Subgroups — C₁₃×#32856 #15719195

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2647	C₂	1	2	yes	maximal
2	C₁₃×#2101	C₂	1	4	yes	maximal
3	C₁₃×#2087	C₂	1	2	yes	maximal
4	C₁₃×#2086	C₂	1	2	yes	maximal
5	C₁₃×#2083	C₂	1	4	yes	maximal
6	C₁₃×#1832	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#107	C₂²	1	2	yes	—
8	C₂×C₁₃×#107	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₃×#400	—	2	4	no	—
12	C₁₃×#398	—	2	4	no	—
13	C₁₃×#389	C₂²	1	4	yes	—
14	C₁₃×#389	C₂²	1	4	yes	—
15	C₁₃×#384	C₂²	1	2	yes	—
16	C₁₃×#382	C₂²	1	2	yes	—
17	C₁₃×#376	C₂²	1	1	yes	characteristic
18	C₁₃×#340	C₂²	1	4	yes	—
19	C₁₃×#340	C₂²	1	4	yes	—
20	C₁₃×#340	C₂²	1	2	yes	—
21	C₁₃×#340	C₂²	1	2	yes	—
22	C₁₃×#336	C₂²	1	4	yes	—
23	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
24	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
29	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
30	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
31	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
32	C₁₃×#107	—	4	2	no	—
33	C₁₃×#107	—	4	2	no	—
34	C₁₃×C₄⋊C₈	—	4	1	no	—
35	C₁₃×C₄⋊C₈	—	4	1	no	—
36	C₁₃×#95	—	2	4	no	—
37	C₁₃×#95	—	2	4	no	—
38	C₁₃×#95	—	2	4	no	—
39	C₁₃×#95	D₄	1	2	yes	—
40	C₁₃×#95	D₄	1	2	yes	—
41	#32856	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₄×C₁₃	—	2	4	no	—
43	C₂²×C₄×C₁₃	—	2	4	no	—
44	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
46	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
48	C₂×C₈×C₁₃	—	2	2	no	—
49	C₂×C₈×C₁₃	—	2	2	no	—
50	C₂×C₈×C₁₃	—	2	4	no	—
51	C₂×C₈×C₁₃	—	2	4	no	—
52	C₁₃×C₄⋊C₄	—	2	4	no	—
53	C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₁₃×C₄⋊C₄	—	8	4	no	—
57	C₁₃×C₄⋊C₄	—	8	4	no	—
58	C₁₃×C₄⋊C₄	—	8	4	no	—
59	C₄²×C₁₃	—	2	1	no	—
60	C₄²×C₁₃	—	2	2	no	—
61	C₄²×C₁₃	—	2	2	no	—
62	C₄²×C₁₃	—	2	1	no	—
63	#2647	C₂×C₁₃	1	2	yes	—
64	#2101	C₂×C₁₃	1	4	yes	—
65	#2087	C₂×C₁₃	1	2	yes	—
66	#2086	C₂×C₁₃	1	2	yes	—
67	#2083	C₂×C₁₃	1	4	yes	—
68	#1832	C₂×C₁₃	1	1	yes	characteristic
69	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₃	—	2	4	no	—
71	C₂×C₄×C₁₃	—	2	1	no	—
72	C₂×C₄×C₁₃	—	2	1	no	—
73	C₂×C₄×C₁₃	—	2	4	no	—
74	C₂×C₄×C₁₃	—	2	2	no	—
75	C₂×C₄×C₁₃	—	2	4	no	—
76	C₂×C₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	—	4	4	no	—
78	C₂×C₄×C₁₃	—	4	4	no	—
79	C₂×C₄×C₁₃	—	4	4	no	—
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	—	4	4	no	—
82	C₂×C₄×C₁₃	—	4	4	no	—
83	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
84	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
85	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
86	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
87	C₈×C₁₃	—	4	2	no	—
88	C₈×C₁₃	—	4	2	no	—
89	C₂×#107	C₂²×C₁₃	1	2	yes	—
90	C₂×#107	C₂²×C₁₃	1	2	yes	—
91	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
92	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
93	#400	—	2	4	no	—
94	#398	—	2	4	no	—
95	#389	C₂²×C₁₃	1	4	yes	—
96	#389	C₂²×C₁₃	1	4	yes	—
97	#384	C₂²×C₁₃	1	2	yes	—
98	#382	C₂²×C₁₃	1	2	yes	—
99	#376	C₂²×C₁₃	1	1	yes	characteristic
