Finite Group Databasebeta

← #14306016

Subgroups — #14306016

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5832C211yesmaximal, characteristic
2C2×#91121C211yesmaximal, characteristic, complemented
3C2×C3×#3969C211yesmaximal, characteristic, complemented
4C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
5#11748440C211yesmaximal, characteristic, complemented
6C2×#90979C211yesmaximal, characteristic, complemented
7C2×#90978C211yesmaximal, characteristic, complemented
8#10602608—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#947C411yescharacteristic, complemented
14C5×#944C411yescharacteristic, complemented
15C5×#940C411yescharacteristic, complemented
16C5×#939—22no—
17C5×#936C411yescharacteristic, complemented
18C4×C5×#67—22no—
19C2×C4×C5×Dic3C2211yescharacteristic
20C2×C3×C4×Dic5C2211yescharacteristic
21C2×C3×#681C2211yescharacteristic
22C2×Dic3×Dic5—22no—
23#91121—22no—
24C3×#3969—22no—
25Dic3⋊#168—22no—
26#90979—22no—
27#90978—22no—
28#70356—51nomaximal, Hall
29C5×#532—31no—
30C2×#3969—31no—
31C2×#3969—31no—
32C2×#3969—31no—
33C2×#3969D311yescharacteristic, complemented
34C42×Dic5—31no—
35#65213—31no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C22×Dic15—21no—
46C2×C5×#67—21no—
47C2×C5×#67—22no—
48C22×C5×Dic3D412yes—
49C5×#235—21no—
50C5×#235—21no—
51C5×#235—21no—
52C5×#235—21no—
53C2×C5×D12C2×C411yescharacteristic
54C2×C4×C5×D3—21no—
55C2×C5×Dic6C2×C411yescharacteristic
56C22×C3×Dic5—21no—
57C4×Dic15—21no—
58C4×Dic15D412yescomplemented
59#6710—21no—
60#6710—21no—
61C2×C3⋊#168—21no—
62C5×#217—22no—
63C5×(C2×D3)⋊C4—22no—
64C5×Dic3⋊C4—22no—
65C4×C5×Dic3C2×C411yescharacteristic
66C4×C5×Dic3C2×C411yescharacteristic
67C4×C5×Dic3D412yes—
68C3×C4×Dic5—21no—
69C3×C4×Dic5D412yescomplemented
70C3×#681—21no—
71C3×#681—21no—
72C2×C3×#168—21no—
73Dic3×Dic5—28no—
74#5832D511yescharacteristic
75C2×C3×#104—51no—
76C2×#837—51no—
77C2×#825—51no—
78#5118—51no—
79C42×Dic3—51no—
80C2×#805—51no—
81C2×C5×#41—31no—
82C2×C5×#41C2×D311yescharacteristic
83C5×C4⋊Q8—31no—
84C5×#127—31no—
85C5×#124—31no—
86C5×#124—31no—
87C5×#121—62no—
88C4×C5×D4—62no—
89C2×C42×C5—31no—
90C2×C4×Dic5—31no—
91C2×C4×Dic5—62no—
92C2×C4×Dic5C2×D311yescharacteristic
93C2×#681—31no—
94C2×#681C2×D311yescharacteristic
95#3969—22no—
96#3969—62no—
97#3969—62no—
98#3969—62no—
99C4⋊#168—62no—
100#1962—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3—21no—
104C3×C5×Q8—21no—
105C3×C5×Q8—21no—
106C3×C5×D4—21no—
107C3×C5×D4—21no—
108C3×C5×D4—41no—
109C3×C5×D4—41no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×Dic15—24no—
120C2×Dic15—22no—
121C5×#67—41no—
122C5×#67—41no—
123C5×#67—44no—
124C2×C5×Dic3—24no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3C22⋊C412yes—
127C2×C5×Dic3C22⋊C412yes—
128C5×D12—21no—
129C5×D12—21no—
130C4×C5×D3—41no—
131C4×C5×D3—41no—
132C5×Dic6—21no—
