Subgroups — C₁₃×#14665 #15701004

Order 3328.

1530 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#126	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1441	C₂	1	6	yes	maximal, complemented
5	C₁₃×#1439	C₂	1	6	yes	maximal
6	C₂×C₁₃×#126	—	2	4	no	—
7	C₂×C₁₃×#126	—	2	4	no	—
8	C₂×C₁₃×#126	C₄	1	8	yes	complemented
9	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	6	yes	—
11	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
12	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
13	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#384	—	2	4	no	—
15	C₁₃×#383	—	2	4	no	—
16	C₂×C₁₃×#95	C₂²	1	6	yes	—
17	C₂×C₁₃×#95	C₂²	1	12	yes	—
18	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
19	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
20	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
21	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
23	C₁₃×#126	—	2	32	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	12	no	—
27	C₂×C₁₃×C₄⋊C₄	—	4	12	no	—
28	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	12	yes	—
29	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
30	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
31	C₂×C₁₃×C₂²⋊C₄	—	4	12	no	—
32	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	12	yes	—
33	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
34	C₂×C₄²×C₁₃	D₄	1	4	yes	—
35	C₂×C₄²×C₁₃	D₄	1	4	yes	—
36	C₁₃×#95	—	2	12	no	—
37	C₁₃×#95	—	4	12	no	—
38	#14665	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂⁴×C₁₃	—	2	1	no	—
40	C₂⁴×C₁₃	—	2	1	no	—
41	C₂⁴×C₁₃	—	2	6	no	—
42	C₂⁴×C₁₃	—	2	6	no	—
43	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
44	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	—	2	6	no	—
46	C₂²×C₄×C₁₃	—	2	6	no	—
47	C₂²×C₄×C₁₃	—	2	3	no	—
48	C₂²×C₄×C₁₃	—	2	3	no	—
49	C₂²×C₄×C₁₃	—	2	6	no	—
50	C₂²×C₄×C₁₃	—	2	6	no	—
51	C₂²×C₄×C₁₃	—	2	4	no	—
52	C₂²×C₄×C₁₃	—	2	4	no	—
53	C₂²×C₄×C₁₃	—	2	12	no	—
54	C₂²×C₄×C₁₃	—	2	12	no	—
55	C₂²×C₄×C₁₃	—	2	12	no	—
56	C₂²×C₄×C₁₃	—	2	12	no	—
57	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
58	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
59	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
60	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
61	C₁₃×C₄⋊C₄	—	2	24	no	—
62	C₁₃×C₄⋊C₄	—	4	24	no	—
63	C₁₃×C₂²⋊C₄	—	2	24	no	—
64	C₁₃×C₂²⋊C₄	—	4	16	no	—
65	C₄²×C₁₃	C₂²⋊C₄	1	16	yes	complemented
66	C₂²×#126	C₂×C₁₃	1	1	yes	characteristic
67	C₂×#384	C₂×C₁₃	1	1	yes	characteristic, complemented
68	C₂×#383	C₂×C₁₃	1	1	yes	characteristic, complemented
69	#1441	C₂×C₁₃	1	6	yes	complemented
70	#1439	C₂×C₁₃	1	6	yes	—
71	C₂³×C₁₃	—	2	2	no	—
72	C₂³×C₁₃	—	2	12	no	—
73	C₂³×C₁₃	—	4	3	no	—
74	C₂³×C₁₃	—	4	3	no	—
