Finite Group Databasebeta

← #14304712

Subgroups — #14304712

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752439C211yesmaximal, characteristic
2C2×#91236C211yesmaximal, characteristic
3C2×#91221C211yesmaximal, characteristic, complemented
4#11752371C211yesmaximal, characteristic, complemented
5C3×D5×#102C211yesmaximal, characteristic
6#11746764C211yesmaximal, characteristic, complemented
7#11746745C211yesmaximal, characteristic, complemented
8#10603964—31nomaximal, Hall
9C2×C3×D4×D5C2211yescharacteristic
10C2×#6763—21no—
11C2×#6763—21no—
12C2×C4⋊ΓL(1,𝔽16)—21no—
13C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
16C2×D5⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C8×D5C2211yescharacteristic
18C3×D5×C4⋊C4C2211yescharacteristic
19#91236—22no—
20#91235—21no—
21#91221—22no—
22C3×C5×#102C411yescharacteristic, complemented
23C3×#3964C411yescharacteristic, complemented
24C3×#3953C411yescharacteristic, complemented
25C3×#3941C411yescharacteristic, complemented
26#70187—51nomaximal, Hall
27#65780—31no—
28C2×#4007—31no—
29C2×#3992—31no—
30#65712—31no—
31D5×#102D311yescharacteristic
32#64893—31no—
33#64874—31no—
34C23×C3×D5—21no—
35C22×ΓL(1,𝔽16)—21no—
36C22×ΓL(1,𝔽16)—21no—
37C22×ΓL(1,𝔽16)D411yescharacteristic
38C22×ΓL(1,𝔽16)D411yescharacteristic
39C2×C3×C5×D4C2×C411yescharacteristic
40C2×C3×C22⋊D5—21no—
41C3×D4×D5—21no—
42C3×D4×D5—21no—
43C3×D4×D5—21no—
44C3×D4×D5—21no—
45C2×C3×D20C2×C411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×C4×D5C2311yescharacteristic
48#6763—42no—
49#6763—42no—
50C2×C3⋊#170—21no—
51C4⋊ΓL(1,𝔽16)—21no—
52C4⋊ΓL(1,𝔽16)—21no—
53C4⋊ΓL(1,𝔽16)—21no—
54C4⋊ΓL(1,𝔽16)—21no—
55C4⋊ΓL(1,𝔽16)—42no—
56C4×ΓL(1,𝔽16)—21no—
57C4×ΓL(1,𝔽16)—21no—
58D5⋊(C3⋊C8)—21no—
59D5⋊(C3⋊C8)D412yes—
60C2×C3×C5×C8C2×C411yescharacteristic
61C3×C5×C4⋊C4C2×C411yescharacteristic
62C3×C4⋊Dic5C2×C411yescharacteristic
63C3×#683—21no—
64C2×C3×#168C2×C411yescharacteristic
65C3×C8×D5—21no—
66C3×C8×D5—21no—
67C2×C3×#102—51no—
68#5221—51no—
69C2×#832—51no—
70C2×#815—51no—
71#4984—51no—
72#4551—51no—
73#4529—51no—
74C2×D4×D5C2×D311yescharacteristic
75C2×C22⋊AGL(1,𝔽5)—61no—
76C2×C22⋊AGL(1,𝔽5)—61no—
77C2×C4⋊AGL(1,𝔽5)—31no—
78C2×C4⋊AGL(1,𝔽5)—31no—
79C2×C4⋊AGL(1,𝔽5)—61no—
80C2×C4×AGL(1,𝔽5)—31no—
81C2×D5⋊C8—31no—
82C2×C8×D5C2×D311yescharacteristic
83D5×C4⋊C4C2×D311yescharacteristic
84#4007—62no—
85(C2×AGL(1,𝔽5))⋊C4—61no—
86#3992—62no—
87C5×#102Dic311yescharacteristic, complemented
88#3964Dic311yescharacteristic, complemented
89#3953Dic311yescharacteristic, complemented
90#3941Dic311yescharacteristic, complemented
91#1936—151noSylow
