Finite Group Databasebeta

← #14301773

Subgroups — #14301773

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C8×D5C211yesmaximal, characteristic
2C2×#91359C211yesmaximal, characteristic
3C2×C5×#816C211yesmaximal, characteristic, complemented
4#11748759C211yesmaximal, characteristic
5C2×#90973C211yesmaximal, characteristic, complemented
6#11746372C211yesmaximal, characteristic, complemented
7#11745981C211yesmaximal, characteristic, complemented
8#10601063—31nomaximal, Hall
9C22×C5×Dic6C2211yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×C4⋊Dic15C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C2×C3×C8×D5—22no—
17C2×C3×C8×D5—22no—
18C2×C3×C8×D5—22no—
19C2×#6669—21no—
20C2×#6665—21no—
21C2×#6665—21no—
22#91359—22no—
23#91359C414yescomplemented
24C5×#816—22no—
25#90994—21no—
26#90973—22no—
27#71972—51nomaximal, Hall
28C2×#4092—31no—
29C22×C8×D5D311yescharacteristic
30C2×C5×#103—31no—
31C2×#3967—31no—
32#65276—31no—
33#64771—31no—
34#64749—31no—
35C23×C3×D5D411yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C22×Dic15—21no—
39C22×C5×Dic3—21no—
40C22×C5×Dic3—21no—
41C2×C5×Dic6—21no—
42C2×C5×Dic6—21no—
43C2×C5×Dic6—21no—
44C2×C5×Dic6—21no—
45C2×C5×Dic6—21no—
46C2×C5×Dic6C2×C412yes—
47C22×C3×Dic5D411yescharacteristic
48C2×C3×C4×D5—21no—
49C2×C3×C4×D5—21no—
50C2×C3×C4×D5—21no—
51C2×C3×C4×D5—21no—
52C2×C3×C4×D5C2×C412yes—
53C2×C3×C4×D5D412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8D412yes—
57C4⋊Dic15—21no—
58C4⋊Dic15—21no—
59C4⋊Dic15—21no—
60C4⋊Dic15C2×C412yes—
61C5×C4⋊Dic3—21no—
62C5×C4⋊Dic3—21no—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C2×C3×#168D412yes—
66C3×C8×D5—28no—
67#6669—24no—
68#6665—24no—
69#6665—42no—
70C23×C3×C8—51no—
71C2×#924—51no—
72#5212—51no—
73C2×#816—51no—
74C2×#816D511yescharacteristic, complemented
75#4551—51no—
76#4551—51no—
77C22×C5×Q8—31no—
78C22×C4×D5C2×D311yescharacteristic
79C22×C5×C8C2×D311yescharacteristic
80C2×C5×C4⋊C4—31no—
81#4092—34no—
82#4092—62no—
83C2×#685—61no—
84C2×#685—61no—
85C2×C4⋊Dic5—31no—
86C2×C4⋊Dic5—31no—
87C2×#683—61no—
88C22×#168C2×D311yescharacteristic
89C2×C8×D5—22no—
90C2×C8×D5—22no—
91C2×C8×D5—22no—
92C5×#103—62no—
93#3967—62no—
94#3963—61no—
95#1892—151noSylow
96C23×C3×C5C2×D411yescharacteristic
97C22×C3×D5—21no—
98C22×C3×D5—21no—
99C22×C3×D5—21no—
100C22×C3×D5—21no—
101C22×C3×D5C22⋊C412yes—
102C22×C3×D5SD1612yes—
103C22×C3×D5Q1612yes—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15—41no—
115C2×Dic15—41no—
116C2×C5×Dic3—22no—
117C2×C5×Dic3—41no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C5×Dic6—22no—
123C5×Dic6—22no—
124C5×Dic6—41no—
125C5×Dic6—41no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—21no—
128C2×C3×Dic5C22⋊C412yes—
129C3×C4×D5—22no—
130C3×C4×D5—22no—
131C3×C4×D5—22no—
132C3×C4×D5—22no—
133C3×C5×C8—22no—
134C3×#168—22no—
135C23×C3×C4—51no—
136C22×Dic6C2×D511yescharacteristic
137C22×C3×C8—51no—
138C22×C3×C8—102no—
139C22×C3×C8—102no—
140C22×C3×C8—102no—
