Subgroups — C₁₃×#24710 #15711049

Order 3328.

828 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#432	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×#2077	C₂	1	2	yes	maximal
6	C₁₃×#2036	C₂	1	2	yes	maximal
7	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1943	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1935	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#475	—	2	4	no	—
18	C₁₃×#432	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#97	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	2	yes	—
37	C₁₃×#380	C₂²	1	1	yes	characteristic
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	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₂²⋊Q₈	—	2	2	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	4	4	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	2	no	—
75	C₂×C₄²×C₁₃	—	2	2	no	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×#107	—	2	4	no	—
83	C₁₃×#106	—	2	4	no	—
84	C₁₃×C₄⋊C₈	—	2	2	no	—
85	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
86	C₁₃×#103	—	2	4	no	—
87	C₁₃×#103	—	2	4	no	—
88	C₁₃×C₂²⋊C₈	—	2	4	no	—
89	C₁₃×#97	—	2	4	no	—
90	C₁₃×#95	—	2	1	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	1	no	—
94	C₁₃×#95	—	2	1	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	#24710	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
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	—	4	2	no	—
105	C₂×Q₈×C₁₃	—	4	2	no	—
106	C₂×Q₈×C₁₃	—	4	2	no	—
107	C₂×Q₈×C₁₃	#41	1	2	yes	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	4	1	no	—
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	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
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	C₂×D₄	1	4	yes	—
138	C₁₃×C₄⋊C₄	—	2	4	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₄⋊C₄	—	4	2	no	—
150	C₁₃×C₄⋊C₄	—	4	4	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	—	4	2	no	—
153	C₁₃×C₄⋊C₄	—	4	2	no	—
154	C₁₃×C₄⋊C₄	#41	1	2	yes	—
155	C₁₃×C₂²⋊C₄	—	2	4	no	—
156	C₁₃×C₂²⋊C₄	—	4	4	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	4	2	no	—
163	C₄²×C₁₃	—	4	2	no	—
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₄²×C₁₃	#41	1	2	yes	—
166	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂×#432	C₂×C₁₃	1	1	yes	characteristic
168	#2857	C₂×C₁₃	1	1	yes	characteristic
169	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
170	#2077	C₂×C₁₃	1	2	yes	—
171	#2036	C₂×C₁₃	1	2	yes	—
172	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1943	C₂×C₁₃	1	2	yes	complemented
175	#1935	C₂×C₁₃	1	2	yes	complemented
176	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂³×C₁₃	—	2	1	no	—
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	2	1	no	—
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	#137	1	2	yes	—
184	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	Q₈×C₁₃	—	2	2	no	—
186	Q₈×C₁₃	—	2	2	no	—
187	Q₈×C₁₃	—	4	1	no	—
188	Q₈×C₁₃	—	4	1	no	—
189	Q₈×C₁₃	—	8	4	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	4	4	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	4	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	#121	1	2	yes	—
226	C₂×C₄×C₁₃	#121	1	2	yes	—
227	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₁₃	#137	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
235	C₈×C₁₃	—	2	4	no	—
236	C₈×C₁₃	—	4	2	no	—
237	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×C₂²⋊Q₈	—	2	1	no	—
239	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
242	#475	—	2	4	no	—
243	#432	—	2	4	no	—
244	C₂×#107	C₂²×C₁₃	1	2	yes	—
245	C₂×#106	C₂²×C₁₃	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×#103	C₂²×C₁₃	1	2	yes	—
249	C₂×#103	C₂²×C₁₃	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
251	C₂×#97	C₂²×C₁₃	1	2	yes	—
252	#391	—	2	1	no	—
253	#391	C₂²×C₁₃	1	1	yes	characteristic
254	#389	—	2	1	no	—
255	#389	C₂²×C₁₃	1	2	yes	—
256	#389	C₂²×C₁₃	1	1	yes	characteristic
257	#387	—	2	1	no	—
258	#385	—	2	1	no	—
259	#384	C₂²×C₁₃	1	1	yes	characteristic
260	#380	—	2	1	no	—
261	#380	C₂²×C₁₃	1	1	yes	characteristic
262	#380	C₂²×C₁₃	1	2	yes	—
263	C₄×C₄⋊C₄	—	2	1	no	—
264	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	—	2	1	no	—
266	#340	C₂²×C₁₃	1	2	yes	—
267	#340	C₂²×C₁₃	1	2	yes	—
268	#340	C₂²×C₁₃	1	2	yes	—
269	#340	C₂²×C₁₃	1	2	yes	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	4	1	no	—
274	C₂²×C₁₃	—	4	1	no	—
275	C₂²×C₁₃	—	4	1	no	—
276	C₂²×C₁₃	—	4	1	no	—
277	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
278	C₂²×C₁₃	#525	1	1	yes	characteristic
279	C₂²×C₁₃	#536	1	1	yes	characteristic
280	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
282	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
