Finite Group Databasebeta

← #14415964

Subgroups — #14415964

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4131C211yesmaximal, characteristic, complemented
2C2×#91916C211yesmaximal, characteristic, complemented
3#11754794C211yesmaximal, characteristic
4#11752435C211yesmaximal, characteristic, complemented
5#11752046C212yesmaximal, complemented
6#11752037C212yesmaximal, complemented
7#11752036C212yesmaximal, complemented
8#11751987C212yesmaximal, complemented
9D5⋊(Dic3⋊C8)C211yesmaximal, characteristic, complemented
10#11751813C211yesmaximal, characteristic, complemented
11Dic3×#700C211yesmaximal, characteristic, complemented
12#10617311—31nomaximal, Hall
13C2×C3×#711C2211yescharacteristic
14C2×#6773C2211yescharacteristic
15C2×#6758C2211yescharacteristic
16C2×D5⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#704C2212yes—
18C22×C3×#170C2212yes—
19C3×#4131—24no—
20C2×C3×#700C2211yescharacteristic
21C2×C3×D5⋊C8C2211yescharacteristic
22C2×#6740C2212yes—
23C2×#6738C2212yes—
24#91916—24no—
25#91829C411yescharacteristic
26C5×#936C411yescharacteristic
27#91552C2212yes—
28#91552C2212yes—
29#91550C412yes—
30#91550C412yes—
31C4×D5×Dic3C2211yescharacteristic
32#91385C411yescharacteristic
33#91374C411yescharacteristic
34#91241C2212yes—
35#91241C2212yes—
36#91177C2211yescharacteristic
37#91177C2211yescharacteristic
38Dic3⋊#170C2211yescharacteristic
39Dic3⋊#170C2211yescharacteristic
40#91171C2212yes—
41#91171C2212yes—
42#91169C2212yes—
43Dic3×#170C2212yes—
44#83788—51nomaximal, Hall
45C2×#4133—31no—
46C2×#4131D311yescharacteristic, complemented
47#66002—31no—
48#65787—31no—
49#65776—31no—
50#65695—32no—
51#65694—32no—
52#65693—32no—
53#65692—32no—
54D5⋊(C4⋊C8)—31no—
55C4×#700—31no—
56C2×C3×C5×D4C2×C411yescharacteristic
57C2×#1220C2×C412yes—
58C2×#1220C2×C412yes—
59C2×D60C2×C411yescharacteristic
60C2×C5×Dic6C2×C411yescharacteristic
61C2×C3×C22⋊D5C2×C412yes—
62C22×C3×Dic5C2312yes—
63C3×#711—22no—
64C3×#711—22no—
65C2×C3×C4×D5C2311yescharacteristic
66C2×C3×Dic10C2×C411yescharacteristic
67C2×#1202C2×C412yes—
68C2×#1200C2312yes—
69C2×D5×Dic3C2×C411yescharacteristic
70C2×D5×Dic3C2×C411yescharacteristic
71#6773—22no—
72#6773—22no—
73C2×C3⋊#170C2311yescharacteristic
74C2×C3⋊#170C2311yescharacteristic
75C2×C3⋊#170C2312yes—
76#6758—22no—
77D5⋊(C3⋊C8)—22no—
78C3×#704—24no—
79C2×C3×#170—24no—
80C2×C3×#170C2311yescharacteristic
81C2×C3×#170C2311yescharacteristic
82C2×C3×#170C2312yes—
83C3×#700D414yescomplemented
84C3×D5⋊C8—22no—
85#6740—24no—
86#6738—24no—
87C4×Dic15C2×C411yescharacteristic
88C5×#217C2×C412yes—
89C5×#217C2×C412yes—
90C4×C5×Dic3C2×C411yescharacteristic
91#6669C2×C412yes—
92#6669C2×C412yes—
93#6667C2×C412yes—
94#6667C2×C412yes—
95Dic3×Dic5C2311yescharacteristic
96Dic3×Dic5C2311yescharacteristic
97C2×C3×#131—51no—
98#5832—51no—
99C2×#907—51no—
100#5234—51no—
101#5128—52no—
102#5127—52no—
103Dic3×M16—51no—
104#5111—52no—
105#5110—51no—
106C8×#67—52no—
107C2×Dic3⋊C8—51no—
108C2×#713—31no—
109C2×#711C2×D311yescharacteristic
110C2×#704C2×D312yes—
111C22×#170C2×D312yes—
112#4133—64no—
113#4131—24no—
114C2×#700—31no—
115C2×#700—32no—
116C2×#700C2×D311yescharacteristic
117C2×D5⋊C8—31no—
