Finite Group Databasebeta

← #14283283

Subgroups — #14283283

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#930C211yesmaximal, characteristic
2#11751312C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4#11745957C214yesmaximal, complemented
5#10602467—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C5×#67—21no—
8C22×C5×D12C411yescharacteristic, complemented
9C2×#6719—21no—
10C5×#930—21no—
11C5×#930—21no—
12C5×#930C412yescomplemented
13C5×#930C2212yes—
14C2×C5×(C2×D3)⋊C4—21no—
15C2×C5×C4⋊Dic3C411yescharacteristic, complemented
16C2×C3×#681—21no—
17#91115—21no—
18#91115C2212yescomplemented
19C3×C22⋊#168—21no—
20C3×C22⋊#168C2212yescomplemented
21#69978—51nomaximal, Hall
22C2×C5×#121—31no—
23#65500—31no—
24#65496D311yescharacteristic, complemented
25#64757—34no—
26C24×C3×C5D411yescharacteristic
27C23×C5×D3—21no—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—22no—
36C2×C5×#67—22no—
37C2×C5×#67—22no—
38C2×C5×#67—44no—
39C22×C5×Dic3—21no—
40C2×C5×D12—21no—
41C2×C5×D12—42no—
42C2×C5×D12C2×C412yes—
43#6719—42no—
44C5×(C2×D3)⋊C4—22no—
45C5×(C2×D3)⋊C4—22no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3C2×C412yes—
48C3×#681—42no—
49C2×C3×#168—22no—
50C2×#930D511yescharacteristic
51C3×#407—51no—
52#5211—51no—
53#4470—54no—
54C22×C5×D4—31no—
55C22×C5×D4—61no—
56C23×C4×C5C2×D311yescharacteristic
57C5×#121—32no—
58C5×#121—32no—
59C5×#121—61no—
60C5×#121—61no—
61C2×C5×C4⋊C4—31no—
62C2×C5×C22⋊C4—61no—
63C2×C22⋊Dic5—61no—
64C2×#681—21no—
65#3963—32no—
66#3963—61no—
67C22⋊#168—21no—
68C22⋊#168C2×D312yescomplemented
69#1510—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
76C22×C5×D3—22no—
77C22×C5×D3—42no—
78C22×C5×D3—42no—
79C22×C5×D3—42no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—42no—
91C2×Dic15—42no—
92C2×Dic15—42no—
93C5×#67—44no—
94C5×#67—44no—
95C2×C5×Dic3—22no—
96C2×C5×Dic3—42no—
97C5×D12—42no—
98C5×D12—42no—
99C3×#168—42no—
100C23×C3×C4C2×D511yescharacteristic
101C22×#67—21no—
102C22×D12Dic511yescharacteristic, complemented
103C2×C3×M16—101no—
104C2×#217—101no—
105#930—21no—
106#930—21no—
107#930Dic512yescomplemented
108#930C2×D512yes—
109C2×(C2×D3)⋊C4—21no—
110C2×C4⋊Dic3Dic511yescharacteristic, complemented
111C3×C22⋊C8—52no—
112C3×C22⋊C8—101no—
113C3⋊#95—52no—
114C3⋊#95—101no—
115C24×C5—61no—
116C24×C5D1211yescharacteristic
117C2×C5×D4—32no—
118C2×C5×D4—62no—
119C2×C5×D4—62no—
120C2×C5×D4—61no—
121C2×C5×D4—122no—
122C2×C5×D4—124no—
123C22×C4×C5—42no—
124C22×C4×C5—61no—
125C22×C4×C5C4×D311yescharacteristic
126C22×C4×C5C4×D311yescharacteristic
127C22×C4×C5D1211yescharacteristic
128C22×C4×C5#6711yescharacteristic
129C22×C4×C5#6711yescharacteristic
130C22×C4×C5C22×D311yescharacteristic
131C22×Dic5—62no—
132C5×C4⋊C4—32no—
133C5×C4⋊C4—61no—
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C22⋊Dic5—122no—
137#681—42no—
138C2×#168—22no—
139C2×#121—31no—
140#407—51no—
141#381—151no—
142#327—154no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—44no—
151C22×C3×C5#9912yes—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C22×C3×C5AGL(1,ℤ/8)12yes—
154C2×C5×D3—42no—
155C2×C5×D3—42no—
156C2×C5×D3—42no—
157C2×C5×D3—84no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162Dic15—82no—
163C5×Dic3—42no—
164C24×C3C22⋊D511yescharacteristic
165C23×D3—21no—
166C22×C3×C4—42no—
167C22×C3×C4C2×Dic511yescharacteristic
168C22×C3×C4C2×Dic511yescharacteristic
169C22×C3×C4C22⋊D511yescharacteristic
170C22×C3×C4C22⋊D511yescharacteristic
171C22×C3×C4C22⋊D511yescharacteristic
172C22×C3×C4C22×D511yescharacteristic
173C2×#67—22no—
174C2×#67—22no—
175C2×#67—44no—
176C22×Dic3—21no—
177C22×Dic3—102no—
178C2×D12—21no—
179C2×D12—42no—
180C2×D12C2×Dic512yes—
181C3×M16—202no—
182C2×C3×C8—102no—
183#217—202no—
184(C2×D3)⋊C4—22no—
185(C2×D3)⋊C4—22no—
186C4⋊Dic3—21no—
187C4⋊Dic3C2×Dic512yes—
188C23×C5—22no—
189C23×C5—22no—
190C23×C5—41no—
191C23×C5—62no—
192C23×C5—122no—
193C23×C5—122no—
194C23×C5—122no—
195C23×C5(C2×D3)⋊C411yescharacteristic
196C23×C5(C2×D3)⋊C411yescharacteristic
197C23×C5C2×D1211yescharacteristic
198C5×D4—122no—
199C5×D4—122no—
200C5×D4—124no—
201C5×D4—124no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—62no—
209C2×C4×C5—122no—
210C2×C4×C5(C2×D3)⋊C411yescharacteristic
211C2×C4×C5(C2×D3)⋊C411yescharacteristic
212C2×C4×C5C2×C4×D311yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C2×Dic5—122no—
