Finite Group Databasebeta

← #14278033

Subgroups — #14278033

Order 1920.

220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#11751236C211yesmaximal, characteristic
2C3×C5×#349C211yesmaximal, characteristic, complemented
3#11746381C211yesmaximal, characteristic, complemented
4#10598026—31nomaximal, Hall
5C2×C3×C5×M16C2211yescharacteristic
6#91819—21no—
7C2×#6710—21no—
8C2×D120C411yescharacteristic
9C3×C5×M32—21no—
10#91105—21no—
11#91101C411yescharacteristic
12#67535—51nomaximal, Hall
13#65424—31no—
14C5×#349D311yescharacteristic, complemented
15#64780—31no—
16C22×C3×C4×C5D411yescharacteristic
17C2×#1220—41no—
18C2×D60—21no—
19C3×C5×M16—41no—
20C2×C3×C5×C8C2×C411yescharacteristic
21C2×C3×C5×C8D411yescharacteristic
22#6714—41no—
23C4⋊Dic15—21no—
24#6710—41no—
25#6710—41no—
26C2×C3⋊#168—22no—
27D120—41no—
28C3×C5×C16—41no—
29#5135—51no—
30C3×#349D511yescharacteristic, complemented
31C3⋊#338—51no—
32C2×C5×M16C2×D311yescharacteristic
33#4076—61no—
34C2×#681—61no—
35C2×D40—31no—
36C5×M32—21no—
37#3953—61no—
38#3949—31no—
39#1341—151noSylow
40C23×C3×C5SD1611yescharacteristic
41C22×D15—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×C3×C4×C5D811yescharacteristic
46#1220—82no—
47C2×Dic15—41no—
48D60—41no—
49D60—41no—
50C3×C5×C8—21no—
51C3×C5×C8—21no—
52C3⋊#168—42no—
53C2×C3×M16C2×D511yescharacteristic
54#930—101no—
55C2×#208—101no—
56C2×D24—51no—
57C3×M32—21no—
58#821—101no—
59#817—51no—
60C22×C4×C5D1211yescharacteristic
61C2×C22⋊D5—121no—
62C2×D20—61no—
63C5×M16—41no—
64C2×C5×C8C4×D311yescharacteristic
65C2×C5×C8#6711yescharacteristic
66#685—121no—
67C4⋊Dic5—61no—
68#681—121no—
69#681—121no—
70C2×#168—62no—
71D40—121no—
72C5×C16—41no—
73#469—151no—
74#349D1511yescharacteristic, complemented
75#338—151no—
76C22×C3×C5—21no—
77C22×C3×C5—41no—
78C22×C3×C5#10211yescharacteristic
79C2×D15—81no—
80C2×D15—81no—
81C2×D15—81no—
82C3×C4×C5—21no—
83C3×C4×C5#9911yescharacteristic
84C3×C4×C5#10411yescharacteristic
85Dic15—81no—
86C22×C3×C4D2011yescharacteristic
87C2×#67—201no—
88C2×D12—101no—
89C3×M16—41no—
90C2×C3×C8C4×D511yescharacteristic
91C2×C3×C8C22⋊D511yescharacteristic
92(C2×D3)⋊C4—201no—
93C4⋊Dic3—101no—
94#208—201no—
95#208—201no—
96C2×C3⋊C8—102no—
97D24—201no—
98C3×C16—41no—
99C23×C5#20411yescharacteristic
100C22×D5—121no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5D2411yescharacteristic
104C2×C4×C5(C2×D3)⋊C411yescharacteristic
105C22⋊D5—242no—
106C2×Dic5—121no—
107D20—121no—
108D20—121no—
109C5×C8—21no—
110C5×C8—21no—
111#168—122no—
112C2×D8—151no—
113C2×M16—301no—
114C2×M16C2×D1511yescharacteristic
115#121—301no—
116M32—21no—
117#106—151no—
118#102—301no—
119C2×C3×C5—21no—
120C2×C3×C5—41no—
121C2×C3×C5#32711yescharacteristic
122D15—161no—
123C23×C3#67711yescharacteristic
124C22×D3—201no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4D4011yescharacteristic
128C2×C3×C4#68511yescharacteristic
129#67—402no—
130C2×Dic3—201no—
131D12—201no—
132D12—201no—
133C3×C8—21no—
134C3×C8—21no—
135C3⋊C8—202no—
136C22×C5—21no—
137C22×C5—41no—
138C22×C5#82111yescharacteristic
139C2×D5—241no—
140C2×D5—241no—
141C2×D5—241no—
142C4×C5—21no—
143C4×C5#80611yescharacteristic
144C4×C5#82511yescharacteristic
145Dic5—241no—
146C2×D4—301no—
147C2×D4—601no—
148C22×C4D6011yescharacteristic
149D8—601no—
150M16—41no—
151M16—601no—
152M16—601no—
153C2×C8—302no—
154C2×C8C4×D1511yescharacteristic
155C2×C8#122011yescharacteristic
156C4⋊C4—301no—
157C22⋊C4—601no—
158C16—41no—
159C3×C5#134111yescharacteristic, complemented, Hall
160C22×C3—21no—
161C22×C3—41no—
162C22×C3#395311yescharacteristic
163C2×D3—401no—
164C2×D3—401no—
165C2×D3—401no—
166C3×C4—21no—
167C3×C4#393811yescharacteristic
168C3×C4#395711yescharacteristic
169Dic3—401no—
170C2×C5—21no—
171C2×C5—41no—
172C2×C5#447011yescharacteristic
173D5—481no—
174C23—601no—
175C23#670611yescharacteristic
176D4—601no—
177D4—601no—
178D4—1202no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—601no—
182C2×C4D12011yescharacteristic
183C2×C4#671411yescharacteristic
184C8—21no—
185C8—21no—
186C8—602no—
187C2×C3—21no—
188C2×C3—41no—
189C2×C3#6469011yescharacteristic
190D3—801no—
191C5#6753511yescharacteristic, complemented, Sylow
192C22—21no—
193C22—41no—
194C22—1201no—
195C22—1201no—
196C22—1201no—
197C22#9110511yescharacteristic
198C4—21no—
199C4—1201no—
200C4#9109011yescharacteristic
201C4#9110911yescharacteristic
202C3#1059802611yescharacteristic, complemented, Sylow
203C2—21no—
204C2—41no—
205C2—2401no—
206C2#1174629111yescharacteristic
subgroupG/H
centerC2#11746291
commutatorC2×C3×C5×C8C2×C4
FrattiniC2×M16C2×D15
FittingC3×C5×#349C2
socleC2×C3×C5#327
prime radical#11751236C2
cosocleC2×C3×C5×M16C22
hypercenter#349D15
hypocenterC3×C5#1341
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. C3×C5×#349C2semidirect
3. #11746381C2semidirect
14. C5×#349D3semidirect
30. C3×#349D5semidirect
74. #349D15semidirect
159. C3×C5#1341semidirect
191. C5#67535semidirect
202. C3#10598026semidirect

Maximal subgroups

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

subgroupindex
#117512362
C3×C5×#3492
#117463812
#105980263
#675355