Subgroups — C₁₃×#13207 #15699546

Order 3328.

486 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#358	C₂	1	4	yes	maximal
3	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×Q₁₆	—	2	1	no	—
6	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
8	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
9	C₁₃×#494	—	2	2	no	—
10	C₁₃×#494	C₄	1	4	yes	complemented
11	C₂×C₁₃×#107	C₂²	1	2	yes	—
12	C₂×C₁₃×#106	—	2	1	no	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#382	—	2	1	no	—
15	C₁₃×#358	—	2	8	no	—
16	C₁₃×#346	—	2	2	no	—
17	C₂²×Q₈×C₁₃	—	2	2	no	—
18	C₂×C₁₃×Q₁₆	—	2	4	no	—
19	C₂×C₁₃×Q₁₆	—	2	4	no	—
20	C₂×C₁₃×Q₁₆	—	2	2	no	—
21	C₂×C₁₃×Q₁₆	—	2	4	no	—
22	C₂×C₁₃×Q₁₆	—	4	2	no	—
23	C₂×C₁₃×Q₁₆	—	4	2	no	—
24	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
25	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₁₃×C₄⋊Q₈	—	2	4	no	—
28	C₁₃×C₄⋊Q₈	—	4	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
30	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
31	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
32	C₂×C₁₃×C₁₆	—	2	2	no	—
33	C₂×C₁₃×C₁₆	—	2	2	no	—
34	C₂×C₁₃×C₁₆	D₄	1	4	yes	—
35	C₁₃×#107	—	2	4	no	—
36	C₁₃×#106	—	4	2	no	—
37	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
38	C₄×C₈×C₁₃	D₄	1	2	yes	—
39	C₁₃×#95	—	4	2	no	—
40	#13207	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×Q₈×C₁₃	—	2	4	no	—
42	C₂×Q₈×C₁₃	—	4	2	no	—
43	C₂×Q₈×C₁₃	—	4	2	no	—
44	C₂×Q₈×C₁₃	—	4	2	no	—
45	C₂×Q₈×C₁₃	—	4	2	no	—
46	C₂×Q₈×C₁₃	—	4	2	no	—
47	C₂²×C₄×C₁₃	—	4	2	no	—
48	C₂²×C₄×C₁₃	—	4	2	no	—
49	C₂²×C₄×C₁₃	D₈	1	2	yes	—
50	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₁₃×Q₁₆	—	2	8	no	—
52	C₁₃×Q₁₆	—	4	8	no	—
53	C₁₃×Q₁₆	—	4	4	no	—
54	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₃	D₈	1	2	yes	—
56	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
57	C₂×C₈×C₁₃	C₂²×C₄	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	—	4	8	no	—
62	C₁₃×C₄⋊C₄	—	4	2	no	—
63	C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₁₃	SD₁₆	1	2	yes	—
66	C₁₃×C₁₆	—	2	4	no	—
67	C₂×#494	C₂×C₁₃	1	1	yes	characteristic
68	C₂×#358	C₂×C₁₃	1	4	yes	—
69	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
70	#1846	C₂×C₁₃	1	1	yes	characteristic
71	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
72	Q₈×C₁₃	—	4	4	no	—
73	Q₈×C₁₃	—	4	4	no	—
74	Q₈×C₁₃	—	8	2	no	—
75	Q₈×C₁₃	—	8	2	no	—
76	C₂×C₄×C₁₃	—	2	4	no	—
77	C₂×C₄×C₁₃	—	4	4	no	—
78	C₂×C₄×C₁₃	—	8	2	no	—
79	C₂×C₄×C₁₃	—	8	2	no	—
80	C₂×C₄×C₁₃	—	8	2	no	—
81	C₂×C₄×C₁₃	—	8	4	no	—
82	C₂×C₄×C₁₃	#102	1	4	yes	—
83	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
85	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
89	C₈×C₁₃	#102	1	4	yes	—
90	C₈×C₁₃	C₄×D₄	1	2	yes	—
91	C₈×C₁₃	#121	1	2	yes	—
92	C₂²×Q₁₆	—	2	1	no	—
93	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
94	C₂×C₄⋊Q₈	—	2	1	no	—
95	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
96	#494	—	2	2	no	—
97	#494	C₄×C₁₃	1	4	yes	complemented
98	C₂×#107	C₂²×C₁₃	1	2	yes	—
99	C₂×#106	—	2	1	no	—
100	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
101	#382	—	2	1	no	—
102	#358	—	2	8	no	—
103	#346	—	2	2	no	—
104	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
105	C₂²×C₁₃	#486	1	1	yes	characteristic
106	C₂²×C₁₃	#493	1	1	yes	characteristic
107	C₂²×C₁₃	#510	1	4	yes	—
108	C₄×C₁₃	—	2	4	no	—
109	C₄×C₁₃	—	8	4	no	—
110	C₄×C₁₃	—	16	2	no	—
111	C₄×C₁₃	#390	1	1	yes	characteristic
