Subgroups — #13123265

Order 1664.

556 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88161	C₂	1	2	yes	maximal
2	C₄×#6127	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718783	C₂	1	2	yes	maximal, complemented
5	C₂×#88043	C₂	1	1	yes	maximal, characteristic, complemented
6	#11718368	C₂	1	2	yes	maximal, complemented
7	D₁₃×#97	C₂	1	2	yes	maximal, complemented
8	#11718350	C₂	1	4	yes	maximal, complemented
9	C₂×#6127	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₄×C₂²⋊D₁₃	C₄	1	4	yes	—
13	#88180	C₂²	1	1	yes	characteristic
14	C₂²×#1055	C₂²	1	2	yes	—
15	#88161	C₄	1	16	yes	complemented
16	C₂×#6094	C₂²	1	4	yes	—
17	C₂×C₈×D₁₃	C₂²	1	4	yes	—
18	C₄×D₅₂	C₄	1	2	yes	—
19	#88126	C₂²	1	2	yes	—
20	C₄²×D₁₃	C₂²	1	2	yes	—
21	C₄×Dic₂₆	C₄	1	2	yes	—
22	C₁₃×#97	C₂²	1	2	yes	—
23	C₄×C₈×C₁₃	C₂²	1	2	yes	—
24	#88055	C₂²	1	4	yes	—
25	C₈×Dic₁₃	C₂²	1	4	yes	—
26	#88043	C₂²	1	2	yes	—
27	#88043	C₂²	1	1	yes	characteristic
28	#88043	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
32	#6127	C₂×C₄	1	8	yes	—
33	C₂×D₅₂	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₁₃	C₂×C₄	1	4	yes	—
35	C₂×C₄×D₁₃	C₂³	1	2	yes	—
36	C₂×Dic₂₆	C₂×C₄	1	1	yes	characteristic
37	C₁₃×M₁₆	C₂×C₄	1	8	yes	complemented
38	C₂×C₈×C₁₃	C₂³	1	4	yes	—
39	C₄²×C₁₃	C₂×C₄	1	2	yes	—
40	C₄²×C₁₃	C₂³	1	1	yes	characteristic
41	C₄²×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
43	#6103	C₂×C₄	1	4	yes	—
44	C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
45	#6101	C₂×C₄	1	4	yes	—
46	C₄×Dic₁₃	C₂×C₄	1	4	yes	—
47	C₄×Dic₁₃	C₂³	1	2	yes	—
48	C₂×#1055	C₂×C₄	1	8	yes	complemented
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	#2875	—	13	1	no	maximal, Sylow
54	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
55	C₂²×D₁₃	C₂²×C₄	1	2	yes	—
56	C₂×C₄×C₁₃	—	4	2	no	—
57	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
58	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
59	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
61	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
62	C₂²⋊D₁₃	C₄²	1	8	yes	—
63	C₂×Dic₁₃	C₂²×C₄	1	4	yes	—
64	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
65	D₅₂	C₄²	1	4	yes	—
66	C₄×D₁₃	—	4	4	no	—
67	C₄×D₁₃	C₂²×C₄	1	8	yes	—
68	Dic₂₆	C₄²	1	4	yes	—
69	C₈×C₁₃	C₂²×C₄	1	8	yes	—
70	#1055	C₂²×C₄	1	4	yes	—
71	#1055	C₂²×C₄	1	4	yes	—
72	C₂×#131	—	13	2	no	—
73	C₄×#41	—	13	1	no	—
74	#405	—	13	2	no	—
75	#405	—	13	4	no	—
76	C₄×M₁₆	—	13	2	no	—
77	C₄×M₁₆	D₁₃	1	1	yes	characteristic, complemented
78	C₂×#97	—	13	1	no	—
79	C₂×#97	—	13	2	no	—
80	C₂²×C₁₃	—	2	2	no	—
81	C₂²×C₁₃	C₂×C₄²	1	2	yes	—
82	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
83	C₂×D₁₃	—	2	4	no	—
84	C₂×D₁₃	C₂×C₄²	1	4	yes	—
85	C₄×C₁₃	—	2	2	no	—
86	C₄×C₁₃	—	2	2	no	—
87	C₄×C₁₃	C₂×C₄²	1	2	yes	—
88	C₄×C₁₃	C₂³×C₄	1	2	yes	—
89	Dic₁₃	—	2	4	no	—
90	Dic₁₃	C₂×C₄²	1	4	yes	—
91	C₂×#41	—	13	1	no	—
92	#131	—	13	16	no	—
93	C₂×M₁₆	—	13	4	no	—
94	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
95	C₂²×C₈	—	13	2	no	—