141C22×C3×C8C2×D511yescharacteristic
142C2×#217—101no—
143C2×#217—101no—
144C2×C4⋊Dic3—51no—
145C2×C4⋊Dic3—51no—
146C2×C4⋊Dic3C2×D511yescharacteristic
147#924—54no—
148#924—102no—
149C2×Dic3⋊C4—101no—
150C3⋊#95—101no—
151#816—22no—
152#816—102no—
153C23×D5D1211yescharacteristic
154C2×C5×Q8—32no—
155C2×C5×Q8—61no—
156C2×C5×Q8—61no—
157C2×C5×Q8—61no—
158C2×C5×Q8—61no—
159C2×C5×Q8—61no—
160C22×C4×C5—61no—
161C22×C4×C5—61no—
162C22×C4×C5C22×D311yescharacteristic
163C22×Dic5—61no—
164C22×Dic5—61no—
165C22×Dic5D1211yescharacteristic
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—21no—
170C2×C4×D5C4×D312yes—
171C2×C4×D5#6712yes—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8#6712yes—
175C5×C4⋊C4—61no—
176C5×C4⋊C4—61no—
177#685—64no—
178#685—122no—
179C4⋊Dic5—32no—
180C4⋊Dic5—61no—
181C4⋊Dic5—61no—
182C4⋊Dic5—61no—
183#683—64no—
184C2×#168—21no—
185C2×#168—21no—
186C2×#168#6712yes—
187C8×D5—28no—
188C23×C8—51no—
189C2×C22⋊Q8—151no—
190C2×#103—31no—
191C2×#103—151no—
192#380—151no—
193#340—151no—
194#340—151no—
195C22×C3×C5C2×C22⋊C411yescharacteristic
196C22×C3×C5#12111yescharacteristic
197C22×C3×C5#12111yescharacteristic
198C22×C3×C5C2×SD1611yescharacteristic
199C22×C3×C5C2×Q1611yescharacteristic
200C22×C3×C5#13511yescharacteristic
201C22×C3×C5#13511yescharacteristic
202C2×C3×D5—22no—
203C2×C3×D5—22no—
204C2×C3×D5—22no—
205C2×C3×D5—22no—
206C2×C3×D5—22no—
207C2×C3×D5—22no—
208C2×C3×D5#10314yescomplemented
209C3×C4×C5C4×D411yescharacteristic
210C3×C4×C5C4×D411yescharacteristic
211C3×C4×C5#12011yescharacteristic
212C3×C4×C5#12311yescharacteristic
213Dic15—42no—
214Dic15—81no—
215C3×Dic5—22no—
216C5×Dic3—42no—
217C5×Dic3—81no—
218C24×C3—51no—
219C22×C3×C4—51no—
220C22×C3×C4—52no—
221C22×C3×C4—52no—
222C22×C3×C4—101no—
223C22×C3×C4—101no—
224C22×C3×C4—101no—
225C22×C3×C4—101no—
226C22×C3×C4C22×D511yescharacteristic
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—101no—
230C22×Dic3—101no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6C4×D512yes—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—52no—
240C2×C3×C8—108no—
241C2×C3×C8—101no—
242C2×C3×C8—101no—
243C2×C3×C8C22⋊D512yes—
244#217—104no—
245#217—202no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—52no—
249C4⋊Dic3—101no—
250C4⋊Dic3—101no—
251C4⋊Dic3—101no—
252Dic3⋊C4—104no—
253C23×C5C2×D1211yescharacteristic
254C22×D5—21no—
255C22×D5—21no—
256C22×D5—21no—
257C22×D5—21no—
258C22×D5#20412yes—
259C22×D5Dic1212yes—
260C22×D5(C2×D3)⋊C412yes—
261C5×Q8—62no—
262C5×Q8—62no—
263C5×Q8—121no—
264C5×Q8—121no—
265C2×C4×C5—62no—
266C2×C4×C5—121no—
267C2×C4×C5—121no—
268C2×C4×C5—121no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5#23511yescharacteristic
273C2×C4×C5#23511yescharacteristic
274C2×C4×C5C2×#6711yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C2×Dic5—21no—
278C2×Dic5—21no—
279C2×Dic5—62no—
280C2×Dic5—121no—
281C2×Dic5—121no—
282C2×Dic5—121no—
283C2×Dic5—121no—
284C2×Dic5—121no—
