Finite Group Databasebeta

← #14301026

Subgroups — #14301026

Order 1920.

876 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91434C211yesmaximal, characteristic, complemented
2C22×#6652C211yesmaximal, characteristic
3C2×C5×#821C211yesmaximal, characteristic, complemented
4C2×C3×#3953C211yesmaximal, characteristic, complemented
5#11748797C211yesmaximal, characteristic, complemented
6#11746371C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10601001—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C22×D5×Dic3—21no—
12C22×C3×C5×C8C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C2×(C2×D3)⋊Dic5—21no—
18C2×(C2×D3)⋊Dic5—21no—
19C2×#6665—21no—
20#91434—22no—
21#91434—22no—
22C2×#6652—22no—
23C2×#6652—22no—
24C2×#6652C414yescomplemented
25C5×#821—22no—
26C3×#3953—22no—
27#70172—51nomaximal, Hall
28C22×#686—31no—
29C2×#4039—31no—
30C2×C5×#102—31no—
31#65510—31no—
32C2×#3953D311yescharacteristic, complemented
33#64770—31no—
34#64749—31no—
35C23×C5×D3—21no—
36C23×C3×D5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15D411yescharacteristic
39C22×Dic15D411yescharacteristic
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
47C22×C3×Dic5—21no—
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20—21no—
51C2×C3×D20C2×C412yes—
52C2×C3×D20D412yes—
53C2×C3×D20D412yes—
54C2×D5×Dic3—24no—
55C2×D5×Dic3—42no—
56C2×D5×Dic3—42no—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C4×Dic15—21no—
61C4×Dic15—21no—
62C2×C3⋊#168—21no—
63C2×C3⋊#168—21no—
64C2×C3⋊#168C2×C412yescomplemented
65C5×C4⋊Dic3—21no—
66C5×C4⋊Dic3D412yes—
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5—21no—
69(C2×D3)⋊Dic5—42no—
70(C2×D3)⋊Dic5—42no—
71#6665—24no—
72#6652—28no—
73C2×D4×Dic3—51no—
74C22×#213—51no—
75C2×C3×#102—51no—
76C2×#821D511yescharacteristic, complemented
77#4988—51no—
78#4550—51no—
79#4529—51no—
80C22×C5×D4—31no—
81C22×D20C2×D311yescharacteristic
82C22×C4×D5—61no—
83C22×C5×C8C2×D311yescharacteristic
84C2×C5×C4⋊C4—31no—
85C2×C22⋊Dic5—61no—
86C2×C22⋊Dic5—61no—
87C2×#686—34no—
88C2×#686—62no—
89C2×#686—62no—
90C2×#685—61no—
91C2×C4⋊Dic5C2×D311yescharacteristic
92C2×C4×Dic5—31no—
93C22×#168—31no—
94#4039—62no—
95#4039—62no—
96C5×#102—62no—
97#3953—22no—
98#1879—151noSylow
99C23×C3×C5C2×D411yescharacteristic
100C22×C5×D3—22no—
101C22×C5×D3—41no—
102C22×C5×D3—41no—
103C22×C5×D3—41no—
104C22×C5×D3—41no—
105C22×C5×D3—41no—
106C22×C5×D3—41no—
107C22×C3×D5—22no—
108C22×C3×D5—22no—
109C22×C3×D5—22no—
110C22×C3×D5—41no—
111C22×C3×D5—41no—
112C22×C3×D5—41no—
113C22×C3×D5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×Dic15—21no—
121C2×Dic15—21no—
122C2×Dic15—21no—
123C2×Dic15—21no—
124C2×Dic15—21no—
125C2×Dic15D812yescomplemented
126C2×C5×Dic3—22no—
127C2×C5×Dic3—41no—
128C2×C5×Dic3—41no—
129C5×D12—22no—
130C5×D12—22no—
131C5×D12—41no—
132C5×D12—41no—
133C2×C3×Dic5—41no—
134C2×C3×Dic5—41no—
135C2×C3×Dic5—41no—
136C3×D20—22no—
137C3×D20—22no—
138C3×D20—22no—
139C3×D20C22⋊C414yescomplemented
140D5×Dic3—48no—
141C3×C5×C8—41no—
142C3⋊#168—22no—
143C22×C3×D4—51no—
144C23×Dic3—101no—
145C22×D12C2×D511yescharacteristic
146C22×C3×C8C2×D511yescharacteristic
147C2×C3×C4⋊C4—51no—
148C2×#217—101no—
149D4×Dic3—102no—
150D4×Dic3—102no—
151C2×#213—54no—
152C2×#213—102no—
153C2×#213—102no—
154C2×(C2×D3)⋊C4—101no—
