Finite Group Databasebeta

← #14460074

Subgroups — #14460074

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
1C3×#66060C211yesmaximal, characteristic
2#11752507C211yesmaximal, characteristic, complemented
3#11751180C211yesmaximal, characteristic, complemented
4C5×#5090C211yesmaximal, characteristic, complemented
5#11749366C212yesmaximal, complemented
6#11749294C212yesmaximal, complemented
7#11749209C212yesmaximal, complemented
8#11749207C212yesmaximal, complemented
9C4×#6655C211yesmaximal, characteristic, complemented
10#11746996C211yesmaximal, characteristic, complemented
11#11746889C211yesmaximal, characteristic, complemented
12#10612223—31nomaximal, Hall
13C2×C3×#713C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91758C2211yescharacteristic
16C2×C5×#216C2212yes—
17C4×C5×Dic6C2211yescharacteristic
18C3×#4092C2212yes—
19C3×#4041—21no—
20C3×#4040—22no—
21C3×D5×C4⋊C4—21no—
22C3×C4×D20C2211yescharacteristic
23C3×C4×D20C2211yescharacteristic
24#91364—21no—
25#91362—22no—
26#91359C2212yes—
27#91358C2212yes—
28#91340—21no—
29C2×#6655C2211yescharacteristic
30C2×D5×C3⋊C8C2212yes—
31#91119C2212yes—
32#91119C2212yes—
33C4×C3⋊#168C2211yescharacteristic
34C5×#835C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36#90990C2212yes—
37#90986C2211yescharacteristic
38#90972C2211yescharacteristic
39#90965C2212yes—
40#90964C2211yescharacteristic
41#90955C2212yes—
42#83510—51nomaximal, Hall
43#66060D311yescharacteristic
44#65918—31no—
45C5×#462—31no—
46#65477—32no—
47#65476—32no—
48#65370—31no—
49C4×#688—31no—
50#65135—31no—
51#65123—31no—
52#65103—32no—
53#65093—32no—
54C2×C3×C5×Q8C2312yes—
55C2×Dic30—21no—
56C2×C5×Dic6C2311yescharacteristic
57C3×#713—24no—
58C3×#713—42no—
59C2×C3×D20—22no—
60C2×C3×D20D411yescharacteristic
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5C2312yes—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4—21no—
67C3×C42×C5C2311yescharacteristic
68C4⋊Dic15—21no—
69C4⋊Dic15C2312yes—
70C2×C3⋊#168C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72C5×#216—42no—
73C5×C4⋊Dic3C2311yescharacteristic
74C5×Dic3⋊C4—21no—
75C4×C5×Dic3—21no—
76C2×C5×C3⋊C8C2312yes—
77C3×#685—22no—
78C3×#685—21no—
79C3×#685D412yes—
80C3×C4⋊Dic5D411yescharacteristic
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—22no—
83#6669—22no—
84#6665—22no—
85#6665—22no—
86Dic3×Dic5—22no—
87#6655—22no—
88D5×C3⋊C8—42no—
89C3×#547—51no—
90#5542—51no—
91#5239—52no—
92#5233—52no—
93#5090D511yescharacteristic, complemented
94#5079—51no—
95#5051—52no—
96#5045—52no—
97C4×#214—51no—
98D4×C3⋊C8—51no—
99#5007—51no—
100C2×#713C2×D312yes—
101C2×C5×Q16—32no—
102C5×C4⋊Q8C2×D311yescharacteristic
103C4×C5×Q8—31no—
104#4092—32no—
105#4092C2×D312yes—
106C2×#688—31no—
107C2×C8×D5—32no—
108#4044—62no—
109#4041—21no—
110#4040—22no—
111#4038—32no—
112D5×C4⋊C4—21no—
113#4021—61no—
114C4×D20C2×D311yescharacteristic
115C4×D20C2×D311yescharacteristic
116#4015—31no—
117C4×Dic10—61no—
118C5×C4⋊C8—31no—
119C5×#103—32no—
120#3967—32no—
121#3967—32no—
122#3967—31no—
123#3953—32no—
124#3952—32no—
125#3950—32no—
126#3941—31no—
127#3940—31no—
128C4×#168—31no—
129#3302—151noSylow
130C22×C3×D5—21no—
131C22×C3×D5C2×D412yes—
132C3×C5×Q8—22no—
133C3×C5×Q8—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2411yescharacteristic
138C2×Dic15—22no—
139Dic30—42no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C5×Dic6—21no—
143C5×Dic6—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5C2×D412yes—
146C3×D20—22no—
147C3×D20—21no—
