Finite Group Databasebeta

← #14318049

Subgroups — #14318049

Order 1920.

272 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C5×#4878C211yesmaximal, characteristic, complemented
2Dic3×D40C211yesmaximal, characteristic
3#11746311C211yesmaximal, characteristic, complemented
4C3×#64711C211yesmaximal, characteristic
5#11745939C211yesmaximal, characteristic, complemented
6Dic3⋊#672C211yesmaximal, characteristic, complemented
7#11745891C211yesmaximal, characteristic
8#10602149—31nomaximal, Hall
9C5×#890—21no—
10C2×C3×D40C2211yescharacteristic
11Dic3×D20—21no—
12C3×C5×#107C2211yescharacteristic
13#91102C2211yescharacteristic
14C2×C3⋊#672C2211yescharacteristic
15C5×#818C2211yescharacteristic
16C5×C8×Dic3C2211yescharacteristic
17C5×#808—21no—
18C2×C3×#672C2211yescharacteristic
19#90965—21no—
20#69180—51nomaximal, Hall
21C5×#499—31no—
22C4×D40—31no—
23#64711—31no—
24#64711D311yescharacteristic
25#64710—31no—
26#64709—31no—
27C4⋊#672—31no—
28C2×C3×D20—21no—
29C2×D5×Dic3—41no—
30C2×C3×C5×C8C2311yescharacteristic
31C3×C5×C4⋊C4—21no—
32C4⋊Dic15—21no—
33C5×C4⋊Dic3—21no—
34C5×C4⋊Dic3—41no—
35C5×Dic3⋊C4—41no—
36C4×C5×Dic3D411yescharacteristic
37C2×C5×C3⋊C8D411yescharacteristic
38C3×D40—21no—
39C3×D40Q812yes—
40#6665—41no—
41C3⋊#672—21no—
42C3×#672—21no—
43Dic3×D8—51no—
44#4878D511yescharacteristic, complemented
45C3×#357—51no—
46#4562—51no—
47#4504—51no—
48Dic3⋊C16—51no—
49#4490—51no—
50C5×#125—61no—
51C2×D40C2×D311yescharacteristic
52C4×D20—61no—
53C5×#107—31no—
54C5×#107C2×D311yescharacteristic
55C5×#106—61no—
56C4×C5×C8—31no—
57#3953—61no—
58#3950—31no—
59C2×#672—31no—
60C2×#672C2×D311yescharacteristic
61#2228—151noSylow
62C22×C3×D5—41no—
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5C2×D411yescharacteristic
65C2×Dic15—41no—
66C2×C5×Dic3—41no—
67C2×C5×Dic3D811yescharacteristic
68C2×C5×Dic3D811yescharacteristic
69C3×D20—22no—
70C3×D20—41no—
71D5×Dic3—82no—
72C3×C5×C8C2×Q811yescharacteristic
73C3×C5×C8#4111yescharacteristic
74C5×C3⋊C8—21no—
75C2×C3×D8—51no—
76D4×Dic3—101no—
77#890—21no—
78C2×C3×C16—51no—
79C3×#107C2×D511yescharacteristic
80#832—101no—
81#818—51no—
82#818C2×D511yescharacteristic
83C8×Dic3C2×D511yescharacteristic
84C2×C3⋊C16—51no—
85#808—21no—
86C2×D20—21no—
87C2×C4×D5—121no—
88C2×C5×C8—31no—
89C2×C5×C8C22×D311yescharacteristic
90C5×C4⋊C4—21no—
91C5×C4⋊C4—61no—
92C5×C4⋊C4—121no—
93C5×C4⋊C4—121no—
94C42×C5—31no—
95#685—121no—
96C4⋊Dic5—61no—
97D40—21no—
98D40Dic612yes—
99#672—21no—
100#672—61no—
101#499—31no—
102C4×D8—151no—
103#367—151no—
104#366—151no—
105C4⋊C16—151no—
106#357—51no—
107#357—151no—
108C22×C3×C5C2×D811yescharacteristic
109C2×C3×D5—42no—
110C2×C3×D5—81no—
111C2×C3×D5—81no—
112C3×C4×C5—81no—
113C3×C4×C5C22⋊Q811yescharacteristic
114C3×C4×C5#13711yescharacteristic
115Dic15—81no—
116C5×Dic3—21no—
117C5×Dic3—21no—
118C5×Dic3—81no—
119C2×C3×D4—101no—
120C22×Dic3—201no—
121C3×D8—52no—
122C3×D8—101no—
123C2×C3×C8C22×D511yescharacteristic
124C3×C4⋊C4—21no—
125#217—201no—
126C4⋊Dic3—21no—
127C4⋊Dic3—41no—
128C4⋊Dic3—101no—
129Dic3⋊C4—41no—
130C4×Dic3C22⋊D511yescharacteristic
131C2×C3⋊C8C22⋊D511yescharacteristic
