Finite Group Databasebeta

← D3×#66169 #14509977

Subgroups — D3×#66169 #14509977

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2D3×#4149C211yesmaximal, characteristic, complemented
3#11756594C211yesmaximal, characteristic, complemented
4C3×#66169C211yesmaximal, characteristic, complemented
5#11755325C213yesmaximal, complemented
6#11755323C213yesmaximal, complemented
7D3×#4096C213yesmaximal, complemented
8D3×#4095C213yesmaximal, complemented
9#11755305C211yesmaximal, characteristic, complemented
10#11755301C211yesmaximal, characteristic, complemented
11D3×#4094C211yesmaximal, characteristic, complemented
12#11754698C213yesmaximal, complemented
13#11754697C213yesmaximal, complemented
14D3×#4078C213yesmaximal, complemented
15C2×D3×#686C213yesmaximal, complemented
16C2×#66169—31nomaximal, Hall
17C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
18#92100C2211yescharacteristic, complemented
19C5×#1009—21no—
20C5×#1009C2213yescomplemented
21C5×#1009C2211yescharacteristic, complemented
22C5×D3×#41—21no—
23C5×D3×#41C2211yescharacteristic
24C5×D3×#41C2213yescomplemented
25C5×#1004—23no—
26C5×#1004C2213yescomplemented
27C2×C5×D3×D4—23no—
28C2×C5×D3×D4C2213yescomplemented
29C3×#4149C2211yescharacteristic, complemented
30#92035—21no—
31D3×#713—21no—
32#92026—23no—
33D3×D4×D5—23no—
34#92019C2213yescomplemented
35#92017C2213yescomplemented
36D3×#709C2213yescomplemented
37C2×D3×D20C2213yescomplemented
38#91839C2213yescomplemented
39#91838C2213yescomplemented
40#91837C2211yescharacteristic, complemented
41#91821C2213yescomplemented
42C2×#6715C2213yescomplemented
43C3×#4096C2213yescomplemented
44C3×#4095C2213yescomplemented
45C3×#4094C2211yescharacteristic, complemented
46C3×#4078C2213yescomplemented
47C2×C3×#686C2213yescomplemented
48#91519C2213yescomplemented
49#91517C2213yescomplemented
50D3×#689C2211yescharacteristic, complemented
51#91504C2216yescomplemented
52D3×#688C2213yescomplemented
53#91496C2216yescomplemented
54#91495C2213yescomplemented
55#91494C2216yescomplemented
56#91493C2213yescomplemented
57D3×#687C2213yescomplemented
58#91480C2216yescomplemented
59D3×#686C2216yescomplemented
60D3×#686C2213yescomplemented
61D3×#686C2216yescomplemented
62D3×#686C2216yescomplemented
63#91305C2213yescomplemented
64#91304C2213yescomplemented
65#91303C2213yescomplemented
66C2×#6654C2213yescomplemented
67#91299C2213yescomplemented
68#91298C2213yescomplemented
69#91297C2213yescomplemented
70C2×#6652C2213yescomplemented
71#91288C2213yescomplemented
72D3×#681C2213yescomplemented
73#91286C2213yescomplemented
74C2×D3×#168C2213yescomplemented
75D3×#576—51nomaximal, Hall
76C2×C5×H(5,𝔽2)—31no—
77C2×#4149—31no—
78#66169—33no—
79#66169—31no—
80#66169—33no—
81#66169—33no—
82#66169—31no—
83#66169—31no—
84#66169—33no—
85#66169D311yescharacteristic, direct product factor
86C2×#4096—33no—
87C2×#4095—33no—
88C2×#4094—31no—
89C2×#4078—33no—
90C22×#686—33no—
91C23×C5×D3—23no—
92C22×D3×D5—23no—
93C3×C5×#41—21no—
94C3×C5×#41C2311yescharacteristic
95C3×C5×#41C2313yescomplemented
96C2×C3×C5×D4—23no—
97C2×C3×C5×D4C2313yescomplemented
98#6821—21no—
99D4×D15—23no—
