Finite Group Databasebeta

← #14439108

Subgroups — #14439108

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5668C211yesmaximal, characteristic, complemented
2C2×#91519C212yesmaximal, complemented
3C2×#91495C212yesmaximal, complemented
4#11752550C211yesmaximal, characteristic, complemented
5#11751159C211yesmaximal, characteristic, complemented
6C3×#65349C211yesmaximal, characteristic, complemented
7#11749324C212yesmaximal, complemented
8#11749076C212yesmaximal, complemented
9#11747082C211yesmaximal, characteristic, complemented
10#11747032C211yesmaximal, characteristic, complemented
11D3×#3935C211yesmaximal, characteristic, complemented
12#10615017—31nomaximal, Hall
13C2×C5×#239C2211yescharacteristic
14C2×C5×#237C2211yescharacteristic
15C2×#6769C2212yes—
16C3×C5×#124C2211yescharacteristic
17C2×#6717C2212yes—
18C2×#6715C2212yes—
19#91763C2211yescharacteristic
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#91519—28no—
30#91495—28no—
31#91460—22no—
32#91428—22no—
33#91374C2212yes—
34C2×#6661C2212yes—
35C2×#6660C2212yes—
36C2×#6656C2212yes—
37C2×#6654C2212yes—
38C2×D3×#168C2212yes—
39#91087C2211yescharacteristic
40C3×#3935C2211yescharacteristic
41#90953C2212yes—
42#81869—51nomaximal, Hall
43C5×#532—31no—
44C2×#4096—32no—
45C2×#4096—32no—
46#65811—31no—
47#65375—32no—
48#65363—32no—
49#65349—31no—
50#65349D311yescharacteristic, complemented
51#65347—31no—
52#65347—31no—
53C2×#3935—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×C3×C5×D4C2311yescharacteristic
56C2×D60—22no—
57C2×D60C2312yes—
58C2×C5×#67—21no—
59C2×C5×#67—22no—
60C22×C5×Dic3—21no—
61C5×#239—24no—
62C5×#237—24no—
63C2×C5×D12—21no—
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C4×C5×D3D412yes—
67C2×C4×C5×D3C2311yescharacteristic
68C2×C5×Dic6C2311yescharacteristic
69C2×C3×Dic10C2312yes—
70C2×#1203—22no—
71C2×#1200—22no—
72#6769—24no—
73#6769—24no—
74C3×C5×C22⋊C4—22no—
75C3×C42×C5C2311yescharacteristic
76#6717—24no—
77#6715—24no—
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—
87#6667—24no—
88#6661—24no—
89#6660—24no—
90#6656—24no—
91#6654—24no—
92D3×#168D418yescomplemented
93C2×#919—52no—
94C2×#916—52no—
95#5725—51no—
96#5668D511yescharacteristic, complemented
97C3×#497—51no—
98#5190—52no—
99#5176—52no—
100#5086—51no—
101#5058—51no—
102#4712—51no—
103D3×#97—51no—
104C2×C5×#41—31no—
105C2×C5×#41—31no—
106C2×#709—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#4096—68no—
115#4096—68no—
116C2×#689—32no—
117C2×#689C2×D312yes—
118C2×#688—32no—
119C2×#688—32no—
120C2×#687—32no—
121C2×#687C2×D312yes—
122C2×#686—32no—
123C2×#686—32no—
124#4076—62no—
125C22×#168—32no—
126#4021—32no—
127#4020—31no—
128C4×D20—62no—
129#4015C2×D311yescharacteristic
130#3935—31no—
131#3935—32no—
132#3935C2×D311yescharacteristic
