Finite Group Databasebeta

← #14460049

Subgroups — #14460049

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#11756491C211yesmaximal, characteristic, complemented
2#11752533C211yesmaximal, characteristic
3C5×#5093C211yesmaximal, characteristic, complemented
4C3×#65376C211yesmaximal, characteristic, complemented
5#11747519C212yesmaximal, complemented
6#11747506C212yesmaximal, complemented
7#11747450C212yesmaximal, complemented
8#11747360C212yesmaximal, complemented
9#11747105C211yesmaximal, characteristic, complemented
10C4×#6657C211yesmaximal, characteristic, complemented
11#11746994C211yesmaximal, characteristic, complemented
12#10613345—31nomaximal, Hall
13C2×#6766C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91836—21no—
16Q8×Dic15—21no—
17#91787—22no—
18#91786C2212yes—
19#91781C2212yes—
20C4×D60C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C5×#869C2211yescharacteristic
23C3×C4×D20C2211yescharacteristic
24#91450—21no—
25#91413—22no—
26D5×C4⋊Dic3—21no—
27#91383C2212yes—
28C2×#6663C2212yes—
29C2×#6657C2211yescharacteristic
30C2×#6648C2212yes—
31C5×#810C2212yes—
32C5×#810C2212yes—
33C4×C5×C3⋊C8C2211yescharacteristic
34C3×#3941C2212yes—
35C3×#3939C2212yes—
36C3×C4⋊#168C2211yescharacteristic
37#90987C2211yescharacteristic
38#90974C2211yescharacteristic
39#90973C2212yes—
40#90965C2211yescharacteristic
41#90957C2212yes—
42#80981—51nomaximal, Hall
43#66066—31no—
44#66060—31no—
45C5×#487—31no—
46#65379—31no—
47#65376D311yescharacteristic, complemented
48#65104—32no—
49#65102—32no—
50#65099—32no—
51#65093—32no—
52C4×#677—31no—
53C8×D20—31no—
54C2×C3×C5×Q8—21no—
55C2×D60D411yescharacteristic
56C2×C4×D15C2312yes—
57C2×Dic30C2311yescharacteristic
58C2×C5×Dic6C2312yes—
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×#1202—22no—
62C2×D5×Dic3—22no—
63#6766—24no—
64#6766—42no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4C2312yes—
67C3×C42×C5C2311yescharacteristic
68#6714—22no—
69#6714—22no—
70#6714D412yes—
71C4⋊Dic15—22no—
72C4⋊Dic15D411yescharacteristic
73C4⋊Dic15C2311yescharacteristic
74#6712—21no—
75C4×Dic15—21no—
76C4×Dic15—22no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3—21no—
79C2×C5×C3⋊C8C2311yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C3×#685—21no—
82C3×C4⋊Dic5C2311yescharacteristic
83C2×C3×#168C2312yes—
84#6668—22no—
85#6667—22no—
86#6663—42no—
87#6657—22no—
88#6648—42no—
89#5732—51no—
90#5555—51no—
91C3×#474—51no—
92#5093D511yescharacteristic, complemented
93C4×#214—51no—
94#4888—52no—
95#4887—52no—
96#4849—51no—
97#4834—51no—
98#4783—52no—
99#4772—52no—
100C2×#713—32no—
101C5×C4⋊Q8—31no—
102C5×C4⋊Q8C2×D311yescharacteristic
103#4093—61no—
104#4092—32no—
105Q8×Dic5—61no—
106C2×#689—32no—
107C2×#677—31no—
108C2×C8×D5—32no—
109#4044—62no—
110#4043—32no—
111#4041—61no—
112#4040—62no—
113#4038—32no—
114D5×C4⋊C4—61no—
115C4×D20—31no—
116C4×D20C2×D311yescharacteristic
117C4×Dic10—31no—
118C5×#103—32no—
119C5×#103—32no—
120C4×C5×C8—31no—
121#3967—32no—
122#3953—31no—
123#3952—32no—
124#3949—31no—
125#3948—31no—
126#3941C2×D312yes—
127#3939C2×D312yes—
128C4⋊#168C2×D311yescharacteristic
129#3302—151noSylow
130C22×D15C2×D412yes—
131C22×C3×D5—21no—
132C3×C5×Q8—42no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—21no—
138C2×Dic15—21no—
139C2×Dic15C2×D412yes—
140D60—22no—
141C4×D15—22no—
142C4×D15—22no—
143Dic30—21no—
144Dic30—21no—
145C2×C5×Dic3—22no—
146C5×Dic6—22no—
147C5×Dic6—22no—
148C2×C3×Dic5—21no—
149C3×D20—21no—
150C3×D20#4112yes—
151C3×C4×D5—42no—
