Subgroups — C₁₃×#25220 #15711559

Order 3328.

816 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2499	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2360	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2074	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	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	C₁₃×#485	—	2	4	no	—
24	C₁₃×#470	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₃×#397	—	2	1	no	—
38	C₁₃×#397	—	2	1	no	—
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×#389	—	2	1	no	—
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#387	—	2	1	no	—
45	C₁₃×#387	—	2	1	no	—
46	C₁₃×#387	—	2	1	no	—
47	C₁₃×#385	—	2	1	no	—
48	C₁₃×#384	C₂²	1	1	yes	characteristic
49	C₁₃×#382	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
52	C₄×C₁₃×C₂²⋊C₄	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	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×Q₁₆	—	2	2	no	—
66	C₂×C₁₃×Q₁₆	—	2	2	no	—
67	C₂×C₁₃×Q₁₆	—	4	1	no	—
68	C₂×C₁₃×M₁₆	—	2	2	no	—
69	C₂×C₁₃×M₁₆	—	2	2	no	—
70	C₂×C₁₃×M₁₆	—	4	1	no	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₂²⋊Q₈	—	2	2	no	—
76	C₁₃×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	4	1	no	—
81	C₁₃×#117	—	2	2	no	—
82	C₁₃×#117	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
102	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#107	—	2	2	no	—
109	C₁₃×#106	—	2	2	no	—
110	C₁₃×#106	—	2	2	no	—
111	C₁₃×C₄⋊C₈	—	2	2	no	—
112	C₁₃×C₄⋊C₈	—	4	1	no	—
113	C₁₃×#103	—	2	2	no	—
114	C₁₃×#103	—	2	2	no	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	4	1	no	—
119	C₁₃×C₂²⋊C₈	—	2	2	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	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	D₄	1	1	yes	characteristic
131	C₁₃×#95	D₄	1	1	yes	characteristic
132	#25220	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	#41	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₁₃×Q₁₆	—	4	4	no	—
170	C₁₃×M₁₆	—	4	4	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	—	2	1	no	—
182	C₂×C₈×C₁₃	#41	1	2	yes	—
183	C₁₃×C₄⋊C₄	—	2	4	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	—	4	2	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	C₂×D₄	1	2	yes	—
201	C₁₃×C₄⋊C₄	#41	1	2	yes	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	4	1	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	4	2	no	—
212	C₄²×C₁₃	—	4	2	no	—
213	C₄²×C₁₃	—	8	1	no	—
214	C₂×#485	C₂×C₁₃	1	1	yes	characteristic
215	C₂×#470	C₂×C₁₃	1	1	yes	characteristic
216	#2499	C₂×C₁₃	1	1	yes	characteristic
217	#2360	C₂×C₁₃	1	1	yes	characteristic
218	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1872	C₂×C₁₃	1	1	yes	characteristic
226	#1851	C₂×C₁₃	1	1	yes	characteristic
227	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1736	C₂×C₁₃	1	1	yes	characteristic
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	#121	1	2	yes	—
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	1	no	—
242	Q₈×C₁₃	—	4	1	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×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	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	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	2	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	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	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	—	8	4	no	—
287	C₂×C₄×C₁₃	#121	1	2	yes	—
288	C₂×C₄×C₁₃	#137	1	2	yes	—
289	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
295	C₈×C₁₃	—	2	2	no	—
296	C₈×C₁₃	—	4	1	no	—
297	C₈×C₁₃	—	4	1	no	—
298	C₈×C₁₃	—	4	1	no	—
299	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
300	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
306	#485	—	2	4	no	—
307	#470	—	2	4	no	—
308	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×C₄⋊C₈	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×#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×#103	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
320	#397	—	2	1	no	—
321	#397	—	2	1	no	—
322	#391	C₂²×C₁₃	1	1	yes	characteristic
323	#391	C₂²×C₁₃	1	1	yes	characteristic
324	#391	C₂²×C₁₃	1	1	yes	characteristic
325	#389	—	2	1	no	—
326	#389	C₂²×C₁₃	1	1	yes	characteristic
327	#387	—	2	1	no	—
328	#387	—	2	1	no	—
329	#387	—	2	1	no	—
330	#385	—	2	1	no	—
331	#384	C₂²×C₁₃	1	1	yes	characteristic
332	#382	C₂²×C₁₃	1	1	yes	characteristic
333	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
334	C₄×C₂²⋊C₄	—	2	1	no	—
335	C₄×C₂²⋊C₄	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	#336	C₂²×C₁₃	1	1	yes	characteristic
343	#336	C₂²×C₁₃	1	1	yes	characteristic
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	4	1	no	—
348	C₂²×C₁₃	—	4	1	no	—
349	C₂²×C₁₃	—	4	1	no	—
350	C₂²×C₁₃	—	4	1	no	—
351	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
352	C₂²×C₁₃	#546	1	1	yes	characteristic
353	C₂²×C₁₃	#547	1	1	yes	characteristic
354	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
355	C₂²×C₁₃	#575	1	1	yes	characteristic
356	C₂²×C₁₃	#577	1	1	yes	characteristic
357	C₂²×C₁₃	#578	1	1	yes	characteristic
358	C₄×C₁₃	—	2	2	no	—
