Subgroups — C₂×#13114589 #15860390

Order 3328.

1134 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#1055	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718593	C₂	1	1	yes	maximal, characteristic
3	#13114589	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718142	C₂	1	4	yes	maximal
5	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
9	C₂³×#1055	C₂²	1	2	yes	—
10	C₂×C₁₃×#97	C₄	1	8	yes	complemented
11	C₂×C₁₃×#97	C₂²	1	4	yes	—
12	C₂×#88071	C₄	1	4	yes	—
13	#11718593	C₄	1	4	yes	—
14	#11718593	C₂²	1	4	yes	—
15	C₂×C₄×#1055	C₄	1	8	yes	complemented
16	C₂×C₄×#1055	C₂²	1	4	yes	—
17	#11718142	C₂²	1	16	yes	—
18	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
20	C₂³×Dic₁₃	C₂×C₄	1	4	yes	—
21	C₂²×C₈×C₁₃	—	2	8	no	—
22	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
23	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
28	C₂×C₄×Dic₁₃	—	2	8	no	—
29	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
30	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
31	C₂²×#1055	—	2	8	no	—
32	C₂²×#1055	C₂×C₄	1	8	yes	—
33	C₂²×#1055	C₂³	1	4	yes	—
34	C₁₃×#97	C₂×C₄	1	16	yes	complemented
35	#88071	C₂×C₄	1	16	yes	—
36	C₄×#1055	C₂×C₄	1	16	yes	complemented
37	C₂×#1746	—	13	1	no	maximal, Sylow
38	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	—	2	8	no	—
40	C₂²×C₄×C₁₃	C₄²	1	8	yes	—
41	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
42	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
45	C₂²×C₄×C₁₃	#41	1	8	yes	—
46	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
47	C₂²×Dic₁₃	—	2	8	no	—
48	C₂²×Dic₁₃	—	2	16	no	—
49	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
50	C₂×C₈×C₁₃	—	2	16	no	—
51	C₂×C₈×C₁₃	—	2	8	no	—
52	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
53	C₄²×C₁₃	C₄²	1	8	yes	—
54	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
55	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
56	C₄×Dic₁₃	—	2	8	no	—
57	C₄×Dic₁₃	—	2	8	no	—
58	C₂×#1055	—	2	16	no	—
59	C₂×#1055	—	2	8	no	—
60	C₂×#1055	C₂²×C₄	1	8	yes	—
61	C₂²×#97	D₁₃	1	1	yes	characteristic
62	C₂²×C₄×C₈	—	13	1	no	—
63	C₂×#376	—	13	1	no	—
64	#1746	—	13	8	no	—
65	C₂×#336	—	13	4	no	—
66	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
67	C₂³×C₁₃	#117	1	4	yes	—
68	C₂³×C₁₃	#131	1	8	yes	—
69	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₃	—	2	8	no	—
71	C₂×C₄×C₁₃	—	2	16	no	—
72	C₂×C₄×C₁₃	C₂×C₄²	1	8	yes	—
73	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
74	C₂×C₄×C₁₃	#117	1	8	yes	—
75	C₂×C₄×C₁₃	#117	1	8	yes	—
76	C₂×C₄×C₁₃	#117	1	4	yes	—
77	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
80	C₂×Dic₁₃	—	2	8	no	—
81	C₂×Dic₁₃	—	2	16	no	—
82	C₂×Dic₁₃	—	4	16	no	—
83	C₈×C₁₃	—	2	8	no	—
84	#1055	—	2	8	no	—
85	C₂³×C₈	—	13	2	no	—
86	C₂³×C₈	C₂×D₁₃	1	2	yes	—
87	C₂²×C₄²	—	13	2	no	—
88	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
89	C₂×#97	Dic₁₃	1	8	yes	complemented
90	C₂×#97	C₂×D₁₃	1	4	yes	—
91	C₂×C₄×C₈	—	13	8	no	—
92	C₂×C₄×C₈	—	13	4	no	—
93	#376	—	13	4	no	—
94	#376	—	13	4	no	—
95	C₂×#95	—	13	4	no	—
96	#336	—	13	16	no	—
97	C₂²×C₁₃	#376	1	4	yes	—
98	C₂²×C₁₃	#405	1	8	yes	—
99	C₂²×C₁₃	#433	1	16	yes	—
100	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
101	C₂²×C₁₃	C₂×#117	1	2	yes	—
102	C₂²×C₁₃	C₂×#131	1	4	yes	—
103	C₄×C₁₃	—	2	8	no	—
104	C₄×C₁₃	#376	1	4	yes	—
105	C₄×C₁₃	C₂×#117	1	2	yes	—
106	C₄×C₁₃	C₂×#117	1	2	yes	—
107	Dic₁₃	—	4	8	no	—
108	C₂³×C₄	—	13	4	no	—