92C23×C3×C5—21no—
93C22×C3×D5—21no—
94C22×C3×D5—41no—
95C22×C3×D5—41no—
96C22×C3×D5—41no—
97C22×C3×D5—41no—
98C22×C3×D5—41no—
99C22×C3×D5—41no—
100C22×C3×D5C2×D411yescharacteristic
101C2×ΓL(1,𝔽16)—21no—
102C2×ΓL(1,𝔽16)—21no—
103C2×ΓL(1,𝔽16)—21no—
104C2×ΓL(1,𝔽16)—21no—
105C2×ΓL(1,𝔽16)—21no—
106C2×ΓL(1,𝔽16)—21no—
107C2×ΓL(1,𝔽16)—41no—
108C2×ΓL(1,𝔽16)—41no—
109C2×ΓL(1,𝔽16)—41no—
110C2×ΓL(1,𝔽16)—41no—
111C2×ΓL(1,𝔽16)—41no—
112C2×ΓL(1,𝔽16)—41no—
113C3×C5×D4—21no—
114C3×C5×D4—21no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5C22×C411yescharacteristic
117C3×C22⋊D5—41no—
118C3×C22⋊D5—41no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5#4111yescharacteristic
121C3×D20—21no—
122C3×D20—21no—
123C3×C4×D5—41no—
124C3×C4×D5—41no—
125C3×C4×D5C2×D411yescharacteristic
126C3×C4×D5#4111yescharacteristic
127C3×C4×D5#4111yescharacteristic
128C3×C4×D5#4111yescharacteristic
129C3⋊#170—22no—
130C3×C5×C8—21no—
131C3×#168—21no—
132C22×C3×D4—51no—
133C22×C3×C8—51no—
134C2×C3×C4⋊C4—51no—
135C2×#217—101no—
136C2×#217—101no—
137C2×C4⋊Dic3—51no—
138C2×C4⋊Dic3—51no—
139C2×C4⋊Dic3—101no—
140C2×C4×Dic3—51no—
141C22×C3⋊C8—51no—
142C3×#102—51no—
143C3×#102—51no—
144C3×#102—51no—
145C3×#102AGL(1,𝔽5)11yescharacteristic, complemented
146#832—102no—
147C3⋊#95—101no—
148#815—102no—
149C23×D5—21no—
150C22×AGL(1,𝔽5)—31no—
151C22×AGL(1,𝔽5)—31no—
152C22×AGL(1,𝔽5)—61no—
153C22×AGL(1,𝔽5)—61no—
154C2×C5×D4C2×Dic311yescharacteristic
155C2×C22⋊D5—21no—
156D4×D5—21no—
157D4×D5—21no—
158D4×D5—21no—
159D4×D5—21no—
160C2×D20C2×Dic311yescharacteristic
161C2×C4×D5—21no—
162C2×C4×D5C22×D311yescharacteristic
163C22⋊AGL(1,𝔽5)—122no—
164C22⋊AGL(1,𝔽5)—122no—
165C2×#170—61no—
166C4⋊AGL(1,𝔽5)—61no—
167C4⋊AGL(1,𝔽5)—61no—
168C4⋊AGL(1,𝔽5)—61no—
169C4⋊AGL(1,𝔽5)—61no—
170C4⋊AGL(1,𝔽5)—122no—
171C4×AGL(1,𝔽5)—61no—
172C4×AGL(1,𝔽5)—61no—
173D5⋊C8—32no—
174D5⋊C8—61no—
175C2×C5×C8C2×Dic311yescharacteristic
176C5×C4⋊C4C2×Dic311yescharacteristic
177C4⋊Dic5C2×Dic311yescharacteristic
178#683—21no—
179C2×#168C2×Dic311yescharacteristic
180C8×D5—21no—
181C8×D5—21no—
182C2×#102—51no—
183C2×#102—151no—
184C2×#97—151no—
185#390—151no—
186#389—151no—
187#340—151no—
188#340—151no—
189C22×C3×C5—41no—
190C22×C3×C5—41no—
191C22×C3×C5—41no—
192C22×C3×C5C4×D411yescharacteristic
193C2×C3×D5—41no—
194C2×C3×D5—41no—
195C2×C3×D5—41no—
196C2×C3×D5—81no—
197C2×C3×D5—81no—
198C2×C3×D5—81no—
199C2×C3×D5—81no—
200C2×C3×D5#12111yescharacteristic
201C2×C3×D5#12411yescharacteristic
202C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
203C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
