Subgroups — C₁₃×#2667 #13111725

Order 1664.

408 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#399	C₂	1	2	yes	maximal
2	C₁₃×#398	C₂	1	2	yes	maximal, complemented
3	C₁₃×#398	C₂	1	2	yes	maximal, complemented
4	C₁₃×#396	C₂	1	2	yes	maximal
5	C₁₃×#389	C₂	1	2	yes	maximal, complemented
6	C₁₃×#387	C₂	1	2	yes	maximal, complemented
7	C₁₃×#381	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#380	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
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	2	yes	—
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#95	C₂²	1	1	yes	characteristic
24	C₁₃×#95	C₂²	1	1	yes	characteristic
25	C₁₃×#95	C₂²	1	2	yes	—
26	C₁₃×#95	C₂²	1	1	yes	characteristic
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	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₃	—	4	2	no	—
33	C₂²×C₄×C₁₃	Q₈	1	4	yes	—
34	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
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	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
42	C₁₃×C₄⋊C₄	—	2	4	no	—
43	C₁₃×C₄⋊C₄	—	2	4	no	—
44	C₁₃×C₄⋊C₄	—	4	2	no	—
45	C₁₃×C₄⋊C₄	—	4	2	no	—
46	C₁₃×C₄⋊C₄	—	4	2	no	—
47	C₁₃×C₄⋊C₄	—	4	2	no	—
48	C₁₃×C₄⋊C₄	—	4	2	no	—
49	C₁₃×C₂²⋊C₄	—	2	4	no	—
50	C₁₃×C₂²⋊C₄	—	4	1	no	—
51	C₁₃×C₂²⋊C₄	—	4	1	no	—
52	C₁₃×C₂²⋊C₄	—	4	2	no	—
53	C₄²×C₁₃	—	4	2	no	—
54	#2667	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂³×C₁₃	—	2	2	no	—
56	C₂³×C₁₃	—	2	1	no	—
57	C₂³×C₁₃	—	2	2	no	—
58	C₂³×C₁₃	—	2	1	no	—
59	C₂³×C₁₃	C₂×Q₈	1	2	yes	—
60	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
68	C₂×C₄×C₁₃	—	2	2	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	2	no	—
77	C₂×C₄×C₁₃	—	2	2	no	—
78	C₂×C₄×C₁₃	—	2	2	no	—
79	C₂×C₄×C₁₃	—	2	2	no	—
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
82	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
83	C₂×C₄×C₁₃	#41	1	4	yes	—
84	#399	C₂×C₁₃	1	2	yes	—
85	#398	C₂×C₁₃	1	2	yes	complemented
86	#398	C₂×C₁₃	1	2	yes	complemented
87	#396	C₂×C₁₃	1	2	yes	—
88	#389	C₂×C₁₃	1	2	yes	complemented
89	#387	C₂×C₁₃	1	2	yes	complemented
90	#381	C₂×C₁₃	1	1	yes	characteristic
91	#380	C₂×C₁₃	1	1	yes	characteristic
92	C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
93	C₂²×C₁₃	—	2	2	no	—
94	C₂²×C₁₃	—	2	2	no	—
95	C₂²×C₁₃	—	2	2	no	—
96	C₂²×C₁₃	—	4	2	no	—
97	C₂²×C₁₃	—	4	2	no	—
98	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
99	C₂²×C₁₃	C₂×#41	1	2	yes	—
100	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
101	C₂²×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
102	C₂²×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
103	C₄×C₁₃	—	2	4	no	—
104	C₄×C₁₃	—	2	2	no	—
105	C₄×C₁₃	—	2	2	no	—
106	C₄×C₁₃	—	4	2	no	—
107	C₄×C₁₃	—	4	2	no	—
108	C₄×C₁₃	—	4	2	no	—
109	C₄×C₁₃	—	4	2	no	—
110	C₄×C₁₃	—	4	2	no	—
111	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
112	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
113	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
114	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
115	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
116	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
117	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
118	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
