Subgroups — C₁₃×#13271 #15699610

Order 3328.

332 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1389	C₂	1	2	yes	maximal
5	C₁₃×#1384	C₂	1	2	yes	maximal
6	C₁₃×#533	—	2	1	no	—
7	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
8	C₁₃×#500	—	2	1	no	—
9	C₁₃×#499	—	2	1	no	—
10	C₁₃×#499	C₄	1	2	yes	complemented
11	C₁₃×#498	C₄	1	2	yes	complemented
12	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
13	C₁₃×#427	—	2	1	no	—
14	C₁₃×#427	C₂²	1	2	yes	—
15	C₁₃×#427	C₂²	1	1	yes	characteristic
16	C₁₃×#405	—	2	1	no	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#364	—	2	1	no	—
19	C₁₃×#364	—	2	1	no	—
20	C₁₃×#339	—	2	1	no	—
21	C₂×C₁₃×M₁₆	—	2	1	no	—
22	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₁₃×#125	—	2	2	no	—
26	C₁₃×C₂²⋊Q₈	—	4	2	no	—
27	C₄×Q₈×C₁₃	—	4	2	no	—
28	C₁₃×#117	—	2	1	no	—
29	C₁₃×#117	—	2	2	no	—
30	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
31	C₁₃×M₃₂	—	2	2	no	—
32	C₁₃×M₃₂	—	2	2	no	—
33	C₂×C₁₃×C₁₆	—	2	2	no	—
34	C₁₃×#108	—	2	1	no	—
35	C₁₃×#108	Q₈	1	2	yes	complemented
36	C₁₃×#107	—	2	2	no	—
37	C₁₃×#107	—	2	2	no	—
38	C₁₃×#107	—	2	1	no	—
39	C₁₃×#106	—	2	2	no	—
40	C₁₃×#106	C₂×C₄	1	4	yes	—
41	C₁₃×#106	Q₈	1	2	yes	complemented
42	C₁₃×#97	—	4	1	no	—
43	C₄×C₈×C₁₃	—	4	1	no	—
44	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
48	#13271	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂×Q₈×C₁₃	—	4	2	no	—
50	C₂²×C₄×C₁₃	—	2	1	no	—
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₁₃×M₁₆	—	2	2	no	—
53	C₁₃×M₁₆	—	4	1	no	—
54	C₂×C₈×C₁₃	—	4	1	no	—
55	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
58	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
59	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
60	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
61	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
66	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
67	C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₁₃×C₄⋊C₄	—	4	4	no	—
70	C₁₃×C₄⋊C₄	—	4	2	no	—
71	C₁₃×C₂²⋊C₄	—	4	1	no	—
72	C₁₃×C₂²⋊C₄	—	4	2	no	—
73	C₄²×C₁₃	—	2	1	no	—
74	C₄²×C₁₃	—	4	1	no	—
75	C₄²×C₁₃	—	4	2	no	—
76	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₁₃×C₁₆	—	4	2	no	—
79	#3160	C₂×C₁₃	1	1	yes	characteristic
80	C₂×#364	C₂×C₁₃	1	1	yes	characteristic
81	#1772	C₂×C₁₃	1	1	yes	characteristic
82	#1389	C₂×C₁₃	1	2	yes	—
83	#1384	C₂×C₁₃	1	2	yes	—
84	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
85	Q₈×C₁₃	—	8	4	no	—
86	C₂×C₄×C₁₃	—	2	1	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	4	2	no	—
89	C₂×C₄×C₁₃	—	4	4	no	—
90	C₂×C₄×C₁₃	—	4	2	no	—
91	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
95	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
96	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₈×C₁₃	—	4	2	no	—
98	C₈×C₁₃	#103	1	1	yes	characteristic
99	C₈×C₁₃	#103	1	1	yes	characteristic
100	C₈×C₁₃	#103	1	1	yes	characteristic
101	C₈×C₁₃	#103	1	1	yes	characteristic
102	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
103	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
104	C₈×C₁₃	#124	1	1	yes	characteristic
105	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
106	#533	—	2	1	no	—
107	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
108	#500	—	2	1	no	—
109	#499	—	2	1	no	—
110	#499	C₄×C₁₃	1	2	yes	complemented
111	#498	C₄×C₁₃	1	2	yes	complemented
112	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
113	#427	—	2	1	no	—
114	#427	C₂²×C₁₃	1	2	yes	—
115	#427	C₂²×C₁₃	1	1	yes	characteristic
116	#405	—	2	1	no	—
117	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
118	#364	—	2	1	no	—
119	#364	—	2	1	no	—
120	#339	—	2	1	no	—
121	C₂²×C₁₃	—	4	1	no	—
122	C₂²×C₁₃	#418	1	1	yes	characteristic
123	C₂²×C₁₃	#476	1	1	yes	characteristic
124	C₂²×C₁₃	#477	1	1	yes	characteristic
125	C₄×C₁₃	—	2	2	no	—
126	C₄×C₁₃	—	4	1	no	—
127	C₄×C₁₃	—	8	2	no	—
128	C₄×C₁₃	—	8	4	no	—
129	C₄×C₁₃	#391	1	1	yes	characteristic
130	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
131	C₄×C₁₃	#476	1	1	yes	characteristic
