Subgroups — C₁₃×#2769 #13111827

Order 1664.

344 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#400	C₂	1	2	yes	maximal
2	C₁₃×#400	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#398	C₂	1	2	yes	maximal
4	C₁₃×#398	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#389	C₂	1	2	yes	maximal
6	C₁₃×#387	C₂	1	2	yes	maximal
7	C₁₃×#387	C₂	1	2	yes	maximal
8	C₁₃×#383	C₂	1	2	yes	maximal
9	C₁₃×#382	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
20	C₁₃×#95	C₂²	1	2	yes	—
21	C₁₃×#95	C₂²	1	2	yes	—
22	C₁₃×#95	C₂²	1	1	yes	characteristic
23	C₁₃×#95	C₂²	1	2	yes	—
24	C₁₃×#95	C₂²	1	2	yes	—
25	C₁₃×#95	C₂²	1	2	yes	—
26	C₁₃×#95	C₂²	1	2	yes	—
27	C₁₃×#95	C₂²	1	1	yes	characteristic
28	C₁₃×#95	C₂²	1	2	yes	—
29	C₁₃×#95	C₂²	1	2	yes	—
30	C₁₃×#95	C₂²	1	2	yes	—
31	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
32	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
33	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₁₃×C₄⋊C₄	—	2	4	no	—
41	C₁₃×C₄⋊C₄	—	2	4	no	—
42	C₁₃×C₄⋊C₄	—	2	4	no	—
43	C₁₃×C₄⋊C₄	—	4	1	no	—
44	C₁₃×C₄⋊C₄	—	4	1	no	—
45	C₁₃×C₄⋊C₄	—	4	2	no	—
46	C₁₃×C₄⋊C₄	—	4	1	no	—
47	C₁₃×C₄⋊C₄	—	4	1	no	—
48	C₄²×C₁₃	—	2	2	no	—
49	C₄²×C₁₃	—	2	4	no	—
50	#2769	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
52	C₂×C₄×C₁₃	—	2	2	no	—
53	C₂×C₄×C₁₃	—	2	1	no	—
54	C₂×C₄×C₁₃	—	2	1	no	—
55	C₂×C₄×C₁₃	—	2	2	no	—
56	C₂×C₄×C₁₃	—	2	2	no	—
57	C₂×C₄×C₁₃	—	2	2	no	—
58	C₂×C₄×C₁₃	—	2	2	no	—
59	C₂×C₄×C₁₃	—	2	2	no	—
60	C₂×C₄×C₁₃	—	2	2	no	—
61	C₂×C₄×C₁₃	—	2	2	no	—
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	—	2	2	no	—
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	2	1	no	—
68	C₂×C₄×C₁₃	—	2	1	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	#41	1	2	yes	—
76	C₂×C₄×C₁₃	#41	1	4	yes	—
77	#400	C₂×C₁₃	1	2	yes	—
78	#400	C₂×C₁₃	1	1	yes	characteristic
79	#398	C₂×C₁₃	1	2	yes	—
80	#398	C₂×C₁₃	1	1	yes	characteristic
81	#389	C₂×C₁₃	1	2	yes	—
82	#387	C₂×C₁₃	1	2	yes	—
83	#387	C₂×C₁₃	1	2	yes	—
84	#383	C₂×C₁₃	1	2	yes	—
85	#382	C₂×C₁₃	1	1	yes	characteristic
86	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
87	C₂²×C₁₃	C₂×#41	1	2	yes	—
88	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
89	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
90	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
91	C₄×C₁₃	—	2	2	no	—
92	C₄×C₁₃	—	2	4	no	—
93	C₄×C₁₃	—	4	2	no	—
94	C₄×C₁₃	—	4	2	no	—
95	C₄×C₁₃	—	4	2	no	—
96	C₄×C₁₃	—	4	2	no	—
97	C₄×C₁₃	—	4	2	no	—
98	C₄×C₁₃	—	4	1	no	—
99	C₄×C₁₃	—	4	1	no	—
100	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
101	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
102	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
103	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
104	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
105	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
106	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
107	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
108	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
109	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
110	#95	C₂²×C₁₃	1	2	yes	—
111	#95	C₂²×C₁₃	1	2	yes	—
112	#95	C₂²×C₁₃	1	1	yes	characteristic
113	#95	C₂²×C₁₃	1	2	yes	—
114	#95	C₂²×C₁₃	1	2	yes	—
115	#95	C₂²×C₁₃	1	2	yes	—
116	#95	C₂²×C₁₃	1	2	yes	—
117	#95	C₂²×C₁₃	1	1	yes	characteristic
118	#95	C₂²×C₁₃	1	2	yes	—
119	#95	C₂²×C₁₃	1	2	yes	—
120	#95	C₂²×C₁₃	1	2	yes	—
121	C₂×C₁₃	#539	1	1	yes	characteristic
122	C₂×C₁₃	#541	1	2	yes	—
123	C₂×C₁₃	#552	1	2	yes	—
124	C₂×C₁₃	#555	1	1	yes	characteristic
125	C₂×C₁₃	#563	1	1	yes	characteristic
126	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
127	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
128	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
129	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
130	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
131	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
132	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
133	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
134	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
135	C₄⋊C₄	—	2	4	no	—
136	C₄⋊C₄	—	2	4	no	—
137	C₄⋊C₄	—	2	4	no	—
138	C₄⋊C₄	—	4	1	no	—
139	C₄⋊C₄	—	4	1	no	—
140	C₄⋊C₄	—	4	2	no	—
141	C₄⋊C₄	—	4	1	no	—
142	C₄⋊C₄	—	4	1	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	2	4	no	—
145	C₁₃	#2769	1	1	yes	characteristic, direct product factor, Sylow
146	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	1	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	C₁₃×#41	1	2	yes	—
171	C₂×C₄	C₁₃×#41	1	4	yes	—
172	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
173	C₂²	C₂×C₁₃×#41	1	2	yes	—
174	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
176	C₂²	C₁₃×2₋¹⁺⁴	1	2	yes	—
177	C₄	—	2	2	no	—
178	C₄	—	2	4	no	—
179	C₄	—	4	2	no	—
180	C₄	—	4	2	no	—
181	C₄	—	4	2	no	—
182	C₄	—	4	2	no	—
183	C₄	—	4	2	no	—
184	C₄	—	4	1	no	—
185	C₄	—	4	1	no	—
186	C₂	C₁₃×#539	1	1	yes	characteristic
187	C₂	C₁₃×#541	1	2	yes	—
188	C₂	C₁₃×#552	1	2	yes	—
189	C₂	C₁₃×#555	1	1	yes	characteristic
190	C₂	C₁₃×#563	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
50. #2769	C₁₃	direct (N × H)
145. C₁₃	#2769	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×#400	2
C₁₃×#398	2
C₁₃×#389	2
C₁₃×#387	2
C₁₃×#383	2
C₁₃×#382	2
#2769	13

Subgroups — C13×#2769 #13111827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2769 #13111827