Finite Group Databasebeta

← #14312436

Subgroups — #14312436

Order 1920.

316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 104 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
2C3×#65407C211yesmaximal, characteristic
3C5×#4557C211yesmaximal, characteristic
4#11745989C212yesmaximal
5#11745977C212yesmaximal
6#10599494—31nomaximal, Hall
7C2×C3×C5×M16C2211yescharacteristic
8C2×#6710C2212yes—
9C5×#926C2212yes—
10C2×C3×C4×Dic5C2211yescharacteristic
11C2×C3×#681C2211yescharacteristic
12#91103—22no—
13C3×#3946—22no—
14#70526—51nomaximal, Hall
15#65414—31no—
16#65407D311yescharacteristic
17C5×H(3,ℤ/4)—31no—
18#64753—32no—
19#64752—32no—
20C22×C3×C4×C5C2311yescharacteristic
21C22×C3×Dic5—21no—
22C3×C5×M16—22no—
23C2×C3×C5×C8D412yes—
24#6710—22no—
25#6710—22no—
26C2×C3⋊#168—22no—
27C5×#217—22no—
28C5×C4⋊Dic3—22no—
29C4×C5×Dic3—22no—
30C3×C4×Dic5—21no—
31C3×C4×Dic5Q811yescharacteristic
32C3×C4×Dic5Q811yescharacteristic
33C3×#681—22no—
34C2×C3×#168—21no—
35C3×#423—51no—
36#5125—51no—
37#4559—52no—
38#4557D511yescharacteristic
39#4523—52no—
40C2×C5×M16C2×D311yescharacteristic
41C5×#117—32no—
42C2×C4×Dic5C2×D311yescharacteristic
43C2×#681—32no—
44C2×#681C2×D311yescharacteristic
45#3951—62no—
46#3946—22no—
47#2102—151noSylow
48C23×C3×C5#4111yescharacteristic
49C2×C3×C4×C5C2×D411yescharacteristic
50C2×C3×C4×C5C2×Q811yescharacteristic
51C2×C3×C4×C5#4112yes—
52C2×C3×C4×C5#4112yes—
53C2×C5×Dic3—42no—
54C2×C3×Dic5—21no—
55C2×C3×Dic5—21no—
56C2×C3×Dic5—42no—
57C3×C5×C8—22no—
58C3⋊#168—42no—
59C3×#168—41no—
60C2×C3×M16—51no—
61C2×C3×M16C2×D511yescharacteristic
62C2×C3×C42—51no—
63#926C2×D512yes—
64C2×#208—52no—
65C3×C4⋊C8—102no—
66#819—102no—
67C22×C4×C5C22×D311yescharacteristic
68C22×Dic5—21no—
69C5×M16—22no—
70C2×C5×C8#6712yes—
71C5×C4⋊C4—62no—
72C5×C22⋊C4—62no—
73C42×C5—62no—
74C4×Dic5—21no—
75C4×Dic5Dic611yescharacteristic
76C4×Dic5Dic611yescharacteristic
77#681—22no—
78#681—62no—
79#681—62no—
80C2×#168—21no—
81C2×#168—62no—
82#430—151no—
83#423—51no—
84#344—152no—
85#339—152no—
86H(3,ℤ/4)—31no—
87C22×C3×C5—41no—
88C22×C3×C5C22⋊Q811yescharacteristic
89C22×C3×C5#12612yes—
90C3×C4×C5#12311yescharacteristic
91C3×C4×C5#12411yescharacteristic
92C3×C4×C5#12512yes—
93C3×Dic5—22no—
94C3×Dic5—41no—
95C5×Dic3—82no—
96C22×C3×C4—101no—
97C22×C3×C4C22×D511yescharacteristic
98C3×M16—22no—
99C3×M16—102no—
100C2×C3×C8—101no—
101C2×C3×C8D2012yes—
102C3×C42—51no—
103C3×C42—51no—
104C3×C42—101no—
105#217—22no—
106C4⋊Dic3—22no—
107C4×Dic3—22no—
108#208—102no—
109#208—102no—
110C2×C3⋊C8—102no—
111C23×C5#23511yescharacteristic
