Subgroups — C₁₃×#9665 #15696004

Order 3328.

586 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1954	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×D₄⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×D₈	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
8	C₄×C₁₃×D₈	—	2	2	no	—
9	C₄×C₁₃×D₈	—	2	2	no	—
10	C₂×C₁₃×#107	C₄	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₃×#102	C₄	1	2	yes	—
13	C₂×C₁₃×C₂²⋊C₈	—	2	4	no	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#334	—	2	2	no	—
18	C₁₃×D₄⋊C₈	—	2	4	no	—
19	C₁₃×#322	—	2	2	no	—
20	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
21	C₂³×C₄×C₁₃	—	2	2	no	—
22	C₂×C₁₃×D₈	—	2	4	no	—
23	C₂×C₁₃×D₈	—	2	2	no	—
24	C₂²×C₈×C₁₃	—	2	1	no	—
25	C₂²×C₈×C₁₃	—	2	2	no	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	D₄	1	2	yes	—
29	C₄×D₄×C₁₃	—	2	2	no	—
30	C₄×D₄×C₁₃	—	2	2	no	—
31	C₄×D₄×C₁₃	—	2	2	no	—
32	C₄×D₄×C₁₃	—	2	2	no	—
33	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
34	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
35	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×#107	—	2	2	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×#102	—	2	4	no	—
40	C₁₃×C₂²⋊C₈	—	4	8	no	—
41	C₄×C₈×C₁₃	—	2	1	no	—
42	C₄×C₈×C₁₃	—	2	1	no	—
43	C₄×C₈×C₁₃	—	2	1	no	—
44	C₄×C₈×C₁₃	D₄	1	2	yes	—
45	C₄×C₈×C₁₃	D₄	1	2	yes	—
46	C₄×C₈×C₁₃	D₄	1	2	yes	—
47	#9665	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁴×C₁₃	—	2	2	no	—
49	C₂×D₄×C₁₃	—	2	2	no	—
50	C₂×D₄×C₁₃	—	2	2	no	—
51	C₂×D₄×C₁₃	—	2	2	no	—
52	C₂×D₄×C₁₃	—	2	2	no	—
53	C₂×D₄×C₁₃	—	2	2	no	—
54	C₂×D₄×C₁₃	M₁₆	1	4	yes	—
55	C₂²×C₄×C₁₃	—	2	2	no	—
56	C₂²×C₄×C₁₃	—	4	2	no	—
57	C₂²×C₄×C₁₃	—	4	2	no	—
58	C₂²×C₄×C₁₃	—	4	4	no	—
59	C₂²×C₄×C₁₃	—	4	4	no	—
60	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
63	C₁₃×D₈	—	2	8	no	—
64	C₂×C₈×C₁₃	—	2	4	no	—
65	C₂×C₈×C₁₃	—	2	2	no	—
66	C₂×C₈×C₁₃	—	2	2	no	—
67	C₂×C₈×C₁₃	—	2	2	no	—
68	C₂×C₈×C₁₃	—	2	2	no	—
69	C₂×C₈×C₁₃	—	2	4	no	—
70	C₂×C₈×C₁₃	—	4	2	no	—
71	C₂×C₈×C₁₃	—	4	4	no	—
72	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
74	C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₁₃×C₂²⋊C₄	—	4	2	no	—
77	C₁₃×C₂²⋊C₄	—	4	2	no	—
78	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₃	#41	1	1	yes	characteristic
82	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
83	#1954	C₂×C₁₃	1	2	yes	complemented
84	C₂×#334	C₂×C₁₃	1	1	yes	characteristic, complemented
85	C₂×D₄⋊C₈	C₂×C₁₃	1	2	yes	complemented
86	C₂×#322	C₂×C₁₃	1	1	yes	characteristic, complemented
87	C₂³×C₁₃	—	2	4	no	—
88	C₂³×C₁₃	—	4	2	no	—
89	C₂³×C₁₃	—	4	2	no	—
90	C₂³×C₁₃	—	4	4	no	—
91	C₂³×C₁₃	—	4	4	no	—
92	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
93	D₄×C₁₃	—	2	4	no	—
94	D₄×C₁₃	—	2	4	no	—
95	D₄×C₁₃	—	4	2	no	—
96	D₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	—	2	2	no	—
98	C₂×C₄×C₁₃	—	4	2	no	—
99	C₂×C₄×C₁₃	—	4	4	no	—
100	C₂×C₄×C₁₃	—	8	4	no	—
