Finite Group Databasebeta

← #14300269

Subgroups — #14300269

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91291C211yesmaximal, characteristic
2C2×#91089C211yesmaximal, characteristic
3C2×#90993C211yesmaximal, characteristic, complemented
4#11748432C211yesmaximal, characteristic, complemented
5#11748411C211yesmaximal, characteristic
6C5×#4524C211yesmaximal, characteristic, complemented
7C3×#64743C211yesmaximal, characteristic, complemented
8#10599487—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C22×C5×C3⋊C8C2211yescharacteristic
13C22×C5×C3⋊C8C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C2×#6651—21no—
17#91291—22no—
18#91291—22no—
19C2×#6648—21no—
20#91089—22no—
21#90993—22no—
22#90982—21no—
23#90982—21no—
24#90974C411yescharacteristic, complemented
25#90974C411yescharacteristic, complemented
26#90968C411yescharacteristic, complemented
27#90968C411yescharacteristic, complemented
28#68774—51nomaximal, Hall
29C2×#4047—31no—
30#65402—31no—
31C2×#3951—31no—
32#65391—31no—
33C2×#3937—31no—
34C5×#336—31no—
35#64743D311yescharacteristic, complemented
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39#6817—21no—
40#6817—21no—
41#6817D412yes—
42#6817Q812yes—
43C2×D60C2×C411yescharacteristic
44C2×C4×D15—21no—
45C2×Dic30C2×C411yescharacteristic
46C3×C42×C5—21no—
47C3×C42×C5—21no—
48#6710—21no—
49#6710—21no—
50C2×C3⋊#168—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8C2×C411yescharacteristic
56C2×C5×C3⋊C8C2×C411yescharacteristic
57C2×C5×C3⋊C8D411yescharacteristic
58C2×C5×C3⋊C8D411yescharacteristic
59C3×C22⋊Dic5—21no—
60C3×C4⋊Dic5C2×C411yescharacteristic
61C3×C4⋊Dic5C2×C411yescharacteristic
62C3×C4×Dic5—21no—
63C3×#681—21no—
64C3×#681D412yes—
65C2×C3×#168—21no—
66#6651—24no—
67#6648—24no—
68C2×#907—51no—
69C2×#822—51no—
70#5002—51no—
71#4999—51no—
72C2×#805—51no—
73C3×#339—51no—
74#4524D511yescharacteristic, complemented
75C2×#709—31no—
76C22×C5×C8—31no—
77C22×C5×C8—31no—
78C2×C42×C5C2×D311yescharacteristic
79#4072C2×D311yescharacteristic
80C2×#681—31no—
81C2×#681C2×D311yescharacteristic
82#4047—62no—
83#4047—62no—
84C2×#676—61no—
85C2×C8×D5—61no—
86#3953—31no—
87#3953—31no—
88#3951—62no—
89#3948—31no—
90#3948—31no—
91#3946—61no—
92#3946—61no—
93#3937—62no—
94#1866—151noSylow
95C23×C3×C5#4111yescharacteristic
96C22×D15—21no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×Q811yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106#1220—22no—
107#1220—22no—
108C2×Dic15—21no—
109D60—21no—
110D60C4⋊C412yes—
111C4×D15—22no—
112C4×D15—22no—
113Dic30—21no—
114Dic30C4⋊C412yes—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C3⋊#168—41no—
118C3×#168—22no—
119C5×C3⋊C8—21no—
120C5×C3⋊C8—21no—
121C5×C3⋊C8—21no—
122C5×C3⋊C8—21no—
123C2×#235—51no—
124C2×C3×M16—51no—
125C3×#117—51no—
126C2×C3×C42C2×D511yescharacteristic
127C2×#208—51no—
128C22×C3⋊C8C2×D511yescharacteristic
129C22×C3⋊C8C2×D511yescharacteristic
130#907—102no—
131#907—102no—
132C2×ΓL(1,𝔽25)—101no—
133C2×D3×C8—101no—
134#822—102no—
135#810—51no—
136#810—51no—
137#809—51no—
138#809—51no—
139#805—102no—
140C4⋊(C3⋊C8)—101no—
141C4⋊(C3⋊C8)—101no—
142C22×C4×C5—21no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5—61no—
145#709—32no—
146#709—32no—
147#709—61no—
148#709—61no—
149C2×D20—31no—
150C2×C4×D5—61no—
151C2×Dic10—31no—
