Finite Group Databasebeta

← #14294113

Subgroups — #14294113

Order 1920.

396 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 102 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
1#11751189C211yesmaximal, characteristic
2C5×#5092C211yesmaximal, characteristic, complemented
3C3×#65367C211yesmaximal, characteristic, complemented
4#11747075C211yesmaximal, characteristic
5#11746962C211yesmaximal, characteristic, complemented
6#11746912C211yesmaximal, characteristic
7#11745832C211yesmaximal, characteristic, complemented
8#10602094—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91763C2211yescharacteristic
11C2×C5×#216—22no—
12C5×#869C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14C2×#6658—22no—
15#91093—22no—
16C4×C3⋊#168C2211yescharacteristic
17C4×C5×C3⋊C8C2211yescharacteristic
18C3×#3939—22no—
19C3×C4×#168C2211yescharacteristic
20#90989—22no—
21#90969—22no—
22#71366—51nomaximal, Hall
23C5×#494—31no—
24#65377—31no—
25#65377—31no—
26#65367—31no—
27#65367D311yescharacteristic, complemented
28#64982—31no—
29#64675—31no—
30C2×C3×C5×Q8—21no—
31C2×D60—21no—
32C2×D60—21no—
33C2×D60—21no—
34C2×C5×Dic6—21no—
35C2×C3×Dic10—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C42×C5C2311yescharacteristic
39C2×C3⋊#168D412yes—
40C5×#216—44no—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3—21no—
43C2×C5×C3⋊C8D412yes—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5—21no—
46C2×C3×#168D412yes—
47#6658—44no—
48C3×#500—51no—
49#5092D511yescharacteristic, complemented
50#5088—51no—
51#5085—51no—
52#5078—51no—
53#4694—51no—
54#4454—51no—
55C2×C5×Q16—62no—
56C5×C4⋊Q8—31no—
57C5×C4⋊Q8C2×D311yescharacteristic
58C2×#677—62no—
59#4020—31no—
60#4015C2×D311yescharacteristic
61C4×C5×C8—31no—
62#3941—62no—
63#3941—62no—
64#3939—22no—
65#3939—62no—
66C4×#168—31no—
67C4×#168C2×D311yescharacteristic
68#1722—151noSylow
69C22×D15—41no—
70C3×C5×Q8—42no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75D60—42no—
76D60—42no—
77D60—42no—
78C2×C5×Dic3—41no—
79C5×Dic6—42no—
80C2×C3×Dic5—41no—
81C3×Dic10—42no—
82C3⋊#168—22no—
83C3×#168—22no—
84C5×C3⋊C8D814yes—
85C3×C4⋊Q8—51no—
86C3×C4⋊Q8C2×D511yescharacteristic
87C2×#216—22no—
88C2×#215—102no—
89#874—51no—
90#869C2×D511yescharacteristic
91C3×#107—102no—
92C3×C4×C8—51no—
93#821—102no—
94#809—102no—
95#807—102no—
96C4×C3⋊C8—51no—
97C4×C3⋊C8C2×D511yescharacteristic
98C2×C5×Q8—21no—
99C2×C5×Q8—61no—
100C2×D20—61no—
101C2×D20—61no—
102C2×D20—61no—
103C2×Dic10—21no—
104C5×Q16—124no—
105C2×C5×C8—32no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—61no—
109C5×C4⋊C4—61no—
110C42×C5C22×D311yescharacteristic
111C4⋊Dic5—21no—
112C4⋊Dic5—21no—
113C2×#168—32no—
114C2×#168#6712yes—
115#677—124no—
116#500—51no—
117#500—151no—
118#494—31no—
119#492—151no—
120#486—151no—
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×C5C2×D812yes—
129C3×C4×C5#13712yes—
130C3×C4×C5#13712yes—
131C3×Dic5—81no—
132C5×Dic3—81no—
133C2×C3×Q8—21no—
134C2×C3×Q8—101no—
135C2×D12—101no—
136C2×D12—101no—
137C2×D12—101no—
138C2×Dic6—21no—
139C2×C3×C8—52no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—101no—
143C3×C4⋊C4—101no—
144C3×C42C22×D511yescharacteristic
145#216—44no—
146#215—204no—
147C4⋊Dic3—21no—
148C4⋊Dic3—21no—
149C2×C3⋊C8—52no—
