Subgroups — C₁₃×#21676 #15708015

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2402	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1940	C₂	1	2	yes	maximal
3	C₁₃×#1917	C₂	1	4	yes	maximal
4	C₁₃×#1832	C₂	1	1	yes	maximal, characteristic
5	C₈×C₁₃×C₄⋊C₄	C₂	1	4	yes	maximal
6	C₈×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal
7	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
10	C₂×C₁₃×#97	C₂²	1	2	yes	—
11	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#400	C₄	1	4	yes	—
16	C₁₃×#398	C₄	1	4	yes	—
17	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
18	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₁₃×#376	C₂²	1	1	yes	characteristic
20	C₁₃×#336	C₂²	1	4	yes	—
21	C₁₃×#336	C₂²	1	4	yes	—
22	C₁₃×#336	C₂²	1	4	yes	—
23	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
24	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
28	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
29	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
31	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
33	C₁₃×C₄⋊C₈	—	2	8	no	—
34	C₁₃×C₄⋊C₈	—	2	4	no	—
35	C₁₃×#97	—	2	4	no	—
36	C₁₃×#97	—	2	2	no	—
37	C₄×C₈×C₁₃	—	2	4	no	—
38	C₄×C₈×C₁₃	—	2	8	no	—
39	C₄×C₈×C₁₃	Q₈	1	4	yes	—
40	C₁₃×#95	C₂×C₄	1	2	yes	—
41	C₁₃×#95	C₂×C₄	1	4	yes	—
42	C₁₃×#95	C₂×C₄	1	4	yes	—
43	C₁₃×#95	C₂×C₄	1	2	yes	—
44	C₁₃×#95	C₂×C₄	1	4	yes	—
45	#21676	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
50	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
51	C₂×C₈×C₁₃	—	2	2	no	—
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	—	2	4	no	—
56	C₂×C₈×C₁₃	—	2	4	no	—
57	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
58	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
59	C₂×C₈×C₁₃	#41	1	4	yes	—
60	C₂×C₈×C₁₃	#41	1	4	yes	—
61	C₁₃×C₄⋊C₄	—	2	8	no	—
62	C₁₃×C₄⋊C₄	—	2	8	no	—
63	C₁₃×C₄⋊C₄	—	2	8	no	—
64	C₄²×C₁₃	—	2	4	no	—
65	C₄²×C₁₃	—	2	2	no	—
66	C₄²×C₁₃	—	2	2	no	—
67	C₄²×C₁₃	—	2	4	no	—
68	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
69	C₄²×C₁₃	#41	1	2	yes	—
70	#2402	C₂×C₁₃	1	1	yes	characteristic
71	#1940	C₂×C₁₃	1	2	yes	—
72	#1917	C₂×C₁₃	1	4	yes	—
73	#1832	C₂×C₁₃	1	1	yes	characteristic
74	C₈×C₄⋊C₄	C₂×C₁₃	1	4	yes	—
75	C₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	—
76	#1726	C₂×C₁₃	1	1	yes	characteristic
77	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	—	2	4	no	—
79	C₂×C₄×C₁₃	—	2	4	no	—
80	C₂×C₄×C₁₃	—	2	4	no	—
81	C₂×C₄×C₁₃	—	2	4	no	—
82	C₂×C₄×C₁₃	—	2	4	no	—
83	C₂×C₄×C₁₃	—	2	4	no	—
84	C₂×C₄×C₁₃	—	2	4	no	—
85	C₂×C₄×C₁₃	—	2	4	no	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
88	C₂×C₄×C₁₃	#131	1	8	yes	—
89	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
91	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
93	C₈×C₁₃	—	2	4	no	—
94	C₈×C₁₃	—	2	2	no	—
95	C₈×C₁₃	—	4	4	no	—
96	C₈×C₁₃	#125	1	4	yes	—
97	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
98	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
99	C₂×#97	C₂²×C₁₃	1	2	yes	—
100	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
101	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
102	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
103	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
104	#400	C₄×C₁₃	1	4	yes	—
105	#398	C₄×C₁₃	1	4	yes	—
106	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
107	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
108	#376	C₂²×C₁₃	1	1	yes	characteristic
109	#336	C₂²×C₁₃	1	4	yes	—
110	#336	C₂²×C₁₃	1	4	yes	—
111	#336	C₂²×C₁₃	1	4	yes	—
112	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
