Subgroups — C₁₃×#26128 #15712467

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2417	C₂	1	1	yes	maximal, characteristic
4	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2077	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1869	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1853	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	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	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	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₁₃×#483	—	2	4	no	—
25	C₂×C₁₃×#106	—	2	4	no	—
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#106	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	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₃×#398	—	2	1	no	—
40	C₁₃×#396	—	2	1	no	—
41	C₁₃×#391	C₂²	1	1	yes	characteristic
42	C₁₃×#389	—	2	1	no	—
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#386	—	2	1	no	—
45	C₁₃×#385	—	2	1	no	—
46	C₁₃×#385	—	2	1	no	—
47	C₁₃×#384	C₂²	1	1	yes	characteristic
48	C₁₃×#380	—	2	1	no	—
49	C₁₃×#380	C₂²	1	1	yes	characteristic
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₁₃×#380	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₄⋊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×D₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	—	2	2	no	—
69	C₂²×C₈×C₁₃	—	2	2	no	—
70	C₂²×C₈×C₁₃	—	2	2	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	—	4	1	no	—
79	C₄×D₄×C₁₃	—	2	2	no	—
80	C₄×D₄×C₁₃	—	2	2	no	—
81	C₄×D₄×C₁₃	—	4	4	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	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	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
96	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	—	2	1	no	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×#106	—	2	2	no	—
114	C₁₃×#106	—	2	2	no	—
115	C₁₃×#106	—	2	2	no	—
116	C₁₃×#106	—	2	2	no	—
117	C₁₃×#106	—	4	1	no	—
118	C₁₃×#106	D₄	1	4	yes	complemented
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	2	2	no	—
121	C₁₃×#103	—	2	2	no	—
122	C₁₃×#103	—	4	1	no	—
123	C₁₃×C₂²⋊C₈	—	2	2	no	—
124	C₁₃×C₂²⋊C₈	—	2	2	no	—
125	C₁₃×C₂²⋊C₈	—	2	2	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	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	#26128	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
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×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	SD₁₆	1	4	yes	—
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	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	1	no	—
160	C₂²×C₄×C₁₃	—	2	1	no	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	4	2	no	—
166	C₂²×C₄×C₁₃	—	4	2	no	—
167	C₂²×C₄×C₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₃	—	4	2	no	—
169	C₂²×C₄×C₁₃	—	8	1	no	—
170	C₂²×C₄×C₁₃	—	8	1	no	—
171	C₂²×C₄×C₁₃	—	8	1	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	#41	1	2	yes	—
177	C₂²×C₄×C₁₃	#41	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₈×C₁₃	—	2	8	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₁₃	#41	1	2	yes	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	4	2	no	—
206	C₁₃×C₄⋊C₄	—	4	2	no	—
207	C₁₃×C₄⋊C₄	—	4	2	no	—
208	C₁₃×C₄⋊C₄	—	4	2	no	—
209	C₁₃×C₄⋊C₄	—	4	2	no	—
210	C₁₃×C₄⋊C₄	—	4	2	no	—
211	C₁₃×C₄⋊C₄	—	8	1	no	—
212	C₁₃×C₄⋊C₄	—	8	1	no	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
214	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
215	C₁₃×C₂²⋊C₄	—	2	2	no	—
216	C₁₃×C₂²⋊C₄	—	2	2	no	—
217	C₁₃×C₂²⋊C₄	—	4	2	no	—
218	C₁₃×C₂²⋊C₄	—	4	2	no	—
219	C₁₃×C₂²⋊C₄	—	4	2	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	8	1	no	—
222	C₄²×C₁₃	—	2	1	no	—
223	C₄²×C₁₃	—	2	1	no	—
224	C₄²×C₁₃	—	4	2	no	—
225	C₂×#483	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2417	C₂×C₁₃	1	1	yes	characteristic
228	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
229	#2096	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2077	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1920	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1892	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#1869	C₂×C₁₃	1	1	yes	characteristic
238	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₂³×C₁₃	—	2	1	no	—
241	C₂³×C₁₃	—	2	1	no	—
242	C₂³×C₁₃	—	2	1	no	—
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	2	1	no	—
248	C₂³×C₁₃	—	2	1	no	—
249	C₂³×C₁₃	—	2	1	no	—
250	C₂³×C₁₃	#123	1	2	yes	—
