Subgroups — C₁₃×#24974 #15711313

Order 3328.

840 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2535	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2076	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1835	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1825	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#397	—	2	1	no	—
35	C₁₃×#392	—	2	1	no	—
36	C₁₃×#388	—	2	1	no	—
37	C₁₃×#387	—	2	1	no	—
38	C₁₃×#386	—	2	1	no	—
39	C₁₃×#386	—	2	1	no	—
40	C₁₃×#386	—	2	1	no	—
41	C₁₃×#382	C₂²	1	1	yes	characteristic
42	C₁₃×#382	C₂²	1	1	yes	characteristic
43	C₁₃×#380	C₂²	1	1	yes	characteristic
44	C₁₃×#380	C₂²	1	1	yes	characteristic
45	C₁₃×#380	C₂²	1	1	yes	characteristic
46	C₁₃×#380	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#121	—	2	2	no	—
72	C₁₃×#121	—	2	2	no	—
73	C₁₃×#121	—	4	1	no	—
74	C₁₃×#121	—	4	1	no	—
75	C₄×D₄×C₁₃	—	2	2	no	—
76	C₄×D₄×C₁₃	—	2	2	no	—
77	C₄×D₄×C₁₃	—	2	2	no	—
78	C₄×D₄×C₁₃	—	2	2	no	—
79	C₁₃×#117	—	2	2	no	—
80	C₁₃×#117	—	4	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	—	2	1	no	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#107	—	4	1	no	—
106	C₁₃×#106	—	4	1	no	—
107	C₁₃×C₄⋊C₈	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#102	—	4	1	no	—
111	C₁₃×#102	—	4	1	no	—
112	C₁₃×C₂²⋊C₈	—	4	1	no	—
113	C₁₃×C₂²⋊C₈	—	4	1	no	—
114	C₁₃×C₂²⋊C₈	—	4	1	no	—
115	C₁₃×C₂²⋊C₈	—	4	1	no	—
116	C₄×C₈×C₁₃	—	2	2	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	—	2	1	no	—
123	C₁₃×#95	—	2	1	no	—
124	C₁₃×#95	—	2	1	no	—
125	C₁₃×#95	—	2	1	no	—
126	#24974	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	4	1	no	—
138	C₂×D₄×C₁₃	—	4	2	no	—
139	C₂×D₄×C₁₃	—	4	2	no	—
140	C₂×D₄×C₁₃	—	4	2	no	—
141	C₂×D₄×C₁₃	—	4	2	no	—
142	C₂×D₄×C₁₃	—	8	1	no	—
143	C₂×D₄×C₁₃	—	8	1	no	—
144	C₂×D₄×C₁₃	#41	1	2	yes	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	4	2	no	—
166	C₂²×C₄×C₁₃	—	4	2	no	—
167	C₂²×C₄×C₁₃	—	8	1	no	—
168	C₂²×C₄×C₁₃	—	8	1	no	—
169	C₂²×C₄×C₁₃	—	8	1	no	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	4	2	no	—
202	C₁₃×C₄⋊C₄	#41	1	2	yes	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	4	2	no	—
208	C₁₃×C₂²⋊C₄	—	4	2	no	—
209	C₁₃×C₂²⋊C₄	—	4	2	no	—
210	C₁₃×C₂²⋊C₄	—	8	1	no	—
211	C₁₃×C₂²⋊C₄	—	8	1	no	—
212	C₁₃×C₂²⋊C₄	—	8	1	no	—
213	C₄²×C₁₃	—	4	2	no	—
214	C₄²×C₁₃	—	8	1	no	—
215	C₄²×C₁₃	#41	1	2	yes	—
216	C₄²×C₁₃	#41	1	2	yes	—
217	#2535	C₂×C₁₃	1	1	yes	characteristic
218	#2352	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2077	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2076	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1875	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1874	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1835	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1825	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1823	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	2	1	no	—
235	C₂³×C₁₃	—	2	1	no	—
236	C₂³×C₁₃	—	2	1	no	—
237	C₂³×C₁₃	—	2	1	no	—
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	—	2	1	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	1	no	—
242	C₂³×C₁₃	—	2	1	no	—
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	#135	1	2	yes	—
253	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	D₄×C₁₃	—	2	2	no	—
255	D₄×C₁₃	—	2	2	no	—
256	D₄×C₁₃	—	4	4	no	—
257	D₄×C₁₃	—	4	1	no	—
258	D₄×C₁₃	—	4	1	no	—
259	D₄×C₁₃	—	8	4	no	—
260	D₄×C₁₃	—	8	4	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	8	4	no	—
301	C₂×C₄×C₁₃	—	8	4	no	—
302	C₂×C₄×C₁₃	#123	1	2	yes	—
303	C₂×C₄×C₁₃	#123	1	2	yes	—
304	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
310	C₈×C₁₃	—	4	1	no	—
