Subgroups — C₁₃×#26210 #15712549

Order 3328.

816 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2417	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×#2075	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1928	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1869	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1825	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	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	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	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×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	C₁₃×#398	—	2	1	no	—
33	C₁₃×#396	—	2	1	no	—
34	C₁₃×#391	C₂²	1	1	yes	characteristic
35	C₁₃×#389	C₂²	1	1	yes	characteristic
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×#382	C₂²	1	1	yes	characteristic
41	C₁₃×#380	—	2	1	no	—
42	C₁₃×#380	C₂²	1	1	yes	characteristic
43	C₁₃×#380	C₂²	1	1	yes	characteristic
44	C₁₃×#380	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×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	—	2	2	no	—
66	C₂²×C₈×C₁₃	—	4	1	no	—
67	C₂²×C₈×C₁₃	—	4	1	no	—
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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×C₂²⋊Q₈	—	2	2	no	—
75	C₁₃×C₂²⋊Q₈	—	4	1	no	—
76	C₄×D₄×C₁₃	—	2	2	no	—
77	C₄×D₄×C₁₃	—	2	2	no	—
78	C₁₃×#117	—	2	2	no	—
79	C₁₃×#117	—	4	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
89	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#107	—	2	2	no	—
109	C₁₃×#107	—	4	1	no	—
110	C₁₃×#103	—	2	2	no	—
111	C₁₃×#103	—	4	1	no	—
112	C₁₃×#103	—	4	1	no	—
113	C₁₃×#103	—	4	1	no	—
114	C₁₃×C₂²⋊C₈	—	2	2	no	—
115	C₁₃×C₂²⋊C₈	—	4	1	no	—
116	C₁₃×C₂²⋊C₈	—	4	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	#26210	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
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×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	2	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	—	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	—	4	2	no	—
157	C₂²×C₄×C₁₃	—	4	2	no	—
158	C₂²×C₄×C₁₃	—	4	2	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	8	1	no	—
161	C₂²×C₄×C₁₃	—	8	1	no	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	#41	1	2	yes	—
167	C₂²×C₄×C₁₃	#41	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	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	—	4	4	no	—
182	C₁₃×C₄⋊C₄	—	2	2	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	—	2	1	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	—	4	2	no	—
196	C₁₃×C₄⋊C₄	—	4	2	no	—
197	C₁₃×C₄⋊C₄	—	4	2	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	—	8	1	no	—
200	C₁₃×C₄⋊C₄	#41	1	2	yes	—
201	C₁₃×C₄⋊C₄	#41	1	2	yes	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	4	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	—	8	1	no	—
209	C₁₃×C₂²⋊C₄	—	8	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	4	2	no	—
213	C₄²×C₁₃	—	8	1	no	—
214	#2417	C₂×C₁₃	1	1	yes	characteristic
215	#2352	C₂×C₁₃	1	1	yes	characteristic
216	#2101	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2075	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1928	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1892	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1869	C₂×C₁₃	1	1	yes	characteristic
226	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1825	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂×#340	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
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	#123	1	2	yes	—
241	C₂³×C₁₃	#135	1	2	yes	—
242	C₂³×C₁₃	#137	1	2	yes	—
243	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₁₃	—	4	1	no	—
245	Q₈×C₁₃	—	4	1	no	—
