Finite Group Databasebeta

← #14288306

Subgroups — #14288306

Order 1920.

456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756242C211yesmaximal, characteristic
2C3×#65242C211yesmaximal, characteristic
3#11748450C212yesmaximal, complemented
4C5×#4525C211yesmaximal, characteristic
5#11745964C212yesmaximal, complemented
6#10598909—31nomaximal, Hall
7C2×C3×C5×C22⋊C4C2211yescharacteristic
8C2×#6719—21no—
9#91813—21no—
10#91813C2212yes—
11#91767—22no—
12#91767—22no—
13C2×C3×C22⋊Dic5—21no—
14C2×C3×C4⋊Dic5C2211yescharacteristic
15C5×#830C2212yes—
16C3×#3963—21no—
17C3×#3963C2211yescharacteristic
18#90987—22no—
19#90974—22no—
20#69710—51nomaximal, Hall
21#65817—31no—
22#65242D311yescharacteristic
23#65010—32no—
24C5×#323—31no—
25#64687—32no—
26C24×C3×C5D411yescharacteristic
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5C2311yescharacteristic
29C22×Dic15—21no—
30C22×Dic15—21no—
31C2×Dic30—21no—
32C2×Dic30D412yes—
33C22×C3×Dic5—21no—
34C22×C3×Dic5—21no—
35C3×C5×C22⋊C4—22no—
36#6719—22no—
37#6719—22no—
38C4⋊Dic15—21no—
39C4⋊Dic15D412yes—
40#6712—22no—
41#6712—22no—
42C2×C5×C3⋊C8—22no—
43C3×C22⋊Dic5—42no—
44C3×C4⋊Dic5—22no—
45#5483—51no—
46C3×#397—51no—
47#4971—52no—
48#4525D511yescharacteristic
49#4452—52no—
50C2×C5×C22⋊C4C2×D311yescharacteristic
51C2×C22⋊Dic5—21no—
52C2×C22⋊Dic5—61no—
53C2×C4⋊Dic5C2×D311yescharacteristic
54#4070—32no—
55#4070—61no—
56#4024—62no—
57#4024—62no—
58C5×C22⋊C8—32no—
59#3963—21no—
60#3963C2×D311yescharacteristic
61#3949—62no—
62#3948—62no—
63#1608—151noSylow
64C23×C3×C5—21no—
65C23×C3×C5—21no—
66C23×C3×C5—41no—
67C23×C3×C5—41no—
68C23×C3×C5SD1612yes—
69C23×C3×C5C2×D411yescharacteristic
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5C2×D412yes—
74C2×Dic15—22no—
75C2×Dic15—22no—
76C2×Dic15—81no—
77C2×Dic15—81no—
78Dic30—42no—
79Dic30—81no—
80C2×C3×Dic5—41no—
81C2×C3×Dic5—41no—
82C2×C3×Dic5—41no—
83C2×C3×Dic5—41no—
84C2×C3×Dic5—41no—
85C2×C3×Dic5—41no—
86C5×C3⋊C8—42no—
87C2×C3×C4⋊C4—51no—
88C2×C3×C22⋊C4—101no—
89C2×C3×C22⋊C4C2×D511yescharacteristic
90C2×#217—101no—
91#924—52no—
92#924—101no—
93#878—102no—
94#878—102no—
95C3×#95—51no—
96C3×#95—101no—
97#830C2×D512yes—
98#810—102no—
99#808—102no—
100C24×C5#6711yescharacteristic
101C22×C4×C5#6711yescharacteristic
102C22×C4×C5C22×D311yescharacteristic
103C22×Dic5—21no—
104C22×Dic5—21no—
105C22×Dic5—61no—
106C22×Dic5—61no—
107C2×Dic10—32no—
108C2×Dic10—61no—
109C2×C5×C8—62no—
110C5×C22⋊C4—22no—
111C22⋊Dic5—42no—
112C22⋊Dic5—62no—
113C22⋊Dic5—62no—
114C4⋊Dic5—22no—
115C4⋊Dic5—32no—
116C4⋊Dic5—61no—
117#683—62no—
118#683—62no—
119#543—151no—
120#483—152no—
121#397—51no—
122#328—152no—
123#323—31no—
124C22×C3×C5—21no—
125C22×C3×C5—21no—
126C22×C3×C5—22no—
127C22×C3×C5—42no—
128C22×C3×C5—41no—
129C22×C3×C5—41no—
130C22×C3×C5—81no—
131C22×C3×C5#12011yescharacteristic
132C22×C3×C5C2×SD1611yescharacteristic
133C22×C3×C5#13711yescharacteristic
134C3×C4×C5—22no—
135C3×C4×C5—41no—
136Dic15—42no—
137Dic15—42no—
138C3×Dic5—81no—
139C3×Dic5—81no—
140C24×C3D2011yescharacteristic
141C22×C3×C4—101no—
142C22×C3×C4—101no—
143C22×C3×C4D2011yescharacteristic
144C22×C3×C4C22×D511yescharacteristic
145C22×Dic3—101no—
146C22×Dic3—101no—
147C2×Dic6—52no—
148C2×Dic6—101no—
149C3×C4⋊C4—102no—
150C3×C22⋊C4—22no—
151C3×C22⋊C4—202no—
152#217—102no—
153#217—102no—
154C4⋊Dic3—52no—
155C4⋊Dic3—101no—
156Dic3⋊C4—102no—
157Dic3⋊C4—102no—
158C2×C3⋊C8—22no—
159C23×C5—21no—
160C23×C5—21no—
161C23×C5—41no—
162C23×C5—41no—
163C23×C5#21412yes—
164C23×C5C2×#6711yescharacteristic
165C2×C4×C5—21no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5D3×D412yes—
169C2×Dic5—41no—
170C2×Dic5—41no—
171C2×Dic5—41no—
172C2×Dic5—41no—
173C2×Dic5—41no—
174C2×Dic5—41no—