155C2×(C2×D3)⋊C4—101no—
156C2×C4⋊Dic3C2×D511yescharacteristic
157C2×C4×Dic3—51no—
158C22×C3⋊C8—51no—
159C3×#102—102no—
160#821—22no—
161C24×C5—61no—
162C23×D5—21no—
163C2×C5×D4—32no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C2×C5×D4—61no—
167C2×C5×D4—61no—
168C2×C5×D4—61no—
169C22×C4×C5—61no—
170C22×C4×C5C22×D311yescharacteristic
171C22×Dic5—21no—
172C22×Dic5—31no—
173C22×Dic5—31no—
174C2×D20—21no—
175C2×D20—21no—
176C2×D20—21no—
177C2×D20C4×D312yes—
178C2×D20D1212yes—
179C2×D20#6712yes—
180C2×C4×D5—64no—
181C2×C4×D5—122no—
182C2×C4×D5—122no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C5×C4⋊C4—32no—
187C5×C4⋊C4—61no—
188C22⋊Dic5—122no—
189C22⋊Dic5—122no—
190#686—68no—
191#685—64no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4×Dic5—61no—
195C4×Dic5—61no—
196C2×#168—32no—
197C2×#168—61no—
198C2×#168—61no—
199C22×D8—151no—
200C2×C4×D4—151no—
201C2×#102—31no—
202C2×#102—51no—
203#390—151no—
204#340—151no—
205#336—151no—
206C22×C3×C5C4×D411yescharacteristic
207C22×C3×C5#12011yescharacteristic
208C22×C3×C5#12111yescharacteristic
209C22×C3×C5C2×D811yescharacteristic
210C22×C3×C5#13511yescharacteristic
211C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
212C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
213C2×C5×D3—42no—
214C2×C5×D3—42no—
215C2×C5×D3—42no—
216C2×C5×D3—81no—
217C2×C5×D3—81no—
218C2×C5×D3—81no—
219C2×C5×D3—81no—
220C2×C3×D5—24no—
221C2×C3×D5—42no—
222C2×C3×D5—42no—
223C2×C3×D5—42no—
224C2×C3×D5—42no—
225C2×C3×D5—42no—
226C2×C3×D5—42no—
227C3×C4×C5C2×C22⋊C411yescharacteristic
228C3×C4×C5C4×D411yescharacteristic
229C3×C4×C5#12111yescharacteristic
230C3×C4×C5#12311yescharacteristic
231Dic15—22no—
232Dic15—41no—
233C3×Dic5—81no—
234C5×Dic3—42no—
235C24×C3—101no—
236C23×D3—21no—
237C2×C3×D4—52no—
238C2×C3×D4—52no—
239C2×C3×D4—52no—
240C2×C3×D4—101no—
241C2×C3×D4—101no—
242C2×C3×D4—101no—
243C22×C3×C4—101no—
244C22×C3×C4C22×D511yescharacteristic
245C22×Dic3—21no—
246C22×Dic3—51no—
247C22×Dic3—51no—
248C22×Dic3—104no—
249C22×Dic3—202no—
250C22×Dic3—202no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12C4×D512yescomplemented
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C3×C4⋊C4—101no—
261C3×C4⋊C4—101no—
262#217—104no—
263#213—108no—
264(C2×D3)⋊C4—202no—
265(C2×D3)⋊C4—202no—
266C4⋊Dic3—21no—
267C4⋊Dic3C22⋊D512yes—
268C4×Dic3—101no—
269C4×Dic3—101no—
270C2×C3⋊C8—52no—
271C2×C3⋊C8—101no—
272C2×C3⋊C8—101no—
273C23×C5—62no—
274C23×C5—121no—
275C23×C5—121no—
276C23×C5—121no—
277C23×C5—121no—
278C23×C5—121no—
279C23×C5—121no—
280C23×C5D3×D411yescharacteristic
281C22×D5—22no—
282C22×D5—22no—
283C22×D5—22no—
284C22×D5—41no—
285C22×D5—41no—
286C22×D5—41no—
287C22×D5—41no—
288C5×D4—62no—
289C5×D4—62no—
290C5×D4—121no—
291C5×D4—121no—
292C2×C4×C5—62no—
293C2×C4×C5—121no—
294C2×C4×C5—121no—
295C2×C4×C5C2×C4×D311yescharacteristic
296C2×C4×C5C2×D1211yescharacteristic
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5#23711yescharacteristic
299C2×C4×C5#23711yescharacteristic
300C2×C4×C5C2×#6711yescharacteristic
301C2×Dic5—32no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—61no—
306C2×Dic5—61no—
307C2×Dic5—61no—
308C2×Dic5—61no—
309C2×Dic5—61no—
310D20—22no—
311D20—22no—
312D20—22no—
313D20(C2×D3)⋊C414yescomplemented
314C4×D5—128no—
315C5×C8—41no—
316#168—62no—
