Subgroups — #15779265

Order 3328.

366 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#6090	C₂	1	1	yes	maximal, characteristic
2	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#13112913	C₂	1	4	yes	maximal
4	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×Dic₁₃	C₄	1	2	yes	—
8	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
9	C₂²×#6090	C₂²	1	2	yes	—
10	C₄²×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×#1055	C₄	1	1	yes	characteristic
12	C₁₃×C₄⋊C₁₆	—	2	2	no	—
13	C₄⋊#6090	—	2	2	no	—
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₃	C₈	1	1	yes	characteristic
18	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
19	C₂×C₄×Dic₁₃	C₈	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
21	C₂²×#1055	C₂×C₄	1	2	yes	—
22	C₂×C₁₃×C₁₆	—	2	2	no	—
23	C₂×C₁₃×C₁₆	—	2	4	no	—
24	C₄×C₈×C₁₃	D₄	1	2	yes	—
25	C₄×C₈×C₁₃	Q₈	1	2	yes	—
26	C₈×Dic₁₃	—	2	2	no	—
27	C₈×Dic₁₃	—	2	2	no	—
28	C₈×Dic₁₃	—	2	4	no	—
29	C₂×#6090	—	2	2	no	—
30	C₂×#6090	—	2	4	no	—
31	C₄×#1055	—	2	2	no	—
32	#12879	—	13	1	no	maximal, Sylow
33	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
37	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
38	C₂×C₈×C₁₃	—	2	2	no	—
39	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
40	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₈×C₁₃	#41	1	2	yes	—
43	C₂×C₈×C₁₃	#41	1	2	yes	—
44	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₄²×C₁₃	M₁₆	1	2	yes	—
46	C₄×Dic₁₃	—	2	2	no	—
47	C₄×Dic₁₃	—	2	2	no	—
48	C₄×Dic₁₃	—	2	2	no	—
49	C₄×Dic₁₃	—	2	4	no	—
50	C₄×Dic₁₃	C₁₆	1	4	yes	complemented
51	C₂×#1055	—	2	2	no	—
52	C₂×#1055	—	2	2	no	—
53	C₂×#1055	M₁₆	1	4	yes	—
54	C₁₃×C₁₆	—	4	2	no	—
55	#6090	—	4	2	no	—
56	C₂×C₄⋊C₁₆	—	13	1	no	—
57	C₂×C₄⋊C₁₆	D₁₃	1	1	yes	characteristic
58	C₄²×C₈	—	13	1	no	—
59	#1374	—	13	4	no	—
60	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
61	C₂×C₄×C₁₃	—	2	2	no	—
62	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
63	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
64	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
65	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
66	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₃	#117	1	2	yes	—
68	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
69	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
70	C₂×Dic₁₃	—	2	2	no	—
71	C₂×Dic₁₃	—	2	2	no	—
72	C₂×Dic₁₃	—	2	2	no	—
73	C₂×Dic₁₃	—	2	2	no	—
74	C₂×Dic₁₃	C₂×C₁₆	1	4	yes	—
75	C₂×Dic₁₃	M₃₂	1	4	yes	—
76	C₈×C₁₃	—	2	2	no	—
77	C₈×C₁₃	#124	1	1	yes	characteristic
78	C₈×C₁₃	#124	1	1	yes	characteristic
79	C₈×C₁₃	#125	1	2	yes	—
80	#1055	—	2	4	no	—
81	C₂²×C₁₆	—	13	2	no	—
82	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
83	C₂×C₄×C₈	—	13	2	no	—
84	C₂×C₄×C₈	—	13	2	no	—
85	C₂×C₄×C₈	—	13	1	no	—
86	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
87	C₄³	—	13	1	no	—
88	C₄⋊C₁₆	—	2	2	no	—
89	C₄⋊C₁₆	—	26	2	no	—
90	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
91	C₂²×C₁₃	#431	1	2	yes	—
92	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
93	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
94	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
95	C₄×C₁₃	—	2	2	no	—
96	C₄×C₁₃	C₄⋊C₁₆	1	4	yes	—
