Subgroups — C₁₃×#34754 #15721093

Order 3328.

2182 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2518	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2517	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2510	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2505	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2493	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2488	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2437	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2412	C₂	1	2	yes	maximal
11	C₁₃×#2401	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×#120	C₂	1	1	yes	maximal, characteristic
17	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2283	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#123	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#120	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#401	C₂²	1	2	yes	complemented
33	C₁₃×#400	C₂²	1	2	yes	complemented
34	C₁₃×#400	C₂²	1	2	yes	complemented
35	C₁₃×#400	C₂²	1	2	yes	complemented
36	C₁₃×#400	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#400	C₂²	1	2	yes	complemented
38	C₁₃×#399	C₂²	1	1	yes	characteristic
39	C₁₃×#398	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#397	C₂²	1	1	yes	characteristic
41	C₁₃×#397	C₂²	1	2	yes	—
42	C₁₃×#397	C₂²	1	2	yes	—
43	C₁₃×#397	C₂²	1	1	yes	characteristic
44	C₁₃×#397	C₂²	1	2	yes	—
45	C₁₃×#397	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#397	C₂²	1	2	yes	complemented
47	C₁₃×#396	C₂²	1	2	yes	—
48	C₁₃×#394	C₂²	1	2	yes	—
49	C₁₃×#394	C₂²	1	2	yes	—
50	C₁₃×#393	C₂²	1	1	yes	characteristic
51	C₁₃×#393	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#391	C₂²	1	2	yes	complemented
53	C₁₃×#389	C₂²	1	2	yes	complemented
54	C₁₃×#388	C₂²	1	2	yes	complemented
55	C₁₃×#388	C₂²	1	2	yes	complemented
56	C₁₃×#388	C₂²	1	2	yes	complemented
57	C₁₃×#388	C₂²	1	2	yes	complemented
58	C₁₃×#387	C₂²	1	2	yes	complemented
59	C₁₃×#387	C₂²	1	2	yes	complemented
60	C₁₃×#387	C₂²	1	2	yes	complemented
61	C₁₃×#387	C₂²	1	2	yes	complemented
62	C₁₃×#387	C₂²	1	2	yes	complemented
63	C₁₃×#387	C₂²	1	2	yes	complemented
64	C₁₃×#386	C₂²	1	2	yes	—
65	C₁₃×#386	C₂²	1	2	yes	—
66	C₁₃×#386	C₂²	1	2	yes	—
67	C₁₃×#386	C₂²	1	1	yes	characteristic
68	C₁₃×#386	C₂²	1	2	yes	—
69	C₁₃×#385	C₂²	1	2	yes	—
70	C₁₃×#385	C₂²	1	2	yes	—
71	C₁₃×#385	C₂²	1	2	yes	—
72	C₁₃×#385	C₂²	1	2	yes	—
73	C₁₃×#385	C₂²	1	2	yes	—
74	C₁₃×#385	C₂²	1	1	yes	characteristic
75	C₁₃×#385	C₂²	1	2	yes	—
76	C₁₃×#383	C₂²	1	2	yes	complemented
77	C₁₃×#383	C₂²	1	2	yes	complemented
78	C₁₃×#382	C₂²	1	2	yes	complemented
79	C₁₃×#382	C₂²	1	2	yes	complemented
80	C₁₃×#381	C₂²	1	2	yes	—
81	C₁₃×#381	C₂²	1	2	yes	—
82	C₁₃×#381	C₂²	1	2	yes	—
83	C₁₃×#380	C₂²	1	2	yes	—
84	C₁₃×#380	C₂²	1	2	yes	—
85	C₁₃×#380	C₂²	1	2	yes	—
86	C₁₃×#379	C₂²	1	1	yes	characteristic
87	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
88	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
89	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
90	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
91	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
92	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
93	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
94	C₄×C₁₃×C₂²⋊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	2	yes	—
98	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
102	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#376	C₂²	1	1	yes	characteristic, complemented
104	C₁₃×#376	C₂²	1	2	yes	complemented
105	C₂×C₁₃×#95	C₂²	1	2	yes	—
106	C₂×C₁₃×#95	C₂²	1	2	yes	—
