Finite Group Databasebeta

← D5×#5835 #14509975

Subgroups — D5×#5835 #14509975

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
1C3×D5×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2D5×#1009C211yesmaximal, characteristic, complemented
3#11756594C211yesmaximal, characteristic, complemented
4C5×#5835C211yesmaximal, characteristic, complemented
5#11755318C213yesmaximal, complemented
6#11755316C213yesmaximal, complemented
7D5×#950C213yesmaximal, complemented
8D5×#949C213yesmaximal, complemented
9#11755311C211yesmaximal, characteristic, complemented
10#11755301C211yesmaximal, characteristic, complemented
11D5×#948C211yesmaximal, characteristic, complemented
12#11754692C213yesmaximal, complemented
13#11754691C213yesmaximal, complemented
14D5×#932C213yesmaximal, complemented
15C2×D5×#213C213yesmaximal, complemented
16D5×#576—31nomaximal, Hall
17C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
18#92100C2211yescharacteristic, complemented
19C5×#1009C2211yescharacteristic, complemented
20C3×#4149—21no—
21C3×#4149C2213yescomplemented
22C3×#4149C2211yescharacteristic, complemented
23C3×D5×#41—21no—
24C3×D5×#41C2211yescharacteristic
25C3×D5×#41C2213yescomplemented
26C3×#4144—23no—
27C3×#4144C2213yescomplemented
28C2×C3×D4×D5—23no—
29C2×C3×D4×D5C2213yescomplemented
30#92035—21no—
31D5×#239—21no—
32#92027—23no—
33D3×D4×D5—23no—
34#92019C2213yescomplemented
35#92018C2213yescomplemented
36D5×#235C2213yescomplemented
37C2×D5×D12C2213yescomplemented
38#91839C2213yescomplemented
39#91838C2213yescomplemented
40#91837C2211yescharacteristic, complemented
41#91821C2213yescomplemented
42C2×#6715C2213yescomplemented
43C5×#950C2213yescomplemented
44C5×#949C2213yescomplemented
45C5×#948C2211yescharacteristic, complemented
46C5×#932C2213yescomplemented
47C2×C5×#213C2213yescomplemented
48#91516C2213yescomplemented
49#91514C2213yescomplemented
50D5×#216C2211yescharacteristic, complemented
51#91502C2216yescomplemented
52D5×#215C2213yescomplemented
53#91492C2213yescomplemented
54#91491C2216yescomplemented
55#91490C2213yescomplemented
56#91489C2216yescomplemented
57D5×#214C2213yescomplemented
58#91478C2216yescomplemented
59D5×#213C2216yescomplemented
60D5×#213C2213yescomplemented
61D5×#213C2216yescomplemented
62D5×#213C2216yescomplemented
63#91312C2213yescomplemented
64#91311C2213yescomplemented
65#91301C2213yescomplemented
66C2×#6653C2213yescomplemented
67#91299C2213yescomplemented
68#91298C2213yescomplemented
69#91297C2213yescomplemented
70C2×#6652C2213yescomplemented
71#91284C2213yescomplemented
72#91283C2213yescomplemented
73D5×#208C2213yescomplemented
74C2×D5×C3⋊C8C2213yescomplemented
75C2×#5835—51nomaximal, Hall
76D5×H(5,𝔽2)—31no—
77D5×H(5,𝔽2)D311yescharacteristic, complemented
78C5×#576—31no—
79#66169—31no—
80#66169—31no—
81#66108—33no—
82#66108—33no—
83D5×AGL(1,ℤ/8)—33no—
84D5×AGL(1,ℤ/8)—33no—
85#66103—33no—
86D5×#135—33no—
87#66091—33no—
88C2×D5×D8—33no—
89#66086—31no—
90D5×#131—31no—
