Subgroups — C₁₃×#34333 #15720672

Order 3328.

2288 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic
11	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2345	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
21	C₁₃×#2275	C₂	1	1	yes	maximal, characteristic
22	C₁₃×#2275	C₂	1	1	yes	maximal, characteristic
23	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
24	C₁₃×#554	C₄	1	16	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
43	C₁₃×#391	C₂²	1	1	yes	characteristic
44	C₁₃×#391	C₂²	1	1	yes	characteristic
45	C₁₃×#391	C₂²	1	2	yes	—
46	C₁₃×#391	C₂²	1	2	yes	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#391	C₂²	1	2	yes	—
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic
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	2	yes	—
56	C₁₃×#389	C₂²	1	2	yes	—
57	C₁₃×#389	C₂²	1	1	yes	characteristic
58	C₁₃×#389	C₂²	1	1	yes	characteristic
59	C₁₃×#389	C₂²	1	1	yes	characteristic
60	C₁₃×#389	C₂²	1	1	yes	characteristic
61	C₁₃×#387	C₂²	1	1	yes	characteristic
62	C₁₃×#387	C₂²	1	2	yes	—
63	C₁₃×#387	C₂²	1	2	yes	—
64	C₁₃×#387	C₂²	1	2	yes	—
65	C₁₃×#387	C₂²	1	2	yes	—
66	C₁₃×#387	C₂²	1	2	yes	—
67	C₁₃×#387	C₂²	1	2	yes	—
68	C₁₃×#387	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	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×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#385	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×#385	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	2	yes	—
85	C₁₃×#384	C₂²	1	1	yes	characteristic
86	C₁₃×#382	C₂²	1	1	yes	characteristic
87	C₁₃×#382	C₂²	1	1	yes	characteristic
88	C₁₃×#380	C₂²	1	2	yes	—
89	C₁₃×#380	C₂²	1	2	yes	—
90	C₁₃×#380	C₂²	1	2	yes	—
91	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
92	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
93	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
109	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
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	C₁₃×#376	C₂²	1	1	yes	characteristic
118	C₁₃×#376	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#95	C₂²	1	2	yes	—
120	C₂×C₁₃×#95	C₂²	1	2	yes	—
121	C₂×C₁₃×#95	C₂²	1	2	yes	—
122	C₂×C₁₃×#95	C₂²	1	2	yes	—
123	C₄³×C₁₃	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂²×D₄×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	2	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
135	C₁₃×#125	C₂×C₄	1	8	yes	complemented
136	C₁₃×#125	C₂×C₄	1	8	yes	complemented
137	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
138	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
139	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
140	C₄×Q₈×C₁₃	—	4	4	no	—
141	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
142	C₄×D₄×C₁₃	—	2	4	no	—
143	C₄×D₄×C₁₃	—	2	4	no	—
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
146	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
147	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
148	C₄×D₄×C₁₃	Q₈	1	8	yes	complemented
149	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
150	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
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	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	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃	—	4	4	no	—
188	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₁₃×#95	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
215	C₁₃×#95	C₂³	1	1	yes	characteristic
216	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
224	C₁₃×#95	C₂³	1	1	yes	characteristic
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	1	yes	characteristic
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	2	yes	—
230	C₁₃×#95	C₂³	1	2	yes	—
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	1	yes	characteristic
233	C₁₃×#95	C₂³	1	1	yes	characteristic
234	C₁₃×#95	C₂³	1	1	yes	characteristic
235	C₁₃×#95	C₂³	1	2	yes	—
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	2	yes	—
238	C₁₃×#95	C₂³	1	2	yes	—
239	C₁₃×#95	C₂³	1	1	yes	characteristic
240	C₁₃×#95	C₂³	1	1	yes	characteristic
241	#34333	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₁₃	—	4	2	no	—
244	C₂×Q₈×C₁₃	—	4	1	no	—
245	C₂×Q₈×C₁₃	—	4	1	no	—
246	C₂×Q₈×C₁₃	—	4	2	no	—
247	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
248	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
249	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
250	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
251	C₂×D₄×C₁₃	#41	1	4	yes	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	2	4	no	—
254	C₂²×C₄×C₁₃	—	2	4	no	—
255	C₂²×C₄×C₁₃	—	2	4	no	—
256	C₂²×C₄×C₁₃	—	4	2	no	—
257	C₂²×C₄×C₁₃	—	4	2	no	—
258	C₂²×C₄×C₁₃	—	4	2	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	2	no	—
262	C₂²×C₄×C₁₃	—	4	2	no	—
263	C₂²×C₄×C₁₃	—	4	2	no	—
264	C₂²×C₄×C₁₃	—	4	2	no	—
