Finite Group Databasebeta

← #14282838

Subgroups — #14282838

Order 1920.

608 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65940C211yesmaximal, characteristic
2#11748702C211yesmaximal, characteristic, complemented
3D5×#830C211yesmaximal, characteristic, complemented
4#11746358C211yesmaximal, characteristic, complemented
5C5×#4537C211yesmaximal, characteristic, complemented
6#11745961C211yesmaximal, characteristic, complemented
7#11745960C211yesmaximal, characteristic, complemented
8#10599094—31nomaximal, Hall
9C2×C3×#711C411yescharacteristic, complemented
10C22×C3×C4×D5C2211yescharacteristic
11C3×C5×#121C2211yescharacteristic
12C3×#4084C411yescharacteristic, complemented
13C3×#4083—21no—
14C3×D4×Dic5—21no—
15C3×#4070C2211yescharacteristic
16C3×#4043C411yescharacteristic, complemented
17C3×#4038C411yescharacteristic, complemented
18C3×#4029—21no—
19C3×#4027—21no—
20C2×#6665—21no—
21C2×Dic3×Dic5—21no—
22C2×D5×C3⋊C8—21no—
23#91115C2211yescharacteristic
24#91114C2211yescharacteristic
25C5×C3⋊#95C2211yescharacteristic
26C5×#830C2211yescharacteristic
27#90955—21no—
28#71707—51nomaximal, Hall
29#65940D311yescharacteristic
30D5×C22⋊C8—31no—
31#64955—31no—
32C5×#327—31no—
33#64757—31no—
34#64687—31no—
35#64672—31no—
36C23×C3×D5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2×C411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C22×C5×Dic3—21no—
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5D411yescharacteristic
46C3×#711—42no—
47C2×C3×C4×D5—42no—
48C2×C3×C4×D5C2×C411yescharacteristic
49C2×C3×C4×D5C2×C411yescharacteristic
50C2×C3×C4×D5D411yescharacteristic
51C2×C3×C4×D5D411yescharacteristic
52C2×C3×Dic10C2×C411yescharacteristic
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C2×C3⋊#168—21no—
56C2×C5×C3⋊C8—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—21no—
59C3×#685—21no—
60C3×#685—21no—
61C3×C4⋊Dic5—21no—
62C3×C4⋊Dic5C2×C411yescharacteristic
63C3×#683—21no—
64C3×C4×Dic5—21no—
65#6665—24no—
66Dic3×Dic5—42no—
67D5×C3⋊C8—42no—
68C3×#525—51no—
69C4×#217—51no—
70C2×#830—51no—
71#4538—51no—
72#4538—51no—
73#4537—51no—
74#4537D511yescharacteristic, complemented
75C2×#711Dic311yescharacteristic, complemented
76C22×C4×D5C2×D311yescharacteristic
77C5×#121C2×D311yescharacteristic
78#4084Dic311yescharacteristic, complemented
79#4083—21no—
80D4×Dic5—21no—
81C2×#685—61no—
82#4070C2×D311yescharacteristic
83C2×C4×Dic5—61no—
84C2×C8×D5—61no—
85#4043Dic311yescharacteristic, complemented
86#4038Dic311yescharacteristic, complemented
87#4029—21no—
88#4027—21no—
89C5×C22⋊C8—31no—
90C5×#95—31no—
91#3963—31no—
92C22⋊#168—31no—
93#3952—61no—
94#1501—151noSylow
95C23×C3×C5—21no—
96C23×C3×C5C2×D411yescharacteristic
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—22no—
100C22×C3×D5—41no—
101C22×C3×D5C22⋊C411yescharacteristic
102C22×C3×D5C22⋊C411yescharacteristic
103C3×C5×D4—41no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3—41no—
