Subgroups — C₁₃×#13191 #15699530

Order 3328.

450 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#350	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#131	C₂²	1	2	yes	—
6	C₁₃×#532	C₄	1	1	yes	characteristic
7	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
8	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
9	C₁₃×#436	—	2	2	no	—
10	C₈×D₄×C₁₃	—	2	2	no	—
11	C₁₃×#423	C₄	1	1	yes	characteristic
12	C₁₃×#408	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×C₄⋊C₁₆	—	2	2	no	—
15	C₁₃×#350	—	2	8	no	—
16	C₄×C₁₃×C₁₆	—	2	2	no	—
17	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
18	C₁₃×#131	—	2	4	no	—
19	C₁₃×#131	—	2	4	no	—
20	C₂×C₁₃×M₁₆	—	2	2	no	—
21	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₁₃	—	2	2	no	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₁₃×C₄⋊Q₈	C₈	1	1	yes	characteristic
26	C₁₃×#127	C₈	1	1	yes	characteristic
27	C₁₃×#124	C₈	1	2	yes	—
28	C₁₃×#121	—	2	2	no	—
29	C₄×D₄×C₁₃	—	2	2	no	—
30	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₁₃×M₃₂	—	2	4	no	—
32	C₂×C₁₃×C₁₆	—	2	2	no	—
33	C₂×C₁₃×C₁₆	—	2	2	no	—
34	C₂×C₁₃×C₁₆	—	2	2	no	—
35	C₂×C₁₃×C₁₆	D₄	1	4	yes	complemented
36	C₁₃×C₄⋊C₈	—	2	2	no	—
37	C₁₃×C₂²⋊C₈	—	2	4	no	—
38	C₄×C₈×C₁₃	D₄	1	2	yes	—
39	C₄×C₈×C₁₃	D₄	1	2	yes	—
40	#13191	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₁₃×#41	—	2	4	no	—
42	C₁₃×#41	—	2	4	no	—
43	C₂×Q₈×C₁₃	C₂×C₈	1	2	yes	—
44	C₂×D₄×C₁₃	—	2	2	no	—
45	C₂×D₄×C₁₃	—	2	2	no	—
46	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
47	C₂²×C₄×C₁₃	—	2	2	no	—
48	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₁₃×M₁₆	—	2	4	no	—
51	C₁₃×M₁₆	—	4	4	no	—
52	C₂×C₈×C₁₃	—	2	2	no	—
53	C₂×C₈×C₁₃	—	2	2	no	—
54	C₂×C₈×C₁₃	—	4	2	no	—
55	C₂×C₈×C₁₃	—	4	2	no	—
56	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
57	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₃	#41	1	2	yes	—
61	C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₁₃×C₂²⋊C₄	—	2	4	no	—
63	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
64	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
65	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
66	C₁₃×C₁₆	—	2	4	no	—
67	C₁₃×C₁₆	—	4	2	no	—
68	#2931	C₂×C₁₃	1	1	yes	characteristic
69	#2150	C₂×C₁₃	1	1	yes	characteristic, complemented
70	C₂×#350	C₂×C₁₃	1	4	yes	complemented
71	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
72	C₂³×C₁₃	—	2	2	no	—
73	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
74	Q₈×C₁₃	—	2	4	no	—
75	D₄×C₁₃	—	2	4	no	—
76	D₄×C₁₃	—	4	4	no	—
77	D₄×C₁₃	—	4	4	no	—
78	C₂×C₄×C₁₃	—	2	4	no	—
79	C₂×C₄×C₁₃	—	2	2	no	—
80	C₂×C₄×C₁₃	—	4	2	no	—
81	C₂×C₄×C₁₃	—	4	2	no	—
82	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
83	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
84	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	#131	1	2	yes	—
88	C₈×C₁₃	—	2	2	no	—
89	C₈×C₁₃	—	4	2	no	—
90	C₈×C₁₃	#121	1	2	yes	—
91	C₈×C₁₃	#124	1	1	yes	characteristic
92	C₈×C₁₃	#127	1	1	yes	characteristic
93	C₂×#131	C₂²×C₁₃	1	2	yes	—
94	#532	C₄×C₁₃	1	1	yes	characteristic
95	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
96	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
97	#436	—	2	2	no	—
98	C₈×D₄	—	2	2	no	—
99	#423	C₄×C₁₃	1	1	yes	characteristic
100	#408	C₄×C₁₃	1	2	yes	—
101	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
102	C₄⋊C₁₆	—	2	2	no	—
103	#350	—	2	8	no	—
104	C₄×C₁₆	—	2	2	no	—
105	C₂²×C₁₃	—	2	2	no	—
106	C₂²×C₁₃	—	4	4	no	—
107	C₂²×C₁₃	—	4	2	no	—
108	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
109	C₂²×C₁₃	#436	1	2	yes	—
110	C₄×C₁₃	—	2	2	no	—
111	C₄×C₁₃	—	4	2	no	—
112	C₄×C₁₃	#350	1	4	yes	complemented
113	C₄×C₁₃	#390	1	1	yes	characteristic
