Subgroups — C₁₃×#34260 #15720599

Order 3328.

2462 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2352	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2343	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2343	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2313	C₂	1	2	yes	maximal, complemented
18	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
21	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
22	C₁₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₁₃×#520	C₄	1	16	yes	complemented
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#117	C₂²	1	2	yes	—
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
46	C₁₃×#391	C₂²	1	1	yes	characteristic
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic
51	C₁₃×#388	C₂²	1	1	yes	characteristic
52	C₁₃×#388	C₂²	1	2	yes	—
53	C₁₃×#388	C₂²	1	1	yes	characteristic
54	C₁₃×#388	C₂²	1	1	yes	characteristic
55	C₁₃×#388	C₂²	1	1	yes	characteristic
56	C₁₃×#388	C₂²	1	2	yes	—
57	C₁₃×#387	C₂²	1	1	yes	characteristic
58	C₁₃×#387	C₂²	1	2	yes	—
59	C₁₃×#387	C₂²	1	2	yes	—
60	C₁₃×#387	C₂²	1	2	yes	—
61	C₁₃×#387	C₂²	1	2	yes	—
62	C₁₃×#387	C₂²	1	2	yes	—
63	C₁₃×#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	1	yes	characteristic
68	C₁₃×#387	C₂²	1	1	yes	characteristic
69	C₁₃×#387	C₂²	1	1	yes	characteristic
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×#386	C₂²	1	2	yes	—
76	C₁₃×#386	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	2	yes	—
78	C₁₃×#386	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×#384	C₂²	1	1	yes	characteristic
84	C₁₃×#383	C₂²	1	2	yes	—
85	C₁₃×#383	C₂²	1	2	yes	—
86	C₁₃×#382	C₂²	1	1	yes	characteristic
87	C₁₃×#382	C₂²	1	2	yes	—
88	C₁₃×#382	C₂²	1	2	yes	—
89	C₁₃×#381	C₂²	1	2	yes	—
90	C₁₃×#381	C₂²	1	2	yes	—
91	C₁₃×#381	C₂²	1	2	yes	—
92	C₁₃×#380	C₂²	1	2	yes	—
93	C₁₃×#380	C₂²	1	2	yes	—
94	C₁₃×#380	C₂²	1	1	yes	characteristic
95	C₁₃×#380	C₂²	1	1	yes	characteristic
96	C₁₃×#380	C₂²	1	2	yes	—
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	1	yes	characteristic
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₁₃×C₂²⋊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	1	yes	characteristic
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₁₃×#376	C₂²	1	1	yes	characteristic
117	C₁₃×#376	C₂²	1	2	yes	—
118	C₁₃×#376	C₂²	1	2	yes	—
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	C₂×C₁₃×#41	—	2	4	no	—
125	C₂×C₁₃×#41	—	2	4	no	—
126	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
127	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
136	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
139	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
140	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
141	C₄×D₄×C₁₃	—	2	4	no	—
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	16	yes	complemented
148	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
149	C₁₃×#117	—	4	4	no	—
150	C₁₃×#117	C₂×C₄	1	8	yes	complemented
151	C₁₃×#117	C₂×C₄	1	16	yes	complemented
152	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
153	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
154	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	—	4	4	no	—
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
209	C₁₃×#95	C₂³	1	2	yes	—
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
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	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	1	yes	characteristic
220	C₁₃×#95	C₂³	1	1	yes	characteristic
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
229	C₁₃×#95	C₂³	1	2	yes	—
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	2	yes	—
234	C₁₃×#95	C₂³	1	2	yes	—
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	2	yes	—
240	C₁₃×#95	C₂³	1	2	yes	—
241	C₁₃×#95	C₂³	1	2	yes	—
242	C₁₃×#95	C₂³	1	1	yes	characteristic
243	#34260	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
246	C₁₃×#41	—	2	32	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
250	C₂×D₄×C₁₃	—	2	4	no	—
251	C₂×D₄×C₁₃	—	2	4	no	—
252	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
253	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
254	C₂×D₄×C₁₃	#41	1	4	yes	—
255	C₂×D₄×C₁₃	#41	1	4	yes	—
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	—	2	4	no	—
