Finite Group Databasebeta

← #14512658

Subgroups — #14512658

Order 1920.

368 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 51 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#65904⋊C3C211yesmaximal, characteristic
2C4×C5⋊#226C211yesmaximal, characteristic
3C5×C4⋊#226C211yesmaximal, characteristic
4#11751597C212yesmaximal
5#11751594C212yesmaximal
6#10612196—31nomaximal, Hall
7C2×C5⋊#226C2211yescharacteristic
8C2×C5×#226C2212yes—
9C4×C5×SL(2,𝔽3)C2211yescharacteristic
10#91384—41nomaximal
11Dic5×SL(2,𝔽3)C2212yes—
12#91184C2211yescharacteristic
13#85417—51nomaximal, Hall
14#66055—31no—
15#65904D311yescharacteristic
16C5×#462—31no—
17#65473—32no—
18#65471—32no—
19#65370—31no—
20C4×#689—31no—
21#65140—31no—
22#65120—31no—
23#65088—32no—
24#65086—32no—
25C2×C5×SL(2,𝔽3)C2311yescharacteristic
26C5⋊#226—21no—
27C5×#226—22no—
28C4×Dic15—41no—
29C5×C4⋊Dic3—41no—
30C3×C4⋊Dic5—41no—
31Dic3⋊Dic5—42no—
32#6668—42no—
33#557⋊C3—51no—
34C4⋊#226—52no—
35C4⋊#226D511yescharacteristic
36#5388—52no—
37C4×#226—51no—
38C2×C5×Q16—32no—
39C5×C4⋊Q8—31no—
40C4×C5×Q8C2×D311yescharacteristic
41Q8×Dic5—32no—
42Q8×Dic5C2×D312yes—
43#4090—32no—
44C2×#689—31no—
45#4036—32no—
46#4036—61no—
47#4035—62no—
48#4033—61no—
49#4015—31no—
50C4×Dic10—31no—
51C4×Dic10—31no—
52C5×C4⋊C8—31no—
53C5×#103—32no—
54#3967—32no—
55#3967—32no—
56#3967—31no—
57#3949—32no—
58#3948—32no—
59#3947—32no—
60#3946—32no—
61#3942—31no—
62#3939—31no—
63C4×#168—31no—
64#3374—151noSylow
65C2×C3×C4×C5—41no—
66C2×Dic15—41no—
67C2×Dic15—41no—
68C2×C5×Dic3—42no—
69C2×C3×Dic5—42no—
70C5×SL(2,𝔽3)#4111yescharacteristic
71C2×#226—51no—
72C2×#226C2×D512yes—
73#890—201no—
74C4×SL(2,𝔽3)—52no—
75C4×SL(2,𝔽3)C2×D511yescharacteristic
76#859—51no—
77C2×C5×Q8—32no—
78C2×C5×Q8C22×D311yescharacteristic
79C2×Dic10—31no—
80C2×Dic10—31no—
81C5×Q16—62no—
82C5×Q16—62no—
83C2×C5×C8—32no—
84C5×C4⋊C4—31no—
85C5×C4⋊C4—61no—
86C5×C4⋊C4—61no—
87C42×C5—31no—
88#689—61no—
89#689—61no—
90C4⋊Dic5—32no—
91C4⋊Dic5—31no—
92C4⋊Dic5—61no—
93C4⋊Dic5—62no—
94C4⋊Dic5S411yescharacteristic
95#683—32no—
96#683—62no—
97#683—61no—
98#683—62no—
99C4×Dic5—32no—
100C4×Dic5—62no—
101C4×Dic5—61no—
102C2×#168—31no—
103C2×#168—31no—
104#557—51no—
105#557—151no—
106#491—152no—
107#487—151no—
108#479—152no—
109#475—151no—
110#462—31no—
111#462—152no—
112#446—151no—
113#441—152no—
114C4×Q16—151no—
115C22×C3×C5—41no—
116C3×C4×C5—42no—
117Dic15—81no—
118Dic15—81no—
119C3×Dic5—82no—
120C5×Dic3—82no—
121C2×SL(2,𝔽3)C22×D511yescharacteristic
122#226—22no—
123#226—101no—
124C3×C4⋊C4—201no—
125C4⋊Dic3—41no—
126C4⋊Dic3—202no—
127Dic3⋊C4—202no—
128C4×Dic3—201no—
129C5×Q8—31no—
130C5×Q8—62no—
131C5×Q8—62no—
132C5×Q8#23911yescharacteristic
133C2×C4×C5—31no—
134C2×C4×C5—31no—