133C5×Dic6—21no—
134C2×C3×Dic5—24no—
135C2×C3×Dic5—22no—
136C3⋊#168—41no—
137C3×#168—41no—
138C2×C3×#41C2×D511yescharacteristic
139C2×#235C2×D511yescharacteristic
140C2×C3×M16—51no—
141C2×C3×C42—51no—
142#947Dic511yescharacteristic, complemented
143#944Dic511yescharacteristic, complemented
144#940Dic511yescharacteristic, complemented
145#939—22no—
146#936Dic511yescharacteristic, complemented
147C4×#67—22no—
148C2×C4×Dic3—51no—
149C2×C4×Dic3—102no—
150C2×C4×Dic3C2×D511yescharacteristic
151C2×#208—51no—
152C3×#104—102no—
153#837—102no—
154#825—102no—
155Dic3⋊C8—102no—
156#805—102no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C5×#41—21no—
161C5×#41—61no—
162C5×#41—61no—
163C5×#41—61no—
164C5×#41—61no—
165C2×C5×Q8—31no—
166C2×C5×Q8C4×D311yescharacteristic
167C2×C5×D4—21no—
168C2×C5×D4—31no—
169C2×C5×D4—62no—
170C2×C5×D4—61no—
171C2×C5×D4C4×D311yescharacteristic
172C22×C4×C5—21no—
173C22×C4×C5—32no—
174C22×C4×C5—61no—
175C22×C4×C5C22×D311yescharacteristic
176C22×Dic5—21no—
177C22×Dic5—61no—
178C5×C4⋊C4—62no—
179C5×C22⋊C4—62no—
180C5×C22⋊C4—62no—
181C42×C5—31no—
182C42×C5—31no—
183C42×C5—32no—
184C4×Dic5—21no—
185C4×Dic5—32no—
186C4×Dic5—68no—
187C4×Dic5—61no—
188C4×Dic5#6712yescomplemented
189#681—21no—
190#681—21no—
191#681—61no—
192#681—61no—
193C2×#168—21no—
194C2×#168—61no—
195#532—31no—
196#423—151no—
197C2×#104—51no—
198C2×#104—151no—
199C2×#104—151no—
200C2×#104—151no—
201C43—151no—
202C22×C3×C5—22no—
203C22×C3×C5—41no—
204C22×C3×C5—42no—
205C22×C3×C5C2×C22⋊C411yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5#12111yescharacteristic
208C2×C5×D3—41no—
209C2×C5×D3—42no—
210C3×C4×C5—41no—
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12411yescharacteristic
214C3×C4×C5#12711yescharacteristic
215Dic15—24no—
216C3×Dic5—24no—
217C5×Dic3—22no—
218C5×Dic3—41no—
219C5×Dic3#10414yescomplemented
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C2×C3×Q8C2×Dic511yescharacteristic
225C2×C3×D4—21no—
226C2×C3×D4C2×Dic511yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4—101no—
229C22×C3×C4C22×D511yescharacteristic
230C2×#67—21no—
231C2×#67—22no—
232C22×Dic3—101no—
233C22×Dic3C22⋊D512yes—
234#235—21no—
235#235—21no—
236#235—21no—
237#235—21no—
238C2×D12C2×Dic511yescharacteristic
239C2×C4×D3—21no—
240C2×Dic6C2×Dic511yescharacteristic
241C3×M16—101no—
242C3×M16—101no—
243C2×C3×C8—101no—
244C3×C42—52no—
245C3×C42—101no—
246#217—22no—
247(C2×D3)⋊C4—22no—
248Dic3⋊C4—22no—
249C4×Dic3—52no—
250C4×Dic3—108no—
251C4×Dic3—101no—
252C4×Dic3C2×Dic511yescharacteristic
253C4×Dic3C2×Dic511yescharacteristic
254C4×Dic3C22⋊D512yes—
255#208—101no—
256#208—101no—
257C2×C3⋊C8—101no—
258C23×C5—21no—
259C23×C5—61no—
260C23×C5D3×D411yescharacteristic
261C5×Q8—21no—
262C5×Q8—21no—
263C5×Q8—61no—
264C5×Q8—61no—
265C5×D4—21no—
266C5×D4—21no—
267C5×D4—41no—
268C5×D4—41no—
269C5×D4—61no—
