Finite Group Databasebeta

← #14283174

Subgroups — #14283174

Order 1920.

588 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4070C211yesmaximal, characteristic
2#11751308C211yesmaximal, characteristic
3C4×C5×#217C211yesmaximal, characteristic
4#11745961C214yesmaximal, complemented
5#10600238—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C3×Dic10C411yescharacteristic, complemented
8C2×#6710—21no—
9C2×C5×#217—21no—
10C2×C4×C5×Dic3—21no—
11C2×C3×C22⋊Dic5—21no—
12C2×C3×C4⋊Dic5C411yescharacteristic, complemented
13C3×#4070—21no—
14C3×#4070—21no—
15C3×#4070C412yescomplemented
16C3×#4070C2212yes—
17C2×C3×#683—21no—
18#91114—21no—
19#91114C2212yes—
20C5×C3⋊#95C2212yes—
21#71688—51nomaximal, Hall
22C2×#4070D311yescharacteristic
23C4×C5×C22⋊C4—31no—
24#65496—31no—
25#64672—34no—
26C24×C3×C5D411yescharacteristic
27C22×C3×C4×C5—42no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5C2311yescharacteristic
34C22×C5×Dic3—22no—
35C22×C3×Dic5—21no—
36C22×C3×Dic5—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10—42no—
39C2×C3×Dic10C2×C412yes—
40#6710—42no—
41C2×C3⋊#168—22no—
42C5×#217—24no—
43C4×C5×Dic3—42no—
44C3×C22⋊Dic5—22no—
45C3×C22⋊Dic5—22no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5C2×C412yes—
48C3×#683—22no—
49C3×#683—22no—
50C2×C3×C22⋊Q8—51no—
51C4×#217D511yescharacteristic
52#5207—51no—
53#4538—54no—
54C23×C4×C5C2×D311yescharacteristic
55C22×Dic10Dic311yescharacteristic, complemented
56C2×C5×C22⋊C4—61no—
57C2×C42×C5—61no—
58C2×C22⋊Dic5—21no—
59C2×C4⋊Dic5Dic311yescharacteristic, complemented
60#4070—21no—
61#4070—21no—
62#4070Dic312yescomplemented
63#4070C2×D312yes—
64C2×#683—21no—
65C2×#681—61no—
66C5×#95—32no—
67C22⋊#168—32no—
68C22⋊#168—61no—
69#1508—151noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22⋊C411yescharacteristic
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C5×Dic3—24no—
87C2×C5×Dic3—42no—
88C2×C5×Dic3—42no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—22no—
91C2×C3×Dic5—42no—
92C2×C3×Dic5—42no—
93C3×Dic10—42no—
94C3×Dic10—42no—
95C3⋊#168—42no—
96C22×C3×Q8—51no—
97C23×C3×C4C2×D511yescharacteristic
98C3×C22⋊Q8—52no—
99C3×C22⋊Q8—52no—
100C3×C22⋊Q8—101no—
101C3×C22⋊Q8—101no—
102C2×C3×C4⋊C4—51no—
103C2×C3×C4⋊C4—101no—
104C2×C3×C22⋊C4—101no—
105C2×#217—21no—
106C2×C4×Dic3—21no—
107C2×#208—101no—
108C3⋊#95C2×D512yes—
109#830—52no—
110#830—101no—
111C24×C5#6711yescharacteristic
112C22×C4×C5—42no—
113C22×C4×C5—62no—
114C22×C4×C5C2×Dic311yescharacteristic
115C22×C4×C5C2×Dic311yescharacteristic
116C22×C4×C5#6711yescharacteristic
117C22×C4×C5#6711yescharacteristic
118C22×C4×C5#6711yescharacteristic
119C22×C4×C5C22×D311yescharacteristic
120C22×Dic5—21no—
121C22×Dic5—21no—
122C2×Dic10—21no—
123C2×Dic10—42no—
124C2×Dic10C2×Dic312yes—
125C5×C22⋊C4—64no—
126C42×C5—122no—
127C22⋊Dic5—22no—
128C22⋊Dic5—22no—
129C4⋊Dic5—21no—
130C4⋊Dic5C2×Dic312yes—
131#683—22no—
132#683—22no—
133#681—122no—
134C2×#168—62no—
135C2×C22⋊Q8—51no—
136#407—151no—
137C4×C22⋊C4—31no—
138#328—154no—
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—44no—
147C22×C3×C5#10412yes—
148C22×C3×C5C2×C22⋊C411yescharacteristic
149C22×C3×C5#13712yes—
150C3×C4×C5—21no—
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5#9912yes—
154C3×Dic5—42no—
155C3×Dic5—42no—
156C5×Dic3—44no—
157C24×C3C22⋊D511yescharacteristic
158C2×C3×Q8—52no—
159C2×C3×Q8—101no—
160C2×C3×Q8—202no—
161C22×C3×C4—42no—
162C22×C3×C4—101no—
163C22×C3×C4—101no—
164C22×C3×C4C4×D511yescharacteristic
165C22×C3×C4C4×D511yescharacteristic
166C22×C3×C4D2011yescharacteristic
167C22×C3×C4D2011yescharacteristic
168C22×C3×C4C22⋊D511yescharacteristic
169C22×C3×C4C22×D511yescharacteristic
170C22×Dic3—22no—
171C3×C4⋊C4—52no—
172C3×C4⋊C4—102no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—102no—
175C3×C22⋊C4—102no—
176C3×C22⋊C4—102no—
177#217—24no—
178C4×Dic3—42no—
179#208—202no—
180C2×C3⋊C8—102no—
181C23×C5—22no—
182C23×C5—22no—
183C23×C5—41no—
184C23×C5#21711yescharacteristic
185C23×C5#21711yescharacteristic
186C23×C5C2×#6711yescharacteristic
187C2×C4×C5—22no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—64no—