100#6817C2313yescomplemented
101C2×D60C2313yescomplemented
102C2×C5×#67—26no—
103C2×C5×#67—23no—
104C5×#239—21no—
105C5×#239D411yescharacteristic
106C5×#239C2313yescomplemented
107C5×D3×Q8D411yescharacteristic
108C5×D3×Q8C2311yescharacteristic
109C5×#237—23no—
110C5×#237—23no—
111C5×#237D413yes—
112C5×#237C2313yescomplemented
113C5×D3×D4—23no—
114C5×D3×D4—23no—
115C5×D3×D4—26no—
116C5×D3×D4—23no—
117C5×D3×D4—23no—
118C5×D3×D4—23no—
119C5×D3×D4D413yes—
120C5×D3×D4C2313yes—
121C5×D3×D4C2316yescomplemented
122C5×#235—23no—
123C5×#235—23no—
124C5×#235C2313yes—
125C5×#235C2313yescomplemented
126C2×C5×D12—23no—
127C2×C5×D12C2313yescomplemented
128C2×C4×C5×D3—23no—
129C2×C4×C5×D3C2313yes—
130C3×#713—21no—
131C3×D4×D5—23no—
132C3×#709C2313yescomplemented
133C2×C3×D20C2313yescomplemented
134#6790—26no—
135D3×C22⋊D5—23no—
136D5×#67—26no—
137C2×#1202—23no—
138#6779—23no—
139#6777—23no—
140D3×D20—23no—
141D3×D20—23no—
142D3×D20C2313yes—
143D3×D20C2316yescomplemented
144D5×D12—23no—
145C4×D3×D5—23no—
146#6773—23no—
147#6771—23no—
148#6769C2313yescomplemented
149D3×Dic10C2311yescharacteristic
150#6766—23no—
151#6765C2313yescomplemented
152#6718C2311yescharacteristic, complemented
153#6717C2313yescomplemented
154#6716C2313yescomplemented
155#6715C2313yescomplemented
156#6715C2316yescomplemented
157#6710C2313yescomplemented
158C2×C3⋊#168C2313yescomplemented
159C3×#689C2311yescharacteristic, complemented
160C3×#688C2313yescomplemented
161C3×#687C2313yescomplemented
162C3×#686C2313yescomplemented
163C3×#686C2316yescomplemented
164C3×#681C2313yescomplemented
165C2×C3×#168C2313yescomplemented
166#6663C2311yescharacteristic, complemented
167#6661C2311yescharacteristic, complemented
168#6660C2313yescomplemented
169#6659C2313yescomplemented
170#6656C2313yescomplemented
171#6655C2313yescomplemented
172#6654C2313yescomplemented
173#6654C2316yescomplemented
174#6652C2313yescomplemented
175#6652C2316yescomplemented
176#6650C2316yescomplemented
177D3×#168C2311yescharacteristic
178D3×#168C2313yes—
179D3×#168C2313yescomplemented
180D3×#168C2313yescomplemented
181D3×H(5,𝔽2)—51no—
182D3×H(5,𝔽2)D511yescharacteristic, complemented
183C3×#576—51no—
184#5835—51no—
185#5835—51no—
186#5774—53no—
187#5774—53no—
188D3×AGL(1,ℤ/8)—53no—
189D3×AGL(1,ℤ/8)—53no—
190#5769—53no—
191D3×#135—53no—
192#5757—53no—
193C2×D3×D8—53no—
194#5752—51no—
195D3×#131—51no—
196C5×H(5,𝔽2)—31no—
197C5×H(5,𝔽2)—33no—
198C5×H(5,𝔽2)—33no—
199C5×H(5,𝔽2)—63no—
200C5×H(5,𝔽2)—61no—
201C5×H(5,𝔽2)C2×D311yescharacteristic, complemented
202C2×C5×#41—31no—
203C2×C5×#41—33no—
204C2×C5×#41—61no—
205C22×C5×D4—33no—
206C22×C5×D4—63no—
207#4149—31no—
208#4149—33no—
209#4149—33no—
210#4149—63no—
211#4149—61no—
212#4149C2×D311yescharacteristic, complemented
213C2×#713—61no—
214C2×D4×D5—63no—
215C2×#709—33no—
216C22×D20—33no—
217#4096—33no—
218#4096—33no—
219#4096—33no—
220#4096—33no—
221#4096—33no—
222#4096—33no—
223#4096—33no—
224#4096C2×D313yescomplemented
225#4095—33no—
226#4095—33no—
227#4095—36no—
228#4095—36no—
229#4095—33no—
230#4095C2×D313yescomplemented
231#4094—31no—
232#4094—33no—
233#4094—33no—
