Finite Group Databasebeta

← #14304749

Subgroups — #14304749

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
1#11751085C211yesmaximal, characteristic, complemented
2C2×C3×#3941C211yesmaximal, characteristic
3#11748796C211yesmaximal, characteristic
4C2×#90965C211yesmaximal, characteristic
5C2×#90954C211yesmaximal, characteristic, complemented
6C5×#4529C211yesmaximal, characteristic, complemented
7#11745981C211yesmaximal, characteristic, complemented
8#10599650—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic15—21no—
12C2×C4⋊Dic15C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C22×C3×#168C2211yescharacteristic
17C2×#6665—21no—
18C2×#6665—21no—
19#91115—21no—
20C3×#3941C414yescomplemented
21#90965—22no—
22#90954—22no—
23#70187—51nomaximal, Hall
24C2×#3953—31no—
25C2×#3947—31no—
26#65277—31no—
27#65274—31no—
28C2×#3941D311yescharacteristic
29C5×#340—31no—
30#64749—31no—
31C23×C3×D5—21no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C22×Dic15—21no—
35C22×Dic15D411yescharacteristic
36C22×Dic15D411yescharacteristic
37C22×C5×Dic3—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C412yes—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C412yes—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15—42no—
49C4×Dic15—21no—
50C4×Dic15—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8D412yes—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58C2×C3×#168C2×C412yes—
59#6665—42no—
60#6665—42no—
61C2×C3×#102—51no—
62#5221—51no—
63C2×#832—51no—
64C2×#815—51no—
65#4984—51no—
66#4551—51no—
67#4529D511yescharacteristic, complemented
68C22×D20C2×D311yescharacteristic
69C22×C5×C8—31no—
70C2×C5×C4⋊C4—31no—
71C2×C5×C4⋊C4C2×D311yescharacteristic
72C2×#685—61no—
73C2×#685—61no—
74C2×C4⋊Dic5—31no—
75C2×C4⋊Dic5—61no—
76C2×C4×Dic5—31no—
77C22×#168C2×D311yescharacteristic
78#3963—61no—
79#3953—62no—
80#3947—62no—
81#3941Dic314yescomplemented
82#1936—151noSylow
83C23×C3×C5C2×D411yescharacteristic
84C22×C3×D5—22no—
85C22×C3×D5—41no—
86C22×C3×D5—41no—
87C22×C3×D5—41no—
88C22×C3×D5—41no—
89C22×C3×D5—41no—
90C22×C3×D5—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
100C2×Dic15—21no—
101C2×Dic15—21no—
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—41no—
107C2×Dic15—41no—
108C2×Dic15—41no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C3×D20—22no—
113C3×D20—22no—
114C3×D20—41no—
115C3×D20—41no—
116C3×#168—22no—
117C5×C3⋊C8—22no—
118C22×C3×D4—51no—
119C22×C3×C8—51no—
120C2×C3×C4⋊C4C2×D511yescharacteristic
121C2×#217—101no—
122C2×#217—101no—
123C2×C4⋊Dic3—51no—
124C2×C4⋊Dic3—101no—
125C2×C4⋊Dic3C2×D511yescharacteristic
126C2×C4×Dic3—51no—
127C22×C3⋊C8C2×D511yescharacteristic
128C3×#102—54no—
129#832—102no—
130C3⋊#95—101no—
131#815—102no—
132C23×D5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—61no—
135C22×C4×C5C22×D311yescharacteristic
136C22×Dic5—31no—
137C22×Dic5—31no—
138C22×Dic5—61no—
139C2×D20—21no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20—21no—
144C2×D20C2×Dic312yes—
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⋊C4C2×Dic312yes—
152#685—122no—
153#685—122no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156C4⋊Dic5—122no—
157C4×Dic5—61no—
158C4×Dic5—61no—
159C2×#168—21no—
160C2×#168—21no—
161C2×#168C2×Dic312yes—
162C2×#102—51no—
163C2×#102—151no—
164C2×#97—151no—
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×C3×D5—42no—
177C2×C3×D5—42no—
178C2×C3×D5—42no—
179C2×C3×D5—81no—