152#1202—44no—
153D5×Dic3—44no—
154C3×#168—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—21no—
157C2×#237—52no—
158C3×C4⋊Q8C2×D511yescharacteristic
159C3×C4×D4—51no—
160#947—101no—
161Q8×Dic3—101no—
162C2×#214—51no—
163#930—101no—
164C2×C4⋊Dic3—101no—
165C2×Dic12—52no—
166C2×D3×C8—52no—
167#898—102no—
168#897—52no—
169#897—52no—
170#892—52no—
171#886—102no—
172C4×D12—51no—
173#869C2×D511yescharacteristic
174C4×Dic6—51no—
175C3×#107—52no—
176C3×C4⋊C8—51no—
177C3×#102—52no—
178#832—51no—
179(C2×D3)⋊C8—52no—
180#816—52no—
181#810—51no—
182#810C2×D512yes—
183#810C2×D512yes—
184#808—51no—
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×Q8—21no—
187C2×C5×Q8—32no—
188#713—64no—
189#713—122no—
190C2×D20—31no—
191C2×D20—62no—
192C2×D20C22×D311yescharacteristic
193C2×C4×D5—21no—
194C2×C4×D5—32no—
195C2×C4×D5—62no—
196C2×Dic10—31no—
197C2×C5×C8—31no—
198C2×C5×C8—31no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—61no—
201C5×C4⋊C4—61no—
202C5×C4⋊C4C22×D312yes—
203C42×C5C22×D311yescharacteristic
204#689—122no—
205#685—21no—
206#685—32no—
207#685—62no—
208#685—62no—
209#685—62no—
210C4⋊Dic5—31no—
211C4⋊Dic5—31no—
212C4⋊Dic5—62no—
213C4⋊Dic5C22×D311yescharacteristic
214#683—62no—
215#683—61no—
216C4×Dic5—62no—
217C4×Dic5—61no—
218C2×#168C22×D312yes—
219#677—62no—
220C8×D5—122no—
221#556—151no—
222#547—151no—
223#487—31no—
224#485—152no—
225#474—51no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—22no—
234C2×D15—22no—
235C2×D15—22no—
236C2×C3×D5—22no—
237C2×C3×D5—41no—
238C2×C3×D5—41no—
239C3×C4×C5—21no—
240C3×C4×C5—42no—
241C3×C4×C5#13512yes—
242C3×C4×C5C2×#4111yescharacteristic
243C3×C4×C5H(5,𝔽2)11yescharacteristic
244Dic15—22no—
245Dic15—41no—
246Dic15—41no—
247C3×Dic5—41no—
248C5×Dic3—42no—
249C2×C3×Q8—21no—
250C2×C3×D4—51no—
251C22×C3×C4—101no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—104no—
255#237—202no—
256C2×D12—51no—
257C2×C4×D3—52no—
258C2×Dic6—51no—
259C2×Dic6C22×D512yes—
260C2×C3×C8—52no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—51no—
263C3×C4⋊C4C22×D512yes—
264C3×C22⋊C4—101no—
265C3×C42C22×D511yescharacteristic
266#214—102no—
267(C2×D3)⋊C4—52no—
268(C2×D3)⋊C4—102no—
269(C2×D3)⋊C4—102no—
270(C2×D3)⋊C4—102no—
271C4⋊Dic3—21no—
272C4⋊Dic3—21no—
273C4⋊Dic3—51no—
274C4⋊Dic3—51no—
275C4⋊Dic3—102no—
276C4⋊Dic3—102no—
277Dic3⋊C4—101no—
278C4×Dic3—102no—
279C4×Dic3—101no—
280C2×C3⋊C8C22×D511yescharacteristic
281C2×C3⋊C8C22×D511yescharacteristic
282Dic12—202no—
283D3×C8—202no—
284C22×D5—21no—
285C22×D5—32no—
286C5×Q8—42no—
287C5×Q8—62no—
288C5×Q8—62no—
289C2×C4×C5—22no—
290C2×C4×C5—62no—
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5C23×D311yescharacteristic
294C2×Dic5—21no—
295C2×Dic5—32no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298D20—21no—
299D20—62no—
300D20—124no—
301D20#23912yes—
302C4×D5—42no—
303C4×D5—62no—
304C4×D5—62no—
305C4×D5—124no—
306Dic10—61no—
307Dic10—61no—
308C5×C8—61no—
309C5×C8—61no—
310#168—22no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—152no—
315C4⋊Q8—31no—
316C4⋊Q8D3×D511yescharacteristic
317#126—302no—
318#124—301no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—151no—
324C4×Q8—301no—
325C4×D4—51no—
326C4×D4—151no—
327#117—152no—
328C2×C4⋊C4—301no—
329#107—52no—
330#106—151no—
331C4⋊C8—51no—
332#103—32no—
333#103—32no—
334#103—151no—
335#103—152no—
336#102—52no—
337#102—151no—
338C22⋊C8—152no—
339C4×C8—31no—
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343D15—42no—
344C3×D5—42no—
345C23×C3—101no—
