Subgroups — D₁₃×#1454 #15828541

Order 3328.

802 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	D₁₃×#431	C₂	1	3	yes	maximal
2	#13113137	C₂	1	3	yes	maximal, complemented
3	#13113136	C₂	1	3	yes	maximal, complemented
4	#13113135	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₃×#322	C₂	1	3	yes	maximal, complemented
6	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1454	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#431	C₂²	1	3	yes	—
10	#11718586	C₂²	1	3	yes	—
11	#11718494	C₄	1	6	yes	—
12	D₁₃×C₄⋊C₈	C₄	1	6	yes	—
13	D₁₃×C₂²⋊C₈	C₄	1	6	yes	—
14	#11718379	C₄	1	6	yes	—
15	#11718346	C₂²	1	3	yes	—
16	#11718346	C₂²	1	3	yes	—
17	C₄×C₈×D₁₃	C₂²	1	3	yes	—
18	C₄×C₈×D₁₃	C₂²	1	3	yes	—
19	C₁₃×#322	C₂²	1	3	yes	complemented
20	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	#11718047	C₂²	1	3	yes	complemented
22	#11718046	C₂²	1	3	yes	complemented
23	#11718046	C₂²	1	3	yes	complemented
24	C₈×#1055	C₂²	1	3	yes	complemented
25	C₂²×C₄×D₁₃	C₂×C₄	1	3	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
28	C₂×C₈×D₁₃	C₂×C₄	1	6	yes	—
29	C₂×C₈×D₁₃	C₂×C₄	1	6	yes	—
30	C₄²×D₁₃	C₂×C₄	1	3	yes	—
31	C₄²×D₁₃	C₂×C₄	1	3	yes	—
32	C₄²×D₁₃	C₂³	1	1	yes	characteristic
33	C₄²×D₁₃	C₂³	1	1	yes	characteristic
34	C₁₃×C₄⋊C₈	C₂×C₄	1	6	yes	—
35	C₁₃×C₂²⋊C₈	C₂×C₄	1	6	yes	—
36	C₄×C₈×C₁₃	C₂³	1	3	yes	—
37	C₄×C₈×C₁₃	C₂³	1	3	yes	—
38	C₂²⋊#1055	C₂×C₄	1	6	yes	—
39	#88060	C₂×C₄	1	6	yes	—
40	#88060	C₂×C₄	1	6	yes	—
41	#88054	C₂×C₄	1	6	yes	—
42	#88054	C₂×C₄	1	6	yes	—
43	C₈×Dic₁₃	C₂×C₄	1	6	yes	—
44	C₈×Dic₁₃	C₂×C₄	1	6	yes	—
45	C₄⋊#1055	C₂×C₄	1	6	yes	—
46	C₄×#1055	C₂³	1	3	yes	—
47	C₄×#1055	C₂³	1	3	yes	—
48	C₂×#1454	—	13	1	no	maximal, Sylow
49	C₂³×D₁₃	C₄²	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
51	C₂²×Dic₁₃	C₄²	1	3	yes	—
52	C₂×C₄×D₁₃	—	2	12	no	—
53	C₂×C₄×D₁₃	C₄²	1	3	yes	—
54	C₂×C₄×D₁₃	C₄²	1	3	yes	—
55	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
56	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
57	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
58	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
59	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
60	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₄×Dic₁₃	C₄²	1	6	yes	—
62	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
63	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
64	C₂×#1055	C₂²×C₄	1	6	yes	—
65	C₂×#1055	C₂²×C₄	1	6	yes	—
66	C₈×D₁₃	—	2	12	no	—
67	C₈×D₁₃	—	2	12	no	—
68	C₂×#431	—	13	3	no	—
69	#1454	—	13	3	no	—
70	#1454	—	13	3	no	—
71	#1454	—	13	1	no	—
72	#1454	D₁₃	1	1	yes	characteristic, direct product factor
73	C₂×#322	—	13	3	no	—
74	C₂×C₈²	—	13	1	no	—
75	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
76	C₂²×D₁₃	—	2	6	no	—
77	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
78	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
79	C₂×C₄×C₁₃	—	2	6	no	—
80	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
81	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
82	C₂×Dic₁₃	—	2	6	no	—
83	C₂×Dic₁₃	C₂×C₄²	1	3	yes	—
84	C₂×Dic₁₃	C₂×C₄²	1	3	yes	—
85	C₄×D₁₃	—	2	6	no	—
86	C₄×D₁₃	—	2	6	no	—
87	C₄×D₁₃	—	2	6	no	—
88	C₄×D₁₃	#131	1	12	yes	—
89	C₈×C₁₃	—	2	6	no	—
90	C₈×C₁₃	—	2	6	no	—
91	#1055	—	2	6	no	—
92	#1055	—	2	6	no	—
93	C₂²×C₄²	—	13	1	no	—
94	#431	—	13	3	no	—
95	#431	—	13	6	no	—
96	#431	—	13	6	no	—
97	#431	—	13	3	no	—
98	#431	—	13	3	no	—
99	#431	C₂×D₁₃	1	3	yes	—
100	C₂×C₄⋊C₈	—	13	6	no	—
101	C₂×C₂²⋊C₈	—	13	6	no	—
102	C₂×C₄×C₈	—	13	3	no	—