132C3×C16—101no—
133C3⋊C16—101no—
134C22×D5—41no—
135C2×C4×C5—31no—
136C2×C4×C5—31no—
137C2×C4×C5—41no—
138C2×C4×C5—121no—
139C2×C4×C5D3×D411yescharacteristic
140C2×Dic5—121no—
141D20—22no—
142D20—41no—
143C4×D5—242no—
144C5×C8—61no—
145C5×C8C2×Dic611yescharacteristic
146C5×C8#23711yescharacteristic
147C2×D8—51no—
148#125—61no—
149C4×D4—301no—
150C2×C16—51no—
151C2×C16—151no—
152#107—31no—
153#107—151no—
154#107D3×D511yescharacteristic
155#106—61no—
156#102—301no—
157C4×C8—31no—
158C2×C3×C5#47411yescharacteristic
159C2×C3×C5#50811yescharacteristic
160C2×C3×C5#50911yescharacteristic
161C3×D5—82no—
162C23×C3—201no—
163C3×D4—102no—
164C3×D4—201no—
165C2×C3×C4—41no—
166C2×C3×C4C2×C22⋊D511yescharacteristic
167C2×Dic3—41no—
168C2×Dic3—201no—
169C2×Dic3—402no—
170C2×Dic3#68611yescharacteristic
171C2×Dic3#68611yescharacteristic
172C3×C8Q8×D511yescharacteristic
173C3×C8#71311yescharacteristic
174C3⋊C8—21no—
175C22×C5D3×D811yescharacteristic
176C2×D5—42no—
177C2×D5—81no—
178C2×D5—81no—
179C4×C5—61no—
180C4×C5—61no—
181C4×C5—81no—
182C4×C5—241no—
183C4×C5#87811yescharacteristic
184C4×C5#91511yescharacteristic
185Dic5—241no—
186C2×D4—101no—
187C22×C4—601no—
188D8—52no—
189D8—101no—
190C2×C8—31no—
191C2×C8C2×D3×D511yescharacteristic
192C4⋊C4—21no—
193C4⋊C4—61no—
194C4⋊C4—121no—
195C4⋊C4—121no—
196C4⋊C4—301no—
197C22⋊C4—601no—
198C42—31no—
199C16—101no—
200C16—301no—
201C3×C5#222811yescharacteristic, complemented, Hall
202C22×C3—202no—
203C22×C3—401no—
204C22×C3—401no—
205C22×C3C2×#68611yescharacteristic
206C3×C4—81no—
207C3×C4#408811yescharacteristic
208C3×C4#409211yescharacteristic
209Dic3—21no—
210Dic3—21no—
211Dic3—81no—
212Dic3—401no—
213C2×C5#475911yescharacteristic
214C2×C5#491211yescharacteristic
215C2×C5#491411yescharacteristic
216D5—82no—
217C23—201no—
218D4—102no—
219D4—201no—
220C2×C4—31no—
221C2×C4—31no—
222C2×C4—41no—
223C2×C4—121no—
224C2×C4—601no—
225C2×C4—1202no—
226C2×C4D3×C22⋊D511yescharacteristic
227C8—61no—
228C8D5×Dic611yescharacteristic
229C8#676611yescharacteristic
230C2×C3—402no—
231C2×C3#6537611yescharacteristic
232C2×C3#6548211yescharacteristic
233C2×C3#6548311yescharacteristic
234C5#6918011yescharacteristic, complemented, Sylow
235C22—202no—
236C22—401no—
237C22—401no—
238C22D3×#68611yescharacteristic
239C4—61no—
240C4—61no—
241C4—81no—
242C4—241no—
243C4—1201no—
244C4#9142111yescharacteristic
245C4#9151811yescharacteristic
246C3#1060214911yescharacteristic, complemented, Sylow
247C2—402no—
248C2#1174724511yescharacteristic
249C2#1174828011yescharacteristic
250C2#1174829111yescharacteristic
subgroupG/H
centerC22D3×#686
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×C3×D40C22
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. C5×#4878C2semidirect
3. #11746311C2semidirect
5. #11745939C2semidirect
6. Dic3⋊#672C2semidirect
44. #4878D5semidirect
201. C3×C5#2228semidirect
234. C5#69180semidirect
246. C3#10602149semidirect

Maximal subgroups

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

subgroupindex
C5×#48782
Dic3×D402
#117463112
C3×#647112
#117459392
Dic3⋊#6722
#117458912
#106021493
#691805