Finite Group Databasebeta

← #14318053

Subgroups — #14318053

Order 1920.

272 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 78 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×#65167C211yesmaximal, characteristic, complemented
2#11747766C211yesmaximal, characteristic
3#11746312C211yesmaximal, characteristic
4C5×#4490C211yesmaximal, characteristic, complemented
5#11745940C211yesmaximal, characteristic, complemented
6#11745927C211yesmaximal, characteristic, complemented
7#11745895C211yesmaximal, characteristic
8#10600147—31nomaximal, Hall
9C2×D120C2211yescharacteristic
10C3×#4036—21no—
11#91418—21no—
12C3×C5×#107C2211yescharacteristic
13C2×C3⋊#672C2211yescharacteristic
14C5×#818C2211yescharacteristic
15C2×C5×C3⋊C16C2211yescharacteristic
16C3×#3950C2211yescharacteristic
17C3×C8×Dic5C2211yescharacteristic
18C3×#3940—21no—
19#90969—21no—
20#71356—51nomaximal, Hall
21#65167D311yescharacteristic, complemented
22#65161—31no—
23C5×#367—31no—
24#64729—31no—
25#64721—31no—
26#64711—31no—
27#64709—31no—
28C2×D60—21no—
29C2×#1200—41no—
30C2×C3×C5×C8C2311yescharacteristic
31C3×C5×C4⋊C4—21no—
32D120—21no—
33D120Q812yes—
34C5×C4⋊Dic3—21no—
35C3×C4⋊Dic5—21no—
36C3×C4⋊Dic5—41no—
37C3×#683—41no—
38C3×C4×Dic5D411yescharacteristic
39C2×C3×#168D411yescharacteristic
40#6667—41no—
41C3⋊#672—21no—
42C5×C3⋊C16—21no—
43C3×#499—51no—
44C4×D24—51no—
45#4491—51no—
46#4491—51no—
47#4490D511yescharacteristic, complemented
48#4489—51no—
49C4⋊(C3⋊C16)—51no—
50C2×D40—31no—
51#4039—61no—
52#4036—21no—
53C2×C5×C16—31no—
54C5×#107—31no—
55C5×#107C2×D311yescharacteristic
56#3950C2×D311yescharacteristic
57C8×Dic5C2×D311yescharacteristic
58C2×#672—31no—
59#3941—61no—
60#3940—21no—
61#2228—151noSylow
62C22×D15—41no—
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5C2×D411yescharacteristic
65D60—22no—
66D60—41no—
67C2×C5×Dic3—41no—
68C2×C3×Dic5—41no—
69C2×C3×Dic5D811yescharacteristic
70C2×C3×Dic5D811yescharacteristic
71#1200—82no—
72C3×C5×C8C2×Q811yescharacteristic
73C3×C5×C8#4111yescharacteristic
74C3×#168—21no—
75C3×#125—101no—
76C2×D24—51no—
77C4×D12—101no—
78C3×#107—51no—
79C3×#107C2×D511yescharacteristic
80C3×#106—101no—
81C3×C4×C8—51no—
82#821—101no—
83#818C2×D511yescharacteristic
84C2×C3⋊C16—51no—
85C2×C3⋊C16C2×D511yescharacteristic
86C2×D20—61no—
87C2×C4×D5—121no—
88C2×C5×C8C22×D311yescharacteristic
89C5×C4⋊C4—21no—
90C5×C4⋊C4—61no—
91#685—121no—
92C4⋊Dic5—21no—
93C4⋊Dic5—41no—
94#683—41no—
95C4×Dic5#6711yescharacteristic
96C2×#168#6711yescharacteristic
97D40—32no—
98D40—61no—
99C5×C16—61no—
100#672—61no—
101#499—51no—
102C4×D8—151no—
103#367—31no—
104#366—151no—
105C4⋊C16—151no—
106#357—151no—
107#357—151no—
108C22×C3×C5C2×D811yescharacteristic
109C2×D15—42no—
110C2×D15—81no—
111C2×D15—81no—
112C3×C4×C5—81no—
113C3×C4×C5C22⋊Q811yescharacteristic
114C3×C4×C5#13711yescharacteristic
115C3×Dic5—21no—
116C3×Dic5—21no—
117C3×Dic5—81no—
118C5×Dic3—81no—
119C2×D12—101no—
120C2×C4×D3—201no—
121C2×C3×C8—51no—
122C2×C3×C8C22×D511yescharacteristic
123C3×C4⋊C4—21no—
124C3×C4⋊C4—101no—
125C3×C4⋊C4—201no—
126C3×C4⋊C4—201no—
127C3×C42—51no—
128(C2×D3)⋊C4—201no—
129C4⋊Dic3—21no—
