Finite Group Databasebeta

← #14291144

Subgroups — #14291144

Order 1920.

392 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 87 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×#562C211yesmaximal, characteristic
2#11751170C211yesmaximal, characteristic, complemented
3#11751156C212yesmaximal, complemented
4#11746364C211yesmaximal, characteristic, complemented
5#11746361C212yesmaximal, complemented
6#10602747—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C3×C5×#124C2212yes—
9C3×C5×#123—22no—
10C3×C5×C22⋊Q8—22no—
11C3×C5×#121—22no—
12#91758C2211yescharacteristic
13#91119—22no—
14#91116—22no—
15#91094—22no—
16#91087C2211yescharacteristic
17#91087C2212yes—
18#71954—51nomaximal, Hall
19C5×#562D311yescharacteristic
20#65358—31no—
21#65344—32no—
22#64763—31no—
23#64760—32no—
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C22×C3×C4×C5—22no—
28C2×Dic30—21no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C5×C22⋊C4—22no—
33C3×C5×C22⋊C4—22no—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5C2311yescharacteristic
36C4⋊Dic15—22no—
37C2×C3⋊#168—21no—
38C2×C3⋊#168—22no—
39C3×#562D511yescharacteristic
40#5069—51no—
41#5055—52no—
42#4543—51no—
43#4540—52no—
44C5×#125C2×D311yescharacteristic
45C5×#124C2×D312yes—
46C5×#123—22no—
47C5×C22⋊Q8—22no—
48C5×#121—22no—
49#4015—31no—
50#3967—62no—
51#3964—62no—
52#3942—62no—
53#3935—32no—
54#3935—31no—
55#1662—151noSylow
56C23×C3×C5—22no—
57C3×C5×Q8—42no—
58C3×C5×D4—42no—
59C3×C5×D4—82no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—82no—
63C2×C3×C4×C5C2×D412yes—
64C2×C3×C4×C5C2×D411yescharacteristic
65C2×Dic15—41no—
66Dic30—42no—
67C3⋊#168—41no—
68C3⋊#168—42no—
69C3×#125C2×D511yescharacteristic
70C3×#124C2×D512yes—
71C3×#123—22no—
72C3×C22⋊Q8—22no—
73C3×#121—22no—
74#869—51no—
75#835—102no—
76#832—102no—
77#810—102no—
78#803—51no—
79#803—52no—
80C2×C5×Q8#6712yes—
81C2×C5×D4—22no—
82C2×C5×D4#6712yes—
83C22×C4×C5—22no—
84C2×Dic10—61no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4#6712yes—
88C5×C22⋊C4—22no—
89C5×C22⋊C4—22no—
90C5×C22⋊C4—22no—
91C42×C5C22×D311yescharacteristic
92C4⋊Dic5—62no—
93C2×#168—61no—
94C2×#168—62no—
95#562D1511yescharacteristic
96#491—151no—
97#489—152no—
98#330—151no—
99#329—152no—
100C22×C3×C5—42no—
101C22×C3×C5—42no—
102C22×C3×C5—42no—
103C22×C3×C5#12011yescharacteristic
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107C3×C4×C5—42no—
108Dic15—81no—
109C2×C3×Q8C22⋊D512yes—
110C2×C3×D4—22no—
111C2×C3×D4C22⋊D512yes—
112C22×C3×C4—22no—
113C2×Dic6—101no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4C22⋊D512yes—
117C3×C22⋊C4—22no—
118C3×C22⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C42C22×D511yescharacteristic
121C4⋊Dic3—102no—
122C2×C3⋊C8—101no—
123C2×C3⋊C8—102no—
124C23×C5—22no—
125C5×Q8—42no—
126C5×D4—42no—
127C5×D4—82no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—82no—
131C2×C4×C5C2×#6712yes—
132C2×C4×C5C2×#6711yescharacteristic
133C2×Dic5—121no—
134Dic10—122no—
135#168—122no—
136#168—121no—
137C4⋊Q8—151no—
138#125C2×D1511yescharacteristic
139#124C2×D1512yes—
140#123—22no—
141C22⋊Q8—22no—
142#121—22no—
143#103—302no—
144#103—302no—
145#102—302no—
146#97—151no—
147#97—152no—
148C2×C3×C5—82no—
149C2×C3×C5#45411yescharacteristic
150C2×C3×C5#45512yes—
151C23×C3—22no—
152C3×Q8—42no—
153C3×D4—42no—
154C3×D4—82no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—82no—
158C2×C3×C4C2×C22⋊D512yes—
159C2×C3×C4C2×C22⋊D511yescharacteristic
160C2×Dic3—201no—
161Dic6—202no—
162C3⋊C8—202no—
163C3⋊C8—201no—
164C22×C5—42no—
165C22×C5—42no—
166C22×C5—42no—
167C22×C5#95311yescharacteristic
168C4×C5—22no—
169C4×C5—21no—
170C4×C5—42no—
171C4×C5—42no—
172Dic5—241no—
173C2×Q8—301no—
174C2×Q8#122012yes—
175C2×D4—22no—
176C2×D4#122012yes—
177C22×C4—22no—
178C2×C8—302no—
179C2×C8—301no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—302no—
183C4⋊C4#122012yes—
184C22⋊C4—22no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C42C22×D1511yescharacteristic
188C3×C5#166211yescharacteristic, complemented, Hall
189C22×C3—42no—
190C22×C3—42no—
191C22×C3—42no—
192C22×C3#409911yescharacteristic
193C3×C4—22no—
194C3×C4—21no—
195C3×C4—42no—
196C3×C4—42no—
197Dic3—401no—
198C2×C5—82no—
199C2×C5#524212yes—
200C2×C5#524511yescharacteristic
201C23—22no—
202Q8—42no—
203Q8—602no—
204D4—42no—
205D4—82no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—82no—
209C2×C4—601no—
210C2×C4C2×#122011yescharacteristic
211C2×C4C2×#122012yes—
212C8—602no—
213C8—601no—
214C2×C3—82no—
215C2×C3#6553112yes—
216C2×C3#6553411yescharacteristic
217C5#7195411yescharacteristic, complemented, Sylow
218C22—42no—
219C22—42no—
220C22—42no—
221C22#9184211yescharacteristic
222C4—22no—
223C4—21no—
224C4—42no—
225C4—42no—
226C4—1201no—
227C3#1060274711yescharacteristic, complemented, Sylow
228C2—82no—
229C2#1175134312yes—
230C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
Fitting, prime radicalC3×C5×#562C2
socleC22×C3×C5#120
hypercenter#562D15
hypocenterC3×C5#1662
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
2. #11751170C2semidirect
3. #11751156C2semidirect
4. #11746364C2semidirect
5. #11746361C2semidirect
188. C3×C5#1662semidirect
217. C5#71954semidirect
227. C3#10602747semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5622
#117511702
#117511562
#117463642
#117463612
#106027473
#719545