180C2×C3×D5—81no—
181C2×C3×D5—81no—
182C2×C3×D5—81no—
183C3×C4×C5—42no—
184C3×C4×C5#11711yescharacteristic
185C3×C4×C5C4×D411yescharacteristic
186C3×C4×C5#12311yescharacteristic
187C3×C4×C5#12611yescharacteristic
188Dic15—41no—
189Dic15—41no—
190Dic15—81no—
191C5×Dic3—81no—
192C24×C3—101no—
193C2×C3×D4—52no—
194C2×C3×D4—101no—
195C2×C3×D4—101no—
196C2×C3×D4—101no—
197C2×C3×D4—101no—
198C2×C3×D4—101no—
199C22×C3×C4—21no—
200C22×C3×C4C22×D511yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—51no—
203C22×Dic3—51no—
204C22×Dic3—101no—
205C2×C3×C8—52no—
206C2×C3×C8—101no—
207C2×C3×C8—101no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4C4×D512yes—
210#217—202no—
211#217—202no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214C4⋊Dic3—101no—
215C4⋊Dic3—101no—
216C4⋊Dic3—202no—
217C4×Dic3—101no—
218C4×Dic3—101no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8D2012yes—
222C23×C5D3×D411yescharacteristic
223C22×D5—22no—
224C22×D5—41no—
225C22×D5—41no—
226C22×D5—41no—
227C22×D5—41no—
228C22×D5—41no—
229C22×D5—41no—
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×C5#23511yescharacteristic
237C2×C4×C5#23511yescharacteristic
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5#23711yescharacteristic
240C2×C4×C5#23711yescharacteristic
241C2×C4×C5C22×Dic311yescharacteristic
242C2×Dic5—61no—
243C2×Dic5—61no—
244C2×Dic5—61no—
245C2×Dic5—61no—
246C2×Dic5—61no—
247C2×Dic5—61no—
248C2×Dic5—121no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251D20—22no—
252D20—22no—
253D20—41no—
254D20—41no—
255C5×C8—62no—
256#168—22no—
257C22×D4—51no—
258C22×C8—31no—
259C22×C8—51no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—151no—
262C2×C4⋊C4—301no—
263C2×C4⋊C4D3×D511yescharacteristic
264C2×C22⋊C4—301no—
265C2×C22⋊C4—301no—
266C2×C42—151no—
267#102—54no—
268#102—302no—
269#97—302no—
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
278C3×D5—82no—
279C23×C3—102no—
280C23×C3—201no—
281C23×C3—201no—
282C23×C3—201no—
283C23×C3—201no—
284C23×C3—201no—
285C23×C3—201no—
286C23×C3D4×D511yescharacteristic
287C3×D4—102no—
288C3×D4—102no—
289C3×D4—201no—
290C3×D4—201no—
291C2×C3×C4—22no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4C2×C4×D511yescharacteristic
295C2×C3×C4C2×D2011yescharacteristic
296C2×C3×C4#70911yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4#71111yescharacteristic
299C2×C3×C4#71311yescharacteristic
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—101no—
304C2×Dic3—101no—
305C2×Dic3—101no—
306C2×Dic3—101no—
307C2×Dic3—101no—
308C2×Dic3—101no—
309C2×Dic3—201no—
310C2×Dic3—201no—
311C2×Dic3—201no—
312C3×C8—102no—
313C3⋊C8—22no—
314C22×C5#88411yescharacteristic
315C22×C5#88511yescharacteristic
316C22×C5#91111yescharacteristic
317C22×C5#91111yescharacteristic
318C22×C5#91411yescharacteristic
319C22×C5#91511yescharacteristic
320C22×C5D4×Dic311yescharacteristic
321C2×D5—42no—
322C2×D5—42no—
323C2×D5—42no—
324C2×D5—81no—
325C2×D5—81no—
326C2×D5—81no—
327C2×D5—81no—
328C4×C5—42no—
329C4×C5—241no—
330C4×C5#87911yescharacteristic
331C4×C5#88311yescharacteristic
332C4×C5#92611yescharacteristic
333C4×C5D4×Dic311yescharacteristic
334Dic5—121no—
335Dic5—121no—
336Dic5—241no—
337C24—101no—
338C2×D4—52no—
339C2×D4—101no—
340C2×D4—101no—
341C2×D4—101no—
342C2×D4—101no—
343C2×D4—101no—
344C22×C4—21no—
345C22×C4—61no—
346C22×C4—151no—
347C22×C4—151no—
348C22×C4—301no—
349C22×C4C2×D3×D511yescharacteristic
350C2×C8—32no—
351C2×C8—52no—
