Subgroups — C₁₃×#25206 #15711545

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#484	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2502	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2360	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2083	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1928	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1850	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#340	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₁₃×#484	—	2	4	no	—
24	C₁₃×#467	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₃×#398	—	2	1	no	—
38	C₁₃×#398	—	2	1	no	—
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#389	—	2	1	no	—
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#387	—	2	1	no	—
45	C₁₃×#385	—	2	1	no	—
46	C₁₃×#385	—	2	1	no	—
47	C₁₃×#385	—	2	1	no	—
48	C₁₃×#384	C₂²	1	1	yes	characteristic
49	C₁₃×#384	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×Q₁₆	—	2	2	no	—
67	C₂×C₁₃×Q₁₆	—	2	2	no	—
68	C₂×C₁₃×Q₁₆	—	4	1	no	—
69	C₂²×C₈×C₁₃	—	2	2	no	—
70	C₂²×C₈×C₁₃	—	2	2	no	—
71	C₂²×C₈×C₁₃	—	4	1	no	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	2	no	—
79	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	4	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#107	—	2	2	no	—
111	C₁₃×#107	—	2	2	no	—
112	C₁₃×#107	—	2	2	no	—
113	C₁₃×C₄⋊C₈	—	2	2	no	—
114	C₁₃×C₄⋊C₈	—	4	1	no	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	4	1	no	—
121	C₁₃×C₂²⋊C₈	—	2	2	no	—
122	C₁₃×#95	—	2	1	no	—
123	C₁₃×#95	—	2	1	no	—
124	C₁₃×#95	—	2	1	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	D₄	1	1	yes	characteristic
131	C₁₃×#95	D₄	1	1	yes	characteristic
132	#25206	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	4	2	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	8	1	no	—
162	C₂²×C₄×C₁₃	—	8	1	no	—
163	C₂²×C₄×C₁₃	—	8	1	no	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	#41	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₁₃×Q₁₆	—	4	4	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	4	4	no	—
185	C₂×C₈×C₁₃	#41	1	2	yes	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	4	2	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	—	4	2	no	—
200	C₁₃×C₄⋊C₄	—	4	2	no	—
201	C₁₃×C₄⋊C₄	—	8	1	no	—
202	C₁₃×C₄⋊C₄	—	8	1	no	—
203	C₁₃×C₄⋊C₄	—	8	1	no	—
204	C₁₃×C₄⋊C₄	—	8	1	no	—
205	C₁₃×C₄⋊C₄	—	8	1	no	—
206	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
207	C₁₃×C₄⋊C₄	#41	1	2	yes	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₁₃×C₂²⋊C₄	—	4	2	no	—
211	C₁₃×C₂²⋊C₄	Q₁₆	1	4	yes	complemented
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	2	1	no	—
216	C₄²×C₁₃	—	4	2	no	—
217	C₄²×C₁₃	—	8	1	no	—
218	C₂×#484	C₂×C₁₃	1	1	yes	characteristic
219	C₂×#467	C₂×C₁₃	1	1	yes	characteristic
220	#2502	C₂×C₁₃	1	1	yes	characteristic
221	#2360	C₂×C₁₃	1	1	yes	characteristic
222	#2083	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1928	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1872	C₂×C₁₃	1	1	yes	characteristic
230	#1850	C₂×C₁₃	1	1	yes	characteristic
231	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂×#340	C₂×C₁₃	1	1	yes	characteristic
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	2	1	no	—
235	C₂³×C₁₃	—	2	1	no	—
236	C₂³×C₁₃	—	2	1	no	—
237	C₂³×C₁₃	#121	1	2	yes	—
238	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
239	C₂³×C₁₃	#137	1	2	yes	—
240	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₁₃	—	2	2	no	—
242	Q₈×C₁₃	—	2	2	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	4	1	no	—
245	Q₈×C₁₃	—	4	1	no	—
246	Q₈×C₁₃	—	4	1	no	—
247	Q₈×C₁₃	—	4	1	no	—
248	Q₈×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	8	4	no	—
290	C₂×C₄×C₁₃	—	8	4	no	—