100	#340	C₂²×C₁₃	1	4	yes	—
101	#340	C₂²×C₁₃	1	4	yes	—
102	#340	C₂²×C₁₃	1	2	yes	—
103	#340	C₂²×C₁₃	1	2	yes	—
104	#336	C₂²×C₁₃	1	4	yes	—
105	C₂²×C₁₃	#536	1	2	yes	—
106	C₂²×C₁₃	#537	1	1	yes	characteristic
107	C₂²×C₁₃	#576	1	2	yes	—
108	C₂²×C₁₃	#578	1	2	yes	—
109	C₄×C₁₃	—	4	4	no	—
110	C₄×C₁₃	—	4	1	no	—
111	C₄×C₁₃	—	4	1	no	—
112	C₄×C₁₃	—	8	4	no	—
113	C₄×C₁₃	—	8	4	no	—
114	C₄×C₁₃	#563	1	1	yes	characteristic
115	C₄×C₁₃	#563	1	1	yes	characteristic
116	C₄×C₁₃	#564	1	2	yes	—
117	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
118	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
119	C₂×C₄⋊C₄	—	2	4	no	—
120	C₂×C₄⋊C₄	—	2	4	no	—
121	C₂×C₄⋊C₄	—	2	4	no	—
122	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
123	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
124	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
125	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
126	#107	—	4	2	no	—
127	#107	—	4	2	no	—
128	C₄⋊C₈	—	4	1	no	—
129	C₄⋊C₈	—	4	1	no	—
130	#95	—	2	4	no	—
131	#95	—	2	4	no	—
132	#95	—	2	4	no	—
133	#95	D₄×C₁₃	1	2	yes	—
134	#95	D₄×C₁₃	1	2	yes	—
135	C₂×C₁₃	#2822	1	1	yes	characteristic
136	C₂×C₁₃	#3243	1	4	yes	—
137	C₂×C₁₃	#3259	1	1	yes	characteristic
138	C₂×C₁₃	#3261	1	1	yes	characteristic
139	C₂²×C₄	—	2	4	no	—
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
142	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
143	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
144	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	—	2	4	no	—
148	C₂×C₈	—	2	4	no	—
149	C₄⋊C₄	—	2	4	no	—
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	8	4	no	—
154	C₄⋊C₄	—	8	4	no	—
155	C₄⋊C₄	—	8	4	no	—
156	C₄²	—	2	1	no	—
157	C₄²	—	2	2	no	—
158	C₄²	—	2	2	no	—
159	C₄²	—	2	1	no	—
160	C₁₃	#32856	1	1	yes	characteristic, direct product factor, Sylow
161	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	—	4	4	no	—
171	C₂×C₄	—	4	4	no	—
172	C₂×C₄	—	4	4	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
177	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
178	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
179	C₈	—	4	2	no	—
180	C₈	—	4	2	no	—
181	C₂²	C₁₃×#536	1	2	yes	—
182	C₂²	C₁₃×#537	1	1	yes	characteristic
183	C₂²	C₁₃×#576	1	2	yes	—
184	C₂²	C₁₃×#578	1	2	yes	—
185	C₄	—	4	4	no	—
186	C₄	—	4	1	no	—
187	C₄	—	4	1	no	—
188	C₄	—	8	4	no	—
189	C₄	—	8	4	no	—
190	C₄	C₁₃×#563	1	1	yes	characteristic
191	C₄	C₁₃×#563	1	1	yes	characteristic
192	C₄	C₁₃×#564	1	2	yes	—
193	C₂	C₁₃×#2822	1	1	yes	characteristic
194	C₂	C₁₃×#3243	1	4	yes	—
195	C₂	C₁₃×#3259	1	1	yes	characteristic
196	C₂	C₁₃×#3261	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	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
41. #32856	C₁₃	direct (N × H)
160. C₁₃	#32856	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×#2647	2
C₁₃×#2101	2
C₁₃×#2087	2
C₁₃×#2086	2
C₁₃×#2083	2
C₁₃×#1832	2
#32856	13

Subgroups — C13×#32856 #15719195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32856 #15719195