Subgroups — #15777926

Order 3328.

338 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₃₂×Dic₁₃	C₂	1	2	yes	maximal
2	#13114524	C₂	1	1	yes	maximal, characteristic
3	#13112916	C₂	1	1	yes	maximal, characteristic
4	#13112915	C₂	1	2	yes	maximal
5	C₁₃×#1375	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
8	C₂×#88055	C₄	1	1	yes	characteristic
9	C₂×#88055	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×#88052	C₂²	1	2	yes	—
13	#11718593	C₄	1	1	yes	characteristic
14	C₂×C₄×#1055	C₄	1	1	yes	characteristic
15	#11718094	C₄	1	4	yes	complemented
16	C₁₆×Dic₁₃	C₄	1	4	yes	complemented
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
23	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
24	C₁₃×M₃₂	—	2	2	no	—
25	C₁₃×M₃₂	—	2	2	no	—
26	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
27	C₁₃×#97	—	2	2	no	—
28	#88071	—	2	2	no	—
29	#88055	—	2	1	no	—
30	#88055	—	2	1	no	—
31	#88055	—	2	2	no	—
32	C₈×Dic₁₃	C₈	1	4	yes	—
33	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
34	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
35	#88052	—	2	2	no	—
36	#88052	—	2	2	no	—
37	C₂×#6090	C₂×C₄	1	4	yes	—
38	C₄×#1055	C₈	1	4	yes	—
39	#12593	—	13	1	no	maximal, Sylow
40	C₂²×C₄×C₁₃	—	2	1	no	—
41	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×Dic₁₃	—	2	1	no	—
43	C₂²×Dic₁₃	M₁₆	1	2	yes	—
44	C₂×C₈×C₁₃	—	2	1	no	—
45	C₂×C₈×C₁₃	—	2	1	no	—
46	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
47	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
48	C₂×C₈×C₁₃	#41	1	2	yes	—
49	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
50	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
51	C₄²×C₁₃	—	2	1	no	—
52	C₄²×C₁₃	C₂×C₈	1	2	yes	—
53	C₄×Dic₁₃	—	2	1	no	—
54	C₄×Dic₁₃	C₄²	1	2	yes	—
55	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
56	C₄×Dic₁₃	M₁₆	1	2	yes	—
57	C₂×#1055	—	2	1	no	—
58	C₂×#1055	—	2	1	no	—
59	C₂×#1055	C₄²	1	1	yes	characteristic
60	C₂×#1055	C₄²	1	1	yes	characteristic
61	C₂×#1055	C₂×C₈	1	2	yes	—
62	C₂×#1055	C₂×C₈	1	2	yes	—
63	C₂×#1055	C₂×C₈	1	2	yes	—
64	C₁₃×C₁₆	—	2	4	no	—
65	#6090	—	2	4	no	—
66	C₄×M₃₂	—	13	2	no	—
67	#1726	—	13	1	no	—
68	#1375	—	13	2	no	—
69	#1375	—	13	1	no	—
70	#1375	D₁₃	1	1	yes	characteristic
71	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	—	4	2	no	—
74	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
80	C₂×Dic₁₃	—	2	2	no	—
81	C₂×Dic₁₃	—	4	2	no	—
82	C₂×Dic₁₃	—	4	2	no	—
83	C₂×Dic₁₃	#97	1	4	yes	—
84	C₈×C₁₃	—	2	2	no	—
85	C₈×C₁₃	#117	1	2	yes	—
86	C₈×C₁₃	#117	1	2	yes	—
87	#1055	—	2	2	no	—
88	#1055	C₄×C₈	1	2	yes	—
89	#1055	C₄×C₈	1	2	yes	—
90	C₂×M₃₂	—	13	2	no	—
91	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
92	C₂×#97	—	13	1	no	—
93	C₂×#97	—	13	1	no	—
94	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
95	C₂×C₄×C₈	—	13	1	no	—
96	C₂×C₄×C₈	—	13	1	no	—
97	C₂×C₄×C₈	—	13	1	no	—
98	#376	—	13	1	no	—
99	#346	—	13	4	no	—
100	C₄×C₁₆	—	13	4	no	—
101	C₂²×C₁₃	—	2	2	no	—
102	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
103	C₂²×C₁₃	#431	1	1	yes	characteristic
104	C₂²×C₁₃	#431	1	1	yes	characteristic
105	C₄×C₁₃	—	4	2	no	—
106	C₄×C₁₃	#376	1	1	yes	characteristic
107	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
108	C₄×C₁₃	#431	1	1	yes	characteristic