103	C₂×C₄×C₈	—	13	3	no	—
104	#322	—	13	3	no	—
105	#322	—	13	3	no	—
106	#322	—	13	3	no	—
107	#322	C₂×D₁₃	1	3	yes	complemented
108	C₈²	—	13	3	no	—
109	C₈²	C₂×D₁₃	1	1	yes	characteristic, complemented
110	C₂²×C₁₃	—	2	3	no	—
111	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
112	C₂×D₁₃	—	2	3	no	—
113	C₂×D₁₃	—	4	4	no	—
114	C₂×D₁₃	#405	1	6	yes	—
115	C₄×C₁₃	—	2	3	no	—
116	C₄×C₁₃	C₂×#131	1	6	yes	—
117	Dic₁₃	—	2	3	no	—
118	Dic₁₃	#405	1	6	yes	—
119	C₂³×C₄	—	13	3	no	—
120	C₂²×C₈	—	13	6	no	—
121	C₂²×C₈	—	13	6	no	—
122	C₂×C₄²	—	13	3	no	—
123	C₂×C₄²	—	13	3	no	—
124	C₂×C₄²	—	13	3	no	—
125	C₂×C₄²	—	13	1	no	—
126	C₂×C₄²	—	13	1	no	—
127	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
128	C₄⋊C₈	—	13	6	no	—
129	C₄⋊C₈	—	13	6	no	—
130	C₄⋊C₈	—	13	6	no	—
131	C₄⋊C₈	C₄×D₁₃	1	6	yes	—
132	C₂²⋊C₈	—	13	6	no	—
133	C₂²⋊C₈	—	13	6	no	—
134	C₂²⋊C₈	—	13	6	no	—
135	C₂²⋊C₈	C₄×D₁₃	1	6	yes	—
136	C₄×C₈	—	13	6	no	—
137	C₄×C₈	—	13	6	no	—
138	C₄×C₈	—	13	3	no	—
139	C₄×C₈	—	13	3	no	—
140	C₄×C₈	C₂²×D₁₃	1	3	yes	—
141	C₄×C₈	C₂²×D₁₃	1	3	yes	—
142	C₂×C₁₃	—	4	1	no	—
143	C₂×C₁₃	C₂×#405	1	3	yes	—
144	D₁₃	—	4	1	no	—
145	D₁₃	#1454	1	4	yes	direct product factor
146	C₂⁴	—	13	1	no	—
147	C₂²×C₄	—	13	3	no	—
148	C₂²×C₄	—	13	3	no	—
149	C₂²×C₄	—	13	3	no	—
150	C₂²×C₄	—	13	3	no	—
151	C₂²×C₄	—	13	3	no	—
152	C₂²×C₄	—	26	12	no	—
153	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
154	C₂×C₈	—	13	6	no	—
155	C₂×C₈	—	13	6	no	—
156	C₂×C₈	—	26	12	no	—
157	C₂×C₈	—	26	12	no	—
158	C₂×C₈	C₂×C₄×D₁₃	1	6	yes	—
159	C₂×C₈	C₂×C₄×D₁₃	1	6	yes	—
160	C₄²	—	13	6	no	—
161	C₄²	—	13	3	no	—
162	C₄²	—	13	3	no	—
163	C₄²	C₂×C₄×D₁₃	1	3	yes	—
164	C₄²	C₂³×D₁₃	1	1	yes	characteristic
165	C₁₃	C₂×#1454	1	1	yes	characteristic, complemented, Sylow
166	C₂³	—	13	1	no	—
167	C₂³	—	13	1	no	—
168	C₂³	—	26	6	no	—
169	C₂³	C₄²×D₁₃	1	1	yes	characteristic
170	C₂×C₄	—	2	6	no	—
171	C₂×C₄	—	13	3	no	—
172	C₂×C₄	—	13	12	no	—
173	C₂×C₄	—	13	3	no	—
174	C₂×C₄	—	26	6	no	—
175	C₂×C₄	—	26	6	no	—
176	C₂×C₄	—	26	6	no	—
177	C₂×C₄	—	26	6	no	—
178	C₂×C₄	C₄²×D₁₃	1	3	yes	—
179	C₂×C₄	C₂²×C₄×D₁₃	1	3	yes	—
180	C₈	—	2	6	no	—
181	C₈	—	2	6	no	—
182	C₈	—	26	6	no	—
183	C₈	—	26	6	no	—
184	C₂²	—	2	3	no	—
185	C₂²	—	13	6	no	—
186	C₂²	—	26	3	no	—
187	C₂²	—	52	4	no	—
188	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
189	C₄	—	2	3	no	—
190	C₄	—	13	6	no	—
191	C₄	—	26	3	no	—
192	C₄	D₁₃×#131	1	6	yes	—
193	C₂	—	4	1	no	—
194	C₂	—	13	4	no	—
195	C₂	—	52	1	no	—
196	C₂	D₁₃×#405	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1454	C₂
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1454	D₁₃
hypocenter	C₁₃	C₂×#1454
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #1454

Complements

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

N	H ≅ G/N	type
2. #13113137	C₂	semidirect
3. #13113136	C₂	semidirect
4. #13113135	C₂	semidirect
5. D₁₃×#322	C₂	semidirect
6. C₈²×D₁₃	C₂	semidirect
7. C₁₃×#1454	C₂	semidirect
19. C₁₃×#322	C₂²	semidirect
20. C₈²×C₁₃	C₂²	semidirect
21. #11718047	C₂²	semidirect
22. #11718046	C₂²	semidirect
23. #11718046	C₂²	semidirect
24. C₈×#1055	C₂²	semidirect
72. #1454	D₁₃	direct (N × H)
107. #322	C₂×D₁₃	semidirect
109. C₈²	C₂×D₁₃	semidirect
145. D₁₃	#1454	direct (N × H)
165. C₁₃	C₂×#1454	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#431	2
#13113137	2
#13113136	2
#13113135	2
D₁₃×#322	2
C₈²×D₁₃	2
C₁₃×#1454	2
C₂×#1454	13

Subgroups — D13×#1454 #15828541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#1454 #15828541