Finite Group Databasebeta

← #14415644

Subgroups — #14415644

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5⋊M16C211yesmaximal, characteristic, complemented
2C2×#91916C211yesmaximal, characteristic, complemented
3#11754527C211yesmaximal, characteristic
4D5⋊#830C211yesmaximal, characteristic, complemented
5#11752037C212yesmaximal, complemented
6#11751987C212yesmaximal, complemented
7#11751911C212yesmaximal, complemented
8#11751881C212yesmaximal, complemented
9#11751825C211yesmaximal, characteristic, complemented
10#11751814C211yesmaximal, characteristic, complemented
11#11751782C211yesmaximal, characteristic, complemented
12#10617260—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×#6773C2211yescharacteristic
15C2×D5⋊(C3⋊C8)C2211yescharacteristic
16C2×D5⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#704C2212yes—
18C3×D5⋊M16—24no—
19C2×C3×#700C2211yescharacteristic
20C2×C3×#700C2211yescharacteristic
21C2×C3×D5⋊C8C2212yes—
22C2×#6740C2212yescomplemented
23C2×#6738C2212yescomplemented
24#91916—24no—
25#91819C411yescharacteristic
26C5×#924C411yescharacteristic
27#91564C412yes—
28#91552C2212yes—
29#91450C411yescharacteristic
30#91444C2212yes—
31#91359C411yescharacteristic
32#91358C2211yescharacteristic
33#91348C412yes—
34#91241C2211yescharacteristic
35#91241C2211yescharacteristic
36#91232C2211yescharacteristic
37#91232C2211yescharacteristic
38#91177C2212yescomplemented
39Dic3⋊#170C2212yescomplemented
40#91171C2212yescomplemented
41#91171C2212yescomplemented
42#91169C2212yescomplemented
43Dic3×#170C2212yescomplemented
44#83757—51nomaximal, Hall
45C2×#4133—31no—
46C2×D5⋊M16D311yescharacteristic, complemented
47#65961—31no—
48#65787—31no—
49D5⋊(C22⋊C8)—31no—
50#65708—31no—
51#65704—32no—
52#65702—32no—
53#65701—31no—
54#65695—32no—
55#65694—32no—
56C23×C3×D5C2×C411yescharacteristic
57C22×C3×C4×C5C2×C411yescharacteristic
58C2×#1220C2×C412yes—
59C2×D60C2×C411yescharacteristic
60C2×C5×Dic6C2×C411yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5C2×C411yescharacteristic
65C2×C3×C4×D5C2×C411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C2×#1202C2×C412yes—
69C2×#1202C2×C412yes—
70C2×#1200C2312yes—
71#6773—22no—
72#6773—22no—
73C2×C3⋊#170C2311yescharacteristic
74C2×C3⋊#170C2311yescharacteristic
75C2×C3⋊#170C2311yescharacteristic
76C2×C3⋊#170C2311yescharacteristic
77D5⋊(C3⋊C8)—22no—
78D5⋊(C3⋊C8)—22no—
79C3×#704—24no—
80C2×C3×#170C2312yes—
81C2×C3×#170C2312yes—
82C3×#700—22no—
83C3×#700D414yescomplemented
84C3×D5⋊C8—24no—
85#6740—24no—
86#6738—24no—
87#6714C2×C412yes—
88C4⋊Dic15C2×C411yescharacteristic
89C5×#217C2×C412yes—
90C5×C4⋊Dic3C2×C411yescharacteristic
91C5×Dic3⋊C4C2×C412yes—
92#6669C2×C412yes—
93#6667C2×C412yes—
