Subgroups — C₁₃×#22737 #15709076

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#446	C₂	1	2	yes	maximal
2	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1940	C₂	1	2	yes	maximal
4	C₁₃×#1940	C₂	1	2	yes	maximal
5	C₁₃×#1939	C₂	1	2	yes	maximal
6	C₁₃×#1832	C₂	1	2	yes	maximal
7	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1768	C₂	1	2	yes	maximal
9	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#446	—	2	8	no	—
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#97	C₂²	1	2	yes	—
19	C₂×C₁₃×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
21	C₁₃×#391	C₄	1	1	yes	characteristic
22	C₁₃×#391	C₄	1	1	yes	characteristic
23	C₁₃×#389	C₄	1	1	yes	characteristic
24	C₁₃×#389	C₄	1	1	yes	characteristic
25	C₁₃×#387	C₄	1	2	yes	—
26	C₁₃×#387	C₄	1	2	yes	—
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#376	C₂²	1	2	yes	—
30	C₄³×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#336	C₂²	1	1	yes	characteristic
32	C₁₃×#336	C₂²	1	1	yes	characteristic
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	1	yes	characteristic
35	C₁₃×#336	C₂²	1	1	yes	characteristic
36	C₁₃×#336	C₂²	1	2	yes	—
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₄×Q₈×C₁₃	D₄	1	4	yes	—
44	C₄×Q₈×C₁₃	Q₈	1	4	yes	—
45	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊C₈	—	2	4	no	—
61	C₁₃×C₄⋊C₈	—	2	4	no	—
62	C₁₃×C₄⋊C₈	—	2	4	no	—
63	C₁₃×C₄⋊C₈	—	2	4	no	—
64	C₁₃×C₄⋊C₈	—	2	4	no	—
65	C₁₃×C₄⋊C₈	—	2	4	no	—
66	C₁₃×#97	—	2	4	no	—
67	C₁₃×#97	—	2	4	no	—
68	C₄×C₈×C₁₃	—	2	4	no	—
69	C₁₃×#95	C₂×C₄	1	2	yes	—
70	C₁₃×#95	C₂×C₄	1	2	yes	—
71	C₁₃×#95	C₂×C₄	1	2	yes	—
72	C₁₃×#95	C₂×C₄	1	2	yes	—
73	C₁₃×#95	C₂×C₄	1	2	yes	—
74	C₁₃×#95	C₂×C₄	1	2	yes	—
75	C₁₃×#95	C₂×C₄	1	2	yes	—
76	#22737	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂×Q₈×C₁₃	—	4	1	no	—
78	C₂×Q₈×C₁₃	—	4	1	no	—
79	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
91	C₂×C₈×C₁₃	—	2	2	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	2	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	2	2	no	—
100	C₂×C₈×C₁₃	—	2	2	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	#41	1	4	yes	—
103	C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₁₃×C₄⋊C₄	—	4	1	no	—
105	C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₁₃×C₄⋊C₄	—	4	2	no	—
107	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
108	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
109	C₄²×C₁₃	—	2	2	no	—
110	C₄²×C₁₃	—	2	2	no	—
111	C₄²×C₁₃	—	2	2	no	—
112	C₄²×C₁₃	—	2	2	no	—
113	C₄²×C₁₃	—	2	2	no	—
114	C₄²×C₁₃	—	4	1	no	—
115	C₄²×C₁₃	—	4	1	no	—
116	C₄²×C₁₃	—	4	1	no	—
117	C₄²×C₁₃	C₂×D₄	1	4	yes	—
118	C₄²×C₁₃	C₂×D₄	1	2	yes	—
119	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
120	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
121	C₂×#446	C₂×C₁₃	1	2	yes	—
122	#2295	C₂×C₁₃	1	1	yes	characteristic
123	#1940	C₂×C₁₃	1	2	yes	—
124	#1940	C₂×C₁₃	1	2	yes	—
125	#1939	C₂×C₁₃	1	2	yes	—
126	#1832	C₂×C₁₃	1	2	yes	—
127	#1831	C₂×C₁₃	1	1	yes	characteristic
128	#1768	C₂×C₁₃	1	2	yes	—
129	#1767	C₂×C₁₃	1	1	yes	characteristic
130	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
131	Q₈×C₁₃	—	4	4	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	1	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
158	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃	#131	1	2	yes	—
162	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
165	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
166	C₈×C₁₃	—	2	4	no	—
167	C₈×C₁₃	—	4	2	no	—
168	C₈×C₁₃	—	4	2	no	—
169	C₈×C₁₃	—	4	2	no	—
170	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
171	#446	—	2	8	no	—
172	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
173	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
174	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
175	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
176	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
177	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
178	C₂×#97	C₂²×C₁₃	1	2	yes	—
179	C₂×#97	C₂²×C₁₃	1	2	yes	—
180	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
181	#391	C₄×C₁₃	1	1	yes	characteristic
182	#391	C₄×C₁₃	1	1	yes	characteristic
183	#389	C₄×C₁₃	1	1	yes	characteristic
184	#389	C₄×C₁₃	1	1	yes	characteristic
185	#387	C₄×C₁₃	1	2	yes	—
186	#387	C₄×C₁₃	1	2	yes	—
187	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
188	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
