Subgroups — C₁₃×#22615 #15708954

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2345	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2344	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1944	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1920	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1919	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1824	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1823	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1776	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1752	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	—	2	1	no	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₄	1	8	yes	complemented
18	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#97	C₂²	1	2	yes	—
24	C₁₃×#389	C₂²	1	2	yes	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#387	—	2	2	no	—
27	C₁₃×#387	—	2	2	no	—
28	C₁₃×#381	—	2	1	no	—
29	C₁₃×#380	—	2	1	no	—
30	C₁₃×#380	C₂²	1	1	yes	characteristic
31	C₁₃×#380	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
35	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂³×C₄×C₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	—	2	4	no	—
46	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#117	—	4	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
72	C₁₃×#107	—	2	4	no	—
73	C₁₃×#106	C₂×C₄	1	4	yes	—
74	C₁₃×#106	C₂×C₄	1	4	yes	—
75	C₁₃×#106	C₂×C₄	1	4	yes	—
76	C₁₃×#106	C₂×C₄	1	4	yes	—
77	C₁₃×C₂²⋊C₈	—	2	2	no	—
78	C₁₃×#97	—	2	4	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	1	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	D₄	1	2	yes	—
86	#22615	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	—	4	2	no	—
100	C₂²×C₄×C₁₃	—	8	2	no	—
101	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	#41	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	8	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₃	#41	1	4	yes	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	4	4	no	—
126	C₁₃×C₄⋊C₄	—	8	2	no	—
127	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
131	C₁₃×C₂²⋊C₄	—	2	2	no	—
132	C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	4	4	no	—
138	C₄²×C₁₃	—	8	2	no	—
139	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic
140	#2345	C₂×C₁₃	1	1	yes	characteristic
141	#2344	C₂×C₁₃	1	1	yes	characteristic
142	#1944	C₂×C₁₃	1	2	yes	complemented
143	#1920	C₂×C₁₃	1	2	yes	complemented
144	#1919	C₂×C₁₃	1	2	yes	complemented
145	#1824	C₂×C₁₃	1	1	yes	characteristic
146	#1823	C₂×C₁₃	1	1	yes	characteristic
147	#1808	C₂×C₁₃	1	1	yes	characteristic
148	#1776	C₂×C₁₃	1	2	yes	complemented
149	#1752	C₂×C₁₃	1	1	yes	characteristic
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	—	2	2	no	—
152	C₂³×C₁₃	C₄×D₄	1	2	yes	—
153	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
154	C₂³×C₁₃	#137	1	2	yes	—
155	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	8	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	8	4	no	—
184	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
189	C₈×C₁₃	—	2	2	no	—
190	C₈×C₁₃	—	4	2	no	—
191	C₈×C₁₃	#117	1	4	yes	complemented
192	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×#117	—	2	1	no	—
194	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
195	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#107	C₂²×C₁₃	1	2	yes	—
197	C₂×#106	C₄×C₁₃	1	8	yes	complemented
198	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×#97	C₂²×C₁₃	1	2	yes	—
204	#389	C₂²×C₁₃	1	2	yes	—
205	#389	C₂²×C₁₃	1	2	yes	—
206	#387	—	2	2	no	—
207	#387	—	2	2	no	—
208	#381	—	2	1	no	—
209	#380	—	2	1	no	—
210	#380	C₂²×C₁₃	1	1	yes	characteristic
211	#380	C₂²×C₁₃	1	1	yes	characteristic
212	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
213	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
214	C₄×C₂²⋊C₄	—	2	1	no	—
215	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
216	#340	C₂²×C₁₃	1	2	yes	—
217	#340	C₂²×C₁₃	1	2	yes	—
218	#340	C₂²×C₁₃	1	2	yes	—
219	#340	C₂²×C₁₃	1	2	yes	—
220	#340	C₂²×C₁₃	1	2	yes	—
221	#336	C₂²×C₁₃	1	2	yes	—