283	C₂²×C₁₃	#575	1	1	yes	characteristic
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	—	4	1	no	—
290	C₄×C₁₃	—	8	2	no	—
291	C₄×C₁₃	—	8	1	no	—
292	C₄×C₁₃	—	8	2	no	—
293	C₄×C₁₃	—	8	1	no	—
294	C₄×C₁₃	#468	1	4	yes	—
295	C₄×C₁₃	#547	1	1	yes	characteristic
296	C₄×C₁₃	#548	1	1	yes	characteristic
297	C₄×C₁₃	#552	1	1	yes	characteristic
298	C₄×C₁₃	#556	1	1	yes	characteristic
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
301	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
302	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
305	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₂²⋊Q₈	—	2	2	no	—
309	C₂²⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	4	4	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₄²	—	2	2	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
336	#107	—	2	4	no	—
337	#106	—	2	4	no	—
338	C₄⋊C₈	—	2	2	no	—
339	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
340	#103	—	2	4	no	—
341	#103	—	2	4	no	—
342	C₂²⋊C₈	—	2	4	no	—
343	#97	—	2	4	no	—
344	#95	—	2	1	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	#95	—	2	1	no	—
349	#95	—	2	2	no	—
350	#95	—	2	2	no	—
351	C₂×C₁₃	—	4	2	no	—
352	C₂×C₁₃	#2415	1	1	yes	characteristic
353	C₂×C₁₃	C₂×#468	1	1	yes	characteristic
354	C₂×C₁₃	#3056	1	1	yes	characteristic
355	C₂×C₁₃	#3113	1	1	yes	characteristic
356	C₂×C₁₃	#3115	1	1	yes	characteristic
357	C₂×C₁₃	#3237	1	1	yes	characteristic
358	C₂×C₁₃	#3239	1	1	yes	characteristic
359	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	—	4	2	no	—
368	C₂×Q₈	C₁₃×#41	1	2	yes	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
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	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	4	4	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	C₁₃×#41	1	2	yes	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	4	2	no	—
424	C₄²	—	4	2	no	—
425	C₄²	C₂×D₄×C₁₃	1	2	yes	—
426	C₄²	C₁₃×#41	1	2	yes	—
427	C₁₃	#24710	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	C₁₃×#137	1	2	yes	—
435	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	4	1	no	—
440	Q₈	—	8	4	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	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	1	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	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	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	C₁₃×#121	1	2	yes	—
477	C₂×C₄	C₁₃×#121	1	2	yes	—
478	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
479	C₂×C₄	C₁₃×#137	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
481	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
482	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
483	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
484	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
485	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
486	C₈	—	2	4	no	—
487	C₈	—	4	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
496	C₂²	C₁₃×#525	1	1	yes	characteristic
497	C₂²	C₁₃×#536	1	1	yes	characteristic
498	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
499	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
500	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
501	C₂²	C₁₃×#575	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	2	no	—
508	C₄	—	8	2	no	—
509	C₄	—	8	1	no	—
510	C₄	—	8	2	no	—
511	C₄	—	8	1	no	—
512	C₄	C₁₃×#468	1	4	yes	—
513	C₄	C₁₃×#547	1	1	yes	characteristic
514	C₄	C₁₃×#548	1	1	yes	characteristic
515	C₄	C₁₃×#552	1	1	yes	characteristic
516	C₄	C₁₃×#556	1	1	yes	characteristic
517	C₂	—	4	2	no	—
518	C₂	C₁₃×#2415	1	1	yes	characteristic
519	C₂	C₂×C₁₃×#468	1	1	yes	characteristic
520	C₂	C₁₃×#3056	1	1	yes	characteristic
521	C₂	C₁₃×#3113	1	1	yes	characteristic
522	C₂	C₁₃×#3115	1	1	yes	characteristic
523	C₂	C₁₃×#3237	1	1	yes	characteristic
524	C₂	C₁₃×#3239	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×#475	C₂	semidirect
7. C₁₃×#1988	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
9. C₁₃×#1943	C₂	semidirect
10. C₁₃×#1935	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
97. #24710	C₁₃	direct (N × H)
166. C₂×#475	C₂×C₁₃	semidirect
172. #1988	C₂×C₁₃	semidirect
173. #1947	C₂×C₁₃	semidirect
174. #1943	C₂×C₁₃	semidirect
175. #1935	C₂×C₁₃	semidirect
176. #1803	C₂×C₁₃	semidirect
427. C₁₃	#24710	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×#475	2
C₂×C₁₃×#432	2
C₁₃×#2857	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2077	2
C₁₃×#2036	2
C₁₃×#1988	2
C₁₃×#1947	2
C₁₃×#1943	2
C₁₃×#1935	2
C₁₃×#1803	2
#24710	13

Subgroups — C13×#24710 #15711049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24710 #15711049