Finite Group Databasebeta

← #14415207

Subgroups — #14415207

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5⋊M16C211yesmaximal, characteristic, complemented
2C2×#91914C211yesmaximal, characteristic, complemented
3#11754527C211yesmaximal, characteristic
4#11752415C211yesmaximal, characteristic, complemented
5#11752037C212yesmaximal, complemented
6#11751987C212yesmaximal, complemented
7#11751886C212yesmaximal, complemented
8#11751822C211yesmaximal, characteristic, complemented
9#11751813C211yesmaximal, characteristic, complemented
10#11751767C211yesmaximal, characteristic, complemented
11#11751763C212yesmaximal, complemented
12#10617258—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×#6773C2211yescharacteristic
15C2×#6758C2211yescharacteristic
16C2×#6758C2211yescharacteristic
17C2×C3×#704C2211yescharacteristic
18C2×C3×#704C2211yescharacteristic
19C3×D5⋊M16—24no—
20C2×C3×#700C2211yescharacteristic
21C2×C3×#700C2211yescharacteristic
22C2×C3×D5⋊C8C2211yescharacteristic
23C2×C3×D5⋊C8C2211yescharacteristic
24C2×#6740C2212yescomplemented
25C2×#6738C2212yescomplemented
26#91914—24no—
27#91819C411yescharacteristic
28C5×#924C411yescharacteristic
29#91564C412yes—
30#91552C2212yes—
31#91450C411yescharacteristic
32#91444C2212yes—
33#91359C411yescharacteristic
34#91358C2211yescharacteristic
35#91348C412yes—
36#91241C2212yes—
37#91232C2212yes—
38#91177C2212yescomplemented
39Dic3⋊#170C2212yescomplemented
40#91171C2212yescomplemented
41#91171C2212yescomplemented
42#91169C2212yescomplemented
43Dic3×#170C2212yescomplemented
44#83756—51nomaximal, Hall
45C2×#4133—31no—
46C2×D5⋊M16D311yescharacteristic, complemented
47#65961—31no—
48#65787—31no—
49#65756—31no—
50#65708—31no—
51#65705—32no—
52#65704—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⋊#170C2312yes—
74C2×C3⋊#170C2312yes—
75#6758—22no—
76#6758—22no—
77C3×#704—22no—
78C3×#704—22no—
79C2×C3×#170C2311yescharacteristic
80C2×C3×#170C2311yescharacteristic
81C2×C3×#170C2311yescharacteristic
82C2×C3×#170C2311yescharacteristic
83C3×#700—22no—
84C3×#700—22no—
85C3×D5⋊C8—22no—
86C3×D5⋊C8D414yescomplemented
87#6740—24no—
88#6738—24no—
89#6714C2×C412yes—
90C4⋊Dic15C2×C411yescharacteristic
91C5×#217C2×C412yes—
92C5×C4⋊Dic3C2×C411yescharacteristic
93C5×Dic3⋊C4C2×C412yes—
94#6669C2×C412yes—
95#6667C2×C412yes—
96#6665C2×C412yes—
97#6665C2×C412yes—
98Dic3×Dic5C2312yes—
99C22×C3×M16—51no—
100#5791—51no—
101C2×#901—51no—
102#5207—51no—
103#5128—52no—
104#5128—52no—
105#5127—52no—
106#5127—52no—
107#5110—51no—
108#5102—51no—
109#5101—51no—
110C2×#713—31no—
111C22×C4×D5C2×D311yescharacteristic
112C2×#704C2×D311yescharacteristic
