Finite Group Databasebeta

← #14282847

Subgroups — #14282847

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
1#11754526C211yesmaximal, characteristic
2C3×D5×C22⋊C8C211yesmaximal, characteristic, complemented
3#11748702C211yesmaximal, characteristic, complemented
4#11746288C211yesmaximal, characteristic, complemented
5C5×#4470C211yesmaximal, characteristic, complemented
6#11745965C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic, complemented
8#10599094—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×#6772C411yescharacteristic, complemented
11#91813C2211yescharacteristic
12C5×#930C2211yescharacteristic
13C2×C3×C8×D5—21no—
14#91563—21no—
15Dic5×#67—21no—
16C2×#6665—21no—
17C2×Dic3×Dic5—21no—
18#91449C411yescharacteristic, complemented
19#91447—21no—
20#91440—21no—
21#91360C411yescharacteristic, complemented
22#91358C411yescharacteristic, complemented
23C3×C5×C22⋊C8C2211yescharacteristic
24#91115C2211yescharacteristic
25C5×C3⋊#95C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27C3×#3952—21no—
28#69942—51nomaximal, Hall
29#65940—31no—
30D5×C22⋊C8D311yescharacteristic, complemented
31#64955—31no—
32C5×#327—31no—
33#64757—31no—
34#64687—31no—
35#64672—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×Dic30C2×C411yescharacteristic
40C2×C5×#67—21no—
41C22×C5×Dic3—21no—
42C2×C5×D12C2×C411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×C3×C4×D5—42no—
45C2×C3×C4×D5C2×C411yescharacteristic
46C2×C3×C4×D5C2×C411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×#1201—21no—
50C2×#1201—21no—
51C2×D3×Dic5—21no—
52#6772—42no—
53C2×C3×C5×C8—21no—
54#6719—21no—
55C4⋊Dic15C2×C411yescharacteristic
56#6712—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×C4⋊Dic3C2×C411yescharacteristic
59C2×C3×#168—21no—
60C3×C8×D5—42no—
61Dic3⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63#6665—24no—
64#6665—21no—
65#6665—21no—
66Dic3×Dic5—21no—
67Dic3×Dic5—42no—
68#5791—51no—
69C2×C3×C22⋊C8—51no—
70C4×#217—51no—
71#4470—51no—
72#4470D511yescharacteristic, complemented
73#4467—51no—
74#4467—51no—
75C2×#711—31no—
76C22×C4×D5C2×D311yescharacteristic
77C5×#121—31no—
78#4084—31no—
79#4083—61no—
80D4×Dic5—61no—
81C2×#685—61no—
82#4070—31no—
83C2×C4×Dic5—61no—
84C2×C8×D5—21no—
85#4043—31no—
86#4038—31no—
87#4029—61no—
88#4027—61no—
89C5×C22⋊C8C2×D311yescharacteristic
90C5×#95—31no—
91#3963—31no—
92C22⋊#168C2×D311yescharacteristic
93#3952—21no—
94#1501—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—21no—
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—22no—
100C22×C3×D5—41no—
101C22×C3×D5C22⋊C411yescharacteristic
102C22×C3×D5C22⋊C411yescharacteristic
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×Dic15—22no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—41no—
110C2×Dic15—41no—
111Dic30—41no—
112C5×#67—41no—
113C5×#67—41no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3—41no—
118C5×D12—41no—
119C2×C3×Dic5—22no—
120C2×C3×Dic5C22⋊C411yescharacteristic
121C2×C3×Dic5C22⋊C411yescharacteristic
122C3×C4×D5—22no—
123C3×C4×D5—22no—
124C3×C4×D5—41no—
125C3×C4×D5—41no—
126#1201—42no—
127#1201—42no—
128D3×Dic5—42no—
129C3×C5×C8—41no—
130C3×#168—41no—
131C23×C3×C4—51no—
132C2×#235—51no—
133C22×C3×C8—101no—
134#953—101no—
135C2×#217—101no—
136#930—51no—
137#930C2×D511yescharacteristic
138#929—101no—
139C4×#67—101no—
140C4×#67—101no—
141#926—51no—
142#924—51no—
143#924—51no—
144C2×C4×Dic3—101no—
145C3×C22⋊C8—51no—
146C3×C22⋊C8—101no—
147C3×C22⋊C8C2×D511yescharacteristic
148C3⋊#95—51no—
149C3⋊#95C2×D511yescharacteristic
150C23×D5D1211yescharacteristic
151C2×C5×D4—31no—
152C2×C5×D4—61no—
153C22×C4×C5—61no—
154C22×C4×C5C22×D311yescharacteristic
155C2×C22⋊D5—61no—
156C2×C22⋊D5—61no—
