Finite Group Databasebeta

← #14289396

Subgroups — #14289396

Order 1920.

436 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5713C211yesmaximal, characteristic
2C3×#65365C211yesmaximal, characteristic
3#11746959C212yesmaximal, complemented
4#11746365C211yesmaximal, characteristic
5#11745843C212yesmaximal, complemented
6#10602737—31nomaximal, Hall
7C3×C5×#127C2211yescharacteristic
8C5×#936—22no—
9C5×#935—22no—
10C5×D4×Dic3—22no—
11C4×C5×Dic6C2212yes—
12C2×C3×#687—22no—
13C3×#4015C2211yescharacteristic
14C4⋊(C3⋊#168)C2212yes—
15C3×C4×#168C2211yescharacteristic
16#90989—22no—
17#90972—22no—
18#71270—51nomaximal, Hall
19C5×#559—31no—
20#65365D311yescharacteristic
21#65310—32no—
22#64764—31no—
23Q8⋊#168—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4D412yes—
26C22×C5×Dic3—22no—
27C2×C5×Dic6D412yes—
28C2×C3×Dic10—21no—
29C3×C42×C5C2311yescharacteristic
30C2×C3⋊#168—22no—
31C5×#217—24no—
32C5×#217—22no—
33C5×C4⋊Dic3D412yes—
34C5×Dic3⋊C4—22no—
35C4×C5×Dic3—22no—
36C3×#687—44no—
37C3×C4⋊Dic5—22no—
38C2×C3×#168—21no—
39#5713D511yescharacteristic
40C3×#492—51no—
41#5091—52no—
42#4544—51no—
43#4456—52no—
44C5×#127C2×D311yescharacteristic
45C5×#124—62no—
46C5×#123—62no—
47C4×C5×Q8—32no—
48C4×C5×D4—62no—
49C2×#687—22no—
50#4015C2×D311yescharacteristic
51#3967—62no—
52#3939—62no—
53C4⋊#168—32no—
54C4×#168C2×D311yescharacteristic
55#1630—151noSylow
56C23×C3×C5—22no—
57C3×C5×D4—42no—
58C3×C5×D4—42no—
59C3×C5×D4—42no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×C5×Dic3—22no—
63C2×C5×Dic3—22no—
64C2×C5×Dic3—82no—
65C5×Dic6—22no—
66C5×Dic6—22no—
67C2×C3×Dic5—41no—
68C3×Dic10—42no—
69C3⋊#168—42no—
70C3×#168—22no—
71C2×C3×SD16—102no—
72C3×C4⋊Q8—51no—
73C3×#127C2×D511yescharacteristic
74#936—22no—
75#935—22no—
76D4×Dic3—22no—
77C4×Dic6C2×D512yes—
78C3×C4×C8—51no—
79#810—102no—
80#807—102no—
81C4⋊(C3⋊C8)—52no—
82C2×C5×Q8—32no—
83C2×C5×D4—22no—
84C2×C5×D4#6712yes—
85C22×C4×C5—62no—
86C2×Dic10—21no—
87C5×C4⋊C4—32no—
88C5×C4⋊C4—62no—
89C5×C22⋊C4—64no—
90C5×C22⋊C4—62no—
91C42×C5—62no—
92C42×C5C22×D311yescharacteristic
93#687—44no—
94C4⋊Dic5—22no—
95C2×#168—21no—
96C2×#168—62no—
97#559—31no—
98#492—51no—
99#477—152no—
100#331—151no—
101Q8⋊C8—152no—
102C22×C3×C5—44no—
103C22×C3×C5—42no—
104C22×C3×C5#12011yescharacteristic
105C3×C4×C5—21no—
106C3×C4×C5#13512yes—
107C3×C4×C5#13712yes—
108C3×Dic5—81no—
109C5×Dic3—42no—
110C5×Dic3—42no—
111C2×C3×Q8—101no—
112C2×C3×D4—22no—
113C2×C3×D4C22⋊D512yes—
114C22×Dic3—22no—
115C2×Dic6C22⋊D512yes—
116C3×SD16—204no—
117C2×C3×C8—101no—
118C3×C4⋊C4—102no—
119C3×C42C22×D511yescharacteristic
120#217—24no—
121#217—22no—
122C4⋊Dic3C22⋊D512yes—
123Dic3⋊C4—22no—
