Subgroups — C₁₃×#13165 #15699504

Order 3328.

326 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#366	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#366	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1942	C₂	1	2	yes	maximal
5	C₁₃×#1380	C₂	1	2	yes	maximal
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#107	C₂²	1	2	yes	—
9	C₂×C₁₃×#107	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#389	—	2	2	no	—
12	C₁₃×#366	—	2	2	no	—
13	C₁₃×#366	C₄	1	4	yes	complemented
14	C₄×C₁₃×C₁₆	—	2	2	no	—
15	C₁₃×#340	—	2	2	no	—
16	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
20	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
21	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	—	2	1	no	—
23	C₂×C₁₃×C₁₆	—	2	1	no	—
24	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
25	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
26	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
27	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
28	C₁₃×#107	—	2	2	no	—
29	C₁₃×#107	—	2	2	no	—
30	C₁₃×#107	—	2	2	no	—
31	C₁₃×#107	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₁₃	—	2	1	no	—
33	C₄×C₈×C₁₃	—	2	1	no	—
34	C₁₃×#95	—	4	2	no	—
35	#13165	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₄×C₁₃	—	4	2	no	—
37	C₂²×C₄×C₁₃	—	4	2	no	—
38	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	—	2	1	no	—
42	C₂×C₈×C₁₃	—	2	1	no	—
43	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
49	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
50	C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₁₃×C₄⋊C₄	—	4	2	no	—
52	C₁₃×C₄⋊C₄	—	4	2	no	—
53	C₁₃×C₄⋊C₄	—	4	2	no	—
54	C₁₃×C₄⋊C₄	—	8	4	no	—
55	C₄²×C₁₃	—	2	1	no	—
56	C₄²×C₁₃	—	2	1	no	—
57	C₁₃×C₁₆	—	2	2	no	—
58	C₁₃×C₁₆	C₄⋊C₄	1	4	yes	complemented
59	C₂×#366	C₂×C₁₃	1	1	yes	characteristic
60	C₂×#366	C₂×C₁₃	1	1	yes	characteristic
61	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
62	#1942	C₂×C₁₃	1	2	yes	—
63	#1380	C₂×C₁₃	1	2	yes	—
64	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
65	C₂×C₄×C₁₃	—	2	1	no	—
66	C₂×C₄×C₁₃	—	2	1	no	—
67	C₂×C₄×C₁₃	—	2	1	no	—
68	C₂×C₄×C₁₃	—	2	1	no	—
69	C₂×C₄×C₁₃	—	4	4	no	—
70	C₂×C₄×C₁₃	—	8	2	no	—
71	C₂×C₄×C₁₃	—	8	2	no	—
72	C₂×C₄×C₁₃	—	8	2	no	—
73	C₂×C₄×C₁₃	—	8	2	no	—
74	C₂×C₄×C₁₃	—	8	2	no	—
75	C₂×C₄×C₁₃	D₁₆	1	2	yes	—
76	C₂×C₄×C₁₃	Q₃₂	1	2	yes	—
77	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
82	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
83	C₈×C₁₃	—	2	2	no	—
84	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
86	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
87	C₈×C₁₃	#125	1	1	yes	characteristic
88	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
89	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
90	C₂×#107	C₂²×C₁₃	1	2	yes	—
91	C₂×#107	C₂²×C₁₃	1	2	yes	—
92	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
93	#389	—	2	2	no	—
94	#366	—	2	2	no	—
95	#366	C₄×C₁₃	1	4	yes	complemented
96	C₄×C₁₆	—	2	2	no	—
97	#340	—	2	2	no	—
98	C₂²×C₁₃	C₄×D₈	1	1	yes	characteristic
99	C₂²×C₁₃	#466	1	1	yes	characteristic
100	C₂²×C₁₃	#500	1	1	yes	characteristic
101	C₂²×C₁₃	C₂×D₁₆	1	1	yes	characteristic
102	C₂²×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
103	C₂²×C₁₃	#508	1	1	yes	characteristic
104	C₂²×C₁₃	#508	1	1	yes	characteristic
105	C₄×C₁₃	—	2	2	no	—
106	C₄×C₁₃	—	2	2	no	—
107	C₄×C₁₃	—	8	4	no	—
108	C₄×C₁₃	—	16	2	no	—
109	C₄×C₁₃	#389	1	1	yes	characteristic
110	C₄×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
111	C₄×C₁₃	#467	1	1	yes	characteristic
112	C₄×C₁₃	#499	1	1	yes	characteristic
113	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
114	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
115	C₂×C₄⋊C₄	—	2	2	no	—
116	C₂×C₄⋊C₄	—	2	2	no	—
