Finite Group Databasebeta

← #14292817

Subgroups — #14292817

Order 1920.

304 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 94 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#11750780C211yesmaximal, characteristic
2C3×#64971C211yesmaximal, characteristic
3#11747104C212yesmaximal
4C5×#4457C211yesmaximal, characteristic
5#11745856C212yesmaximal
6#10599345—31nomaximal, Hall
7C4×Dic30C2211yescharacteristic
8C3×#4015C2212yes—
9C2×#6662—22no—
10C3×C4×C5×C8C2211yescharacteristic
11#91099—21no—
12#91098—21no—
13C4⋊(C3⋊#168)C2211yescharacteristic
14C5×C4⋊(C3⋊C8)C2212yes—
15C3×#3950—21no—
16C3×#3950—21no—
17#90971—22no—
18#71379—51nomaximal, Hall
19#65138—32no—
20#64971D311yescharacteristic
21#64968—31no—
22C5×#334—31no—
23#64702—32no—
24C2×Dic30D411yescharacteristic
25C2×C3×Dic10—22no—
26C2×C3×C5×C8D411yescharacteristic
27C2×C3×C5×C8D411yescharacteristic
28C3×C42×C5C2311yescharacteristic
29C4⋊Dic15D411yescharacteristic
30#6712—21no—
31C4×Dic15—21no—
32C2×C3⋊#168—21no—
33C2×C5×C3⋊C8—22no—
34C3×C4⋊Dic5—22no—
35C3×C4⋊Dic5—22no—
36#6662—44no—
37C3×#500—51no—
38#5090—52no—
39#4679—51no—
40#4547—52no—
41#4457D511yescharacteristic
42C2×Dic20—62no—
43#4015C2×D312yes—
44C4×Dic10—31no—
45C5×C4⋊C8—32no—
46C4×C5×C8C2×D311yescharacteristic
47#3950—21no—
48#3950—21no—
49#3948—62no—
50#3947—61no—
51#3946—61no—
52C4⋊#168—31no—
53#1694—151noSylow
54C2×C3×C4×C5C2×D411yescharacteristic
55C2×C3×C4×C5C2×D411yescharacteristic
56C2×C3×C4×C5#4111yescharacteristic
57C2×Dic15—21no—
58C2×Dic15—21no—
59Dic30—22no—
60C2×C3×Dic5—42no—
61C3×Dic10—42no—
62C3×Dic10—42no—
63C3×C5×C8—21no—
64C3×C5×C8Q1612yescomplemented
65C3⋊#168—41no—
66C5×C3⋊C8—42no—
67C3×C4⋊Q8—52no—
68C2×#216—102no—
69C4×Dic6—51no—
70C3×#107—101no—
71C3×#107—101no—
72C3×C4×C8C2×D511yescharacteristic
73#835—102no—
74#815—101no—
75Dic3⋊C8—101no—
76C4⋊(C3⋊C8)—51no—
77C4⋊(C3⋊C8)C2×D512yes—
78C2×Dic10—22no—
79C2×Dic10—31no—
80C2×C5×C8—62no—
81C2×C5×C8#6711yescharacteristic
82C2×C5×C8#6711yescharacteristic
83C42×C5C22×D311yescharacteristic
84C4⋊Dic5—22no—
85C4⋊Dic5—22no—
86C4⋊Dic5—31no—
87#683—61no—
88C4×Dic5—61no—
89C2×#168—61no—
90Dic20—124no—
91#500—51no—
92#462—152no—
93#446—151no—
94#334—31no—
95#332—152no—
96C22×C3×C5#12111yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5C2×Q1611yescharacteristic
99C3×C4×C5AGL(1,ℤ/8)12yes—
100C3×C4×C5#13711yescharacteristic
101Dic15—41no—
102Dic15—41no—
103C3×Dic5—82no—
104C2×C3×Q8—102no—
105C2×Dic6—51no—
106C2×C3×C8D2011yescharacteristic
107C2×C3×C8D2011yescharacteristic
108C3×C4⋊C4—102no—
109C3×C4⋊C4—102no—
110C3×C42C22×D511yescharacteristic
111#216—204no—
112C4⋊Dic3—51no—
113Dic3⋊C4—101no—
114C4×Dic3—101no—
115C2×C3⋊C8—22no—
116C2×C3⋊C8—101no—
117C2×C4×C5D3×D411yescharacteristic
118C2×C4×C5#23711yescharacteristic
119C2×C4×C5C2×#6711yescharacteristic
