Finite Group Databasebeta

← #14289543

Subgroups — #14289543

Order 1920.

412 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 95 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
2C3×C5×#494C211yesmaximal, characteristic
3#11751192C212yesmaximal
4#11746367C211yesmaximal, characteristic
5#11746277C212yesmaximal
6#10602100—31nomaximal, Hall
7C2×C3×C5×Q16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91833—22no—
11#91777—22no—
12#91776—22no—
13C4×Dic30C2212yes—
14C3×C4×C5×C8C2211yescharacteristic
15#91094—22no—
16#91091—22no—
17C4⋊(C3⋊#168)C2212yes—
18#71307—51nomaximal, Hall
19#66056—31no—
20C5×#494D311yescharacteristic
21#65380—32no—
22#64766—31no—
23#64676—32no—
24C2×C3×C5×Q8—21no—
25C2×C3×C5×Q8D412yes—
26C2×Dic30—22no—
27C2×Dic30D412yes—
28C3×C5×Q16—44no—
29C2×C3×C5×C8—21no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C4⋊Dic15D412yes—
34#6712—24no—
35#6712—22no—
36C4×Dic15—22no—
37C4×Dic15—22no—
38C2×C3⋊#168—22no—
39#5722—51no—
40C3×#494D511yescharacteristic
41#5091—52no—
42#4546—51no—
43#4456—52no—
44C2×C5×Q16—22no—
45C5×C4⋊Q8C2×D311yescharacteristic
46C5×C4⋊Q8C2×D311yescharacteristic
47#4090—62no—
48#4034—62no—
49#4033—62no—
50C4×Dic10—32no—
51C4×C5×C8C2×D311yescharacteristic
52#3942—62no—
53#3939—62no—
54C4⋊#168—32no—
55#1633—151noSylow
56C3×C5×Q8—42no—
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5—41no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×Dic15—22no—
63C2×Dic15—22no—
64Dic30—22no—
65Dic30—82no—
66Dic30Q1614yescomplemented
67C3×C5×C8—22no—
68C3⋊#168—42no—
69C2×C3×Q16—22no—
70C3×C4⋊Q8C2×D511yescharacteristic
71C3×C4⋊Q8C2×D511yescharacteristic
72#944—102no—
73#888—102no—
74#887—102no—
75C4×Dic6—52no—
76C3×C4×C8C2×D511yescharacteristic
77#810—102no—
78#807—102no—
79C4⋊(C3⋊C8)—52no—
80C2×C5×Q8—21no—
81C2×C5×Q8#6712yes—
82C2×Dic10—32no—
83C2×Dic10—62no—
84C5×Q16—44no—
85C2×C5×C8—21no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—22no—
88C42×C5C22×D311yescharacteristic
89C4⋊Dic5—32no—
90#683—64no—
91#683—62no—
92C4×Dic5—62no—
93C4×Dic5—62no—
94C2×#168—62no—
95Q82—151no—
96#494D1511yescharacteristic
97#477—152no—
98#333—151no—
99Q8⋊C8—152no—
100C22×C3×C5#12011yescharacteristic
101C3×C4×C5—21no—
102C3×C4×C5—42no—
103C3×C4×C5—81no—
104C3×C4×C5C2×Q1612yes—
105C3×C4×C5#13712yes—
106Dic15—24no—
107Dic15—42no—
108C2×C3×Q8—21no—
109C2×C3×Q8C22⋊D512yes—
110C2×Dic6—52no—
111C2×Dic6—102no—
112C3×Q16—44no—
113C2×C3×C8—21no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C42C22×D511yescharacteristic
117C4⋊Dic3—52no—
118Dic3⋊C4—104no—
119Dic3⋊C4—102no—
120C4×Dic3—102no—
121C4×Dic3—102no—
122C2×C3⋊C8—102no—
123C5×Q8—42no—
124C5×Q8—42no—
125C2×C4×C5—22no—
126C2×C4×C5—41no—
127C2×C4×C5D3×D412yes—
128C2×C4×C5C2×#6711yescharacteristic
129C2×Dic5—62no—
130C2×Dic5—62no—
131Dic10—34no—
132Dic10—62no—
133Dic10—242no—
134C5×C8—22no—
135#168—122no—
136C2×Q16—22no—
137C4⋊Q8—302no—
138C4⋊Q8—302no—
139C4⋊Q8C2×D1511yescharacteristic
140C4⋊Q8C2×D1511yescharacteristic
141C4×Q8—152no—
142C4×Q8—302no—
143#107—302no—
144C4⋊C8—152no—
145#103—302no—
146C4×C8C2×D1511yescharacteristic
147C2×C3×C5#45112yes—
148C2×C3×C5#45311yescharacteristic
149C3×Q8—42no—
150C3×Q8—42no—
151C2×C3×C4—22no—
152C2×C3×C4—41no—
153C2×C3×C4D4×D512yes—
154C2×C3×C4C2×C22⋊D511yescharacteristic
155C2×Dic3—102no—
156C2×Dic3—102no—
157Dic6—54no—
158Dic6—102no—
159Dic6—402no—
160C3×C8—22no—
161C3⋊C8—202no—
162C22×C5#93711yescharacteristic
163C4×C5—21no—
164C4×C5—42no—
165C4×C5—81no—
166C4×C5D3×Q1612yes—
167C4×C5#91812yes—
168Dic5—64no—
169Dic5—122no—
170C2×Q8—21no—
171C2×Q8—152no—
172C2×Q8—302no—
173C2×Q8#122012yes—
174Q16—44no—
175C2×C8—21no—
176C2×C8—302no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—152no—
180C4⋊C4—304no—
181C4⋊C4—302no—
182C42—302no—
183C42—302no—
184C42C22×D1511yescharacteristic
185C3×C5#163311yescharacteristic, complemented, Hall
186C22×C3#408311yescharacteristic
187C3×C4—21no—
188C3×C4—42no—
189C3×C4—81no—
190C3×C4D5×Q1612yes—
191C3×C4#406412yes—
192Dic3—104no—
193Dic3—202no—
194C2×C5#507711yescharacteristic
195C2×C5#518612yes—
196Q8—42no—
197Q8—42no—
198Q8—154no—
199Q8—302no—
200Q8—1202no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—302no—
204C2×C4—302no—
205C2×C4D4×D1512yes—
206C2×C4C2×#122011yescharacteristic
207C8—22no—
208C8—602no—
209C2×C3#6536611yescharacteristic
210C2×C3#6547512yes—
211C5#7130711yescharacteristic, complemented, Sylow
212C22#9182611yescharacteristic
213C4—21no—
214C4—42no—
215C4—81no—
216C4—304no—
217C4—602no—
218C4Q16×D1512yes—
219C4#9180712yes—
220C3#1060210011yescharacteristic, complemented, Sylow
221C2#1175117811yescharacteristic
222C2#1175128712yes—
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#494C2
socle, prime radicalC22×C3×C5#120
hypercenter#494D15
hypocenterC3×C5#1633
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
66. Dic30Q16semidirect
185. C3×C5#1633semidirect
211. C5#71307semidirect
220. C3#10602100semidirect

Maximal subgroups

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

subgroupindex
#117564812
C3×C5×#4942
#117511922
#117463672
#117462772
#106021003
#713075