234#4094C2×D311yescharacteristic, complemented
235C2×#689—31no—
236C2×#688—33no—
237C2×#687—33no—
238#4078—33no—
239#4078—33no—
240#4078—36no—
241#4078—36no—
242#4078—33no—
243#4078C2×D313yescomplemented
244C2×#686—33no—
245C2×#686—33no—
246C2×#686—33no—
247C2×#686—36no—
248C2×#686—36no—
249C2×#686—36no—
250C2×#686—33no—
251C2×#686C2×D313yescomplemented
252C2×#681—33no—
253C22×#168—33no—
254C2×#576—151noSylow
255C23×C3×C5—23no—
256C22×D15—23no—
257C22×C5×D3—23no—
258C22×C5×D3—23no—
259C22×C5×D3—26no—
260C22×C5×D3—86no—
261C22×C5×D3C2×D413yes—
262C22×C3×D5—23no—
263C2×D3×D5—23no—
264C2×D3×D5—26no—
265C2×D3×D5—86no—
266C3×C5×Q8C2×D411yescharacteristic
267C3×C5×Q8C2411yescharacteristic
268C3×C5×D4—23no—
269C3×C5×D4—23no—
270C3×C5×D4C2×D413yes—
271C3×C5×D4C2413yes—
272C2×C3×C4×C5—23no—
273C2×C3×C4×C5C2413yes—
274#1220—23no—
275D60—23no—
276D60C2413yes—
277C4×D15—23no—
278Dic30C2411yescharacteristic
279C5×#67—23no—
280C5×#67—23no—
281C5×#67—23no—
282C5×#67—26no—
283C5×#67C2×D416yes—
284C2×C5×Dic3—23no—
285C2×C5×Dic3C2×D413yes—
286C5×D12—23no—
287C5×D12—23no—
288C5×D12C2×D413yes—
289C5×D12C2413yes—
290C4×C5×D3—21no—
291C4×C5×D3—23no—
292C4×C5×D3—23no—
293C4×C5×D3C2×D413yes—
294C4×C5×D3C2×D413yes—
295C4×C5×D3C2413yes—
296C4×C5×D3C2411yescharacteristic
297C5×Dic6—21no—
298C5×Dic6C2×D413yes—
299C5×Dic6C2411yescharacteristic
300C3×C22⋊D5—23no—
301C3×D20—23no—
302C3×D20C2413yes—
303C3×C4×D5—23no—
304C3×Dic10C2411yescharacteristic
305#1204—21no—
306#1203—23no—
307#1202—26no—
308#1202—23no—
309#1201—23no—
310#1200—23no—
311D3×Dic5—21no—
312D5×Dic3—23no—
313C3⋊#168C2413yes—
314C3⋊#168C2411yescharacteristic
315C3×#168C2413yes—
316C3×#168C2411yescharacteristic
317C3×H(5,𝔽2)—51no—
318C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
319#1009—21no—
320#1009—51no—
321#1009—53no—
322#1009—101no—
323#1009C2×D513yescomplemented
324#1009C2×D511yescharacteristic, complemented
325D3×#41—21no—
326D3×#41—53no—
327D3×#41—101no—
328D3×#41C2×D511yescharacteristic
329D3×#41C2×D513yescomplemented
330#1004—23no—
331#1004—53no—
332#1004—103no—
333#1004C2×D513yescomplemented
334C2×D3×D4—23no—
335C2×D3×D4—53no—
336C2×D3×D4—103no—
337C2×D3×D4C2×D513yescomplemented
338C3×AGL(1,ℤ/8)—53no—
339C3×AGL(1,ℤ/8)—53no—
340C3×#135—53no—
341C2×C3×D8—53no—
342C3×#131—51no—
343#950—53no—
344#950—53no—
345#949—53no—
346#949—53no—
347#948—51no—
348#932—53no—
349#932—53no—
350C2×#213—53no—
351C2×#213—53no—
352#919—53no—
353D3×Q16—51no—
354#916—53no—
355#916—53no—
356#914—56no—
357#914—56no—
358D3×SD16—53no—
359D3×SD16—53no—
360#912—53no—
361#911—56no—
362#911—56no—
363D3×D8—53no—
364D3×D8—56no—
365D3×D8—56no—
366D3×D8—56no—
367#908—53no—
368#908—53no—
369#907—53no—
370D3×M16—53no—
371#904—53no—
372C2×D24—53no—
373#901—53no—
374C2×D3×C8—53no—
375C24×C5—63no—
376C23×D5—63no—
377C5×#41—21no—
378C5×#41—31no—
379C5×#41—33no—
380C5×#41—33no—
381C5×#41—33no—
382C5×#41—33no—
383C5×#41—33no—
384C5×#41—63no—
385C5×#41—63no—
386C5×#41—63no—
387C5×#41—63no—
388C5×#41—61no—
389C5×#41C22×D311yescharacteristic
390C5×#41C22×D313yescomplemented
391C2×C5×Q8—31no—
392C2×C5×Q8—31no—
