Subgroups — C₁₃×#13190 #15699529

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
8	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
9	C₈×D₄×C₁₃	—	2	2	no	—
10	C₈×D₄×C₁₃	—	2	2	no	—
11	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×C₄⋊C₁₆	—	2	2	no	—
15	C₁₃×C₂²⋊C₁₆	—	2	8	no	—
16	C₁₃×#346	—	2	2	no	—
17	C₂²×D₄×C₁₃	C₈	1	1	yes	characteristic
18	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₃	—	2	4	no	—
20	C₂²×C₈×C₁₃	—	2	2	no	—
21	C₂²×C₈×C₁₃	—	2	2	no	—
22	C₂²×C₈×C₁₃	—	2	4	no	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
26	C₄×D₄×C₁₃	—	2	2	no	—
27	C₄×D₄×C₁₃	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	C₈	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊C₄	C₈	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₁₃×C₁₆	—	2	2	no	—
32	C₂×C₁₃×C₁₆	—	2	2	no	—
33	C₂×C₁₃×C₁₆	—	2	4	no	—
34	C₂×C₁₃×C₁₆	—	2	2	no	—
35	C₂×C₁₃×C₁₆	D₄	1	4	yes	complemented
36	C₁₃×C₄⋊C₈	—	2	2	no	—
37	C₁₃×C₂²⋊C₈	—	2	4	no	—
38	C₄×C₈×C₁₃	D₄	1	2	yes	—
39	C₄×C₈×C₁₃	D₄	1	2	yes	—
40	#13190	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁴×C₁₃	C₂×C₈	1	2	yes	—
42	C₂×D₄×C₁₃	—	2	4	no	—
43	C₂×D₄×C₁₃	—	2	2	no	—
44	C₂²×C₄×C₁₃	—	2	2	no	—
45	C₂²×C₄×C₁₃	—	2	4	no	—
46	C₂²×C₄×C₁₃	—	2	2	no	—
47	C₂²×C₄×C₁₃	—	2	4	no	—
48	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	—	2	2	no	—
53	C₂×C₈×C₁₃	—	2	2	no	—
54	C₂×C₈×C₁₃	—	2	4	no	—
55	C₂×C₈×C₁₃	—	4	4	no	—
56	C₂×C₈×C₁₃	—	4	2	no	—
57	C₂×C₈×C₁₃	—	4	2	no	—
58	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
59	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
61	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₁₃	#41	1	2	yes	—
63	C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₁₃×C₂²⋊C₄	—	2	4	no	—
65	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
66	C₄²×C₁₃	M₁₆	1	2	yes	—
67	C₁₃×C₁₆	—	2	4	no	—
68	C₁₃×C₁₆	—	4	2	no	—
69	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
70	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
71	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	4	yes	complemented
72	C₂×#346	C₂×C₁₃	1	1	yes	characteristic, complemented
73	C₂³×C₁₃	—	2	2	no	—
74	C₂³×C₁₃	—	2	4	no	—
75	C₂³×C₁₃	—	2	2	no	—
76	C₂³×C₁₃	—	2	4	no	—
77	C₂³×C₁₃	M₃₂	1	4	yes	—
78	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
79	D₄×C₁₃	—	2	8	no	—
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	—	4	4	no	—
87	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
88	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
89	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₃	#131	1	2	yes	—
93	C₈×C₁₃	—	2	2	no	—
94	C₈×C₁₃	—	4	2	no	—
95	C₈×C₁₃	#121	1	2	yes	—
96	C₈×C₁₃	#124	1	1	yes	characteristic
97	C₈×C₁₃	#127	1	1	yes	characteristic
98	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
99	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
100	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
101	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
102	C₈×D₄	—	2	2	no	—
103	C₈×D₄	—	2	2	no	—
104	C₂×C₄⋊C₈	C₄×C₁₃	1	1	yes	characteristic
105	C₂×C₂²⋊C₈	C₄×C₁₃	1	2	yes	—
106	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
107	C₄⋊C₁₆	—	2	2	no	—
108	C₂²⋊C₁₆	—	2	8	no	—
109	#346	—	2	2	no	—
110	C₂²×C₁₃	—	2	4	no	—
111	C₂²×C₁₃	—	2	8	no	—
112	C₂²×C₁₃	—	4	2	no	—
113	C₂²×C₁₃	—	4	4	no	—
114	C₂²×C₁₃	—	4	2	no	—
115	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
116	C₂²×C₁₃	C₈×D₄	1	2	yes	—
117	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
118	C₂²×C₁₃	#504	1	2	yes	—
119	C₄×C₁₃	—	2	2	no	—
120	C₄×C₁₃	—	2	2	no	—
121	C₄×C₁₃	—	4	2	no	—
122	C₄×C₁₃	#390	1	1	yes	characteristic
123	C₄×C₁₃	#408	1	1	yes	characteristic
124	C₄×C₁₃	#436	1	2	yes	—
125	C₂²×D₄	C₈×C₁₃	1	1	yes	characteristic
126	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
