Finite Group Databasebeta

← #14318573

Subgroups — #14318573

Order 1920.

248 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C5×#5125C211yesmaximal, characteristic
2C3×#65426C211yesmaximal, characteristic
3#11746374C211yesmaximal, characteristic
4#11745935C212yesmaximal, complemented
5#11745921C212yesmaximal, complemented
6#10601517—31nomaximal, Hall
7C2×C3×C5×M16C2211yescharacteristic
8C2×C5×#208—21no—
9C3×#4070—21no—
10C2×C3×Dic20C2211yescharacteristic
11#91096C2212yes—
12C5×#819—21no—
13C5×#819C2212yes—
14C3×#3949C2211yescharacteristic
15C3×#3948—21no—
16#71090—51nomaximal, Hall
17C5×#430—31no—
18#65426D311yescharacteristic
19#64773—31no—
20#64716—32no—
21#64714—32no—
22C22×C3×C4×C5D411yescharacteristic
23C2×C3×Dic10—21no—
24C3×C5×M16—22no—
25C2×C3×C5×C8D411yescharacteristic
26C2×C3×C5×C8C2311yescharacteristic
27C5×#208—22no—
28C5×#208—41no—
29C2×C5×C3⋊C8—41no—
30C3×C22⋊Dic5—41no—
31C3×C4⋊Dic5—21no—
32C3×#683—41no—
33C3×Dic20—22no—
34C3⋊#672—22no—
35C3×#470—51no—
36#5125D511yescharacteristic
37#4565—52no—
38#4553—51no—
39#4487—52no—
40C2×C5×M16—61no—
41C2×C5×M16C2×D311yescharacteristic
42#4070—21no—
43C2×Dic20C2×D311yescharacteristic
44C5×#108—32no—
45C5×#108—61no—
46#3949C2×D311yescharacteristic
47#3948—21no—
48#3944—32no—
49#2239—151noSylow
50C23×C3×C5SD1611yescharacteristic
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5—21no—
53C2×C3×C4×C5SD1611yescharacteristic
54C2×C3×C4×C5C2×D411yescharacteristic
55C2×C3×Dic5—41no—
56C2×C3×Dic5—41no—
57C3×Dic10—41no—
58C3×Dic10—41no—
59C3×C5×C8—21no—
60C3×C5×C8#4112yes—
61C5×C3⋊C8—42no—
62C2×C3×Q16—51no—
63C2×C3×M16C2×D511yescharacteristic
64C3×C22⋊Q8—101no—
65C2×#208—21no—
66C3×#106—51no—
67C3×#103—101no—
68#819—21no—
69#819C2×D512yes—
70#812—52no—
71C22×C4×C5#6711yescharacteristic
72C2×Dic10—21no—
73C5×M16—22no—
74C5×M16—62no—
75C5×M16—121no—
76C2×C5×C8—121no—
77C2×C5×C8#6711yescharacteristic
78C2×C5×C8C22×D311yescharacteristic
79C22⋊Dic5—41no—
80C4⋊Dic5—21no—
81#683—41no—
82Dic20—22no—
83#672—62no—
84#470—51no—
85#430—31no—
86#365—152no—
87#362—152no—
88#349—151no—
89C22×C3×C5—21no—
90C22×C3×C5—41no—
91C22×C3×C5C2×SD1611yescharacteristic
92C3×C4×C5—21no—
93C3×C4×C5#12311yescharacteristic
94C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
95C3×Dic5—81no—
96C3×Dic5—81no—
97C2×C3×Q8—101no—
98C22×C3×C4C22⋊D511yescharacteristic
99C3×Q16—102no—
100C3×M16—22no—
101C2×C3×C8C22⋊D511yescharacteristic
102C2×C3×C8C22×D511yescharacteristic
103C3×C4⋊C4—101no—
104C3×C4⋊C4—201no—
105C3×C22⋊C4—201no—
106#208—22no—
107#208—41no—
108C2×C3⋊C8—41no—
109C3⋊C16—102no—
110C23×C5#21411yescharacteristic
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5#21411yescharacteristic
114C2×C4×C5C2×#6711yescharacteristic
115C2×Dic5—41no—
116C2×Dic5—41no—
117Dic10—41no—
118Dic10—41no—
119C5×C8—21no—
120C5×C8—122no—
121C5×C8#23712yes—
122C2×Q16—51no—
123C2×M16—61no—
124C2×M16D3×D511yescharacteristic
125C22⋊Q8—101no—
126M32—152no—
127#108—32no—
128#108—61no—
129#106—51no—
130#103—101no—
131C2×C3×C5—21no—
132C2×C3×C5—41no—
133C2×C3×C5#48111yescharacteristic
134C23×C3#68811yescharacteristic
135C3×Q8—201no—
136C3×Q8—201no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—201no—
140C2×C3×C4—201no—
141C2×C3×C4#68811yescharacteristic
142C2×C3×C4C2×C22⋊D511yescharacteristic
143C3×C8—21no—
144C3×C8#70912yes—
145C3⋊C8—42no—
146C22×C5—21no—
147C22×C5—41no—
148C22×C5C2×#21411yescharacteristic
149C4×C5—21no—
150C4×C5#93511yescharacteristic
151C4×C5#94911yescharacteristic
152Dic5—81no—
153Dic5—81no—
154C2×Q8—101no—
155C22×C4#120111yescharacteristic
156Q16—102no—
157M16—22no—
158M16—62no—
159M16—121no—
160C2×C8—121no—
161C2×C8#120111yescharacteristic
162C2×C8C2×D3×D511yescharacteristic
163C4⋊C4—101no—
164C4⋊C4—201no—
165C22⋊C4—201no—
166C16—302no—
167C3×C5#223911yescharacteristic, complemented, Hall
168C22×C3—21no—
169C22×C3—41no—
170C22×C3C2×#68811yescharacteristic
171C3×C4—21no—
172C3×C4—401no—
173C3×C4—401no—
174C3×C4#407511yescharacteristic
175C3×C4#407811yescharacteristic
176C2×C5—21no—
177C2×C5—41no—
178C2×C5#503411yescharacteristic
179C23#665511yescharacteristic
180Q8—201no—
181Q8—201no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—201no—
185C2×C4—201no—
186C2×C4#665511yescharacteristic
187C2×C4C2×#120111yescharacteristic
188C8—21no—
189C8—122no—
190C8#677912yes—
191C2×C3—21no—
192C2×C3—41no—
193C2×C3#6525711yescharacteristic
194C5#7109011yescharacteristic, complemented, Sylow
195C22—21no—
196C22—41no—
197C22C2×#665511yescharacteristic
198C4—21no—
199C4—401no—
200C4—401no—
201C4#9129911yescharacteristic
202C4#9153611yescharacteristic
203C3#1060151711yescharacteristic, complemented, Sylow
204C2—21no—
205C2—41no—
206C2#1174837211yescharacteristic
subgroupG/H
centerC2#11748372
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#481
prime radicalC23×C3×C5SD16
hypercenterC2×M16D3×D5
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #11745935C2semidirect
5. #11745921C2semidirect
167. C3×C5#2239semidirect
194. C5#71090semidirect
203. C3#10601517semidirect

Maximal subgroups

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

subgroupindex
C5×#51252
C3×#654262
#117463742
#117459352
#117459212
#106015173
#710905