Subgroups — C₁₃×#34916 #15721255

Order 3328.

1750 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2590	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2589	C₂	1	2	yes	maximal
3	C₁₃×#2588	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2587	C₂	1	2	yes	maximal
5	C₁₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2507	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2497	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2492	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2429	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2423	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2402	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2396	C₂	1	2	yes	maximal
15	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
18	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
19	C₁₃×#2298	C₂	1	2	yes	maximal
20	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2295	C₂	1	2	yes	maximal, complemented
22	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#400	C₂²	1	2	yes	—
37	C₁₃×#400	C₂²	1	2	yes	—
38	C₁₃×#400	C₂²	1	2	yes	—
39	C₁₃×#400	C₂²	1	2	yes	—
40	C₁₃×#400	C₂²	1	2	yes	—
41	C₁₃×#399	C₂²	1	2	yes	—
42	C₁₃×#398	C₂²	1	2	yes	—
43	C₁₃×#398	C₂²	1	2	yes	—
44	C₁₃×#398	C₂²	1	2	yes	—
45	C₁₃×#398	C₂²	1	2	yes	—
46	C₁₃×#398	C₂²	1	2	yes	—
47	C₁₃×#398	C₂²	1	2	yes	—
48	C₁₃×#396	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	2	yes	—
50	C₁₃×#395	C₂²	1	2	yes	—
51	C₁₃×#393	C₂²	1	2	yes	—
52	C₁₃×#391	C₂²	1	1	yes	characteristic
53	C₁₃×#391	C₂²	1	1	yes	characteristic
54	C₁₃×#391	C₂²	1	1	yes	characteristic
55	C₁₃×#391	C₂²	1	2	yes	—
56	C₁₃×#391	C₂²	1	2	yes	—
57	C₁₃×#391	C₂²	1	1	yes	characteristic
58	C₁₃×#391	C₂²	1	1	yes	characteristic
59	C₁₃×#391	C₂²	1	2	yes	—
60	C₁₃×#391	C₂²	1	1	yes	characteristic
61	C₁₃×#389	C₂²	1	1	yes	characteristic
62	C₁₃×#389	C₂²	1	1	yes	characteristic
63	C₁₃×#389	C₂²	1	1	yes	characteristic
64	C₁₃×#389	C₂²	1	2	yes	—
65	C₁₃×#389	C₂²	1	1	yes	characteristic
66	C₁₃×#389	C₂²	1	1	yes	characteristic
67	C₁₃×#389	C₂²	1	1	yes	characteristic
68	C₁₃×#389	C₂²	1	2	yes	—
69	C₁₃×#389	C₂²	1	2	yes	—
70	C₁₃×#389	C₂²	1	2	yes	—
71	C₁₃×#389	C₂²	1	2	yes	—
72	C₁₃×#388	C₂²	1	2	yes	—
73	C₁₃×#388	C₂²	1	2	yes	—
74	C₁₃×#388	C₂²	1	2	yes	—
75	C₁₃×#388	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#387	C₂²	1	2	yes	—
78	C₁₃×#387	C₂²	1	2	yes	—
79	C₁₃×#387	C₂²	1	2	yes	—
80	C₁₃×#387	C₂²	1	2	yes	—
81	C₁₃×#387	C₂²	1	2	yes	—
82	C₁₃×#387	C₂²	1	2	yes	—
83	C₁₃×#387	C₂²	1	2	yes	—
84	C₁₃×#387	C₂²	1	2	yes	—
85	C₁₃×#387	C₂²	1	2	yes	—
86	C₁₃×#387	C₂²	1	2	yes	—
87	C₁₃×#387	C₂²	1	2	yes	—
88	C₁₃×#385	C₂²	1	2	yes	—
89	C₁₃×#385	C₂²	1	2	yes	—
90	C₁₃×#384	C₂²	1	1	yes	characteristic
91	C₁₃×#384	C₂²	1	1	yes	characteristic
92	C₁₃×#380	C₂²	1	1	yes	characteristic
93	C₁₃×#380	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	2	yes	—
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	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×C₄⋊C₄	C₂²	1	2	yes	—
110	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	C₁₃×#376	C₂²	1	1	yes	characteristic
118	C₁₃×#376	C₂²	1	1	yes	characteristic
119	C₁₃×#376	C₂²	1	2	yes	—
120	C₄³×C₁₃	C₂²	1	1	yes	characteristic
121	C₄³×C₁₃	C₂²	1	1	yes	characteristic
122	C₄³×C₁₃	C₂²	1	2	yes	—
123	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
125	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×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	C₁₃×C₄⋊Q₈	—	2	4	no	—
130	C₁₃×C₄⋊Q₈	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	2	4	no	—
133	C₄×Q₈×C₁₃	—	2	4	no	—
134	C₄×Q₈×C₁₃	—	2	4	no	—
135	C₄×Q₈×C₁₃	—	2	4	no	—
136	C₄×Q₈×C₁₃	—	2	4	no	—
137	C₄×Q₈×C₁₃	—	2	8	no	—
138	C₁₃×#117	—	2	4	no	—
139	C₁₃×#117	Q₈	1	8	yes	complemented
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃	—	2	4	no	—
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	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	2	yes	—
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₁₃×#95	C₂³	1	1	yes	characteristic
