Finite Group Databasebeta

← #14279345

Subgroups — #14279345

Order 1920.

224 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#454C211yesmaximal, characteristic
2#11746362C211yesmaximal, characteristic, complemented
3#11746361C211yesmaximal, characteristic, complemented
4#10598262—31nomaximal, Hall
5C3×C5×2−1+4C411yescharacteristic, complemented
6C3×C5×AGL(1,ℤ/8)—21no—
7C3×C5×#124C2211yescharacteristic
8C3×C5×#104—21no—
9C3×C5×#101C411yescharacteristic, complemented
10#91118—21no—
11#91087—21no—
12#67771—51nomaximal, Hall
13C5×#454D311yescharacteristic
14#64761—31no—
15#64760—31no—
16C3×C5×#41—21no—
17C3×C5×#41—41no—
18C3×C5×#41—41no—
19C2×C3×C5×Q8—41no—
20C2×C3×C5×Q8C2×C411yescharacteristic
21C2×C3×C5×D4D411yescharacteristic
22C3×C5×SD16—41no—
23C3×C5×D8—41no—
24C3×C5×M16—21no—
25C3×C5×C22⋊C4—41no—
26C3×C42×C5D411yescharacteristic
27#6719—41no—
28C2×C3⋊#168—41no—
29C3×#454D511yescharacteristic
30#4541—51no—
31#4540—51no—
32C5×2−1+4Dic311yescharacteristic, complemented
33C5×AGL(1,ℤ/8)—21no—
34C5×#124C2×D311yescharacteristic
35C5×#104—21no—
36C5×#101Dic311yescharacteristic, complemented
37#3966—61no—
38#3935—61no—
39#1404—151noSylow
40C23×C3×C5—21no—
41C3×C5×Q8—21no—
42C3×C5×Q8—41no—
43C3×C5×Q8—41no—
44C3×C5×D4—21no—
45C3×C5×D4—41no—
46C3×C5×D4—41no—
47C3×C5×D4—41no—
48C2×C3×C4×C5—21no—
49C2×C3×C4×C5—21no—
50C2×C3×C4×C5—41no—
51C2×C3×C4×C5—42no—
52C2×C3×C4×C5C22⋊C411yescharacteristic
53C2×Dic15—81no—
54C3×C5×C8—41no—
55C3⋊#168—42no—
56C3×2−1+4Dic511yescharacteristic, complemented
57C3×AGL(1,ℤ/8)—21no—
58C3×#124C2×D511yescharacteristic
59C3×#104—21no—
60C3×#101Dic511yescharacteristic, complemented
61#834—101no—
62#803—101no—
63C5×#41—21no—
64C5×#41—41no—
65C5×#41—41no—
66C2×C5×Q8—41no—
67C2×C5×Q8C2×Dic311yescharacteristic
68C2×C5×D4#6711yescharacteristic
69C5×SD16—41no—
70C5×D8—41no—
71C5×M16—21no—
72C5×C22⋊C4—41no—
73C42×C5#6711yescharacteristic
74C22⋊Dic5—121no—
75C2×#168—121no—
76#454D1511yescharacteristic
77#354—151no—
78#329—151no—
79C22×C3×C5—41no—
80C22×C3×C5—41no—
81C22×C3×C5—81no—
82C22×C3×C5#9911yescharacteristic
83C3×C4×C5—21no—
84C3×C4×C5—41no—
85C3×C4×C5—41no—
86C3×C4×C5—41no—
87Dic15—161no—
88C3×#41—21no—
89C3×#41—41no—
90C3×#41—41no—
91C2×C3×Q8—41no—
92C2×C3×Q8C2×Dic511yescharacteristic
93C2×C3×D4C22⋊D511yescharacteristic
94C3×SD16—41no—
95C3×D8—41no—
96C3×M16—21no—
97C3×C22⋊C4—41no—
98C3×C42C22⋊D511yescharacteristic
99#217—201no—
100C2×C3⋊C8—201no—
101C23×C5—21no—
102C5×Q8—21no—
103C5×Q8—41no—
104C5×Q8—41no—
105C5×D4—21no—
106C5×D4—41no—
107C5×D4—41no—
108C5×D4—41no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—41no—
112C2×C4×C5—42no—
113C2×C4×C5#21711yescharacteristic
114C2×Dic5—241no—
115C5×C8—41no—
