Finite Group Databasebeta

← #14313519

Subgroups — #14313519

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5830C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic, complemented
3C3×#65529C211yesmaximal, characteristic, complemented
4#11746007C214yesmaximal, complemented
5#10602654—31nomaximal, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C5×D12C411yescharacteristic, complemented
8#91815—21no—
9C5×#947C412yescomplemented
10C5×#940C2212yes—
11C5×#937—21no—
12C5×#937—21no—
13C5×#930—21no—
14C5×#930—21no—
15C5×#926C411yescharacteristic, complemented
16C3×#4072—21no—
17#91118—21no—
18#91118C2212yescomplemented
19C3×#3966—21no—
20C3×#3966C2212yescomplemented
21#70061—51nomaximal, Hall
22C5×#535—31no—
23#65529—31no—
24#65529D311yescharacteristic, complemented
25#64765—34no—
26C23×C5×D3—21no—
27C3×C5×#41—41no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8C2×C411yescharacteristic
30C2×C3×C5×D4D411yescharacteristic
31C2×C3×C5×D4D411yescharacteristic
32C2×C3×C5×D4C2311yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C2×C5×#67—22no—
37C2×C5×#67—22no—
38C2×C5×D12—21no—
39C2×C5×D12—41no—
40C2×C5×D12—41no—
41C2×C5×D12C2×C412yes—
42#6719—22no—
43C4⋊Dic15—41no—
44C4×Dic15—41no—
45C5×#217—21no—
46C5×(C2×D3)⋊C4—22no—
47C5×(C2×D3)⋊C4—22no—
48C5×C4⋊Dic3—21no—
49C4×C5×Dic3C2×C412yes—
50C3×C22⋊Dic5—22no—
51C3×C4⋊Dic5—41no—
52C3×C4×Dic5—41no—
53#5830D511yescharacteristic
54C3×#410—51no—
55#5240—51no—
56#4474—54no—
57C2×C5×#41C2×D311yescharacteristic
58C22×C5×D4—31no—
59C5×#127—32no—
60C5×#124—32no—
61C5×#121—61no—
62C5×#121—61no—
63C5×#120—61no—
64C5×#120—61no—
65C5×#117—31no—
66#4072—21no—
67#4072—61no—
68#3966—21no—
69#3966—32no—
70#3966—61no—
71#3966C2×D312yescomplemented
72#2128—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C2×D411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C22×C5×D3—22no—
77C22×C5×D3—42no—
78C22×C5×D3—82no—
79C3×C5×Q8—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5C22⋊C411yescharacteristic
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22⋊C411yescharacteristic
92C2×C3×C4×C5C22×C411yescharacteristic
93C2×Dic15—42no—
94C5×#67—82no—
95C5×#67—82no—
96C2×C5×Dic3—22no—
97C5×D12—42no—
98C5×D12—41no—
99C5×D12—41no—
100C2×C3×Dic5—42no—
101C2×C3×#41C2×D511yescharacteristic
102C22×D12Dic511yescharacteristic, complemented
103C3×#117—101no—
104#947Dic512yescomplemented
105#940C2×D512yes—
106#937—21no—
107#937—21no—
108#930—21no—
109#930—21no—
110#926—101no—
111#926Dic511yescharacteristic, complemented
112C3×#99—52no—
113C3×#99—101no—
114#834—52no—
115#834—101no—
116C24×C5—61no—
117C5×#41—41no—
118C5×#41—41no—
119C2×C5×Q8C4×D311yescharacteristic
120C2×C5×D4—32no—
121C2×C5×D4—62no—
122C2×C5×D4—62no—
123C2×C5×D4—61no—
124C2×C5×D4—121no—
125C2×C5×D4—121no—
126C2×C5×D4D1211yescharacteristic
127C2×C5×D4#6711yescharacteristic
128C2×C5×D4C22×D311yescharacteristic
129C22×C4×C5C4×D311yescharacteristic
130C22×C4×C5D1211yescharacteristic
