Finite Group Databasebeta

← #14460063

Subgroups — #14460063

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#11752676C211yesmaximal, characteristic
2#11752507C211yesmaximal, characteristic, complemented
3#11750782C211yesmaximal, characteristic, complemented
4C4×C5×#204C211yesmaximal, characteristic, complemented
5C3×C8×D20C211yesmaximal, characteristic, complemented
6#11748155C212yesmaximal, complemented
7#11748135C212yesmaximal, complemented
8#11747939C212yesmaximal, complemented
9#11747676C212yesmaximal, complemented
10#11747101C211yesmaximal, characteristic, complemented
11#11746964C211yesmaximal, characteristic, complemented
12#10611411—31nomaximal, Hall
13C2×#6772C2212yes—
14#91758C2211yescharacteristic
15#91758C2211yescharacteristic
16C2×C5×#204C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18C4×C5×Dic6C2211yescharacteristic
19C2×C3×C8×D5C2212yes—
20C3×C4×D20C2211yescharacteristic
21#91457—22no—
22#91456—21no—
23D3×C4⋊Dic5—21no—
24#91364—21no—
25#91362—22no—
26#91360C2212yes—
27#91359C2212yes—
28#91358C2212yes—
29#91340—21no—
30C2×#6663C2212yes—
31C3×C4×C5×C8C2211yescharacteristic
32#91100C2212yes—
33#91100C2212yes—
34C5×#821C2211yescharacteristic
35C5×#817C2211yescharacteristic
36C5×#816C2211yescharacteristic
37C3×#3952C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90988C2212yes—
40#90975C2212yes—
41#90967C2212yes—
42#79442—51nomaximal, Hall
43#65918—31no—
44#65889—31no—
45C4×C5×SD16—31no—
46#65462—32no—
47#65320—31no—
48#65296—31no—
49#65156—32no—
50#65102—32no—
51#65061—32no—
52C8×D20D311yescharacteristic, complemented
53#64970—31no—
54C2×Dic30—21no—
55C2×Dic30C2312yes—
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C5×Dic6C2311yescharacteristic
59C2×C3×D20D411yescharacteristic
60C2×C3×C4×D5C2312yes—
61C2×#1201—22no—
62C2×D3×Dic5—22no—
63#6772—24no—
64#6772—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)⋊C4—21no—
73C5×C4⋊Dic3C2311yescharacteristic
74C5×C4⋊Dic3C2311yescharacteristic
75C5×Dic3⋊C4—21no—
76C4×C5×Dic3—21no—
77C5×#204—22no—
78C3×#685D412yes—
79C3×C4⋊Dic5D411yescharacteristic
80C2×C3×#168C2312yes—
81C3×C8×D5—42no—
82Dic3⋊Dic5—22no—
83#6669—22no—
84#6665—22no—
85#6665—22no—
86#6665—22no—
87Dic3×Dic5—22no—
88#6663—42no—
89#5551—51no—
90#5542—51no—
91C3×C8×D4—51no—
92#5116—52no—
93#5113—52no—
94#4849—51no—
95#4846—51no—
96#4733—52no—
97#4723—52no—
98C4×#204D511yescharacteristic, complemented
99#4681—51no—
100C2×#711—32no—
101C2×C5×SD16—31no—
102C4×C5×Q8—31no—
103C4×C5×D4—31no—
104#4092—32no—
105C2×#689—32no—
106#4076—61no—
107C2×C4⋊Dic5—61no—
108C2×C8×D5C2×D312yes—
109#4044—62no—
110#4043—32no—
111#4038—32no—
112#4032—62no—
113#4021—61no—
114C4×D20C2×D311yescharacteristic
115#4015—31no—
116#4015—31no—
117C4×Dic10—61no—
118C5×#106—31no—
119C5×#103—31no—
120C5×#102—31no—
121C4×C5×C8C2×D311yescharacteristic
122#3964—32no—
123#3952C2×D312yes—
124#3948—32no—
125#3948—32no—
126#3942—32no—
127#3939—32no—
128C4⋊#168C2×D311yescharacteristic
129#3302—151noSylow
130C22×C5×D3—21no—
131C22×C3×D5C2×D412yes—
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×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—21no—
143C5×D12—21no—
144C5×D12#4112yes—
145C4×C5×D3—42no—
146C5×Dic6—21no—
147C5×Dic6—21no—
148C2×C3×Dic5C2×D412yes—
149C3×D20—22no—
150C3×C4×D5—22no—
151C3×C4×D5—22no—
152#1201—44no—
153D3×Dic5—44no—
