Subgroups — C₁₃×#21671 #15708010

Order 3328.

676 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2401	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1924	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1923	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1923	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1917	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1840	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#401	C₄	1	1	yes	characteristic
33	C₁₃×#400	C₄	1	1	yes	characteristic
34	C₁₃×#400	C₄	1	1	yes	characteristic
35	C₁₃×#400	C₄	1	1	yes	characteristic
36	C₁₃×#397	C₄	1	1	yes	characteristic
37	C₁₃×#397	C₄	1	1	yes	characteristic
38	C₁₃×#397	C₄	1	1	yes	characteristic
39	C₁₃×#396	C₄	1	1	yes	characteristic
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₁₃×#376	C₂²	1	1	yes	characteristic
47	C₁₃×#336	C₂²	1	1	yes	characteristic
48	C₁₃×#336	C₂²	1	1	yes	characteristic
49	C₁₃×#336	C₂²	1	1	yes	characteristic
50	C₁₃×#336	C₂²	1	1	yes	characteristic
51	C₁₃×#336	C₂²	1	1	yes	characteristic
52	C₁₃×#336	C₂²	1	1	yes	characteristic
53	C₁₃×#336	C₂²	1	1	yes	characteristic
54	C₁₃×#336	C₂²	1	1	yes	characteristic
55	C₁₃×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	—	2	2	no	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×C₄⋊C₈	—	2	2	no	—
90	C₁₃×C₄⋊C₈	—	2	2	no	—
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×C₂²⋊C₈	—	2	2	no	—
93	C₁₃×C₂²⋊C₈	—	2	2	no	—
94	C₁₃×C₂²⋊C₈	—	2	2	no	—
95	C₁₃×#97	—	2	2	no	—
96	C₁₃×#97	—	2	2	no	—
97	C₁₃×#97	—	2	2	no	—
98	C₁₃×#97	—	2	2	no	—
99	C₄×C₈×C₁₃	—	2	2	no	—
100	C₄×C₈×C₁₃	—	2	2	no	—
101	C₄×C₈×C₁₃	—	2	2	no	—
102	C₄×C₈×C₁₃	—	2	2	no	—
103	C₄×C₈×C₁₃	—	2	2	no	—
104	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
105	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
106	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
107	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
108	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
109	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
110	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
114	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
115	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
117	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
120	#21671	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₁₃×M₁₆	—	4	4	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	#41	1	2	yes	—
162	C₂×C₈×C₁₃	#41	1	2	yes	—
163	C₂×C₈×C₁₃	#41	1	2	yes	—
164	C₂×C₈×C₁₃	#41	1	2	yes	—
165	C₂×C₈×C₁₃	#41	1	2	yes	—
166	C₂×C₈×C₁₃	#41	1	2	yes	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	4	1	no	—
172	C₁₃×C₄⋊C₄	—	4	1	no	—
173	C₁₃×C₂²⋊C₄	—	2	2	no	—
174	C₁₃×C₂²⋊C₄	—	2	2	no	—
175	C₁₃×C₂²⋊C₄	—	4	1	no	—
176	C₁₃×C₂²⋊C₄	—	4	1	no	—
177	C₁₃×C₂²⋊C₄	—	4	1	no	—
178	C₁₃×C₂²⋊C₄	—	4	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	—	2	1	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	2	1	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	#2401	C₂×C₁₃	1	1	yes	characteristic
192	#1924	C₂×C₁₃	1	1	yes	characteristic
193	#1923	C₂×C₁₃	1	1	yes	characteristic
194	#1923	C₂×C₁₃	1	1	yes	characteristic
195	#1917	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#1916	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#1916	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#1840	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#1770	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1753	C₂×C₁₃	1	1	yes	characteristic
203	#1753	C₂×C₁₃	1	1	yes	characteristic
204	#1753	C₂×C₁₃	1	1	yes	characteristic
205	#1726	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂³×C₁₃	—	2	1	no	—
207	C₂³×C₁₃	—	2	1	no	—
208	C₂³×C₁₃	—	2	1	no	—
209	C₂³×C₁₃	—	2	1	no	—
210	C₂³×C₁₃	—	2	1	no	—
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	#131	1	2	yes	—
256	C₂×C₄×C₁₃	#131	1	2	yes	—
257	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
263	C₈×C₁₃	—	2	2	no	—
264	C₈×C₁₃	—	2	2	no	—
265	C₈×C₁₃	—	2	2	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	#126	1	4	yes	—
271	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
287	#401	C₄×C₁₃	1	1	yes	characteristic
288	#400	C₄×C₁₃	1	1	yes	characteristic
289	#400	C₄×C₁₃	1	1	yes	characteristic
290	#400	C₄×C₁₃	1	1	yes	characteristic
291	#397	C₄×C₁₃	1	1	yes	characteristic
292	#397	C₄×C₁₃	1	1	yes	characteristic
293	#397	C₄×C₁₃	1	1	yes	characteristic
294	#396	C₄×C₁₃	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
298	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
301	#376	C₂²×C₁₃	1	1	yes	characteristic
302	#336	C₂²×C₁₃	1	1	yes	characteristic
303	#336	C₂²×C₁₃	1	1	yes	characteristic
304	#336	C₂²×C₁₃	1	1	yes	characteristic
305	#336	C₂²×C₁₃	1	1	yes	characteristic
306	#336	C₂²×C₁₃	1	1	yes	characteristic
307	#336	C₂²×C₁₃	1	1	yes	characteristic
308	#336	C₂²×C₁₃	1	1	yes	characteristic
309	#336	C₂²×C₁₃	1	1	yes	characteristic
310	#336	C₂²×C₁₃	1	1	yes	characteristic
311	#336	C₂²×C₁₃	1	1	yes	characteristic
312	#336	C₂²×C₁₃	1	1	yes	characteristic
313	#336	C₂²×C₁₃	1	1	yes	characteristic
314	C₂²×C₁₃	—	4	1	no	—
315	C₂²×C₁₃	—	4	1	no	—
316	C₂²×C₁₃	—	4	1	no	—
317	C₂²×C₁₃	—	4	1	no	—
