Finite Group Databasebeta

← #14300273

Subgroups — #14300273

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×C5×#901C211yesmaximal, characteristic
2C3×#65391C211yesmaximal, characteristic, complemented
3C2×#90992C211yesmaximal, characteristic, complemented
4C2×#90978C211yesmaximal, characteristic
5#11748382C211yesmaximal, characteristic
6#11746371C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10602810—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C5×#901—22no—
15C5×#901—22no—
16C2×C5×ΓL(1,𝔽25)—21no—
17C2×C5×D3×C8—21no—
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#3946—21no—
21C3×#3946—21no—
22#90992—22no—
23#90978—22no—
24#90972C411yescharacteristic, complemented
25#90972C411yescharacteristic, complemented
26#90966C411yescharacteristic, complemented
27#90966C411yescharacteristic, complemented
28#70545—51nomaximal, Hall
29C2×C5×#131—31no—
30C2×#3969—31no—
31#65522—31no—
32C2×#3954—31no—
33#65391D311yescharacteristic, complemented
34#64775—31no—
35#64770—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×C5×#67—21no—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235D412yes—
42C5×#235Q812yes—
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C5×Dic6C2×C411yescharacteristic
46C2×C3×C5×C8—21no—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8D411yescharacteristic
49C2×C3×C5×C8D411yescharacteristic
50C4×Dic15—21no—
51C4×Dic15—21no—
52C2×C3⋊#168—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168C2×C411yescharacteristic
55C2×C3⋊#168C2×C411yescharacteristic
56C5×#208—21no—
57C5×#208D412yes—
58C2×C5×C3⋊C8—21no—
59C5×ΓL(1,𝔽25)—24no—
60C5×D3×C8—24no—
61C3×C22⋊Dic5—21no—
62C3×C4⋊Dic5C2×C411yescharacteristic
63C3×C4⋊Dic5C2×C411yescharacteristic
64C3×C4×Dic5—21no—
65C3×#681—21no—
66C3×#681—21no—
67C2×C3×#168—21no—
68C2×#901D511yescharacteristic
69C3×#424—51no—
70C2×#825—51no—
71C2×#822—51no—
72#5002—51no—
73#4550—51no—
74#4532—51no—
75C2×C5×#41—31no—
76C5×#131—62no—
77C5×#131—62no—
78C2×C5×M16—31no—
79C2×C5×M16—61no—
80C22×C5×C8—61no—
81C22×C5×C8C2×D311yescharacteristic
82#4072C2×D311yescharacteristic
83C2×C4×Dic5—31no—
84C2×#681C2×D311yescharacteristic
85C22×#168—31no—
86#3969—62no—
87#3967—31no—
88#3967—31no—
89#3964—31no—
90#3964—31no—
91#3954—62no—
92#3946—21no—
93#3946—21no—
94#1866—151noSylow
95C23×C3×C5#4111yescharacteristic
96C22×C5×D3—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×Q811yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—22no—
104C2×Dic15—41no—
105C2×Dic15—41no—
106C5×#67—22no—
107C5×#67—22no—
108C2×C5×Dic3—21no—
109C5×D12—21no—
110C5×D12C4⋊C412yes—
111C4×C5×D3—22no—
112C4×C5×D3—22no—
113C5×Dic6—21no—
114C5×Dic6C4⋊C412yes—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C3×C5×C8—21no—
118C3×C5×C8—21no—
119C3⋊#168—21no—
120C3⋊#168—21no—
121C3×#168—41no—
122C5×C3⋊C8—22no—
123C2×#235C2×D511yescharacteristic
124C2×C3×M16—51no—
125C22×C3×C8C2×D511yescharacteristic
126C3×#117—51no—
127C2×C4×Dic3—51no—
128C2×#208C2×D511yescharacteristic
129C22×C3⋊C8—51no—
130#901—22no—
131#901—22no—
132C2×ΓL(1,𝔽25)—21no—
133C2×D3×C8—21no—
134C3×C4⋊C8—101no—
135C3×C4⋊C8—101no—
136#825—102no—
137#822—102no—
138#810—51no—
139#810—51no—
140#809—51no—
141#809—51no—
142C5×#41—32no—
143C5×#41—32no—
144C5×#41—61no—
145C5×#41—61no—
146C2×C5×Q8—31no—
147C2×C5×D4—31no—