317C22×D4—31no—
318C22×D4—51no—
319C23×C4—301no—
320C2×D8—154no—
321C2×D8—302no—
322C2×D8—302no—
323C22×C8—151no—
324C22×C8D3×D511yescharacteristic
325C4×D4—302no—
326C4×D4—302no—
327C2×C4⋊C4—31no—
328C2×C4⋊C4—51no—
329C2×C22⋊C4—301no—
330C2×C22⋊C4—301no—
331C2×C22⋊C4—301no—
332C2×C42—151no—
333#102—62no—
334#102—102no—
335C2×C3×C5#38611yescharacteristic
336C2×C3×C5C4×D811yescharacteristic
337C2×C3×C5#44211yescharacteristic
338C2×C3×C5#44711yescharacteristic
339C2×C3×C5#44911yescharacteristic
340C2×C3×C5#45911yescharacteristic
341C2×C3×C5#46311yescharacteristic
342C3×D5—44no—
343C5×D3—82no—
344C23×C3—102no—
345C23×C3—102no—
346C23×C3—102no—
347C23×C3—201no—
348C23×C3—201no—
349C23×C3—201no—
350C23×C3—201no—
351C23×C3D4×D511yescharacteristic
352C22×D3—22no—
353C22×D3—41no—
354C22×D3—41no—
355C22×D3—41no—
356C22×D3—41no—
357C22×D3—41no—
358C22×D3—41no—
359C3×D4—54no—
360C3×D4—102no—
361C3×D4—102no—
362C3×D4—102no—
363C2×C3×C4—201no—
364C2×C3×C4—201no—
365C2×C3×C4—201no—
366C2×C3×C4C2×C4×D511yescharacteristic
367C2×C3×C4#70911yescharacteristic
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4#71111yescharacteristic
371C2×C3×C4C2×C22⋊D511yescharacteristic
372C2×Dic3—22no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—52no—
376C2×Dic3—101no—
377C2×Dic3—101no—
378C2×Dic3—101no—
379C2×Dic3—101no—
380C2×Dic3—101no—
381C2×Dic3—208no—
382D12—22no—
383D12—22no—
384D12—41no—
385D12—41no—
386C3×C8—41no—
387C3⋊C8—102no—
388C22×C5—122no—
389C22×C5—122no—
390C22×C5—122no—
391C22×C5—241no—
392C22×C5—241no—
393C22×C5—241no—
394C22×C5—241no—
395C22×C5#67⋊C411yescharacteristic
396C22×C5#88211yescharacteristic
397C22×C5D3×D811yescharacteristic
398C22×C5#91111yescharacteristic
399C22×C5#91411yescharacteristic
400C22×C5#91611yescharacteristic
401C22×C5#93911yescharacteristic
402C2×D5—24no—
403C2×D5—42no—
404C2×D5—42no—
405C2×D5—42no—
406C2×D5—42no—
407C2×D5—42no—
408C2×D5—42no—
409C4×C5—122no—
410C4×C5#67⋊C411yescharacteristic
411C4×C5#88611yescharacteristic
412C4×C5C2×(C2×D3)⋊C411yescharacteristic
413C4×C5#93911yescharacteristic
414Dic5—62no—
415Dic5—81no—
416Dic5—121no—
417C24—61no—
418C24—101no—
419C2×D4—32no—
420C2×D4—52no—
421C2×D4—52no—
422C2×D4—52no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—101no—
429C2×D4—101no—
430C2×D4—101no—
431C22×C4—61no—
432C22×C4—101no—
433C22×C4—151no—
434C22×C4—151no—
435C22×C4—304no—
436C22×C4—602no—
437C22×C4—602no—
438C22×C4C2×D3×D511yescharacteristic
439D8—308no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—152no—
444C2×C8—301no—
445C2×C8—301no—
446C4⋊C4—32no—
447C4⋊C4—61no—
448C4⋊C4—101no—
449C4⋊C4—101no—
450C22⋊C4—304no—
451C22⋊C4—602no—
452C22⋊C4—602no—
453C42—301no—
454C42—301no—
455C3×C5#187911yescharacteristic, complemented, Hall
456C22×C3—104no—
457C22×C3—202no—
458C22×C3—202no—
459C22×C3—202no—
460C22×C3—202no—
461C22×C3—202no—
462C22×C3—202no—
463C22×C3#402711yescharacteristic
464C22×C3#403011yescharacteristic
465C22×C3D5×D811yescharacteristic
466C22×C3#405711yescharacteristic
467C22×C3#406011yescharacteristic
468C22×C3#406211yescharacteristic
469C22×C3#408311yescharacteristic
470C2×D3—42no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—81no—
474C2×D3—81no—
475C2×D3—81no—
476C2×D3—81no—
477C3×C4—401no—
478C3×C4D5×C22⋊C411yescharacteristic
