388	C₂²	1	2	yes	—
52	C₁₃×#388	C₂²	1	2	yes	—
53	C₁₃×#388	C₂²	1	2	yes	—
54	C₁₃×#388	C₂²	1	2	yes	—
55	C₁₃×#387	C₂²	1	2	yes	—
56	C₁₃×#387	C₂²	1	2	yes	—
57	C₁₃×#387	C₂²	1	2	yes	—
58	C₁₃×#387	C₂²	1	2	yes	—
59	C₁₃×#387	C₂²	1	2	yes	—
60	C₁₃×#387	C₂²	1	2	yes	—
61	C₁₃×#387	C₂²	1	2	yes	—
62	C₁₃×#387	C₂²	1	2	yes	—
63	C₁₃×#386	C₂²	1	2	yes	—
64	C₁₃×#386	C₂²	1	2	yes	—
65	C₁₃×#386	C₂²	1	1	yes	characteristic
66	C₁₃×#386	C₂²	1	2	yes	—
67	C₁₃×#386	C₂²	1	2	yes	—
68	C₁₃×#386	C₂²	1	1	yes	characteristic
69	C₁₃×#386	C₂²	1	2	yes	—
70	C₁₃×#386	C₂²	1	2	yes	—
71	C₁₃×#386	C₂²	1	2	yes	—
72	C₁₃×#386	C₂²	1	2	yes	—
73	C₁₃×#386	C₂²	1	2	yes	—
74	C₁₃×#385	C₂²	1	2	yes	—
75	C₁₃×#385	C₂²	1	2	yes	—
76	C₁₃×#385	C₂²	1	1	yes	characteristic
77	C₁₃×#385	C₂²	1	2	yes	—
78	C₁₃×#385	C₂²	1	2	yes	—
79	C₁₃×#385	C₂²	1	1	yes	characteristic
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#383	C₂²	1	2	yes	—
82	C₁₃×#383	C₂²	1	2	yes	—
83	C₁₃×#383	C₂²	1	2	yes	—
84	C₁₃×#382	C₂²	1	2	yes	—
85	C₁₃×#382	C₂²	1	1	yes	characteristic
86	C₁₃×#382	C₂²	1	2	yes	—
87	C₁₃×#381	C₂²	1	1	yes	characteristic
88	C₁₃×#381	C₂²	1	1	yes	characteristic
89	C₁₃×#380	C₂²	1	2	yes	—
90	C₁₃×#380	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
96	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₁₃×#376	C₂²	1	2	yes	—
105	C₁₃×#376	C₂²	1	2	yes	—
106	C₁₃×#376	C₂²	1	1	yes	characteristic
107	C₂×C₁₃×#95	C₂²	1	2	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₁₃×#127	C₂×C₄	1	8	yes	—
123	C₁₃×#124	C₂×C₄	1	16	yes	complemented
124	C₁₃×#124	C₂×C₄	1	16	yes	complemented
125	C₁₃×#123	C₂×C₄	1	8	yes	complemented
126	C₁₃×#123	C₂×C₄	1	8	yes	complemented
127	C₁₃×#123	C₂×C₄	1	16	yes	complemented
128	C₄×Q₈×C₁₃	C₂×C₄	1	16	yes	complemented
129	C₄×D₄×C₁₃	—	4	2	no	—
130	C₄×D₄×C₁₃	—	4	2	no	—
131	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
132	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
133	C₁₃×#117	—	4	4	no	—
134	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	—	4	2	no	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₁₃×#95	C₂³	1	2	yes	—
184	C₁₃×#95	C₂³	1	2	yes	—
185	C₁₃×#95	C₂³	1	2	yes	—
186	C₁₃×#95	C₂³	1	2	yes	—
187	C₁₃×#95	C₂³	1	2	yes	—
188	C₁₃×#95	C₂³	1	2	yes	—
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	2	yes	—
192	C₁₃×#95	C₂³	1	2	yes	—
193	C₁₃×#95	C₂³	1	2	yes	—
194	C₁₃×#95	C₂³	1	2	yes	—
195	C₁₃×#95	C₂³	1	2	yes	—
196	C₁₃×#95	C₂³	1	2	yes	—
197	C₁₃×#95	C₂³	1	2	yes	—
198	C₁₃×#95	C₂³	1	2	yes	—
199	C₁₃×#95	C₂³	1	2	yes	—
200	C₁₃×#95	C₂³	1	2	yes	—
201	C₁₃×#95	C₂³	1	2	yes	—
202	C₁₃×#95	C₂³	1	2	yes	—
203	C₁₃×#95	C₂³	1	2	yes	—
204	C₁₃×#95	C₂³	1	2	yes	—
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	C₁₃×#95	C₂³	1	2	yes	—
208	C₁₃×#95	C₂³	1	2	yes	—
209	#34510	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
211	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂×Q₈×C₁₃	—	4	2	no	—
214	C₂×Q₈×C₁₃	—	4	2	no	—
215	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
216	C₂×D₄×C₁₃	—	4	1	no	—
217	C₂×D₄×C₁₃	—	4	1	no	—
218	C₂×D₄×C₁₃	—	4	1	no	—
219	C₂×D₄×C₁₃	—	4	1	no	—
220	C₂×D₄×C₁₃	—	4	2	no	—
