Subgroups — C₁₃×#20490 #15706829

Order 3328.

1138 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2290	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#436	C₄	1	8	yes	complemented
24	C₁₃×#435	C₄	1	8	yes	complemented
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊C₈	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	C₁₃×#405	—	2	4	no	—
32	C₄×C₁₃×M₁₆	—	2	4	no	—
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#388	C₄	1	2	yes	—
46	C₁₃×#387	C₄	1	2	yes	—
47	C₁₃×#386	C₄	1	2	yes	—
48	C₁₃×#385	C₄	1	2	yes	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₁₃×#376	C₂²	1	1	yes	characteristic
53	C₁₃×#336	C₂²	1	1	yes	characteristic
54	C₁₃×#336	C₂²	1	1	yes	characteristic
55	C₁₃×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	—	2	2	no	—
64	C₂×C₁₃×M₁₆	—	2	2	no	—
65	C₂×C₁₃×M₁₆	—	2	2	no	—
66	C₂×C₁₃×M₁₆	—	2	2	no	—
67	C₂×C₁₃×M₁₆	—	2	2	no	—
68	C₂×C₁₃×M₁₆	—	2	2	no	—
69	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
70	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
71	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	complemented
72	C₂²×C₈×C₁₃	—	2	2	no	—
73	C₂²×C₈×C₁₃	—	2	2	no	—
74	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
84	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
85	C₁₃×#117	—	2	2	no	—
86	C₁₃×#117	—	2	2	no	—
87	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	—	2	2	no	—
96	C₂×C₄²×C₁₃	—	2	2	no	—
97	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
104	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
105	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
106	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
107	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
108	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
109	C₁₃×#97	—	2	2	no	—
110	C₁₃×#97	—	2	2	no	—
111	C₁₃×#97	—	2	2	no	—
112	C₁₃×#97	C₂×C₄	1	4	yes	complemented
113	C₁₃×#97	D₄	1	4	yes	complemented
114	C₄×C₈×C₁₃	—	2	2	no	—
115	C₄×C₈×C₁₃	—	2	2	no	—
116	C₄×C₈×C₁₃	—	2	2	no	—
117	C₄×C₈×C₁₃	—	2	2	no	—
118	C₄×C₈×C₁₃	—	2	2	no	—
119	C₄×C₈×C₁₃	—	2	2	no	—
120	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
121	C₁₃×#95	C₂×C₄	1	2	yes	—
122	C₁₃×#95	C₂×C₄	1	2	yes	—
123	C₁₃×#95	C₂×C₄	1	2	yes	—
124	C₁₃×#95	C₂×C₄	1	2	yes	—
125	C₁₃×#95	C₂×C₄	1	2	yes	—
126	#20490	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₁₃	—	4	2	no	—
130	C₂×D₄×C₁₃	C₄²	1	4	yes	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₁₃×M₁₆	—	2	8	no	—
156	C₁₃×M₁₆	—	2	8	no	—
157	C₁₃×M₁₆	—	2	8	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
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	8	no	—
171	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
172	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
173	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
175	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
178	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
179	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
181	C₂×C₈×C₁₃	#41	1	2	yes	—
182	C₂×C₈×C₁₃	#41	1	2	yes	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	—	4	2	no	—
189	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
190	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
191	C₄²×C₁₃	—	2	4	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	—	2	1	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
199	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
200	C₄²×C₁₃	C₂×D₄	1	2	yes	—
201	C₄²×C₁₃	#41	1	2	yes	—
202	C₂×#436	C₂×C₁₃	1	1	yes	characteristic
203	C₂×#435	C₂×C₁₃	1	1	yes	characteristic
204	C₂×#405	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2290	C₂×C₁₃	1	1	yes	characteristic
207	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1768	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1750	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1726	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	—	2	1	no	—
219	C₂³×C₁₃	—	2	1	no	—
220	C₂³×C₁₃	—	2	1	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
226	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
227	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
228	D₄×C₁₃	—	4	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	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	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	4	8	no	—
254	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
255	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
256	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
257	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
258	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
259	C₂×C₄×C₁₃	#131	1	4	yes	—
260	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
266	C₈×C₁₃	—	2	2	no	—
267	C₈×C₁₃	—	2	2	no	—