118C2×D5⋊C8—32no—
119C2×D5⋊C8C2×D311yescharacteristic
120C5×#124—31no—
121#4090—31no—
122#4086—31no—
123#4030—32no—
124#4030—32no—
125#4027—32no—
126#4027—32no—
127#4021—31no—
128C42×D5—31no—
129C22⋊#170—32no—
130C22⋊#170—32no—
131#4004—31no—
132#4004—31no—
133#4003—32no—
134#4003—32no—
135#4002—32no—
136C4⋊#170—31no—
137C4⋊#170—31no—
138C4×#170—32no—
139#2935—151noSylow
140C23×C3×C5C22×C412yes—
141C22×D15C22×C412yes—
142C22×C3×D5C22×C411yescharacteristic
143C3×C5×D4—22no—
144C2×C3×C4×C5C22×C411yescharacteristic
145#1220—24no—
146#1220—42no—
147C2×Dic15C22×C411yescharacteristic
148C2×Dic15C22×C411yescharacteristic
149D60—22no—
150C2×C5×Dic3C22×C411yescharacteristic
151C2×C5×Dic3C22×C411yescharacteristic
152C2×C5×Dic3C22×C412yes—
153C5×Dic6—22no—
154C3×C22⋊D5—24no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5C22×C412yes—
158C2×C3×Dic5C2411yescharacteristic
159C3×C4×D5C2×D412yes—
160C3×C4×D5#4112yes—
161C3×Dic10—22no—
162#1202—24no—
163#1200—22no—
164#1200—22no—
165D5×Dic3—22no—
166D5×Dic3—41no—
167C3⋊#170—21no—
168C3⋊#170—21no—
169C3⋊#170—22no—
170C3×#170—21no—
171C3×#170—21no—
172C3×#170C2×D414yes—
173C2×C3×#41—51no—
174C2×#235—51no—
175C3×#131—104no—
176C2×C3×M16—51no—
177C2×C3×M16—52no—
178C22×C3×C8—51no—
179C22×C3×C8—52no—
180#947—51no—
181#944—51no—
182#940—51no—
183#939—52no—
184#939—52no—
185#936AGL(1,𝔽5)11yescharacteristic
186C4×#67—52no—
187C4×#67—52no—
188C2×C4×Dic3—51no—
189C2×#208—51no—
190C22×C3⋊C8—51no—
191#907—104no—
192C2×ΓL(1,𝔽25)—52no—
193C2×D3×C8—52no—
194#830—52no—
195#830—52no—
196(C2×D3)⋊C8—52no—
197(C2×D3)⋊C8—52no—
198#815—52no—
199Dic3⋊C8—51no—
200Dic3⋊C8—51no—
201Dic3⋊C8—51no—
202Dic3⋊C8—51no—
203C8×Dic3—52no—
204C2×C5×Q8—31no—
205C2×C5×D4C4×D311yescharacteristic
206C2×C22⋊D5—32no—
207C2×C22⋊D5—32no—
208C2×C22⋊D5C4×D312yes—
209C22×Dic5C22×D312yes—
210#713—62no—
211#713—62no—
212#711—22no—
213#711—22no—
214C2×D20—32no—
215C2×D20—31no—
216C2×C4×D5—31no—
217C2×C4×D5—32no—
218C2×C4×D5—31no—
219C2×C4×D5C22×D311yescharacteristic
220C2×Dic10C4×D311yescharacteristic
221#704—24no—
222C2×#170—24no—
223C2×#170—31no—
224C2×#170—31no—
225C2×#170—32no—
226C2×#170C22×D311yescharacteristic
227C2×#170C22×D311yescharacteristic
228C2×#170C22×D312yes—
229#700—62no—
230#700—64no—
231#700#6714yescomplemented
232D5⋊C8—22no—
233D5⋊C8—62no—
234D5⋊C8—64no—
235C5×C22⋊C4—32no—
236C5×C22⋊C4—32no—
237C42×C5—31no—
238#685—32no—
239#685—32no—
240#683—32no—
241#683—32no—
242C4×Dic5—31no—
243C4×Dic5—31no—
244C4×Dic5—31no—
245C2×#131—51no—
246C2×#131—151no—
247#532—151no—
248#436—152no—
249#435—152no—
250#435—152no—
251C8×D4—152no—
252C2×C4⋊C8—151no—
253#408—151no—
254#408—151no—
255C4×M16—151no—
256C22×C3×C5—22no—
257C22×C3×C5—22no—
258C22×C3×C5—22no—
259C22×C3×C5C23×C411yescharacteristic
260C2×D15—22no—
261C2×D15—22no—
262C2×D15—22no—
263C2×C3×D5—21no—
264C2×C3×D5—21no—
265C2×C3×D5C4×D412yes—
266C3×C4×C5C4×D412yes—
267Dic15—21no—
268Dic15#13112yescomplemented
269C3×Dic5—22no—
270C3×Dic5C22×D411yescharacteristic
271C3×Dic5C2×#4111yescharacteristic
272C5×Dic3—22no—
273C5×Dic3—21no—
274C5×Dic3—21no—
275C3×#41—102no—
276C3×#41—102no—
277C2×C3×Q8—51no—
278C2×C3×D4—52no—