120C2×Dic5—42no—
121C2×Dic5—61no—
122C2×Dic5—61no—
123Dic10—42no—
124Dic10—42no—
125Dic10—62no—
126C5×C8—21no—
127C5×C8—122no—
128C5×C8#21612yescomplemented
129#168—121no—
130C2×Q16—302no—
131C4⋊Q8—52no—
132C4×Q8—151no—
133#107—101no—
134#107—101no—
135C4⋊C8—32no—
136C4⋊C8—151no—
137C4⋊C8—301no—
138#103—302no—
139#97—301no—
140C4×C8D3×D511yescharacteristic
141C2×C3×C5#46211yescharacteristic
142C2×C3×C5#46911yescharacteristic
143C2×C3×C5#47311yescharacteristic
144C3×Q8—202no—
145C3×Q8—202no—
146C2×C3×C4—202no—
147C2×C3×C4C2×D2011yescharacteristic
148C2×C3×C4D4×D511yescharacteristic
149C2×C3×C4#71311yescharacteristic
150C2×Dic3—101no—
151C2×Dic3—101no—
152Dic6—102no—
153C3×C8—21no—
154C3×C8Dic2012yescomplemented
155C3⋊C8—42no—
156C3⋊C8—201no—
157C22×C5#93811yescharacteristic
158C4×C5—21no—
159C4×C5#91112yes—
160C4×C5#94211yescharacteristic
161C4×C5C2×#21611yescharacteristic
162Dic5—82no—
163Dic5—121no—
164Dic5—121no—
165C2×Q8—102no—
166C2×Q8—151no—
167Q16—604no—
168C2×C8—62no—
169C2×C8—301no—
170C2×C8#120211yescharacteristic
171C2×C8#120211yescharacteristic
172C4⋊C4—102no—
173C4⋊C4—102no—
174C4⋊C4—151no—
175C4⋊C4—301no—
176C42—301no—
177C42C2×D3×D511yescharacteristic
178C3×C5#169411yescharacteristic, complemented, Hall
179C22×C3#404111yescharacteristic
180C3×C4—21no—
181C3×C4—402no—
182C3×C4C2×Dic2011yescharacteristic
183C3×C4#405511yescharacteristic
184C3×C4#406012yes—
185Dic3—201no—
186Dic3—201no—
187C2×C5#509011yescharacteristic
188C2×C5#515911yescharacteristic
189C2×C5#519211yescharacteristic
190Q8—202no—
191Q8—202no—
192Q8—302no—
193C2×C4—202no—
194C2×C4—301no—
195C2×C4—301no—
196C2×C4#676611yescharacteristic
197C2×C4#677711yescharacteristic
198C2×C4C2×#120211yescharacteristic
199C8—21no—
200C8—122no—
201C8—601no—
202C8#666212yescomplemented
203C2×C3#6513811yescharacteristic
204C2×C3#6515411yescharacteristic
205C2×C3#6518511yescharacteristic
206C5#7137911yescharacteristic, complemented, Sylow
207C22#9146511yescharacteristic
208C4—21no—
209C4—402no—
210C4—601no—
211C4—601no—
212C4#9125812yes—
213C4#9131511yescharacteristic
214C4C2×#666211yescharacteristic
215C3#1059934511yescharacteristic, complemented, Sylow
216C2#1174710411yescharacteristic
217C2#1174793611yescharacteristic
218C2#1174809611yescharacteristic
subgroupG/H
centerC22#91465
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socle, prime radicalC22×C3×C5#121
hypercenterC4×C8D3×D5
hypocenterC3×C5#1694
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
64. C3×C5×C8Q16semidirect
128. C5×C8#216semidirect
154. C3×C8Dic20semidirect
178. C3×C5#1694semidirect
202. C8#6662semidirect
206. C5#71379semidirect
215. C3#10599345semidirect

Maximal subgroups

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

subgroupindex
#117507802
C3×#649712
#117471042
C5×#44572
#117458562
#105993453
#713795