Subgroups — C₁₃×#32616 #15718955

Order 3328.

700 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2592	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2582	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2094	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2015	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1936	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
33	C₁₃×#398	—	2	1	no	—
34	C₁₃×#398	—	2	1	no	—
35	C₁₃×#397	—	2	1	no	—
36	C₁₃×#393	—	2	1	no	—
37	C₁₃×#391	—	2	1	no	—
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#390	C₂²	1	1	yes	characteristic
44	C₁₃×#389	—	2	1	no	—
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#388	—	2	1	no	—
48	C₁₃×#388	—	2	1	no	—
49	C₁₃×#384	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	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×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×Q₁₆	—	2	2	no	—
64	C₂×C₁₃×Q₁₆	—	2	2	no	—
65	C₂×C₁₃×Q₁₆	—	4	1	no	—
66	C₂×C₁₃×SD₁₆	—	2	2	no	—
67	C₂×C₁₃×SD₁₆	—	4	1	no	—
68	C₂×C₁₃×SD₁₆	—	4	1	no	—
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#124	—	4	1	no	—
74	C₁₃×#124	—	4	1	no	—
75	C₄×Q₈×C₁₃	—	4	1	no	—
76	C₄×Q₈×C₁₃	—	4	1	no	—
77	C₄×Q₈×C₁₃	—	4	1	no	—
78	C₄×Q₈×C₁₃	—	4	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	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	—	2	1	no	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#106	—	2	2	no	—
104	C₁₃×#106	—	4	1	no	—
105	C₁₃×C₄⋊C₈	—	4	1	no	—
106	C₁₃×#103	—	2	2	no	—
107	C₁₃×#103	—	4	1	no	—
108	C₁₃×#103	—	4	1	no	—
109	C₁₃×#103	—	4	1	no	—
110	C₁₃×#103	—	4	1	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×#102	—	4	1	no	—
113	C₁₃×#102	—	4	1	no	—
114	C₁₃×#97	—	4	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	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	#32616	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	—	2	2	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	4	1	no	—
141	C₂×Q₈×C₁₃	—	4	1	no	—
142	C₂×Q₈×C₁₃	#41	1	2	yes	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×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	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×Q₁₆	—	4	4	no	—
164	C₁₃×SD₁₆	—	4	4	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	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	4	1	no	—
188	C₁₃×C₄⋊C₄	—	4	1	no	—
189	C₁₃×C₄⋊C₄	—	4	1	no	—
190	C₁₃×C₄⋊C₄	—	4	2	no	—
191	C₁₃×C₄⋊C₄	—	4	2	no	—
192	C₁₃×C₄⋊C₄	—	8	1	no	—
193	C₁₃×C₄⋊C₄	—	8	1	no	—
194	C₁₃×C₄⋊C₄	—	8	1	no	—
195	C₁₃×C₂²⋊C₄	—	4	2	no	—
196	C₁₃×C₂²⋊C₄	—	4	2	no	—
197	C₁₃×C₂²⋊C₄	—	4	2	no	—
198	C₁₃×C₂²⋊C₄	—	4	2	no	—
199	C₁₃×C₂²⋊C₄	—	8	1	no	—
200	C₁₃×C₂²⋊C₄	—	8	1	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	4	2	no	—
208	C₄²×C₁₃	—	8	1	no	—
209	#2592	C₂×C₁₃	1	1	yes	characteristic
210	#2582	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#2094	C₂×C₁₃	1	1	yes	characteristic
212	#2072	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2055	C₂×C₁₃	1	1	yes	characteristic
215	#2042	C₂×C₁₃	1	1	yes	characteristic
216	#2015	C₂×C₁₃	1	1	yes	characteristic
217	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1971	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1936	C₂×C₁₃	1	1	yes	characteristic
220	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1880	C₂×C₁₃	1	1	yes	characteristic
223	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂³×C₁₃	—	4	1	no	—
225	C₂³×C₁₃	—	4	1	no	—
226	C₂³×C₁₃	—	4	1	no	—
227	C₂³×C₁₃	—	4	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₁₃	—	2	2	no	—
