Subgroups — C₁₃×#34913 #15721252

Order 3328.

1870 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2578	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2577	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2576	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2575	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2508	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2495	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2489	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2454	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×#2420	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2401	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2395	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#125	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	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
19	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
21	C₁₃×#2283	C₂	1	2	yes	maximal, 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×#125	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
37	C₁₃×#401	C₂²	1	2	yes	—
38	C₁₃×#400	C₂²	1	2	yes	—
39	C₁₃×#400	C₂²	1	2	yes	—
40	C₁₃×#400	C₂²	1	2	yes	—
41	C₁₃×#400	C₂²	1	2	yes	—
42	C₁₃×#399	C₂²	1	2	yes	—
43	C₁₃×#398	C₂²	1	2	yes	—
44	C₁₃×#397	C₂²	1	2	yes	—
45	C₁₃×#397	C₂²	1	2	yes	—
46	C₁₃×#397	C₂²	1	2	yes	—
47	C₁₃×#397	C₂²	1	2	yes	—
48	C₁₃×#397	C₂²	1	2	yes	—
49	C₁₃×#397	C₂²	1	2	yes	—
50	C₁₃×#396	C₂²	1	2	yes	—
51	C₁₃×#394	C₂²	1	2	yes	—
52	C₁₃×#394	C₂²	1	2	yes	—
53	C₁₃×#391	C₂²	1	1	yes	characteristic
54	C₁₃×#391	C₂²	1	1	yes	characteristic
55	C₁₃×#391	C₂²	1	1	yes	characteristic
56	C₁₃×#391	C₂²	1	1	yes	characteristic
57	C₁₃×#390	C₂²	1	1	yes	characteristic
58	C₁₃×#390	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	1	yes	characteristic
62	C₁₃×#389	C₂²	1	1	yes	characteristic
63	C₁₃×#389	C₂²	1	1	yes	characteristic
64	C₁₃×#389	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
71	C₁₃×#387	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	2	yes	—
78	C₁₃×#386	C₂²	1	2	yes	—
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	2	yes	—
81	C₁₃×#385	C₂²	1	2	yes	—
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#383	C₂²	1	2	yes	—
84	C₁₃×#383	C₂²	1	2	yes	—
85	C₁₃×#382	C₂²	1	1	yes	characteristic
86	C₁₃×#382	C₂²	1	2	yes	—
87	C₁₃×#382	C₂²	1	1	yes	characteristic
88	C₁₃×#382	C₂²	1	2	yes	—
89	C₁₃×#381	C₂²	1	2	yes	—
90	C₁₃×#381	C₂²	1	2	yes	—
91	C₁₃×#380	C₂²	1	1	yes	characteristic
92	C₁₃×#380	C₂²	1	1	yes	characteristic
93	C₁₃×#380	C₂²	1	2	yes	—
94	C₁₃×#380	C₂²	1	2	yes	—
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	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	2	yes	—
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₁₃×#125	—	2	4	no	—
133	C₁₃×#124	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×#121	—	2	4	no	—
136	C₄×Q₈×C₁₃	—	2	4	no	—
137	C₄×D₄×C₁₃	—	2	4	no	—
138	C₄×D₄×C₁₃	—	2	8	no	—
139	C₄×D₄×C₁₃	—	2	4	no	—
140	C₄×D₄×C₁₃	—	2	4	no	—
141	C₁₃×#117	—	2	4	no	—
142	C₁₃×#117	—	2	4	no	—
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	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₃	—	2	8	no	—
181	C₂×C₄²×C₁₃	—	2	4	no	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	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	1	yes	characteristic
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	1	yes	characteristic
207	C₁₃×#95	C₂³	1	1	yes	characteristic
208	C₁₃×#95	C₂³	1	1	yes	characteristic
209	C₁₃×#95	C₂³	1	1	yes	characteristic
210	C₁₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
215	C₁₃×#95	C₂³	1	2	yes	—
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	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	#34913	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×D₄×C₁₃	—	2	4	no	—
242	C₂×D₄×C₁₃	—	2	4	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	4	2	no	—