150C2×C3⋊C8C22⋊D512yes—
151C22×D5—121no—
152C5×Q8—42no—
153C5×Q8—122no—
154C2×C4×C5—41no—
155C2×C4×C5—121no—
156C2×C4×C5D3×D411yescharacteristic
157C2×C4×C5D3×D411yescharacteristic
158C2×C4×C5C2×#6711yescharacteristic
159C2×Dic5—41no—
160D20—122no—
161D20—122no—
162D20—122no—
163Dic10—42no—
164C5×C8—34no—
165#168—22no—
166#168—62no—
167C2×Q16—62no—
168C2×SD16—302no—
169C4⋊Q8—31no—
170C4⋊Q8—51no—
171C4⋊Q8D3×D511yescharacteristic
172#127—151no—
173#107—102no—
174#107—302no—
175#102—302no—
176#102—302no—
177C4×C8—31no—
178C4×C8—51no—
179C4×C8—151no—
180C2×C3×C5#49311yescharacteristic
181C2×C3×C5#49711yescharacteristic
182C2×C3×C5#49711yescharacteristic
183D15—161no—
184C22×D3—201no—
185C3×Q8—42no—
186C3×Q8—202no—
187C2×C3×C4—41no—
188C2×C3×C4—201no—
189C2×C3×C4D4×D511yescharacteristic
190C2×C3×C4D4×D511yescharacteristic
191C2×C3×C4C2×C22⋊D511yescharacteristic
192C2×Dic3—41no—
193D12—202no—
194D12—202no—
195D12—202no—
196Dic6—42no—
197C3×C8—102no—
198C3⋊C8—102no—
199C3⋊C8#68614yes—
200C22×C5#94011yescharacteristic
201C2×D5—241no—
202C2×D5—241no—
203C2×D5—241no—
204C4×C5—81no—
205C4×C5—241no—
206C4×C5D3×D812yes—
207C4×C5#91812yes—
208C4×C5#94212yes—
209Dic5—81no—
210C2×Q8—21no—
211C2×Q8—61no—
212C2×Q8—101no—
213C2×D4—301no—
214C2×D4—301no—
215C2×D4—301no—
216Q16—124no—
217SD16—604no—
218C2×C8—32no—
219C2×C8—52no—
220C2×C8—152no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—61no—
224C4⋊C4—61no—
225C4⋊C4—101no—
226C4⋊C4—101no—
227C42C2×D3×D511yescharacteristic
228C3×C5#172211yescharacteristic, complemented, Hall
229C22×C3#408611yescharacteristic
230C2×D3—401no—
231C2×D3—401no—
232C2×D3—401no—
233C3×C4—81no—
234C3×C4—401no—
235C3×C4#406412yes—
236C3×C4#406412yes—
237C3×C4C2×#68612yes—
238Dic3—81no—
239C2×C5#508611yescharacteristic
240C2×C5#515111yescharacteristic
241C2×C5#519011yescharacteristic
242D5—481no—
243C23—601no—
244Q8—42no—
245Q8—122no—
246Q8—202no—
247D4—602no—
248D4—602no—
249D4—602no—
250C2×C4—41no—
251C2×C4—121no—
252C2×C4—201no—
253C2×C4D5×#6711yescharacteristic
254C2×C4D3×C22⋊D511yescharacteristic
255C2×C4#679011yescharacteristic
256C8—34no—
257C8—102no—
258C8—302no—
259C2×C3#6536211yescharacteristic
260C2×C3#6547911yescharacteristic
261C2×C3#6547911yescharacteristic
262D3—801no—
263C5#7136611yescharacteristic, complemented, Sylow
264C22—1201no—
265C22—1201no—
266C22—1201no—
267C22#9156711yescharacteristic
268C4—81no—
269C4—241no—
270C4—401no—
271C4D3×#68612yes—
272C4#9151212yes—
273C4#9151512yes—
274C3#1060209411yescharacteristic, complemented, Sylow
275C2—2401no—
276C2#1174909711yescharacteristic
277C2#1174931511yescharacteristic
278C2#1174935611yescharacteristic
subgroupG/H
centerC22#91567
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#127
prime radical#91763C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1722
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5092C2semidirect
3. C3×#65367C2semidirect
5. #11746962C2semidirect
7. #11745832C2semidirect
27. #65367D3semidirect
49. #5092D5semidirect
228. C3×C5#1722semidirect
263. C5#71366semidirect
274. C3#10602094semidirect

Maximal subgroups

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

subgroupindex
#117511892
C5×#50922
C3×#653672
#117470752
#117469622
#117469122
#117458322
#106020943
#713665