Subgroups — C₁₃×#34307 #15720646

Order 3328.

2136 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2373	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2372	C₂	1	2	yes	maximal
5	C₁₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2356	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2352	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2337	C₂	1	2	yes	maximal
14	C₁₃×#2334	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×#126	C₂	1	2	yes	maximal, complemented
18	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2295	C₂	1	2	yes	maximal, complemented
20	C₁₃×#2290	C₂	1	1	yes	maximal, characteristic
21	C₁₃×#2276	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#556	C₄	1	16	yes	complemented
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#126	C₂²	1	2	yes	—
27	C₂×C₁₃×#126	C₂²	1	2	yes	—
28	C₂×C₁₃×#124	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#391	C₂²	1	2	yes	—
43	C₁₃×#391	C₂²	1	2	yes	—
44	C₁₃×#391	C₂²	1	1	yes	characteristic
45	C₁₃×#391	C₂²	1	1	yes	characteristic
46	C₁₃×#391	C₂²	1	2	yes	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#389	C₂²	1	2	yes	—
49	C₁₃×#389	C₂²	1	2	yes	—
50	C₁₃×#389	C₂²	1	1	yes	characteristic
51	C₁₃×#389	C₂²	1	1	yes	characteristic
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×#388	C₂²	1	1	yes	characteristic
56	C₁₃×#388	C₂²	1	1	yes	characteristic
57	C₁₃×#388	C₂²	1	2	yes	—
58	C₁₃×#388	C₂²	1	2	yes	—
59	C₁₃×#388	C₂²	1	2	yes	—
60	C₁₃×#388	C₂²	1	2	yes	—
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#387	C₂²	1	1	yes	characteristic
67	C₁₃×#387	C₂²	1	1	yes	characteristic
68	C₁₃×#387	C₂²	1	2	yes	—
69	C₁₃×#387	C₂²	1	2	yes	—
70	C₁₃×#387	C₂²	1	2	yes	—
71	C₁₃×#387	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	1	yes	characteristic
78	C₁₃×#386	C₂²	1	1	yes	characteristic
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#385	C₂²	1	1	yes	characteristic
81	C₁₃×#385	C₂²	1	1	yes	characteristic
82	C₁₃×#385	C₂²	1	2	yes	—
83	C₁₃×#385	C₂²	1	2	yes	—
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×#380	C₂²	1	1	yes	characteristic
89	C₁₃×#380	C₂²	1	1	yes	characteristic
90	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
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×C₄⋊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	1	yes	characteristic
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₁₃×#376	C₂²	1	2	yes	—
119	C₁₃×#376	C₂²	1	1	yes	characteristic
120	C₁₃×#376	C₂²	1	2	yes	—
121	C₁₃×#376	C₂²	1	2	yes	—
122	C₁₃×#376	C₂²	1	2	yes	—
123	C₄³×C₁₃	C₂²	1	2	yes	—
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	1	yes	characteristic
128	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
133	C₁₃×#126	C₂×C₄	1	16	yes	complemented
134	C₁₃×#126	C₂×C₄	1	16	yes	complemented
135	C₁₃×#124	C₂×C₄	1	16	yes	—
136	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
137	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
138	C₄×Q₈×C₁₃	—	2	4	no	—
139	C₄×Q₈×C₁₃	—	2	4	no	—
140	C₄×Q₈×C₁₃	C₂×C₄	1	16	yes	complemented
141	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
142	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
143	C₁₃×#117	—	2	4	no	—
144	C₁₃×#117	—	2	4	no	—
145	C₁₃×#117	C₂×C₄	1	8	yes	complemented
146	C₁₃×#117	C₂×C₄	1	8	yes	complemented
147	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
179	C₂×C₁₃×C₂²⋊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	1	yes	characteristic
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	1	yes	characteristic
186	C₂×C₄²×C₁₃	—	2	4	no	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
193	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
222	C₁₃×#95	C₂³	1	2	yes	—
223	C₁₃×#95	C₂³	1	2	yes	—
224	C₁₃×#95	C₂³	1	1	yes	characteristic
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	2	yes	—
