Finite Group Databasebeta

← #14460056

Subgroups — #14460056

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752507C211yesmaximal, characteristic, complemented
2#11752493C211yesmaximal, characteristic
3#11750947C211yesmaximal, characteristic, complemented
4C5×#4849C211yesmaximal, characteristic, complemented
5C3×#65123C211yesmaximal, characteristic, complemented
6#11748157C212yesmaximal, complemented
7#11747942C212yesmaximal, complemented
8#11747674C212yesmaximal, complemented
9#11747642C212yesmaximal, complemented
10C4×#6660C211yesmaximal, characteristic, complemented
11#11746929C211yesmaximal, characteristic, complemented
12#10612223—31nomaximal, Hall
13C2×#6773C2212yes—
14C4×D60C2211yescharacteristic
15#91758C2211yescharacteristic
16C2×C5×Dic12C2212yes—
17C5×#869C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic
19C2×C3×C8×D5C2212yes—
20C3×C4×D20C2211yescharacteristic
21#91465—21no—
22#91437—21no—
23#91364—21no—
24#91362—22no—
25#91359C2212yes—
26#91359C2212yes—
27#91358C2212yes—
28#91356—22no—
29#91340—21no—
30C2×#6660C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic
32#91105C2212yes—
33#91102C2212yes—
34C5×#816C2212yes—
35C3×#3952C2212yes—
36C3×C4×#168C2211yescharacteristic
37#90985C2211yescharacteristic
38#90973C2212yes—
39#90973C2212yes—
40#90973C2211yescharacteristic
41#90969C2211yescharacteristic
42#79442—51nomaximal, Hall
43#66060—31no—
44#65918—31no—
45C5×#462—31no—
46#65477—32no—
47#65476—32no—
48#65370—31no—
49C4×#688—31no—
50#65135—31no—
51#65123D311yescharacteristic, complemented
52#65103—32no—
53#65093—32no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30—21no—
57C2×C5×Dic6C2311yescharacteristic
58C2×C5×Dic6C2312yes—
59C2×C3×D20D411yescharacteristic
60C2×C3×C4×D5C2312yes—
61C2×#1202—22no—
62C2×#1200—22no—
63#6773—24no—
64#6773—42no—
65C2×C3×C5×C8C2312yes—
66C3×C42×C5C2311yescharacteristic
67#6714—21no—
68C4⋊Dic15—21no—
69C4⋊Dic15C2312yes—
70C4⋊Dic15C2311yescharacteristic
71C5×C4⋊Dic3—21no—
72C5×C4⋊Dic3—21no—
73C5×C4⋊Dic3C2311yescharacteristic
74C5×Dic3⋊C4—21no—
75C4×C5×Dic3—21no—
76C5×Dic12—42no—
77C3×#685D412yes—
78C3×C4⋊Dic5D411yescharacteristic
79C2×C3×#168C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81C3×C8×D5—42no—
82#6669—22no—
83#6669—22no—
84#6665—22no—
85#6665—22no—
86#6665—22no—
87Dic3×Dic5—22no—
88#6660—22no—
89#5551—51no—
90#5542—51no—
91C3×C8×D4—51no—
92#5116—52no—
93#5113—52no—
94#4849D511yescharacteristic, complemented
95#4846—51no—
96#4733—52no—
97#4723—52no—
98C4×#204—51no—
99#4681—51no—
100C2×#713—32no—
101C2×C5×Q16—32no—
102C5×C4⋊Q8—31no—
103C4×C5×Q8—31no—
104#4092—32no—
105#4092—32no—
106C2×#688—31no—
107C2×C8×D5C2×D312yes—
108#4044—62no—
109#4041—61no—
110#4040—62no—
111#4038—32no—
112D5×C4⋊C4—61no—
113#4021—61no—
114C4×D20—31no—
115C4×D20C2×D311yescharacteristic
116#4015—31no—
117C4×Dic10—61no—
118C5×C4⋊C8C2×D311yescharacteristic
119C5×#103—32no—
120#3967—31no—
121#3967—32no—
122#3967—32no—
123#3953—32no—
124#3952C2×D312yes—
125#3950—32no—
126#3941—31no—
127#3940—31no—
128C4×#168C2×D311yescharacteristic
129#3302—151noSylow
130C22×D15—21no—
131C22×C3×D5C2×D412yes—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136C2×Dic15—21no—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140Dic30—42no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—22no—
144C5×Dic6—21no—
145C5×Dic6—22no—
146C5×Dic6—21no—
147C5×Dic6—22no—
148C2×C3×Dic5C2×D412yes—
149C3×D20—22no—
150C3×C4×D5—22no—
151C3×C4×D5—22no—
152#1202—44no—
153#1200—44no—
