Finite Group Databasebeta

← #14290986

Subgroups — #14290986

Order 1920.

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

normal subgroups only

This group has 364 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, complemented
2C5×#5067C211yesmaximal, characteristic
3#11746905C212yesmaximal
4#11746364C211yesmaximal, characteristic, complemented
5#11745849C212yesmaximal, complemented
6#10602043—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C5×#874C2211yescharacteristic
9C3×#4036—22no—
10C3×#4035—22no—
11C3×#4035—22no—
12C3×#4016C2212yes—
13#91087C2212yes—
14C5×#809—22no—
15C5×#803C2211yescharacteristic
16#90966—22no—
17#90966—22no—
18#71960—51nomaximal, Hall
19C5⋊#564D311yescharacteristic, complemented
20C5×#490—31no—
21#65360—32no—
22#64763—31no—
23#64685—32no—
24C2×C5×D12—22no—
25C2×C5×D12—21no—
26C3×C5×C4⋊C4—22no—
27C3×C5×C4⋊C4D412yes—
28C3×C42×C5C2311yescharacteristic
29C2×C3⋊#168—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#5067—52no—
41#5067D511yescharacteristic
42#4543—51no—
43#4543—52no—
44C5×#127—31no—
45C5×#125C2×D311yescharacteristic
46#4036—22no—
47#4035—22no—
48#4035—22no—
49#4016C2×D312yes—
50C5×#102—62no—
51C5×#97—31no—
52#3964—62no—
53#3964—62no—
54#3935—32no—
55#1658—151noSylow
56C22×C5×D3—41no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D412yes—
59C2×C3×C4×C5C2×D411yescharacteristic
60C5×D12—42no—
61C5×D12—44no—
62C2×C3×Dic5—22no—
63C2×C3×Dic5—22no—
64C3⋊#168—42no—
65C5×C3⋊C8—41no—
66C3×#125—52no—
67C3×#125—102no—
68C3×#125—102no—
69C3×#125—102no—
70C3×#125C2×D511yescharacteristic
71#874C2×D511yescharacteristic
72#809—22no—
73#809—102no—
74#809—102no—
75#803—52no—
76#803C2×D511yescharacteristic
77C2×C5×D4—62no—
78C2×C5×D4—61no—
79C2×C5×C8—61no—
80C5×C4⋊C4—22no—
81C5×C4⋊C4#6712yes—
82C42×C5C22×D311yescharacteristic
83C4⋊Dic5—22no—
84C4⋊Dic5#6712yes—
85C4⋊Dic5#6712yes—
86#683—22no—
87#683—22no—
88#683—22no—
89#683—22no—
90C4×Dic5—22no—
91C2×#168—62no—
92#564—51no—
93#490—31no—
94#490—152no—
95#330—152no—
96#330—151no—
97C22×C3×C5#12011yescharacteristic
98C2×C5×D3—81no—
99C2×C5×D3—82no—
100C3×C4×C5—21no—
101C3×C4×C5—22no—
102C3×C4×C5—42no—
103C3×Dic5—42no—
104C3×Dic5—42no—
105C2×D12—22no—
106C2×D12—21no—
107C3×C4⋊C4—22no—
108C3×C4⋊C4—52no—
109C3×C4⋊C4—52no—
110C3×C4⋊C4—102no—
111C3×C4⋊C4—102no—
112C3×C4⋊C4—102no—
113C3×C4⋊C4—102no—
114C3×C4⋊C4—102no—
115C3×C4⋊C4C22⋊D512yes—
116C3×C42—102no—
117C3×C42C22×D511yescharacteristic
118C2×C3⋊C8—21no—
119C2×C3⋊C8—102no—
120C23×C5—121no—
121C5×D4—124no—
122C5×D4—122no—
123C2×C4×C5—22no—
124C2×C4×C5C2×#6711yescharacteristic
125C2×C4×C5C2×#6712yes—
126C2×Dic5—22no—
127C2×Dic5—22no—
128C5×C8—121no—
129#168—122no—
130#127—31no—
131#125—52no—
132#125—102no—
133#125—102no—
134#125—102no—
135#125D3×D511yescharacteristic
136#102—62no—
137#102—302no—
138#102—302no—
139#97—31no—
140#97—152no—
141C2×C3×C5#45411yescharacteristic
142C2×C3×C5#45412yes—
143C5×D3—161no—
144C22×D3—41no—
145C2×C3×C4—22no—
146C2×C3×C4—102no—
147C2×C3×C4—102no—
148C2×C3×C4D4×D512yes—
149C2×C3×C4C2×C22⋊D511yescharacteristic
150D12—42no—
151D12—44no—
152C3⋊C8—41no—
153C3⋊C8—202no—
154C22×C5—241no—
155C22×C5—242no—
156C22×C5#95311yescharacteristic
157C4×C5—22no—
158C4×C5—21no—
159C4×C5—42no—
160Dic5—42no—
161Dic5—42no—
162C2×D4—61no—
163C2×D4—62no—
164C2×C8—61no—
165C2×C8—302no—
166C4⋊C4—22no—
167C4⋊C4—52no—
168C4⋊C4—52no—
169C4⋊C4—102no—
170C4⋊C4—102no—
171C4⋊C4—102no—
172C4⋊C4—102no—
173C4⋊C4—102no—
174C4⋊C4#120112yes—
175C42—102no—
176C42C2×D3×D511yescharacteristic
177C3×C5#165811yescharacteristic, complemented, Hall
178C22×C3#408311yescharacteristic
179C2×D3—81no—
180C2×D3—82no—
181C3×C4—21no—
182C3×C4—22no—
183C3×C4—42no—
184C3×C4—202no—
185C3×C4—202no—
186C2×C5—481no—
187C2×C5#524511yescharacteristic
188C2×C5#524512yes—
189C23—121no—
190D4—122no—
191D4—124no—
192C2×C4—22no—
193C2×C4—102no—
194C2×C4—102no—
195C2×C4C2×#120111yescharacteristic
196C2×C4D5×#6712yes—
197C8—121no—
198C8—602no—
199C2×C3#6535111yescharacteristic
200C2×C3#6549012yes—
201D3—161no—
202C5#7196011yescharacteristic, complemented, Sylow
203C22—241no—
204C22—242no—
205C22#9156311yescharacteristic
206C4—21no—
207C4—22no—
208C4—42no—
209C4—202no—
210C4—202no—
211C3#1060204311yescharacteristic, complemented, Sylow
212C2—481no—
213C2#1174938311yescharacteristic
214C2#1174945612yes—
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenter#125D3×D5
hypocenterC3×C5#1658
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
1. C3×C5⋊#564C2semidirect
4. #11746364C2semidirect
5. #11745849C2semidirect
19. C5⋊#564D3semidirect
177. C3×C5#1658semidirect
202. C5#71960semidirect
211. C3#10602043semidirect

Maximal subgroups

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

subgroupindex
C3×C5⋊#5642
C5×#50672
#117469052
#117463642
#117458492
#106020433
#719605