Subgroups — C₁₃×#24127 #15710466

Order 3328.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#552	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2536	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₁₃×#552	—	2	4	no	—
18	C₁₃×#552	—	2	4	no	—
19	C₂×C₁₃×#126	—	2	1	no	—
20	C₂×C₁₃×#125	—	2	1	no	—
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#123	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	—	2	1	no	—
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₁₃×#479	—	2	4	no	—
34	C₄×C₁₃×Q₁₆	—	2	4	no	—
35	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#398	—	2	1	no	—
51	C₁₃×#394	—	2	1	no	—
52	C₁₃×#388	—	2	1	no	—
53	C₁₃×#388	—	2	1	no	—
54	C₁₃×#382	C₂²	1	1	yes	characteristic
55	C₁₃×#380	C₂²	1	1	yes	characteristic
56	C₁₃×#380	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	C₁₃×#340	C₂²	1	1	yes	characteristic
62	C₁₃×#340	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×Q₁₆	—	2	2	no	—
70	C₂×C₁₃×Q₁₆	—	2	2	no	—
71	C₂×C₁₃×Q₁₆	—	2	2	no	—
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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#126	—	2	8	no	—
77	C₁₃×#125	—	2	8	no	—
78	C₁₃×#125	—	2	2	no	—
79	C₁₃×#125	D₄	1	4	yes	—
80	C₁₃×#123	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	4	1	no	—
88	C₁₃×C₂²⋊Q₈	—	4	1	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	D₄	1	4	yes	—
93	C₄×D₄×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₁₃×#117	—	2	8	no	—
96	C₁₃×#117	—	2	2	no	—
97	C₁₃×#117	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
124	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₂×C₄²×C₁₃	—	2	1	no	—
127	C₂×C₄²×C₁₃	—	2	1	no	—
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×#107	—	2	2	no	—
130	C₁₃×#107	—	2	2	no	—
131	C₁₃×#106	—	2	2	no	—
132	C₁₃×C₄⋊C₈	—	2	2	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	4	1	no	—
138	C₁₃×#103	—	4	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	2	no	—
140	C₁₃×C₂²⋊C₈	—	2	2	no	—
141	C₁₃×C₂²⋊C₈	—	4	1	no	—
142	C₁₃×C₂²⋊C₈	—	4	1	no	—
143	C₄×C₈×C₁₃	—	2	2	no	—
144	C₁₃×#95	—	2	1	no	—
145	C₁₃×#95	—	2	1	no	—
146	C₁₃×#95	—	2	1	no	—
147	C₁₃×#95	—	2	1	no	—
148	#24127	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
162	C₂×Q₈×C₁₃	#41	1	2	yes	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	—	2	2	no	—
165	C₂×D₄×C₁₃	—	4	1	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	4	2	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₁₃×Q₁₆	—	2	8	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	no	—
205	C₂×C₈×C₁₃	—	2	1	no	—
206	C₂×C₈×C₁₃	#41	1	2	yes	—
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	2	4	no	—
212	C₁₃×C₄⋊C₄	—	2	4	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	1	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	1	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	4	2	no	—
224	C₁₃×C₄⋊C₄	—	4	2	no	—
225	C₁₃×C₄⋊C₄	—	4	2	no	—
226	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
227	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
228	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
229	C₁₃×C₂²⋊C₄	—	2	4	no	—
230	C₁₃×C₂²⋊C₄	—	2	4	no	—
231	C₁₃×C₂²⋊C₄	—	2	4	no	—
232	C₁₃×C₂²⋊C₄	—	2	2	no	—