116C3×C22⋊D5—42no—
117C3×C22⋊D5—42no—
118C2×C3×Dic5—22no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—42no—
122C2×C3×Dic5C22⋊C411yescharacteristic
123C2×C3×Dic5C22⋊C411yescharacteristic
124C3×C4×D5—22no—
125C3×C4×D5—22no—
126C3×C4×D5—41no—
127C3×C4×D5—41no—
128C3×Dic10—41no—
129C3⋊#168—41no—
130C5×C3⋊C8—41no—
131C2×C3×#41—51no—
132C23×C3×C4—51no—
133C3×#123—101no—
134C3×C22⋊Q8—51no—
135C3×C22⋊Q8—51no—
136C3×#121—51no—
137C3×#121C2×D511yescharacteristic
138C3×#120—101no—
139C3×C4×D4—101no—
140C3×C4×D4—101no—
141C3×#117—51no—
142C2×#217—101no—
143C2×C4×Dic3—101no—
144C22×C3⋊C8—101no—
145C3⋊#95—51no—
146C3⋊#95C2×D511yescharacteristic
147#830—51no—
148#830—101no—
149#830C2×D511yescharacteristic
150C23×D5#6711yescharacteristic
151C2×C5×D4—21no—
152C2×C5×D4C2×Dic311yescharacteristic
153C22×C4×C5—61no—
154C22×C4×C5C22×D311yescharacteristic
155C2×C22⋊D5—21no—
156C2×C22⋊D5—21no—
157C22×Dic5—21no—
158C22×Dic5—61no—
159C22×Dic5#6711yescharacteristic
160#711—42no—
161C2×C4×D5—42no—
162C2×C4×D5C2×Dic311yescharacteristic
163C2×C4×D5C2×Dic311yescharacteristic
164C2×C4×D5#6711yescharacteristic
165C2×C4×D5#6711yescharacteristic
166C2×Dic10C2×Dic311yescharacteristic
167C2×C5×C8—61no—
168C5×C4⋊C4C2×Dic311yescharacteristic
169C5×C22⋊C4—21no—
170C22⋊Dic5—21no—
171C22⋊Dic5—21no—
172#685—21no—
173#685—21no—
174#685—64no—
175C4⋊Dic5—21no—
176C4⋊Dic5C2×Dic311yescharacteristic
177#683—21no—
178C4×Dic5—21no—
179C4×Dic5—122no—
180C2×#168—61no—
181C8×D5—122no—
182#525—51no—
183C2×C22⋊C8—151no—
184C4×C22⋊C4—151no—
185#328—151no—
186#328—151no—
187#327—31no—
188#327—151no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5—41no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5#13511yescharacteristic
196C22×C3×C5#13511yescharacteristic
197C2×C3×D5—21no—
198C2×C3×D5—21no—
199C2×C3×D5—21no—
200C2×C3×D5—21no—
201C2×C3×D5—21no—
202C2×C3×D5—42no—
203C2×C3×D5—42no—
204C2×C3×D5#10412yes—
205C3×C4×C5—21no—
206C3×C4×C5—21no—
207C3×C4×C5—41no—
208Dic15—42no—
209C3×Dic5—21no—
210C3×Dic5—41no—
211C3×Dic5—41no—
212C3×Dic5#9912yes—
213C5×Dic3—42no—
214C24×C3—51no—
215C3×#41—202no—
216C2×C3×Q8—51no—
217C2×C3×D4—21no—
218C2×C3×D4—101no—
219C2×C3×D4—101no—
220C2×C3×D4C4×D511yescharacteristic
221C22×C3×C4—51no—
222C22×C3×C4—51no—
223C22×C3×C4—51no—
224C22×C3×C4—51no—
225C22×C3×C4—51no—
226C22×C3×C4—101no—
227C22×C3×C4—202no—
228C22×C3×C4C22×D511yescharacteristic
229C22×Dic3—21no—
230C22×Dic3—101no—
231C3×C4⋊C4—51no—
232C3×C4⋊C4—101no—
233C3×C4⋊C4—101no—
234C3×C4⋊C4C4×D511yescharacteristic
235C3×C22⋊C4—21no—
236C3×C22⋊C4—101no—
237C3×C22⋊C4—101no—
238C3×C22⋊C4—101no—
239C3×C22⋊C4—101no—
240C3×C42—101no—
241#217—104no—
242C4×Dic3—202no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—101no—
245C2×C3⋊C8—202no—
246C23×C5—21no—
247C23×C5C2×#6711yescharacteristic
248C22×D5—21no—
249C22×D5—21no—
250C22×D5—22no—
251C22×D5—41no—
