Subgroups — C₂×#11718494 #13123451

Order 1664.

528 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	C₂×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88060	C₂	1	2	yes	maximal
4	C₂×C₈×Dic₁₃	C₂	1	2	yes	maximal, complemented
5	C₂×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
6	#11718494	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×D₁₃	C₄	1	1	yes	characteristic
8	C₂²×C₄×D₁₃	C₄	1	1	yes	characteristic
9	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₁₃	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
15	C₂²×#1055	C₂²	1	2	yes	—
16	C₄²×D₁₃	C₄	1	4	yes	—
17	C₄²×D₁₃	C₂²	1	4	yes	—
18	C₁₃×C₄⋊C₈	C₂²	1	4	yes	complemented
19	#88060	C₂²	1	8	yes	—
20	C₈×Dic₁₃	C₂²	1	8	yes	complemented
21	C₄⋊#1055	C₂²	1	4	yes	complemented
22	C₂³×D₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×D₁₃	—	2	2	no	—
30	C₂×C₄×D₁₃	—	2	2	no	—
31	C₂×C₄×D₁₃	—	2	4	no	—
32	C₂×C₄×D₁₃	C₈	1	8	yes	complemented
33	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₄×D₁₃	C₂×C₄	1	4	yes	—
35	C₂×C₄×D₁₃	C₂×C₄	1	4	yes	—
36	C₂×C₄×D₁₃	C₂³	1	2	yes	—
37	C₂×C₈×C₁₃	—	2	4	no	—
38	C₂×C₈×C₁₃	C₂³	1	4	yes	—
39	C₄²×C₁₃	C₂×C₄	1	2	yes	—
40	C₄²×C₁₃	C₂³	1	2	yes	—
41	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
42	C₄×Dic₁₃	C₂×C₄	1	4	yes	—
43	C₄×Dic₁₃	C₂×C₄	1	4	yes	—
44	C₄×Dic₁₃	C₂³	1	2	yes	—
45	C₂×#1055	—	2	4	no	—
46	C₂×#1055	C₂³	1	4	yes	—
47	C₂×#431	—	13	1	no	maximal, Sylow
48	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²×D₁₃	—	2	2	no	—
50	C₂²×D₁₃	—	2	2	no	—
51	C₂²×D₁₃	C₂×C₈	1	4	yes	—
52	C₂²×D₁₃	C₂²×C₄	1	2	yes	—
53	C₂×C₄×C₁₃	—	2	2	no	—
54	C₂×C₄×C₁₃	C₂×C₈	1	4	yes	—
55	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
56	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
58	C₂×C₄×C₁₃	#41	1	2	yes	—
59	C₂×C₄×C₁₃	#41	1	2	yes	—
60	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₂×Dic₁₃	—	2	2	no	—
62	C₂×Dic₁₃	C₂×C₈	1	4	yes	—
63	C₂×Dic₁₃	M₁₆	1	4	yes	—
64	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
65	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
66	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
67	C₄×D₁₃	—	2	4	no	—
68	C₄×D₁₃	—	2	2	no	—
69	C₄×D₁₃	—	2	2	no	—
70	C₄×D₁₃	—	2	8	no	—
71	C₄×D₁₃	C₂×C₈	1	16	yes	complemented
72	C₈×C₁₃	—	2	4	no	—
73	#1055	—	2	4	no	—
74	C₂²×C₄²	—	13	1	no	—
75	#431	—	13	8	no	—
76	C₂×C₄⋊C₈	—	13	1	no	—
77	C₂×C₄⋊C₈	D₁₃	1	1	yes	characteristic, complemented
78	C₂×C₂²⋊C₈	—	13	2	no	—
79	C₂×C₄×C₈	—	13	2	no	—
80	C₂²×C₁₃	#117	1	2	yes	—
81	C₂²×C₁₃	C₂²×C₈	1	2	yes	—
82	C₂²×C₁₃	C₂×M₁₆	1	2	yes	—
83	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
84	C₂×D₁₃	—	2	2	no	—
85	C₂×D₁₃	—	2	2	no	—
86	C₂×D₁₃	—	2	8	no	—
87	C₂×D₁₃	C₂²×C₈	1	4	yes	—
88	C₄×C₁₃	—	2	2	no	—
89	C₄×C₁₃	#117	1	2	yes	—
90	C₄×C₁₃	C₂²×C₈	1	4	yes	—
91	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
92	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
93	Dic₁₃	—	2	2	no	—
94	Dic₁₃	C₂²×C₈	1	4	yes	—
95	Dic₁₃	C₂×M₁₆	1	4	yes	—
96	C₂³×C₄	—	13	1	no	—
97	C₂³×C₄	—	13	1	no	—
98	C₂³×C₄	—	13	1	no	—
99	C₂²×C₈	—	13	2	no	—
100	C₂²×C₈	C₂×D₁₃	1	2	yes	—
101	C₂×C₄²	—	13	1	no	—
102	C₂×C₄²	—	13	1	no	—
103	C₂×C₄²	—	13	1	no	—
104	C₂×C₄²	—	13	4	no	—
105	C₂×C₄²	—	13	4	no	—
106	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
107	C₄⋊C₈	—	13	4	no	—
108	C₄⋊C₈	C₂×D₁₃	1	4	yes	complemented