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	4	4	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	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	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	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	—	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	#137	1	2	yes	—
284	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
290	C₈×C₁₃	—	2	2	no	—
291	C₈×C₁₃	—	4	1	no	—
292	C₈×C₁₃	—	4	1	no	—
293	C₈×C₁₃	—	4	1	no	—
294	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
295	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
311	#398	—	2	1	no	—
312	#398	—	2	1	no	—
313	#397	—	2	1	no	—
314	#393	—	2	1	no	—
315	#391	—	2	1	no	—
316	#391	C₂²×C₁₃	1	1	yes	characteristic
317	#391	C₂²×C₁₃	1	1	yes	characteristic
318	#391	C₂²×C₁₃	1	1	yes	characteristic
319	#391	C₂²×C₁₃	1	1	yes	characteristic
320	#390	C₂²×C₁₃	1	1	yes	characteristic
321	#390	C₂²×C₁₃	1	1	yes	characteristic
322	#389	—	2	1	no	—
323	#389	C₂²×C₁₃	1	1	yes	characteristic
324	#389	C₂²×C₁₃	1	1	yes	characteristic
325	#388	—	2	1	no	—
326	#388	—	2	1	no	—
327	#384	C₂²×C₁₃	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
329	#340	C₂²×C₁₃	1	1	yes	characteristic
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#340	C₂²×C₁₃	1	1	yes	characteristic
332	#340	C₂²×C₁₃	1	1	yes	characteristic
333	#336	C₂²×C₁₃	1	1	yes	characteristic
334	#336	C₂²×C₁₃	1	1	yes	characteristic
335	#336	C₂²×C₁₃	1	1	yes	characteristic
336	#336	C₂²×C₁₃	1	1	yes	characteristic
337	C₂²×C₁₃	—	8	1	no	—
338	C₂²×C₁₃	—	8	1	no	—
339	C₂²×C₁₃	—	8	1	no	—
340	C₂²×C₁₃	—	8	1	no	—
341	C₂²×C₁₃	—	8	1	no	—
342	C₂²×C₁₃	—	8	1	no	—
343	C₂²×C₁₃	—	8	1	no	—
344	C₂²×C₁₃	#534	1	1	yes	characteristic
345	C₂²×C₁₃	#548	1	1	yes	characteristic
346	C₂²×C₁₃	#550	1	1	yes	characteristic
347	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
348	C₂²×C₁₃	#575	1	1	yes	characteristic
349	C₂²×C₁₃	#577	1	1	yes	characteristic
350	C₂²×C₁₃	#577	1	1	yes	characteristic
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	—	4	2	no	—
358	C₄×C₁₃	—	8	1	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	#538	1	1	yes	characteristic
365	C₄×C₁₃	#542	1	1	yes	characteristic
366	C₄×C₁₃	#551	1	1	yes	characteristic
367	C₄×C₁₃	#562	1	1	yes	characteristic
368	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
370	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×Q₁₆	—	2	2	no	—
373	C₂×Q₁₆	—	2	2	no	—
374	C₂×Q₁₆	—	4	1	no	—
375	C₂×SD₁₆	—	2	2	no	—
376	C₂×SD₁₆	—	4	1	no	—
377	C₂×SD₁₆	—	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	#124	—	4	1	no	—
383	#124	—	4	1	no	—
384	C₄×Q₈	—	4	1	no	—
385	C₄×Q₈	—	4	1	no	—
386	C₄×Q₈	—	4	1	no	—
387	C₄×Q₈	—	4	1	no	—
388	C₂×C₄⋊C₄	—	2	1	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	D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	D₄×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×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
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×C₄²	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
412	#106	—	2	2	no	—
413	#106	—	4	1	no	—
414	C₄⋊C₈	—	4	1	no	—
415	#103	—	2	2	no	—
416	#103	—	4	1	no	—
417	#103	—	4	1	no	—
418	#103	—	4	1	no	—
419	#103	—	4	1	no	—
420	#102	—	2	2	no	—
421	#102	—	4	1	no	—
422	#102	—	4	1	no	—
423	#97	—	4	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	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	C₂×C₁₃	—	16	1	no	—
436	C₂×C₁₃	#2730	1	1	yes	characteristic
437	C₂×C₁₃	#3196	1	1	yes	characteristic