112	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
113	C₄×C₁₃	#486	1	1	yes	characteristic
114	C₄×C₁₃	#492	1	1	yes	characteristic
115	C₂²×Q₈	—	2	2	no	—
116	C₂×Q₁₆	—	2	4	no	—
117	C₂×Q₁₆	—	2	4	no	—
118	C₂×Q₁₆	—	2	2	no	—
119	C₂×Q₁₆	—	2	4	no	—
120	C₂×Q₁₆	—	4	2	no	—
121	C₂×Q₁₆	—	4	2	no	—
122	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
123	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
124	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
125	C₄⋊Q₈	—	2	4	no	—
126	C₄⋊Q₈	—	4	2	no	—
127	C₂×C₄⋊C₄	—	2	2	no	—
128	C₂×C₄⋊C₄	—	4	2	no	—
129	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
130	C₂×C₁₆	—	2	2	no	—
131	C₂×C₁₆	—	2	2	no	—
132	C₂×C₁₆	D₄×C₁₃	1	4	yes	—
133	#107	—	2	4	no	—
134	#106	—	4	2	no	—
135	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
136	C₄×C₈	D₄×C₁₃	1	2	yes	—
137	#95	—	4	2	no	—
138	C₂×C₁₃	#1957	1	1	yes	characteristic
139	C₂×C₁₃	#2141	1	2	yes	—
140	C₂×C₁₃	#2245	1	2	yes	—
141	C₂×C₁₃	#2251	1	2	yes	—
142	C₂×Q₈	—	2	4	no	—
143	C₂×Q₈	—	4	2	no	—
144	C₂×Q₈	—	4	2	no	—
145	C₂×Q₈	—	4	2	no	—
146	C₂×Q₈	—	4	2	no	—
147	C₂×Q₈	—	4	2	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	—	4	2	no	—
150	C₂²×C₄	C₁₃×D₈	1	2	yes	—
151	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
152	Q₁₆	—	2	8	no	—
153	Q₁₆	—	4	8	no	—
154	Q₁₆	—	4	4	no	—
155	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
156	C₂×C₈	C₁₃×D₈	1	2	yes	—
157	C₂×C₈	C₁₃×SD₁₆	1	2	yes	—
158	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
159	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
160	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
161	C₂×C₈	C₁₃×#41	1	2	yes	—
162	C₄⋊C₄	—	4	8	no	—
163	C₄⋊C₄	—	4	2	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
166	C₄²	C₁₃×SD₁₆	1	2	yes	—
167	C₁₆	—	2	4	no	—
168	C₁₃	#13207	1	1	yes	characteristic, direct product factor, Sylow
169	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
170	Q₈	—	4	4	no	—
171	Q₈	—	4	4	no	—
172	Q₈	—	8	2	no	—
173	Q₈	—	8	2	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	8	2	no	—
177	C₂×C₄	—	8	2	no	—
178	C₂×C₄	—	8	2	no	—
179	C₂×C₄	—	8	4	no	—
180	C₂×C₄	C₁₃×#102	1	4	yes	—
181	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
183	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
184	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
185	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
186	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
187	C₈	C₁₃×#102	1	4	yes	—
188	C₈	C₄×D₄×C₁₃	1	2	yes	—
189	C₈	C₁₃×#121	1	2	yes	—
190	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
191	C₂²	C₁₃×#486	1	1	yes	characteristic
192	C₂²	C₁₃×#493	1	1	yes	characteristic
193	C₂²	C₁₃×#510	1	4	yes	—
194	C₄	—	2	4	no	—
195	C₄	—	8	4	no	—
196	C₄	—	16	2	no	—
197	C₄	C₁₃×#390	1	1	yes	characteristic
198	C₄	C₂×C₁₃×#102	1	1	yes	characteristic
199	C₄	C₁₃×#486	1	1	yes	characteristic
200	C₄	C₁₃×#492	1	1	yes	characteristic
201	C₂	C₁₃×#1957	1	1	yes	characteristic
202	C₂	C₁₃×#2141	1	2	yes	—
203	C₂	C₁₃×#2245	1	2	yes	—
204	C₂	C₁₃×#2251	1	2	yes	—

	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
10. C₁₃×#494	C₄	semidirect
40. #13207	C₁₃	direct (N × H)
97. #494	C₄×C₁₃	semidirect
168. C₁₃	#13207	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×#494	2
C₂×C₁₃×#358	2
C₂×C₁₃×#346	2
C₁₃×#1846	2
#13207	13

Subgroups — C13×#13207 #15699546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13207 #15699546