148C3×D20—44no—
149C3×D20#4112yes—
150C3×C4×D5—22no—
151C3×C4×D5—22no—
152C3×C4×D5—44no—
153C3×C4×D5—42no—
154C3⋊#168—21no—
155C3⋊#168—21no—
156C5×C3⋊C8—22no—
157C2×C3×#41—52no—
158C3×C4⋊Q8C2×D511yescharacteristic
159C3×#123—102no—
160C3×C22⋊Q8—52no—
161C3×#121—101no—
162C3×C4×D4—51no—
163C3×C4×D4—51no—
164C2×C3×C4⋊C4—101no—
165C2×#216C2×D512yes—
166#936—101no—
167C2×#214—51no—
168#926—52no—
169#924—52no—
170C22×C3⋊C8—52no—
171#887—101no—
172#879—102no—
173#869—51no—
174C4×Dic6C2×D511yescharacteristic
175#835—52no—
176#835—52no—
177#835C2×D512yes—
178#832—51no—
179#832—52no—
180#830—52no—
181#810—51no—
182#808—51no—
183#807—52no—
184C4⋊(C3⋊C8)C2×D511yescharacteristic
185C4×C3⋊C8—51no—
186C2×C5×Q8—31no—
187C2×C5×Q8C22×D312yes—
188#713—24no—
189#713—42no—
190C2×D20—22no—
191C2×D20#6711yescharacteristic
192C2×D20C22×D311yescharacteristic
193C2×C4×D5—21no—
194C2×C4×D5—22no—
195C2×C4×D5C22×D312yes—
196C2×Dic10—61no—
197C5×Q16—122no—
198C2×C5×C8—32no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—31no—
202C5×C4⋊C4—61no—
203C42×C5—61no—
204C42×C5C22×D311yescharacteristic
205#688—62no—
206#685—22no—
207#685—21no—
208#685—62no—
209#685—62no—
210#685#6712yes—
211C4⋊Dic5—32no—
212C4⋊Dic5—61no—
213C4⋊Dic5#6711yescharacteristic
214C4⋊Dic5C22×D311yescharacteristic
215#683—22no—
216#683—62no—
217C4×Dic5—62no—
218C2×#168—31no—
219C2×#168—31no—
220C8×D5—122no—
221#556—151no—
222#547—51no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—31no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5—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—42no—
245C3×Dic5—22no—
246C3×Dic5—41no—
247C5×Dic3—41no—
248C5×Dic3—41no—
249C3×#41—104no—
250C3×#41—202no—
251C2×C3×Q8C22×D512yes—
252C2×C3×D4—51no—
253C2×C3×D4—51no—
254C2×C3×D4—102no—
255C22×C3×C4—52no—
256C22×C3×C4—102no—
257C22×C3×C4—101no—
258C2×Dic6—101no—
259C2×Dic6C22×D511yescharacteristic
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—51no—
263C3×C4⋊C4—51no—
264C3×C4⋊C4—102no—
265C3×C22⋊C4—52no—
266C3×C22⋊C4—102no—
267C3×C22⋊C4—101no—
268C3×C42C22×D511yescharacteristic
269#217—102no—
270#217—102no—
271#216—42no—
272#214—102no—
273C4⋊Dic3—52no—
274C4⋊Dic3—101no—
275C4⋊Dic3C22×D511yescharacteristic
276Dic3⋊C4—21no—
277Dic3⋊C4—102no—
278C4×Dic3—21no—
279C4×Dic3—102no—
280C2×C3⋊C8—51no—
281C2×C3⋊C8—51no—
282C2×C3⋊C8—202no—
283C2×C3⋊C8C22×D512yes—
284C22×D5—21no—
285C22×D5C2×#6712yes—
286C5×Q8—22no—
287C5×Q8—22no—
288C5×Q8—61no—
289C5×Q8—61no—
290C2×C4×C5—22no—
291C2×C4×C5—61no—
292C2×C4×C5—61no—
293C2×C4×C5C2×#6711yescharacteristic
294C2×C4×C5C2×#6711yescharacteristic
295C2×C4×C5C23×D311yescharacteristic
296C2×Dic5—21no—
297C2×Dic5—62no—
298C2×Dic5C2×#6712yes—
299D20—22no—
300D20—21no—
301D20—44no—
302D20#23712yes—
303C4×D5—22no—
304C4×D5—22no—
305C4×D5—44no—
306C4×D5—42no—
307Dic10—122no—
308C5×C8—62no—
309#168—61no—
310#168—61no—
311C2×#41—52no—
312C2×Q16—32no—
313C2×SD16—151no—
314C22×C8—152no—
315C4⋊Q8—151no—
316C4⋊Q8D3×D511yescharacteristic
317#126—302no—
318#124—301no—
319#123—102no—
320C22⋊Q8—52no—
321C22⋊Q8—152no—
322#121—101no—
323C4×Q8—31no—
324C4×Q8—301no—
325C4×D4—51no—
326C4×D4—51no—
327#117—152no—
328C2×C4⋊C4—101no—
329#107—152no—
330#106—151no—
331C4⋊C8—31no—
332#103—32no—
333#103—151no—
334#103—152no—
335#103—152no—
336#102—151no—
337#102—152no—
338C22⋊C8—152no—
339C4×C8—151no—
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343C3×D5—42no—
344C3×D5—42no—
345C23×C3—52no—
346C23×C3—101no—
347C3×Q8—22no—
348C3×Q8—22no—