148C2×C5×D4—61no—
149C22×C4×C5—61no—
150C22×C4×C5C22×D311yescharacteristic
151C22×Dic5—61no—
152C5×M16—32no—
153C5×M16—64no—
154C5×M16—61no—
155C2×C5×C8—21no—
156C2×C5×C8—21no—
157C2×C5×C8—64no—
158C2×C5×C8—61no—
159C2×C5×C8#6711yescharacteristic
160C2×C5×C8#6711yescharacteristic
161C22⋊Dic5—21no—
162C4⋊Dic5C4×D311yescharacteristic
163C4⋊Dic5C4×D311yescharacteristic
164C4×Dic5—21no—
165C4×Dic5—61no—
166C4×Dic5—61no—
167#681—21no—
168#681—21no—
169C2×#168—21no—
170C2×#168—31no—
171C2×#168—31no—
172C2×#168—61no—
173C2×#168—61no—
174C2×#131—31no—
175C2×#108—151no—
176#424—51no—
177C2×#104—151no—
178#416—151no—
179#339—151no—
180#336—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5C22⋊Q811yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×C5×D3—22no—
187C2×C5×D3—41no—
188C2×C5×D3—41no—
189C3×C4×C5C2×C4⋊C411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193Dic15—42no—
194C3×Dic5—41no—
195C3×Dic5—41no—
196C5×Dic3—22no—
197C22×C3×C4C22×D511yescharacteristic
198C2×#67—21no—
199C22×Dic3—101no—
200#235—21no—
201#235—21no—
202#235Dic1012yes—
203#235C22⋊D512yes—
204C2×D12C4×D511yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6C4×D511yescharacteristic
207C3×M16—101no—
208C3×M16—101no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—101no—
212C2×C3×C8C22⋊D511yescharacteristic
213C2×C3×C8C22⋊D511yescharacteristic
214C3×C4⋊C4—51no—
215C3×C4⋊C4—51no—
216C3×C22⋊C4—101no—
217C3×C42—101no—
218C4×Dic3—101no—
219C4×Dic3—101no—
220#208—21no—
221#208C22⋊D512yes—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—51no—
224C2×C3⋊C8—51no—
225C2×C3⋊C8—101no—
226C2×C3⋊C8—101no—
227ΓL(1,𝔽25)—24no—
228D3×C8—24no—
229C23×C5—61no—
230C23×C5#23511yescharacteristic
231C5×Q8—32no—
232C5×Q8—61no—
233C5×D4—32no—
234C5×D4—62no—
235C5×D4—62no—
236C5×D4—61no—
237C2×C4×C5—61no—
238C2×C4×C5—62no—
239C2×C4×C5—62no—
240C2×C4×C5C2×C4×D311yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5D3×D411yescharacteristic
243C2×C4×C5D3×Q811yescharacteristic
244C2×C4×C5#23911yescharacteristic
245C2×C4×C5C2×#6711yescharacteristic
246C2×Dic5—21no—
247C2×Dic5—21no—
248C2×Dic5—62no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251C5×C8—21no—
252C5×C8—21no—
253C5×C8—62no—
254#168—41no—
255#168—61no—
256#168—61no—
257C2×#41—31no—
258#131—62no—
259#131—62no—
260C2×M16—31no—
261C2×M16—51no—
262C2×M16—61no—
263C22×C8—61no—
264C22×C8—151no—
265C22×C8D3×D511yescharacteristic
266#117—51no—
267C2×C42—151no—
268#108—302no—
269C4⋊C8—101no—
270C4⋊C8—101no—
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
281C5×D3—42no—
282C23×C3#70911yescharacteristic
283C22×D3—21no—
284C2×C3×C4—101no—
285C2×C3×C4—101no—
286C2×C3×C4C2×Dic1011yescharacteristic
287C2×C3×C4C2×C4×D511yescharacteristic
288C2×C3×C4#70911yescharacteristic
289C2×C3×C4C2×C22⋊D511yescharacteristic
290C2×C3×C4C2×C22⋊D511yescharacteristic
291C2×C3×C4C2×C22⋊D511yescharacteristic
292#67—22no—
293#67—22no—
294C2×Dic3—21no—
295C2×Dic3—102no—
296C2×Dic3—201no—
297C2×Dic3—201no—
298D12—21no—
299D12#68312yes—
300C4×D3—22no—
301C4×D3—22no—
302Dic6—21no—
303Dic6#68312yes—
304C3×C8—21no—
305C3×C8—21no—
306C3×C8—201no—
307C3⋊C8—22no—
308C3⋊C8—101no—
309C3⋊C8—101no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—62no—
313C22×C5—121no—
314C22×C5—121no—
315C22×C5#89411yescharacteristic
