Finite Group Databasebeta

← #14289549

Subgroups — #14289549

Order 1920.

412 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 119 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×Q82C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic
3#11751122C212yesmaximal
4#11746367C211yesmaximal, characteristic
5#11746356C212yesmaximal
6#10602733—31nomaximal, Hall
7C3×C5×C4⋊Q8—22no—
8C3×C5×C4⋊Q8—22no—
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×Q8—22no—
11C3×C4×C5×Q8C2212yes—
12C2×#6718—22no—
13#91758C2211yescharacteristic
14#91119—22no—
15#91091—22no—
16C4⋊(C3⋊#168)C2212yes—
17C4×C3⋊#168C2211yescharacteristic
18#71940—51nomaximal, Hall
19C5×Q82D311yescharacteristic
20#65381—31no—
21#65310—32no—
22#64766—31no—
23Q8⋊#168—32no—
24C2×C3×C5×Q8—22no—
25C2×C3×C5×Q8D412yes—
26C2×C3×C5×Q8D412yes—
27C2×Dic30—21no—
28C3×C5×C4⋊C4—24no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C42×C5—22no—
33C3×C42×C5—22no—
34C3×C42×C5C2311yescharacteristic
35#6718—44no—
36C4⋊Dic15—22no—
37C2×C3⋊#168—21no—
38C2×C3⋊#168—22no—
39C3×Q82D511yescharacteristic
40#5092—51no—
41#5021—52no—
42#4546—51no—
43#4535—52no—
44C5×C4⋊Q8—22no—
45C5×C4⋊Q8—22no—
46C5×C4⋊Q8C2×D311yescharacteristic
47C4×C5×Q8—22no—
48C4×C5×Q8C2×D312yes—
49C2×#689—62no—
50#4015—31no—
51#3967—62no—
52#3939—62no—
53C4⋊#168—32no—
54C4×#168—31no—
55#1633—151noSylow
56C3×C5×Q8—22no—
57C3×C5×Q8—42no—
58C3×C5×Q8—82no—
59C3×C5×Q8Q1614yescomplemented
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5C2×D411yescharacteristic
64C2×C3×C4×C5C2×D412yes—
65C2×Dic15—41no—
66Dic30—42no—
67C3⋊#168—22no—
68C3⋊#168—42no—
69C3×C4⋊Q8—22no—
70C3×C4⋊Q8—22no—
71C3×C4⋊Q8C2×D511yescharacteristic
72C3×C4×Q8—22no—
73C3×C4×Q8C2×D512yes—
74C2×#216—102no—
75#869—51no—
76#835—102no—
77#807—102no—
78C4⋊(C3⋊C8)—52no—
79C4×C3⋊C8—51no—
80C2×C5×Q8—22no—
81C2×C5×Q8#6712yes—
82C2×C5×Q8#6712yes—
83C2×Dic10—61no—
84C5×C4⋊C4—24no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4#6712yes—
88C42×C5—22no—
89C42×C5—22no—
90C42×C5C22×D311yescharacteristic
91#689—124no—
92C4⋊Dic5—62no—
93C2×#168—61no—
94C2×#168—62no—
95Q82D1511yescharacteristic
96#494—151no—
97#477—152no—
98#333—151no—
99Q8⋊C8—152no—
100C22×C3×C5#12011yescharacteristic
101C3×C4×C5—24no—
102C3×C4×C5—21no—
103C3×C4×C5—42no—
104C3×C4×C5—42no—
105C3×C4×C5C2×Q1612yes—
106C3×C4×C5#13712yes—
107Dic15—81no—
108C2×C3×Q8—22no—
109C2×C3×Q8C22⋊D512yes—
110C2×C3×Q8C22⋊D512yes—
111C2×Dic6—101no—
112C3×C4⋊C4—24no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4C22⋊D512yes—
116C3×C42—22no—
117C3×C42—22no—
118C3×C42C22×D511yescharacteristic
119#216—204no—
120C4⋊Dic3—102no—
121C2×C3⋊C8—101no—
122C2×C3⋊C8—102no—
123C5×Q8—22no—
124C5×Q8—42no—
125C5×Q8—82no—
126C5×Q8#21614yescomplemented
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5C2×#6711yescharacteristic
131C2×C4×C5C2×#6712yes—
132C2×Dic5—121no—
133Dic10—122no—
134#168—62no—
135#168—122no—
136C2×Q16—302no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—151no—
140C4⋊Q8C2×D1511yescharacteristic
141C4×Q8—22no—
142C4×Q8C2×D1512yes—
143#107—302no—
144C4⋊C8—152no—
145#103—302no—
146C4×C8—151no—
147C2×C3×C5#45112yes—
148C2×C3×C5#45311yescharacteristic
149C3×Q8—22no—
150C3×Q8—42no—
151C3×Q8—82no—
152C3×Q8#68914yescomplemented
153C2×C3×C4—22no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4C2×C22⋊D511yescharacteristic
157C2×C3×C4C2×C22⋊D512yes—
158C2×Dic3—201no—
159Dic6—202no—
160C3⋊C8—102no—
161C3⋊C8—202no—
162C22×C5#95311yescharacteristic
163C4×C5—24no—
164C4×C5—21no—
165C4×C5—42no—
166C4×C5—42no—
167C4×C5#94212yes—
168C4×C5C2×#21612yes—
169Dic5—241no—
170C2×Q8—22no—
171C2×Q8—301no—
172C2×Q8#122012yes—
173C2×Q8#122012yes—
174Q16—604no—
175C2×C8—301no—
176C2×C8—302no—
177C4⋊C4—24no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—302no—
181C4⋊C4#122012yes—
182C42—22no—
183C42—22no—
184C42C22×D1511yescharacteristic
185C3×C5#163311yescharacteristic, complemented, Hall
186C22×C3#409911yescharacteristic
187C3×C4—24no—
188C3×C4—21no—
189C3×C4—42no—
190C3×C4—42no—
191C3×C4#408812yes—
192C3×C4C2×#68912yes—
193Dic3—401no—
194C2×C5#522812yes—
195C2×C5#524111yescharacteristic
196Q8—22no—
197Q8—42no—
198Q8—82no—
199Q8—602no—
200Q8#671814yescomplemented
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—601no—
205C2×C4C2×#122011yescharacteristic
206C2×C4C2×#122012yes—
207C8—302no—
208C8—602no—
209C2×C3#6551712yes—
210C2×C3#6553011yescharacteristic
211C5#7194011yescharacteristic, complemented, Sylow
212C22#9184211yescharacteristic
213C4—24no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—1201no—
218C4#9183112yes—
219C4C2×#671812yes—
220C3#1060273311yescharacteristic, complemented, Sylow
221C2#1175132912yes—
222C2#1175134211yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×Q82C2
socle, prime radicalC22×C3×C5#120
hypercenterQ82D15
hypocenterC3×C5#1633
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ Q82

Complements

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

NH ≅ G/Ntype
59. C3×C5×Q8Q16semidirect
126. C5×Q8#216semidirect
152. C3×Q8#689semidirect
185. C3×C5#1633semidirect
200. Q8#6718semidirect
211. C5#71940semidirect
220. C3#10602733semidirect

Maximal subgroups

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

subgroupindex
C3×C5×Q822
#117511932
#117511222
#117463672
#117463562
#106027333
#719405