251	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
252	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
253	C₂³×C₁₃	#137	1	2	yes	—
254	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	Q₈×C₁₃	—	4	1	no	—
256	Q₈×C₁₃	—	4	1	no	—
257	Q₈×C₁₃	—	4	1	no	—
258	Q₈×C₁₃	—	4	1	no	—
259	D₄×C₁₃	—	2	8	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	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	8	4	no	—
303	C₂×C₄×C₁₃	—	8	4	no	—
304	C₂×C₄×C₁₃	—	8	4	no	—
305	C₂×C₄×C₁₃	#123	1	2	yes	—
306	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
307	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
311	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
313	C₈×C₁₃	—	2	2	no	—
314	C₈×C₁₃	—	2	2	no	—
315	C₈×C₁₃	—	4	1	no	—
316	C₈×C₁₃	—	4	1	no	—
317	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×C₄×D₄	—	2	1	no	—
321	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
324	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
325	#483	—	2	4	no	—
326	C₂×#106	—	2	4	no	—
327	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
340	#398	—	2	1	no	—
341	#396	—	2	1	no	—
342	#391	C₂²×C₁₃	1	1	yes	characteristic
343	#389	—	2	1	no	—
344	#389	C₂²×C₁₃	1	1	yes	characteristic
345	#386	—	2	1	no	—
346	#385	—	2	1	no	—
347	#385	—	2	1	no	—
348	#384	C₂²×C₁₃	1	1	yes	characteristic
349	#380	—	2	1	no	—
350	#380	C₂²×C₁₃	1	1	yes	characteristic
351	#380	C₂²×C₁₃	1	1	yes	characteristic
352	#380	C₂²×C₁₃	1	1	yes	characteristic
353	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
354	#340	C₂²×C₁₃	1	1	yes	characteristic
355	#340	C₂²×C₁₃	1	1	yes	characteristic
356	#340	C₂²×C₁₃	1	1	yes	characteristic
357	#340	C₂²×C₁₃	1	1	yes	characteristic
358	#340	C₂²×C₁₃	1	1	yes	characteristic
359	#340	C₂²×C₁₃	1	1	yes	characteristic
360	#336	C₂²×C₁₃	1	1	yes	characteristic
361	#336	C₂²×C₁₃	1	1	yes	characteristic
362	C₂²×C₁₃	—	2	2	no	—
363	C₂²×C₁₃	—	2	2	no	—
364	C₂²×C₁₃	—	2	2	no	—
365	C₂²×C₁₃	—	2	2	no	—
366	C₂²×C₁₃	—	2	2	no	—
367	C₂²×C₁₃	—	2	2	no	—
368	C₂²×C₁₃	—	2	2	no	—
369	C₂²×C₁₃	—	2	2	no	—
370	C₂²×C₁₃	—	2	2	no	—
371	C₂²×C₁₃	—	4	1	no	—
372	C₂²×C₁₃	—	4	1	no	—
373	C₂²×C₁₃	—	4	1	no	—
374	C₂²×C₁₃	—	4	1	no	—
375	C₂²×C₁₃	#483	1	4	yes	complemented
376	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
377	C₂²×C₁₃	D₄²	1	1	yes	characteristic
378	C₂²×C₁₃	#547	1	1	yes	characteristic
379	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
380	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
381	C₂²×C₁₃	#577	1	1	yes	characteristic
382	C₂²×C₁₃	#577	1	1	yes	characteristic
383	C₄×C₁₃	—	2	2	no	—
384	C₄×C₁₃	—	2	2	no	—
385	C₄×C₁₃	—	4	1	no	—
386	C₄×C₁₃	—	4	1	no	—
387	C₄×C₁₃	—	4	2	no	—
388	C₄×C₁₃	—	4	2	no	—
389	C₄×C₁₃	—	8	1	no	—
390	C₄×C₁₃	—	8	1	no	—
391	C₄×C₁₃	—	8	1	no	—
392	C₄×C₁₃	—	8	1	no	—
393	C₄×C₁₃	—	8	1	no	—
394	C₄×C₁₃	—	8	1	no	—
395	C₄×C₁₃	#525	1	1	yes	characteristic
396	C₄×C₁₃	#539	1	1	yes	characteristic
397	C₄×C₁₃	#548	1	1	yes	characteristic
398	C₄×C₁₃	#553	1	1	yes	characteristic
399	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
401	C₂³×C₄	—	2	1	no	—
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	—	2	1	no	—
404	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
406	C₂²×C₈	—	2	2	no	—
407	C₂²×C₈	—	2	2	no	—
408	C₂²×C₈	—	2	2	no	—
409	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₂²⋊Q₈	—	2	2	no	—
414	C₂²⋊Q₈	—	2	2	no	—
415	C₂²⋊Q₈	—	2	2	no	—
416	C₂²⋊Q₈	—	4	1	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	4	4	no	—
420	C₂×C₄⋊C₄	—	2	2	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	—	2	2	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	4	1	no	—
432	C₂×C₄⋊C₄	—	4	1	no	—
433	C₂×C₄⋊C₄	—	4	1	no	—
434	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
451	#106	—	2	2	no	—
452	#106	—	2	2	no	—
453	#106	—	2	2	no	—
454	#106	—	2	2	no	—
455	#106	—	4	1	no	—
456	#106	D₄×C₁₃	1	4	yes	complemented
457	#103	—	2	2	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#103	—	4	1	no	—
461	C₂²⋊C₈	—	2	2	no	—
462	C₂²⋊C₈	—	2	2	no	—
463	C₂²⋊C₈	—	2	2	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	C₂×C₁₃	—	2	4	no	—
472	C₂×C₁₃	—	4	2	no	—
473	C₂×C₁₃	#2443	1	1	yes	characteristic
474	C₂×C₁₃	C₂×#483	1	1	yes	characteristic
475	C₂×C₁₃	#3099	1	1	yes	characteristic
476	C₂×C₁₃	#3266	1	1	yes	characteristic
477	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
478	C₂×C₁₃	#3335	1	1	yes	characteristic
479	C₂×C₁₃	#3344	1	1	yes	characteristic