215C2×Dic5—122no—
216C2×Dic5—122no—
217#168—42no—
218C22×D4—31no—
219C22×D4—61no—
220C23×C4D3×D511yescharacteristic
221C2×M16—101no—
222#121—32no—
223#121—32no—
224#121—61no—
225#121—61no—
226C2×C4⋊C4—31no—
227C2×C22⋊C4—61no—
228C2×C22⋊C4—301no—
229C22⋊C8—52no—
230C22⋊C8—101no—
231#95—152no—
232#95—301no—
233C2×C3×C5—22no—
234C2×C3×C5—22no—
235C2×C3×C5—41no—
236C2×C3×C5C2×#9911yescharacteristic
237C2×C3×C5#41811yescharacteristic
238C2×C3×C5#42111yescharacteristic
239C5×D3—82no—
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—41no—
243C23×C3C22⋊Dic511yescharacteristic
244C23×C3C22⋊Dic511yescharacteristic
245C23×C3C2×C22⋊D511yescharacteristic
246C22×D3—22no—
247C22×D3—42no—
248C22×D3—42no—
249C22×D3—42no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4C22⋊Dic511yescharacteristic
257C2×C3×C4C22⋊Dic511yescharacteristic
258C2×C3×C4C22×Dic511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260#67—44no—
261#67—44no—
262C2×Dic3—22no—
263C2×Dic3—42no—
264C2×Dic3—202no—
265C2×Dic3—202no—
266C2×Dic3—202no—
267D12—42no—
268D12—42no—
269C3×C8—202no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—44no—
278C22×C5—122no—
279C22×C5—122no—
280C22×C5—122no—
281C22×C5—244no—
282C22×C5#80612yes—
283C22×C5#90812yes—
284C22×C5C2×(C2×D3)⋊C411yescharacteristic
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—122no—
290Dic5—242no—
291C24—61no—
292C24#120311yescharacteristic
293C2×D4—32no—
294C2×D4—62no—
295C2×D4—62no—
296C2×D4—61no—
297C2×D4—122no—
298C2×D4—124no—
299C22×C4—42no—
300C22×C4—61no—
301C22×C4—302no—
302C22×C4D3×Dic511yescharacteristic
303C22×C4D3×Dic511yescharacteristic
304C22×C4#120111yescharacteristic
305C22×C4#120111yescharacteristic
306C22×C4#120311yescharacteristic
307C22×C4C2×D3×D511yescharacteristic
308M16—202no—
309C2×C8—102no—
310C4⋊C4—32no—
311C4⋊C4—61no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C22⋊C4—602no—
315C3×C5#151011yescharacteristic, complemented, Hall
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—44no—
324C22×C3#396612yes—
325C22×C3#407812yes—
326C22×C3C2×C22⋊Dic511yescharacteristic
327C2×D3—42no—
328C2×D3—42no—
329C2×D3—42no—
330C2×D3—84no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335Dic3—42no—
336Dic3—402no—
337C2×C5—22no—
338C2×C5—22no—
339C2×C5—41no—
340C2×C5—242no—
341C2×C5C2×#80611yescharacteristic
342C2×C5#513111yescharacteristic
343C2×C5#513911yescharacteristic
344C23—22no—
345C23—22no—
346C23—41no—
347C23—62no—
348C23—122no—
349C23—122no—
350C23—122no—
351C23(C2×D3)⋊Dic511yescharacteristic
352C23(C2×D3)⋊Dic511yescharacteristic
353C23C2×#120311yescharacteristic
354D4—122no—
355D4—122no—
356D4—124no—
357D4—124no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—62no—
365C2×C4—122no—
366C2×C4—602no—
367C2×C4—602no—
368C2×C4—602no—
369C2×C4(C2×D3)⋊Dic511yescharacteristic
370C2×C4(C2×D3)⋊Dic511yescharacteristic
371C2×C4C2×D3×Dic511yescharacteristic
372C2×C4C2×#120111yescharacteristic
373C8—202no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—41no—
377C2×C3#6550411yescharacteristic
378C2×C3C2×#396611yescharacteristic
379C2×C3#6552511yescharacteristic
380D3—82no—
381C5#6997811yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—44no—
390C22—122no—
391C22—122no—
392C22—122no—
393C22—244no—
394C22#9099612yes—
395C22#9130412yes—
396C22C2×(C2×D3)⋊Dic511yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—122no—
402C4—1202no—
403C3#1060246711yescharacteristic, complemented, Sylow
404C2—22no—
405C2—22no—
406C2—41no—
407C2—242no—
408C2#1174838911yescharacteristic
409C2#1174842411yescharacteristic
410C2C2×#9099611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×#930C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1510
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
2. #11751312C2semidirect
3. C3×#65496C2semidirect
4. #11745957C2semidirect
8. C22×C5×D12C4semidirect
12. C5×#930C4semidirect
15. C2×C5×C4⋊Dic3C4semidirect
18. #91115C22semidirect
20. C3×C22⋊#168C22semidirect
24. #65496D3semidirect
68. C22⋊#168C2×D3semidirect
102. C22×D12Dic5semidirect
107. #930Dic5semidirect
110. C2×C4⋊Dic3Dic5semidirect
315. C3×C5#1510semidirect
381. C5#69978semidirect
403. C3#10602467semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9302
#117513122
C3×#654962
#117459572
#106024673
#699785