204C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
205C2×C3×D5#13711yescharacteristic
206ΓL(1,𝔽16)—41no—
207ΓL(1,𝔽16)—41no—
208ΓL(1,𝔽16)—81no—
209ΓL(1,𝔽16)—81no—
210C3×C4×C5—41no—
211C3×C4×C5#11711yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×Dic5—41no—
214C3×Dic5#12311yescharacteristic
215C3×Dic5#12611yescharacteristic
216C24×C3—101no—
217C2×C3×D4—51no—
218C2×C3×D4—101no—
219C2×C3×D4—101no—
220C2×C3×D4—101no—
221C2×C3×D4—101no—
222C2×C3×D4—101no—
223C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
224C22×C3×C4—51no—
225C22×C3×C4—101no—
226C22×Dic3—51no—
227C22×Dic3—51no—
228C22×Dic3—101no—
229C22×Dic3—101no—
230C2×C3×C8—51no—
231C2×C3×C8—101no—
232C2×C3×C8—101no—
233C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
234C3×C4⋊C4—51no—
235C3×C4⋊C4—101no—
236C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
237#217—202no—
238#217—202no—
239C4⋊Dic3—101no—
240C4⋊Dic3—101no—
241C4⋊Dic3—101no—
242C4⋊Dic3—101no—
243C4⋊Dic3—202no—
244C4×Dic3—101no—
245C4×Dic3—101no—
246C2×C3⋊C8—52no—
247C2×C3⋊C8—101no—
248C2×C3⋊C8—101no—
249C23×C5—21no—
250C22×D5—21no—
251C22×D5—41no—
252C22×D5—41no—
253C22×D5—41no—
254C22×D5—41no—
255C22×D5—41no—
256C22×D5—41no—
257C22×D5D3×D411yescharacteristic
258C2×AGL(1,𝔽5)—61no—
259C2×AGL(1,𝔽5)—61no—
260C2×AGL(1,𝔽5)—61no—
261C2×AGL(1,𝔽5)—61no—
262C2×AGL(1,𝔽5)—61no—
263C2×AGL(1,𝔽5)—61no—
264C2×AGL(1,𝔽5)—121no—
265C2×AGL(1,𝔽5)—121no—
266C2×AGL(1,𝔽5)—121no—
267C2×AGL(1,𝔽5)—121no—
268C2×AGL(1,𝔽5)—121no—
269C2×AGL(1,𝔽5)—121no—
270C5×D4—21no—
271C5×D4—21no—
272C2×C4×C5—21no—
273C2×C4×C5C22×Dic311yescharacteristic
274C22⋊D5—41no—
275C22⋊D5—41no—
276C2×Dic5—21no—
277C2×Dic5#23711yescharacteristic
278D20—21no—
279D20—21no—
280C4×D5—41no—
281C4×D5—41no—
282C4×D5#23511yescharacteristic
283C4×D5#23511yescharacteristic
284C4×D5D3×D411yescharacteristic
285C4×D5#23711yescharacteristic
286#170—62no—
287C5×C8—21no—
288#168—21no—
289C22×D4—51no—
290C22×C8—51no—
291C22×C8—151no—
292C2×C4⋊C4—51no—
293C2×C4⋊C4—151no—
294C2×C4⋊C4—151no—
295C2×C4⋊C4—301no—
296C2×C22⋊C4—301no—
297C2×C22⋊C4—301no—
298C2×C42—151no—
299#102—51no—
300#102—51no—
301#102—51no—
302#102—302no—
303#102ΓL(1,𝔽16)11yescharacteristic, complemented
304#97—302no—
305#95—301no—
306C2×C3×C5—81no—
307C2×C3×C5#38811yescharacteristic
308C2×C3×C5#44011yescharacteristic
309C2×C3×C5#44211yescharacteristic
310C3×D5—81no—
311C3×D5#46811yescharacteristic
312C3×D5#46911yescharacteristic
313C3×D5#48911yescharacteristic
314C3×D5#49011yescharacteristic
315C23×C3—21no—
316C23×C3—51no—
317C23×C3—101no—
318C23×C3—201no—
319C23×C3—201no—
320C23×C3—201no—