261	C₂²×C₄×C₁₃	—	2	4	no	—
262	C₂²×C₄×C₁₃	—	2	4	no	—
263	C₂²×C₄×C₁₃	—	2	4	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	2	4	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	—	4	2	no	—
270	C₂²×C₄×C₁₃	—	4	2	no	—
271	C₂²×C₄×C₁₃	—	4	2	no	—
272	C₂²×C₄×C₁₃	—	4	2	no	—
273	C₂²×C₄×C₁₃	—	4	2	no	—
274	C₂²×C₄×C₁₃	—	4	2	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	—	4	2	no	—
277	C₂²×C₄×C₁₃	—	4	2	no	—
278	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
279	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
280	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
281	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
282	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
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	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	4	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
311	C₁₃×C₄⋊C₄	—	4	2	no	—
312	C₁₃×C₄⋊C₄	—	4	2	no	—
313	C₁₃×C₄⋊C₄	—	4	1	no	—
314	C₁₃×C₄⋊C₄	—	4	2	no	—
315	C₁₃×C₄⋊C₄	—	4	1	no	—
316	C₁₃×C₄⋊C₄	—	4	2	no	—
317	C₁₃×C₄⋊C₄	—	4	2	no	—
318	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
319	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
320	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
321	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
322	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
323	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
324	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	4	no	—
328	C₁₃×C₂²⋊C₄	—	2	4	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	4	1	no	—
332	C₁₃×C₂²⋊C₄	—	4	1	no	—
333	C₁₃×C₂²⋊C₄	—	4	2	no	—
334	C₁₃×C₂²⋊C₄	—	4	2	no	—
335	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
336	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
337	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
338	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
339	C₄²×C₁₃	—	2	2	no	—
340	C₄²×C₁₃	—	2	2	no	—
341	C₄²×C₁₃	—	2	2	no	—
342	C₄²×C₁₃	—	2	2	no	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	4	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	4	2	no	—
347	C₄²×C₁₃	—	4	2	no	—
348	C₄²×C₁₃	—	4	1	no	—
349	C₄²×C₁₃	—	4	2	no	—
350	C₄²×C₁₃	—	4	2	no	—
351	C₄²×C₁₃	—	4	1	no	—
352	C₄²×C₁₃	—	4	2	no	—
353	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
354	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
355	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
356	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
357	C₂×#520	C₂×C₁₃	1	1	yes	characteristic
358	#2356	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#2353	C₂×C₁₃	1	2	yes	complemented
361	#2352	C₂×C₁₃	1	2	yes	complemented
362	#2349	C₂×C₁₃	1	1	yes	characteristic, complemented
363	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#2345	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#2344	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#2343	C₂×C₁₃	1	2	yes	complemented
367	#2343	C₂×C₁₃	1	2	yes	complemented
368	#2339	C₂×C₁₃	1	1	yes	characteristic
369	#2339	C₂×C₁₃	1	1	yes	characteristic
370	#2320	C₂×C₁₃	1	1	yes	characteristic, complemented
371	#2318	C₂×C₁₃	1	2	yes	complemented
372	#2314	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#2313	C₂×C₁₃	1	2	yes	complemented
374	#2298	C₂×C₁₃	1	1	yes	characteristic, complemented
375	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
376	#2290	C₂×C₁₃	1	2	yes	complemented
377	C₂×#387	C₂×C₁₃	1	2	yes	complemented
378	#2275	C₂×C₁₃	1	1	yes	characteristic, complemented
379	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	2	no	—
382	C₂³×C₁₃	—	2	2	no	—
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	2	1	no	—
385	C₂³×C₁₃	—	2	1	no	—
386	C₂³×C₁₃	—	2	1	no	—
387	C₂³×C₁₃	—	2	1	no	—
388	C₂³×C₁₃	—	2	1	no	—
389	C₂³×C₁₃	—	2	1	no	—
390	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
391	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
392	C₂³×C₁₃	C₂×#41	1	4	yes	—
393	C₂³×C₁₃	C₂×#41	1	4	yes	—
394	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
395	Q₈×C₁₃	—	2	8	no	—
396	D₄×C₁₃	—	2	16	no	—
397	D₄×C₁₃	#117	1	16	yes	complemented
398	C₂×C₄×C₁₃	—	2	16	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	1	no	—
