Subgroups — C₁₃×#20561 #15706900

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 574 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	C₁₃×#2290	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1746	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1728	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	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#388	C₄	1	2	yes	—
40	C₁₃×#387	C₄	1	2	yes	—
41	C₁₃×#386	C₄	1	2	yes	—
42	C₁₃×#385	C₄	1	2	yes	—
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₁₃×#376	C₂²	1	1	yes	characteristic
47	C₁₃×#336	C₂²	1	1	yes	characteristic
48	C₁₃×#336	C₂²	1	1	yes	characteristic
49	C₁₃×#336	C₂²	1	1	yes	characteristic
50	C₁₃×#336	C₂²	1	1	yes	characteristic
51	C₁₃×#336	C₂²	1	1	yes	characteristic
52	C₁₃×#336	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	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×M₁₆	—	4	1	no	—
62	C₂×C₁₃×M₁₆	—	4	1	no	—
63	C₂×C₁₃×M₁₆	—	4	1	no	—
64	C₂×C₁₃×M₁₆	—	4	1	no	—
65	C₂×C₁₃×M₁₆	—	4	1	no	—
66	C₂×C₁₃×M₁₆	—	4	1	no	—
67	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
68	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
69	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	complemented
70	C₂²×C₈×C₁₃	—	4	1	no	—
71	C₂²×C₈×C₁₃	—	4	1	no	—
72	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
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	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	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
82	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
83	C₁₃×#117	—	4	1	no	—
84	C₁₃×#117	—	4	1	no	—
85	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	—	4	1	no	—
94	C₂×C₄²×C₁₃	—	4	1	no	—
95	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
102	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
103	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
104	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
105	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
106	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
107	C₁₃×#97	—	4	1	no	—
108	C₁₃×#97	—	4	1	no	—
109	C₁₃×#97	C₂×C₄	1	4	yes	complemented
110	C₄×C₈×C₁₃	—	4	1	no	—
111	C₄×C₈×C₁₃	—	4	1	no	—
112	C₄×C₈×C₁₃	—	4	1	no	—
113	C₄×C₈×C₁₃	—	4	1	no	—
114	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
115	C₁₃×#95	C₂×C₄	1	2	yes	—
116	C₁₃×#95	C₂×C₄	1	2	yes	—
117	C₁₃×#95	C₂×C₄	1	2	yes	—
118	C₁₃×#95	C₂×C₄	1	2	yes	—
119	C₁₃×#95	C₂×C₄	1	2	yes	—
120	#20561	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	C₄²	1	4	yes	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	4	2	no	—
135	C₂²×C₄×C₁₃	—	4	2	no	—
136	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×M₁₆	—	4	4	no	—
150	C₁₃×M₁₆	—	4	4	no	—
151	C₁₃×M₁₆	—	4	4	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	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	—	4	4	no	—
169	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
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	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	4	2	no	—
179	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₁₃×C₂²⋊C₄	—	4	2	no	—
182	C₁₃×C₂²⋊C₄	—	4	2	no	—
183	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
184	C₁₃×C₂²⋊C₄	C₄²	1	4	yes	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	2	1	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	C₄²×C₁₃	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	4	2	no	—
194	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
195	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
196	C₂×#436	C₂×C₁₃	1	1	yes	characteristic
197	C₂×#435	C₂×C₁₃	1	1	yes	characteristic
198	#2290	C₂×C₁₃	1	1	yes	characteristic
199	#1771	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#1768	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1750	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1746	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1728	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	2	1	no	—
214	C₂³×C₁₃	—	2	1	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
220	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
221	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
222	D₄×C₁₃	—	4	4	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	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	—	4	8	no	—
249	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
250	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
251	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
252	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
253	C₂×C₄×C₁₃	#131	1	4	yes	—
