Finite Group Databasebeta

← #14304750

Subgroups — #14304750

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×#91093C211yesmaximal, characteristic
2C3×#65274C211yesmaximal, characteristic, complemented
3#11748768C211yesmaximal, characteristic
4C2×#90968C211yesmaximal, characteristic
5C2×#90952C211yesmaximal, characteristic, complemented
6C5×#4529C211yesmaximal, characteristic, complemented
7#11745979C211yesmaximal, characteristic, complemented
8#10599650—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C22×C3⋊#168C2211yescharacteristic
12C2×C5×C4⋊Dic3C2211yescharacteristic
13C22×C5×C3⋊C8C2211yescharacteristic
14C2×C3×C4⋊Dic5—21no—
15C2×C3×C4⋊Dic5C2211yescharacteristic
16C2×C3×C4×Dic5C2211yescharacteristic
17C2×#6667—21no—
18C2×#6667—21no—
19#91093C414yescomplemented
20C3×#3963—21no—
21#90968—22no—
22#90952—22no—
23#69617—51nomaximal, Hall
24C2×#3953—31no—
25C2×#3947—31no—
26#65277—31no—
27#65274D311yescharacteristic, complemented
28C2×#3941—31no—
29C5×#340—31no—
30#64749—31no—
31C23×D15—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60C2×C412yes—
40C22×C5×Dic3—21no—
41C22×C3×Dic5—21no—
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C412yes—
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C3⋊#168C2×C412yes—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C2×C5×C3⋊C8D412yes—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—42no—
57C3×C4×Dic5—21no—
58C3×C4×Dic5—21no—
59#6667—42no—
60#6667—42no—
61C3×#389—51no—
62C2×#809—51no—
63C2×#809—51no—
64#4939—51no—
65C2×#803—51no—
66#4529—51no—
67#4529D511yescharacteristic, complemented
68C22×D20—31no—
69C22×C5×C8—31no—
70C2×C5×C4⋊C4—31no—
71C2×C5×C4⋊C4C2×D311yescharacteristic
72C2×#685—61no—
73C2×#685—61no—
74C2×C4⋊Dic5—21no—
75C2×C4⋊Dic5C2×D311yescharacteristic
76C2×C4×Dic5C2×D311yescharacteristic
77C22×#168—31no—
78#3963—21no—
79#3953—62no—
80#3947—62no—
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×C5—22no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5#4111yescharacteristic
97C2×C3×C4×C5#4111yescharacteristic
98C2×C3×C4×C5#4111yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100D60—22no—
101D60—22no—
102D60—41no—
103D60—41no—
104C2×C5×Dic3—41no—
105C2×C5×Dic3—41no—
106C2×C5×Dic3—41no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C2×C3×Dic5—41no—
114C2×C3×Dic5—41no—
115C2×C3×Dic5—41no—
116C3⋊#168—22no—
117C5×C3⋊C8—22no—
118C22×D12—51no—
119C2×C3×C4⋊C4—51no—
120C2×C3×C4⋊C4—101no—
121C2×C3×C4⋊C4C2×D511yescharacteristic
122C2×C3×C42—51no—
123C2×(C2×D3)⋊C4—101no—
124C2×(C2×D3)⋊C4—101no—
125C2×C4⋊Dic3C2×D511yescharacteristic
126C22×C3⋊C8—51no—
127C22×C3⋊C8C2×D511yescharacteristic
128C3×#95—101no—
129#809—54no—
130#809—102no—
131#803—102no—
132C23×D5—61no—
133C22×C4×C5—21no—
134C22×C4×C5—61no—
135C22×C4×C5C22×D311yescharacteristic
136C22×Dic5—21no—
137C22×Dic5#6711yescharacteristic
138C22×Dic5#6711yescharacteristic
139C2×D20—32no—
140C2×D20—61no—
141C2×D20—61no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—61no—
145C2×C5×C8—32no—
146C2×C5×C8—61no—
147C2×C5×C8—61no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—61no—
150C5×C4⋊C4—61no—
151C5×C4⋊C4C4×D312yes—
152#685—122no—
153#685—122no—
154C4⋊Dic5—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5—42no—
