Finite Group Databasebeta

← #14289588

Subgroups — #14289588

Order 1920.

436 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 103 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×#555C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic, complemented
3#11751109C212yesmaximal, complemented
4#11746367C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C212yesmaximal, complemented
6#10602721—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×#124—22no—
9C3×C5×#121—22no—
10C3×C4×C5×D4C2212yes—
11C3×C5×#117—22no—
12C2×#6718—22no—
13#91758C2211yescharacteristic
14#91116—22no—
15#91092—22no—
16C4⋊(C3⋊#168)C2212yes—
17C4×C3⋊#168C2211yescharacteristic
18#71928—51nomaximal, Hall
19C5×#555D311yescharacteristic
20#65381—31no—
21#65297—32no—
22#64766—31no—
23D4⋊#168—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⋊C4D412yes—
31C3×C5×C22⋊C4—24no—
32C3×C5×C22⋊C4—22no—
33C3×C42×C5—22no—
34C3×C42×C5C2311yescharacteristic
35#6718—44no—
36C4⋊Dic15—22no—
37C2×C3⋊#168—21no—
38C2×C3⋊#168—22no—
39C3×#555D511yescharacteristic
40#5092—51no—
41#5008—52no—
42#4546—51no—
43D4⋊(C3⋊C8)—52no—
44C5×C4⋊Q8C2×D311yescharacteristic
45C5×#124—22no—
46C5×#121—22no—
47C4×C5×D4C2×D312yes—
48C5×#117—22no—
49C2×#689—62no—
50#4015—31no—
51#3964—62no—
52#3940—62no—
53C4⋊#168—32no—
54C4×#168—31no—
55#1634—151noSylow
56C23×C3×C5—22no—
57C3×C5×Q8—42no—
58C3×C5×D4—22no—
59C3×C5×D4—22no—
60C3×C5×D4—82no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5—42no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C2×Dic15—41no—
68Dic30—42no—
69C3⋊#168—22no—
70C3⋊#168—42no—
71C3×C4⋊Q8C2×D511yescharacteristic
72C3×#124—22no—
73C3×#121—22no—
74C3×C4×D4C2×D512yes—
75C3×#117—22no—
76C2×#216—102no—
77#869—51no—
78#832—102no—
79#808—102no—
80C4⋊(C3⋊C8)—52no—
81C4×C3⋊C8—51no—
82C2×C5×Q8#6712yes—
83C2×C5×D4—22no—
84C2×C5×D4#6712yes—
85C22×C4×C5—22no—
86C2×Dic10—61no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4#6712yes—
89C5×C22⋊C4—24no—
90C5×C22⋊C4—22no—
91C42×C5—22no—
92C42×C5C22×D311yescharacteristic
93#689—124no—
94C4⋊Dic5—62no—
95C2×#168—61no—
96C2×#168—62no—
97#555D1511yescharacteristic
98#494—151no—
99#476—152no—
100#333—151no—
101D4⋊C8—152no—
102C22×C3×C5—42no—
103C22×C3×C5—42no—
104C22×C3×C5—42no—
105C22×C3×C5#12011yescharacteristic
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5—42no—
109C3×C4×C5#13512yes—
110C3×C4×C5#13712yes—
111Dic15—81no—
112C2×C3×Q8C22⋊D512yes—
113C2×C3×D4—22no—
114C2×C3×D4C22⋊D512yes—
115C22×C3×C4—22no—
116C2×Dic6—101no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4C22⋊D512yes—
119C3×C22⋊C4—24no—
120C3×C22⋊C4—22no—
121C3×C42—22no—
122C3×C42C22×D511yescharacteristic
123#216—204no—
124C4⋊Dic3—102no—
125C2×C3⋊C8—101no—
126C2×C3⋊C8—102no—
127C23×C5—22no—
128C5×Q8—42no—
129C5×D4—22no—
130C5×D4—22no—
131C5×D4—82no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—42no—
135C2×C4×C5—42no—
136C2×C4×C5C2×#6711yescharacteristic
137C2×C4×C5C2×#6712yes—
138C2×Dic5—121no—
139Dic10—122no—
140#168—62no—
141#168—122no—
142C2×Q16—302no—
143C4⋊Q8—151no—
144C4⋊Q8C2×D1511yescharacteristic
145#124—22no—
146#121—22no—
147C4×D4C2×D1512yes—
148#117—22no—
149#106—302no—
150C4⋊C8—152no—
151#102—302no—
152C4×C8—151no—
153C2×C3×C5—82no—
154C2×C3×C5#45212yes—
155C2×C3×C5#45311yescharacteristic
156C23×C3—22no—
157C3×Q8—42no—
158C3×D4—22no—
159C3×D4—22no—
160C3×D4—82no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—42no—
164C2×C3×C4—42no—
165C2×C3×C4C2×C22⋊D511yescharacteristic
166C2×C3×C4C2×C22⋊D512yes—
167C2×Dic3—201no—
168Dic6—202no—
169C3⋊C8—102no—
170C3⋊C8—202no—
171C22×C5—42no—
172C22×C5—42no—
173C22×C5—42no—
174C22×C5#95311yescharacteristic
175C4×C5—21no—
176C4×C5—42no—
177C4×C5—42no—
178C4×C5#95012yes—
179C4×C5#95112yes—
180Dic5—241no—
181C2×Q8—301no—
182C2×Q8#122012yes—
183C2×D4—22no—
184C2×D4#122012yes—
185C22×C4—22no—
186Q16—604no—
187C2×C8—301no—
188C2×C8—302no—
189C4⋊C4—22no—
190C4⋊C4—302no—
191C4⋊C4#122012yes—
192C22⋊C4—24no—
193C22⋊C4—22no—
194C42—22no—
195C42C22×D1511yescharacteristic
196C3×C5#163411yescharacteristic, complemented, Hall
197C22×C3—42no—
198C22×C3—42no—
199C22×C3—42no—
200C22×C3#409911yescharacteristic
201C3×C4—21no—
202C3×C4—42no—
203C3×C4—42no—
204C3×C4#409612yes—
205C3×C4#409712yes—
206Dic3—401no—
207C2×C5—82no—
208C2×C5#523912yes—
209C2×C5#524111yescharacteristic
210C23—22no—
211Q8—42no—
212Q8—602no—
213D4—22no—
214D4—22no—
215D4—82no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—601no—
221C2×C4C2×#122011yescharacteristic
222C2×C4C2×#122012yes—
223C8—302no—
224C8—602no—
225C2×C3—82no—
226C2×C3#6552812yes—
227C2×C3#6553011yescharacteristic
228C5#7192811yescharacteristic, complemented, Sylow
229C22—42no—
230C22—42no—
231C22—42no—
232C22#9184211yescharacteristic
233C4—21no—
234C4—42no—
235C4—42no—
236C4—1201no—
237C4#9183912yes—
238C4#9184012yes—
239C3#1060272111yescharacteristic, complemented, Sylow
240C2—82no—
241C2#1175134012yes—
242C2#1175134211yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
Fitting, prime radicalC3×C5×#555C2
socleC22×C3×C5#120
hypercenter#555D15
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
2. #11751193C2semidirect
3. #11751109C2semidirect
4. #11746367C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
196. C3×C5#1634semidirect
228. C5#71928semidirect
239. C3#10602721semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5552
#117511932
#117511092
#117463672
D4⋊(C3⋊#168)2
#106027213
#719285