Finite Group Databasebeta

← #14471849

Subgroups — #14471849

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5730C211yesmaximal, characteristic, complemented
2#11752636C211yesmaximal, characteristic, complemented
3#11751192C211yesmaximal, characteristic, complemented
4C3×#65377C211yesmaximal, characteristic, complemented
5#11747375C212yesmaximal, complemented
6#11747374C212yesmaximal, complemented
7#11747249C212yesmaximal, complemented
8#11747219C212yesmaximal, complemented
9C4×#6659C211yesmaximal, characteristic, complemented
10#11747033C211yesmaximal, characteristic
11Dic6×#168C211yesmaximal, characteristic, complemented
12#10615374—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C4×Dic30C2211yescharacteristic
15C5×#946—22no—
16C5×#897—21no—
17C5×#893C2212yes—
18C5×D3×C4⋊C4—21no—
19C5×#890C2212yes—
20C4×C5×D12C2211yescharacteristic
21C4×C5×Dic6C2211yescharacteristic
22C3×#4020C2211yescharacteristic
23#91434—21no—
24Dic3×D20C2212yes—
25#91407—22no—
26#91368—21no—
27#91364C2212yes—
28C2×#6659C2211yescharacteristic
29C2×#6652C2212yes—
30#91094C2212yes—
31#91091C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C3×#3941C2212yes—
34C3×#3941C2212yes—
35C3×C4×#168C2211yescharacteristic
36#90985C2211yescharacteristic
37Dic3⋊#168C2212yes—
38#90975C2211yescharacteristic
39#90967C2211yescharacteristic
40#90964C2212yes—
41Dic3×#168C2212yes—
42#81585—51nomaximal, Hall
43C5×#554—31no—
44#65919—31no—
45#65380—31no—
46#65377D311yescharacteristic, complemented
47#65357—32no—
48#65355—32no—
49Q8×#168—31no—
50C4×#687—31no—
51#65305—32no—
52#65304—31no—
53C4×#686—32no—
54C2×C3×C5×Q8—21no—
55C2×Dic30C2311yescharacteristic
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C4×C5×D3—22no—
59C2×C5×Dic6D411yescharacteristic
60C2×C3×D20—21no—
61C2×C3×D20—21no—
62C2×C3×D20C2312yes—
63C2×D5×Dic3—22no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2312yes—
66C3×C42×C5C2311yescharacteristic
67C4⋊Dic15C2311yescharacteristic
68#6712—21no—
69C4×Dic15—21no—
70C2×C3⋊#168C2312yes—
71C5×(C2×D3)⋊C4—21no—
72C5×(C2×D3)⋊C4—22no—
73C5×C4⋊Dic3—22no—
74C5×C4⋊Dic3D411yescharacteristic
75C5×C4⋊Dic3C2311yescharacteristic
76C5×Dic3⋊C4—22no—
77C5×Dic3⋊C4D412yes—
78C4×C5×Dic3C2312yes—
79C2×C3×#168C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81#6665—22no—
82#6665—22no—
83#6665—22no—
84#6659—22no—
85#6652—24no—
86#5730D511yescharacteristic, complemented
87#5713—51no—
88C3×#486—51no—
89#5091—51no—
90#5072—51no—
91#4787—52no—
92#4768—52no—
93#4763—52no—
94#4756—52no—
95C4×#204—51no—
96C8×Dic6—51no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C5×#125—32no—
99C5×C22⋊Q8—61no—
100C5×C22⋊Q8—62no—
101C4×C5×Q8—31no—
102C4×C5×D4—32no—
103C4×C5×D4—31no—
104C2×C5×C4⋊C4—61no—
105#4093—61no—
106C2×#687—31no—
107C2×#686—32no—
108#4040—62no—
109#4039—61no—
110#4021—32no—
111#4020C2×D311yescharacteristic
112C4×D20—32no—
113C4×Dic10—31no—
114#3964—31no—
115#3942—32no—
116#3942—31no—
117#3941—32no—
118#3941C2×D312yes—
119#3941C2×D312yes—
120#3940—31no—
121#3939—32no—
122C4⋊#168—31no—
123C4⋊#168—32no—
124C4×#168—32no—
125C4×#168C2×D311yescharacteristic
126#3361—151noSylow
127C22×C5×D3—21no—
128C22×C3×D5—22no—
129C3×C5×Q8—81no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—21no—
135C2×Dic15—21no—
136Dic30—21no—
137Dic30—21no—
138C2×C5×Dic3—21no—
139C2×C5×Dic3C2×D412yes—
140C2×C5×Dic3C2×D412yes—
141C5×D12—21no—
142C5×D12#4112yes—
143C4×C5×D3—42no—
144C4×C5×D3—82no—
145C5×Dic6—22no—
146C3×D20—22no—
147C3×D20—22no—
148C3×D20—42no—
149C3×D20—81no—