285C2×Dic5(C2×D3)⋊C412yes—
286C4×D5—22no—
287C4×D5—22no—
288C4×D5—22no—
289C4×D5—22no—
290C5×C8—22no—
291#168—22no—
292C22×Q8—31no—
293C23×C4—51no—
294C22×C8—51no—
295C22×C8—102no—
296C22×C8—102no—
297C22×C8—102no—
298C22×C8D3×D511yescharacteristic
299C22⋊Q8—154no—
300C22⋊Q8—302no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—151no—
303C2×C4⋊C4—151no—
304C2×C4⋊C4—301no—
305C2×C22⋊C4—301no—
306C2×C22⋊C4—301no—
307#103—62no—
308#103—302no—
309#95—301no—
310C2×C3×C5#38611yescharacteristic
311C2×C3×C5C2×#10311yescharacteristic
312C2×C3×C5#41611yescharacteristic
313C2×C3×C5#46511yescharacteristic
314C2×C3×C5#46511yescharacteristic
315C2×C3×C5#46711yescharacteristic
316C2×C3×C5#46711yescharacteristic
317C3×D5—24no—
318C23×C3—52no—
319C23×C3—52no—
320C23×C3—52no—
321C23×C3—101no—
322C23×C3—101no—
323C23×C3—101no—
324C23×C3—101no—
325C23×C3D4×D511yescharacteristic
326C2×C3×C4—52no—
327C2×C3×C4—101no—
328C2×C3×C4—101no—
329C2×C3×C4—102no—
330C2×C3×C4—102no—
331C2×C3×C4—102no—
332C2×C3×C4—102no—
333C2×C3×C4C2×C4×D511yescharacteristic
334C2×C3×C4#70911yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4#71111yescharacteristic
338C2×C3×C4C2×C22⋊D511yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—41no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—102no—
346C2×Dic3—201no—
347C2×Dic3—201no—
348C2×Dic3—201no—
349C2×Dic3—201no—
350C2×Dic3—201no—
351Dic6—22no—
352Dic6—22no—
353Dic6—41no—
354Dic6—41no—
355C3×C8—22no—
356C3×C8—102no—
357C22×C5C2×#20411yescharacteristic
358C22×C5#90411yescharacteristic
359C22×C5#90411yescharacteristic
360C22×C5C2×Dic1211yescharacteristic
361C22×C5C2×(C2×D3)⋊C411yescharacteristic
362C22×C5#93011yescharacteristic
363C22×C5#93011yescharacteristic
364C2×D5—22no—
365C2×D5—22no—
366C2×D5—22no—
367C2×D5—22no—
368C2×D5—22no—
369C2×D5—22no—
370C2×D5#81614yescomplemented
371C4×C5—122no—
372C4×C5—241no—
373C4×C5C4×#6711yescharacteristic
374C4×C5C4×#6711yescharacteristic
375C4×C5#92911yescharacteristic
376C4×C5#95311yescharacteristic
377Dic5—22no—
378Dic5—122no—
379Dic5—241no—
380C24—51no—
381C2×Q8—32no—
382C2×Q8—61no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8—61no—
387C22×C4—51no—
388C22×C4—52no—
389C22×C4—52no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—101no—
393C22×C4—101no—
394C22×C4—101no—
395C22×C4—101no—
396C22×C4—301no—
397C22×C4—301no—
398C22×C4C2×D3×D511yescharacteristic
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—52no—
402C2×C8—108no—
403C2×C8—101no—
404C2×C8—101no—
405C2×C8#120112yes—
406C4⋊C4—61no—
407C4⋊C4—61no—
408C4⋊C4—152no—
409C4⋊C4—304no—
410C4⋊C4—301no—
411C4⋊C4—301no—
412C4⋊C4—301no—
413C22⋊C4—304no—
414C22⋊C4—602no—
415C3×C5#189211yescharacteristic, complemented, Hall
416C22×C3—54no—
417C22×C3—102no—
418C22×C3—102no—
419C22×C3—102no—
420C22×C3—102no—
421C22×C3—102no—
422C22×C3—102no—
423C22×C3D5×C22⋊C411yescharacteristic
424C22×C3#403011yescharacteristic
425C22×C3D5×SD1611yescharacteristic
426C22×C3#406211yescharacteristic