408	C₂×C₄×C₁₃	—	2	1	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	1	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	8	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	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	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	1	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	1	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	1	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	1	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	1	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	1	no	—
448	C₂×C₄×C₁₃	—	2	1	no	—
449	C₂×C₄×C₁₃	—	2	1	no	—
450	C₂×C₄×C₁₃	—	4	8	no	—
451	C₂×C₄×C₁₃	—	4	8	no	—
452	C₂×C₄×C₁₃	—	4	8	no	—
453	C₂×C₄×C₁₃	—	4	8	no	—
454	C₂×C₄×C₁₃	—	4	8	no	—
455	C₂×C₄×C₁₃	—	8	4	no	—
456	C₂×C₄×C₁₃	—	8	4	no	—
457	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
460	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
461	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
463	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
464	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
467	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
468	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
469	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
470	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
471	#520	C₄×C₁₃	1	16	yes	complemented
472	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
474	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
475	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
476	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
477	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
478	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
480	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
481	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
482	C₂×#117	C₂²×C₁₃	1	2	yes	—
483	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×#117	C₂²×C₁₃	1	2	yes	—
485	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
486	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
487	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
488	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
489	#391	C₂²×C₁₃	1	1	yes	characteristic
490	#391	C₂²×C₁₃	1	1	yes	characteristic
491	#391	C₂²×C₁₃	1	1	yes	characteristic
492	#391	C₂²×C₁₃	1	1	yes	characteristic
493	#389	C₂²×C₁₃	1	1	yes	characteristic
494	#389	C₂²×C₁₃	1	1	yes	characteristic
495	#389	C₂²×C₁₃	1	1	yes	characteristic
496	#389	C₂²×C₁₃	1	1	yes	characteristic
497	#388	C₂²×C₁₃	1	2	yes	—
498	#388	C₂²×C₁₃	1	2	yes	—
499	#388	C₂²×C₁₃	1	1	yes	characteristic
500	#388	C₂²×C₁₃	1	1	yes	characteristic
501	#388	C₂²×C₁₃	1	1	yes	characteristic
502	#388	C₂²×C₁₃	1	1	yes	characteristic
503	#387	C₂²×C₁₃	1	1	yes	characteristic
504	#387	C₂²×C₁₃	1	2	yes	—
505	#387	C₂²×C₁₃	1	2	yes	—
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	2	yes	—
510	#387	C₂²×C₁₃	1	2	yes	—
511	#387	C₂²×C₁₃	1	2	yes	—
512	#387	C₂²×C₁₃	1	2	yes	—
513	#387	C₂²×C₁₃	1	1	yes	characteristic
514	#387	C₂²×C₁₃	1	1	yes	characteristic
515	#387	C₂²×C₁₃	1	2	yes	—
516	#387	C₂²×C₁₃	1	2	yes	—
517	#387	C₂²×C₁₃	1	2	yes	—
518	#387	C₂²×C₁₃	1	2	yes	—
519	#387	C₂²×C₁₃	1	1	yes	characteristic
520	#387	C₂²×C₁₃	1	2	yes	—
521	#386	C₂²×C₁₃	1	2	yes	—
522	#386	C₂²×C₁₃	1	2	yes	—
523	#386	C₂²×C₁₃	1	2	yes	—
524	#386	C₂²×C₁₃	1	2	yes	—
525	#385	C₂²×C₁₃	1	2	yes	—
526	#385	C₂²×C₁₃	1	2	yes	—
527	#385	C₂²×C₁₃	1	2	yes	—
528	#385	C₂²×C₁₃	1	2	yes	—
529	#384	C₂²×C₁₃	1	1	yes	characteristic
530	#383	C₂²×C₁₃	1	2	yes	—
531	#383	C₂²×C₁₃	1	2	yes	—
532	#382	C₂²×C₁₃	1	1	yes	characteristic
533	#382	C₂²×C₁₃	1	2	yes	—
534	#382	C₂²×C₁₃	1	2	yes	—
535	#381	C₂²×C₁₃	1	2	yes	—
536	#381	C₂²×C₁₃	1	2	yes	—
537	#381	C₂²×C₁₃	1	2	yes	—
538	#380	C₂²×C₁₃	1	2	yes	—
539	#380	C₂²×C₁₃	1	2	yes	—
540	#380	C₂²×C₁₃	1	1	yes	characteristic
541	#380	C₂²×C₁₃	1	1	yes	characteristic
542	#380	C₂²×C₁₃	1	2	yes	—
543	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
544	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
545	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
546	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
547	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
