Finite Group Databasebeta

← #14513475

Subgroups — #14513475

Order 1920.

434 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 63 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
1Dic5×#41⋊C3C211yesmaximal, characteristic
2#11752145C211yesmaximal, characteristic
3C5×#5426C211yesmaximal, characteristic
4#11751608C212yesmaximal, complemented
5#11751598C212yesmaximal, complemented
6#10610601—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8#91468—41nomaximal
9Dic5×SL(2,𝔽3)C2211yescharacteristic
10Dic5×SL(2,𝔽3)C2211yescharacteristic
11#91184C2212yes—
12C5×#859C2212yes—
13#85337—51nomaximal, Hall
14#41×Dic5D311yescharacteristic
15C2×#4034—31no—
16C5×#417—31no—
17#65521—31no—
18#65410—31no—
19#65407—31no—
20#65253—31no—
21#65083—32no—
22#65080—32no—
23#65050—32no—
24#65048—32no—
25C5×#41⋊C3Q812yescomplemented
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C2×#1204—42no—
28C4⋊Dic15—41no—
29C5×C4⋊Dic3—41no—
30C3×C4×Dic5—41no—
31#6668—42no—
32C4×#41⋊C3—51no—
33#5426—51no—
34#5426D511yescharacteristic
35#5391—52no—
36#5386—52no—
37C2×C5×#41C2×D311yescharacteristic
38C22×Dic10—61no—
39C2×C5×M16—31no—
40C2×C5×C4⋊C4—31no—
41Q8×Dic5C2×D311yescharacteristic
42Q8×Dic5C2×D311yescharacteristic
43D4×Dic5—31no—
44D4×Dic5—31no—
45#4072—31no—
46C2×C4⋊Dic5—31no—
47C2×#683—61no—
48C2×C4×Dic5—31no—
49C2×#681—31no—
50#4034—32no—
51#4034—32no—
52#4034—61no—
53#4034—61no—
54C5×#103—32no—
55C5×#102—32no—
56#3967—32no—
57#3964—32no—
58#3950—32no—
59#3949—32no—
60#3946—32no—
61#3946—32no—
62#3940—32no—
63#3939—32no—
64#3079—151noSylow
65C2×C3×C4×C5—41no—
66C2×Dic15—42no—
67C2×C5×Dic3—42no—
68C2×C3×Dic5—41no—
69C2×C3×Dic5—41no—
70C5×SL(2,𝔽3)C2×Q811yescharacteristic, complemented
71#1204—84no—
72C2×#41⋊C3C2×D511yescharacteristic
73#869—201no—
74C4×SL(2,𝔽3)—51no—
75C4×SL(2,𝔽3)—51no—
76#859—52no—
77#859C2×D512yes—
78C5×#41—32no—
79C5×#41Dic612yescomplemented
80C2×C5×Q8C22×D311yescharacteristic
81C2×C5×D4—31no—
82C22×C4×C5—31no—
83C22×C4×C5—61no—
84C22×Dic5—31no—
85C22×Dic5—31no—
86C22×Dic5—61no—
87C2×Dic10—62no—
88C2×Dic10—62no—
89C2×Dic10—124no—
90C5×M16—62no—
91C2×C5×C8—32no—
92C5×C4⋊C4—32no—
93C5×C4⋊C4—61no—
94C22⋊Dic5—61no—
95C4⋊Dic5—31no—
96C4⋊Dic5—31no—
97C4⋊Dic5—32no—
98C4⋊Dic5—61no—
99#683—62no—
100#683—62no—
101C4×Dic5—31no—
102C4×Dic5—31no—
103C4×Dic5—31no—
104C4×Dic5S411yescharacteristic
105#681—62no—
106C2×#168—32no—
107C2×C4⋊Q8—151no—
108C4×#41—51no—
109#477—152no—
110#476—152no—
111#475—152no—
112#474—152no—
113#428—151no—
114#428—151no—
115#423—151no—
116#417—31no—
117#417—151no—
118C22×C3×C5—41no—
119C3×C4×C5—42no—
120Dic15—82no—
121C3×Dic5—42no—
122C3×Dic5—42no—
123C5×Dic3—82no—
124C2×Dic6—202no—
125#41⋊C3Dic1012yescomplemented
126C2×SL(2,𝔽3)C22×D511yescharacteristic
127C3×C42—201no—
128C4⋊Dic3—41no—
129C4⋊Dic3—202no—
130C4⋊Dic3—201no—
131C23×C5—31no—
132C5×Q8—31no—
133C5×Q8C2×Dic611yescharacteristic
134C5×D4—32no—
135C5×D4—61no—
136C2×C4×C5—31no—
137C2×C4×C5—32no—
138C2×C4×C5—32no—
139C2×C4×C5—62no—
140C2×C4×C5—122no—
141C2×C4×C5C2×S411yescharacteristic
142C2×Dic5—31no—
143C2×Dic5—31no—
144C2×Dic5—62no—
145C2×Dic5—62no—
146C2×Dic5—62no—
147C2×Dic5—122no—
