Finite Group Databasebeta

← Dic5×#984 #14513402

Subgroups — Dic5×#984 #14513402

Order 1920.

520 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×C5×#984C211yesmaximal, characteristic
2Dic5×#41⋊C3C211yesmaximal, characteristic
3#11752145C211yesmaximal, characteristic
4#11751594C212yesmaximal, complemented
5Dic5×#226C212yesmaximal, complemented
6Dic5×#137—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C5×#984C414yescomplemented
9C2×C5×#226C2212yes—
10Dic5×Dic6—41nomaximal
11Dic5×SL(2,𝔽3)C2211yescharacteristic
12Dic5×SL(2,𝔽3)C2211yescharacteristic
13#91184C2212yes—
14C4×#984—51nomaximal, Hall
15C2×C5×#137—31no—
16#41×Dic5D311yescharacteristic
17C2×Q8×Dic5—31no—
18#65521—31no—
19#65514—31no—
20#65473—32no—
21Q16×Dic5—32no—
22#65453—32no—
23SD16×Dic5—32no—
24#65410—31no—
25M16×Dic5—31no—
26C2×C5×Dic6—41no—
27C5×#41⋊C3C2×C412yes—
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29C5×#226C2×C414yescomplemented
30C4⋊Dic15—41no—
31C3×C4×Dic5—41no—
32Dic3⋊Dic5—42no—
33Dic3×Dic5—42no—
34C2×#984D511yescharacteristic
35C4×#41⋊C3—51no—
36#5426—51no—
37#5388—52no—
38C4×#226—52no—
39C2×C5×#41C2×D311yescharacteristic
40C22×C5×Q8—31no—
41C5×#137—34no—
42C5×#137—34no—
43C2×C5×Q16—32no—
44C2×C5×SD16—32no—
45C2×C5×M16—31no—
46Q8×Dic5—32no—
47Q8×Dic5—32no—
48Q8×Dic5—61no—
49Q8×Dic5—61no—
50Q8×Dic5C2×D311yescharacteristic
51Q8×Dic5C2×D311yescharacteristic
52D4×Dic5—31no—
53D4×Dic5—31no—
54#4072—31no—
55C2×C4⋊Dic5—31no—
56C2×C4⋊Dic5—61no—
57C2×C4×Dic5—31no—
58C2×C4×Dic5—61no—
59C2×#681—31no—
60#3967—32no—
61#3967—32no—
62#3967—32no—
63#3964—32no—
64#3950—32no—
65#3949—32no—
66#3947—32no—
67C8×Dic5—32no—
68C4×#137—151noSylow
69C2×C3×C4×C5—41no—
70C2×Dic15—42no—
71C2×C5×Dic3—42no—
72C5×Dic6—44no—
73C2×C3×Dic5—41no—
74C2×C3×Dic5—41no—
75C5×SL(2,𝔽3)C22×C411yescharacteristic
76C2×#41⋊C3C2×D511yescharacteristic
77#984Dic514yesdirect product factor
78C2×#226C2×D512yes—
79C4×Dic6—201no—
80C4×SL(2,𝔽3)—51no—
81C4×SL(2,𝔽3)—51no—
82#859—52no—
83C5×#41—32no—
84C5×#41C4×D312yes—
85C2×C5×Q8—32no—
86C2×C5×Q8—34no—
87C2×C5×Q8—62no—
88C2×C5×Q8—61no—
89C2×C5×Q8C22×D311yescharacteristic
90C2×C5×D4—31no—
91C22×C4×C5—31no—
92C22×C4×C5—61no—
93C22×Dic5—31no—
94C22×Dic5—31no—
95C22×Dic5—61no—
96C5×Q16—34no—
97C5×Q16—34no—
98C5×SD16—38no—
99C5×M16—34no—
100C2×C5×C8—32no—
101C22⋊Dic5—61no—
102C4⋊Dic5—31no—
103C4⋊Dic5—31no—
104C4⋊Dic5—32no—
105C4⋊Dic5—62no—
106C4⋊Dic5—61no—
107C4⋊Dic5—62no—
108C4×Dic5—31no—
109C4×Dic5—31no—
110C4×Dic5—31no—
111C4×Dic5—62no—
112C4×Dic5—62no—
113C4×Dic5S411yescharacteristic
114#681—62no—
115C2×#168—32no—
116C2×#137—31no—
117C4×#41—51no—
118C2×C4×Q8—151no—
119#441—152no—
120#440—152no—
121C4×Q16—152no—
122C4×SD16—152no—
123#428—151no—
124#419—151no—
125#417—151no—
126C4×M16—151no—
127C22×C3×C5—41no—
128C3×C4×C5—42no—
129Dic15—82no—
130C3×Dic5—42no—
131C3×Dic5—81no—
132C5×Dic3—44no—
133C2×Dic6—41no—
134#41⋊C3C2×Dic512yes—
135C2×SL(2,𝔽3)C22×D511yescharacteristic
136#226C2×Dic514yescomplemented
137C3×C42—201no—
138C4⋊Dic3—201no—
139Dic3⋊C4—202no—
140C4×Dic3—202no—
141C23×C5—31no—
142C5×Q8—31no—
143C5×Q8—34no—
144C5×Q8—62no—
145C5×Q8—64no—
146C5×Q8C2×C4×D311yescharacteristic
147C5×D4—32no—
148C5×D4—61no—
149C2×C4×C5—31no—
150C2×C4×C5—32no—
151C2×C4×C5—32no—
152C2×C4×C5—64no—
153C2×C4×C5—62no—
154C2×C4×C5C2×S411yescharacteristic
