Finite Group Databasebeta

← #14291193

Subgroups — #14291193

Order 1920.

344 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 76 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⋊#564C211yesmaximal, characteristic
2C5×#5069C211yesmaximal, characteristic
3#11746970C212yesmaximal
4#11746364C211yesmaximal, characteristic
5#11745849C212yesmaximal
6#10602045—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C5×#869C2211yescharacteristic
9C3×#4036—22no—
10C3×#4035—22no—
11C3×#4035—22no—
12C3×#4016C2212yes—
13#91087C2212yes—
14C5×#810—22no—
15C5×#803C2211yescharacteristic
16#90989—22no—
17#90986—22no—
18#71961—51nomaximal, Hall
19C5⋊#564D311yescharacteristic
20C5×#491—31no—
21#65369—32no—
22#64763—31no—
23#64685—32no—
24C2×C5×Dic6—21no—
25C3×C5×C4⋊C4—22no—
26C3×C5×C4⋊C4D412yes—
27C3×C42×C5C2311yescharacteristic
28C2×C3⋊#168—22no—
29C5×C4⋊Dic3—22no—
30C2×C5×C3⋊C8—21no—
31C3×C4⋊Dic5—22no—
32C3×C4⋊Dic5D412yes—
33C3×C4⋊Dic5D412yes—
34C3×#683—22no—
35C3×#683—22no—
36C3×#683—22no—
37C3×#683—22no—
38C3×C4×Dic5—22no—
39C3×#564—51no—
40#5069D511yescharacteristic
41#5064—52no—
42#4543—51no—
43#4543—52no—
44C5×C4⋊Q8—31no—
45C5×#125C2×D311yescharacteristic
46#4036—22no—
47#4035—22no—
48#4035—22no—
49#4016C2×D312yes—
50C5×#103—62no—
51C5×#97—31no—
52#3940—62no—
53#3939—62no—
54#3935—32no—
55#1663—151noSylow
56C2×C3×C4×C5—22no—
57C2×C3×C4×C5C2×D412yes—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C5×Dic3—41no—
60C5×Dic6—42no—
61C2×C3×Dic5—22no—
62C2×C3×Dic5—22no—
63C3⋊#168—24no—
64C5×C3⋊C8—41no—
65C3×#125—52no—
66C3×#125—102no—
67C3×#125—102no—
68C3×#125—102no—
69C3×#125C2×D511yescharacteristic
70#869C2×D511yescharacteristic
71#810—22no—
72#808—102no—
73#807—102no—
74#803—52no—
75#803C2×D511yescharacteristic
76C2×C5×Q8—61no—
77C2×C5×C8—61no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4—62no—
80C5×C4⋊C4#6712yes—
81C42×C5C22×D311yescharacteristic
82C4⋊Dic5—22no—
83C4⋊Dic5#6712yes—
84C4⋊Dic5#6712yes—
85#683—22no—
86#683—22no—
87#683—22no—
88#683—22no—
89C4×Dic5—22no—
90C2×#168—62no—
91#564—51no—
92#501—152no—
93#491—31no—
94#330—152no—
95#330—151no—
96C22×C3×C5#12011yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5—22no—
99C3×C4×C5—42no—
100C3×Dic5—42no—
101C3×Dic5—42no—
102C5×Dic3—81no—
103C2×Dic6—21no—
104C3×C4⋊C4—22no—
105C3×C4⋊C4—52no—
106C3×C4⋊C4—52no—
107C3×C4⋊C4—102no—
108C3×C4⋊C4—102no—
109C3×C4⋊C4—102no—
110C3×C4⋊C4—102no—
111C3×C4⋊C4—102no—
112C3×C4⋊C4C22⋊D512yes—
113C3×C42—102no—
114C3×C42C22×D511yescharacteristic
115C4⋊Dic3—22no—
116C2×C3⋊C8—21no—
117C2×C3⋊C8—102no—
118C5×Q8—122no—
119C2×C4×C5—22no—
120C2×C4×C5—121no—
121C2×C4×C5C2×#6711yescharacteristic
122C2×C4×C5C2×#6712yes—
123C2×Dic5—22no—
124C2×Dic5—22no—
125C5×C8—121no—
126#168—64no—
127C4⋊Q8—31no—
128#125—52no—
129#125—102no—
130#125—102no—
131#125—102no—
132#125D3×D511yescharacteristic
133#107—302no—
134#106—302no—
135#103—62no—
136#97—31no—
137#97—152no—
138C2×C3×C5#45411yescharacteristic
139C2×C3×C5#45612yes—
140C2×C3×C4—22no—
141C2×C3×C4—102no—
142C2×C3×C4—102no—
143C2×C3×C4D4×D512yes—
144C2×C3×C4C2×C22⋊D511yescharacteristic
145C2×Dic3—41no—
146Dic6—42no—
147C3⋊C8—41no—
148C3⋊C8—104no—
149C22×C5#95311yescharacteristic
150C4×C5—21no—
151C4×C5—22no—
152C4×C5—42no—
153C4×C5—241no—
154Dic5—42no—
155Dic5—42no—
156C2×Q8—61no—
157C2×C8—61no—
158C2×C8—302no—
159C4⋊C4—22no—
160C4⋊C4—52no—
161C4⋊C4—52no—
162C4⋊C4—62no—
163C4⋊C4—102no—
164C4⋊C4—102no—
165C4⋊C4—102no—
166C4⋊C4—102no—
167C4⋊C4—102no—
168C4⋊C4#120112yes—
169C42—102no—
170C42C2×D3×D511yescharacteristic
171C3×C5#166311yescharacteristic, complemented, Hall
172C22×C3#408311yescharacteristic
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—42no—
176C3×C4—202no—
177C3×C4—202no—
178Dic3—81no—
179C2×C5#524511yescharacteristic
180C2×C5#524612yes—
181Q8—122no—
182C2×C4—22no—
183C2×C4—102no—
184C2×C4—102no—
185C2×C4—121no—
186C2×C4C2×#120111yescharacteristic
187C2×C4D5×#6712yes—
188C8—121no—
189C8—304no—
190C2×C3#6535111yescharacteristic
191C2×C3#6549412yes—
192C5#7196111yescharacteristic, complemented, Sylow
193C22#9156311yescharacteristic
194C4—21no—
195C4—22no—
196C4—42no—
197C4—202no—
198C4—202no—
199C4—241no—
200C3#1060204511yescharacteristic, complemented, Sylow
201C2#1174938311yescharacteristic
202C2#1174946212yes—
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socle, prime radicalC22×C3×C5#120
hypercenter#125D3×D5
hypocenterC3×C5#1663
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
171. C3×C5#1663semidirect
192. C5#71961semidirect
200. C3#10602045semidirect

Maximal subgroups

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

subgroupindex
C3×C5⋊#5642
C5×#50692
#117469702
#117463642
#117458492
#106020453
#719615