393C2×C5×D4—23no—
394C2×C5×D4—33no—
395C2×C5×D4—33no—
396C2×C5×D4—36no—
397C2×C5×D4—33no—
398C2×C5×D4—63no—
399C2×C5×D4—63no—
400C2×C5×D4—63no—
401C2×C5×D4—63no—
402C2×C5×D4—66no—
403C2×C5×D4—63no—
404C2×C5×D4—63no—
405C2×C5×D4—66no—
406C2×C5×D4—63no—
407C2×C5×D4C22×D313yescomplemented
408C22×C4×C5—33no—
409C22×C4×C5—63no—
410C2×C22⋊D5—63no—
411#713—21no—
412#713—63no—
413#713—63no—
414#713—61no—
415D4×D5—23no—
416D4×D5—63no—
417D4×D5—63no—
418D4×D5—66no—
419D4×D5—66no—
420D4×D5—63no—
421#709—33no—
422#709—33no—
423#709—33no—
424#709—63no—
425#709—63no—
426#709C22×D313yescomplemented
427C2×D20—33no—
428C2×D20—33no—
429C2×D20—36no—
430C2×D20—63no—
431C2×D20—63no—
432C2×D20—63no—
433C2×D20C22×D313yescomplemented
434C2×C4×D5—63no—
435C2×Dic10—31no—
436#689—31no—
437#689—31no—
438#689—31no—
439#689C22×D311yescharacteristic, complemented
440#688—33no—
441#688—33no—
442#688—33no—
443#688C22×D313yescomplemented
444#687—33no—
445#687—33no—
446#687—33no—
447#687C22×D313yescomplemented
448#686—33no—
449#686—36no—
450#686—33no—
451#686—36no—
452#686—33no—
453#686—36no—
454#686C22×D313yescomplemented
455#686C22×D316yescomplemented
456#681—33no—
457#681—36no—
458#681C22×D313yescomplemented
459C2×#168—33no—
460C2×#168—33no—
461C2×#168—33no—
462C2×#168—31no—
463C2×#168—33no—
464C2×#168C22×D313yescomplemented
465C2×H(5,𝔽2)—31no—
466C2×H(5,𝔽2)—151no—
467#576—51no—
468#576—151no—
469#576—153no—
470#576—153no—
471#576—153no—
472#576—153no—
473#576—151no—
474#576—151no—
475C2×AGL(1,ℤ/8)—153no—
476C2×AGL(1,ℤ/8)—153no—
477C2×#135—153no—
478C22×D8—153no—
479C2×#131—151no—
480C22×C3×C5—23no—
481C22×C3×C5—83no—
482C22×C3×C5C22×D413yes—
483C2×D15—23no—
484C2×D15—83no—
485C2×C5×D3—26no—
486C2×C5×D3—23no—
487C2×C5×D3—46no—
488C2×C5×D3—86no—
489C2×C5×D3—83no—
490C2×C5×D3C22×D413yes—
491C2×C5×D3C22×D411yescharacteristic
492C2×C3×D5—23no—
493C2×C3×D5—83no—
494D3×D5—46no—
495D3×D5—86no—
496C3×C4×C5—21no—
497C3×C4×C5C22×D413yes—
498C3×C4×C5C2511yescharacteristic
499Dic15—21no—
500C3×Dic5—21no—
501C5×Dic3—21no—
502C5×Dic3C22×D413yes—
503C5×Dic3C22×D411yescharacteristic
504C23×D3—23no—
505C23×D3—103no—
506C3×#41—21no—
507C3×#41—53no—
508C3×#41—101no—
509C3×#41C22×D511yescharacteristic
510C3×#41C22×D513yescomplemented
511C2×C3×D4—23no—
512C2×C3×D4—53no—
513C2×C3×D4—103no—
514C2×C3×D4C22×D513yescomplemented
515C2×#67—26no—
516C2×#67—23no—
517C2×#67—106no—
518C2×#67—103no—
519#239—21no—
520#239—53no—
521#239—101no—
522#239C22⋊D511yescharacteristic
523#239C22×D513yescomplemented
524D3×Q8—51no—
525D3×Q8C22⋊D511yescharacteristic
526D3×Q8C22×D511yescharacteristic
527#237—23no—
528#237—23no—
529#237—53no—
530#237—103no—
531#237—103no—
532#237C22⋊D513yes—
533#237C22×D513yescomplemented
534D3×D4—23no—
535D3×D4—23no—
536D3×D4—26no—
537D3×D4—23no—
538D3×D4—23no—
539D3×D4—23no—
540D3×D4—53no—
541D3×D4—56no—
542D3×D4—103no—
543D3×D4—103no—
544D3×D4—106no—
545D3×D4—103no—
546D3×D4—103no—
547D3×D4—103no—
548D3×D4C22⋊D513yes—
549D3×D4C22×D513yes—
550D3×D4C22×D516yescomplemented
551#235—23no—
552#235—23no—
553#235—53no—
554#235—103no—
555#235—103no—
556#235C22×D513yes—
557#235C22×D513yescomplemented
