Finite Group Databasebeta

← #14312424

Subgroups — #14312424

Order 1920.

316 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 105 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#11751226C211yesmaximal, characteristic
2#11751219C211yesmaximal, characteristic
3C3×C5×H(3,ℤ/4)C211yesmaximal, characteristic
4#11746354C212yesmaximal
5#11746353C212yesmaximal
6#10599494—31nomaximal, Hall
7C2×C3×C5×M16C2211yescharacteristic
8C3×C5×#117C2212yes—
9C2×C4×Dic15C2211yescharacteristic
10C2×#6710C2212yes—
11C2×#6710C2211yescharacteristic
12#91103—22no—
13#91098—22no—
14#68701—51nomaximal, Hall
15#65414—31no—
16#65407—31no—
17C5×H(3,ℤ/4)D311yescharacteristic
18#64753—32no—
19#64752—32no—
20C22×C3×C4×C5C2311yescharacteristic
21C22×Dic15—21no—
22C3×C5×M16—22no—
23C2×C3×C5×C8D412yes—
24C3×C5×C4⋊C4—22no—
25C3×C5×C22⋊C4—22no—
26C3×C42×C5—22no—
27C4×Dic15—21no—
28C4×Dic15Q811yescharacteristic
29C4×Dic15Q811yescharacteristic
30#6710—22no—
31#6710—22no—
32#6710—22no—
33C2×C3⋊#168—21no—
34C2×C3⋊#168—22no—
35#5125—51no—
36#5118—51no—
37C3×H(3,ℤ/4)D511yescharacteristic
38#4533—52no—
39#4532—52no—
40C2×C5×M16C2×D311yescharacteristic
41C5×#117C2×D312yes—
42C2×C4×Dic5—31no—
43C2×#681—31no—
44C2×#681—32no—
45#3951—62no—
46#3946—62no—
47#2102—151noSylow
48C23×C3×C5#4111yescharacteristic
49C2×C3×C4×C5—42no—
50C2×C3×C4×C5C2×D411yescharacteristic
51C2×C3×C4×C5C2×Q811yescharacteristic
52C2×C3×C4×C5#4112yes—
53C2×C3×C4×C5#4112yes—
54C2×Dic15—21no—
55C2×Dic15—21no—
56C2×Dic15—42no—
57C3×C5×C8—22no—
58C3⋊#168—41no—
59C3⋊#168—42no—
60C2×C3×M16C2×D511yescharacteristic
61C3×#117C2×D512yes—
62C2×C4×Dic3—51no—
63C2×#208—52no—
64C2×#208—51no—
65#819—102no—
66Dic3⋊C8—102no—
67C22×C4×C5C22×D311yescharacteristic
68C22×Dic5—61no—
69C5×M16—22no—
70C2×C5×C8D1212yes—
71C5×C4⋊C4—22no—
72C5×C22⋊C4—22no—
73C42×C5—22no—
74C4×Dic5—31no—
75C4×Dic5—31no—
76C4×Dic5—61no—
77#681—62no—
78#681—62no—
79#681—62no—
80C2×#168—61no—
81C2×#168—62no—
82#430—151no—
83#423—151no—
84#344—152no—
85#339—152no—
86H(3,ℤ/4)D1511yescharacteristic
87C22×C3×C5—41no—
88C22×C3×C5C22⋊Q811yescharacteristic
89C22×C3×C5#12612yes—
90C3×C4×C5—82no—
91C3×C4×C5#12311yescharacteristic
92C3×C4×C5#12411yescharacteristic
93C3×C4×C5#12512yes—
94Dic15—22no—
95Dic15—41no—
96C22×C3×C4C22×D511yescharacteristic
97C22×Dic3—101no—
98C3×M16—22no—
99C2×C3×C8D2012yes—
100C3×C4⋊C4—22no—
101C3×C22⋊C4—22no—
102C3×C42—22no—
103C4×Dic3—51no—
104C4×Dic3—51no—
105C4×Dic3—101no—
106#208—102no—
107#208—102no—
108#208—102no—
109C2×C3⋊C8—101no—
110C2×C3⋊C8—102no—
111C23×C5#23711yescharacteristic
112C2×C4×C5—42no—
