Finite Group Databasebeta

← #14460065

Subgroups — #14460065

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#11752532C211yesmaximal, characteristic
2#11752491C211yesmaximal, characteristic, complemented
3#11750782C211yesmaximal, characteristic, complemented
4C5×C8×D12C211yesmaximal, characteristic, complemented
5C3×C4×#677C211yesmaximal, characteristic, complemented
6#11748147C212yesmaximal, complemented
7#11748137C212yesmaximal, complemented
8#11747947C212yesmaximal, complemented
9#11747681C212yesmaximal, complemented
10#11747095C211yesmaximal, characteristic, complemented
11#11746889C211yesmaximal, characteristic, complemented
12#10611173—31nomaximal, Hall
13C2×#6765C2212yes—
14#91758C2211yescharacteristic
15#91758C2211yescharacteristic
16C2×C5×D3×C8C2212yes—
17C4×C5×D12C2211yescharacteristic
18C2×C3×#677C2211yescharacteristic
19C3×C4×D20C2211yescharacteristic
20C3×C4×Dic10C2211yescharacteristic
21#91449—21no—
22#91414—22no—
23D5×C4⋊Dic3—21no—
24#91373—21no—
25#91369C2212yes—
26#91365C2212yes—
27#91342—22no—
28#91338C2212yes—
29#91333—21no—
30C2×#6662C2212yes—
31C3×C4×C5×C8C2211yescharacteristic
32#91100C2212yes—
33#91100C2212yes—
34C5×(C2×D3)⋊C8C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×#3953C2211yescharacteristic
37C3×#3949C2211yescharacteristic
38C3×#3948C2211yescharacteristic
39#90990C2212yes—
40#90974C2212yes—
41#90965C2212yes—
42#79680—51nomaximal, Hall
43#65885—31no—
44#65876—31no—
45C5×C8×D4—31no—
46#65405—32no—
47#65402—32no—
48#65138—31no—
49#65135—31no—
50#65022—32no—
51#65012—32no—
52C4×#677D311yescharacteristic, complemented
53#64970—31no—
54C2×Dic30—21no—
55C2×Dic30C2312yes—
56C2×C5×D12D411yescharacteristic
57C2×C4×C5×D3C2312yes—
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×C3×Dic10C2311yescharacteristic
61C2×#1201—22no—
62C2×D5×Dic3—22no—
63#6765—24no—
64#6765—42no—
65C2×C3×C5×C8C2311yescharacteristic
66C2×C3×C5×C8C2311yescharacteristic
67C3×C42×C5C2311yescharacteristic
68C4⋊Dic15—21no—
69C4⋊Dic15—21no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2312yes—
72C5×(C2×D3)⋊C4D412yes—
73C5×C4⋊Dic3D411yescharacteristic
74C2×C5×C3⋊C8C2312yes—
75C5×D3×C8—42no—
76C3×#685—21no—
77C3×C4⋊Dic5C2311yescharacteristic
78C3×C4⋊Dic5C2311yescharacteristic
79C3×#683—21no—
80C3×C4×Dic5—21no—
81C3×#677—22no—
82#6669—22no—
83#6668—22no—
84(C2×D3)⋊Dic5—22no—
85(C2×D3)⋊Dic5—22no—
86(C2×D3)⋊Dic5—22no—
87Dic3×Dic5—22no—
88#6662—42no—
89#5584—51no—
90#5555—51no—
91C3×C4×SD16—51no—
92#5173—52no—
93#5031—51no—
94#5007—51no—
95#4868—52no—
96#4813—52no—
97#4772—52no—
98C8×D12D511yescharacteristic, complemented
99#4681—51no—
100C2×#709—32no—
101C22×C5×C8—32no—
102C4×C5×D4—31no—
103#4084—61no—
104#4082—61no—
105#4072—32no—
106#4070—32no—
107#4070—32no—
108C2×Dic20—32no—
109C2×#677C2×D311yescharacteristic
110D5×C4⋊C4—61no—
111#4033—61no—
112#4029—62no—
113#4025—62no—
114C4×D20C2×D311yescharacteristic
115#4015—31no—
116#4015—31no—
117C4×Dic10C2×D311yescharacteristic
118C5×C4⋊C8—31no—
119C5×C22⋊C8—32no—
120C4×C5×C8C2×D311yescharacteristic
121#3953—32no—
122#3953C2×D311yescharacteristic
123#3950—32no—
124#3949C2×D311yescharacteristic
125#3948—32no—
126#3948—32no—
127#3948—32no—
128#3948C2×D311yescharacteristic
129#3302—151noSylow
130C22×C5×D3C2×D412yes—
131C22×C3×D5—21no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136C2×Dic15—22no—
137Dic30—22no—
138Dic30—22no—
139Dic30—42no—
140C2×C5×Dic3C2×D412yes—
141C5×D12—22no—
142C4×C5×D3—22no—
143C4×C5×D3—22no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C3×D20—21no—
148C3×D20#4112yes—
149C3×C4×D5—42no—
150C3×Dic10—21no—
151C3×Dic10—21no—
152#1201—44no—
