Subgroups — C₁₃×#22642 #15708981

Order 3328.

680 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1940	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1924	C₂	1	2	yes	maximal
4	C₁₃×#1923	C₂	1	2	yes	maximal
5	C₁₃×#1840	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1771	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1768	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#97	C₂²	1	2	yes	—
18	C₂×C₁₃×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
20	C₁₃×#383	C₄	1	2	yes	—
21	C₁₃×#382	C₄	1	1	yes	characteristic
22	C₁₃×#382	C₄	1	1	yes	characteristic
23	C₁₃×#381	C₄	1	2	yes	—
24	C₁₃×#380	C₄	1	1	yes	characteristic
25	C₁₃×#380	C₄	1	1	yes	characteristic
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₁₃×#376	C₂²	1	2	yes	—
30	C₁₃×#336	C₂²	1	1	yes	characteristic
31	C₁₃×#336	C₂²	1	1	yes	characteristic
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₁₃×#336	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	2	yes	—
37	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₁₃	—	2	4	no	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊C₈	—	2	4	no	—
58	C₁₃×C₄⋊C₈	—	2	4	no	—
59	C₁₃×C₄⋊C₈	—	2	4	no	—
60	C₁₃×C₂²⋊C₈	—	2	4	no	—
61	C₁₃×C₂²⋊C₈	—	4	1	no	—
62	C₁₃×C₂²⋊C₈	—	4	1	no	—
63	C₁₃×#97	—	2	4	no	—
64	C₁₃×#97	—	4	2	no	—
65	C₄×C₈×C₁₃	—	4	2	no	—
66	C₁₃×#95	C₂×C₄	1	2	yes	—
67	C₁₃×#95	C₂×C₄	1	2	yes	—
68	C₁₃×#95	C₂×C₄	1	2	yes	—
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	#22642	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	1	no	—
82	C₂²×C₄×C₁₃	—	2	1	no	—
83	C₂²×C₄×C₁₃	—	4	1	no	—
84	C₂²×C₄×C₁₃	—	4	1	no	—
85	C₂²×C₄×C₁₃	—	4	1	no	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	#41	1	4	yes	—
108	C₁₃×C₄⋊C₄	—	4	1	no	—
109	C₁₃×C₄⋊C₄	—	4	1	no	—
110	C₁₃×C₄⋊C₄	—	4	1	no	—
111	C₁₃×C₄⋊C₄	—	4	1	no	—
112	C₁₃×C₂²⋊C₄	—	2	4	no	—
113	C₁₃×C₂²⋊C₄	—	4	2	no	—
114	C₄²×C₁₃	—	2	2	no	—
115	C₄²×C₁₃	—	2	2	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	2	2	no	—
119	C₄²×C₁₃	—	2	2	no	—
120	C₄²×C₁₃	—	2	2	no	—
121	C₄²×C₁₃	#41	1	4	yes	—
122	#2283	C₂×C₁₃	1	1	yes	characteristic
123	#1940	C₂×C₁₃	1	2	yes	complemented
124	#1924	C₂×C₁₃	1	2	yes	—
125	#1923	C₂×C₁₃	1	2	yes	—
126	#1840	C₂×C₁₃	1	2	yes	complemented
127	#1797	C₂×C₁₃	1	1	yes	characteristic
128	#1771	C₂×C₁₃	1	2	yes	complemented
129	#1768	C₂×C₁₃	1	2	yes	complemented
130	#1749	C₂×C₁₃	1	1	yes	characteristic
131	C₂³×C₁₃	—	2	1	no	—
132	C₂³×C₁₃	—	2	1	no	—
133	C₂³×C₁₃	—	2	1	no	—
134	C₂³×C₁₃	—	2	1	no	—
135	C₂³×C₁₃	—	2	1	no	—
136	C₂³×C₁₃	—	2	1	no	—
137	C₂³×C₁₃	#131	1	2	yes	—
138	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	1	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
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	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	4	4	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	#117	1	2	yes	—
169	C₂×C₄×C₁₃	#117	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
174	C₈×C₁₃	—	2	4	no	—
175	C₈×C₁₃	—	4	2	no	—
176	C₈×C₁₃	—	4	2	no	—
177	C₈×C₁₃	—	4	2	no	—
178	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
180	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
181	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
182	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
183	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×#97	C₂²×C₁₃	1	2	yes	—
186	C₂×#97	C₂²×C₁₃	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
188	#383	C₄×C₁₃	1	2	yes	—
189	#382	C₄×C₁₃	1	1	yes	characteristic
190	#382	C₄×C₁₃	1	1	yes	characteristic
191	#381	C₄×C₁₃	1	2	yes	—
192	#380	C₄×C₁₃	1	1	yes	characteristic
193	#380	C₄×C₁₃	1	1	yes	characteristic
194	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
195	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
196	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
197	#376	C₂²×C₁₃	1	2	yes	—
198	#336	C₂²×C₁₃	1	2	yes	—
199	#336	C₂²×C₁₃	1	1	yes	characteristic
200	#336	C₂²×C₁₃	1	2	yes	—
