Subgroups — C₁₃×#26306 #15712645

Order 3328.

732 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2562	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2352	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2076	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2075	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1824	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#125	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	C₂×C₁₃×#107	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×C₄⋊C₈	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	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#400	—	2	1	no	—
31	C₁₃×#394	—	2	1	no	—
32	C₁₃×#388	—	2	1	no	—
33	C₁₃×#388	—	2	1	no	—
34	C₁₃×#388	—	2	1	no	—
35	C₁₃×#387	—	2	1	no	—
36	C₁₃×#386	—	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	C₁₃×#380	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	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	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#125	—	2	2	no	—
68	C₁₃×#125	—	2	2	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₁₃×#117	—	2	2	no	—
72	C₁₃×#117	—	4	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	—	2	2	no	—
101	C₁₃×#107	—	2	2	no	—
102	C₁₃×#107	—	4	1	no	—
103	C₁₃×#106	—	4	1	no	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×C₂²⋊C₈	—	2	2	no	—
106	C₁₃×C₂²⋊C₈	—	2	2	no	—
107	C₁₃×C₂²⋊C₈	—	4	1	no	—
108	C₁₃×C₂²⋊C₈	—	4	1	no	—
109	C₄×C₈×C₁₃	—	2	2	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	#26306	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	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	4	2	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	8	1	no	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	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	#41	1	2	yes	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	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	—	4	2	no	—
183	C₁₃×C₄⋊C₄	—	4	2	no	—
184	C₁₃×C₄⋊C₄	—	4	2	no	—
185	C₁₃×C₄⋊C₄	#41	1	2	yes	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₁₃×C₂²⋊C₄	—	4	2	no	—
189	C₁₃×C₂²⋊C₄	—	4	2	no	—
190	C₁₃×C₂²⋊C₄	—	4	2	no	—
191	C₁₃×C₂²⋊C₄	—	4	2	no	—
192	C₁₃×C₂²⋊C₄	—	8	1	no	—
193	C₁₃×C₂²⋊C₄	—	8	1	no	—
194	C₁₃×C₂²⋊C₄	—	8	1	no	—
195	C₄²×C₁₃	—	4	2	no	—
196	C₄²×C₁₃	—	8	1	no	—
197	C₄²×C₁₃	—	8	1	no	—
198	C₄²×C₁₃	#41	1	2	yes	—
199	C₄²×C₁₃	#41	1	2	yes	—
200	#2562	C₂×C₁₃	1	1	yes	characteristic
201	#2352	C₂×C₁₃	1	1	yes	characteristic
202	#2077	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2076	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#2075	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2075	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1991	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1989	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1954	C₂×C₁₃	1	1	yes	characteristic
209	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1825	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1824	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂³×C₁₃	—	2	1	no	—
216	C₂³×C₁₃	—	2	1	no	—
217	C₂³×C₁₃	—	2	1	no	—
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	#135	1	2	yes	—
229	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	D₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
274	C₂×C₄×C₁₃	#123	1	2	yes	—
275	C₂×C₄×C₁₃	#123	1	2	yes	—
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
281	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
282	C₈×C₁₃	—	2	2	no	—
283	C₈×C₁₃	—	4	1	no	—
284	C₈×C₁₃	—	4	1	no	—
285	C₈×C₁₃	—	4	1	no	—
286	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
289	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
300	#400	—	2	1	no	—
301	#394	—	2	1	no	—
302	#388	—	2	1	no	—
303	#388	—	2	1	no	—
304	#388	—	2	1	no	—
305	#387	—	2	1	no	—
306	#386	—	2	1	no	—
307	#382	C₂²×C₁₃	1	1	yes	characteristic
308	#380	C₂²×C₁₃	1	1	yes	characteristic
309	#380	C₂²×C₁₃	1	1	yes	characteristic
310	#380	C₂²×C₁₃	1	1	yes	characteristic
311	#380	C₂²×C₁₃	1	1	yes	characteristic
312	#380	C₂²×C₁₃	1	1	yes	characteristic
313	#380	C₂²×C₁₃	1	1	yes	characteristic
314	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
315	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
316	C₄×C₂²⋊C₄	—	2	1	no	—
317	#340	C₂²×C₁₃	1	1	yes	characteristic
318	#340	C₂²×C₁₃	1	1	yes	characteristic
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	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	4	1	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	C₂×#123	1	1	yes	characteristic
344	C₂²×C₁₃	#546	1	1	yes	characteristic
345	C₂²×C₁₃	#547	1	1	yes	characteristic
346	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
347	C₂²×C₁₃	#575	1	1	yes	characteristic
348	C₂²×C₁₃	#576	1	1	yes	characteristic
349	C₂²×C₁₃	#578	1	1	yes	characteristic
