Finite Group Databasebeta

← #14288142

Subgroups — #14288142

Order 1920.

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

normal subgroups only

This group has 476 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×#395C211yesmaximal, characteristic
3#11751329C212yesmaximal
4#11746349C211yesmaximal, characteristic
5#11746273C212yesmaximal
6#10600500—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C2×C3×C5×C4⋊C4—21no—
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10C2×#6718—22no—
11#91815—21no—
12#91813—21no—
13#91813C2212yes—
14#91779—22no—
15#91777—22no—
16C3×C5×#95—21no—
17C3×C5×#95C2211yescharacteristic
18#91119—22no—
19#91114C2212yes—
20#69707—51nomaximal, Hall
21#65834—31no—
22C5×#395D311yescharacteristic
23#65517—32no—
24#64748—31no—
25#64672—32no—
26C2×C3×C5×Q8—22no—
27C2×C3×C5×Q8—42no—
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5C2311yescharacteristic
33C2×Dic30—21no—
34C2×Dic30D412yes—
35C3×C5×C4⋊C4—22no—
36C3×C5×C4⋊C4—42no—
37#6719—22no—
38#6718—44no—
39C4⋊Dic15—21no—
40C4⋊Dic15—21no—
41C4⋊Dic15—21no—
42C4⋊Dic15D412yes—
43#6712—22no—
44#6712—22no—
45C4×Dic15—22no—
46C2×C3⋊#168—22no—
47#5500—51no—
48C3×#395D511yescharacteristic
49#5228—52no—
50#4528—51no—
51#4452—52no—
52C22×C5×Q8C2×D311yescharacteristic
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4C2×D311yescharacteristic
55C2×#689—62no—
56#4072—61no—
57#4070—32no—
58#4070—61no—
59#4036—62no—
60#4034—62no—
61C5×#95—21no—
62C5×#95C2×D311yescharacteristic
63#3967—62no—
64C22⋊#168—32no—
65#1605—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C3×C5×Q8—24no—
68C3×C5×Q8—42no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5Q1612yescomplemented
81C2×C3×C4×C5C2×D412yes—
82C2×Dic15—22no—
83C2×Dic15—22no—
84Dic30—42no—
85Dic30—81no—
86C3⋊#168—42no—
87C22×C3×Q8C2×D511yescharacteristic
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4C2×D511yescharacteristic
90C2×#216—102no—
91#926—101no—
92#924—52no—
93#924—101no—
94#890—102no—
95#888—102no—
96C3×#95—21no—
97C3×#95C2×D511yescharacteristic
98#835—102no—
99#830—52no—
100C2×C5×Q8—22no—
101C2×C5×Q8—42no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5#6711yescharacteristic
105C22×C4×C5#6711yescharacteristic
106C22×C4×C5C22×D311yescharacteristic
107C2×Dic10—32no—
108C2×Dic10—61no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—42no—
111C22⋊Dic5—62no—
112#689—124no—
113C4⋊Dic5—32no—
114C4⋊Dic5—61no—
115C4⋊Dic5—61no—
116C4⋊Dic5—61no—
117#683—62no—
118#683—62no—
119C4×Dic5—62no—
120C2×#168—62no—
121#544—151no—
122#451—152no—
123#395D1511yescharacteristic
124#328—152no—
125#324—151no—
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5#12011yescharacteristic
129C22×C3×C5C2×Q1611yescharacteristic
130C22×C3×C5#13711yescharacteristic
131C3×C4×C5—22no—
132C3×C4×C5—22no—
133C3×C4×C5—42no—
134C3×C4×C5—41no—
135C3×C4×C5—42no—
136Dic15—42no—
137Dic15—42no—
138C2×C3×Q8—22no—
139C2×C3×Q8—42no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4C22⋊D511yescharacteristic
143C22×C3×C4C22⋊D511yescharacteristic
144C22×C3×C4C22×D511yescharacteristic
145C2×Dic6—52no—
146C2×Dic6—101no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—42no—
149#217—102no—
150#216—204no—
151C4⋊Dic3—52no—
152C4⋊Dic3—101no—
153C4⋊Dic3—101no—
154C4⋊Dic3—101no—
155Dic3⋊C4—102no—
156Dic3⋊C4—102no—
157C4×Dic3—102no—
158C2×C3⋊C8—102no—
159C23×C5C2×#6711yescharacteristic
160C5×Q8—24no—