96	C₂²×C₈	—	13	4	no	—
97	C₄×Q₈	—	13	2	no	—
98	C₄×D₄	—	13	4	no	—
99	C₄×D₄	—	13	2	no	—
100	#117	—	13	1	no	—
101	#117	—	13	2	no	—
102	C₂×C₄²	—	13	2	no	—
103	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
104	#97	—	13	4	no	—
105	#97	—	13	1	no	—
106	#97	—	13	1	no	—
107	#97	—	13	2	no	—
108	#97	C₂×D₁₃	1	2	yes	—
109	C₄×C₈	—	13	4	no	—
110	C₄×C₈	C₂×D₁₃	1	2	yes	—
111	C₂×C₁₃	—	2	2	no	—
112	C₂×C₁₃	C₂²×C₄²	1	1	yes	characteristic
113	C₂×C₁₃	#568	1	2	yes	—
114	D₁₃	—	2	4	no	—
115	#41	—	13	8	no	—
116	C₂×Q₈	—	13	1	no	—
117	C₂×D₄	—	13	2	no	—
118	C₂×D₄	—	13	1	no	—
119	C₂²×C₄	—	13	2	no	—
120	C₂²×C₄	—	13	4	no	—
121	C₂²×C₄	C₄×D₁₃	1	2	yes	—
122	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
123	M₁₆	—	13	16	no	—
124	M₁₆	C₄×D₁₃	1	8	yes	complemented
125	C₂×C₈	—	13	8	no	—
126	C₂×C₈	—	13	2	no	—
127	C₂×C₈	—	13	2	no	—
128	C₂×C₈	—	13	16	no	—
129	C₂×C₈	C₂²×D₁₃	1	4	yes	—
130	C₄⋊C₄	—	13	4	no	—
131	C₄⋊C₄	—	13	2	no	—
132	C₂²⋊C₄	—	13	2	no	—
133	C₂²⋊C₄	—	13	4	no	—
134	C₄²	—	13	4	no	—
135	C₄²	—	13	2	no	—
136	C₄²	C₄×D₁₃	1	2	yes	—
137	C₄²	C₂²×D₁₃	1	1	yes	characteristic
138	C₄²	C₂²×D₁₃	1	1	yes	characteristic
139	C₁₃	#2875	1	1	yes	characteristic, complemented, Sylow
140	C₂³	—	13	2	no	—
141	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
142	Q₈	—	13	4	no	—
143	D₄	—	13	8	no	—
144	D₄	—	13	4	no	—
145	C₂×C₄	—	4	2	no	—
146	C₂×C₄	—	13	2	no	—
147	C₂×C₄	—	13	8	no	—
148	C₂×C₄	—	13	4	no	—
149	C₂×C₄	—	52	4	no	—
150	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
151	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
152	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
153	C₂×C₄	C₂×C₄×D₁₃	1	4	yes	—
154	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
155	C₈	—	13	4	no	—
156	C₈	—	13	4	no	—
157	C₈	C₂×C₄×D₁₃	1	8	yes	—
158	C₂²	—	2	2	no	—
159	C₂²	—	13	4	no	—
160	C₂²	—	26	4	no	—
161	C₂²	C₄²×D₁₃	1	2	yes	—
162	C₂²	C₂²×C₄×D₁₃	1	1	yes	characteristic
163	C₄	—	2	2	no	—
164	C₄	—	2	2	no	—
165	C₄	—	13	4	no	—
166	C₄	—	26	4	no	—
167	C₄	C₄²×D₁₃	1	2	yes	—
168	C₄	C₂²×C₄×D₁₃	1	2	yes	—
169	C₂	—	2	2	no	—
170	C₂	—	26	4	no	—
171	C₂	C₂×C₄²×D₁₃	1	1	yes	characteristic
172	C₂	#11719450	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₃
commutator	C₂×C₁₃	C₂²×C₄²
Fitting	C₄×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂³×C₄
prime radical	C₂×#6127	C₂²
cosocle	C₂×C₄×C₁₃	C₂⁴
hypercenter	C₄×M₁₆	D₁₃
hypocenter	C₁₃	#2875
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₄×C₁₃×M₁₆	C₂	semidirect
4. #11718783	C₂	semidirect
5. C₂×#88043	C₂	semidirect
6. #11718368	C₂	semidirect
7. D₁₃×#97	C₂	semidirect
8. #11718350	C₂	semidirect
15. #88161	C₄	semidirect
37. C₁₃×M₁₆	C₂×C₄	semidirect
48. C₂×#1055	C₂×C₄	semidirect
51. #6094	C₂×C₄	semidirect
52. C₈×D₁₃	C₂×C₄	semidirect
77. C₄×M₁₆	D₁₃	semidirect
124. M₁₆	C₄×D₁₃	semidirect
139. C₁₃	#2875	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88161	2
C₄×#6127	2
C₄×C₁₃×M₁₆	2
#11718783	2
C₂×#88043	2
#11718368	2
D₁₃×#97	2
#11718350	2
#2875	13