Finite Group Databasebeta

← #14301353

Subgroups — #14301353

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65838C211yesmaximal, characteristic, complemented
2C2×#91299C211yesmaximal, characteristic
3C5×#4988C211yesmaximal, characteristic, complemented
4C2×#90977C211yesmaximal, characteristic, complemented
5#11748386C211yesmaximal, characteristic, complemented
6#11746351C211yesmaximal, characteristic, complemented
7#11745974C211yesmaximal, characteristic, complemented
8#10600456—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×(C2×D3)⋊C4—22no—
15C2×C4×C5×Dic3C2211yescharacteristic
16C3×C4×C22⋊D5—22no—
17C3×#4072C2211yescharacteristic
18C3×#4039—21no—
19C3×#4038—21no—
20C3×D5×C4⋊C4—21no—
21C3×#4033—21no—
22C2×#6656—21no—
23#91299—22no—
24#91299C414yescomplemented
25C2×#6652—21no—
26#90977—22no—
27#90966—21no—
28#90966—21no—
29#71667—51nomaximal, Hall
30C2×#4078—31no—
31#65838D311yescharacteristic, complemented
32C5×#390—31no—
33#65504—31no—
34C2×#3937—31no—
35#64750—31no—
36#64743—31no—
37C23×C5×D3—21no—
38C22×C3×C4×C5D412yes—
39C22×C3×C4×C5C2311yescharacteristic
40C22×C5×Dic3—21no—
41C2×C5×D12—21no—
42C2×C5×D12—21no—
43C2×C5×D12—21no—
44C2×C5×D12—21no—
45C2×C5×D12—21no—
46C2×C5×D12C2×C412yescomplemented
47C2×C3×C22⋊D5—21no—
48C3×#709—21no—
49C3×#709—21no—
50C3×#709C2×C412yes—
51C3×#709D412yes—
52C2×C3×D20D411yescharacteristic
53C2×C3×C4×D5—21no—
54C2×C3×C4×D5—22no—
55C2×C3×Dic10D411yescharacteristic
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4—21no—
58#6710—21no—
59#6710—21no—
60#6710—21no—
61#6710C2×C412yescomplemented
62C2×C3⋊#168—21no—
63C2×C3⋊#168—21no—
64C5×(C2×D3)⋊C4—44no—
65C4×C5×Dic3—21no—
66C4×C5×Dic3—21no—
67C3×C22⋊Dic5—21no—
68C3×#685—22no—
69C3×C4⋊Dic5D411yescharacteristic
70C3×C4⋊Dic5D411yescharacteristic
71C3×#683—22no—
72C3×C4×Dic5—22no—
73C3×C4×Dic5—21no—
74#6656—24no—
75#6652—24no—
76C3×#520—51no—
77C2×#949—51no—
78C2×#837—51no—
79#5001—51no—
80#4988D511yescharacteristic, complemented
81#4532—51no—
82#4530—51no—
83C22×C5×D4—31no—
84C2×#709C2×D311yescharacteristic
85C2×C5×C4⋊C4C2×D311yescharacteristic
86C2×C5×C22⋊C4—62no—
87C2×C42×C5—31no—
88C2×#687—61no—
89#4078—34no—
90#4078—62no—
91C2×#686—61no—
92C4×C22⋊D5—22no—
93#4072C2×D311yescharacteristic
94C2×#681—31no—
95C2×#681—31no—
96#4039—21no—
97#4038—21no—
98D5×C4⋊C4—21no—
99#4033—21no—
100#3964—61no—
101#3964—61no—
102#3937—62no—
103#1883—151noSylow
104C23×C3×C5C2×D411yescharacteristic
105C22×C5×D3—22no—
106C22×C5×D3—42no—
107C22×C5×D3—42no—
108C22×C5×D3—41no—
109C22×C5×D3—41no—
110C22×C3×D5—21no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—42no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C5×Dic3—22no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C5×D12—22no—
123C5×D12—22no—
124C5×D12—41no—
125C5×D12—41no—
126C3×C22⋊D5—22no—
127C3×C22⋊D5—22no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5—21no—
130C2×C3×Dic5—21no—
131C3×D20—21no—
132C3×D20C22⋊C412yescomplemented