254	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
260	C₈×C₁₃	—	2	2	no	—
261	C₈×C₁₃	—	2	2	no	—
262	C₈×C₁₃	—	2	2	no	—
263	C₈×C₁₃	—	2	2	no	—
264	C₈×C₁₃	—	2	2	no	—
265	C₈×C₁₃	—	2	2	no	—
266	C₈×C₁₃	—	2	2	no	—
267	C₈×C₁₃	—	2	2	no	—
268	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
269	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
270	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
271	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
274	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
275	#436	C₄×C₁₃	1	8	yes	complemented
276	#435	C₄×C₁₃	1	8	yes	complemented
277	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
291	#388	C₄×C₁₃	1	2	yes	—
292	#387	C₄×C₁₃	1	2	yes	—
293	#386	C₄×C₁₃	1	2	yes	—
294	#385	C₄×C₁₃	1	2	yes	—
295	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
298	#376	C₂²×C₁₃	1	1	yes	characteristic
299	#336	C₂²×C₁₃	1	1	yes	characteristic
300	#336	C₂²×C₁₃	1	1	yes	characteristic
301	#336	C₂²×C₁₃	1	1	yes	characteristic
302	#336	C₂²×C₁₃	1	1	yes	characteristic
303	#336	C₂²×C₁₃	1	1	yes	characteristic
304	#336	C₂²×C₁₃	1	1	yes	characteristic
305	#336	C₂²×C₁₃	1	1	yes	characteristic
306	#336	C₂²×C₁₃	1	1	yes	characteristic
307	#336	C₂²×C₁₃	1	1	yes	characteristic
308	#336	C₂²×C₁₃	1	1	yes	characteristic
309	C₂²×C₁₃	—	2	2	no	—
310	C₂²×C₁₃	—	2	2	no	—
311	C₂²×C₁₃	—	2	2	no	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	2	2	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	4	2	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
320	C₂²×C₁₃	#518	1	1	yes	characteristic
321	C₂²×C₁₃	#520	1	1	yes	characteristic
322	C₂²×C₁₃	C₂×#131	1	2	yes	—
323	C₂²×C₁₃	#568	1	2	yes	—
324	C₄×C₁₃	—	2	2	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	4	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	2	no	—
332	C₄×C₁₃	#518	1	1	yes	characteristic
333	C₄×C₁₃	#518	1	1	yes	characteristic
334	C₄×C₁₃	#520	1	1	yes	characteristic
335	C₄×C₁₃	#520	1	1	yes	characteristic
336	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
337	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
340	C₂×M₁₆	—	4	1	no	—
341	C₂×M₁₆	—	4	1	no	—
342	C₂×M₁₆	—	4	1	no	—
343	C₂×M₁₆	—	4	1	no	—
344	C₂×M₁₆	—	4	1	no	—
345	C₂×M₁₆	—	4	1	no	—
346	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
347	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
348	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
349	C₂²×C₈	—	4	1	no	—
350	C₂²×C₈	—	4	1	no	—
351	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
352	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
360	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
361	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
362	#117	—	4	1	no	—
363	#117	—	4	1	no	—
364	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
368	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
369	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
370	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄²	—	4	1	no	—
373	C₂×C₄²	—	4	1	no	—
374	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
380	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
381	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
382	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
383	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
384	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
385	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
386	#97	—	4	1	no	—
387	#97	—	4	1	no	—
388	#97	C₂×C₄×C₁₃	1	4	yes	complemented
389	C₄×C₈	—	4	1	no	—
390	C₄×C₈	—	4	1	no	—
391	C₄×C₈	—	4	1	no	—
392	C₄×C₈	—	4	1	no	—
393	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
394	#95	C₂×C₄×C₁₃	1	2	yes	—
395	#95	C₂×C₄×C₁₃	1	2	yes	—
396	#95	C₂×C₄×C₁₃	1	2	yes	—
397	#95	C₂×C₄×C₁₃	1	2	yes	—
398	#95	C₂×C₄×C₁₃	1	2	yes	—
399	C₂×C₁₃	—	4	2	no	—
400	C₂×C₁₃	—	4	2	no	—
401	C₂×C₁₃	#2275	1	1	yes	characteristic
402	C₂×C₁₃	#2873	1	1	yes	characteristic
403	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
404	C₂×C₁₃	#2976	1	2	yes	—
405	C₂×C₁₃	#2993	1	2	yes	—
406	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
407	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	C₄²×C₁₃	1	4	yes	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
422	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
423	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
424	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
429	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
430	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
431	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
434	M₁₆	—	4	4	no	—
