Finite Group Databasebeta

← #14279442

Subgroups — #14279442

Order 1920.

240 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 42 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×#65362C211yesmaximal, characteristic
2#11746366C211yesmaximal, characteristic, complemented
3C5×#4545C211yesmaximal, characteristic, complemented
4#10598032—31nomaximal, Hall
5C3×C5×#127C2211yescharacteristic
6C2×C3×#686—21no—
7C2×C3×#686—21no—
8C3×#4020C411yescharacteristic, complemented
9#91118—21no—
10C5×#834—21no—
11C3×C4×#168C411yescharacteristic, complemented
12#67792—51nomaximal, Hall
13#65362D311yescharacteristic
14C5×#353—31no—
15#64765—31no—
16C2×C3×C5×D4—41no—
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×C5×D4D411yescharacteristic
19C2×C3×D20—21no—
20C2×C3×D20—41no—
21C3×C42×C5C2×C411yescharacteristic
22#6719—41no—
23C5×#217—41no—
24C3×#686—42no—
25C3×#686—42no—
26C2×C3×#168—21no—
27C3×#493—51no—
28#4545—51no—
29#4545D511yescharacteristic, complemented
30C5×#127C2×D311yescharacteristic
31C2×#686—21no—
32C2×#686—21no—
33#4020Dic311yescharacteristic, complemented
34C5×#99—61no—
35#3966—61no—
36C4×#168Dic311yescharacteristic, complemented
37#1408—151noSylow
38C23×C3×C5—21no—
39C23×C3×C5—21no—
40C22×C3×D5—41no—
41C3×C5×D4—41no—
42C3×C5×D4—41no—
43C3×C5×D4—82no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C2×Dic15—81no—
47C2×C5×Dic3—81no—
48C3×D20—41no—
49C3×D20—41no—
50C3×D20—82no—
51C3×#168—22no—
52C2×C3×D8—101no—
53C2×C3×D8—101no—
54C3×#127—51no—
55C3×#127C2×D511yescharacteristic
56C3×C4×C8—51no—
57#834—21no—
58#834—101no—
59C2×C5×D4—41no—
60C2×C5×D4#6711yescharacteristic
61C2×C5×D4#6711yescharacteristic
62C2×D20—21no—
63C2×D20—41no—
64C5×C22⋊C4—121no—
65C42×C5C2×Dic311yescharacteristic
66C22⋊Dic5—121no—
67#686—42no—
68#686—42no—
69C2×#168—21no—
70#493—51no—
71#353—31no—
72#353—151no—
73C22×C3×C5—41no—
74C22×C3×C5—41no—
75C22×C3×C5—81no—
76C22×C3×C5—81no—
77C22×C3×C5#9911yescharacteristic
78C2×C3×D5—82no—
79C2×C3×D5—81no—
80C3×C4×C5—22no—
81C3×C4×C5—21no—
82Dic15—161no—
83C5×Dic3—161no—
84C2×C3×D4—41no—
85C2×C3×D4—101no—
86C2×C3×D4—201no—
87C2×C3×D4D2011yescharacteristic
88C2×C3×D4C22⋊D511yescharacteristic
89C3×D8—202no—
90C3×D8—202no—
91C2×C3×C8—101no—
92C3×C42C4×D511yescharacteristic
93#217—41no—
94#217—201no—
95C23×C5—21no—
96C23×C5—21no—
97C22×D5—41no—
98C5×D4—41no—
99C5×D4—41no—
100C5×D4—82no—
101C2×C4×C5—21no—
102C2×C4×C5—241no—
103C2×C4×C5#21711yescharacteristic
104C2×Dic5—241no—
105D20—41no—
106D20—41no—
107D20—82no—
108#168—22no—
109C2×D8—101no—
110C2×D8—101no—
111#127—51no—
112#127D3×D511yescharacteristic
113#99—61no—
114#99—301no—
115C4×C8—51no—
116C2×C3×C5—21no—
117C2×C3×C5—81no—
118C2×C3×C5—81no—
119C2×C3×C5#35311yescharacteristic
120C3×D5—161no—
121C23×C3—21no—
122C23×C3—21no—
123C23×C3—201no—
124C3×D4—41no—
125C3×D4—41no—
126C3×D4—82no—
127C3×D4—201no—
128C3×D4—201no—
129C3×D4—402no—
130C2×C3×C4—21no—
131C2×C3×C4#68511yescharacteristic
132C2×Dic3—81no—
133C2×Dic3—401no—
134C3×C8—102no—
135C22×C5—41no—
136C22×C5—41no—
137C22×C5—81no—
138C22×C5—81no—
139C22×C5#83411yescharacteristic
140C2×D5—82no—
141C2×D5—81no—
142C4×C5—22no—
143C4×C5—21no—
144C4×C5—481no—
145Dic5—481no—
146C2×D4—41no—
147C2×D4—101no—
148C2×D4—201no—
149C2×D4#120111yescharacteristic
150C2×D4#120211yescharacteristic
151D8—202no—
152D8—202no—
153C2×C8—101no—
154C22⋊C4—121no—
155C22⋊C4—601no—
156C42D5×Dic311yescharacteristic
157C3×C5#140811yescharacteristic, complemented, Hall
158C22×C3—41no—
159C22×C3—41no—
160C22×C3—81no—
161C22×C3—81no—
162C22×C3—402no—
163C22×C3—401no—
164C22×C3#393811yescharacteristic
165C3×C4—22no—
166C3×C4—21no—
167Dic3—161no—
168Dic3—801no—
169C2×C5—21no—
170C2×C5—81no—
171C2×C5—81no—
172C2×C5#454511yescharacteristic
173D5—161no—
174C23—21no—
175C23—21no—
176C23—201no—
177D4—41no—
178D4—41no—
179D4—82no—
180D4—201no—
181D4—201no—
182D4—402no—
183C2×C4—21no—
184C2×C4—241no—
185C2×C4—1201no—
186C2×C4#666511yescharacteristic
187C8—102no—
188C2×C3—21no—
189C2×C3—81no—
190C2×C3—81no—
191C2×C3—801no—
192C2×C3#6469411yescharacteristic
193C5#6779211yescharacteristic, complemented, Sylow
194C22—41no—
195C22—41no—
196C22—81no—
197C22—81no—
198C22—402no—
199C22—401no—
200C22#9099511yescharacteristic
201C4—22no—
202C4—21no—
203C4—481no—
204C4—2401no—
205C3#1059803211yescharacteristic, complemented, Sylow
206C2—21no—
207C2—81no—
208C2—81no—
209C2—801no—
210C2#1174600611yescharacteristic
subgroupG/H
centerC2#11746006
commutatorC3×C42×C5C2×C4
Frattini, hypercenter#127D3×D5
Fitting, cosocleC3×C5×#127C22
socleC2×C3×C5#353
prime radicalC3×#65362C2
hypocenterC3×C5#1408
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11746366C2semidirect
3. C5×#4545C2semidirect
8. C3×#4020C4semidirect
11. C3×C4×#168C4semidirect
29. #4545D5semidirect
33. #4020Dic3semidirect
36. C4×#168Dic3semidirect
157. C3×C5#1408semidirect
193. C5#67792semidirect
205. C3#10598032semidirect

Maximal subgroups

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

subgroupindex
C3×#653622
#117463662
C5×#45452
#105980323
#677925