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	—	2	2	no	—
270	C₈×C₁₃	—	2	2	no	—
271	C₈×C₁₃	—	2	2	no	—
272	C₈×C₁₃	C₄×D₄	1	4	yes	—
273	C₈×C₁₃	C₄×D₄	1	4	yes	—
274	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
275	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
276	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
277	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
280	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
281	#436	C₄×C₁₃	1	8	yes	complemented
282	#435	C₄×C₁₃	1	8	yes	complemented
283	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
289	#405	—	2	4	no	—
290	C₄×M₁₆	—	2	4	no	—
291	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
303	#388	C₄×C₁₃	1	2	yes	—
304	#387	C₄×C₁₃	1	2	yes	—
305	#386	C₄×C₁₃	1	2	yes	—
306	#385	C₄×C₁₃	1	2	yes	—
307	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
310	#376	C₂²×C₁₃	1	1	yes	characteristic
311	#336	C₂²×C₁₃	1	1	yes	characteristic
312	#336	C₂²×C₁₃	1	1	yes	characteristic
313	#336	C₂²×C₁₃	1	1	yes	characteristic
314	#336	C₂²×C₁₃	1	1	yes	characteristic
315	#336	C₂²×C₁₃	1	1	yes	characteristic
316	#336	C₂²×C₁₃	1	1	yes	characteristic
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	—	4	2	no	—
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	4	2	no	—
327	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
328	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
329	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
330	C₂²×C₁₃	C₂×#131	1	2	yes	—
331	C₂²×C₁₃	#568	1	2	yes	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	4	no	—
335	C₄×C₁₃	—	2	4	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	4	2	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
341	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
342	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
343	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
344	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
345	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×M₁₆	—	2	2	no	—
349	C₂×M₁₆	—	2	2	no	—
350	C₂×M₁₆	—	2	2	no	—
351	C₂×M₁₆	—	2	2	no	—
352	C₂×M₁₆	—	2	2	no	—
353	C₂×M₁₆	—	2	2	no	—
354	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
355	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
356	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
357	C₂²×C₈	—	2	2	no	—
358	C₂²×C₈	—	2	2	no	—
359	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
360	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
369	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
374	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
376	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
377	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
378	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
380	C₂×C₄²	—	2	2	no	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
388	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
389	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
390	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
391	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
392	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
393	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
394	#97	—	2	2	no	—
395	#97	—	2	2	no	—
396	#97	—	2	2	no	—
397	#97	C₂×C₄×C₁₃	1	4	yes	complemented
398	#97	D₄×C₁₃	1	4	yes	complemented
399	C₄×C₈	—	2	2	no	—
400	C₄×C₈	—	2	2	no	—
401	C₄×C₈	—	2	2	no	—
402	C₄×C₈	—	2	2	no	—
403	C₄×C₈	—	2	2	no	—
404	C₄×C₈	—	2	2	no	—
405	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
406	#95	C₂×C₄×C₁₃	1	2	yes	—
407	#95	C₂×C₄×C₁₃	1	2	yes	—
408	#95	C₂×C₄×C₁₃	1	2	yes	—
409	#95	C₂×C₄×C₁₃	1	2	yes	—
410	#95	C₂×C₄×C₁₃	1	2	yes	—
411	C₂×C₁₃	—	4	2	no	—
412	C₂×C₁₃	—	4	2	no	—
413	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
414	C₂×C₁₃	#2873	1	1	yes	characteristic
415	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
416	C₂×C₁₃	#2933	1	2	yes	—
417	C₂×C₁₃	#2969	1	2	yes	—
418	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
419	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	C₄²×C₁₃	1	4	yes	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
434	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
435	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
440	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
441	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
444	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
446	M₁₆	—	2	8	no	—
447	M₁₆	—	2	8	no	—
448	M₁₆	—	2	8	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	8	no	—
462	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
463	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
464	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
465	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
