Finite Group Databasebeta

← #14293653

Subgroups — #14293653

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×#492C211yesmaximal, characteristic
2#11751181C211yesmaximal, characteristic, complemented
3#11751179C211yesmaximal, characteristic, complemented
4#11751177C211yesmaximal, characteristic
5#11751171C211yesmaximal, characteristic
6#11750782C211yesmaximal, characteristic, complemented
7#11746275C211yesmaximal, characteristic, complemented
8#10602050—31nomaximal, Hall
9C2×C3×C5×SD16—22no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#127C2211yescharacteristic
12C2×#6716—22no—
13#91758C2211yescharacteristic
14#91758C2211yescharacteristic
15C3×C4×C5×C8C2211yescharacteristic
16#91116—22no—
17#91100—22no—
18#91092—22no—
19#91091—22no—
20C4×C3⋊#168C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22#71257—51nomaximal, Hall
23C5×#492D311yescharacteristic
24#65368—31no—
25#65367—31no—
26#65365—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
41#6716—44no—
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C2×C3⋊#168D412yes—
47C2×C3⋊#168D412yes—
48C3×#492D511yescharacteristic
49#5080—51no—
50#5078—51no—
51#5076—51no—
52#5070—51no—
53#4681—51no—
54#4454—51no—
55C2×C5×SD16—22no—
56C5×C4⋊Q8C2×D311yescharacteristic
57C5×#127C2×D311yescharacteristic
58C2×#687—62no—
59#4015—31no—
60#4015—31no—
61C4×C5×C8C2×D311yescharacteristic
62#3964—62no—
63#3948—62no—
64#3940—62no—
65#3939—62no—
66C4×#168—31no—
67C4×#168—31no—
68#1714—151noSylow
69C23×C3×C5—41no—
70C3×C5×Q8—42no—
71C3×C5×D4—42no—
72C3×C5×D4—42no—
73C3×C5×D4—42no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×Dic15—41no—
79C2×Dic15—41no—
80Dic30—42no—
81Dic30—42no—
82C3×C5×C8—22no—
83C3⋊#168—22no—
84C3⋊#168SD1614yescomplemented
85C2×C3×SD16—22no—
86C3×C4⋊Q8C2×D511yescharacteristic
87C3×#127C2×D511yescharacteristic
88C2×#214—102no—
89#869—51no—
90#869—51no—
91C3×C4×C8C2×D511yescharacteristic
92#832—102no—
93#816—102no—
94#808—102no—
95#807—102no—
96C4×C3⋊C8—51no—
97C4×C3⋊C8—51no—
98C2×C5×Q8—21no—
99C2×C5×D4—21no—
100C2×C5×D4—21no—
101C2×C5×D4—21no—
102C2×Dic10—61no—
103C2×Dic10—61no—
104C5×SD16—44no—
105C2×C5×C8#6712yes—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—21no—
108C42×C5C22×D311yescharacteristic
109#687—124no—
110C4⋊Dic5—61no—
111C4⋊Dic5—61no—
112C4⋊Dic5—61no—
113C4⋊Dic5—61no—
114C2×#168—32no—
115C2×#168—32no—
116#500—151no—
117#498—151no—
118#492—151no—
119#492D1511yescharacteristic
120#487—151no—
121#486—151no—
122#322—151no—
123C22×C3×C5—81no—
124C22×C3×C5—81no—
125C22×C3×C5—81no—
126C22×C3×C5#12711yescharacteristic
127C3×C4×C5—81no—
128C3×C4×C5C2×SD1612yes—
129C3×C4×C5AGL(1,ℤ/8)12yes—
130C3×C4×C5#13712yes—
131Dic15—81no—
132Dic15—81no—
133C2×C3×Q8—21no—
134C2×C3×D4—21no—
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×Dic6—101no—
138C2×Dic6—101no—
139C3×SD16—44no—
140C2×C3×C8C22⋊D512yes—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C42C22×D511yescharacteristic
144#214—204no—
145C4⋊Dic3—101no—
146C4⋊Dic3—101no—
147C4⋊Dic3—101no—
148C4⋊Dic3—101no—
149C2×C3⋊C8—52no—
150C2×C3⋊C8—52no—
151C23×C5—41no—
152C5×Q8—42no—
