Finite Group Databasebeta

← C4×#91954 #14513735

Subgroups — C4×#91954 #14513735

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×#91954C211yesmaximal, characteristic
2C4×C5×#41⋊C3C211yesmaximal, characteristic
3#11752145C211yesmaximal, characteristic
4#11752107C212yesmaximal, complemented
5C4×C5⋊#226C212yesmaximal, complemented
6C4×#4097—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8#91954C414yesdirect product factor
9C2×C5⋊#226C2212yes—
10C4×Dic30—41nomaximal
11C4×C5×SL(2,𝔽3)C2211yescharacteristic
12C4×C5×SL(2,𝔽3)C2211yescharacteristic
13#91184C2212yes—
14C4×#984—51nomaximal, Hall
15C4×C5×#41D311yescharacteristic
16C2×#4097—31no—
17C2×C4×Dic10—31no—
18#65521—31no—
19#65319—32no—
20C4×#689—32no—
21#65307—32no—
22C4×#687—32no—
23#65293—31no—
24#65284—31no—
25C4×#681—31no—
26C2×Dic30—41no—
27C5×#41⋊C3C2×C412yes—
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29C5⋊#226C2×C414yescomplemented
30C3×C42×C5—41no—
31C4⋊Dic15—41no—
32#6712—42no—
33C4×Dic15—42no—
34C2×#984—51no—
35C4×#41⋊C3D511yescharacteristic
36#5426—51no—
37#5388—52no—
38C4×#226—52no—
39C2×C5×#41C2×D311yescharacteristic
40C22×Dic10—31no—
41C4×C5×Q8C2×D311yescharacteristic
42C4×C5×Q8C2×D311yescharacteristic
43C4×C5×D4—31no—
44C4×C5×D4—31no—
45C5×#117—31no—
46C2×C42×C5—31no—
47#4097—34no—
48#4097—34no—
49C2×#689—32no—
50C2×#687—32no—
51C2×C4⋊Dic5—31no—
52C2×#683—61no—
53C2×C4×Dic5—61no—
54C2×#681—31no—
55C2×#681—31no—
56C4×Dic10—32no—
57C4×Dic10—32no—
58C4×Dic10—61no—
59C4×Dic10—61no—
60#3967—32no—
61#3964—32no—
62#3942—32no—
63#3942—32no—
64#3940—32no—
65#3939—32no—
66#3935—32no—
67C4×#168—32no—
68C4×#137—151noSylow
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×Dic15—42no—
73C2×Dic15—42no—
74Dic30—44no—
75C5×SL(2,𝔽3)C22×C411yescharacteristic
76C2×#41⋊C3C2×D511yescharacteristic
77#984—54no—
78C2×#226—52no—
79C4×Dic6—201no—
80C4×SL(2,𝔽3)C2×D511yescharacteristic
81C4×SL(2,𝔽3)C2×D511yescharacteristic
82#859—52no—
83C5×#41—32no—
84C5×#41C4×D312yes—
85C2×C5×Q8C22×D311yescharacteristic
86C2×C5×D4—31no—
87C22×C4×C5—31no—
88C22×C4×C5—31no—
89C22×C4×C5—31no—
90C22×Dic5—61no—
91C22×Dic5—61no—
92C2×Dic10—34no—
93C2×Dic10—32no—
94C2×Dic10—62no—
95C2×Dic10—61no—
96C5×C4⋊C4—31no—
97C5×C4⋊C4—31no—
98C5×C22⋊C4—61no—
99C42×C5—31no—
100C42×C5—31no—
101C42×C5—31no—
102C42×C5S411yescharacteristic
103#689—34no—
104#689—34no—
105#687—38no—
106C4⋊Dic5—32no—
107C4⋊Dic5—61no—
108#683—62no—
109#683—62no—
110C4×Dic5—62no—
111C4×Dic5—62no—
112#681—34no—
113#681—62no—
114C2×#168—32no—
115C2×#168—32no—
116C2×#137—151no—
117C4×#41D1511yescharacteristic
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—
129C3×C4×C5—42no—
130C3×C4×C5—81no—
131Dic15—44no—
132Dic15—82no—
133C2×Dic6—201no—
134#41⋊C3C4×D512yes—
135C2×SL(2,𝔽3)C22×D511yescharacteristic
136#226—54no—
137C3×C42—41no—
138C4⋊Dic3—201no—
139Dic3⋊C4—202no—
140C4×Dic3—202no—
141C23×C5—31no—
142C5×Q8—31no—
143C5×Q8C2×C4×D311yescharacteristic
144C5×D4—32no—
145C5×D4—61no—
146C2×C4×C5—31no—
147C2×C4×C5—32no—
148C2×C4×C5—32no—
149C2×C4×C5—31no—
150C2×C4×C5—31no—
151C2×C4×C5—62no—
152C2×C4×C5—121no—
153C2×C4×C5C2×S411yescharacteristic
154C2×C4×C5C2×S411yescharacteristic
