Finite Group Databasebeta

← #14277997

Subgroups — #14277997

Order 1920.

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

normal subgroups only

This group has 228 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#11746378C211yesmaximal, characteristic, complemented
3C5×#4553C211yesmaximal, characteristic, complemented
4#10598025—31nomaximal, Hall
5C2×C3×C5×M16C2211yescharacteristic
6#91815—21no—
7C3×#4076—21no—
8C2×C3×D40C411yescharacteristic, complemented
9C5×#812—21no—
10C3×#3953—21no—
11C3×#3949C411yescharacteristic, complemented
12#67778—51nomaximal, Hall
13#65424D311yescharacteristic
14C5×#349—31no—
15#64777—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
22#6719—41no—
23C4⋊Dic15—41no—
24C4×Dic15—22no—
25C3×#685—41no—
26C3×C4⋊Dic5—21no—
27C3×D40—41no—
28C5×C3⋊C16—41no—
29C3×#469—51no—
30#4557—51no—
31#4553D511yescharacteristic, complemented
32C2×C5×M16C2×D311yescharacteristic
33#4076—21no—
34#4072—61no—
35C2×D40Dic311yescharacteristic, complemented
36C5×M32—61no—
37#3953—21no—
38#3949Dic311yescharacteristic, complemented
39#1339—151noSylow
40C23×C3×C5D811yescharacteristic
41C22×C3×D5—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×C3×C4×C5SD1611yescharacteristic
46C2×Dic15—42no—
47C3×C22⋊D5—82no—
48C2×C3×Dic5—41no—
49C3×D20—41no—
50C3×D20—41no—
51C3×C5×C8—21no—
52C3×C5×C8—21no—
53C2×C3×D8—51no—
54C2×C3×M16C2×D511yescharacteristic
55C3×#121—101no—
56#926—101no—
57C3×#106—51no—
58C3×#102—101no—
59#812—21no—
60C22×C4×C5#6711yescharacteristic
61C2×C22⋊D5—41no—
62C2×D20—21no—
63C5×M16—41no—
64C2×C5×C8C2×Dic311yescharacteristic
65C2×C5×C8#6711yescharacteristic
66C22⋊Dic5—121no—
67#685—41no—
68C4⋊Dic5—21no—
69C4⋊Dic5—121no—
70C4×Dic5—62no—
71D40—41no—
72C5×C16—121no—
73#469—51no—
74#349—31no—
75H(3,ℤ/4)—151no—
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
85Dic15—82no—
86C3×Dic5—81no—
87C2×C3×D4—101no—
88C2×C3×D4—201no—
89C22×C3×C4D2011yescharacteristic
90C3×D8—201no—
91C3×M16—41no—
92C2×C3×C8C4×D511yescharacteristic
93C2×C3×C8C22⋊D511yescharacteristic
94C3×C4⋊C4—101no—
95C3×C22⋊C4—201no—
96#217—201no—
97C4⋊Dic3—201no—
98C4×Dic3—102no—
99C3⋊C16—41no—
100C23×C5#21311yescharacteristic
101C22×D5—41no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5#21411yescharacteristic
105C2×C4×C5#21711yescharacteristic
106C22⋊D5—82no—
107C2×Dic5—41no—
108C2×Dic5—122no—
109D20—41no—
110D20—41no—
111C5×C8—21no—
112C5×C8—21no—
113C2×D8—51no—
114C2×M16D3×D511yescharacteristic
115#121—101no—
116#117—301no—
117M32—61no—
118#106—51no—
119#102—101no—
120C2×C3×C5—21no—
121C2×C3×C5—41no—
122C2×C3×C5#32711yescharacteristic
123C3×D5—161no—
124C23×C3—201no—
125C23×C3D4011yescharacteristic
126C3×D4—201no—
127C3×D4—201no—
128C3×D4—402no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—201no—
132C2×C3×C4#67711yescharacteristic
133C2×C3×C4#68511yescharacteristic
134C2×Dic3—202no—
135C3×C8—21no—
136C3×C8—21no—
137C22×C5—21no—
138C22×C5—41no—
139C22×C5#83211yescharacteristic
140C2×D5—81no—
141C2×D5—81no—
142C2×D5—81no—
143C4×C5—21no—
144C4×C5#83411yescharacteristic
145C4×C5#83711yescharacteristic
146Dic5—81no—
147Dic5—242no—
148C2×D4—101no—
149C2×D4—201no—
150C22×C4#120211yescharacteristic
151D8—201no—
152M16—41no—
153C2×C8D5×Dic311yescharacteristic
154C2×C8#120111yescharacteristic
155C4⋊C4—101no—
156C4⋊C4—601no—
157C22⋊C4—201no—
158C22⋊C4—601no—
159C42—302no—
160C16—121no—
161C3×C5#133911yescharacteristic, complemented, Hall
162C22×C3—21no—
163C22×C3—41no—
164C22×C3—401no—
165C22×C3—401no—
166C22×C3—401no—
167C22×C3#395311yescharacteristic
168C3×C4—21no—
169C3×C4—401no—
170C3×C4#393811yescharacteristic
171C3×C4#395711yescharacteristic
172Dic3—402no—
173C2×C5—21no—
174C2×C5—41no—
175C2×C5#453711yescharacteristic
176D5—161no—
177C23—201no—
178C23#665311yescharacteristic
179D4—201no—
180D4—201no—
181D4—402no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—201no—
185C2×C4—602no—
186C2×C4#665711yescharacteristic
187C2×C4#666511yescharacteristic
188C8—21no—
189C8—21no—
190C2×C3—21no—
191C2×C3—41no—
192C2×C3—801no—
193C2×C3#6469011yescharacteristic
194C5#6777811yescharacteristic, complemented, Sylow
195C22—21no—
196C22—41no—
197C22—401no—
198C22—401no—
199C22—401no—
200C22#9096511yescharacteristic
201C4—21no—
202C4—401no—
203C4—1202no—
204C4#9097611yescharacteristic
205C4#9099511yescharacteristic
206C3#1059802511yescharacteristic, complemented, Sylow
207C2—21no—
208C2—41no—
209C2—801no—
210C2#1174595511yescharacteristic
subgroupG/H
centerC2#11745955
commutatorC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×M16D3×D5
Fitting, cosocleC2×C3×C5×M16C22
socleC2×C3×C5#327
prime radicalC3×#65424C2
hypocenterC3×C5#1339
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. #11746378C2semidirect
3. C5×#4553C2semidirect
8. C2×C3×D40C4semidirect
11. C3×#3949C4semidirect
31. #4553D5semidirect
35. C2×D40Dic3semidirect
38. #3949Dic3semidirect
161. C3×C5#1339semidirect
194. C5#67778semidirect
206. C3#10598025semidirect

Maximal subgroups

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

subgroupindex
C3×#654242
#117463782
C5×#45532
#105980253
#677785