132	C₄×C₁₃	#477	1	1	yes	characteristic
133	C₂×M₁₆	—	2	1	no	—
134	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
135	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
136	C₄⋊Q₈	—	2	2	no	—
137	#125	—	2	2	no	—
138	C₂²⋊Q₈	—	4	2	no	—
139	C₄×Q₈	—	4	2	no	—
140	#117	—	2	2	no	—
141	#117	—	2	1	no	—
142	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
143	M₃₂	—	2	2	no	—
144	M₃₂	—	2	2	no	—
145	C₂×C₁₆	—	2	2	no	—
146	#108	—	2	1	no	—
147	#108	Q₈×C₁₃	1	2	yes	complemented
148	#107	—	2	2	no	—
149	#107	—	2	2	no	—
150	#107	—	2	1	no	—
151	#106	—	2	2	no	—
152	#106	C₂×C₄×C₁₃	1	4	yes	—
153	#106	Q₈×C₁₃	1	2	yes	complemented
154	#97	—	4	1	no	—
155	C₄×C₈	—	4	1	no	—
156	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
157	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
158	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
159	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
160	C₂×C₁₃	—	2	1	no	—
161	C₂×C₁₃	—	2	1	no	—
162	C₂×C₁₃	—	2	1	no	—
163	C₂×C₁₃	#1987	1	1	yes	characteristic
164	C₂×Q₈	—	4	2	no	—
165	C₂²×C₄	—	2	1	no	—
166	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
167	M₁₆	—	2	2	no	—
168	M₁₆	—	4	1	no	—
169	C₂×C₈	—	4	1	no	—
170	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₈	C₁₃×SD₁₆	1	1	yes	characteristic
173	C₂×C₈	C₁₃×SD₁₆	1	1	yes	characteristic
174	C₂×C₈	C₁₃×Q₁₆	1	1	yes	characteristic
175	C₂×C₈	C₁₃×Q₁₆	1	1	yes	characteristic
176	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
177	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
178	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
179	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
180	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
181	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
182	C₄⋊C₄	—	2	4	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	4	4	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₂²⋊C₄	—	4	2	no	—
187	C₂²⋊C₄	—	4	1	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	4	1	no	—
190	C₄²	—	4	2	no	—
191	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
192	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
193	C₁₆	—	4	2	no	—
194	C₁₃	#13271	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
196	Q₈	—	8	4	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
205	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
206	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
207	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₈	—	4	2	no	—
209	C₈	C₁₃×#103	1	1	yes	characteristic
210	C₈	C₁₃×#103	1	1	yes	characteristic
211	C₈	C₁₃×#103	1	1	yes	characteristic
212	C₈	C₁₃×#103	1	1	yes	characteristic
213	C₈	C₄×Q₈×C₁₃	1	1	yes	characteristic
214	C₈	C₄×Q₈×C₁₃	1	1	yes	characteristic
215	C₈	C₁₃×#124	1	1	yes	characteristic
216	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
217	C₂²	—	4	1	no	—
218	C₂²	C₁₃×#418	1	1	yes	characteristic
219	C₂²	C₁₃×#476	1	1	yes	characteristic
220	C₂²	C₁₃×#477	1	1	yes	characteristic
221	C₄	—	2	2	no	—
222	C₄	—	4	1	no	—
223	C₄	—	8	2	no	—
224	C₄	—	8	4	no	—
225	C₄	C₁₃×#391	1	1	yes	characteristic
226	C₄	C₂×C₁₃×#103	1	1	yes	characteristic
227	C₄	C₁₃×#476	1	1	yes	characteristic
228	C₄	C₁₃×#477	1	1	yes	characteristic
229	C₂	—	2	1	no	—
230	C₂	—	2	1	no	—
231	C₂	—	2	1	no	—
232	C₂	C₁₃×#1987	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#476
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1987
prime radical	C₂³×C₁₃	AGL(1,ℤ/8)
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₁₃×#499	C₄	semidirect
11. C₁₃×#498	C₄	semidirect
35. C₁₃×#108	Q₈	semidirect
41. C₁₃×#106	Q₈	semidirect
48. #13271	C₁₃	direct (N × H)
110. #499	C₄×C₁₃	semidirect
111. #498	C₄×C₁₃	semidirect
147. #108	Q₈×C₁₃	semidirect
153. #106	Q₈×C₁₃	semidirect
194. C₁₃	#13271	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3160	2
C₂×C₁₃×#364	2
C₁₃×#1772	2
C₁₃×#1389	2
C₁₃×#1384	2
#13271	13

Subgroups — C13×#13271 #15699610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13271 #15699610