Subgroups — C₁₃×#24956 #15711295

Order 3328.

764 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2487	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2352	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2076	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1870	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	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×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₃×#400	—	2	1	no	—
29	C₁₃×#399	—	2	1	no	—
30	C₁₃×#389	C₂²	1	1	yes	characteristic
31	C₁₃×#389	C₂²	1	1	yes	characteristic
32	C₁₃×#388	—	2	1	no	—
33	C₁₃×#387	—	2	1	no	—
34	C₁₃×#386	—	2	1	no	—
35	C₁₃×#386	—	2	1	no	—
36	C₁₃×#385	—	2	1	no	—
37	C₁₃×#382	C₂²	1	1	yes	characteristic
38	C₁₃×#380	C₂²	1	1	yes	characteristic
39	C₁₃×#380	C₂²	1	1	yes	characteristic
40	C₁₃×#380	C₂²	1	1	yes	characteristic
41	C₁₃×#380	C₂²	1	1	yes	characteristic
42	C₁₃×#380	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
45	C₁₃×#340	C₂²	1	1	yes	characteristic
46	C₁₃×#340	C₂²	1	1	yes	characteristic
47	C₁₃×#340	C₂²	1	1	yes	characteristic
48	C₁₃×#340	C₂²	1	1	yes	characteristic
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×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	—	2	2	no	—
65	C₂×C₁₃×M₁₆	—	2	2	no	—
66	C₂×C₁₃×M₁₆	—	4	1	no	—
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	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₁₃×#117	—	2	2	no	—
74	C₁₃×#117	—	4	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
83	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	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	D₄	1	1	yes	characteristic
99	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	—	2	1	no	—
101	C₂×C₄²×C₁₃	—	2	1	no	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#107	—	2	2	no	—
104	C₁₃×#107	—	4	1	no	—
105	C₁₃×#106	—	2	2	no	—
106	C₁₃×#106	—	4	1	no	—
107	C₁₃×C₂²⋊C₈	—	2	2	no	—
108	C₁₃×C₂²⋊C₈	—	2	2	no	—
109	C₁₃×C₂²⋊C₈	—	4	1	no	—
110	C₁₃×#95	—	2	1	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	#24956	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	4	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	4	2	no	—
145	C₂²×C₄×C₁₃	—	4	2	no	—
146	C₂²×C₄×C₁₃	—	4	2	no	—
147	C₂²×C₄×C₁₃	—	8	1	no	—
148	C₂²×C₄×C₁₃	—	8	1	no	—
149	C₂²×C₄×C₁₃	—	8	1	no	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	#41	1	2	yes	—
155	C₂²×C₄×C₁₃	#41	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×M₁₆	—	4	4	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	#41	1	2	yes	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	4	2	no	—
187	C₁₃×C₄⋊C₄	—	4	2	no	—
188	C₁₃×C₄⋊C₄	—	8	1	no	—
189	C₁₃×C₄⋊C₄	—	8	1	no	—
190	C₁₃×C₄⋊C₄	#41	1	2	yes	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	2	2	no	—
193	C₁₃×C₂²⋊C₄	—	4	2	no	—
194	C₁₃×C₂²⋊C₄	—	4	2	no	—
195	C₁₃×C₂²⋊C₄	—	4	2	no	—
196	C₁₃×C₂²⋊C₄	—	8	1	no	—
197	C₁₃×C₂²⋊C₄	—	8	1	no	—
198	C₁₃×C₂²⋊C₄	—	8	1	no	—
199	C₄²×C₁₃	—	2	1	no	—
200	C₄²×C₁₃	—	2	1	no	—
201	C₄²×C₁₃	—	4	2	no	—
202	C₄²×C₁₃	—	8	1	no	—
203	#2487	C₂×C₁₃	1	1	yes	characteristic
204	#2352	C₂×C₁₃	1	1	yes	characteristic
205	#2101	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2085	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2076	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#2076	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1870	C₂×C₁₃	1	1	yes	characteristic
212	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1823	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1823	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂³×C₁₃	—	2	1	no	—