157C4×Dic5—21no—
158C4×Dic5—21no—
159C2×#168—32no—
160C2×#168—61no—
161C2×#168—61no—
162C2×#102—151no—
163C2×#102—151no—
164C2×#97—151no—
165#390—151no—
166#389—51no—
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—42no—
184C3×C4×C5#11711yescharacteristic
185C3×C4×C5C4×D411yescharacteristic
186C3×C4×C5#12311yescharacteristic
187C3×C4×C5#12611yescharacteristic
188C3×Dic5—41no—
189C3×Dic5—41no—
190C3×Dic5—81no—
191C5×Dic3—81no—
192C23×D3—101no—
193C22×C3×C4—21no—
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4—101no—
197C22×C3×C4C22×D511yescharacteristic
198C22×Dic3—21no—
199C2×D12—52no—
200C2×D12—101no—
201C2×D12—101no—
202C2×D12—101no—
203C2×D12—101no—
204C2×D12—101no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—101no—
207C3×C4⋊C4—101no—
208C3×C4⋊C4—202no—
209C3×C4⋊C4C4×D512yes—
210C3×C42—101no—
211C3×C42—101no—
212(C2×D3)⋊C4—202no—
213(C2×D3)⋊C4—202no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—52no—
219C2×C3⋊C8—101no—
220C2×C3⋊C8—101no—
221C2×C3⋊C8D2012yes—
222C23×C5C2×#6711yescharacteristic
223C22×D5—62no—
224C22×D5—121no—
225C22×D5—121no—
226C22×D5—121no—
227C22×D5—121no—
228C22×D5—121no—
229C22×D5—121no—
230C2×C4×C5—22no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5—121no—
234C2×C4×C5—121no—
235C2×C4×C5—121no—
236C2×C4×C5C2×C4×D311yescharacteristic
237C2×C4×C5#23511yescharacteristic
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5#23711yescharacteristic
240C2×C4×C5#23911yescharacteristic
241C2×C4×C5#23911yescharacteristic
242C2×Dic5—21no—
243C2×Dic5—21no—
244C2×Dic5—21no—
245C2×Dic5—21no—
246C2×Dic5—21no—
247C2×Dic5—21no—
248C2×Dic5—41no—
249C2×Dic5—41no—
250C2×Dic5—41no—
251D20—62no—
252D20—62no—
253D20—121no—
254D20—121no—
255C5×C8—62no—
256#168—62no—
257C22×D4—151no—
258C22×C8—31no—
259C22×C8—151no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—51no—
262C2×C4⋊C4—101no—
263C2×C4⋊C4D3×D511yescharacteristic
264C2×C22⋊C4—301no—
265C2×C22⋊C4—301no—
266C2×C42—51no—
267#102—154no—
268#102—302no—
269#97—302no—
270#95—101no—
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—22no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—101no—
291C2×C3×C4—101no—
292C2×C3×C4—101no—
293C2×C3×C4—101no—
294C2×C3×C4—101no—
295C2×C3×C4—101no—
296C2×C3×C4—201no—
297C2×C3×C4—201no—
298C2×C3×C4—201no—
299C2×C3×C4C2×C4×D511yescharacteristic
300C2×C3×C4C2×D2011yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4#71111yescharacteristic
303C2×C3×C4#71111yescharacteristic
304C2×C3×C4#71311yescharacteristic
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308D12—102no—
309D12—102no—
310D12—201no—
311D12—201no—
312C3⋊C8—22no—
313C3⋊C8—102no—
314C22×C5C4×#6711yescharacteristic
315C22×C5#93211yescharacteristic
316C22×C5#93911yescharacteristic
317C22×C5#94211yescharacteristic
318C22×C5#94711yescharacteristic
319C22×C5#94911yescharacteristic
320C22×C5#94911yescharacteristic
321C2×D5—122no—
322C2×D5—122no—
323C2×D5—122no—
324C2×D5—241no—
325C2×D5—241no—
326C2×D5—241no—
327C2×D5—241no—
328C4×C5—42no—
329C4×C5—241no—
330C4×C5#89211yescharacteristic
331C4×C5#89311yescharacteristic
332C4×C5#89411yescharacteristic
333C4×C5#89811yescharacteristic
334Dic5—41no—
335Dic5—41no—
336Dic5—81no—
337C24—301no—
