Finite Group Databasebeta

← #14289069

Subgroups — #14289069

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×#66068C211yesmaximal, characteristic, complemented
2#11751186C211yesmaximal, characteristic, complemented
3#11747028C212yesmaximal, complemented
4C5×#4546C211yesmaximal, characteristic, complemented
5#11745834C212yesmaximal, complemented
6#10599284—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C2×#6717—22no—
9#91763C2211yescharacteristic
10C3×#4093—22no—
11C3×#4041—22no—
12C3×#4038—22no—
13C3×C4×D20C2212yes—
14C2×#6653—22no—
15C4×C3⋊#168C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2212yes—
17#90968—22no—
18#71927—51nomaximal, Hall
19#66068D311yescharacteristic, complemented
20#65374—31no—
21#65132—32no—
22C5×#333—31no—
23#64703—32no—
24C2×C3×C5×Q8D412yes—
25C2×D60—22no—
26C2×D60—21no—
27C2×C3×D20—22no—
28C2×C3×D20D412yes—
29C2×C3×C4×D5—22no—
30C3×C5×C4⋊C4—22no—
31C3×C42×C5C2311yescharacteristic
32#6717—44no—
33C2×C3⋊#168—21no—
34C2×C5×C3⋊C8—22no—
35C3×#685—24no—
36C3×#685—22no—
37C3×C4⋊Dic5D412yes—
38C3×C4×Dic5—22no—
39#6653—44no—
40C3×#555—51no—
41#5085—51no—
42#5015—52no—
43#4546D511yescharacteristic, complemented
44D4⋊(C3⋊C8)—52no—
45C5×C4⋊Q8C2×D311yescharacteristic
46#4093—22no—
47C2×#688—62no—
48C2×D40—62no—
49#4041—22no—
50#4038—22no—
51#4020—31no—
52C4×D20C2×D312yes—
53C5×C4⋊C8—32no—
54#3953—62no—
55C4×#168—31no—
56#1624—151noSylow
57C22×D15—41no—
58C22×C3×D5—22no—
59C3×C5×Q8—42no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63D60—42no—
64D60—42no—
65D60—42no—
66C2×C3×Dic5—22no—
67C3×D20—22no—
68C3×D20—22no—
69C3×D20—82no—
70C3×C4×D5—42no—
71C3×C4×D5—42no—
72C3⋊#168—22no—
73C5×C3⋊C8—42no—
74C3×C4⋊Q8C2×D511yescharacteristic
75C3×#124—102no—
76C3×#121—102no—
77C3×C4×D4—52no—
78C3×#117—102no—
79C2×#215—102no—
80C2×#213—102no—
81#874—51no—
82#809—102no—
83C4⋊(C3⋊C8)C2×D512yes—
84C4×C3⋊C8—51no—
85C2×C5×Q8#6712yes—
86C2×D20—22no—
87C2×D20—62no—
88C2×D20—61no—
89C2×D20#6712yes—
90C2×C4×D5—22no—
91C2×C5×C8—62no—
92C5×C4⋊C4—22no—
93C42×C5C22×D311yescharacteristic
94#688—124no—
95#685—24no—
96#685—22no—
97C4⋊Dic5#6712yes—
98C4×Dic5—22no—
99C2×#168—61no—
100D40—124no—
101#555—51no—
102#492—151no—
103#459—152no—
104#333—31no—
105D4⋊C8—152no—
106C22×C3×C5#12011yescharacteristic
107C2×D15—82no—
108C2×D15—81no—
109C2×C3×D5—42no—
110C2×C3×D5—42no—
111C2×C3×D5—42no—
112C3×C4×C5—21no—
113C3×C4×C5—42no—
114C3×C4×C5#13512yes—
115C3×C4×C5AGL(1,ℤ/8)12yes—
116C3×Dic5—42no—
117C2×C3×Q8D2012yes—
118C2×C3×D4—52no—
119C2×C3×D4—102no—
120C22×C3×C4—102no—
121C2×D12—101no—
122C2×D12—102no—
123C3×C4⋊C4—22no—
124C3×C4⋊C4—52no—
125C3×C22⋊C4—104no—
126C3×C22⋊C4—102no—
127C3×C42—102no—
128C3×C42C22×D511yescharacteristic
129#215—204no—
130#213—204no—
131C2×C3⋊C8—22no—
132C2×C3⋊C8—101no—
133C22×D5—22no—
134C22×D5—121no—
135C5×Q8—42no—
