Subgroups — C₁₃×#26226 #15712565

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2415	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×#2077	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×#1927	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1921	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1894	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×#1870	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1825	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×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	C₂×C₁₃×#117	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×#106	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×#397	—	2	1	no	—
33	C₁₃×#394	—	2	1	no	—
34	C₁₃×#391	C₂²	1	1	yes	characteristic
35	C₁₃×#389	—	2	1	no	—
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#388	—	2	1	no	—
38	C₁₃×#388	—	2	1	no	—
39	C₁₃×#387	—	2	1	no	—
40	C₁₃×#386	—	2	1	no	—
41	C₁₃×#382	C₂²	1	1	yes	characteristic
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	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	—	4	1	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	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×C₂²⋊Q₈	—	2	2	no	—
74	C₁₃×C₂²⋊Q₈	—	4	1	no	—
75	C₄×D₄×C₁₃	—	2	2	no	—
76	C₄×D₄×C₁₃	—	2	2	no	—
77	C₁₃×#117	—	2	2	no	—
78	C₁₃×#117	—	2	2	no	—
79	C₁₃×#117	—	4	1	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	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
87	C₂×C₁₃×C₄⋊C₄	D₄	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×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×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	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	—	2	1	no	—
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×#106	—	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	#26226	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	—	4	1	no	—
137	C₂×D₄×C₁₃	—	4	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	—	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	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	#41	1	2	yes	—
164	C₂²×C₄×C₁₃	#41	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₁₃×M₁₆	—	4	4	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	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	2	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	—	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	—	4	2	no	—
193	C₁₃×C₄⋊C₄	—	4	2	no	—
194	C₁₃×C₄⋊C₄	—	4	2	no	—
195	C₁₃×C₄⋊C₄	—	4	2	no	—
196	C₁₃×C₄⋊C₄	#41	1	2	yes	—
197	C₁₃×C₄⋊C₄	#41	1	2	yes	—
198	C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	4	2	no	—
201	C₁₃×C₂²⋊C₄	—	4	2	no	—
202	C₁₃×C₂²⋊C₄	—	4	2	no	—
203	C₁₃×C₂²⋊C₄	—	4	2	no	—
204	C₁₃×C₂²⋊C₄	—	4	2	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	8	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	4	2	no	—
210	C₄²×C₁₃	—	4	2	no	—
211	C₄²×C₁₃	—	8	1	no	—
212	#2415	C₂×C₁₃	1	1	yes	characteristic
213	#2352	C₂×C₁₃	1	1	yes	characteristic
214	#2101	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2077	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1921	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1894	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1870	C₂×C₁₃	1	1	yes	characteristic
224	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1825	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	2	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
242	Q₈×C₁₃	—	4	1	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	4	1	no	—
245	Q₈×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	4	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	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	2	no	—