265	C₂²×C₄×C₁₃	—	4	2	no	—
266	C₂²×C₄×C₁₃	—	4	2	no	—
267	C₂²×C₄×C₁₃	—	4	2	no	—
268	C₂²×C₄×C₁₃	—	4	2	no	—
269	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
270	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
271	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
272	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	4	no	—
300	C₁₃×C₄⋊C₄	—	2	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	—	4	1	no	—
306	C₁₃×C₄⋊C₄	—	4	1	no	—
307	C₁₃×C₄⋊C₄	—	4	2	no	—
308	C₁₃×C₄⋊C₄	—	4	1	no	—
309	C₁₃×C₄⋊C₄	—	4	2	no	—
310	C₁₃×C₄⋊C₄	—	4	1	no	—
311	C₁₃×C₄⋊C₄	—	4	2	no	—
312	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
313	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
314	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
315	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
316	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
317	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
318	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
319	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
320	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
321	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
322	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
323	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
328	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
329	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
330	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	2	no	—
335	C₄²×C₁₃	—	2	4	no	—
336	C₄²×C₁₃	—	4	2	no	—
337	C₄²×C₁₃	—	4	2	no	—
338	C₄²×C₁₃	—	4	2	no	—
339	C₄²×C₁₃	—	4	1	no	—
340	C₄²×C₁₃	—	4	1	no	—
341	C₄²×C₁₃	—	4	2	no	—
342	C₄²×C₁₃	—	4	2	no	—
343	C₄²×C₁₃	—	4	2	no	—
344	C₄²×C₁₃	—	4	1	no	—
345	C₄²×C₁₃	—	4	2	no	—
346	C₄²×C₁₃	—	4	2	no	—
347	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
348	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
349	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
350	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
351	C₂×#554	C₂×C₁₃	1	1	yes	characteristic
352	#2370	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#2370	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2368	C₂×C₁₃	1	2	yes	complemented
355	#2368	C₂×C₁₃	1	2	yes	complemented
356	#2365	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#2360	C₂×C₁₃	1	2	yes	complemented
358	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#2349	C₂×C₁₃	1	1	yes	characteristic
360	#2349	C₂×C₁₃	1	1	yes	characteristic
361	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
362	#2345	C₂×C₁₃	1	2	yes	complemented
363	#2331	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#2330	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#2329	C₂×C₁₃	1	2	yes	complemented
366	#2329	C₂×C₁₃	1	2	yes	complemented
367	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
369	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
370	C₂×#387	C₂×C₁₃	1	2	yes	complemented
371	#2275	C₂×C₁₃	1	1	yes	characteristic
372	#2275	C₂×C₁₃	1	1	yes	characteristic
373	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
374	C₂³×C₁₃	—	2	2	no	—
375	C₂³×C₁₃	—	2	2	no	—
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	2	2	no	—
378	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
379	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
380	C₂³×C₁₃	C₂×#41	1	4	yes	—
381	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
382	Q₈×C₁₃	—	4	4	no	—
383	Q₈×C₁₃	—	4	8	no	—
384	D₄×C₁₃	C₄×Q₈	1	16	yes	complemented
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	2	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	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	1	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	2	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	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	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	1	no	—
434	C₂×C₄×C₁₃	—	2	1	no	—
435	C₂×C₄×C₁₃	—	4	8	no	—
436	C₂×C₄×C₁₃	—	4	8	no	—
437	C₂×C₄×C₁₃	—	4	8	no	—
438	C₂×C₄×C₁₃	—	4	8	no	—
439	C₂×C₄×C₁₃	—	4	8	no	—
440	C₂×C₄×C₁₃	—	8	4	no	—
441	C₂×C₄×C₁₃	—	8	4	no	—
442	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
443	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
444	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
445	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
446	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
447	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
448	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
449	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
450	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
451	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
452	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
453	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