221	C₂×D₄×C₁₃	—	4	2	no	—
222	C₂×D₄×C₁₃	—	4	2	no	—
223	C₂×D₄×C₁₃	—	4	2	no	—
224	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
225	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
226	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	4	1	no	—
231	C₂²×C₄×C₁₃	—	4	1	no	—
232	C₂²×C₄×C₁₃	—	4	1	no	—
233	C₂²×C₄×C₁₃	—	4	2	no	—
234	C₂²×C₄×C₁₃	—	4	1	no	—
235	C₂²×C₄×C₁₃	—	4	2	no	—
236	C₂²×C₄×C₁₃	—	4	2	no	—
237	C₂²×C₄×C₁₃	—	4	1	no	—
238	C₂²×C₄×C₁₃	—	4	2	no	—
239	C₂²×C₄×C₁₃	—	4	1	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	4	2	no	—
244	C₂²×C₄×C₁₃	—	4	2	no	—
245	C₂²×C₄×C₁₃	—	4	2	no	—
246	C₂²×C₄×C₁₃	—	4	2	no	—
247	C₂²×C₄×C₁₃	—	4	2	no	—
248	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
249	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
250	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	4	2	no	—
269	C₁₃×C₄⋊C₄	—	4	2	no	—
270	C₁₃×C₄⋊C₄	—	4	2	no	—
271	C₁₃×C₄⋊C₄	—	4	2	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	—	4	2	no	—
274	C₁₃×C₄⋊C₄	—	4	2	no	—
275	C₁₃×C₄⋊C₄	—	4	1	no	—
276	C₁₃×C₄⋊C₄	—	4	1	no	—
277	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
278	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
279	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	4	2	no	—
282	C₁₃×C₂²⋊C₄	—	4	2	no	—
283	C₁₃×C₂²⋊C₄	—	4	1	no	—
284	C₁₃×C₂²⋊C₄	—	4	2	no	—
285	C₁₃×C₂²⋊C₄	—	4	2	no	—
286	C₁₃×C₂²⋊C₄	—	4	2	no	—
287	C₁₃×C₂²⋊C₄	—	4	2	no	—
288	C₁₃×C₂²⋊C₄	—	4	2	no	—
289	C₁₃×C₂²⋊C₄	—	4	1	no	—
290	C₁₃×C₂²⋊C₄	—	4	2	no	—
291	C₁₃×C₂²⋊C₄	—	4	2	no	—
292	C₁₃×C₂²⋊C₄	—	4	1	no	—
293	C₁₃×C₂²⋊C₄	—	4	1	no	—
294	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
295	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
296	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
297	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
298	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
299	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
300	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
301	C₄²×C₁₃	—	2	4	no	—
302	C₄²×C₁₃	—	2	2	no	—
303	C₄²×C₁₃	—	4	2	no	—
304	C₄²×C₁₃	—	4	2	no	—
305	C₄²×C₁₃	—	4	2	no	—
306	C₄²×C₁₃	—	4	2	no	—
307	C₄²×C₁₃	—	4	2	no	—
308	C₄²×C₁₃	—	4	2	no	—
309	C₄²×C₁₃	—	4	1	no	—
310	C₄²×C₁₃	—	4	2	no	—
311	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
312	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
313	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
314	C₂×#559	C₂×C₁₃	1	1	yes	characteristic
315	#2380	C₂×C₁₃	1	1	yes	characteristic
316	#2379	C₂×C₁₃	1	2	yes	complemented
317	#2376	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#2374	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#2372	C₂×C₁₃	1	2	yes	complemented
320	#2359	C₂×C₁₃	1	2	yes	complemented
321	#2356	C₂×C₁₃	1	2	yes	complemented
322	#2353	C₂×C₁₃	1	2	yes	complemented
323	#2352	C₂×C₁₃	1	2	yes	complemented
324	#2337	C₂×C₁₃	1	2	yes	complemented
325	#2337	C₂×C₁₃	1	2	yes	complemented
326	#2335	C₂×C₁₃	1	2	yes	complemented
327	#2328	C₂×C₁₃	1	1	yes	characteristic
328	#2322	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#2320	C₂×C₁₃	1	2	yes	complemented
