Subgroups — C₁₃×#34434 #15720773

Order 3328.

1974 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2381	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2378	C₂	1	2	yes	maximal
4	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2365	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2362	C₂	1	2	yes	maximal
10	C₁₃×#2347	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2347	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2345	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2344	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#2336	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2336	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2332	C₂	1	2	yes	maximal
17	C₁₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2323	C₂	1	2	yes	maximal
20	C₁₃×#2314	C₂	1	1	yes	maximal, characteristic
21	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic
24	C₁₃×#544	C₄	1	16	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#125	C₂²	1	2	yes	—
30	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#391	C₂²	1	2	yes	—
42	C₁₃×#391	C₂²	1	2	yes	—
43	C₁₃×#391	C₂²	1	2	yes	—
44	C₁₃×#391	C₂²	1	2	yes	—
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#389	C₂²	1	2	yes	—
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	2	yes	—
51	C₁₃×#389	C₂²	1	2	yes	—
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#389	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	2	yes	—
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#388	C₂²	1	1	yes	characteristic
60	C₁₃×#388	C₂²	1	1	yes	characteristic
61	C₁₃×#388	C₂²	1	1	yes	characteristic
62	C₁₃×#388	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	1	yes	characteristic
70	C₁₃×#387	C₂²	1	1	yes	characteristic
71	C₁₃×#387	C₂²	1	1	yes	characteristic
72	C₁₃×#387	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#387	C₂²	1	2	yes	—
86	C₁₃×#387	C₂²	1	2	yes	—
87	C₁₃×#387	C₂²	1	2	yes	—
88	C₁₃×#387	C₂²	1	2	yes	—
89	C₁₃×#387	C₂²	1	2	yes	—
90	C₁₃×#387	C₂²	1	2	yes	—
91	C₁₃×#384	C₂²	1	1	yes	characteristic
92	C₁₃×#383	C₂²	1	2	yes	—
93	C₁₃×#383	C₂²	1	2	yes	—
94	C₁₃×#382	C₂²	1	1	yes	characteristic
95	C₁₃×#381	C₂²	1	2	yes	—
96	C₁₃×#380	C₂²	1	1	yes	characteristic
97	C₁₃×#380	C₂²	1	1	yes	characteristic
98	C₁₃×#380	C₂²	1	2	yes	—
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	2	yes	—
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
114	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
115	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
118	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
121	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₁₃×#376	C₂²	1	1	yes	characteristic
123	C₄³×C₁₃	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
125	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
129	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
130	C₁₃×C₄⋊Q₈	C₂×C₄	1	16	yes	—
131	C₁₃×#125	C₂×C₄	1	8	yes	—
132	C₁₃×#125	C₂×C₄	1	16	yes	—
133	C₁₃×#125	C₂×C₄	1	8	yes	—
134	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
135	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
136	C₄×Q₈×C₁₃	—	4	4	no	—
137	C₄×Q₈×C₁₃	—	4	4	no	—
138	C₁₃×#117	—	4	4	no	—
139	C₁₃×#117	C₂×C₄	1	8	yes	—
140	C₁₃×#117	C₂×C₄	1	8	yes	—
141	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	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	1	yes	characteristic
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	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
193	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
194	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	2	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₁₃×#95	C₂³	1	1	yes	characteristic
204	C₁₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
209	C₁₃×#95	C₂³	1	1	yes	characteristic
210	C₁₃×#95	C₂³	1	1	yes	characteristic
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	C₁₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
230	C₁₃×#95	C₂³	1	2	yes	—
231	C₁₃×#95	C₂³	1	1	yes	characteristic
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	1	yes	characteristic
234	C₁₃×#95	C₂³	1	1	yes	characteristic
235	C₁₃×#95	C₂³	1	1	yes	characteristic
236	C₁₃×#95	C₂³	1	1	yes	characteristic
237	#34434	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₁₃	—	4	2	no	—