311	C₈×C₁₃	—	4	1	no	—
312	C₈×C₁₃	—	4	1	no	—
313	C₈×C₁₃	—	4	1	no	—
314	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
319	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
332	#397	—	2	1	no	—
333	#392	—	2	1	no	—
334	#388	—	2	1	no	—
335	#387	—	2	1	no	—
336	#386	—	2	1	no	—
337	#386	—	2	1	no	—
338	#386	—	2	1	no	—
339	#382	C₂²×C₁₃	1	1	yes	characteristic
340	#382	C₂²×C₁₃	1	1	yes	characteristic
341	#380	C₂²×C₁₃	1	1	yes	characteristic
342	#380	C₂²×C₁₃	1	1	yes	characteristic
343	#380	C₂²×C₁₃	1	1	yes	characteristic
344	#380	C₂²×C₁₃	1	1	yes	characteristic
345	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
346	C₄×C₂²⋊C₄	—	2	1	no	—
347	#340	C₂²×C₁₃	1	1	yes	characteristic
348	#340	C₂²×C₁₃	1	1	yes	characteristic
349	#340	C₂²×C₁₃	1	1	yes	characteristic
350	#340	C₂²×C₁₃	1	1	yes	characteristic
351	#340	C₂²×C₁₃	1	1	yes	characteristic
352	#340	C₂²×C₁₃	1	1	yes	characteristic
353	#340	C₂²×C₁₃	1	1	yes	characteristic
354	#340	C₂²×C₁₃	1	1	yes	characteristic
355	#340	C₂²×C₁₃	1	1	yes	characteristic
356	#340	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×C₁₃	—	2	2	no	—
358	C₂²×C₁₃	—	2	2	no	—
359	C₂²×C₁₃	—	2	2	no	—
360	C₂²×C₁₃	—	4	1	no	—
361	C₂²×C₁₃	—	4	1	no	—
362	C₂²×C₁₃	—	4	1	no	—
363	C₂²×C₁₃	—	4	1	no	—
364	C₂²×C₁₃	—	4	1	no	—
365	C₂²×C₁₃	—	4	1	no	—
366	C₂²×C₁₃	—	4	1	no	—
367	C₂²×C₁₃	—	4	2	no	—
368	C₂²×C₁₃	—	4	2	no	—
369	C₂²×C₁₃	—	4	1	no	—
370	C₂²×C₁₃	—	4	1	no	—
371	C₂²×C₁₃	—	4	1	no	—
372	C₂²×C₁₃	—	4	2	no	—
373	C₂²×C₁₃	—	4	1	no	—
374	C₂²×C₁₃	—	8	1	no	—
375	C₂²×C₁₃	—	8	1	no	—
376	C₂²×C₁₃	—	8	1	no	—
377	C₂²×C₁₃	—	8	1	no	—
378	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
379	C₂²×C₁₃	#546	1	1	yes	characteristic
380	C₂²×C₁₃	#546	1	1	yes	characteristic
381	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
382	C₂²×C₁₃	#575	1	1	yes	characteristic
383	C₂²×C₁₃	#576	1	1	yes	characteristic
384	C₂²×C₁₃	#577	1	1	yes	characteristic
385	C₄×C₁₃	—	2	2	no	—
386	C₄×C₁₃	—	2	2	no	—
387	C₄×C₁₃	—	4	1	no	—
388	C₄×C₁₃	—	4	1	no	—
389	C₄×C₁₃	—	4	2	no	—
390	C₄×C₁₃	—	8	1	no	—
391	C₄×C₁₃	—	8	1	no	—
392	C₄×C₁₃	—	8	1	no	—
393	C₄×C₁₃	—	8	1	no	—
394	C₄×C₁₃	—	8	1	no	—
395	C₄×C₁₃	—	8	1	no	—
396	C₄×C₁₃	#529	1	1	yes	characteristic
397	C₄×C₁₃	#540	1	1	yes	characteristic
398	C₄×C₁₃	#553	1	1	yes	characteristic
399	C₄×C₁₃	#555	1	1	yes	characteristic
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
403	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₂³×C₄	—	2	1	no	—
405	C₂³×C₄	—	2	1	no	—
406	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
412	#121	—	2	2	no	—
413	#121	—	2	2	no	—
414	#121	—	4	1	no	—
415	#121	—	4	1	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	#117	—	2	2	no	—
421	#117	—	4	1	no	—
422	C₂×C₄⋊C₄	—	2	2	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	4	1	no	—
425	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
443	C₂×C₄²	—	2	1	no	—
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
446	#107	—	4	1	no	—
447	#106	—	4	1	no	—
448	C₄⋊C₈	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	—	4	1	no	—
452	#102	—	4	1	no	—
453	C₂²⋊C₈	—	4	1	no	—
454	C₂²⋊C₈	—	4	1	no	—
455	C₂²⋊C₈	—	4	1	no	—
456	C₂²⋊C₈	—	4	1	no	—
457	C₄×C₈	—	2	2	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	C₂×C₁₃	—	4	2	no	—
468	C₂×C₁₃	—	8	1	no	—
469	C₂×C₁₃	—	8	2	no	—
470	C₂×C₁₃	#2420	1	1	yes	characteristic
471	C₂×C₁₃	#3091	1	1	yes	characteristic
472	C₂×C₁₃	#3096	1	1	yes	characteristic
473	C₂×C₁₃	#3296	1	1	yes	characteristic
474	C₂×C₁₃	#3297	1	1	yes	characteristic
475	C₂×C₁₃	#3322	1	1	yes	characteristic
476	C₂×C₁₃	#3326	1	1	yes	characteristic
477	C₂⁴	—	2	1	no	—
478	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	4	1	no	—
