Finite Group Databasebeta

← #14288424

Subgroups — #14288424

Order 1920.

420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#11756259C211yesmaximal, characteristic
2C3×C5×#398C211yesmaximal, characteristic
3#11751072C212yesmaximal
4#11746349C211yesmaximal, characteristic
5#11746273C212yesmaximal
6#10600506—31nomaximal, Hall
7C2×C3×C5×C4⋊C4—21no—
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10#91815—21no—
11#91813—21no—
12#91813C2212yes—
13#91779—22no—
14#91777—22no—
15C3×C5×#95—21no—
16C3×C5×#95C2211yescharacteristic
17#91114C2212yes—
18#91094—22no—
19#91092—22no—
20#69713—51nomaximal, Hall
21#65834—31no—
22C5×#398D311yescharacteristic
23#65260—32no—
24#64748—31no—
25#64672—32no—
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5—21no—
28C22×C3×C4×C5D411yescharacteristic
29C22×C3×C4×C5D411yescharacteristic
30C22×C3×C4×C5C2311yescharacteristic
31C2×Dic30—21no—
32C2×Dic30D412yes—
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4—22no—
35C3×C5×C4⋊C4—42no—
36#6719—22no—
37C4⋊Dic15—21no—
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C4⋊Dic15D412yes—
41#6712—22no—
42#6712—22no—
43C4×Dic15—22no—
44C2×C3⋊#168—22no—
45#5500—51no—
46C3×#398D511yescharacteristic
47#4971—52no—
48#4528—51no—
49#4452—52no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4C2×D311yescharacteristic
52C2×C5×C4⋊C4C2×D311yescharacteristic
53#4072—61no—
54#4070—32no—
55#4070—61no—
56#4036—62no—
57#4034—62no—
58C5×#95—21no—
59C5×#95C2×D311yescharacteristic
60C22⋊#168—32no—
61#3942—62no—
62#3940—62no—
63#1611—151noSylow
64C23×C3×C5C2×D411yescharacteristic
65C2×C3×C4×C5—21no—
66C2×C3×C4×C5—21no—
67C2×C3×C4×C5—22no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5SD1612yes—
77C2×C3×C4×C5C2×D412yes—
78C2×Dic15—22no—
79C2×Dic15—22no—
80Dic30—42no—
81Dic30—81no—
82C3⋊#168—42no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4C2×D511yescharacteristic
85C2×C3×C4⋊C4C2×D511yescharacteristic
86#926—101no—
87#924—52no—
88#924—101no—
89#890—102no—
90#888—102no—
91C3×#95—21no—
92C3×#95C2×D511yescharacteristic
93#830—52no—
94#810—102no—
95#808—102no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5#6711yescharacteristic
99C22×C4×C5#6711yescharacteristic
100C22×C4×C5C22×D311yescharacteristic
101C2×Dic10—32no—
102C2×Dic10—61no—
103C5×C4⋊C4—22no—
104C5×C4⋊C4—22no—
105C5×C4⋊C4—42no—
106C22⋊Dic5—62no—
107C4⋊Dic5—32no—
108C4⋊Dic5—61no—
109C4⋊Dic5—61no—
110C4⋊Dic5—61no—
111#683—62no—
112#683—62no—
113C4×Dic5—62no—
114C2×#168—62no—
115#544—151no—
116#483—152no—
117#398D1511yescharacteristic
118#328—152no—
119#324—151no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5#12011yescharacteristic
123C22×C3×C5C2×SD1611yescharacteristic
124C22×C3×C5#13711yescharacteristic
125C3×C4×C5—22no—
126C3×C4×C5—22no—
127C3×C4×C5—42no—
128C3×C4×C5—41no—
129C3×C4×C5—81no—
130Dic15—42no—
131Dic15—42no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4C22⋊D511yescharacteristic
135C22×C3×C4C22⋊D511yescharacteristic
136C22×C3×C4C22×D511yescharacteristic
137C2×Dic6—52no—
138C2×Dic6—101no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—42no—
142#217—102no—
143C4⋊Dic3—52no—
144C4⋊Dic3—101no—
145C4⋊Dic3—101no—
146C4⋊Dic3—101no—
147Dic3⋊C4—102no—
148Dic3⋊C4—102no—
149C4×Dic3—102no—
150C2×C3⋊C8—102no—