107	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃	—	2	8	no	—
112	C₂³×C₄×C₁₃	—	4	2	no	—
113	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
122	C₁₃×#123	—	2	8	no	—
123	C₁₃×C₂²⋊Q₈	—	2	8	no	—
124	C₁₃×#120	—	2	4	no	—
125	C₄×Q₈×C₁₃	—	4	2	no	—
126	C₄×D₄×C₁₃	—	2	8	no	—
127	C₄×D₄×C₁₃	—	4	2	no	—
128	C₁₃×#117	—	4	2	no	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊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	2	yes	—
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	2	yes	—
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃	—	2	8	no	—
166	C₂×C₄²×C₁₃	—	4	4	no	—
167	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
177	C₁₃×#95	C₂³	1	2	yes	—
178	C₁₃×#95	C₂³	1	2	yes	—
179	C₁₃×#95	C₂³	1	2	yes	—
180	C₁₃×#95	C₂³	1	2	yes	—
181	C₁₃×#95	C₂³	1	2	yes	—
182	C₁₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
189	C₁₃×#95	C₂³	1	2	yes	—
190	C₁₃×#95	C₂³	1	2	yes	—
191	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
205	C₁₃×#95	C₂³	1	2	yes	—
206	C₁₃×#95	C₂³	1	2	yes	—
207	#34754	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂⁴×C₁₃	—	2	4	no	—
209	C₂⁴×C₁₃	—	2	4	no	—
210	C₂⁴×C₁₃	—	4	1	no	—
211	C₂⁴×C₁₃	—	4	1	no	—
212	C₂⁴×C₁₃	#41	1	4	yes	—
213	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₁₃	—	2	4	no	—
217	C₂×Q₈×C₁₃	—	4	1	no	—
218	C₂×D₄×C₁₃	—	2	4	no	—
219	C₂×D₄×C₁₃	—	2	2	no	—
220	C₂×D₄×C₁₃	—	2	4	no	—
221	C₂×D₄×C₁₃	—	2	4	no	—
222	C₂×D₄×C₁₃	—	4	1	no	—
223	C₂×D₄×C₁₃	—	4	1	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	—	2	4	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	2	4	no	—
237	C₂²×C₄×C₁₃	—	2	4	no	—
238	C₂²×C₄×C₁₃	—	2	4	no	—
239	C₂²×C₄×C₁₃	—	2	2	no	—
240	C₂²×C₄×C₁₃	—	2	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	4	1	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	16	no	—
248	C₂²×C₄×C₁₃	#41	1	8	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	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	1	no	—
275	C₁₃×C₄⋊C₄	—	4	1	no	—
276	C₁₃×C₄⋊C₄	—	4	1	no	—
277	C₁₃×C₄⋊C₄	—	4	2	no	—
278	C₁₃×C₄⋊C₄	—	4	1	no	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	4	no	—
282	C₁₃×C₂²⋊C₄	—	2	4	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	4	1	no	—
294	C₁₃×C₂²⋊C₄	—	4	2	no	—
295	C₁₃×C₂²⋊C₄	—	4	2	no	—
296	C₁₃×C₂²⋊C₄	—	4	1	no	—
297	C₁₃×C₂²⋊C₄	—	4	1	no	—
298	C₁₃×C₂²⋊C₄	#41	1	8	yes	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	—	2	4	no	—
301	C₄²×C₁₃	—	2	4	no	—
302	C₄²×C₁₃	—	2	4	no	—
303	C₄²×C₁₃	—	2	4	no	—
304	C₄²×C₁₃	—	2	4	no	—
305	C₄²×C₁₃	—	2	4	no	—
306	C₄²×C₁₃	—	2	2	no	—
307	C₄²×C₁₃	—	4	2	no	—
308	C₄²×C₁₃	—	4	2	no	—
309	#2523	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#2518	C₂×C₁₃	1	2	yes	complemented
311	#2517	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#2510	C₂×C₁₃	1	2	yes	complemented
313	#2505	C₂×C₁₃	1	2	yes	complemented
314	#2493	C₂×C₁₃	1	2	yes	complemented
315	#2488	C₂×C₁₃	1	2	yes	complemented
316	#2483	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#2437	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#2412	C₂×C₁₃	1	2	yes	—
319	#2401	C₂×C₁₃	1	2	yes	complemented
320	#2398	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#2395	C₂×C₁₃	1	1	yes	characteristic, complemented
322	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
323	C₄×#123	C₂×C₁₃	1	2	yes	complemented
324	C₄×#120	C₂×C₁₃	1	1	yes	characteristic
325	#2290	C₂×C₁₃	1	2	yes	complemented
326	#2283	C₂×C₁₃	1	2	yes	complemented
327	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
328	C₂³×C₁₃	—	2	2	no	—
329	C₂³×C₁₃	—	2	2	no	—
330	C₂³×C₁₃	—	2	2	no	—
331	C₂³×C₁₃	—	2	2	no	—
332	C₂³×C₁₃	—	2	16	no	—
333	C₂³×C₁₃	—	2	2	no	—