161C5×Q8—42no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—22no—
165C2×C4×C5—22no—
166C2×C4×C5—21no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5#21612yescomplemented
174C2×C4×C5D3×D412yes—
175C2×Dic5—62no—
176C2×Dic5—62no—
177Dic10—122no—
178Dic10—241no—
179#168—122no—
180C22×Q8C2×D1511yescharacteristic
181C2×Q16—302no—
182C4⋊Q8—302no—
183#125—302no—
184C22⋊Q8—152no—
185C22⋊Q8—301no—
186#117—301no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C2×D1511yescharacteristic
189#103—302no—
190C22⋊C8—152no—
191#95—21no—
192#95C2×D1511yescharacteristic
193C2×C3×C5—21no—
194C2×C3×C5—21no—
195C2×C3×C5#45111yescharacteristic
196C2×C3×C5#45611yescharacteristic
197C2×C3×C5B(4,𝔽2)11yescharacteristic
198C23×C3C2×C22⋊D511yescharacteristic
199C3×Q8—24no—
200C3×Q8—42no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4#68912yescomplemented
213C2×C3×C4D4×D512yes—
214C2×Dic3—102no—
215C2×Dic3—102no—
216Dic6—202no—
217Dic6—401no—
218C3⋊C8—202no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5#93711yescharacteristic
222C22×C5C2×#21611yescharacteristic
223C22×C5#95111yescharacteristic
224C4×C5—22no—
225C4×C5—22no—
226C4×C5—42no—
227C4×C5—41no—
228C4×C5—42no—
229Dic5—122no—
230Dic5—122no—
231C2×Q8—22no—
232C2×Q8—42no—
233C2×Q8—152no—
234C2×Q8—301no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4#122011yescharacteristic
238C22×C4#122011yescharacteristic
239C22×C4C22×D1511yescharacteristic
240Q16—604no—
241C2×C8—302no—
242C4⋊C4—22no—
243C4⋊C4—42no—
244C4⋊C4—152no—
245C4⋊C4—301no—
246C4⋊C4—301no—
247C4⋊C4—301no—
248C4⋊C4—302no—
249C4⋊C4—302no—
250C22⋊C4—302no—
251C42—302no—
252C3×C5#160511yescharacteristic, complemented, Hall
253C22×C3—21no—
254C22×C3—21no—
255C22×C3#408311yescharacteristic
256C22×C3C2×#68911yescharacteristic
257C22×C3#409711yescharacteristic
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—42no—
261C3×C4—41no—
262C3×C4—42no—
263Dic3—202no—
264Dic3—202no—
265C2×C5—21no—
266C2×C5—21no—
267C2×C5#503211yescharacteristic
268C2×C5#505011yescharacteristic
269C2×C5#509511yescharacteristic
270C23C2×#122011yescharacteristic
271Q8—24no—
272Q8—42no—
273Q8—602no—
274Q8—1201no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—302no—
287C2×C4—302no—
288C2×C4#671812yescomplemented
289C2×C4D4×D1512yes—
290C8—602no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3#6532111yescharacteristic
294C2×C3#6533911yescharacteristic
295C2×C3#6538411yescharacteristic
296C5#6970711yescharacteristic, complemented, Sylow
297C22—21no—
298C22—21no—
299C22#9182611yescharacteristic
300C22C2×#671811yescharacteristic
301C22#9184011yescharacteristic
302C4—22no—
303C4—22no—
304C4—42no—
305C4—42no—
306C4—41no—
307C4—602no—
308C4—602no—
309C3#1060050011yescharacteristic, complemented, Sylow
310C2—21no—
311C2—21no—
312C2#1175113311yescharacteristic
313C2#1175115111yescharacteristic
314C2#1175119611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#395C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenter#395D15
hypocenterC3×C5#1605
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
80. C2×C3×C4×C5Q16semidirect
173. C2×C4×C5#216semidirect
212. C2×C3×C4#689semidirect
252. C3×C5#1605semidirect
288. C2×C4#6718semidirect
296. C5#69707semidirect
309. C3#10600500semidirect

Maximal subgroups

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

subgroupindex
#117562592
C3×C5×#3952
#117513292
#117463492
#117462732
#106005003
#697075