Subgroups — C₁₃×#23810 #15710149

Order 3328.

1150 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#442	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2328	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2092	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2011	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
8	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
9	C₂×C₁₃×#127	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
11	C₁₃×#442	—	2	8	no	—
12	C₄×C₁₃×D₈	—	2	8	no	—
13	C₂×C₁₃×#107	C₂²	1	2	yes	—
14	C₂×C₁₃×#106	C₂²	1	2	yes	—
15	C₂×C₁₃×#102	C₂²	1	4	yes	—
16	C₂×C₁₃×#102	C₂²	1	4	yes	—
17	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#390	C₂²	1	4	yes	—
20	C₁₃×#386	—	2	8	no	—
21	C₁₃×#382	C₂²	1	2	yes	—
22	C₁₃×#376	C₂²	1	1	yes	characteristic
23	C₁₃×#336	C₂²	1	4	yes	—
24	C₂²×D₄×C₁₃	—	2	4	no	—
25	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
26	C₂³×C₄×C₁₃	—	2	4	no	—
27	C₂×C₁₃×D₈	—	2	8	no	—
28	C₂×C₁₃×D₈	—	2	8	no	—
29	C₂×C₁₃×D₈	—	2	4	no	—
30	C₂×C₁₃×D₈	—	2	4	no	—
31	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
32	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
33	C₁₃×#127	—	2	8	no	—
34	C₄×D₄×C₁₃	—	2	8	no	—
35	C₄×D₄×C₁₃	—	2	8	no	—
36	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
37	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
38	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
39	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
40	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
41	C₁₃×#107	—	2	4	no	—
42	C₁₃×#106	—	2	4	no	—
43	C₁₃×#102	—	2	8	no	—
44	C₁₃×#102	—	2	8	no	—
45	C₁₃×#97	D₄	1	4	yes	complemented
46	C₄×C₈×C₁₃	D₄	1	4	yes	complemented
47	C₁₃×#95	—	2	4	no	—
48	C₁₃×#95	D₄	1	4	yes	—
49	#23810	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂⁴×C₁₃	—	2	4	no	—
51	C₂×D₄×C₁₃	—	2	16	no	—
52	C₂×D₄×C₁₃	—	2	4	no	—
53	C₂×D₄×C₁₃	—	2	4	no	—
54	C₂×D₄×C₁₃	—	2	4	no	—
55	C₂×D₄×C₁₃	—	2	4	no	—
56	C₂×D₄×C₁₃	—	2	4	no	—
57	C₂×D₄×C₁₃	—	8	8	no	—
58	C₂×D₄×C₁₃	#41	1	8	yes	—
59	C₂²×C₄×C₁₃	—	2	4	no	—
60	C₂²×C₄×C₁₃	—	4	8	no	—
61	C₂²×C₄×C₁₃	—	8	8	no	—
62	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
63	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
65	C₁₃×D₈	—	2	16	no	—
66	C₁₃×D₈	—	2	16	no	—
67	C₂×C₈×C₁₃	—	2	4	no	—
68	C₂×C₈×C₁₃	—	2	4	no	—
69	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
70	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
71	C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₁₃×C₄⋊C₄	—	2	4	no	—
73	C₁₃×C₂²⋊C₄	—	4	8	no	—
74	C₁₃×C₂²⋊C₄	—	8	8	no	—
75	C₄²×C₁₃	—	2	4	no	—
76	C₄²×C₁₃	C₂×D₄	1	2	yes	—
77	C₄²×C₁₃	C₂×D₄	1	2	yes	—
78	C₂×#442	C₂×C₁₃	1	2	yes	complemented