91C23×C3×D5—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
102C5×#239—21no—
103C5×D3×D4—23no—
104C5×#235C2313yescomplemented
105C2×C5×D12C2313yescomplemented
106C2×C3×C22⋊D5—26no—
107C2×C3×C22⋊D5—23no—
108C3×#713—21no—
109C3×#713D411yescharacteristic
110C3×#713C2313yescomplemented
111C3×Q8×D5D411yescharacteristic
112C3×Q8×D5C2311yescharacteristic
113C3×#711—23no—
114C3×#711—23no—
115C3×#711D413yes—
116C3×#711C2313yescomplemented
117C3×D4×D5—23no—
118C3×D4×D5—23no—
119C3×D4×D5—26no—
120C3×D4×D5—23no—
121C3×D4×D5—23no—
122C3×D4×D5—23no—
123C3×D4×D5D413yes—
124C3×D4×D5C2313yes—
125C3×D4×D5C2316yescomplemented
126C3×#709—23no—
127C3×#709—23no—
128C3×#709C2313yes—
129C3×#709C2313yescomplemented
130C2×C3×D20—23no—
131C2×C3×D20C2313yescomplemented
132C2×C3×C4×D5—23no—
133C2×C3×C4×D5C2313yes—
134#6790—26no—
135D3×C22⋊D5—26no—
136D5×#67—23no—
137C2×#1203—23no—
138#6782—23no—
139#6777—23no—
140D3×D20—23no—
141D5×D12—23no—
142D5×D12—23no—
143D5×D12C2313yes—
144D5×D12C2316yescomplemented
145C4×D3×D5—23no—
146#6773C2313yescomplemented
147#6772C2313yescomplemented
148#6771—23no—
149#6769—23no—
150#6768—23no—
151D5×Dic6C2311yescharacteristic
152#6718C2311yescharacteristic, complemented
153#6717C2313yescomplemented
154#6716C2313yescomplemented
155#6715C2313yescomplemented
156#6715C2316yescomplemented
157#6710C2313yescomplemented
158C2×C3⋊#168C2313yescomplemented
159C5×#216C2311yescharacteristic, complemented
160C5×#215C2313yescomplemented
161C5×#214C2313yescomplemented
162C5×#213C2313yescomplemented
163C5×#213C2316yescomplemented
164C5×#208C2313yescomplemented
165C2×C5×C3⋊C8C2313yescomplemented
166#6662C2311yescharacteristic, complemented
167#6661C2311yescharacteristic, complemented
168#6658C2313yescomplemented
169#6657C2313yescomplemented
170#6656C2313yescomplemented
171#6655C2313yescomplemented
172#6653C2313yescomplemented
173#6653C2316yescomplemented
174#6652C2313yescomplemented
175#6652C2316yescomplemented
176#6649C2316yescomplemented
177D5×C3⋊C8C2311yescharacteristic
178D5×C3⋊C8C2313yes—
179D5×C3⋊C8C2313yescomplemented
180D5×C3⋊C8C2313yescomplemented
181C2×C3×H(5,𝔽2)—51no—
182C2×#1009—51no—
183#5835—51no—
184#5835—51no—
185#5835—53no—
186#5835—53no—
187#5835—51no—
188#5835—53no—
189#5835—53no—
190#5835D511yescharacteristic, direct product factor
191C2×#950—53no—
192C2×#949—53no—
193C2×#948—51no—
194C2×#932—53no—
195C22×#213—53no—
196C5×H(5,𝔽2)—31no—
197C5×H(5,𝔽2)C2×D311yescharacteristic, complemented
198#4149—21no—
199#4149—31no—
200#4149—33no—
201#4149—61no—
202#4149C2×D313yescomplemented
203#4149C2×D311yescharacteristic, complemented
204D5×#41—21no—
205D5×#41—33no—
206D5×#41—61no—
207D5×#41C2×D311yescharacteristic
208D5×#41C2×D313yescomplemented
209#4144—23no—
210#4144—33no—
211#4144—63no—
212#4144C2×D313yescomplemented
213C2×D4×D5—23no—
214C2×D4×D5—33no—
215C2×D4×D5—63no—
216C2×D4×D5C2×D313yescomplemented
217C5×AGL(1,ℤ/8)—33no—
218C5×AGL(1,ℤ/8)—33no—
219C5×#135—33no—
220C2×C5×D8—33no—
221C5×#131—31no—
222#4096—33no—
223#4096—33no—