222	C₂²×C₁₃	—	2	4	no	—
223	C₂²×C₁₃	—	2	4	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	#440	1	4	yes	—
227	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₁₃	#547	1	2	yes	—
229	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
231	C₂²×C₁₃	#577	1	2	yes	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	4	2	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	—	4	2	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	—	8	2	no	—
241	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
242	C₄×C₁₃	#519	1	1	yes	characteristic
243	C₄×C₁₃	#552	1	2	yes	—
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
247	C₂²×C₈	—	2	4	no	—
248	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
249	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	#117	—	4	4	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
261	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
274	#107	—	2	4	no	—
275	#106	C₂×C₄×C₁₃	1	4	yes	—
276	#106	C₂×C₄×C₁₃	1	4	yes	—
277	#106	C₂×C₄×C₁₃	1	4	yes	—
278	#106	C₂×C₄×C₁₃	1	4	yes	—
279	C₂²⋊C₈	—	2	2	no	—
280	#97	—	2	4	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	1	no	—
285	#95	—	2	1	no	—
286	#95	—	2	2	no	—
287	#95	D₄×C₁₃	1	2	yes	—
288	C₂×C₁₃	—	2	4	no	—
289	C₂×C₁₃	#2344	1	1	yes	characteristic
290	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
291	C₂×C₁₃	#2949	1	1	yes	characteristic
292	C₂×C₁₃	#3344	1	2	yes	—
293	C₂×C₁₃	#3345	1	2	yes	—
294	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₁₃×#41	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	8	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
320	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
321	C₂×C₈	C₁₃×#41	1	4	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
335	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
336	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
337	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	4	4	no	—
345	C₄²	—	8	2	no	—
346	C₁₃	#22615	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₄×D₄×C₁₃	1	2	yes	—
350	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
351	C₂³	C₁₃×#137	1	2	yes	—
352	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	8	4	no	—
381	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
382	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
383	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
384	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
385	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
386	C₈	—	2	2	no	—
387	C₈	—	4	2	no	—
388	C₈	C₁₃×#117	1	4	yes	complemented
389	C₂²	—	2	4	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	C₁₃×#440	1	4	yes	—
394	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
395	C₂²	C₁₃×#547	1	2	yes	—
396	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
398	C₂²	C₁₃×#577	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	8	2	no	—
407	C₄	—	8	2	no	—
408	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
409	C₄	C₁₃×#519	1	1	yes	characteristic
410	C₄	C₁₃×#552	1	2	yes	—
411	C₂	—	2	4	no	—
412	C₂	C₁₃×#2344	1	1	yes	characteristic
413	C₂	C₂×C₁₃×#440	1	1	yes	characteristic
414	C₂	C₁₃×#2949	1	1	yes	characteristic
415	C₂	C₁₃×#3344	1	2	yes	—
416	C₂	C₁₃×#3345	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×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
4. C₁₃×#1944	C₂	semidirect
5. C₁₃×#1920	C₂	semidirect
6. C₁₃×#1919	C₂	semidirect
10. C₁₃×#1776	C₂	semidirect
17. C₂×C₁₃×#106	C₄	semidirect
86. #22615	C₁₃	direct (N × H)
142. #1944	C₂×C₁₃	semidirect
143. #1920	C₂×C₁₃	semidirect
144. #1919	C₂×C₁₃	semidirect
148. #1776	C₂×C₁₃	semidirect
191. C₈×C₁₃	#117	semidirect
197. C₂×#106	C₄×C₁₃	semidirect
346. C₁₃	#22615	direct (N × H)
388. C₈	C₁₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#106	2
C₁₃×#2345	2
C₁₃×#2344	2
C₁₃×#1944	2
C₁₃×#1920	2
C₁₃×#1919	2
C₁₃×#1824	2
C₁₃×#1823	2
C₁₃×#1808	2
C₁₃×#1776	2
C₁₃×#1752	2
#22615	13

Subgroups — C13×#22615 #15708954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22615 #15708954