Finite Group Databasebeta

← #14291198

Subgroups — #14291198

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
2#11751170C211yesmaximal, characteristic
3#11746953C212yesmaximal
4C5×#4543C211yesmaximal, characteristic
5#11745849C212yesmaximal
6#10599170—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91758C2211yescharacteristic
9C3×#4036—22no—
10C3×#4035—22no—
11C3×#4035—22no—
12C3×#4016C2212yes—
13#91094—22no—
14#91087C2211yescharacteristic
15C5×#803C2212yes—
16#90990—22no—
17#90987—22no—
18#71961—51nomaximal, Hall
19C5⋊#564D311yescharacteristic
20#65358—31no—
21#64991—32no—
22C5×#330—31no—
23#64685—32no—
24C2×Dic30—21no—
25C3×C5×C4⋊C4—22no—
26C3×C5×C4⋊C4D412yes—
27C3×C42×C5C2311yescharacteristic
28C4⋊Dic15—22no—
29C2×C3⋊#168—21no—
30C2×C5×C3⋊C8—22no—
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#5069—51no—
41#5064—52no—
42#4543—52no—
43#4543D511yescharacteristic
44C5×#125C2×D311yescharacteristic
45#4036—22no—
46#4035—22no—
47#4035—22no—
48#4016C2×D312yes—
49#4015—31no—
50C5×#97—32no—
51#3950—62no—
52#3949—62no—
53#3942—62no—
54#3935—31no—
55#1663—151noSylow
56C2×C3×C4×C5—22no—
57C2×C3×C4×C5C2×D411yescharacteristic
58C2×C3×C4×C5C2×D412yes—
59C2×Dic15—41no—
60Dic30—42no—
61C2×C3×Dic5—22no—
62C2×C3×Dic5—22no—
63C3⋊#168—41no—
64C5×C3⋊C8—24no—
65C3×#125—52no—
66C3×#125—102no—
67C3×#125—102no—
68C3×#125—102no—
69C3×#125C2×D511yescharacteristic
70#869—51no—
71#810—102no—
72#808—102no—
73#807—102no—
74#803—51no—
75#803C2×D512yes—
76C2×Dic10—61no—
77C2×C5×C8—62no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4#6712yes—
80C42×C5C22×D311yescharacteristic
81C4⋊Dic5—22no—
82C4⋊Dic5—62no—
83C4⋊Dic5#6712yes—
84C4⋊Dic5#6712yes—
85#683—22no—
86#683—22no—
87#683—22no—
88#683—22no—
89C4×Dic5—22no—
90C2×#168—61no—
91#564—51no—
92#501—152no—
93#491—151no—
94#330—31no—
95#330—152no—
96C22×C3×C5#12011yescharacteristic
97C3×C4×C5—21no—
98C3×C4×C5—22no—
99C3×C4×C5—42no—
100Dic15—81no—
101C3×Dic5—42no—
102C3×Dic5—42no—
103C2×Dic6—101no—
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⋊C4D2012yes—
113C3×C42—102no—
114C3×C42C22×D511yescharacteristic
115C4⋊Dic3—102no—
116C2×C3⋊C8—22no—
117C2×C3⋊C8—101no—
118C2×C4×C5—22no—
119C2×C4×C5C2×#6711yescharacteristic
120C2×C4×C5C2×#6712yes—
121C2×Dic5—22no—
122C2×Dic5—22no—
123C2×Dic5—121no—
124Dic10—122no—
125C5×C8—64no—
126#168—121no—
127C4⋊Q8—151no—
128#125—52no—
129#125—102no—
130#125—102no—
131#125—102no—
132#125D3×D511yescharacteristic
133#107—302no—
134#106—302no—
135#103—302no—
136#97—32no—
137#97—151no—
138C2×C3×C5#45411yescharacteristic
139C2×C3×C5#45612yes—
140C2×C3×C4—22no—
141C2×C3×C4—102no—
142C2×C3×C4—102no—
143C2×C3×C4C2×D2011yescharacteristic
144C2×C3×C4D4×D512yes—
145C2×Dic3—201no—
146Dic6—202no—
147C3⋊C8—24no—
148C3⋊C8—201no—
149C22×C5#95311yescharacteristic
150C4×C5—21no—
151C4×C5—22no—
152C4×C5—42no—
153Dic5—42no—
154Dic5—42no—
155Dic5—241no—
156C2×Q8—301no—
157C2×C8—62no—
158C2×C8—301no—
159C4⋊C4—22no—
160C4⋊C4—52no—
161C4⋊C4—52no—
162C4⋊C4—102no—
163C4⋊C4—102no—
164C4⋊C4—102no—
165C4⋊C4—102no—
166C4⋊C4—102no—
167C4⋊C4—302no—
168C4⋊C4#120212yes—
169C42—102no—
170C42C2×D3×D511yescharacteristic
171C3×C5#166311yescharacteristic, complemented, Hall
172C22×C3#402811yescharacteristic
173C3×C4—21no—
174C3×C4—22no—
175C3×C4—42no—
176C3×C4—202no—
177C3×C4—202no—
178Dic3—401no—
179C2×C5#524511yescharacteristic
180C2×C5#524612yes—
181Q8—602no—
182C2×C4—22no—
183C2×C4—102no—
184C2×C4—102no—
185C2×C4—601no—
186C2×C4C2×#120211yescharacteristic
187C2×C4D5×#6712yes—
188C8—64no—
189C8—601no—
190C2×C3#6504211yescharacteristic
191C2×C3#6511512yes—
192C5#7196111yescharacteristic, complemented, Sylow
193C22#9156411yescharacteristic
194C4—21no—
195C4—22no—
196C4—42no—
197C4—202no—
198C4—202no—
199C4—1201no—
200C3#1059917011yescharacteristic, complemented, Sylow
201C2#1174938411yescharacteristic
202C2#1174946412yes—
subgroupG/H
centerC22#91564
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#10599170semidirect

Maximal subgroups

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

subgroupindex
C3×C5⋊#5642
#117511702
#117469532
C5×#45432
#117458492
#105991703
#719615