349C3×D4—52no—
350C3×D4—101no—
351C3×D4—102no—
352C3×D4—204no—
353C2×C3×C4—22no—
354C2×C3×C4—52no—
355C2×C3×C4—102no—
356C2×C3×C4—102no—
357C2×C3×C4—101no—
358C2×C3×C4—204no—
359C2×C3×C4—202no—
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4D4×D511yescharacteristic
362C2×C3×C4C23×D511yescharacteristic
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—102no—
366Dic6—21no—
367Dic6—21no—
368Dic6—202no—
369C3⋊C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5C22×#6711yescharacteristic
373C2×D5—22no—
374C2×D5—22no—
375C2×D5—22no—
376C2×D5—22no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—21no—
380C4×C5—42no—
381C4×C5—121no—
382C4×C5—121no—
383C4×C5#95012yes—
384C4×C5C2×#23711yescharacteristic
385C4×C5#100411yescharacteristic
386Dic5—22no—
387Dic5—41no—
388Dic5—122no—
389#41—104no—
390#41—202no—
391C2×Q8—31no—
392C2×Q8—301no—
393C2×Q8C2×D3×D512yes—
394C2×D4—51no—
395C2×D4—51no—
396C2×D4—102no—
397C22×C4—52no—
398C22×C4—102no—
399C22×C4—101no—
400Q16—122no—
401SD16—302no—
402C2×C8—32no—
403C2×C8—151no—
404C2×C8—151no—
405C2×C8—602no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—31no—
409C4⋊C4—51no—
410C4⋊C4—51no—
411C4⋊C4—61no—
412C4⋊C4—102no—
413C4⋊C4—152no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C22⋊C4—52no—
417C22⋊C4—102no—
418C22⋊C4—101no—
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×C3—102no—
429C22×C3—201no—
430C22×C3—201no—
431C22×C3C2×D4×D511yescharacteristic
432C3×C4—21no—
433C3×C4—42no—
434C3×C4—102no—
435C3×C4—201no—
436C3×C4#406512yes—
437C3×C4#414411yescharacteristic
438C3×C4D5×#4111yescharacteristic
439Dic3—41no—
440Dic3—41no—
441Dic3—202no—
442C2×C5#580611yescharacteristic
443C2×C5C2×#95011yescharacteristic
444C2×C5#583811yescharacteristic
445D5—42no—
446D5—42no—
447C23—52no—
448C23—101no—
449Q8—22no—
450Q8—22no—
451Q8—61no—
452Q8—61no—
453Q8—602no—
454D4—52no—
455D4—101no—
456D4—102no—
457D4—204no—
458C2×C4—22no—
459C2×C4—52no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—101no—
465C2×C4—204no—
466C2×C4—202no—
467C2×C4—302no—
468C2×C4D5×#6711yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—301no—
473C8—301no—
474C2×C3—202no—
475C2×C3—202no—
476C2×C3#6594611yescharacteristic
477C2×C3C2×#406511yescharacteristic
478C2×C3#6611311yescharacteristic
479C5#8351011yescharacteristic, complemented, Sylow
480C22—102no—
481C22—102no—
482C22—102no—
483C22—102no—
484C22—201no—
485C22—201no—
486C22C2×D5×#6711yescharacteristic
487C4—21no—
488C4—42no—
489C4—102no—
490C4—121no—
491C4—121no—
492C4—201no—
493C4—602no—
494C4#9151612yes—
495C4D5×#23711yescharacteristic
496C4#9202511yescharacteristic
497C3#1061222311yescharacteristic, complemented, Sylow
498C2—202no—
499C2—202no—
500C2#1175493011yescharacteristic
501C2#1175510211yescharacteristic
502C2C2×#9151611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC3×#66060C2
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
2. #11752507C2semidirect
3. #11751180C2semidirect
4. C5×#5090C2semidirect
5. #11749366C2semidirect
6. #11749294C2semidirect
7. #11749209C2semidirect
8. #11749207C2semidirect
9. C4×#6655C2semidirect
10. #11746996C2semidirect
11. #11746889C2semidirect
93. #5090D5semidirect
424. C3×C5#3302semidirect
479. C5#83510semidirect
497. C3#10612223semidirect

Maximal subgroups

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

subgroupindex
C3×#660602
#117525072
#117511802
C5×#50902
#117493662
#117492942
#117492092
#117492072
C4×#66552
#117469962
#117468892
#106122233
#835105