480	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	C₁₃×SD₁₆	1	4	yes	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	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	C₂²×C₄	—	8	1	no	—
518	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
519	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
520	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
522	C₂²×C₄	C₁₃×#41	1	2	yes	—
523	C₂²×C₄	C₁₃×#41	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
525	C₂×C₈	—	2	8	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
537	C₂×C₈	C₁₃×#41	1	2	yes	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	4	2	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	8	1	no	—
558	C₄⋊C₄	—	8	1	no	—
559	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
560	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₂²⋊C₄	—	8	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	4	2	no	—
571	C₁₃	#26128	1	1	yes	characteristic, direct product factor, Sylow
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	C₁₃×#123	1	2	yes	—
583	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
584	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
585	C₂³	C₁₃×#137	1	2	yes	—
586	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
587	Q₈	—	4	1	no	—
588	Q₈	—	4	1	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	D₄	—	2	8	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	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	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	8	4	no	—
635	C₂×C₄	—	8	4	no	—
636	C₂×C₄	—	8	4	no	—
637	C₂×C₄	C₁₃×#123	1	2	yes	—
638	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
639	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
640	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
641	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
642	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
643	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
644	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
645	C₈	—	2	2	no	—
646	C₈	—	2	2	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	C₁₃×#483	1	4	yes	complemented
663	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
664	C₂²	D₄²×C₁₃	1	1	yes	characteristic
665	C₂²	C₁₃×#547	1	1	yes	characteristic
666	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
667	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
668	C₂²	C₁₃×#577	1	1	yes	characteristic
669	C₂²	C₁₃×#577	1	1	yes	characteristic
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	—	8	1	no	—
679	C₄	—	8	1	no	—
680	C₄	—	8	1	no	—
681	C₄	—	8	1	no	—
682	C₄	C₁₃×#525	1	1	yes	characteristic
683	C₄	C₁₃×#539	1	1	yes	characteristic
684	C₄	C₁₃×#548	1	1	yes	characteristic
685	C₄	C₁₃×#553	1	1	yes	characteristic
686	C₂	—	2	4	no	—
687	C₂	—	4	2	no	—
688	C₂	C₁₃×#2443	1	1	yes	characteristic
689	C₂	C₂×C₁₃×#483	1	1	yes	characteristic
690	C₂	C₁₃×#3099	1	1	yes	characteristic
691	C₂	C₁₃×#3266	1	1	yes	characteristic
692	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
693	C₂	C₁₃×#3335	1	1	yes	characteristic
694	C₂	C₁₃×#3344	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
1. C₂×C₁₃×#483	C₂	semidirect
2. C₂²×C₁₃×#106	C₂	semidirect
5. C₁₃×#2096	C₂	semidirect
6. C₁₃×#2084	C₂	semidirect
7. C₁₃×#2077	C₂	semidirect
8. C₁₃×#2035	C₂	semidirect
9. C₁₃×#1927	C₂	semidirect
10. C₁₃×#1920	C₂	semidirect
11. C₁₃×#1892	C₂	semidirect
12. C₁₃×#1872	C₂	semidirect
14. C₁₃×#1853	C₂	semidirect
15. C₁₃×#1853	C₂	semidirect
118. C₁₃×#106	D₄	semidirect
133. #26128	C₁₃	direct (N × H)
225. C₂×#483	C₂×C₁₃	semidirect
226. C₂²×#106	C₂×C₁₃	semidirect
229. #2096	C₂×C₁₃	semidirect
230. #2084	C₂×C₁₃	semidirect
231. #2077	C₂×C₁₃	semidirect
232. #2035	C₂×C₁₃	semidirect
233. #1927	C₂×C₁₃	semidirect
234. #1920	C₂×C₁₃	semidirect
235. #1892	C₂×C₁₃	semidirect
236. #1872	C₂×C₁₃	semidirect
238. #1853	C₂×C₁₃	semidirect
239. #1853	C₂×C₁₃	semidirect
375. C₂²×C₁₃	#483	semidirect
456. #106	D₄×C₁₃	semidirect
571. C₁₃	#26128	direct (N × H)
662. C₂²	C₁₃×#483	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#483	2
C₂²×C₁₃×#106	2
C₁₃×#2417	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2096	2
C₁₃×#2084	2
C₁₃×#2077	2
C₁₃×#2035	2
C₁₃×#1927	2
C₁₃×#1920	2
C₁₃×#1892	2
C₁₃×#1872	2
C₁₃×#1869	2
C₁₃×#1853	2
#26128	13

Subgroups — C13×#26128 #15712467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26128 #15712467