113C2×#704C2×D311yescharacteristic
114#4133—64no—
115D5⋊M16—24no—
116C2×#700—31no—
117C2×#700—31no—
118C2×#700—32no—
119C2×#700C2×D311yescharacteristic
120C2×#700C2×D311yescharacteristic
121C2×D5⋊C8—32no—
122C2×D5⋊C8C2×D311yescharacteristic
123C2×D5⋊C8C2×D311yescharacteristic
124C5×C22⋊Q8—31no—
125#4092—31no—
126#4076—31no—
127#4041—31no—
128#4040—32no—
129#4039—32no—
130#4038—31no—
131#4028—32no—
132#4027—32no—
133C22⋊#170—32no—
134#4004—32no—
135#4003—32no—
136#4003—32no—
137#4003—32no—
138#4002—32no—
139C4⋊#170—32no—
140C4×#170—32no—
141#2930—151noSylow
142C23×C3×C5C22×C411yescharacteristic
143C22×D15C22×C412yes—
144C22×C3×D5—22no—
145C22×C3×D5—41no—
146C22×C3×D5—41no—
147C22×C3×D5C22×C411yescharacteristic
148C22×C3×D5C22×C411yescharacteristic
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C22×C411yescharacteristic
151C2×C3×C4×C5C22×C411yescharacteristic
152#1220—42no—
153C2×Dic15C22×C412yes—
154D60—22no—
155C2×C5×Dic3C22×C412yes—
156C2×C5×Dic3C22×C412yes—
157C5×Dic6—22no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5C22×C411yescharacteristic
161C2×C3×Dic5C2411yescharacteristic
162C3×C4×D5—22no—
163C3×C4×D5—22no—
164C3×C4×D5—21no—
165C3×C4×D5—21no—
166C3×C4×D5C2×D412yes—
167C3×C4×D5#4112yes—
168#1202—24no—
169#1202—42no—
170#1200—22no—
171#1200—22no—
172C3⋊#170—22no—
173C3⋊#170—22no—
174C3×#170—21no—
175C3×#170—21no—
176C3×#170C2×D412yes—
177C3×#170C2×D412yes—
178C23×C3×C4—51no—
179C2×#235—51no—
180C2×C3×M16—51no—
181C2×C3×M16—51no—
182C2×C3×M16—51no—
183C2×C3×M16—51no—
184C2×C3×M16—104no—
185C22×C3×C8—51no—
186C22×C3×C8—51no—
187#953—52no—
188#930—51no—
189#930—51no—
190#929—52no—
191C4×#67—52no—
192C4×#67—52no—
193#926—51no—
194#924—51no—
195#924AGL(1,𝔽5)11yescharacteristic
196C2×#208—51no—
197C2×#208—51no—
198#901—104no—
199C2×ΓL(1,𝔽25)—52no—
200C2×D3×C8—52no—
201#830—52no—
202#830—52no—
203(C2×D3)⋊C8—52no—
204(C2×D3)⋊C8—52no—
205#815—52no—
206Dic3⋊C8—52no—
207Dic3⋊C8—52no—
208C8×Dic3—52no—
209C23×D5C4×D311yescharacteristic
210C2×C5×Q8—31no—
211C22×C4×C5C4×D311yescharacteristic
212C2×C22⋊D5—32no—
213C22×Dic5C22×D311yescharacteristic
214#713—62no—
215#713—62no—
216C2×D20—32no—
217C2×D20—31no—
218C2×D20—32no—
219C2×C4×D5—22no—
220C2×C4×D5—22no—
221C2×C4×D5—32no—
222C2×C4×D5C4×D311yescharacteristic
223C2×C4×D5C4×D311yescharacteristic
224C2×C4×D5C22×D311yescharacteristic
225C2×C4×D5C22×D311yescharacteristic
226#704—22no—
227#704—22no—
228C2×#170—32no—
229C2×#170—32no—
230C2×#170C22×D311yescharacteristic
231C2×#170C22×D311yescharacteristic
232C2×#170C22×D311yescharacteristic
233C2×#170C22×D311yescharacteristic
234#700—22no—
235#700—22no—
236#700—62no—
237#700—62no—
