Subgroups — C₁₃×#20477 #15706816

Order 3328.

922 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1771	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1753	C₂	1	4	yes	maximal
6	C₁₃×#1746	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1726	C₂	1	2	yes	maximal, complemented
8	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#432	C₄	1	8	yes	complemented
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
13	C₄×C₁₃×M₁₆	C₄	1	8	yes	complemented
14	C₂×C₁₃×#97	C₂²	1	4	yes	—
15	C₂×C₁₃×#97	C₂²	1	2	yes	—
16	C₂×C₁₃×#97	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#383	C₄	1	2	yes	—
21	C₁₃×#382	C₄	1	2	yes	—
22	C₁₃×#381	C₄	1	2	yes	—
23	C₁₃×#380	C₄	1	2	yes	—
24	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₁₃×#376	C₂²	1	2	yes	—
27	C₁₃×#336	C₂²	1	8	yes	—
28	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₁₃×M₁₆	—	2	8	no	—
32	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
33	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
34	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
35	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
36	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
37	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
38	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
41	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
43	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
45	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
46	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
47	C₁₃×#97	—	2	8	no	—
48	C₁₃×#97	C₂×C₄	1	8	yes	—
49	C₁₃×#97	C₂×C₄	1	8	yes	—
50	C₄×C₈×C₁₃	—	2	8	no	—
51	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
52	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
53	C₁₃×#95	C₂×C₄	1	4	yes	—
54	C₁₃×#95	C₂×C₄	1	4	yes	—
55	C₁₃×#95	C₂×C₄	1	4	yes	—
56	C₁₃×#95	C₂×C₄	1	4	yes	—
57	#20477	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	—	2	4	no	—
60	C₂²×C₄×C₁₃	—	4	2	no	—
61	C₂²×C₄×C₁₃	—	4	2	no	—
62	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
63	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
64	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
65	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
71	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
73	C₁₃×M₁₆	—	2	16	no	—
74	C₂×C₈×C₁₃	—	2	4	no	—
75	C₂×C₈×C₁₃	—	2	4	no	—
76	C₂×C₈×C₁₃	—	2	4	no	—
77	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
78	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
79	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
80	C₂×C₈×C₁₃	#41	1	8	yes	—
81	C₁₃×C₄⋊C₄	—	4	4	no	—
82	C₁₃×C₂²⋊C₄	—	4	4	no	—
83	C₄²×C₁₃	—	2	4	no	—
84	C₄²×C₁₃	—	2	4	no	—
85	C₄²×C₁₃	C₄²	1	4	yes	—
86	C₄²×C₁₃	C₄²	1	4	yes	—
87	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
88	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
89	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
90	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂×#432	C₂×C₁₃	1	1	yes	characteristic
92	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
93	#2283	C₂×C₁₃	1	1	yes	characteristic
94	#1771	C₂×C₁₃	1	4	yes	complemented
95	#1753	C₂×C₁₃	1	4	yes	—
96	#1746	C₂×C₁₃	1	2	yes	complemented
97	#1726	C₂×C₁₃	1	2	yes	complemented
98	C₂³×C₁₃	—	2	2	no	—
99	C₂³×C₁₃	—	2	2	no	—
100	C₂³×C₁₃	—	2	2	no	—
101	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
102	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	—	2	2	no	—
104	C₂×C₄×C₁₃	—	2	2	no	—
105	C₂×C₄×C₁₃	—	2	2	no	—
106	C₂×C₄×C₁₃	—	2	2	no	—
107	C₂×C₄×C₁₃	—	2	2	no	—
108	C₂×C₄×C₁₃	—	2	4	no	—
109	C₂×C₄×C₁₃	—	2	4	no	—
110	C₂×C₄×C₁₃	—	2	8	no	—
111	C₂×C₄×C₁₃	—	2	8	no	—
112	C₂×C₄×C₁₃	—	2	8	no	—
113	C₂×C₄×C₁₃	—	4	4	no	—
114	C₂×C₄×C₁₃	—	4	4	no	—
115	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
116	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
117	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
118	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
119	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
120	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
123	C₈×C₁₃	—	2	4	no	—
124	C₈×C₁₃	—	2	8	no	—
125	C₈×C₁₃	#117	1	8	yes	—
126	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
127	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
128	#432	C₄×C₁₃	1	8	yes	complemented
129	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
130	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
131	C₄×M₁₆	C₄×C₁₃	1	8	yes	complemented
132	C₂×#97	C₂²×C₁₃	1	4	yes	—
133	C₂×#97	C₂²×C₁₃	1	2	yes	—
134	C₂×#97	C₂²×C₁₃	1	2	yes	—
135	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
136	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
137	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
138	#383	C₄×C₁₃	1	2	yes	—
139	#382	C₄×C₁₃	1	2	yes	—
140	#381	C₄×C₁₃	1	2	yes	—
141	#380	C₄×C₁₃	1	2	yes	—
142	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
143	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
144	#376	C₂²×C₁₃	1	2	yes	—
145	#336	C₂²×C₁₃	1	8	yes	—
146	C₂²×C₁₃	—	2	2	no	—
147	C₂²×C₁₃	—	2	2	no	—
148	C₂²×C₁₃	—	2	2	no	—
149	C₂²×C₁₃	—	4	4	no	—
150	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
151	C₂²×C₁₃	C₄×#41	1	2	yes	—
152	C₂²×C₁₃	#568	1	2	yes	—
153	C₂²×C₁₃	#568	1	2	yes	—
154	C₄×C₁₃	—	2	2	no	—
155	C₄×C₁₃	—	2	2	no	—
156	C₄×C₁₃	—	2	2	no	—
157	C₄×C₁₃	—	2	2	no	—
158	C₄×C₁₃	—	2	2	no	—