548	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
549	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
550	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
551	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
553	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
554	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
555	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
556	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
557	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
558	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
559	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
560	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
562	#376	C₂²×C₁₃	1	1	yes	characteristic
563	#376	C₂²×C₁₃	1	2	yes	—
564	#376	C₂²×C₁₃	1	2	yes	—
565	C₂×#95	C₂²×C₁₃	1	2	yes	—
566	C₂×#95	C₂²×C₁₃	1	2	yes	—
567	C₂×#95	C₂²×C₁₃	1	2	yes	—
568	C₂×#95	C₂²×C₁₃	1	2	yes	—
569	C₄³	C₂²×C₁₃	1	1	yes	characteristic
570	C₂²×C₁₃	—	2	4	no	—
571	C₂²×C₁₃	—	2	4	no	—
572	C₂²×C₁₃	—	2	4	no	—
573	C₂²×C₁₃	—	2	4	no	—
574	C₂²×C₁₃	—	2	4	no	—
575	C₂²×C₁₃	—	2	4	no	—
576	C₂²×C₁₃	—	2	2	no	—
577	C₂²×C₁₃	—	2	2	no	—
578	C₂²×C₁₃	—	2	2	no	—
579	C₂²×C₁₃	—	4	1	no	—
580	C₂²×C₁₃	—	4	1	no	—
581	C₂²×C₁₃	—	4	1	no	—
582	C₂²×C₁₃	—	4	1	no	—
583	C₂²×C₁₃	C₂×#117	1	8	yes	—
584	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
585	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
586	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
587	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
589	C₂²×C₁₃	#585	1	1	yes	characteristic
590	C₂²×C₁₃	#585	1	1	yes	characteristic
591	C₄×C₁₃	—	2	2	no	—
592	C₄×C₁₃	—	2	4	no	—
593	C₄×C₁₃	—	2	2	no	—
594	C₄×C₁₃	—	2	4	no	—
595	C₄×C₁₃	—	2	2	no	—
596	C₄×C₁₃	—	2	4	no	—
597	C₄×C₁₃	—	2	2	no	—
598	C₄×C₁₃	—	2	2	no	—
599	C₄×C₁₃	—	2	2	no	—
600	C₄×C₁₃	—	2	2	no	—
601	C₄×C₁₃	—	4	2	no	—
602	C₄×C₁₃	—	4	2	no	—
603	C₄×C₁₃	—	4	1	no	—
604	C₄×C₁₃	—	4	1	no	—
605	C₄×C₁₃	—	4	1	no	—
606	C₄×C₁₃	—	4	1	no	—
607	C₄×C₁₃	—	4	2	no	—
608	C₄×C₁₃	—	4	1	no	—
609	C₄×C₁₃	—	4	2	no	—
610	C₄×C₁₃	—	4	1	no	—
611	C₄×C₁₃	C₂×#117	1	4	yes	—
612	C₂×#41	—	2	4	no	—
613	C₂×#41	—	2	4	no	—
614	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
615	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
616	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
617	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
619	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
620	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
621	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
623	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
624	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
625	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
626	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
627	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
628	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
629	C₄×D₄	—	2	4	no	—
630	C₄×D₄	—	2	4	no	—
631	C₄×D₄	—	2	4	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
634	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
635	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
636	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
637	#117	—	4	4	no	—
638	#117	C₂×C₄×C₁₃	1	8	yes	complemented
639	#117	C₂×C₄×C₁₃	1	16	yes	complemented
640	C₂×C₄⋊C₄	—	4	4	no	—
641	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
642	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×C₄²	—	4	4	no	—
679	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
680	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
687	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
690	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
691	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
692	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
693	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
694	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
695	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
696	C₂×C₄²	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	1	yes	characteristic
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	#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	2	yes	—