94#6665C2×C412yes—
95#6665C2×C412yes—
96Dic3×Dic5C2312yes—
97C22×C3×M16—51no—
98#5791—51no—
99C2×#907—51no—
100C2×#830—51no—
101#5129—51no—
102#5128—52no—
103#5127—52no—
104#5122—51no—
105#5119—51no—
106#5111—52no—
107C8×#67—52no—
108C2×#713—31no—
109C22×C4×D5C2×D311yescharacteristic
110C2×#704C2×D312yes—
111#4133—64no—
112D5⋊M16—24no—
113C2×#700—32no—
114C2×#700C2×D311yescharacteristic
115C2×#700C2×D311yescharacteristic
116C2×D5⋊C8—31no—
117C2×D5⋊C8—31no—
118C2×D5⋊C8—32no—
119C2×D5⋊C8C2×D312yes—
120C5×C22⋊Q8—31no—
121#4092—31no—
122#4076—31no—
123#4041—31no—
124#4040—32no—
125#4039—32no—
126#4038—31no—
127#4028—32no—
128#4027—32no—
129C22⋊#170—31no—
130C22⋊#170—31no—
131#4004—32no—
132#4003—31no—
133#4003—31no—
134#4003—32no—
135#4003—32no—
136#4002—32no—
137C4⋊#170—32no—
138C4×#170—32no—
139#2933—151noSylow
140C23×C3×C5C22×C411yescharacteristic
141C22×D15C22×C412yes—
142C22×C3×D5—22no—
143C22×C3×D5—22no—
144C22×C3×D5—41no—
145C22×C3×D5C22×C411yescharacteristic
146C22×C3×D5C22×C411yescharacteristic
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5C22×C411yescharacteristic
149C2×C3×C4×C5C22×C411yescharacteristic
150#1220—42no—
151C2×Dic15C22×C412yes—
152D60—22no—
153C2×C5×Dic3C22×C412yes—
154C2×C5×Dic3C22×C412yes—
155C5×Dic6—22no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5C22×C411yescharacteristic
159C2×C3×Dic5C2411yescharacteristic
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×C4×D5—21no—
163C3×C4×D5—21no—
164C3×C4×D5C2×D412yes—
165C3×C4×D5#4112yes—
166#1202—24no—
167#1202—24no—
168#1200—22no—
169#1200—22no—
170C3⋊#170—21no—
171C3⋊#170—21no—
172C3⋊#170—21no—
173C3⋊#170—21no—
174C3×#170—22no—
175C3×#170C2×D414yes—
176C23×C3×C4—51no—
177C2×#235—51no—
178C2×C3×M16—51no—
179C2×C3×M16—52no—
180C2×C3×M16—51no—
181C2×C3×M16—104no—
182C22×C3×C8—52no—
183#953—52no—
184#930—51no—
185#930—51no—
186#929—52no—
187C4×#67—52no—
188C4×#67—52no—
189#926—51no—
190#924—51no—
191#924AGL(1,𝔽5)11yescharacteristic
192C22×C3⋊C8—51no—
193C22×C3⋊C8—51no—
194#907—104no—
195C2×ΓL(1,𝔽25)—52no—
196C2×D3×C8—52no—
197#830—51no—
198#830—51no—
199#830—51no—
200#830—51no—
201(C2×D3)⋊C8—52no—
202(C2×D3)⋊C8—52no—
203#815—52no—
204Dic3⋊C8—52no—
205Dic3⋊C8—52no—
206C8×Dic3—52no—
207C23×D5C4×D311yescharacteristic
208C2×C5×Q8—31no—
209C22×C4×C5C4×D311yescharacteristic
210C2×C22⋊D5—32no—
211C22×Dic5C22×D311yescharacteristic
212#713—62no—
213#713—62no—
214C2×D20—32no—
215C2×D20—32no—
216C2×D20—31no—
217C2×C4×D5—22no—
218C2×C4×D5—22no—
219C2×C4×D5—32no—
220C2×C4×D5C4×D311yescharacteristic
221C2×C4×D5C4×D311yescharacteristic
222C2×C4×D5C22×D311yescharacteristic
223C2×C4×D5C22×D311yescharacteristic
224#704—24no—
225C2×#170—31no—
226C2×#170—31no—
227C2×#170—31no—