133C3×C4×D5—22no—
134C3×C4×D5—22no—
135C3×C4×D5—82no—
136C3×Dic10—21no—
137C3×Dic10C22⋊C412yescomplemented
138C3⋊#168—22no—
139C3⋊#168—41no—
140C2×C3×#41—51no—
141C22×D12C2×D511yescharacteristic
142C3×C4×Q8—101no—
143C3×C4×D4—101no—
144C3×C4×D4—102no—
145C3×#117—51no—
146C3×#117—101no—
147C2×C3×C4⋊C4—101no—
148C2×C3×C4⋊C4C2×D511yescharacteristic
149#949—54no—
150#949—102no—
151C2×#215—101no—
152C2×#213—101no—
153C2×(C2×D3)⋊C4—22no—
154C2×C4×Dic3C2×D511yescharacteristic
155C2×#208—51no—
156C2×#208—51no—
157#837—102no—
158#809—101no—
159#809—101no—
160C24×C5—61no—
161C2×C5×D4—32no—
162C2×C5×D4—61no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C2×C5×D4—61no—
167C22×C4×C5—61no—
168C22×C4×C5#6712yes—
169C22×C4×C5C22×D311yescharacteristic
170C2×C22⋊D5—21no—
171#709—21no—
172#709—21no—
173#709C4×D312yes—
174#709D1212yes—
175C2×D20#6711yescharacteristic
176C2×C4×D5—21no—
177C2×C4×D5—22no—
178C2×Dic10#6711yescharacteristic
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C22⋊C4—124no—
182C42×C5—61no—
183C42×C5—61no—
184C22⋊Dic5—21no—
185#687—64no—
186#686—64no—
187#685—22no—
188C4⋊Dic5#6711yescharacteristic
189C4⋊Dic5#6711yescharacteristic
190#683—22no—
191C4×Dic5—22no—
192C4×Dic5—21no—
193#681—32no—
194#681—61no—
195#681—61no—
196#681—61no—
197C2×#168—61no—
198C2×#168—61no—
199C2×AGL(1,ℤ/8)—151no—
200#520—51no—
201C2×#104—151no—
202#418—151no—
203#390—31no—
204#343—151no—
205#339—151no—
206C22×C3×C5—21no—
207C22×C3×C5—21no—
208C22×C3×C5C4×D411yescharacteristic
209C22×C3×C5#12011yescharacteristic
210C22×C3×C5#12111yescharacteristic
211C2×C5×D3—44no—
212C2×C5×D3—42no—
213C2×C5×D3—82no—
214C2×C5×D3—81no—
215C2×C5×D3—81no—
216C2×C3×D5—22no—
217C2×C3×D5—41no—
218C2×C3×D5—41no—
219C3×C4×C5—42no—
220C3×C4×C5C2×C22⋊C411yescharacteristic
221C3×C4×C5C4×D411yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5#12311yescharacteristic
224C3×Dic5—22no—
225C3×Dic5—41no—
226C3×Dic5—41no—
227C5×Dic3—42no—
228C23×D3—21no—
229C3×#41—52no—
230C3×#41—52no—
231C3×#41—101no—
232C3×#41—101no—
233C2×C3×Q8—51no—
234C2×C3×D4—51no—
235C2×C3×D4—101no—
236C22×C3×C4—102no—
237C22×C3×C4—101no—
238C22×C3×C4C22⋊D512yes—
239C22×C3×C4C22×D511yescharacteristic
240C22×Dic3—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12C4×D512yescomplemented
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—51no—
250C3×C4⋊C4—51no—
251C3×C4⋊C4—102no—
252C3×C22⋊C4—102no—
253C3×C22⋊C4—101no—
254C3×C42—102no—
255C3×C42—101no—
256#215—104no—
257#213—104no—
258(C2×D3)⋊C4—44no—
259C4×Dic3—21no—
260C4×Dic3—21no—
261#208—52no—
262#208—101no—
263#208—101no—
264#208—101no—
265C2×C3⋊C8—101no—
266C2×C3⋊C8—101no—
267C23×C5—62no—
268C23×C5—122no—
269C23×C5—122no—
270C23×C5—121no—
271C23×C5—121no—
272C23×C5C2×#6711yescharacteristic
273C22×D5—21no—
274C5×D4—62no—
275C5×D4—62no—
276C5×D4—121no—
277C5×D4—121no—
278C2×C4×C5—22no—
279C2×C4×C5—42no—
280C2×C4×C5—62no—
281C2×C4×C5—121no—
282C2×C4×C5—121no—
