Subgroups — C₁₃×#12844 #15699183

Order 3328.

542 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	2	yes	maximal
3	C₁₃×#1374	C₂	1	4	yes	maximal, complemented
4	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄²×C₁₃	C₄	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	—
8	C₂×C₄×C₈×C₁₃	—	2	4	no	—
9	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
11	C₁₃×C₂²⋊C₁₆	—	2	4	no	—
12	C₂³×C₄×C₁₃	C₈	1	1	yes	characteristic
13	C₂³×C₄×C₁₃	C₈	1	1	yes	characteristic
14	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	—	2	2	no	—
16	C₂²×C₈×C₁₃	—	2	4	no	—
17	C₂²×C₈×C₁₃	—	2	4	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₃	D₄	1	4	yes	—
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	—	2	2	no	—
23	C₂×C₄²×C₁₃	—	2	2	no	—
24	C₂×C₄²×C₁₃	C₈	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₁₃×C₁₆	—	2	4	no	—
27	C₂×C₁₃×C₁₆	—	2	8	no	—
28	C₄×C₈×C₁₃	—	2	4	no	—
29	C₄×C₈×C₁₃	—	2	4	no	—
30	#12844	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₂²×C₄×C₁₃	—	2	2	no	—
33	C₂²×C₄×C₁₃	—	2	2	no	—
34	C₂²×C₄×C₁₃	—	2	2	no	—
35	C₂²×C₄×C₁₃	—	2	4	no	—
36	C₂²×C₄×C₁₃	—	2	2	no	—
37	C₂²×C₄×C₁₃	—	2	2	no	—
38	C₂²×C₄×C₁₃	C₁₆	1	4	yes	complemented
39	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
42	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
43	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	—	2	8	no	—
46	C₂×C₈×C₁₃	—	2	2	no	—
47	C₂×C₈×C₁₃	—	2	2	no	—
48	C₂×C₈×C₁₃	—	2	2	no	—
49	C₂×C₈×C₁₃	—	2	8	no	—
50	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
52	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₁₃	#41	1	4	yes	—
54	C₄²×C₁₃	—	2	4	no	—
55	C₄²×C₁₃	—	2	2	no	—
56	C₄²×C₁₃	—	2	2	no	—
57	C₁₃×C₁₆	—	4	4	no	—
58	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic
59	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	2	yes	—
60	#1374	C₂×C₁₃	1	4	yes	complemented
61	C₂³×C₁₃	—	2	2	no	—
62	C₂³×C₁₃	—	2	2	no	—
63	C₂³×C₁₃	C₂²⋊C₈	1	2	yes	—
64	C₂³×C₁₃	C₂×C₁₆	1	2	yes	—
65	C₂³×C₁₃	M₃₂	1	2	yes	—
66	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
67	C₂×C₄×C₁₃	—	2	8	no	—
68	C₂×C₄×C₁₃	—	2	8	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	2	2	no	—
74	C₂×C₄×C₁₃	—	2	2	no	—
75	C₂×C₄×C₁₃	—	2	2	no	—
76	C₂×C₄×C₁₃	—	2	4	no	—
77	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×C₁₆	1	4	yes	—
79	C₂×C₄×C₁₃	M₃₂	1	4	yes	—
80	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#117	1	2	yes	—
82	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
83	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
84	C₈×C₁₃	—	2	2	no	—
85	C₈×C₁₃	—	2	4	no	—
86	C₈×C₁₃	#123	1	4	yes	—
87	C₂³×C₈	C₄×C₁₃	1	1	yes	characteristic
88	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
89	C₂²×C₄²	C₄×C₁₃	1	1	yes	characteristic
90	C₂²×C₁₆	C₂²×C₁₃	1	4	yes	—
91	C₂×C₄×C₈	—	2	4	no	—
92	C₂×C₄×C₈	C₄×C₁₃	1	2	yes	—
93	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
94	C₂²⋊C₁₆	—	2	4	no	—
95	C₂²×C₁₃	—	2	2	no	—
96	C₂²×C₁₃	—	2	2	no	—
97	C₂²×C₁₃	—	2	4	no	—
98	C₂²×C₁₃	—	2	4	no	—
99	C₂²×C₁₃	C₂²⋊C₁₆	1	4	yes	—
100	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
101	C₂²×C₁₃	#431	1	2	yes	—
102	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
103	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
104	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
105	C₄×C₁₃	—	2	2	no	—
106	C₄×C₁₃	—	2	4	no	—
107	C₄×C₁₃	—	2	4	no	—
108	C₄×C₁₃	#381	1	1	yes	characteristic
109	C₄×C₁₃	#407	1	1	yes	characteristic
110	C₄×C₁₃	#432	1	2	yes	—
111	C₂³×C₄	C₈×C₁₃	1	1	yes	characteristic
112	C₂³×C₄	C₈×C₁₃	1	1	yes	characteristic
113	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