133#3150—151noSylow
134C23×C3×C5—21no—
135C22×D15—22no—
136C22×C5×D3—21no—
137C22×C5×D3C2×D411yescharacteristic
138C3×C5×Q8—22no—
139C3×C5×D4—22no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2411yescharacteristic
143D60—22no—
144D60—22no—
145D60—44no—
146C5×#67—44no—
147C5×#67—42no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—42no—
150C2×C5×Dic3C2×D412yes—
151C2×C5×Dic3C2×D411yescharacteristic
152C5×D12—22no—
153C5×D12—42no—
154C4×C5×D3—42no—
155C4×C5×D3—42no—
156C4×C5×D3C2×D414yes—
157C5×Dic6—22no—
158C2×C3×Dic5—22no—
159C3×Dic10—22no—
160C3×Dic10—22no—
161#1203—44no—
162#1200—44no—
163C3⋊#168C2×D414yes—
164C3×#168C2×D414yes—
165C2×#239—52no—
166C2×#239C2×D511yescharacteristic
167C2×#237C2×D511yescharacteristic
168C2×C3×Q16—52no—
169C2×C3×SD16—52no—
170C3×C4⋊Q8—51no—
171C3×#124C2×D511yescharacteristic
172#947—52no—
173#944C2×D511yescharacteristic
174C2×#216—52no—
175C2×#215—52no—
176C2×#215—52no—
177#940C2×D511yescharacteristic
178C2×#213—52no—
179#919—108no—
180#916—108no—
181C2×D24—52no—
182C2×#204—52no—
183C2×D3×C8—52no—
184#895—102no—
185#893—102no—
186#884—22no—
187#67⋊C4—22no—
188#875C2×D511yescharacteristic
189#874—51no—
190C42×D3C2×D511yescharacteristic
191C3×#97—51no—
192#815—52no—
193#803—51no—
194C5×#41—64no—
195C5×#41—64no—
196C2×C5×Q8—31no—
197C2×C5×Q8C22×D311yescharacteristic
198C2×C5×D4—31no—
199C2×C5×D4—61no—
200C2×C5×D4—62no—
201C2×C5×D4—61no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—31no—
204C22×C4×C5—32no—
205C22×C4×C5—61no—
206C22×C4×C5—61no—
207C2×C22⋊D5—62no—
208#709—64no—
209#709—64no—
210C2×D20—32no—
211C2×D20—62no—
212C2×C4×D5—62no—
213C2×Dic10C22×D312yes—
214C5×C4⋊C4—62no—
215C5×C22⋊C4—22no—
216C5×C22⋊C4—62no—
217C42×C5—32no—
218C42×C5—31no—
219C42×C5C22×D311yescharacteristic
220#689—24no—
221#689—64no—
222#688—64no—
223#688—64no—
224#687—24no—
225#687—64no—
226#686—64no—
227#686—64no—
228#685—64no—
229C4⋊Dic5—22no—
230C2×#168—32no—
231C2×#168—38no—
232C2×#168C22×D312yes—
233C2×#135—152no—
234C2×#135—152no—
235#532—31no—
236#532—151no—
237#497—51no—
238#497—151no—
239#497—152no—
240#496—151no—
241#496—152no—
242#496—151no—
243C2×#97—151no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5C22×D411yescharacteristic
247C2×D15—42no—
248C2×D15—44no—
249C2×C5×D3—22no—
250C2×C5×D3—41no—
251C2×C5×D3—42no—
252C2×C5×D3#12712yes—
253C3×C4×C5—22no—
254C3×C4×C5—41no—
255C3×C4×C5C22×D412yes—
256C3×Dic5—42no—
257C5×Dic3—22no—
258C5×Dic3—41no—
259C5×Dic3#12712yes—
260C2×C3×Q8—52no—
261C2×C3×Q8C22×D511yescharacteristic
262C2×C3×D4C22×D511yescharacteristic
263C2×#67—21no—
264C2×#67—22no—
265C22×Dic3—21no—
266#239—24no—
267#239—104no—
268#239—104no—
269#237—24no—
270C2×D12—21no—
271C2×D12—52no—
272C2×D12—102no—
273C2×D12—102no—
