Finite Group Databasebeta

← #14293874

Subgroups — #14293874

Order 1920.

328 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 94 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#11751181C211yesmaximal, characteristic
2C5×#5079C211yesmaximal, characteristic
3C3×#65367C211yesmaximal, characteristic
4#11746930C211yesmaximal, characteristic
5#11746923C211yesmaximal, characteristic
6#11746920C211yesmaximal, characteristic
7#11745832C211yesmaximal, characteristic
8#10602013—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91092—22no—
14C4×C3⋊#168C2211yescharacteristic
15C5×#835—22no—
16C4×C5×C3⋊C8C2211yescharacteristic
17C3×#3939—22no—
18C3×C4×#168C2211yescharacteristic
19#90975—22no—
20#90972—22no—
21#90971—22no—
22#71364—51nomaximal, Hall
23C5×#487—31no—
24#65382—31no—
25#65370—31no—
26#65368—31no—
27#65367D311yescharacteristic
28#64970—31no—
29#64675—31no—
30C2×C3×C5×Q8—21no—
31C2×Dic30—21no—
32C2×C5×Dic6—21no—
33C2×C3×Dic10—21no—
34C3×C5×C4⋊C4—21no—
35C3×C5×C4⋊C4—21no—
36C3×C42×C5C2311yescharacteristic
37C4⋊Dic15—21no—
38C4⋊Dic15—21no—
39C2×C3⋊#168D412yes—
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3—21no—
42C2×C5×C3⋊C8D412yes—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C2×C3×#168D412yes—
46C3×#500—51no—
47#5093—51no—
48#5080—51no—
49#5079—51no—
50#5079D511yescharacteristic
51#4681—51no—
52#4454—51no—
53C5×C4⋊Q8—31no—
54C5×C4⋊Q8C2×D311yescharacteristic
55#4015—31no—
56#4015C2×D311yescharacteristic
57C5×#103—62no—
58C4×C5×C8—31no—
59#3967—62no—
60#3948—62no—
61#3942—62no—
62#3940—62no—
63#3939—22no—
64C4×#168—31no—
65C4×#168C2×D311yescharacteristic
66#1718—151noSylow
67C3×C5×Q8—42no—
68C2×C3×C4×C5—41no—
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×Dic15—41no—
73Dic30—42no—
74C2×C5×Dic3—41no—
75C5×Dic6—42no—
76C2×C3×Dic5—41no—
77C3×Dic10—42no—
78C3⋊#168—22no—
79C3×#168—22no—
80C5×C3⋊C8—22no—
81C3×C4⋊Q8—51no—
82C3×C4⋊Q8C2×D511yescharacteristic
83#869—51no—
84#869C2×D511yescharacteristic
85C3×#107—102no—
86C3×C4×C8—51no—
87#835—22no—
88#835—102no—
89#816—102no—
90#810—102no—
91#808—102no—
92C4×C3⋊C8—51no—
93C4×C3⋊C8C2×D511yescharacteristic
94C2×C5×Q8—21no—
95C2×C5×Q8—61no—
96C2×Dic10—21no—
97C2×Dic10—61no—
98C2×C5×C8—32no—
99C5×C4⋊C4—21no—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—61no—
102C5×C4⋊C4—61no—
103C42×C5C22×D311yescharacteristic
104C4⋊Dic5—21no—
105C4⋊Dic5—21no—
106C4⋊Dic5—61no—
107C4⋊Dic5—61no—
108C2×#168—32no—
109C2×#168#6712yes—
110#500—51no—
111#498—151no—
112#487—31no—
113#487—151no—
114#487—151no—
115#487—151no—
116#322—151no—
117C22×C3×C5#12711yescharacteristic
118C3×C4×C5—81no—
119C3×C4×C5#13512yes—
120C3×C4×C5#13712yes—
121C3×C4×C5#13712yes—
122Dic15—81no—
123C3×Dic5—81no—
124C5×Dic3—81no—
125C2×C3×Q8—21no—
126C2×C3×Q8—101no—
127C2×Dic6—21no—
128C2×Dic6—101no—
129C2×C3×C8—52no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—101no—
133C3×C4⋊C4—101no—
134C3×C42C22×D511yescharacteristic