283C2×C4×C5C2×C4×D311yescharacteristic
284C2×C4×C5C2×D1211yescharacteristic
285C2×C4×C5#23511yescharacteristic
286C2×C4×C5#23511yescharacteristic
287C2×C4×C5C2×#6711yescharacteristic
288C2×C4×C5C2×#6711yescharacteristic
289C22⋊D5—22no—
290C22⋊D5—22no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294D20—21no—
295D20(C2×D3)⋊C412yescomplemented
296C4×D5—22no—
297C4×D5—22no—
298C4×D5—82no—
299Dic10—21no—
300Dic10(C2×D3)⋊C412yescomplemented
301#168—62no—
302#168—121no—
303C2×#41—51no—
304C22×D4—31no—
305AGL(1,ℤ/8)—154no—
306AGL(1,ℤ/8)—302no—
307C2×SD16—301no—
308C2×D8—301no—
309C2×M16—151no—
310C2×M16—151no—
311C4×Q8—101no—
312C4×D4—101no—
313C4×D4—102no—
314#117—51no—
315#117—101no—
316C2×C4⋊C4—101no—
317C2×C4⋊C4D3×D511yescharacteristic
318C2×C22⋊C4—62no—
319C2×C42—31no—
320#104—302no—
321#102—301no—
322#102—301no—
323C2×C3×C5—21no—
324C2×C3×C5—21no—
325C2×C3×C5#38611yescharacteristic
326C2×C3×C5#45311yescharacteristic
327C2×C3×C5#45411yescharacteristic
328C3×D5—42no—
329C5×D3—82no—
330C23×C3—101no—
331C23×C3C2×C22⋊D511yescharacteristic
332C22×D3—22no—
333C22×D3—42no—
334C22×D3—42no—
335C22×D3—41no—
336C22×D3—41no—
337C3×Q8—52no—
338C3×Q8—101no—
339C3×D4—52no—
340C3×D4—102no—
341C3×D4—102no—
342C3×D4—101no—
343C2×C3×C4—22no—
344C2×C3×C4—42no—
345C2×C3×C4—101no—
346C2×C3×C4—102no—
347C2×C3×C4—102no—
348C2×C3×C4—101no—
349C2×C3×C4—101no—
350C2×C3×C4—402no—
351C2×C3×C4C2×C4×D511yescharacteristic
352C2×C3×C4#70911yescharacteristic
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4#71111yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360D12—22no—
361D12—22no—
362D12—41no—
363D12—41no—
364C3⋊C8—102no—
365C3⋊C8—201no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—124no—
369C22×C5—122no—
370C22×C5—242no—
371C22×C5—241no—
372C22×C5—241no—
373C22×C5C4×#6711yescharacteristic
374C22×C5#93011yescharacteristic
375C22×C5#95311yescharacteristic
376C2×D5—22no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—42no—
380C4×C5—122no—
381C4×C5C2×(C2×D3)⋊C411yescharacteristic
382C4×C5C4×#6711yescharacteristic
383C4×C5#92911yescharacteristic
384C4×C5#93011yescharacteristic
385Dic5—22no—
386Dic5—41no—
387Dic5—41no—
388C24—61no—
389#41—52no—
390#41—52no—
391#41—101no—
392#41—101no—
393C2×Q8—51no—
394C2×D4—32no—
395C2×D4—51no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—101no—
402C22×C4—61no—
403C22×C4—102no—
404C22×C4—101no—
405C22×C4#120112yes—
406C22×C4C2×D3×D511yescharacteristic
407SD16—304no—
408D8—304no—
409M16—152no—
410M16—301no—
411M16—301no—
412M16—301no—
413C2×C8—301no—
414C2×C8—301no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—51no—
418C4⋊C4—51no—
419C4⋊C4—102no—
420C22⋊C4—102no—
421C22⋊C4—101no—
422C22⋊C4—124no—
423C42—61no—
424C42—61no—
425C42—102no—
426C42—101no—
427C3×C5#188311yescharacteristic, complemented, Hall
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—102no—
431C22×C3—201no—
432C22×C3—201no—
433C22×C3C4×C22⋊D511yescharacteristic
