Finite Group Databasebeta

← #14304724

Subgroups — #14304724

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91105C211yesmaximal, characteristic
2C2×C3×#3947C211yesmaximal, characteristic, complemented
3#11748842C211yesmaximal, characteristic, complemented
4#11748768C211yesmaximal, characteristic
5C2×#90969C211yesmaximal, characteristic
6C5×#4551C211yesmaximal, characteristic, complemented
7#11745981C211yesmaximal, characteristic, complemented
8#10599650—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C2×C5×C4⋊Dic3C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4×Dic5C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C2×Dic3⋊Dic5—21no—
17C2×#6667—21no—
18C2×#6667—21no—
19#91105—22no—
20C3×#3947—22no—
21#90994—21no—
22#90969C414yescomplemented
23#69818—51nomaximal, Hall
24C2×#3953—31no—
25C2×#3947D311yescharacteristic, complemented
26#65277—31no—
27#65274—31no—
28C2×#3941—31no—
29C5×#340—31no—
30#64749—31no—
31C23×D15—21no—
32C22×C3×C4×C5C2311yescharacteristic
33C22×Dic15—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60C2×C412yes—
40C22×C5×Dic3—21no—
41C22×C5×Dic3—21no—
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8D412yes—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3C2×C412yes—
53C3×C4×Dic5—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57C2×C3×#168C2×C412yes—
58Dic3⋊Dic5—42no—
59#6667—42no—
60#6667—42no—
61C2×C3×#97—51no—
62C2×#821—51no—
63C2×#821—51no—
64#4939—51no—
65#4928—51no—
66#4551—51no—
67#4551D511yescharacteristic, complemented
68C22×D20—31no—
69C22×C5×C8C2×D311yescharacteristic
70C2×C5×C4⋊C4—31no—
71C2×C5×C4⋊C4—31no—
72C2×#685—61no—
73C2×#685—61no—
74C2×C4⋊Dic5—31no—
75C2×C4⋊Dic5—61no—
76C2×C4×Dic5C2×D311yescharacteristic
77C22×#168C2×D311yescharacteristic
78#3963—61no—
79#3953—62no—
80#3947—22no—
81#3941—34no—
82#1936—151noSylow
83C23×C3×C5C2×D411yescharacteristic
84C22×D15—22no—
85C22×D15—41no—
86C22×D15—41no—
87C22×D15—41no—
88C22×D15—41no—
89C22×D15—41no—
90C22×D15—41no—
91C2×C3×C4×C5C22×C411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×Dic15—41no—
98C2×Dic15—41no—
99C2×Dic15—41no—
100D60—22no—
101D60—22no—
102D60—41no—
103D60—41no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—41no—
106C2×C5×Dic3—41no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—41no—
109C2×C5×Dic3—41no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C3×C5×C8—22no—
117C3×#168—22no—
118C22×D12—51no—
119C22×C3×C8—51no—
120C22×C3×C8C2×D511yescharacteristic
121C2×C3×C42—51no—
122C2×(C2×D3)⋊C4—101no—
123C2×(C2×D3)⋊C4—101no—
124C2×C4⋊Dic3—51no—
125C2×C4⋊Dic3C2×D511yescharacteristic
126C2×C4⋊Dic3C2×D511yescharacteristic
127C2×Dic3⋊C4—101no—
128C3×#97—102no—
129C3⋊#95—101no—
130#821—54no—
131#821—102no—
132C23×D5—61no—
133C22×C4×C5—61no—
134C22×C4×C5—61no—
135C22×C4×C5C22×D311yescharacteristic
136C22×Dic5—61no—
137C22×Dic5D1211yescharacteristic
138C22×Dic5D1211yescharacteristic
139C2×D20—32no—
140C2×D20—61no—
141C2×D20—61no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—61no—
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C2×C5×C8#6712yes—
148C5×C4⋊C4—32no—
149C5×C4⋊C4—61no—
150C5×C4⋊C4—61no—
151C5×C4⋊C4—61no—
152#685—122no—
153#685—122no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5—122no—
157C4×Dic5—21no—
158C4×Dic5—21no—
159C2×#168—21no—
160C2×#168—21no—
161C2×#168C4×D312yes—
162C2×#102—151no—
163C2×#102—151no—
164C2×#97—51no—
165#390—151no—
166#389—151no—
167#340—31no—
168#340—151no—
169C22×C3×C5C4×D411yescharacteristic
170C22×C3×C5#12111yescharacteristic
171C22×C3×C5#12411yescharacteristic
172C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