318	C₂²×C₁₃	—	4	1	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
322	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
323	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
324	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
325	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
326	C₂²×C₁₃	#568	1	1	yes	characteristic
327	C₂²×C₁₃	#568	1	1	yes	characteristic
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	4	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
342	C₄×C₁₃	#529	1	1	yes	characteristic
343	C₄×C₁₃	#529	1	1	yes	characteristic
344	C₄×C₁₃	#529	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×M₁₆	—	2	2	no	—
347	C₂×M₁₆	—	2	2	no	—
348	C₂×M₁₆	—	2	2	no	—
349	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	C₄⋊C₈	—	2	2	no	—
376	C₄⋊C₈	—	2	2	no	—
377	C₄⋊C₈	—	2	2	no	—
378	C₂²⋊C₈	—	2	2	no	—
379	C₂²⋊C₈	—	2	2	no	—
380	C₂²⋊C₈	—	2	2	no	—
381	#97	—	2	2	no	—
382	#97	—	2	2	no	—
383	#97	—	2	2	no	—
384	#97	—	2	2	no	—
385	C₄×C₈	—	2	2	no	—
386	C₄×C₈	—	2	2	no	—
387	C₄×C₈	—	2	2	no	—
388	C₄×C₈	—	2	2	no	—
389	C₄×C₈	—	2	2	no	—
390	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
391	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
392	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
393	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
394	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
395	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
396	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
397	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
398	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
399	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
400	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
401	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
402	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
403	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
404	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
405	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
406	C₂×C₁₃	—	8	1	no	—
407	C₂×C₁₃	C₄×#126	1	1	yes	characteristic
408	C₂×C₁₃	#2966	1	1	yes	characteristic
409	C₂×C₁₃	#2967	1	1	yes	characteristic
410	C₂×C₁₃	#2968	1	1	yes	characteristic
411	C₂×C₁₃	#2969	1	1	yes	characteristic
412	C₂×C₁₃	#2969	1	1	yes	characteristic
413	C₂×C₁₃	#2969	1	1	yes	characteristic
414	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
435	M₁₆	—	4	4	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	C₁₃×#41	1	2	yes	—
455	C₂×C₈	C₁₃×#41	1	2	yes	—
456	C₂×C₈	C₁₃×#41	1	2	yes	—
457	C₂×C₈	C₁₃×#41	1	2	yes	—
458	C₂×C₈	C₁₃×#41	1	2	yes	—
459	C₂×C₈	C₁₃×#41	1	2	yes	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₁₃	#21671	1	1	yes	characteristic, direct product factor, Sylow
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	C₁₃×#131	1	2	yes	—
535	C₂×C₄	C₁₃×#131	1	2	yes	—
536	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
537	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
538	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
539	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
540	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
541	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
542	C₈	—	2	2	no	—
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	C₁₃×#126	1	4	yes	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
558	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
559	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
560	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
561	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
562	C₂²	C₁₃×#568	1	1	yes	characteristic
563	C₂²	C₁₃×#568	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	C₂×C₁₃×#126	1	1	yes	characteristic
578	C₄	C₁₃×#529	1	1	yes	characteristic
579	C₄	C₁₃×#529	1	1	yes	characteristic
580	C₄	C₁₃×#529	1	1	yes	characteristic
581	C₂	—	8	1	no	—
582	C₂	C₄×C₁₃×#126	1	1	yes	characteristic
583	C₂	C₁₃×#2966	1	1	yes	characteristic
584	C₂	C₁₃×#2967	1	1	yes	characteristic
585	C₂	C₁₃×#2968	1	1	yes	characteristic
586	C₂	C₁₃×#2969	1	1	yes	characteristic
587	C₂	C₁₃×#2969	1	1	yes	characteristic
588	C₂	C₁₃×#2969	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
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
5. C₁₃×#1917	C₂	semidirect
6. C₁₃×#1916	C₂	semidirect
7. C₁₃×#1916	C₂	semidirect
8. C₁₃×#1840	C₂	semidirect
9. C₁₃×#1771	C₂	semidirect
10. C₁₃×#1770	C₂	semidirect
11. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
15. C₁₃×#1726	C₂	semidirect
120. #21671	C₁₃	direct (N × H)
195. #1917	C₂×C₁₃	semidirect
196. #1916	C₂×C₁₃	semidirect
197. #1916	C₂×C₁₃	semidirect
198. #1840	C₂×C₁₃	semidirect
199. #1771	C₂×C₁₃	semidirect
200. #1770	C₂×C₁₃	semidirect
201. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
205. #1726	C₂×C₁₃	semidirect
484. C₁₃	#21671	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×#2401	2
C₁₃×#1924	2
C₁₃×#1923	2
C₁₃×#1917	2
C₁₃×#1916	2
C₁₃×#1840	2
C₁₃×#1771	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1753	2
C₁₃×#1726	2
#21671	13

Subgroups — C13×#21671 #15708010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21671 #15708010