454	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
455	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
456	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
457	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
458	#554	C₄×C₁₃	1	16	yes	complemented
459	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
461	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
463	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
465	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
466	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
474	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
475	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
476	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
477	#391	C₂²×C₁₃	1	1	yes	characteristic
478	#391	C₂²×C₁₃	1	2	yes	—
479	#391	C₂²×C₁₃	1	2	yes	—
480	#391	C₂²×C₁₃	1	2	yes	—
481	#391	C₂²×C₁₃	1	2	yes	—
482	#391	C₂²×C₁₃	1	1	yes	characteristic
483	#389	C₂²×C₁₃	1	1	yes	characteristic
484	#389	C₂²×C₁₃	1	1	yes	characteristic
485	#389	C₂²×C₁₃	1	1	yes	characteristic
486	#389	C₂²×C₁₃	1	2	yes	—
487	#389	C₂²×C₁₃	1	2	yes	—
488	#389	C₂²×C₁₃	1	2	yes	—
489	#389	C₂²×C₁₃	1	2	yes	—
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	#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	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	1	yes	characteristic
506	#387	C₂²×C₁₃	1	2	yes	—
507	#387	C₂²×C₁₃	1	2	yes	—
508	#387	C₂²×C₁₃	1	2	yes	—
509	#387	C₂²×C₁₃	1	1	yes	characteristic
510	#387	C₂²×C₁₃	1	2	yes	—
511	#387	C₂²×C₁₃	1	1	yes	characteristic
512	#387	C₂²×C₁₃	1	1	yes	characteristic
513	#385	C₂²×C₁₃	1	2	yes	—
514	#385	C₂²×C₁₃	1	2	yes	—
515	#385	C₂²×C₁₃	1	2	yes	—
516	#385	C₂²×C₁₃	1	2	yes	—
517	#385	C₂²×C₁₃	1	2	yes	—
518	#385	C₂²×C₁₃	1	2	yes	—
519	#384	C₂²×C₁₃	1	1	yes	characteristic
520	#382	C₂²×C₁₃	1	1	yes	characteristic
521	#382	C₂²×C₁₃	1	1	yes	characteristic
522	#380	C₂²×C₁₃	1	2	yes	—
523	#380	C₂²×C₁₃	1	2	yes	—
524	#380	C₂²×C₁₃	1	2	yes	—
525	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
526	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
527	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
528	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
530	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
531	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
532	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
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	2	yes	—
536	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
537	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
539	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
540	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
541	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
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	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
548	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
549	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
550	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
551	#376	C₂²×C₁₃	1	1	yes	characteristic
552	#376	C₂²×C₁₃	1	1	yes	characteristic
553	C₂×#95	C₂²×C₁₃	1	2	yes	—
554	C₂×#95	C₂²×C₁₃	1	2	yes	—
555	C₂×#95	C₂²×C₁₃	1	2	yes	—
556	C₂×#95	C₂²×C₁₃	1	2	yes	—
557	C₄³	C₂²×C₁₃	1	1	yes	characteristic
558	C₂²×C₁₃	—	2	4	no	—
559	C₂²×C₁₃	—	2	4	no	—
560	C₂²×C₁₃	—	2	4	no	—
561	C₂²×C₁₃	—	2	4	no	—
562	C₂²×C₁₃	—	2	4	no	—
563	C₂²×C₁₃	—	2	4	no	—
564	C₂²×C₁₃	C₂×C₄×Q₈	1	8	yes	—
565	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
566	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
567	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
568	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂²×C₁₃	#585	1	1	yes	characteristic
570	C₂²×C₁₃	#585	1	1	yes	characteristic
571	C₂²×C₁₃	#585	1	1	yes	characteristic
572	C₄×C₁₃	—	2	2	no	—
573	C₄×C₁₃	—	2	4	no	—
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	—	2	4	no	—
580	C₄×C₁₃	—	2	2	no	—
581	C₄×C₁₃	—	2	2	no	—
582	C₄×C₁₃	—	2	4	no	—
583	C₄×C₁₃	—	2	2	no	—
584	C₄×C₁₃	—	2	2	no	—
585	C₄×C₁₃	—	4	1	no	—
586	C₄×C₁₃	—	4	2	no	—
587	C₄×C₁₃	—	4	2	no	—
588	C₄×C₁₃	—	4	1	no	—
589	C₄×C₁₃	—	4	1	no	—
590	C₄×C₁₃	—	4	1	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	1	no	—
593	C₄×C₁₃	C₂×C₄×Q₈	1	4	yes	—
594	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
595	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
598	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
599	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
600	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
601	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
602	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
603	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
604	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
605	#125	C₂×C₄×C₁₃	1	8	yes	complemented