240	C₂×Q₈×C₁₃	—	4	2	no	—
241	C₂×Q₈×C₁₃	—	4	2	no	—
242	C₂×Q₈×C₁₃	—	4	2	no	—
243	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
244	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	4	2	no	—
248	C₂²×C₄×C₁₃	—	4	2	no	—
249	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
250	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
262	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	4	1	no	—
283	C₁₃×C₄⋊C₄	—	4	2	no	—
284	C₁₃×C₄⋊C₄	—	4	2	no	—
285	C₁₃×C₄⋊C₄	—	4	2	no	—
286	C₁₃×C₄⋊C₄	—	4	1	no	—
287	C₁₃×C₄⋊C₄	—	4	2	no	—
288	C₁₃×C₄⋊C₄	—	4	2	no	—
289	C₁₃×C₄⋊C₄	—	4	2	no	—
290	C₁₃×C₄⋊C₄	—	4	2	no	—
291	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
292	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
293	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
294	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
295	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
296	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
297	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
298	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
299	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
300	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
301	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
302	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
303	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	4	2	no	—
307	C₁₃×C₂²⋊C₄	—	4	1	no	—
308	C₁₃×C₂²⋊C₄	—	4	1	no	—
309	C₁₃×C₂²⋊C₄	—	4	2	no	—
310	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
311	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
312	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
313	C₄²×C₁₃	—	2	4	no	—
314	C₄²×C₁₃	—	2	2	no	—
315	C₄²×C₁₃	—	2	2	no	—
316	C₄²×C₁₃	—	2	2	no	—
317	C₄²×C₁₃	—	2	2	no	—
318	C₄²×C₁₃	—	2	2	no	—
319	C₄²×C₁₃	—	2	2	no	—
320	C₄²×C₁₃	—	4	2	no	—
321	C₄²×C₁₃	—	4	1	no	—
322	C₄²×C₁₃	—	4	2	no	—
323	C₄²×C₁₃	—	4	2	no	—
324	C₄²×C₁₃	—	4	2	no	—
325	C₄²×C₁₃	—	4	1	no	—
326	C₄²×C₁₃	—	4	2	no	—
327	C₄²×C₁₃	—	4	2	no	—
328	C₄²×C₁₃	—	4	2	no	—
329	C₄²×C₁₃	—	4	2	no	—
330	C₄²×C₁₃	—	4	2	no	—
331	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
332	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
333	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
334	C₂×#544	C₂×C₁₃	1	1	yes	characteristic
335	#2381	C₂×C₁₃	1	2	yes	complemented
336	#2378	C₂×C₁₃	1	2	yes	—
337	#2370	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#2370	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#2369	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#2365	C₂×C₁₃	1	2	yes	complemented
341	#2365	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#2362	C₂×C₁₃	1	2	yes	—
343	#2347	C₂×C₁₃	1	1	yes	characteristic
344	#2347	C₂×C₁₃	1	1	yes	characteristic
345	#2345	C₂×C₁₃	1	1	yes	characteristic
346	#2344	C₂×C₁₃	1	1	yes	characteristic
347	#2336	C₂×C₁₃	1	2	yes	complemented
348	#2336	C₂×C₁₃	1	2	yes	complemented
349	#2332	C₂×C₁₃	1	2	yes	—
350	#2331	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#2330	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#2323	C₂×C₁₃	1	2	yes	—
353	#2314	C₂×C₁₃	1	1	yes	characteristic
354	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#2298	C₂×C₁₃	1	1	yes	characteristic
357	C₂³×C₁₃	—	2	1	no	—
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	—	2	1	no	—
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
364	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
365	Q₈×C₁₃	—	4	8	no	—
366	Q₈×C₁₃	—	4	8	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	2	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	2	no	—
389	C₂×C₄×C₁₃	—	2	8	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	1	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	1	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	1	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	4	8	no	—
421	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
422	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
423	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
424	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
425	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
426	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
427	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