233	C₁₃×C₂²⋊C₄	—	2	2	no	—
234	C₁₃×C₂²⋊C₄	—	4	2	no	—
235	C₁₃×C₂²⋊C₄	—	4	2	no	—
236	C₁₃×C₂²⋊C₄	—	4	2	no	—
237	C₁₃×C₂²⋊C₄	—	4	2	no	—
238	C₄²×C₁₃	—	2	4	no	—
239	C₄²×C₁₃	—	2	4	no	—
240	C₄²×C₁₃	—	4	2	no	—
241	C₄²×C₁₃	C₂×D₄	1	2	yes	—
242	C₄²×C₁₃	C₂×D₄	1	2	yes	—
243	C₂×#552	C₂×C₁₃	1	1	yes	characteristic
244	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
245	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#2536	C₂×C₁₃	1	1	yes	characteristic
247	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#2001	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#2001	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1991	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1954	C₂×C₁₃	1	1	yes	characteristic
253	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
258	C₂³×C₁₃	—	2	1	no	—
259	C₂³×C₁₃	—	2	1	no	—
260	C₂³×C₁₃	—	2	1	no	—
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	1	no	—
263	C₂³×C₁₃	—	2	1	no	—
264	C₂³×C₁₃	—	2	1	no	—
265	C₂³×C₁₃	—	2	1	no	—
266	C₂³×C₁₃	—	2	1	no	—
267	C₂³×C₁₃	—	2	1	no	—
268	C₂³×C₁₃	—	2	1	no	—
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	1	no	—
271	C₂³×C₁₃	#135	1	2	yes	—
272	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	Q₈×C₁₃	—	2	2	no	—
274	Q₈×C₁₃	—	2	2	no	—
275	Q₈×C₁₃	—	2	2	no	—
276	Q₈×C₁₃	—	2	2	no	—
277	Q₈×C₁₃	—	4	1	no	—
278	Q₈×C₁₃	—	4	1	no	—
279	Q₈×C₁₃	—	4	1	no	—
280	Q₈×C₁₃	—	4	1	no	—
281	D₄×C₁₃	—	4	4	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	1	no	—
297	C₂×C₄×C₁₃	—	4	8	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	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	#120	1	2	yes	—
326	C₂×C₄×C₁₃	#120	1	2	yes	—
327	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
333	C₈×C₁₃	—	2	2	no	—
334	C₈×C₁₃	—	4	1	no	—
335	C₈×C₁₃	—	4	1	no	—
336	C₈×C₁₃	—	4	1	no	—
337	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
338	#552	—	2	4	no	—
339	#552	—	2	4	no	—
340	C₂×#126	—	2	1	no	—
341	C₂×#125	—	2	1	no	—
342	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#123	—	2	1	no	—
344	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#117	—	2	1	no	—
352	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
353	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
354	#479	—	2	4	no	—
355	C₄×Q₁₆	—	2	4	no	—
356	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
363	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
371	#398	—	2	1	no	—
372	#394	—	2	1	no	—
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#382	C₂²×C₁₃	1	1	yes	characteristic
376	#380	C₂²×C₁₃	1	1	yes	characteristic
377	#380	C₂²×C₁₃	1	1	yes	characteristic
378	#340	C₂²×C₁₃	1	1	yes	characteristic
379	#340	C₂²×C₁₃	1	1	yes	characteristic
380	#340	C₂²×C₁₃	1	1	yes	characteristic
381	#340	C₂²×C₁₃	1	1	yes	characteristic
382	#340	C₂²×C₁₃	1	1	yes	characteristic
383	#340	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	2	2	no	—
386	C₂²×C₁₃	—	2	2	no	—
387	C₂²×C₁₃	—	4	1	no	—
388	C₂²×C₁₃	—	4	1	no	—
389	C₂²×C₁₃	—	4	1	no	—
390	C₂²×C₁₃	—	4	1	no	—
391	C₂²×C₁₃	—	4	1	no	—
392	C₂²×C₁₃	—	4	1	no	—
393	C₂²×C₁₃	—	4	1	no	—
394	C₂²×C₁₃	—	4	1	no	—
395	C₂²×C₁₃	—	4	1	no	—
396	C₂²×C₁₃	—	4	1	no	—
397	C₂²×C₁₃	—	4	1	no	—