466	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
467	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
468	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
469	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
470	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
471	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
472	C₂×C₈	C₁₃×#41	1	2	yes	—
473	C₂×C₈	C₁₃×#41	1	2	yes	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
481	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
482	C₄²	—	2	4	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
490	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
491	C₄²	C₂×D₄×C₁₃	1	2	yes	—
492	C₄²	C₁₃×#41	1	2	yes	—
493	C₁₃	#20490	1	1	yes	characteristic, direct product factor, Sylow
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
503	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
504	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
505	D₄	—	4	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
532	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
533	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
534	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
535	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
536	C₂×C₄	C₁₃×#131	1	4	yes	—
537	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
538	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
540	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
541	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
542	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	2	2	no	—
547	C₈	—	2	2	no	—
548	C₈	—	2	2	no	—
549	C₈	C₄×D₄×C₁₃	1	4	yes	—
550	C₈	C₄×D₄×C₁₃	1	4	yes	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
562	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
563	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
564	C₂²	C₂×C₁₃×#131	1	2	yes	—
565	C₂²	C₁₃×#568	1	2	yes	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	4	no	—
571	C₄	—	2	4	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
575	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
576	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
577	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
578	C₂	—	4	2	no	—
579	C₂	—	4	2	no	—
580	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
581	C₂	C₁₃×#2873	1	1	yes	characteristic
582	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
583	C₂	C₁₃×#2933	1	2	yes	—
584	C₂	C₁₃×#2969	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#405	C₂	semidirect
4. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
6. C₁₃×#1771	C₂	semidirect
7. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
8. C₁₃×#1768	C₂	semidirect
9. C₁₃×#1753	C₂	semidirect
10. C₁₃×#1753	C₂	semidirect
11. C₁₃×#1753	C₂	semidirect
12. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
13. C₁₃×#1750	C₂	semidirect
14. C₄×C₁₃×C₂²⋊C₈	C₂	semidirect
15. C₁₃×#1726	C₂	semidirect
23. C₁₃×#436	C₄	semidirect
24. C₁₃×#435	C₄	semidirect
71. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
74. C₂²×C₈×C₁₃	C₂×C₄	semidirect
103. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
104. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
107. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
108. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
112. C₁₃×#97	C₂×C₄	semidirect
113. C₁₃×#97	D₄	semidirect
120. C₄×C₈×C₁₃	C₂×C₄	semidirect
126. #20490	C₁₃	direct (N × H)
204. C₂×#405	C₂×C₁₃	semidirect
205. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
207. #1771	C₂×C₁₃	semidirect
208. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
209. #1768	C₂×C₁₃	semidirect
210. #1753	C₂×C₁₃	semidirect
211. #1753	C₂×C₁₃	semidirect
212. #1753	C₂×C₁₃	semidirect
213. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
214. #1750	C₂×C₁₃	semidirect
215. C₄×C₂²⋊C₈	C₂×C₁₃	semidirect
216. #1726	C₂×C₁₃	semidirect
281. #436	C₄×C₁₃	semidirect
282. #435	C₄×C₁₃	semidirect
356. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
359. C₂²×C₈	C₂×C₄×C₁₃	semidirect
388. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
389. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
392. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
393. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
397. #97	C₂×C₄×C₁₃	semidirect
398. #97	D₄×C₁₃	semidirect
405. C₄×C₈	C₂×C₄×C₁₃	semidirect
493. C₁₃	#20490	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×#436	2
C₂×C₁₃×#435	2
C₂×C₁₃×#405	2
C₂×C₄×C₁₃×M₁₆	2
C₁₃×#2290	2
C₁₃×#1771	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1768	2
C₁₃×#1753	2
C₈×C₁₃×C₂²⋊C₄	2
C₁₃×#1750	2
C₄×C₁₃×C₂²⋊C₈	2
C₁₃×#1726	2
#20490	13

Subgroups — C13×#20490 #15706829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20490 #15706829