234	C₁₃×#95	C₂³	1	1	yes	characteristic
235	C₁₃×#95	C₂³	1	2	yes	—
236	C₁₃×#95	C₂³	1	2	yes	—
237	C₁₃×#95	C₂³	1	1	yes	characteristic
238	C₁₃×#95	C₂³	1	2	yes	—
239	C₁₃×#95	C₂³	1	2	yes	—
240	#34307	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	—	4	2	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	—	4	1	no	—
250	C₂×D₄×C₁₃	—	4	1	no	—
251	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
252	C₂²×C₄×C₁₃	—	2	2	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	4	no	—
260	C₂²×C₄×C₁₃	—	4	1	no	—
261	C₂²×C₄×C₁₃	—	4	1	no	—
262	C₂²×C₄×C₁₃	—	4	1	no	—
263	C₂²×C₄×C₁₃	—	4	2	no	—
264	C₂²×C₄×C₁₃	—	4	2	no	—
265	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
266	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₁₃×C₄⋊C₄	—	2	4	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	4	1	no	—
298	C₁₃×C₄⋊C₄	—	4	2	no	—
299	C₁₃×C₄⋊C₄	—	4	2	no	—
300	C₁₃×C₄⋊C₄	—	4	2	no	—
301	C₁₃×C₄⋊C₄	—	4	2	no	—
302	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
303	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
304	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
305	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
306	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
307	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
308	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
309	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
310	C₁₃×C₄⋊C₄	#41	1	4	yes	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	4	2	no	—
316	C₁₃×C₂²⋊C₄	—	4	1	no	—
317	C₁₃×C₂²⋊C₄	—	4	1	no	—
318	C₁₃×C₂²⋊C₄	—	4	2	no	—
319	C₁₃×C₂²⋊C₄	—	4	1	no	—
320	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
321	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
322	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
323	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
324	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
325	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	4	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	4	no	—
332	C₄²×C₁₃	—	2	4	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	4	no	—
335	C₄²×C₁₃	—	4	2	no	—
336	C₄²×C₁₃	—	4	2	no	—
337	C₄²×C₁₃	—	4	2	no	—
338	C₄²×C₁₃	—	4	2	no	—
339	C₄²×C₁₃	—	4	2	no	—
340	C₄²×C₁₃	—	4	2	no	—
341	C₄²×C₁₃	—	4	2	no	—
342	C₄²×C₁₃	—	4	2	no	—
343	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
344	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
345	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
346	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
347	C₄²×C₁₃	#41	1	4	yes	—
348	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
349	#2373	C₂×C₁₃	1	2	yes	complemented
350	#2373	C₂×C₁₃	1	2	yes	complemented
351	#2372	C₂×C₁₃	1	2	yes	—
352	#2369	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#2362	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2360	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#2356	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#2356	C₂×C₁₃	1	2	yes	complemented
357	#2352	C₂×C₁₃	1	1	yes	characteristic
358	#2347	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#2346	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#2337	C₂×C₁₃	1	2	yes	—
361	#2334	C₂×C₁₃	1	2	yes	complemented
362	#2331	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#2323	C₂×C₁₃	1	1	yes	characteristic, complemented
364	C₄×#126	C₂×C₁₃	1	2	yes	complemented
365	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#2295	C₂×C₁₃	1	2	yes	complemented
367	#2290	C₂×C₁₃	1	1	yes	characteristic
368	#2276	C₂×C₁₃	1	1	yes	characteristic, complemented
369	#2274	C₂×C₁₃	1	1	yes	characteristic, complemented
370	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
371	C₂³×C₁₃	—	2	1	no	—
372	C₂³×C₁₃	—	2	1	no	—