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C3×#168—22no—
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×Dic12—52no—
166C2×#204C2×D511yescharacteristic
167D3×C4⋊C4—101no—
168#887—101no—
169#883—102no—
170#879—102no—
171C4×D12C2×D511yescharacteristic
172#869—51no—
173#869—51no—
174C4×Dic6C2×D511yescharacteristic
175C3×C4⋊C8—51no—
176C3×C22⋊C8—52no—
177C3×C4×C8C2×D511yescharacteristic
178#821—52no—
179#821C2×D511yescharacteristic
180#818—52no—
181#817C2×D511yescharacteristic
182#816—52no—
183#816—52no—
184#816—52no—
185#816C2×D511yescharacteristic
186C2×C5×Q8—31no—
187C2×C5×D4—31no—
188C22×C4×C5—61no—
189C2×C22⋊D5—62no—
190C22×Dic5—62no—
191#711—64no—
192#711—122no—
193C2×D20D1211yescharacteristic
194C2×C4×D5C22×D312yes—
195C2×Dic10—32no—
196C2×Dic10—61no—
197C5×SD16—62no—
198C2×C5×C8C22×D311yescharacteristic
199C2×C5×C8C22×D311yescharacteristic
200C5×C4⋊C4—31no—
201C5×C4⋊C4—31no—
202C5×C4⋊C4—61no—
203C5×C22⋊C4—61no—
204C42×C5—61no—
205C42×C5C22×D311yescharacteristic
206#689—122no—
207#685—62no—
208#685—62no—
209#685—62no—
210#685D1212yes—
211C4⋊Dic5—32no—
212C4⋊Dic5—61no—
213C4⋊Dic5—61no—
214C4⋊Dic5—61no—
215C4⋊Dic5—62no—
216C4⋊Dic5D1211yescharacteristic
217#683—62no—
218C4×Dic5—62no—
219C2×#168C22×D312yes—
220C8×D5—42no—
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—31no—
230C8×D4—51no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×C5×D3—22no—
234C2×C5×D3—41no—
235C2×C5×D3—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—42no—
245C3×Dic5—22no—
246C5×Dic3—41no—
247C5×Dic3—41no—
248C5×Dic3—41no—
249C2×C3×D4—51no—
250C22×C3×C4—52no—
251C2×#67—102no—
252#235—104no—
253#235—202no—
254C2×D12C22×D511yescharacteristic
255C2×C4×D3—21no—
256C2×C4×D3—102no—
257C2×Dic6—52no—
258C2×Dic6—101no—
259C2×Dic6C22×D511yescharacteristic
260C2×C3×C8—52no—
261C2×C3×C8—202no—
262C2×C3×C8C22×D511yescharacteristic
263C2×C3×C8C22×D511yescharacteristic
264C3×C4⋊C4—51no—
265C3×C22⋊C4—52no—
266C3×C42C22×D511yescharacteristic
267#217—102no—
268#217—102no—
269#217—102no—
270(C2×D3)⋊C4—21no—
271C4⋊Dic3—52no—
272C4⋊Dic3—101no—
273C4⋊Dic3—101no—
274C4⋊Dic3—101no—
275C4⋊Dic3C22×D511yescharacteristic
276C4⋊Dic3C22×D511yescharacteristic
277Dic3⋊C4—21no—
278Dic3⋊C4—102no—
279Dic3⋊C4—102no—
280C4×Dic3—21no—
281C4×Dic3—102no—
282Dic12—202no—
283#204—22no—
284C23×C5—61no—
285C22×D5C2×D1212yes—
286C5×Q8—61no—
287C5×Q8—61no—
288C5×D4—32no—
289C5×D4—61no—
290C2×C4×C5—61no—
291C2×C4×C5—61no—
292C2×C4×C5—61no—
293C2×C4×C5—122no—
294C2×C4×C5C2×D1211yescharacteristic
295C2×C4×C5C2×D1211yescharacteristic
296C2×C4×C5C23×D311yescharacteristic
297C22⋊D5—124no—
298C2×Dic5—62no—
299C2×Dic5—62no—
300C2×Dic5—124no—
301C2×Dic5C2×D1212yes—
302D20—22no—
303C4×D5—22no—
304C4×D5—22no—
305Dic10—62no—
306Dic10—62no—
307Dic10—122no—
308C5×C8—21no—
309C5×C8—21no—
310#168—22no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—31no—
314C22×C8—52no—
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—31no—
324C4×Q8—301no—
325C4×D4—31no—
326C4×D4—51no—
327#117—152no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—31no—
331C4⋊C8—51no—
332#103—31no—
333#103—152no—
334#103—152no—
335#103—152no—
336#102—31no—
337#102—152no—
338C22⋊C8—52no—
339C4×C8D3×D511yescharacteristic
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343C3×D5—42no—
344C5×D3—42no—
345C23×C3—52no—