150D5×Dic3—82no—
151C3⋊#168—22no—
152C3×#168—21no—
153C3×#168—21no—
154C3×C4⋊Q8C2×D511yescharacteristic
155C3×#127—51no—
156#946—22no—
157#936—52no—
158#936—101no—
159#935—102no—
160D4×Dic3—52no—
161D4×Dic3—101no—
162C2×#213—52no—
163C2×#204—51no—
164#897—21no—
165#893C2×D512yes—
166D3×C4⋊C4—21no—
167#890C2×D512yes—
168C4×D12C2×D511yescharacteristic
169C4×Dic6—51no—
170C4×Dic6C2×D511yescharacteristic
171C3×#102—52no—
172C3×#102—52no—
173C3×C4×C8—51no—
174#832—52no—
175#821—51no—
176#817—51no—
177#816—51no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#810—52no—
181#807—52no—
182C4⋊(C3⋊C8)—51no—
183C2×C5×Q8—21no—
184C2×C5×Q8—31no—
185C2×C5×D4—31no—
186C22×C4×C5—62no—
187C22×C4×C5—61no—
188C2×D20—21no—
189C2×D20—21no—
190C2×D20C22×D312yes—
191C2×C4×D5—62no—
192C2×Dic10—31no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—31no—
195C5×C4⋊C4—32no—
196C5×C4⋊C4—31no—
197C5×C4⋊C4—62no—
198C5×C4⋊C4—62no—
199C5×C4⋊C4C22×D312yes—
200C5×C22⋊C4—62no—
201C5×C22⋊C4—61no—
202C42×C5—32no—
203C42×C5C22×D311yescharacteristic
204#687—62no—
205#686—64no—
206#685—62no—
207#685—62no—
208#685—62no—
209C4⋊Dic5—31no—
210#683—61no—
211C4×Dic5—61no—
212C2×#168—32no—
213C2×#168C22×D311yescharacteristic
214C2×#168C22×D311yescharacteristic
215#559—151no—
216#554—31no—
217#488—152no—
218#486—51no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—22no—
228C2×C5×D3—41no—
229C2×C5×D3—41no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—42no—
233C3×C4×C5—21no—
234C3×C4×C5—42no—
235C3×C4×C5#13512yes—
236C3×C4×C5C2×#4111yescharacteristic
237C3×C4×C52−1+411yescharacteristic
238Dic15—41no—
239Dic15—41no—
240C5×Dic3—22no—
241C5×Dic3—22no—
242C5×Dic3—41no—
243C2×C3×Q8—21no—
244C2×C3×D4—52no—
245C2×C3×D4—101no—
246C2×C3×D4—101no—
247C22×Dic3—102no—
248C2×D12C22×D511yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—22no—
251C2×Dic6—51no—
252C2×Dic6C22⋊D511yescharacteristic
253C2×C3×C8—51no—
254C2×C3×C8—51no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4C22×D512yes—
257C3×C42C22×D511yescharacteristic
258#217—102no—
259#217—102no—
260#217—102no—
261#213—104no—
262(C2×D3)⋊C4—21no—
263(C2×D3)⋊C4—22no—
264C4⋊Dic3—22no—
265C4⋊Dic3—51no—
266C4⋊Dic3C22⋊D511yescharacteristic
267C4⋊Dic3C22×D511yescharacteristic
268Dic3⋊C4—22no—
269Dic3⋊C4—101no—
270Dic3⋊C4C22⋊D512yes—
271C4×Dic3—101no—
272C4×Dic3C22×D512yes—
273C2×C3⋊C8—52no—
274#204—102no—
275C23×C5—61no—
276C22×D5—22no—
277C5×Q8—62no—
278C5×Q8—81no—
279C5×D4—32no—
280C5×D4—61no—
281C2×C4×C5—22no—
282C2×C4×C5—32no—
283C2×C4×C5—32no—
284C2×C4×C5—61no—
285C2×C4×C5—122no—
286C2×C4×C5—242no—
287C2×C4×C5D3×D411yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5C23×D311yescharacteristic
290C2×Dic5—61no—
291C2×Dic5—61no—
292D20—22no—
293D20—22no—
294D20—42no—
295D20—81no—
296C4×D5—242no—
297Dic10—61no—
298Dic10—61no—
299#168—21no—
300#168—21no—
301#168—62no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8D3×D511yescharacteristic
305#127—51no—
306#125—32no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—61no—
311C22⋊Q8—62no—
312C4×Q8—31no—
313C4×Q8—151no—
314C4×D4—32no—
315C4×D4—31no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—61no—
319#107—152no—
320#106—151no—
321C4⋊C8—152no—
322C4⋊C8—151no—
323#103—151no—
324#103—152no—
325#102—52no—
326#102—52no—
327#102—152no—
328#102—151no—
329C4×C8—51no—
330C4×C8—152no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334C3×D5—82no—
335C5×D3—42no—
336C23×C3—102no—
337C22×D3—21no—
338C3×Q8—81no—
339C3×D4—102no—
340C3×D4—102no—
341C3×D4—202no—