316C22×C5#89611yescharacteristic
317C22×C5C4×#6711yescharacteristic
318C4×C5—62no—
319C4×C5D3×C4⋊C411yescharacteristic
320C4×C5#89311yescharacteristic
321C4×C5#93711yescharacteristic
322C4×C5#94611yescharacteristic
323Dic5—41no—
324Dic5—41no—
325Dic5—122no—
326#41—32no—
327#41—32no—
328#41—61no—
329#41—61no—
330C2×Q8—31no—
331C2×D4—31no—
332C2×D4—61no—
333C22×C4—61no—
334C22×C4—301no—
335C22×C4C2×D3×D511yescharacteristic
336M16—32no—
337M16—64no—
338M16—61no—
339M16—101no—
340M16—101no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—64no—
344C2×C8—61no—
345C2×C8—101no—
346C2×C8—151no—
347C2×C8—151no—
348C2×C8—301no—
349C2×C8—301no—
350C2×C8#120111yescharacteristic
351C2×C8#120111yescharacteristic
352C4⋊C4—51no—
353C4⋊C4—51no—
354C22⋊C4—101no—
355C42—101no—
356C42—301no—
357C42—301no—
358C3×C5#186611yescharacteristic, complemented, Hall
359C22×C3—21no—
360C22×C3—21no—
361C22×C3#407011yescharacteristic
362C22×C3C4×C22⋊D511yescharacteristic
363C22×C3#407511yescharacteristic
364C2×D3—22no—
365C2×D3—41no—
366C2×D3—41no—
367C3×C4—201no—
368C3×C4—201no—
369C3×C4C2×#68311yescharacteristic
370C3×C4#407011yescharacteristic
371C3×C4C4×C22⋊D511yescharacteristic
372C3×C4#409911yescharacteristic
373Dic3—22no—
374Dic3—202no—
375C2×C5—21no—
376C2×C5—21no—
377C2×C5—122no—
378C2×C5#498911yescharacteristic
379C2×C5#514411yescharacteristic
380C2×C5#514511yescharacteristic
381C23—61no—
382C23#677111yescharacteristic
383Q8—32no—
384Q8—61no—
385D4—32no—
386D4—62no—
387D4—62no—
388D4—61no—
389C2×C4—61no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—101no—
393C2×C4—101no—
394C2×C4—302no—
395C2×C4—601no—
396C2×C4—601no—
397C2×C4D3×Dic1011yescharacteristic
398C2×C4#676911yescharacteristic
399C2×C4C4×D3×D511yescharacteristic
400C2×C4C2×#120111yescharacteristic
401C2×C4D3×C22⋊D511yescharacteristic
402C2×C4D3×C22⋊D511yescharacteristic
403C8—21no—
404C8—21no—
405C8—62no—
406C8—201no—
407C8—301no—
408C8—301no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3#6543311yescharacteristic
412C2×C3#6543411yescharacteristic
413C2×C3#6549911yescharacteristic
414D3—42no—
415C5#7054511yescharacteristic, complemented, Sylow
416C22—21no—
417C22—21no—
418C22—62no—
419C22—121no—
420C22—121no—
421C22#9135111yescharacteristic
422C22#9135211yescharacteristic
423C22C4×#120111yescharacteristic
424C4—62no—
425C4—201no—
426C4—201no—
427C4—602no—
428C4#9136911yescharacteristic
429C4D3×#68311yescharacteristic
430C4#9144611yescharacteristic
431C4#9156811yescharacteristic
432C3#1060281011yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—122no—
436C2#1174807411yescharacteristic
437C2#1174807511yescharacteristic
438C2#1174871611yescharacteristic
subgroupG/H
centerC2×C4C2×#1201
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C4×D4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1866
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C3×#65391C2semidirect
3. C2×#90992C2semidirect
6. #11746371C2semidirect
7. #11745973C2semidirect
24. #90972C4semidirect
25. #90972C4semidirect
26. #90966C4semidirect
27. #90966C4semidirect
33. #65391D3semidirect
358. C3×C5#1866semidirect
415. C5#70545semidirect
432. C3#10602810semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9012
C3×#653912
C2×#909922
C2×#909782
#117483822
#117463712
#117459732
#106028103
#705455