Finite Group Databasebeta

← #14471952

Subgroups — #14471952

Order 1920.

784 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
1Q8×Dic30C211yesmaximal, characteristic, complemented
2#11752554C211yesmaximal, characteristic
3C4×C5×#215C211yesmaximal, characteristic, complemented
4C3×#65316C211yesmaximal, characteristic, complemented
5#11749346C212yesmaximal, complemented
6#11749239C212yesmaximal, complemented
7#11747407C212yesmaximal, complemented
8#11747255C212yesmaximal, complemented
9#11746890C211yesmaximal, characteristic, complemented
10#11746883C211yesmaximal, characteristic, complemented
11#11746855C211yesmaximal, characteristic, complemented
12#10611353—31nomaximal, Hall
13C2×#6765—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15Q8×Dic15C2212yes—
16#91777—22no—
17#91777C2212yes—
18#91758—21no—
19#91758C2211yescharacteristic
20C4×Dic30—21no—
21C4×Dic30C2211yescharacteristic
22C2×C5×#215C2211yescharacteristic
23C4×C5×D12C2211yescharacteristic
24C2×C3×#688C2212yes—
25C3×#4020C2211yescharacteristic
26#91463C2212yes—
27#91456—21no—
28#91434C2212yes—
29#91408—22no—
30C5×#835C2211yescharacteristic
31C5×#809C2211yescharacteristic
32C5×#808C2211yescharacteristic
33C4×C5×C3⋊C8C2211yescharacteristic
34C3×#3941C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90985C2212yes—
37#90983C2212yes—
38#90967C2212yes—
39#90965C2212yes—
40#90965C2212yes—
41#90951C2212yes—
42#80369—51nomaximal, Hall
43Q8×Dic10—31no—
44#65887—31no—
45C4×C5×SD16—31no—
46#65452—32no—
47#65316D311yescharacteristic, complemented
48#65297—31no—
49#65159—32no—
50#65077—32no—
51#65049—32no—
52#64983—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×Dic30—21no—
56C2×Dic30—22no—
57C2×Dic30D411yescharacteristic
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C3×D20—21no—
61C2×C3×D20—21no—
62C2×C3×D20C2312yes—
63C2×#1201—22no—
64C2×#1201—22no—
65C2×D5×Dic3—22no—
66#6765—44no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C42×C5—21no—
70C3×C42×C5C2311yescharacteristic
71C4⋊Dic15—21no—
72C4⋊Dic15—22no—
73C4⋊Dic15D411yescharacteristic
74C4⋊Dic15C2312yes—
75#6712—22no—
76#6712D412yes—
77C4×Dic15—22no—
78C4×Dic15C2312yes—
79C5×#215—22no—
80C5×(C2×D3)⋊C4—21no—
81C5×C4⋊Dic3C2311yescharacteristic
82C2×C5×C3⋊C8C2311yescharacteristic
83C2×C5×C3⋊C8C2311yescharacteristic
84C3×#688—24no—
85C2×C3×#168C2312yes—
86#6665—22no—
87#5718—51no—
88Q8×Dic6—51no—
89C3×#460—51no—
90#5163—52no—
91Dic3×SD16—52no—
92#5070—51no—
93C4×#215D511yescharacteristic, complemented
94#4842—51no—
95#4830—51no—
96#4761—52no—
97#4760—52no—
98C2×#709—61no—
99C2×C5×SD16—31no—
100C4×C5×Q8C2×D311yescharacteristic
101C4×C5×D4—31no—
102Q8×Dic5—32no—
103C2×#688C2×D312yes—
104#4086—32no—
105#4076—61no—
106#4039—32no—
107#4034—32no—
108#4034—62no—
109#4030—62no—
110#4020C2×D311yescharacteristic
111#4015—31no—
112#4015—61no—
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×#106—31no—
116C5×#103—31no—
117C5×#102—31no—
118C4×C5×C8—31no—
119#3964—32no—
120#3953—32no—
121#3953—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3941C2×D312yes—
125#3940—32no—
126C4⋊#168C2×D311yescharacteristic
127#3362—151noSylow
128C22×C5×D3—21no—
129C22×C3×D5—22no—
130C3×C5×Q8—21no—
131C3×C5×Q8#4112yescomplemented
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—22no—
138C2×Dic15C2×D412yes—
139C2×Dic15C2×D412yes—
140Dic30—82no—
141Dic30—81no—
142Dic30SD1614yescomplemented
143C2×C5×Dic3—21no—
144C5×D12—21no—
145C5×D12—21no—
146C4×C5×D3—42no—
147C3×D20—22no—
148C3×D20—22no—
149C3×D20—42no—
150C3×D20—81no—
151#1201—44no—
152#1201—82no—
153D5×Dic3—44no—