148C2×Dic5C2×S411yescharacteristic
149C2×Dic5C2×S411yescharacteristic
150Dic10—124no—
151Dic10—124no—
152C5×C8—62no—
153#168—62no—
154C2×#41D3×D511yescharacteristic
155C22×Q8—301no—
156C2×M16—31no—
157C2×M16—151no—
158C4⋊Q8—152no—
159C4⋊Q8—152no—
160C4⋊Q8—301no—
161C4⋊Q8—301no—
162C4×Q8—51no—
163C4×Q8—51no—
164C4×D4—151no—
165C4×D4—151no—
166#117—151no—
167C2×C4⋊C4—31no—
168C2×C4⋊C4—151no—
169C2×C4⋊C4—301no—
170C2×C42—151no—
171#107—152no—
172#107—152no—
173#106—152no—
174#106—152no—
175C4⋊C8—152no—
176C4⋊C8—152no—
177#103—32no—
178#103—152no—
179#102—32no—
180#102—152no—
181C2×C3×C5—41no—
182C2×C3×C5—41no—
183C2×C3×C5—41no—
184C2×C3×C4—41no—
185C2×C3×C4—201no—
186C2×C3×C4—201no—
187C2×Dic3—42no—
188C2×Dic3—202no—
189Dic6—404no—
190SL(2,𝔽3)C2×Dic1011yescharacteristic, complemented
191C22×C5—32no—
192C22×C5—61no—
193C22×C5—61no—
194C22×C5C22×S411yescharacteristic
195C4×C5—31no—
196C4×C5—31no—
197C4×C5—122no—
198C4×C5A4⋊Q812yes—
199Dic5—61no—
200Dic5—61no—
201Dic5—122no—
202Dic5#98412yes—
203Dic5#98612yes—
204#41—32no—
205#41#120412yescomplemented
206C2×Q8—302no—
207C2×Q8—302no—
208C2×Q8—604no—
209C2×Q8C2×D3×D511yescharacteristic
210C2×D4—31no—
211C22×C4—31no—
212C22×C4—61no—
213C22×C4—151no—
214C22×C4—151no—
215C22×C4—301no—
216M16—62no—
217M16—302no—
218C2×C8—32no—
219C2×C8—152no—
220C4⋊C4—32no—
221C4⋊C4—61no—
222C4⋊C4—151no—
223C4⋊C4—151no—
224C4⋊C4—152no—
225C4⋊C4—302no—
226C4⋊C4—302no—
227C4⋊C4—301no—
228C22⋊C4—301no—
229C42—51no—
230C42—151no—
231C42—151no—
232C42—151no—
233C3×C5—41noHall
234C22×C3—41no—
235C3×C4—42no—
236C3×C4—202no—
237C3×C4—202no—
238Dic3—82no—
239Dic3—402no—
240C2×C5—62no—
241C2×C5C2×A4⋊Q811yescharacteristic
242C2×C5C2×#98411yescharacteristic
243C2×C5C2×#98611yescharacteristic
244C23—31no—
245Q8—31no—
246Q8—604no—
247Q8—604no—
248Q8C2×#120411yescharacteristic
249D4—32no—
250D4—61no—
251C2×C4—31no—
252C2×C4—32no—
253C2×C4—32no—
254C2×C4—51no—
255C2×C4—51no—
256C2×C4—62no—
257C2×C4—122no—
258C2×C4—151no—
259C2×C4—151no—
260C2×C4—302no—
261C2×C4—302no—
262C2×C4—302no—
263C2×C4—602no—
264C2×C4D5×S411yescharacteristic
265C8—62no—
266C8—302no—
267C2×C3—41no—
268C2×C3—41no—
269C2×C3—41no—
270C5#8533711yescharacteristic, complemented, Sylow
271C22—32no—
272C22—61no—
273C22—61no—
274C22C2×D5×S411yescharacteristic
275C4—31no—
276C4—31no—
277C4—52no—
278C4—52no—
279C4—122no—
280C4—301no—
281C4—301no—
282C4—602no—
283C4#9189912yes—
284C3—41noSylow
285C2—62no—
286C2D5×#98411yescharacteristic
287C2D5×#98611yescharacteristic
288C2C2×#9189911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC2×C5×#41C2×D3
socleC22×C5C22×S4
prime radicalC2×C5×#41⋊C3C22
hypercenterC2×C4D5×S4
hypocenterC5×SL(2,𝔽3)C2×Q8
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
4. #11751608C2semidirect
5. #11751598C2semidirect
25. C5×#41⋊C3Q8semidirect
70. C5×SL(2,𝔽3)C2×Q8semidirect
79. C5×#41Dic6semidirect
125. #41⋊C3Dic10semidirect
190. SL(2,𝔽3)C2×Dic10semidirect
205. #41#1204semidirect
270. C5#85337semidirect

Maximal subgroups

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

subgroupindex
Dic5×#41⋊C32
#117521452
C5×#54262
#117516082
#117515982
#106106013
#914684
#853375