246	C₂×D₄×C₁₃	#41	1	4	yes	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	4	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	2	2	no	—
253	C₂²×C₄×C₁₃	—	2	4	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	4	no	—
256	C₂²×C₄×C₁₃	—	2	4	no	—
257	C₂²×C₄×C₁₃	—	2	4	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	4	1	no	—
261	C₂²×C₄×C₁₃	—	4	1	no	—
262	C₂²×C₄×C₁₃	—	4	2	no	—
263	C₂²×C₄×C₁₃	—	4	2	no	—
264	C₂²×C₄×C₁₃	#41	1	4	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	4	2	no	—
301	C₁₃×C₄⋊C₄	—	4	2	no	—
302	C₁₃×C₄⋊C₄	—	4	2	no	—
303	C₁₃×C₄⋊C₄	—	4	2	no	—
304	C₁₃×C₄⋊C₄	—	4	2	no	—
305	C₁₃×C₄⋊C₄	#41	1	4	yes	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	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	—	4	2	no	—
320	C₁₃×C₂²⋊C₄	—	4	2	no	—
321	C₁₃×C₂²⋊C₄	—	4	2	no	—
322	C₁₃×C₂²⋊C₄	—	4	2	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	4	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	4	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	2	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	4	no	—
335	C₄²×C₁₃	—	2	4	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	—	2	2	no	—
338	C₄²×C₁₃	—	4	1	no	—
339	C₄²×C₁₃	—	4	1	no	—
340	C₄²×C₁₃	—	4	1	no	—
341	C₄²×C₁₃	—	4	1	no	—
342	C₄²×C₁₃	#41	1	4	yes	—
343	C₄²×C₁₃	#41	1	4	yes	—
344	#2578	C₂×C₁₃	1	2	yes	complemented
345	#2577	C₂×C₁₃	1	2	yes	complemented
346	#2576	C₂×C₁₃	1	2	yes	complemented
347	#2575	C₂×C₁₃	1	2	yes	complemented
348	#2514	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#2508	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#2495	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#2489	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2454	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#2447	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2427	C₂×C₁₃	1	1	yes	characteristic
355	#2420	C₂×C₁₃	1	1	yes	characteristic
356	#2401	C₂×C₁₃	1	2	yes	complemented
357	#2395	C₂×C₁₃	1	2	yes	complemented
358	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₄×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
360	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
361	C₄×#121	C₂×C₁₃	1	1	yes	characteristic
362	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#2290	C₂×C₁₃	1	2	yes	complemented
364	#2283	C₂×C₁₃	1	2	yes	complemented
365	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
366	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
367	C₂³×C₁₃	—	2	1	no	—
368	C₂³×C₁₃	—	2	1	no	—
369	C₂³×C₁₃	—	2	2	no	—
370	C₂³×C₁₃	—	2	2	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	2	1	no	—
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	2	1	no	—
375	C₂³×C₁₃	—	2	2	no	—
376	C₂³×C₁₃	—	2	1	no	—
377	C₂³×C₁₃	—	2	2	no	—
378	C₂³×C₁₃	—	2	1	no	—
379	C₂³×C₁₃	C₂×#41	1	4	yes	—
380	C₂³×C₁₃	C₂×#41	1	2	yes	—
381	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
382	Q₈×C₁₃	—	4	4	no	—
383	D₄×C₁₃	—	2	8	no	—
384	D₄×C₁₃	—	4	8	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	8	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	1	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	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	2	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	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	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	1	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	1	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	4	8	no	—
439	C₂×C₄×C₁₃	—	4	8	no	—
440	C₂×C₄×C₁₃	—	4	4	no	—
441	C₂×C₄×C₁₃	—	4	8	no	—
442	C₂×C₄×C₁₃	—	4	4	no	—
443	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
444	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
445	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
446	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
447	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
448	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