113	C₂²×C₁₃	C₄×#41	1	2	yes	—
114	C₂²×C₁₃	C₂×#131	1	4	yes	—
115	C₄×C₁₃	—	2	4	no	—
116	C₄×C₁₃	—	2	8	no	—
117	C₄×C₁₃	—	4	4	no	—
118	C₄×C₁₃	—	4	4	no	—
119	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
120	C₄×C₁₃	#529	1	2	yes	—
121	C₄×C₁₃	#533	1	1	yes	characteristic
122	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
123	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
124	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
125	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
126	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
127	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
128	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
129	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
130	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
131	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
132	C₄⋊C₈	—	2	8	no	—
133	C₄⋊C₈	—	2	4	no	—
134	#97	—	2	4	no	—
135	#97	—	2	2	no	—
136	C₄×C₈	—	2	4	no	—
137	C₄×C₈	—	2	8	no	—
138	C₄×C₈	Q₈×C₁₃	1	4	yes	—
139	#95	C₂×C₄×C₁₃	1	4	yes	—
140	#95	C₂×C₄×C₁₃	1	2	yes	—
141	#95	C₂×C₄×C₁₃	1	4	yes	—
142	#95	C₂×C₄×C₁₃	1	4	yes	—
143	#95	C₂×C₄×C₁₃	1	2	yes	—
144	C₂×C₁₃	C₄×#125	1	1	yes	characteristic
145	C₂×C₁₃	#2960	1	2	yes	—
146	C₂×C₁₃	#2966	1	4	yes	—
147	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
148	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
149	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
150	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
151	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
152	C₂×C₈	—	2	2	no	—
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	—	2	4	no	—
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	2	4	no	—
158	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
159	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
160	C₂×C₈	C₁₃×#41	1	4	yes	—
161	C₂×C₈	C₁₃×#41	1	4	yes	—
162	C₄⋊C₄	—	2	8	no	—
163	C₄⋊C₄	—	2	8	no	—
164	C₄⋊C₄	—	2	8	no	—
165	C₄²	—	2	4	no	—
166	C₄²	—	2	2	no	—
167	C₄²	—	2	2	no	—
168	C₄²	—	2	4	no	—
169	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
170	C₄²	C₁₃×#41	1	2	yes	—
171	C₁₃	#21676	1	1	yes	characteristic, direct product factor, Sylow
172	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	2	4	no	—
176	C₂×C₄	—	2	4	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
183	C₂×C₄	C₁₃×#131	1	8	yes	—
184	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
185	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
186	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
187	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
188	C₈	—	2	4	no	—
189	C₈	—	2	2	no	—
190	C₈	—	4	4	no	—
191	C₈	C₁₃×#125	1	4	yes	—
192	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
193	C₂²	C₄×C₁₃×#41	1	2	yes	—
194	C₂²	C₂×C₁₃×#131	1	4	yes	—
195	C₄	—	2	4	no	—
196	C₄	—	2	8	no	—
197	C₄	—	4	4	no	—
198	C₄	—	4	4	no	—
199	C₄	C₂×C₁₃×#125	1	1	yes	characteristic
200	C₄	C₁₃×#529	1	2	yes	—
201	C₄	C₁₃×#533	1	1	yes	characteristic
202	C₂	C₄×C₁₃×#125	1	1	yes	characteristic
203	C₂	C₁₃×#2960	1	2	yes	—
204	C₂	C₁₃×#2966	1	4	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle, prime radical	C₂³×C₁₃	C₂³×C₄
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
45. #21676	C₁₃	direct (N × H)
171. C₁₃	#21676	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2402	2
C₁₃×#1940	2
C₁₃×#1917	2
C₁₃×#1832	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1726	2
#21676	13

Subgroups — C13×#21676 #15708015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21676 #15708015