434C22×C3#408311yescharacteristic
435C22×C3#408411yescharacteristic
436C2×D3—44no—
437C2×D3—42no—
438C2×D3—82no—
439C2×D3—81no—
440C2×D3—81no—
441C3×C4—42no—
442C3×C4—102no—
443C3×C4—201no—
444C3×C4—201no—
445C3×C4D5×C22⋊C411yescharacteristic
446C3×C4#402711yescharacteristic
447C3×C4#402911yescharacteristic
448C3×C4#403011yescharacteristic
449Dic3—42no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—242no—
453C2×C5#521311yescharacteristic
454C2×C5#524111yescharacteristic
455C2×C5#524511yescharacteristic
456D5—42no—
457C23—62no—
458C23—101no—
459C23—122no—
460C23—122no—
461C23—121no—
462C23—121no—
463C23C2×#120111yescharacteristic
464Q8—52no—
465Q8—101no—
466D4—52no—
467D4—62no—
468D4—62no—
469D4—102no—
470D4—102no—
471D4—101no—
472D4—121no—
473D4—121no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—62no—
477C2×C4—101no—
478C2×C4—102no—
479C2×C4—102no—
480C2×C4—101no—
481C2×C4—101no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—402no—
485C2×C4#677111yescharacteristic
486C2×C4#677211yescharacteristic
487C2×C4C4×D3×D511yescharacteristic
488C2×C4D5×D1211yescharacteristic
489C2×C4D5×#6711yescharacteristic
490C2×C4D5×#6711yescharacteristic
491C8—302no—
492C8—601no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—202no—
496C2×C3#6524511yescharacteristic
497C2×C3#6535111yescharacteristic
498C2×C3#6536611yescharacteristic
499D3—82no—
500C5#7166711yescharacteristic, complemented, Sylow
501C22—21no—
502C22—21no—
503C22—102no—
504C22—124no—
505C22—122no—
506C22—201no—
507C22—201no—
508C22—242no—
509C22—241no—
510C22—241no—
511C22C4×#120111yescharacteristic
512C22#9144911yescharacteristic
513C22#9156311yescharacteristic
514C4—42no—
515C4—102no—
516C4—122no—
517C4—201no—
518C4—201no—
519C4#9144011yescharacteristic
520C4#9144711yescharacteristic
521C4#9144811yescharacteristic
522C4D5×(C2×D3)⋊C411yescharacteristic
523C3#1060045611yescharacteristic, complemented, Sylow
524C2—21no—
525C2—21no—
526C2—202no—
527C2—242no—
528C2#1174890511yescharacteristic
529C2#1174913711yescharacteristic
530C2#1174938311yescharacteristic
subgroupG/H
centerC22#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#91299C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1883
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65838C2semidirect
3. C5×#4988C2semidirect
4. C2×#90977C2semidirect
5. #11748386C2semidirect
6. #11746351C2semidirect
7. #11745974C2semidirect
24. #91299C4semidirect
31. #65838D3semidirect
46. C2×C5×D12C2×C4semidirect
61. #6710C2×C4semidirect
80. #4988D5semidirect
132. C3×D20C22⋊C4semidirect
137. C3×Dic10C22⋊C4semidirect
246. C2×D12C4×D5semidirect
295. D20(C2×D3)⋊C4semidirect
300. Dic10(C2×D3)⋊C4semidirect
427. C3×C5#1883semidirect
500. C5#71667semidirect
523. C3#10600456semidirect

Maximal subgroups

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

subgroupindex
C3×#658382
C2×#912992
C5×#49882
C2×#909772
#117483862
#117463512
#117459742
#106004563
#716675