558C2×D12—23no—
559C2×D12—53no—
560C2×D12—103no—
561C2×D12C22×D513yescomplemented
562C2×C4×D3—23no—
563C2×C4×D3—103no—
564C2×C4×D3C22×D513yes—
565C3×Q16—51no—
566C3×SD16—53no—
567C3×SD16—53no—
568C3×D8—53no—
569C3×D8—56no—
570C3×M16—53no—
571C2×C3×C8—53no—
572#216—51no—
573#216—51no—
574#215—53no—
575#215—53no—
576#214—53no—
577#214—53no—
578#213—53no—
579#213—56no—
580#213—53no—
581#213—56no—
582#208—53no—
583C2×C3⋊C8—53no—
584Dic12—51no—
585D24—53no—
586D24—56no—
587#204—53no—
588#204—53no—
589ΓL(1,𝔽25)—56no—
590D3×C8—51no—
591D3×C8—53no—
592D3×C8—53no—
593D3×C8—53no—
594C23×C5—23no—
595C23×C5—33no—
596C23×C5—63no—
597C23×C5—66no—
598C23×C5—63no—
599C23×C5—246no—
600C22×D5—23no—
601C22×D5—63no—
602C22×D5—66no—
603C22×D5—63no—
604C22×D5—246no—
605C5×Q8—33no—
606C5×Q8—31no—
607C5×Q8—61no—
608C5×Q8D3×D411yescharacteristic
609C5×Q8C23×D311yescharacteristic
610C5×D4—23no—
611C5×D4—23no—
612C5×D4—36no—
613C5×D4—33no—
614C5×D4—33no—
615C5×D4—63no—
616C5×D4—63no—
617C5×D4—66no—
618C5×D4—63no—
619C5×D4—63no—
620C5×D4—63no—
621C5×D4D3×D413yes—
622C5×D4C23×D313yes—
623C2×C4×C5—23no—
624C2×C4×C5—33no—
625C2×C4×C5—33no—
626C2×C4×C5—33no—
627C2×C4×C5—31no—
628C2×C4×C5—33no—
629C2×C4×C5—63no—
630C2×C4×C5—61no—
631C2×C4×C5—63no—
632C2×C4×C5—63no—
633C2×C4×C5C23×D313yes—
634C22⋊D5—23no—
635C22⋊D5—63no—
636C22⋊D5—63no—
637C22⋊D5—63no—
638C2×Dic5—61no—
639D20—23no—
640D20—33no—
641D20—63no—
642D20—66no—
643D20—63no—
644D20C23×D313yes—
645C4×D5—23no—
646C4×D5—63no—
647C4×D5—63no—
648C4×D5—63no—
649Dic10—31no—
650Dic10—61no—
651Dic10C23×D311yescharacteristic
652#168—31no—
653#168—33no—
654#168C23×D311yescharacteristic
655#168C23×D313yes—
656H(5,𝔽2)—31no—
657H(5,𝔽2)—33no—
658H(5,𝔽2)—33no—
659H(5,𝔽2)—51no—
660H(5,𝔽2)—63no—
661H(5,𝔽2)—61no—
662H(5,𝔽2)—153no—
663H(5,𝔽2)—153no—
664H(5,𝔽2)—151no—
665H(5,𝔽2)—303no—
666H(5,𝔽2)—301no—
667H(5,𝔽2)D3×D511yescharacteristic, complemented
668C2×#41—31no—
669C2×#41—33no—
670C2×#41—61no—
671C2×#41—153no—
672C2×#41—301no—
673C22×D4—33no—
674C22×D4—63no—
675C22×D4—153no—
676C22×D4—303no—
677AGL(1,ℤ/8)—53no—
678AGL(1,ℤ/8)—53no—
679AGL(1,ℤ/8)—153no—
680AGL(1,ℤ/8)—153no—
681AGL(1,ℤ/8)—156no—
682AGL(1,ℤ/8)—156no—
683AGL(1,ℤ/8)—156no—
684AGL(1,ℤ/8)—156no—
685AGL(1,ℤ/8)—153no—
686AGL(1,ℤ/8)—153no—
687AGL(1,ℤ/8)—153no—
688AGL(1,ℤ/8)—153no—
689#135—53no—
690#135—153no—
691#135—153no—
692#135—153no—
693#135—153no—
694#135—153no—
695#135—153no—
696#135—153no—
697C2×Q16—151no—
698C2×SD16—153no—
699C2×SD16—153no—
700C2×D8—53no—
701C2×D8—153no—
702C2×D8—153no—
703C2×D8—156no—
704C2×D8—156no—
705C2×D8—156no—
706C2×D8—153no—
707C2×D8—153no—
708#131—51no—
709#131—153no—
710#131—153no—
711#131—151no—
712C2×M16—153no—
713C22×C8—153no—
714C2×C3×C5—23no—
715C2×C3×C5—43no—
716C2×C3×C5C23×D411yescharacteristic
717D15—43no—
718C3×D5—43no—
719C5×D3—23no—
720C5×D3—43no—
721C5×D3#57612yescomplemented
722C23×C3—23no—
723C23×C3—103no—
724C22×D3—23no—
725C22×D3—23no—
726C22×D3—26no—
727C22×D3—86no—
728C22×D3—103no—
729C22×D3—103no—
730C22×D3—106no—
731C22×D3—406no—
732C22×D3C2×C22⋊D513yes—
733C3×Q8—51no—
734C3×Q8C2×C22⋊D511yescharacteristic