135C2×C4×C5—62no—
136C2×C4×C5C2×S411yescharacteristic
137C2×Dic5—32no—
138C2×Dic5—61no—
139C2×Dic5—61no—
140C2×Dic5C2×S412yes—
141Dic10—62no—
142Dic10—61no—
143Dic10—61no—
144C5×C8—62no—
145#168—61no—
146#168—61no—
147C2×Q16—32no—
148C2×Q16—151no—
149C4⋊Q8—31no—
150C4⋊Q8—151no—
151C4⋊Q8—152no—
152#125—152no—
153#125—301no—
154#125—302no—
155C4×Q8—52no—
156C4×Q8—151no—
157C4×Q8—151no—
158C4×Q8—152no—
159C4×Q8—301no—
160C4×Q8D3×D511yescharacteristic
161#107—151no—
162#106—152no—
163C4⋊C8—31no—
164C4⋊C8—152no—
165#103—32no—
166#103—151no—
167#103—152no—
168#103—152no—
169#103—152no—
170#103—151no—
171#97—152no—
172C4×C8—151no—
173C2×C3×C5—41no—
174C2×C3×C5—41no—
175C2×C3×C5—41no—
176C2×C3×C4—41no—
177C2×C3×C4—202no—
178C2×Dic3—42no—
179C2×Dic3—201no—
180C2×Dic3—201no—
181SL(2,𝔽3)#71111yescharacteristic
182C22×C5C22×S411yescharacteristic
183C4×C5—31no—
184C4×C5—31no—
185C4×C5—61no—
186C4×C5—122no—
187C4×C5#98412yes—
188Dic5—22no—
189Dic5—62no—
190Dic5—121no—
191Dic5—121no—
192C2×Q8—32no—
193C2×Q8—151no—
194C2×Q8—151no—
195C2×Q8C2×D3×D511yescharacteristic
196Q16—62no—
197Q16—62no—
198Q16—301no—
199Q16—301no—
200C2×C8—32no—
201C2×C8—151no—
202C2×C8—151no—
203C4⋊C4—31no—
204C4⋊C4—51no—
205C4⋊C4—61no—
206C4⋊C4—61no—
207C4⋊C4—152no—
208C4⋊C4—152no—
209C4⋊C4—151no—
210C4⋊C4—301no—
211C4⋊C4—301no—
212C4⋊C4—302no—
213C4⋊C4—302no—
214C4⋊C4—302no—
215C42—31no—
216C42—152no—
217C42—302no—
218C42—301no—
219C3×C5—41noHall
220C22×C3—41no—
221C3×C4—42no—
222C3×C4—402no—
223Dic3—82no—
224Dic3—401no—
225Dic3—401no—
226C2×C5#591911yescharacteristic
227C2×C5C2×#98411yescharacteristic
228C2×C5#592711yescharacteristic
229Q8—31no—
230Q8—62no—
231Q8—62no—
232Q8—301no—
233Q8—301no—
234Q8—302no—
235Q8#676811yescharacteristic
236C2×C4—31no—
237C2×C4—31no—
238C2×C4—52no—
239C2×C4—62no—
240C2×C4—152no—
241C2×C4—301no—
242C2×C4—301no—
243C2×C4D5×S411yescharacteristic
244C8—62no—
245C8—301no—
246C8—301no—
247C2×C3—41no—
248C2×C3—41no—
249C2×C3—41no—
250C5#8541711yescharacteristic, complemented, Sylow
251C22C2×D5×S411yescharacteristic
252C4—31no—
253C4—31no—
254C4—61no—
255C4—102no—
256C4—122no—
257C4—302no—
258C4—601no—
259C4—601no—
260C4#9189112yes—
261C3—41noSylow
262C2#1175674611yescharacteristic
263C2C2×#9189111yescharacteristic
264C2#1175677911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, prime radical, cosocleC2×C5×SL(2,𝔽3)C23
FittingC4×C5×Q8C2×D3
socleC22×C5C22×S4
hypercenterC2×C4D5×S4
hypocenterC5×SL(2,𝔽3)#41
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
250. C5#85417semidirect

Maximal subgroups

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

subgroupindex
#65904⋊C32
C4×C5⋊#2262
C5×C4⋊#2262
#117515972
#117515942
#106121963
#913844
#854175