157C22×Dic5—61no—
158C22×Dic5—61no—
159C22×Dic5D1211yescharacteristic
160#711—122no—
161C2×C4×D5—42no—
162C2×C4×D5C4×D311yescharacteristic
163C2×C4×D5C4×D311yescharacteristic
164C2×C4×D5#6711yescharacteristic
165C2×C4×D5#6711yescharacteristic
166C2×Dic10—31no—
167C2×C5×C8—21no—
168C5×C4⋊C4—31no—
169C5×C22⋊C4—61no—
170C22⋊Dic5—61no—
171C22⋊Dic5—61no—
172#685—64no—
173#685—61no—
174#685—61no—
175C4⋊Dic5—31no—
176C4⋊Dic5—61no—
177#683—61no—
178C4×Dic5—61no—
179C4×Dic5—122no—
180C2×#168—21no—
181C8×D5—42no—
182#525—151no—
183C2×C22⋊C8—51no—
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×C5C2×C22⋊C411yescharacteristic
192C22×C3×C5#13511yescharacteristic
193C22×C3×C5#13511yescharacteristic
194C2×C5×D3—41no—
195C2×C5×D3—41no—
196C2×C5×D3—41no—
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—
207Dic15—42no—
208Dic15—41no—
209Dic15—41no—
210C3×Dic5—21no—
211C3×Dic5#9912yes—
212C5×Dic3—42no—
213C5×Dic3—41no—
214C24×C3—51no—
215C22×C3×C4—51no—
216C22×C3×C4—51no—
217C22×C3×C4—51no—
218C22×C3×C4—51no—
219C22×C3×C4—51no—
220C22×C3×C4—202no—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—21no—
223C2×#67—101no—
224C2×#67—101no—
225C22×Dic3—21no—
226C22×Dic3—101no—
227#235—202no—
228C2×D12C4×D511yescharacteristic
229C2×C4×D3—101no—
230C2×Dic6—51no—
231C2×C3×C8—21no—
232C2×C3×C8—101no—
233C2×C3×C8—202no—
234#217—101no—
235#217—101no—
236#217—104no—
237#217—101no—
238(C2×D3)⋊C4—21no—
239(C2×D3)⋊C4—101no—
240C4⋊Dic3—51no—
241C4⋊Dic3C4×D511yescharacteristic
242Dic3⋊C4—101no—
243Dic3⋊C4—101no—
244C4×Dic3—101no—
245C4×Dic3—202no—
246C23×C5—61no—
247C23×C5C2×D1211yescharacteristic
248C22×D5—21no—
249C22×D5—21no—
250C22×D5—22no—
251C22×D5—41no—
252C22×D5(C2×D3)⋊C411yescharacteristic
253C22×D5(C2×D3)⋊C411yescharacteristic
254C5×D4—121no—
255C5×D4—121no—
256C5×D4—121no—
257C2×C4×C5—41no—
258C2×C4×C5—62no—
259C2×C4×C5—61no—
260C2×C4×C5—121no—
261C2×C4×C5—121no—
262C2×C4×C5C2×C4×D311yescharacteristic
263C2×C4×C5C2×#6711yescharacteristic
264C22⋊D5—122no—
265C22⋊D5—122no—
266C2×Dic5—22no—
267C2×Dic5—62no—
268C2×Dic5—61no—
269C2×Dic5—61no—
270C2×Dic5—121no—
271C2×Dic5—121no—
272C2×Dic5—122no—
273C2×Dic5(C2×D3)⋊C411yescharacteristic
274C2×Dic5(C2×D3)⋊C411yescharacteristic
275C4×D5—22no—
276C4×D5—22no—
277C4×D5—41no—
278C4×D5—41no—
279Dic10—121no—
280C5×C8—41no—
281#168—41no—
282C2×#41—151no—
283C23×C4—51no—
284C22×C8—101no—
285#123—301no—
286C22⋊Q8—151no—
287C22⋊Q8—151no—
288#121—31no—
289#121—151no—
290#120—301no—
291C4×D4—301no—
292C4×D4—301no—
293#117—151no—
294C2×C22⋊C4—301no—
295C2×C42—301no—
296C22⋊C8—51no—
297C22⋊C8—101no—
298C22⋊C8D3×D511yescharacteristic
299#95—31no—
300#95—151no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5C2×#9911yescharacteristic
304C2×C3×C5#41611yescharacteristic
305C2×C3×C5C2×#10411yescharacteristic
306C3×D5—22no—
307C3×D5—41no—
308C5×D3—81no—
309C23×C3—51no—
310C23×C3—51no—
311C23×C3—102no—
312C23×C3—101no—
313C23×C3—101no—
314C23×C3—201no—
315C23×C3D4×D511yescharacteristic
316C22×D3—21no—
317C2×C3×C4—41no—
318C2×C3×C4—51no—
319C2×C3×C4—51no—
320C2×C3×C4—102no—
321C2×C3×C4—102no—
322C2×C3×C4—102no—
323C2×C3×C4—201no—
324C2×C3×C4—201no—
325C2×C3×C4C2×C4×D511yescharacteristic
326C2×C3×C4D4×D511yescharacteristic
327#67—41no—
328#67—41no—
329#67—202no—
330#67—202no—
331C2×Dic3—22no—
332C2×Dic3—21no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—102no—
336C2×Dic3—101no—
337C2×Dic3—101no—
338C2×Dic3—201no—
339C2×Dic3—201no—
340D12—41no—
341C4×D3—202no—
342Dic6—201no—
343C3×C8—41no—
344C3×C8—201no—
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—121no—
348C22×C5—121no—
349C22×C5—121no—
350C22×C5#90411yescharacteristic
351C22×C5#90411yescharacteristic
352C22×C5C2×(C2×D3)⋊C411yescharacteristic