228C2×#170—31no—
229C2×#170C22×D312yes—
230C2×#170C22×D312yes—
231#700—22no—
232#700—64no—
233#700#6714yescomplemented
234D5⋊C8—24no—
235D5⋊C8—62no—
236D5⋊C8—62no—
237D5⋊C8—64no—
238C5×C4⋊C4—32no—
239C5×C4⋊C4—31no—
240C5×C22⋊C4—32no—
241#685—32no—
242#685—32no—
243#685—32no—
244#685—32no—
245C4⋊Dic5—31no—
246#683—32no—
247C4×Dic5—32no—
248C2×#131—151no—
249C22×M16—51no—
250#525—151no—
251#436—152no—
252#435—152no—
253#435—152no—
254C8×D4—152no—
255#424—151no—
256#408—151no—
257C2×C22⋊C8—151no—
258#405—151no—
259C22×C3×C5—21no—
260C22×C3×C5—21no—
261C22×C3×C5—21no—
262C22×C3×C5C23×C411yescharacteristic
263C2×D15—22no—
264C2×D15—22no—
265C2×D15—22no—
266C2×C3×D5—21no—
267C2×C3×D5—21no—
268C2×C3×D5—21no—
269C2×C3×D5—21no—
270C2×C3×D5—44no—
271C2×C3×D5C4×D412yes—
272C2×C3×D5#13112yescomplemented
273C3×C4×C5—21no—
274C3×C4×C5C4×D412yes—
275Dic15—22no—
276C3×Dic5—21no—
277C3×Dic5C22×D411yescharacteristic
278C3×Dic5C2×#4111yescharacteristic
279C5×Dic3—22no—
280C5×Dic3—22no—
281C24×C3—51no—
282C22×C3×C4—51no—
283C22×C3×C4—51no—
284C22×C3×C4—51no—
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4—102no—
288C22×C3×C4—102no—
289C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
290C2×#67—52no—
291C2×#67—52no—
292C2×#67—52no—
293#235—102no—
294#235—102no—
295C2×D12—51no—
296C2×C4×D3—52no—
297C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
298C3×M16—54no—
299C3×M16—104no—
300C3×M16—102no—
301C2×C3×C8—52no—
302C2×C3×C8—52no—
303C2×C3×C8—104no—
304#217—52no—
305#217—52no—
306#217C2×AGL(1,𝔽5)12yes—
307(C2×D3)⋊C4—52no—
308(C2×D3)⋊C4—52no—
309C4⋊Dic3—51no—
310C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
311Dic3⋊C4—52no—
312Dic3⋊C4C2×AGL(1,𝔽5)12yes—
313C4×Dic3—52no—
314C2×C3⋊C8—51no—
315C2×C3⋊C8—51no—
316C2×C3⋊C8—51no—
317C2×C3⋊C8—51no—
318C2×C3⋊C8—102no—
319C2×C3⋊C8—102no—
320ΓL(1,𝔽25)—104no—
321D3×C8—104no—
322C23×C5C2×C4×D311yescharacteristic
323C22×D5—22no—
324C22×D5—22no—
325C22×D5—32no—
326C22×D5—41no—
327C22×D5C2×C4×D311yescharacteristic
328C22×D5C2×C4×D311yescharacteristic
329C5×Q8—62no—
330C2×C4×C5—22no—
331C2×C4×C5—32no—
332C2×C4×C5—32no—
333C2×C4×C5C2×C4×D311yescharacteristic
334C2×C4×C5C2×C4×D311yescharacteristic
335C22⋊D5—122no—
336C2×Dic5—21no—
337C2×Dic5—21no—
338C2×Dic5—32no—
339C2×Dic5C2×C4×D311yescharacteristic
340C2×Dic5C23×D311yescharacteristic
341D20—64no—
342D20—64no—
343D20—62no—
344C4×D5—22no—
345C4×D5—22no—
346C4×D5—21no—
347C4×D5—21no—
348C4×D5—62no—
349C4×D5—62no—
350C4×D5#23512yes—
351C4×D5C2×#6712yes—
352#170—22no—
353#170—61no—
354#170—61no—
355#170—61no—
356#170—61no—
357#170C2×#6714yes—
358C2×#41—151no—
359C23×C4—51no—
360#131—304no—
361C2×M16—51no—
362C2×M16—51no—
363C2×M16—52no—
364C2×M16—104no—