119	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
120	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
121	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
122	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
123	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
124	#95	C₂²×C₁₃	1	1	yes	characteristic
125	#95	C₂²×C₁₃	1	1	yes	characteristic
126	#95	C₂²×C₁₃	1	2	yes	—
127	#95	C₂²×C₁₃	1	1	yes	characteristic
128	#95	C₂²×C₁₃	1	1	yes	characteristic
129	#95	C₂²×C₁₃	1	2	yes	—
130	#95	C₂²×C₁₃	1	2	yes	—
131	#95	C₂²×C₁₃	1	2	yes	—
132	C₂×C₁₃	—	4	2	no	—
133	C₂×C₁₃	#533	1	1	yes	characteristic
134	C₂×C₁₃	#539	1	2	yes	—
135	C₂×C₁₃	#540	1	2	yes	—
136	C₂×C₁₃	#543	1	1	yes	characteristic
137	C₂×C₁₃	#544	1	1	yes	characteristic
138	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	Q₈×C₁₃	1	4	yes	—
141	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
142	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
143	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
144	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
145	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
146	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
147	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
148	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
149	C₄⋊C₄	—	2	4	no	—
150	C₄⋊C₄	—	2	4	no	—
151	C₄⋊C₄	—	4	2	no	—
152	C₄⋊C₄	—	4	2	no	—
153	C₄⋊C₄	—	4	2	no	—
154	C₄⋊C₄	—	4	2	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₂²⋊C₄	—	2	4	no	—
157	C₂²⋊C₄	—	4	1	no	—
158	C₂²⋊C₄	—	4	1	no	—
159	C₂²⋊C₄	—	4	2	no	—
160	C₄²	—	4	2	no	—
161	C₁₃	#2667	1	1	yes	characteristic, direct product factor, Sylow
162	C₂³	—	2	2	no	—
163	C₂³	—	2	1	no	—
164	C₂³	—	2	2	no	—
165	C₂³	—	2	1	no	—
166	C₂³	C₂×Q₈×C₁₃	1	2	yes	—
167	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	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	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
189	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
190	C₂×C₄	C₁₃×#41	1	4	yes	—
191	C₂²	—	2	2	no	—
192	C₂²	—	2	2	no	—
193	C₂²	—	2	2	no	—
194	C₂²	—	4	2	no	—
195	C₂²	—	4	2	no	—
196	C₂²	C₂²×Q₈×C₁₃	1	1	yes	characteristic
197	C₂²	C₂×C₁₃×#41	1	2	yes	—
198	C₂²	C₁₃×H(5,𝔽₂)	1	2	yes	—
199	C₂²	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
200	C₂²	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
201	C₄	—	2	4	no	—
202	C₄	—	2	2	no	—
203	C₄	—	2	2	no	—
204	C₄	—	4	2	no	—
205	C₄	—	4	2	no	—
206	C₄	—	4	2	no	—
207	C₄	—	4	2	no	—
208	C₄	—	4	2	no	—
209	C₂	—	4	2	no	—
210	C₂	C₁₃×#533	1	1	yes	characteristic
211	C₂	C₁₃×#539	1	2	yes	—
212	C₂	C₁₃×#540	1	2	yes	—
213	C₂	C₁₃×#543	1	1	yes	characteristic
214	C₂	C₁₃×#544	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂³
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
2. C₁₃×#398	C₂	semidirect
3. C₁₃×#398	C₂	semidirect
5. C₁₃×#389	C₂	semidirect
6. C₁₃×#387	C₂	semidirect
54. #2667	C₁₃	direct (N × H)
85. #398	C₂×C₁₃	semidirect
86. #398	C₂×C₁₃	semidirect
88. #389	C₂×C₁₃	semidirect
89. #387	C₂×C₁₃	semidirect
161. C₁₃	#2667	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×#399	2
C₁₃×#398	2
C₁₃×#396	2
C₁₃×#389	2
C₁₃×#387	2
C₁₃×#381	2
C₁₃×#380	2
C₄×C₁₃×C₂²⋊C₄	2
#2667	13

Subgroups — C13×#2667 #13111725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2667 #13111725