Finite Group Databasebeta

← #14313281

Subgroups — #14313281

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5830C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic, complemented
3C3×#65526C211yesmaximal, characteristic, complemented
4#11745997C214yesmaximal, complemented
5#10602652—31nomaximal, Hall
6C2×C3×C5×#41C2211yescharacteristic
7C22×C5×D12C411yescharacteristic, complemented
8#91815—21no—
9C5×#947—21no—
10C5×#940—21no—
11C5×#937C412yescomplemented
12C5×#937C2212yes—
13C5×#930—21no—
14C5×#930—21no—
15C5×#926C411yescharacteristic, complemented
16C2×C3×#681—21no—
17#91118—21no—
18#91118C2212yes—
19C3×#3968—21no—
20C3×#3965C2212yes—
21#70146—51nomaximal, Hall
22C5×#535—31no—
23#65529—31no—
24#65526D311yescharacteristic, complemented
25#64756—34no—
26C23×C5×D3C2×C412yes—
27C3×C5×#41—41no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8D411yescharacteristic
30C2×C3×C5×D4C2×C411yescharacteristic
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—21no—
40C2×C5×D12—41no—
41C2×C5×D12—41no—
42#6719—22no—
43C4⋊Dic15—41no—
44C4×Dic15—41no—
45C5×#217C2×C412yes—
46C5×(C2×D3)⋊C4—22no—
47C5×(C2×D3)⋊C4—22no—
48C5×C4⋊Dic3—21no—
49C4×C5×Dic3—21no—
50C3×#681—22no—
51C3×#681—41no—
52C2×C3×#168—41no—
53#5830D511yescharacteristic
54C3×#413—51no—
55#5240—51no—
56#4475—54no—
57C2×C5×#41C2×D311yescharacteristic
58C22×C5×D4—31no—
59C5×#127—61no—
60C5×#124—61no—
61C5×#121—61no—
62C5×#121—61no—
63C5×#120—32no—
64C5×#120—32no—
65C5×#117—31no—
66#4072—61no—
67C2×#681—21no—
68#3968—21no—
69#3966—32no—
70#3966—61no—
71#3965C2×D312yes—
72#2122—151noSylow
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22×C411yescharacteristic
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×C5C2×D411yescharacteristic
93C2×Dic15—42no—
94C5×#67—82no—
95C5×#67—82no—
96C2×C5×Dic3—22no—
97C5×D12—42no—
98C5×D12—41no—
99C5×D12—41no—
100C3×#168—42no—
101C2×C3×#41C2×D511yescharacteristic
102C22×D12Dic511yescharacteristic, complemented
103C2×C3×M16—101no—
104#947—21no—
105#940—21no—
106#937Dic512yescomplemented
107#937C2×D512yes—
108#930—21no—
109#930—21no—
110#926—101no—
111#926Dic511yescharacteristic, complemented
112C3×#101—101no—
113C3×#100—52no—
114#834—52no—
115#834—101no—
116C24×C5—32no—
117C5×#41—41no—
118C5×#41—41no—
119C2×C5×Q8#6711yescharacteristic
120C2×C5×D4—62no—
121C2×C5×D4—62no—
122C2×C5×D4—61no—
123C2×C5×D4—61no—
124C2×C5×D4—121no—
125C2×C5×D4—121no—
126C2×C5×D4C4×D311yescharacteristic
127C2×C5×D4D1211yescharacteristic
128C2×C5×D4C22×D311yescharacteristic
129C22×C4×C5C4×D311yescharacteristic
130C22×C4×C5D1211yescharacteristic
131C22×C4×C5#6711yescharacteristic
132C5×C4⋊C4—61no—
133C5×C22⋊C4—32no—
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C42×C5—61no—
137C22⋊Dic5—62no—
138C4⋊Dic5—121no—
139C4×Dic5—121no—
140#681—22no—
141#681—41no—
142C2×#168—41no—
143#535—31no—
144#413—51no—
145#410—151no—
146AΣL(1,𝔽16)—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—
164C5×Dic3—42no—
165C23×D3C2×Dic512yes—
166C3×#41—41no—
167C3×#41—41no—
168C2×C3×Q8C22⋊D511yescharacteristic
169C2×C3×D4C2×Dic511yescharacteristic
170C2×C3×D4C22⋊D511yescharacteristic
171C2×C3×D4C22×D511yescharacteristic
172C22×C3×C4C2×Dic511yescharacteristic
173C22×C3×C4C22⋊D511yescharacteristic
174C22×C3×C4C22⋊D511yescharacteristic
175C2×#67—22no—
176C2×#67—22no—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—41no—
180C2×D12—41no—
181C3×M16—102no—
182C3×M16—201no—
183C2×C3×C8—201no—
184#217—102no—
185#217C2×Dic512yes—
186(C2×D3)⋊C4—22no—
187(C2×D3)⋊C4—22no—
188C4⋊Dic3—21no—
189C4⋊Dic3—201no—
190C4×Dic3—21no—
191C4×Dic3—201no—
192C23×C5—62no—
193C23×C5—122no—
194C23×C5—242no—
195C23×C5(C2×D3)⋊C411yescharacteristic
196C23×C5C2×C4×D311yescharacteristic
197C23×C5C2×D1211yescharacteristic
198C5×Q8—41no—
199C5×D4—41no—
200C5×D4—41no—
201C5×D4—41no—
202C5×D4—122no—
203C5×D4—121no—
204C5×D4—121no—
205C5×D4—242no—
206C5×D4—242no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—62no—
214C2×C4×C5(C2×D3)⋊C411yescharacteristic
215C2×C4×C5(C2×D3)⋊C411yescharacteristic
216C2×C4×C5(C2×D3)⋊C411yescharacteristic
