Finite Group Databasebeta

← #14278038

Subgroups — #14278038

Order 1920.

220 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 58 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×#65424C211yesmaximal, characteristic
2#11746374C211yesmaximal, characteristic, complemented
3C5×C3⋊#338C211yesmaximal, characteristic, complemented
4#10597974—31nomaximal, Hall
5C2×C3×C5×M16C2211yescharacteristic
6C2×C5×#208—21no—
7C3×#4076—21no—
8C2×C3×D40C411yescharacteristic
9#91096—21no—
10C3×#3953—21no—
11C3×#3949C411yescharacteristic
12#67779—51nomaximal, Hall
13#65424D311yescharacteristic
14C5×#338—31no—
15#64773—31no—
16C22×C3×C4×C5D411yescharacteristic
17C2×C3×C22⋊D5—41no—
18C2×C3×D20—21no—
19C3×C5×M16—41no—
20C2×C3×C5×C8C2×C411yescharacteristic
21C2×C3×C5×C8D411yescharacteristic
22C5×#208—41no—
23C5×#208—41no—
24C2×C5×C3⋊C8—22no—
25C3×#685—41no—
26C3×C4⋊Dic5—21no—
27C3×D40—41no—
28C3⋊#672—41no—
29C3×#469—51no—
30C3⋊#338D511yescharacteristic, complemented
31#4553—51no—
32C2×C5×M16—61no—
33C2×C5×M16C2×D311yescharacteristic
34#4076—21no—
35C2×D40Dic311yescharacteristic
36#3953—21no—
37#3949Dic311yescharacteristic
38#3944—61no—
39#1341—151noSylow
40C23×C3×C5SD1611yescharacteristic
41C22×C3×D5—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×C3×C4×C5D811yescharacteristic
46C3×C22⋊D5—82no—
47C2×C3×Dic5—41no—
48C3×D20—41no—
49C3×D20—41no—
50C3×C5×C8—21no—
51C3×C5×C8—21no—
52C5×C3⋊C8—42no—
53C2×C3×D8—51no—
54C2×C3×M16C2×D511yescharacteristic
55C3×#121—101no—
56C2×#208—21no—
57C3×#106—51no—
58C3×#102—101no—
59#812—101no—
60C22×C4×C5#6711yescharacteristic
61C2×C22⋊D5—41no—
62C2×D20—21no—
63C5×M16—41no—
64C5×M16—121no—
65C5×M16—121no—
66C2×C5×C8—62no—
67C2×C5×C8C2×Dic311yescharacteristic
68C2×C5×C8#6711yescharacteristic
69#685—41no—
70C4⋊Dic5—21no—
71D40—41no—
72#672—121no—
73#469—51no—
74#349—151no—
75#338—31no—
76C22×C3×C5—21no—
77C22×C3×C5—41no—
78C22×C3×C5#10211yescharacteristic
79C2×C3×D5—81no—
80C2×C3×D5—81no—
81C2×C3×D5—81no—
82C3×C4×C5—21no—
83C3×C4×C5#9911yescharacteristic
84C3×C4×C5#10411yescharacteristic
85C3×Dic5—81no—
86C2×C3×D4—101no—
87C2×C3×D4—201no—
88C22×C3×C4C22⋊D511yescharacteristic
89C3×D8—201no—
90C3×M16—41no—
91C2×C3×C8C4×D511yescharacteristic
92C2×C3×C8D2011yescharacteristic
93C3×C4⋊C4—101no—
94C3×C22⋊C4—201no—
95#208—41no—
96#208—41no—
97C2×C3⋊C8—22no—
98C3⋊C16—201no—
99C23×C5#21411yescharacteristic
100C22×D5—41no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5#21311yescharacteristic
104C2×C4×C5#21711yescharacteristic
105C22⋊D5—82no—
106C2×Dic5—41no—
107D20—41no—
108D20—41no—
109C5×C8—21no—
110C5×C8—21no—
111C5×C8—122no—
112C2×D8—51no—
113C2×M16—61no—
114C2×M16D3×D511yescharacteristic
115#121—101no—
116M32—301no—
117#106—51no—
118#102—101no—
119C2×C3×C5—21no—
120C2×C3×C5—41no—
121C2×C3×C5#32711yescharacteristic
122C3×D5—161no—
123C23×C3—201no—
124C23×C3#68811yescharacteristic
125C3×D4—201no—
126C3×D4—201no—
127C3×D4—402no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—201no—
131C2×C3×C4#68511yescharacteristic
132C2×C3×C4#68611yescharacteristic
133C3×C8—21no—
134C3×C8—21no—
135C3⋊C8—42no—
136C22×C5—21no—
137C22×C5—41no—
138C22×C5#83211yescharacteristic
139C2×D5—81no—
140C2×D5—81no—
141C2×D5—81no—
142C4×C5—21no—
143C4×C5#83411yescharacteristic
144C4×C5#83711yescharacteristic
145Dic5—81no—
146C2×D4—101no—
147C2×D4—201no—
148C22×C4#120111yescharacteristic
149D8—201no—
150M16—41no—
151M16—121no—
152M16—121no—
153C2×C8—62no—
154C2×C8D5×Dic311yescharacteristic
155C2×C8#120211yescharacteristic
156C4⋊C4—101no—
157C22⋊C4—201no—
158C16—601no—
159C3×C5#134111yescharacteristic, complemented, Hall
160C22×C3—21no—
161C22×C3—41no—
162C22×C3—401no—
163C22×C3—401no—
164C22×C3—401no—
165C22×C3#394111yescharacteristic
166C3×C4—21no—
167C3×C4—401no—
168C3×C4#393711yescharacteristic
169C3×C4#393811yescharacteristic
170C2×C5—21no—
171C2×C5—41no—
172C2×C5#453711yescharacteristic
173D5—161no—
174C23—201no—
175C23#665511yescharacteristic
176D4—201no—
177D4—201no—
178D4—402no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—201no—
182C2×C4#665211yescharacteristic
183C2×C4#666511yescharacteristic
184C8—21no—
185C8—21no—
186C8—122no—
187C2×C3—21no—
188C2×C3—41no—
189C2×C3—801no—
190C2×C3#6467111yescharacteristic
191C5#6777911yescharacteristic, complemented, Sylow
192C22—21no—
193C22—41no—
194C22—401no—
195C22—401no—
196C22—401no—
197C22#9096411yescharacteristic
198C4—21no—
199C4—401no—
200C4#9097711yescharacteristic
201C4#9099511yescharacteristic
202C3#1059797411yescharacteristic, complemented, Sylow
203C2—21no—
204C2—41no—
205C2—801no—
206C2#1174595411yescharacteristic
subgroupG/H
centerC2#11745954
commutatorC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×M16D3×D5
Fitting, cosocleC2×C3×C5×M16C22
socleC2×C3×C5#327
prime radicalC3×#65424C2
hypocenterC3×C5#1341
LCSG ▷ C2×C3×C5×C8 ▷ C2×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
2. #11746374C2semidirect
3. C5×C3⋊#338C2semidirect
30. C3⋊#338D5semidirect
159. C3×C5#1341semidirect
191. C5#67779semidirect
202. C3#10597974semidirect

Maximal subgroups

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

subgroupindex
C3×#654242
#117463742
C5×C3⋊#3382
#105979743
#677795