321C23×C3—201no—
322C23×C3—201no—
323C23×C3—201no—
324C3×D4—21no—
325C3×D4—21no—
326C3×D4—101no—
327C3×D4—101no—
328C3×D4—201no—
329C3×D4—201no—
330C2×C3×C4—21no—
331C2×C3×C4—51no—
332C2×C3×C4—51no—
333C2×C3×C4—51no—
334C2×C3×C4—51no—
335C2×C3×C4—51no—
336C2×C3×C4—101no—
337C2×C3×C4—201no—
338C2×C3×C4—201no—
339C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
340C2×Dic3—101no—
341C2×Dic3—101no—
342C2×Dic3—101no—
343C2×Dic3—101no—
344C2×Dic3—101no—
345C2×Dic3—101no—
346C2×Dic3—201no—
347C2×Dic3—201no—
348C2×Dic3—201no—
349C2×Dic3—201no—
350C2×Dic3—201no—
351C2×Dic3—201no—
352C3×C8—21no—
353C3×C8—101no—
354C3⋊C8—102no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—41no—
358C22×C5D4×Dic311yescharacteristic
359C2×D5—41no—
360C2×D5—41no—
361C2×D5—41no—
362C2×D5—81no—
363C2×D5—81no—
364C2×D5—81no—
365C2×D5—81no—
366C2×D5#88411yescharacteristic
367C2×D5#88511yescharacteristic
368C2×D5#91111yescharacteristic
369C2×D5#91111yescharacteristic
370C2×D5#91411yescharacteristic
371C2×D5#91511yescharacteristic
372AGL(1,𝔽5)—121no—
373AGL(1,𝔽5)—121no—
374AGL(1,𝔽5)—241no—
375AGL(1,𝔽5)—241no—
376C4×C5—41no—
377C4×C5#92611yescharacteristic
378C4×C5D4×Dic311yescharacteristic
379Dic5—41no—
380Dic5#87911yescharacteristic
381Dic5#88311yescharacteristic
382C24—101no—
383C2×D4—51no—
384C2×D4—101no—
385C2×D4—101no—
386C2×D4—101no—
387C2×D4—101no—
388C2×D4—101no—
389C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
390C22×C4—51no—
391C22×C4—101no—
392C22×C4—151no—
393C22×C4—151no—
394C22×C4—301no—
395C22×C4—301no—
396C2×C8—51no—
397C2×C8—101no—
398C2×C8—101no—
399C2×C8—152no—
400C2×C8—301no—
401C2×C8—301no—
402C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
403C4⋊C4—51no—
404C4⋊C4—101no—
405C4⋊C4—301no—
406C4⋊C4—301no—
407C4⋊C4—301no—
408C4⋊C4—301no—
409C4⋊C4—602no—
410C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
411C22⋊C4—602no—
412C22⋊C4—602no—
413C42—301no—
414C42—301no—
415C3×C5#193611yescharacteristic, complemented, Hall
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—51no—
420C22×C3—51no—
421C22×C3—51no—
422C22×C3—51no—
423C22×C3—51no—
424C22×C3—51no—
425C22×C3—201no—
426C22×C3—201no—
427C22×C3—201no—
428C22×C3—401no—
429C22×C3—401no—
430C22×C3—401no—
431C22×C3—401no—
432C22×C3D4×AGL(1,𝔽5)11yescharacteristic
433C3×C4—41no—
434C3×C4—51no—
435C3×C4—51no—
436C3×C4—201no—
437C3×C4#413011yescharacteristic
438C3×C4D4×AGL(1,𝔽5)11yescharacteristic
439Dic3—201no—
440Dic3—201no—
441Dic3—401no—
442Dic3—401no—
443C2×C5—81no—
444C2×C5#495111yescharacteristic
445C2×C5#515211yescharacteristic
446C2×C5#516411yescharacteristic