735C3×Q8C23×D511yescharacteristic
736C3×D4—23no—
737C3×D4—23no—
738C3×D4—53no—
739C3×D4—103no—
740C3×D4—103no—
741C3×D4C2×C22⋊D513yes—
742C3×D4C23×D513yes—
743C2×C3×C4—23no—
744C2×C3×C4—103no—
745C2×C3×C4C23×D513yes—
746#67—23no—
747#67—23no—
748#67—23no—
749#67—26no—
750#67—103no—
751#67—103no—
752#67—103no—
753#67—106no—
754#67C2×C22⋊D516yes—
755C2×Dic3—23no—
756C2×Dic3—103no—
757C2×Dic3C2×C22⋊D513yes—
758D12—23no—
759D12—23no—
760D12—53no—
761D12—103no—
762D12—103no—
763D12C2×C22⋊D513yes—
764D12C23×D513yes—
765C4×D3—21no—
766C4×D3—23no—
767C4×D3—23no—
768C4×D3—101no—
769C4×D3—103no—
770C4×D3—103no—
771C4×D3C2×C22⋊D513yes—
772C4×D3C2×C22⋊D513yes—
773C4×D3C23×D511yescharacteristic
774C4×D3C23×D513yes—
775Dic6—21no—
776Dic6—51no—
777Dic6—101no—
778Dic6C2×C22⋊D513yes—
779Dic6C23×D511yescharacteristic
780C3×C8—51no—
781C3×C8—53no—
782C3⋊C8—51no—
783C3⋊C8—53no—
784C22×C5—23no—
785C22×C5—31no—
786C22×C5—33no—
787C22×C5—66no—
788C22×C5—63no—
789C22×C5—83no—
790C22×C5—126no—
791C22×C5—243no—
792C22×C5—246no—
793C22×C5C2×D3×D413yes—
794C2×D5—23no—
795C2×D5—63no—
796C2×D5—83no—
797C2×D5—126no—
798C2×D5—246no—
799C2×D5—243no—
800C4×C5—21no—
801C4×C5—31no—
802C4×C5—33no—
803C4×C5—61no—
804C4×C5C2×D3×D413yes—
805C4×C5C24×D311yescharacteristic
806Dic5—21no—
807Dic5—61no—
808C24—63no—
809C24—303no—
810#41—21no—
811#41—31no—
812#41—33no—
813#41—33no—
814#41—33no—
815#41—33no—
816#41—33no—
817#41—53no—
818#41—63no—
819#41—63no—
820#41—63no—
821#41—63no—
822#41—61no—
823#41—101no—
824#41—153no—
825#41—153no—
826#41—153no—
827#41—303no—
828#41—303no—
829#41—303no—
830#41—303no—
831#41—301no—
832#41C2×D3×D511yescharacteristic
833#41C2×D3×D513yescomplemented
834C2×Q8—31no—
835C2×Q8—31no—
836C2×Q8—151no—
837C2×D4—23no—
838C2×D4—33no—
839C2×D4—33no—
840C2×D4—36no—
841C2×D4—33no—
842C2×D4—53no—
843C2×D4—63no—
844C2×D4—63no—
845C2×D4—63no—
846C2×D4—63no—
847C2×D4—66no—
848C2×D4—63no—
849C2×D4—63no—
850C2×D4—66no—
851C2×D4—63no—
852C2×D4—103no—
853C2×D4—153no—
854C2×D4—156no—
855C2×D4—153no—
856C2×D4—303no—
857C2×D4—303no—
858C2×D4—303no—
859C2×D4—303no—
860C2×D4—306no—
861C2×D4—303no—
862C2×D4—306no—
863C2×D4—303no—
864C2×D4—303no—
865C2×D4C2×D3×D513yescomplemented
866C22×C4—33no—
867C22×C4—63no—
868C22×C4—303no—
869Q16—51no—
870Q16—151no—
871Q16—151no—
872Q16—151no—
873SD16—53no—
874SD16—53no—
875SD16—153no—
876SD16—153no—
877SD16—153no—
878SD16—153no—
879SD16—153no—
880SD16—153no—
881D8—53no—
882D8—56no—
883D8—153no—
884D8—156no—
885D8—153no—
886D8—156no—
887D8—153no—
888D8—156no—
889M16—53no—
890M16—156no—
891M16—153no—
892C2×C8—53no—
893C2×C8—151no—
894C2×C8—153no—
895C2×C8—153no—
896C2×C8—153no—
897C2×C8—153no—
898C3×C5C2×#57611yescharacteristic, complemented, Hall
899C22×C3—23no—
900C22×C3—83no—
901C22×C3—103no—
902C22×C3—403no—
903C22×C3C22×C22⋊D513yes—
904C2×D3—26no—
905C2×D3—23no—
906C2×D3—46no—
907C2×D3—86no—
908C2×D3—83no—
909C2×D3—103no—
910C2×D3—206no—
911C2×D3—406no—
912C2×D3—403no—
913C2×D3C22×C22⋊D513yes—
914C2×D3C22×C22⋊D511yescharacteristic
915C3×C4—21no—
916C3×C4—101no—
917C3×C4C22×C22⋊D513yes—
918C3×C4C24×D511yescharacteristic