353C2×D5—21no—
354C2×D5—21no—
355C2×D5—21no—
356C2×D5—21no—
357C2×D5—21no—
358C2×D5—42no—
359C2×D5—42no—
360C2×D5#82512yes—
361C4×C5—21no—
362C4×C5—21no—
363C4×C5—122no—
364C4×C5—121no—
365Dic5—21no—
366Dic5—122no—
367Dic5—121no—
368Dic5—121no—
369Dic5#80612yes—
370C24—51no—
371#41—602no—
372C2×Q8—151no—
373C2×D4—31no—
374C2×D4—61no—
375C2×D4—301no—
376C2×D4—301no—
377C22×C4—51no—
378C22×C4—51no—
379C22×C4—51no—
380C22×C4—51no—
381C22×C4—51no—
382C22×C4—61no—
383C22×C4—202no—
384C22×C4—301no—
385C22×C4—301no—
386C22×C4C2×D3×D511yescharacteristic
387C2×C8—21no—
388C2×C8—101no—
389C2×C8—202no—
390C4⋊C4—31no—
391C4⋊C4—151no—
392C4⋊C4—301no—
393C4⋊C4—301no—
394C22⋊C4—61no—
395C22⋊C4—301no—
396C22⋊C4—301no—
397C22⋊C4—301no—
398C22⋊C4—304no—
399C22⋊C4—301no—
400C42—301no—
401C42—602no—
402C3×C5#150111yescharacteristic, complemented, Hall
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—52no—
406C22×C3—101no—
407C22×C3—101no—
408C22×C3—101no—
409C22×C3—101no—
410C22×C3—101no—
411C22×C3—202no—
412C22×C3—202no—
413C22×C3D5×C22⋊C411yescharacteristic
414C22×C3#405811yescharacteristic
415C22×C3#406211yescharacteristic
416C2×D3—41no—
417C2×D3—41no—
418C2×D3—41no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—52no—
422C3×C4—101no—
423Dic3—42no—
424Dic3—41no—
425Dic3—202no—
426Dic3—201no—
427Dic3—201no—
428C2×C5—21no—
429C2×C5—21no—
430C2×C5—241no—
431C2×C5C2×#80611yescharacteristic
432C2×C5#511311yescharacteristic
433C2×C5C2×#82511yescharacteristic
434D5—22no—
435D5—41no—
436C23—51no—
437C23—51no—
438C23—61no—
439C23—102no—
440C23—101no—
441C23—101no—
442C23—201no—
443C23D5×D1211yescharacteristic
444Q8—601no—
445D4—121no—
446D4—121no—
447D4—121no—
448D4—602no—
449D4—602no—
450C2×C4—41no—
451C2×C4—51no—
452C2×C4—51no—
453C2×C4—62no—
454C2×C4—61no—
455C2×C4—102no—
456C2×C4—102no—
457C2×C4—102no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—201no—
461C2×C4—201no—
462C2×C4—302no—
463C2×C4—301no—
464C2×C4—301no—
465C2×C4—602no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4C4×D3×D511yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C8—41no—
471C8—201no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—102no—
475C2×C3—201no—
476C2×C3D5×#9911yescharacteristic
477C2×C3#6506111yescharacteristic
478C2×C3D5×#10411yescharacteristic
479D3—81no—
480C5#6994211yescharacteristic, complemented, Sylow
481C22—21no—
482C22—21no—
483C22—52no—
484C22—101no—
485C22—101no—
486C22—101no—
487C22—101no—
488C22—101no—
489C22—121no—
490C22—121no—
491C22—121no—
492C22—202no—
493C22—202no—
494C22#9126911yescharacteristic
495C22#9127011yescharacteristic
496C22D5×(C2×D3)⋊C411yescharacteristic
497C4—21no—
498C4—21no—
499C4—52no—
500C4—101no—
501C4—122no—
502C4—121no—
503C4—602no—
504C4—601no—
505C4—601no—
506C3#1059909411yescharacteristic, complemented, Sylow
507C2—21no—
508C2—21no—
509C2—102no—
510C2—201no—
511C2—241no—
512C2D5×#80611yescharacteristic
513C2#1174813511yescharacteristic
514C2D5×#82511yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754526C2
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1501
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×D5×C22⋊C8C2semidirect
3. #11748702C2semidirect
4. #11746288C2semidirect
5. C5×#4470C2semidirect
6. #11745965C2semidirect
7. #11745957C2semidirect
10. C2×#6772C4semidirect
18. #91449C4semidirect
21. #91360C4semidirect
22. #91358C4semidirect
30. D5×C22⋊C8D3semidirect
72. #4470D5semidirect
402. C3×C5#1501semidirect
480. C5#69942semidirect
506. C3#10599094semidirect

Maximal subgroups

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

subgroupindex
#117545262
C3×D5×C22⋊C82
#117487022
#117462882
C5×#44702
#117459652
#117459572
#105990943
#699425