136C2×C4×C5—22no—
137C2×C4×C5C2×#6711yescharacteristic
138C2×C4×C5C2×#6712yes—
139C2×Dic5—22no—
140D20—22no—
141D20—22no—
142D20—82no—
143D20—122no—
144D20—122no—
145D20—122no—
146C4×D5—42no—
147C4×D5—42no—
148C5×C8—122no—
149#168—62no—
150C2×SD16—302no—
151C2×D8—302no—
152C4⋊Q8D3×D511yescharacteristic
153#127—151no—
154#124—102no—
155#121—102no—
156C4×D4—52no—
157#117—102no—
158C4⋊C8—32no—
159#102—302no—
160C4×C8—151no—
161C2×C3×C5#44912yes—
162C2×C3×C5#45311yescharacteristic
163D15—161no—
164C3×D5—82no—
165C23×C3—102no—
166C22×D3—201no—
167C3×Q8—42no—
168C3×D4—102no—
169C3×D4—102no—
170C3×D4—402no—
171C2×C3×C4—22no—
172C2×C3×C4—102no—
173C2×C3×C4—202no—
174C2×C3×C4—202no—
175C2×C3×C4C2×D2011yescharacteristic
176C2×C3×C4D4×D512yes—
177D12—202no—
178D12—202no—
179D12—202no—
180C3⋊C8—42no—
181C3⋊C8—102no—
182C22×C5#95311yescharacteristic
183C2×D5—42no—
184C2×D5—42no—
185C2×D5—42no—
186C2×D5—242no—
187C2×D5—241no—
188C4×C5—21no—
189C4×C5—42no—
190C4×C5#94912yes—
191C4×C5#95012yes—
192Dic5—42no—
193C2×Q8#120212yes—
194C2×D4—52no—
195C2×D4—102no—
196C2×D4—301no—
197C2×D4—302no—
198C22×C4—102no—
199SD16—604no—
200D8—604no—
201C2×C8—62no—
202C2×C8—301no—
203C4⋊C4—22no—
204C4⋊C4—52no—
205C22⋊C4—104no—
206C22⋊C4—102no—
207C42—102no—
208C42C2×D3×D511yescharacteristic
209C3×C5#162411yescharacteristic, complemented, Hall
210C22×C3—202no—
211C22×C3—202no—
212C22×C3—202no—
213C22×C3#402811yescharacteristic
214C2×D3—401no—
215C2×D3—402no—
216C3×C4—21no—
217C3×C4—42no—
218C3×C4—202no—
219C3×C4#406012yes—
220C3×C4#406512yes—
221C2×C5#523812yes—
222C2×C5#524111yescharacteristic
223D5—82no—
224D5—481no—
225C23—102no—
226C23—601no—
227Q8—42no—
228D4—102no—
229D4—102no—
230D4—402no—
231D4—602no—
232D4—602no—
233D4—602no—
234C2×C4—22no—
235C2×C4—102no—
236C2×C4—202no—
237C2×C4—202no—
238C2×C4C2×#120211yescharacteristic
239C2×C4D5×#6712yes—
240C8—122no—
241C8—302no—
242C2×C3—402no—
243C2×C3#6503611yescharacteristic
244C2×C3#6510012yes—
245D3—801no—
246C5#7192711yescharacteristic, complemented, Sylow
247C22—202no—
248C22—202no—
249C22—202no—
250C22—1201no—
251C22—1202no—
252C22#9156411yescharacteristic
253C4—21no—
254C4—42no—
255C4—202no—
256C4#9150212yes—
257C4#9151612yes—
258C3#1059928411yescharacteristic, complemented, Sylow
259C2—402no—
260C2—2401no—
261C2#1174913811yescharacteristic
262C2#1174927212yes—
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66068C2semidirect
2. #11751186C2semidirect
3. #11747028C2semidirect
4. C5×#4546C2semidirect
5. #11745834C2semidirect
19. #66068D3semidirect
43. #4546D5semidirect
209. C3×C5#1624semidirect
246. C5#71927semidirect
258. C3#10599284semidirect

Maximal subgroups

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

subgroupindex
C3×#660682
#117511862
#117470282
C5×#45462
#117458342
#105992843
#719275