154C3×#168—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—21no—
157C2×#237—101no—
158C2×C3×SD16—52no—
159C3×#127—51no—
160C3×C4×Q8C2×D511yescharacteristic
161Q8×Dic3—52no—
162C2×#215C2×D511yescharacteristic
163#940—52no—
164#939—102no—
165#938—101no—
166D4×Dic3—52no—
167#888—52no—
168#888—102no—
169C4×D12C2×D511yescharacteristic
170#869—51no—
171#869—101no—
172C4×Dic6—51no—
173C4×Dic6—101no—
174C3×C4⋊C8—51no—
175C3×#102—52no—
176#835C2×D511yescharacteristic
177#832—52no—
178#832—52no—
179#821—52no—
180#817—52no—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809C2×D511yescharacteristic
184#808C2×D511yescharacteristic
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×Q8C22×D311yescharacteristic
187C2×C5×D4—31no—
188C22×C4×C5—61no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191#709—124no—
192C2×D20—21no—
193C2×D20—21no—
194C2×D20C22×D312yes—
195C2×C4×D5—62no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10—61no—
199C5×SD16—62no—
200C2×C5×C8—31no—
201C2×C5×C8—31no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4C22×D311yescharacteristic
205C5×C22⋊C4—61no—
206C42×C5—21no—
207C42×C5C22×D311yescharacteristic
208#688—24no—
209#685—62no—
210C4⋊Dic5—31no—
211C4⋊Dic5—32no—
212C4⋊Dic5—62no—
213C4⋊Dic5—61no—
214#683—32no—
215#683—62no—
216C4×Dic5—32no—
217C4×Dic5—62no—
218C2×#168C22×D312yes—
219Q82—151no—
220#550—151no—
221#486—151no—
222#486—152no—
223#476—152no—
224#476—151no—
225#460—51no—
226#460—152no—
227C8×Q8—151no—
228C4×SD16—31no—
229C4×SD16—152no—
230C22×C3×C5C22×D411yescharacteristic
231C2×C5×D3—41no—
232C2×C5×D3—41no—
233C2×C5×D3—41no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—42no—
237C3×C4×C5—22no—
238C3×C4×C5—21no—
239C3×C4×C5—41no—
240C3×C4×C5C2×SD1612yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C52−1+411yescharacteristic
243Dic15—22no—
244Dic15—42no—
245Dic15C2×SD1614yes—
246C5×Dic3—41no—
247C2×C3×Q8C22×D511yescharacteristic
248C2×C3×D4—52no—
249C2×C3×D4—101no—
250C2×C3×D4—101no—
251C2×#67—102no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—204no—
255C2×D12C22×D511yescharacteristic
256C2×C4×D3—21no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6—101no—
260C3×SD16—104no—
261C2×C3×C8—52no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4C22×D511yescharacteristic
264C3×C42—21no—
265C3×C42C22×D511yescharacteristic
266#217—102no—
267#215—22no—
268(C2×D3)⋊C4—21no—
269C4⋊Dic3—51no—
270C4⋊Dic3—52no—
271C4⋊Dic3—102no—
272C4⋊Dic3—101no—
273C4⋊Dic3C22×D511yescharacteristic
274Dic3⋊C4—52no—
275Dic3⋊C4—102no—
276C4×Dic3—52no—
277C4×Dic3—102no—
278C2×C3⋊C8C22×D511yescharacteristic
279C2×C3⋊C8C22×D511yescharacteristic
280C23×C5—61no—
281C22×D5—22no—
282C5×Q8—21no—
283C5×Q8#23712yescomplemented
284C5×D4—61no—
285C5×D4—61no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—61no—
289C2×C4×C5—122no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—32no—
296C2×Dic5—32no—
297C2×Dic5—62no—
298D20—22no—
299D20—22no—
300D20—42no—
301D20—81no—
302C4×D5—124no—
303Dic10—34no—
304Dic10—242no—
305Dic10—241no—
306C5×C8—61no—
307C5×C8—61no—
308#168—22no—
309C2×#41—301no—
310C2×SD16—31no—
311C2×SD16—52no—
312C4⋊Q8—152no—
313C4⋊Q8—151no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—51no—
317#127—152no—
318#121—302no—
319#121—301no—
320C4×Q8—151no—
321C4×Q8—152no—
322C4×Q8—301no—
323C4×Q8D3×D511yescharacteristic
324C4×D4—31no—
325C4×D4—152no—
326#106—31no—
327#106—152no—
328C4⋊C8—51no—
329C4⋊C8—152no—
330#103—31no—
331#102—31no—
332#102—52no—
333#102—152no—
334#102—152no—
335#102—152no—
336C4×C8—31no—
337C4×C8—152no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341C3×D5—82no—
342C5×D3—81no—