606	#125	C₂×C₄×C₁₃	1	8	yes	complemented
607	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
608	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
609	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
610	C₄×Q₈	—	4	4	no	—
611	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	4	no	—
614	C₄×D₄	—	2	4	no	—
615	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
616	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
617	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
618	C₄×D₄	Q₈×C₁₃	1	8	yes	complemented
619	C₂×C₄⋊C₄	—	4	4	no	—
620	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₄²	—	4	4	no	—
658	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
664	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
665	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
669	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
670	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
671	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
672	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
674	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×C₄²	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	2	yes	—
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	1	yes	characteristic
695	#95	C₂³×C₁₃	1	1	yes	characteristic
696	#95	C₂³×C₁₃	1	1	yes	characteristic
697	#95	C₂³×C₁₃	1	1	yes	characteristic
698	#95	C₂³×C₁₃	1	1	yes	characteristic
699	#95	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
704	#95	C₂³×C₁₃	1	1	yes	characteristic
705	#95	C₂³×C₁₃	1	1	yes	characteristic
706	#95	C₂³×C₁₃	1	2	yes	—
707	#95	C₂³×C₁₃	1	2	yes	—
708	#95	C₂³×C₁₃	1	2	yes	—
709	#95	C₂³×C₁₃	1	2	yes	—
710	#95	C₂³×C₁₃	1	1	yes	characteristic
711	C₂×C₁₃	—	2	8	no	—
712	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
713	C₂×C₁₃	#3428	1	1	yes	characteristic
714	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
715	C₂×C₁₃	#3501	1	1	yes	characteristic
716	C₂×C₁₃	#3504	1	1	yes	characteristic
717	C₂×C₁₃	#3513	1	1	yes	characteristic
718	C₂×C₁₃	#3521	1	1	yes	characteristic
719	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
720	C₂×Q₈	—	4	2	no	—
721	C₂×Q₈	—	4	1	no	—
722	C₂×Q₈	—	4	1	no	—
723	C₂×Q₈	—	4	2	no	—
724	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
725	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
726	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
727	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
728	C₂×D₄	C₁₃×#41	1	4	yes	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
747	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
748	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
749	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
750	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
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	2	yes	—
756	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	2	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	1	no	—
784	C₄⋊C₄	—	4	1	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	1	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
790	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
791	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
792	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
793	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
794	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
795	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
796	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
797	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
798	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
799	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
800	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
805	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
806	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
807	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	4	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	—	4	2	no	—
818	C₄²	—	4	1	no	—
819	C₄²	—	4	1	no	—
820	C₄²	—	4	2	no	—
821	C₄²	—	4	2	no	—
822	C₄²	—	4	2	no	—
823	C₄²	—	4	1	no	—
824	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
825	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
826	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
827	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
828	C₁₃	#34333	1	1	yes	characteristic, direct product factor, Sylow
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
834	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
835	C₂³	C₂×C₁₃×#41	1	4	yes	—
836	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
837	Q₈	—	4	4	no	—
838	Q₈	—	4	8	no	—
839	D₄	C₄×Q₈×C₁₃	1	16	yes	complemented