159	C₄×C₁₃	—	4	8	no	—
160	C₄×C₁₃	C₂×#117	1	2	yes	—
161	C₄×C₁₃	C₄×#41	1	2	yes	—
162	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
163	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
164	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
165	C₂×M₁₆	—	2	8	no	—
166	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
167	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
168	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
169	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
170	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
171	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
172	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
173	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
174	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
175	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
176	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
177	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
178	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
179	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
180	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
181	#97	—	2	8	no	—
182	#97	C₂×C₄×C₁₃	1	8	yes	—
183	#97	C₂×C₄×C₁₃	1	8	yes	—
184	C₄×C₈	—	2	8	no	—
185	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
186	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
187	#95	C₂×C₄×C₁₃	1	4	yes	—
188	#95	C₂×C₄×C₁₃	1	4	yes	—
189	#95	C₂×C₄×C₁₃	1	4	yes	—
190	#95	C₂×C₄×C₁₃	1	4	yes	—
191	C₂×C₁₃	—	4	2	no	—
192	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
193	C₂×C₁₃	#2873	1	1	yes	characteristic
194	C₂×C₁₃	#2873	1	1	yes	characteristic
195	C₂×C₁₃	#2967	1	4	yes	—
196	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
197	C₂²×C₄	—	2	4	no	—
198	C₂²×C₄	—	4	2	no	—
199	C₂²×C₄	—	4	2	no	—
200	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
201	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
202	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
203	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
204	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
205	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
206	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
207	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
208	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
209	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
210	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
211	M₁₆	—	2	16	no	—
212	C₂×C₈	—	2	4	no	—
213	C₂×C₈	—	2	4	no	—
214	C₂×C₈	—	2	4	no	—
215	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
216	C₂×C₈	C₂²×C₄×C₁₃	1	8	yes	—
217	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
218	C₂×C₈	C₁₃×#41	1	8	yes	—
219	C₄⋊C₄	—	4	4	no	—
220	C₂²⋊C₄	—	4	4	no	—
221	C₄²	—	2	4	no	—
222	C₄²	—	2	4	no	—
223	C₄²	C₄²×C₁₃	1	4	yes	—
224	C₄²	C₄²×C₁₃	1	4	yes	—
225	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
226	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
227	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
228	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
229	C₁₃	#20477	1	1	yes	characteristic, direct product factor, Sylow
230	C₂³	—	2	2	no	—
231	C₂³	—	2	2	no	—
232	C₂³	—	2	2	no	—
233	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
234	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	2	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	4	no	—
241	C₂×C₄	—	2	4	no	—
242	C₂×C₄	—	2	8	no	—
243	C₂×C₄	—	2	8	no	—
244	C₂×C₄	—	2	8	no	—
245	C₂×C₄	—	4	4	no	—
246	C₂×C₄	—	4	4	no	—
247	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
248	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
249	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
250	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
251	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
252	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
253	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
254	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
255	C₈	—	2	4	no	—
256	C₈	—	2	8	no	—
257	C₈	C₁₃×#117	1	8	yes	—
258	C₂²	—	2	2	no	—
259	C₂²	—	2	2	no	—
260	C₂²	—	2	2	no	—
261	C₂²	—	4	4	no	—
262	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
263	C₂²	C₄×C₁₃×#41	1	2	yes	—
264	C₂²	C₁₃×#568	1	2	yes	—
265	C₂²	C₁₃×#568	1	2	yes	—
266	C₄	—	2	2	no	—
267	C₄	—	2	2	no	—
268	C₄	—	2	2	no	—
269	C₄	—	2	2	no	—
270	C₄	—	2	2	no	—
271	C₄	—	4	8	no	—
272	C₄	C₂×C₁₃×#117	1	2	yes	—
273	C₄	C₄×C₁₃×#41	1	2	yes	—
274	C₂	—	4	2	no	—
275	C₂	C₄×C₁₃×#117	1	1	yes	characteristic
276	C₂	C₁₃×#2873	1	1	yes	characteristic
277	C₂	C₁₃×#2873	1	1	yes	characteristic
278	C₂	C₁₃×#2967	1	4	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	C₂⁴×C₁₃	C₂²×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
6. C₁₃×#1746	C₂	semidirect
7. C₁₃×#1726	C₂	semidirect
10. C₁₃×#432	C₄	semidirect
13. C₄×C₁₃×M₁₆	C₄	semidirect
57. #20477	C₁₃	direct (N × H)
94. #1771	C₂×C₁₃	semidirect
96. #1746	C₂×C₁₃	semidirect
97. #1726	C₂×C₁₃	semidirect
128. #432	C₄×C₁₃	semidirect
131. C₄×M₁₆	C₄×C₁₃	semidirect
229. C₁₃	#20477	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×#432	2
C₂×C₄×C₁₃×M₁₆	2
C₁₃×#2283	2
C₁₃×#1771	2
C₁₃×#1753	2
C₁₃×#1746	2
C₁₃×#1726	2
#20477	13

Subgroups — C13×#20477 #15706816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20477 #15706816