203	C₁₃×#95	C₂³	1	1	yes	characteristic
204	C₁₃×#95	C₂³	1	1	yes	characteristic
205	C₁₃×#95	C₂³	1	1	yes	characteristic
206	C₁₃×#95	C₂³	1	1	yes	characteristic
207	C₁₃×#95	C₂³	1	1	yes	characteristic
208	C₁₃×#95	C₂³	1	1	yes	characteristic
209	C₁₃×#95	C₂³	1	1	yes	characteristic
210	C₁₃×#95	C₂³	1	2	yes	—
211	C₁₃×#95	C₂³	1	2	yes	—
212	C₁₃×#95	C₂³	1	2	yes	—
213	C₁₃×#95	C₂³	1	2	yes	—
214	C₁₃×#95	C₂³	1	2	yes	—
215	C₁₃×#95	C₂³	1	2	yes	—
216	C₁₃×#95	C₂³	1	2	yes	—
217	C₁₃×#95	C₂³	1	2	yes	—
218	C₁₃×#95	C₂³	1	2	yes	—
219	C₁₃×#95	C₂³	1	2	yes	—
220	C₁₃×#95	C₂³	1	2	yes	—
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	2	yes	—
223	C₁₃×#95	C₂³	1	2	yes	—
224	C₁₃×#95	C₂³	1	2	yes	—
225	C₁₃×#95	C₂³	1	2	yes	—
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	2	yes	—
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	2	yes	—
230	C₁₃×#95	C₂³	1	2	yes	—
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	2	yes	—
234	#34916	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	4	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	4	no	—
242	C₂×Q₈×C₁₃	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	4	2	no	—
244	C₂×Q₈×C₁₃	#41	1	4	yes	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	4	1	no	—
252	C₂²×C₄×C₁₃	—	4	1	no	—
253	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	4	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	4	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	4	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	4	2	no	—
296	C₁₃×C₄⋊C₄	—	4	2	no	—
297	C₁₃×C₄⋊C₄	—	4	2	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	C₂×Q₈	1	4	yes	—
303	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
304	C₁₃×C₄⋊C₄	#41	1	4	yes	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	4	2	no	—
310	C₁₃×C₂²⋊C₄	—	4	2	no	—
311	C₁₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
312	C₁₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
313	C₄²×C₁₃	—	2	2	no	—
314	C₄²×C₁₃	—	2	2	no	—
315	C₄²×C₁₃	—	2	2	no	—
316	C₄²×C₁₃	—	2	2	no	—
317	C₄²×C₁₃	—	2	4	no	—
318	C₄²×C₁₃	—	2	4	no	—
319	C₄²×C₁₃	—	2	2	no	—
320	C₄²×C₁₃	—	2	2	no	—
321	C₄²×C₁₃	—	2	4	no	—
322	C₄²×C₁₃	—	2	4	no	—
323	C₄²×C₁₃	—	2	4	no	—
324	C₄²×C₁₃	—	2	4	no	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	4	1	no	—
328	C₄²×C₁₃	—	4	1	no	—
329	C₄²×C₁₃	—	4	2	no	—
330	C₄²×C₁₃	—	4	2	no	—
331	C₄²×C₁₃	—	4	1	no	—
332	C₄²×C₁₃	—	4	1	no	—
333	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
334	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
335	C₄²×C₁₃	#41	1	4	yes	—
336	C₄²×C₁₃	#41	1	4	yes	—
337	#2590	C₂×C₁₃	1	2	yes	complemented
338	#2589	C₂×C₁₃	1	2	yes	—
339	#2588	C₂×C₁₃	1	2	yes	complemented
340	#2587	C₂×C₁₃	1	2	yes	—
341	#2511	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#2507	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#2497	C₂×C₁₃	1	1	yes	characteristic
344	#2492	C₂×C₁₃	1	1	yes	characteristic
345	#2451	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#2446	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#2429	C₂×C₁₃	1	1	yes	characteristic
348	#2423	C₂×C₁₃	1	1	yes	characteristic
349	#2402	C₂×C₁₃	1	2	yes	complemented
350	#2396	C₂×C₁₃	1	2	yes	—
351	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
354	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
355	#2298	C₂×C₁₃	1	2	yes	—
356	#2295	C₂×C₁₃	1	2	yes	complemented
357	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	—	2	1	no	—
364	C₂³×C₁₃	—	2	1	no	—
365	C₂³×C₁₃	—	2	1	no	—
366	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
367	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
368	Q₈×C₁₃	—	2	8	no	—
369	Q₈×C₁₃	—	4	8	no	—
370	Q₈×C₁₃	—	4	4	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	1	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	1	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	8	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	1	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	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	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	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	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	4	4	no	—
