Finite Group Databasebeta

← #14439272

Subgroups — #14439272

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5668C211yesmaximal, characteristic
2C2×#91510C212yesmaximal, complemented
3C2×#91486C212yesmaximal, complemented
4D3×#4015C211yesmaximal, characteristic, complemented
5#11751161C211yesmaximal, characteristic, complemented
6C3×#65349C211yesmaximal, characteristic, complemented
7#11749357C212yesmaximal, complemented
8#11749108C212yesmaximal, complemented
9#11747098C211yesmaximal, characteristic, complemented
10#11747082C211yesmaximal, characteristic, complemented
11#11747005C211yesmaximal, characteristic, complemented
12#10615019—31nomaximal, Hall
13C2×C5×#239C2211yescharacteristic
14C2×C5×#237C2211yescharacteristic
15C2×D3×Dic10C2212yes—
16C3×C5×#124C2211yescharacteristic
17C2×#6718C2212yes—
18C2×#6716C2212yes—
19#91758C2211yescharacteristic
20C5×#944C2211yescharacteristic
21C5×#940C2211yescharacteristic
22C5×#884—22no—
23C5×#67⋊C4—22no—
24C5×#875C2211yescharacteristic
25C42×C5×D3C2211yescharacteristic
26C2×C3×#689C2212yes—
27C2×C3×#687C2212yes—
28C3×#4015C2211yescharacteristic
29#91510—28no—
30#91486—28no—
31#91469—22no—
32D3×C4⋊Dic5—22no—
33#91389C2212yes—
34C2×#6663C2212yes—
35C2×#6661C2212yes—
36C2×#6659C2212yes—
37C2×#6656C2212yes—
38C2×#6650C2212yes—
39#91087C2211yescharacteristic
40C3×#3935C2211yescharacteristic
41Dic3×#168C2212yes—
42#81870—51nomaximal, Hall
43C5×#532—31no—
44C2×#4097—32no—
45C2×#4097—32no—
46C2×#4015—31no—
47#65381—32no—
48#65365—32no—
49#65349—31no—
50#65349—31no—
51#65349—31no—
52#65349D311yescharacteristic, complemented
53C4×#681—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×C3×C5×D4C2311yescharacteristic
56C2×Dic30C2312yes—
57C2×C5×#67—21no—
58C2×C5×#67—22no—
59C22×C5×Dic3—21no—
60C5×#239—24no—
61C5×#237—24no—
62C2×C5×D12—21no—
63C2×C5×D12C2311yescharacteristic
64C2×C4×C5×D3—21no—
65C2×C4×C5×D3D412yes—
66C2×C4×C5×D3C2311yescharacteristic
67C2×C5×Dic6C2311yescharacteristic
68C2×C3×Dic10C2312yes—
69C2×#1204—22no—
70C2×D3×Dic5—22no—
71D3×Dic10—24no—
72D3×Dic10—24no—
73C3×C5×C22⋊C4—22no—
74C3×C42×C5C2311yescharacteristic
75#6718—24no—
76#6716—24no—
77C4⋊Dic15—22no—
78C2×C3⋊#168C2312yes—
79C5×(C2×D3)⋊C4—22no—
80C5×Dic3⋊C4—22no—
81C4×C5×Dic3D412yes—
82C4×C5×Dic3C2311yescharacteristic
83C3×#689—24no—
84C3×#687—24no—
85C3×C4⋊Dic5—22no—
86C2×C3×#168C2312yes—
87Dic3⋊Dic5—24no—
88#6663—24no—
89#6661—24no—
90#6659—24no—
91#6656—24no—
92#6650D418yescomplemented
93C2×#918—52no—
94C2×#915—52no—
95D3×C4⋊Q8—51no—
96#5668D511yescharacteristic
97C3×#497—51no—
98#5183—52no—
99#5175—52no—
100#5086—51no—
101#5060—51no—
102#4715—51no—
103#4707—51no—
104C2×C5×#41—31no—
105C2×C5×#41—31no—
106C22×Dic10—32no—
107C5×C4⋊Q8—31no—
108C5×#127—31no—
109C5×#124—31no—
110C5×#124C2×D311yescharacteristic
111C5×#121—62no—
112C4×C5×D4—62no—