75	C₂³×C₁₃	—	4	6	no	—
76	C₂³×C₁₃	—	4	4	no	—
77	C₂³×C₁₃	—	4	12	no	—
78	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
79	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
80	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
81	C₂³×C₁₃	H(5,𝔽₂)	1	6	yes	—
82	C₂³×C₁₃	2₋¹⁺⁴	1	6	yes	—
83	C₂×C₄×C₁₃	—	2	12	no	—
84	C₂×C₄×C₁₃	—	2	6	no	—
85	C₂×C₄×C₁₃	—	2	6	no	—
86	C₂×C₄×C₁₃	—	2	12	no	—
87	C₂×C₄×C₁₃	—	2	6	no	—
88	C₂×C₄×C₁₃	—	2	12	no	—
89	C₂×C₄×C₁₃	—	4	3	no	—
90	C₂×C₄×C₁₃	—	4	3	no	—
91	C₂×C₄×C₁₃	—	4	6	no	—
92	C₂×C₄×C₁₃	—	4	12	no	—
93	C₂×C₄×C₁₃	—	4	12	no	—
94	C₂×C₄×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	—	4	4	no	—
96	C₂×C₄×C₁₃	—	4	12	no	—
97	C₂×C₄×C₁₃	—	4	12	no	—
98	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	12	yes	—
99	C₂×#126	—	2	4	no	—
100	C₂×#126	—	2	4	no	—
101	C₂×#126	C₄×C₁₃	1	8	yes	complemented
102	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
103	C₂²×C₄⋊C₄	C₂²×C₁₃	1	6	yes	—
104	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
105	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
106	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
107	#384	—	2	4	no	—
108	#383	—	2	4	no	—
109	C₂×#95	C₂²×C₁₃	1	6	yes	—
110	C₂×#95	C₂²×C₁₃	1	12	yes	—
111	C₂²×C₁₃	—	4	6	no	—
112	C₂²×C₁₃	—	4	8	no	—
113	C₂²×C₁₃	—	8	1	no	—
114	C₂²×C₁₃	—	8	3	no	—
115	C₂²×C₁₃	—	8	4	no	—
116	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₁₃	#520	1	6	yes	—
118	C₂²×C₁₃	#535	1	3	yes	—
119	C₂²×C₁₃	#536	1	3	yes	—
120	C₂²×C₁₃	#537	1	6	yes	—
121	C₂²×C₁₃	#560	1	4	yes	—
122	C₂²×C₁₃	#563	1	12	yes	—
123	C₄×C₁₃	—	2	12	no	—
124	C₄×C₁₃	—	4	6	no	—
125	C₄×C₁₃	—	8	4	no	—
126	C₄×C₁₃	—	8	4	no	—
127	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
128	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
129	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
130	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
131	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
132	#126	—	2	32	no	—
133	C₂×C₄⋊C₄	—	2	6	no	—
134	C₂×C₄⋊C₄	—	2	6	no	—
135	C₂×C₄⋊C₄	—	2	12	no	—
136	C₂×C₄⋊C₄	—	4	12	no	—
137	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	12	yes	—
138	C₂×C₂²⋊C₄	—	2	6	no	—
139	C₂×C₂²⋊C₄	—	2	6	no	—
140	C₂×C₂²⋊C₄	—	4	12	no	—
141	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	12	yes	—
142	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
143	C₂×C₄²	D₄×C₁₃	1	4	yes	—
144	C₂×C₄²	D₄×C₁₃	1	4	yes	—
145	#95	—	2	12	no	—
146	#95	—	4	12	no	—
147	C₂×C₁₃	—	8	2	no	—
148	C₂×C₁₃	#2311	1	3	yes	—
149	C₂×C₁₃	#2383	1	4	yes	—
150	C₂×C₁₃	#2818	1	1	yes	characteristic
151	C₂×C₁₃	#2821	1	3	yes	—
152	C₂×C₁₃	#2823	1	4	yes	—
153	C₂⁴	—	2	1	no	—
154	C₂⁴	—	2	1	no	—
155	C₂⁴	—	2	6	no	—
156	C₂⁴	—	2	6	no	—