330	#2318	C₂×C₁₃	1	2	yes	complemented
331	C₄×#123	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#2290	C₂×C₁₃	1	2	yes	complemented
333	C₂³×C₁₃	—	2	2	no	—
334	C₂³×C₁₃	—	2	1	no	—
335	C₂³×C₁₃	—	2	1	no	—
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	2	2	no	—
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	1	no	—
343	C₂³×C₁₃	—	2	1	no	—
344	C₂³×C₁₃	—	2	2	no	—
345	C₂³×C₁₃	—	2	2	no	—
346	C₂³×C₁₃	—	2	2	no	—
347	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
348	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
349	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
350	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
351	Q₈×C₁₃	—	4	8	no	—
352	D₄×C₁₃	—	4	8	no	—
353	D₄×C₁₃	—	4	8	no	—
354	D₄×C₁₃	—	4	4	no	—
355	D₄×C₁₃	—	4	4	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	4	4	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	8	no	—
396	C₂×C₄×C₁₃	—	4	4	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	8	2	no	—
399	C₂×C₄×C₁₃	—	8	2	no	—
400	C₂×C₄×C₁₃	—	8	4	no	—
401	C₂×C₄×C₁₃	—	8	4	no	—
402	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
403	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
404	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
405	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
406	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
407	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
408	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
409	#559	C₄×C₁₃	1	16	yes	complemented
410	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#124	C₂²×C₁₃	1	2	yes	—
412	C₂×#124	C₂²×C₁₃	1	2	yes	—
413	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#123	C₂²×C₁₃	1	2	yes	—
415	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
417	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
421	C₂×#117	C₂²×C₁₃	1	2	yes	—
422	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
423	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
424	#391	C₂²×C₁₃	1	2	yes	—
425	#391	C₂²×C₁₃	1	2	yes	—
426	#391	C₂²×C₁₃	1	2	yes	—
427	#391	C₂²×C₁₃	1	2	yes	—
428	#390	C₂²×C₁₃	1	1	yes	characteristic
429	#390	C₂²×C₁₃	1	1	yes	characteristic
430	#389	C₂²×C₁₃	1	2	yes	—
431	#389	C₂²×C₁₃	1	2	yes	—
432	#388	C₂²×C₁₃	1	2	yes	—
433	#388	C₂²×C₁₃	1	2	yes	—
434	#388	C₂²×C₁₃	1	2	yes	—
435	#388	C₂²×C₁₃	1	2	yes	—
436	#388	C₂²×C₁₃	1	2	yes	—
437	#388	C₂²×C₁₃	1	2	yes	—
438	#388	C₂²×C₁₃	1	2	yes	—
439	#388	C₂²×C₁₃	1	2	yes	—
440	#388	C₂²×C₁₃	1	2	yes	—
441	#388	C₂²×C₁₃	1	2	yes	—
442	#388	C₂²×C₁₃	1	2	yes	—
443	#388	C₂²×C₁₃	1	2	yes	—
444	#387	C₂²×C₁₃	1	2	yes	—
445	#387	C₂²×C₁₃	1	2	yes	—
446	#387	C₂²×C₁₃	1	2	yes	—
447	#387	C₂²×C₁₃	1	2	yes	—
448	#387	C₂²×C₁₃	1	2	yes	—
449	#387	C₂²×C₁₃	1	2	yes	—
450	#387	C₂²×C₁₃	1	2	yes	—
451	#387	C₂²×C₁₃	1	2	yes	—
452	#386	C₂²×C₁₃	1	2	yes	—
453	#386	C₂²×C₁₃	1	2	yes	—
454	#386	C₂²×C₁₃	1	1	yes	characteristic
455	#386	C₂²×C₁₃	1	2	yes	—
456	#386	C₂²×C₁₃	1	2	yes	—
457	#386	C₂²×C₁₃	1	2	yes	—
458	#386	C₂²×C₁₃	1	2	yes	—
459	#386	C₂²×C₁₃	1	2	yes	—
460	#386	C₂²×C₁₃	1	2	yes	—