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	1	no	—
336	C₂³×C₁₃	—	2	1	no	—
337	C₂³×C₁₃	—	2	2	no	—
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	2	1	no	—
340	C₂³×C₁₃	—	2	1	no	—
341	C₂³×C₁₃	—	2	1	no	—
342	C₂³×C₁₃	—	4	4	no	—
343	C₂³×C₁₃	—	4	4	no	—
344	C₂³×C₁₃	—	4	8	no	—
345	C₂³×C₁₃	—	4	4	no	—
346	C₂³×C₁₃	C₂×#41	1	2	yes	—
347	C₂³×C₁₃	C₂×#41	1	4	yes	—
348	C₂³×C₁₃	C₂×#41	1	4	yes	—
349	C₂³×C₁₃	C₂×#41	1	4	yes	—
350	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
351	Q₈×C₁₃	—	4	4	no	—
352	D₄×C₁₃	—	4	4	no	—
353	D₄×C₁₃	—	4	8	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	16	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	2	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	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	2	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	1	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	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	—	2	1	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	8	no	—
396	C₂×C₄×C₁₃	—	4	8	no	—
397	C₂×C₄×C₁₃	—	4	8	no	—
398	C₂×C₄×C₁₃	—	4	8	no	—
399	C₂×C₄×C₁₃	—	4	8	no	—
400	C₂×C₄×C₁₃	—	4	4	no	—
401	C₂×C₄×C₁₃	—	4	4	no	—
402	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
403	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
404	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
405	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
406	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
407	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#123	C₂²×C₁₃	1	2	yes	—
409	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
410	C₂×#120	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
416	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
417	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
418	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
419	#401	C₂²×C₁₃	1	2	yes	complemented
420	#400	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	#400	C₂²×C₁₃	1	2	yes	complemented
422	#400	C₂²×C₁₃	1	2	yes	complemented
423	#400	C₂²×C₁₃	1	2	yes	complemented
424	#400	C₂²×C₁₃	1	2	yes	complemented
425	#399	C₂²×C₁₃	1	1	yes	characteristic
426	#398	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	#397	C₂²×C₁₃	1	1	yes	characteristic
428	#397	C₂²×C₁₃	1	1	yes	characteristic
429	#397	C₂²×C₁₃	1	2	yes	—
430	#397	C₂²×C₁₃	1	2	yes	—
431	#397	C₂²×C₁₃	1	2	yes	—
432	#397	C₂²×C₁₃	1	2	yes	complemented
433	#397	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	#396	C₂²×C₁₃	1	2	yes	—
435	#394	C₂²×C₁₃	1	2	yes	—
436	#394	C₂²×C₁₃	1	2	yes	—
437	#393	C₂²×C₁₃	1	1	yes	characteristic
438	#393	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#391	C₂²×C₁₃	1	2	yes	complemented
440	#389	C₂²×C₁₃	1	2	yes	complemented
441	#388	C₂²×C₁₃	1	2	yes	complemented
442	#388	C₂²×C₁₃	1	2	yes	complemented
443	#388	C₂²×C₁₃	1	2	yes	complemented
444	#388	C₂²×C₁₃	1	2	yes	complemented
445	#387	C₂²×C₁₃	1	2	yes	complemented
446	#387	C₂²×C₁₃	1	2	yes	complemented
447	#387	C₂²×C₁₃	1	2	yes	complemented
448	#387	C₂²×C₁₃	1	2	yes	complemented
449	#387	C₂²×C₁₃	1	2	yes	complemented
450	#387	C₂²×C₁₃	1	2	yes	complemented
451	#386	C₂²×C₁₃	1	2	yes	—
452	#386	C₂²×C₁₃	1	2	yes	—
453	#386	C₂²×C₁₃	1	2	yes	—
454	#386	C₂²×C₁₃	1	2	yes	—
455	#386	C₂²×C₁₃	1	1	yes	characteristic
456	#385	C₂²×C₁₃	1	2	yes	—
457	#385	C₂²×C₁₃	1	2	yes	—
458	#385	C₂²×C₁₃	1	2	yes	—
459	#385	C₂²×C₁₃	1	2	yes	—
460	#385	C₂²×C₁₃	1	2	yes	—
461	#385	C₂²×C₁₃	1	2	yes	—
462	#385	C₂²×C₁₃	1	1	yes	characteristic
463	#383	C₂²×C₁₃	1	2	yes	complemented
464	#383	C₂²×C₁₃	1	2	yes	complemented
465	#382	C₂²×C₁₃	1	2	yes	complemented