423	C₂×C₄×C₁₃	—	4	4	no	—
424	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
425	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
426	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
427	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
428	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
429	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
430	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
431	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
432	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
433	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
434	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
435	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
436	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
437	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
438	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
439	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
440	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
445	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
451	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
452	#400	C₂²×C₁₃	1	2	yes	—
453	#400	C₂²×C₁₃	1	2	yes	—
454	#400	C₂²×C₁₃	1	2	yes	—
455	#400	C₂²×C₁₃	1	2	yes	—
456	#400	C₂²×C₁₃	1	2	yes	—
457	#399	C₂²×C₁₃	1	2	yes	—
458	#398	C₂²×C₁₃	1	2	yes	—
459	#398	C₂²×C₁₃	1	2	yes	—
460	#398	C₂²×C₁₃	1	2	yes	—
461	#398	C₂²×C₁₃	1	2	yes	—
462	#398	C₂²×C₁₃	1	2	yes	—
463	#398	C₂²×C₁₃	1	2	yes	—
464	#396	C₂²×C₁₃	1	2	yes	—
465	#396	C₂²×C₁₃	1	2	yes	—
466	#395	C₂²×C₁₃	1	2	yes	—
467	#393	C₂²×C₁₃	1	2	yes	—
468	#391	C₂²×C₁₃	1	2	yes	—
469	#391	C₂²×C₁₃	1	1	yes	characteristic
470	#391	C₂²×C₁₃	1	1	yes	characteristic
471	#391	C₂²×C₁₃	1	2	yes	—
472	#391	C₂²×C₁₃	1	2	yes	—
473	#391	C₂²×C₁₃	1	1	yes	characteristic
474	#391	C₂²×C₁₃	1	1	yes	characteristic
475	#391	C₂²×C₁₃	1	1	yes	characteristic
476	#391	C₂²×C₁₃	1	1	yes	characteristic
477	#389	C₂²×C₁₃	1	2	yes	—
478	#389	C₂²×C₁₃	1	2	yes	—
479	#389	C₂²×C₁₃	1	2	yes	—
480	#389	C₂²×C₁₃	1	1	yes	characteristic
481	#389	C₂²×C₁₃	1	1	yes	characteristic
482	#389	C₂²×C₁₃	1	2	yes	—
483	#389	C₂²×C₁₃	1	2	yes	—
484	#389	C₂²×C₁₃	1	1	yes	characteristic
485	#389	C₂²×C₁₃	1	1	yes	characteristic
486	#389	C₂²×C₁₃	1	1	yes	characteristic
487	#389	C₂²×C₁₃	1	1	yes	characteristic
488	#388	C₂²×C₁₃	1	2	yes	—
489	#388	C₂²×C₁₃	1	2	yes	—
490	#388	C₂²×C₁₃	1	2	yes	—
491	#388	C₂²×C₁₃	1	2	yes	—
492	#387	C₂²×C₁₃	1	2	yes	—
493	#387	C₂²×C₁₃	1	2	yes	—
494	#387	C₂²×C₁₃	1	2	yes	—
495	#387	C₂²×C₁₃	1	2	yes	—
496	#387	C₂²×C₁₃	1	2	yes	—
497	#387	C₂²×C₁₃	1	2	yes	—
498	#387	C₂²×C₁₃	1	2	yes	—
499	#387	C₂²×C₁₃	1	2	yes	—
500	#387	C₂²×C₁₃	1	2	yes	—
501	#387	C₂²×C₁₃	1	2	yes	—
502	#387	C₂²×C₁₃	1	2	yes	—
503	#387	C₂²×C₁₃	1	2	yes	—
504	#385	C₂²×C₁₃	1	2	yes	—
505	#385	C₂²×C₁₃	1	2	yes	—
506	#384	C₂²×C₁₃	1	1	yes	characteristic
507	#384	C₂²×C₁₃	1	1	yes	characteristic
508	#380	C₂²×C₁₃	1	1	yes	characteristic
509	#380	C₂²×C₁₃	1	1	yes	characteristic
510	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
511	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
512	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
513	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
514	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
515	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
516	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
517	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
518	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
519	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
520	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
521	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
522	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
523	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
524	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