461	#386	C₂²×C₁₃	1	1	yes	characteristic
462	#386	C₂²×C₁₃	1	2	yes	—
463	#385	C₂²×C₁₃	1	2	yes	—
464	#385	C₂²×C₁₃	1	2	yes	—
465	#385	C₂²×C₁₃	1	1	yes	characteristic
466	#385	C₂²×C₁₃	1	2	yes	—
467	#385	C₂²×C₁₃	1	2	yes	—
468	#385	C₂²×C₁₃	1	2	yes	—
469	#385	C₂²×C₁₃	1	1	yes	characteristic
470	#383	C₂²×C₁₃	1	2	yes	—
471	#383	C₂²×C₁₃	1	2	yes	—
472	#383	C₂²×C₁₃	1	2	yes	—
473	#382	C₂²×C₁₃	1	2	yes	—
474	#382	C₂²×C₁₃	1	1	yes	characteristic
475	#382	C₂²×C₁₃	1	2	yes	—
476	#381	C₂²×C₁₃	1	1	yes	characteristic
477	#381	C₂²×C₁₃	1	1	yes	characteristic
478	#380	C₂²×C₁₃	1	2	yes	—
479	#380	C₂²×C₁₃	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
483	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
486	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
493	#376	C₂²×C₁₃	1	2	yes	—
494	#376	C₂²×C₁₃	1	1	yes	characteristic
495	#376	C₂²×C₁₃	1	2	yes	—
496	C₂×#95	C₂²×C₁₃	1	2	yes	—
497	C₂²×C₁₃	—	2	4	no	—
498	C₂²×C₁₃	—	2	4	no	—
499	C₂²×C₁₃	—	2	4	no	—
500	C₂²×C₁₃	—	2	4	no	—
501	C₂²×C₁₃	—	2	4	no	—
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	4	1	no	—
505	C₂²×C₁₃	—	4	1	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	4	2	no	—
514	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
515	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂²×C₁₃	#585	1	2	yes	—
517	C₂²×C₁₃	#585	1	2	yes	—
518	C₂²×C₁₃	#585	1	1	yes	characteristic
519	C₄×C₁₃	—	2	4	no	—
520	C₄×C₁₃	—	2	4	no	—
521	C₄×C₁₃	—	2	4	no	—
522	C₄×C₁₃	—	2	4	no	—
523	C₄×C₁₃	—	2	4	no	—
524	C₄×C₁₃	—	2	2	no	—
525	C₄×C₁₃	—	2	2	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	1	no	—
529	C₄×C₁₃	—	4	2	no	—
530	C₄×C₁₃	—	4	2	no	—
531	C₄×C₁₃	—	4	1	no	—
532	C₄×C₁₃	—	4	2	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
536	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
539	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
540	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
544	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
545	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
548	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
549	#127	C₂×C₄×C₁₃	1	8	yes	—
550	#124	C₂×C₄×C₁₃	1	16	yes	complemented
551	#124	C₂×C₄×C₁₃	1	16	yes	complemented
552	#123	C₂×C₄×C₁₃	1	8	yes	complemented
553	#123	C₂×C₄×C₁₃	1	16	yes	complemented
554	#123	C₂×C₄×C₁₃	1	8	yes	complemented
555	C₄×Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
556	C₄×D₄	—	4	2	no	—
557	C₄×D₄	—	4	2	no	—
558	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
559	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
560	#117	—	4	4	no	—
561	C₂×C₄⋊C₄	—	4	2	no	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₄²	—	4	2	no	—
597	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
605	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
607	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
608	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
610	#95	C₂³×C₁₃	1	2	yes	—
611	#95	C₂³×C₁₃	1	2	yes	—
612	#95	C₂³×C₁₃	1	2	yes	—
613	#95	C₂³×C₁₃	1	2	yes	—
614	#95	C₂³×C₁₃	1	2	yes	—
615	#95	C₂³×C₁₃	1	2	yes	—
616	#95	C₂³×C₁₃	1	2	yes	—