246	Q₈×C₁₃	—	4	1	no	—
247	Q₈×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	4	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	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	2	no	—
260	C₂×C₄×C₁₃	—	2	2	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	—	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	—	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	—	8	4	no	—
293	C₂×C₄×C₁₃	—	8	4	no	—
294	C₂×C₄×C₁₃	#123	1	2	yes	—
295	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
301	C₈×C₁₃	—	4	1	no	—
302	C₈×C₁₃	—	4	1	no	—
303	C₈×C₁₃	—	4	1	no	—
304	C₈×C₁₃	—	4	1	no	—
305	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	#398	—	2	1	no	—
322	#396	—	2	1	no	—
323	#391	C₂²×C₁₃	1	1	yes	characteristic
324	#389	C₂²×C₁₃	1	1	yes	characteristic
325	#388	—	2	1	no	—
326	#387	—	2	1	no	—
327	#386	—	2	1	no	—
328	#386	—	2	1	no	—
329	#382	C₂²×C₁₃	1	1	yes	characteristic
330	#380	—	2	1	no	—
331	#380	C₂²×C₁₃	1	1	yes	characteristic
332	#380	C₂²×C₁₃	1	1	yes	characteristic
333	#380	C₂²×C₁₃	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
335	C₄×C₂²⋊C₄	—	2	1	no	—
336	#340	C₂²×C₁₃	1	1	yes	characteristic
337	#340	C₂²×C₁₃	1	1	yes	characteristic
338	#340	C₂²×C₁₃	1	1	yes	characteristic
339	#340	C₂²×C₁₃	1	1	yes	characteristic
340	#340	C₂²×C₁₃	1	1	yes	characteristic
341	#340	C₂²×C₁₃	1	1	yes	characteristic
342	#340	C₂²×C₁₃	1	1	yes	characteristic
343	#340	C₂²×C₁₃	1	1	yes	characteristic
344	#340	C₂²×C₁₃	1	1	yes	characteristic
345	#340	C₂²×C₁₃	1	1	yes	characteristic
346	#336	C₂²×C₁₃	1	1	yes	characteristic
347	#336	C₂²×C₁₃	1	1	yes	characteristic
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	—	2	2	no	—
350	C₂²×C₁₃	—	2	2	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	2	no	—
353	C₂²×C₁₃	—	2	2	no	—
354	C₂²×C₁₃	—	4	1	no	—
355	C₂²×C₁₃	—	4	1	no	—
356	C₂²×C₁₃	—	4	1	no	—
357	C₂²×C₁₃	—	4	1	no	—
358	C₂²×C₁₃	—	4	1	no	—
359	C₂²×C₁₃	—	4	1	no	—
360	C₂²×C₁₃	—	4	1	no	—
361	C₂²×C₁₃	#485	1	4	yes	—
362	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
363	C₂²×C₁₃	#546	1	1	yes	characteristic
364	C₂²×C₁₃	#546	1	1	yes	characteristic
365	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
366	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
367	C₂²×C₁₃	#576	1	1	yes	characteristic
368	C₂²×C₁₃	#578	1	1	yes	characteristic
369	C₄×C₁₃	—	2	2	no	—
370	C₄×C₁₃	—	4	1	no	—
371	C₄×C₁₃	—	4	1	no	—
372	C₄×C₁₃	—	4	1	no	—
373	C₄×C₁₃	—	4	2	no	—
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	8	1	no	—
376	C₄×C₁₃	—	8	1	no	—
377	C₄×C₁₃	—	8	1	no	—
378	C₄×C₁₃	—	8	1	no	—
379	C₄×C₁₃	—	8	1	no	—
380	C₄×C₁₃	—	8	1	no	—
381	C₄×C₁₃	#529	1	1	yes	characteristic
382	C₄×C₁₃	#538	1	1	yes	characteristic
383	C₄×C₁₃	#553	1	1	yes	characteristic
384	C₄×C₁₃	#553	1	1	yes	characteristic
385	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₂²×C₈	—	2	2	no	—
392	C₂²×C₈	—	4	1	no	—
393	C₂²×C₈	—	4	1	no	—
394	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	4	1	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	#117	—	2	2	no	—
405	#117	—	4	1	no	—
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	2	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	4	1	no	—
414	C₂×C₄⋊C₄	—	4	1	no	—
415	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
434	#107	—	2	2	no	—
435	#107	—	4	1	no	—
436	#103	—	2	2	no	—
437	#103	—	4	1	no	—
438	#103	—	4	1	no	—
439	#103	—	4	1	no	—
440	C₂²⋊C₈	—	2	2	no	—
441	C₂²⋊C₈	—	4	1	no	—
442	C₂²⋊C₈	—	4	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	C₂×C₁₃	—	2	4	no	—
453	C₂×C₁₃	—	8	1	no	—
454	C₂×C₁₃	#2444	1	1	yes	characteristic
455	C₂×C₁₃	C₂×#485	1	1	yes	characteristic
456	C₂×C₁₃	#3098	1	1	yes	characteristic
457	C₂×C₁₃	#3297	1	1	yes	characteristic
458	C₂×C₁₃	#3300	1	1	yes	characteristic