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×#125	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
459	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
460	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
465	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
466	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
467	#401	C₂²×C₁₃	1	2	yes	—
468	#400	C₂²×C₁₃	1	2	yes	—
469	#400	C₂²×C₁₃	1	2	yes	—
470	#400	C₂²×C₁₃	1	2	yes	—
471	#400	C₂²×C₁₃	1	2	yes	—
472	#399	C₂²×C₁₃	1	2	yes	—
473	#398	C₂²×C₁₃	1	2	yes	—
474	#397	C₂²×C₁₃	1	2	yes	—
475	#397	C₂²×C₁₃	1	2	yes	—
476	#397	C₂²×C₁₃	1	2	yes	—
477	#397	C₂²×C₁₃	1	2	yes	—
478	#397	C₂²×C₁₃	1	2	yes	—
479	#397	C₂²×C₁₃	1	2	yes	—
480	#396	C₂²×C₁₃	1	2	yes	—
481	#394	C₂²×C₁₃	1	2	yes	—
482	#394	C₂²×C₁₃	1	2	yes	—
483	#391	C₂²×C₁₃	1	1	yes	characteristic
484	#391	C₂²×C₁₃	1	1	yes	characteristic
485	#391	C₂²×C₁₃	1	1	yes	characteristic
486	#391	C₂²×C₁₃	1	1	yes	characteristic
487	#390	C₂²×C₁₃	1	1	yes	characteristic
488	#390	C₂²×C₁₃	1	1	yes	characteristic
489	#389	C₂²×C₁₃	1	1	yes	characteristic
490	#389	C₂²×C₁₃	1	1	yes	characteristic
491	#389	C₂²×C₁₃	1	1	yes	characteristic
492	#389	C₂²×C₁₃	1	1	yes	characteristic
493	#389	C₂²×C₁₃	1	1	yes	characteristic
494	#389	C₂²×C₁₃	1	1	yes	characteristic
495	#388	C₂²×C₁₃	1	2	yes	—
496	#388	C₂²×C₁₃	1	2	yes	—
497	#388	C₂²×C₁₃	1	2	yes	—
498	#388	C₂²×C₁₃	1	2	yes	—
499	#388	C₂²×C₁₃	1	2	yes	—
500	#387	C₂²×C₁₃	1	2	yes	—
501	#387	C₂²×C₁₃	1	2	yes	—
502	#387	C₂²×C₁₃	1	2	yes	—
503	#387	C₂²×C₁₃	1	2	yes	—
504	#387	C₂²×C₁₃	1	2	yes	—
505	#387	C₂²×C₁₃	1	2	yes	—
506	#387	C₂²×C₁₃	1	2	yes	—
507	#386	C₂²×C₁₃	1	2	yes	—
508	#386	C₂²×C₁₃	1	2	yes	—
509	#386	C₂²×C₁₃	1	2	yes	—
510	#385	C₂²×C₁₃	1	2	yes	—
511	#385	C₂²×C₁₃	1	2	yes	—
512	#385	C₂²×C₁₃	1	2	yes	—
513	#383	C₂²×C₁₃	1	2	yes	—
514	#383	C₂²×C₁₃	1	2	yes	—
515	#382	C₂²×C₁₃	1	1	yes	characteristic
516	#382	C₂²×C₁₃	1	2	yes	—
517	#382	C₂²×C₁₃	1	2	yes	—
518	#382	C₂²×C₁₃	1	1	yes	characteristic
519	#381	C₂²×C₁₃	1	2	yes	—
520	#381	C₂²×C₁₃	1	2	yes	—
521	#380	C₂²×C₁₃	1	2	yes	—
522	#380	C₂²×C₁₃	1	2	yes	—
523	#380	C₂²×C₁₃	1	1	yes	characteristic
524	#380	C₂²×C₁₃	1	1	yes	characteristic
525	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
526	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
527	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
528	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
529	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
530	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
531	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
532	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
533	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
535	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
536	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
537	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
539	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
540	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
541	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
542	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
543	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
547	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
548	#376	C₂²×C₁₃	1	1	yes	characteristic
549	#376	C₂²×C₁₃	1	1	yes	characteristic
550	#376	C₂²×C₁₃	1	2	yes	—
551	C₄³	C₂²×C₁₃	1	1	yes	characteristic
552	C₄³	C₂²×C₁₃	1	1	yes	characteristic
553	C₂²×C₁₃	—	2	2	no	—
554	C₂²×C₁₃	—	2	4	no	—
555	C₂²×C₁₃	—	2	4	no	—
556	C₂²×C₁₃	—	2	2	no	—
557	C₂²×C₁₃	—	2	4	no	—
558	C₂²×C₁₃	—	2	2	no	—
559	C₂²×C₁₃	—	4	2	no	—
560	C₂²×C₁₃	—	4	1	no	—
561	C₂²×C₁₃	—	4	1	no	—
562	C₂²×C₁₃	—	4	2	no	—
563	C₂²×C₁₃	—	4	2	no	—
564	C₂²×C₁₃	—	4	1	no	—
565	C₂²×C₁₃	—	4	1	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
568	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