154C3×C5×C8—22no—
155C3×#168—21no—
156C3×#168—21no—
157C2×#235—52no—
158C22×C3×C8—52no—
159C3×C4×D4—51no—
160#938—101no—
161#936—101no—
162#926—52no—
163#924—52no—
164#924—52no—
165C2×Dic12C2×D512yes—
166C2×#204—51no—
167D3×C4⋊C4—101no—
168#887—101no—
169#883—102no—
170#879—102no—
171C4×D12—51no—
172#869—51no—
173#869C2×D511yescharacteristic
174C4×Dic6C2×D511yescharacteristic
175C3×C4⋊C8C2×D511yescharacteristic
176C3×C22⋊C8—52no—
177C3×C4×C8—51no—
178#821—52no—
179#821—51no—
180#818—52no—
181#817—51no—
182#816—52no—
183#816—52no—
184#816—51no—
185#816C2×D512yes—
186C2×C5×Q8—31no—
187C2×C5×Q8—32no—
188#713—64no—
189#713—122no—
190C2×D20—31no—
191C2×D20—62no—
192C2×D20D1211yescharacteristic
193C2×C4×D5—61no—
194C2×C4×D5—62no—
195C2×C4×D5C22×D312yes—
196C2×Dic10—61no—
197C5×Q16—122no—
198C2×C5×C8C22×D312yes—
199C5×C4⋊C4—31no—
200C5×C4⋊C4—61no—
201C5×C4⋊C4—61no—
202C5×C4⋊C4—61no—
203C42×C5—61no—
204C42×C5C22×D311yescharacteristic
205#688—62no—
206#685—62no—
207#685—62no—
208#685—62no—
209#685—61no—
210#685D1212yes—
211C4⋊Dic5—31no—
212C4⋊Dic5—32no—
213C4⋊Dic5—61no—
214C4⋊Dic5D1211yescharacteristic
215#683—62no—
216#683—62no—
217C4×Dic5—62no—
218C2×#168C22×D311yescharacteristic
219C2×#168C22×D311yescharacteristic
220C8×D5—42no—
221#556—151no—
222#547—151no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—31no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—51no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—22no—
234C2×D15—41no—
235C2×D15—41no—
236C2×C3×D5—22no—
237C2×C3×D5—22no—
238C2×C3×D5—22no—
239C3×C4×C5—21no—
240C3×C4×C5#13512yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C5H(5,𝔽2)11yescharacteristic
243Dic15—42no—
244Dic15—41no—
245C3×Dic5—22no—
246C5×Dic3—42no—
247C5×Dic3—41no—
248C5×Dic3—41no—
249C2×C3×D4—51no—
250C22×C3×C4—52no—
251C2×#67—102no—
252#235—104no—
253#235—202no—
254C2×D12—51no—
255C2×C4×D3—102no—
256C2×C4×D3—101no—
257C2×Dic6—101no—
258C2×Dic6C22×D512yes—
259C2×Dic6C22×D511yescharacteristic
260C2×C3×C8—51no—
261C2×C3×C8—51no—
262C2×C3×C8—202no—
263C2×C3×C8C22×D512yes—
264C3×C4⋊C4—51no—
265C3×C22⋊C4—52no—
266C3×C42C22×D511yescharacteristic
267#217—102no—
268#217—102no—
269#217—102no—
270(C2×D3)⋊C4—101no—
271C4⋊Dic3—21no—
272C4⋊Dic3—21no—
273C4⋊Dic3—52no—
274C4⋊Dic3—51no—
275C4⋊Dic3—101no—
276C4⋊Dic3C22×D511yescharacteristic
277Dic3⋊C4—21no—
278Dic3⋊C4—102no—
279Dic3⋊C4—102no—
280C4×Dic3—21no—
281C4×Dic3—102no—
282Dic12—42no—
283#204—102no—
284C22×D5—61no—
285C22×D5C2×D1212yes—
286C5×Q8—61no—
287C5×Q8—62no—
288C5×Q8—61no—
289C5×Q8—62no—
290C2×C4×C5—61no—
291C2×C4×C5—61no—
292C2×C4×C5—62no—
293C2×C4×C5C2×D1211yescharacteristic
294C2×C4×C5C2×D1211yescharacteristic
295C2×C4×C5C23×D311yescharacteristic
296C2×Dic5—62no—
297C2×Dic5—61no—
298C2×Dic5C2×D1212yes—
299D20—22no—
300D20—32no—
301D20—61no—
302D20—124no—
303C4×D5—22no—
304C4×D5—22no—
305C4×D5—124no—
306C4×D5—122no—
307Dic10—122no—
308C5×C8—22no—
309#168—21no—
310#168—21no—
311C2×#41—152no—
312C2×Q16—32no—
313C2×SD16—151no—
314C22×C8—52no—
315C4⋊Q8—31no—
316C4⋊Q8—151no—
317#126—302no—
318#124—301no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—31no—
324C4×Q8—301no—
325C4×D4—51no—
326C4×D4—151no—
327#117—152no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—151no—
331C4⋊C8D3×D511yescharacteristic
332#103—32no—
333#103—152no—
334#103—151no—
335#103—152no—
336#102—151no—
337#102—152no—
338C22⋊C8—52no—
339C4×C8—51no—
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343D15—42no—
344C3×D5—42no—
