Finite Group Databasebeta

← #14293920

Subgroups — #14293920

Order 1920.

372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C3×C5×#492C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11751179C211yesmaximal, characteristic, complemented
4#11751171C211yesmaximal, characteristic
5#11751171C211yesmaximal, characteristic
6#11750782C211yesmaximal, characteristic, complemented
7#11746275C211yesmaximal, characteristic, complemented
8#10602054—31nomaximal, Hall
9C2×C3×C5×SD16—22no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#127C2211yescharacteristic
12#91758C2211yescharacteristic
13#91758C2211yescharacteristic
14C3×C4×C5×C8C2211yescharacteristic
15#91116—22no—
16#91116—22no—
17#91100—22no—
18#91094—22no—
19#91091—22no—
20C4×C3⋊#168C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22#71261—51nomaximal, Hall
23C5×#492D311yescharacteristic
24#65382—31no—
25#65367—31no—
26#65359—31no—
27#65359—31no—
28#64970—31no—
29#64674—31no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×Dic30—21no—
35C2×Dic30—21no—
36C3×C5×SD16—44no—
37C2×C3×C5×C8D412yes—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C2×C3⋊#168D412yes—
46C2×C3⋊#168D412yes—
47C3×#492D511yescharacteristic
48#5093—51no—
49#5078—51no—
50#5070—51no—
51#5070—51no—
52#4681—51no—
53#4454—51no—
54C2×C5×SD16—22no—
55C5×C4⋊Q8C2×D311yescharacteristic
56C5×#127C2×D311yescharacteristic
57#4015—31no—
58#4015—31no—
59C4×C5×C8C2×D311yescharacteristic
60#3964—62no—
61#3964—62no—
62#3948—62no—
63#3942—62no—
64#3939—62no—
65C4×#168—31no—
66C4×#168—31no—
67#1719—151noSylow
68C23×C3×C5—41no—
69C3×C5×Q8—42no—
70C3×C5×D4—42no—
71C3×C5×D4—42no—
72C3×C5×D4—42no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×Dic15—41no—
78C2×Dic15—41no—
79Dic30—42no—
80Dic30—42no—
81C3×C5×C8—22no—
82C3⋊#168—22no—
83C3⋊#168—22no—
84C2×C3×SD16—22no—
85C3×C4⋊Q8C2×D511yescharacteristic
86C3×#127C2×D511yescharacteristic
87#869—51no—
88#869—51no—
89C3×C4×C8C2×D511yescharacteristic
90#832—102no—
91#832—102no—
92#816—102no—
93#810—102no—
94#807—102no—
95C4×C3⋊C8—51no—
96C4×C3⋊C8—51no—
97C2×C5×Q8—21no—
98C2×C5×D4—21no—
99C2×C5×D4—21no—
100C2×C5×D4—21no—
101C2×Dic10—61no—
102C2×Dic10—61no—
103C5×SD16—44no—
104C2×C5×C8#6712yes—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C42×C5C22×D311yescharacteristic
108C4⋊Dic5—61no—
109C4⋊Dic5—61no—
110C4⋊Dic5—61no—
111C4⋊Dic5—61no—
112C2×#168—32no—
113C2×#168—32no—
114#500—151no—
115#492D1511yescharacteristic
116#487—151no—
117#487—151no—
118#486—151no—
119#486—151no—
120#322—151no—
121C22×C3×C5—81no—
122C22×C3×C5—81no—
123C22×C3×C5—81no—
124C22×C3×C5#12711yescharacteristic
125C3×C4×C5—81no—
126C3×C4×C5#13512yes—
127C3×C4×C5AGL(1,ℤ/8)12yes—
128C3×C4×C5#13712yes—
129Dic15—81no—
130Dic15—81no—
131C2×C3×Q8—21no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—21no—
135C2×Dic6—101no—
136C2×Dic6—101no—
137C3×SD16—44no—
138C2×C3×C8C22⋊D512yes—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C42C22×D511yescharacteristic
142C4⋊Dic3—101no—
143C4⋊Dic3—101no—
144C4⋊Dic3—101no—
145C4⋊Dic3—101no—
146C2×C3⋊C8—52no—
147C2×C3⋊C8—52no—
148C23×C5—41no—
149C5×Q8—42no—
150C5×D4—42no—
