Finite Group Databasebeta

← #14299754

Subgroups — #14299754

Order 1920.

604 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754509C211yesmaximal, characteristic
2C3×#65422C211yesmaximal, characteristic
3#11748861C211yesmaximal, characteristic, complemented
4#11748470C211yesmaximal, characteristic, complemented
5C2×#90977C211yesmaximal, characteristic
6#11746375C211yesmaximal, characteristic, complemented
7C5×#4555C211yesmaximal, characteristic, complemented
8#10599564—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic5C2211yescharacteristic
16#91559—22no—
17C2×Dic3⋊Dic5—22no—
18Dic3×D20—21no—
19D5×C4⋊Dic3—21no—
20#91358—21no—
21Dic3×Dic10—21no—
22C3×#3953—21no—
23C3×#3948—21no—
24#90989—21no—
25#90986—21no—
26#90977C414yescomplemented
27#70297—51nomaximal, Hall
28#65857—31no—
29#65422D311yescharacteristic
30#65284—31no—
31#65224—31no—
32C2×#3937—31no—
33C5×#339—31no—
34#64774—31no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15D412yes—
37C22×C5×Dic3—21no—
38C2×C3×C22⋊D5—21no—
39C22×C3×Dic5—21no—
40C3×#709—21no—
41C3×#709—21no—
42C3×#709C2×C412yes—
43C3×#709Q812yes—
44C2×C3×D20D411yescharacteristic
45C2×C3×C4×D5—21no—
46C2×C3×Dic10D411yescharacteristic
47C2×D5×Dic3—22no—
48C3×C5×M16—21no—
49C3×C5×M16—21no—
50C2×C3×C5×C8—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53#6710—21no—
54#6710C2×C412yescomplemented
55C2×C3⋊#168—21no—
56C5×#217—21no—
57C5×C4⋊Dic3D411yescharacteristic
58C5×C4⋊Dic3D411yescharacteristic
59C4×C5×Dic3—21no—
60C4×C5×Dic3—21no—
61C4×C5×Dic3C2×C412yescomplemented
62C3×C4⋊Dic5—21no—
63C3×C4⋊Dic5—21no—
64Dic3⋊Dic5—44no—
65#6668—22no—
66#6665—22no—
67Dic3×Dic5—22no—
68#5827—51no—
69C3×#417—51no—
70C2×#837—51no—
71#4975—51no—
72#4964—51no—
73#4555D511yescharacteristic, complemented
74#4554—51no—
75C2×#709C2×D311yescharacteristic
76C2×C5×M16C2×D311yescharacteristic
77C5×#117—31no—
78C2×C42×C5—31no—
79C2×C4⋊Dic5—31no—
80C2×C4⋊Dic5—62no—
81C2×C4⋊Dic5C2×D311yescharacteristic
82C2×#681—31no—
83#4038—61no—
84D5×C4⋊C4—61no—
85#4027—62no—
86C4×D20—61no—
87C4×Dic10—61no—
88#3953—21no—
89#3948—21no—
90#3940—61no—
91#3939—61no—
92#3937—34no—
93#1859—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×Q811yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×Dic15—22no—
103C2×Dic15—42no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—21no—
109C3×C22⋊D5—22no—
110C3×C22⋊D5—22no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—42no—
113C2×C3×Dic5—41no—
114C3×D20—21no—
115C3×D20C4⋊C412yescomplemented
116C3×C4×D5—22no—
117C3×C4×D5—22no—
118C3×Dic10—21no—
119C3×Dic10C4⋊C412yescomplemented
120D5×Dic3—82no—
121C3×C5×C8—41no—
122C3⋊#168—22no—
123C2×C3×#41—51no—
124C2×C3×M16C2×D511yescharacteristic
125C2×C3×C4⋊C4—51no—
126Q8×Dic3—101no—
127D4×Dic3—101no—
128D4×Dic3—102no—
129#926—101no—
130#926C2×D511yescharacteristic
131C2×C4⋊Dic3—51no—
132C2×C4⋊Dic3—101no—
133C2×Dic3⋊C4—102no—
134C2×C4×Dic3C2×D511yescharacteristic
135C2×#208—51no—
136C3×#103—101no—
137C3×#102—101no—
138#837—54no—
139#808—101no—
140#807—101no—
141C22×C4×C5—61no—
142C22×C4×C5C22×D311yescharacteristic
143C2×C22⋊D5—21no—
144C22×Dic5—21no—
145C22×Dic5—32no—
146#709—21no—
147#709—21no—
148#709Dic612yes—
149#709C4×D312yes—
150C2×D20#6711yescharacteristic
151C2×C4×D5—21no—
152C2×C4×D5—62no—
153C2×Dic10#6711yescharacteristic
154C5×M16—21no—
155C5×M16—21no—
156C2×C5×C8—21no—