373	C₂³×C₁₃	—	2	1	no	—
374	C₂³×C₁₃	—	2	1	no	—
375	C₂³×C₁₃	—	2	1	no	—
376	C₂³×C₁₃	—	2	1	no	—
377	C₂³×C₁₃	—	2	1	no	—
378	C₂³×C₁₃	—	2	1	no	—
379	C₂³×C₁₃	—	2	1	no	—
380	C₂³×C₁₃	—	2	1	no	—
381	C₂³×C₁₃	—	2	1	no	—
382	C₂³×C₁₃	—	2	1	no	—
383	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
384	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
385	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
386	Q₈×C₁₃	—	2	8	no	—
387	Q₈×C₁₃	—	4	8	no	—
388	D₄×C₁₃	—	4	4	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	2	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	2	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	8	no	—
414	C₂×C₄×C₁₃	—	2	8	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	1	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	1	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	1	no	—
434	C₂×C₄×C₁₃	—	2	2	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	1	no	—
439	C₂×C₄×C₁₃	—	4	4	no	—
440	C₂×C₄×C₁₃	—	4	4	no	—
441	C₂×C₄×C₁₃	—	8	4	no	—
442	C₂×C₄×C₁₃	C₂³×C₄	1	4	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	4	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	2	yes	—
451	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
452	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
453	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
454	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
455	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
456	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
457	#556	C₄×C₁₃	1	16	yes	complemented
458	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
459	C₂×#126	C₂²×C₁₃	1	2	yes	—
460	C₂×#126	C₂²×C₁₃	1	2	yes	—
461	C₂×#124	C₂²×C₁₃	1	2	yes	—
462	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
464	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
465	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
468	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
470	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
473	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
474	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
475	#391	C₂²×C₁₃	1	1	yes	characteristic
476	#391	C₂²×C₁₃	1	2	yes	—
477	#391	C₂²×C₁₃	1	2	yes	—
478	#391	C₂²×C₁₃	1	2	yes	—
479	#391	C₂²×C₁₃	1	1	yes	characteristic
480	#391	C₂²×C₁₃	1	2	yes	—
481	#389	C₂²×C₁₃	1	2	yes	—
482	#389	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	2	yes	—
486	#389	C₂²×C₁₃	1	1	yes	characteristic
487	#389	C₂²×C₁₃	1	2	yes	—
488	#388	C₂²×C₁₃	1	1	yes	characteristic
489	#388	C₂²×C₁₃	1	2	yes	—
490	#388	C₂²×C₁₃	1	2	yes	—
491	#388	C₂²×C₁₃	1	2	yes	—
492	#388	C₂²×C₁₃	1	2	yes	—
493	#388	C₂²×C₁₃	1	2	yes	—
494	#388	C₂²×C₁₃	1	2	yes	—
495	#388	C₂²×C₁₃	1	2	yes	—
496	#388	C₂²×C₁₃	1	2	yes	—
497	#388	C₂²×C₁₃	1	2	yes	—
498	#388	C₂²×C₁₃	1	1	yes	characteristic
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	2	yes	—
506	#387	C₂²×C₁₃	1	2	yes	—
507	#387	C₂²×C₁₃	1	1	yes	characteristic
508	#387	C₂²×C₁₃	1	2	yes	—
509	#387	C₂²×C₁₃	1	1	yes	characteristic
510	#386	C₂²×C₁₃	1	1	yes	characteristic
511	#386	C₂²×C₁₃	1	2	yes	—
512	#386	C₂²×C₁₃	1	1	yes	characteristic
513	#385	C₂²×C₁₃	1	1	yes	characteristic
514	#385	C₂²×C₁₃	1	2	yes	—
515	#385	C₂²×C₁₃	1	2	yes	—
516	#385	C₂²×C₁₃	1	1	yes	characteristic
517	#383	C₂²×C₁₃	1	2	yes	—
518	#383	C₂²×C₁₃	1	2	yes	—
519	#382	C₂²×C₁₃	1	1	yes	characteristic
520	#382	C₂²×C₁₃	1	2	yes	—
521	#380	C₂²×C₁₃	1	1	yes	characteristic
522	#380	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	1	yes	characteristic
527	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
528	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
530	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
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	2	yes	—