279C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
280C22×C3×C4—51no—
281C22×C3×C4—52no—
282C2×#67—52no—
283C2×#67—52no—
284C2×#67—52no—
285C22×Dic3—51no—
286C22×Dic3—51no—
287#235—102no—
288#235—102no—
289C2×D12—51no—
290C2×C4×D3—52no—
291C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
292C3×M16—54no—
293C3×M16—104no—
294C2×C3×C8—52no—
295C2×C3×C8—51no—
296C2×C3×C8—51no—
297C2×C3×C8—104no—
298C2×C3×C8—102no—
299#217C2×AGL(1,𝔽5)12yes—
300#217C2×AGL(1,𝔽5)12yes—
301(C2×D3)⋊C4—52no—
302(C2×D3)⋊C4—52no—
303Dic3⋊C4—52no—
304Dic3⋊C4—52no—
305C4×Dic3—51no—
306C4×Dic3—51no—
307C4×Dic3—51no—
308C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
309#208—102no—
310C2×C3⋊C8—52no—
311C2×C3⋊C8—51no—
312C2×C3⋊C8—51no—
313C2×C3⋊C8—102no—
314ΓL(1,𝔽25)—104no—
315D3×C8—104no—
316C23×C5C2×C4×D312yes—
317C22×D5—32no—
318C22×D5C2×C4×D311yescharacteristic
319C5×Q8—62no—
320C5×D4—22no—
321C2×C4×C5—31no—
322C2×C4×C5—31no—
323C2×C4×C5—32no—
324C2×C4×C5C2×C4×D311yescharacteristic
325C22⋊D5—24no—
326C22⋊D5—64no—
327C22⋊D5—122no—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—31no—
331C2×Dic5—31no—
332C2×Dic5C2×C4×D312yes—
333C2×Dic5C23×D311yescharacteristic
334D20—64no—
335D20—62no—
336C4×D5—62no—
337C4×D5—62no—
338C4×D5—62no—
339C4×D5—121no—
340C4×D5#23512yes—
341C4×D5C2×#6712yes—
342Dic10—22no—
343#170—21no—
344#170—21no—
345#170—62no—
346#170—61no—
347#170—61no—
348#170C2×#6714yes—
349C2×#41—51no—
350C2×#41—151no—
351#131—104no—
352#131—304no—
353C2×M16—51no—
354C2×M16—52no—
355C2×M16—152no—
356C2×M16—151no—
357C22×C8—51no—
358C22×C8—52no—
359C22×C8—152no—
360C22×C8—151no—
361C4⋊Q8—151no—
362#127—151no—
363#124—31no—
364#124—151no—
365#121—152no—
366#121—152no—
367C4×D4—152no—
368C4×D4—152no—
369C2×C42—151no—
370C4⋊C8—151no—
371C4⋊C8—151no—
372C4⋊C8—151no—
373C4⋊C8—151no—
374C22⋊C8—152no—
375C22⋊C8—152no—
376C22⋊C8—152no—
377C22⋊C8—152no—
378#97—152no—
379C4×C8—152no—
380C2×C3×C5—42no—
381C2×C3×C5C2×C4×D411yescharacteristic
382C2×C3×C5C2×#13111yescharacteristic
383C2×C3×C5#56811yescharacteristic
384D15—42no—
385C3×D5—22no—
386C23×C3—51no—
387C23×C3C22×AGL(1,𝔽5)12yes—
388C22×D3—52no—
389C3×Q8—102no—
390C3×D4—22no—
391C3×D4—104no—
392C2×C3×C4—51no—
393C2×C3×C4—52no—
394C2×C3×C4—52no—
395C2×C3×C4—52no—
396C2×C3×C4—102no—
397C2×C3×C4—102no—
398C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
399#67—104no—
400#67—104no—
401#67—202no—
402C2×Dic3—51no—
403C2×Dic3—51no—
404C2×Dic3—102no—
405C2×Dic3—201no—
406C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
407C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
408C2×Dic3C22×AGL(1,𝔽5)12yes—
409D12—102no—
410C4×D3—102no—
411C4×D3—102no—
412Dic6—22no—
413C3×C8—54no—
414C3×C8—101no—
415C3×C8—101no—
416C3⋊C8—101no—
417C3⋊C8—101no—
418C3⋊C8—102no—
419C22×C5—22no—
420C22×C5—22no—
421C22×C5—22no—
422C22×C5C22×C4×D311yescharacteristic
423C2×D5—21no—
424C2×D5—21no—
425C2×D5—62no—
426C2×D5—62no—
427C2×D5—62no—
428C2×D5C4×#6712yes—
429C4×C5—61no—
430C4×C5—61no—
431C4×C5—62no—
432C4×C5C4×#6712yes—
433Dic5—22no—
434Dic5—32no—
435Dic5—61no—
436Dic5C2×#23511yescharacteristic
437Dic5C22×#6711yescharacteristic
438#41—102no—
439#41—102no—
440#41—302no—
441#41—302no—