488	C₂×D₄	—	4	2	no	—
489	C₂×D₄	—	4	2	no	—
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	8	1	no	—
493	C₂×D₄	—	8	1	no	—
494	C₂×D₄	C₁₃×#41	1	2	yes	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	8	1	no	—
518	C₂²×C₄	—	8	1	no	—
519	C₂²×C₄	—	8	1	no	—
520	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	C₁₃×#41	1	2	yes	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	8	1	no	—
561	C₂²⋊C₄	—	8	1	no	—
562	C₂²⋊C₄	—	8	1	no	—
563	C₄²	—	4	2	no	—
564	C₄²	—	8	1	no	—
565	C₄²	C₁₃×#41	1	2	yes	—
566	C₄²	C₁₃×#41	1	2	yes	—
567	C₁₃	#24974	1	1	yes	characteristic, direct product factor, Sylow
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	C₁₃×#135	1	2	yes	—
589	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	4	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	8	4	no	—
596	D₄	—	8	4	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	8	4	no	—
637	C₂×C₄	—	8	4	no	—
638	C₂×C₄	C₁₃×#123	1	2	yes	—
639	C₂×C₄	C₁₃×#123	1	2	yes	—
640	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
641	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
642	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
643	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
644	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
645	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
672	C₂²	C₁₃×#546	1	1	yes	characteristic
673	C₂²	C₁₃×#546	1	1	yes	characteristic
674	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
675	C₂²	C₁₃×#575	1	1	yes	characteristic
676	C₂²	C₁₃×#576	1	1	yes	characteristic
677	C₂²	C₁₃×#577	1	1	yes	characteristic
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	8	1	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	—	8	1	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	C₁₃×#529	1	1	yes	characteristic
690	C₄	C₁₃×#540	1	1	yes	characteristic
691	C₄	C₁₃×#553	1	1	yes	characteristic
692	C₄	C₁₃×#555	1	1	yes	characteristic
693	C₂	—	4	2	no	—
694	C₂	—	8	1	no	—
695	C₂	—	8	2	no	—
696	C₂	C₁₃×#2420	1	1	yes	characteristic
697	C₂	C₁₃×#3091	1	1	yes	characteristic
698	C₂	C₁₃×#3096	1	1	yes	characteristic
699	C₂	C₁₃×#3296	1	1	yes	characteristic
700	C₂	C₁₃×#3297	1	1	yes	characteristic
701	C₂	C₁₃×#3322	1	1	yes	characteristic
702	C₂	C₁₃×#3326	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2535	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2352	C₂	semidirect
3. C₁₃×#2077	C₂	semidirect
4. C₁₃×#2076	C₂	semidirect
5. C₁₃×#2034	C₂	semidirect
6. C₁₃×#2033	C₂	semidirect
7. C₁₃×#1954	C₂	semidirect
8. C₁₃×#1949	C₂	semidirect
9. C₁₃×#1875	C₂	semidirect
10. C₁₃×#1874	C₂	semidirect
11. C₁₃×#1835	C₂	semidirect
12. C₁₃×#1825	C₂	semidirect
13. C₁₃×#1823	C₂	semidirect
14. C₁₃×#1804	C₂	semidirect
15. C₄×C₁₃×#102	C₂	semidirect
126. #24974	C₁₃	direct (N × H)
218. #2352	C₂×C₁₃	semidirect
219. #2077	C₂×C₁₃	semidirect
220. #2076	C₂×C₁₃	semidirect
221. #2034	C₂×C₁₃	semidirect
222. #2033	C₂×C₁₃	semidirect
223. #1954	C₂×C₁₃	semidirect
224. #1949	C₂×C₁₃	semidirect
225. #1875	C₂×C₁₃	semidirect
226. #1874	C₂×C₁₃	semidirect
227. #1835	C₂×C₁₃	semidirect
228. #1825	C₂×C₁₃	semidirect
229. #1823	C₂×C₁₃	semidirect
230. #1804	C₂×C₁₃	semidirect
231. C₄×#102	C₂×C₁₃	semidirect
567. C₁₃	#24974	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×#2535	2
C₁₃×#2352	2
C₁₃×#2077	2
C₁₃×#2076	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#1954	2
C₁₃×#1949	2
C₁₃×#1875	2
C₁₃×#1874	2
C₁₃×#1835	2
C₁₃×#1825	2
C₁₃×#1823	2
C₁₃×#1804	2
C₄×C₁₃×#102	2
#24974	13

Subgroups — C13×#24974 #15711313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24974 #15711313