79	C₂×C₄×D₈	C₂×C₁₃	1	2	yes	complemented
80	#2328	C₂×C₁₃	1	2	yes	complemented
81	#2092	C₂×C₁₃	1	4	yes	complemented
82	#2011	C₂×C₁₃	1	4	yes	complemented
83	#1746	C₂×C₁₃	1	1	yes	characteristic, complemented
84	C₂³×C₁₃	—	2	8	no	—
85	C₂³×C₁₃	—	4	4	no	—
86	C₂³×C₁₃	—	4	4	no	—
87	C₂³×C₁₃	—	4	8	no	—
88	C₂³×C₁₃	—	4	8	no	—
89	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
90	D₄×C₁₃	—	2	8	no	—
91	D₄×C₁₃	—	2	8	no	—
92	D₄×C₁₃	—	4	4	no	—
93	D₄×C₁₃	—	4	4	no	—
94	D₄×C₁₃	—	8	16	no	—
95	C₂×C₄×C₁₃	—	2	4	no	—
96	C₂×C₄×C₁₃	—	2	4	no	—
97	C₂×C₄×C₁₃	—	2	8	no	—
98	C₂×C₄×C₁₃	—	4	4	no	—
99	C₂×C₄×C₁₃	—	4	8	no	—
100	C₂×C₄×C₁₃	—	8	16	no	—
101	C₂×C₄×C₁₃	#127	1	4	yes	—
102	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
105	C₈×C₁₃	—	2	4	no	—
106	C₈×C₁₃	—	2	4	no	—
107	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
108	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
109	C₂×#127	C₂²×C₁₃	1	2	yes	—
110	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
111	#442	—	2	8	no	—
112	C₄×D₈	—	2	8	no	—
113	C₂×#107	C₂²×C₁₃	1	2	yes	—
114	C₂×#106	C₂²×C₁₃	1	2	yes	—
115	C₂×#102	C₂²×C₁₃	1	4	yes	—
116	C₂×#102	C₂²×C₁₃	1	4	yes	—
117	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
119	#390	C₂²×C₁₃	1	4	yes	—
120	#386	—	2	8	no	—
121	#382	C₂²×C₁₃	1	2	yes	—
122	#376	C₂²×C₁₃	1	1	yes	characteristic
123	#336	C₂²×C₁₃	1	4	yes	—
124	C₂²×C₁₃	—	4	16	no	—
125	C₂²×C₁₃	—	4	8	no	—
126	C₂²×C₁₃	—	8	8	no	—
127	C₂²×C₁₃	—	8	4	no	—
128	C₂²×C₁₃	—	8	4	no	—
129	C₂²×C₁₃	#525	1	2	yes	—
130	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
131	C₂²×C₁₃	#576	1	4	yes	—
132	C₄×C₁₃	—	2	4	no	—
133	C₄×C₁₃	—	4	4	no	—
134	C₄×C₁₃	—	8	4	no	—
135	C₄×C₁₃	#525	1	2	yes	—
136	C₄×C₁₃	#525	1	2	yes	—
137	C₂²×D₄	—	2	4	no	—
138	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
139	C₂³×C₄	—	2	4	no	—
140	C₂×D₈	—	2	8	no	—
141	C₂×D₈	—	2	8	no	—
142	C₂×D₈	—	2	4	no	—
143	C₂×D₈	—	2	4	no	—
144	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
145	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
146	#127	—	2	8	no	—
147	C₄×D₄	—	2	8	no	—
148	C₄×D₄	—	2	8	no	—
149	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
150	C₂×C₂²⋊C₄	—	2	4	no	—
151	C₂×C₂²⋊C₄	—	2	8	no	—
152	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
153	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
154	#107	—	2	4	no	—
155	#106	—	2	4	no	—
156	#102	—	2	8	no	—
157	#102	—	2	8	no	—
158	#97	D₄×C₁₃	1	4	yes	complemented
159	C₄×C₈	D₄×C₁₃	1	4	yes	complemented
160	#95	—	2	4	no	—
161	#95	D₄×C₁₃	1	4	yes	—
162	C₂×C₁₃	—	8	8	no	—
163	C₂×C₁₃	#2397	1	1	yes	characteristic
164	C₂×C₁₃	#3122	1	4	yes	—
165	C₂×C₁₃	#3155	1	2	yes	—
166	C₂⁴	—	2	4	no	—
167	C₂×D₄	—	2	16	no	—
168	C₂×D₄	—	2	4	no	—