525	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
526	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
527	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
528	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
529	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
530	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
532	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
533	#376	C₂²×C₁₃	1	1	yes	characteristic
534	#376	C₂²×C₁₃	1	1	yes	characteristic
535	#376	C₂²×C₁₃	1	2	yes	—
536	C₄³	C₂²×C₁₃	1	1	yes	characteristic
537	C₄³	C₂²×C₁₃	1	1	yes	characteristic
538	C₄³	C₂²×C₁₃	1	2	yes	—
539	C₂²×C₁₃	—	2	2	no	—
540	C₂²×C₁₃	—	2	2	no	—
541	C₂²×C₁₃	—	2	2	no	—
542	C₂²×C₁₃	—	4	1	no	—
543	C₂²×C₁₃	—	4	1	no	—
544	C₂²×C₁₃	—	4	1	no	—
545	C₂²×C₁₃	—	4	1	no	—
546	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
547	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
548	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
549	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
550	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
551	C₂²×C₁₃	#585	1	1	yes	characteristic
552	C₂²×C₁₃	#585	1	1	yes	characteristic
553	C₄×C₁₃	—	2	4	no	—
554	C₄×C₁₃	—	2	2	no	—
555	C₄×C₁₃	—	2	2	no	—
556	C₄×C₁₃	—	2	4	no	—
557	C₄×C₁₃	—	2	2	no	—
558	C₄×C₁₃	—	2	2	no	—
559	C₄×C₁₃	—	2	2	no	—
560	C₄×C₁₃	—	2	2	no	—
561	C₄×C₁₃	—	2	2	no	—
562	C₄×C₁₃	—	2	2	no	—
563	C₄×C₁₃	—	4	1	no	—
564	C₄×C₁₃	—	4	2	no	—
565	C₄×C₁₃	—	4	2	no	—
566	C₄×C₁₃	—	4	2	no	—
567	C₄×C₁₃	—	4	1	no	—
568	C₄×C₁₃	—	4	1	no	—
569	C₄×C₁₃	—	4	2	no	—
570	C₄×C₁₃	—	4	1	no	—
571	C₄×C₁₃	—	4	2	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	#529	1	4	yes	—
574	C₄×C₁₃	#533	1	4	yes	—
575	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
576	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
577	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₄⋊Q₈	—	2	4	no	—
582	C₄⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	C₂²⋊Q₈	—	2	4	no	—
585	C₄×Q₈	—	2	4	no	—
586	C₄×Q₈	—	2	4	no	—
587	C₄×Q₈	—	2	4	no	—
588	C₄×Q₈	—	2	4	no	—
589	C₄×Q₈	—	2	8	no	—
590	#117	—	2	4	no	—
591	#117	Q₈×C₁₃	1	8	yes	complemented
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₂×C₄²	—	2	4	no	—
630	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
639	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
650	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
654	#95	C₂³×C₁₃	1	1	yes	characteristic
655	#95	C₂³×C₁₃	1	1	yes	characteristic
656	#95	C₂³×C₁₃	1	1	yes	characteristic
657	#95	C₂³×C₁₃	1	1	yes	characteristic
658	#95	C₂³×C₁₃	1	1	yes	characteristic
659	#95	C₂³×C₁₃	1	1	yes	characteristic
660	#95	C₂³×C₁₃	1	1	yes	characteristic
661	#95	C₂³×C₁₃	1	1	yes	characteristic
662	#95	C₂³×C₁₃	1	2	yes	—
663	#95	C₂³×C₁₃	1	2	yes	—
664	#95	C₂³×C₁₃	1	2	yes	—
665	#95	C₂³×C₁₃	1	2	yes	—
666	#95	C₂³×C₁₃	1	2	yes	—
667	#95	C₂³×C₁₃	1	2	yes	—
668	#95	C₂³×C₁₃	1	2	yes	—
669	#95	C₂³×C₁₃	1	2	yes	—
670	#95	C₂³×C₁₃	1	2	yes	—
671	#95	C₂³×C₁₃	1	2	yes	—
672	#95	C₂³×C₁₃	1	2	yes	—
673	#95	C₂³×C₁₃	1	2	yes	—
674	#95	C₂³×C₁₃	1	2	yes	—
675	#95	C₂³×C₁₃	1	2	yes	—
676	#95	C₂³×C₁₃	1	2	yes	—
677	#95	C₂³×C₁₃	1	2	yes	—
678	#95	C₂³×C₁₃	1	2	yes	—
679	#95	C₂³×C₁₃	1	2	yes	—
680	#95	C₂³×C₁₃	1	2	yes	—
681	#95	C₂³×C₁₃	1	2	yes	—
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	C₂×C₁₃	—	4	2	no	—
687	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
688	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
689	C₂×C₁₃	#3455	1	1	yes	characteristic
690	C₂×C₁₃	#3475	1	1	yes	characteristic
691	C₂×C₁₃	Q₈×#41	1	1	yes	characteristic
692	C₂×C₁₃	Q₈×#41	1	1	yes	characteristic
693	C₂×C₁₃	#3480	1	1	yes	characteristic
694	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	4	2	no	—
703	C₂×Q₈	C₁₃×#41	1	4	yes	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	4	1	no	—
711	C₂²×C₄	—	4	1	no	—
712	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
762	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
763	C₄⋊C₄	C₁₃×#41	1	4	yes	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