919Dic3—21no—
920Dic3—101no—
921Dic3C22×C22⋊D511yescharacteristic
922Dic3C22×C22⋊D513yes—
923C2×C5—23no—
924C2×C5—32no—
925C2×C5—43no—
926C2×C5—63no—
927C2×C5—123no—
928C2×C5C22×D3×D411yescharacteristic
929D5—43no—
930D5—123no—
931C23—23no—
932C23—33no—
933C23—63no—
934C23—66no—
935C23—63no—
936C23—103no—
937C23—246no—
938C23—303no—
939C23—306no—
940C23—303no—
941C23—1206no—
942Q8—33no—
943Q8—31no—
944Q8—51no—
945Q8—61no—
946Q8—151no—
947Q8—301no—
948Q8D3×C22⋊D511yescharacteristic
949Q8C22×D3×D511yescharacteristic
950D4—23no—
951D4—23no—
952D4—36no—
953D4—33no—
954D4—33no—
955D4—53no—
956D4—63no—
957D4—63no—
958D4—66no—
959D4—63no—
960D4—63no—
961D4—63no—
962D4—103no—
963D4—103no—
964D4—153no—
965D4—303no—
966D4—306no—
967D4—303no—
968D4—303no—
969D4—303no—
970D4—303no—
971D4D3×C22⋊D513yes—
972D4C22×D3×D513yes—
973C2×C4—23no—
974C2×C4—33no—
975C2×C4—33no—
976C2×C4—33no—
977C2×C4—31no—
978C2×C4—33no—
979C2×C4—63no—
980C2×C4—61no—
981C2×C4—63no—
982C2×C4—63no—
983C2×C4—103no—
984C2×C4—303no—
985C2×C4—303no—
986C2×C4—301no—
987C2×C4—303no—
988C2×C4C22×D3×D513yes—
989C8—51no—
990C8—53no—
991C8—151no—
992C8—153no—
993C2×C3—23no—
994C2×C3—43no—
995C2×C3—203no—
996C2×C3C23×C22⋊D511yescharacteristic
997D3—23no—
998D3—43no—
999D3—203no—
1000D3#6616912yesdirect product factor
1001C5D3×#57611yescharacteristic, complemented, Sylow
1002C22—23no—
1003C22—31no—
1004C22—33no—
1005C22—66no—
1006C22—63no—
1007C22—83no—
1008C22—103no—
1009C22—126no—
1010C22—243no—
1011C22—246no—
1012C22—303no—
1013C22—403no—
1014C22—606no—
1015C22—1203no—
1016C22—1206no—
1017C22C2×D3×C22⋊D513yes—
1018C4—21no—
1019C4—31no—
1020C4—33no—
1021C4—61no—
1022C4—101no—
1023C4—301no—
1024C4C2×D3×C22⋊D513yes—
1025C4C23×D3×D511yescharacteristic
1026C3C2×#6616911yescharacteristic, complemented, Sylow
1027C2—23no—
1028C2—32no—
1029C2—43no—
1030C2—63no—
1031C2—123no—
1032C2—203no—
1033C2—603no—
1034C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC2C22×D3×C22⋊D5
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC3×C5×H(5,𝔽2)C22
socleC2×C3×C5C23×D4
hypercenterH(5,𝔽2)D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C5×D3×H(5,𝔽2)C2semidirect
2. D3×#4149C2semidirect
3. #11756594C2semidirect
4. C3×#66169C2semidirect
5. #11755325C2semidirect
6. #11755323C2semidirect
7. D3×#4096C2semidirect
8. D3×#4095C2semidirect
9. #11755305C2semidirect
10. #11755301C2semidirect
11. D3×#4094C2semidirect
12. #11754698C2semidirect
13. #11754697C2semidirect
14. D3×#4078C2semidirect
15. C2×D3×#686C2semidirect
17. C3×C5×H(5,𝔽2)C22semidirect
18. #92100C22semidirect
20. C5×#1009C22semidirect
21. C5×#1009C22semidirect
24. C5×D3×#41C22semidirect
26. C5×#1004C22semidirect
28. C2×C5×D3×D4C22semidirect
29. C3×#4149C22semidirect
34. #92019C22semidirect
35. #92017C22semidirect
36. D3×#709C22semidirect
37. C2×D3×D20C22semidirect
38. #91839C22semidirect
39. #91838C22semidirect
40. #91837C22semidirect
41. #91821C22semidirect
42. C2×#6715C22semidirect
43. C3×#4096C22semidirect
44. C3×#4095C22semidirect
45. C3×#4094C22semidirect
46. C3×#4078C22semidirect
47. C2×C3×#686C22semidirect