152C2×C5×C8—31no—
153C2×C5×C8—31no—
154C2×C5×C8—31no—
155C2×C5×C8—31no—
156C2×C5×C8—61no—
157C2×C5×C8—61no—
158C2×C5×C8—61no—
159C2×C5×C8—61no—
160C42×C5—21no—
161C42×C5—21no—
162C22⋊Dic5—21no—
163C4⋊Dic5C4×D311yescharacteristic
164C4⋊Dic5C4×D311yescharacteristic
165C4×Dic5—21no—
166#681—21no—
167#681—61no—
168#681—61no—
169#681D1212yes—
170C2×#168—21no—
171C2×#168—61no—
172#676—64no—
173C8×D5—64no—
174C2×#131—151no—
175C2×#108—151no—
176#424—151no—
177C2×#104—151no—
178#416—151no—
179#339—51no—
180#336—31no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5C22⋊Q811yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×D15—22no—
187C2×D15—41no—
188C2×D15—41no—
189C3×C4×C5—42no—
190C3×C4×C5C2×C4⋊C411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5#12011yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194Dic15—22no—
195C3×Dic5—41no—
196C3×Dic5—41no—
197C22×C3×C4—21no—
198C22×C3×C4C22×D511yescharacteristic
199C2×#67—101no—
200#235—52no—
201#235—52no—
202#235—101no—
203#235—101no—
204C2×D12—51no—
205C2×C4×D3—101no—
206C2×Dic6—51no—
207C3×M16—52no—
208C3×M16—101no—
209C2×C3×C8—101no—
210C3×C4⋊C4—51no—
211C3×C4⋊C4—51no—
212C3×C22⋊C4—101no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—101no—
216#208—101no—
217#208—101no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—101no—
223C2×C3⋊C8C4×D511yescharacteristic
224C2×C3⋊C8C4×D511yescharacteristic
225C2×C3⋊C8D2011yescharacteristic
226C2×C3⋊C8D2011yescharacteristic
227ΓL(1,𝔽25)—104no—
228D3×C8—104no—
229C23×C5#23711yescharacteristic
230C22×D5—61no—
231C2×C4×C5—22no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5C2×C4×D311yescharacteristic
235C2×C4×C5C2×D1211yescharacteristic
236C2×C4×C5#23511yescharacteristic
237C2×C4×C5D3×D411yescharacteristic
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5D3×Q811yescharacteristic
240C22⋊D5—62no—
241C22⋊D5—62no—
242C2×Dic5—21no—
243C2×Dic5—21no—
244C2×Dic5—61no—
245D20—32no—
246D20—61no—
247C4×D5—62no—
248C4×D5—62no—
249Dic10—32no—
250Dic10—61no—
251C5×C8—61no—
252C5×C8—61no—
253C5×C8—61no—
254C5×C8—61no—
255#168—22no—
256#168—121no—
257C2×#41—151no—
258#131—302no—
259#131—302no—
260C2×M16—51no—
261C2×M16—151no—
262C2×M16—301no—
263C22×C8—31no—
264C22×C8—31no—
265C22×C8—301no—
266#117—51no—
267C2×C42D3×D511yescharacteristic
268#108—302no—
269C4⋊C8—301no—
270C4⋊C8—301no—
271#104—302no—
272#103—151no—
273#103—151no—
274#102—151no—
275#102—151no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5#38511yescharacteristic
279C2×C3×C5#44311yescharacteristic
280C2×C3×C5#44411yescharacteristic
281D15—42no—
282C23×C3#70911yescharacteristic
283C22×D3—101no—
284C2×C3×C4—22no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—101no—
288C2×C3×C4—101no—
289C2×C3×C4C2×C4×D511yescharacteristic
290C2×C3×C4C2×D2011yescharacteristic
291C2×C3×C4D4×D511yescharacteristic
292C2×C3×C4D4×D511yescharacteristic
293C2×C3×C4#71111yescharacteristic
294C2×C3×C4Q8×D511yescharacteristic
295#67—102no—
296#67—102no—
297C2×Dic3—101no—
298D12—52no—
299D12—101no—
300C4×D3—102no—
301C4×D3—102no—
302Dic6—52no—
303Dic6—101no—
304C3×C8—102no—
305C3⋊C8—21no—
306C3⋊C8—21no—
307C3⋊C8—21no—
308C3⋊C8—21no—
309C3⋊C8—201no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5#67⋊C411yescharacteristic
313C22×C5#88311yescharacteristic
