Finite Group Databasebeta

← #14513737

Subgroups — #14513737

Order 1920.

412 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 61 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
3C4⋊(C5⋊#226)C211yesmaximal, characteristic, complemented
4C4×C5⋊#226C212yesmaximal, complemented
5#11752105C211yesmaximal, characteristic, complemented
6#10614265—31nomaximal, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C2×C5⋊#226C2212yes—
9C4×Dic30—41nomaximal
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11C4×C5×SL(2,𝔽3)C2211yescharacteristic
12#91184C2212yes—
13#85335—51nomaximal, Hall
14C4×C5×#41D311yescharacteristic
15#65804—31no—
16#65528—32no—
17#65320—31no—
18C4×#689—32no—
19#65309—31no—
20#65308—31no—
21C4×#687—32no—
22#65296—31no—
23#65285—32no—
24#65214—31no—
25C2×Dic30—41no—
26C5×#41⋊C3—21no—
27C2×C5×SL(2,𝔽3)C2311yescharacteristic
28C5⋊#226—22no—
29C3×C42×C5—41no—
30C4⋊Dic15—41no—
31#6712—42no—
32C4×Dic15—42no—
33C4×#41⋊C3D511yescharacteristic
34#5425—52no—
35C4⋊#226—51no—
36C4×#226—52no—
37#5386—51no—
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—
64C4×#168—32no—
65#3107—151noSylow
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5—41no—
68C2×C3×C4×C5—41no—
69C2×Dic15—42no—
70C2×Dic15—42no—
71Dic30—44no—
72C5×SL(2,𝔽3)#4111yescharacteristic
73C2×#41⋊C3C2×D511yescharacteristic
74C2×#226—52no—
75C4×Dic6—201no—
76C4×SL(2,𝔽3)C2×D511yescharacteristic
77C4×SL(2,𝔽3)C2×D511yescharacteristic
78#859—52no—
79C5×#41—21no—
80C5×#41—61no—
81C2×C5×Q8C22×D311yescharacteristic
82C2×C5×D4—31no—
83C22×C4×C5—31no—
84C22×C4×C5—31no—
85C22×C4×C5—31no—
86C2×Dic10—32no—
87C2×Dic10—61no—
88C5×C4⋊C4—31no—
89C5×C4⋊C4—31no—
90C5×C22⋊C4—61no—
91C42×C5—31no—
92C42×C5—31no—
93C42×C5—31no—
94C42×C5S411yescharacteristic
95C22⋊Dic5—62no—
96#689—62no—
97#689—62no—
98#687—64no—
99C4⋊Dic5—32no—
100C4⋊Dic5—61no—
101C4⋊Dic5—61no—
102C4⋊Dic5—61no—
103#683—62no—
104#683—62no—
105C4×Dic5—62no—
106C2×#168—32no—
107C2×#168—32no—
108#533—151no—
109C4×#41D1511yescharacteristic
110#485—152no—
111#475—151no—
112#474—151no—
113#462—151no—
114#461—151no—
115#452—152no—
116C4×Q16—152no—
117C4×SD16—152no—
118#431—151no—
119C22×C3×C5—41no—
120C3×C4×C5—42no—
121C3×C4×C5—42no—
122C3×C4×C5—81no—
123Dic15—44no—
124Dic15—82no—
125C2×Dic6—201no—
126#41⋊C3—21no—
127C2×SL(2,𝔽3)C22×D511yescharacteristic
128#226—102no—
129C3×C42—41no—
130C4⋊Dic3—201no—
131Dic3⋊C4—202no—
132C4×Dic3—202no—
133C23×C5—31no—
134C5×Q8—31no—
135C5×Q8#23511yescharacteristic
136C5×D4—32no—
137C5×D4—61no—
138C2×C4×C5—31no—
139C2×C4×C5—31no—
140C2×C4×C5—31no—
141C2×C4×C5—61no—
142C2×C4×C5—61no—
143C2×C4×C5—62no—
144C2×C4×C5—62no—
145C2×C4×C5C2×S411yescharacteristic
146C2×C4×C5C2×S411yescharacteristic
147C2×C4×C5C2×S411yescharacteristic
148C2×Dic5—62no—
149C2×Dic5—62no—
150Dic10—62no—
151Dic10—62no—
152Dic10—122no—
153#168—62no—
154#168—62no—
