Finite Group Databasebeta

← D5×#5386 #14512793

Subgroups — D5×#5386 #14512793

Order 1920.

534 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 71 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×D5×SL(2,𝔽3)C211yesmaximal, characteristic
2#11752105C211yesmaximal, characteristic, complemented
3C5×#5386C211yesmaximal, characteristic, complemented
4D5×#859C212yesmaximal
5#11751608C212yesmaximal, complemented
6D5×#475—31nomaximal, Hall
7C2×D5×Dic6—41nomaximal
8C2×D5×SL(2,𝔽3)C2211yescharacteristic
9C4×C5×SL(2,𝔽3)C2211yescharacteristic
10Dic5×SL(2,𝔽3)C2211yescharacteristic
11#91184C2212yes—
12C5×#859C2212yes—
13C2×#5386—51nomaximal, Hall
14D5×C4⋊Q8—31no—
15C4×Q8×D5D311yescharacteristic
16C5×#475—31no—
17#65383—31no—
18#65309—31no—
19D5×#106—32no—
20#65143—32no—
21#65140—31no—
22D5×C4⋊C8—31no—
23D5×#103—32no—
24#65080—32no—
25C2×Dic30—41no—
26C2×C5×Dic6—41no—
27C2×C3×C4×D5—41no—
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29C2×#1204—42no—
30C2×D5×Dic3—42no—
31D5×Dic6—48no—
32D5×SL(2,𝔽3)Q812yescomplemented
33C2×C4×SL(2,𝔽3)—51no—
34C2×#859—52no—
35#5386—51no—
36#5386—52no—
37#5386D511yescharacteristic, direct product factor
38C2×Q8×D5—61no—
39C2×Q8×D5C2×D311yescharacteristic
40C5×C4⋊Q8—31no—
41C4×C5×Q8C2×D311yescharacteristic
42Q8×Dic5C2×D311yescharacteristic
43#4090—61no—
44C2×C8×D5—32no—
45D5×C4⋊C4—31no—
46D5×C4⋊C4—32no—
47D5×C4⋊C4—61no—
48#4034—32no—
49#4034—61no—
50#4033—31no—
51C42×D5—31no—
52#4015—31no—
53C4×Dic10—31no—
54C5×#106—32no—
55C5×C4⋊C8—31no—
56C5×#103—32no—
57#3967—32no—
58#3949—32no—
59#3948—32no—
60#3946—32no—
61#3942—32no—
62#3940—32no—
63#3940—32no—
64C4⋊#168—31no—
65C2×#475—151noSylow
66C22×C3×D5—41no—
67C2×C3×C4×C5—41no—
68C2×Dic15—42no—
69Dic30—44no—
70C2×C5×Dic3—42no—
71C5×Dic6—44no—
72C2×C3×Dic5—41no—
73C3×C4×D5—44no—
74C5×SL(2,𝔽3)C2×Q811yescharacteristic, complemented
75#1204—48no—
76D5×Dic3—48no—
77C22×Dic6—201no—
78C22×SL(2,𝔽3)—51no—
79C4×SL(2,𝔽3)—51no—
80C4×SL(2,𝔽3)C2×D511yescharacteristic
81#859—52no—
82#859C2×D512yes—
83C2×C5×Q8—61no—
84C2×C5×Q8C22×D311yescharacteristic
85Q8×D5—32no—
86Q8×D5—124no—
87Q8×D5Dic612yescomplemented
88C2×C4×D5—31no—
89C2×C4×D5—31no—
90C2×C4×D5—62no—
91C2×C4×D5S411yescharacteristic
92C2×Dic10—31no—
93C2×Dic10—61no—
94C2×Dic10—62no—
95C2×C5×C8—32no—
96C5×C4⋊C4—31no—
97C5×C4⋊C4—32no—
98C5×C4⋊C4—61no—
99C42×C5—31no—
100C4⋊Dic5—31no—
101C4⋊Dic5—32no—
102C4⋊Dic5—61no—
103#683—61no—
104#683—62no—
105#683—62no—
106C4×Dic5—31no—
107C4×Dic5—31no—
108C4×Dic5—31no—
109C2×#168—32no—
110C8×D5—64no—
111C2×C4⋊Q8—151no—
112C2×C4×Q8—51no—
113#475—31no—
114#475—152no—
115#475—151no—
116#475—152no—
117#475—151no—
118#475—151no—
119C2×#106—152no—
120C2×C4⋊C8—151no—
121C2×#103—152no—
122C22×C3×C5—41no—
123C2×C3×D5—42no—
124C2×C3×D5—42no—
125C2×C3×D5—42no—
126C3×C4×C5—42no—
127Dic15—44no—
128C3×Dic5—42no—
129C5×Dic3—44no—
130C22×C3×C4—201no—
131C22×Dic3—202no—
132C2×Dic6—41no—
133C2×Dic6—202no—
134C2×Dic6—201no—
135C2×Dic6—208no—
136C2×SL(2,𝔽3)—52no—
137C2×SL(2,𝔽3)C22×D511yescharacteristic
138C22×D5C2×S411yescharacteristic
139C5×Q8—31no—
140C5×Q8—122no—
141C5×Q8C2×Dic611yescharacteristic, complemented
142C2×C4×C5—31no—
143C2×C4×C5—31no—
144C2×C4×C5—62no—
145C2×C4×C5C2×S411yescharacteristic
146C2×Dic5—31no—
147C2×Dic5—31no—
148C2×Dic5—62no—
149C2×Dic5C2×S411yescharacteristic
150C4×D5—32no—
151C4×D5—32no—
152C4×D5—62no—
153C4×D5—124no—
