Subgroups — C₂×#11718350 #13123247

Order 1664.

592 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6094	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#88126	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#88043	C₂	1	1	yes	maximal, characteristic, complemented
8	#11718350	C₂	1	8	yes	maximal, direct product factor
9	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#6103	C₄	1	2	yes	—
14	C₂×#6101	C₄	1	2	yes	—
15	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₂²×#1055	C₂²	1	1	yes	characteristic
17	C₂²×#1055	C₂²	1	1	yes	characteristic
18	C₂×#6094	C₄	1	8	yes	complemented
19	C₂×#6094	C₂²	1	4	yes	—
20	C₂×C₈×D₁₃	C₄	1	8	yes	complemented
21	C₂×C₈×D₁₃	C₂²	1	4	yes	—
22	#88126	C₄	1	4	yes	—
23	#88126	C₂²	1	4	yes	—
24	C₄×C₈×C₁₃	C₂²	1	4	yes	complemented
25	#88055	C₂²	1	4	yes	complemented
26	C₈×Dic₁₃	C₂²	1	4	yes	complemented
27	#88043	C₂²	1	4	yes	complemented
28	C₂³×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₃	C₂×C₄	1	2	yes	—
32	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄	1	4	yes	—
38	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
39	C₂×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂×C₈×C₁₃	C₂³	1	2	yes	—
41	C₄²×C₁₃	C₂×C₄	1	2	yes	—
42	C₄²×C₁₃	C₂³	1	2	yes	—
43	#6103	C₂×C₄	1	8	yes	—
44	#6101	C₂×C₄	1	8	yes	—
45	C₄×Dic₁₃	C₂×C₄	1	2	yes	—
46	C₄×Dic₁₃	C₂³	1	2	yes	—
47	C₂×#1055	C₂×C₄	1	4	yes	—
48	C₂×#1055	C₂×C₄	1	4	yes	—
49	C₂×#1055	C₂³	1	2	yes	—
50	C₂×#1055	C₂³	1	2	yes	—
51	#6094	C₂×C₄	1	16	yes	complemented
52	C₈×D₁₃	C₂×C₄	1	16	yes	complemented
53	C₂×#405	—	13	1	no	maximal, Sylow
54	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
55	C₂²×D₁₃	—	2	4	no	—
56	C₂²×D₁₃	C₄²	1	4	yes	—
57	C₂²×D₁₃	C₂²×C₄	1	2	yes	—
58	C₂×C₄×C₁₃	—	2	4	no	—
59	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
60	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
62	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
63	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
64	C₂×Dic₁₃	—	2	4	no	—
65	C₂×Dic₁₃	C₄²	1	4	yes	—
66	C₂×Dic₁₃	C₂²×C₄	1	4	yes	—
67	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
68	C₄×D₁₃	C₄²	1	8	yes	—
69	C₄×D₁₃	C₂²×C₄	1	4	yes	—
70	C₄×D₁₃	C₂²×C₄	1	4	yes	—
71	C₈×C₁₃	C₂²×C₄	1	4	yes	—
72	C₈×C₁₃	C₂²×C₄	1	4	yes	—
73	#1055	C₂²×C₄	1	4	yes	—
74	#1055	C₂²×C₄	1	4	yes	—
75	C₂²×M₁₆	—	13	1	no	—
76	C₂³×C₈	—	13	1	no	—
77	C₂×#117	—	13	1	no	—
78	#405	—	13	8	no	—
79	C₂×#97	—	13	1	no	—
80	C₂×#97	—	13	1	no	—
81	C₂×C₄×C₈	—	13	1	no	—
82	C₂×C₄×C₈	D₁₃	1	1	yes	characteristic, complemented
83	C₂²×C₁₃	C₂×C₄²	1	2	yes	—
84	C₂²×C₁₃	#131	1	4	yes	—
85	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
86	C₂×D₁₃	—	2	4	no	—
87	C₂×D₁₃	—	2	8	no	—
88	C₂×D₁₃	C₂×C₄²	1	4	yes	—
89	C₄×C₁₃	—	2	4	no	—
90	C₄×C₁₃	C₂×C₄²	1	2	yes	—
91	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
92	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
93	Dic₁₃	—	2	4	no	—
94	Dic₁₃	C₂×C₄²	1	4	yes	—
95	C₂³×C₄	—	13	1	no	—
96	C₂×M₁₆	—	13	8	no	—
97	C₂×M₁₆	—	13	4	no	—
98	C₂²×C₈	—	13	1	no	—
99	C₂²×C₈	—	13	1	no	—
100	C₂²×C₈	—	13	8	no	—
101	C₂²×C₈	—	13	4	no	—
102	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
103	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