224#4095—33no—
225#4095—33no—
226#4094—31no—
227#4078—33no—
228#4078—33no—
229C2×#686—33no—
230C2×#686—33no—
231#4065—33no—
232D5×Q16—31no—
233#4062—33no—
234#4062—33no—
235#4060—36no—
236#4060—36no—
237D5×SD16—33no—
238D5×SD16—33no—
239#4058—33no—
240#4057—36no—
241#4057—36no—
242D5×D8—33no—
243D5×D8—36no—
244D5×D8—36no—
245D5×D8—36no—
246#4054—33no—
247#4054—33no—
248#4053—33no—
249D5×M16—33no—
250#4050—33no—
251C2×D40—33no—
252#4047—33no—
253C2×C8×D5—33no—
254C2×#576—151noSylow
255C23×C3×C5—23no—
256C22×D15—23no—
257C22×C5×D3—23no—
258C22×C3×D5—23no—
259C22×C3×D5—23no—
260C22×C3×D5—26no—
261C22×C3×D5—86no—
262C22×C3×D5C2×D413yes—
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×D12—23no—
281C5×D12C2413yes—
282C4×C5×D3—23no—
283C5×Dic6C2411yescharacteristic
284C3×C22⋊D5—23no—
285C3×C22⋊D5—23no—
286C3×C22⋊D5—23no—
287C3×C22⋊D5—26no—
288C3×C22⋊D5C2×D416yes—
289C2×C3×Dic5—23no—
290C2×C3×Dic5C2×D413yes—
291C3×D20—23no—
292C3×D20—23no—
293C3×D20C2×D413yes—
294C3×D20C2413yes—
295C3×C4×D5—21no—
296C3×C4×D5—23no—
297C3×C4×D5—23no—
298C3×C4×D5C2×D413yes—
299C3×C4×D5C2×D413yes—
300C3×C4×D5C2411yescharacteristic
301C3×C4×D5C2413yes—
302C3×Dic10—21no—
303C3×Dic10C2×D413yes—
304C3×Dic10C2411yescharacteristic
305#1204—21no—
306#1203—26no—
307#1203—23no—
308#1202—23no—
309#1201—23no—
310#1200—23no—
311D3×Dic5—23no—
312D5×Dic3—21no—
313C3⋊#168C2413yes—
314C3⋊#168C2411yescharacteristic
315C5×C3⋊C8C2413yes—
316C5×C3⋊C8C2411yescharacteristic
317C3×H(5,𝔽2)—51no—
318C3×H(5,𝔽2)—53no—
319C3×H(5,𝔽2)—53no—
320C3×H(5,𝔽2)—103no—
321C3×H(5,𝔽2)—101no—
322C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
323C2×C3×#41—51no—
324C2×C3×#41—53no—
325C2×C3×#41—101no—
326C22×C3×D4—53no—
327C22×C3×D4—103no—
328#1009—51no—
329#1009—53no—
330#1009—53no—
331#1009—103no—
332#1009—101no—
333#1009C2×D511yescharacteristic, complemented
334C2×#239—101no—
335C2×D3×D4—103no—
336C2×#235—53no—
337C22×D12—53no—
338#950—53no—
339#950—53no—
340#950—53no—
341#950—53no—
342#950—53no—
343#950—53no—
344#950—53no—
345#950C2×D513yescomplemented
346#949—53no—
347#949—53no—
348#949—56no—
349#949—56no—
350#949—53no—
351#949C2×D513yescomplemented
352#948—51no—
353#948—53no—
354#948—53no—
355#948C2×D511yescharacteristic, complemented
356C2×#216—51no—
357C2×#215—53no—
358C2×#214—53no—
359#932—53no—
360#932—53no—
361#932—56no—
362#932—56no—
363#932—53no—
364#932C2×D513yescomplemented
365C2×#213—53no—
366C2×#213—53no—
367C2×#213—53no—
368C2×#213—56no—
369C2×#213—56no—
370C2×#213—56no—
371C2×#213—53no—
372C2×#213C2×D513yescomplemented
373C2×#208—53no—
374C22×C3⋊C8—53no—
375C23×D5—23no—
376C23×D5—63no—
377C5×#41—21no—
378C5×#41—33no—
379C5×#41—61no—
380C5×#41C22×D311yescharacteristic
381C5×#41C22×D313yescomplemented
382C2×C5×D4—23no—
383C2×C5×D4—33no—
384C2×C5×D4—63no—
385C2×C5×D4C22×D313yescomplemented
386C2×C22⋊D5—26no—
387C2×C22⋊D5—23no—
388C2×C22⋊D5—66no—
389C2×C22⋊D5—63no—
390#713—21no—
391#713—33no—
392#713—61no—
393#713#6711yescharacteristic
