Subgroups — C₁₃×#24840 #15711179

Order 3328.

860 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	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2851	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1892	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1892	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	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	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#479	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₈	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	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#389	C₂²	1	1	yes	characteristic
40	C₁₃×#387	—	2	1	no	—
41	C₁₃×#387	—	2	1	no	—
42	C₁₃×#387	—	2	1	no	—
43	C₁₃×#385	—	2	1	no	—
44	C₁₃×#385	—	2	1	no	—
45	C₁₃×#385	—	2	1	no	—
46	C₁₃×#382	C₂²	1	1	yes	characteristic
47	C₁₃×#380	C₂²	1	1	yes	characteristic
48	C₁₃×#380	C₂²	1	1	yes	characteristic
49	C₁₃×#380	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	—	2	2	no	—
66	C₂²×C₈×C₁₃	—	2	2	no	—
67	C₂²×C₈×C₁₃	—	2	2	no	—
68	C₂²×C₈×C₁₃	—	2	2	no	—
69	C₂²×C₈×C₁₃	—	4	1	no	—
70	C₂²×C₈×C₁₃	—	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×#125	—	2	2	no	—
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	Q₈	1	4	yes	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	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	—	2	1	no	—
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×C₄²×C₁₃	—	2	2	no	—
100	C₂×C₄²×C₁₃	—	2	2	no	—
101	C₂×C₄²×C₁₃	—	2	1	no	—
102	C₂×C₄²×C₁₃	—	2	1	no	—
103	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#107	—	2	2	no	—
108	C₁₃×#107	—	4	1	no	—
109	C₁₃×#106	—	2	2	no	—
110	C₁₃×#106	—	4	1	no	—
111	C₁₃×C₄⋊C₈	—	2	2	no	—
112	C₁₃×C₄⋊C₈	—	2	2	no	—
113	C₁₃×C₄⋊C₈	—	2	2	no	—
114	C₁₃×C₄⋊C₈	D₄	1	4	yes	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	4	1	no	—
118	C₁₃×#103	—	4	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	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	#24840	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
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	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	2	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	2	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	2	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	—	4	1	no	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	2	yes	—
162	C₂²×C₄×C₁₃	#41	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	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	—	4	4	no	—
175	C₂×C₈×C₁₃	—	4	4	no	—
176	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
178	C₁₃×C₄⋊C₄	—	2	4	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	—	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	—	4	2	no	—
197	C₁₃×C₄⋊C₄	—	4	2	no	—
198	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	4	2	no	—
201	C₁₃×C₂²⋊C₄	—	4	2	no	—
202	C₁₃×C₂²⋊C₄	—	4	2	no	—
203	C₄²×C₁₃	—	2	2	no	—
204	C₄²×C₁₃	—	2	2	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	4	2	no	—
208	C₄²×C₁₃	—	4	2	no	—
209	C₄²×C₁₃	C₂×D₄	1	2	yes	—
210	C₄²×C₁₃	#41	1	2	yes	—
211	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
213	#2851	C₂×C₁₃	1	1	yes	characteristic
214	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
215	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2086	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1989	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1892	C₂×C₁₃	1	1	yes	characteristic
222	#1892	C₂×C₁₃	1	1	yes	characteristic
223	#1808	C₂×C₁₃	1	1	yes	characteristic
224	#1807	C₂×C₁₃	1	1	yes	characteristic
225	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
231	C₂³×C₁₃	#135	1	2	yes	—
232	C₂³×C₁₃	#137	1	2	yes	—
233	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	2	no	—
235	Q₈×C₁₃	—	2	2	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	2	8	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	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	4	4	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	—	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	#121	1	2	yes	—
280	C₂×C₄×C₁₃	#121	1	2	yes	—
281	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
282	C₂×C₄×C₁₃	#135	1	2	yes	—
283	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
289	C₈×C₁₃	—	2	2	no	—
290	C₈×C₁₃	—	2	2	no	—
291	C₈×C₁₃	—	4	1	no	—
292	C₈×C₁₃	—	4	1	no	—
293	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
299	#479	—	2	4	no	—
300	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₄⋊C₈	—	2	4	no	—
305	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#103	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	#391	C₂²×C₁₃	1	1	yes	characteristic
314	#389	C₂²×C₁₃	1	1	yes	characteristic
315	#389	C₂²×C₁₃	1	1	yes	characteristic
316	#389	C₂²×C₁₃	1	1	yes	characteristic
317	#387	—	2	1	no	—
318	#387	—	2	1	no	—
319	#387	—	2	1	no	—
320	#385	—	2	1	no	—
321	#385	—	2	1	no	—
322	#385	—	2	1	no	—
323	#382	C₂²×C₁₃	1	1	yes	characteristic
324	#380	C₂²×C₁₃	1	1	yes	characteristic
325	#380	C₂²×C₁₃	1	1	yes	characteristic
326	#380	C₂²×C₁₃	1	1	yes	characteristic
327	C₄×C₄⋊C₄	—	2	1	no	—
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
329	C₄×C₂²⋊C₄	—	2	1	no	—
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#340	C₂²×C₁₃	1	1	yes	characteristic
332	#340	C₂²×C₁₃	1	1	yes	characteristic
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	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	2	2	no	—
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	2	2	no	—
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	2	2	no	—
344	C₂²×C₁₃	#479	1	4	yes	complemented