771	C₂²⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	4	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	4	1	no	—
787	C₄²	—	4	1	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	1	no	—
791	C₄²	—	4	1	no	—
792	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
793	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
794	C₄²	C₁₃×#41	1	4	yes	—
795	C₄²	C₁₃×#41	1	4	yes	—
796	C₁₃	#34916	1	1	yes	characteristic, direct product factor, Sylow
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
804	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
805	Q₈	—	2	8	no	—
806	Q₈	—	4	8	no	—
807	Q₈	—	4	4	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	8	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	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	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
862	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
863	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
864	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
865	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
866	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
867	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
868	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
869	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
870	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
871	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
872	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
873	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
874	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
875	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
876	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
885	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
886	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
887	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
888	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
889	C₂²	C₁₃×#585	1	1	yes	characteristic
890	C₂²	C₁₃×#585	1	1	yes	characteristic
891	C₄	—	2	4	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	4	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	C₁₃×#529	1	4	yes	—
912	C₄	C₁₃×#533	1	4	yes	—
913	C₂	—	4	2	no	—
914	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
915	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
916	C₂	C₁₃×#3455	1	1	yes	characteristic
917	C₂	C₁₃×#3475	1	1	yes	characteristic
918	C₂	Q₈×C₁₃×#41	1	1	yes	characteristic
919	C₂	Q₈×C₁₃×#41	1	1	yes	characteristic
920	C₂	C₁₃×#3480	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2590	C₂	semidirect
3. C₁₃×#2588	C₂	semidirect
5. C₁₃×#2511	C₂	semidirect
6. C₁₃×#2507	C₂	semidirect
9. C₁₃×#2451	C₂	semidirect
10. C₁₃×#2446	C₂	semidirect
13. C₁₃×#2402	C₂	semidirect
15. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
16. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
20. C₁₃×#2295	C₂	semidirect
21. C₁₃×#2295	C₂	semidirect
22. C₄²×Q₈×C₁₃	C₂	semidirect
139. C₁₃×#117	Q₈	semidirect
234. #34916	C₁₃	direct (N × H)
337. #2590	C₂×C₁₃	semidirect
339. #2588	C₂×C₁₃	semidirect
341. #2511	C₂×C₁₃	semidirect
342. #2507	C₂×C₁₃	semidirect
345. #2451	C₂×C₁₃	semidirect
346. #2446	C₂×C₁₃	semidirect
349. #2402	C₂×C₁₃	semidirect
351. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
352. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
356. #2295	C₂×C₁₃	semidirect
357. #2295	C₂×C₁₃	semidirect
358. C₄²×Q₈	C₂×C₁₃	semidirect
591. #117	Q₈×C₁₃	semidirect
796. C₁₃	#34916	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2590	2
C₁₃×#2589	2
C₁₃×#2588	2
C₁₃×#2587	2
C₁₃×#2511	2
C₁₃×#2507	2
C₁₃×#2497	2
C₁₃×#2492	2
C₁₃×#2451	2
C₁₃×#2446	2
C₁₃×#2429	2
C₁₃×#2423	2
C₁₃×#2402	2
C₁₃×#2396	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2298	2
C₁₃×#2295	2
C₄²×Q₈×C₁₃	2
C₄×C₁₃×#117	2
#34916	13

Subgroups — C13×#34916 #15721255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34916 #15721255