104	#117	—	13	4	no	—
105	#117	—	13	4	no	—
106	C₂×C₄⋊C₄	—	13	2	no	—
107	C₂×C₂²⋊C₄	—	13	2	no	—
108	C₂×C₄²	—	13	1	no	—
109	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
110	#97	—	13	4	no	—
111	#97	—	13	4	no	—
112	C₄×C₈	—	13	4	no	—
113	C₄×C₈	C₂×D₁₃	1	4	yes	complemented
114	C₂×C₁₃	#405	1	4	yes	complemented
115	C₂×C₁₃	C₂²×C₄²	1	1	yes	characteristic
116	C₂×C₁₃	C₂×#131	1	2	yes	—
117	D₁₃	—	2	4	no	—
118	C₂⁴	—	13	1	no	—
119	C₂²×C₄	—	13	1	no	—
120	C₂²×C₄	—	13	2	no	—
121	C₂²×C₄	—	13	4	no	—
122	C₂²×C₄	—	13	4	no	—
123	C₂²×C₄	—	13	2	no	—
124	C₂²×C₄	—	13	2	no	—
125	C₂²×C₄	C₄×D₁₃	1	2	yes	—
126	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
127	M₁₆	—	13	16	no	—
128	C₂×C₈	—	13	4	no	—
129	C₂×C₈	—	13	4	no	—
130	C₂×C₈	—	13	2	no	—
131	C₂×C₈	—	13	2	no	—
132	C₂×C₈	—	13	16	no	—
133	C₂×C₈	C₄×D₁₃	1	4	yes	—
134	C₂×C₈	C₄×D₁₃	1	4	yes	—
135	C₂×C₈	C₂²×D₁₃	1	2	yes	—
136	C₂×C₈	C₂²×D₁₃	1	2	yes	—
137	C₄⋊C₄	—	13	8	no	—
138	C₂²⋊C₄	—	13	8	no	—
139	C₄²	—	13	2	no	—
140	C₄²	—	13	2	no	—
141	C₄²	C₄×D₁₃	1	2	yes	—
142	C₄²	C₂²×D₁₃	1	2	yes	—
143	C₁₃	C₂×#405	1	1	yes	characteristic, complemented, Sylow
144	C₂³	—	13	4	no	—
145	C₂³	—	13	2	no	—
146	C₂³	—	26	4	no	—
147	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	13	4	no	—
150	C₂×C₄	—	13	2	no	—
151	C₂×C₄	—	13	8	no	—
152	C₂×C₄	—	13	4	no	—
153	C₂×C₄	—	13	4	no	—
154	C₂×C₄	—	13	4	no	—
155	C₂×C₄	—	26	4	no	—
156	C₂×C₄	C₂×C₄×D₁₃	1	4	yes	—
157	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
158	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
159	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
160	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
161	C₈	—	13	4	no	—
162	C₈	—	13	4	no	—
163	C₈	C₂×C₄×D₁₃	1	4	yes	—
164	C₈	C₂×C₄×D₁₃	1	4	yes	—
165	C₂²	—	13	4	no	—
166	C₂²	—	26	4	no	—
167	C₂²	—	26	8	no	—
168	C₂²	C₄²×D₁₃	1	2	yes	—
169	C₂²	#88155	1	4	yes	—
170	C₂²	C₂²×C₄×D₁₃	1	1	yes	characteristic
171	C₄	—	2	4	no	—
172	C₄	—	13	4	no	—
173	C₄	—	26	4	no	—
174	C₄	C₄²×D₁₃	1	2	yes	—
175	C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
176	C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
177	C₂	—	26	4	no	—
178	C₂	#11718350	1	4	yes	direct product factor
179	C₂	C₂×C₄²×D₁₃	1	1	yes	characteristic
180	C₂	C₂×#88155	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₁₃
Fitting	C₂×C₄×C₈×C₁₃	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×#405
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₄×C₈×C₁₃	C₂	semidirect
5. C₂×#88055	C₂	semidirect
6. C₂×C₈×Dic₁₃	C₂	semidirect
7. C₂×#88043	C₂	semidirect
8. #11718350	C₂	direct (N × H)
18. C₂×#6094	C₄	semidirect
20. C₂×C₈×D₁₃	C₄	semidirect
24. C₄×C₈×C₁₃	C₂²	semidirect
25. #88055	C₂²	semidirect
26. C₈×Dic₁₃	C₂²	semidirect
27. #88043	C₂²	semidirect
51. #6094	C₂×C₄	semidirect
52. C₈×D₁₃	C₂×C₄	semidirect
82. C₂×C₄×C₈	D₁₃	semidirect
113. C₄×C₈	C₂×D₁₃	semidirect
114. C₂×C₁₃	#405	semidirect
143. C₁₃	C₂×#405	semidirect
178. C₂	#11718350	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×#6094	2
C₂²×C₈×D₁₃	2
C₂×#88126	2
C₂×C₄×C₈×C₁₃	2
C₂×#88055	2
C₂×C₈×Dic₁₃	2
C₂×#88043	2
#11718350	2
C₂×#405	13

Subgroups — C2×#11718350 #13123247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718350 #13123247