153D5×Dic3—44no—
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C5×C3⋊C8—22no—
157C2×#237—52no—
158C2×C3×SD16—51no—
159C3×C4×Q8—51no—
160C3×C4×D4—51no—
161#946—52no—
162C2×#216—52no—
163#930—101no—
164C2×C4⋊Dic3—101no—
165C2×D3×C8C2×D512yes—
166#898—102no—
167#897—52no—
168#892—52no—
169#886—102no—
170#875—101no—
171C4×D12C2×D511yescharacteristic
172#869—51no—
173#869—51no—
174C4×Dic6—101no—
175C3×#106—51no—
176C3×#103—51no—
177C3×#102—51no—
178C3×C4×C8C2×D511yescharacteristic
179#832—52no—
180(C2×D3)⋊C8C2×D512yes—
181#816—52no—
182#816—52no—
183#810—52no—
184#807—52no—
185C4⋊(C3⋊C8)C2×D511yescharacteristic
186C2×C5×D4—31no—
187C22×C4×C5—32no—
188C2×C22⋊D5—62no—
189#709—64no—
190#709—122no—
191C2×D20C22×D311yescharacteristic
192C2×C4×D5—21no—
193C2×C4×D5—62no—
194C2×Dic10—32no—
195C2×Dic10—61no—
196C2×Dic10C22×D311yescharacteristic
197C2×C5×C8—32no—
198C2×C5×C8—122no—
199C2×C5×C8C22×D311yescharacteristic
200C2×C5×C8C22×D311yescharacteristic
201C5×C4⋊C4—31no—
202C5×C22⋊C4—32no—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—62no—
205C22⋊Dic5—62no—
206C22⋊Dic5—62no—
207#685—21no—
208C4⋊Dic5—32no—
209C4⋊Dic5—61no—
210C4⋊Dic5—61no—
211C4⋊Dic5—61no—
212C4⋊Dic5C22×D311yescharacteristic
213C4⋊Dic5C22×D311yescharacteristic
214#683—21no—
215#683—62no—
216#683—62no—
217C4×Dic5—21no—
218C4×Dic5—62no—
219Dic20—122no—
220#677—22no—
221#556—151no—
222#547—151no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—51no—
230C8×D4—31no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×C5×D3—22no—
234C2×C5×D3—22no—
235C2×C5×D3—22no—
236C2×C3×D5—22no—
237C2×C3×D5—41no—
238C2×C3×D5—41no—
239C3×C4×C5—21no—
240C3×C4×C5#13512yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C5H(5,𝔽2)11yescharacteristic
243Dic15—42no—
244Dic15—42no—
245C3×Dic5—41no—
246C3×Dic5—41no—
247C3×Dic5—41no—
248C5×Dic3—22no—
249C2×C3×Q8—51no—
250C2×C3×D4—51no—
251C22×C3×C4—101no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—104no—
255#237—202no—
256C2×D12D2011yescharacteristic
257C2×C4×D3C22×D512yes—
258C2×Dic6—52no—
259C2×Dic6—101no—
260C3×SD16—102no—
261C2×C3×C8C22×D511yescharacteristic
262C2×C3×C8C22×D511yescharacteristic
263C3×C4⋊C4—51no—
264C3×C4⋊C4—51no—
265C3×C4⋊C4—101no—
266C3×C22⋊C4—101no—
267C3×C42—101no—
268C3×C42C22×D511yescharacteristic
269#216—202no—
270(C2×D3)⋊C4—102no—
271(C2×D3)⋊C4—102no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4D2012yes—
274C4⋊Dic3—52no—
275C4⋊Dic3—101no—
276C4⋊Dic3—101no—
277C4⋊Dic3—101no—
278C4⋊Dic3—102no—
279C4⋊Dic3D2011yescharacteristic
280Dic3⋊C4—102no—
281C4×Dic3—102no—
282C2×C3⋊C8C22×D512yes—
283D3×C8—42no—
284C23×C5—32no—
285C22×D5—21no—
286C5×D4—62no—
287C2×C4×C5—32no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—62no—
298C2×Dic5—62no—
299D20—21no—
300D20#23512yes—
301C4×D5—42no—
302C4×D5—124no—
303Dic10—21no—
304Dic10—21no—
305Dic10—62no—
306Dic10—62no—
307Dic10—122no—
308C5×C8—21no—
309C5×C8—21no—
310C5×C8—62no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—51no—
314C22×C8—32no—
315C4⋊Q8—151no—
316C4⋊Q8—151no—
317#126—302no—
318#124—301no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—51no—
324C4×Q8—301no—
325C4×D4—31no—
326C4×D4—51no—
327#117—152no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—51no—
331C4⋊C8—31no—
332#103—51no—
333#103—152no—
334#103—152no—
335#103—152no—
336#102—51no—
337#102—152no—
338C22⋊C8—32no—
339C4×C8D3×D511yescharacteristic
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343C3×D5—42no—
344C5×D3—42no—
345C23×C3—101no—
346C22×D3C2×D2012yes—
347C3×Q8—101no—
348C3×Q8—101no—
349C3×D4—52no—
350C3×D4—101no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4—101no—