101	C₂×C₄×C₁₃	—	8	2	no	—
102	C₂×C₄×C₁₃	—	8	2	no	—
103	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
106	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
107	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
108	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
109	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
110	C₂×C₄×C₁₃	#131	1	2	yes	—
111	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
112	C₈×C₁₃	—	2	4	no	—
113	C₈×C₁₃	—	2	2	no	—
114	C₈×C₁₃	—	2	2	no	—
115	C₈×C₁₃	—	4	2	no	—
116	C₈×C₁₃	—	8	2	no	—
117	C₂²×D₈	C₄×C₁₃	1	1	yes	characteristic
118	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
119	C₄×D₈	—	2	2	no	—
120	C₄×D₈	—	2	2	no	—
121	C₂×#107	C₄×C₁₃	1	1	yes	characteristic
122	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
123	C₂×#102	C₄×C₁₃	1	2	yes	—
124	C₂×C₂²⋊C₈	—	2	4	no	—
125	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
126	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
128	#334	—	2	2	no	—
129	D₄⋊C₈	—	2	4	no	—
130	#322	—	2	2	no	—
131	C₂²×C₁₃	—	4	8	no	—
132	C₂²×C₁₃	—	4	4	no	—
133	C₂²×C₁₃	—	8	4	no	—
134	C₂²×C₁₃	—	8	2	no	—
135	C₂²×C₁₃	—	8	2	no	—
136	C₂²×C₁₃	#390	1	1	yes	characteristic
137	C₂²×C₁₃	#435	1	2	yes	—
138	C₂²×C₁₃	#442	1	2	yes	—
139	C₂²×C₁₃	#443	1	2	yes	—
140	C₄×C₁₃	—	2	1	no	—
141	C₄×C₁₃	—	2	1	no	—
142	C₄×C₁₃	—	8	2	no	—
143	C₄×C₁₃	#407	1	1	yes	characteristic
144	C₄×C₁₃	#408	1	1	yes	characteristic
145	C₄×C₁₃	#435	1	2	yes	—
146	C₄×C₁₃	#469	1	2	yes	—
147	C₄×C₁₃	#496	1	2	yes	—
148	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
149	C₂³×C₄	—	2	2	no	—
150	C₂×D₈	—	2	4	no	—
151	C₂×D₈	—	2	2	no	—
152	C₂²×C₈	—	2	1	no	—
153	C₂²×C₈	—	2	2	no	—
154	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
155	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
156	C₂²×C₈	D₄×C₁₃	1	2	yes	—
157	C₄×D₄	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₄×D₄	—	2	2	no	—
160	C₄×D₄	—	2	2	no	—
161	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
162	C₂×C₂²⋊C₄	—	2	2	no	—
163	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
164	#107	—	2	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	C₄⋊C₈	—	2	2	no	—
167	#102	—	2	4	no	—
168	C₂²⋊C₈	—	4	8	no	—
169	C₄×C₈	—	2	1	no	—
170	C₄×C₈	—	2	1	no	—
171	C₄×C₈	—	2	1	no	—
172	C₄×C₈	D₄×C₁₃	1	2	yes	—
173	C₄×C₈	D₄×C₁₃	1	2	yes	—
174	C₄×C₈	D₄×C₁₃	1	2	yes	—
175	C₂×C₁₃	—	8	4	no	—
176	C₂×C₁₃	#1586	1	4	yes	—
177	C₂×C₁₃	#1955	1	1	yes	characteristic
178	C₂×C₁₃	#1972	1	1	yes	characteristic
179	C₂×C₁₃	#1974	1	1	yes	characteristic
180	C₂⁴	—	2	2	no	—
181	C₂×D₄	—	2	2	no	—
182	C₂×D₄	—	2	2	no	—
183	C₂×D₄	—	2	2	no	—
184	C₂×D₄	—	2	2	no	—
185	C₂×D₄	—	2	2	no	—
186	C₂×D₄	C₁₃×M₁₆	1	4	yes	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	4	2	no	—
189	C₂²×C₄	—	4	2	no	—
190	C₂²×C₄	—	4	4	no	—
191	C₂²×C₄	—	4	4	no	—
192	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