338C2×D4—152no—
339C2×D4—301no—
340C2×D4—301no—
341C2×D4—301no—
342C2×D4—301no—
343C2×D4—301no—
344C22×C4—21no—
345C22×C4—51no—
346C22×C4—51no—
347C22×C4—61no—
348C22×C4—101no—
349C22×C4C2×D3×D511yescharacteristic
350C2×C8—32no—
351C2×C8—61no—
352C2×C8—61no—
353C2×C8—152no—
354C2×C8—301no—
355C2×C8—301no—
356C4⋊C4—21no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—101no—
360C4⋊C4—101no—
361C4⋊C4—202no—
362C4⋊C4#120012yes—
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—42no—
383C3×C4—201no—
384C3×C4—201no—
385C3×C4—401no—
386C3×C4C4×D2011yescharacteristic
387C3×C4#403211yescharacteristic
388C3×C4#403811yescharacteristic
389C3×C4#404411yescharacteristic
390Dic3—81no—
391C2×C5#499011yescharacteristic
392C2×C5#501411yescharacteristic
393C2×C5#502611yescharacteristic
394C2×C5#503911yescharacteristic
395C2×C5#504911yescharacteristic
396C2×C5#506711yescharacteristic
397C2×C5#508911yescharacteristic
398D5—242no—
399C23—302no—
400C23—601no—
401C23—601no—
402C23—601no—
403C23—601no—
404C23—601no—
405C23—601no—
406C23D5×#6711yescharacteristic
407D4—302no—
408D4—302no—
409D4—601no—
410D4—601no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—101no—
415C2×C4—101no—
416C2×C4—101no—
417C2×C4—101no—
418C2×C4—101no—
419C2×C4—101no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—201no—
424C2×C4—201no—
425C2×C4—201no—
426C2×C4#676611yescharacteristic
427C2×C4#676811yescharacteristic
428C2×C4#676911yescharacteristic
429C2×C4D3×D2011yescharacteristic
430C2×C4#678211yescharacteristic
431C2×C4C2×#120011yescharacteristic
432C8—62no—
433C8—302no—
434C2×C3#6495911yescharacteristic
435C2×C3#6505311yescharacteristic
436C2×C3#6507411yescharacteristic
437C2×C3#6508411yescharacteristic
438C2×C3#6510611yescharacteristic
439C2×C3#6515411yescharacteristic
440C2×C3#6517511yescharacteristic
441D3—402no—
442C5#6961711yescharacteristic, complemented, Sylow
443C22—602no—
444C22—602no—
445C22—602no—
446C22—1201no—
447C22—1201no—
448C22—1201no—
449C22—1201no—
450C22#9132611yescharacteristic
451C22#9140911yescharacteristic
452C22#9147811yescharacteristic
453C22#9149111yescharacteristic
454C22#9150211yescharacteristic
455C22#9151511yescharacteristic
456C22#9155211yescharacteristic
457C4—42no—
458C4—201no—
459C4—201no—
460C4—241no—
461C4—401no—
462C4#9134511yescharacteristic
463C4#9134711yescharacteristic
464C4#9142711yescharacteristic
465C4#9142811yescharacteristic
466C3#1059965011yescharacteristic, complemented, Sylow
467C2—1202no—
468C2#1174715911yescharacteristic
469C2#1174740111yescharacteristic
470C2#1174746011yescharacteristic
471C2#1174746111yescharacteristic
472C2#1174867811yescharacteristic
473C2#1174897911yescharacteristic
474C2#1174922511yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1936
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#65274C2semidirect
5. C2×#90952C2semidirect
6. C5×#4529C2semidirect
7. #11745979C2semidirect
19. #91093C4semidirect
27. #65274D3semidirect
67. #4529D5semidirect
367. C3×C5#1936semidirect
442. C5#69617semidirect
466. C3#10599650semidirect

Maximal subgroups

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

subgroupindex
C2×#910932
C3×#652742
#117487682
C2×#909682
C2×#909522
C5×#45292
#117459792
#105996503
#696175