97	C₄×C₁₃	#382	1	1	yes	characteristic
98	C₄×C₁₃	#423	1	1	yes	characteristic
99	C₄×C₁₃	#432	1	2	yes	—
100	Dic₁₃	—	2	4	no	—
101	Dic₁₃	—	2	4	no	—
102	C₂²×C₈	—	13	2	no	—
103	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
104	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
105	C₂×C₄²	—	13	1	no	—
106	C₂×C₄²	—	13	2	no	—
107	C₂×C₄²	—	13	1	no	—
108	C₂×C₄²	—	13	2	no	—
109	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
110	C₂×C₁₆	—	2	4	no	—
111	C₂×C₁₆	—	2	2	no	—
112	C₂×C₁₆	—	26	4	no	—
113	C₂×C₁₆	—	26	2	no	—
114	C₄×C₈	—	26	4	no	—
115	C₄×C₈	—	26	2	no	—
116	C₄×C₈	—	26	2	no	—
117	C₄×C₈	—	26	2	no	—
118	C₄×C₈	Dic₂₆	1	2	yes	—
119	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
120	C₂×C₁₃	#1831	1	1	yes	characteristic
121	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
122	C₂×C₁₃	#2150	1	1	yes	characteristic
123	C₂×C₁₃	#2162	1	2	yes	—
124	C₂×C₁₃	#2163	1	2	yes	—
125	C₂²×C₄	—	13	2	no	—
126	C₂²×C₄	—	13	2	no	—
127	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
128	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
129	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
130	C₂×C₈	—	2	2	no	—
131	C₂×C₈	—	13	4	no	—
132	C₂×C₈	—	26	2	no	—
133	C₂×C₈	—	26	2	no	—
134	C₂×C₈	#6101	1	2	yes	—
135	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
136	C₂×C₈	#6129	1	2	yes	—
137	C₂×C₈	#6131	1	2	yes	—
138	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
139	C₄²	—	13	4	no	—
140	C₄²	—	26	4	no	—
141	C₄²	—	26	2	no	—
142	C₄²	—	26	2	no	—
143	C₄²	—	26	2	no	—
144	C₄²	#6094	1	2	yes	—
145	C₄²	#6101	1	2	yes	—
146	C₁₆	—	4	2	no	—
147	C₁₆	—	52	2	no	—
148	C₁₃	#12879	1	1	yes	characteristic, complemented, Sylow
149	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	13	4	no	—
152	C₂×C₄	—	13	4	no	—
153	C₂×C₄	—	26	2	no	—
154	C₂×C₄	—	26	2	no	—
155	C₂×C₄	—	26	2	no	—
156	C₂×C₄	—	26	2	no	—
157	C₂×C₄	C₁₆×D₁₃	1	2	yes	—
158	C₂×C₄	#88038	1	2	yes	—
159	C₂×C₄	#88054	1	2	yes	—
160	C₂×C₄	#88054	1	2	yes	—
161	C₂×C₄	#88146	1	2	yes	—
162	C₂×C₄	C₂×#6094	1	1	yes	characteristic
163	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
164	C₂×C₄	C₂×#6101	1	1	yes	characteristic
165	C₈	—	2	2	no	—
166	C₈	—	26	4	no	—
167	C₈	#88144	1	2	yes	—
168	C₈	#88190	1	1	yes	characteristic
169	C₈	#88201	1	1	yes	characteristic
170	C₂²	#11718494	1	2	yes	—
171	C₂²	C₂×C₁₆×D₁₃	1	1	yes	characteristic
172	C₂²	C₂×#88038	1	1	yes	characteristic
173	C₂²	D₁₃×M₃₂	1	2	yes	—
174	C₂²	C₂×#88054	1	1	yes	characteristic
175	C₄	—	2	2	no	—
176	C₄	—	26	4	no	—
177	C₄	—	26	4	no	—
178	C₄	#11718093	1	4	yes	—
179	C₄	#11718496	1	2	yes	—
180	C₄	#11718638	1	1	yes	characteristic
181	C₄	#11718779	1	1	yes	characteristic
182	C₂	#13114952	1	1	yes	characteristic
183	C₂	C₂×#11718093	1	1	yes	characteristic
184	C₂	#13116591	1	1	yes	characteristic
185	C₂	#13116634	1	2	yes	—
186	C₂	#13116638	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₁₆
Fitting	C₂×C₁₃×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₁₃
hypocenter	C₁₃	#12879
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
50. C₄×Dic₁₃	C₁₆	semidirect
148. C₁₃	#12879	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#6090	2
C₄×C₈×Dic₁₃	2
#13112913	2
C₂×C₁₃×C₄⋊C₁₆	2
#12879	13