Subgroups — #15783097

Order 3328.

238 conjugacy classes of subgroups.

The subgroup lattice has 160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718039	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#13116431	C₂	1	1	yes	maximal, characteristic
4	#13112970	C₂	1	1	yes	maximal, characteristic, complemented
5	#13112969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₂×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88038	C₄	1	1	yes	characteristic
9	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
10	#11718350	C₄	1	1	yes	characteristic
11	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
14	#11718094	C₄	1	1	yes	characteristic
15	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₂×#88034	C₂²	1	1	yes	characteristic
17	C₂×#88034	C₂²	1	1	yes	characteristic
18	#11718053	C₄	1	1	yes	characteristic
19	#11718039	C₄	1	4	yes	complemented
20	D₁₃×C₃₂	C₄	1	4	yes	complemented
21	C₂×#6094	C₈	1	1	yes	characteristic
22	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
23	#88126	C₈	1	1	yes	characteristic
24	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
26	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	#88055	C₈	1	1	yes	characteristic
28	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×#6090	C₂×C₄	1	1	yes	characteristic
30	C₂×#6090	C₂×C₄	1	1	yes	characteristic
31	#88043	C₈	1	1	yes	characteristic
32	#88038	C₈	1	4	yes	—
33	C₁₆×D₁₃	C₂×C₄	1	2	yes	—
34	C₁₆×D₁₃	C₂×C₄	1	2	yes	—
35	C₁₃×C₃₂	C₂×C₄	1	2	yes	—
36	C₁₃×C₃₂	C₂×C₄	1	2	yes	—
37	#88034	C₂×C₄	1	2	yes	—
38	#88034	C₂×C₄	1	2	yes	—
39	#13549	—	13	1	no	maximal, Sylow
40	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
44	#6103	C₁₆	1	2	yes	—
45	#6101	C₁₆	1	2	yes	—
46	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
47	C₂×#1055	C₂×C₈	1	1	yes	characteristic
48	C₂×#1055	C₂×C₈	1	1	yes	characteristic
49	#6094	C₁₆	1	4	yes	—
50	C₈×D₁₃	C₄²	1	2	yes	—
51	C₈×D₁₃	C₂×C₈	1	2	yes	—
52	C₁₃×C₁₆	C₂×C₈	1	2	yes	—
53	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
54	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
55	#6090	C₄²	1	2	yes	—
56	#6090	C₂×C₈	1	2	yes	—
57	C₂×M₆₄	—	13	1	no	—
58	C₂²×C₃₂	—	13	1	no	—
59	#2108	—	13	1	no	—
60	#1397	—	13	1	no	—
61	#1397	—	13	1	no	—
62	C₄×C₃₂	—	13	1	no	—
63	C₄×C₃₂	D₁₃	1	1	yes	characteristic, complemented
64	C₂²×D₁₃	C₂×C₁₆	1	1	yes	characteristic
65	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
66	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
67	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
68	C₂×Dic₁₃	C₂×C₁₆	1	1	yes	characteristic
69	C₄×D₁₃	C₄×C₈	1	2	yes	—
70	C₄×D₁₃	C₂×C₁₆	1	2	yes	—
71	C₈×C₁₃	C₂×C₁₆	1	2	yes	—
72	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
73	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
74	#1055	C₄×C₈	1	2	yes	—
75	#1055	C₂×C₁₆	1	2	yes	—
76	C₂×M₃₂	—	13	1	no	—
77	C₂²×C₁₆	—	13	1	no	—
78	#405	—	13	1	no	—
79	M₆₄	—	13	4	no	—
80	C₂×C₃₂	—	13	1	no	—
81	C₂×C₃₂	—	13	1	no	—
82	C₂×C₃₂	—	13	4	no	—
83	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
