Finite Group Databasebeta

← #14289397

Subgroups — #14289397

Order 1920.

436 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×#5713C211yesmaximal, characteristic
2#11751177C211yesmaximal, characteristic
3#11746961C212yesmaximal, complemented
4C3×#64764C211yesmaximal, characteristic
5#11745842C212yesmaximal, complemented
6#10602737—31nomaximal, Hall
7C3×C5×#127C2211yescharacteristic
8C2×#6716—22no—
9#91758C2211yescharacteristic
10C5×#936—22no—
11C5×#935—22no—
12C5×D4×Dic3—22no—
13C4×C5×Dic6C2212yes—
14C4×C3⋊#168C2211yescharacteristic
15C3×C4⋊#168C2212yes—
16#90988—22no—
17#90973—22no—
18#68404—51nomaximal, Hall
19C5×#559—31no—
20#65365—31no—
21#65310—32no—
22#64764D311yescharacteristic
23Q8⋊#168—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4D412yes—
26C2×Dic30—21no—
27C22×C5×Dic3—22no—
28C2×C5×Dic6D412yes—
29C3×C42×C5C2311yescharacteristic
30#6716—44no—
31C4⋊Dic15—22no—
32C2×C3⋊#168—21no—
33C5×#217—24no—
34C5×#217—22no—
35C5×C4⋊Dic3D412yes—
36C5×Dic3⋊C4—22no—
37C4×C5×Dic3—22no—
38C2×C3×#168—22no—
39#5713D511yescharacteristic
40#5076—51no—
41#4850—52no—
42C3×#331—51no—
43#4484—52no—
44C5×#127C2×D311yescharacteristic
45C5×#124—62no—
46C5×#123—62no—
47C4×C5×Q8—32no—
48C4×C5×D4—62no—
49C2×#687—62no—
50#4015—31no—
51#3967—62no—
52#3939—62no—
53C4⋊#168C2×D312yes—
54C4×#168—31no—
55#1630—151noSylow
56C23×C3×C5—22no—
57C3×C5×D4—42no—
58C3×C5×D4—42no—
59C3×C5×D4—42no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×Dic15—41no—
63Dic30—42no—
64C2×C5×Dic3—22no—
65C2×C5×Dic3—22no—
66C2×C5×Dic3—82no—
67C5×Dic6—22no—
68C5×Dic6—22no—
69C3⋊#168—22no—
70C3×#168—42no—
71C3×#127C2×D511yescharacteristic
72#936—22no—
73#935—22no—
74D4×Dic3—22no—
75C2×#214—102no—
76#869—51no—
77C4×Dic6C2×D512yes—
78C3×C4⋊C8—52no—
79#818—102no—
80#816—102no—
81C4×C3⋊C8—51no—
82C2×C5×Q8—32no—
83C2×C5×D4—22no—
84C2×C5×D4D1212yes—
85C22×C4×C5—62no—
86C2×Dic10—61no—
87C5×C4⋊C4—32no—
88C5×C4⋊C4—62no—
89C5×C22⋊C4—64no—
90C5×C22⋊C4—62no—
91C42×C5—62no—
92C42×C5C22×D311yescharacteristic
93#687—124no—
94C4⋊Dic5—62no—
95C2×#168—22no—
96C2×#168—61no—
97#559—31no—
98#492—151no—
99#477—152no—
100#331—51no—
101Q8⋊C8—152no—
102C22×C3×C5—44no—
103C22×C3×C5—42no—
104C22×C3×C5#12011yescharacteristic
105C3×C4×C5—21no—
106C3×C4×C5#13512yes—
107C3×C4×C5#13712yes—
108Dic15—81no—
109C5×Dic3—42no—
110C5×Dic3—42no—
111C2×C3×D4—22no—
112C2×C3×D4C22⋊D512yes—
113C22×Dic3—22no—
114C2×Dic6—101no—
115C2×Dic6C22⋊D512yes—
116C2×C3×C8—102no—
117C3×C42C22×D511yescharacteristic
118#217—24no—
119#217—22no—
120#214—204no—
121C4⋊Dic3—102no—
122C4⋊Dic3C22⋊D512yes—
123Dic3⋊C4—22no—
124C4×Dic3—22no—