252C22×D5#21711yescharacteristic
253C22×D5#21711yescharacteristic
254C5×D4—41no—
255C5×D4—41no—
256C5×D4—41no—
257C2×C4×C5—21no—
258C2×C4×C5—41no—
259C2×C4×C5—62no—
260C2×C4×C5—121no—
261C2×C4×C5—121no—
262C2×C4×C5C22×Dic311yescharacteristic
263C2×C4×C5C2×#6711yescharacteristic
264C22⋊D5—42no—
265C22⋊D5—42no—
266C2×Dic5—22no—
267C2×Dic5—21no—
268C2×Dic5—21no—
269C2×Dic5—42no—
270C2×Dic5—62no—
271C2×Dic5—121no—
272C2×Dic5—121no—
273C2×Dic5#21711yescharacteristic
274C2×Dic5#21711yescharacteristic
275C4×D5—22no—
276C4×D5—22no—
277C4×D5—41no—
278C4×D5—41no—
279Dic10—41no—
280C5×C8—121no—
281#168—121no—
282C2×#41—51no—
283C23×C4—51no—
284C22×C8—301no—
285#123—101no—
286C22⋊Q8—51no—
287C22⋊Q8—51no—
288#121—51no—
289#121D3×D511yescharacteristic
290#120—101no—
291C4×D4—101no—
292C4×D4—101no—
293#117—51no—
294C2×C22⋊C4—301no—
295C2×C42—301no—
296C22⋊C8—31no—
297C22⋊C8—151no—
298C22⋊C8—301no—
299#95—31no—
300#95—151no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—81no—
304C2×C3×C5C2×#9911yescharacteristic
305C2×C3×C5#41611yescharacteristic
306C2×C3×C5C2×#10411yescharacteristic
307C3×D5—22no—
308C3×D5—41no—
309C23×C3—21no—
310C23×C3—51no—
311C23×C3—51no—
312C23×C3—102no—
313C23×C3—101no—
314C23×C3—101no—
315C23×C3—201no—
316C23×C3D4×D511yescharacteristic
317C3×Q8—201no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—41no—
321C3×D4—202no—
322C3×D4—202no—
323C2×C3×C4—21no—
324C2×C3×C4—41no—
325C2×C3×C4—51no—
326C2×C3×C4—51no—
327C2×C3×C4—102no—
328C2×C3×C4—102no—
329C2×C3×C4—102no—
330C2×C3×C4—101no—
331C2×C3×C4—101no—
332C2×C3×C4—201no—
333C2×C3×C4—201no—
334C2×C3×C4—202no—
335C2×C3×C4C2×C4×D511yescharacteristic
336C2×C3×C4D4×D511yescharacteristic
337C2×Dic3—22no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—102no—
341C2×Dic3—201no—
342C2×Dic3—201no—
343C3⋊C8—41no—
344C3⋊C8—201no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—41no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5#95011yescharacteristic
351C22×C5#95011yescharacteristic
352C22×C5C2×#21711yescharacteristic
353C2×D5—21no—
354C2×D5—21no—
355C2×D5—21no—
356C2×D5—21no—
357C2×D5—21no—
358C2×D5—42no—
359C2×D5—42no—
360C2×D5#83712yes—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—41no—
364C4×C5—122no—
365Dic5—21no—
366Dic5—41no—
367Dic5—41no—
368Dic5—122no—
369Dic5#83412yes—
370C24—51no—
371#41—202no—
372C2×Q8—51no—
373C2×D4—21no—
374C2×D4—101no—
375C2×D4—101no—
376C2×D4D5×Dic311yescharacteristic
377C22×C4—51no—
378C22×C4—51no—
379C22×C4—51no—
380C22×C4—51no—
381C22×C4—51no—
382C22×C4—61no—
383C22×C4—101no—
384C22×C4—202no—
385C22×C4—301no—
386C22×C4C2×D3×D511yescharacteristic
387C2×C8—61no—
388C2×C8—301no—
389C2×C8—602no—
390C4⋊C4—51no—
391C4⋊C4—101no—
392C4⋊C4—101no—
393C4⋊C4D5×Dic311yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—101no—
396C22⋊C4—101no—
397C22⋊C4—101no—
398C22⋊C4—101no—
399C22⋊C4—304no—
400C42—101no—
401C42—602no—
