Finite Group Databasebeta

← #14293665

Subgroups — #14293665

Order 1920.

396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 103 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×#487C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic
3#11751186C211yesmaximal, characteristic
4#11751181C211yesmaximal, characteristic, complemented
5#11751179C211yesmaximal, characteristic, complemented
6#11750794C211yesmaximal, characteristic
7#11746275C211yesmaximal, characteristic, complemented
8#10602009—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×C4⋊Q8C2211yescharacteristic
11C2×#6717—22no—
12C2×#6706—22no—
13#91763C2211yescharacteristic
14#91758C2211yescharacteristic
15C3×C5×#103—22no—
16C3×C4×C5×C8C2211yescharacteristic
17#91093—22no—
18#91092—22no—
19#91091—22no—
20C4×C3⋊#168C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22#71216—51nomaximal, Hall
23C5×#487D311yescharacteristic, complemented
24#65377—31no—
25#65374—31no—
26#65368—31no—
27#65367—31no—
28#64982—31no—
29#64674—31no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×Q8—21no—
32C2×D60—21no—
33C2×D60—21no—
34C2×D60—21no—
35C2×Dic30—21no—
36C2×C3×C5×C8D412yes—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42#6717—44no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C2×C3⋊#168D412yes—
46C2×C3⋊#168D412yes—
47#6706—44no—
48C3×#487D511yescharacteristic, complemented
49#5088—51no—
50#5085—51no—
51#5080—51no—
52#5078—51no—
53#4693—51no—
54#4454—51no—
55C5×C4⋊Q8C2×D311yescharacteristic
56C5×C4⋊Q8C2×D311yescharacteristic
57C2×#688—62no—
58C2×#677—62no—
59#4020—31no—
60#4015—31no—
61C5×#103—22no—
62C4×C5×C8C2×D311yescharacteristic
63#3941—62no—
64#3940—62no—
65#3939—62no—
66C4×#168—31no—
67C4×#168—31no—
68#1714—151noSylow
69C22×D15—41no—
70C3×C5×Q8—42no—
71C3×C5×Q8—42no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×Dic15—41no—
78D60—42no—
79D60—42no—
80D60—42no—
81Dic30—42no—
82C3×C5×C8—22no—
83C3⋊#168—22no—
84C3⋊#168SD1614yescomplemented
85C3×C4⋊Q8C2×D511yescharacteristic
86C3×C4⋊Q8C2×D511yescharacteristic
87C2×#215—102no—
88C2×#204—102no—
89#874—51no—
90#869—51no—
91C3×#103—22no—
92C3×C4×C8C2×D511yescharacteristic
93#809—102no—
94#808—102no—
95#807—102no—
96C4×C3⋊C8—51no—
97C4×C3⋊C8—51no—
98C2×C5×Q8—21no—
99C2×C5×Q8—21no—
100C2×D20—61no—
101C2×D20—61no—
102C2×D20—61no—
103C2×Dic10—61no—
104C2×C5×C8#6712yes—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C42×C5C22×D311yescharacteristic
110#688—124no—
111C4⋊Dic5—61no—
112C4⋊Dic5—61no—
113C2×#168—32no—
114C2×#168—32no—
115#677—124no—
116#500—151no—
117#498—151no—
118#492—151no—
119#492—151no—
120#487D1511yescharacteristic, complemented
121#486—151no—
122#322—151no—
123C22×C3×C5#12711yescharacteristic
124C2×D15—81no—
125C2×D15—81no—
126C2×D15—81no—
127C3×C4×C5—81no—
128C3×C4×C5—81no—
129C3×C4×C5C2×SD1612yes—
130C3×C4×C5AGL(1,ℤ/8)12yes—
131C3×C4×C5#13712yes—
132Dic15—81no—
133C2×C3×Q8—21no—
134C2×C3×Q8—21no—
135C2×D12—101no—
136C2×D12—101no—
137C2×D12—101no—
138C2×Dic6—101no—
139C2×C3×C8C22⋊D512yes—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C42C22×D511yescharacteristic
145#215—204no—
146C4⋊Dic3—101no—
147C4⋊Dic3—101no—
148C2×C3⋊C8—52no—
149C2×C3⋊C8—52no—
150#204—204no—
151C22×D5—121no—
152C5×Q8—42no—