438	C₂×C₁₃	#3204	1	1	yes	characteristic
439	C₂×C₁₃	#3369	1	1	yes	characteristic
440	C₂×C₁₃	#3371	1	1	yes	characteristic
441	C₂×C₁₃	#3400	1	1	yes	characteristic
442	C₂×C₁₃	#3401	1	1	yes	characteristic
443	C₂⁴	—	2	1	no	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	4	1	no	—
457	C₂×Q₈	—	4	1	no	—
458	C₂×Q₈	C₁₃×#41	1	2	yes	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	Q₁₆	—	4	4	no	—
480	SD₁₆	—	4	4	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	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	C₁₃×#41	1	2	yes	—
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	—	4	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	8	1	no	—
509	C₄⋊C₄	—	8	1	no	—
510	C₄⋊C₄	—	8	1	no	—
511	C₂²⋊C₄	—	4	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	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	4	2	no	—
524	C₄²	—	8	1	no	—
525	C₁₃	#32616	1	1	yes	characteristic, direct product factor, Sylow
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	4	4	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	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	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	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	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	C₁₃×#137	1	2	yes	—
586	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
587	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
588	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
589	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
592	C₈	—	2	2	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	4	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	C₁₃×#534	1	1	yes	characteristic
604	C₂²	C₁₃×#548	1	1	yes	characteristic
605	C₂²	C₁₃×#550	1	1	yes	characteristic
606	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
607	C₂²	C₁₃×#575	1	1	yes	characteristic
608	C₂²	C₁₃×#577	1	1	yes	characteristic
609	C₂²	C₁₃×#577	1	1	yes	characteristic
610	C₄	—	2	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	2	no	—
617	C₄	—	8	1	no	—
618	C₄	—	8	1	no	—
619	C₄	—	8	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	C₁₃×#538	1	1	yes	characteristic
624	C₄	C₁₃×#542	1	1	yes	characteristic
625	C₄	C₁₃×#551	1	1	yes	characteristic
626	C₄	C₁₃×#562	1	1	yes	characteristic
627	C₂	—	16	1	no	—
628	C₂	C₁₃×#2730	1	1	yes	characteristic
629	C₂	C₁₃×#3196	1	1	yes	characteristic
630	C₂	C₁₃×#3204	1	1	yes	characteristic
631	C₂	C₁₃×#3369	1	1	yes	characteristic
632	C₂	C₁₃×#3371	1	1	yes	characteristic
633	C₂	C₁₃×#3400	1	1	yes	characteristic
634	C₂	C₁₃×#3401	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	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2582	C₂	semidirect
4. C₁₃×#2072	C₂	semidirect
5. C₁₃×#2066	C₂	semidirect
9. C₁₃×#1985	C₂	semidirect
10. C₁₃×#1971	C₂	semidirect
12. C₁₃×#1927	C₂	semidirect
13. C₁₃×#1919	C₂	semidirect
15. C₁₃×#1878	C₂	semidirect
126. #32616	C₁₃	direct (N × H)
210. #2582	C₂×C₁₃	semidirect
212. #2072	C₂×C₁₃	semidirect
213. #2066	C₂×C₁₃	semidirect
217. #1985	C₂×C₁₃	semidirect
218. #1971	C₂×C₁₃	semidirect
220. #1927	C₂×C₁₃	semidirect
221. #1919	C₂×C₁₃	semidirect
223. #1878	C₂×C₁₃	semidirect
525. C₁₃	#32616	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×#2592	2
C₁₃×#2582	2
C₁₃×#2094	2
C₁₃×#2072	2
C₁₃×#2066	2
C₁₃×#2055	2
C₁₃×#2042	2
C₁₃×#2015	2
C₁₃×#1985	2
C₁₃×#1971	2
C₁₃×#1936	2
C₁₃×#1927	2
C₁₃×#1919	2
C₁₃×#1880	2
C₁₃×#1878	2
#32616	13

Subgroups — C13×#32616 #15718955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32616 #15718955