711	#95	C₂³×C₁₃	1	2	yes	—
712	#95	C₂³×C₁₃	1	2	yes	—
713	#95	C₂³×C₁₃	1	1	yes	characteristic
714	#95	C₂³×C₁₃	1	1	yes	characteristic
715	#95	C₂³×C₁₃	1	1	yes	characteristic
716	#95	C₂³×C₁₃	1	1	yes	characteristic
717	#95	C₂³×C₁₃	1	2	yes	—
718	#95	C₂³×C₁₃	1	2	yes	—
719	#95	C₂³×C₁₃	1	2	yes	—
720	#95	C₂³×C₁₃	1	2	yes	—
721	#95	C₂³×C₁₃	1	2	yes	—
722	#95	C₂³×C₁₃	1	2	yes	—
723	#95	C₂³×C₁₃	1	2	yes	—
724	#95	C₂³×C₁₃	1	2	yes	—
725	#95	C₂³×C₁₃	1	1	yes	characteristic
726	#95	C₂³×C₁₃	1	1	yes	characteristic
727	#95	C₂³×C₁₃	1	1	yes	characteristic
728	#95	C₂³×C₁₃	1	2	yes	—
729	#95	C₂³×C₁₃	1	2	yes	—
730	#95	C₂³×C₁₃	1	1	yes	characteristic
731	C₂×C₁₃	—	2	8	no	—
732	C₂×C₁₃	—	4	2	no	—
733	C₂×C₁₃	C₂²×#117	1	1	yes	characteristic
734	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
735	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
736	C₂×C₁₃	#3513	1	1	yes	characteristic
737	C₂×C₁₃	#3515	1	1	yes	characteristic
738	C₂×C₁₃	#3520	1	1	yes	characteristic
739	C₂×C₁₃	#3521	1	1	yes	characteristic
740	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
741	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
742	#41	—	2	32	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	2	4	no	—
748	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
749	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
750	C₂×D₄	C₁₃×#41	1	4	yes	—
751	C₂×D₄	C₁₃×#41	1	4	yes	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	4	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	4	2	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	—	4	2	no	—
765	C₂²×C₄	—	4	2	no	—
766	C₂²×C₄	—	4	2	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
775	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
776	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
777	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
778	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
779	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
797	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	1	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	1	no	—
813	C₄⋊C₄	—	4	2	no	—
814	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
815	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
816	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
817	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
818	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
819	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
820	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	4	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	4	2	no	—
828	C₂²⋊C₄	—	4	1	no	—
829	C₂²⋊C₄	—	4	1	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
832	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
833	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
834	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	4	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	4	2	no	—
843	C₄²	—	4	2	no	—
844	C₄²	—	4	2	no	—
845	C₄²	—	4	1	no	—
846	C₄²	—	4	2	no	—
847	C₄²	—	4	2	no	—
848	C₄²	—	4	1	no	—
849	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
850	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
851	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
852	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
853	C₁₃	#34260	1	1	yes	characteristic, direct product factor, Sylow
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
865	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
866	C₂³	C₂×C₁₃×#41	1	4	yes	—
867	C₂³	C₂×C₁₃×#41	1	4	yes	—
868	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
869	Q₈	—	2	8	no	—
870	D₄	—	2	16	no	—
871	D₄	C₁₃×#117	1	16	yes	complemented
872	C₂×C₄	—	2	16	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	8	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	4	8	no	—
925	C₂×C₄	—	4	8	no	—
926	C₂×C₄	—	4	8	no	—
927	C₂×C₄	—	4	8	no	—
928	C₂×C₄	—	4	8	no	—
929	C₂×C₄	—	8	4	no	—
930	C₂×C₄	—	8	4	no	—
931	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
932	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
933	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
934	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
935	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