124C4×Dic3—22no—
125C2×C3⋊C8—102no—
126C23×C5—22no—
127C5×Q8—62no—
128C5×Q8—62no—
129C5×D4—42no—
130C5×D4—42no—
131C5×D4—42no—
132C2×C4×C5—62no—
133C2×C4×C5—62no—
134C2×C4×C5—242no—
135C2×C4×C5D3×D412yes—
136C2×C4×C5C2×#6711yescharacteristic
137C2×Dic5—41no—
138Dic10—42no—
139#168—22no—
140#168—122no—
141C2×SD16—102no—
142C4⋊Q8—51no—
143#127D3×D511yescharacteristic
144#124—62no—
145#123—62no—
146C4×Q8—32no—
147C4×D4—62no—
148#107—302no—
149C4⋊C8—152no—
150#103—302no—
151C4×C8—51no—
152C2×C3×C5—82no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155C23×C3—22no—
156C3×Q8—202no—
157C3×D4—42no—
158C3×D4—42no—
159C3×D4—42no—
160C2×C3×C4—201no—
161C2×C3×C4C2×C22⋊D511yescharacteristic
162C2×C3×C4C2×C22⋊D512yes—
163C2×Dic3—22no—
164C2×Dic3—22no—
165C2×Dic3—82no—
166Dic6—22no—
167Dic6—22no—
168C3×C8—102no—
169C3⋊C8—202no—
170C22×C5—44no—
171C22×C5—42no—
172C22×C5#93711yescharacteristic
173C4×C5—21no—
174C4×C5—122no—
175C4×C5—122no—
176C4×C5#91512yes—
177C4×C5#91612yes—
178Dic5—81no—
179C2×Q8—32no—
180C2×Q8—101no—
181C2×D4—22no—
182C2×D4#120112yes—
183C22×C4—62no—
184SD16—204no—
185C2×C8—101no—
186C2×C8—302no—
187C4⋊C4—32no—
188C4⋊C4—62no—
189C4⋊C4—102no—
190C22⋊C4—64no—
191C22⋊C4—62no—
192C42—62no—
193C42C2×D3×D511yescharacteristic
194C3×C5#163011yescharacteristic, complemented, Hall
195C22×C3—44no—
196C22×C3—42no—
197C22×C3#409911yescharacteristic
198C3×C4—21no—
199C3×C4—401no—
200C3×C4#409612yes—
201C3×C4#409712yes—
202Dic3—42no—
203Dic3—42no—
204C2×C5—82no—
205C2×C5#507711yescharacteristic
206C2×C5#517312yes—
207C23—22no—
208Q8—62no—
209Q8—62no—
210Q8—202no—
211D4—42no—
212D4—42no—
213D4—42no—
214C2×C4—62no—
215C2×C4—62no—
216C2×C4—201no—
217C2×C4—242no—
218C2×C4C2×#120111yescharacteristic
219C2×C4D3×C22⋊D512yes—
220C8—102no—
221C8—602no—
222C2×C3—82no—
223C2×C3#6552812yes—
224C2×C3#6553011yescharacteristic
225C5#7127011yescharacteristic, complemented, Sylow
226C22—42no—
227C22—44no—
228C22#9156811yescharacteristic
229C4—21no—
230C4—122no—
231C4—122no—
232C4—401no—
233C4#9148612yes—
234C4#9149512yes—
235C3#1060273711yescharacteristic, complemented, Sylow
236C2—82no—
237C2#1174905912yes—
238C2#1174914011yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
Fitting, prime radicalC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1630
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
3. #11746959C2semidirect
5. #11745843C2semidirect
194. C3×C5#1630semidirect
225. C5#71270semidirect
235. C3#10602737semidirect

Maximal subgroups

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

subgroupindex
C5×#57132
C3×#653652
#117469592
#117463652
#117458432
#106027373
#712705