274C2×D12C22×D511yescharacteristic
275C2×C4×D3—21no—
276C2×C4×D3—102no—
277C2×C4×D3C22⋊D512yes—
278C2×C4×D3C22×D511yescharacteristic
279C2×Dic6C22×D511yescharacteristic
280C3×Q16—104no—
281C3×SD16—104no—
282C2×C3×C8—52no—
283C3×C4⋊C4—102no—
284C3×C22⋊C4—22no—
285C3×C42C22×D511yescharacteristic
286#216—104no—
287#215—104no—
288#215—104no—
289#213—104no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—104no—
292Dic3⋊C4—22no—
293C4×Dic3C22⋊D512yes—
294C4×Dic3C22×D511yescharacteristic
295C2×C3⋊C8—52no—
296D24—104no—
297#204—104no—
298D3×C8—58no—
299C23×C5—21no—
300C23×C5—31no—
301C23×C5—61no—
302C22×D5—62no—
303C5×Q8—22no—
304C5×Q8—62no—
305C5×D4—22no—
306C5×D4—62no—
307C5×D4—122no—
308C5×D4—124no—
309C5×D4—122no—
310C2×C4×C5—21no—
311C2×C4×C5—31no—
312C2×C4×C5—34no—
313C2×C4×C5—32no—
314C2×C4×C5—61no—
315C2×C4×C5—122no—
316C2×C4×C5—122no—
317C2×C4×C5—122no—
318C2×C4×C5D3×D412yes—
319C2×C4×C5C23×D311yescharacteristic
320C22⋊D5—124no—
321C2×Dic5—22no—
322D20—62no—
323D20—62no—
324D20—124no—
325C4×D5—124no—
326Dic10—22no—
327Dic10—22no—
328#168—34no—
329#168D3×D414yes—
330C2×#41—31no—
331C2×#41—31no—
332C2×#41—152no—
333#135—308no—
334#135—308no—
335C2×Q16—52no—
336C2×Q16—152no—
337C2×SD16—52no—
338C2×SD16—152no—
339C2×SD16—152no—
340C2×SD16—152no—
341C2×D8—152no—
342C2×D8—152no—
343C22×C8—152no—
344C4⋊Q8—31no—
345C4⋊Q8—51no—
346#127—31no—
347#127—151no—
348#124—31no—
349#124—152no—
350#124D3×D511yescharacteristic
351#121—62no—
352#121—302no—
353C4×D4—62no—
354C4×D4—302no—
355C2×C42—31no—
356#97—51no—
357#97—152no—
358#97—151no—
359C2×C3×C5—81no—
360C2×C3×C5C2×#12711yescharacteristic
361C2×C3×C5#57512yes—
362D15—82no—
363C5×D3—22no—
364C5×D3—81no—
365C23×C3—21no—
366C22×D3—21no—
367C22×D3—102no—
368C22×D3C2×C22⋊D511yescharacteristic
369C3×Q8—22no—
370C3×Q8—102no—
371C3×Q8—102no—
372C3×D4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—102no—
375C2×C3×C4C2×C22⋊D512yes—
376C2×C3×C4C23×D511yescharacteristic
377#67—44no—
378#67—42no—
379C2×Dic3—21no—
380C2×Dic3—42no—
381C2×Dic3C2×C22⋊D512yes—
382C2×Dic3C2×C22⋊D511yescharacteristic
383D12—22no—
384D12—42no—
385D12—102no—
386D12—102no—
387D12—204no—
388D12—204no—
389C4×D3—42no—
390C4×D3—42no—
391C4×D3—204no—
392C4×D3D4×D514yes—
393Dic6—22no—
394C3×C8—54no—
395C3⋊C8—54no—
396C22×C5—32no—
397C22×C5—41no—
398C22×C5—42no—
399C22×C5—62no—
400C22×C5—121no—
401C22×C5—122no—
402C22×C5C2×D3×D411yescharacteristic
403C2×D5—122no—
404C2×D5—124no—
405C4×C5—22no—
406C4×C5—32no—
407C4×C5—41no—
408C4×C5—62no—
409C4×C5—121no—
410C4×C5C2×D3×D412yes—
411Dic5—42no—
412#41—64no—
413#41—64no—
414#41—304no—
415#41—304no—
416C2×Q8—31no—
417C2×Q8—52no—
418C2×Q8C2×D3×D511yescharacteristic
419C2×D4—31no—
420C2×D4—61no—
421C2×D4—62no—
422C2×D4—61no—
423C2×D4—152no—
