Subgroups — C₁₃×#2935 #13111993

Order 1664.

492 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	C₂×C₁₃×#131	C₂	1	2	yes	maximal, complemented
2	C₁₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#436	C₂	1	2	yes	maximal, complemented
4	C₁₃×#435	C₂	1	4	yes	maximal, complemented
5	C₈×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#408	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#41	C₂²	1	2	yes	—
10	C₁₃×#131	—	2	8	no	—
11	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×M₁₆	C₂²	1	4	yes	—
13	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
15	C₂²×C₈×C₁₃	C₂²	1	4	yes	—
16	C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
17	C₁₃×#127	C₄	1	1	yes	characteristic
18	C₁₃×#124	C₄	1	2	yes	—
19	C₁₃×#121	C₄	1	2	yes	—
20	C₁₃×#121	C₄	1	2	yes	—
21	C₄×D₄×C₁₃	C₂²	1	2	yes	—
22	C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
28	C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
29	C₁₃×#97	C₂²	1	2	yes	—
30	C₄×C₈×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#41	—	2	4	no	—
32	C₁₃×#41	—	2	4	no	—
33	C₂×Q₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₂×D₄×C₁₃	C₂×C₄	1	2	yes	—
35	C₂×D₄×C₁₃	C₂×C₄	1	4	yes	—
36	C₂×D₄×C₁₃	C₂×C₄	1	2	yes	—
37	C₂×D₄×C₁₃	C₂×C₄	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
41	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×M₁₆	—	2	2	no	—
43	C₁₃×M₁₆	—	2	8	no	—
44	C₁₃×M₁₆	D₄	1	4	yes	complemented
45	C₂×C₈×C₁₃	—	2	4	no	—
46	C₂×C₈×C₁₃	—	2	8	no	—
47	C₂×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
54	C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
55	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	#2935	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂³×C₁₃	C₂²×C₄	1	4	yes	—
61	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	Q₈×C₁₃	—	2	4	no	—
63	D₄×C₁₃	—	2	8	no	—
64	D₄×C₁₃	—	2	4	no	—
65	D₄×C₁₃	—	2	4	no	—
66	D₄×C₁₃	—	4	2	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	4	no	—
69	C₂×C₄×C₁₃	—	2	4	no	—
70	C₂×C₄×C₁₃	—	4	1	no	—
71	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
75	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₁₃	#41	1	2	yes	—
79	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
80	C₈×C₁₃	—	2	2	no	—
81	C₈×C₁₃	—	2	2	no	—
82	C₈×C₁₃	—	2	2	no	—
83	C₈×C₁₃	C₂×D₄	1	4	yes	—
84	C₂×#131	C₂×C₁₃	1	2	yes	complemented
85	#532	C₂×C₁₃	1	1	yes	characteristic
86	#436	C₂×C₁₃	1	2	yes	complemented
87	#435	C₂×C₁₃	1	4	yes	complemented
88	C₈×D₄	C₂×C₁₃	1	2	yes	complemented
89	C₂×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
90	#408	C₂×C₁₃	1	2	yes	complemented
91	C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
92	C₂²×C₁₃	—	2	1	no	—
93	C₂²×C₁₃	—	2	1	no	—
94	C₂²×C₁₃	—	2	4	no	—
95	C₂²×C₁₃	—	2	4	no	—
96	C₂²×C₁₃	—	2	4	no	—
97	C₂²×C₁₃	C₄×D₄	1	2	yes	—
98	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
99	C₄×C₁₃	—	2	4	no	—
100	C₄×C₁₃	—	2	1	no	—
101	C₄×C₁₃	—	2	1	no	—
102	C₄×C₁₃	—	2	1	no	—
103	C₄×C₁₃	C₄×D₄	1	2	yes	—
104	C₄×C₁₃	#131	1	2	yes	complemented
105	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
106	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
107	C₂×#41	C₂²×C₁₃	1	2	yes	—
108	#131	—	2	8	no	—
109	C₂×M₁₆	C₂²×C₁₃	1	4	yes	—
110	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
111	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
112	C₂²×C₈	C₂²×C₁₃	1	2	yes	—
113	C₂²×C₈	C₂²×C₁₃	1	4	yes	—
114	C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
115	#127	C₄×C₁₃	1	1	yes	characteristic
116	#124	C₄×C₁₃	1	2	yes	—
117	#121	C₄×C₁₃	1	2	yes	—
118	#121	C₄×C₁₃	1	2	yes	—
119	C₄×D₄	C₂²×C₁₃	1	2	yes	—
120	C₄×D₄	C₂²×C₁₃	1	2	yes	—
121	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
122	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
123	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
124	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