394#713C22×D313yescomplemented
395Q8×D5—31no—
396Q8×D5#6711yescharacteristic
397Q8×D5C22×D311yescharacteristic
398#711—23no—
399#711—23no—
400#711—33no—
401#711—63no—
402#711—63no—
403#711#6713yes—
404#711C22×D313yescomplemented
405D4×D5—23no—
406D4×D5—23no—
407D4×D5—26no—
408D4×D5—23no—
409D4×D5—23no—
410D4×D5—23no—
411D4×D5—33no—
412D4×D5—36no—
413D4×D5—63no—
414D4×D5—63no—
415D4×D5—66no—
416D4×D5—63no—
417D4×D5—63no—
418D4×D5—63no—
419D4×D5#6713yes—
420D4×D5C22×D313yes—
421D4×D5C22×D316yescomplemented
422#709—23no—
423#709—23no—
424#709—33no—
425#709—63no—
426#709—63no—
427#709C22×D313yes—
428#709C22×D313yescomplemented
429C2×D20—23no—
430C2×D20—33no—
431C2×D20—63no—
432C2×D20C22×D313yescomplemented
433C2×C4×D5—23no—
434C2×C4×D5—63no—
435C2×C4×D5C22×D313yes—
436C5×Q16—31no—
437C5×SD16—33no—
438C5×SD16—33no—
439C5×D8—33no—
440C5×D8—36no—
441C5×M16—33no—
442C2×C5×C8—33no—
443#689—31no—
444#689—31no—
445#688—33no—
446#688—33no—
447#687—33no—
448#687—33no—
449#686—33no—
450#686—36no—
451#686—33no—
452#686—36no—
453#681—33no—
454C2×#168—33no—
455Dic20—31no—
456D40—33no—
457D40—36no—
458#677—33no—
459#677—33no—
460#676—36no—
461C8×D5—31no—
462C8×D5—33no—
463C8×D5—33no—
464C8×D5—33no—
465C2×H(5,𝔽2)—51no—
466C2×H(5,𝔽2)—151no—
467#576—31no—
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—23no—
486C2×C5×D3—83no—
487C2×C3×D5—26no—
488C2×C3×D5—23no—
489C2×C3×D5—46no—
490C2×C3×D5—86no—
491C2×C3×D5—83no—
492C2×C3×D5C22×D413yes—
493C2×C3×D5C22×D411yescharacteristic
494D3×D5—46no—
495D3×D5—86no—
496C3×C4×C5—21no—
497C3×C4×C5C22×D413yes—
498C3×C4×C5C2511yescharacteristic
499Dic15—21no—
500C3×Dic5—21no—
501C3×Dic5C22×D413yes—
502C3×Dic5C22×D411yescharacteristic
503C5×Dic3—21no—
504C24×C3—103no—
505C23×D3—103no—
506C3×#41—21no—
507C3×#41—51no—
508C3×#41—53no—
509C3×#41—53no—
510C3×#41—53no—
511C3×#41—53no—
512C3×#41—53no—
513C3×#41—103no—
514C3×#41—103no—
515C3×#41—103no—
516C3×#41—103no—
517C3×#41—101no—
518C3×#41C22×D511yescharacteristic
519C3×#41C22×D513yescomplemented
520C2×C3×Q8—51no—
521C2×C3×Q8—51no—
522C2×C3×D4—23no—
523C2×C3×D4—53no—
524C2×C3×D4—53no—
525C2×C3×D4—56no—
526C2×C3×D4—53no—
527C2×C3×D4—103no—
528C2×C3×D4—103no—
529C2×C3×D4—103no—
530C2×C3×D4—103no—
531C2×C3×D4—106no—
532C2×C3×D4—103no—
533C2×C3×D4—103no—
534C2×C3×D4—106no—
535C2×C3×D4—103no—
536C2×C3×D4C22×D513yescomplemented
537C22×C3×C4—53no—
538C22×C3×C4—103no—
539C2×#67—103no—
540#239—21no—
541#239—103no—
542#239—103no—
543#239—101no—
544D3×D4—23no—
545D3×D4—103no—
546D3×D4—103no—
547D3×D4—106no—
548D3×D4—106no—
549D3×D4—103no—
550#235—53no—
551#235—53no—
552#235—53no—
553#235—103no—
554#235—103no—
555#235C22×D513yescomplemented
556C2×D12—53no—
557C2×D12—53no—
558C2×D12—56no—
559C2×D12—103no—
560C2×D12—103no—
561C2×D12—103no—
562C2×D12C22×D513yescomplemented
563C2×C4×D3—103no—
564C2×Dic6—51no—
565#216—51no—
566#216—51no—
567#216—51no—
568#216C22×D511yescharacteristic, complemented
569#215—53no—
570#215—53no—
571#215—53no—
572#215C22×D513yescomplemented
