Subgroups — C₁₃×#24837 #15711176

Order 3328.

904 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2087	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2068	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1892	C₂	1	2	yes	maximal
10	C₁₃×#1808	C₂	1	2	yes	maximal
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#477	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	—	2	4	no	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₁₃×#391	—	2	1	no	—
28	C₁₃×#391	C₂²	1	1	yes	characteristic
29	C₁₃×#389	—	2	1	no	—
30	C₁₃×#389	C₂²	1	1	yes	characteristic
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#387	—	2	1	no	—
33	C₁₃×#385	—	2	1	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₁₃×#380	—	2	1	no	—
36	C₁₃×#380	C₂²	1	1	yes	characteristic
37	C₁₃×#380	C₂²	1	2	yes	—
38	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	—	2	4	no	—
51	C₂²×C₈×C₁₃	—	2	4	no	—
52	C₂²×C₈×C₁₃	—	4	2	no	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₂²⋊Q₈	—	2	2	no	—
58	C₁₃×C₂²⋊Q₈	—	4	4	no	—
59	C₁₃×C₂²⋊Q₈	Q₈	1	4	yes	complemented
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₄²×C₁₃	—	2	2	no	—
78	C₂×C₄²×C₁₃	—	2	2	no	—
79	C₂×C₄²×C₁₃	—	2	1	no	—
80	C₂×C₄²×C₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#107	—	2	4	no	—
86	C₁₃×#107	—	4	2	no	—
87	C₁₃×C₄⋊C₈	—	2	4	no	—
88	C₁₃×C₄⋊C₈	—	2	2	no	—
89	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
90	C₁₃×#103	—	2	4	no	—
91	C₁₃×#103	—	4	2	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	1	no	—
94	C₁₃×#95	—	2	1	no	—
95	C₁₃×#95	—	2	1	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	2	no	—
98	C₁₃×#95	—	2	2	no	—
99	#24837	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	4	2	no	—
107	C₂×Q₈×C₁₃	—	4	2	no	—
108	C₂×Q₈×C₁₃	—	4	2	no	—
109	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	4	1	no	—
125	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
132	C₂²×C₄×C₁₃	#41	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	4	8	no	—
140	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
141	C₁₃×C₄⋊C₄	—	2	4	no	—
142	C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	—	4	2	no	—
153	C₁₃×C₄⋊C₄	—	4	4	no	—
154	C₁₃×C₄⋊C₄	—	4	2	no	—
155	C₁₃×C₄⋊C₄	—	4	2	no	—
156	C₁₃×C₄⋊C₄	—	4	2	no	—
157	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
158	C₁₃×C₂²⋊C₄	—	2	4	no	—
159	C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₁₃×C₂²⋊C₄	—	4	4	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	2	2	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	—	2	1	no	—
165	C₄²×C₁₃	—	4	2	no	—
166	C₄²×C₁₃	—	4	2	no	—
167	C₄²×C₁₃	C₂×D₄	1	2	yes	—
168	C₄²×C₁₃	#41	1	2	yes	—
169	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
171	#2857	C₂×C₁₃	1	1	yes	characteristic
172	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
173	#2087	C₂×C₁₃	1	2	yes	complemented
174	#2068	C₂×C₁₃	1	2	yes	complemented
175	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1892	C₂×C₁₃	1	2	yes	—
178	#1808	C₂×C₁₃	1	2	yes	—
179	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	2	1	no	—
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	—	2	1	no	—
184	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
185	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
186	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
187	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	2	2	no	—
190	Q₈×C₁₃	—	4	1	no	—
191	Q₈×C₁₃	—	4	1	no	—
192	Q₈×C₁₃	—	8	4	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	8	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	4	4	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	1	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	#121	1	2	yes	—
227	C₂×C₄×C₁₃	#121	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
231	C₂×C₄×C₁₃	#135	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
238	C₈×C₁₃	—	2	4	no	—
239	C₈×C₁₃	—	4	2	no	—
240	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
241	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×C₂²⋊Q₈	—	2	1	no	—
243	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
246	#477	—	2	4	no	—
247	C₂×#107	C₂²×C₁₃	1	2	yes	—
248	C₂×#107	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄⋊C₈	—	2	4	no	—
250	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
252	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#103	C₂²×C₁₃	1	2	yes	—
254	C₂×#103	C₂²×C₁₃	1	2	yes	—
255	#391	—	2	1	no	—
256	#391	C₂²×C₁₃	1	1	yes	characteristic
257	#389	—	2	1	no	—
258	#389	C₂²×C₁₃	1	2	yes	—
259	#389	C₂²×C₁₃	1	1	yes	characteristic
260	#387	—	2	1	no	—
261	#385	—	2	1	no	—
262	#384	C₂²×C₁₃	1	1	yes	characteristic
263	#380	—	2	1	no	—
264	#380	C₂²×C₁₃	1	1	yes	characteristic
265	#380	C₂²×C₁₃	1	2	yes	—
266	C₄×C₄⋊C₄	—	2	1	no	—
267	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₄×C₂²⋊C₄	—	2	1	no	—
269	#340	C₂²×C₁₃	1	2	yes	—
270	#340	C₂²×C₁₃	1	2	yes	—
271	#340	C₂²×C₁₃	1	2	yes	—
272	#340	C₂²×C₁₃	1	2	yes	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	#477	1	4	yes	complemented
280	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