127	C₂²×C₈	—	2	4	no	—
128	C₂²×C₈	—	2	2	no	—
129	C₂²×C₈	—	2	2	no	—
130	C₂²×C₈	—	2	4	no	—
131	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
132	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
133	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
134	C₄×D₄	—	2	2	no	—
135	C₄×D₄	—	2	2	no	—
136	C₂×C₄⋊C₄	C₈×C₁₃	1	1	yes	characteristic
137	C₂×C₂²⋊C₄	C₈×C₁₃	1	2	yes	—
138	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
139	C₂×C₁₆	—	2	2	no	—
140	C₂×C₁₆	—	2	2	no	—
141	C₂×C₁₆	—	2	4	no	—
142	C₂×C₁₆	—	2	2	no	—
143	C₂×C₁₆	D₄×C₁₃	1	4	yes	complemented
144	C₄⋊C₈	—	2	2	no	—
145	C₂²⋊C₈	—	2	4	no	—
146	C₄×C₈	D₄×C₁₃	1	2	yes	—
147	C₄×C₈	D₄×C₁₃	1	2	yes	—
148	C₂×C₁₃	—	4	4	no	—
149	C₂×C₁₃	#1954	1	1	yes	characteristic
150	C₂×C₁₃	#2112	1	1	yes	characteristic
151	C₂×C₁₃	#2113	1	1	yes	characteristic
152	C₂×C₁₃	#2168	1	4	yes	—
153	C₂⁴	C₂×C₈×C₁₃	1	2	yes	—
154	C₂×D₄	—	2	4	no	—
155	C₂×D₄	—	2	2	no	—
156	C₂²×C₄	—	2	2	no	—
157	C₂²×C₄	—	2	4	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	2	4	no	—
160	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
161	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
162	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
163	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	2	4	no	—
167	C₂×C₈	—	4	4	no	—
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
171	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
172	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
173	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
174	C₂×C₈	C₁₃×#41	1	2	yes	—
175	C₄⋊C₄	—	2	2	no	—
176	C₂²⋊C₄	—	2	4	no	—
177	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
178	C₄²	C₁₃×M₁₆	1	2	yes	—
179	C₁₆	—	2	4	no	—
180	C₁₆	—	4	2	no	—
181	C₁₃	#13190	1	1	yes	characteristic, direct product factor, Sylow
182	C₂³	—	2	2	no	—
183	C₂³	—	2	4	no	—
184	C₂³	—	2	2	no	—
185	C₂³	—	2	4	no	—
186	C₂³	C₁₃×M₃₂	1	4	yes	—
187	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
188	D₄	—	2	8	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
197	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
198	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
200	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
201	C₂×C₄	C₁₃×#131	1	2	yes	—
202	C₈	—	2	2	no	—
203	C₈	—	4	2	no	—
204	C₈	C₁₃×#121	1	2	yes	—
205	C₈	C₁₃×#124	1	1	yes	characteristic
206	C₈	C₁₃×#127	1	1	yes	characteristic
207	C₂²	—	2	4	no	—
208	C₂²	—	2	8	no	—
209	C₂²	—	4	2	no	—
210	C₂²	—	4	4	no	—
211	C₂²	—	4	2	no	—
212	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
213	C₂²	C₈×D₄×C₁₃	1	2	yes	—
214	C₂²	C₂×C₁₃×M₃₂	1	2	yes	—
215	C₂²	C₁₃×#504	1	2	yes	—
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	4	2	no	—
219	C₄	C₁₃×#390	1	1	yes	characteristic
220	C₄	C₁₃×#408	1	1	yes	characteristic
221	C₄	C₁₃×#436	1	2	yes	—
222	C₂	—	4	4	no	—
223	C₂	C₁₃×#1954	1	1	yes	characteristic
224	C₂	C₁₃×#2112	1	1	yes	characteristic
225	C₂	C₁₃×#2113	1	1	yes	characteristic
226	C₂	C₁₃×#2168	1	4	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂³	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂³×C₁₃	C₂²×C₈
prime radical	C₂²×D₄×C₁₃	C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×C₄⋊C₁₆	C₂	semidirect
3. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
4. C₂×C₁₃×#346	C₂	semidirect
35. C₂×C₁₃×C₁₆	D₄	semidirect
40. #13190	C₁₃	direct (N × H)
70. C₂×C₄⋊C₁₆	C₂×C₁₃	semidirect
71. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
72. C₂×#346	C₂×C₁₃	semidirect
143. C₂×C₁₆	D₄×C₁₃	semidirect
181. C₁₃	#13190	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×C₈×D₄×C₁₃	2
C₂×C₁₃×C₄⋊C₁₆	2
C₂×C₁₃×C₂²⋊C₁₆	2
C₂×C₁₃×#346	2
#13190	13

Subgroups — C13×#13190 #15699529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13190 #15699529