435	M₁₆	—	4	4	no	—
436	M₁₆	—	4	4	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	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	—	4	4	no	—
454	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
455	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
456	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
457	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
458	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
459	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
460	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
461	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₂²⋊C₄	—	4	2	no	—
468	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
469	C₂²⋊C₄	C₄²×C₁₃	1	4	yes	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	4	2	no	—
479	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
480	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
481	C₁₃	#20561	1	1	yes	characteristic, direct product factor, Sylow
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
491	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
492	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
493	D₄	—	4	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	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	—	4	8	no	—
520	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
521	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
522	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
523	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
524	C₂×C₄	C₁₃×#131	1	4	yes	—
525	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
526	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
531	C₈	—	2	2	no	—
532	C₈	—	2	2	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	2	no	—
535	C₈	—	2	2	no	—
536	C₈	—	2	2	no	—
537	C₈	—	2	2	no	—
538	C₈	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
550	C₂²	C₁₃×#518	1	1	yes	characteristic
551	C₂²	C₁₃×#520	1	1	yes	characteristic
552	C₂²	C₂×C₁₃×#131	1	2	yes	—
553	C₂²	C₁₃×#568	1	2	yes	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	4	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	C₁₃×#518	1	1	yes	characteristic
563	C₄	C₁₃×#518	1	1	yes	characteristic
564	C₄	C₁₃×#520	1	1	yes	characteristic
565	C₄	C₁₃×#520	1	1	yes	characteristic
566	C₂	—	4	2	no	—
567	C₂	—	4	2	no	—
568	C₂	C₁₃×#2275	1	1	yes	characteristic
569	C₂	C₁₃×#2873	1	1	yes	characteristic
570	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
571	C₂	C₁₃×#2976	1	2	yes	—
572	C₂	C₁₃×#2993	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
4. C₁₃×#1771	C₂	semidirect
5. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
6. C₁₃×#1768	C₂	semidirect
7. C₁₃×#1753	C₂	semidirect
8. C₁₃×#1753	C₂	semidirect
9. C₁₃×#1753	C₂	semidirect
10. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
11. C₁₃×#1750	C₂	semidirect
12. C₄×C₁₃×C₂²⋊C₈	C₂	semidirect
13. C₁₃×#1746	C₂	semidirect
14. C₁₃×#1729	C₂	semidirect
15. C₁₃×#1728	C₂	semidirect
23. C₁₃×#436	C₄	semidirect
24. C₁₃×#435	C₄	semidirect
69. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
72. C₂²×C₈×C₁₃	C₂×C₄	semidirect
101. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
102. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
105. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
106. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
109. C₁₃×#97	C₂×C₄	semidirect
114. C₄×C₈×C₁₃	C₂×C₄	semidirect
120. #20561	C₁₃	direct (N × H)
199. #1771	C₂×C₁₃	semidirect
200. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
201. #1768	C₂×C₁₃	semidirect
202. #1753	C₂×C₁₃	semidirect
203. #1753	C₂×C₁₃	semidirect
204. #1753	C₂×C₁₃	semidirect
205. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
206. #1750	C₂×C₁₃	semidirect
207. C₄×C₂²⋊C₈	C₂×C₁₃	semidirect
208. #1746	C₂×C₁₃	semidirect
209. #1729	C₂×C₁₃	semidirect
210. #1728	C₂×C₁₃	semidirect
275. #436	C₄×C₁₃	semidirect
276. #435	C₄×C₁₃	semidirect
348. C₂×M₁₆	C₂×C₄×C₁₃	semidirect
351. C₂²×C₈	C₂×C₄×C₁₃	semidirect
380. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
381. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
384. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
385. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
388. #97	C₂×C₄×C₁₃	semidirect
393. C₄×C₈	C₂×C₄×C₁₃	semidirect
481. C₁₃	#20561	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
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×#1746	2
C₁₃×#1729	2
C₁₃×#1728	2
#20561	13

Subgroups — C13×#20561 #15706900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20561 #15706900