Finite Group Databasebeta

← #14471831

Subgroups — #14471831

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×#5543C211yesmaximal, characteristic, complemented
2#11752636C211yesmaximal, characteristic, complemented
3C4×#6716C211yesmaximal, characteristic, complemented
4C3×#65304C211yesmaximal, characteristic
5#11749079C212yesmaximal, complemented
6Dic3×#686C212yesmaximal, complemented
7#11747374C212yesmaximal, complemented
8#11747251C212yesmaximal, complemented
9#11746963C211yesmaximal, characteristic, complemented
10#11746895C211yesmaximal, characteristic, complemented
11#11746857C211yesmaximal, characteristic, complemented
12#10615374—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14C2×#6716C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C5×D4×Dic3C2212yes—
17C2×C5×C4⋊Dic3—21no—
18C5×#924—21no—
19C5×#890C2212yes—
20C5×#878—22no—
21C5×#869C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C2×C3×#686C2212yes—
24C3×#4020C2211yescharacteristic
25#91434—21no—
26Dic3×D20C2212yes—
27#91407—22no—
28#91368—21no—
29#91364C2212yes—
30#91116C2211yescharacteristic
31#91094C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C3×#3941C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90988C2212yes—
37Dic3⋊#168C2212yes—
38#90975C2212yes—
39#90964C2212yes—
40#90964C2212yes—
41Dic3×#168C2212yes—
42#80319—51nomaximal, Hall
43C5×#554—31no—
44#65919—31no—
45#65380—31no—
46#65377—31no—
47#65357—32no—
48#65355—32no—
49Q8×#168—31no—
50C4×#687—31no—
51#65305—32no—
52#65304D311yescharacteristic
53C4×#686—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30C2311yescharacteristic
57C22×C5×Dic3—22no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6D411yescharacteristic
60C2×C3×D20—21no—
61C2×C3×D20—21no—
62C2×C3×D20C2312yes—
63C2×D5×Dic3—22no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C5×C22⋊C4—21no—
66C3×C42×C5C2311yescharacteristic
67#6716—22no—
68C4⋊Dic15C2311yescharacteristic
69#6712—21no—
70C4×Dic15—21no—
71C2×C3⋊#168C2311yescharacteristic
72C2×C3⋊#168C2311yescharacteristic
73C5×#217—22no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3—22no—
76C5×C4⋊Dic3D411yescharacteristic
77C5×C4⋊Dic3C2312yes—
78C5×Dic3⋊C4—22no—
79C5×Dic3⋊C4D412yes—
80C4×C5×Dic3C2312yes—
81C3×#686—24no—
82C2×C3×#168C2312yes—
83#6665—22no—
84#6665—22no—
85#6665—22no—
86#5713—51no—
87#5543D511yescharacteristic, complemented
88C3×#459—51no—
89#5153—52no—
90Dic3×D8—52no—
91#5070—51no—
92C4×#214—51no—
93#4850—51no—
94#4830—51no—
95#4768—52no—
96#4766—52no—
97C5×C4⋊Q8—31no—
98C5×#125—32no—
99C5×C22⋊Q8—62no—
100C5×C22⋊Q8—61no—
101C4×C5×Q8—31no—
102C4×C5×D4—32no—
103C4×C5×D4C2×D311yescharacteristic
104C2×C5×C4⋊C4—61no—
105#4093—61no—
106C2×#687—31no—
107C2×#686C2×D312yes—
108#4040—62no—
109#4039—61no—
110#4021—32no—
111#4020C2×D311yescharacteristic
112C4×D20—32no—
113C4×Dic10—31no—
114#3964—31no—
115#3942—31no—
116#3942—32no—
117#3941—32no—
118#3941—32no—
119#3941C2×D312yes—
120#3940—31no—
121#3939—32no—
122C4⋊#168—32no—
123C4⋊#168C2×D311yescharacteristic
124C4×#168—31no—
125C4×#168—32no—
126#3361—151noSylow
127C23×C3×C5—21no—
128C22×C3×D5—22no—
129C3×C5×D4—21no—
130C3×C5×D4#4112yes—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—21no—
137C2×Dic15—21no—
138Dic30—21no—
139Dic30—21no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—82no—
142C2×C5×Dic3C2×D412yes—
143C2×C5×Dic3C2×D412yes—
144C5×Dic6—22no—
145C5×Dic6—81no—