427C22×C3D5×Q1611yescharacteristic
428C22×C3#406511yescharacteristic
429C22×C3#408411yescharacteristic
430C3×C4—102no—
431C3×C4#402711yescharacteristic
432C3×C4#402911yescharacteristic
433C3×C4C4×C22⋊D511yescharacteristic
434C3×C4#408311yescharacteristic
435Dic3—42no—
436Dic3—81no—
437Dic3—202no—
438Dic3—401no—
439C2×C5C2×#81611yescharacteristic
440C2×C5#511311yescharacteristic
441C2×C5#511411yescharacteristic
442C2×C5#511411yescharacteristic
443C2×C5#511611yescharacteristic
444C2×C5#511611yescharacteristic
445C2×C5#521311yescharacteristic
446D5—24no—
447C23—52no—
448C23—52no—
449C23—52no—
450C23—101no—
451C23—101no—
452C23—101no—
453C23—101no—
454C23D5×D1211yescharacteristic
455Q8—62no—
456Q8—62no—
457Q8—121no—
458Q8—121no—
459C2×C4—52no—
460C2×C4—62no—
461C2×C4—101no—
462C2×C4—101no—
463C2×C4—102no—
464C2×C4—102no—
465C2×C4—102no—
466C2×C4—102no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—302no—
473C2×C4—601no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4—601no—
477C2×C4—601no—
478C2×C4#677111yescharacteristic
479C2×C4#677211yescharacteristic
480C2×C4C4×D3×D511yescharacteristic
481C2×C4C2×#120111yescharacteristic
482C2×C4D5×#6711yescharacteristic
483C2×C4D5×#6711yescharacteristic
484C8—22no—
485C8—102no—
486C2×C3—104no—
487C2×C3D5×#10311yescharacteristic
488C2×C3#6509311yescharacteristic
489C2×C3#6509611yescharacteristic
490C2×C3#6510211yescharacteristic
491C2×C3#6524511yescharacteristic
492C2×C3#6546011yescharacteristic
493C2×C3#6547711yescharacteristic
494C5#7197211yescharacteristic, complemented, Sylow
495C22—54no—
496C22—102no—
497C22—102no—
498C22—102no—
499C22—102no—
500C22—102no—
501C22—102no—
502C22D5×#20411yescharacteristic
503C22D5×Dic1211yescharacteristic
504C22#9126911yescharacteristic
505C22#9127111yescharacteristic
506C22#9144811yescharacteristic
507C22#9144911yescharacteristic
508C22D5×(C2×D3)⋊C411yescharacteristic
509C4—102no—
510C4—122no—
511C4—241no—
512C4—602no—
513C4—1201no—
514C4C4×#120111yescharacteristic
515C4#9144011yescharacteristic
516C4#9144711yescharacteristic
517C4#9156311yescharacteristic
518C3#1060106311yescharacteristic, complemented, Sylow
519C2—104no—
520C2D5×#81611yescharacteristic
521C2#1174764211yescharacteristic
522C2#1174789611yescharacteristic
523C2#1174793811yescharacteristic
524C2#1174793911yescharacteristic
525C2#1174794211yescharacteristic
526C2#1174890511yescharacteristic
subgroupG/H
centerC23D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1892
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C5×#816C2semidirect
5. C2×#90973C2semidirect
6. #11746372C2semidirect
7. #11745981C2semidirect
23. #91359C4semidirect
74. C2×#816D5semidirect
208. C2×C3×D5#103semidirect
370. C2×D5#816semidirect
415. C3×C5#1892semidirect
494. C5#71972semidirect
518. C3#10601063semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C8×D52
C2×#913592
C2×C5×#8162
#117487592
C2×#909732
#117463722
#117459812
#106010633
#719725