157	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
158	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
159	C₂²×C₄	—	2	6	no	—
160	C₂²×C₄	—	2	6	no	—
161	C₂²×C₄	—	2	3	no	—
162	C₂²×C₄	—	2	3	no	—
163	C₂²×C₄	—	2	6	no	—
164	C₂²×C₄	—	2	6	no	—
165	C₂²×C₄	—	2	4	no	—
166	C₂²×C₄	—	2	4	no	—
167	C₂²×C₄	—	2	12	no	—
168	C₂²×C₄	—	2	12	no	—
169	C₂²×C₄	—	2	12	no	—
170	C₂²×C₄	—	2	12	no	—
171	C₂²×C₄	C₂²×C₄×C₁₃	1	6	yes	—
172	C₂²×C₄	C₂²×C₄×C₁₃	1	6	yes	—
173	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
174	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
175	C₄⋊C₄	—	2	24	no	—
176	C₄⋊C₄	—	4	24	no	—
177	C₂²⋊C₄	—	2	24	no	—
178	C₂²⋊C₄	—	4	16	no	—
179	C₄²	C₁₃×C₂²⋊C₄	1	16	yes	complemented
180	C₁₃	#14665	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³	—	2	2	no	—
182	C₂³	—	2	12	no	—
183	C₂³	—	4	3	no	—
184	C₂³	—	4	3	no	—
185	C₂³	—	4	6	no	—
186	C₂³	—	4	4	no	—
187	C₂³	—	4	12	no	—
188	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
189	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
190	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
191	C₂³	C₁₃×H(5,𝔽₂)	1	6	yes	—
192	C₂³	C₁₃×2₋¹⁺⁴	1	6	yes	—
193	C₂×C₄	—	2	12	no	—
194	C₂×C₄	—	2	6	no	—
195	C₂×C₄	—	2	6	no	—
196	C₂×C₄	—	2	12	no	—
197	C₂×C₄	—	2	6	no	—
198	C₂×C₄	—	2	12	no	—
199	C₂×C₄	—	4	3	no	—
200	C₂×C₄	—	4	3	no	—
201	C₂×C₄	—	4	6	no	—
202	C₂×C₄	—	4	12	no	—
203	C₂×C₄	—	4	12	no	—
204	C₂×C₄	—	4	4	no	—
205	C₂×C₄	—	4	4	no	—
206	C₂×C₄	—	4	12	no	—
207	C₂×C₄	—	4	12	no	—
208	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	12	yes	—
209	C₂²	—	4	6	no	—
210	C₂²	—	4	8	no	—
211	C₂²	—	8	1	no	—
212	C₂²	—	8	3	no	—
213	C₂²	—	8	4	no	—
214	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²	C₁₃×#520	1	6	yes	—
216	C₂²	C₁₃×#535	1	3	yes	—
217	C₂²	C₁₃×#536	1	3	yes	—
218	C₂²	C₁₃×#537	1	6	yes	—
219	C₂²	C₁₃×#560	1	4	yes	—
220	C₂²	C₁₃×#563	1	12	yes	—
221	C₄	—	2	12	no	—
222	C₄	—	4	6	no	—
223	C₄	—	8	4	no	—
224	C₄	—	8	4	no	—
225	C₂	—	8	2	no	—
226	C₂	C₁₃×#2311	1	3	yes	—
227	C₂	C₁₃×#2383	1	4	yes	—
228	C₂	C₁₃×#2818	1	1	yes	characteristic
229	C₂	C₁₃×#2821	1	3	yes	—
230	C₂	C₁₃×#2823	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#384	C₂	semidirect
3. C₂×C₁₃×#383	C₂	semidirect
4. C₁₃×#1441	C₂	semidirect
8. C₂×C₁₃×#126	C₄	semidirect
38. #14665	C₁₃	direct (N × H)
65. C₄²×C₁₃	C₂²⋊C₄	semidirect
67. C₂×#384	C₂×C₁₃	semidirect
68. C₂×#383	C₂×C₁₃	semidirect
69. #1441	C₂×C₁₃	semidirect
101. C₂×#126	C₄×C₁₃	semidirect
179. C₄²	C₁₃×C₂²⋊C₄	semidirect
180. C₁₃	#14665	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#126	2
C₂×C₁₃×#384	2
C₂×C₁₃×#383	2
C₁₃×#1441	2
C₁₃×#1439	2
#14665	13

Subgroups — C13×#14665 #15701004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14665 #15701004