Finite Group Databasebeta

← #14289562

Subgroups — #14289562

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
1C5×#5722C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic
3#11746961C212yesmaximal
4C3×#64766C211yesmaximal, characteristic
5#11745842C212yesmaximal
6#10602733—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C2×#6718—22no—
9#91758C2211yescharacteristic
10C5×#944—22no—
11C5×#888—22no—
12C5×#887—22no—
13C4×C5×Dic6C2212yes—
14C4×C3⋊#168C2211yescharacteristic
15C3×C4⋊#168C2212yes—
16#90988—22no—
17#90973—22no—
18#68505—51nomaximal, Hall
19C5×Q82—31no—
20#65381—31no—
21#65310—32no—
22#64766D311yescharacteristic
23Q8⋊#168—32no—
24C2×C3×C5×Q8D412yes—
25C2×Dic30—21no—
26C2×C5×Dic6—22no—
27C2×C5×Dic6D412yes—
28C3×C5×C4⋊C4—22no—
29C3×C42×C5C2311yescharacteristic
30#6718—44no—
31C4⋊Dic15—22no—
32C2×C3⋊#168—21no—
33C5×C4⋊Dic3D412yes—
34C5×Dic3⋊C4—24no—
35C5×Dic3⋊C4—22no—
36C4×C5×Dic3—22no—
37C4×C5×Dic3—22no—
38C2×C3×#168—22no—
39#5722D511yescharacteristic
40#5092—51no—
41#4850—52no—
42C3×#333—51no—
43#4484—52no—
44C5×C4⋊Q8—62no—
45C5×C4⋊Q8—62no—
46C5×C4⋊Q8C2×D311yescharacteristic
47C4×C5×Q8—32no—
48C4×C5×Q8—62no—
49C2×#689—62no—
50#4015—31no—
51#3967—62no—
52#3939—62no—
53C4⋊#168C2×D312yes—
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×C5×Dic3—22no—
63C2×C5×Dic3—22no—
64C5×Dic6—22no—
65C5×Dic6—82no—
66C5×Dic6Q1614yescomplemented
67C3⋊#168—22no—
68C3×#168—42no—
69C3×C4⋊Q8C2×D511yescharacteristic
70#944—22no—
71C2×#216—102no—
72#888—22no—
73#887—22no—
74#869—51no—
75C4×Dic6C2×D512yes—
76C3×C4⋊C8—52no—
77#818—102no—
78#816—102no—
79C4×C3⋊C8—51no—
80C2×C5×Q8—32no—
81C2×C5×Q8—62no—
82C2×C5×Q8D1212yes—
83C2×Dic10—61no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—32no—
86C5×C4⋊C4—64no—
87C5×C4⋊C4—62no—
88C42×C5—62no—
89C42×C5—62no—
90C42×C5C22×D311yescharacteristic
91#689—124no—
92C4⋊Dic5—62no—
93C2×#168—22no—
94C2×#168—61no—
95Q82—31no—
96#494—151no—
97#477—152no—
98#333—51no—
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—
106C5×Dic3—24no—
107C5×Dic3—42no—
108C2×C3×Q8C22⋊D512yes—
109C2×Dic6—22no—
110C2×Dic6—101no—
111C2×Dic6C22⋊D512yes—
112C2×C3×C8—102no—
113C3×C4⋊C4—22no—
114C3×C42C22×D511yescharacteristic
115#216—204no—
116C4⋊Dic3—102no—
117C4⋊Dic3C22⋊D512yes—
118Dic3⋊C4—24no—
119Dic3⋊C4—22no—
120C4×Dic3—22no—
121C4×Dic3—22no—
122C2×C3⋊C8—101no—
123C5×Q8—34no—
124C5×Q8—42no—
125C5×Q8—62no—
126C5×Q8—242no—
127C2×C4×C5—22no—
128C2×C4×C5—62no—
129C2×C4×C5—62no—
130C2×C4×C5C2×D1211yescharacteristic
131C2×C4×C5D3×D412yes—
132C2×Dic5—121no—
133Dic10—122no—
134#168—42no—
135#168—62no—
136C2×Q16—302no—
137C4⋊Q8—62no—
138C4⋊Q8—62no—
139C4⋊Q8—151no—
140C4⋊Q8D3×D511yescharacteristic
141C4×Q8—32no—
142C4×Q8—62no—
143#107—302no—
144C4⋊C8—52no—
145#103—302no—
146C4×C8—151no—
147C2×C3×C5#45112yes—
148C2×C3×C5#45311yescharacteristic
149C3×Q8—42no—
150C2×C3×C4—22no—
151C2×C3×C4C2×C22⋊D511yescharacteristic
152C2×C3×C4C2×C22⋊D512yes—
153C2×Dic3—22no—
154C2×Dic3—22no—
155C2×Dic3—201no—
156Dic6—22no—
157Dic6—82no—
158Dic6—202no—
159Dic6#68914yescomplemented
160C3×C8—202no—
161C3⋊C8—102no—
162C22×C5#88211yescharacteristic
163C4×C5—21no—
164C4×C5—42no—
165C4×C5—64no—
166C4×C5—122no—
167C4×C5#91512yes—
168C4×C5D3×Q1612yes—
169Dic5—241no—
170C2×Q8—32no—
171C2×Q8—62no—
172C2×Q8—301no—
173C2×Q8#120312yes—
174Q16—604no—
175C2×C8—102no—
176C2×C8—301no—
177C4⋊C4—22no—
178C4⋊C4—32no—
179C4⋊C4—64no—
180C4⋊C4—62no—
181C4⋊C4—302no—
182C42—62no—
183C42—62no—
184C42C2×D3×D511yescharacteristic
185C3×C5#163311yescharacteristic, complemented, Hall
186C22×C3#409911yescharacteristic
187C3×C4—21no—
188C3×C4—42no—
189C3×C4#408812yes—
190C3×C4C2×#68912yes—
191Dic3—24no—
192Dic3—42no—
193Dic3—401no—
194C2×C5#474711yescharacteristic
195C2×C5#480912yes—
196Q8—34no—
197Q8—42no—
198Q8—62no—
199Q8—242no—
200Q8—602no—
201C2×C4—22no—
202C2×C4—62no—
203C2×C4—62no—
204C2×C4—601no—
205C2×C4C2×#120311yescharacteristic
206C2×C4D3×C22⋊D512yes—
207C8—202no—
208C8—302no—
209C2×C3#6551712yes—
210C2×C3#6553011yescharacteristic
211C5#6850511yescharacteristic, complemented, Sylow
212C22#9157011yescharacteristic
213C4—21no—
214C4—42no—
215C4—64no—
216C4—122no—
217C4—1201no—
218C4D3×#68912yes—
219C4#9151812yes—
220C3#1060273311yescharacteristic, complemented, Sylow
221C2#1174914111yescharacteristic
222C2#1174930212yes—
subgroupG/H
centerC22#91570
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. C5×Dic6Q16semidirect
159. Dic6#689semidirect
185. C3×C5#1633semidirect
211. C5#68505semidirect
220. C3#10602733semidirect

Maximal subgroups

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

subgroupindex
C5×#57222
#117511932
#117469612
C3×#647662
#117458422
#106027333
#685055