479C3×C4#402911yescharacteristic
480C3×C4C4×C22⋊D511yescharacteristic
481C3×C4#408411yescharacteristic
482Dic3—42no—
483Dic3—102no—
484Dic3—201no—
485C2×C5—242no—
486C2×C5#475611yescharacteristic
487C2×C5#477311yescharacteristic
488C2×C5#478111yescharacteristic
489C2×C5#478511yescharacteristic
490C2×C5#495811yescharacteristic
491C2×C5#515011yescharacteristic
492C2×C5#516511yescharacteristic
493D5—44no—
494C23—62no—
495C23—102no—
496C23—102no—
497C23—102no—
498C23—121no—
499C23—121no—
500C23—121no—
501C23—121no—
502C23—121no—
503C23—121no—
504C23—201no—
505C23—201no—
506C23—201no—
507C23—201no—
508C23#677711yescharacteristic
509D4—54no—
510D4—62no—
511D4—62no—
512D4—102no—
513D4—102no—
514D4—102no—
515D4—121no—
516D4—121no—
517C2×C4—62no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—152no—
521C2×C4—201no—
522C2×C4—201no—
523C2×C4—201no—
524C2×C4—301no—
525C2×C4—301no—
526C2×C4—301no—
527C2×C4—301no—
528C2×C4—301no—
529C2×C4—608no—
530C2×C4#676511yescharacteristic
531C2×C4C4×D3×D511yescharacteristic
532C2×C4D5×D1211yescharacteristic
533C2×C4#678011yescharacteristic
534C2×C4D5×#6711yescharacteristic
535C2×C4D3×C22⋊D511yescharacteristic
536C8—41no—
537C8—302no—
538C2×C3—204no—
539C2×C3#6504511yescharacteristic
540C2×C3#6507411yescharacteristic
541C2×C3#6507511yescharacteristic
542C2×C3#6507611yescharacteristic
543C2×C3#6524511yescharacteristic
544C2×C3#6544511yescharacteristic
545C2×C3#6546111yescharacteristic
546D3—82no—
547C5#7017211yescharacteristic, complemented, Sylow
548C22—104no—
549C22—122no—
550C22—122no—
551C22—122no—
552C22—202no—
553C22—202no—
554C22—202no—
555C22—202no—
556C22—202no—
557C22—202no—
558C22—241no—
559C22—241no—
560C22—241no—
561C22—241no—
562C22#9125611yescharacteristic
563C22#9125711yescharacteristic
564C22#9125811yescharacteristic
565C22#9127611yescharacteristic
566C22#9140811yescharacteristic
567C22#9144211yescharacteristic
568C22#9147511yescharacteristic
569C4—122no—
570C4—302no—
571C4—401no—
572C4—601no—
573C4#9141411yescharacteristic
574C4#9144111yescharacteristic
575C4D5×(C2×D3)⋊C411yescharacteristic
576C4#9154911yescharacteristic
577C3#1060100111yescharacteristic, complemented, Sylow
578C2—204no—
579C2—242no—
580C2#1174773311yescharacteristic
581C2#1174773411yescharacteristic
582C2#1174775011yescharacteristic
583C2#1174775111yescharacteristic
584C2#1174811911yescharacteristic
585C2#1174815311yescharacteristic
586C2#1174890611yescharacteristic
subgroupG/H
centerC23#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×#6652C2
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1879
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
1. C2×#91434C2semidirect
3. C2×C5×#821C2semidirect
4. C2×C3×#3953C2semidirect
5. #11748797C2semidirect
6. #11746371C2semidirect
7. #11745979C2semidirect
24. C2×#6652C4semidirect
32. C2×#3953D3semidirect
46. C2×C5×D12C2×C4semidirect
64. C2×C3⋊#168C2×C4semidirect
76. C2×#821D5semidirect
125. C2×Dic15D8semidirect
139. C3×D20C22⋊C4semidirect
256. C2×D12C4×D5semidirect
313. D20(C2×D3)⋊C4semidirect
455. C3×C5#1879semidirect
547. C5#70172semidirect
577. C3#10601001semidirect

Maximal subgroups

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

subgroupindex
C2×#914342
C22×#66522
C2×C5×#8212
C2×C3×#39532
#117487972
#117463712
#117459792
#106010013
#701725