201	#336	C₂²×C₁₃	1	2	yes	—
202	#336	C₂²×C₁₃	1	2	yes	—
203	#336	C₂²×C₁₃	1	2	yes	—
204	#336	C₂²×C₁₃	1	1	yes	characteristic
205	C₂²×C₁₃	—	2	2	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	4	1	no	—
209	C₂²×C₁₃	—	4	1	no	—
210	C₂²×C₁₃	—	4	1	no	—
211	C₂²×C₁₃	—	4	1	no	—
212	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
213	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
214	C₂²×C₁₃	#520	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
216	C₂²×C₁₃	#568	1	1	yes	characteristic
217	C₂²×C₁₃	#568	1	1	yes	characteristic
218	C₂²×C₁₃	#568	1	1	yes	characteristic
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	4	1	no	—
222	C₄×C₁₃	—	4	1	no	—
223	C₄×C₁₃	—	4	1	no	—
224	C₄×C₁₃	—	4	2	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	4	2	no	—
228	C₄×C₁₃	#553	1	2	yes	—
229	C₄×C₁₃	#556	1	2	yes	—
230	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
231	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
234	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
235	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
236	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
248	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
249	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	4	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	4	1	no	—
255	C₂²⋊C₈	—	4	1	no	—
256	#97	—	2	4	no	—
257	#97	—	4	2	no	—
258	C₄×C₈	—	4	2	no	—
259	#95	C₂×C₄×C₁₃	1	2	yes	—
260	#95	C₂×C₄×C₁₃	1	2	yes	—
261	#95	C₂×C₄×C₁₃	1	2	yes	—
262	#95	C₂×C₄×C₁₃	1	2	yes	—
263	#95	C₂×C₄×C₁₃	1	2	yes	—
264	#95	C₂×C₄×C₁₃	1	2	yes	—
265	#95	C₂×C₄×C₁₃	1	2	yes	—
266	#95	C₂×C₄×C₁₃	1	2	yes	—
267	C₂×C₁₃	—	4	2	no	—
268	C₂×C₁₃	#2347	1	1	yes	characteristic
269	C₂×C₁₃	#2921	1	1	yes	characteristic
270	C₂×C₁₃	#2924	1	1	yes	characteristic
271	C₂×C₁₃	#2967	1	1	yes	characteristic
272	C₂×C₁₃	#2968	1	1	yes	characteristic
273	C₂×C₁₃	#2992	1	1	yes	characteristic
274	C₂×C₁₃	#2995	1	1	yes	characteristic
275	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	C₁₃×#41	1	4	yes	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	C₁₃×#41	1	4	yes	—
322	C₁₃	#22642	1	1	yes	characteristic, direct product factor, Sylow
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	C₁₃×#131	1	2	yes	—
330	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	C₁₃×#117	1	2	yes	—
361	C₂×C₄	C₁₃×#117	1	2	yes	—
362	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
363	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
364	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
366	C₈	—	2	4	no	—
367	C₈	—	4	2	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
378	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
379	C₂²	C₁₃×#520	1	1	yes	characteristic
380	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
381	C₂²	C₁₃×#568	1	1	yes	characteristic
382	C₂²	C₁₃×#568	1	1	yes	characteristic
383	C₂²	C₁₃×#568	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	C₁₃×#553	1	2	yes	—
394	C₄	C₁₃×#556	1	2	yes	—
395	C₂	—	4	2	no	—
396	C₂	C₁₃×#2347	1	1	yes	characteristic
397	C₂	C₁₃×#2921	1	1	yes	characteristic
398	C₂	C₁₃×#2924	1	1	yes	characteristic
399	C₂	C₁₃×#2967	1	1	yes	characteristic
400	C₂	C₁₃×#2968	1	1	yes	characteristic
401	C₂	C₁₃×#2992	1	1	yes	characteristic
402	C₂	C₁₃×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×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
2. C₁₃×#1940	C₂	semidirect
5. C₁₃×#1840	C₂	semidirect
7. C₁₃×#1771	C₂	semidirect
8. C₁₃×#1768	C₂	semidirect
74. #22642	C₁₃	direct (N × H)
123. #1940	C₂×C₁₃	semidirect
126. #1840	C₂×C₁₃	semidirect
128. #1771	C₂×C₁₃	semidirect
129. #1768	C₂×C₁₃	semidirect
322. C₁₃	#22642	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2283	2
C₁₃×#1940	2
C₁₃×#1924	2
C₁₃×#1923	2
C₁₃×#1840	2
C₁₃×#1797	2
C₁₃×#1771	2
C₁₃×#1768	2
C₁₃×#1749	2
#22642	13

Subgroups — C13×#22642 #15708981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22642 #15708981