116#168—122no—
1172−1+4Dic1511yescharacteristic, complemented
118AGL(1,ℤ/8)—21no—
119#124C2×D1511yescharacteristic
120#104—21no—
121#101Dic1511yescharacteristic, complemented
122#99—301no—
123#97—301no—
124C2×C3×C5—21no—
125C2×C3×C5—81no—
126C2×C3×C5—81no—
127C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
128C23×C3—21no—
129C3×Q8—21no—
130C3×Q8—41no—
131C3×Q8—41no—
132C3×D4—21no—
133C3×D4—41no—
134C3×D4—41no—
135C3×D4—41no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—41no—
139C2×C3×C4—42no—
140C2×C3×C4C22⋊Dic511yescharacteristic
141C2×Dic3—401no—
142C3×C8—41no—
143C3⋊C8—202no—
144C22×C5—41no—
145C22×C5—41no—
146C22×C5—81no—
147C22×C5#83411yescharacteristic
148C4×C5—21no—
149C4×C5—41no—
150C4×C5—41no—
151C4×C5—41no—
152Dic5—481no—
153#41—21no—
154#41—41no—
155#41—41no—
156C2×Q8—41no—
157C2×Q8C2×Dic1511yescharacteristic
158C2×D4#122011yescharacteristic
159SD16—41no—
160D8—41no—
161M16—21no—
162C2×C8—601no—
163C22⋊C4—41no—
164C22⋊C4—601no—
165C42#122011yescharacteristic
166C3×C5#140411yescharacteristic, complemented, Hall
167C22×C3—41no—
168C22×C3—41no—
169C22×C3—81no—
170C22×C3#396611yescharacteristic
171C3×C4—21no—
172C3×C4—41no—
173C3×C4—41no—
174C3×C4—41no—
175Dic3—801no—
176C2×C5—21no—
177C2×C5—81no—
178C2×C5—81no—
179C2×C5#453611yescharacteristic
180C23—21no—
181Q8—21no—
182Q8—41no—
183Q8—41no—
184D4—21no—
185D4—41no—
186D4—41no—
187D4—41no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—1201no—
193C2×C4#671911yescharacteristic
194C8—41no—
195C8—602no—
196C2×C3—21no—
197C2×C3—81no—
198C2×C3—81no—
199C2×C3#6475611yescharacteristic
200C5#6777111yescharacteristic, complemented, Sylow
201C22—41no—
202C22—41no—
203C22—81no—
204C22#9111811yescharacteristic
205C4—21no—
206C4—41no—
207C4—41no—
208C4—41no—
209C4—2401no—
210C3#1059826211yescharacteristic, complemented, Sylow
211C2—21no—
212C2—81no—
213C2—81no—
214C2#1174635711yescharacteristic
subgroupG/H
centerC2#11746357
commutatorC2×C3×C5×Q8C2×C4
Frattini#124C2×D15
Fitting, prime radicalC3×C5×#454C2
socleC2×C3×C5AΣL(1,𝔽16)
cosocleC3×C5×#124C22
hypercenter#454D15
hypocenterC3×C5#1404
LCSG ▷ C2×C3×C5×Q8 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #454

Complements

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

NH ≅ G/Ntype
2. #11746362C2semidirect
3. #11746361C2semidirect
5. C3×C5×2−1+4C4semidirect
9. C3×C5×#101C4semidirect
32. C5×2−1+4Dic3semidirect
36. C5×#101Dic3semidirect
56. C3×2−1+4Dic5semidirect
60. C3×#101Dic5semidirect
117. 2−1+4Dic15semidirect
121. #101Dic15semidirect
166. C3×C5#1404semidirect
200. C5#67771semidirect
210. C3#10598262semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4542
#117463622
#117463612
#105982623
#677715