194C2×C4×C5—122no—
195C2×C4×C5—122no—
196C2×C4×C5#21711yescharacteristic
197C2×C4×C5#21711yescharacteristic
198C2×C4×C5C22×Dic311yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—22no—
201C2×Dic5—22no—
202C2×Dic5—42no—
203C2×Dic5—42no—
204Dic10—42no—
205Dic10—42no—
206#168—122no—
207C22×Q8—51no—
208C23×C4D3×D511yescharacteristic
209C2×M16—301no—
210C22⋊Q8—52no—
211C22⋊Q8—52no—
212C22⋊Q8—101no—
213C22⋊Q8—101no—
214C2×C4⋊C4—51no—
215C2×C4⋊C4—101no—
216C2×C22⋊C4—61no—
217C2×C22⋊C4—101no—
218C2×C42—61no—
219C22⋊C8—152no—
220C22⋊C8—301no—
221#95—32no—
222C2×C3×C5—22no—
223C2×C3×C5—22no—
224C2×C3×C5—41no—
225C2×C3×C5C2×#9911yescharacteristic
226C2×C3×C5#41911yescharacteristic
227C2×C3×C5C2×#10411yescharacteristic
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—41no—
231C23×C3#68511yescharacteristic
232C23×C3#68511yescharacteristic
233C23×C3C2×C22⋊D511yescharacteristic
234C3×Q8—202no—
235C3×Q8—202no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—102no—
243C2×C3×C4—102no—
244C2×C3×C4—202no—
245C2×C3×C4—202no—
246C2×C3×C4#68511yescharacteristic
247C2×C3×C4#68511yescharacteristic
248C2×C3×C4C2×C4×D511yescharacteristic
249C2×C3×C4C2×D2011yescharacteristic
250C2×Dic3—24no—
251C2×Dic3—42no—
252C2×Dic3—42no—
253C3⋊C8—202no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—44no—
262C22×C5#83712yes—
263C22×C5#94212yes—
264C22×C5C2×#21711yescharacteristic
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—124no—
269C4×C5#83412yes—
270Dic5—42no—
271Dic5—42no—
272C24#120111yescharacteristic
273C2×Q8—52no—
274C2×Q8—101no—
275C2×Q8—202no—
276C22×C4—42no—
277C22×C4—62no—
278C22×C4—101no—
279C22×C4—101no—
280C22×C4D5×Dic311yescharacteristic
281C22×C4D5×Dic311yescharacteristic
282C22×C4#120111yescharacteristic
283C22×C4#120211yescharacteristic
284C22×C4#120211yescharacteristic
285C22×C4C2×D3×D511yescharacteristic
286M16—602no—
287C2×C8—302no—
288C4⋊C4—52no—
289C4⋊C4—101no—
290C4⋊C4—102no—
291C4⋊C4—102no—
292C22⋊C4—64no—
293C22⋊C4—102no—
294C22⋊C4—102no—
295C42—122no—
296C3×C5#150811yescharacteristic, complemented, Hall
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—44no—
305C22×C3#393712yes—
306C22×C3C2×#68511yescharacteristic
307C22×C3#409712yes—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—202no—
312C3×C4—202no—
313C3×C4#393812yes—
314Dic3—44no—
315C2×C5—22no—
316C2×C5—22no—
317C2×C5—41no—
318C2×C5C2×#83411yescharacteristic
319C2×C5#522511yescharacteristic
320C2×C5C2×#83711yescharacteristic
321C23—22no—
322C23—22no—
323C23—41no—
324C23#666511yescharacteristic
325C23#666511yescharacteristic
326C23C2×#120111yescharacteristic
327Q8—202no—
328Q8—202no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—64no—
336C2×C4—102no—
337C2×C4—102no—
338C2×C4—122no—
339C2×C4—122no—
340C2×C4—202no—
341C2×C4—202no—
342C2×C4#666511yescharacteristic
343C2×C4#666511yescharacteristic
344C2×C4C2×D5×Dic311yescharacteristic
345C2×C4C2×#120211yescharacteristic
346C8—602no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—41no—
350C2×C3C2×#393711yescharacteristic
351C2×C3C2×#393811yescharacteristic
352C2×C3#6529311yescharacteristic
353C5#7168811yescharacteristic, complemented, Sylow
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—44no—
362C22#9097712yes—
363C22#9130912yes—
364C22C2×#666511yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—124no—
369C4—202no—
370C4—202no—
371C4#9099512yes—
372C3#1060023811yescharacteristic, complemented, Sylow
373C2—22no—
374C2—22no—
375C2—41no—
376C2#1174839911yescharacteristic
377C2C2×#9097711yescharacteristic
378C2C2×#9099511yescharacteristic
subgroupG/H
centerC22C2×#6665
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1508
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #11745961C2semidirect
7. C22×C3×Dic10C4semidirect
12. C2×C3×C4⋊Dic5C4semidirect
15. C3×#4070C4semidirect
55. C22×Dic10Dic3semidirect
59. C2×C4⋊Dic5Dic3semidirect
62. #4070Dic3semidirect
296. C3×C5#1508semidirect
353. C5#71688semidirect
372. C3#10600238semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40702
#117513082
C4×C5×#2172
#117459612
#106002383
#716885