258	C₂×C₄×C₁₃	—	2	2	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	—	2	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	—	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	—	8	4	no	—
291	C₂×C₄×C₁₃	#123	1	2	yes	—
292	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
297	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
298	C₈×C₁₃	—	4	1	no	—
299	C₈×C₁₃	—	4	1	no	—
300	C₈×C₁₃	—	4	1	no	—
301	C₈×C₁₃	—	4	1	no	—
302	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
308	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
318	#397	—	2	1	no	—
319	#394	—	2	1	no	—
320	#391	C₂²×C₁₃	1	1	yes	characteristic
321	#389	—	2	1	no	—
322	#389	C₂²×C₁₃	1	1	yes	characteristic
323	#388	—	2	1	no	—
324	#388	—	2	1	no	—
325	#387	—	2	1	no	—
326	#386	—	2	1	no	—
327	#382	C₂²×C₁₃	1	1	yes	characteristic
328	#380	C₂²×C₁₃	1	1	yes	characteristic
329	#380	C₂²×C₁₃	1	1	yes	characteristic
330	#380	C₂²×C₁₃	1	1	yes	characteristic
331	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
332	C₄×C₂²⋊C₄	—	2	1	no	—
333	#340	C₂²×C₁₃	1	1	yes	characteristic
334	#340	C₂²×C₁₃	1	1	yes	characteristic
335	#340	C₂²×C₁₃	1	1	yes	characteristic
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	#336	C₂²×C₁₃	1	1	yes	characteristic
344	#336	C₂²×C₁₃	1	1	yes	characteristic
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	2	no	—
348	C₂²×C₁₃	—	4	1	no	—
349	C₂²×C₁₃	—	4	1	no	—
350	C₂²×C₁₃	—	4	1	no	—
351	C₂²×C₁₃	—	4	1	no	—
352	C₂²×C₁₃	—	4	1	no	—
353	C₂²×C₁₃	—	4	1	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	C₂×#123	1	1	yes	characteristic
360	C₂²×C₁₃	#546	1	1	yes	characteristic
361	C₂²×C₁₃	#546	1	1	yes	characteristic
362	C₂²×C₁₃	#575	1	1	yes	characteristic
363	C₂²×C₁₃	#575	1	1	yes	characteristic
364	C₂²×C₁₃	#577	1	1	yes	characteristic
365	C₂²×C₁₃	#578	1	1	yes	characteristic
366	C₄×C₁₃	—	2	2	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	4	2	no	—
371	C₄×C₁₃	—	4	2	no	—
372	C₄×C₁₃	—	8	1	no	—
373	C₄×C₁₃	—	8	1	no	—
374	C₄×C₁₃	—	8	1	no	—
375	C₄×C₁₃	—	8	1	no	—
376	C₄×C₁₃	—	8	1	no	—
377	C₄×C₁₃	—	8	1	no	—
378	C₄×C₁₃	#529	1	1	yes	characteristic
379	C₄×C₁₃	#538	1	1	yes	characteristic
380	C₄×C₁₃	#553	1	1	yes	characteristic
381	C₄×C₁₃	#553	1	1	yes	characteristic
382	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
383	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×M₁₆	—	2	2	no	—
388	C₂×M₁₆	—	4	1	no	—
389	C₂×M₁₆	—	4	1	no	—
390	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	—	4	1	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	#117	—	2	2	no	—
401	#117	—	2	2	no	—
402	#117	—	4	1	no	—
403	#117	—	4	1	no	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	4	1	no	—
410	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×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×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	#107	—	2	2	no	—
432	#106	—	4	1	no	—
433	#103	—	2	2	no	—
434	#103	—	4	1	no	—
435	#103	—	4	1	no	—
436	#103	—	4	1	no	—
437	C₂²⋊C₈	—	2	2	no	—
438	C₂²⋊C₈	—	4	1	no	—
439	C₂²⋊C₈	—	4	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	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	C₂×C₁₃	—	4	2	no	—
450	C₂×C₁₃	—	8	1	no	—
451	C₂×C₁₃	#2444	1	1	yes	characteristic
452	C₂×C₁₃	#3093	1	1	yes	characteristic
453	C₂×C₁₃	#3097	1	1	yes	characteristic
454	C₂×C₁₃	#3307	1	1	yes	characteristic
455	C₂×C₁₃	#3313	1	1	yes	characteristic
456	C₂×C₁₃	#3323	1	1	yes	characteristic
457	C₂×C₁₃	#3327	1	1	yes	characteristic
458	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	—	4	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	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	—	4	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	8	1	no	—
490	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₁₃×#41	1	2	yes	—