151C5×D4—42no—
152C5×D4—42no—
153C2×C4×C5—41no—
154C2×C4×C5D3×D411yescharacteristic
155C2×C4×C5D3×D411yescharacteristic
156C2×C4×C5C2×#6711yescharacteristic
157C2×Dic5—121no—
158C2×Dic5—121no—
159Dic10—122no—
160Dic10—122no—
161C5×C8—22no—
162#168—62no—
163#168—62no—
164C2×SD16—22no—
165C4⋊Q8—151no—
166C4⋊Q8—151no—
167C4⋊Q8C2×D1511yescharacteristic
168#127C2×D1511yescharacteristic
169#107—302no—
170#103—302no—
171#103—302no—
172#102—302no—
173#102—302no—
174C4×C8—151no—
175C4×C8—151no—
176C4×C8C2×D1511yescharacteristic
177C2×C3×C5—161no—
178C2×C3×C5#49511yescharacteristic
179C2×C3×C5#49611yescharacteristic
180C2×C3×C5#49711yescharacteristic
181C23×C3—41no—
182C3×Q8—42no—
183C3×D4—42no—
184C3×D4—42no—
185C3×D4—42no—
186C2×C3×C4—41no—
187C2×C3×C4D4×D511yescharacteristic
188C2×C3×C4D4×D511yescharacteristic
189C2×C3×C4C2×C22⋊D511yescharacteristic
190C2×Dic3—201no—
191C2×Dic3—201no—
192Dic6—202no—
193Dic6—202no—
194C3×C8—22no—
195C3⋊C8—102no—
196C3⋊C8—102no—
197C22×C5—81no—
198C22×C5—81no—
199C22×C5—81no—
200C22×C5#94011yescharacteristic
201C4×C5—81no—
202C4×C5#91512yes—
203C4×C5#91612yes—
204C4×C5#93212yes—
205Dic5—241no—
206Dic5—241no—
207C2×Q8—21no—
208C2×Q8—301no—
209C2×Q8—301no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213SD16—44no—
214C2×C8—152no—
215C2×C8—152no—
216C2×C8#122012yes—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—301no—
220C4⋊C4—301no—
221C4⋊C4—301no—
222C4⋊C4—301no—
223C42C22×D1511yescharacteristic
224C3×C5#171911yescharacteristic, complemented, Hall
225C22×C3—81no—
226C22×C3—81no—
227C22×C3—81no—
228C22×C3#408611yescharacteristic
229C3×C4—81no—
230C3×C4#406112yes—
231C3×C4#406212yes—
232C3×C4#407812yes—
233Dic3—401no—
234Dic3—401no—
235C2×C5—161no—
236C2×C5#507411yescharacteristic
237C2×C5#516711yescharacteristic
238C2×C5#516811yescharacteristic
239C23—41no—
240Q8—42no—
241Q8—602no—
242Q8—602no—
243D4—42no—
244D4—42no—
245D4—42no—
246C2×C4—41no—
247C2×C4—601no—
248C2×C4—601no—
249C2×C4D4×D1511yescharacteristic
250C2×C4D4×D1511yescharacteristic
251C2×C4C2×#122011yescharacteristic
252C8—22no—
253C8—302no—
254C8—302no—
255C2×C3—161no—
256C2×C3#6536311yescharacteristic
257C2×C3#6545611yescharacteristic
258C2×C3#6545711yescharacteristic
259C5#7126111yescharacteristic, complemented, Sylow
260C22—81no—
261C22—81no—
262C22—81no—
263C22#9182911yescharacteristic
264C4—81no—
265C4—1201no—
266C4—1201no—
267C4#9180412yes—
268C4#9180512yes—
269C4#9182112yes—
270C3#1060205411yescharacteristic, complemented, Sylow
271C2—161no—
272C2#1175117511yescharacteristic
273C2#1175126811yescharacteristic
274C2#1175126911yescharacteristic
subgroupG/H
centerC22#91829
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#492C2
socleC22×C3×C5#127
prime radicalC3×C5×#127C22
hypercenter#492D15
hypocenterC3×C5#1719
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #11751194C2semidirect
3. #11751179C2semidirect
6. #11750782C2semidirect
7. #11746275C2semidirect
224. C3×C5#1719semidirect
259. C5#71261semidirect
270. C3#10602054semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4922
#117511942
#117511792
#117511712
#117507822
#117462752
#106020543
#712615