428	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
429	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
430	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
431	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
432	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
433	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
434	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
435	#544	C₄×C₁₃	1	16	yes	complemented
436	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
439	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#125	C₂²×C₁₃	1	2	yes	—
441	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
443	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
444	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
445	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
446	C₂×#117	C₂²×C₁₃	1	2	yes	—
447	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
449	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
450	#391	C₂²×C₁₃	1	2	yes	—
451	#391	C₂²×C₁₃	1	2	yes	—
452	#391	C₂²×C₁₃	1	2	yes	—
453	#391	C₂²×C₁₃	1	2	yes	—
454	#391	C₂²×C₁₃	1	2	yes	—
455	#391	C₂²×C₁₃	1	2	yes	—
456	#389	C₂²×C₁₃	1	1	yes	characteristic
457	#389	C₂²×C₁₃	1	1	yes	characteristic
458	#389	C₂²×C₁₃	1	2	yes	—
459	#389	C₂²×C₁₃	1	1	yes	characteristic
460	#389	C₂²×C₁₃	1	1	yes	characteristic
461	#389	C₂²×C₁₃	1	2	yes	—
462	#389	C₂²×C₁₃	1	2	yes	—
463	#389	C₂²×C₁₃	1	1	yes	characteristic
464	#389	C₂²×C₁₃	1	1	yes	characteristic
465	#389	C₂²×C₁₃	1	2	yes	—
466	#389	C₂²×C₁₃	1	1	yes	characteristic
467	#389	C₂²×C₁₃	1	1	yes	characteristic
468	#389	C₂²×C₁₃	1	2	yes	—
469	#389	C₂²×C₁₃	1	2	yes	—
470	#388	C₂²×C₁₃	1	2	yes	—
471	#388	C₂²×C₁₃	1	2	yes	—
472	#388	C₂²×C₁₃	1	1	yes	characteristic
473	#388	C₂²×C₁₃	1	2	yes	—
474	#388	C₂²×C₁₃	1	2	yes	—
475	#388	C₂²×C₁₃	1	1	yes	characteristic
476	#388	C₂²×C₁₃	1	2	yes	—
477	#388	C₂²×C₁₃	1	2	yes	—
478	#388	C₂²×C₁₃	1	1	yes	characteristic
479	#388	C₂²×C₁₃	1	1	yes	characteristic
480	#387	C₂²×C₁₃	1	2	yes	—
481	#387	C₂²×C₁₃	1	2	yes	—
482	#387	C₂²×C₁₃	1	2	yes	—
483	#387	C₂²×C₁₃	1	2	yes	—
484	#387	C₂²×C₁₃	1	2	yes	—
485	#387	C₂²×C₁₃	1	2	yes	—
486	#387	C₂²×C₁₃	1	2	yes	—
487	#387	C₂²×C₁₃	1	2	yes	—
488	#387	C₂²×C₁₃	1	2	yes	—
489	#387	C₂²×C₁₃	1	2	yes	—
490	#387	C₂²×C₁₃	1	1	yes	characteristic
491	#387	C₂²×C₁₃	1	1	yes	characteristic
492	#387	C₂²×C₁₃	1	2	yes	—
493	#387	C₂²×C₁₃	1	2	yes	—
494	#387	C₂²×C₁₃	1	2	yes	—
495	#387	C₂²×C₁₃	1	2	yes	—
496	#387	C₂²×C₁₃	1	2	yes	—
497	#387	C₂²×C₁₃	1	2	yes	—
498	#387	C₂²×C₁₃	1	2	yes	—
499	#387	C₂²×C₁₃	1	2	yes	—
500	#387	C₂²×C₁₃	1	1	yes	characteristic
501	#387	C₂²×C₁₃	1	1	yes	characteristic
502	#384	C₂²×C₁₃	1	1	yes	characteristic
503	#383	C₂²×C₁₃	1	2	yes	—
504	#383	C₂²×C₁₃	1	2	yes	—
505	#382	C₂²×C₁₃	1	1	yes	characteristic
506	#381	C₂²×C₁₃	1	2	yes	—
507	#380	C₂²×C₁₃	1	1	yes	characteristic
508	#380	C₂²×C₁₃	1	1	yes	characteristic
509	#380	C₂²×C₁₃	1	2	yes	—
510	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
511	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
512	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
513	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
514	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
515	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
516	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
517	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
518	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
519	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
520	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
521	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
522	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
523	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
524	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
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	2	yes	—
528	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
529	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
530	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
532	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
533	#376	C₂²×C₁₃	1	1	yes	characteristic
534	C₄³	C₂²×C₁₃	1	1	yes	characteristic
535	C₂²×C₁₃	—	2	2	no	—
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	2	no	—
538	C₂²×C₁₃	—	4	1	no	—