154C4×D5GL(2,𝔽3)14yes—
155Dic10—32no—
156Dic10—61no—
157Dic10—122no—
158Dic10—124no—
159C5×C8—62no—
160#168—62no—
161C22×Q8—51no—
162C22×Q8—301no—
163C22×C8—152no—
164C4⋊Q8—31no—
165C4⋊Q8—151no—
166C4⋊Q8—152no—
167C4⋊Q8—301no—
168C4⋊Q8—301no—
169C4×Q8—51no—
170C4×Q8—151no—
171C4×Q8—151no—
172C4×Q8D3×D511yescharacteristic
173C2×C4⋊C4—151no—
174C2×C4⋊C4—152no—
175C2×C4⋊C4—301no—
176C2×C42—151no—
177#106—32no—
178#106—152no—
179#106—152no—
180#106—152no—
181C4⋊C8—31no—
182C4⋊C8—151no—
183C4⋊C8—152no—
184#103—32no—
185#103—152no—
186#103—152no—
187#103—152no—
188C2×C3×C5—41no—
189C2×C3×C5—41no—
190C2×C3×C5—41no—
191C3×D5—44no—
192C23×C3—201no—
193C2×C3×C4—41no—
194C2×C3×C4—204no—
195C2×C3×C4—201no—
196C2×Dic3—42no—
197C2×Dic3—202no—
198C2×Dic3—208no—
199Dic6—44no—
200Dic6—208no—
201Dic6—204no—
202SL(2,𝔽3)Q8×D511yescharacteristic, complemented
203C22×C5C22×S411yescharacteristic
204C2×D5A4⋊Q812yes—
205C2×D5C2×GL(2,𝔽3)12yes—
206C2×D5#98412yes—
207C4×C5—31no—
208C4×C5—31no—
209C4×C5—61no—
210C4×C5—122no—
211C4×C5C2×GL(2,𝔽3)12yes—
212Dic5—32no—
213Dic5—61no—
214Dic5—122no—
215Dic5C2×GL(2,𝔽3)12yes—
216C2×Q8—52no—
217C2×Q8—61no—
218C2×Q8—151no—
219C2×Q8—152no—
220C2×Q8—302no—
221C2×Q8—301no—
222C2×Q8—604no—
223C2×Q8C2×D3×D511yescharacteristic
224C22×C4—51no—
225C22×C4—151no—
226C22×C4—151no—
227C22×C4—302no—
228C2×C8—32no—
229C2×C8—152no—
230C2×C8—304no—
231C4⋊C4—31no—
232C4⋊C4—32no—
233C4⋊C4—61no—
234C4⋊C4—151no—
235C4⋊C4—152no—
236C4⋊C4—301no—
237C4⋊C4—301no—
238C4⋊C4—302no—
239C4⋊C4—302no—
240C42—31no—
241C42—151no—
242C42—151no—
243C42—151no—
244C3×C5—41noHall
245C22×C3—41no—
246C22×C3—202no—
247C22×C3—202no—
248C22×C3—202no—
249C3×C4—42no—
250C3×C4—202no—
251Dic3—44no—
252Dic3—204no—
253C2×C5C2×A4⋊Q811yescharacteristic
254C2×C5C22×GL(2,𝔽3)11yescharacteristic
255C2×C5C2×#98411yescharacteristic
256D5#538614yesdirect product factor
257C23—51no—
258Q8—31no—
259Q8—122no—
260Q8—152no—
261Q8—301no—
262Q8—604no—
263Q8—602no—
264Q8D5×Dic611yescharacteristic, complemented
265C2×C4—31no—
266C2×C4—31no—
267C2×C4—51no—
268C2×C4—54no—
269C2×C4—62no—
270C2×C4—152no—
271C2×C4—152no—
272C2×C4—151no—
273C2×C4—151no—
274C2×C4—302no—
275C2×C4—302no—
276C2×C4—604no—
277C2×C4D5×S411yescharacteristic
278C8—62no—
279C8—302no—
280C2×C3—41no—
281C2×C3—41no—
282C2×C3—41no—
283C2×C3—204no—
284C5C2×#538611yescharacteristic, complemented, Sylow
285C22—52no—
286C22—52no—
287C22—52no—
288C22C2×D5×S411yescharacteristic
289C4—31no—
290C4—31no—
291C4—52no—
292C4—61no—
293C4—122no—
294C4—152no—
295C4—301no—
296C4—602no—
297C4D5×GL(2,𝔽3)12yes—
298C3—41noSylow
299C2—54no—
300C2D5×A4⋊Q811yescharacteristic
301C2C2×D5×GL(2,𝔽3)11yescharacteristic
302C2D5×#98411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FittingC4×C5×Q8C2×D3
socleC22×C5C22×S4
prime radicalC2×D5×SL(2,𝔽3)C22
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
2. #11752105C2semidirect
3. C5×#5386C2semidirect
5. #11751608C2semidirect
32. D5×SL(2,𝔽3)Q8semidirect
37. #5386D5direct (N × H)
74. C5×SL(2,𝔽3)C2×Q8semidirect
87. Q8×D5Dic6semidirect
141. C5×Q8C2×Dic6semidirect
202. SL(2,𝔽3)Q8×D5semidirect
256. D5#5386direct (N × H)
264. Q8D5×Dic6semidirect
284. C5C2×#5386semidirect

Maximal subgroups

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

subgroupindex
C4×D5×SL(2,𝔽3)2
#117521052
C5×#53862
D5×#8592
#117516082
D5×#4753
C2×D5×Dic64
C2×#53865