270C5×D4—61no—
271C5×D4—124no—
272C5×D4—121no—
273C5×D4—121no—
274C2×C4×C5—21no—
275C2×C4×C5—32no—
276C2×C4×C5—32no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—64no—
280C2×C4×C5—61no—
281C2×C4×C5—121no—
282C2×C4×C5—121no—
283C2×C4×C5C2×C4×D311yescharacteristic
284C2×C4×C5#23511yescharacteristic
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5#23711yescharacteristic
288C2×C4×C5C2×#6711yescharacteristic
289C2×Dic5—24no—
290C2×Dic5—22no—
291C2×Dic5—64no—
292C2×Dic5—62no—
293#168—41no—
294#168—121no—
295C2×#41—31no—
296C2×#41D3×D511yescharacteristic
297C2×M16—51no—
298C2×M16—151no—
299C4⋊Q8—31no—
300#127—31no—
301#124—31no—
302#124—31no—
303#121—62no—
304C4×D4—62no—
305C2×C42—31no—
306C2×C42—51no—
307C2×C42—151no—
308C2×C42—302no—
309C4⋊C8—302no—
310#104—102no—
311#104—302no—
312#104—302no—
313#104—302no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—81no—
317C2×C3×C5#39011yescharacteristic
318C2×C3×C5C2×#10412yes—
319C5×D3—81no—
320C23×C3—21no—
321C23×C3C2×C22⋊D511yescharacteristic
322C22×D3—21no—
323C3×Q8—21no—
324C3×Q8—21no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—41no—
328C3×D4—41no—
329C2×C3×C4—21no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—104no—
333C2×C3×C4—102no—
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4#71111yescharacteristic
337C2×C3×C4#71111yescharacteristic
338C2×C3×C4C22×Dic511yescharacteristic
339C2×C3×C4C2×C22⋊D511yescharacteristic
340#67—41no—
341#67—41no—
342#67—44no—
343C2×Dic3—24no—
344C2×Dic3—21no—
345C2×Dic3—104no—
346C2×Dic3—102no—
347C2×Dic3C22⋊Dic512yes—
348C2×Dic3C22⋊Dic512yes—
349D12—21no—
350D12—21no—
351C4×D3—41no—
352C4×D3—41no—
353Dic6—21no—
354Dic6—21no—
355C3×C8—201no—
356C3⋊C8—201no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—42no—
360C22×C5—121no—
361C22×C5—122no—
362C22×C5D3×C22⋊C411yescharacteristic
363C22×C5#88411yescharacteristic
364C22×C5#93911yescharacteristic
365C4×C5—34no—
366C4×C5—41no—
367C4×C5—62no—
368C4×C5—121no—
369C4×C5#67⋊C411yescharacteristic
370C4×C5#88511yescharacteristic
371C4×C5C4×#6711yescharacteristic
372C4×C5#94011yescharacteristic
373Dic5—24no—
374Dic5—64no—
375#41—21no—
376#41—21no—
377#41—21no—
378#41—21no—
379#41—61no—
380#41—61no—
381#41—61no—
382#41—61no—
383C2×Q8—31no—
384C2×Q8D3×Dic511yescharacteristic
385C2×D4—21no—
386C2×D4—31no—
387C2×D4—62no—
388C2×D4—61no—
389C2×D4D3×Dic511yescharacteristic
390C22×C4—21no—
391C22×C4—32no—
392C22×C4—61no—
393C22×C4—101no—
394C22×C4—301no—
395C22×C4C2×D3×D511yescharacteristic
396M16—101no—
397M16—101no—
398M16—301no—
399M16—301no—
400C2×C8—101no—
401C2×C8—301no—
402C4⋊C4—62no—
403C22⋊C4—62no—
404C22⋊C4—62no—
405C42—31no—
406C42—31no—
407C42—32no—
408C42—52no—
409C42—101no—
410C42—152no—
411C42—308no—
412C42—301no—
413C3×C5#196211yescharacteristic, complemented, Hall
414C22×C3—22no—
415C22×C3—41no—