117	C₂×C₄⋊C₄	—	4	2	no	—
118	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
119	C₂×C₁₆	—	2	1	no	—
120	C₂×C₁₆	—	2	1	no	—
121	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
122	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
123	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
124	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
125	#107	—	2	2	no	—
126	#107	—	2	2	no	—
127	#107	—	2	2	no	—
128	#107	C₂×C₄×C₁₃	1	4	yes	—
129	C₄×C₈	—	2	1	no	—
130	C₄×C₈	—	2	1	no	—
131	#95	—	4	2	no	—
132	C₂×C₁₃	#1942	1	1	yes	characteristic
133	C₂×C₁₃	C₄×D₁₆	1	1	yes	characteristic
134	C₂×C₁₃	C₄×Q₃₂	1	1	yes	characteristic
135	C₂×C₁₃	#2215	1	1	yes	characteristic
136	C₂×C₁₃	#2216	1	1	yes	characteristic
137	C₂×C₁₃	#2252	1	1	yes	characteristic
138	C₂×C₁₃	#2253	1	1	yes	characteristic
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	—	4	2	no	—
141	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
142	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
143	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
144	C₂×C₈	—	2	1	no	—
145	C₂×C₈	—	2	1	no	—
146	C₂×C₈	C₁₃×Q₁₆	1	2	yes	—
147	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
148	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
149	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
150	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
151	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
152	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	4	2	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₄⋊C₄	—	4	2	no	—
157	C₄⋊C₄	—	8	4	no	—
158	C₄²	—	2	1	no	—
159	C₄²	—	2	1	no	—
160	C₁₆	—	2	2	no	—
161	C₁₆	C₁₃×C₄⋊C₄	1	4	yes	complemented
162	C₁₃	#13165	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	—	8	2	no	—
170	C₂×C₄	—	8	2	no	—
171	C₂×C₄	—	8	2	no	—
172	C₂×C₄	—	8	2	no	—
173	C₂×C₄	—	8	2	no	—
174	C₂×C₄	C₁₃×D₁₆	1	2	yes	—
175	C₂×C₄	C₁₃×Q₃₂	1	2	yes	—
176	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
177	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
178	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
179	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
180	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
181	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
182	C₈	—	2	2	no	—
183	C₈	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
184	C₈	C₄×Q₈×C₁₃	1	1	yes	characteristic
185	C₈	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
186	C₈	C₁₃×#125	1	1	yes	characteristic
187	C₂²	C₄×C₁₃×D₈	1	1	yes	characteristic
188	C₂²	C₁₃×#466	1	1	yes	characteristic
189	C₂²	C₁₃×#500	1	1	yes	characteristic
190	C₂²	C₂×C₁₃×D₁₆	1	1	yes	characteristic
191	C₂²	C₂×C₁₃×Q₃₂	1	1	yes	characteristic
192	C₂²	C₁₃×#508	1	1	yes	characteristic
193	C₂²	C₁₃×#508	1	1	yes	characteristic
194	C₄	—	2	2	no	—
195	C₄	—	2	2	no	—
196	C₄	—	8	4	no	—
197	C₄	—	16	2	no	—
198	C₄	C₁₃×#389	1	1	yes	characteristic
199	C₄	C₄×C₁₃×Q₁₆	1	1	yes	characteristic
200	C₄	C₁₃×#467	1	1	yes	characteristic
201	C₄	C₁₃×#499	1	1	yes	characteristic
202	C₂	C₁₃×#1942	1	1	yes	characteristic
203	C₂	C₄×C₁₃×D₁₆	1	1	yes	characteristic
204	C₂	C₄×C₁₃×Q₃₂	1	1	yes	characteristic
205	C₂	C₁₃×#2215	1	1	yes	characteristic
206	C₂	C₁₃×#2216	1	1	yes	characteristic
207	C₂	C₁₃×#2252	1	1	yes	characteristic
208	C₂	C₁₃×#2253	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
13. C₁₃×#366	C₄	semidirect
35. #13165	C₁₃	direct (N × H)
58. C₁₃×C₁₆	C₄⋊C₄	semidirect
95. #366	C₄×C₁₃	semidirect
161. C₁₆	C₁₃×C₄⋊C₄	semidirect
162. C₁₃	#13165	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×#366	2
C₂×C₄×C₁₃×C₁₆	2
C₁₃×#1942	2
C₁₃×#1380	2
#13165	13

Subgroups — C13×#13165 #15699504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13165 #15699504