936	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
937	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
938	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
939	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
940	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
941	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
942	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
943	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	2	4	no	—
947	C₂²	—	2	4	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	4	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	C₂×C₁₃×#117	1	8	yes	—
958	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
959	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
960	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
961	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
963	C₂²	C₁₃×#585	1	1	yes	characteristic
964	C₂²	C₁₃×#585	1	1	yes	characteristic
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	2	4	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	4	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	4	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	1	no	—
978	C₄	—	4	2	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	1	no	—
985	C₄	C₂×C₁₃×#117	1	4	yes	—
986	C₂	—	2	8	no	—
987	C₂	—	4	2	no	—
988	C₂	C₂²×C₁₃×#117	1	1	yes	characteristic
989	C₂	C₄×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
990	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
991	C₂	C₁₃×#3513	1	1	yes	characteristic
992	C₂	C₁₃×#3515	1	1	yes	characteristic
993	C₂	C₁₃×#3520	1	1	yes	characteristic
994	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×C₁₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#2356	C₂	semidirect
3. C₁₃×#2355	C₂	semidirect
4. C₁₃×#2353	C₂	semidirect
5. C₁₃×#2352	C₂	semidirect
6. C₁₃×#2349	C₂	semidirect
7. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
8. C₁₃×#2345	C₂	semidirect
9. C₁₃×#2344	C₂	semidirect
10. C₁₃×#2343	C₂	semidirect
11. C₁₃×#2343	C₂	semidirect
14. C₁₃×#2320	C₂	semidirect
15. C₁₃×#2318	C₂	semidirect
16. C₁₃×#2314	C₂	semidirect
17. C₁₃×#2313	C₂	semidirect
18. C₁₃×#2298	C₂	semidirect
19. C₁₃×#2295	C₂	semidirect
20. C₁₃×#2290	C₂	semidirect
21. C₂×C₁₃×#387	C₂	semidirect
22. C₁₃×#2275	C₂	semidirect
23. C₄²×D₄×C₁₃	C₂	semidirect
25. C₁₃×#520	C₄	semidirect
139. C₄×Q₈×C₁₃	C₂×C₄	semidirect
140. C₄×Q₈×C₁₃	C₂×C₄	semidirect
147. C₄×D₄×C₁₃	C₂×C₄	semidirect
148. C₄×D₄×C₁₃	C₂×C₄	semidirect
150. C₁₃×#117	C₂×C₄	semidirect
151. C₁₃×#117	C₂×C₄	semidirect
153. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
154. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
243. #34260	C₁₃	direct (N × H)
358. #2356	C₂×C₁₃	semidirect
359. #2355	C₂×C₁₃	semidirect
360. #2353	C₂×C₁₃	semidirect
361. #2352	C₂×C₁₃	semidirect
362. #2349	C₂×C₁₃	semidirect
363. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
364. #2345	C₂×C₁₃	semidirect
365. #2344	C₂×C₁₃	semidirect
366. #2343	C₂×C₁₃	semidirect
367. #2343	C₂×C₁₃	semidirect
370. #2320	C₂×C₁₃	semidirect
371. #2318	C₂×C₁₃	semidirect
372. #2314	C₂×C₁₃	semidirect
373. #2313	C₂×C₁₃	semidirect
374. #2298	C₂×C₁₃	semidirect
375. #2295	C₂×C₁₃	semidirect
376. #2290	C₂×C₁₃	semidirect
377. C₂×#387	C₂×C₁₃	semidirect
378. #2275	C₂×C₁₃	semidirect
379. C₄²×D₄	C₂×C₁₃	semidirect
397. D₄×C₁₃	#117	semidirect
471. #520	C₄×C₁₃	semidirect
627. C₄×Q₈	C₂×C₄×C₁₃	semidirect
628. C₄×Q₈	C₂×C₄×C₁₃	semidirect
635. C₄×D₄	C₂×C₄×C₁₃	semidirect
636. C₄×D₄	C₂×C₄×C₁₃	semidirect
638. #117	C₂×C₄×C₁₃	semidirect
639. #117	C₂×C₄×C₁₃	semidirect
641. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
642. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
853. C₁₃	#34260	direct (N × H)
871. D₄	C₁₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#520	2
C₁₃×#2356	2
C₁₃×#2355	2
C₁₃×#2353	2
C₁₃×#2352	2
C₁₃×#2349	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2345	2
C₁₃×#2344	2
C₁₃×#2343	2
C₁₃×#2339	2
C₁₃×#2320	2
C₁₃×#2318	2
C₁₃×#2314	2
C₁₃×#2313	2
C₁₃×#2298	2
C₁₃×#2295	2
C₁₃×#2290	2
C₂×C₁₃×#387	2
C₁₃×#2275	2
C₄²×D₄×C₁₃	2
#34260	13

Subgroups — C13×#34260 #15720599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34260 #15720599