Finite Group Databasebeta

← #14513740

Subgroups — #14513740

Order 1920.

394 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C4×C5×#41⋊C3C211yesmaximal, characteristic
2#11752144C212yesmaximal
3#11752110C211yesmaximal, characteristic, complemented
4C4⋊(C5⋊#226)C211yesmaximal, characteristic, complemented
5#11752107C212yesmaximal, complemented
6#10614266—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C2×C5⋊#226C2212yes—
9#91759—41nomaximal
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11C4×C5×SL(2,𝔽3)C2211yescharacteristic
12#91184C2212yes—
13#85338—51nomaximal, Hall
14C4×C5×#41D311yescharacteristic
15#65804—31no—
16#65528—32no—
17#65320—31no—
18#65319—32no—
19#65310—31no—
20#65308—31no—
21#65307—32no—
22#65297—31no—
23#65285—32no—
24#65215—31no—
25C5×#41⋊C3—21no—
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C5⋊#226—22no—
28C3×C42×C5—41no—
29C4⋊Dic15—41no—
30C4⋊Dic15—41no—
31#6712—42no—
32#6712—42no—
33C4×#41⋊C3D511yescharacteristic
34#5425—52no—
35#5391—51no—
36C4⋊#226—51no—
37#5388—52no—
38C2×C5×#41C2×D311yescharacteristic
39C4×C5×Q8C2×D311yescharacteristic
40C4×C5×Q8C2×D311yescharacteristic
41C4×C5×D4—31no—
42C4×C5×D4—31no—
43C5×#117—31no—
44C2×C42×C5—31no—
45C2×#689—32no—
46C2×#687—32no—
47#4072—61no—
48#4070—32no—
49#4070—61no—
50#4016—61no—
51#4015—31no—
52#4015—31no—
53C4×Dic10—32no—
54C4×Dic10—61no—
55#3967—32no—
56#3964—32no—
57C22⋊#168—32no—
58#3942—32no—
59#3942—32no—
60#3940—32no—
61#3939—32no—
62C4⋊#168—31no—
63C4⋊#168—31no—
64#3935—32no—
65#3116—151noSylow
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5—41no—
68C2×C3×C4×C5—41no—
69C2×Dic15—42no—
70C2×Dic15—42no—
71C5×SL(2,𝔽3)#4111yescharacteristic
72C2×#41⋊C3C2×D511yescharacteristic
73C2×#226—52no—
74#870—201no—
75C4×SL(2,𝔽3)C2×D511yescharacteristic
76C4×SL(2,𝔽3)C2×D511yescharacteristic
77#859—52no—
78C5×#41—21no—
79C5×#41—61no—
80C2×C5×Q8C22×D311yescharacteristic
81C2×C5×D4—31no—
82C22×C4×C5—31no—
83C22×C4×C5—31no—
84C22×C4×C5—31no—
85C2×Dic10—32no—
86C2×Dic10—61no—
87C5×C4⋊C4—31no—
88C5×C4⋊C4—31no—
89C5×C22⋊C4—61no—
90C42×C5—31no—
91C42×C5—31no—
92C42×C5—31no—
93C42×C5S411yescharacteristic
94C22⋊Dic5—62no—
95#689—62no—
96#689—62no—
97#687—64no—
98C4⋊Dic5—32no—
99C4⋊Dic5—61no—
100C4⋊Dic5—61no—
101C4⋊Dic5—61no—
102#683—62no—
103#683—62no—
104C4×Dic5—62no—
105C2×#168—32no—
106C2×#168—32no—
107#533—151no—
108C4×#41D1511yescharacteristic
109#485—152no—
110#477—151no—
111#476—151no—
112#462—151no—
113#461—151no—
114#452—152no—
115#441—152no—
116#440—152no—
117#432—151no—
118C22×C3×C5—41no—
119C3×C4×C5—42no—
120C3×C4×C5—81no—
121C3×C4×C5—81no—
122Dic15—82no—
123Dic15—82no—
124#41⋊C3—21no—
125C2×SL(2,𝔽3)C22×D511yescharacteristic
126#226—102no—
127C3×C42—41no—
128C4⋊Dic3—201no—
129C4⋊Dic3—201no—
130Dic3⋊C4—202no—
131Dic3⋊C4—202no—
132C23×C5—31no—
133C5×Q8—31no—
134C5×Q8#23511yescharacteristic
135C5×D4—32no—
136C5×D4—61no—
137C2×C4×C5—31no—
138C2×C4×C5—31no—
139C2×C4×C5—31no—
140C2×C4×C5—61no—
141C2×C4×C5—61no—
142C2×C4×C5—62no—
143C2×C4×C5—121no—
144C2×C4×C5C2×S411yescharacteristic