346C22×D3—21no—
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—21no—
358C2×Dic3—102no—
359C2×Dic3—102no—
360D12—21no—
361D12#70912yes—
362C4×D3—42no—
363C4×D3—204no—
364Dic6—21no—
365Dic6—21no—
366Dic6—102no—
367Dic6—102no—
368Dic6—202no—
369C3×C8—21no—
370C3×C8—21no—
371C3×C8—102no—
372C22×C5—62no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5C22×D1211yescharacteristic
376C2×D5—22no—
377C2×D5—22no—
378C2×D5—22no—
379C4×C5—21no—
380C4×C5—121no—
381C4×C5—121no—
382C4×C5—121no—
383C4×C5#90412yes—
384C4×C5#100411yescharacteristic
385C4×C5D3×#4111yescharacteristic
386Dic5—22no—
387Dic5—122no—
388Dic5—122no—
389#41—304no—
390#41—602no—
391C2×Q8—31no—
392C2×Q8—152no—
393C2×Q8—301no—
394C2×D4—31no—
395C2×D4—51no—
396C2×D4—302no—
397C22×C4—52no—
398C22×C4—61no—
399C22×C4—302no—
400Q16—602no—
401SD16—62no—
402C2×C8—52no—
403C2×C8—202no—
404C2×C8C2×D3×D511yescharacteristic
405C2×C8C2×D3×D511yescharacteristic
406C4⋊C4—31no—
407C4⋊C4—31no—
408C4⋊C4—51no—
409C4⋊C4—61no—
410C4⋊C4—152no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—301no—
414C4⋊C4—301no—
415C4⋊C4—301no—
416C22⋊C4—52no—
417C22⋊C4—61no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—302no—
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—22no—
430C2×D3—41no—
431C2×D3—41no—
432C3×C4—21no—
433C3×C4—102no—
434C3×C4#406212yes—
435C3×C4C2×#70911yescharacteristic
436C3×C4#414911yescharacteristic
437Dic3—41no—
438Dic3—41no—
439Dic3—41no—
440Dic3—202no—
441Dic3—202no—
442C2×C5—122no—
443C2×C5#555411yescharacteristic
444C2×C5C2×#90411yescharacteristic
445C2×C5#575311yescharacteristic
446D5—42no—
447C23—52no—
448C23—61no—
449Q8—61no—
450Q8—61no—
451Q8—302no—
452Q8—302no—
453Q8—602no—
454D4—32no—
455D4—61no—
456D4—102no—
457D4—604no—
458C2×C4—52no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—122no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4D5×D1211yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—21no—
472C8—21no—
473C8—102no—
474C2×C3—202no—
475C2×C3#6588411yescharacteristic
476C2×C3C2×#406211yescharacteristic
477C2×C3#6610511yescharacteristic
478D3—42no—
479C5#7944211yescharacteristic, complemented, Sylow
480C22—62no—
481C22—102no—
482C22—102no—
483C22—102no—
484C22—121no—
485C22—121no—
486C22C2×D5×D1211yescharacteristic
487C4—21no—
488C4—102no—
489C4—121no—
490C4—121no—
491C4—121no—
492C4—602no—
493C4—602no—
494C4#9126912yes—
495C4D3×#70911yescharacteristic
496C4#9201711yescharacteristic
497C3#1061141111yescharacteristic, complemented, Sylow
498C2—122no—
499C2—202no—
500C2#1175273611yescharacteristic
501C2#1175398811yescharacteristic
502C2C2×#9126911yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11752676C2
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. #11752507C2semidirect
3. #11750782C2semidirect
4. C4×C5×#204C2semidirect
5. C3×C8×D20C2semidirect
6. #11748155C2semidirect
7. #11748135C2semidirect
8. #11747939C2semidirect
9. #11747676C2semidirect
10. #11747101C2semidirect
11. #11746964C2semidirect
52. C8×D20D3semidirect
98. C4×#204D5semidirect
424. C3×C5#3302semidirect
479. C5#79442semidirect
497. C3#10611411semidirect

Maximal subgroups

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

subgroupindex
#117526762
#117525072
#117507822
C4×C5×#2042
C3×C8×D202
#117481552
#117481352
#117479392
#117476762
#117471012
#117469642
#106114113
#794425