155C2×#41C2×D1511yescharacteristic
156C2×Q16—152no—
157C2×SD16—152no—
158C4⋊Q8—151no—
159C4⋊Q8—151no—
160#125—301no—
161C22⋊Q8—152no—
162C22⋊Q8—301no—
163C4×Q8—152no—
164C4×Q8—301no—
165C4×Q8C2×D1511yescharacteristic
166C4×Q8C2×D1511yescharacteristic
167C4×D4—31no—
168C4×D4—31no—
169#117—31no—
170#117—301no—
171C2×C42—31no—
172#107—152no—
173#106—152no—
174C4⋊C8—151no—
175C4⋊C8—151no—
176#103—152no—
177#103—152no—
178#103—152no—
179#102—152no—
180C22⋊C8—152no—
181C4×C8—152no—
182C2×C3×C5—41no—
183C2×C3×C5—41no—
184C2×C3×C5—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×Dic3—202no—
189C2×Dic3—202no—
190Dic6—204no—
191SL(2,𝔽3)#70911yescharacteristic
192C22×C5—61no—
193C22×C5—61no—
194C22×C5—61no—
195C22×C5C22×S411yescharacteristic
196C4×C5—21no—
197C4×C5—31no—
198C4×C5—31no—
199C4×C5—61no—
200C4×C5—61no—
201C4×C5#98412yes—
202C4×C5#98512yes—
203Dic5—122no—
204Dic5—122no—
205#41—21no—
206#41—61no—
207C2×Q8—152no—
208C2×Q8—301no—
209C2×Q8C22×D1511yescharacteristic
210C2×D4—31no—
211C22×C4—31no—
212C22×C4—31no—
213C22×C4—31no—
214Q16—302no—
215Q16—302no—
216SD16—304no—
217C2×C8—152no—
218C2×C8—152no—
219C4⋊C4—31no—
220C4⋊C4—31no—
221C4⋊C4—152no—
222C4⋊C4—301no—
223C4⋊C4—301no—
224C4⋊C4—302no—
225C4⋊C4—302no—
226C4⋊C4—301no—
227C22⋊C4—61no—
228C22⋊C4—302no—
229C42—31no—
230C42—31no—
231C42—31no—
232C42—302no—
233C42C5⋊S411yescharacteristic
234C3×C5—41noHall
235C22×C3—41no—
236C3×C4—42no—
237C3×C4—42no—
238C3×C4—81no—
239Dic3—204no—
240Dic3—402no—
241C2×C5—121no—
242C2×C5#591211yescharacteristic
243C2×C5C2×#98411yescharacteristic
244C2×C5C2×#98511yescharacteristic
245C23—31no—
246Q8—31no—
247Q8—302no—
248Q8—302no—
249Q8—602no—
250Q8#681711yescharacteristic
251D4—32no—
252D4—61no—
253C2×C4—31no—
254C2×C4—31no—
255C2×C4—31no—
256C2×C4—61no—
257C2×C4—61no—
258C2×C4—62no—
259C2×C4—62no—
260C2×C4—302no—
261C2×C4—302no—
262C2×C4C2×C5⋊S411yescharacteristic
263C2×C4C2×C5⋊S411yescharacteristic
264C2×C4C2×C5⋊S411yescharacteristic
265C8—302no—
266C8—302no—
267C2×C3—41no—
268C2×C3—41no—
269C2×C3—41no—
270C5#8533511yescharacteristic, complemented, Sylow
271C22—61no—
272C22—61no—
273C22—61no—
274C22C22×C5⋊S411yescharacteristic
275C4—21no—
276C4—31no—
277C4—31no—
278C4—61no—
279C4—61no—
280C4—602no—
281C4—602no—
282C4#9195412yes—
283C4#9195512yes—
284C3—41noSylow
285C2—121no—
286C2#1175689611yescharacteristic
287C2C2×#9195411yescharacteristic
288C2C2×#9195511yescharacteristic
subgroupG/H
centerC2×C4C2×C5⋊S4
commutator, cosocleC2×C5×SL(2,𝔽3)C23
FrattiniC22C22×C5⋊S4
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 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. C4⋊(C5⋊#226)C2semidirect
4. C4×C5⋊#226C2semidirect
5. #11752105C2semidirect
270. C5#85335semidirect

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
C4⋊(C5⋊#226)2
C4×C5⋊#2262
#117521052
#106142653
C4×Dic304
#853355