466	#382	C₂²×C₁₃	1	2	yes	complemented
467	#381	C₂²×C₁₃	1	2	yes	—
468	#381	C₂²×C₁₃	1	2	yes	—
469	#381	C₂²×C₁₃	1	2	yes	—
470	#380	C₂²×C₁₃	1	2	yes	—
471	#380	C₂²×C₁₃	1	2	yes	—
472	#380	C₂²×C₁₃	1	2	yes	—
473	#379	C₂²×C₁₃	1	1	yes	characteristic
474	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
475	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
476	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
477	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
478	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
479	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
480	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
481	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
482	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
483	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
484	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
489	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
490	#376	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	#376	C₂²×C₁₃	1	2	yes	complemented
492	C₂×#95	C₂²×C₁₃	1	2	yes	—
493	C₂×#95	C₂²×C₁₃	1	2	yes	—
494	C₂²×C₁₃	—	2	4	no	—
495	C₂²×C₁₃	—	2	4	no	—
496	C₂²×C₁₃	—	2	4	no	—
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	2	no	—
502	C₂²×C₁₃	—	4	16	no	—
503	C₂²×C₁₃	—	4	1	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	4	1	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	#529	1	8	yes	—
512	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
513	C₂²×C₁₃	C₂²×#41	1	2	yes	—
514	C₂²×C₁₃	C₂²×#41	1	2	yes	—
515	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂²×C₁₃	#585	1	1	yes	characteristic
517	C₄×C₁₃	—	2	4	no	—
518	C₄×C₁₃	—	2	4	no	—
519	C₄×C₁₃	—	2	4	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	2	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	—	4	1	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	2	no	—
530	C₄×C₁₃	—	4	2	no	—
531	C₄×C₁₃	—	4	1	no	—
532	C₄×C₁₃	#551	1	4	yes	—
533	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
534	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
536	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂³×C₄	—	2	8	no	—
538	C₂³×C₄	—	4	2	no	—
539	C₂³×C₄	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	2	yes	—
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	2	yes	—
547	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
548	#123	—	2	8	no	—
549	C₂²⋊Q₈	—	2	8	no	—
550	#120	—	2	4	no	—
551	C₄×Q₈	—	4	2	no	—
552	C₄×D₄	—	2	8	no	—
553	C₄×D₄	—	4	2	no	—
554	#117	—	4	2	no	—
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
569	C₂×C₂²⋊C₄	—	2	8	no	—
570	C₂×C₂²⋊C₄	—	2	8	no	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
574	C₂×C₂²⋊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	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄²	—	2	8	no	—
592	C₂×C₄²	—	4	4	no	—
593	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
594	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
596	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
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	#95	C₂³×C₁₃	1	2	yes	—
604	#95	C₂³×C₁₃	1	2	yes	—
605	#95	C₂³×C₁₃	1	2	yes	—
606	#95	C₂³×C₁₃	1	2	yes	—
607	#95	C₂³×C₁₃	1	2	yes	—
608	#95	C₂³×C₁₃	1	2	yes	—
609	#95	C₂³×C₁₃	1	2	yes	—
610	#95	C₂³×C₁₃	1	2	yes	—
611	#95	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
622	#95	C₂³×C₁₃	1	2	yes	—
623	#95	C₂³×C₁₃	1	2	yes	—
624	#95	C₂³×C₁₃	1	1	yes	characteristic
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	C₂×C₁₃	—	2	8	no	—
634	C₂×C₁₃	—	4	2	no	—
635	C₂×C₁₃	—	8	1	no	—
636	C₂×C₁₃	C₂×#529	1	2	yes	—
637	C₂×C₁₃	#3459	1	1	yes	characteristic