424C2×D4—302no—
425C2×D4—302no—
426C2×D4C2×D3×D511yescharacteristic
427C22×C4—31no—
428C22×C4—32no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—302no—
432Q16—104no—
433Q16—304no—
434SD16—104no—
435SD16—304no—
436SD16—304no—
437SD16—304no—
438D8—304no—
439D8—304no—
440C2×C8—52no—
441C2×C8—158no—
442C2×C8—152no—
443C4⋊C4—62no—
444C4⋊C4—102no—
445C22⋊C4—22no—
446C22⋊C4—62no—
447C22⋊C4—304no—
448C42—32no—
449C42—31no—
450C42C2×D3×D511yescharacteristic
451C3×C5#315011yescharacteristic, complemented, Hall
452C22×C3—41no—
453C22×C3—42no—
454C22×C3C22×C22⋊D511yescharacteristic
455C2×D3—22no—
456C2×D3—41no—
457C2×D3—42no—
458C2×D3—202no—
459C2×D3—204no—
460C2×D3#408612yes—
461C3×C4—22no—
462C3×C4—41no—
463C3×C4—202no—
464C3×C4C2×D4×D512yes—
465Dic3—22no—
466Dic3—41no—
467Dic3#408612yes—
468C2×C5—62no—
469C2×C5—81no—
470C2×C5—241no—
471C2×C5D3×#12711yescharacteristic
472C2×C5#577712yes—
473D5—242no—
474C23—21no—
475C23—31no—
476C23—61no—
477C23—302no—
478Q8—22no—
479Q8—62no—
480Q8—102no—
481Q8—102no—
482D4—22no—
483D4—62no—
484D4—122no—
485D4—124no—
486D4—122no—
487D4—302no—
488D4—302no—
489D4—604no—
490D4—604no—
491C2×C4—21no—
492C2×C4—31no—
493C2×C4—34no—
494C2×C4—32no—
495C2×C4—61no—
496C2×C4—102no—
497C2×C4—122no—
498C2×C4—122no—
499C2×C4—122no—
500C2×C4—604no—
501C2×C4D3×C22⋊D512yes—
502C2×C4C22×D3×D511yescharacteristic
503C8—54no—
504C8—154no—
505C2×C3—81no—
506C2×C3C2×#408611yescharacteristic
507C2×C3#6615612yes—
508D3—22no—
509D3—81no—
510D3—402no—
511C5#8186911yescharacteristic, complemented, Sylow
512C22—32no—
513C22—41no—
514C22—42no—
515C22—62no—
516C22—121no—
517C22—122no—
518C22—602no—
519C22—604no—
520C22C2×D3×C22⋊D511yescharacteristic
521C4—22no—
522C4—32no—
523C4—41no—
524C4—62no—
525C4—121no—
526C4—202no—
527C4D3×D4×D512yes—
528C3#1061501711yescharacteristic, complemented, Sylow
529C2—62no—
530C2—81no—
531C2—241no—
532C2—1202no—
533C2D3×#408611yescharacteristic
534C2#1175534812yes—
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
hypercenter#124D3×D5
hypocenterC3×C5#3150
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
1. C5×#5668C2semidirect
2. C2×#91519C2semidirect
3. C2×#91495C2semidirect
4. #11752550C2semidirect
5. #11751159C2semidirect
6. C3×#65349C2semidirect
7. #11749324C2semidirect
8. #11749076C2semidirect
9. #11747082C2semidirect
10. #11747032C2semidirect
11. D3×#3935C2semidirect
50. #65349D3semidirect
92. D3×#168D4semidirect
96. #5668D5semidirect
451. C3×C5#3150semidirect
511. C5#81869semidirect
528. C3#10615017semidirect

Maximal subgroups

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

subgroupindex
C5×#56682
C2×#915192
C2×#914952
#117525502
#117511592
C3×#653492
#117493242
#117490762
#117470822
#117470322
D3×#39352
#106150173
#818695