145C2×C4×C5C2×S411yescharacteristic
146C2×C4×C5C2×S411yescharacteristic
147C2×Dic5—62no—
148C2×Dic5—62no—
149Dic10—62no—
150Dic10—62no—
151Dic10—122no—
152#168—62no—
153#168—62no—
154C2×#41C2×D1511yescharacteristic
155C2×Q16—152no—
156C2×SD16—152no—
157C4⋊Q8—151no—
158C4⋊Q8—151no—
159#125—301no—
160C22⋊Q8—152no—
161C22⋊Q8—301no—
162C4×Q8—152no—
163C4×Q8—301no—
164C4×Q8C2×D1511yescharacteristic
165C4×Q8C2×D1511yescharacteristic
166C4×D4—31no—
167C4×D4—31no—
168#117—31no—
169#117—301no—
170C2×C42—31no—
171#107—152no—
172#106—152no—
173C4⋊C8—151no—
174C4⋊C8—151no—
175#103—152no—
176#103—152no—
177#103—152no—
178#102—152no—
179C22⋊C8—152no—
180#97—152no—
181C2×C3×C5—41no—
182C2×C3×C5—41no—
183C2×C3×C5—41no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×Dic3—202no—
188C2×Dic3—202no—
189SL(2,𝔽3)#70911yescharacteristic
190C22×C5—61no—
191C22×C5—61no—
192C22×C5—61no—
193C22×C5C22×S411yescharacteristic
194C4×C5—21no—
195C4×C5—21no—
196C4×C5—31no—
197C4×C5—31no—
198C4×C5—61no—
199C4×C5—61no—
200C4×C5#98412yes—
201Dic5—122no—
202Dic5—122no—
203#41—21no—
204#41—61no—
205C2×Q8—152no—
206C2×Q8—301no—
207C2×Q8C22×D1511yescharacteristic
208C2×D4—31no—
209C22×C4—31no—
210C22×C4—31no—
211C22×C4—31no—
212Q16—302no—
213Q16—302no—
214SD16—304no—
215C2×C8—152no—
216C2×C8—152no—
217C4⋊C4—31no—
218C4⋊C4—31no—
219C4⋊C4—152no—
220C4⋊C4—301no—
221C4⋊C4—301no—
222C4⋊C4—301no—
223C4⋊C4—302no—
224C4⋊C4—302no—
225C22⋊C4—61no—
226C22⋊C4—302no—
227C42—31no—
228C42—31no—
229C42—31no—
230C42—302no—
231C42C5⋊S411yescharacteristic
232C3×C5—41noHall
233C22×C3—41no—
234C3×C4—42no—
235C3×C4—81no—
236C3×C4—81no—
237Dic3—402no—
238Dic3—402no—
239C2×C5—121no—
240C2×C5#591211yescharacteristic
241C2×C5C2×#98411yescharacteristic
242C2×C5#592311yescharacteristic
243C23—31no—
244Q8—31no—
245Q8—302no—
246Q8—302no—
247Q8—602no—
248Q8#681711yescharacteristic
249D4—32no—
250D4—61no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—61no—
255C2×C4—61no—
256C2×C4—62no—
257C2×C4—121no—
258C2×C4—302no—
259C2×C4—302no—
260C2×C4C2×C5⋊S411yescharacteristic
261C2×C4C2×C5⋊S411yescharacteristic
262C2×C4C2×C5⋊S411yescharacteristic
263C8—302no—
264C8—302no—
265C2×C3—41no—
266C2×C3—41no—
267C2×C3—41no—
268C5#8533811yescharacteristic, complemented, Sylow
269C22—61no—
270C22—61no—
271C22—61no—
272C22C22×C5⋊S411yescharacteristic
273C4—21no—
274C4—21no—
275C4—31no—
276C4—31no—
277C4—61no—
278C4—61no—
279C4—602no—
280C4—602no—
281C4#9195412yes—
282C3—41noSylow
283C2—121no—
284C2#1175689611yescharacteristic
285C2C2×#9195411yescharacteristic
286C2#1175690711yescharacteristic
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC4×C5×#41D3
socleC22×C5C22×S4
prime radicalC2×C5×#41⋊C3C22
hypercenterC42C5⋊S4
hypocenterC5×SL(2,𝔽3)#41
LCSG ▷ C2×C5×SL(2,𝔽3) ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #11752110C2semidirect
4. C4⋊(C5⋊#226)C2semidirect
5. #11752107C2semidirect
268. C5#85338semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#41⋊C32
#117521442
#117521102
C4⋊(C5⋊#226)2
#117521072
#106142663
#917594
#853385