638	C₂×C₁₃	C₂×#551	1	1	yes	characteristic
639	C₂×C₁₃	#3475	1	2	yes	—
640	C₂×C₁₃	#3481	1	1	yes	characteristic
641	C₂⁴	—	2	4	no	—
642	C₂⁴	—	2	4	no	—
643	C₂⁴	—	4	1	no	—
644	C₂⁴	—	4	1	no	—
645	C₂⁴	C₁₃×#41	1	4	yes	—
646	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
647	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
648	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
649	C₂×Q₈	—	2	4	no	—
650	C₂×Q₈	—	4	1	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	4	1	no	—
656	C₂×D₄	—	4	1	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	4	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	16	no	—
681	C₂²×C₄	C₁₃×#41	1	8	yes	—
682	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	4	1	no	—
705	C₄⋊C₄	—	4	1	no	—
706	C₄⋊C₄	—	4	1	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	1	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	1	no	—
728	C₂²⋊C₄	—	4	1	no	—
729	C₂²⋊C₄	—	4	1	no	—
730	C₂²⋊C₄	—	4	2	no	—
731	C₂²⋊C₄	C₁₃×#41	1	8	yes	—
732	C₄²	—	2	4	no	—
733	C₄²	—	2	4	no	—
734	C₄²	—	2	4	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	4	2	no	—
741	C₄²	—	4	2	no	—
742	C₁₃	#34754	1	1	yes	characteristic, direct product factor, Sylow
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	16	no	—
748	C₂³	—	2	2	no	—
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	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	8	no	—
760	C₂³	—	4	4	no	—
761	C₂³	C₂×C₁₃×#41	1	2	yes	—
762	C₂³	C₂×C₁₃×#41	1	4	yes	—
763	C₂³	C₂×C₁₃×#41	1	4	yes	—
764	C₂³	C₂×C₁₃×#41	1	4	yes	—
765	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
766	Q₈	—	4	4	no	—
767	D₄	—	4	4	no	—
768	D₄	—	4	8	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	16	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	2	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	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	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	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	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	1	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
818	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
819	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
820	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
821	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	16	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	C₁₃×#529	1	8	yes	—
840	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
841	C₂²	C₂²×C₁₃×#41	1	2	yes	—
842	C₂²	C₂²×C₁₃×#41	1	2	yes	—
843	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂²	C₁₃×#585	1	1	yes	characteristic
845	C₄	—	2	4	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	4	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	C₁₃×#551	1	4	yes	—
861	C₂	—	2	8	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	1	no	—
864	C₂	C₂×C₁₃×#529	1	2	yes	—
865	C₂	C₁₃×#3459	1	1	yes	characteristic
866	C₂	C₂×C₁₃×#551	1	1	yes	characteristic
867	C₂	C₁₃×#3475	1	2	yes	—
868	C₂	C₁₃×#3481	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×#120	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×#2523	C₂	semidirect
2. C₁₃×#2518	C₂	semidirect
3. C₁₃×#2517	C₂	semidirect
4. C₁₃×#2510	C₂	semidirect
5. C₁₃×#2505	C₂	semidirect
6. C₁₃×#2493	C₂	semidirect
7. C₁₃×#2488	C₂	semidirect
8. C₁₃×#2483	C₂	semidirect
9. C₁₃×#2437	C₂	semidirect
11. C₁₃×#2401	C₂	semidirect
12. C₁₃×#2398	C₂	semidirect
13. C₁₃×#2395	C₂	semidirect
14. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₁₃×#123	C₂	semidirect
17. C₁₃×#2290	C₂	semidirect
18. C₁₃×#2283	C₂	semidirect
19. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
27. C₂×C₁₃×#117	C₂²	semidirect
32. C₁₃×#401	C₂²	semidirect
33. C₁₃×#400	C₂²	semidirect
34. C₁₃×#400	C₂²	semidirect
35. C₁₃×#400	C₂²	semidirect
36. C₁₃×#400	C₂²	semidirect
37. C₁₃×#400	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
45. C₁₃×#397	C₂²	semidirect
46. C₁₃×#397	C₂²	semidirect
51. C₁₃×#393	C₂²	semidirect
52. C₁₃×#391	C₂²	semidirect
53. C₁₃×#389	C₂²	semidirect
54. C₁₃×#388	C₂²	semidirect
55. C₁₃×#388	C₂²	semidirect
56. C₁₃×#388	C₂²	semidirect
57. C₁₃×#388	C₂²	semidirect
58. C₁₃×#387	C₂²	semidirect
59. C₁₃×#387	C₂²	semidirect
60. C₁₃×#387	C₂²	semidirect
61. C₁₃×#387	C₂²	semidirect
62. C₁₃×#387	C₂²	semidirect
63. C₁₃×#387	C₂²	semidirect
76. C₁₃×#383	C₂²	semidirect
77. C₁₃×#383	C₂²	semidirect
78. C₁₃×#382	C₂²	semidirect
79. C₁₃×#382	C₂²	semidirect
87. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
88. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
89. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
90. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
101. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
102. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
103. C₁₃×#376	C₂²	semidirect
104. C₁₃×#376	C₂²	semidirect
207. #34754	C₁₃	direct (N × H)
309. #2523	C₂×C₁₃	semidirect
310. #2518	C₂×C₁₃	semidirect
311. #2517	C₂×C₁₃	semidirect
312. #2510	C₂×C₁₃	semidirect
313. #2505	C₂×C₁₃	semidirect
314. #2493	C₂×C₁₃	semidirect
315. #2488	C₂×C₁₃	semidirect
316. #2483	C₂×C₁₃	semidirect
317. #2437	C₂×C₁₃	semidirect
319. #2401	C₂×C₁₃	semidirect
320. #2398	C₂×C₁₃	semidirect
321. #2395	C₂×C₁₃	semidirect
322. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
323. C₄×#123	C₂×C₁₃	semidirect
325. #2290	C₂×C₁₃	semidirect
326. #2283	C₂×C₁₃	semidirect
327. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
411. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
414. C₂×#117	C₂²×C₁₃	semidirect
419. #401	C₂²×C₁₃	semidirect
420. #400	C₂²×C₁₃	semidirect
421. #400	C₂²×C₁₃	semidirect
422. #400	C₂²×C₁₃	semidirect
423. #400	C₂²×C₁₃	semidirect
424. #400	C₂²×C₁₃	semidirect
426. #398	C₂²×C₁₃	semidirect
432. #397	C₂²×C₁₃	semidirect
433. #397	C₂²×C₁₃	semidirect
438. #393	C₂²×C₁₃	semidirect
439. #391	C₂²×C₁₃	semidirect
440. #389	C₂²×C₁₃	semidirect
441. #388	C₂²×C₁₃	semidirect
442. #388	C₂²×C₁₃	semidirect
443. #388	C₂²×C₁₃	semidirect
444. #388	C₂²×C₁₃	semidirect
445. #387	C₂²×C₁₃	semidirect
446. #387	C₂²×C₁₃	semidirect
447. #387	C₂²×C₁₃	semidirect
448. #387	C₂²×C₁₃	semidirect
449. #387	C₂²×C₁₃	semidirect
450. #387	C₂²×C₁₃	semidirect
463. #383	C₂²×C₁₃	semidirect
464. #383	C₂²×C₁₃	semidirect
465. #382	C₂²×C₁₃	semidirect
466. #382	C₂²×C₁₃	semidirect
474. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
475. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
476. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
477. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
488. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
489. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
490. #376	C₂²×C₁₃	semidirect
491. #376	C₂²×C₁₃	semidirect
742. C₁₃	#34754	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×#2523	2
C₁₃×#2518	2
C₁₃×#2517	2
C₁₃×#2510	2
C₁₃×#2505	2
C₁₃×#2493	2
C₁₃×#2488	2
C₁₃×#2483	2
C₁₃×#2437	2
C₁₃×#2412	2
C₁₃×#2401	2
C₁₃×#2398	2
C₁₃×#2395	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#123	2
C₄×C₁₃×#120	2
C₁₃×#2290	2
C₁₃×#2283	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34754	13

Subgroups — C13×#34754 #15721093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34754 #15721093