84	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
85	#346	—	13	1	no	—
86	#346	—	13	1	no	—
87	C₄×C₁₆	—	13	1	no	—
88	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
89	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
90	C₂×D₁₃	—	2	2	no	—
91	C₂×D₁₃	C₄×C₁₆	1	2	yes	—
92	C₄×C₁₃	—	2	2	no	—
93	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
94	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
95	Dic₁₃	—	2	2	no	—
96	Dic₁₃	C₄×C₁₆	1	2	yes	—
97	C₂×M₁₆	—	13	1	no	—
98	C₂²×C₈	—	13	1	no	—
99	#117	—	13	1	no	—
100	M₃₂	—	13	4	no	—
101	C₂×C₁₆	—	13	1	no	—
102	C₂×C₁₆	—	13	1	no	—
103	C₂×C₁₆	—	13	2	no	—
104	C₂×C₁₆	—	13	2	no	—
105	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
106	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
107	#97	—	13	1	no	—
108	#97	—	13	1	no	—
109	C₄×C₈	—	13	1	no	—
110	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
111	C₃₂	—	13	2	no	—
112	C₃₂	—	13	2	no	—
113	C₃₂	C₄×D₁₃	1	2	yes	—
114	C₃₂	C₄×D₁₃	1	2	yes	—
115	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
116	C₂×C₁₃	#2258	1	2	yes	—
117	D₁₃	—	2	2	no	—
118	C₂²×C₄	—	13	1	no	—
119	M₁₆	—	13	4	no	—
120	C₂×C₈	—	13	1	no	—
121	C₂×C₈	—	13	1	no	—
122	C₂×C₈	—	13	2	no	—
123	C₂×C₈	—	13	2	no	—
124	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
125	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
126	C₄⋊C₄	—	13	2	no	—
127	C₂²⋊C₄	—	13	2	no	—
128	C₄²	—	13	1	no	—
129	C₄²	C₈×D₁₃	1	1	yes	characteristic
130	C₁₆	—	13	2	no	—
131	C₁₆	—	13	2	no	—
132	C₁₆	C₈×D₁₃	1	2	yes	—
133	C₁₆	C₂×C₄×D₁₃	1	1	yes	characteristic
134	C₁₆	C₂×C₄×D₁₃	1	1	yes	characteristic
135	C₁₃	#13549	1	1	yes	characteristic, complemented, Sylow
136	C₂³	—	13	1	no	—
137	C₂×C₄	—	13	1	no	—
138	C₂×C₄	—	13	2	no	—
139	C₂×C₄	—	13	2	no	—
140	C₂×C₄	—	13	2	no	—
141	C₂×C₄	C₁₆×D₁₃	1	2	yes	—
142	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
143	C₈	—	13	2	no	—
144	C₈	—	13	2	no	—
145	C₈	C₁₆×D₁₃	1	2	yes	—
146	C₈	C₄²×D₁₃	1	1	yes	characteristic
147	C₈	C₂×C₈×D₁₃	1	1	yes	characteristic
148	C₂²	—	13	2	no	—
149	C₂²	—	26	2	no	—
150	C₂²	C₂×C₁₆×D₁₃	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	13	2	no	—
153	C₄	—	26	2	no	—
154	C₄	C₄×C₈×D₁₃	1	1	yes	characteristic
155	C₄	C₂×C₁₆×D₁₃	1	1	yes	characteristic
156	C₂	—	26	2	no	—
157	C₂	C₄×C₁₆×D₁₃	1	1	yes	characteristic
158	C₂	#13117129	1	2	yes	—

	subgroup	G/H
center	C₂×C₃₂	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₄×C₁₃×C₃₂	C₂
socle	C₂²×C₁₃	C₂²×C₁₆
prime radical	C₂²×D₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	C₄×C₃₂	D₁₃
hypocenter	C₁₃	#13549
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃₂ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
4. #13112970	C₂	semidirect
5. #13112969	C₂	semidirect
6. C₃₂×Dic₁₃	C₂	semidirect
7. C₄×C₁₃×C₃₂	C₂	semidirect
19. #11718039	C₄	semidirect
20. D₁₃×C₃₂	C₄	semidirect
63. C₄×C₃₂	D₁₃	semidirect
135. C₁₃	#13549	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718039	2
C₂×D₁₃×C₃₂	2
#13116431	2
#13112970	2
#13112969	2
C₃₂×Dic₁₃	2
C₄×C₁₃×C₃₂	2
#13549	13