281	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
282	C₂²×C₁₃	#537	1	1	yes	characteristic
283	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
284	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
285	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₂²×C₁₃	#575	1	1	yes	characteristic
287	C₄×C₁₃	—	2	2	no	—
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	4	2	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	1	no	—
293	C₄×C₁₃	—	8	1	no	—
294	C₄×C₁₃	—	8	2	no	—
295	C₄×C₁₃	—	8	1	no	—
296	C₄×C₁₃	—	8	2	no	—
297	C₄×C₁₃	#467	1	4	yes	—
298	C₄×C₁₃	#546	1	1	yes	characteristic
299	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
300	C₄×C₁₃	#552	1	1	yes	characteristic
301	C₄×C₁₃	#554	1	1	yes	characteristic
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
304	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
305	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²×C₈	—	2	4	no	—
308	C₂²×C₈	—	2	4	no	—
309	C₂²×C₈	—	4	2	no	—
310	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
311	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	4	4	no	—
316	C₂²⋊Q₈	Q₈×C₁₃	1	4	yes	complemented
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
342	#107	—	2	4	no	—
343	#107	—	4	2	no	—
344	C₄⋊C₈	—	2	4	no	—
345	C₄⋊C₈	—	2	2	no	—
346	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
347	#103	—	2	4	no	—
348	#103	—	4	2	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	2	no	—
355	#95	—	2	2	no	—
356	C₂×C₁₃	—	2	4	no	—
357	C₂×C₁₃	#2417	1	1	yes	characteristic
358	C₂×C₁₃	C₂×#467	1	1	yes	characteristic
359	C₂×C₁₃	#3055	1	1	yes	characteristic
360	C₂×C₁₃	C₂×#477	1	1	yes	characteristic
361	C₂×C₁₃	#3076	1	1	yes	characteristic
362	C₂×C₁₃	#3247	1	1	yes	characteristic
363	C₂×C₁₃	#3249	1	1	yes	characteristic
364	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	—	4	2	no	—
373	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
390	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
396	C₂²×C₄	C₁₃×#41	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	4	8	no	—
404	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	4	2	no	—
430	C₄²	—	4	2	no	—
431	C₄²	C₂×D₄×C₁₃	1	2	yes	—
432	C₄²	C₁₃×#41	1	2	yes	—
433	C₁₃	#24837	1	1	yes	characteristic, direct product factor, Sylow
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
439	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
440	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
441	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	8	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	C₁₃×#121	1	2	yes	—
481	C₂×C₄	C₁₃×#121	1	2	yes	—
482	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
483	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
484	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
485	C₂×C₄	C₁₃×#135	1	2	yes	—
486	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
489	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
490	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
491	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
492	C₈	—	2	4	no	—
493	C₈	—	4	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	C₁₃×#477	1	4	yes	complemented
501	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
502	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
503	C₂²	C₁₃×#537	1	1	yes	characteristic
504	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
505	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
506	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
507	C₂²	C₁₃×#575	1	1	yes	characteristic
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	2	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	2	no	—
518	C₄	C₁₃×#467	1	4	yes	—
519	C₄	C₁₃×#546	1	1	yes	characteristic
520	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
521	C₄	C₁₃×#552	1	1	yes	characteristic
522	C₄	C₁₃×#554	1	1	yes	characteristic
523	C₂	—	2	4	no	—
524	C₂	C₁₃×#2417	1	1	yes	characteristic
525	C₂	C₂×C₁₃×#467	1	1	yes	characteristic
526	C₂	C₁₃×#3055	1	1	yes	characteristic
527	C₂	C₂×C₁₃×#477	1	1	yes	characteristic
528	C₂	C₁₃×#3076	1	1	yes	characteristic
529	C₂	C₁₃×#3247	1	1	yes	characteristic
530	C₂	C₁₃×#3249	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#477	C₂	semidirect
5. C₁₃×#2087	C₂	semidirect
6. C₁₃×#2068	C₂	semidirect
7. C₁₃×#1987	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
59. C₁₃×C₂²⋊Q₈	Q₈	semidirect
99. #24837	C₁₃	direct (N × H)
169. C₂×#477	C₂×C₁₃	semidirect
173. #2087	C₂×C₁₃	semidirect
174. #2068	C₂×C₁₃	semidirect
175. #1987	C₂×C₁₃	semidirect
176. #1947	C₂×C₁₃	semidirect
179. #1803	C₂×C₁₃	semidirect
279. C₂²×C₁₃	#477	semidirect
316. C₂²⋊Q₈	Q₈×C₁₃	semidirect
433. C₁₃	#24837	direct (N × H)
500. C₂²	C₁₃×#477	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#477	2
C₂²×C₁₃×C₄⋊C₈	2
C₁₃×#2857	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2087	2
C₁₃×#2068	2
C₁₃×#1987	2
C₁₃×#1947	2
C₁₃×#1892	2
C₁₃×#1808	2
C₁₃×#1803	2
#24837	13

Subgroups — C13×#24837 #15711176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24837 #15711176