219	C₂³×C₁₃	—	2	1	no	—
220	C₂³×C₁₃	—	2	1	no	—
221	C₂³×C₁₃	—	2	1	no	—
222	C₂³×C₁₃	—	2	1	no	—
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	—	2	1	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	#123	1	2	yes	—
231	C₂³×C₁₃	#137	1	2	yes	—
232	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	D₄×C₁₃	—	4	4	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
278	C₂×C₄×C₁₃	—	8	4	no	—
279	C₂×C₄×C₁₃	#123	1	2	yes	—
280	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
285	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
286	C₈×C₁₃	—	2	2	no	—
287	C₈×C₁₃	—	4	1	no	—
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
293	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
294	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
302	#400	—	2	1	no	—
303	#399	—	2	1	no	—
304	#389	C₂²×C₁₃	1	1	yes	characteristic
305	#389	C₂²×C₁₃	1	1	yes	characteristic
306	#388	—	2	1	no	—
307	#387	—	2	1	no	—
308	#386	—	2	1	no	—
309	#386	—	2	1	no	—
310	#385	—	2	1	no	—
311	#382	C₂²×C₁₃	1	1	yes	characteristic
312	#380	C₂²×C₁₃	1	1	yes	characteristic
313	#380	C₂²×C₁₃	1	1	yes	characteristic
314	#380	C₂²×C₁₃	1	1	yes	characteristic
315	#380	C₂²×C₁₃	1	1	yes	characteristic
316	#380	C₂²×C₁₃	1	1	yes	characteristic
317	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
318	C₄×C₂²⋊C₄	—	2	1	no	—
319	#340	C₂²×C₁₃	1	1	yes	characteristic
320	#340	C₂²×C₁₃	1	1	yes	characteristic
321	#340	C₂²×C₁₃	1	1	yes	characteristic
322	#340	C₂²×C₁₃	1	1	yes	characteristic
323	#340	C₂²×C₁₃	1	1	yes	characteristic
324	#340	C₂²×C₁₃	1	1	yes	characteristic
325	#340	C₂²×C₁₃	1	1	yes	characteristic
326	#340	C₂²×C₁₃	1	1	yes	characteristic
327	#340	C₂²×C₁₃	1	1	yes	characteristic
328	#340	C₂²×C₁₃	1	1	yes	characteristic
329	#340	C₂²×C₁₃	1	1	yes	characteristic
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#336	C₂²×C₁₃	1	1	yes	characteristic
332	#336	C₂²×C₁₃	1	1	yes	characteristic
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	—	2	2	no	—
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
348	C₂²×C₁₃	#546	1	1	yes	characteristic
349	C₂²×C₁₃	#547	1	1	yes	characteristic
350	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
351	C₂²×C₁₃	#575	1	1	yes	characteristic
352	C₂²×C₁₃	#576	1	1	yes	characteristic
353	C₂²×C₁₃	#577	1	1	yes	characteristic
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	—	4	1	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	8	1	no	—
360	C₄×C₁₃	—	8	1	no	—
361	C₄×C₁₃	—	8	1	no	—
362	C₄×C₁₃	—	8	1	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	—	8	1	no	—
365	C₄×C₁₃	—	8	1	no	—
366	C₄×C₁₃	#529	1	1	yes	characteristic
367	C₄×C₁₃	#539	1	1	yes	characteristic
368	C₄×C₁₃	#551	1	1	yes	characteristic
369	C₄×C₁₃	#552	1	1	yes	characteristic
370	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	4	1	no	—
378	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	2	no	—
384	#117	—	2	2	no	—
385	#117	—	4	1	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	4	1	no	—
394	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	#107	—	2	2	no	—
415	#107	—	4	1	no	—
416	#106	—	2	2	no	—
417	#106	—	4	1	no	—
418	C₂²⋊C₈	—	2	2	no	—
419	C₂²⋊C₈	—	2	2	no	—
420	C₂²⋊C₈	—	4	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	C₂×C₁₃	—	4	2	no	—
432	C₂×C₁₃	—	4	2	no	—
433	C₂×C₁₃	#2419	1	1	yes	characteristic
434	C₂×C₁₃	#3095	1	1	yes	characteristic
435	C₂×C₁₃	#3096	1	1	yes	characteristic
436	C₂×C₁₃	#3314	1	1	yes	characteristic