189	#376	C₂²×C₁₃	1	2	yes	—
190	C₄³	C₂²×C₁₃	1	1	yes	characteristic
191	#336	C₂²×C₁₃	1	2	yes	—
192	#336	C₂²×C₁₃	1	1	yes	characteristic
193	#336	C₂²×C₁₃	1	1	yes	characteristic
194	#336	C₂²×C₁₃	1	1	yes	characteristic
195	#336	C₂²×C₁₃	1	2	yes	—
196	#336	C₂²×C₁₃	1	2	yes	—
197	#336	C₂²×C₁₃	1	1	yes	characteristic
198	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
200	C₂²×C₁₃	#519	1	1	yes	characteristic
201	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
202	C₂²×C₁₃	#568	1	1	yes	characteristic
203	C₂²×C₁₃	#568	1	1	yes	characteristic
204	C₂²×C₁₃	#568	1	1	yes	characteristic
205	C₄×C₁₃	—	2	2	no	—
206	C₄×C₁₃	—	2	4	no	—
207	C₄×C₁₃	—	2	2	no	—
208	C₄×C₁₃	—	2	4	no	—
209	C₄×C₁₃	—	2	2	no	—
210	C₄×C₁₃	—	4	1	no	—
211	C₄×C₁₃	—	4	2	no	—
212	C₄×C₁₃	—	4	2	no	—
213	C₄×C₁₃	—	4	1	no	—
214	C₄×C₁₃	—	4	1	no	—
215	C₄×C₁₃	#548	1	2	yes	—
216	C₄×C₁₃	#557	1	2	yes	—
217	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
219	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
220	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
221	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
222	C₄×Q₈	D₄×C₁₃	1	4	yes	—
223	C₄×Q₈	Q₈×C₁₃	1	4	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
225	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
237	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
239	C₄⋊C₈	—	2	4	no	—
240	C₄⋊C₈	—	2	4	no	—
241	C₄⋊C₈	—	2	4	no	—
242	C₄⋊C₈	—	2	4	no	—
243	C₄⋊C₈	—	2	4	no	—
244	C₄⋊C₈	—	2	4	no	—
245	#97	—	2	4	no	—
246	#97	—	2	4	no	—
247	C₄×C₈	—	2	4	no	—
248	#95	C₂×C₄×C₁₃	1	2	yes	—
249	#95	C₂×C₄×C₁₃	1	2	yes	—
250	#95	C₂×C₄×C₁₃	1	2	yes	—
251	#95	C₂×C₄×C₁₃	1	2	yes	—
252	#95	C₂×C₄×C₁₃	1	2	yes	—
253	#95	C₂×C₄×C₁₃	1	2	yes	—
254	#95	C₂×C₄×C₁₃	1	2	yes	—
255	C₂×C₁₃	#2351	1	1	yes	characteristic
256	C₂×C₁₃	#2905	1	1	yes	characteristic
257	C₂×C₁₃	#2906	1	1	yes	characteristic
258	C₂×C₁₃	#2967	1	1	yes	characteristic
259	C₂×C₁₃	#2968	1	1	yes	characteristic
260	C₂×C₁₃	#2985	1	1	yes	characteristic
261	C₂×C₁₃	#2987	1	1	yes	characteristic
262	C₂×Q₈	—	4	1	no	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×Q₈	C₁₃×C₄⋊C₄	1	4	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
269	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₁₃×#41	1	4	yes	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
293	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	4	1	no	—
300	C₄²	—	4	1	no	—
301	C₄²	—	4	1	no	—
302	C₄²	C₂×D₄×C₁₃	1	4	yes	—
303	C₄²	C₂×D₄×C₁₃	1	2	yes	—
304	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
305	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
306	C₁₃	#22737	1	1	yes	characteristic, direct product factor, Sylow
307	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
308	Q₈	—	4	4	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
335	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
336	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
337	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
338	C₂×C₄	C₁₃×#131	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
341	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
342	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
343	C₈	—	2	4	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
348	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
349	C₂²	C₁₃×#519	1	1	yes	characteristic
350	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
351	C₂²	C₁₃×#568	1	1	yes	characteristic
352	C₂²	C₁₃×#568	1	1	yes	characteristic
353	C₂²	C₁₃×#568	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	4	no	—
358	C₄	—	2	2	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	C₁₃×#548	1	2	yes	—
365	C₄	C₁₃×#557	1	2	yes	—
366	C₂	C₁₃×#2351	1	1	yes	characteristic
367	C₂	C₁₃×#2905	1	1	yes	characteristic
368	C₂	C₁₃×#2906	1	1	yes	characteristic
369	C₂	C₁₃×#2967	1	1	yes	characteristic
370	C₂	C₁₃×#2968	1	1	yes	characteristic
371	C₂	C₁₃×#2985	1	1	yes	characteristic
372	C₂	C₁₃×#2987	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle, prime radical	C₂³×C₁₃	C₂³×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
76. #22737	C₁₃	direct (N × H)
306. C₁₃	#22737	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×#446	2
C₁₃×#2295	2
C₁₃×#1940	2
C₁₃×#1939	2
C₁₃×#1832	2
C₁₃×#1831	2
C₁₃×#1768	2
C₁₃×#1767	2
#22737	13

Subgroups — C13×#22737 #15709076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22737 #15709076