153C5×D4—42no—
154C5×D4—42no—
155C5×D4—42no—
156C2×C4×C5—41no—
157C2×C4×C5D3×D411yescharacteristic
158C2×C4×C5D3×D411yescharacteristic
159C2×C4×C5C2×#6711yescharacteristic
160C2×Dic5—121no—
161C2×Dic5—121no—
162Dic10—122no—
163Dic10—122no—
164C5×C8—22no—
165#168—34no—
166#168—62no—
167C2×SD16—22no—
168C2×SD16—302no—
169C4⋊Q8—151no—
170C4⋊Q8—151no—
171C4⋊Q8C2×D1511yescharacteristic
172#127C2×D1511yescharacteristic
173#107—302no—
174#106—302no—
175#103—302no—
176#102—302no—
177C4×C8—151no—
178C4×C8—151no—
179C4×C8C2×D1511yescharacteristic
180C2×C3×C5—161no—
181C2×C3×C5#49211yescharacteristic
182C2×C3×C5#49611yescharacteristic
183C2×C3×C5#49711yescharacteristic
184C23×C3—41no—
185C3×Q8—42no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—42no—
189C2×C3×C4—41no—
190C2×C3×C4D4×D511yescharacteristic
191C2×C3×C4D4×D511yescharacteristic
192C2×C3×C4C2×C22⋊D511yescharacteristic
193C2×Dic3—201no—
194C2×Dic3—201no—
195Dic6—202no—
196Dic6—202no—
197C3×C8—22no—
198C3⋊C8—54no—
199C3⋊C8—102no—
200C22×C5—81no—
201C22×C5—81no—
202C22×C5—81no—
203C22×C5#94011yescharacteristic
204C4×C5—81no—
205C4×C5D3×SD1612yes—
206C4×C5#91512yes—
207C4×C5#93212yes—
208Dic5—241no—
209Dic5—241no—
210C2×Q8—21no—
211C2×Q8—301no—
212C2×Q8—301no—
213C2×D4—21no—
214C2×D4—21no—
215C2×D4—21no—
216SD16—44no—
217SD16—604no—
218C2×C8—152no—
219C2×C8—152no—
220C2×C8#122012yes—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—301no—
224C4⋊C4—301no—
225C4⋊C4—301no—
226C4⋊C4—301no—
227C42C22×D1511yescharacteristic
228C3×C5#171411yescharacteristic, complemented, Hall
229C22×C3—81no—
230C22×C3—81no—
231C22×C3—81no—
232C22×C3#408611yescharacteristic
233C3×C4—81no—
234C3×C4D5×SD1612yes—
235C3×C4#406112yes—
236C3×C4#407812yes—
237Dic3—401no—
238Dic3—401no—
239C2×C5—161no—
240C2×C5#507411yescharacteristic
241C2×C5#516711yescharacteristic
242C2×C5#517511yescharacteristic
243C23—41no—
244Q8—42no—
245Q8—602no—
246Q8—602no—
247D4—42no—
248D4—42no—
249D4—42no—
250C2×C4—41no—
251C2×C4—601no—
252C2×C4—601no—
253C2×C4D4×D1511yescharacteristic
254C2×C4D4×D1511yescharacteristic
255C2×C4C2×#122011yescharacteristic
256C8—22no—
257C8—154no—
258C8—302no—
259C2×C3—161no—
260C2×C3#6536311yescharacteristic
261C2×C3#6545611yescharacteristic
262C2×C3#6546411yescharacteristic
263C5#7125711yescharacteristic, complemented, Sylow
264C22—81no—
265C22—81no—
266C22—81no—
267C22#9182911yescharacteristic
268C4—81no—
269C4—1201no—
270C4—1201no—
271C4SD16×D1512yes—
272C4#9180412yes—
273C4#9182112yes—
274C3#1060205011yescharacteristic, complemented, Sylow
275C2—161no—
276C2#1175117511yescharacteristic
277C2#1175126811yescharacteristic
278C2#1175127611yescharacteristic
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#1714
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. #11751181C2semidirect
3. #11751179C2semidirect
6. #11750782C2semidirect
7. #11746275C2semidirect
84. C3⋊#168SD16semidirect
228. C3×C5#1714semidirect
263. C5#71257semidirect
274. C3#10602050semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4922
#117511812
#117511792
#117511772
#117511712
#117507822
#117462752
#106020503
#712575