345	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
346	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
347	C₂²×C₁₃	#537	1	1	yes	characteristic
348	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
349	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
350	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
351	C₂²×C₁₃	#575	1	1	yes	characteristic
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	—	4	2	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	8	1	no	—
360	C₄×C₁₃	—	8	1	no	—
361	C₄×C₁₃	—	8	1	no	—
362	C₄×C₁₃	—	8	1	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	—	8	1	no	—
365	C₄×C₁₃	#546	1	1	yes	characteristic
366	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
367	C₄×C₁₃	#552	1	1	yes	characteristic
368	C₄×C₁₃	#554	1	1	yes	characteristic
369	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
370	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
371	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂²×C₈	—	2	2	no	—
374	C₂²×C₈	—	2	2	no	—
375	C₂²×C₈	—	2	2	no	—
376	C₂²×C₈	—	2	2	no	—
377	C₂²×C₈	—	4	1	no	—
378	C₂²×C₈	—	4	1	no	—
379	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
383	#125	—	2	2	no	—
384	#125	—	2	2	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	Q₈×C₁₃	1	4	yes	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₄²	—	2	2	no	—
408	C₂×C₄²	—	2	2	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
415	#107	—	2	2	no	—
416	#107	—	4	1	no	—
417	#106	—	2	2	no	—
418	#106	—	4	1	no	—
419	C₄⋊C₈	—	2	2	no	—
420	C₄⋊C₈	—	2	2	no	—
421	C₄⋊C₈	—	2	2	no	—
422	C₄⋊C₈	D₄×C₁₃	1	4	yes	—
423	#103	—	2	2	no	—
424	#103	—	2	2	no	—
425	#103	—	4	1	no	—
426	#103	—	4	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	C₂×C₁₃	—	2	4	no	—
439	C₂×C₁₃	#2417	1	1	yes	characteristic
440	C₂×C₁₃	#3050	1	1	yes	characteristic
441	C₂×C₁₃	#3056	1	1	yes	characteristic
442	C₂×C₁₃	C₂×#479	1	1	yes	characteristic
443	C₂×C₁₃	#3076	1	1	yes	characteristic
444	C₂×C₁₃	#3248	1	1	yes	characteristic
445	C₂×C₁₃	#3250	1	1	yes	characteristic
446	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	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	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
477	C₂²×C₄	C₁₃×#41	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	4	4	no	—
490	C₂×C₈	—	4	4	no	—
491	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
492	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	4	2	no	—
516	C₂²⋊C₄	—	4	2	no	—
517	C₂²⋊C₄	—	4	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	4	2	no	—
523	C₄²	—	4	2	no	—
524	C₄²	C₂×D₄×C₁₃	1	2	yes	—
525	C₄²	C₁₃×#41	1	2	yes	—
526	C₁₃	#24840	1	1	yes	characteristic, direct product factor, Sylow
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
532	C₂³	C₁₃×#135	1	2	yes	—
533	C₂³	C₁₃×#137	1	2	yes	—
534	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
535	Q₈	—	2	2	no	—
536	Q₈	—	2	2	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	C₂×C₄	—	2	8	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	4	4	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	—	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	C₁₃×#121	1	2	yes	—
581	C₂×C₄	C₁₃×#121	1	2	yes	—
582	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
583	C₂×C₄	C₁₃×#135	1	2	yes	—
584	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
587	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
588	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
589	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
590	C₈	—	2	2	no	—
591	C₈	—	2	2	no	—
592	C₈	—	4	1	no	—
593	C₈	—	4	1	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	C₁₃×#479	1	4	yes	complemented
601	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
602	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
603	C₂²	C₁₃×#537	1	1	yes	characteristic
604	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
605	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
606	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
607	C₂²	C₁₃×#575	1	1	yes	characteristic
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	2	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	—	8	1	no	—
621	C₄	C₁₃×#546	1	1	yes	characteristic
622	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
623	C₄	C₁₃×#552	1	1	yes	characteristic
624	C₄	C₁₃×#554	1	1	yes	characteristic
625	C₂	—	2	4	no	—
626	C₂	C₁₃×#2417	1	1	yes	characteristic
627	C₂	C₁₃×#3050	1	1	yes	characteristic
628	C₂	C₁₃×#3056	1	1	yes	characteristic
629	C₂	C₂×C₁₃×#479	1	1	yes	characteristic
630	C₂	C₁₃×#3076	1	1	yes	characteristic
631	C₂	C₁₃×#3248	1	1	yes	characteristic
632	C₂	C₁₃×#3250	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#479	C₂	semidirect
5. C₁₃×#2088	C₂	semidirect
6. C₁₃×#2086	C₂	semidirect
7. C₁₃×#2068	C₂	semidirect
8. C₁₃×#2066	C₂	semidirect
9. C₁₃×#1989	C₂	semidirect
10. C₁₃×#1949	C₂	semidirect
15. C₁₃×#1805	C₂	semidirect
130. #24840	C₁₃	direct (N × H)
211. C₂×#479	C₂×C₁₃	semidirect
215. #2088	C₂×C₁₃	semidirect
216. #2086	C₂×C₁₃	semidirect
217. #2068	C₂×C₁₃	semidirect
218. #2066	C₂×C₁₃	semidirect
219. #1989	C₂×C₁₃	semidirect
220. #1949	C₂×C₁₃	semidirect
225. #1805	C₂×C₁₃	semidirect
344. C₂²×C₁₃	#479	semidirect
526. C₁₃	#24840	direct (N × H)
600. C₂²	C₁₃×#479	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#479	2
C₂²×C₁₃×C₄⋊C₈	2
C₁₃×#2851	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2088	2
C₁₃×#2086	2
C₁₃×#2068	2
C₁₃×#2066	2
C₁₃×#1989	2
C₁₃×#1949	2
C₁₃×#1892	2
C₁₃×#1808	2
C₁₃×#1807	2
C₁₃×#1805	2
#24840	13

Subgroups — C13×#24840 #15711179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24840 #15711179