131C22×C4×C5#6711yescharacteristic
132C5×C4⋊C4—61no—
133C5×C22⋊C4—61no—
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C42×C5—32no—
137C22⋊Dic5—22no—
138C22⋊Dic5—62no—
139C4⋊Dic5—41no—
140C4⋊Dic5—121no—
141C4×Dic5—41no—
142C4×Dic5—121no—
143#535—31no—
144#410—51no—
145#410—151no—
146#353—154no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—41no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
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#9911yescharacteristic
162C3×C4×C5#9911yescharacteristic
163Dic15—82no—
164C3×Dic5—82no—
165C5×Dic3—42no—
166C23×D3—21no—
167C3×#41—41no—
168C3×#41—41no—
169C2×C3×Q8C2×Dic511yescharacteristic
170C2×C3×D4C22⋊D511yescharacteristic
171C2×C3×D4C22⋊D511yescharacteristic
172C2×C3×D4C22×D511yescharacteristic
173C22×C3×C4C2×Dic511yescharacteristic
174C22×C3×C4C22⋊D511yescharacteristic
175C22×C3×C4C22⋊D511yescharacteristic
176C2×#67—22no—
177C2×#67—22no—
178C2×D12—21no—
179C2×D12—41no—
180C2×D12—41no—
181C2×D12C2×Dic512yes—
182C3×C4⋊C4—201no—
183C3×C22⋊C4—102no—
184C3×C42—201no—
185#217—21no—
186#217—102no—
187(C2×D3)⋊C4—22no—
188(C2×D3)⋊C4—22no—
189C4⋊Dic3—21no—
190C4⋊Dic3—201no—
191C4×Dic3—201no—
192C4×Dic3C2×Dic512yes—
193C23×C5—62no—
194C23×C5—122no—
195C23×C5—242no—
196C23×C5(C2×D3)⋊C411yescharacteristic
197C23×C5C2×D1211yescharacteristic
198C23×C5C2×#6711yescharacteristic
199C5×Q8—41no—
200C5×D4—41no—
201C5×D4—41no—
202C5×D4—41no—
203C5×D4—122no—
204C5×D4—121no—
205C5×D4—121no—
206C5×D4—242no—
207C5×D4—242no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—21no—
214C2×C4×C5—62no—
215C2×C4×C5(C2×D3)⋊C411yescharacteristic
216C2×C4×C5(C2×D3)⋊C411yescharacteristic
217C2×C4×C5(C2×D3)⋊C411yescharacteristic
218C2×C4×C5C2×C4×D311yescharacteristic
219C2×Dic5—42no—
220C2×Dic5—122no—
221C2×#41D3×D511yescharacteristic
222C22×D4—31no—
223#127—32no—
224#124—32no—
225#121—61no—
226#121—61no—
227#120—61no—
228#120—61no—
229#117—31no—
230#117—101no—
231#117—301no—
232#99—52no—
233#99—101no—
234#99—152no—
235#99—301no—
236C2×C3×C5—21no—
237C2×C3×C5—41no—
238C2×C3×C5—41no—
239C2×C3×C5—41no—
240C2×C3×C5C2×#9911yescharacteristic
241C5×D3—82no—
242C23×C3C22⋊Dic511yescharacteristic
243C23×C3C2×C22⋊D511yescharacteristic
244C23×C3C2×C22⋊D511yescharacteristic
245C22×D3—22no—
246C22×D3—42no—
247C22×D3—82no—
248C3×Q8—41no—
249C3×D4—41no—
250C3×D4—41no—
251C3×D4—41no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—202no—
259C2×C3×C4C22⋊Dic511yescharacteristic
260C2×C3×C4C22⋊Dic511yescharacteristic
261C2×C3×C4C22⋊Dic511yescharacteristic
262C2×C3×C4C22×Dic511yescharacteristic
263#67—82no—
264#67—82no—
265C2×Dic3—22no—
266C2×Dic3—202no—
267D12—42no—
268D12—41no—
269D12—41no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—41no—
274C22×C5—41no—
275C22×C5—41no—
276C22×C5—122no—
277C22×C5—122no—
278C22×C5—122no—
279C22×C5—244no—
280C22×C5C2×(C2×D3)⋊C411yescharacteristic
281C4×C5—21no—
282C4×C5—21no—
283C4×C5—21no—
284C4×C5—122no—
285C4×C5#80611yescharacteristic