109	C₂³×C₄	C₄×D₁₃	1	2	yes	—
110	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
111	C₂²×C₈	—	2	8	no	—
112	C₂²×C₈	—	13	8	no	—
113	C₂²×C₈	—	13	4	no	—
114	C₂²×C₈	—	26	8	no	—
115	C₂²×C₈	C₂×Dic₁₃	1	8	yes	—
116	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
117	C₂×C₄²	—	13	4	no	—
118	C₂×C₄²	—	13	4	no	—
119	C₂×C₄²	—	26	8	no	—
120	C₂×C₄²	C₄×D₁₃	1	2	yes	—
121	C₂×C₄²	C₄×D₁₃	1	4	yes	—
122	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
123	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
124	#97	C₂×Dic₁₃	1	16	yes	complemented
125	C₄×C₈	—	13	16	no	—
126	#95	—	13	16	no	—
127	C₂×C₁₃	#1746	1	8	yes	complemented
128	C₂×C₁₃	C₂×#376	1	1	yes	characteristic
129	C₂×C₁₃	C₂×#405	1	2	yes	—
130	C₂×C₁₃	C₂×#433	1	4	yes	—
131	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
132	C₂²×C₄	—	2	8	no	—
133	C₂²×C₄	—	13	8	no	—
134	C₂²×C₄	—	26	8	no	—
135	C₂²×C₄	—	26	16	no	—
136	C₂²×C₄	C₄×Dic₁₃	1	8	yes	—
137	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
138	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
139	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
140	C₂²×C₄	#6127	1	8	yes	—
141	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
142	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
143	C₂×C₈	—	2	16	no	—
144	C₂×C₈	—	2	8	no	—
145	C₂×C₈	—	13	8	no	—
146	C₂×C₈	—	26	16	no	—
147	C₂×C₈	—	26	8	no	—
148	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
149	C₄²	—	26	8	no	—
150	C₄²	—	26	8	no	—
151	C₄²	C₄×Dic₁₃	1	8	yes	—
152	C₄²	C₂×C₄×D₁₃	1	4	yes	—
153	C₄²	C₂²×Dic₁₃	1	4	yes	—
154	C₁₃	C₂×#1746	1	1	yes	characteristic, complemented, Sylow
155	C₂³	#88126	1	4	yes	—
156	C₂³	#88161	1	8	yes	—
157	C₂³	C₂×C₄×Dic₁₃	1	2	yes	—
158	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
159	C₂×C₄	—	2	8	no	—
160	C₂×C₄	—	2	16	no	—
161	C₂×C₄	—	26	8	no	—
162	C₂×C₄	—	26	16	no	—
163	C₂×C₄	—	52	16	no	—
164	C₂×C₄	#88126	1	8	yes	—
165	C₂×C₄	#88126	1	4	yes	—
166	C₂×C₄	C₂×C₄×Dic₁₃	1	8	yes	—
167	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
168	C₂×C₄	#88180	1	8	yes	—
169	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
170	C₂×C₄	C₂×#6127	1	4	yes	—
171	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
172	C₈	—	2	8	no	—
173	C₈	—	26	8	no	—
174	C₂²	#11718370	1	16	yes	—
175	C₂²	#11718593	1	4	yes	—
176	C₂²	#11718783	1	8	yes	—
177	C₂²	C₂×#88126	1	2	yes	—
178	C₂²	C₂×#88161	1	4	yes	—
179	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
180	C₄	—	2	8	no	—
181	C₄	—	52	8	no	—
182	C₄	#11718593	1	4	yes	—
183	C₄	C₂×#88126	1	2	yes	—
184	C₄	C₂×#88180	1	2	yes	—
185	C₂	#13114589	1	8	yes	direct product factor
186	C₂	C₂×#11718593	1	1	yes	characteristic
187	C₂	C₂×#11718783	1	2	yes	—
188	C₂	C₂×#11718370	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×#97	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	C₂×#1746
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
3. #13114589	C₂	direct (N × H)
10. C₂×C₁₃×#97	C₄	semidirect
15. C₂×C₄×#1055	C₄	semidirect
34. C₁₃×#97	C₂×C₄	semidirect
36. C₄×#1055	C₂×C₄	semidirect
89. C₂×#97	Dic₁₃	semidirect
124. #97	C₂×Dic₁₃	semidirect
127. C₂×C₁₃	#1746	semidirect
154. C₁₃	C₂×#1746	semidirect
185. C₂	#13114589	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×#1055	2
C₂×#11718593	2
#13114589	2
C₂×#11718142	2
C₂²×C₁₃×#97	2
C₂×#1746	13

Subgroups — C2×#13114589 #15860390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114589 #15860390