114	C₂²×C₈	—	2	2	no	—
115	C₂²×C₈	—	2	4	no	—
116	C₂²×C₈	—	2	4	no	—
117	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
118	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
119	C₂²×C₈	D₄×C₁₃	1	4	yes	—
120	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
121	C₂×C₄²	—	2	2	no	—
122	C₂×C₄²	—	2	2	no	—
123	C₂×C₄²	C₈×C₁₃	1	2	yes	—
124	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
125	C₂×C₁₆	—	2	4	no	—
126	C₂×C₁₆	—	2	8	no	—
127	C₄×C₈	—	2	4	no	—
128	C₄×C₈	—	2	4	no	—
129	C₂×C₁₃	—	2	4	no	—
130	C₂×C₁₃	#1817	1	1	yes	characteristic
131	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
132	C₂×C₁₃	#2112	1	1	yes	characteristic
133	C₂×C₁₃	#2162	1	2	yes	—
134	C₂×C₁₃	#2163	1	2	yes	—
135	C₂⁴	C₂×C₈×C₁₃	1	1	yes	characteristic
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	2	4	no	—
140	C₂²×C₄	—	2	2	no	—
141	C₂²×C₄	—	2	2	no	—
142	C₂²×C₄	C₁₃×C₁₆	1	4	yes	complemented
143	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
144	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
145	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
146	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
147	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
148	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
149	C₂×C₈	—	2	8	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	—	2	8	no	—
154	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
155	C₂×C₈	C₁₃×M₁₆	1	4	yes	—
156	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
157	C₂×C₈	C₁₃×#41	1	4	yes	—
158	C₄²	—	2	4	no	—
159	C₄²	—	2	2	no	—
160	C₄²	—	2	2	no	—
161	C₁₆	—	4	4	no	—
162	C₁₃	#12844	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	—	2	2	no	—
164	C₂³	—	2	2	no	—
165	C₂³	C₁₃×C₂²⋊C₈	1	2	yes	—
166	C₂³	C₂×C₁₃×C₁₆	1	2	yes	—
167	C₂³	C₁₃×M₃₂	1	2	yes	—
168	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
169	C₂×C₄	—	2	8	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	8	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
180	C₂×C₄	C₂×C₁₃×C₁₆	1	4	yes	—
181	C₂×C₄	C₁₃×M₃₂	1	4	yes	—
182	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄	C₁₃×#117	1	2	yes	—
184	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
185	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
186	C₈	—	2	2	no	—
187	C₈	—	2	4	no	—
188	C₈	C₁₃×#123	1	4	yes	—
189	C₂²	—	2	2	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	2	4	no	—
192	C₂²	—	2	4	no	—
193	C₂²	C₁₃×C₂²⋊C₁₆	1	4	yes	—
194	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
195	C₂²	C₁₃×#431	1	2	yes	—
196	C₂²	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
197	C₂²	C₂×C₁₃×M₃₂	1	1	yes	characteristic
198	C₂²	C₂×C₁₃×M₃₂	1	2	yes	—
199	C₄	—	2	2	no	—
200	C₄	—	2	4	no	—
201	C₄	—	2	4	no	—
202	C₄	C₁₃×#381	1	1	yes	characteristic
203	C₄	C₁₃×#407	1	1	yes	characteristic
204	C₄	C₁₃×#432	1	2	yes	—
205	C₂	—	2	4	no	—
206	C₂	C₁₃×#1817	1	1	yes	characteristic
207	C₂	C₂×C₁₃×C₂²⋊C₁₆	1	1	yes	characteristic
208	C₂	C₁₃×#2112	1	1	yes	characteristic
209	C₂	C₁₃×#2162	1	2	yes	—
210	C₂	C₁₃×#2163	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂²	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂³×C₁₃	C₂²×C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1374	C₂	semidirect
30. #12844	C₁₃	direct (N × H)
38. C₂²×C₄×C₁₃	C₁₆	semidirect
60. #1374	C₂×C₁₃	semidirect
142. C₂²×C₄	C₁₃×C₁₆	semidirect
162. C₁₃	#12844	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×C₄×C₈×C₁₃	2
C₂×C₁₃×C₂²⋊C₁₆	2
C₁₃×#1374	2
#12844	13

Subgroups — C13×#12844 #15699183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12844 #15699183