157C5×C4⋊C4—31no—
158C5×C4⋊C4—31no—
159C5×C22⋊C4—61no—
160C42×C5—32no—
161C42×C5—61no—
162C42×C5—61no—
163#685—62no—
164C4⋊Dic5—21no—
165C4⋊Dic5—21no—
166C4⋊Dic5—61no—
167C4⋊Dic5—61no—
168C4⋊Dic5—124no—
169#683—62no—
170C4×Dic5—62no—
171#681—32no—
172#681—61no—
173C2×#168—61no—
174#520—151no—
175#428—151no—
176C2×#104—151no—
177#417—51no—
178#384—151no—
179#343—151no—
180#339—31no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5C22⋊Q811yescharacteristic
186C2×C3×D5—22no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5C2×C4⋊C411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C22⋊Q811yescharacteristic
192C3×C4×C5#12311yescharacteristic
193Dic15—42no—
194C3×Dic5—22no—
195C3×Dic5—81no—
196C5×Dic3—24no—
197C5×Dic3—41no—
198C5×Dic3—41no—
199C3×#41—52no—
200C3×#41—52no—
201C3×#41—101no—
202C3×#41—101no—
203C2×C3×Q8—51no—
204C2×C3×D4—51no—
205C2×C3×D4—101no—
206C22×C3×C4—101no—
207C22×C3×C4—101no—
208C22×C3×C4C22×D511yescharacteristic
209C22×Dic3—21no—
210C22×Dic3—52no—
211C22×Dic3—102no—
212C3×M16—21no—
213C3×M16—21no—
214C2×C3×C8—21no—
215C3×C4⋊C4—101no—
216C3×C4⋊C4—101no—
217#217—21no—
218#217—102no—
219C4⋊Dic3—102no—
220C4⋊Dic3—101no—
221C4⋊Dic3—101no—
222C4⋊Dic3D2011yescharacteristic
223C4⋊Dic3D2011yescharacteristic
224Dic3⋊C4—204no—
225C4×Dic3—21no—
226C4×Dic3—21no—
227C4×Dic3—102no—
228C4×Dic3C4×D512yescomplemented
229#208—52no—
230#208—101no—
231C2×C3⋊C8—101no—
232C23×C5D3×D411yescharacteristic
233C22×D5—21no—
234C2×C4×C5—62no—
235C2×C4×C5—62no—
236C2×C4×C5—62no—
237C2×C4×C5—61no—
238C2×C4×C5—61no—
239C2×C4×C5C2×Dic611yescharacteristic
240C2×C4×C5C2×C4×D311yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5#23711yescharacteristic
243C2×C4×C5#23711yescharacteristic
244C2×C4×C5C2×#6711yescharacteristic
245C22⋊D5—22no—
246C22⋊D5—22no—
247C2×Dic5—21no—
248C2×Dic5—42no—
249C2×Dic5—41no—
250C2×Dic5—62no—
251C2×Dic5—122no—
252D20—21no—
253D20Dic3⋊C412yescomplemented
254C4×D5—22no—
255C4×D5—22no—
256C4×D5—242no—
257Dic10—21no—
258Dic10Dic3⋊C412yescomplemented
259C5×C8—41no—
260#168—62no—
261C2×#41—51no—
262C2×M16—151no—
263C2×M16D3×D511yescharacteristic
264C4×Q8—301no—
265C4×D4—301no—
266C4×D4—302no—
267#117—31no—
268#117—301no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—151no—
271C2×C4⋊C4—301no—
272C2×C4⋊C4—302no—
273C2×C42—31no—
274#107—301no—
275#106—301no—
276#104—154no—
277#103—101no—
278#102—101no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38511yescharacteristic
282C2×C3×C5#45311yescharacteristic
283C2×C3×C5#45611yescharacteristic
284C3×D5—42no—
285C23×C3—101no—
286C23×C3D4×D511yescharacteristic
287C3×Q8—52no—
288C3×Q8—101no—
289C3×D4—52no—
290C3×D4—102no—
291C3×D4—102no—
292C3×D4—101no—
293C2×C3×C4—101no—
294C2×C3×C4—102no—
295C2×C3×C4—102no—
296C2×C3×C4—202no—
297C2×C3×C4—201no—
298C2×C3×C4C2×C4×D511yescharacteristic
299C2×C3×C4C2×D2011yescharacteristic
300C2×C3×C4#70911yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4#71111yescharacteristic
303C2×C3×C4Q8×D511yescharacteristic
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—102no—
310C2×Dic3—202no—
311C2×Dic3—402no—
312C3×C8—41no—
313C3⋊C8—102no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5#87811yescharacteristic
317C22×C5#67⋊C411yescharacteristic
318C22×C5#93711yescharacteristic
319C2×D5—22no—
320C2×D5—41no—
321C2×D5—41no—
322C4×C5—64no—