286C4×C5#80611yescharacteristic
287Dic5—82no—
288Dic5—242no—
289C24—61no—
290#41—41no—
291#41—41no—
292C2×Q8D3×Dic511yescharacteristic
293C2×D4—32no—
294C2×D4—62no—
295C2×D4—62no—
296C2×D4—61no—
297C2×D4—121no—
298C2×D4—121no—
299C2×D4#120111yescharacteristic
300C2×D4#120311yescharacteristic
301C2×D4C2×D3×D511yescharacteristic
302C22×C4D3×Dic511yescharacteristic
303C22×C4#120111yescharacteristic
304C22×C4#120311yescharacteristic
305C4⋊C4—61no—
306C4⋊C4—201no—
307C4⋊C4—601no—
308C22⋊C4—61no—
309C22⋊C4—62no—
310C22⋊C4—62no—
311C22⋊C4—102no—
312C22⋊C4—302no—
313C42—32no—
314C42—201no—
315C42—601no—
316C3×C5#212811yescharacteristic, complemented, Hall
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3C2×C22⋊Dic511yescharacteristic
324C2×D3—42no—
325C2×D3—42no—
326C2×D3—42no—
327C2×D3—84no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—402no—
332C3×C4#396611yescharacteristic
333C3×C4#396611yescharacteristic
334Dic3—42no—
335Dic3—402no—
336C2×C5—21no—
337C2×C5—41no—
338C2×C5—41no—
339C2×C5—41no—
340C2×C5—242no—
341C2×C5C2×#80611yescharacteristic
342C23—62no—
343C23—122no—
344C23—242no—
345C23(C2×D3)⋊Dic511yescharacteristic
346C23C2×#120111yescharacteristic
347C23C2×#120311yescharacteristic
348Q8—41no—
349D4—41no—
350D4—41no—
351D4—41no—
352D4—122no—
353D4—121no—
354D4—121no—
355D4—242no—
356D4—242no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—62no—
364C2×C4—202no—
365C2×C4—602no—
366C2×C4(C2×D3)⋊Dic511yescharacteristic
367C2×C4(C2×D3)⋊Dic511yescharacteristic
368C2×C4(C2×D3)⋊Dic511yescharacteristic
369C2×C4C2×D3×Dic511yescharacteristic
370C2×C3—21no—
371C2×C3—41no—
372C2×C3—41no—
373C2×C3—41no—
374C2×C3C2×#396611yescharacteristic
375D3—82no—
376C5#7006111yescharacteristic, complemented, Sylow
377C22—21no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—122no—
384C22—122no—
385C22—122no—
386C22—244no—
387C22C2×(C2×D3)⋊Dic511yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—122no—
392C4—402no—
393C4—1202no—
394C4#9099611yescharacteristic
395C4#9099611yescharacteristic
396C3#1060265411yescharacteristic, complemented, Sylow
397C2—21no—
398C2—41no—
399C2—41no—
400C2—41no—
401C2—242no—
402C2C2×#9099611yescharacteristic
subgroupG/H
centerC2C2×#90996
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
prime radicalC5×#5830C2
cosocleC2×C3×C5×D4C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2128
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11751341C2semidirect
3. C3×#65529C2semidirect
4. #11746007C2semidirect
7. C22×C5×D12C4semidirect
9. C5×#947C4semidirect
15. C5×#926C4semidirect
18. #91118C22semidirect
20. C3×#3966C22semidirect
24. #65529D3semidirect
71. #3966C2×D3semidirect
102. C22×D12Dic5semidirect
104. #947Dic5semidirect
111. #926Dic5semidirect
316. C3×C5#2128semidirect
376. C5#70061semidirect
396. C3#10602654semidirect

Maximal subgroups

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

subgroupindex
C5×#58302
#117513412
C3×#655292
#117460072
#106026543
#700615