437	C₂×C₁₃	#3326	1	1	yes	characteristic
438	C₂×C₁₃	#3344	1	1	yes	characteristic
439	C₂×C₁₃	#3355	1	1	yes	characteristic
440	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	8	1	no	—
467	C₂²×C₄	—	8	1	no	—
468	C₂²×C₄	—	8	1	no	—
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₁₃×#41	1	2	yes	—
474	C₂²×C₄	C₁₃×#41	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
476	M₁₆	—	4	4	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	C₁₃×#41	1	2	yes	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	8	1	no	—
508	C₄⋊C₄	—	8	1	no	—
509	C₄⋊C₄	C₁₃×#41	1	2	yes	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	8	1	no	—
516	C₂²⋊C₄	—	8	1	no	—
517	C₂²⋊C₄	—	8	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	4	2	no	—
521	C₄²	—	8	1	no	—
522	C₁₃	#24956	1	1	yes	characteristic, direct product factor, Sylow
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	C₁₃×#123	1	2	yes	—
536	C₂³	C₁₃×#137	1	2	yes	—
537	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
538	D₄	—	4	4	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	8	4	no	—
583	C₂×C₄	—	8	4	no	—
584	C₂×C₄	C₁₃×#123	1	2	yes	—
585	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
586	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
587	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
588	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
589	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
591	C₈	—	2	2	no	—
592	C₈	—	4	1	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
610	C₂²	C₁₃×#546	1	1	yes	characteristic
611	C₂²	C₁₃×#547	1	1	yes	characteristic
612	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
613	C₂²	C₁₃×#575	1	1	yes	characteristic
614	C₂²	C₁₃×#576	1	1	yes	characteristic
615	C₂²	C₁₃×#577	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	—	8	1	no	—
627	C₄	—	8	1	no	—
628	C₄	C₁₃×#529	1	1	yes	characteristic
629	C₄	C₁₃×#539	1	1	yes	characteristic
630	C₄	C₁₃×#551	1	1	yes	characteristic
631	C₄	C₁₃×#552	1	1	yes	characteristic
632	C₂	—	4	2	no	—
633	C₂	—	4	2	no	—
634	C₂	C₁₃×#2419	1	1	yes	characteristic
635	C₂	C₁₃×#3095	1	1	yes	characteristic
636	C₂	C₁₃×#3096	1	1	yes	characteristic
637	C₂	C₁₃×#3314	1	1	yes	characteristic
638	C₂	C₁₃×#3326	1	1	yes	characteristic
639	C₂	C₁₃×#3344	1	1	yes	characteristic
640	C₂	C₁₃×#3355	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
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
3. C₁₃×#2101	C₂	semidirect
4. C₁₃×#2085	C₂	semidirect
5. C₁₃×#2076	C₂	semidirect
6. C₁₃×#2076	C₂	semidirect
7. C₁₃×#1919	C₂	semidirect
8. C₁₃×#1918	C₂	semidirect
10. C₁₃×#1854	C₂	semidirect
11. C₁₃×#1853	C₂	semidirect
12. C₁₃×#1823	C₂	semidirect
13. C₁₃×#1823	C₂	semidirect
14. C₁₃×#1809	C₂	semidirect
15. C₁₃×#1736	C₂	semidirect
120. #24956	C₁₃	direct (N × H)
205. #2101	C₂×C₁₃	semidirect
206. #2085	C₂×C₁₃	semidirect
207. #2076	C₂×C₁₃	semidirect
208. #2076	C₂×C₁₃	semidirect
209. #1919	C₂×C₁₃	semidirect
210. #1918	C₂×C₁₃	semidirect
212. #1854	C₂×C₁₃	semidirect
213. #1853	C₂×C₁₃	semidirect
214. #1823	C₂×C₁₃	semidirect
215. #1823	C₂×C₁₃	semidirect
216. #1809	C₂×C₁₃	semidirect
217. #1736	C₂×C₁₃	semidirect
522. C₁₃	#24956	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×#2487	2
C₁₃×#2352	2
C₁₃×#2101	2
C₁₃×#2085	2
C₁₃×#2076	2
C₁₃×#1919	2
C₁₃×#1918	2
C₁₃×#1870	2
C₁₃×#1854	2
C₁₃×#1853	2
C₁₃×#1823	2
C₁₃×#1809	2
C₁₃×#1736	2
#24956	13

Subgroups — C13×#24956 #15711295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24956 #15711295