442C2×Q8—31no—
443C2×Q8—51no—
444C2×D4—52no—
445C2×D4—152no—
446C2×D4—152no—
447C2×D4—152no—
448C2×D4—151no—
449C2×D4D3×AGL(1,𝔽5)11yescharacteristic
450C22×C4—51no—
451C22×C4—52no—
452C22×C4—152no—
453C22×C4—151no—
454C22×C4—151no—
455M16—54no—
456M16—104no—
457M16—304no—
458M16—302no—
459C2×C8—52no—
460C2×C8—51no—
461C2×C8—51no—
462C2×C8—104no—
463C2×C8—102no—
464C2×C8—152no—
465C2×C8—151no—
466C2×C8—151no—
467C2×C8—304no—
468C2×C8—302no—
469C4⋊C4—152no—
470C4⋊C4—152no—
471C22⋊C4—32no—
472C22⋊C4—32no—
473C22⋊C4—152no—
474C22⋊C4—152no—
475C42—31no—
476C42—151no—
477C42—151no—
478C42—151no—
479C3×C5#293511yescharacteristic, complemented, Hall
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—52no—
484C22×C3—101no—
485C22×C3—101no—
486C22×C3C23×AGL(1,𝔽5)11yescharacteristic
487C2×D3—102no—
488C2×D3—102no—
489C2×D3—102no—
490C3×C4—51no—
491C3×C4—51no—
492C3×C4—102no—
493C3×C4D4×AGL(1,𝔽5)12yes—
494Dic3—22no—
495Dic3—21no—
496Dic3—21no—
497Dic3—52no—
498Dic3—101no—
499C2×C5—42no—
500C2×C5D3×#13111yescharacteristic
501C2×C5#575011yescharacteristic
502C2×C5C2×C4×#6711yescharacteristic
503D5—22no—
504D5—122no—
505C23—51no—
506C23—152no—
507C23C2×D3×AGL(1,𝔽5)12yes—
508Q8—62no—
509Q8—102no—
510D4—22no—
511D4—104no—
512D4—304no—
513D4—304no—
514D4—302no—
515D4—602no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—32no—
519C2×C4—51no—
520C2×C4—52no—
521C2×C4—52no—
522C2×C4—52no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—151no—
526C2×C4—151no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4—601no—
531C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
532C8—54no—
533C8—101no—
534C8—101no—
535C8—301no—
536C8—301no—
537C8—302no—
538C2×C3—42no—
539C2×C3—102no—
540C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
541C2×C3D5⋊#13111yescharacteristic
542C2×C3#6626411yescharacteristic
543D3—202no—
544C5#8378811yescharacteristic, complemented, Sylow
545C22—22no—
546C22—22no—
547C22—22no—
548C22—52no—
549C22—101no—
550C22—101no—
551C22—302no—
552C22—302no—
553C22—302no—
554C22C22×D3×AGL(1,𝔽5)11yescharacteristic
555C4—51no—
556C4—51no—
557C4—61no—
558C4—61no—
559C4—62no—
560C4—102no—
561C4—152no—
562C4—301no—
563C4AGL(1,𝔽5)×#6712yes—
564C3#1061731111yescharacteristic, complemented, Sylow
565C2—42no—
566C2—102no—
567C2—602no—
568C2#1175684011yescharacteristic
569C2#1175684211yescharacteristic
570C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radical#11754794C2
cosocleC2×C3×Dic5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2935
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4131C2semidirect
2. C2×#91916C2semidirect
4. #11752435C2semidirect
5. #11752046C2semidirect
6. #11752037C2semidirect
7. #11752036C2semidirect
8. #11751987C2semidirect
9. D5⋊(Dic3⋊C8)C2semidirect
10. #11751813C2semidirect
11. Dic3×#700C2semidirect
46. C2×#4131D3semidirect
83. C3×#700D4semidirect
231. #700#67semidirect
268. Dic15#131semidirect
479. C3×C5#2935semidirect
544. C5#83788semidirect
564. C3#10617311semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41312
C2×#919162
#117547942
#117524352
#117520462
#117520372
#117520362
#117519872
D5⋊(Dic3⋊C8)2
#117518132
Dic3×#7002
#106173113
#837885