Finite Group Databasebeta

← #14289560

Subgroups — #14289560

Order 1920.

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

normal subgroups only

This group has 412 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
1#11756481C211yesmaximal, characteristic
2C5×#5092C211yesmaximal, characteristic
3#11746963C212yesmaximal
4C3×#64766C211yesmaximal, characteristic
5#11745844C212yesmaximal
6#10602100—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8#91833—22no—
9#91777—22no—
10#91776—22no—
11C4×Dic30C2212yes—
12C2×C5×#216—22no—
13C5×#869C2211yescharacteristic
14C4×C5×C3⋊C8C2211yescharacteristic
15C3×C4⋊#168C2212yes—
16#90988—22no—
17#90975—22no—
18#68505—51nomaximal, Hall
19#66056—31no—
20C5×#494—31no—
21#65380—32no—
22#64766D311yescharacteristic
23#64676—32no—
24C2×C3×C5×Q8D412yes—
25C2×Dic30—22no—
26C2×Dic30D412yes—
27C2×C5×Dic6—21no—
28C3×C5×C4⋊C4—22no—
29C3×C42×C5C2311yescharacteristic
30C4⋊Dic15D412yes—
31#6712—24no—
32#6712—22no—
33C4×Dic15—22no—
34C4×Dic15—22no—
35C5×#216—44no—
36C5×C4⋊Dic3—22no—
37C2×C5×C3⋊C8—21no—
38C2×C3×#168—22no—
39#5722—51no—
40#5092D511yescharacteristic
41#4850—52no—
42C3×#333—51no—
43#4484—52no—
44C2×C5×Q16—62no—
45C5×C4⋊Q8—31no—
46C5×C4⋊Q8C2×D311yescharacteristic
47#4090—62no—
48#4034—62no—
49#4033—62no—
50C4×Dic10—32no—
51C4×C5×C8—31no—
52#3942—62no—
53#3939—62no—
54C4⋊#168C2×D312yes—
55#1633—151noSylow
56C3×C5×Q8—42no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×Dic15—22no—
61C2×Dic15—22no—
62Dic30—22no—
63Dic30—82no—
64Dic30Q1614yescomplemented
65C2×C5×Dic3—41no—
66C5×Dic6—42no—
67C3×#168—42no—
68C5×C3⋊C8—22no—
69C3×C4⋊Q8C2×D511yescharacteristic
70#944—102no—
71C2×#216—22no—
72#888—102no—
73#887—102no—
74#869C2×D511yescharacteristic
75C4×Dic6—52no—
76C3×C4⋊C8—52no—
77#818—102no—
78#816—102no—
79C4×C3⋊C8C2×D511yescharacteristic
80C2×C5×Q8—61no—
81C2×C5×Q8D1212yes—
82C2×Dic10—32no—
83C2×Dic10—62no—
84C5×Q16—124no—
85C2×C5×C8—61no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—62no—
88C42×C5C22×D311yescharacteristic
89C4⋊Dic5—32no—
90#683—64no—
91#683—62no—
92C4×Dic5—62no—
93C4×Dic5—62no—
94C2×#168—22no—
95Q82—151no—
96#494—31no—
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—24no—
106Dic15—42no—
107C5×Dic3—81no—
108C2×C3×Q8C22⋊D512yes—
109C2×Dic6—21no—
110C2×Dic6—52no—
111C2×Dic6—102no—
112C2×C3×C8—102no—
113C3×C4⋊C4—22no—
114C3×C42C22×D511yescharacteristic
115#216—44no—
116C4⋊Dic3—22no—
117C4⋊Dic3—52no—
118Dic3⋊C4—104no—
119Dic3⋊C4—102no—
120C4×Dic3—102no—
121C4×Dic3—102no—
122C2×C3⋊C8—21no—
123C5×Q8—42no—
124C5×Q8—122no—
125C2×C4×C5—22no—
126C2×C4×C5—121no—
127C2×C4×C5C2×D1211yescharacteristic
128C2×C4×C5D3×D412yes—
129C2×Dic5—62no—
130C2×Dic5—62no—
131Dic10—34no—
132Dic10—62no—
133Dic10—242no—
134C5×C8—62no—
135#168—42no—
136C2×Q16—62no—
137C4⋊Q8—31no—
138C4⋊Q8—302no—
139C4⋊Q8—302no—
140C4⋊Q8D3×D511yescharacteristic
141C4×Q8—152no—
142C4×Q8—302no—
143#107—302no—
144C4⋊C8—52no—
145#103—302no—
146C4×C8—31no—
147C2×C3×C5#45112yes—
148C2×C3×C5#45311yescharacteristic
149C3×Q8—42no—
150C2×C3×C4—22no—
151C2×C3×C4D4×D512yes—
152C2×C3×C4C2×C22⋊D511yescharacteristic
153C2×Dic3—41no—
154C2×Dic3—102no—
155C2×Dic3—102no—
156Dic6—42no—
157Dic6—54no—
158Dic6—102no—
159Dic6—402no—
160C3×C8—202no—
161C3⋊C8—22no—
162C22×C5#88211yescharacteristic
163C4×C5—21no—
164C4×C5—42no—
165C4×C5—241no—
166C4×C5#91512yes—
167C4×C5D3×Q1612yes—
168Dic5—64no—
169Dic5—122no—
170C2×Q8—61no—
171C2×Q8—152no—
172C2×Q8—302no—
173C2×Q8#120312yes—
174Q16—124no—
175C2×C8—61no—
176C2×C8—102no—
177C4⋊C4—22no—
178C4⋊C4—62no—
179C4⋊C4—152no—
180C4⋊C4—304no—
181C4⋊C4—302no—
182C42—302no—
183C42—302no—
184C42C2×D3×D511yescharacteristic
185C3×C5#163311yescharacteristic, complemented, Hall
186C22×C3#408311yescharacteristic
187C3×C4—21no—
188C3×C4—42no—
189C3×C4D5×Q1612yes—
190C3×C4#406412yes—
191Dic3—81no—
192Dic3—104no—
193Dic3—202no—
194C2×C5#474711yescharacteristic
195C2×C5#480912yes—
196Q8—42no—
197Q8—122no—
198Q8—154no—
199Q8—302no—
200Q8—1202no—
201C2×C4—22no—
202C2×C4—121no—
203C2×C4—302no—
204C2×C4—302no—
205C2×C4C2×#120311yescharacteristic
206C2×C4#679012yes—
207C8—62no—
208C8—202no—
209C2×C3#6536611yescharacteristic
210C2×C3#6547512yes—
211C5#6850511yescharacteristic, complemented, Sylow
212C22#9157311yescharacteristic
213C4—21no—
214C4—42no—
215C4—241no—
216C4—304no—
217C4—602no—
218C4#9151112yes—
219C4#9152212yes—
220C3#1060210011yescharacteristic, complemented, Sylow
221C2#1174914311yescharacteristic
222C2#1174930812yes—
subgroupG/H
centerC22#91573
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
64. Dic30Q16semidirect
185. C3×C5#1633semidirect
211. C5#68505semidirect
220. C3#10602100semidirect

Maximal subgroups

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

subgroupindex
#117564812
C5×#50922
#117469632
C3×#647662
#117458442
#106021003
#685055