314C22×C5#89711yescharacteristic
315C2×D5—62no—
316C2×D5—121no—
317C2×D5—121no—
318C4×C5—42no—
319C4×C5C4×D1211yescharacteristic
320C4×C5#88211yescharacteristic
321C4×C5D3×C4⋊C411yescharacteristic
322C4×C5#89611yescharacteristic
323Dic5—41no—
324Dic5—41no—
325Dic5—62no—
326#41—152no—
327#41—152no—
328#41—301no—
329#41—301no—
330C2×Q8—151no—
331C2×D4—151no—
332C2×D4—301no—
333C22×C4—21no—
334C22×C4—301no—
335C22×C4C2×D3×D511yescharacteristic
336M16—52no—
337M16—101no—
338M16—304no—
339M16—301no—
340M16—301no—
341C2×C8—31no—
342C2×C8—31no—
343C2×C8—31no—
344C2×C8—31no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—61no—
348C2×C8—61no—
349C2×C8—101no—
350C2×C8—304no—
351C2×C8—301no—
352C4⋊C4—51no—
353C4⋊C4—51no—
354C22⋊C4—101no—
355C42—21no—
356C42—21no—
357C42—101no—
358C3×C5#186611yescharacteristic, complemented, Hall
359C22×C3—21no—
360C22×C3—21no—
361C22×C3C4×D2011yescharacteristic
362C22×C3#402911yescharacteristic
363C22×C3#404211yescharacteristic
364C2×D3—102no—
365C2×D3—201no—
366C2×D3—201no—
367C3×C4—42no—
368C3×C4—201no—
369C3×C4—201no—
370C3×C4#402711yescharacteristic
371C3×C4#402811yescharacteristic
372C3×C4D5×C4⋊C411yescharacteristic
373C3×C4#404311yescharacteristic
374Dic3—102no—
375C2×C5—21no—
376C2×C5—21no—
377C2×C5#466811yescharacteristic
378C2×C5#482311yescharacteristic
379C2×C5#482411yescharacteristic
380D5—122no—
381C23—301no—
382C23#677911yescharacteristic
383Q8—152no—
384Q8—301no—
385D4—152no—
386D4—302no—
387D4—302no—
388D4—301no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—101no—
393C2×C4—101no—
394C2×C4—301no—
395C2×C4—302no—
396C2×C4—302no—
397C2×C4D15⋊Q811yescharacteristic
398C2×C4C4×D3×D511yescharacteristic
399C2×C4D5×D1211yescharacteristic
400C2×C4D3×D2011yescharacteristic
401C2×C4#678211yescharacteristic
402C2×C4#679011yescharacteristic
403C8—61no—
404C8—61no—
405C8—61no—
406C8—61no—
407C8—102no—
408C8—601no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3#6495711yescharacteristic
412C2×C3#6498911yescharacteristic
413C2×C3#6500611yescharacteristic
414D3—202no—
415C5#6877411yescharacteristic, complemented, Sylow
416C22—21no—
417C22—21no—
418C22—302no—
419C22—601no—
420C22—601no—
421C22#9139511yescharacteristic
422C22#9141911yescharacteristic
423C22#9156211yescharacteristic
424C4—42no—
425C4—201no—
426C4—201no—
427C4—302no—
428C4#9140411yescharacteristic
429C4#9140511yescharacteristic
430C4#9142911yescharacteristic
431C4#9147611yescharacteristic
432C3#1059948711yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—602no—
436C2#1174701611yescharacteristic
437C2#1174701711yescharacteristic
438C2#1174889511yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C4×D4
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1866
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#90993C2semidirect
4. #11748432C2semidirect
6. C5×#4524C2semidirect
7. C3×#64743C2semidirect
24. #90974C4semidirect
25. #90974C4semidirect
26. #90968C4semidirect
27. #90968C4semidirect
35. #64743D3semidirect
74. #4524D5semidirect
358. C3×C5#1866semidirect
415. C5#68774semidirect
432. C3#10599487semidirect

Maximal subgroups

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

subgroupindex
C2×#912912
C2×#910892
C2×#909932
#117484322
#117484112
C5×#45242
C3×#647432
#105994873
#687745