217C2×C4×C5C2×#6711yescharacteristic
218C2×Dic5—122no—
219#168—42no—
220C2×#41D3×D511yescharacteristic
221C22×D4—31no—
222C2×M16—101no—
223#127—61no—
224#124—61no—
225#121—61no—
226#121—61no—
227#120—32no—
228#120—32no—
229#117—31no—
230#117—301no—
231#101—101no—
232#100—52no—
233#99—152no—
234#99—301no—
235C2×C3×C5—21no—
236C2×C3×C5—41no—
237C2×C3×C5—41no—
238C2×C3×C5—41no—
239C2×C3×C5C2×#9911yescharacteristic
240C5×D3—82no—
241C23×C3C22⋊Dic511yescharacteristic
242C23×C3C22×Dic511yescharacteristic
243C23×C3C2×C22⋊D511yescharacteristic
244C22×D3—22no—
245C22×D3—42no—
246C22×D3—82no—
247C3×Q8—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—41no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4C22⋊Dic511yescharacteristic
258C2×C3×C4C22⋊Dic511yescharacteristic
259C2×C3×C4C22⋊Dic511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261#67—82no—
262#67—82no—
263C2×Dic3—22no—
264C2×Dic3—202no—
265D12—42no—
266D12—41no—
267D12—41no—
268C3×C8—202no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5—41no—
275C22×C5—122no—
276C22×C5—122no—
277C22×C5—122no—
278C22×C5—244no—
279C22×C5C2×(C2×D3)⋊C411yescharacteristic
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—21no—
283C4×C5—122no—
284C4×C5#80611yescharacteristic
285C4×C5#80611yescharacteristic
286Dic5—242no—
287C24—32no—
288#41—41no—
289#41—41no—
290C2×Q8#120111yescharacteristic
291C2×D4—62no—
292C2×D4—62no—
293C2×D4—61no—
294C2×D4—61no—
295C2×D4—121no—
296C2×D4—121no—
297C2×D4D3×Dic511yescharacteristic
298C2×D4#120311yescharacteristic
299C2×D4C2×D3×D511yescharacteristic
300C22×C4D3×Dic511yescharacteristic
301C22×C4#120111yescharacteristic
302C22×C4#120311yescharacteristic
303M16—102no—
304M16—201no—
305C2×C8—201no—
306C4⋊C4—61no—
307C4⋊C4—601no—
308C22⋊C4—32no—
309C22⋊C4—62no—
310C22⋊C4—62no—
311C22⋊C4—302no—
312C42—61no—
313C42—601no—
314C3×C5#212211yescharacteristic, complemented, Hall
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3C2×C22⋊Dic511yescharacteristic
322C2×D3—42no—
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—84no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4#396611yescharacteristic
330C3×C4#396611yescharacteristic
331Dic3—42no—
332Dic3—402no—
333C2×C5—21no—
334C2×C5—41no—
335C2×C5—41no—
336C2×C5—41no—
337C2×C5—242no—
338C2×C5C2×#80611yescharacteristic
339C23—62no—
340C23—122no—
341C23—242no—
342C23(C2×D3)⋊Dic511yescharacteristic
343C23C2×D3×Dic511yescharacteristic
344C23C2×#120311yescharacteristic
345Q8—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—122no—
350D4—121no—
351D4—121no—
352D4—242no—
353D4—242no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—62no—
361C2×C4—602no—
362C2×C4(C2×D3)⋊Dic511yescharacteristic
363C2×C4(C2×D3)⋊Dic511yescharacteristic
364C2×C4(C2×D3)⋊Dic511yescharacteristic
365C2×C4C2×#120111yescharacteristic
366C8—202no—
367C2×C3—21no—
368C2×C3—41no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3C2×#396611yescharacteristic
372D3—82no—
373C5#7014611yescharacteristic, complemented, Sylow
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—122no—
381C22—122no—
382C22—122no—
383C22—244no—
384C22C2×(C2×D3)⋊Dic511yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—122no—
389C4—1202no—
390C4#9099611yescharacteristic
391C4#9099611yescharacteristic
392C3#1060265211yescharacteristic, complemented, Sylow
393C2—21no—
394C2—41no—
395C2—41no—
396C2—41no—
397C2—242no—
398C2C2×#9099611yescharacteristic
subgroupG/H
centerC2C2×#90996
commutatorC23×C3×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#2122
LCSG ▷ C23×C3×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×#65526C2semidirect
4. #11745997C2semidirect
7. C22×C5×D12C4semidirect
11. C5×#937C4semidirect
15. C5×#926C4semidirect
24. #65526D3semidirect
102. C22×D12Dic5semidirect
106. #937Dic5semidirect
111. #926Dic5semidirect
314. C3×C5#2122semidirect
373. C5#70146semidirect
392. C3#10602652semidirect

Maximal subgroups

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

subgroupindex
C5×#58302
#117513412
C3×#655262
#117459972
#106026523
#701465