617	#95	C₂³×C₁₃	1	2	yes	—
618	#95	C₂³×C₁₃	1	2	yes	—
619	#95	C₂³×C₁₃	1	2	yes	—
620	#95	C₂³×C₁₃	1	2	yes	—
621	#95	C₂³×C₁₃	1	2	yes	—
622	#95	C₂³×C₁₃	1	2	yes	—
623	#95	C₂³×C₁₃	1	2	yes	—
624	#95	C₂³×C₁₃	1	2	yes	—
625	#95	C₂³×C₁₃	1	2	yes	—
626	#95	C₂³×C₁₃	1	2	yes	—
627	#95	C₂³×C₁₃	1	2	yes	—
628	#95	C₂³×C₁₃	1	2	yes	—
629	#95	C₂³×C₁₃	1	2	yes	—
630	#95	C₂³×C₁₃	1	2	yes	—
631	#95	C₂³×C₁₃	1	2	yes	—
632	#95	C₂³×C₁₃	1	2	yes	—
633	#95	C₂³×C₁₃	1	2	yes	—
634	#95	C₂³×C₁₃	1	2	yes	—
635	#95	C₂³×C₁₃	1	2	yes	—
636	C₂×C₁₃	—	4	2	no	—
637	C₂×C₁₃	—	4	2	no	—
638	C₂×C₁₃	—	4	4	no	—
639	C₂×C₁₃	#3428	1	2	yes	—
640	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
641	C₂×C₁₃	#3533	1	1	yes	characteristic
642	C₂×C₁₃	#3540	1	1	yes	characteristic
643	C₂×C₁₃	#3566	1	2	yes	—
644	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
645	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
646	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
647	C₂×Q₈	—	4	2	no	—
648	C₂×Q₈	—	4	2	no	—
649	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
650	C₂×D₄	—	4	1	no	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	1	no	—
653	C₂×D₄	—	4	1	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
659	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
660	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
661	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	4	1	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	1	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
683	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
684	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
685	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
712	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
713	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	1	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	1	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	1	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
729	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
730	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
731	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
732	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
733	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
734	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	4	2	no	—
738	C₄²	—	4	2	no	—
739	C₄²	—	4	2	no	—
740	C₄²	—	4	2	no	—
741	C₄²	—	4	2	no	—
742	C₄²	—	4	2	no	—
743	C₄²	—	4	2	no	—
744	C₄²	—	4	1	no	—
745	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
746	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
747	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
748	C₁₃	#34510	1	1	yes	characteristic, direct product factor, Sylow
749	C₂³	—	2	2	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
764	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
765	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
766	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
767	Q₈	—	4	8	no	—
768	D₄	—	4	8	no	—
769	D₄	—	4	8	no	—
770	D₄	—	4	4	no	—