146C3×D20—22no—
147C3×D20—22no—
148C3×D20—42no—
149C3×D20—81no—
150D5×Dic3—82no—
151C3⋊#168—21no—
152C3⋊#168—21no—
153C3×#168—22no—
154C2×C3×D8—52no—
155C3×#127—51no—
156C3×C4×D4C2×D511yescharacteristic
157#936—52no—
158#936—101no—
159#935—102no—
160D4×Dic3—52no—
161D4×Dic3—101no—
162D4×Dic3C2×D512yes—
163C2×#214—51no—
164C2×C4⋊Dic3—21no—
165#924—21no—
166#890C2×D512yes—
167#878—22no—
168#869C2×D511yescharacteristic
169C4×Dic6—51no—
170C4×Dic6C2×D511yescharacteristic
171C3×C4⋊C8—51no—
172C3×#102—52no—
173#832—51no—
174#832—52no—
175#832—52no—
176#818—52no—
177#816—52no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#810—51no—
181#808—51no—
182C4×C3⋊C8—51no—
183C2×C5×Q8—31no—
184C2×C5×Q8—61no—
185C2×C5×D4C22×D311yescharacteristic
186C22×C4×C5—21no—
187C22×C4×C5—62no—
188C2×D20—21no—
189C2×D20—21no—
190C2×D20C22×D312yes—
191C2×C4×D5—62no—
192C2×Dic10—31no—
193C5×C4⋊C4—31no—
194C5×C4⋊C4—32no—
195C5×C4⋊C4—32no—
196C5×C4⋊C4—62no—
197C5×C4⋊C4—62no—
198C5×C4⋊C4—61no—
199C5×C4⋊C4C22×D311yescharacteristic
200C5×C22⋊C4—21no—
201C5×C22⋊C4—62no—
202C42×C5—32no—
203C42×C5C22×D311yescharacteristic
204#687—62no—
205#686—24no—
206#685—62no—
207#685—62no—
208#685—62no—
209C4⋊Dic5—31no—
210#683—61no—
211C4×Dic5—61no—
212C2×#168—31no—
213C2×#168—31no—
214C2×#168C22×D312yes—
215#559—151no—
216#554—31no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—51no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5—22no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5C22×D411yescharacteristic
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—42no—
233C3×C4×C5—21no—
234C3×C4×C5—41no—
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—42no—
243C2×C3×D4—52no—
244C2×C3×D4—101no—
245C2×C3×D4—101no—
246C2×C3×D4C22×D511yescharacteristic
247C22×C3×C4—21no—
248C22×Dic3—22no—
249C22×Dic3—102no—
250C2×Dic6—21no—
251C2×Dic6—51no—
252C2×Dic6C22⋊D511yescharacteristic
253C3×D8—104no—
254C2×C3×C8—52no—
255C3×C4⋊C4C22×D511yescharacteristic
256C3×C22⋊C4—21no—
257C3×C42C22×D511yescharacteristic
258#217—22no—
259#217—102no—
260#217—102no—
261#217—102no—
262#214—102no—
263C4⋊Dic3—21no—
264C4⋊Dic3—22no—
265C4⋊Dic3—51no—
266C4⋊Dic3C22⋊D511yescharacteristic
267C4⋊Dic3C22×D512yes—
268Dic3⋊C4—22no—
269Dic3⋊C4—101no—
270Dic3⋊C4C22⋊D512yes—
271C4×Dic3—101no—
272C4×Dic3C22×D512yes—
273C2×C3⋊C8—51no—
274C2×C3⋊C8—51no—
275C23×C5—21no—
276C22×D5—22no—
277C5×Q8—62no—
278C5×Q8—241no—
279C5×D4—21no—
280C5×D4#23712yes—
281C2×C4×C5—21no—
282C2×C4×C5—32no—
283C2×C4×C5—32no—
284C2×C4×C5—42no—
285C2×C4×C5—62no—
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—22no—
300#168—61no—
301#168—61no—
302C2×SD16—151no—
303C2×D8—52no—
304C4⋊Q8—31no—
305#127—51no—
306#125—32no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—62no—
311C22⋊Q8—61no—
312C4×Q8—31no—
313C4×Q8—151no—
314C4×D4—32no—
315C4×D4—152no—
316C4×D4—301no—
317C4×D4D3×D511yescharacteristic
318C2×C4⋊C4—61no—
319#107—152no—
320#106—151no—
321C4⋊C8—51no—
322C4⋊C8—152no—
323#103—152no—
324#103—151no—
325#102—52no—
326#102—152no—
327#102—152no—
328#102—151no—
329C4×C8—152no—
330C4×C8—151no—
331C2×C3×C5—42no—
332C2×C3×C5#54811yescharacteristic
333C2×C3×C5C2×#13511yescharacteristic
334C2×C3×C5#57611yescharacteristic
335C3×D5—82no—
336C23×C3—21no—
337C23×C3—102no—
338C3×D4—21no—
339C3×D4—102no—
340C3×D4—102no—
341C3×D4—202no—
342C3×D4—401no—
343C3×D4#71312yes—
344C2×C3×C4—21no—
345C2×C3×C4—42no—