398	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
399	C₂²×C₁₃	#546	1	1	yes	characteristic
400	C₂²×C₁₃	#547	1	1	yes	characteristic
401	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
402	C₂²×C₁₃	#575	1	1	yes	characteristic
403	C₂²×C₁₃	#578	1	1	yes	characteristic
404	C₂²×C₁₃	#578	1	1	yes	characteristic
405	C₄×C₁₃	—	2	2	no	—
406	C₄×C₁₃	—	2	2	no	—
407	C₄×C₁₃	—	4	1	no	—
408	C₄×C₁₃	—	4	1	no	—
409	C₄×C₁₃	—	4	2	no	—
410	C₄×C₁₃	—	4	2	no	—
411	C₄×C₁₃	—	4	2	no	—
412	C₄×C₁₃	—	4	2	no	—
413	C₄×C₁₃	—	4	2	no	—
414	C₄×C₁₃	—	8	1	no	—
415	C₄×C₁₃	—	8	1	no	—
416	C₄×C₁₃	—	8	1	no	—
417	C₄×C₁₃	#525	1	1	yes	characteristic
418	C₄×C₁₃	#537	1	1	yes	characteristic
419	C₄×C₁₃	#548	1	1	yes	characteristic
420	C₄×C₁₃	#550	1	1	yes	characteristic
421	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
424	C₂³×C₄	—	2	1	no	—
425	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×Q₁₆	—	2	2	no	—
428	C₂×Q₁₆	—	2	2	no	—
429	C₂×Q₁₆	—	2	2	no	—
430	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	#126	—	2	8	no	—
435	#125	—	2	8	no	—
436	#125	—	2	2	no	—
437	#125	D₄×C₁₃	1	4	yes	—
438	#123	—	2	8	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	2	no	—
441	C₂²⋊Q₈	—	2	2	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	2	no	—
445	C₂²⋊Q₈	—	4	1	no	—
446	C₂²⋊Q₈	—	4	1	no	—
447	C₄×Q₈	—	2	2	no	—
448	C₄×Q₈	—	2	2	no	—
449	C₄×Q₈	—	2	2	no	—
450	C₄×Q₈	D₄×C₁₃	1	4	yes	—
451	C₄×D₄	—	2	2	no	—
452	C₄×D₄	—	2	2	no	—
453	#117	—	2	8	no	—
454	#117	—	2	2	no	—
455	#117	—	2	2	no	—
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	2	2	no	—
463	C₂×C₄⋊C₄	—	2	2	no	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	—	2	1	no	—
466	C₂×C₄⋊C₄	—	2	1	no	—
467	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	1	no	—
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
483	C₂×C₄²	—	2	1	no	—
484	C₂×C₄²	—	2	1	no	—
485	C₂×C₄²	—	2	1	no	—
486	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
487	#107	—	2	2	no	—
488	#107	—	2	2	no	—
489	#106	—	2	2	no	—
490	C₄⋊C₈	—	2	2	no	—
491	#103	—	2	2	no	—
492	#103	—	2	2	no	—
493	#103	—	2	2	no	—
494	#103	—	2	2	no	—
495	#103	—	4	1	no	—
496	#103	—	4	1	no	—
497	C₂²⋊C₈	—	2	2	no	—
498	C₂²⋊C₈	—	2	2	no	—
499	C₂²⋊C₈	—	4	1	no	—
500	C₂²⋊C₈	—	4	1	no	—
501	C₄×C₈	—	2	2	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	#95	—	2	1	no	—
505	#95	—	2	1	no	—
506	C₂×C₁₃	—	4	2	no	—
507	C₂×C₁₃	—	8	1	no	—
508	C₂×C₁₃	#2407	1	1	yes	characteristic
509	C₂×C₁₃	#3002	1	1	yes	characteristic
510	C₂×C₁₃	#3011	1	1	yes	characteristic
511	C₂×C₁₃	#3300	1	1	yes	characteristic
512	C₂×C₁₃	#3327	1	1	yes	characteristic
513	C₂×C₁₃	#3336	1	1	yes	characteristic
514	C₂×C₁₃	#3352	1	1	yes	characteristic
515	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
528	C₂×Q₈	C₁₃×#41	1	2	yes	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	4	1	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
556	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
557	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
560	Q₁₆	—	2	8	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	C₁₃×#41	1	2	yes	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