155C2×C4×C5C2×S411yescharacteristic
156C2×Dic5—64no—
157C2×Dic5—62no—
158C2×Dic5—62no—
159C2×Dic5—122no—
160Dic10—34no—
161Dic10—62no—
162Dic10—64no—
163#168—34no—
164#168—62no—
165C2×#41C2×D1511yescharacteristic
166C22×Q8—151no—
167#137—154no—
168#137—154no—
169C2×Q16—152no—
170C2×SD16—152no—
171C2×M16—151no—
172C2×M16—151no—
173C4×Q8—152no—
174C4×Q8—152no—
175C4×Q8—301no—
176C4×Q8—301no—
177C4×Q8C2×D1511yescharacteristic
178C4×Q8C2×D1511yescharacteristic
179C4×D4—31no—
180C4×D4—31no—
181#117—31no—
182C2×C4⋊C4—151no—
183C2×C4⋊C4—301no—
184C2×C42—31no—
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—41no—
199C2×C3×C4—41no—
200C2×Dic3—202no—
201C2×Dic3—202no—
202Dic6—204no—
203SL(2,𝔽3)C2×C4×D511yescharacteristic
204C22×C5—32no—
205C22×C5—61no—
206C22×C5—61no—
207C22×C5C22×S411yescharacteristic
208C4×C5—21no—
209C4×C5—31no—
210C4×C5—31no—
211C4×C5—61no—
212C4×C5—61no—
213C4×C5C4×S412yes—
214C4×C5#98412yescomplemented
215Dic5—64no—
216Dic5—122no—
217#41—32no—
218#41C4×D1512yes—
219C2×Q8—152no—
220C2×Q8—154no—
221C2×Q8—302no—
222C2×Q8—301no—
223C2×Q8C22×D1511yescharacteristic
224C2×D4—31no—
225C22×C4—31no—
226C22×C4—31no—
227C22×C4—31no—
228C22×C4—301no—
229C22×C4—301no—
230Q16—154no—
231Q16—154no—
232SD16—158no—
233M16—154no—
234M16—302no—
235C2×C8—152no—
236C2×C8—152no—
237C4⋊C4—31no—
238C4⋊C4—31no—
239C4⋊C4—152no—
240C4⋊C4—302no—
241C4⋊C4—301no—
242C4⋊C4—302no—
243C22⋊C4—61no—
244C42—31no—
245C42—31no—
246C42—31no—
247C42—302no—
248C42—302no—
249C42C5⋊S411yescharacteristic
250C3×C5—41noHall
251C22×C3—41no—
252C3×C4—42no—
253C3×C4—42no—
254C3×C4—81no—
255Dic3—204no—
256Dic3—402no—
257C2×C5—62no—
258C2×C5C2×C4×S411yescharacteristic
259C2×C5C2×#98411yescharacteristic
260C2×C5#592311yescharacteristic
261C23—31no—
262Q8—31no—
263Q8—154no—
264Q8—302no—
265Q8—304no—
266Q8C2×C4×D1511yescharacteristic
267D4—32no—
268D4—61no—
269C2×C4—31no—
270C2×C4—32no—
271C2×C4—32no—
272C2×C4—31no—
273C2×C4—31no—
274C2×C4—62no—
275C2×C4—121no—
276C2×C4—304no—
277C2×C4—302no—
278C2×C4—302no—
279C2×C4—602no—
280C2×C4C2×C5⋊S411yescharacteristic
281C2×C4C2×C5⋊S411yescharacteristic
282C2×C4C2×C5⋊S411yescharacteristic
283C8—154no—
284C8—302no—
285C2×C3—41no—
286C2×C3—41no—
287C2×C3—41no—
288C5C4×#98411yescharacteristic, complemented, Sylow
289C22—32no—
290C22—61no—
291C22—61no—
292C22C22×C5⋊S411yescharacteristic
293C4—21no—
294C4—31no—
295C4—31no—
296C4—61no—
297C4—61no—
298C4—304no—
299C4—602no—
300C4C4×C5⋊S412yes—
301C4#9195412yesdirect product factor
302C3—41noSylow
303C2—62no—
304C2C2×C4×C5⋊S411yescharacteristic
305C2C2×#9195411yescharacteristic
306C2#1175690711yescharacteristic
subgroupG/H
centerC2×C4C2×C5⋊S4
commutator, hypocenterC5×SL(2,𝔽3)C22×C4
FrattiniC22C22×C5⋊S4
FittingC4×C5×#41D3
socleC22×C5C22×S4
prime radicalC2×C5×#41⋊C3C22
cosocleC2×C5×SL(2,𝔽3)C23
hypercenterC42C5⋊S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #11752107C2semidirect
5. C4×C5⋊#226C2semidirect
8. #91954C4direct (N × H)
29. C5⋊#226C2×C4semidirect
214. C4×C5#984semidirect
288. C5C4×#984semidirect
301. C4#91954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#919542
C4×C5×#41⋊C32
#117521452
#117521072
C4×C5⋊#2262
C4×#40973
C4×Dic304
C4×#9845