539	C₂²×C₁₃	—	4	1	no	—
540	C₂²×C₁₃	—	4	1	no	—
541	C₂²×C₁₃	—	4	1	no	—
542	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
543	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
544	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
545	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
546	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
547	C₂²×C₁₃	#585	1	1	yes	characteristic
548	C₂²×C₁₃	#585	1	1	yes	characteristic
549	C₄×C₁₃	—	2	2	no	—
550	C₄×C₁₃	—	2	4	no	—
551	C₄×C₁₃	—	2	4	no	—
552	C₄×C₁₃	—	2	2	no	—
553	C₄×C₁₃	—	2	4	no	—
554	C₄×C₁₃	—	2	2	no	—
555	C₄×C₁₃	—	2	2	no	—
556	C₄×C₁₃	—	2	2	no	—
557	C₄×C₁₃	—	2	4	no	—
558	C₄×C₁₃	—	2	2	no	—
559	C₄×C₁₃	—	2	2	no	—
560	C₄×C₁₃	—	4	2	no	—
561	C₄×C₁₃	—	4	1	no	—
562	C₄×C₁₃	—	4	1	no	—
563	C₄×C₁₃	—	4	1	no	—
564	C₄×C₁₃	—	4	2	no	—
565	C₄×C₁₃	—	4	1	no	—
566	C₄×C₁₃	—	4	2	no	—
567	C₄×C₁₃	—	4	1	no	—
568	C₄×C₁₃	—	4	1	no	—
569	C₄×C₁₃	—	4	2	no	—
570	C₄×C₁₃	#519	1	4	yes	—
571	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
572	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
573	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
575	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
576	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
577	C₄⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
578	#125	C₂×C₄×C₁₃	1	8	yes	—
579	#125	C₂×C₄×C₁₃	1	16	yes	—
580	#125	C₂×C₄×C₁₃	1	8	yes	—
581	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
582	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	—
583	C₄×Q₈	—	4	4	no	—
584	C₄×Q₈	—	4	4	no	—
585	#117	—	4	4	no	—
586	#117	C₂×C₄×C₁₃	1	8	yes	—
587	#117	C₂×C₄×C₁₃	1	8	yes	—
588	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
632	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
633	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
639	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
641	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
646	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
650	#95	C₂³×C₁₃	1	1	yes	characteristic
651	#95	C₂³×C₁₃	1	1	yes	characteristic
652	#95	C₂³×C₁₃	1	1	yes	characteristic
653	#95	C₂³×C₁₃	1	1	yes	characteristic
654	#95	C₂³×C₁₃	1	1	yes	characteristic
655	#95	C₂³×C₁₃	1	1	yes	characteristic
656	#95	C₂³×C₁₃	1	2	yes	—
657	#95	C₂³×C₁₃	1	1	yes	characteristic
658	#95	C₂³×C₁₃	1	1	yes	characteristic
659	#95	C₂³×C₁₃	1	2	yes	—
660	#95	C₂³×C₁₃	1	1	yes	characteristic
661	#95	C₂³×C₁₃	1	1	yes	characteristic
662	#95	C₂³×C₁₃	1	2	yes	—
663	#95	C₂³×C₁₃	1	2	yes	—
664	#95	C₂³×C₁₃	1	2	yes	—
665	#95	C₂³×C₁₃	1	2	yes	—
666	#95	C₂³×C₁₃	1	2	yes	—
667	#95	C₂³×C₁₃	1	2	yes	—
668	#95	C₂³×C₁₃	1	2	yes	—
669	#95	C₂³×C₁₃	1	2	yes	—
670	#95	C₂³×C₁₃	1	2	yes	—
671	#95	C₂³×C₁₃	1	2	yes	—
672	#95	C₂³×C₁₃	1	2	yes	—
673	#95	C₂³×C₁₃	1	2	yes	—
674	#95	C₂³×C₁₃	1	2	yes	—
675	#95	C₂³×C₁₃	1	2	yes	—
676	#95	C₂³×C₁₃	1	2	yes	—
677	#95	C₂³×C₁₃	1	2	yes	—
678	#95	C₂³×C₁₃	1	2	yes	—
679	#95	C₂³×C₁₃	1	2	yes	—
680	#95	C₂³×C₁₃	1	1	yes	characteristic
681	#95	C₂³×C₁₃	1	2	yes	—
682	#95	C₂³×C₁₃	1	1	yes	characteristic
683	#95	C₂³×C₁₃	1	2	yes	—
684	C₂×C₁₃	—	4	2	no	—
685	C₂×C₁₃	C₂×#519	1	1	yes	characteristic
686	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
688	C₂×C₁₃	#3552	1	1	yes	characteristic
689	C₂×C₁₃	#3555	1	1	yes	characteristic
690	C₂×C₁₃	#3559	1	1	yes	characteristic
691	C₂×C₁₃	#3565	1	1	yes	characteristic
692	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	—	4	2	no	—
695	C₂×Q₈	—	4	2	no	—
696	C₂×Q₈	—	4	2	no	—
697	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
698	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
704	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
705	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	1	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	1	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
746	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
747	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
748	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
749	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
750	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
751	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
752	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
753	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