534	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
535	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
536	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
537	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
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	1	yes	characteristic
547	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
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	2	yes	—
553	#376	C₂²×C₁₃	1	2	yes	—
554	#376	C₂²×C₁₃	1	2	yes	—
555	#376	C₂²×C₁₃	1	2	yes	—
556	C₄³	C₂²×C₁₃	1	2	yes	—
557	C₂²×C₁₃	—	2	2	no	—
558	C₂²×C₁₃	—	2	2	no	—
559	C₂²×C₁₃	—	2	2	no	—
560	C₂²×C₁₃	—	2	2	no	—
561	C₂²×C₁₃	—	2	2	no	—
562	C₂²×C₁₃	—	2	2	no	—
563	C₂²×C₁₃	—	4	1	no	—
564	C₂²×C₁₃	—	4	1	no	—
565	C₂²×C₁₃	—	4	1	no	—
566	C₂²×C₁₃	—	4	1	no	—
567	C₂²×C₁₃	—	4	1	no	—
568	C₂²×C₁₃	—	4	1	no	—
569	C₂²×C₁₃	—	4	1	no	—
570	C₂²×C₁₃	—	4	1	no	—
571	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
572	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
573	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
574	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
575	C₂²×C₁₃	#585	1	1	yes	characteristic
576	C₂²×C₁₃	#585	1	1	yes	characteristic
577	C₂²×C₁₃	#585	1	1	yes	characteristic
578	C₄×C₁₃	—	2	2	no	—
579	C₄×C₁₃	—	2	2	no	—
580	C₄×C₁₃	—	2	4	no	—
581	C₄×C₁₃	—	2	2	no	—
582	C₄×C₁₃	—	2	4	no	—
583	C₄×C₁₃	—	2	4	no	—
584	C₄×C₁₃	—	2	4	no	—
585	C₄×C₁₃	—	2	2	no	—
586	C₄×C₁₃	—	2	2	no	—
587	C₄×C₁₃	—	2	2	no	—
588	C₄×C₁₃	—	2	2	no	—
589	C₄×C₁₃	—	2	4	no	—
590	C₄×C₁₃	—	4	1	no	—
591	C₄×C₁₃	—	4	2	no	—
592	C₄×C₁₃	—	4	1	no	—
593	C₄×C₁₃	—	4	1	no	—
594	C₄×C₁₃	—	4	1	no	—
595	C₄×C₁₃	—	4	2	no	—
596	C₄×C₁₃	—	4	1	no	—
597	C₄×C₁₃	—	4	2	no	—
598	C₄×C₁₃	C₄×#41	1	4	yes	—
599	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
601	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
606	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
608	#126	C₂×C₄×C₁₃	1	16	yes	complemented
609	#126	C₂×C₄×C₁₃	1	16	yes	complemented
610	#124	C₂×C₄×C₁₃	1	16	yes	—
611	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
612	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
613	C₄×Q₈	—	2	4	no	—
614	C₄×Q₈	—	2	4	no	—
615	C₄×Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
616	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
617	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
618	#117	—	2	4	no	—
619	#117	—	2	4	no	—
620	#117	C₂×C₄×C₁₃	1	8	yes	complemented
621	#117	C₂×C₄×C₁₃	1	8	yes	complemented
622	C₂×C₄⋊C₄	—	2	4	no	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₂²⋊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	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
661	C₂×C₄²	—	2	4	no	—
662	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
663	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
666	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
667	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
669	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
675	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
676	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
677	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
678	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
679	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
680	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
681	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
683	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
684	#95	C₂³×C₁₃	1	1	yes	characteristic
685	#95	C₂³×C₁₃	1	2	yes	—
686	#95	C₂³×C₁₃	1	1	yes	characteristic
687	#95	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
698	#95	C₂³×C₁₃	1	2	yes	—
699	#95	C₂³×C₁₃	1	2	yes	—
700	#95	C₂³×C₁₃	1	2	yes	—
701	#95	C₂³×C₁₃	1	2	yes	—
702	#95	C₂³×C₁₃	1	2	yes	—
703	#95	C₂³×C₁₃	1	1	yes	characteristic