345C23×C3—52no—
346C22×D3—101no—
347C3×D4—102no—
348C2×C3×C4—52no—
349C2×C3×C4—102no—
350C2×C3×C4—102no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3—102no—
359C2×Dic3—101no—
360D12—52no—
361D12—101no—
362C4×D3—204no—
363C4×D3—202no—
364Dic6—21no—
365Dic6—22no—
366Dic6—21no—
367Dic6—22no—
368Dic6—202no—
369C3×C8—22no—
370C3×C8—101no—
371C3×C8—101no—
372C22×C5C22×D1211yescharacteristic
373C2×D5—22no—
374C2×D5—22no—
375C2×D5—22no—
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—121no—
381C4×C5—122no—
382C4×C5—121no—
383C4×C5#90412yes—
384C4×C5#100411yescharacteristic
385C4×C5D3×#4111yescharacteristic
386Dic5—22no—
387Dic5—122no—
388Dic5—121no—
389#41—304no—
390#41—602no—
391C2×Q8—32no—
392C2×Q8—31no—
393C2×Q8—301no—
394C2×D4—51no—
395C2×D4—151no—
396C2×D4—302no—
397C22×C4—52no—
398C22×C4—302no—
399C22×C4—301no—
400Q16—122no—
401SD16—302no—
402C2×C8—51no—
403C2×C8—51no—
404C2×C8—202no—
405C2×C8C2×D3×D512yes—
406C4⋊C4—31no—
407C4⋊C4—51no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—152no—
412C4⋊C4—151no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C22⋊C4—52no—
417C22⋊C4—302no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—301no—
421C42—61no—
422C42—302no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—102no—
426C22×C3—102no—
427C22×C3—102no—
428C22×C3C2×D4×D511yescharacteristic
429C2×D3—102no—
430C2×D3—201no—
431C2×D3—201no—
432C3×C4—21no—
433C3×C4—102no—
434C3×C4#406512yes—
435C3×C4#414411yescharacteristic
436C3×C4D5×#4111yescharacteristic
437Dic3—41no—
438Dic3—42no—
439Dic3—41no—
440Dic3—202no—
441Dic3—201no—
442C2×C5#555411yescharacteristic
443C2×C5C2×#90411yescharacteristic
444C2×C5#575311yescharacteristic
445D5—42no—
446D5—122no—
447C23—52no—
448C23—301no—
449Q8—61no—
450Q8—62no—
451Q8—61no—
452Q8—62no—
453Q8—602no—
454D4—102no—
455D4—152no—
456D4—301no—
457D4—604no—
458C2×C4—52no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—62no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—302no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D5×D1211yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—22no—
472C8—101no—
473C8—101no—
474C2×C3—202no—
475C2×C3#6594611yescharacteristic
476C2×C3C2×#406511yescharacteristic
477C2×C3#6611311yescharacteristic
478D3—202no—
479C5#7944211yescharacteristic, complemented, Sylow
480C22—102no—
481C22—102no—
482C22—102no—
483C22—302no—
484C22—601no—
485C22—601no—
486C22C2×D5×D1211yescharacteristic
487C4—21no—
488C4—102no—
489C4—121no—
490C4—122no—
491C4—121no—
492C4—601no—
493C4—602no—
494C4#9127112yes—
495C4#9202511yescharacteristic
496C4#9203411yescharacteristic
497C3#1061222311yescharacteristic, complemented, Sylow
498C2—202no—
499C2—602no—
500C2#1175387711yescharacteristic
501C2C2×#9127111yescharacteristic
502C2#1175404011yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11752493C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752507C2semidirect
3. #11750947C2semidirect
4. C5×#4849C2semidirect
5. C3×#65123C2semidirect
6. #11748157C2semidirect
7. #11747942C2semidirect
8. #11747674C2semidirect
9. #11747642C2semidirect
10. C4×#6660C2semidirect
11. #11746929C2semidirect
51. #65123D3semidirect
94. #4849D5semidirect
424. C3×C5#3302semidirect
479. C5#79442semidirect
497. C3#10612223semidirect

Maximal subgroups

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

subgroupindex
#117525072
#117524932
#117509472
C5×#48492
C3×#651232
#117481572
#117479422
#117476742
#117476422
C4×#66602
#117469292
#106122233
#794425