Finite Group Databasebeta

← #14293752

Subgroups — #14293752

Order 1920.

352 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 115 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×#494C211yesmaximal, characteristic
2#11751194C212yesmaximal
3#11751181C212yesmaximal
4#11750781C211yesmaximal, characteristic
5#11746276C211yesmaximal, characteristic
6#10602092—31nomaximal, Hall
7C2×C3×C5×Q16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2212yes—
11C3×C4×C5×C8C2211yescharacteristic
12#91101—22no—
13#91094—24no—
14#91092—24no—
15C4×C3⋊#168C2212yes—
16#71299—51nomaximal, Hall
17C5×#494D311yescharacteristic
18#65382—32no—
19#65368—32no—
20#64969—31no—
21#64675—31no—
22C2×C3×C5×Q8—21no—
23C2×C3×C5×Q8—21no—
24C2×Dic30—22no—
25C3×C5×Q16—44no—
26C2×C3×C5×C8D412yes—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4—22no—
29C3×C42×C5C2311yescharacteristic
30C4⋊Dic15—22no—
31C4⋊Dic15—22no—
32C2×C3⋊#168D414yes—
33C3×#494D511yescharacteristic
34#5093—52no—
35#5080—52no—
36#4680—51no—
37#4455—51no—
38C2×C5×Q16—22no—
39C5×C4⋊Q8C2×D311yescharacteristic
40C5×C4⋊Q8C2×D311yescharacteristic
41#4015—32no—
42C4×C5×C8C2×D311yescharacteristic
43#3949—62no—
44#3942—64no—
45#3940—64no—
46C4×#168—32no—
47#1716—151noSylow
48C3×C5×Q8—42no—
49C3×C5×Q8—42no—
50C2×C3×C4×C5—41no—
51C2×C3×C4×C5—41no—
52C2×C3×C4×C5C2×D411yescharacteristic
53C2×C3×C4×C5C2×D412yes—
54C2×Dic15—42no—
55Dic30—44no—
56C3×C5×C8SD1614yes—
57C3⋊#168—24no—
58C2×C3×Q16—22no—
59C3×C4⋊Q8C2×D511yescharacteristic
60C3×C4⋊Q8C2×D511yescharacteristic
61#869—52no—
62C3×C4×C8C2×D511yescharacteristic
63#817—102no—
64#810—104no—
65#808—104no—
66C4×C3⋊C8—52no—
67C2×C5×Q8—21no—
68C2×C5×Q8—21no—
69C2×Dic10—62no—
70C5×Q16—44no—
71C2×C5×C8#6712yes—
72C5×C4⋊C4—22no—
73C5×C4⋊C4—22no—
74C42×C5C22×D311yescharacteristic
75C4⋊Dic5—62no—
76C4⋊Dic5—62no—
77C2×#168—34no—
78#498—152no—
79#498—151no—
80#494D1511yescharacteristic
81#487—152no—
82#322—151no—
83C22×C3×C5#12711yescharacteristic
84C3×C4×C5—81no—
85C3×C4×C5—81no—
86C3×C4×C5C2×SD1612yes—
87C3×C4×C5#13714yes—
88Dic15—82no—
89C2×C3×Q8—21no—
90C2×C3×Q8—21no—
91C2×Dic6—102no—
92C3×Q16—44no—
93C2×C3×C8C22⋊D512yes—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—22no—
96C3×C42C22×D511yescharacteristic
97C4⋊Dic3—102no—
98C4⋊Dic3—102no—
99C2×C3⋊C8—54no—
100C5×Q8—42no—
101C5×Q8—42no—
102C2×C4×C5—41no—
103C2×C4×C5—41no—
104C2×C4×C5D3×D412yes—
105C2×C4×C5C2×#6711yescharacteristic
106C2×Dic5—122no—
107Dic10—124no—
108C5×C8#21414yes—
109#168—64no—
110C2×Q16—22no—
111C4⋊Q8—152no—
112C4⋊Q8C2×D1511yescharacteristic
113C4⋊Q8C2×D1511yescharacteristic
114#106—304no—
115#106—302no—
116#103—304no—
117C4×C8—152no—
118C4×C8C2×D1511yescharacteristic
119C2×C3×C5#49211yescharacteristic
120C2×C3×C5#49712yes—
121C3×Q8—42no—
122C3×Q8—42no—
123C2×C3×C4—41no—
124C2×C3×C4—41no—
125C2×C3×C4D4×D512yes—
126C2×C3×C4C2×C22⋊D511yescharacteristic
127C2×Dic3—202no—
128Dic6—204no—
129C3×C8#68714yes—
130C3⋊C8—104no—
131C22×C5#94011yescharacteristic
132C4×C5—81no—
133C4×C5—81no—
134C4×C5#91814yes—
135C4×C5C2×#21412yes—
136Dic5—242no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—302no—
140Q16—44no—
141C2×C8—154no—
142C2×C8#122012yes—
143C4⋊C4—22no—
144C4⋊C4—22no—
145C4⋊C4—302no—
146C4⋊C4—302no—
147C42C22×D1511yescharacteristic
148C3×C5#171611yescharacteristic, complemented, Hall
149C22×C3#408611yescharacteristic
150C3×C4—81no—
151C3×C4—81no—
152C3×C4#406414yes—
153C3×C4C2×#68712yes—
154Dic3—402no—
155C2×C5#507611yescharacteristic
156C2×C5#519012yes—
157Q8—42no—
158Q8—42no—
159Q8—604no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—602no—
163C2×C4D4×D1512yes—
164C2×C4C2×#122011yescharacteristic
165C8—304no—
166C8#671614yes—
167C2×C3#6536511yescharacteristic
168C2×C3#6547912yes—
169C5#7129911yescharacteristic, complemented, Sylow
170C22#9182911yescharacteristic
171C4—81no—
172C4—81no—
173C4—1202no—
174C4#9180714yes—
175C4C2×#671612yes—
176C3#1060209211yescharacteristic, complemented, Sylow
177C2#1175117711yescharacteristic
178C2#1175129112yes—
subgroupG/H
centerC22#91829
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#494C2
socle, prime radicalC22×C3×C5#127
hypercenter#494D15
hypocenterC3×C5#1716
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
148. C3×C5#1716semidirect
169. C5#71299semidirect
176. C3#10602092semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4942
#117511942
#117511812
#117507812
#117462762
#106020923
#712995