Finite Group Databasebeta

← #14277996

Subgroups — #14277996

Order 1920.

228 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 56 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
2C5×#4553C211yesmaximal, characteristic, complemented
3C3×#64777C211yesmaximal, characteristic, complemented
4#10598025—31nomaximal, Hall
5C2×C3×C5×M16C2211yescharacteristic
6#91819—21no—
7C2×D120C411yescharacteristic, complemented
8C3×#4072—21no—
9#91105—21no—
10#91101C411yescharacteristic, complemented
11C5×#812—21no—
12#67481—51nomaximal, Hall
13#65424—31no—
14C5×#349—31no—
15#64777D311yescharacteristic, complemented
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—
24D120—41no—
25C3×C22⋊Dic5—41no—
26C3×C4⋊Dic5—41no—
27C3×C4×Dic5—22no—
28C5×C3⋊C16—41no—
29#5135—51no—
30C3×H(3,ℤ/4)—51no—
31#4553D511yescharacteristic, complemented
32C2×C5×M16C2×D311yescharacteristic
33#4076—61no—
34#4072—21no—
35C2×D40—31no—
36C5×M32—61no—
37#3953—61no—
38#3949—31no—
39#1339—151noSylow
40C23×C3×C5D811yescharacteristic
41C22×D15—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×C3×C4×C5SD1611yescharacteristic
46#1220—82no—
47C2×Dic15—41no—
48D60—41no—
49D60—41no—
50C2×C3×Dic5—42no—
51C3×C5×C8—21no—
52C3×C5×C8—21no—
53C2×C3×M16C2×D511yescharacteristic
54C3×#117—101no—
55#930—101no—
56C2×D24—51no—
57#821—101no—
58#817—51no—
59#812—21no—
60C22×C4×C5#6711yescharacteristic
61C2×C22⋊D5—121no—
62C2×D20—61no—
63C5×M16—41no—
64C2×C5×C8C4×D311yescharacteristic
65C2×C5×C8D1211yescharacteristic
66C22⋊Dic5—41no—
67#685—121no—
68C4⋊Dic5—41no—
69C4⋊Dic5—61no—
70C4×Dic5—22no—
71D40—121no—
72C5×C16—121no—
73#469—151no—
74#349—31no—
75H(3,ℤ/4)—51no—
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—
86C3×Dic5—82no—
87C22×C3×C4D2011yescharacteristic
88C2×#67—201no—
89C2×D12—101no—
90C3×M16—41no—
91C2×C3×C8C4×D511yescharacteristic
92C2×C3×C8C22⋊D511yescharacteristic
93C3×C4⋊C4—201no—
94C3×C22⋊C4—201no—
95C3×C42—102no—
96(C2×D3)⋊C4—201no—
97C4⋊Dic3—101no—
98D24—201no—
99C3⋊C16—41no—
100C23×C5#21311yescharacteristic
101C22×D5—121no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5(C2×D3)⋊C411yescharacteristic
105C2×C4×C5#21511yescharacteristic
106C22⋊D5—242no—
107C2×Dic5—42no—
108C2×Dic5—121no—
109D20—121no—
110D20—121no—
111C5×C8—21no—
112C5×C8—21no—
113C2×D8—151no—
114C2×M16D3×D511yescharacteristic
115#121—301no—
116#117—101no—
117M32—61no—
118#106—151no—
119#102—301no—
120C2×C3×C5—21no—
121C2×C3×C5—41no—
122C2×C3×C5#32711yescharacteristic
123D15—161no—
124C23×C3D4011yescharacteristic
125C22×D3—201no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—202no—
129C2×C3×C4#67711yescharacteristic
130C2×C3×C4#68511yescharacteristic
131#67—402no—
132C2×Dic3—201no—
133D12—201no—
134D12—201no—
135C3×C8—21no—
136C3×C8—21no—
137C22×C5—21no—
138C22×C5—41no—
139C22×C5#80911yescharacteristic
140C2×D5—241no—
141C2×D5—241no—
142C2×D5—241no—
143C4×C5—21no—
144C4×C5#80511yescharacteristic
145C4×C5#80611yescharacteristic
146Dic5—82no—
147Dic5—241no—
148C2×D4—301no—
149C2×D4—601no—
150C22×C4#120211yescharacteristic
151D8—601no—
152M16—41no—
153C2×C8#120011yescharacteristic
154C2×C8#120311yescharacteristic
155C4⋊C4—201no—
156C4⋊C4—301no—
157C22⋊C4—201no—
158C22⋊C4—601no—
159C42—102no—
160C16—121no—
161C3×C5#133911yescharacteristic, complemented, Hall
162C22×C3—21no—
163C22×C3—41no—
164C22×C3#395311yescharacteristic
165C2×D3—401no—
166C2×D3—401no—
167C2×D3—401no—
168C3×C4—21no—
169C3×C4—402no—
170C3×C4#393811yescharacteristic
171C3×C4#395711yescharacteristic
172Dic3—401no—
173C2×C5—21no—
174C2×C5—41no—
175C2×C5#445111yescharacteristic
176D5—481no—
177C23—601no—
178C23#665311yescharacteristic
179D4—601no—
180D4—601no—
181D4—1202no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—202no—
185C2×C4—601no—
186C2×C4#665811yescharacteristic
187C2×C4#666711yescharacteristic
188C8—21no—
189C8—21no—
190C2×C3—21no—
191C2×C3—41no—
192C2×C3#6469011yescharacteristic
193D3—801no—
194C5#6748111yescharacteristic, complemented, Sylow
195C22—21no—
196C22—41no—
197C22—1201no—
198C22—1201no—
199C22—1201no—
200C22#9096811yescharacteristic
201C4—21no—
202C4—402no—
203C4—1201no—
204C4#9098111yescharacteristic
205C4#9099711yescharacteristic
206C3#1059802511yescharacteristic, complemented, Sylow
207C2—21no—
208C2—41no—
209C2—2401no—
210C2#1174595811yescharacteristic
subgroupG/H
centerC2#11745958
commutatorC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×M16D3×D5
Fitting, cosocleC2×C3×C5×M16C22
socleC2×C3×C5#327
prime radical#11751236C2
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. C5×#4553C2semidirect
3. C3×#64777C2semidirect
7. C2×D120C4semidirect
10. #91101C4semidirect
15. #64777D3semidirect
31. #4553D5semidirect
161. C3×C5#1339semidirect
194. C5#67481semidirect
206. C3#10598025semidirect

Maximal subgroups

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

subgroupindex
#117512362
C5×#45532
C3×#647772
#105980253
#674815