569	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
570	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
571	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
572	C₂²×C₁₃	#585	1	1	yes	characteristic
573	C₂²×C₁₃	#585	1	1	yes	characteristic
574	C₄×C₁₃	—	2	2	no	—
575	C₄×C₁₃	—	2	2	no	—
576	C₄×C₁₃	—	2	2	no	—
577	C₄×C₁₃	—	2	2	no	—
578	C₄×C₁₃	—	2	4	no	—
579	C₄×C₁₃	—	4	2	no	—
580	C₄×C₁₃	—	4	1	no	—
581	C₄×C₁₃	—	4	2	no	—
582	C₄×C₁₃	—	4	2	no	—
583	C₄×C₁₃	—	4	1	no	—
584	C₄×C₁₃	—	4	1	no	—
585	C₄×C₁₃	—	4	1	no	—
586	C₄×C₁₃	—	4	1	no	—
587	C₄×C₁₃	—	4	1	no	—
588	C₄×C₁₃	—	4	2	no	—
589	C₄×C₁₃	—	4	2	no	—
590	C₄×C₁₃	—	4	1	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	1	no	—
593	C₄×C₁₃	#529	1	4	yes	—
594	C₄×C₁₃	#529	1	4	yes	—
595	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
597	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
599	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
601	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
602	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
604	#125	—	2	4	no	—
605	#124	—	2	4	no	—
606	C₂²⋊Q₈	—	2	4	no	—
607	#121	—	2	4	no	—
608	C₄×Q₈	—	2	4	no	—
609	C₄×D₄	—	2	4	no	—
610	C₄×D₄	—	2	8	no	—
611	C₄×D₄	—	2	4	no	—
612	C₄×D₄	—	2	4	no	—
613	#117	—	2	4	no	—
614	#117	—	2	4	no	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₄²	—	2	8	no	—
653	C₂×C₄²	—	2	4	no	—
654	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
660	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
665	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
666	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
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	#95	C₂³×C₁₃	1	1	yes	characteristic
676	#95	C₂³×C₁₃	1	1	yes	characteristic
677	#95	C₂³×C₁₃	1	1	yes	characteristic
678	#95	C₂³×C₁₃	1	1	yes	characteristic
679	#95	C₂³×C₁₃	1	1	yes	characteristic
680	#95	C₂³×C₁₃	1	1	yes	characteristic
681	#95	C₂³×C₁₃	1	1	yes	characteristic
682	#95	C₂³×C₁₃	1	1	yes	characteristic
683	#95	C₂³×C₁₃	1	2	yes	—
684	#95	C₂³×C₁₃	1	2	yes	—
685	#95	C₂³×C₁₃	1	2	yes	—
686	#95	C₂³×C₁₃	1	2	yes	—
687	#95	C₂³×C₁₃	1	2	yes	—
688	#95	C₂³×C₁₃	1	2	yes	—
689	#95	C₂³×C₁₃	1	2	yes	—
690	#95	C₂³×C₁₃	1	2	yes	—
691	#95	C₂³×C₁₃	1	2	yes	—
692	#95	C₂³×C₁₃	1	2	yes	—
693	#95	C₂³×C₁₃	1	2	yes	—
694	#95	C₂³×C₁₃	1	2	yes	—
695	#95	C₂³×C₁₃	1	2	yes	—
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	C₂×C₁₃	—	4	2	no	—
708	C₂×C₁₃	—	4	4	no	—
709	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
710	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
711	C₂×C₁₃	#3455	1	1	yes	characteristic
712	C₂×C₁₃	#3475	1	1	yes	characteristic
713	C₂×C₁₃	#3475	1	1	yes	characteristic
714	C₂×C₁₃	#3475	1	1	yes	characteristic
715	C₂×C₁₃	#3480	1	1	yes	characteristic
716	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
717	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	C₁₃×#41	1	4	yes	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	4	1	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	C₁₃×#41	1	4	yes	—
745	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
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	2	yes	—
764	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	C₁₃×#41	1	4	yes	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	—	4	2	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₄²	—	2	4	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	4	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	4	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	4	no	—
815	C₄²	—	2	4	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	4	1	no	—
819	C₄²	—	4	1	no	—
820	C₄²	—	4	1	no	—
821	C₄²	—	4	1	no	—
822	C₄²	C₁₃×#41	1	4	yes	—
823	C₄²	C₁₃×#41	1	4	yes	—
824	C₁₃	#34913	1	1	yes	characteristic, direct product factor, Sylow
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	1	no	—
837	C₂³	C₂×C₁₃×#41	1	4	yes	—
838	C₂³	C₂×C₁₃×#41	1	2	yes	—