113C2×C42×C5—31no—
114#4097—68no—
115#4097—68no—
116C2×#689—32no—
117C2×#689—32no—
118C2×#689—32no—
119C2×#689C2×D312yes—
120C2×#687—32no—
121C2×#687—32no—
122C2×#687—32no—
123C2×#687C2×D312yes—
124C2×C4⋊Dic5—62no—
125C2×#681—32no—
126#4015—32no—
127#4015—31no—
128#4015—62no—
129#4015C2×D311yescharacteristic
130#3935—31no—
131#3935C2×D311yescharacteristic
132C4×#168—32no—
133#3152—151noSylow
134C23×C3×C5—21no—
135C22×C5×D3—21no—
136C22×C5×D3C2×D411yescharacteristic
137C3×C5×Q8—22no—
138C3×C5×D4—22no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—22no—
143Dic30—22no—
144Dic30—22no—
145C5×#67—42no—
146C5×#67—44no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—42no—
149C2×C5×Dic3C2×D411yescharacteristic
150C2×C5×Dic3C2×D412yes—
151C5×D12—22no—
152C5×D12—42no—
153C4×C5×D3—24no—
154C4×C5×D3—42no—
155C4×C5×D3C2×D414yes—
156C5×Dic6—22no—
157C2×C3×Dic5—22no—
158C3×Dic10—22no—
159C3×Dic10—22no—
160#1204—44no—
161D3×Dic5—44no—
162C3⋊#168C2×D414yes—
163C3×#168C2×D414yes—
164C2×#239C2×D511yescharacteristic
165C2×D3×Q8—52no—
166C2×#237C2×D511yescharacteristic
167C2×C3×Q16—52no—
168C2×C3×SD16—52no—
169C3×C4⋊Q8—51no—
170C3×#124C2×D511yescharacteristic
171#944—52no—
172#944C2×D511yescharacteristic
173C2×#216—52no—
174C2×#216—52no—
175C2×#215—52no—
176#940C2×D511yescharacteristic
177C2×#214—52no—
178#918—108no—
179#915—108no—
180C2×Dic12—52no—
181C2×#204—52no—
182C2×ΓL(1,𝔽25)—52no—
183D3×C4⋊C4—102no—
184#888—102no—
185#884—22no—
186#67⋊C4—22no—
187#875C2×D511yescharacteristic
188C42×D3C2×D511yescharacteristic
189#869—51no—
190C3×#97—51no—
191C8×Dic3—52no—
192#803—51no—
193C5×#41—64no—
194C5×#41—64no—
195C2×C5×Q8—31no—
196C2×C5×Q8C22×D311yescharacteristic
197C2×C5×D4—31no—
198C2×C5×D4—61no—
199C2×C5×D4—62no—
200C2×C5×D4—61no—
201C2×C5×D4C22×D311yescharacteristic
202C22×C4×C5—31no—
203C22×C4×C5—32no—
204C22×C4×C5—61no—
205C22×C4×C5—61no—
206C22×Dic5—62no—
207C2×Dic10—32no—
208C2×Dic10—64no—
209C2×Dic10—64no—
210C2×Dic10—62no—
211C2×Dic10C22×D312yes—
212C5×C4⋊C4—62no—
213C5×C22⋊C4—22no—
214C5×C22⋊C4—62no—
215C42×C5—32no—
216C42×C5—31no—
217C42×C5C22×D311yescharacteristic
218#689—24no—
219#689—64no—
220#689—64no—
221#689—64no—
222#687—24no—
223#687—64no—
224#687—64no—
225#687—64no—
226C4⋊Dic5—22no—
227C4⋊Dic5—64no—
228C4⋊Dic5—62no—
229#681—38no—
230C2×#168—32no—
231C2×#168C22×D312yes—
232C2×#137—152no—
233C2×#137—152no—
234#532—31no—
235C2×C4⋊Q8—151no—
236#497—51no—
237#497—151no—
238#497—151no—
239#497—151no—
240#494—152no—
241#492—152no—
242C4×M16—151no—
243C22×C3×C5—41no—
244C22×C3×C5—42no—
245C22×C3×C5C22×D411yescharacteristic
246C2×C5×D3—22no—
247C2×C5×D3—41no—
248C2×C5×D3—42no—
249C2×C5×D3#12712yes—
250C3×C4×C5—22no—
251C3×C4×C5—41no—
252C3×C4×C5C22×D412yes—
253Dic15—42no—
254C3×Dic5—42no—
255C5×Dic3—41no—
256C5×Dic3#12712yes—
257C5×Dic3#13714yescomplemented
258C2×C3×Q8—52no—