193	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
194	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
195	D₈	—	2	8	no	—
196	C₂×C₈	—	2	4	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	2	4	no	—
202	C₂×C₈	—	4	2	no	—
203	C₂×C₈	—	4	4	no	—
204	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
205	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
206	C₄⋊C₄	—	2	2	no	—
207	C₄⋊C₄	—	2	2	no	—
208	C₂²⋊C₄	—	4	2	no	—
209	C₂²⋊C₄	—	4	2	no	—
210	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
211	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
212	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
213	C₄²	C₁₃×#41	1	1	yes	characteristic
214	C₁₃	#9665	1	1	yes	characteristic, direct product factor, Sylow
215	C₂³	—	2	4	no	—
216	C₂³	—	4	2	no	—
217	C₂³	—	4	2	no	—
218	C₂³	—	4	4	no	—
219	C₂³	—	4	4	no	—
220	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
221	D₄	—	2	4	no	—
222	D₄	—	2	4	no	—
223	D₄	—	4	2	no	—
224	D₄	—	4	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	4	no	—
228	C₂×C₄	—	8	4	no	—
229	C₂×C₄	—	8	2	no	—
230	C₂×C₄	—	8	2	no	—
231	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
233	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
234	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
235	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
236	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
237	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
238	C₂×C₄	C₁₃×#131	1	2	yes	—
239	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
240	C₈	—	2	4	no	—
241	C₈	—	2	2	no	—
242	C₈	—	2	2	no	—
243	C₈	—	4	2	no	—
244	C₈	—	8	2	no	—
245	C₂²	—	4	8	no	—
246	C₂²	—	4	4	no	—
247	C₂²	—	8	4	no	—
248	C₂²	—	8	2	no	—
249	C₂²	—	8	2	no	—
250	C₂²	C₁₃×#390	1	1	yes	characteristic
251	C₂²	C₁₃×#435	1	2	yes	—
252	C₂²	C₁₃×#442	1	2	yes	—
253	C₂²	C₁₃×#443	1	2	yes	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	8	2	no	—
257	C₄	C₁₃×#407	1	1	yes	characteristic
258	C₄	C₁₃×#408	1	1	yes	characteristic
259	C₄	C₁₃×#435	1	2	yes	—
260	C₄	C₁₃×#469	1	2	yes	—
261	C₄	C₁₃×#496	1	2	yes	—
262	C₂	—	8	4	no	—
263	C₂	C₁₃×#1586	1	4	yes	—
264	C₂	C₁₃×#1955	1	1	yes	characteristic
265	C₂	C₁₃×#1972	1	1	yes	characteristic
266	C₂	C₁₃×#1974	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×C₁₃×D₈	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1954	C₂	semidirect
3. C₂×C₁₃×#334	C₂	semidirect
4. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
5. C₂×C₁₃×#322	C₂	semidirect
47. #9665	C₁₃	direct (N × H)
83. #1954	C₂×C₁₃	semidirect
84. C₂×#334	C₂×C₁₃	semidirect
85. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
86. C₂×#322	C₂×C₁₃	semidirect
214. C₁₃	#9665	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×C₄×C₁₃×D₈	2
C₁₃×#1954	2
C₂×C₁₃×#334	2
C₂×C₁₃×D₄⋊C₈	2
C₂×C₁₃×#322	2
#9665	13

Subgroups — C13×#9665 #15696004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9665 #15696004