173C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
174C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C2×D15—42no—
177C2×D15—42no—
178C2×D15—42no—
179C2×D15—81no—
180C2×D15—81no—
181C2×D15—81no—
182C2×D15—81no—
183C3×C4×C5#11711yescharacteristic
184C3×C4×C5C4×D411yescharacteristic
185C3×C4×C5#12311yescharacteristic
186C3×C4×C5#12611yescharacteristic
187Dic15—81no—
188C3×Dic5—41no—
189C3×Dic5—41no—
190C5×Dic3—42no—
191C5×Dic3—81no—
192C23×D3—101no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4C22×D511yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—101no—
199C2×D12—52no—
200C2×D12—101no—
201C2×D12—101no—
202C2×D12—101no—
203C2×D12—101no—
204C2×D12—101no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—52no—
208C2×C3×C8—101no—
209C2×C3×C8—101no—
210C2×C3×C8D2012yes—
211C3×C42—101no—
212C3×C42—101no—
213(C2×D3)⋊C4—202no—
214(C2×D3)⋊C4—202no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—21no—
218C4⋊Dic3—101no—
219C4⋊Dic3—101no—
220C4⋊Dic3C4×D512yes—
221Dic3⋊C4—202no—
222C23×C5C2×D1211yescharacteristic
223C22×D5—62no—
224C22×D5—121no—
225C22×D5—121no—
226C22×D5—121no—
227C22×D5—121no—
228C22×D5—121no—
229C22×D5—121no—
230C2×C4×C5—62no—
231C2×C4×C5—121no—
232C2×C4×C5—121no—
233C2×C4×C5—121no—
234C2×C4×C5—121no—
235C2×C4×C5—121no—
236C2×C4×C5C2×C4×D311yescharacteristic
237C2×C4×C5#23511yescharacteristic
238C2×C4×C5#23511yescharacteristic
239C2×C4×C5#23511yescharacteristic
240C2×C4×C5#23511yescharacteristic
241C2×C4×C5C2×#6711yescharacteristic
242C2×Dic5—21no—
243C2×Dic5—21no—
244C2×Dic5—21no—
245C2×Dic5—21no—
246C2×Dic5—21no—
247C2×Dic5—21no—
248C2×Dic5—121no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251D20—62no—
252D20—62no—
253D20—121no—
254D20—121no—
255C5×C8—22no—
256#168—22no—
257C22×D4—151no—
258C22×C8—51no—
259C22×C8D3×D511yescharacteristic
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—151no—
263C2×C4⋊C4—301no—
264C2×C22⋊C4—301no—
265C2×C22⋊C4—301no—
266C2×C42—51no—
267#102—154no—
268#102—302no—
269#97—102no—
270#95—301no—
271C2×C3×C5#38811yescharacteristic
272C2×C3×C5#44011yescharacteristic
273C2×C3×C5#44211yescharacteristic
274C2×C3×C5#46811yescharacteristic
275C2×C3×C5#46911yescharacteristic
276C2×C3×C5#48911yescharacteristic
277C2×C3×C5#49011yescharacteristic
278D15—82no—
279C23×C3D4×D511yescharacteristic
280C22×D3—102no—
281C22×D3—201no—
282C22×D3—201no—
283C22×D3—201no—
284C22×D3—201no—
285C22×D3—201no—
286C22×D3—201no—
287C2×C3×C4—101no—
288C2×C3×C4—101no—
289C2×C3×C4—101no—
290C2×C3×C4—101no—
291C2×C3×C4—101no—
292C2×C3×C4—101no—
293C2×C3×C4C2×C4×D511yescharacteristic
294C2×C3×C4C2×D2011yescharacteristic
295C2×C3×C4#70911yescharacteristic
296C2×C3×C4#71111yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4#71311yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—201no—
306C2×Dic3—201no—
307C2×Dic3—201no—
308D12—102no—
309D12—102no—
310D12—201no—
311D12—201no—
312C3×C8—22no—
313C3×C8—102no—
314C22×C5C4×D1211yescharacteristic
315C22×C5#87511yescharacteristic
316C22×C5#90811yescharacteristic
317C22×C5#90811yescharacteristic
318C22×C5#90811yescharacteristic
319C22×C5#90911yescharacteristic
320C22×C5#93011yescharacteristic
321C2×D5—122no—
322C2×D5—122no—
323C2×D5—122no—
324C2×D5—241no—
325C2×D5—241no—
326C2×D5—241no—
327C2×D5—241no—
328C4×C5—122no—
329C4×C5—241no—
330C4×C5#87211yescharacteristic
331C4×C5#87611yescharacteristic
332C4×C5C4×#6711yescharacteristic
333C4×C5#92911yescharacteristic
334Dic5—41no—
335Dic5—41no—
336Dic5—241no—
337C24—301no—
338C2×D4—152no—
339C2×D4—301no—
340C2×D4—301no—
341C2×D4—301no—
342C2×D4—301no—