459	C₂×C₁₃	#3312	1	1	yes	characteristic
460	C₂×C₁₃	#3314	1	1	yes	characteristic
461	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	8	1	no	—
495	C₂²×C₄	—	8	1	no	—
496	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₁₃×#41	1	2	yes	—
501	C₂²×C₄	C₁₃×#41	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	4	4	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₄⋊C₄	—	4	2	no	—
532	C₄⋊C₄	—	4	2	no	—
533	C₄⋊C₄	—	8	1	no	—
534	C₄⋊C₄	C₁₃×#41	1	2	yes	—
535	C₄⋊C₄	C₁₃×#41	1	2	yes	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	4	2	no	—
539	C₂²⋊C₄	—	4	2	no	—
540	C₂²⋊C₄	—	4	2	no	—
541	C₂²⋊C₄	—	4	2	no	—
542	C₂²⋊C₄	—	8	1	no	—
543	C₂²⋊C₄	—	8	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	4	2	no	—
547	C₄²	—	8	1	no	—
548	C₁₃	#26210	1	1	yes	characteristic, direct product factor, Sylow
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	C₁₃×#123	1	2	yes	—
561	C₂³	C₁₃×#135	1	2	yes	—
562	C₂³	C₁₃×#137	1	2	yes	—
563	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
564	Q₈	—	4	1	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	—	4	1	no	—
568	D₄	—	4	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	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	—	8	4	no	—
613	C₂×C₄	—	8	4	no	—
614	C₂×C₄	C₁₃×#123	1	2	yes	—
615	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
616	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
617	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
618	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
619	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₈	—	4	1	no	—
624	C₈	—	4	1	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	C₁₃×#485	1	4	yes	—
639	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
640	C₂²	C₁₃×#546	1	1	yes	characteristic
641	C₂²	C₁₃×#546	1	1	yes	characteristic
642	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
643	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
644	C₂²	C₁₃×#576	1	1	yes	characteristic
645	C₂²	C₁₃×#578	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	8	1	no	—
653	C₄	—	8	1	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	C₁₃×#529	1	1	yes	characteristic
659	C₄	C₁₃×#538	1	1	yes	characteristic
660	C₄	C₁₃×#553	1	1	yes	characteristic
661	C₄	C₁₃×#553	1	1	yes	characteristic
662	C₂	—	2	4	no	—
663	C₂	—	8	1	no	—
664	C₂	C₁₃×#2444	1	1	yes	characteristic
665	C₂	C₂×C₁₃×#485	1	1	yes	characteristic
666	C₂	C₁₃×#3098	1	1	yes	characteristic
667	C₂	C₁₃×#3297	1	1	yes	characteristic
668	C₂	C₁₃×#3300	1	1	yes	characteristic
669	C₂	C₁₃×#3312	1	1	yes	characteristic
670	C₂	C₁₃×#3314	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×#2075	C₂	semidirect
5. C₁₃×#2074	C₂	semidirect
6. C₁₃×#2036	C₂	semidirect
7. C₁₃×#1928	C₂	semidirect
8. C₁₃×#1918	C₂	semidirect
9. C₁₃×#1892	C₂	semidirect
10. C₁₃×#1873	C₂	semidirect
11. C₁₃×#1872	C₂	semidirect
13. C₁₃×#1852	C₂	semidirect
14. C₁₃×#1825	C₂	semidirect
15. C₂×C₁₃×#340	C₂	semidirect
126. #26210	C₁₃	direct (N × H)
216. #2101	C₂×C₁₃	semidirect
217. #2075	C₂×C₁₃	semidirect
218. #2074	C₂×C₁₃	semidirect
219. #2036	C₂×C₁₃	semidirect
220. #1928	C₂×C₁₃	semidirect
221. #1918	C₂×C₁₃	semidirect
222. #1892	C₂×C₁₃	semidirect
223. #1873	C₂×C₁₃	semidirect
224. #1872	C₂×C₁₃	semidirect
226. #1852	C₂×C₁₃	semidirect
227. #1825	C₂×C₁₃	semidirect
228. C₂×#340	C₂×C₁₃	semidirect
548. C₁₃	#26210	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×#2417	2
C₁₃×#2352	2
C₁₃×#2101	2
C₁₃×#2075	2
C₁₃×#2074	2
C₁₃×#2036	2
C₁₃×#1928	2
C₁₃×#1918	2
C₁₃×#1892	2
C₁₃×#1873	2
C₁₃×#1872	2
C₁₃×#1869	2
C₁₃×#1852	2
C₁₃×#1825	2
C₂×C₁₃×#340	2
#26210	13

Subgroups — C13×#26210 #15712549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26210 #15712549