153C5×Q8—42no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5D3×D411yescharacteristic
157C2×C4×C5D3×D411yescharacteristic
158C2×C4×C5C2×#6711yescharacteristic
159C2×Dic5—121no—
160D20—122no—
161D20—122no—
162D20—122no—
163Dic10—122no—
164C5×C8—22no—
165#168—34no—
166#168—62no—
167C2×SD16—302no—
168C2×SD16—302no—
169C4⋊Q8—151no—
170C4⋊Q8C2×D1511yescharacteristic
171C4⋊Q8C2×D1511yescharacteristic
172#127—151no—
173#107—302no—
174#106—302no—
175#103—22no—
176#102—302no—
177C4×C8—151no—
178C4×C8—151no—
179C4×C8C2×D1511yescharacteristic
180C2×C3×C5#49211yescharacteristic
181C2×C3×C5#49611yescharacteristic
182C2×C3×C5#49711yescharacteristic
183D15—161no—
184C22×D3—201no—
185C3×Q8—42no—
186C3×Q8—42no—
187C2×C3×C4—41no—
188C2×C3×C4—41no—
189C2×C3×C4D4×D511yescharacteristic
190C2×C3×C4D4×D511yescharacteristic
191C2×C3×C4C2×C22⋊D511yescharacteristic
192C2×Dic3—201no—
193D12—202no—
194D12—202no—
195D12—202no—
196Dic6—202no—
197C3×C8—22no—
198C3⋊C8—54no—
199C3⋊C8—102no—
200C22×C5#94011yescharacteristic
201C2×D5—241no—
202C2×D5—241no—
203C2×D5—241no—
204C4×C5—81no—
205C4×C5—81no—
206C4×C5D3×SD1612yes—
207C4×C5#91812yes—
208C4×C5#94912yes—
209Dic5—241no—
210C2×Q8—21no—
211C2×Q8—21no—
212C2×Q8—301no—
213C2×D4—301no—
214C2×D4—301no—
215C2×D4—301no—
216SD16—604no—
217SD16—604no—
218C2×C8—152no—
219C2×C8—152no—
220C2×C8#122012yes—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—301no—
226C4⋊C4—301no—
227C42C22×D1511yescharacteristic
228C3×C5#171411yescharacteristic, complemented, Hall
229C22×C3#408611yescharacteristic
230C2×D3—401no—
231C2×D3—401no—
232C2×D3—401no—
233C3×C4—81no—
234C3×C4—81no—
235C3×C4D5×SD1612yes—
236C3×C4#406412yes—
237C3×C4#409512yes—
238Dic3—401no—
239C2×C5#505811yescharacteristic
240C2×C5#517511yescharacteristic
241C2×C5#519011yescharacteristic
242D5—481no—
243C23—601no—
244Q8—42no—
245Q8—42no—
246Q8—602no—
247D4—602no—
248D4—602no—
249D4—602no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—601no—
253C2×C4D4×D1511yescharacteristic
254C2×C4D4×D1511yescharacteristic
255C2×C4C2×#122011yescharacteristic
256C8—22no—
257C8—154no—
258C8—302no—
259C2×C3#6534711yescharacteristic
260C2×C3#6546411yescharacteristic
261C2×C3#6547911yescharacteristic
262D3—801no—
263C5#7121611yescharacteristic, complemented, Sylow
264C22—1201no—
265C22—1201no—
266C22—1201no—
267C22#9182911yescharacteristic
268C4—81no—
269C4—81no—
270C4—1201no—
271C4SD16×D1512yes—
272C4#9180712yes—
273C4#9183812yes—
274C3#1060200911yescharacteristic, complemented, Sylow
275C2—2401no—
276C2#1175115911yescharacteristic
277C2#1175127611yescharacteristic
278C2#1175129111yescharacteristic
subgroupG/H
centerC22#91829
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#487C2
socleC22×C3×C5#127
prime radical#91763C22
hypercenter#487D15
hypocenterC3×C5#1714
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. C3×C5×#487C2semidirect
4. #11751181C2semidirect
5. #11751179C2semidirect
7. #11746275C2semidirect
23. C5×#487D3semidirect
48. C3×#487D5semidirect
84. C3⋊#168SD16semidirect
120. #487D15semidirect
228. C3×C5#1714semidirect
263. C5#71216semidirect
274. C3#10602009semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4872
#117511892
#117511862
#117511812
#117511792
#117507942
#117462752
#106020093
#712165