259C2×C3×Q8C22×D511yescharacteristic
260C2×C3×D4C22×D511yescharacteristic
261C2×#67—21no—
262C2×#67—22no—
263C22×Dic3—21no—
264#239—24no—
265D3×Q8—104no—
266D3×Q8—104no—
267#237—24no—
268C2×D12—21no—
269C2×D12C22×D511yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—102no—
272C2×C4×D3C22⋊D512yes—
273C2×C4×D3C22×D511yescharacteristic
274C2×Dic6—52no—
275C2×Dic6—102no—
276C2×Dic6C22×D511yescharacteristic
277C3×Q16—104no—
278C3×SD16—104no—
279C2×C3×C8—52no—
280C3×C4⋊C4—102no—
281C3×C22⋊C4—22no—
282C3×C42C22×D511yescharacteristic
283#216—104no—
284#216—104no—
285#215—104no—
286#214—104no—
287(C2×D3)⋊C4—22no—
288C4⋊Dic3—102no—
289Dic3⋊C4—22no—
290Dic3⋊C4—104no—
291C4×Dic3C22⋊D512yes—
292C4×Dic3C22×D511yescharacteristic
293C2×C3⋊C8—52no—
294Dic12—104no—
295#204—104no—
296ΓL(1,𝔽25)—58no—
297C23×C5—21no—
298C23×C5—31no—
299C23×C5—61no—
300C5×Q8—22no—
301C5×Q8—62no—
302C5×D4—22no—
303C5×D4—62no—
304C5×D4—124no—
305C5×D4—122no—
306C5×D4—122no—
307C2×C4×C5—21no—
308C2×C4×C5—32no—
309C2×C4×C5—31no—
310C2×C4×C5—34no—
311C2×C4×C5—64no—
312C2×C4×C5—61no—
313C2×C4×C5—122no—
314C2×C4×C5—122no—
315C2×C4×C5D3×D412yes—
316C2×C4×C5C23×D311yescharacteristic
317C2×Dic5—22no—
318C2×Dic5—62no—
319C2×Dic5—124no—
320Dic10—22no—
321Dic10—22no—
322Dic10—62no—
323Dic10—62no—
324Dic10—124no—
325#168—34no—
326#168D3×D414yes—
327C2×#41—31no—
328C2×#41—31no—
329C22×Q8—152no—
330#137—308no—
331#137—308no—
332C2×Q16—52no—
333C2×Q16—152no—
334C2×Q16—152no—
335C2×Q16—152no—
336C2×SD16—52no—
337C2×SD16—152no—
338C2×SD16—152no—
339C2×SD16—152no—
340C2×M16—152no—
341C4⋊Q8—31no—
342C4⋊Q8—51no—
343C4⋊Q8—152no—
344C4⋊Q8—151no—
345C4⋊Q8—302no—
346#127—31no—
347#124—31no—
348#124D3×D511yescharacteristic
349#121—62no—
350C4×D4—62no—
351C2×C4⋊C4—302no—
352C2×C42—31no—
353#97—51no—
354#97—151no—
355C4×C8—152no—
356C2×C3×C5—81no—
357C2×C3×C5C2×#12711yescharacteristic
358C2×C3×C5C2×#13712yes—
359C5×D3—22no—
360C5×D3—81no—
361C23×C3—21no—
362C22×D3—21no—
363C22×D3C2×C22⋊D511yescharacteristic
364C3×Q8—22no—
365C3×Q8—102no—
366C3×Q8—102no—
367C3×D4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—102no—
370C2×C3×C4C2×C22⋊D512yes—
371C2×C3×C4C23×D511yescharacteristic
372#67—42no—
373#67—44no—
374C2×Dic3—21no—
375C2×Dic3—42no—
376C2×Dic3—102no—
377C2×Dic3C2×C22⋊D512yes—
378C2×Dic3C2×C22⋊D511yescharacteristic
379D12—22no—
380D12—42no—
381C4×D3—24no—
382C4×D3—42no—
383C4×D3—204no—
384C4×D3D4×D514yes—
385Dic6—22no—
386Dic6—102no—
387Dic6—102no—
388Dic6—204no—
389C3×C8—54no—
390C3⋊C8—54no—
391C22×C5—32no—
392C22×C5—41no—
393C22×C5—42no—
394C22×C5—62no—
395C22×C5—121no—
396C22×C5—122no—
397C22×C5C2×D3×D411yescharacteristic
398C4×C5—22no—
399C4×C5—32no—
400C4×C5—34no—
401C4×C5—41no—
402C4×C5—121no—
403C4×C5C2×D3×D412yes—
404Dic5—42no—
405Dic5—122no—
406#41—64no—
407#41—64no—
408C2×Q8—31no—
409C2×Q8—52no—