238#700—64no—
239D5⋊C8—22no—
240D5⋊C8—64no—
241D5⋊C8#6714yescomplemented
242C5×C4⋊C4—32no—
243C5×C4⋊C4—31no—
244C5×C22⋊C4—32no—
245#685—32no—
246#685—32no—
247#685—32no—
248#685—32no—
249C4⋊Dic5—31no—
250#683—32no—
251C4×Dic5—32no—
252C2×#131—151no—
253C22×M16—51no—
254#525—151no—
255#436—152no—
256#436—152no—
257#435—152no—
258#435—152no—
259#424—151no—
260#408—151no—
261#407—151no—
262#405—151no—
263C22×C3×C5—21no—
264C22×C3×C5—21no—
265C22×C3×C5—21no—
266C22×C3×C5C23×C411yescharacteristic
267C2×D15—22no—
268C2×D15—22no—
269C2×D15—22no—
270C2×C3×D5—21no—
271C2×C3×D5—21no—
272C2×C3×D5—21no—
273C2×C3×D5—21no—
274C2×C3×D5—21no—
275C2×C3×D5—44no—
276C2×C3×D5C4×D412yes—
277C3×C4×C5—21no—
278C3×C4×C5C4×D412yes—
279Dic15—22no—
280C3×Dic5—21no—
281C3×Dic5C22×D411yescharacteristic
282C3×Dic5C2×#4111yescharacteristic
283C5×Dic3—22no—
284C5×Dic3—22no—
285C24×C3—51no—
286C22×C3×C4—51no—
287C22×C3×C4—51no—
288C22×C3×C4—51no—
289C22×C3×C4—51no—
290C22×C3×C4—51no—
291C22×C3×C4—102no—
292C22×C3×C4—102no—
293C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
294C2×#67—52no—
295C2×#67—52no—
296C2×#67—52no—
297#235—102no—
298#235—102no—
299C2×D12—51no—
300C2×C4×D3—52no—
301C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
302C3×M16—102no—
303C3×M16—102no—
304C3×M16—102no—
305C3×M16—102no—
306C2×C3×C8—51no—
307C2×C3×C8—51no—
308C2×C3×C8—54no—
309C2×C3×C8—51no—
310C2×C3×C8—51no—
311C2×C3×C8—102no—
312#217—52no—
313#217—52no—
314#217C2×AGL(1,𝔽5)12yes—
315(C2×D3)⋊C4—52no—
316(C2×D3)⋊C4—52no—
317C4⋊Dic3—51no—
318C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
319Dic3⋊C4—52no—
320Dic3⋊C4C2×AGL(1,𝔽5)12yes—
321C4×Dic3—52no—
322#208—102no—
323#208—102no—
324C2×C3⋊C8—52no—
325C2×C3⋊C8—52no—
326ΓL(1,𝔽25)—104no—
327D3×C8—104no—
328C23×C5C2×C4×D311yescharacteristic
329C22×D5—22no—
330C22×D5—32no—
331C22×D5—41no—
332C22×D5—41no—
333C22×D5C2×C4×D311yescharacteristic
334C22×D5C2×C4×D311yescharacteristic
335C5×Q8—62no—
336C2×C4×C5—22no—
337C2×C4×C5—32no—
338C2×C4×C5—32no—
339C2×C4×C5C2×C4×D311yescharacteristic
340C2×C4×C5C2×C4×D311yescharacteristic
341C22⋊D5—122no—
342C2×Dic5—21no—
343C2×Dic5—21no—
344C2×Dic5—32no—
345C2×Dic5C2×C4×D311yescharacteristic
346C2×Dic5C23×D311yescharacteristic
347D20—64no—
348D20—62no—
349D20—122no—
350C4×D5—22no—
351C4×D5—22no—
352C4×D5—21no—
353C4×D5—21no—
354C4×D5—62no—
355C4×D5—62no—
356C4×D5#23512yes—
357C4×D5C2×#6712yes—
358#170—21no—
359#170—21no—
360#170—62no—
361#170—62no—
362#170C2×#6712yes—
363#170C2×#6712yes—
364C2×#41—151no—
365C23×C4—51no—
366#131—304no—
367C2×M16—51no—
368C2×M16—51no—
369C2×M16—51no—
370C2×M16—51no—
371C2×M16—104no—