704	#95	C₂³×C₁₃	1	2	yes	—
705	#95	C₂³×C₁₃	1	2	yes	—
706	#95	C₂³×C₁₃	1	1	yes	characteristic
707	#95	C₂³×C₁₃	1	2	yes	—
708	#95	C₂³×C₁₃	1	1	yes	characteristic
709	#95	C₂³×C₁₃	1	2	yes	—
710	#95	C₂³×C₁₃	1	2	yes	—
711	#95	C₂³×C₁₃	1	1	yes	characteristic
712	#95	C₂³×C₁₃	1	2	yes	—
713	#95	C₂³×C₁₃	1	2	yes	—
714	#95	C₂³×C₁₃	1	2	yes	—
715	C₂×C₁₃	—	4	2	no	—
716	C₂×C₁₃	—	4	2	no	—
717	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
718	C₂×C₁₃	#3428	1	1	yes	characteristic
719	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
720	C₂×C₁₃	#3493	1	1	yes	characteristic
721	C₂×C₁₃	#3495	1	1	yes	characteristic
722	C₂×C₁₃	#3518	1	1	yes	characteristic
723	C₂×C₁₃	#3521	1	1	yes	characteristic
724	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	4	2	no	—
729	C₂×Q₈	—	4	2	no	—
730	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
731	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
732	C₂×D₄	—	4	1	no	—
733	C₂×D₄	—	4	1	no	—
734	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	4	1	no	—
744	C₂²×C₄	—	4	1	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
749	C₂²×C₄	C₂²×C₄×C₁₃	1	4	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	2	yes	—
755	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
771	C₄⋊C₄	—	2	4	no	—
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	4	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
786	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
787	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
788	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
789	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	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	C₁₃×#41	1	4	yes	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	1	no	—
800	C₂²⋊C₄	—	4	1	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	1	no	—
803	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
804	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
805	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
806	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
807	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
808	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	4	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	4	no	—
815	C₄²	—	2	4	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	4	no	—
818	C₄²	—	4	2	no	—
819	C₄²	—	4	2	no	—
820	C₄²	—	4	2	no	—
821	C₄²	—	4	2	no	—
822	C₄²	—	4	2	no	—
823	C₄²	—	4	2	no	—
824	C₄²	—	4	2	no	—
825	C₄²	—	4	2	no	—
826	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
827	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
828	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
829	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
830	C₄²	C₁₃×#41	1	4	yes	—
831	C₁₃	#34307	1	1	yes	characteristic, direct product factor, Sylow
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
845	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
846	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
847	Q₈	—	2	8	no	—
848	Q₈	—	4	8	no	—
849	D₄	—	4	4	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	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	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	8	no	—
875	C₂×C₄	—	2	8	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
904	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
905	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
906	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
907	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
908	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
909	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
910	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
911	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