109	C₂²⋊C₈	—	13	8	no	—
110	C₄×C₈	—	13	8	no	—
111	C₂×C₁₃	#431	1	4	yes	complemented
112	C₂×C₁₃	C₂×#117	1	1	yes	characteristic
113	C₂×C₁₃	C₂³×C₈	1	1	yes	characteristic
114	C₂×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
115	D₁₃	—	2	4	no	—
116	C₂⁴	—	13	1	no	—
117	C₂²×C₄	—	13	1	no	—
118	C₂²×C₄	—	13	1	no	—
119	C₂²×C₄	—	13	8	no	—
120	C₂²×C₄	—	13	4	no	—
121	C₂²×C₄	—	13	1	no	—
122	C₂²×C₄	—	13	4	no	—
123	C₂²×C₄	—	13	2	no	—
124	C₂²×C₄	—	13	2	no	—
125	C₂²×C₄	—	26	4	no	—
126	C₂²×C₄	—	26	2	no	—
127	C₂²×C₄	—	26	2	no	—
128	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
129	C₂²×C₄	C₄×D₁₃	1	1	yes	characteristic
130	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
131	C₂×C₈	—	2	4	no	—
132	C₂×C₈	—	13	4	no	—
133	C₂×C₈	—	26	4	no	—
134	C₂×C₈	C₂²×D₁₃	1	4	yes	—
135	C₄²	—	13	2	no	—
136	C₄²	—	13	4	no	—
137	C₄²	—	13	4	no	—
138	C₄²	—	13	2	no	—
139	C₄²	C₄×D₁₃	1	2	yes	—
140	C₄²	C₂²×D₁₃	1	2	yes	—
141	C₁₃	C₂×#431	1	1	yes	characteristic, complemented, Sylow
142	C₂³	—	13	4	no	—
143	C₂³	—	13	2	no	—
144	C₂³	—	26	2	no	—
145	C₂³	—	26	2	no	—
146	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	13	4	no	—
149	C₂×C₄	—	13	4	no	—
150	C₂×C₄	—	13	2	no	—
151	C₂×C₄	—	13	2	no	—
152	C₂×C₄	—	13	16	no	—
153	C₂×C₄	—	13	2	no	—
154	C₂×C₄	—	26	8	no	—
155	C₂×C₄	—	26	2	no	—
156	C₂×C₄	—	26	4	no	—
157	C₂×C₄	—	26	2	no	—
158	C₂×C₄	—	26	2	no	—
159	C₂×C₄	C₈×D₁₃	1	4	yes	—
160	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
161	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
162	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
163	C₂×C₄	#6129	1	2	yes	—
164	C₂×C₄	#6131	1	2	yes	—
165	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
166	C₈	—	2	4	no	—
167	C₈	—	26	4	no	—
168	C₂²	—	13	4	no	—
169	C₂²	—	26	2	no	—
170	C₂²	—	26	2	no	—
171	C₂²	—	26	8	no	—
172	C₂²	#88146	1	2	yes	—
173	C₂²	C₂×C₈×D₁₃	1	2	yes	—
174	C₂²	M₁₆×D₁₃	1	2	yes	—
175	C₂²	C₂²×C₄×D₁₃	1	1	yes	characteristic
176	C₄	—	2	2	no	—
177	C₄	—	13	4	no	—
178	C₄	—	13	4	no	—
179	C₄	—	26	2	no	—
180	C₄	#88146	1	2	yes	—
181	C₄	C₂×C₈×D₁₃	1	4	yes	—
182	C₄	C₂×#6129	1	1	yes	characteristic
183	C₄	C₂×#6131	1	1	yes	characteristic
184	C₂	—	26	4	no	—
185	C₂	#11718494	1	4	yes	direct product factor
186	C₂	C₂×#88146	1	1	yes	characteristic
187	C₂	C₂²×C₈×D₁₃	1	1	yes	characteristic
188	C₂	C₂×M₁₆×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₃
commutator	C₂×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×C₄⋊C₈	C₂
socle	C₂³×C₁₃	C₂²×C₄
prime radical	C₂³×D₁₃	C₂×C₄
cosocle	C₂×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄⋊C₈	D₁₃
hypocenter	C₁₃	C₂×#431
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×C₄⋊C₈	C₂	semidirect
4. C₂×C₈×Dic₁₃	C₂	semidirect
5. C₂×C₄⋊#1055	C₂	semidirect
6. #11718494	C₂	direct (N × H)
18. C₁₃×C₄⋊C₈	C₂²	semidirect
20. C₈×Dic₁₃	C₂²	semidirect
21. C₄⋊#1055	C₂²	semidirect
32. C₂×C₄×D₁₃	C₈	semidirect
71. C₄×D₁₃	C₂×C₈	semidirect
77. C₂×C₄⋊C₈	D₁₃	semidirect
108. C₄⋊C₈	C₂×D₁₃	semidirect
111. C₂×C₁₃	#431	semidirect
141. C₁₃	C₂×#431	semidirect
185. C₂	#11718494	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₁₃	2
C₂×C₁₃×C₄⋊C₈	2
C₂×#88060	2
C₂×C₈×Dic₁₃	2
C₂×C₄⋊#1055	2
#11718494	2
C₂×#431	13

Subgroups — C2×#11718494 #13123451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718494 #13123451