323C4×C5—121no—
324C4×C5—121no—
325C4×C5#87811yescharacteristic
326C4×C5#67⋊C411yescharacteristic
327C4×C5C2×Dic3⋊C411yescharacteristic
328C4×C5#93511yescharacteristic
329Dic5—22no—
330Dic5—81no—
331Dic5—122no—
332#41—52no—
333#41—52no—
334#41—101no—
335#41—101no—
336C2×Q8—51no—
337C2×D4—51no—
338C2×D4—101no—
339C22×C4—61no—
340C22×C4—101no—
341C22×C4—101no—
342C22×C4—152no—
343C22×C4—302no—
344C22×C4C2×D3×D511yescharacteristic
345M16—21no—
346M16—21no—
347M16—152no—
348M16—301no—
349C2×C8—21no—
350C2×C8—301no—
351C4⋊C4—31no—
352C4⋊C4—31no—
353C4⋊C4—101no—
354C4⋊C4—101no—
355C4⋊C4—302no—
356C4⋊C4—301no—
357C4⋊C4—301no—
358C4⋊C4—604no—
359C22⋊C4—61no—
360C22⋊C4—302no—
361C42—32no—
362C42—61no—
363C42—61no—
364C42—302no—
365C3×C5#185911yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—102no—
369C22×C3—201no—
370C22×C3—201no—
371C22×C3#402711yescharacteristic
372C22×C3#402811yescharacteristic
373C22×C3#404211yescharacteristic
374C3×C4—102no—
375C3×C4—401no—
376C3×C4C4×D2011yescharacteristic
377C3×C4#402911yescharacteristic
378C3×C4D5×C4⋊C411yescharacteristic
379C3×C4#404311yescharacteristic
380Dic3—24no—
381Dic3—41no—
382Dic3—41no—
383Dic3—202no—
384C2×C5—21no—
385C2×C5—21no—
386C2×C5#494611yescharacteristic
387C2×C5#519811yescharacteristic
388C2×C5#520511yescharacteristic
389D5—42no—
390C23—101no—
391C23#677711yescharacteristic
392Q8—52no—
393Q8—101no—
394D4—52no—
395D4—102no—
396D4—102no—
397D4—101no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—101no—
404C2×C4—102no—
405C2×C4—102no—
406C2×C4—202no—
407C2×C4—201no—
408C2×C4—302no—
409C2×C4—602no—
410C2×C4—1202no—
411C2×C4D5×Dic611yescharacteristic
412C2×C4C4×D3×D511yescharacteristic
413C2×C4D3×D2011yescharacteristic
414C2×C4#677911yescharacteristic
415C2×C4#678011yescharacteristic
416C2×C4D5×#6711yescharacteristic
417C8—41no—
418C8—302no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—202no—
422C2×C3#6495711yescharacteristic
423C2×C3#6511111yescharacteristic
424C2×C3#6511511yescharacteristic
425C5#7029711yescharacteristic, complemented, Sylow
426C22—21no—
427C22—21no—
428C22—102no—
429C22—201no—
430C22—201no—
431C22#9143011yescharacteristic
432C22#9144211yescharacteristic
433C22#9147411yescharacteristic
434C4—64no—
435C4—102no—
436C4—121no—
437C4—121no—
438C4—401no—
439C4—602no—
440C4D5×Dic3⋊C411yescharacteristic
441C4#9139511yescharacteristic
442C4#9142211yescharacteristic
443C4#9154811yescharacteristic
444C3#1059956411yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—202no—
448C2#1174824211yescharacteristic
449C2#1174825211yescharacteristic
450C2#1174889011yescharacteristic
subgroupG/H
centerC22#91474
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1859
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #11748861C2semidirect
4. #11748470C2semidirect
6. #11746375C2semidirect
7. C5×#4555C2semidirect
26. #90977C4semidirect
54. #6710C2×C4semidirect
61. C4×C5×Dic3C2×C4semidirect
73. #4555D5semidirect
115. C3×D20C4⋊C4semidirect
119. C3×Dic10C4⋊C4semidirect
228. C4×Dic3C4×D5semidirect
253. D20Dic3⋊C4semidirect
258. Dic10Dic3⋊C4semidirect
365. C3×C5#1859semidirect
425. C5#70297semidirect
444. C3#10599564semidirect

Maximal subgroups

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

subgroupindex
#117545092
C3×#654222
#117488612
#117484702
C2×#909772
#117463752
C5×#45552
#105995643
#702975