447D5—81no—
448D5#476411yescharacteristic
449D5#476511yescharacteristic
450D5#478011yescharacteristic
451D5#478211yescharacteristic
452C23—21no—
453C23—51no—
454C23—101no—
455C23—201no—
456C23—201no—
457C23—201no—
458C23—201no—
459C23—201no—
460C23—201no—
461D4—21no—
462D4—21no—
463D4—101no—
464D4—101no—
465D4—201no—
466D4—201no—
467C2×C4—21no—
468C2×C4—51no—
469C2×C4—51no—
470C2×C4—51no—
471C2×C4—51no—
472C2×C4—51no—
473C2×C4—101no—
474C2×C4—201no—
475C2×C4—201no—
476C2×C4—301no—
477C2×C4—301no—
478C2×C4—301no—
479C2×C4—301no—
480C2×C4—301no—
481C2×C4—301no—
482C2×C4—601no—
483C2×C4—601no—
484C2×C4—601no—
485C2×C4—601no—
486C2×C4—601no—
487C2×C4—601no—
488C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
489C8—21no—
490C8—101no—
491C8—302no—
492C2×C3—51no—
493C2×C3—51no—
494C2×C3—51no—
495C2×C3—51no—
496C2×C3—81no—
497C2×C3—401no—
498C2×C3#6570011yescharacteristic
499C2×C3#6573111yescharacteristic
500C2×C3#6573511yescharacteristic
501C5#7018711yescharacteristic, complemented, Sylow
502C22—41no—
503C22—41no—
504C22—41no—
505C22—51no—
506C22—51no—
507C22—51no—
508C22—51no—
509C22—51no—
510C22—51no—
511C22—201no—
512C22—201no—
513C22—201no—
514C22—401no—
515C22—401no—
516C22—401no—
517C22—401no—
518C22D4×ΓL(1,𝔽16)11yescharacteristic
519C4—41no—
520C4—51no—
521C4—51no—
522C4—201no—
523C4—601no—
524C4—601no—
525C4—1201no—
526C4—1201no—
527C4#9198911yescharacteristic
528C4D4×ΓL(1,𝔽16)11yescharacteristic
529C3#1060396411yescharacteristic, complemented, Sylow
530C2—51no—
531C2—51no—
532C2—51no—
533C2—51no—
534C2—81no—
535C2—401no—
536C2#1175235911yescharacteristic
537C2#1175239011yescharacteristic
538C2#1175239411yescharacteristic
subgroupG/H
centerC22D4×ΓL(1,𝔽16)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#102C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D4×D5C22
cosocleC2×C3×C4×D5C23
hypercenter#102ΓL(1,𝔽16)
hypocenterC3×C5#1936
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
3. C2×#91221C2semidirect
4. #11752371C2semidirect
6. #11746764C2semidirect
7. #11746745C2semidirect
22. C3×C5×#102C4semidirect
23. C3×#3964C4semidirect
24. C3×#3953C4semidirect
25. C3×#3941C4semidirect
87. C5×#102Dic3semidirect
88. #3964Dic3semidirect
89. #3953Dic3semidirect
90. #3941Dic3semidirect
145. C3×#102AGL(1,𝔽5)semidirect
303. #102ΓL(1,𝔽16)semidirect
415. C3×C5#1936semidirect
501. C5#70187semidirect
529. C3#10603964semidirect

Maximal subgroups

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

subgroupindex
#117524392
C2×#912362
C2×#912212
#117523712
C3×D5×#1022
#117467642
#117467452
#106039643
#701875