Subgroups — C₁₃×#12868 #15699207

Order 3328.

426 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×#427	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1380	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1380	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#117	—	2	1	no	—
8	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
9	C₁₃×#427	—	2	2	no	—
10	C₁₃×#427	C₄	1	4	yes	complemented
11	C₂×C₁₃×#107	C₂²	1	2	yes	—
12	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#106	—	2	1	no	—
15	C₁₃×#380	—	2	1	no	—
16	C₁₃×C₂²⋊C₁₆	—	2	2	no	—
17	C₁₃×#340	—	2	1	no	—
18	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	—	2	4	no	—
20	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	D₄	1	2	yes	—
23	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₁₃×#117	—	2	4	no	—
25	C₁₃×#117	—	4	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
30	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
31	C₂×C₄²×C₁₃	—	4	1	no	—
32	C₂×C₁₃×C₁₆	—	2	2	no	—
33	C₂×C₁₃×C₁₆	—	2	4	no	—
34	C₁₃×#107	—	2	1	no	—
35	C₁₃×#107	—	2	1	no	—
36	C₁₃×#107	—	2	4	no	—
37	C₁₃×#107	C₂×C₄	1	2	yes	—
38	C₁₃×#107	C₂×C₄	1	2	yes	—
39	C₁₃×#106	—	2	4	no	—
40	C₁₃×#95	—	4	1	no	—
41	#12868	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	—	2	2	no	—
44	C₂²×C₄×C₁₃	—	2	2	no	—
45	C₂²×C₄×C₁₃	—	4	1	no	—
46	C₂²×C₄×C₁₃	—	4	1	no	—
47	C₂²×C₄×C₁₃	—	4	2	no	—
48	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	—	2	2	no	—
53	C₂×C₈×C₁₃	—	2	4	no	—
54	C₂×C₈×C₁₃	—	2	4	no	—
55	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
56	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	#41	1	4	yes	—
59	C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₁₃×C₄⋊C₄	—	4	1	no	—
62	C₁₃×C₄⋊C₄	—	4	1	no	—
63	C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₁₃×C₂²⋊C₄	—	4	4	no	—
66	C₁₃×C₂²⋊C₄	—	8	2	no	—
67	C₄²×C₁₃	—	4	4	no	—
68	C₁₃×C₁₆	—	4	2	no	—
69	C₂×#427	C₂×C₁₃	1	1	yes	characteristic
70	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic
71	#1808	C₂×C₁₃	1	1	yes	characteristic
72	#1380	C₂×C₁₃	1	2	yes	complemented
73	#1380	C₂×C₁₃	1	2	yes	complemented
74	C₂³×C₁₃	—	2	2	no	—
75	C₂³×C₁₃	—	2	2	no	—
76	C₂³×C₁₃	—	2	1	no	—
77	C₂³×C₁₃	—	2	1	no	—
78	C₂³×C₁₃	#102	1	2	yes	—
79	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₁₃	—	2	2	no	—
81	C₂×C₄×C₁₃	—	2	2	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	—	2	4	no	—
84	C₂×C₄×C₁₃	—	4	2	no	—
85	C₂×C₄×C₁₃	—	4	2	no	—
86	C₂×C₄×C₁₃	—	8	2	no	—
87	C₂×C₄×C₁₃	—	8	1	no	—
88	C₂×C₄×C₁₃	—	8	1	no	—
89	C₂×C₄×C₁₃	—	8	2	no	—
90	C₂×C₄×C₁₃	—	8	2	no	—
91	C₂×C₄×C₁₃	—	8	2	no	—
92	C₂×C₄×C₁₃	#102	1	2	yes	—
93	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#123	1	2	yes	—
95	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#137	1	2	yes	—
97	C₈×C₁₃	—	2	2	no	—
98	C₈×C₁₃	#117	1	2	yes	—
99	C₈×C₁₃	#123	1	2	yes	—
100	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
101	C₂×#117	—	2	1	no	—
102	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
103	#427	—	2	2	no	—
104	#427	C₄×C₁₃	1	4	yes	complemented
105	C₂×#107	C₂²×C₁₃	1	2	yes	—
106	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
107	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
108	C₂×#106	—	2	1	no	—
109	#380	—	2	1	no	—
110	C₂²⋊C₁₆	—	2	2	no	—
111	#340	—	2	1	no	—
112	C₂²×C₁₃	—	2	2	no	—
113	C₂²×C₁₃	—	2	2	no	—
114	C₂²×C₁₃	—	2	2	no	—
115	C₂²×C₁₃	—	4	2	no	—
116	C₂²×C₁₃	—	4	2	no	—
117	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
118	C₂²×C₁₃	#480	1	2	yes	—
119	C₂²×C₁₃	#508	1	2	yes	—
120	C₂²×C₁₃	#509	1	1	yes	characteristic