372C2×M16—152no—
373C2×M16—151no—
374C2×M16—151no—
375C22×C8—51no—
376C22×C8—51no—
377C22×C8—152no—
378#123—152no—
379C22⋊Q8—31no—
380C22⋊Q8—151no—
381#121—151no—
382#121—151no—
383#120—152no—
384C4×D4—152no—
385C4×D4—152no—
386#117—151no—
387C4⋊C8—152no—
388C4⋊C8—152no—
389C22⋊C8—152no—
390C22⋊C8—152no—
391C22⋊C8—152no—
392C22⋊C8—152no—
393#97—152no—
394C4×C8—152no—
395C2×C3×C5—41no—
396C2×C3×C5C2×C4×D411yescharacteristic
397C2×C3×C5#56811yescharacteristic
398C2×C3×C5#56811yescharacteristic
399D15—42no—
400C3×D5—22no—
401C3×D5—41no—
402C23×C3—51no—
403C23×C3—51no—
404C23×C3—102no—
405C23×C3—201no—
406C23×C3—201no—
407C23×C3C22×AGL(1,𝔽5)11yescharacteristic
408C22×D3—52no—
409C2×C3×C4—22no—
410C2×C3×C4—51no—
411C2×C3×C4—52no—
412C2×C3×C4—52no—
413C2×C3×C4—51no—
414C2×C3×C4—101no—
415C2×C3×C4—101no—
416C2×C3×C4—102no—
417C2×C3×C4—101no—
418C2×C3×C4—101no—
419C2×C3×C4—102no—
420C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
421C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
422#67—104no—
423#67—202no—
424#67—202no—
425C2×Dic3—52no—
426C2×Dic3C22×AGL(1,𝔽5)12yes—
427C2×Dic3C22×AGL(1,𝔽5)12yes—
428D12—102no—
429C4×D3—102no—
430C4×D3—102no—
431Dic6—22no—
432C3×C8—52no—
433C3×C8—52no—
434C3×C8—101no—
435C3×C8—101no—
436C3⋊C8—102no—
437C3⋊C8—102no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5—21no—
441C22×C5C22×C4×D311yescharacteristic
442C2×D5—21no—
443C2×D5—21no—
444C2×D5—21no—
445C2×D5—21no—
446C2×D5—21no—
447C2×D5—44no—
448C2×D5—62no—
449C2×D5—62no—
450C2×D5—62no—
451C2×D5C4×#6712yes—
452C4×C5—21no—
453C4×C5—62no—
454C4×C5—62no—
455C4×C5C4×#6712yes—
456Dic5—21no—
457Dic5—62no—
458Dic5C2×#23511yescharacteristic
459Dic5C22×#6711yescharacteristic
460C24—51no—
461#41—302no—
462#41—302no—
463C2×Q8—31no—
464C2×D4—152no—
465C2×D4—152no—
466C2×D4—152no—
467C2×D4—151no—
468C22×C4—51no—
469C22×C4—51no—
470C22×C4—51no—
471C22×C4—51no—
472C22×C4—51no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—152no—
476C22×C4D3×AGL(1,𝔽5)11yescharacteristic
477M16—102no—
478M16—102no—
479M16—102no—
480M16—102no—
481M16—304no—
482M16—302no—
483M16—302no—
484C2×C8—51no—
485C2×C8—51no—
486C2×C8—54no—
487C2×C8—51no—
488C2×C8—51no—
489C2×C8—102no—
490C2×C8—152no—
491C2×C8—152no—
492C2×C8—304no—
493C4⋊C4—31no—
494C4⋊C4—32no—
495C4⋊C4—152no—
496C4⋊C4—151no—
497C22⋊C4—32no—
498C22⋊C4—152no—
499C22⋊C4—152no—
500C22⋊C4—152no—
501C22⋊C4—152no—
502C42—152no—
503C3×C5#293011yescharacteristic, complemented, Hall
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—52no—
508C22×C3—101no—
509C22×C3—101no—
510C22×C3—101no—
511C22×C3—101no—
512C22×C3—101no—
513C22×C3—204no—