125	C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
126	C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
127	#97	C₂²×C₁₃	1	2	yes	—
128	C₄×C₈	C₂²×C₁₃	1	2	yes	—
129	C₂×C₁₃	—	2	2	no	—
130	C₂×C₁₃	—	4	4	no	—
131	C₂×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
132	C₂×C₁₃	C₂×#131	1	1	yes	characteristic
133	C₂×C₁₃	#568	1	1	yes	characteristic
134	#41	—	2	4	no	—
135	#41	—	2	4	no	—
136	C₂×Q₈	C₂×C₄×C₁₃	1	2	yes	—
137	C₂×D₄	C₂×C₄×C₁₃	1	2	yes	—
138	C₂×D₄	C₂×C₄×C₁₃	1	4	yes	—
139	C₂×D₄	C₂×C₄×C₁₃	1	2	yes	—
140	C₂×D₄	C₂×C₄×C₁₃	1	2	yes	—
141	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
142	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
143	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
144	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
145	M₁₆	—	2	2	no	—
146	M₁₆	—	2	8	no	—
147	M₁₆	D₄×C₁₃	1	4	yes	complemented
148	C₂×C₈	—	2	4	no	—
149	C₂×C₈	—	2	8	no	—
150	C₂×C₈	C₂³×C₁₃	1	2	yes	—
151	C₂×C₈	C₂³×C₁₃	1	2	yes	—
152	C₂×C₈	C₂³×C₁₃	1	2	yes	—
153	C₂×C₈	C₂³×C₁₃	1	2	yes	—
154	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
155	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
156	C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
157	C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
158	C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
159	C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
160	C₄²	C₂³×C₁₃	1	1	yes	characteristic
161	C₄²	C₂³×C₁₃	1	1	yes	characteristic
162	C₁₃	#2935	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	C₂²×C₄×C₁₃	1	4	yes	—
164	C₂³	C₂²×C₄×C₁₃	1	1	yes	characteristic
165	Q₈	—	2	4	no	—
166	D₄	—	2	8	no	—
167	D₄	—	2	4	no	—
168	D₄	—	2	4	no	—
169	D₄	—	4	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	4	1	no	—
174	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
175	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
176	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
177	C₂×C₄	C₂²×C₄×C₁₃	1	4	yes	—
178	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
179	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
180	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
181	C₂×C₄	C₁₃×#41	1	2	yes	—
182	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
183	C₈	—	2	2	no	—
184	C₈	—	2	2	no	—
185	C₈	—	2	2	no	—
186	C₈	C₂×D₄×C₁₃	1	4	yes	—
187	C₂²	—	2	1	no	—
188	C₂²	—	2	1	no	—
189	C₂²	—	2	4	no	—
190	C₂²	—	2	4	no	—
191	C₂²	—	2	4	no	—
192	C₂²	C₄×D₄×C₁₃	1	2	yes	—
193	C₂²	C₂³×C₄×C₁₃	1	1	yes	characteristic
194	C₄	—	2	4	no	—
195	C₄	—	2	1	no	—
196	C₄	—	2	1	no	—
197	C₄	—	2	1	no	—
198	C₄	C₄×D₄×C₁₃	1	2	yes	—
199	C₄	C₁₃×#131	1	2	yes	complemented
200	C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
201	C₄	C₂×C₁₃×#41	1	1	yes	characteristic
202	C₂	—	2	2	no	—
203	C₂	—	4	4	no	—
204	C₂	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
205	C₂	C₂×C₁₃×#131	1	1	yes	characteristic
206	C₂	C₁₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₄
prime radical	C₁₃×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#131	C₂	semidirect
3. C₁₃×#436	C₂	semidirect
4. C₁₃×#435	C₂	semidirect
5. C₈×D₄×C₁₃	C₂	semidirect
6. C₂×C₁₃×C₄⋊C₈	C₂	semidirect
7. C₁₃×#408	C₂	semidirect
8. C₄×C₁₃×M₁₆	C₂	semidirect
44. C₁₃×M₁₆	D₄	semidirect
59. #2935	C₁₃	direct (N × H)
84. C₂×#131	C₂×C₁₃	semidirect
86. #436	C₂×C₁₃	semidirect
87. #435	C₂×C₁₃	semidirect
88. C₈×D₄	C₂×C₁₃	semidirect
89. C₂×C₄⋊C₈	C₂×C₁₃	semidirect
90. #408	C₂×C₁₃	semidirect
91. C₄×M₁₆	C₂×C₁₃	semidirect
104. C₄×C₁₃	#131	semidirect
147. M₁₆	D₄×C₁₃	semidirect
162. C₁₃	#2935	direct (N × H)
199. C₄	C₁₃×#131	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#131	2
C₁₃×#532	2
C₁₃×#436	2
C₁₃×#435	2
C₈×D₄×C₁₃	2
C₂×C₁₃×C₄⋊C₈	2
C₁₃×#408	2
C₄×C₁₃×M₁₆	2
#2935	13

Subgroups — C13×#2935 #13111993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2935 #13111993