593	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
594	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	4	2	no	—
603	C₂²⋊C₄	—	4	2	no	—
604	C₄²	—	2	4	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	4	2	no	—
607	C₄²	C₂×D₄×C₁₃	1	2	yes	—
608	C₄²	C₂×D₄×C₁₃	1	2	yes	—
609	C₁₃	#24127	1	1	yes	characteristic, direct product factor, Sylow
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	C₁₃×#135	1	2	yes	—
624	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
625	Q₈	—	2	2	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	1	no	—
632	Q₈	—	4	1	no	—
633	D₄	—	4	4	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	C₁₃×#120	1	2	yes	—
678	C₂×C₄	C₁₃×#120	1	2	yes	—
679	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
681	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
682	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
683	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
684	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
685	C₈	—	2	2	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
704	C₂²	C₁₃×#546	1	1	yes	characteristic
705	C₂²	C₁₃×#547	1	1	yes	characteristic
706	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
707	C₂²	C₁₃×#575	1	1	yes	characteristic
708	C₂²	C₁₃×#578	1	1	yes	characteristic
709	C₂²	C₁₃×#578	1	1	yes	characteristic
710	C₄	—	2	2	no	—
711	C₄	—	2	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	8	1	no	—
720	C₄	—	8	1	no	—
721	C₄	—	8	1	no	—
722	C₄	C₁₃×#525	1	1	yes	characteristic
723	C₄	C₁₃×#537	1	1	yes	characteristic
724	C₄	C₁₃×#548	1	1	yes	characteristic
725	C₄	C₁₃×#550	1	1	yes	characteristic
726	C₂	—	4	2	no	—
727	C₂	—	8	1	no	—
728	C₂	C₁₃×#2407	1	1	yes	characteristic
729	C₂	C₁₃×#3002	1	1	yes	characteristic
730	C₂	C₁₃×#3011	1	1	yes	characteristic
731	C₂	C₁₃×#3300	1	1	yes	characteristic
732	C₂	C₁₃×#3327	1	1	yes	characteristic
733	C₂	C₁₃×#3336	1	1	yes	characteristic
734	C₂	C₁₃×#3352	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
2. C₂×C₁₃×#479	C₂	semidirect
3. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#2036	C₂	semidirect
6. C₁₃×#2035	C₂	semidirect
7. C₁₃×#2001	C₂	semidirect
8. C₁₃×#2001	C₂	semidirect
9. C₁₃×#1991	C₂	semidirect
11. C₁₃×#1873	C₂	semidirect
12. C₁₃×#1872	C₂	semidirect
13. C₁₃×#1854	C₂	semidirect
14. C₁₃×#1852	C₂	semidirect
15. C₁₃×#1805	C₂	semidirect
148. #24127	C₁₃	direct (N × H)
244. C₂×#479	C₂×C₁₃	semidirect
245. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
247. #2036	C₂×C₁₃	semidirect
248. #2035	C₂×C₁₃	semidirect
249. #2001	C₂×C₁₃	semidirect
250. #2001	C₂×C₁₃	semidirect
251. #1991	C₂×C₁₃	semidirect
253. #1873	C₂×C₁₃	semidirect
254. #1872	C₂×C₁₃	semidirect
255. #1854	C₂×C₁₃	semidirect
256. #1852	C₂×C₁₃	semidirect
257. #1805	C₂×C₁₃	semidirect
609. C₁₃	#24127	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×#552	2
C₂×C₁₃×#479	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2536	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#2001	2
C₁₃×#1991	2
C₁₃×#1954	2
C₁₃×#1873	2
C₁₃×#1872	2
C₁₃×#1854	2
C₁₃×#1852	2
C₁₃×#1805	2
#24127	13

Subgroups — C13×#24127 #15710466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24127 #15710466