771	D₄	—	4	4	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	—	8	2	no	—
816	C₂×C₄	—	8	4	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
819	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
820	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
821	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
822	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
823	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
824	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	4	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
843	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂²	C₁₃×#585	1	2	yes	—
845	C₂²	C₁₃×#585	1	2	yes	—
846	C₂²	C₁₃×#585	1	1	yes	characteristic
847	C₄	—	2	2	no	—
848	C₄	—	2	4	no	—
849	C₄	—	2	4	no	—
850	C₄	—	2	4	no	—
851	C₄	—	2	4	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₂	—	4	2	no	—
864	C₂	—	4	2	no	—
865	C₂	—	4	4	no	—
866	C₂	C₁₃×#3428	1	2	yes	—
867	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
868	C₂	C₁₃×#3533	1	1	yes	characteristic
869	C₂	C₁₃×#3540	1	1	yes	characteristic
870	C₂	C₁₃×#3566	1	2	yes	—

	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
3. C₁₃×#2379	C₂	semidirect
4. C₁₃×#2376	C₂	semidirect
5. C₁₃×#2374	C₂	semidirect
6. C₁₃×#2372	C₂	semidirect
7. C₁₃×#2359	C₂	semidirect
8. C₁₃×#2356	C₂	semidirect
9. C₁₃×#2353	C₂	semidirect
10. C₁₃×#2352	C₂	semidirect
11. C₁₃×#2337	C₂	semidirect
12. C₁₃×#2337	C₂	semidirect
13. C₁₃×#2335	C₂	semidirect
15. C₁₃×#2322	C₂	semidirect
16. C₁₃×#2320	C₂	semidirect
17. C₁₃×#2318	C₂	semidirect
18. C₄×C₁₃×#123	C₂	semidirect
19. C₁₃×#2290	C₂	semidirect
20. C₁₃×#559	C₄	semidirect
123. C₁₃×#124	C₂×C₄	semidirect
124. C₁₃×#124	C₂×C₄	semidirect
125. C₁₃×#123	C₂×C₄	semidirect
126. C₁₃×#123	C₂×C₄	semidirect
127. C₁₃×#123	C₂×C₄	semidirect
128. C₄×Q₈×C₁₃	C₂×C₄	semidirect
131. C₄×D₄×C₁₃	C₂×C₄	semidirect
132. C₄×D₄×C₁₃	C₂×C₄	semidirect
209. #34510	C₁₃	direct (N × H)
316. #2379	C₂×C₁₃	semidirect
317. #2376	C₂×C₁₃	semidirect
318. #2374	C₂×C₁₃	semidirect
319. #2372	C₂×C₁₃	semidirect
320. #2359	C₂×C₁₃	semidirect
321. #2356	C₂×C₁₃	semidirect
322. #2353	C₂×C₁₃	semidirect
323. #2352	C₂×C₁₃	semidirect
324. #2337	C₂×C₁₃	semidirect
325. #2337	C₂×C₁₃	semidirect
326. #2335	C₂×C₁₃	semidirect
328. #2322	C₂×C₁₃	semidirect
329. #2320	C₂×C₁₃	semidirect
330. #2318	C₂×C₁₃	semidirect
331. C₄×#123	C₂×C₁₃	semidirect
332. #2290	C₂×C₁₃	semidirect
409. #559	C₄×C₁₃	semidirect
550. #124	C₂×C₄×C₁₃	semidirect
551. #124	C₂×C₄×C₁₃	semidirect
552. #123	C₂×C₄×C₁₃	semidirect
553. #123	C₂×C₄×C₁₃	semidirect
554. #123	C₂×C₄×C₁₃	semidirect
555. C₄×Q₈	C₂×C₄×C₁₃	semidirect
558. C₄×D₄	C₂×C₄×C₁₃	semidirect
559. C₄×D₄	C₂×C₄×C₁₃	semidirect
748. C₁₃	#34510	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×#2380	2
C₁₃×#2379	2
C₁₃×#2376	2
C₁₃×#2374	2
C₁₃×#2372	2
C₁₃×#2359	2
C₁₃×#2356	2
C₁₃×#2353	2
C₁₃×#2352	2
C₁₃×#2337	2
C₁₃×#2335	2
C₁₃×#2328	2
C₁₃×#2322	2
C₁₃×#2320	2
C₁₃×#2318	2
C₄×C₁₃×#123	2
C₁₃×#2290	2
#34510	13

Subgroups — C13×#34510 #15720849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34510 #15720849