112C2×C4×C5—122no—
113C2×C4×C5C2×Dic611yescharacteristic
114C2×C4×C5#23712yes—
115C2×C4×C5#23912yes—
116C2×C4×C5C2×#6711yescharacteristic
117C2×Dic5—21no—
118C2×Dic5—21no—
119C2×Dic5—42no—
120C5×C8—22no—
121#168—41no—
122#168—122no—
123C2×M16—51no—
124C2×M16—152no—
125C2×M16D3×D511yescharacteristic
126#117—32no—
127C2×C42—51no—
128#108—302no—
129C4⋊C8—102no—
130C2×C3×C5—22no—
131C2×C3×C5—21no—
132C2×C3×C5#40011yescharacteristic
133C23×C3#71111yescharacteristic
134C2×C3×C4—101no—
135C2×C3×C4—101no—
136C2×C3×C4—202no—
137C2×C3×C4C2×D2011yescharacteristic
138C2×C3×C4#70912yes—
139C2×C3×C4#71112yes—
140C2×C3×C4Q8×D511yescharacteristic
141C2×Dic3—42no—
142C3×C8—22no—
143C3×C8—201no—
144C3⋊C8—202no—
145C22×C5—41no—
146C22×C5#89812yes—
147C22×C5#92411yescharacteristic
148C4×C5—242no—
149C4×C5#89012yes—
150C4×C5#93511yescharacteristic
151C4×C5#94711yescharacteristic
152Dic5—22no—
153Dic5—41no—
154C22×C4—101no—
155C22×C4C2×D3×D511yescharacteristic
156M16—22no—
157M16—102no—
158M16—302no—
159M16—302no—
160C2×C8—101no—
161C2×C8—302no—
162C2×C8#120212yes—
163C4⋊C4—62no—
164C22⋊C4—62no—
165C42—51no—
166C42—51no—
167C42—62no—
168C42—101no—
169C3×C5#210211yescharacteristic, complemented, Hall
170C22×C3—41no—
171C22×C3#402512yes—
172C22×C3#404311yescharacteristic
173C3×C4—102no—
174C3×C4—201no—
175C3×C4#402111yescharacteristic
176C3×C4#403211yescharacteristic
177C3×C4#403512yes—
178Dic3—82no—
179C2×C5—21no—
180C2×C5—22no—
181C2×C5#498611yescharacteristic
182C23#677211yescharacteristic
183C2×C4—101no—
184C2×C4—101no—
185C2×C4—122no—
186C2×C4—202no—
187C2×C4D5×Dic611yescharacteristic
188C2×C4#676912yes—
189C2×C4#678012yes—
190C2×C4C2×#120211yescharacteristic
191C8—22no—
192C8—201no—
193C8—602no—
194C2×C3—22no—
195C2×C3—21no—
196C2×C3#6494811yescharacteristic
197C5#7052611yescharacteristic, complemented, Sylow
198C22—41no—
199C22#9134212yes—
200C22#9136011yescharacteristic
201C4—102no—
202C4—201no—
203C4—242no—
204C4#9133412yes—
205C4#9137411yescharacteristic
206C4#9153711yescharacteristic
207C3#1059949411yescharacteristic, complemented, Sylow
208C2—21no—
209C2—22no—
210C2#1174861411yescharacteristic
subgroupG/H
centerC4#91374
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#400
prime radicalC23×C3×C5#41
hypercenterC2×M16D3×D5
hypocenterC3×C5#2102
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
169. C3×C5#2102semidirect
197. C5#70526semidirect
207. C3#10599494semidirect

Maximal subgroups

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

subgroupindex
#117512262
C3×#654072
C5×#45572
#117459892
#117459772
#105994943
#705265