155C2×Dic5—31no—
156C2×Dic5—31no—
157C2×Dic5—62no—
158C2×Dic5—62no—
159C2×Dic5—121no—
160C2×Dic5—122no—
161C2×Dic5C2×S411yescharacteristic
162C2×Dic5C2×S411yescharacteristic
163C5×C8—34no—
164#168—62no—
165C2×#41D3×D511yescharacteristic
166C22×Q8—31no—
167#137—34no—
168#137—34no—
169C2×Q16—32no—
170C2×SD16—32no—
171C2×M16—31no—
172C2×M16—151no—
173C4×Q8—51no—
174C4×Q8—51no—
175C4×Q8—152no—
176C4×Q8—152no—
177C4×Q8—301no—
178C4×Q8—301no—
179C4×D4—151no—
180C4×D4—151no—
181#117—151no—
182C2×C4⋊C4—151no—
183C2×C4⋊C4—301no—
184C2×C42—151no—
185C2×C42—301no—
186#107—152no—
187#106—152no—
188#103—152no—
189#103—152no—
190#103—152no—
191#102—152no—
192#97—152no—
193C4×C8—152no—
194C2×C3×C5—41no—
195C2×C3×C5—41no—
196C2×C3×C5—41no—
197C2×C3×C4—41no—
198C2×C3×C4—201no—
199C2×C3×C4—201no—
200C2×Dic3—42no—
201C2×Dic3—202no—
202Dic6—44no—
203SL(2,𝔽3)C22×Dic511yescharacteristic
204C22×C5—32no—
205C22×C5—61no—
206C22×C5—61no—
207C22×C5C22×S411yescharacteristic
208C4×C5—31no—
209C4×C5—31no—
210C4×C5—64no—
211C4×C5C4×S412yes—
212Dic5—21no—
213Dic5—61no—
214Dic5—61no—
215Dic5—122no—
216Dic5#98412yesdirect product factor
217#41—32no—
218#41D3×Dic512yes—
219C2×Q8—32no—
220C2×Q8—34no—
221C2×Q8—62no—
222C2×Q8—61no—
223C2×Q8C2×D3×D511yescharacteristic
224C2×D4—31no—
225C22×C4—31no—
226C22×C4—61no—
227C22×C4—151no—
228C22×C4—151no—
229C22×C4—301no—
230Q16—34no—
231Q16—34no—
232SD16—38no—
233M16—34no—
234M16—302no—
235C2×C8—32no—
236C2×C8—152no—
237C4⋊C4—151no—
238C4⋊C4—151no—
239C4⋊C4—152no—
240C4⋊C4—302no—
241C4⋊C4—302no—
242C4⋊C4—301no—
243C22⋊C4—301no—
244C42—51no—
245C42—151no—
246C42—151no—
247C42—151no—
248C42—302no—
249C42—302no—
250C3×C5—41noHall
251C22×C3—41no—
252C3×C4—42no—
253C3×C4—202no—
254C3×C4—401no—
255Dic3—44no—
256Dic3—402no—
257C2×C5—62no—
258C2×C5C2×C4×S411yescharacteristic
259C2×C5C2×#98411yescharacteristic
260C2×C5#592311yescharacteristic
261C23—31no—
262Q8—31no—
263Q8—34no—
264Q8—62no—
265Q8—64no—
266Q8C2×D3×Dic511yescharacteristic
267D4—32no—
268D4—61no—
269C2×C4—31no—
270C2×C4—32no—
271C2×C4—32no—
272C2×C4—51no—
273C2×C4—51no—
274C2×C4—64no—
275C2×C4—62no—
276C2×C4—151no—
277C2×C4—151no—
278C2×C4—302no—
279C2×C4—302no—
280C2×C4—601no—
281C2×C4—602no—
282C2×C4D5×S411yescharacteristic
283C8—34no—
284C8—302no—
285C2×C3—41no—
286C2×C3—41no—
287C2×C3—41no—
288C5C4×#98411yescharacteristic, complemented, Sylow
289C22—32no—
290C22—61no—
291C22—61no—
292C22C2×D5×S411yescharacteristic
293C4—31no—
294C4—31no—
295C4—52no—
296C4—64no—
297C4—101no—
298C4—301no—
299C4—301no—
300C4—602no—
301C4Dic5×S412yes—
302C3—41noSylow
303C2—62no—
304C2D5×#98411yescharacteristic
305C2#1175678211yescharacteristic
306C2C2×Dic5×S411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×S4
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FittingC2×C5×#41C2×D3
socleC22×C5C22×S4
prime radicalC2×C5×#41⋊C3C22
cosocleC2×C5×SL(2,𝔽3)C23
hypercenterC2×C4D5×S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #11751594C2semidirect
5. Dic5×#226C2semidirect
8. C5×#984C4semidirect
29. C5×#226C2×C4semidirect
77. #984Dic5direct (N × H)
136. #226C2×Dic5semidirect
216. Dic5#984direct (N × H)
288. C5C4×#984semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9842
Dic5×#41⋊C32
#117521452
#117515942
Dic5×#2262
Dic5×#1373
Dic5×Dic64
C4×#9845