114	C₄×C₁₃	#408	1	1	yes	characteristic
115	C₄×C₁₃	C₈×D₄	1	2	yes	—
116	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
117	#131	—	2	4	no	—
118	#131	—	2	4	no	—
119	C₂×M₁₆	—	2	2	no	—
120	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
121	C₂²×C₈	—	2	2	no	—
122	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
123	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
124	C₄⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
125	#127	C₈×C₁₃	1	1	yes	characteristic
126	#124	C₈×C₁₃	1	2	yes	—
127	#121	—	2	2	no	—
128	C₄×D₄	—	2	2	no	—
129	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
130	M₃₂	—	2	4	no	—
131	C₂×C₁₆	—	2	2	no	—
132	C₂×C₁₆	—	2	2	no	—
133	C₂×C₁₆	—	2	2	no	—
134	C₂×C₁₆	D₄×C₁₃	1	4	yes	complemented
135	C₄⋊C₈	—	2	2	no	—
136	C₂²⋊C₈	—	2	4	no	—
137	C₄×C₈	D₄×C₁₃	1	2	yes	—
138	C₄×C₈	D₄×C₁₃	1	2	yes	—
139	C₂×C₁₃	—	2	2	no	—
140	C₂×C₁₃	—	8	2	no	—
141	C₂×C₁₃	#1954	1	1	yes	characteristic
142	C₂×C₁₃	C₂×#350	1	2	yes	—
143	#41	—	2	4	no	—
144	#41	—	2	4	no	—
145	C₂×Q₈	C₂×C₈×C₁₃	1	2	yes	—
146	C₂×D₄	—	2	2	no	—
147	C₂×D₄	—	2	2	no	—
148	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
151	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
152	M₁₆	—	2	4	no	—
153	M₁₆	—	4	4	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	4	2	no	—
157	C₂×C₈	—	4	2	no	—
158	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
159	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
160	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
161	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
162	C₂×C₈	C₁₃×#41	1	2	yes	—
163	C₄⋊C₄	—	2	2	no	—
164	C₂²⋊C₄	—	2	4	no	—
165	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
166	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
167	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
168	C₁₆	—	2	4	no	—
169	C₁₆	—	4	2	no	—
170	C₁₃	#13191	1	1	yes	characteristic, direct product factor, Sylow
171	C₂³	—	2	2	no	—
172	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
173	Q₈	—	2	4	no	—
174	D₄	—	2	4	no	—
175	D₄	—	4	4	no	—
176	D₄	—	4	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	4	2	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
182	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
183	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
185	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
186	C₂×C₄	C₁₃×#131	1	2	yes	—
187	C₈	—	2	2	no	—
188	C₈	—	4	2	no	—
189	C₈	C₁₃×#121	1	2	yes	—
190	C₈	C₁₃×#124	1	1	yes	characteristic
191	C₈	C₁₃×#127	1	1	yes	characteristic
192	C₂²	—	2	2	no	—
193	C₂²	—	4	4	no	—
194	C₂²	—	4	2	no	—
195	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
196	C₂²	C₁₃×#436	1	2	yes	—
197	C₄	—	2	2	no	—
198	C₄	—	4	2	no	—
199	C₄	C₁₃×#350	1	4	yes	complemented
200	C₄	C₁₃×#390	1	1	yes	characteristic
201	C₄	C₁₃×#408	1	1	yes	characteristic
202	C₄	C₈×D₄×C₁₃	1	2	yes	—
203	C₂	—	2	2	no	—
204	C₂	—	8	2	no	—
205	C₂	C₁₃×#1954	1	1	yes	characteristic
206	C₂	C₂×C₁₃×#350	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₁₃×#532	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2150	C₂	semidirect
3. C₂×C₁₃×#350	C₂	semidirect
4. C₂×C₄×C₁₃×C₁₆	C₂	semidirect
35. C₂×C₁₃×C₁₆	D₄	semidirect
40. #13191	C₁₃	direct (N × H)
69. #2150	C₂×C₁₃	semidirect
70. C₂×#350	C₂×C₁₃	semidirect
71. C₂×C₄×C₁₆	C₂×C₁₃	semidirect
112. C₄×C₁₃	#350	semidirect
134. C₂×C₁₆	D₄×C₁₃	semidirect
170. C₁₃	#13191	direct (N × H)
199. C₄	C₁₃×#350	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#2931	2
C₁₃×#2150	2
C₂×C₁₃×#350	2
C₂×C₄×C₁₃×C₁₆	2
#13191	13

Subgroups — C13×#13191 #15699530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13191 #15699530