416C22×C3—42no—
417C22×C3#408411yescharacteristic
418C22×C3#408411yescharacteristic
419C22×C3C2×C22⋊Dic511yescharacteristic
420C2×D3—41no—
421C2×D3—42no—
422C3×C4—41no—
423C3×C4—104no—
424C3×C4D4×Dic511yescharacteristic
425C3×C4D4×Dic511yescharacteristic
426C3×C4#408211yescharacteristic
427C3×C4#408611yescharacteristic
428Dic3—22no—
429Dic3—41no—
430Dic3—104no—
431Dic3#396914yescomplemented
432C2×C5—21no—
433C2×C5—21no—
434C2×C5—81no—
435C2×C5—241no—
436C2×C5D3×#10412yes—
437C2×C5#495711yescharacteristic
438C23—21no—
439C23—61no—
440C23D3×C22⋊D511yescharacteristic
441Q8—21no—
442Q8—21no—
443Q8—61no—
444Q8—61no—
445D4—21no—
446D4—21no—
447D4—41no—
448D4—41no—
449D4—61no—
450D4—61no—
451D4—124no—
452D4—121no—
453D4—121no—
454C2×C4—21no—
455C2×C4—32no—
456C2×C4—32no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—64no—
460C2×C4—61no—
461C2×C4—104no—
462C2×C4—102no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—304no—
466C2×C4—302no—
467C2×C4#678011yescharacteristic
468C2×C4C2×D3×Dic511yescharacteristic
469C2×C4#678211yescharacteristic
470C2×C4D5×#6711yescharacteristic
471C2×C4D3×C22⋊D511yescharacteristic
472C2×C4#679011yescharacteristic
473C8—201no—
474C8—601no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—81no—
478C2×C3#6551011yescharacteristic
479C2×C3C2×#396912yes—
480D3—81no—
481C5#7035611yescharacteristic, complemented, Sylow
482C22—22no—
483C22—42no—
484C22—41no—
485C22—122no—
486C22—121no—
487C22#9154911yescharacteristic
488C22D3×C22⋊Dic511yescharacteristic
489C22#9155711yescharacteristic
490C4—34no—
491C4—41no—
492C4—62no—
493C4—104no—
494C4—121no—
495C4—304no—
496C4#9152511yescharacteristic
497C4Dic5×#6711yescharacteristic
498C4#67⋊Dic511yescharacteristic
499C4#9156711yescharacteristic
500C3#1060260811yescharacteristic, complemented, Sylow
501C2—21no—
502C2—21no—
503C2—81no—
504C2—241no—
505C2D3×#396912yes—
506C2#1174948211yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5832C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1962
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91121C2semidirect
3. C2×C3×#3969C2semidirect
4. C4×Dic3×Dic5C2semidirect
5. #11748440C2semidirect
6. C2×#90979C2semidirect
7. C2×#90978C2semidirect
13. C5×#947C4semidirect
14. C5×#944C4semidirect
15. C5×#940C4semidirect
17. C5×#936C4semidirect
33. C2×#3969D3semidirect
58. C4×Dic15D4semidirect
69. C3×C4×Dic5D4semidirect
142. #947Dic5semidirect
143. #944Dic5semidirect
144. #940Dic5semidirect
146. #936Dic5semidirect
188. C4×Dic5#67semidirect
219. C5×Dic3#104semidirect
413. C3×C5#1962semidirect
431. Dic3#3969semidirect
481. C5#70356semidirect
500. C3#10602608semidirect

Maximal subgroups

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

subgroupindex
C5×#58322
C2×#911212
C2×C3×#39692
C4×Dic3×Dic52
#117484402
C2×#909792
C2×#909782
#106026083
#703565