291	C₂×C₄×C₁₃	#121	1	2	yes	—
292	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
293	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
294	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
300	C₈×C₁₃	—	2	2	no	—
301	C₈×C₁₃	—	4	1	no	—
302	C₈×C₁₃	—	4	1	no	—
303	C₈×C₁₃	—	4	1	no	—
304	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
305	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
311	#484	—	2	4	no	—
312	#467	—	2	4	no	—
313	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
325	#398	—	2	1	no	—
326	#398	—	2	1	no	—
327	#391	C₂²×C₁₃	1	1	yes	characteristic
328	#391	C₂²×C₁₃	1	1	yes	characteristic
329	#391	C₂²×C₁₃	1	1	yes	characteristic
330	#389	—	2	1	no	—
331	#389	C₂²×C₁₃	1	1	yes	characteristic
332	#387	—	2	1	no	—
333	#385	—	2	1	no	—
334	#385	—	2	1	no	—
335	#385	—	2	1	no	—
336	#384	C₂²×C₁₃	1	1	yes	characteristic
337	#384	C₂²×C₁₃	1	1	yes	characteristic
338	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
339	C₄×C₂²⋊C₄	—	2	1	no	—
340	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
341	#340	C₂²×C₁₃	1	1	yes	characteristic
342	#340	C₂²×C₁₃	1	1	yes	characteristic
343	#340	C₂²×C₁₃	1	1	yes	characteristic
344	#340	C₂²×C₁₃	1	1	yes	characteristic
345	#340	C₂²×C₁₃	1	1	yes	characteristic
346	#340	C₂²×C₁₃	1	1	yes	characteristic
347	#336	C₂²×C₁₃	1	1	yes	characteristic
348	#336	C₂²×C₁₃	1	1	yes	characteristic
349	C₂²×C₁₃	—	2	2	no	—
350	C₂²×C₁₃	—	2	2	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	2	no	—
353	C₂²×C₁₃	—	2	2	no	—
354	C₂²×C₁₃	—	2	2	no	—
355	C₂²×C₁₃	#462	1	4	yes	—
356	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
357	C₂²×C₁₃	#546	1	1	yes	characteristic
358	C₂²×C₁₃	#547	1	1	yes	characteristic
359	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
360	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
361	C₂²×C₁₃	#576	1	1	yes	characteristic
362	C₂²×C₁₃	#577	1	1	yes	characteristic
363	C₄×C₁₃	—	2	2	no	—
364	C₄×C₁₃	—	2	2	no	—
365	C₄×C₁₃	—	2	2	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	—	4	2	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	4	2	no	—
371	C₄×C₁₃	—	8	1	no	—
372	C₄×C₁₃	—	8	1	no	—
373	C₄×C₁₃	—	8	1	no	—
374	C₄×C₁₃	—	8	1	no	—
375	C₄×C₁₃	—	8	1	no	—
376	C₄×C₁₃	#529	1	1	yes	characteristic
377	C₄×C₁₃	#539	1	1	yes	characteristic
378	C₄×C₁₃	#546	1	1	yes	characteristic
379	C₄×C₁₃	#547	1	1	yes	characteristic
380	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×Q₁₆	—	2	2	no	—
386	C₂×Q₁₆	—	2	2	no	—
387	C₂×Q₁₆	—	4	1	no	—
388	C₂²×C₈	—	2	2	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	—	4	1	no	—
391	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	2	2	no	—
398	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	—	4	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	2	no	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	4	1	no	—
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
429	#107	—	2	2	no	—
430	#107	—	2	2	no	—
431	#107	—	2	2	no	—
432	C₄⋊C₈	—	2	2	no	—
433	C₄⋊C₈	—	4	1	no	—
434	#103	—	2	2	no	—
435	#103	—	2	2	no	—
436	#103	—	2	2	no	—
437	#103	—	2	2	no	—
438	#103	—	2	2	no	—
439	#103	—	4	1	no	—
440	C₂²⋊C₈	—	2	2	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	D₄×C₁₃	1	1	yes	characteristic
450	#95	D₄×C₁₃	1	1	yes	characteristic
451	C₂×C₁₃	—	2	4	no	—
452	C₂×C₁₃	#2425	1	1	yes	characteristic
453	C₂×C₁₃	C₂×#462	1	1	yes	characteristic
454	C₂×C₁₃	#3045	1	1	yes	characteristic
455	C₂×C₁₃	#3299	1	1	yes	characteristic
456	C₂×C₁₃	#3314	1	1	yes	characteristic
457	C₂×C₁₃	#3338	1	1	yes	characteristic
458	C₂×C₁₃	#3344	1	1	yes	characteristic
459	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	8	1	no	—
488	C₂²×C₄	—	8	1	no	—
489	C₂²×C₄	—	8	1	no	—