113C2×C4×C5C2×D1211yescharacteristic
114C2×C4×C5#23512yes—
115C2×C4×C5#23712yes—
116C2×C4×C5D3×Q811yescharacteristic
117C2×Dic5—61no—
118C2×Dic5—61no—
119C2×Dic5—122no—
120C5×C8—22no—
121#168—122no—
122#168—121no—
123C2×M16—152no—
124C2×M16—151no—
125C2×M16C2×D1511yescharacteristic
126#117C2×D1512yes—
127C2×C42—151no—
128#108—302no—
129C4⋊C8—302no—
130C2×C3×C5—21no—
131C2×C3×C5—22no—
132C2×C3×C5#40011yescharacteristic
133C23×C3#71111yescharacteristic
134C2×C3×C4—42no—
135C2×C3×C4C2×D2011yescharacteristic
136C2×C3×C4#70912yes—
137C2×C3×C4#71112yes—
138C2×C3×C4Q8×D511yescharacteristic
139C2×Dic3—101no—
140C2×Dic3—101no—
141C2×Dic3—202no—
142C3×C8—22no—
143C3⋊C8—202no—
144C3⋊C8—201no—
145C22×C5—41no—
146C22×C5#87912yes—
147C22×C5#89711yescharacteristic
148C4×C5—82no—
149C4×C5#87511yescharacteristic
150C4×C5#88611yescharacteristic
151C4×C5#88912yes—
152Dic5—62no—
153Dic5—121no—
154C22×C4—301no—
155C22×C4C22×D1511yescharacteristic
156M16—22no—
157M16—302no—
158M16—302no—
159M16—302no—
160C2×C8—301no—
161C2×C8—302no—
162C2×C8D6012yes—
163C4⋊C4—22no—
164C22⋊C4—22no—
165C42—22no—
166C42—151no—
167C42—151no—
168C42—301no—
169C3×C5#210211yescharacteristic, complemented, Hall
170C22×C3—41no—
171C22×C3#402512yes—
172C22×C3#404311yescharacteristic
173C3×C4—82no—
174C3×C4#402111yescharacteristic
175C3×C4#403211yescharacteristic
176C3×C4#403512yes—
177Dic3—102no—
178Dic3—201no—
179C2×C5—21no—
180C2×C5—22no—
181C2×C5#465911yescharacteristic
182C23#681911yescharacteristic
183C2×C4—42no—
184C2×C4—301no—
185C2×C4—301no—
186C2×C4—602no—
187C2×C4C2×D6011yescharacteristic
188C2×C4#681712yes—
189C2×C4#681912yes—
190C2×C4Q8×D1511yescharacteristic
191C8—22no—
192C8—602no—
193C8—601no—
194C2×C3—21no—
195C2×C3—22no—
196C2×C3#6494811yescharacteristic
197C5#6870111yescharacteristic, complemented, Sylow
198C22—41no—
199C22#9176812yes—
200C22#9178611yescharacteristic
201C4—82no—
202C4—302no—
203C4—601no—
204C4#9176411yescharacteristic
205C4#9177511yescharacteristic
206C4#9177812yes—
207C3#1059949411yescharacteristic, complemented, Sylow
208C2—22no—
209C2—21no—
210C2#1175076011yescharacteristic
subgroupG/H
centerC4#91764
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×H(3,ℤ/4)C2
socleC2×C3×C5#400
prime radicalC23×C3×C5#41
hypercenterH(3,ℤ/4)D15
hypocenterC3×C5#2102
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
169. C3×C5#2102semidirect
197. C5#68701semidirect
207. C3#10599494semidirect

Maximal subgroups

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

subgroupindex
#117512262
#117512192
C3×C5×H(3,ℤ/4)2
#117463542
#117463532
#105994943
#687015