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	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	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	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	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	4	8	no	—
891	C₂×C₄	—	4	8	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	4	8	no	—
895	C₂×C₄	—	8	4	no	—
896	C₂×C₄	—	8	4	no	—
897	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
898	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
899	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
900	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
901	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
902	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
903	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
904	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
905	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
906	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
907	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
908	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
909	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
910	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
911	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
912	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
913	C₂²	—	2	4	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	2	4	no	—
916	C₂²	—	2	4	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	C₂×C₄×Q₈×C₁₃	1	8	yes	—
920	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
921	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
922	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
923	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
924	C₂²	C₁₃×#585	1	1	yes	characteristic
925	C₂²	C₁₃×#585	1	1	yes	characteristic
926	C₂²	C₁₃×#585	1	1	yes	characteristic
927	C₄	—	2	2	no	—
928	C₄	—	2	4	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	4	no	—
934	C₄	—	2	4	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	1	no	—
948	C₄	C₂×C₄×Q₈×C₁₃	1	4	yes	—
949	C₂	—	2	8	no	—
950	C₂	C₂²×C₄×Q₈×C₁₃	1	1	yes	characteristic
951	C₂	C₁₃×#3428	1	1	yes	characteristic
952	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂	C₁₃×#3501	1	1	yes	characteristic
954	C₂	C₁₃×#3504	1	1	yes	characteristic
955	C₂	C₁₃×#3513	1	1	yes	characteristic
956	C₂	C₁₃×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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×#2370	C₂	semidirect
3. C₁₃×#2370	C₂	semidirect
4. C₁₃×#2368	C₂	semidirect
5. C₁₃×#2368	C₂	semidirect
6. C₁₃×#2365	C₂	semidirect
7. C₁₃×#2360	C₂	semidirect
8. C₁₃×#2355	C₂	semidirect
12. C₁₃×#2345	C₂	semidirect
13. C₁₃×#2331	C₂	semidirect
14. C₁₃×#2330	C₂	semidirect
15. C₁₃×#2329	C₂	semidirect
16. C₁₃×#2329	C₂	semidirect
17. C₄×C₁₃×#125	C₂	semidirect
18. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
19. C₁₃×#2295	C₂	semidirect
20. C₂×C₁₃×#387	C₂	semidirect
24. C₁₃×#554	C₄	semidirect
134. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
135. C₁₃×#125	C₂×C₄	semidirect
136. C₁₃×#125	C₂×C₄	semidirect
137. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
138. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
139. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
141. C₄×Q₈×C₁₃	C₂×C₄	semidirect
148. C₄×D₄×C₁₃	Q₈	semidirect
150. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
241. #34333	C₁₃	direct (N × H)
352. #2370	C₂×C₁₃	semidirect
353. #2370	C₂×C₁₃	semidirect
354. #2368	C₂×C₁₃	semidirect
355. #2368	C₂×C₁₃	semidirect
356. #2365	C₂×C₁₃	semidirect
357. #2360	C₂×C₁₃	semidirect
358. #2355	C₂×C₁₃	semidirect
362. #2345	C₂×C₁₃	semidirect
363. #2331	C₂×C₁₃	semidirect
364. #2330	C₂×C₁₃	semidirect
365. #2329	C₂×C₁₃	semidirect
366. #2329	C₂×C₁₃	semidirect
367. C₄×#125	C₂×C₁₃	semidirect
368. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
369. #2295	C₂×C₁₃	semidirect
370. C₂×#387	C₂×C₁₃	semidirect
384. D₄×C₁₃	C₄×Q₈	semidirect
458. #554	C₄×C₁₃	semidirect
604. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
605. #125	C₂×C₄×C₁₃	semidirect
606. #125	C₂×C₄×C₁₃	semidirect
607. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
608. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
609. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
611. C₄×Q₈	C₂×C₄×C₁₃	semidirect
618. C₄×D₄	Q₈×C₁₃	semidirect
620. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
828. C₁₃	#34333	direct (N × H)
839. D₄	C₄×Q₈×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#554	2
C₁₃×#2370	2
C₁₃×#2368	2
C₁₃×#2365	2
C₁₃×#2360	2
C₁₃×#2355	2
C₁₃×#2349	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2345	2
C₁₃×#2331	2
C₁₃×#2330	2
C₁₃×#2329	2
C₄×C₁₃×#125	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2295	2
C₂×C₁₃×#387	2
C₁₃×#2275	2
C₄²×D₄×C₁₃	2
#34333	13

Subgroups — C13×#34333 #15720672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34333 #15720672