Finite Group Databasebeta

← #14289027

Subgroups — #14289027

Order 1920.

456 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C5×#5722C211yesmaximal, characteristic, complemented
2C3×#65374C211yesmaximal, characteristic
3#11747068C212yesmaximal
4#11746367C211yesmaximal, characteristic, complemented
5#11745843C212yesmaximal, complemented
6#10602732—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C5×#944—22no—
9C5×#888—22no—
10C5×#887—22no—
11C4×C5×Dic6C2212yes—
12C2×C3×#688—22no—
13C3×#4020C2211yescharacteristic
14C2×#6655—22no—
15C4⋊(C3⋊#168)C2212yes—
16C3×C4×#168C2211yescharacteristic
17#90964—22no—
18#71269—51nomaximal, Hall
19C5×Q82—31no—
20#65374D311yescharacteristic
21#65316—32no—
22#64766—31no—
23Q8⋊#168—32no—
24C2×C3×C5×Q8D412yes—
25C2×C5×Dic6—22no—
26C2×C5×Dic6D412yes—
27C2×C3×D20—21no—
28C2×C3×D20—22no—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2311yescharacteristic
31C2×C3⋊#168—22no—
32C5×C4⋊Dic3D412yes—
33C5×Dic3⋊C4—24no—
34C5×Dic3⋊C4—22no—
35C4×C5×Dic3—22no—
36C4×C5×Dic3—22no—
37C3×#688—44no—
38C2×C3×#168—21no—
39#6655—44no—
40#5722D511yescharacteristic, complemented
41C3×#492—51no—
42#5075—52no—
43#4546—51no—
44#4456—52no—
45C5×C4⋊Q8—62no—
46C5×C4⋊Q8—62no—
47C5×C4⋊Q8C2×D311yescharacteristic
48C4×C5×Q8—32no—
49C4×C5×Q8—62no—
50C2×#688—22no—
51C2×#688—62no—
52#4020C2×D311yescharacteristic
53#3941—62no—
54C4⋊#168—32no—
55C4×#168C2×D311yescharacteristic
56#1623—151noSylow
57C22×C3×D5—41no—
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×C5×Dic3—22no—
63C2×C5×Dic3—22no—
64C5×Dic6—22no—
65C5×Dic6—82no—
66C5×Dic6SD1614yescomplemented
67C3×D20—42no—
68C3×D20—42no—
69C3×D20—42no—
70C3⋊#168—42no—
71C3×#168—22no—
72C2×C3×SD16—102no—
73C3×C4⋊Q8C2×D511yescharacteristic
74C3×#127—51no—
75#944—22no—
76C2×#214—102no—
77#888—22no—
78#887—22no—
79C4×Dic6C2×D512yes—
80C3×C4×C8—51no—
81#832—102no—
82C4⋊(C3⋊C8)—52no—
83C2×C5×Q8—32no—
84C2×C5×Q8—62no—
85C2×C5×Q8#6712yes—
86C2×D20—22no—
87C2×D20—21no—
88C5×C4⋊C4—22no—
89C5×C4⋊C4—32no—
90C5×C4⋊C4—64no—
91C5×C4⋊C4—62no—
92C42×C5—62no—
93C42×C5—62no—
94C42×C5C22×D311yescharacteristic
95#688—44no—
96#688—124no—
97C2×#168—21no—
98C2×#168—62no—
99Q82—31no—
100#492—51no—
101#460—152no—
102#333—151no—
103Q8⋊C8—152no—
104C22×C3×C5#12011yescharacteristic
105C2×C3×D5—82no—
106C2×C3×D5—81no—
107C3×C4×C5—21no—
108C3×C4×C5—42no—
109C3×C4×C5C2×SD1612yes—
110C3×C4×C5#13712yes—
111C5×Dic3—24no—
112C5×Dic3—42no—
113C2×C3×Q8C22⋊D512yes—
114C2×C3×D4—102no—
115C2×C3×D4—101no—
116C2×Dic6—22no—
117C2×Dic6C22⋊D512yes—
118C3×SD16—204no—
119C2×C3×C8—101no—
120C3×C4⋊C4—22no—
121C3×C42C22×D511yescharacteristic
122#214—204no—
123C4⋊Dic3C22⋊D512yes—
124Dic3⋊C4—24no—
125Dic3⋊C4—22no—
126C4×Dic3—22no—