514C22×C3C23×AGL(1,𝔽5)11yescharacteristic
515C2×D3—102no—
516C2×D3—102no—
517C2×D3—102no—
518C3×C4—21no—
519C3×C4—51no—
520C3×C4—51no—
521C3×C4—101no—
522C3×C4D4×AGL(1,𝔽5)12yes—
523Dic3—22no—
524Dic3—22no—
525Dic3—102no—
526C2×C5—41no—
527C2×C5#574511yescharacteristic
528C2×C5#574511yescharacteristic
529C2×C5C2×C4×#6711yescharacteristic
530D5—22no—
531D5—41no—
532D5—122no—
533C23—51no—
534C23—51no—
535C23—102no—
536C23—152no—
537C23—201no—
538C23—201no—
539C23C2×D3×AGL(1,𝔽5)11yescharacteristic
540Q8—62no—
541D4—304no—
542D4—302no—
543D4—602no—
544D4—602no—
545C2×C4—22no—
546C2×C4—32no—
547C2×C4—32no—
548C2×C4—51no—
549C2×C4—52no—
550C2×C4—52no—
551C2×C4—51no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—102no—
555C2×C4—101no—
556C2×C4—101no—
557C2×C4—102no—
558C2×C4—152no—
559C2×C4—302no—
560C2×C4—302no—
561C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
562C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
563C8—52no—
564C8—52no—
565C8—101no—
566C8—101no—
567C8—302no—
568C8—302no—
569C2×C3—41no—
570C2×C3—102no—
571C2×C3—201no—
572C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
573C2×C3#6626011yescharacteristic
574C2×C3#6626411yescharacteristic
575D3—202no—
576C5#8375611yescharacteristic, complemented, Sylow
577C22—21no—
578C22—21no—
579C22—21no—
580C22—52no—
581C22—101no—
582C22—101no—
583C22—101no—
584C22—101no—
585C22—101no—
586C22—204no—
587C22—302no—
588C22—302no—
589C22—302no—
590C22C22×D3×AGL(1,𝔽5)11yescharacteristic
591C4—21no—
592C4—51no—
593C4—51no—
594C4—62no—
595C4—62no—
596C4—101no—
597C4—302no—
598C4AGL(1,𝔽5)×#6712yes—
599C3#1061725811yescharacteristic, complemented, Sylow
600C2—41no—
601C2—102no—
602C2—201no—
603C2—602no—
604C2#1175682311yescharacteristic
605C2#1175682711yescharacteristic
606C2C2×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#2930
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×#91914C2semidirect
4. #11752415C2semidirect
5. #11752037C2semidirect
6. #11751987C2semidirect
7. #11751886C2semidirect
8. #11751822C2semidirect
9. #11751813C2semidirect
10. #11751767C2semidirect
11. #11751763C2semidirect
24. C2×#6740C22semidirect
25. C2×#6738C22semidirect
38. #91177C22semidirect
39. Dic3⋊#170C22semidirect
40. #91171C22semidirect
41. #91171C22semidirect
42. #91169C22semidirect
43. Dic3×#170C22semidirect
46. C2×D5⋊M16D3semidirect
86. C3×D5⋊C8D4semidirect
241. D5⋊C8#67semidirect
503. C3×C5#2930semidirect
576. C5#83756semidirect
599. C3#10617258semidirect

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×#919142
#117545272
#117524152
#117520372
#117519872
#117518862
#117518222
#117518132
#117517672
#117517632
#106172583
#837565