Finite Group Databasebeta

← #14288865

Subgroups — #14288865

Order 1920.

480 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 92 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×#66047C211yesmaximal, characteristic, complemented
2#11751174C211yesmaximal, characteristic
3#11747064C212yesmaximal, complemented
4C5×#4544C211yesmaximal, characteristic, complemented
5#11745840C212yesmaximal, complemented
6#10599195—31nomaximal, Hall
7C3×C5×#127C2211yescharacteristic
8C2×#6715—22no—
9#91763C2211yescharacteristic
10C3×#4082—22no—
11C3×#4081—22no—
12C3×D4×Dic5—22no—
13C3×C4×Dic10C2212yes—
14C2×#6658—22no—
15C4×C3⋊#168C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2212yes—
17#90968—22no—
18#71943—51nomaximal, Hall
19#66047D311yescharacteristic, complemented
20#65362—31no—
21#65137—32no—
22C5×#331—31no—
23#64704—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4D412yes—
26C2×D60—22no—
27C2×D60—21no—
28C22×C3×Dic5—22no—
29C2×C3×Dic10D412yes—
30C3×C42×C5C2311yescharacteristic
31#6715—44no—
32C2×C3⋊#168—21no—
33C2×C5×C3⋊C8—22no—
34C3×C22⋊Dic5—24no—
35C3×C22⋊Dic5—22no—
36C3×C4⋊Dic5D412yes—
37C3×#683—22no—
38C3×C4×Dic5—22no—
39#6658—44no—
40C3×#559—51no—
41#5073—51no—
42#5027—52no—
43#4544D511yescharacteristic, complemented
44#4535—52no—
45C5×#127C2×D311yescharacteristic
46#4082—22no—
47#4081—22no—
48D4×Dic5—22no—
49C2×#686—62no—
50C2×#677—62no—
51#4020—31no—
52C4×Dic10C2×D312yes—
53C5×C4⋊C8—32no—
54#3953—62no—
55C4×#168—31no—
56#1620—151noSylow
57C23×C3×C5—22no—
58C22×D15—41no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C2×C3×C4×C5C2×D411yescharacteristic
63C2×C3×C4×C5C2×D412yes—
64D60—42no—
65D60—42no—
66D60—42no—
67C2×C3×Dic5—22no—
68C2×C3×Dic5—22no—
69C2×C3×Dic5—82no—
70C3×Dic10—22no—
71C3×Dic10—22no—
72C3⋊#168—22no—
73C5×C3⋊C8—42no—
74C3×#127C2×D511yescharacteristic
75C3×#124—102no—
76C3×#123—102no—
77C3×C4×Q8—52no—
78C3×C4×D4—102no—
79C2×#215—102no—
80C2×#213—102no—
81#874—51no—
82#809—102no—
83C4⋊(C3⋊C8)C2×D512yes—
84C4×C3⋊C8—51no—
85C2×C5×D4—22no—
86C2×C5×D4#6712yes—
87C22×Dic5—22no—
88C2×D20—62no—
89C2×D20—61no—
90C2×Dic10#6712yes—
91C2×C5×C8—62no—
92C42×C5C22×D311yescharacteristic
93C22⋊Dic5—24no—
94C22⋊Dic5—22no—
95#686—124no—
96C4⋊Dic5#6712yes—
97#683—22no—
98C4×Dic5—22no—
99C2×#168—61no—
100#677—124no—
101#559—51no—
102#493—151no—
103#460—152no—
104#331—31no—
105Q8⋊C8—152no—
106C22×C3×C5—44no—
107C22×C3×C5—42no—
108C22×C3×C5#12011yescharacteristic
109C2×D15—82no—
110C2×D15—81no—
111C3×C4×C5—21no—
112C3×C4×C5#13512yes—
113C3×C4×C5AGL(1,ℤ/8)12yes—
114C3×Dic5—42no—
115C3×Dic5—42no—
116C2×C3×Q8—52no—
117C2×C3×D4—22no—
118C2×C3×D4D2012yes—
119C22×C3×C4—102no—
120C2×D12—101no—
121C2×D12—102no—
122C3×C4⋊C4—52no—
123C3×C4⋊C4—102no—
124C3×C22⋊C4—104no—
125C3×C22⋊C4—102no—
126C3×C42—102no—
127C3×C42C22×D511yescharacteristic
128#215—204no—
129#213—204no—
130C2×C3⋊C8—22no—
131C2×C3⋊C8—101no—