410C2×Q8—152no—
411C2×Q8—302no—
412C2×Q8—304no—
413C2×Q8—304no—
414C2×Q8C2×D3×D511yescharacteristic
415C2×D4—31no—
416C2×D4—61no—
417C2×D4—62no—
418C2×D4—61no—
419C2×D4C2×D3×D511yescharacteristic
420C22×C4—31no—
421C22×C4—32no—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4—302no—
425Q16—104no—
426Q16—304no—
427Q16—304no—
428Q16—304no—
429SD16—104no—
430SD16—304no—
431SD16—304no—
432SD16—304no—
433M16—158no—
434C2×C8—52no—
435C2×C8—152no—
436C4⋊C4—62no—
437C4⋊C4—102no—
438C4⋊C4—304no—
439C4⋊C4—302no—
440C22⋊C4—22no—
441C22⋊C4—62no—
442C42—32no—
443C42—31no—
444C42C2×D3×D511yescharacteristic
445C3×C5#315211yescharacteristic, complemented, Hall
446C22×C3—41no—
447C22×C3—42no—
448C22×C3C22×C22⋊D511yescharacteristic
449C2×D3—22no—
450C2×D3—41no—
451C2×D3—42no—
452C2×D3#408612yes—
453C3×C4—22no—
454C3×C4—41no—
455C3×C4—202no—
456C3×C4C2×D4×D512yes—
457Dic3—41no—
458Dic3—202no—
459Dic3#408612yes—
460Dic3#409714yescomplemented
461C2×C5—62no—
462C2×C5—81no—
463C2×C5—241no—
464C2×C5D3×#12711yescharacteristic
465C2×C5D3×#13712yes—
466C23—21no—
467C23—31no—
468C23—61no—
469Q8—22no—
470Q8—62no—
471Q8—102no—
472Q8—102no—
473Q8—302no—
474Q8—302no—
475Q8—604no—
476D4—22no—
477D4—62no—
478D4—124no—
479D4—122no—
480D4—122no—
481C2×C4—21no—
482C2×C4—32no—
483C2×C4—31no—
484C2×C4—34no—
485C2×C4—64no—
486C2×C4—61no—
487C2×C4—102no—
488C2×C4—122no—
489C2×C4—122no—
490C2×C4—302no—
491C2×C4—604no—
492C2×C4D3×C22⋊D512yes—
493C2×C4C22×D3×D511yescharacteristic
494C8—54no—
495C8—154no—
496C2×C3—81no—
497C2×C3C2×#408611yescharacteristic
498C2×C3C2×#409712yes—
499D3—22no—
500D3—81no—
501C5#8187011yescharacteristic, complemented, Sylow
502C22—32no—
503C22—41no—
504C22—42no—
505C22—62no—
506C22—121no—
507C22—122no—
508C22C2×D3×C22⋊D511yescharacteristic
509C4—22no—
510C4—32no—
511C4—34no—
512C4—41no—
513C4—121no—
514C4—202no—
515C4—602no—
516C4D3×D4×D512yes—
517C3#1061501911yescharacteristic, complemented, Sylow
518C2—62no—
519C2—81no—
520C2—241no—
521C2D3×#408611yescharacteristic
522C2D3×#409712yes—
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC5×#5668C2
hypercenter#124D3×D5
hypocenterC3×C5#3152
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C2×#91510C2semidirect
3. C2×#91486C2semidirect
4. D3×#4015C2semidirect
5. #11751161C2semidirect
6. C3×#65349C2semidirect
7. #11749357C2semidirect
8. #11749108C2semidirect
9. #11747098C2semidirect
10. #11747082C2semidirect
11. #11747005C2semidirect
52. #65349D3semidirect
92. #6650D4semidirect
257. C5×Dic3#137semidirect
445. C3×C5#3152semidirect
460. Dic3#4097semidirect
501. C5#81870semidirect
517. C3#10615019semidirect

Maximal subgroups

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

subgroupindex
C5×#56682
C2×#915102
C2×#914862
D3×#40152
#117511612
C3×#653492
#117493572
#117491082
#117470982
#117470822
#117470052
#106150193
#818705