175C2×Dic5—62no—
176C2×Dic5—62no—
177C2×Dic5—241no—
178C2×Dic5—241no—
179Dic10—122no—
180Dic10—241no—
181C5×C8—122no—
182C22⋊Q8—152no—
183C22⋊Q8—302no—
184C22⋊Q8—302no—
185C22⋊Q8—301no—
186C2×C4⋊C4—51no—
187C2×C22⋊C4—101no—
188C2×C22⋊C4—301no—
189C2×C22⋊C4D3×D511yescharacteristic
190#106—302no—
191#103—302no—
192C22⋊C8—32no—
193#95—51no—
194#95—101no—
195C2×C3×C5—21no—
196C2×C3×C5—21no—
197C2×C3×C5—42no—
198C2×C3×C5#44811yescharacteristic
199C2×C3×C5#45511yescharacteristic
200C2×C3×C5#45811yescharacteristic
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—41no—
204C23×C3—41no—
205C23×C3#67712yes—
206C23×C3C2×D2011yescharacteristic
207C2×C3×C4—21no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—201no—
211C2×C3×C4—201no—
212C2×C3×C4—201no—
213C2×C3×C4—201no—
214C2×C3×C4—201no—
215C2×C3×C4—201no—
216C2×C3×C4D4×D512yes—
217C2×Dic3—102no—
218C2×Dic3—102no—
219C2×Dic3—401no—
220C2×Dic3—401no—
221Dic6—202no—
222Dic6—401no—
223C3⋊C8—42no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5—22no—
227C22×C5—42no—
228C22×C5—41no—
229C22×C5—41no—
230C22×C5—81no—
231C22×C5C2×#21411yescharacteristic
232C22×C5#93711yescharacteristic
233C22×C5#95111yescharacteristic
234C4×C5—22no—
235C4×C5—41no—
236Dic5—81no—
237Dic5—81no—
238Dic5—122no—
239Dic5—122no—
240C24#120211yescharacteristic
241C2×Q8—152no—
242C2×Q8—301no—
243C22×C4—101no—
244C22×C4—101no—
245C22×C4—301no—
246C22×C4—301no—
247C22×C4#120211yescharacteristic
248C22×C4C2×D3×D511yescharacteristic
249C2×C8—62no—
250C4⋊C4—102no—
251C4⋊C4—152no—
252C4⋊C4—302no—
253C4⋊C4—301no—
254C4⋊C4—302no—
255C22⋊C4—22no—
256C22⋊C4—202no—
257C22⋊C4—302no—
258C22⋊C4—302no—
259C3×C5#160811yescharacteristic, complemented, Hall
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—42no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—81no—
267C22×C3#402811yescharacteristic
268C22×C3C2×#67711yescharacteristic
269C22×C3#405511yescharacteristic
270C3×C4—22no—
271C3×C4—41no—
272C3×C4—401no—
273C3×C4—401no—
274Dic3—202no—
275Dic3—202no—
276C2×C5—21no—
277C2×C5—21no—
278C2×C5—42no—
279C2×C5#504011yescharacteristic
280C2×C5#505311yescharacteristic
281C2×C5#506111yescharacteristic
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23#665712yes—
287C23C2×#120211yescharacteristic
288Q8—602no—
289Q8—1201no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—201no—
294C2×C4—201no—
295C2×C4—201no—
296C2×C4—201no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4—302no—
300C2×C4—302no—
301C2×C4—1201no—
302C2×C4—1201no—
303C2×C4#679012yes—
304C8—122no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—42no—
308C2×C3#6502711yescharacteristic
309C2×C3#6503111yescharacteristic
310C2×C3#6503511yescharacteristic
311C5#6971011yescharacteristic, complemented, Sylow
312C22—21no—
313C22—21no—
314C22—22no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—81no—
319C22C2×#665711yescharacteristic
320C22#9131311yescharacteristic
321C22#9157211yescharacteristic
322C4—22no—
323C4—41no—
324C4—401no—
325C4—401no—
326C4—602no—
327C4—602no—
328C3#1059890911yescharacteristic, complemented, Sylow
329C2—21no—
330C2—21no—
331C2—42no—
332C2#1174854911yescharacteristic
333C2#1174914911yescharacteristic
334C2#1174918511yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
prime radicalC24×C3×C5D4
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1608
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #11748450C2semidirect
5. #11745964C2semidirect
259. C3×C5#1608semidirect
311. C5#69710semidirect
328. C3#10598909semidirect

Maximal subgroups

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

subgroupindex
#117562422
C3×#652422
#117484502
C5×#45252
#117459642
#105989093
#697105