839	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
840	Q₈	—	4	4	no	—
841	D₄	—	2	8	no	—
842	D₄	—	4	8	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	8	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	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	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	4	8	no	—
897	C₂×C₄	—	4	8	no	—
898	C₂×C₄	—	4	4	no	—
899	C₂×C₄	—	4	8	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
902	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
903	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
904	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
905	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
906	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
907	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
908	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
909	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
910	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
911	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	4	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	4	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	2	no	—
926	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
927	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
928	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
929	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
930	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
931	C₂²	C₁₃×#585	1	1	yes	characteristic
932	C₂²	C₁₃×#585	1	1	yes	characteristic
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	4	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	1	no	—
952	C₄	C₁₃×#529	1	4	yes	—
953	C₄	C₁₃×#529	1	4	yes	—
954	C₂	—	4	2	no	—
955	C₂	—	4	4	no	—
956	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
957	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
958	C₂	C₁₃×#3455	1	1	yes	characteristic
959	C₂	C₁₃×#3475	1	1	yes	characteristic
960	C₂	C₁₃×#3475	1	1	yes	characteristic
961	C₂	C₁₃×#3475	1	1	yes	characteristic
962	C₂	C₁₃×#3480	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×#2578	C₂	semidirect
2. C₁₃×#2577	C₂	semidirect
3. C₁₃×#2576	C₂	semidirect
4. C₁₃×#2575	C₂	semidirect
5. C₁₃×#2514	C₂	semidirect
6. C₁₃×#2508	C₂	semidirect
7. C₁₃×#2495	C₂	semidirect
8. C₁₃×#2489	C₂	semidirect
9. C₁₃×#2454	C₂	semidirect
10. C₁₃×#2447	C₂	semidirect
13. C₁₃×#2401	C₂	semidirect
14. C₁₃×#2395	C₂	semidirect
15. C₄×C₁₃×#125	C₂	semidirect
16. C₄×C₁₃×#124	C₂	semidirect
17. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
19. C₁₃×#2295	C₂	semidirect
20. C₁₃×#2290	C₂	semidirect
21. C₁₃×#2283	C₂	semidirect
22. C₄²×D₄×C₁₃	C₂	semidirect
23. C₄×C₁₃×#117	C₂	semidirect
235. #34913	C₁₃	direct (N × H)
344. #2578	C₂×C₁₃	semidirect
345. #2577	C₂×C₁₃	semidirect
346. #2576	C₂×C₁₃	semidirect
347. #2575	C₂×C₁₃	semidirect
348. #2514	C₂×C₁₃	semidirect
349. #2508	C₂×C₁₃	semidirect
350. #2495	C₂×C₁₃	semidirect
351. #2489	C₂×C₁₃	semidirect
352. #2454	C₂×C₁₃	semidirect
353. #2447	C₂×C₁₃	semidirect
356. #2401	C₂×C₁₃	semidirect
357. #2395	C₂×C₁₃	semidirect
358. C₄×#125	C₂×C₁₃	semidirect
359. C₄×#124	C₂×C₁₃	semidirect
360. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
362. #2295	C₂×C₁₃	semidirect
363. #2290	C₂×C₁₃	semidirect
364. #2283	C₂×C₁₃	semidirect
365. C₄²×D₄	C₂×C₁₃	semidirect
366. C₄×#117	C₂×C₁₃	semidirect
824. C₁₃	#34913	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×#2578	2
C₁₃×#2577	2
C₁₃×#2576	2
C₁₃×#2575	2
C₁₃×#2514	2
C₁₃×#2508	2
C₁₃×#2495	2
C₁₃×#2489	2
C₁₃×#2454	2
C₁₃×#2447	2
C₁₃×#2427	2
C₁₃×#2420	2
C₁₃×#2401	2
C₁₃×#2395	2
C₄×C₁₃×#125	2
C₄×C₁₃×#124	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2295	2
C₁₃×#2290	2
C₁₃×#2283	2
C₄²×D₄×C₁₃	2
C₄×C₁₃×#117	2
#34913	13

Subgroups — C13×#34913 #15721252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34913 #15721252