151C23×C5C2×#6711yescharacteristic
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—22no—
155C2×C4×C5—21no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5#21412yes—
164C2×C4×C5D3×D412yes—
165C2×Dic5—62no—
166C2×Dic5—62no—
167Dic10—122no—
168Dic10—241no—
169#168—122no—
170C4⋊Q8—302no—
171#125—302no—
172C22⋊Q8—152no—
173C22⋊Q8—301no—
174#117—301no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4C2×D1511yescharacteristic
177C2×C4⋊C4C2×D1511yescharacteristic
178#106—302no—
179#103—302no—
180C22⋊C8—152no—
181#95—21no—
182#95C2×D1511yescharacteristic
183C2×C3×C5—21no—
184C2×C3×C5—21no—
185C2×C3×C5#44811yescharacteristic
186C2×C3×C5#45611yescharacteristic
187C2×C3×C5#45811yescharacteristic
188C23×C3C2×C22⋊D511yescharacteristic
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4—41no—
198C2×C3×C4—41no—
199C2×C3×C4—41no—
200C2×C3×C4#68712yes—
201C2×C3×C4D4×D512yes—
202C2×Dic3—102no—
203C2×Dic3—102no—
204Dic6—202no—
205Dic6—401no—
206C3⋊C8—202no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5C2×#21411yescharacteristic
210C22×C5#93711yescharacteristic
211C22×C5#95111yescharacteristic
212C4×C5—22no—
213C4×C5—22no—
214C4×C5—42no—
215C4×C5—41no—
216C4×C5—81no—
217Dic5—122no—
218Dic5—122no—
219C2×Q8—152no—
220C2×Q8—301no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4#122011yescharacteristic
224C22×C4#122011yescharacteristic
225C22×C4C22×D1511yescharacteristic
226C2×C8—302no—
227C4⋊C4—22no—
228C4⋊C4—22no—
229C4⋊C4—42no—
230C4⋊C4—152no—
231C4⋊C4—301no—
232C4⋊C4—301no—
233C4⋊C4—301no—
234C4⋊C4—302no—
235C4⋊C4—302no—
236C22⋊C4—302no—
237C42—302no—
238C3×C5#161111yescharacteristic, complemented, Hall
239C22×C3—21no—
240C22×C3—21no—
241C22×C3C2×#68711yescharacteristic
242C22×C3#408311yescharacteristic
243C22×C3#409711yescharacteristic
244C3×C4—22no—
245C3×C4—22no—
246C3×C4—42no—
247C3×C4—41no—
248C3×C4—81no—
249Dic3—202no—
250Dic3—202no—
251C2×C5—21no—
252C2×C5—21no—
253C2×C5#504011yescharacteristic
254C2×C5#505311yescharacteristic
255C2×C5#509511yescharacteristic
256C23C2×#122011yescharacteristic
257Q8—602no—
258Q8—1201no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—302no—
271C2×C4—302no—
272C2×C4#671612yes—
273C2×C4D4×D1512yes—
274C8—602no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3#6532911yescharacteristic
278C2×C3#6534211yescharacteristic
279C2×C3#6538411yescharacteristic
280C5#6971311yescharacteristic, complemented, Sylow
281C22—21no—
282C22—21no—
283C22C2×#671611yescharacteristic
284C22#9182611yescharacteristic
285C22#9184011yescharacteristic
286C4—22no—
287C4—22no—
288C4—42no—
289C4—41no—
290C4—81no—
291C4—602no—
292C4—602no—
293C3#1060050611yescharacteristic, complemented, Sylow
294C2—21no—
295C2—21no—
296C2#1175114111yescharacteristic
297C2#1175115411yescharacteristic
298C2#1175119611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#398C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenter#398D15
hypocenterC3×C5#1611
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
238. C3×C5#1611semidirect
280. C5#69713semidirect
293. C3#10600506semidirect

Maximal subgroups

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

subgroupindex
#117562592
C3×C5×#3982
#117510722
#117463492
#117462732
#106005063
#697135