490	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
494	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₁₃×#41	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
498	Q₁₆	—	4	4	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	4	4	no	—
511	C₂×C₈	C₁₃×#41	1	2	yes	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	4	2	no	—
524	C₄⋊C₄	—	4	2	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	8	1	no	—
528	C₄⋊C₄	—	8	1	no	—
529	C₄⋊C₄	—	8	1	no	—
530	C₄⋊C₄	—	8	1	no	—
531	C₄⋊C₄	—	8	1	no	—
532	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
533	C₄⋊C₄	C₁₃×#41	1	2	yes	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	C₁₃×Q₁₆	1	4	yes	complemented
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	4	2	no	—
543	C₄²	—	8	1	no	—
544	C₁₃	#25206	1	1	yes	characteristic, direct product factor, Sylow
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	C₁₃×#121	1	2	yes	—
550	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
551	C₂³	C₁₃×#137	1	2	yes	—
552	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
553	Q₈	—	2	2	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	4	1	no	—
556	Q₈	—	4	1	no	—
557	Q₈	—	4	1	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	—	8	4	no	—
603	C₂×C₄	C₁₃×#121	1	2	yes	—
604	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
605	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
606	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
607	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
608	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
609	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
610	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
612	C₈	—	2	2	no	—
613	C₈	—	4	1	no	—
614	C₈	—	4	1	no	—
615	C₈	—	4	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	C₁₃×#462	1	4	yes	—
623	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
624	C₂²	C₁₃×#546	1	1	yes	characteristic
625	C₂²	C₁₃×#547	1	1	yes	characteristic
626	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
627	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
628	C₂²	C₁₃×#576	1	1	yes	characteristic
629	C₂²	C₁₃×#577	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	2	no	—
638	C₄	—	8	1	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	C₁₃×#529	1	1	yes	characteristic
644	C₄	C₁₃×#539	1	1	yes	characteristic
645	C₄	C₁₃×#546	1	1	yes	characteristic
646	C₄	C₁₃×#547	1	1	yes	characteristic
647	C₂	—	2	4	no	—
648	C₂	C₁₃×#2425	1	1	yes	characteristic
649	C₂	C₂×C₁₃×#462	1	1	yes	characteristic
650	C₂	C₁₃×#3045	1	1	yes	characteristic
651	C₂	C₁₃×#3299	1	1	yes	characteristic
652	C₂	C₁₃×#3314	1	1	yes	characteristic
653	C₂	C₁₃×#3338	1	1	yes	characteristic
654	C₂	C₁₃×#3344	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₃×#2083	C₂	semidirect
6. C₁₃×#2072	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2056	C₂	semidirect
9. C₁₃×#1947	C₂	semidirect
10. C₁₃×#1928	C₂	semidirect
11. C₁₃×#1878	C₂	semidirect
14. C₁₃×#1803	C₂	semidirect
132. #25206	C₁₃	direct (N × H)
211. C₁₃×C₂²⋊C₄	Q₁₆	semidirect
222. #2083	C₂×C₁₃	semidirect
223. #2072	C₂×C₁₃	semidirect
224. #2068	C₂×C₁₃	semidirect
225. #2056	C₂×C₁₃	semidirect
226. #1947	C₂×C₁₃	semidirect
227. #1928	C₂×C₁₃	semidirect
228. #1878	C₂×C₁₃	semidirect
231. #1803	C₂×C₁₃	semidirect
537. C₂²⋊C₄	C₁₃×Q₁₆	semidirect
544. C₁₃	#25206	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×#484	2
C₂×C₁₃×#467	2
C₁₃×#2502	2
C₁₃×#2360	2
C₁₃×#2083	2
C₁₃×#2072	2
C₁₃×#2068	2
C₁₃×#2056	2
C₁₃×#1947	2
C₁₃×#1928	2
C₁₃×#1878	2
C₁₃×#1872	2
C₁₃×#1850	2
C₁₃×#1803	2
C₂×C₁₃×#340	2
#25206	13

Subgroups — C13×#25206 #15711545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25206 #15711545