125C2×C3⋊C8—101no—
126C23×C5—22no—
127C5×Q8—62no—
128C5×Q8—62no—
129C5×D4—42no—
130C5×D4—42no—
131C5×D4—42no—
132C2×C4×C5—62no—
133C2×C4×C5—62no—
134C2×C4×C5—242no—
135C2×C4×C5C2×D1211yescharacteristic
136C2×C4×C5D3×D412yes—
137C2×Dic5—121no—
138Dic10—122no—
139#168—42no—
140#168—62no—
141C2×SD16—302no—
142C4⋊Q8—151no—
143#127D3×D511yescharacteristic
144#124—62no—
145#123—62no—
146C4×Q8—32no—
147C4×D4—62no—
148#107—302no—
149C4⋊C8—52no—
150#103—302no—
151C4×C8—151no—
152C2×C3×C5—82no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155C23×C3—22no—
156C3×D4—42no—
157C3×D4—42no—
158C3×D4—42no—
159C2×C3×C4C2×C22⋊D511yescharacteristic
160C2×C3×C4C2×C22⋊D512yes—
161C2×Dic3—22no—
162C2×Dic3—22no—
163C2×Dic3—82no—
164C2×Dic3—201no—
165Dic6—22no—
166Dic6—22no—
167Dic6—202no—
168C3×C8—202no—
169C3⋊C8—102no—
170C22×C5—42no—
171C22×C5—44no—
172C22×C5#88211yescharacteristic
173C4×C5—21no—
174C4×C5—122no—
175C4×C5—122no—
176C4×C5#91212yes—
177C4×C5#91512yes—
178Dic5—241no—
179C2×Q8—32no—
180C2×Q8—301no—
181C2×D4—22no—
182C2×D4#120312yes—
183C22×C4—62no—
184SD16—604no—
185C2×C8—102no—
186C2×C8—301no—
187C4⋊C4—32no—
188C4⋊C4—62no—
189C4⋊C4—302no—
190C22⋊C4—64no—
191C22⋊C4—62no—
192C42—62no—
193C42C2×D3×D511yescharacteristic
194C3×C5#163011yescharacteristic, complemented, Hall
195C22×C3—44no—
196C22×C3—42no—
197C22×C3#409911yescharacteristic
198C3×C4—21no—
199C3×C4#409612yes—
200C3×C4#409712yes—
201Dic3—42no—
202Dic3—42no—
203Dic3—401no—
204C2×C5—82no—
205C2×C5#474711yescharacteristic
206C2×C5#478312yes—
207C23—22no—
208Q8—62no—
209Q8—62no—
210Q8—602no—
211D4—42no—
212D4—42no—
213D4—42no—
214C2×C4—62no—
215C2×C4—62no—
216C2×C4—242no—
217C2×C4—601no—
218C2×C4C2×#120311yescharacteristic
219C2×C4D3×C22⋊D512yes—
220C8—202no—
221C8—302no—
222C2×C3—82no—
223C2×C3#6552812yes—
224C2×C3#6553011yescharacteristic
225C5#6840411yescharacteristic, complemented, Sylow
226C22—42no—
227C22—44no—
228C22#9157011yescharacteristic
229C4—21no—
230C4—122no—
231C4—122no—
232C4—1201no—
233C4#9148612yes—
234C4#9149312yes—
235C3#1060273711yescharacteristic, complemented, Sylow
236C2—82no—
237C2#1174905412yes—
238C2#1174914111yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
Fitting, prime radicalC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1630
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
3. #11746961C2semidirect
5. #11745842C2semidirect
194. C3×C5#1630semidirect
225. C5#68404semidirect
235. C3#10602737semidirect

Maximal subgroups

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

subgroupindex
C5×#57132
#117511772
#117469612
C3×#647642
#117458422
#106027373
#684045