Finite Group Databasebeta

← #14289564

Subgroups — #14289564

Order 1920.

412 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 100 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×#66056C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic
3#11746916C212yesmaximal
4C5×#4546C211yesmaximal, characteristic
5#11745840C212yesmaximal
6#10599298—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C2×#6718—22no—
9#91758C2211yescharacteristic
10C3×#4090—22no—
11C3×#4034—22no—
12C3×#4033—22no—
13C3×C4×Dic10C2212yes—
14C4×C3⋊#168C2211yescharacteristic
15C5×C4⋊(C3⋊C8)C2212yes—
16#90990—22no—
17#90971—22no—
18#71940—51nomaximal, Hall
19#66056D311yescharacteristic
20#65381—31no—
21#65139—32no—
22C5×#333—31no—
23#64704—32no—
24C2×C3×C5×Q8D412yes—
25C2×Dic30—21no—
26C2×C3×Dic10—22no—
27C2×C3×Dic10D412yes—
28C3×C5×C4⋊C4—22no—
29C3×C42×C5C2311yescharacteristic
30#6718—44no—
31C4⋊Dic15—22no—
32C2×C3⋊#168—21no—
33C2×C5×C3⋊C8—22no—
34C3×C4⋊Dic5D412yes—
35C3×#683—24no—
36C3×#683—22no—
37C3×C4×Dic5—22no—
38C3×C4×Dic5—22no—
39C3×Q82—51no—
40#5092—51no—
41#5021—52no—
42#4546D511yescharacteristic
43#4535—52no—
44C5×C4⋊Q8C2×D311yescharacteristic
45#4090—22no—
46C2×#689—62no—
47#4034—22no—
48#4033—22no—
49#4015—31no—
50C4×Dic10C2×D312yes—
51C5×C4⋊C8—32no—
52#3950—62no—
53#3948—62no—
54C4×#168—31no—
55#1633—151noSylow
56C3×C5×Q8—42no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×Dic15—41no—
61Dic30—42no—
62C2×C3×Dic5—22no—
63C2×C3×Dic5—22no—
64C3×Dic10—22no—
65C3×Dic10—82no—
66C3×Dic10Q1614yescomplemented
67C3⋊#168—22no—
68C5×C3⋊C8—42no—
69C3×C4⋊Q8—102no—
70C3×C4⋊Q8—102no—
71C3×C4⋊Q8C2×D511yescharacteristic
72C3×C4×Q8—52no—
73C3×C4×Q8—102no—
74C2×#216—102no—
75#869—51no—
76#835—102no—
77#807—102no—
78C4⋊(C3⋊C8)C2×D512yes—
79C4×C3⋊C8—51no—
80C2×C5×Q8#6712yes—
81C2×Dic10—22no—
82C2×Dic10—61no—
83C2×Dic10#6712yes—
84C2×C5×C8—62no—
85C5×C4⋊C4—22no—
86C42×C5C22×D311yescharacteristic
87#689—124no—
88C4⋊Dic5—62no—
89C4⋊Dic5#6712yes—
90#683—24no—
91#683—22no—
92C4×Dic5—22no—
93C4×Dic5—22no—
94C2×#168—61no—
95Q82—51no—
96#494—151no—
97#477—152no—
98#333—31no—
99Q8⋊C8—152no—
100C22×C3×C5#12011yescharacteristic
101C3×C4×C5—21no—
102C3×C4×C5—42no—
103C3×C4×C5C2×Q1612yes—
104C3×C4×C5#13712yes—
105Dic15—81no—
106C3×Dic5—24no—
107C3×Dic5—42no—
108C2×C3×Q8—52no—
109C2×C3×Q8—102no—
110C2×C3×Q8D2012yes—
111C2×Dic6—101no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—52no—
114C3×C4⋊C4—104no—
115C3×C4⋊C4—102no—
116C3×C42—102no—
117C3×C42—102no—
118C3×C42C22×D511yescharacteristic
119#216—204no—
120C4⋊Dic3—102no—
121C2×C3⋊C8—22no—
122C2×C3⋊C8—101no—
123C5×Q8—42no—
124C2×C4×C5—22no—
125C2×C4×C5C2×#6711yescharacteristic
126C2×C4×C5C2×#6712yes—
127C2×Dic5—22no—
128C2×Dic5—22no—
129C2×Dic5—121no—
130Dic10—22no—
131Dic10—82no—
132Dic10—122no—
133Dic10#21614yescomplemented
134C5×C8—122no—
135#168—62no—
136C2×Q16—302no—
137C4⋊Q8—102no—
138C4⋊Q8—102no—
139C4⋊Q8—151no—
140C4⋊Q8D3×D511yescharacteristic
141C4×Q8—52no—
142C4×Q8—102no—
143#107—302no—
144C4⋊C8—32no—
145#103—302no—
146C4×C8—151no—
147C2×C3×C5#45112yes—
148C2×C3×C5#45311yescharacteristic
149C3×Q8—42no—
150C3×Q8—54no—
151C3×Q8—102no—
152C3×Q8—402no—
153C2×C3×C4—22no—
154C2×C3×C4—102no—
155C2×C3×C4—102no—
156C2×C3×C4C2×D2011yescharacteristic
157C2×C3×C4D4×D512yes—
158C2×Dic3—201no—
159Dic6—202no—
160C3⋊C8—42no—
161C3⋊C8—102no—
162C22×C5#95311yescharacteristic
163C4×C5—21no—
164C4×C5—42no—
165C4×C5#94212yes—
166C4×C5C2×#21612yes—
167Dic5—24no—
168Dic5—42no—
169Dic5—241no—
170C2×Q8—52no—
171C2×Q8—102no—
172C2×Q8—301no—
173C2×Q8#120212yes—
174Q16—604no—
175C2×C8—62no—
176C2×C8—301no—
177C4⋊C4—22no—
178C4⋊C4—52no—
179C4⋊C4—104no—
180C4⋊C4—102no—
181C4⋊C4—302no—
182C42—102no—
183C42—102no—
184C42C2×D3×D511yescharacteristic
185C3×C5#163311yescharacteristic, complemented, Hall
186C22×C3#402811yescharacteristic
187C3×C4—21no—
188C3×C4—42no—
189C3×C4—104no—
190C3×C4—202no—
191C3×C4#406112yes—
192C3×C4D5×Q1612yes—
193Dic3—401no—
194C2×C5#522812yes—
195C2×C5#524111yescharacteristic
196Q8—42no—
197Q8—54no—
198Q8—102no—
199Q8—402no—
200Q8—602no—
201C2×C4—22no—
202C2×C4—102no—
203C2×C4—102no—
204C2×C4—601no—
205C2×C4C2×#120211yescharacteristic
206C2×C4D5×#6712yes—
207C8—122no—
208C8—302no—
209C2×C3#6503611yescharacteristic
210C2×C3#6509712yes—
211C5#7194011yescharacteristic, complemented, Sylow
212C22#9156411yescharacteristic
213C4—21no—
214C4—42no—
215C4—104no—
216C4—202no—
217C4—1201no—
218C4D5×#21612yes—
219C4#9151312yes—
220C3#1059929811yescharacteristic, complemented, Sylow
221C2#1174913811yescharacteristic
222C2#1174929112yes—
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socle, prime radicalC22×C3×C5#120
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1633
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
66. C3×Dic10Q16semidirect
133. Dic10#216semidirect
185. C3×C5#1633semidirect
211. C5#71940semidirect
220. C3#10599298semidirect

Maximal subgroups

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

subgroupindex
C3×#660562
#117511932
#117469162
C5×#45462
#117458402
#105992983
#719405