354C2×C3×C4—202no—
355C2×C3×C4C2×D2011yescharacteristic
356C2×C3×C4C2×D2011yescharacteristic
357C2×C3×C4C23×D511yescharacteristic
358#67—204no—
359C2×Dic3—102no—
360C2×Dic3—102no—
361C2×Dic3—204no—
362C2×Dic3C2×D2012yes—
363D12—22no—
364C4×D3—22no—
365C4×D3—22no—
366Dic6—102no—
367Dic6—102no—
368Dic6—202no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—22no—
372C22×C5—62no—
373C22×C5—62no—
374C22×C5—62no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—22no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—21no—
380C4×C5—62no—
381C4×C5#91612yes—
382C4×C5C2×#23511yescharacteristic
383C4×C5#100911yescharacteristic
384Dic5—41no—
385Dic5—41no—
386Dic5—41no—
387Dic5—122no—
388Dic5—122no—
389#41—304no—
390#41—602no—
391C2×Q8—51no—
392C2×Q8—152no—
393C2×Q8—301no—
394C2×D4—31no—
395C2×D4—51no—
396C2×D4—302no—
397C22×C4—32no—
398C22×C4—101no—
399C22×C4—302no—
400Q16—602no—
401SD16—102no—
402C2×C8—32no—
403C2×C8—122no—
404C2×C8C2×D3×D511yescharacteristic
405C2×C8C2×D3×D511yescharacteristic
406C4⋊C4—31no—
407C4⋊C4—51no—
408C4⋊C4—51no—
409C4⋊C4—101no—
410C4⋊C4—152no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—301no—
414C4⋊C4—301no—
415C4⋊C4—301no—
416C22⋊C4—32no—
417C22⋊C4—101no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C42—101no—
422C42—302no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—102no—
426C22×C3—201no—
427C22×C3—201no—
428C22×C3C22×D2011yescharacteristic
429C2×D3—22no—
430C2×D3—22no—
431C2×D3—22no—
432C3×C4—21no—
433C3×C4—201no—
434C3×C4—201no—
435C3×C4—201no—
436C3×C4#405012yes—
437C3×C4#414411yescharacteristic
438C3×C4D5×#4111yescharacteristic
439Dic3—22no—
440Dic3—202no—
441Dic3—202no—
442C2×C5—122no—
443C2×C5#555011yescharacteristic
444C2×C5C2×#91611yescharacteristic
445C2×C5#577111yescharacteristic
446D5—42no—
447C23—32no—
448C23—101no—
449Q8—101no—
450Q8—101no—
451Q8—302no—
452Q8—302no—
453Q8—602no—
454D4—52no—
455D4—62no—
456D4—101no—
457D4—604no—
458C2×C4—32no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—101no—
462C2×C4—101no—
463C2×C4—101no—
464C2×C4—202no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4D3×D2011yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—21no—
472C8—21no—
473C8—62no—
474C2×C3—202no—
475C2×C3#6588811yescharacteristic
476C2×C3C2×#405011yescharacteristic
477C2×C3#6608711yescharacteristic
478D3—42no—
479C5#7968011yescharacteristic, complemented, Sylow
480C22—62no—
481C22—62no—
482C22—62no—
483C22—102no—
484C22—201no—
485C22—201no—
486C22C2×D3×D2011yescharacteristic
487C4—21no—
488C4—62no—
489C4—201no—
490C4—201no—
491C4—201no—
492C4—602no—
493C4—602no—
494C4#9127212yes—
495C4D5×#23511yescharacteristic
496C4#9201811yescharacteristic
497C3#1061117311yescharacteristic, complemented, Sylow
498C2—122no—
499C2—202no—
500C2#1175274011yescharacteristic
501C2C2×#9127211yescharacteristic
502C2#1175400311yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11752532C2
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
2. #11752491C2semidirect
3. #11750782C2semidirect
4. C5×C8×D12C2semidirect
5. C3×C4×#677C2semidirect
6. #11748147C2semidirect
7. #11748137C2semidirect
8. #11747947C2semidirect
9. #11747681C2semidirect
10. #11747095C2semidirect
11. #11746889C2semidirect
52. C4×#677D3semidirect
98. C8×D12D5semidirect
424. C3×C5#3302semidirect
479. C5#79680semidirect
497. C3#10611173semidirect

Maximal subgroups

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

subgroupindex
#117525322
#117524912
#117507822
C5×C8×D122
C3×C4×#6772
#117481472
#117481372
#117479472
#117476812
#117470952
#117468892
#106111733
#796805