130D24—52no—
131D24—101no—
132C3⋊C16—21no—
133C3⋊C16—101no—
134C22×D5—121no—
135C2×C4×C5—41no—
136C2×C4×C5—121no—
137C2×C4×C5C2×#6711yescharacteristic
138C2×Dic5—41no—
139C2×Dic5#21311yescharacteristic
140C2×Dic5#21311yescharacteristic
141D20—62no—
142D20—121no—
143C4×D5—242no—
144C5×C8D3×Q811yescharacteristic
145C5×C8#23911yescharacteristic
146#168—21no—
147C2×D8—151no—
148#125—101no—
149C4×D4—301no—
150C2×C16—31no—
151C2×C16—151no—
152#107—31no—
153#107—51no—
154#107D3×D511yescharacteristic
155#106—101no—
156#102—301no—
157C4×C8—51no—
158C2×C3×C5#47411yescharacteristic
159C2×C3×C5#50811yescharacteristic
160C2×C3×C5#50911yescharacteristic
161D15—82no—
162C22×D3—201no—
163C2×C3×C4—41no—
164C2×C3×C4—51no—
165C2×C3×C4—51no—
166C2×C3×C4—201no—
167C2×C3×C4D4×D511yescharacteristic
168C2×Dic3—41no—
169D12—102no—
170D12—201no—
171C4×D3—402no—
172C3×C8—101no—
173C3×C8#70911yescharacteristic
174C3×C8Q8×D511yescharacteristic
175C22×C5C2×#21311yescharacteristic
176C2×D5—122no—
177C2×D5—241no—
178C2×D5—241no—
179C4×C5—81no—
180C4×C5—241no—
181C4×C5#94211yescharacteristic
182C4×C5#94611yescharacteristic
183Dic5—21no—
184Dic5—21no—
185Dic5—81no—
186C2×D4—301no—
187C22×C4—601no—
188D8—152no—
189D8—301no—
190C2×C8—51no—
191C2×C8C2×D3×D511yescharacteristic
192C4⋊C4—21no—
193C4⋊C4—61no—
194C4⋊C4—101no—
195C4⋊C4—201no—
196C4⋊C4—201no—
197C22⋊C4—601no—
198C42—51no—
199C16—61no—
200C16—301no—
201C3×C5#222811yescharacteristic, complemented, Hall
202C22×C3D5×D811yescharacteristic
203C2×D3—202no—
204C2×D3—401no—
205C2×D3—401no—
206C3×C4—81no—
207C3×C4—101no—
208C3×C4—101no—
209C3×C4—401no—
210C3×C4#404211yescharacteristic
211C3×C4#406411yescharacteristic
212Dic3—81no—
213C2×C5#508711yescharacteristic
214C2×C5#519311yescharacteristic
215C2×C5#519411yescharacteristic
216D5—242no—
217C23—601no—
218D4—302no—
219D4—601no—
220C2×C4—41no—
221C2×C4—51no—
222C2×C4—51no—
223C2×C4—121no—
224C2×C4—201no—
225C2×C4—1202no—
226C2×C4D5×#6711yescharacteristic
227C8—101no—
228C8#676911yescharacteristic
229C8D15⋊Q811yescharacteristic
230C2×C3#6517911yescharacteristic
231C2×C3#6520311yescharacteristic
232C2×C3#6520511yescharacteristic
233D3—402no—
234C5#7135611yescharacteristic, complemented, Sylow
235C22—602no—
236C22—1201no—
237C22—1201no—
238C22D5×#21311yescharacteristic
239C4—81no—
240C4—101no—
241C4—101no—
242C4—241no—
243C4—401no—
244C4#9141111yescharacteristic
245C4#9151511yescharacteristic
246C3#1060014711yescharacteristic, complemented, Sylow
247C2—1202no—
248C2#1174723811yescharacteristic
249C2#1174827911yescharacteristic
250C2#1174828911yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×D120C22
hypercenter#107D3×D5
hypocenterC3×C5#2228
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C3×#65167C2semidirect
4. C5×#4490C2semidirect
5. #11745940C2semidirect
6. #11745927C2semidirect
21. #65167D3semidirect
47. #4490D5semidirect
201. C3×C5#2228semidirect
234. C5#71356semidirect
246. C3#10600147semidirect

Maximal subgroups

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

subgroupindex
C3×#651672
#117477662
#117463122
C5×#44902
#117459402
#117459272
#117458952
#106001473
#713565