365C2×M16—152no—
366C22×C8—52no—
367C22×C8—152no—
368C22×C8—151no—
369C22×C8—151no—
370#123—152no—
371C22⋊Q8—31no—
372C22⋊Q8—151no—
373#121—151no—
374#121—151no—
375#120—152no—
376C4×D4—152no—
377C4×D4—152no—
378#117—151no—
379C4⋊C8—152no—
380C4⋊C8—152no—
381C22⋊C8—152no—
382C22⋊C8—152no—
383C22⋊C8—151no—
384C22⋊C8—151no—
385C22⋊C8—151no—
386C22⋊C8—151no—
387#97—152no—
388C4×C8—152no—
389C2×C3×C5—41no—
390C2×C3×C5C2×C4×D411yescharacteristic
391C2×C3×C5C2×#13111yescharacteristic
392C2×C3×C5#56811yescharacteristic
393D15—42no—
394C3×D5—22no—
395C3×D5—22no—
396C23×C3—51no—
397C23×C3—51no—
398C23×C3—102no—
399C23×C3—102no—
400C23×C3—201no—
401C23×C3C22×AGL(1,𝔽5)11yescharacteristic
402C22×D3—52no—
403C2×C3×C4—22no—
404C2×C3×C4—51no—
405C2×C3×C4—52no—
406C2×C3×C4—52no—
407C2×C3×C4—51no—
408C2×C3×C4—101no—
409C2×C3×C4—101no—
410C2×C3×C4—102no—
411C2×C3×C4—101no—
412C2×C3×C4—101no—
413C2×C3×C4—102no—
414C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
415C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
416#67—104no—
417#67—104no—
418#67—202no—
419C2×Dic3—52no—
420C2×Dic3C22×AGL(1,𝔽5)12yes—
421C2×Dic3C22×AGL(1,𝔽5)12yes—
422D12—102no—
423C4×D3—102no—
424C4×D3—102no—
425Dic6—22no—
426C3×C8—54no—
427C3×C8—102no—
428C3⋊C8—101no—
429C3⋊C8—101no—
430C3⋊C8—101no—
431C3⋊C8—101no—
432C22×C5—21no—
433C22×C5—21no—
434C22×C5—21no—
435C22×C5C22×C4×D311yescharacteristic
436C2×D5—21no—
437C2×D5—21no—
438C2×D5—21no—
439C2×D5—21no—
440C2×D5—44no—
441C2×D5—62no—
442C2×D5—62no—
443C2×D5—62no—
444C2×D5#90712yescomplemented
445C2×D5C4×#6712yes—
446C4×C5—21no—
447C4×C5—62no—
448C4×C5—62no—
449C4×C5C4×#6712yes—
450Dic5—21no—
451Dic5—62no—
452Dic5C2×#23511yescharacteristic
453Dic5C22×#6711yescharacteristic
454C24—51no—
455#41—302no—
456#41—302no—
457C2×Q8—31no—
458C2×D4—152no—
459C2×D4—152no—
460C2×D4—152no—
461C2×D4—151no—
462C22×C4—51no—
463C22×C4—51no—
464C22×C4—51no—
465C22×C4—51no—
466C22×C4—51no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—152no—
470C22×C4D3×AGL(1,𝔽5)11yescharacteristic
471M16—54no—
472M16—104no—
473M16—102no—
474M16—304no—
475C2×C8—52no—
476C2×C8—52no—
477C2×C8—104no—
478C2×C8—151no—
479C2×C8—151no—
480C2×C8—151no—
481C2×C8—151no—
482C2×C8—304no—
483C2×C8—302no—
484C2×C8—302no—
485C4⋊C4—31no—
486C4⋊C4—32no—
487C4⋊C4—152no—
488C4⋊C4—151no—
489C22⋊C4—32no—
490C22⋊C4—152no—
491C22⋊C4—152no—
492C22⋊C4—152no—
493C22⋊C4—152no—
494C42—152no—
495C3×C5#293311yescharacteristic, complemented, Hall
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—52no—
500C22×C3—52no—
501C22×C3—101no—
502C22×C3—101no—
503C22×C3—101no—
504C22×C3—101no—
505C22×C3—204no—
506C22×C3C23×AGL(1,𝔽5)11yescharacteristic
507C2×D3—102no—
508C2×D3—102no—
509C2×D3—102no—