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—101no—
138C4⋊Dic3—101no—
139C2×C3⋊C8—52no—
140C2×C3⋊C8C22⋊D512yes—
141C5×Q8—42no—
142C5×Q8—122no—
143C2×C4×C5—41no—
144C2×C4×C5—121no—
145C2×C4×C5D3×D411yescharacteristic
146C2×C4×C5D3×D411yescharacteristic
147C2×C4×C5C2×#6711yescharacteristic
148C2×Dic5—41no—
149C2×Dic5—121no—
150Dic10—42no—
151Dic10—122no—
152C5×C8—62no—
153#168—22no—
154#168—62no—
155C4⋊Q8—31no—
156C4⋊Q8—51no—
157C4⋊Q8—151no—
158C4⋊Q8D3×D511yescharacteristic
159#107—102no—
160#106—302no—
161#103—62no—
162#103—302no—
163#103—302no—
164#103—302no—
165C4×C8—31no—
166C4×C8—51no—
167C4×C8—151no—
168C2×C3×C5#49511yescharacteristic
169C2×C3×C5#49711yescharacteristic
170C2×C3×C5#49711yescharacteristic
171C3×Q8—42no—
172C3×Q8—202no—
173C2×C3×C4—41no—
174C2×C3×C4—201no—
175C2×C3×C4D4×D511yescharacteristic
176C2×C3×C4D4×D511yescharacteristic
177C2×C3×C4C2×C22⋊D511yescharacteristic
178C2×Dic3—41no—
179C2×Dic3—201no—
180Dic6—42no—
181Dic6—202no—
182C3×C8—102no—
183C3⋊C8—22no—
184C3⋊C8—102no—
185C22×C5#94011yescharacteristic
186C4×C5—81no—
187C4×C5—241no—
188C4×C5#91212yes—
189C4×C5#91812yes—
190C4×C5#94212yes—
191Dic5—81no—
192Dic5—241no—
193C2×Q8—21no—
194C2×Q8—61no—
195C2×Q8—101no—
196C2×Q8—301no—
197C2×C8—32no—
198C2×C8—52no—
199C2×C8—152no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—61no—
203C4⋊C4—61no—
204C4⋊C4—101no—
205C4⋊C4—101no—
206C4⋊C4—301no—
207C4⋊C4—301no—
208C42C2×D3×D511yescharacteristic
209C3×C5#171811yescharacteristic, complemented, Hall
210C22×C3#408611yescharacteristic
211C3×C4—81no—
212C3×C4—401no—
213C3×C4#406112yes—
214C3×C4#406412yes—
215C3×C4#409612yes—
216Dic3—81no—
217Dic3—401no—
218C2×C5#508611yescharacteristic
219C2×C5#515511yescharacteristic
220C2×C5#519011yescharacteristic
221Q8—42no—
222Q8—122no—
223Q8—202no—
224Q8—602no—
225C2×C4—41no—
226C2×C4—121no—
227C2×C4—201no—
228C2×C4—601no—
229C2×C4D5×#6711yescharacteristic
230C2×C4D3×C22⋊D511yescharacteristic
231C2×C4#679011yescharacteristic
232C8—62no—
233C8—102no—
234C8—302no—
235C2×C3#6534811yescharacteristic
236C2×C3#6545611yescharacteristic
237C2×C3#6547911yescharacteristic
238C5#7136411yescharacteristic, complemented, Sylow
239C22#9156711yescharacteristic
240C4—81no—
241C4—241no—
242C4—401no—
243C4—1201no—
244C4#9149312yes—
245C4#9151512yes—
246C4#9152412yes—
247C3#1060201311yescharacteristic, complemented, Sylow
248C2#1174907411yescharacteristic
249C2#1174931511yescharacteristic
250C2#1174932211yescharacteristic
subgroupG/H
centerC22#91567
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socle, prime radicalC22×C3×C5#127
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1718
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
209. C3×C5#1718semidirect
238. C5#71364semidirect
247. C3#10602013semidirect

Maximal subgroups

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

subgroupindex
#117511812
C5×#50792
C3×#653672
#117469302
#117469232
#117469202
#117458322
#106020133
#713645