127C4×Dic3—22no—
128C2×C3⋊C8—102no—
129C22×D5—41no—
130C5×Q8—34no—
131C5×Q8—42no—
132C5×Q8—62no—
133C5×Q8—242no—
134C2×C4×C5—22no—
135C2×C4×C5—62no—
136C2×C4×C5—62no—
137C2×C4×C5D3×D412yes—
138C2×C4×C5C2×#6711yescharacteristic
139D20—42no—
140D20—42no—
141D20—42no—
142#168—22no—
143#168—122no—
144C2×SD16—102no—
145C2×SD16—302no—
146C4⋊Q8—62no—
147C4⋊Q8—62no—
148C4⋊Q8D3×D511yescharacteristic
149#127—51no—
150C4×Q8—32no—
151C4×Q8—62no—
152C4⋊C8—152no—
153#102—302no—
154C4×C8—51no—
155C2×C3×C5#44812yes—
156C2×C3×C5#45311yescharacteristic
157C3×D5—161no—
158C23×C3—201no—
159C3×Q8—42no—
160C3×D4—202no—
161C3×D4—202no—
162C3×D4—202no—
163C2×C3×C4—22no—
164C2×C3×C4C2×C22⋊D511yescharacteristic
165C2×C3×C4C2×C22⋊D512yes—
166C2×Dic3—22no—
167C2×Dic3—22no—
168Dic6—22no—
169Dic6—82no—
170Dic6#68814yescomplemented
171C3×C8—102no—
172C3⋊C8—202no—
173C22×C5#93711yescharacteristic
174C2×D5—82no—
175C2×D5—81no—
176C4×C5—21no—
177C4×C5—42no—
178C4×C5—64no—
179C4×C5—122no—
180C4×C5D3×SD1612yes—
181C4×C5#91512yes—
182C2×Q8—32no—
183C2×Q8—62no—
184C2×Q8#120112yes—
185C2×D4—101no—
186C2×D4—102no—
187SD16—204no—
188SD16—604no—
189C2×C8—101no—
190C2×C8—302no—
191C4⋊C4—22no—
192C4⋊C4—32no—
193C4⋊C4—64no—
194C4⋊C4—62no—
195C42—62no—
196C42—62no—
197C42C2×D3×D511yescharacteristic
198C3×C5#162311yescharacteristic, complemented, Hall
199C22×C3—402no—
200C22×C3—401no—
201C22×C3#409911yescharacteristic
202C3×C4—21no—
203C3×C4—42no—
204C3×C4C2×#68812yes—
205C3×C4#408812yes—
206Dic3—24no—
207Dic3—42no—
208C2×C5#507711yescharacteristic
209C2×C5#517012yes—
210D5—161no—
211C23—201no—
212Q8—34no—
213Q8—42no—
214Q8—62no—
215Q8—242no—
216D4—202no—
217D4—202no—
218D4—202no—
219C2×C4—22no—
220C2×C4—62no—
221C2×C4—62no—
222C2×C4C2×#120111yescharacteristic
223C2×C4D3×C22⋊D512yes—
224C8—102no—
225C8—602no—
226C2×C3—801no—
227C2×C3#6551612yes—
228C2×C3#6553011yescharacteristic
229C5#7126911yescharacteristic, complemented, Sylow
230C22—401no—
231C22—402no—
232C22#9156811yescharacteristic
233C4—21no—
234C4—42no—
235C4—64no—
236C4—122no—
237C4D3×#68812yes—
238C4#9151812yes—
239C3#1060273211yescharacteristic, complemented, Sylow
240C2—801no—
241C2#1174914011yescharacteristic
242C2#1174927812yes—
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1623
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. C5×#5722C2semidirect
4. #11746367C2semidirect
5. #11745843C2semidirect
40. #5722D5semidirect
66. C5×Dic6SD16semidirect
170. Dic6#688semidirect
198. C3×C5#1623semidirect
229. C5#71269semidirect
239. C3#10602732semidirect

Maximal subgroups

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

subgroupindex
C5×#57222
C3×#653742
#117470682
#117463672
#117458432
#106027323
#712695