510C3×C4—21no—
511C3×C4—51no—
512C3×C4—51no—
513C3×C4—101no—
514C3×C4D4×AGL(1,𝔽5)12yes—
515Dic3—22no—
516Dic3—22no—
517Dic3—102no—
518C2×C5—41no—
519C2×C5C2×#90711yescharacteristic
520C2×C5#574511yescharacteristic
521C2×C5C2×C4×#6711yescharacteristic
522D5—22no—
523D5—22no—
524D5—122no—
525C23—51no—
526C23—51no—
527C23—102no—
528C23—102no—
529C23—152no—
530C23—201no—
531C23C2×D3×AGL(1,𝔽5)11yescharacteristic
532Q8—62no—
533D4—304no—
534D4—304no—
535D4—302no—
536D4—602no—
537C2×C4—22no—
538C2×C4—32no—
539C2×C4—32no—
540C2×C4—51no—
541C2×C4—52no—
542C2×C4—52no—
543C2×C4—51no—
544C2×C4—101no—
545C2×C4—101no—
546C2×C4—102no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—102no—
550C2×C4—152no—
551C2×C4—302no—
552C2×C4—302no—
553C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
554C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
555C8—54no—
556C8—102no—
557C8—301no—
558C8—301no—
559C8—301no—
560C8—301no—
561C2×C3—41no—
562C2×C3—102no—
563C2×C3—102no—
564C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
565C2×C3#6626011yescharacteristic
566C2×C3D5⋊#13111yescharacteristic
567D3—202no—
568C5#8375711yescharacteristic, complemented, Sylow
569C22—21no—
570C22—21no—
571C22—21no—
572C22—52no—
573C22—52no—
574C22—101no—
575C22—101no—
576C22—101no—
577C22—101no—
578C22—204no—
579C22—302no—
580C22—302no—
581C22—302no—
582C22C22×D3×AGL(1,𝔽5)11yescharacteristic
583C4—21no—
584C4—51no—
585C4—51no—
586C4—62no—
587C4—62no—
588C4—101no—
589C4—302no—
590C4AGL(1,𝔽5)×#6712yes—
591C3#1061726011yescharacteristic, complemented, Sylow
592C2—41no—
593C2—102no—
594C2—102no—
595C2—602no—
596C2D5⋊#90711yescharacteristic
597C2#1175682711yescharacteristic
598C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radical#11754527C2
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2933
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5⋊M16C2semidirect
2. C2×#91916C2semidirect
4. D5⋊#830C2semidirect
5. #11752037C2semidirect
6. #11751987C2semidirect
7. #11751911C2semidirect
8. #11751881C2semidirect
9. #11751825C2semidirect
10. #11751814C2semidirect
11. #11751782C2semidirect
22. C2×#6740C22semidirect
23. C2×#6738C22semidirect
38. #91177C22semidirect
39. Dic3⋊#170C22semidirect
40. #91171C22semidirect
41. #91171C22semidirect
42. #91169C22semidirect
43. Dic3×#170C22semidirect
46. C2×D5⋊M16D3semidirect
83. C3×#700D4semidirect
233. #700#67semidirect
272. C2×C3×D5#131semidirect
444. C2×D5#907semidirect
495. C3×C5#2933semidirect
568. C5#83757semidirect
591. C3#10617260semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5⋊M162
C2×#919162
#117545272
D5⋊#8302
#117520372
#117519872
#117519112
#117518812
#117518252
#117518142
#117517822
#106172603
#837575