352C2×C8—61no—
353C2×C8—61no—
354C2×C8—101no—
355C2×C8—101no—
356C4⋊C4—21no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—301no—
360C4⋊C4—301no—
361C4⋊C4—602no—
362C4⋊C4D5×Dic312yes—
363C22⋊C4—602no—
364C22⋊C4—602no—
365C42—301no—
366C42—301no—
367C3×C5#193611yescharacteristic, complemented, Hall
368C22×C3—202no—
369C22×C3—202no—
370C22×C3—202no—
371C22×C3—401no—
372C22×C3—401no—
373C22×C3—401no—
374C22×C3—401no—
375C22×C3#402711yescharacteristic
376C22×C3#403111yescharacteristic
377C22×C3#404111yescharacteristic
378C22×C3#405711yescharacteristic
379C22×C3#406011yescharacteristic
380C22×C3#406011yescharacteristic
381C22×C3#406411yescharacteristic
382C3×C4—42no—
383C3×C4C4×D2011yescharacteristic
384C3×C4#403211yescharacteristic
385C3×C4#403811yescharacteristic
386C3×C4#404411yescharacteristic
387Dic3—81no—
388Dic3—201no—
389Dic3—201no—
390Dic3—401no—
391C2×C5#476411yescharacteristic
392C2×C5#476511yescharacteristic
393C2×C5#478011yescharacteristic
394C2×C5#478211yescharacteristic
395C2×C5#495111yescharacteristic
396C2×C5#515211yescharacteristic
397C2×C5#516411yescharacteristic
398D5—82no—
399C23—102no—
400C23—201no—
401C23—201no—
402C23—201no—
403C23—201no—
404C23—201no—
405C23—201no—
406C23#679011yescharacteristic
407D4—102no—
408D4—102no—
409D4—201no—
410D4—201no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—301no—
418C2×C4—301no—
419C2×C4—301no—
420C2×C4—301no—
421C2×C4—301no—
422C2×C4—301no—
423C2×C4—601no—
424C2×C4—601no—
425C2×C4—601no—
426C2×C4#676511yescharacteristic
427C2×C4#677211yescharacteristic
428C2×C4#677311yescharacteristic
429C2×C4D3×D2011yescharacteristic
430C2×C4C2×D5×Dic311yescharacteristic
431C2×C4#678011yescharacteristic
432C8—62no—
433C8—102no—
434C2×C3—402no—
435C2×C3#6495911yescharacteristic
436C2×C3#6505311yescharacteristic
437C2×C3#6507411yescharacteristic
438C2×C3#6508411yescharacteristic
439C2×C3#6510611yescharacteristic
440C2×C3#6515411yescharacteristic
441C2×C3#6517511yescharacteristic
442C5#7018711yescharacteristic, complemented, Sylow
443C22—202no—
444C22—202no—
445C22—202no—
446C22—401no—
447C22—401no—
448C22—401no—
449C22—401no—
450C22#9145911yescharacteristic
451C22#9146211yescharacteristic
452C22#9148211yescharacteristic
453C22#9149811yescharacteristic
454C22#9150611yescharacteristic
455C22#9152211yescharacteristic
456C22#9155911yescharacteristic
457C4—42no—
458C4—241no—
459C4—601no—
460C4—601no—
461C4—1201no—
462C4#9135811yescharacteristic
463C4#9136211yescharacteristic
464C4Dic3×D2011yescharacteristic
465C4#9145711yescharacteristic
466C3#1059965011yescharacteristic, complemented, Sylow
467C2—402no—
468C2#1174732611yescharacteristic
469C2#1174732811yescharacteristic
470C2#1174738411yescharacteristic
471C2#1174740911yescharacteristic
472C2#1174877211yescharacteristic
473C2#1174899511yescharacteristic
474C2#1174924111yescharacteristic
subgroupG/H
centerC23#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D20C22
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
1. #11751085C2semidirect
5. C2×#90954C2semidirect
6. C5×#4529C2semidirect
7. #11745981C2semidirect
20. C3×#3941C4semidirect
67. #4529D5semidirect
81. #3941Dic3semidirect
367. C3×C5#1936semidirect
442. C5#70187semidirect
466. C3#10599650semidirect

Maximal subgroups

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

subgroupindex
#117510852
C2×C3×#39412
#117487962
C2×#909652
C2×#909542
C5×#45292
#117459812
#105996503
#701875