343C2×D4—301no—
344C22×C4—51no—
345C22×C4—51no—
346C22×C4—61no—
347C22×C4—61no—
348C22×C4—301no—
349C22×C4C2×D3×D511yescharacteristic
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—52no—
353C2×C8—101no—
354C2×C8—101no—
355C2×C8#120212yes—
356C4⋊C4—32no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—301no—
361C4⋊C4—301no—
362C4⋊C4—602no—
363C22⋊C4—602no—
364C22⋊C4—602no—
365C42—101no—
366C42—101no—
367C3×C5#193611yescharacteristic, complemented, Hall
368C22×C3#402711yescharacteristic
369C22×C3#403111yescharacteristic
370C22×C3#404111yescharacteristic
371C22×C3#405711yescharacteristic
372C22×C3#406011yescharacteristic
373C22×C3#406011yescharacteristic
374C22×C3#406411yescharacteristic
375C2×D3—202no—
376C2×D3—202no—
377C2×D3—202no—
378C2×D3—401no—
379C2×D3—401no—
380C2×D3—401no—
381C2×D3—401no—
382C3×C4—201no—
383C3×C4—201no—
384C3×C4C4×D2011yescharacteristic
385C3×C4#403211yescharacteristic
386C3×C4#403811yescharacteristic
387C3×C4#404411yescharacteristic
388Dic3—42no—
389Dic3—81no—
390Dic3—401no—
391C2×C5#471011yescharacteristic
392C2×C5#471111yescharacteristic
393C2×C5#471311yescharacteristic
394C2×C5#471411yescharacteristic
395C2×C5#494011yescharacteristic
396C2×C5#513411yescharacteristic
397C2×C5#513511yescharacteristic
398D5—242no—
399C23—302no—
400C23—601no—
401C23—601no—
402C23—601no—
403C23—601no—
404C23—601no—
405C23—601no—
406C23D5×D1211yescharacteristic
407D4—302no—
408D4—302no—
409D4—601no—
410D4—601no—
411C2×C4—62no—
412C2×C4—101no—
413C2×C4—101no—
414C2×C4—101no—
415C2×C4—101no—
416C2×C4—101no—
417C2×C4—101no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—601no—
424C2×C4—601no—
425C2×C4—601no—
426C2×C4#677111yescharacteristic
427C2×C4#677311yescharacteristic
428C2×C4C4×D3×D511yescharacteristic
429C2×C4#678211yescharacteristic
430C2×C4#678211yescharacteristic
431C2×C4C2×#120211yescharacteristic
432C8—22no—
433C8—102no—
434C2×C3#6495911yescharacteristic
435C2×C3#6505311yescharacteristic
436C2×C3#6507411yescharacteristic
437C2×C3#6508411yescharacteristic
438C2×C3#6510611yescharacteristic
439C2×C3#6515411yescharacteristic
440C2×C3#6517511yescharacteristic
441D3—402no—
442C5#6981811yescharacteristic, complemented, Sylow
443C22—602no—
444C22—602no—
445C22—602no—
446C22—1201no—
447C22—1201no—
448C22—1201no—
449C22—1201no—
450C22#9124911yescharacteristic
451C22#9124911yescharacteristic
452C22#9125011yescharacteristic
453C22#9126111yescharacteristic
454C22#9135011yescharacteristic
455C22#9140511yescharacteristic
456C22#9145011yescharacteristic
457C4—122no—
458C4—201no—
459C4—201no—
460C4—241no—
461C4—1201no—
462C4#9138711yescharacteristic
463C4#9140211yescharacteristic
464C4C4×#120211yescharacteristic
465C4#9154611yescharacteristic
466C3#1059965011yescharacteristic, complemented, Sylow
467C2—1202no—
468C2#1174774611yescharacteristic
469C2#1174774811yescharacteristic
470C2#1174790411yescharacteristic
471C2#1174790711yescharacteristic
472C2#1174799811yescharacteristic
473C2#1174802211yescharacteristic
474C2#1174872611yescharacteristic
subgroupG/H
centerC23D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1936
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
2. C2×C3×#3947C2semidirect
3. #11748842C2semidirect
6. C5×#4551C2semidirect
7. #11745981C2semidirect
22. #90969C4semidirect
25. C2×#3947D3semidirect
67. #4551D5semidirect
367. C3×C5#1936semidirect
442. C5#69818semidirect
466. C3#10599650semidirect

Maximal subgroups

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

subgroupindex
C2×#911052
C2×C3×#39472
#117488422
#117487682
C2×#909692
C5×#45512
#117459812
#105996503
#698185