402C3×C5#150111yescharacteristic, complemented, Hall
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—52no—
409C22×C3—101no—
410C22×C3—101no—
411C22×C3—101no—
412C22×C3—101no—
413C22×C3—101no—
414C22×C3—202no—
415C22×C3—202no—
416C22×C3D5×C22⋊C411yescharacteristic
417C22×C3#405811yescharacteristic
418C22×C3#406211yescharacteristic
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—52no—
423C3×C4—101no—
424C3×C4—201no—
425C3×C4—201no—
426Dic3—42no—
427Dic3—202no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—81no—
431C2×C5C2×#83411yescharacteristic
432C2×C5#523311yescharacteristic
433C2×C5C2×#83711yescharacteristic
434D5—22no—
435D5—41no—
436C23—21no—
437C23—51no—
438C23—51no—
439C23—102no—
440C23—101no—
441C23—101no—
442C23—201no—
443C23D5×#6711yescharacteristic
444Q8—201no—
445D4—41no—
446D4—41no—
447D4—41no—
448D4—202no—
449D4—202no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—51no—
453C2×C4—51no—
454C2×C4—62no—
455C2×C4—102no—
456C2×C4—102no—
457C2×C4—102no—
458C2×C4—101no—
459C2×C4—101no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—201no—
463C2×C4—201no—
464C2×C4—202no—
465C2×C4—302no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4C2×D5×Dic311yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C8—121no—
471C8—601no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—81no—
475C2×C3—102no—
476C2×C3—201no—
477C2×C3D5×#9911yescharacteristic
478C2×C3#6506111yescharacteristic
479C2×C3D5×#10411yescharacteristic
480C5#7170711yescharacteristic, complemented, Sylow
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—52no—
487C22—101no—
488C22—101no—
489C22—101no—
490C22—101no—
491C22—101no—
492C22—202no—
493C22—202no—
494C22#9149011yescharacteristic
495C22#9149211yescharacteristic
496C22D5×#21711yescharacteristic
497C4—21no—
498C4—21no—
499C4—41no—
500C4—52no—
501C4—101no—
502C4—122no—
503C4—201no—
504C4—201no—
505C4—602no—
506C3#1059909411yescharacteristic, complemented, Sylow
507C2—21no—
508C2—21no—
509C2—81no—
510C2—102no—
511C2—201no—
512C2#1174896111yescharacteristic
513C2D5×#83411yescharacteristic
514C2D5×#83711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#65940C2
cosocleC22×C3×C4×C5C23
hypercenter#121D3×D5
hypocenterC3×C5#1501
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11748702C2semidirect
3. D5×#830C2semidirect
4. #11746358C2semidirect
5. C5×#4537C2semidirect
6. #11745961C2semidirect
7. #11745960C2semidirect
9. C2×C3×#711C4semidirect
12. C3×#4084C4semidirect
16. C3×#4043C4semidirect
17. C3×#4038C4semidirect
74. #4537D5semidirect
75. C2×#711Dic3semidirect
78. #4084Dic3semidirect
85. #4043Dic3semidirect
86. #4038Dic3semidirect
402. C3×C5#1501semidirect
480. C5#71707semidirect
506. C3#10599094semidirect

Maximal subgroups

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

subgroupindex
C3×#659402
#117487022
D5×#8302
#117463582
C5×#45372
#117459612
#117459602
#105990943
#717075