121	C₂²×C₁₃	#510	1	1	yes	characteristic
122	C₄×C₁₃	—	2	2	no	—
123	C₄×C₁₃	—	8	2	no	—
124	C₄×C₁₃	—	8	2	no	—
125	C₄×C₁₃	—	16	2	no	—
126	C₄×C₁₃	#381	1	1	yes	characteristic
127	C₄×C₁₃	#419	1	1	yes	characteristic
128	C₄×C₁₃	#483	1	2	yes	—
129	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
130	C₂²×C₈	—	2	4	no	—
131	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
132	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
133	C₂²×C₈	D₄×C₁₃	1	2	yes	—
134	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
135	#117	—	2	4	no	—
136	#117	—	4	2	no	—
137	C₂×C₄⋊C₄	—	2	1	no	—
138	C₂×C₄⋊C₄	—	2	1	no	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₂²⋊C₄	—	4	1	no	—
141	C₂×C₂²⋊C₄	—	4	1	no	—
142	C₂×C₄²	—	4	1	no	—
143	C₂×C₁₆	—	2	2	no	—
144	C₂×C₁₆	—	2	4	no	—
145	#107	—	2	1	no	—
146	#107	—	2	1	no	—
147	#107	—	2	4	no	—
148	#107	C₂×C₄×C₁₃	1	2	yes	—
149	#107	C₂×C₄×C₁₃	1	2	yes	—
150	#106	—	2	4	no	—
151	#95	—	4	1	no	—
152	C₂×C₁₃	—	4	2	no	—
153	C₂×C₁₃	#1823	1	1	yes	characteristic
154	C₂×C₁₃	#2138	1	1	yes	characteristic
155	C₂×C₁₃	#2139	1	1	yes	characteristic
156	C₂×C₁₃	#2234	1	2	yes	—
157	C₂×C₁₃	#2237	1	2	yes	—
158	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	4	1	no	—
162	C₂²×C₄	—	4	1	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
165	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
166	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
167	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	2	4	no	—
171	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
172	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
173	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
174	C₂×C₈	C₁₃×#41	1	4	yes	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	4	1	no	—
178	C₄⋊C₄	—	4	1	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₂²⋊C₄	—	4	4	no	—
182	C₂²⋊C₄	—	8	2	no	—
183	C₄²	—	4	4	no	—
184	C₁₆	—	4	2	no	—
185	C₁₃	#12868	1	1	yes	characteristic, direct product factor, Sylow
186	C₂³	—	2	2	no	—
187	C₂³	—	2	2	no	—
188	C₂³	—	2	1	no	—
189	C₂³	—	2	1	no	—
190	C₂³	C₁₃×#102	1	2	yes	—
191	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	8	2	no	—
199	C₂×C₄	—	8	1	no	—
200	C₂×C₄	—	8	1	no	—
201	C₂×C₄	—	8	2	no	—
202	C₂×C₄	—	8	2	no	—
203	C₂×C₄	—	8	2	no	—
204	C₂×C₄	C₁₃×#102	1	2	yes	—
205	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄	C₁₃×#123	1	2	yes	—
207	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
208	C₂×C₄	C₁₃×#137	1	2	yes	—
209	C₈	—	2	2	no	—
210	C₈	C₁₃×#117	1	2	yes	—
211	C₈	C₁₃×#123	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
218	C₂²	C₁₃×#480	1	2	yes	—
219	C₂²	C₁₃×#508	1	2	yes	—
220	C₂²	C₁₃×#509	1	1	yes	characteristic
221	C₂²	C₁₃×#510	1	1	yes	characteristic
222	C₄	—	2	2	no	—
223	C₄	—	8	2	no	—
224	C₄	—	8	2	no	—
225	C₄	—	16	2	no	—
226	C₄	C₁₃×#381	1	1	yes	characteristic
227	C₄	C₁₃×#419	1	1	yes	characteristic
228	C₄	C₁₃×#483	1	2	yes	—
229	C₂	—	4	2	no	—
230	C₂	C₁₃×#1823	1	1	yes	characteristic
231	C₂	C₁₃×#2138	1	1	yes	characteristic
232	C₂	C₁₃×#2139	1	1	yes	characteristic
233	C₂	C₁₃×#2234	1	2	yes	—
234	C₂	C₁₃×#2237	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1380	C₂	semidirect
5. C₁₃×#1380	C₂	semidirect
10. C₁₃×#427	C₄	semidirect
41. #12868	C₁₃	direct (N × H)
72. #1380	C₂×C₁₃	semidirect
73. #1380	C₂×C₁₃	semidirect
104. #427	C₄×C₁₃	semidirect
185. C₁₃	#12868	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×#427	2
C₂×C₁₃×C₂²⋊C₁₆	2
C₁₃×#1808	2
C₁₃×#1380	2
#12868	13

Subgroups — C13×#12868 #15699207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12868 #15699207