132C23×C5—22no—
133C22×D5—121no—
134C5×D4—42no—
135C5×D4—42no—
136C5×D4—42no—
137C2×C4×C5C2×#6711yescharacteristic
138C2×C4×C5C2×#6712yes—
139C2×Dic5—22no—
140C2×Dic5—22no—
141C2×Dic5—82no—
142D20—122no—
143D20—122no—
144D20—122no—
145Dic10—22no—
146Dic10—22no—
147C5×C8—122no—
148#168—62no—
149C2×SD16—302no—
150C2×D8—302no—
151#127—151no—
152#127D3×D511yescharacteristic
153#124—102no—
154#123—102no—
155C4×Q8—52no—
156C4×D4—102no—
157C4⋊C8—32no—
158#102—302no—
159C4×C8—151no—
160C2×C3×C5—82no—
161C2×C3×C5#44912yes—
162C2×C3×C5#45311yescharacteristic
163D15—161no—
164C23×C3—22no—
165C22×D3—201no—
166C3×Q8—102no—
167C3×Q8—102no—
168C3×D4—42no—
169C3×D4—42no—
170C3×D4—42no—
171C2×C3×C4—102no—
172C2×C3×C4—102no—
173C2×C3×C4—402no—
174C2×C3×C4C2×D2011yescharacteristic
175C2×C3×C4D4×D512yes—
176D12—202no—
177D12—202no—
178D12—202no—
179C3⋊C8—42no—
180C3⋊C8—102no—
181C22×C5—44no—
182C22×C5—42no—
183C22×C5#95311yescharacteristic
184C2×D5—242no—
185C2×D5—241no—
186C4×C5—21no—
187C4×C5#94912yes—
188C4×C5#95012yes—
189Dic5—42no—
190Dic5—42no—
191C2×Q8—52no—
192C2×D4—22no—
193C2×D4—301no—
194C2×D4—302no—
195C2×D4#120212yes—
196C22×C4—102no—
197SD16—604no—
198D8—604no—
199C2×C8—62no—
200C2×C8—301no—
201C4⋊C4—52no—
202C4⋊C4—102no—
203C22⋊C4—104no—
204C22⋊C4—102no—
205C42—102no—
206C42C2×D3×D511yescharacteristic
207C3×C5#162011yescharacteristic, complemented, Hall
208C22×C3—42no—
209C22×C3—44no—
210C22×C3#402811yescharacteristic
211C2×D3—401no—
212C2×D3—402no—
213C3×C4—21no—
214C3×C4—202no—
215C3×C4—202no—
216C3×C4#405712yes—
217C3×C4#406212yes—
218C2×C5—82no—
219C2×C5#523812yes—
220C2×C5#524111yescharacteristic
221D5—481no—
222C23—22no—
223C23—601no—
224Q8—102no—
225Q8—102no—
226D4—42no—
227D4—42no—
228D4—42no—
229D4—602no—
230D4—602no—
231D4—602no—
232C2×C4—102no—
233C2×C4—102no—
234C2×C4—402no—
235C2×C4C2×#120211yescharacteristic
236C2×C4D5×#6712yes—
237C8—122no—
238C8—302no—
239C2×C3—82no—
240C2×C3#6503611yescharacteristic
241C2×C3#6507012yes—
242D3—801no—
243C5#7194311yescharacteristic, complemented, Sylow
244C22—42no—
245C22—44no—
246C22—1201no—
247C22—1202no—
248C22#9156411yescharacteristic
249C4—21no—
250C4—202no—
251C4—202no—
252C4#9147812yes—
253C4#9149212yes—
254C3#1059919511yescharacteristic, complemented, Sylow
255C2—82no—
256C2—2401no—
257C2#1174902612yes—
258C2#1174913811yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radical#11751174C2
hypercenter#127D3×D5
hypocenterC3×C5#1620
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#66047C2semidirect
3. #11747064C2semidirect
4. C5×#4544C2semidirect
5. #11745840C2semidirect
19. #66047D3semidirect
43. #4544D5semidirect
207. C3×C5#1620semidirect
243. C5#71943semidirect
254. C3#10599195semidirect

Maximal subgroups

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

subgroupindex
C3×#660472
#117511742
#117470642
C5×#45442
#117458402
#105991953
#719435