109	C₄×C₁₃	#431	1	1	yes	characteristic
110	Dic₁₃	—	2	4	no	—
111	Dic₁₃	—	4	2	no	—
112	C₂²×C₈	—	13	1	no	—
113	C₂²×C₈	—	13	1	no	—
114	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
115	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
116	C₂×C₄²	—	13	1	no	—
117	C₂×C₄²	—	13	1	no	—
118	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
119	M₃₂	—	2	2	no	—
120	M₃₂	—	2	2	no	—
121	M₃₂	—	26	2	no	—
122	M₃₂	—	26	2	no	—
123	C₂×C₁₆	—	13	4	no	—
124	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
125	#97	—	2	2	no	—
126	#97	—	26	2	no	—
127	#97	—	26	1	no	—
128	#97	—	26	1	no	—
129	C₄×C₈	—	13	4	no	—
130	C₄×C₈	—	13	2	no	—
131	C₄×C₈	—	13	2	no	—
132	C₄×C₈	—	13	4	no	—
133	#95	—	26	2	no	—
134	C₂×C₁₃	—	2	1	no	—
135	C₂×C₁₃	—	2	1	no	—
136	C₂×C₁₃	#1744	1	1	yes	characteristic
137	C₂×C₁₃	#2110	1	2	yes	—
138	C₂²×C₄	—	2	1	no	—
139	C₂²×C₄	—	13	2	no	—
140	C₂²×C₄	—	26	1	no	—
141	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	2	1	no	—
144	C₂×C₈	—	13	1	no	—
145	C₂×C₈	—	13	1	no	—
146	C₂×C₈	—	13	2	no	—
147	C₂×C₈	—	13	2	no	—
148	C₂×C₈	—	13	2	no	—
149	C₂×C₈	—	26	1	no	—
150	C₂×C₈	—	26	1	no	—
151	C₂×C₈	C₈×D₁₃	1	2	yes	—
152	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
153	C₂×C₈	#6129	1	1	yes	characteristic
154	C₂×C₈	#6129	1	2	yes	—
155	C₂×C₈	#6131	1	1	yes	characteristic
156	C₄²	—	2	1	no	—
157	C₄²	—	13	2	no	—
158	C₄²	—	13	2	no	—
159	C₄²	—	13	2	no	—
160	C₄²	—	26	1	no	—
161	C₄²	C₈×D₁₃	1	2	yes	—
162	C₁₆	—	2	4	no	—
163	C₁₆	—	26	4	no	—
164	C₁₃	#12593	1	1	yes	characteristic, complemented, Sylow
165	C₂³	M₁₆×D₁₃	1	1	yes	characteristic
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	4	2	no	—
168	C₂×C₄	—	13	4	no	—
169	C₂×C₄	—	26	2	no	—
170	C₂×C₄	—	52	2	no	—
171	C₂×C₄	—	52	2	no	—
172	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
173	C₂×C₄	#88131	1	1	yes	characteristic
174	C₂×C₄	#88146	1	1	yes	characteristic
175	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
176	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
177	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
178	C₈	—	2	2	no	—
179	C₈	—	13	2	no	—
180	C₈	—	13	2	no	—
181	C₈	—	26	2	no	—
182	C₈	#88131	1	2	yes	—
183	C₈	#88146	1	2	yes	—
184	C₂²	—	2	2	no	—
185	C₂²	D₁₃×#97	1	1	yes	characteristic
186	C₂²	#11718379	1	1	yes	characteristic
187	C₂²	#11718494	1	1	yes	characteristic
188	C₄	—	4	2	no	—
189	C₄	—	26	4	no	—
190	C₄	—	52	2	no	—
191	C₄	#11718309	1	1	yes	characteristic
192	C₄	C₄×C₈×D₁₃	1	1	yes	characteristic
193	C₄	#11718379	1	1	yes	characteristic
194	C₄	#11718494	1	1	yes	characteristic
195	C₂	—	2	1	no	—
196	C₂	—	2	1	no	—
197	C₂	#13114580	1	1	yes	characteristic
198	C₂	#13116439	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄²×D₁₃
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1375	C₂
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1375	D₁₃
hypocenter	C₁₃	#12593
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #1375

Complements

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

N	H ≅ G/N	type
15. #11718094	C₄	semidirect
16. C₁₆×Dic₁₃	C₄	semidirect
164. C₁₃	#12593	semidirect

Maximal subgroups

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

subgroup	index
M₃₂×Dic₁₃	2
#13114524	2
#13112916	2
#13112915	2
C₁₃×#1375	2
#12593	13