48. #91519C22semidirect
49. #91517C22semidirect
50. D3×#689C22semidirect
51. #91504C22semidirect
52. D3×#688C22semidirect
53. #91496C22semidirect
54. #91495C22semidirect
55. #91494C22semidirect
56. #91493C22semidirect
57. D3×#687C22semidirect
58. #91480C22semidirect
59. D3×#686C22semidirect
60. D3×#686C22semidirect
61. D3×#686C22semidirect
62. D3×#686C22semidirect
63. #91305C22semidirect
64. #91304C22semidirect
65. #91303C22semidirect
66. C2×#6654C22semidirect
67. #91299C22semidirect
68. #91298C22semidirect
69. #91297C22semidirect
70. C2×#6652C22semidirect
71. #91288C22semidirect
72. D3×#681C22semidirect
73. #91286C22semidirect
74. C2×D3×#168C22semidirect
85. #66169D3direct (N × H)
95. C3×C5×#41C23semidirect
97. C2×C3×C5×D4C23semidirect
100. #6817C23semidirect
101. C2×D60C23semidirect
106. C5×#239C23semidirect
112. C5×#237C23semidirect
121. C5×D3×D4C23semidirect
125. C5×#235C23semidirect
127. C2×C5×D12C23semidirect
132. C3×#709C23semidirect
133. C2×C3×D20C23semidirect
143. D3×D20C23semidirect
148. #6769C23semidirect
151. #6765C23semidirect
152. #6718C23semidirect
153. #6717C23semidirect
154. #6716C23semidirect
155. #6715C23semidirect
156. #6715C23semidirect
157. #6710C23semidirect
158. C2×C3⋊#168C23semidirect
159. C3×#689C23semidirect
160. C3×#688C23semidirect
161. C3×#687C23semidirect
162. C3×#686C23semidirect
163. C3×#686C23semidirect
164. C3×#681C23semidirect
165. C2×C3×#168C23semidirect
166. #6663C23semidirect
167. #6661C23semidirect
168. #6660C23semidirect
169. #6659C23semidirect
170. #6656C23semidirect
171. #6655C23semidirect
172. #6654C23semidirect
173. #6654C23semidirect
174. #6652C23semidirect
175. #6652C23semidirect
176. #6650C23semidirect
179. D3×#168C23semidirect
180. D3×#168C23semidirect
182. D3×H(5,𝔽2)D5semidirect
201. C5×H(5,𝔽2)C2×D3semidirect
212. #4149C2×D3semidirect
224. #4096C2×D3semidirect
230. #4095C2×D3semidirect
234. #4094C2×D3semidirect
243. #4078C2×D3semidirect
251. C2×#686C2×D3semidirect
318. C3×H(5,𝔽2)C2×D5semidirect
323. #1009C2×D5semidirect
324. #1009C2×D5semidirect
329. D3×#41C2×D5semidirect
333. #1004C2×D5semidirect
337. C2×D3×D4C2×D5semidirect
390. C5×#41C22×D3semidirect
407. C2×C5×D4C22×D3semidirect
426. #709C22×D3semidirect
433. C2×D20C22×D3semidirect
439. #689C22×D3semidirect
443. #688C22×D3semidirect
447. #687C22×D3semidirect
454. #686C22×D3semidirect
455. #686C22×D3semidirect
458. #681C22×D3semidirect
464. C2×#168C22×D3semidirect
510. C3×#41C22×D5semidirect
514. C2×C3×D4C22×D5semidirect
523. #239C22×D5semidirect
533. #237C22×D5semidirect
550. D3×D4C22×D5semidirect
557. #235C22×D5semidirect
561. C2×D12C22×D5semidirect
667. H(5,𝔽2)D3×D5semidirect
721. C5×D3#576semidirect
833. #41C2×D3×D5semidirect
865. C2×D4C2×D3×D5semidirect
898. C3×C5C2×#576semidirect
1000. D3#66169direct (N × H)
1001. C5D3×#576semidirect
1026. C3C2×#66169semidirect

Maximal subgroups

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

subgroupindex
C5×D3×H(5,𝔽2)2
D3×#41492
#117565942
C3×#661692
#117553252
#117553232
D3×#40962
D3×#40952
#117553052
#117553012
D3×#40942
#117546982
#117546972
D3×#40782
C2×D3×#6862
C2×#661693
D3×#5765