343C23×C3—102no—
344C22×D3—21no—
345C3×Q8—21no—
346C3×Q8#70912yescomplemented
347C3×D4—102no—
348C3×D4—102no—
349C3×D4—202no—
350C3×D4—401no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357#67—402no—
358C2×Dic3—21no—
359C2×Dic3—52no—
360C2×Dic3—52no—
361C2×Dic3—102no—
362C2×Dic3—204no—
363D12—21no—
364D12—21no—
365C4×D3—42no—
366Dic6—54no—
367Dic6—402no—
368Dic6—401no—
369C3×C8—102no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C22×C5—121no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—42no—
377C2×D5—42no—
378C2×D5—42no—
379C4×C5—21no—
380C4×C5—22no—
381C4×C5—41no—
382C4×C5—121no—
383C4×C5D3×SD1612yes—
384C4×C5C2×#23711yescharacteristic
385C4×C5#101011yescharacteristic
386Dic5—34no—
387Dic5—62no—
388Dic5—122no—
389#41—604no—
390C2×Q8—151no—
391C2×Q8—302no—
392C2×Q8—301no—
393C2×Q8C2×D3×D511yescharacteristic
394C2×D4—31no—
395C2×D4—52no—
396C2×D4—101no—
397C2×D4—101no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—61no—
401C22×C4—302no—
402SD16—62no—
403SD16—104no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—52no—
407C4⋊C4—21no—
408C4⋊C4—31no—
409C4⋊C4—152no—
410C4⋊C4—151no—
411C4⋊C4—152no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C2×D3×D511yescharacteristic
416C22⋊C4—61no—
417C22⋊C4—302no—
418C42—21no—
419C42—152no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—202no—
424C22×C3—202no—
425C22×C3—202no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4D5×SD1612yes—
434C3×C4C2×#70911yescharacteristic
435C3×C4#415011yescharacteristic
436Dic3—41no—
437Dic3—54no—
438Dic3—102no—
439Dic3—202no—
440C2×C5—241no—
441C2×C5#559811yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#577411yescharacteristic
444D5—82no—
445C23—61no—
446C23—102no—
447Q8—21no—
448Q8—154no—
449Q8—1201no—
450Q8—1202no—
451Q8#676512yescomplemented
452D4—61no—
453D4—61no—
454D4—102no—
455D4—102no—
456D4—202no—
457D4—401no—
458D4—604no—
459D4—1202no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—61no—
463C2×C4—122no—
464C2×C4—152no—
465C2×C4—152no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—61no—
472C8—61no—
473C8—102no—
474C2×C3—402no—
475C2×C3#6588611yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610311yescharacteristic
478D3—81no—
479C5#8036911yescharacteristic, complemented, Sylow
480C22—121no—
481C22—121no—
482C22—121no—
483C22—202no—
484C22—202no—
485C22—202no—
486C22C2×#679011yescharacteristic
487C4—21no—
488C4—22no—
489C4—41no—
490C4—121no—
491C4—154no—
492C4—302no—
493C4—602no—
494C4#9150512yes—
495C4C2×#676511yescharacteristic
496C4#9200111yescharacteristic
497C3#1061135311yescharacteristic, complemented, Sylow
498C2—241no—
499C2—402no—
500C2#1175436911yescharacteristic
501C2C2×#9150511yescharacteristic
502C2#1175533011yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11752554C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3362
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. Q8×Dic30C2semidirect
3. C4×C5×#215C2semidirect
4. C3×#65316C2semidirect
5. #11749346C2semidirect
6. #11749239C2semidirect
7. #11747407C2semidirect
8. #11747255C2semidirect
9. #11746890C2semidirect
10. #11746883C2semidirect
11. #11746855C2semidirect
47. #65316D3semidirect
93. C4×#215D5semidirect
131. C3×C5×Q8#41semidirect
142. Dic30SD16semidirect
283. C5×Q8#237semidirect
346. C3×Q8#709semidirect
422. C3×C5#3362semidirect
451. Q8#6765semidirect
479. C5#80369semidirect
497. C3#10611353semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic302
#117525542
C4×C5×#2152
C3×#653162
#117493462
#117492392
#117474072
#117472552
#117468902
#117468832
#117468552
#106113533
#803695