Finite Group Databasebeta

← #14289384

Subgroups — #14289384

Order 1920.

436 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 103 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×C5×#559C211yesmaximal, characteristic
2#11751177C211yesmaximal, characteristic
3#11751122C212yesmaximal, complemented
4#11746365C211yesmaximal, characteristic
5#11746356C212yesmaximal, complemented
6#10602737—31nomaximal, Hall
7C3×C5×#127C2211yescharacteristic
8C3×C5×#124—22no—
9C3×C5×#123—22no—
10C3×C4×C5×Q8C2212yes—
11C3×C4×C5×D4—22no—
12C2×#6716—22no—
13#91758C2211yescharacteristic
14#91119—22no—
15#91091—22no—
16C4⋊(C3⋊#168)C2212yes—
17C4×C3⋊#168C2211yescharacteristic
18#71944—51nomaximal, Hall
19C5×#559D311yescharacteristic
20#65365—31no—
21#65310—32no—
22#64764—31no—
23Q8⋊#168—32no—
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C22×C3×C4×C5—22no—
28C2×Dic30—21no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4D412yes—
31C3×C5×C22⋊C4—24no—
32C3×C5×C22⋊C4—22no—
33C3×C42×C5—22no—
34C3×C42×C5C2311yescharacteristic
35#6716—44no—
36C4⋊Dic15—22no—
37C2×C3⋊#168—21no—
38C2×C3⋊#168—22no—
39C3×#559D511yescharacteristic
40#5076—51no—
41#5021—52no—
42#4544—51no—
43#4535—52no—
44C5×#127C2×D311yescharacteristic
45C5×#124—22no—
46C5×#123—22no—
47C4×C5×Q8C2×D312yes—
48C4×C5×D4—22no—
49C2×#687—62no—
50#4015—31no—
51#3967—62no—
52#3939—62no—
53C4⋊#168—32no—
54C4×#168—31no—
55#1630—151noSylow
56C23×C3×C5—22no—
57C3×C5×Q8—22no—
58C3×C5×Q8—22no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—82no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C2×Dic15—41no—
68Dic30—42no—
69C3⋊#168—22no—
70C3⋊#168—42no—
71C3×#127C2×D511yescharacteristic
72C3×#124—22no—
73C3×#123—22no—
74C3×C4×Q8C2×D512yes—
75C3×C4×D4—22no—
76C2×#214—102no—
77#869—51no—
78#835—102no—
79#807—102no—
80C4⋊(C3⋊C8)—52no—
81C4×C3⋊C8—51no—
82C2×C5×Q8#6712yes—
83C2×C5×D4—22no—
84C2×C5×D4#6712yes—
85C22×C4×C5—22no—
86C2×Dic10—61no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4#6712yes—
89C5×C22⋊C4—24no—
90C5×C22⋊C4—22no—
91C42×C5—22no—
92C42×C5C22×D311yescharacteristic
93#687—124no—
94C4⋊Dic5—62no—
95C2×#168—61no—
96C2×#168—62no—
97#559D1511yescharacteristic
98#492—151no—
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—42no—
107C3×C4×C5—42no—
108C3×C4×C5#13512yes—
109C3×C4×C5#13712yes—
110Dic15—81no—
111C2×C3×Q8C22⋊D512yes—
112C2×C3×D4—22no—
113C2×C3×D4C22⋊D512yes—
114C22×C3×C4—22no—
115C2×Dic6—101no—
116C3×C4⋊C4—22no—
117C3×C4⋊C4C22⋊D512yes—
118C3×C22⋊C4—24no—
119C3×C22⋊C4—22no—
120C3×C42—22no—
121C3×C42C22×D511yescharacteristic
122#214—204no—
123C4⋊Dic3—102no—
124C2×C3⋊C8—101no—
125C2×C3⋊C8—102no—
126C23×C5—22no—
127C5×Q8—22no—
128C5×Q8—22no—
129C5×D4—42no—
130C5×D4—42no—
131C5×D4—42no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—82no—
135C2×C4×C5C2×#6711yescharacteristic
136C2×C4×C5C2×#6712yes—
137C2×Dic5—121no—
138Dic10—122no—
139#168—62no—
140#168—122no—
141C2×SD16—302no—
142C4⋊Q8—151no—
143#127C2×D1511yescharacteristic
144#124—22no—
145#123—22no—
146C4×Q8C2×D1512yes—
147C4×D4—22no—
148#107—302no—
149C4⋊C8—152no—
150#103—302no—
151C4×C8—151no—
152C2×C3×C5—82no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155C23×C3—22no—
156C3×Q8—22no—
157C3×Q8—22no—
158C3×D4—42no—
159C3×D4—42no—
160C3×D4—42no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—82no—
164C2×C3×C4C2×C22⋊D511yescharacteristic
165C2×C3×C4C2×C22⋊D512yes—
166C2×Dic3—201no—
167Dic6—202no—
168C3⋊C8—102no—
169C3⋊C8—202no—
170C22×C5—44no—
171C22×C5—42no—
172C22×C5#95311yescharacteristic
173C4×C5—21no—
174C4×C5—42no—
175C4×C5—42no—
176C4×C5#95012yes—
177C4×C5#95112yes—
178Dic5—241no—
179C2×Q8—301no—
180C2×Q8#122012yes—
181C2×D4—22no—
182C2×D4#122012yes—
183C22×C4—22no—
184SD16—604no—
185C2×C8—301no—
186C2×C8—302no—
187C4⋊C4—22no—
188C4⋊C4—302no—
189C4⋊C4#122012yes—
190C22⋊C4—24no—
191C22⋊C4—22no—
192C42—22no—
193C42C22×D1511yescharacteristic
194C3×C5#163011yescharacteristic, complemented, Hall
195C22×C3—44no—
196C22×C3—42no—
197C22×C3#409911yescharacteristic
198C3×C4—21no—
199C3×C4—42no—
200C3×C4—42no—
201C3×C4#409612yes—
202C3×C4#409712yes—
203Dic3—401no—
204C2×C5—82no—
205C2×C5#523912yes—
206C2×C5#524111yescharacteristic
207C23—22no—
208Q8—22no—
209Q8—22no—
210Q8—602no—
211D4—42no—
212D4—42no—
213D4—42no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—82no—
217C2×C4—601no—
218C2×C4C2×#122011yescharacteristic
219C2×C4C2×#122012yes—
220C8—302no—
221C8—602no—
222C2×C3—82no—
223C2×C3#6552812yes—
224C2×C3#6553011yescharacteristic
225C5#7194411yescharacteristic, complemented, Sylow
226C22—44no—
227C22—42no—
228C22#9184211yescharacteristic
229C4—21no—
230C4—42no—
231C4—42no—
232C4—1201no—
233C4#9183912yes—
234C4#9184012yes—
235C3#1060273711yescharacteristic, complemented, Sylow
236C2—82no—
237C2#1175134012yes—
238C2#1175134211yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#559C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenter#559D15
hypocenterC3×C5#1630
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #559

Complements

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

NH ≅ G/Ntype
3. #11751122C2semidirect
5. #11746356C2semidirect
194. C3×C5#1630semidirect
225. C5#71944semidirect
235. C3#10602737semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5592
#117511772
#117511222
#117463652
#117463562
#106027373
#719445