346C22×D3—52no—
347C3×Q8—42no—
348C3×D4—52no—
349C3×D4—101no—
350C2×C3×C4—22no—
351C2×C3×C4—101no—
352C2×C3×C4—202no—
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357C2×Dic3—22no—
358C2×Dic3—52no—
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—204no—
362D12—102no—
363C4×D3—102no—
364C4×D3—102no—
365Dic6—22no—
366Dic6—22no—
367Dic6—101no—
368Dic6—101no—
369C3×C8—102no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C22×C5C2×D3×D411yescharacteristic
373C2×D5—22no—
374C2×D5—41no—
375C2×D5—41no—
376C2×D5—62no—
377C2×D5—62no—
378C2×D5—62no—
379C4×C5—21no—
380C4×C5—42no—
381C4×C5—122no—
382C4×C5#91212yes—
383C4×C5C2×#23911yescharacteristic
384C4×C5#100911yescharacteristic
385Dic5—41no—
386Dic5—62no—
387Dic5—121no—
388Dic5—121no—
389#41—304no—
390#41—602no—
391C2×Q8—21no—
392C2×Q8—32no—
393C2×Q8—151no—
394C2×D4—51no—
395C2×D4—151no—
396C2×D4—302no—
397C22×C4—101no—
398C22×C4—152no—
399C22×C4—302no—
400Q16—602no—
401SD16—302no—
402C2×C8—31no—
403C2×C8—31no—
404C2×C8—52no—
405C2×C8—602no—
406C4⋊C4—21no—
407C4⋊C4—51no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—151no—
411C4⋊C4—151no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C2×D3×D512yes—
416C22⋊C4—101no—
417C22⋊C4—152no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C42—302no—
422C42—301no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—102no—
426C22×C3—201no—
427C22×C3—201no—
428C22×C3C2×D4×D511yescharacteristic
429C2×D3—102no—
430C2×D3—102no—
431C2×D3—102no—
432C3×C4—21no—
433C3×C4—42no—
434C3×C4—201no—
435C3×C4#406212yes—
436C3×C4D5×#4111yescharacteristic
437C3×C4#414911yescharacteristic
438Dic3—42no—
439Dic3—102no—
440Dic3—201no—
441Dic3—201no—
442C2×C5#563011yescharacteristic
443C2×C5C2×#91211yescharacteristic
444C2×C5#577911yescharacteristic
445D5—42no—
446D5—122no—
447C23—101no—
448C23—152no—
449Q8—42no—
450Q8—62no—
451Q8—62no—
452Q8—301no—
453Q8—301no—
454D4—52no—
455D4—101no—
456D4—302no—
457D4—604no—
458C2×C4—22no—
459C2×C4—62no—
460C2×C4—101no—
461C2×C4—152no—
462C2×C4—202no—
463C2×C4—302no—
464C2×C4—302no—
465C2×C4—301no—
466C2×C4—301no—
467C2×C4—604no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—61no—
472C8—61no—
473C8—102no—
474C2×C3—202no—
475C2×C3#6601011yescharacteristic
476C2×C3C2×#406211yescharacteristic
477C2×C3#6610011yescharacteristic
478D3—202no—
479C5#8098111yescharacteristic, complemented, Sylow
480C22—102no—
481C22—201no—
482C22—201no—
483C22—302no—
484C22—302no—
485C22—302no—
486C22C2×#679011yescharacteristic
487C4—21no—
488C4—42no—
489C4—122no—
490C4—201no—
491C4—302no—
492C4—601no—
493C4—601no—
494C4#9149712yes—
495C4D5×#23911yescharacteristic
496C4#9203511yescharacteristic
497C3#1061334511yescharacteristic, complemented, Sylow
498C2—202no—
499C2—602no—
500C2C2×#9149711yescharacteristic
501C2#1175511911yescharacteristic
502C2#1175528311yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752533C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11756491C2semidirect
3. C5×#5093C2semidirect
4. C3×#65376C2semidirect
5. #11747519C2semidirect
6. #11747506C2semidirect
7. #11747450C2semidirect
8. #11747360C2semidirect
9. #11747105C2semidirect
10. C4×#6657C2semidirect
11. #11746994C2semidirect
47. #65376D3semidirect
92. #5093D5semidirect
424. C3×C5#3302semidirect
479. C5#80981semidirect
497. C3#10613345semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117525332
C5×#50932
C3×#653762
#117475192
#117475062
#117474502
#117473602
#117471052
C4×#66572
#117469942
#106133453
#809815