495	C₂²×C₄	C₁₃×#41	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	M₁₆	—	4	4	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
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	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	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	—	4	2	no	—
524	C₄⋊C₄	—	4	2	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	C₁₃×#41	1	2	yes	—
528	C₄⋊C₄	C₁₃×#41	1	2	yes	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	4	2	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	—	8	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	4	2	no	—
541	C₄²	—	4	2	no	—
542	C₄²	—	8	1	no	—
543	C₁₃	#26226	1	1	yes	characteristic, direct product factor, Sylow
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
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	C₁₃×#123	1	2	yes	—
558	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
559	Q₈	—	4	1	no	—
560	Q₈	—	4	1	no	—
561	Q₈	—	4	1	no	—
562	Q₈	—	4	1	no	—
563	D₄	—	4	4	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	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	—	4	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	—	8	4	no	—
608	C₂×C₄	C₁₃×#123	1	2	yes	—
609	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
610	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
611	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
612	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
613	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
614	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
615	C₈	—	4	1	no	—
616	C₈	—	4	1	no	—
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	4	1	no	—
630	C₂²	—	4	1	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
634	C₂²	C₁₃×#546	1	1	yes	characteristic
635	C₂²	C₁₃×#546	1	1	yes	characteristic
636	C₂²	C₁₃×#575	1	1	yes	characteristic
637	C₂²	C₁₃×#575	1	1	yes	characteristic
638	C₂²	C₁₃×#577	1	1	yes	characteristic
639	C₂²	C₁₃×#578	1	1	yes	characteristic
640	C₄	—	2	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	8	1	no	—
647	C₄	—	8	1	no	—
648	C₄	—	8	1	no	—
649	C₄	—	8	1	no	—
650	C₄	—	8	1	no	—
651	C₄	—	8	1	no	—
652	C₄	C₁₃×#529	1	1	yes	characteristic
653	C₄	C₁₃×#538	1	1	yes	characteristic
654	C₄	C₁₃×#553	1	1	yes	characteristic
655	C₄	C₁₃×#553	1	1	yes	characteristic
656	C₂	—	4	2	no	—
657	C₂	—	8	1	no	—
658	C₂	C₁₃×#2444	1	1	yes	characteristic
659	C₂	C₁₃×#3093	1	1	yes	characteristic
660	C₂	C₁₃×#3097	1	1	yes	characteristic
661	C₂	C₁₃×#3307	1	1	yes	characteristic
662	C₂	C₁₃×#3313	1	1	yes	characteristic
663	C₂	C₁₃×#3323	1	1	yes	characteristic
664	C₂	C₁₃×#3327	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×#2077	C₂	semidirect
5. C₁₃×#2074	C₂	semidirect
6. C₁₃×#2036	C₂	semidirect
7. C₁₃×#1927	C₂	semidirect
8. C₁₃×#1921	C₂	semidirect
9. C₁₃×#1894	C₂	semidirect
10. C₁₃×#1873	C₂	semidirect
11. C₁₃×#1872	C₂	semidirect
13. C₁₃×#1854	C₂	semidirect
14. C₁₃×#1825	C₂	semidirect
15. C₁₃×#1736	C₂	semidirect
126. #26226	C₁₃	direct (N × H)
214. #2101	C₂×C₁₃	semidirect
215. #2077	C₂×C₁₃	semidirect
216. #2074	C₂×C₁₃	semidirect
217. #2036	C₂×C₁₃	semidirect
218. #1927	C₂×C₁₃	semidirect
219. #1921	C₂×C₁₃	semidirect
220. #1894	C₂×C₁₃	semidirect
221. #1873	C₂×C₁₃	semidirect
222. #1872	C₂×C₁₃	semidirect
224. #1854	C₂×C₁₃	semidirect
225. #1825	C₂×C₁₃	semidirect
226. #1736	C₂×C₁₃	semidirect
543. C₁₃	#26226	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×#2415	2
C₁₃×#2352	2
C₁₃×#2101	2
C₁₃×#2077	2
C₁₃×#2074	2
C₁₃×#2036	2
C₁₃×#1927	2
C₁₃×#1921	2
C₁₃×#1894	2
C₁₃×#1873	2
C₁₃×#1872	2
C₁₃×#1870	2
C₁₃×#1854	2
C₁₃×#1825	2
C₁₃×#1736	2
#26226	13

Subgroups — C13×#26226 #15712565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26226 #15712565