754	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
755	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
756	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
757	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	1	no	—
763	C₂²⋊C₄	—	4	1	no	—
764	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
765	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
766	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
767	C₄²	—	2	4	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	—	4	2	no	—
779	C₄²	—	4	2	no	—
780	C₄²	—	4	1	no	—
781	C₄²	—	4	2	no	—
782	C₄²	—	4	2	no	—
783	C₄²	—	4	2	no	—
784	C₄²	—	4	1	no	—
785	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
786	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
787	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
788	C₁₃	#34434	1	1	yes	characteristic, direct product factor, Sylow
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
796	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
797	Q₈	—	4	8	no	—
798	Q₈	—	4	8	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	8	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	4	8	no	—
853	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
854	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
855	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
856	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
857	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
858	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
859	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
860	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
861	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
862	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
863	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
864	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
865	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
866	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
875	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
876	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
877	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
878	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
879	C₂²	C₁₃×#585	1	1	yes	characteristic
880	C₂²	C₁₃×#585	1	1	yes	characteristic
881	C₄	—	2	2	no	—
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	4	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	1	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	2	no	—
902	C₄	C₁₃×#519	1	4	yes	—
903	C₂	—	4	2	no	—
904	C₂	C₂×C₁₃×#519	1	1	yes	characteristic
905	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
906	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
907	C₂	C₁₃×#3552	1	1	yes	characteristic
908	C₂	C₁₃×#3555	1	1	yes	characteristic
909	C₂	C₁₃×#3559	1	1	yes	characteristic
910	C₂	C₁₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁴×C₁₃	C₂⁴
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×#2381	C₂	semidirect
4. C₁₃×#2370	C₂	semidirect
5. C₁₃×#2370	C₂	semidirect
6. C₁₃×#2369	C₂	semidirect
7. C₁₃×#2365	C₂	semidirect
8. C₁₃×#2365	C₂	semidirect
14. C₁₃×#2336	C₂	semidirect
15. C₁₃×#2336	C₂	semidirect
17. C₁₃×#2331	C₂	semidirect
18. C₁₃×#2330	C₂	semidirect
21. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
22. C₄×C₁₃×#125	C₂	semidirect
24. C₁₃×#544	C₄	semidirect
237. #34434	C₁₃	direct (N × H)
335. #2381	C₂×C₁₃	semidirect
337. #2370	C₂×C₁₃	semidirect
338. #2370	C₂×C₁₃	semidirect
339. #2369	C₂×C₁₃	semidirect
340. #2365	C₂×C₁₃	semidirect
341. #2365	C₂×C₁₃	semidirect
347. #2336	C₂×C₁₃	semidirect
348. #2336	C₂×C₁₃	semidirect
350. #2331	C₂×C₁₃	semidirect
351. #2330	C₂×C₁₃	semidirect
354. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
355. C₄×#125	C₂×C₁₃	semidirect
435. #544	C₄×C₁₃	semidirect
788. C₁₃	#34434	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×#544	2
C₁₃×#2381	2
C₁₃×#2378	2
C₁₃×#2370	2
C₁₃×#2369	2
C₁₃×#2365	2
C₁₃×#2362	2
C₁₃×#2347	2
C₁₃×#2345	2
C₁₃×#2344	2
C₁₃×#2336	2
C₁₃×#2332	2
C₁₃×#2331	2
C₁₃×#2330	2
C₁₃×#2323	2
C₁₃×#2314	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#125	2
C₁₃×#2298	2
#34434	13

Subgroups — C13×#34434 #15720773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34434 #15720773