169	C₂×D₄	—	2	4	no	—
170	C₂×D₄	—	2	4	no	—
171	C₂×D₄	—	2	4	no	—
172	C₂×D₄	—	2	4	no	—
173	C₂×D₄	—	8	8	no	—
174	C₂×D₄	C₁₃×#41	1	8	yes	—
175	C₂²×C₄	—	2	4	no	—
176	C₂²×C₄	—	4	8	no	—
177	C₂²×C₄	—	8	8	no	—
178	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
179	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
180	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
181	D₈	—	2	16	no	—
182	D₈	—	2	16	no	—
183	C₂×C₈	—	2	4	no	—
184	C₂×C₈	—	2	4	no	—
185	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
186	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
187	C₄⋊C₄	—	2	4	no	—
188	C₄⋊C₄	—	2	4	no	—
189	C₂²⋊C₄	—	4	8	no	—
190	C₂²⋊C₄	—	8	8	no	—
191	C₄²	—	2	4	no	—
192	C₄²	C₂×D₄×C₁₃	1	2	yes	—
193	C₄²	C₂×D₄×C₁₃	1	2	yes	—
194	C₁₃	#23810	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³	—	2	8	no	—
196	C₂³	—	4	4	no	—
197	C₂³	—	4	4	no	—
198	C₂³	—	4	8	no	—
199	C₂³	—	4	8	no	—
200	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
201	D₄	—	2	8	no	—
202	D₄	—	2	8	no	—
203	D₄	—	4	4	no	—
204	D₄	—	4	4	no	—
205	D₄	—	8	16	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	2	8	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	4	8	no	—
211	C₂×C₄	—	8	16	no	—
212	C₂×C₄	C₁₃×#127	1	4	yes	—
213	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
214	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
215	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
216	C₈	—	2	4	no	—
217	C₈	—	2	4	no	—
218	C₂²	—	4	16	no	—
219	C₂²	—	4	8	no	—
220	C₂²	—	8	8	no	—
221	C₂²	—	8	4	no	—
222	C₂²	—	8	4	no	—
223	C₂²	C₁₃×#525	1	2	yes	—
224	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
225	C₂²	C₁₃×#576	1	4	yes	—
226	C₄	—	2	4	no	—
227	C₄	—	4	4	no	—
228	C₄	—	8	4	no	—
229	C₄	C₁₃×#525	1	2	yes	—
230	C₄	C₁₃×#525	1	2	yes	—
231	C₂	—	8	8	no	—
232	C₂	C₁₃×#2397	1	1	yes	characteristic
233	C₂	C₁₃×#3122	1	4	yes	—
234	C₂	C₁₃×#3155	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#442	C₂	semidirect
2. C₂×C₄×C₁₃×D₈	C₂	semidirect
3. C₁₃×#2328	C₂	semidirect
4. C₁₃×#2092	C₂	semidirect
5. C₁₃×#2011	C₂	semidirect
6. C₁₃×#1746	C₂	semidirect
45. C₁₃×#97	D₄	semidirect
46. C₄×C₈×C₁₃	D₄	semidirect
49. #23810	C₁₃	direct (N × H)
78. C₂×#442	C₂×C₁₃	semidirect
79. C₂×C₄×D₈	C₂×C₁₃	semidirect
80. #2328	C₂×C₁₃	semidirect
81. #2092	C₂×C₁₃	semidirect
82. #2011	C₂×C₁₃	semidirect
83. #1746	C₂×C₁₃	semidirect
158. #97	D₄×C₁₃	semidirect
159. C₄×C₈	D₄×C₁₃	semidirect
194. C₁₃	#23810	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×#442	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2328	2
C₁₃×#2092	2
C₁₃×#2011	2
C₁₃×#1746	2
#23810	13

Subgroups — C13×#23810 #15710149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23810 #15710149