342C3×D4—401no—
343C2×C3×C4—22no—
344C2×C3×C4C2×C22⋊D511yescharacteristic
345C2×C3×C4C2×C22⋊D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—101no—
349C2×Dic3—101no—
350C2×Dic3—402no—
351C2×Dic3C2×C22⋊D512yes—
352C2×Dic3C2×C22⋊D512yes—
353D12—21no—
354D12#71312yes—
355C4×D3—42no—
356C4×D3—82no—
357Dic6—22no—
358Dic6—101no—
359Dic6—101no—
360C3×C8—101no—
361C3×C8—101no—
362C3⋊C8—102no—
363C22×C5—62no—
364C22×C5—121no—
365C22×C5—121no—
366C22×C5C2×D3×D411yescharacteristic
367C2×D5—42no—
368C2×D5—42no—
369C2×D5—42no—
370C4×C5—21no—
371C4×C5—42no—
372C4×C5—62no—
373C4×C5—62no—
374C4×C5—121no—
375C4×C5#91612yes—
376C4×C5D3×#4111yescharacteristic
377C4×C5#101011yescharacteristic
378Dic5—121no—
379Dic5—121no—
380C2×Q8—21no—
381C2×Q8—31no—
382C2×Q8—151no—
383C2×D4—31no—
384C2×D4—52no—
385C2×D4—101no—
386C2×D4—101no—
387C22×C4—62no—
388C22×C4—61no—
389C22×C4—302no—
390SD16—302no—
391D8—304no—
392C2×C8—51no—
393C2×C8—51no—
394C2×C8—152no—
395C4⋊C4—21no—
396C4⋊C4—31no—
397C4⋊C4—32no—
398C4⋊C4—31no—
399C4⋊C4—62no—
400C4⋊C4—62no—
401C4⋊C4—151no—
402C4⋊C4—301no—
403C4⋊C4C2×D3×D512yes—
404C22⋊C4—62no—
405C22⋊C4—61no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—32no—
410C42—301no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—202no—
414C22×C3—202no—
415C22×C3—202no—
416C22×C3C22×C22⋊D511yescharacteristic
417C2×D3—22no—
418C2×D3—41no—
419C2×D3—41no—
420C3×C4—21no—
421C3×C4—42no—
422C3×C4#409612yes—
423C3×C4C2×#71311yescharacteristic
424C3×C4#414711yescharacteristic
425Dic3—22no—
426Dic3—22no—
427Dic3—41no—
428Dic3—201no—
429Dic3—201no—
430C2×C5—122no—
431C2×C5#567711yescharacteristic
432C2×C5#575711yescharacteristic
433C2×C5C2×#91611yescharacteristic
434D5—82no—
435C23—61no—
436C23—102no—
437Q8—62no—
438Q8—81no—
439Q8—301no—
440Q8—301no—
441D4—32no—
442D4—61no—
443D4—102no—
444D4—102no—
445D4—202no—
446D4—401no—
447C2×C4—22no—
448C2×C4—32no—
449C2×C4—32no—
450C2×C4—61no—
451C2×C4—122no—
452C2×C4—242no—
453C2×C4—301no—
454C2×C4—301no—
455C2×C4—1202no—
456C2×C4D3×C22⋊D511yescharacteristic
457C2×C4D3×C22⋊D511yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—101no—
460C8—101no—
461C8—302no—
462C2×C3—402no—
463C2×C3#6615111yescharacteristic
464C2×C3C2×#409611yescharacteristic
465C2×C3#6616911yescharacteristic
466D3—42no—
467C5#8158511yescharacteristic, complemented, Sylow
468C22—62no—
469C22—121no—
470C22—121no—
471C22—202no—
472C22—202no—
473C22—202no—
474C22C2×D3×C22⋊D511yescharacteristic
475C4—21no—
476C4—42no—
477C4—62no—
478C4—62no—
479C4—121no—
480C4—601no—
481C4—601no—
482C4#9151712yes—
483C4#9202811yescharacteristic
484C4D3×#71311yescharacteristic
485C3#1061537411yescharacteristic, complemented, Sylow
486C2—122no—
487C2—402no—
488C2#1175469711yescharacteristic
489C2C2×#9151711yescharacteristic
490C2#1175523011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11747033C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5730C2semidirect
2. #11752636C2semidirect
3. #11751192C2semidirect
4. C3×#65377C2semidirect
5. #11747375C2semidirect
6. #11747374C2semidirect
7. #11747249C2semidirect
8. #11747219C2semidirect
9. C4×#6659C2semidirect
11. Dic6×#168C2semidirect
46. #65377D3semidirect
86. #5730D5semidirect
412. C3×C5#3361semidirect
467. C5#81585semidirect
485. C3#10615374semidirect

Maximal subgroups

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

subgroupindex
C5×#57302
#117526362
#117511922
C3×#653772
#117473752
#117473742
#117472492
#117472192
C4×#66592
#117470332
Dic6×#1682
#106153743
#815855