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	—	8	1	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	#529	1	1	yes	characteristic
363	C₄×C₁₃	#542	1	1	yes	characteristic
364	C₄×C₁₃	#556	1	1	yes	characteristic
365	C₄×C₁₃	#559	1	1	yes	characteristic
366	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
367	C₂³×C₄	—	2	1	no	—
368	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
374	#125	—	2	2	no	—
375	#125	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	#117	—	2	2	no	—
379	#117	—	4	1	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	4	1	no	—
385	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
407	#107	—	2	2	no	—
408	#107	—	2	2	no	—
409	#107	—	4	1	no	—
410	#106	—	4	1	no	—
411	C₄⋊C₈	—	2	2	no	—
412	C₂²⋊C₈	—	2	2	no	—
413	C₂²⋊C₈	—	2	2	no	—
414	C₂²⋊C₈	—	4	1	no	—
415	C₂²⋊C₈	—	4	1	no	—
416	C₄×C₈	—	2	2	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	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	C₂×C₁₃	—	4	2	no	—
428	C₂×C₁₃	—	8	1	no	—
429	C₂×C₁₃	#2447	1	1	yes	characteristic
430	C₂×C₁₃	#3091	1	1	yes	characteristic
431	C₂×C₁₃	#3098	1	1	yes	characteristic
432	C₂×C₁₃	#3300	1	1	yes	characteristic
433	C₂×C₁₃	#3322	1	1	yes	characteristic
434	C₂×C₁₃	#3339	1	1	yes	characteristic
435	C₂×C₁₃	#3352	1	1	yes	characteristic
436	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	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	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	8	1	no	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	C₁₃×#41	1	2	yes	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	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	—	4	2	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	C₁₃×#41	1	2	yes	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	4	2	no	—
504	C₂²⋊C₄	—	4	2	no	—
505	C₂²⋊C₄	—	4	2	no	—
506	C₂²⋊C₄	—	4	2	no	—
507	C₂²⋊C₄	—	8	1	no	—
508	C₂²⋊C₄	—	8	1	no	—
509	C₂²⋊C₄	—	8	1	no	—
510	C₄²	—	4	2	no	—
511	C₄²	—	8	1	no	—
512	C₄²	—	8	1	no	—
513	C₄²	C₁₃×#41	1	2	yes	—
514	C₄²	C₁₃×#41	1	2	yes	—
515	C₁₃	#26306	1	1	yes	characteristic, direct product factor, Sylow
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
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	C₁₃×#135	1	2	yes	—
530	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
531	D₄	—	4	4	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	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	—	8	4	no	—
575	C₂×C₄	C₁₃×#123	1	2	yes	—
576	C₂×C₄	C₁₃×#123	1	2	yes	—
577	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
578	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
579	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
580	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
581	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
583	C₈	—	2	2	no	—
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
602	C₂²	C₁₃×#546	1	1	yes	characteristic
603	C₂²	C₁₃×#547	1	1	yes	characteristic
604	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
605	C₂²	C₁₃×#575	1	1	yes	characteristic
606	C₂²	C₁₃×#576	1	1	yes	characteristic
607	C₂²	C₁₃×#578	1	1	yes	characteristic
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	—	8	1	no	—
616	C₄	—	8	1	no	—
617	C₄	—	8	1	no	—
618	C₄	—	8	1	no	—
619	C₄	—	8	1	no	—
620	C₄	C₁₃×#529	1	1	yes	characteristic
621	C₄	C₁₃×#542	1	1	yes	characteristic
622	C₄	C₁₃×#556	1	1	yes	characteristic
623	C₄	C₁₃×#559	1	1	yes	characteristic
624	C₂	—	4	2	no	—
625	C₂	—	8	1	no	—
626	C₂	C₁₃×#2447	1	1	yes	characteristic
627	C₂	C₁₃×#3091	1	1	yes	characteristic
628	C₂	C₁₃×#3098	1	1	yes	characteristic
629	C₂	C₁₃×#3300	1	1	yes	characteristic
630	C₂	C₁₃×#3322	1	1	yes	characteristic
631	C₂	C₁₃×#3339	1	1	yes	characteristic
632	C₂	C₁₃×#3352	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×#2077	C₂	semidirect
4. C₁₃×#2076	C₂	semidirect
5. C₁₃×#2075	C₂	semidirect
6. C₁₃×#2075	C₂	semidirect
7. C₁₃×#1991	C₂	semidirect
8. C₁₃×#1989	C₂	semidirect
10. C₁₃×#1949	C₂	semidirect
11. C₁₃×#1854	C₂	semidirect
12. C₁₃×#1852	C₂	semidirect
13. C₁₃×#1825	C₂	semidirect
14. C₁₃×#1824	C₂	semidirect
15. C₄×C₁₃×#107	C₂	semidirect
120. #26306	C₁₃	direct (N × H)
202. #2077	C₂×C₁₃	semidirect
203. #2076	C₂×C₁₃	semidirect
204. #2075	C₂×C₁₃	semidirect
205. #2075	C₂×C₁₃	semidirect
206. #1991	C₂×C₁₃	semidirect
207. #1989	C₂×C₁₃	semidirect
209. #1949	C₂×C₁₃	semidirect
210. #1854	C₂×C₁₃	semidirect
211. #1852	C₂×C₁₃	semidirect
212. #1825	C₂×C₁₃	semidirect
213. #1824	C₂×C₁₃	semidirect
214. C₄×#107	C₂×C₁₃	semidirect
515. C₁₃	#26306	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×#2562	2
C₁₃×#2352	2
C₁₃×#2077	2
C₁₃×#2076	2
C₁₃×#2075	2
C₁₃×#1991	2
C₁₃×#1989	2
C₁₃×#1954	2
C₁₃×#1949	2
C₁₃×#1854	2
C₁₃×#1852	2
C₁₃×#1825	2
C₁₃×#1824	2
C₄×C₁₃×#107	2
#26306	13

Subgroups — C13×#26306 #15712645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26306 #15712645