359	C₄×C₁₃	—	2	2	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	4	2	no	—
364	C₄×C₁₃	—	4	1	no	—
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	—	8	1	no	—
367	C₄×C₁₃	—	8	1	no	—
368	C₄×C₁₃	—	8	1	no	—
369	C₄×C₁₃	—	8	1	no	—
370	C₄×C₁₃	—	8	1	no	—
371	C₄×C₁₃	#529	1	1	yes	characteristic
372	C₄×C₁₃	#539	1	1	yes	characteristic
373	C₄×C₁₃	#546	1	1	yes	characteristic
374	C₄×C₁₃	#547	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
377	C₂³×C₄	—	2	1	no	—
378	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×Q₁₆	—	2	2	no	—
380	C₂×Q₁₆	—	2	2	no	—
381	C₂×Q₁₆	—	4	1	no	—
382	C₂×M₁₆	—	2	2	no	—
383	C₂×M₁₆	—	2	2	no	—
384	C₂×M₁₆	—	4	1	no	—
385	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	4	1	no	—
395	#117	—	2	2	no	—
396	#117	—	2	2	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	4	1	no	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
422	#107	—	2	2	no	—
423	#106	—	2	2	no	—
424	#106	—	2	2	no	—
425	C₄⋊C₈	—	2	2	no	—
426	C₄⋊C₈	—	4	1	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#103	—	2	2	no	—
430	#103	—	2	2	no	—
431	#103	—	2	2	no	—
432	#103	—	4	1	no	—
433	C₂²⋊C₈	—	2	2	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	D₄×C₁₃	1	1	yes	characteristic
445	#95	D₄×C₁₃	1	1	yes	characteristic
446	C₂×C₁₃	—	4	2	no	—
447	C₂×C₁₃	#2425	1	1	yes	characteristic
448	C₂×C₁₃	#3037	1	1	yes	characteristic
449	C₂×C₁₃	#3046	1	1	yes	characteristic
450	C₂×C₁₃	#3312	1	1	yes	characteristic
451	C₂×C₁₃	#3323	1	1	yes	characteristic
452	C₂×C₁₃	#3349	1	1	yes	characteristic
453	C₂×C₁₃	#3356	1	1	yes	characteristic
454	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
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×Q₈	C₂×D₄×C₁₃	1	2	yes	—
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	—	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	—	4	2	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	8	1	no	—
482	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
487	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₁₃×#41	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
490	Q₁₆	—	4	4	no	—
491	M₁₆	—	4	4	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	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	C₁₃×#41	1	2	yes	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	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	—	4	2	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	8	1	no	—
521	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
522	C₄⋊C₄	C₁₃×#41	1	2	yes	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	4	2	no	—
533	C₄²	—	4	2	no	—
534	C₄²	—	8	1	no	—
535	C₁₃	#25220	1	1	yes	characteristic, direct product factor, Sylow
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	C₁₃×#121	1	2	yes	—
543	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	Q₈	—	2	2	no	—
545	Q₈	—	2	2	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	4	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	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	—	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	—	8	4	no	—
594	C₂×C₄	C₁₃×#121	1	2	yes	—
595	C₂×C₄	C₁₃×#137	1	2	yes	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
598	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
599	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
600	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
614	C₂²	C₁₃×#546	1	1	yes	characteristic
615	C₂²	C₁₃×#547	1	1	yes	characteristic
616	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
617	C₂²	C₁₃×#575	1	1	yes	characteristic
618	C₂²	C₁₃×#577	1	1	yes	characteristic
619	C₂²	C₁₃×#578	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	8	1	no	—
629	C₄	—	8	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	C₁₃×#529	1	1	yes	characteristic
634	C₄	C₁₃×#539	1	1	yes	characteristic
635	C₄	C₁₃×#546	1	1	yes	characteristic
636	C₄	C₁₃×#547	1	1	yes	characteristic
637	C₂	—	4	2	no	—
638	C₂	C₁₃×#2425	1	1	yes	characteristic
639	C₂	C₁₃×#3037	1	1	yes	characteristic
640	C₂	C₁₃×#3046	1	1	yes	characteristic
641	C₂	C₁₃×#3312	1	1	yes	characteristic
642	C₂	C₁₃×#3323	1	1	yes	characteristic
643	C₂	C₁₃×#3349	1	1	yes	characteristic
644	C₂	C₁₃×#3356	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₃×#2084	C₂	semidirect
6. C₁₃×#2074	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2056	C₂	semidirect
9. C₁₃×#1949	C₂	semidirect
10. C₁₃×#1927	C₂	semidirect
11. C₁₃×#1878	C₂	semidirect
14. C₁₃×#1803	C₂	semidirect
132. #25220	C₁₃	direct (N × H)
218. #2084	C₂×C₁₃	semidirect
219. #2074	C₂×C₁₃	semidirect
220. #2068	C₂×C₁₃	semidirect
221. #2056	C₂×C₁₃	semidirect
222. #1949	C₂×C₁₃	semidirect
223. #1927	C₂×C₁₃	semidirect
224. #1878	C₂×C₁₃	semidirect
227. #1803	C₂×C₁₃	semidirect
535. C₁₃	#25220	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#485	2
C₂×C₁₃×#470	2
C₁₃×#2499	2
C₁₃×#2360	2
C₁₃×#2084	2
C₁₃×#2074	2
C₁₃×#2068	2
C₁₃×#2056	2
C₁₃×#1949	2
C₁₃×#1927	2
C₁₃×#1878	2
C₁₃×#1872	2
C₁₃×#1851	2
C₁₃×#1803	2
C₁₃×#1736	2
#25220	13

Subgroups — C13×#25220 #15711559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25220 #15711559