346C2×C3×C4C2×C22⋊D511yescharacteristic
347C2×C3×C4C2×C22⋊D511yescharacteristic
348C2×C3×C4C23×D511yescharacteristic
349C2×Dic3—22no—
350C2×Dic3—82no—
351C2×Dic3—101no—
352C2×Dic3—101no—
353C2×Dic3—402no—
354C2×Dic3C2×C22⋊D512yes—
355C2×Dic3C2×C22⋊D512yes—
356Dic6—22no—
357Dic6—81no—
358Dic6—101no—
359Dic6—101no—
360C3×C8—102no—
361C3⋊C8—101no—
362C3⋊C8—101no—
363C22×C5—22no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5C2×D3×D411yescharacteristic
367C2×D5—42no—
368C2×D5—42no—
369C2×D5—42no—
370C4×C5—21no—
371C4×C5—41no—
372C4×C5—62no—
373C4×C5—62no—
374C4×C5—122no—
375C4×C5#91212yes—
376C4×C5C2×#23711yescharacteristic
377C4×C5#101011yescharacteristic
378Dic5—121no—
379Dic5—121no—
380C2×Q8—31no—
381C2×Q8—61no—
382C2×Q8—151no—
383C2×D4—52no—
384C2×D4—101no—
385C2×D4—101no—
386C2×D4C2×D3×D511yescharacteristic
387C22×C4—21no—
388C22×C4—62no—
389C22×C4—302no—
390SD16—302no—
391D8—104no—
392C2×C8—52no—
393C2×C8—151no—
394C2×C8—151no—
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—62no—
399C4⋊C4—62no—
400C4⋊C4—61no—
401C4⋊C4—151no—
402C4⋊C4—301no—
403C4⋊C4C2×D3×D511yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—62no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—32no—
410C42—301no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—22no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—202no—
417C22×C3—202no—
418C22×C3—202no—
419C22×C3C22×C22⋊D511yescharacteristic
420C3×C4—21no—
421C3×C4—41no—
422C3×C4#409612yes—
423C3×C4C2×#71311yescharacteristic
424C3×C4#414711yescharacteristic
425Dic3—22no—
426Dic3—22no—
427Dic3—42no—
428Dic3—201no—
429Dic3—201no—
430C2×C5—42no—
431C2×C5#559811yescharacteristic
432C2×C5C2×#91211yescharacteristic
433C2×C5#577411yescharacteristic
434D5—82no—
435C23—21no—
436C23—102no—
437Q8—62no—
438Q8—241no—
439Q8—301no—
440Q8—301no—
441D4—21no—
442D4—102no—
443D4—102no—
444D4—202no—
445D4—401no—
446D4#676612yes—
447C2×C4—21no—
448C2×C4—32no—
449C2×C4—32no—
450C2×C4—42no—
451C2×C4—62no—
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—102no—
460C8—301no—
461C8—301no—
462C2×C3—42no—
463C2×C3—402no—
464C2×C3#6615111yescharacteristic
465C2×C3C2×#409611yescharacteristic
466C2×C3#6616911yescharacteristic
467C5#8031911yescharacteristic, complemented, Sylow
468C22—22no—
469C22—41no—
470C22—41no—
471C22—202no—
472C22—202no—
473C22—202no—
474C22C2×D3×C22⋊D511yescharacteristic
475C4—21no—
476C4—41no—
477C4—62no—
478C4—62no—
479C4—122no—
480C4—601no—
481C4—601no—
482C4#9149312yes—
483C4C2×#676611yescharacteristic
484C4#9200011yescharacteristic
485C3#1061537411yescharacteristic, complemented, Sylow
486C2—42no—
487C2—402no—
488C2#1175434411yescharacteristic
489C2C2×#9149311yescharacteristic
490C2#1175532311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC3×#65304C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5543C2semidirect
2. #11752636C2semidirect
3. C4×#6716C2semidirect
5. #11749079C2semidirect
6. Dic3×#686C2semidirect
7. #11747374C2semidirect
8. #11747251C2semidirect
9. #11746963C2semidirect
10. #11746895C2semidirect
11. #11746857C2semidirect
87. #5543D5semidirect
412. C3×C5#3361semidirect
467. C5#80319semidirect
485. C3#10615374semidirect

Maximal subgroups

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

subgroupindex
C5×#55432
#117526362
C4×#67162
C3×#653042
#117490792
Dic3×#6862
#117473742
#117472512
#117469632
#117468952
#117468572
#106153743
#803195