912	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
913	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
914	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
915	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
916	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
917	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	1	no	—
932	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
933	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
934	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
935	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
936	C₂²	C₁₃×#585	1	1	yes	characteristic
937	C₂²	C₁₃×#585	1	1	yes	characteristic
938	C₂²	C₁₃×#585	1	1	yes	characteristic
939	C₄	—	2	4	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	4	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	4	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	1	no	—
958	C₄	—	4	1	no	—
959	C₄	C₄×C₁₃×#41	1	4	yes	—
960	C₂	—	4	2	no	—
961	C₂	—	4	2	no	—
962	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
963	C₂	C₁₃×#3428	1	1	yes	characteristic
964	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
965	C₂	C₁₃×#3493	1	1	yes	characteristic
966	C₂	C₁₃×#3495	1	1	yes	characteristic
967	C₂	C₁₃×#3518	1	1	yes	characteristic
968	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×#2373	C₂	semidirect
3. C₁₃×#2373	C₂	semidirect
5. C₁₃×#2369	C₂	semidirect
6. C₁₃×#2362	C₂	semidirect
7. C₁₃×#2360	C₂	semidirect
8. C₁₃×#2356	C₂	semidirect
9. C₁₃×#2356	C₂	semidirect
11. C₁₃×#2347	C₂	semidirect
12. C₁₃×#2346	C₂	semidirect
14. C₁₃×#2334	C₂	semidirect
15. C₁₃×#2331	C₂	semidirect
16. C₁₃×#2323	C₂	semidirect
17. C₄×C₁₃×#126	C₂	semidirect
18. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
19. C₁₃×#2295	C₂	semidirect
21. C₁₃×#2276	C₂	semidirect
22. C₁₃×#2274	C₂	semidirect
23. C₄×C₁₃×#117	C₂	semidirect
24. C₁₃×#556	C₄	semidirect
132. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
133. C₁₃×#126	C₂×C₄	semidirect
134. C₁₃×#126	C₂×C₄	semidirect
136. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
137. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
140. C₄×Q₈×C₁₃	C₂×C₄	semidirect
141. C₄×Q₈×C₁₃	C₂×C₄	semidirect
145. C₁₃×#117	C₂×C₄	semidirect
146. C₁₃×#117	C₂×C₄	semidirect
240. #34307	C₁₃	direct (N × H)
349. #2373	C₂×C₁₃	semidirect
350. #2373	C₂×C₁₃	semidirect
352. #2369	C₂×C₁₃	semidirect
353. #2362	C₂×C₁₃	semidirect
354. #2360	C₂×C₁₃	semidirect
355. #2356	C₂×C₁₃	semidirect
356. #2356	C₂×C₁₃	semidirect
358. #2347	C₂×C₁₃	semidirect
359. #2346	C₂×C₁₃	semidirect
361. #2334	C₂×C₁₃	semidirect
362. #2331	C₂×C₁₃	semidirect
363. #2323	C₂×C₁₃	semidirect
364. C₄×#126	C₂×C₁₃	semidirect
365. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
366. #2295	C₂×C₁₃	semidirect
368. #2276	C₂×C₁₃	semidirect
369. #2274	C₂×C₁₃	semidirect
370. C₄×#117	C₂×C₁₃	semidirect
457. #556	C₄×C₁₃	semidirect
607. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
608. #126	C₂×C₄×C₁₃	semidirect
609. #126	C₂×C₄×C₁₃	semidirect
611. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
612. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
615. C₄×Q₈	C₂×C₄×C₁₃	semidirect
616. C₄×Q₈	C₂×C₄×C₁₃	semidirect
620. #117	C₂×C₄×C₁₃	semidirect
621. #117	C₂×C₄×C₁₃	semidirect
831. C₁₃	#34307	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×#556	2
C₁₃×#2373	2
C₁₃×#2372	2
C₁₃×#2369	2
C₁₃×#2362	2
C₁₃×#2360	2
C₁₃×#2356	2
C₁₃×#2352	2
C₁₃×#2347	2
C₁₃×#2346	2
C₁₃×#2337	2
C₁₃×#2334	2
C₁₃×#2331	2
C₁₃×#2323	2
C₄×C₁₃×#126	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2295	2
C₁₃×#2290	2
C₁₃×#2276	2
C₁₃×#2274	2
C₄×C₁₃×#117	2
#34307	13

Subgroups — C13×#34307 #15720646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34307 #15720646