573#214—53no—
574#214—53no—
575#214—53no—
576#214C22×D513yescomplemented
577#213—53no—
578#213—56no—
579#213—53no—
580#213—56no—
581#213—53no—
582#213—56no—
583#213C22×D513yescomplemented
584#213C22×D516yescomplemented
585#208—53no—
586#208—56no—
587#208C22×D513yescomplemented
588C2×C3⋊C8—53no—
589C2×C3⋊C8—51no—
590C2×C3⋊C8—53no—
591C2×C3⋊C8—53no—
592C2×C3⋊C8—53no—
593C2×C3⋊C8C22×D513yescomplemented
594C23×C5—23no—
595C23×C5—63no—
596C22×D5—23no—
597C22×D5—23no—
598C22×D5—26no—
599C22×D5—63no—
600C22×D5—63no—
601C22×D5—66no—
602C22×D5—86no—
603C22×D5—246no—
604C22×D5C2×#6713yes—
605C5×Q8—31no—
606C5×Q8C2×#6711yescharacteristic
607C5×Q8C23×D311yescharacteristic
608C5×D4—23no—
609C5×D4—23no—
610C5×D4—33no—
611C5×D4—63no—
612C5×D4—63no—
613C5×D4C2×#6713yes—
614C5×D4C23×D313yes—
615C2×C4×C5—23no—
616C2×C4×C5—63no—
617C2×C4×C5C23×D313yes—
618C22⋊D5—23no—
619C22⋊D5—23no—
620C22⋊D5—23no—
621C22⋊D5—26no—
622C22⋊D5—63no—
623C22⋊D5—63no—
624C22⋊D5—63no—
625C22⋊D5—66no—
626C22⋊D5C2×#6716yes—
627C2×Dic5—23no—
628C2×Dic5—63no—
629C2×Dic5C2×#6713yes—
630D20—23no—
631D20—23no—
632D20—33no—
633D20—63no—
634D20—63no—
635D20C2×#6713yes—
636D20C23×D313yes—
637C4×D5—21no—
638C4×D5—23no—
639C4×D5—23no—
640C4×D5—61no—
641C4×D5—63no—
642C4×D5—63no—
643C4×D5C2×#6713yes—
644C4×D5C2×#6713yes—
645C4×D5C23×D311yescharacteristic
646C4×D5C23×D313yes—
647Dic10—21no—
648Dic10—31no—
649Dic10—61no—
650Dic10C2×#6713yes—
651Dic10C23×D311yescharacteristic
652C5×C8—31no—
653C5×C8—33no—
654#168—31no—
655#168—33no—
656H(5,𝔽2)—31no—
657H(5,𝔽2)—51no—
658H(5,𝔽2)—53no—
659H(5,𝔽2)—53no—
660H(5,𝔽2)—103no—
661H(5,𝔽2)—101no—
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—51no—
669C2×#41—53no—
670C2×#41—101no—
671C2×#41—153no—
672C2×#41—301no—
673C22×D4—53no—
674C22×D4—103no—
675C22×D4—153no—
676C22×D4—303no—
677AGL(1,ℤ/8)—33no—
678AGL(1,ℤ/8)—33no—
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—33no—
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—33no—
701C2×D8—153no—
702C2×D8—153no—
703C2×D8—156no—
704C2×D8—156no—
705C2×D8—156no—
706C2×D8—153no—
707C2×D8—153no—
708#131—31no—
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—23no—
719C3×D5—43no—
720C3×D5#57612yescomplemented
721C5×D3—43no—
722C23×C3—23no—
723C23×C3—53no—
724C23×C3—103no—
725C23×C3—106no—
726C23×C3—103no—
727C23×C3—406no—
728C22×D3—23no—
729C22×D3—103no—
730C22×D3—106no—
731C22×D3—103no—
732C22×D3—406no—
733C3×Q8—53no—
734C3×Q8—51no—
735C3×Q8—101no—
736C3×Q8D4×D511yescharacteristic
737C3×Q8C23×D511yescharacteristic
738C3×D4—23no—
739C3×D4—23no—
740C3×D4—56no—
741C3×D4—53no—
742C3×D4—53no—
743C3×D4—103no—
744C3×D4—103no—
745C3×D4—106no—
746C3×D4—103no—
747C3×D4—103no—
748C3×D4—103no—
749C3×D4D4×D513yes—
750C3×D4C23×D513yes—
751C2×C3×C4—23no—
752C2×C3×C4—53no—
753C2×C3×C4—53no—
754C2×C3×C4—53no—
755C2×C3×C4—51no—
756C2×C3×C4—53no—
757C2×C3×C4—103no—
758C2×C3×C4—101no—
759C2×C3×C4—103no—
760C2×C3×C4—103no—
761C2×C3×C4C23×D513yes—
762#67—23no—
763#67—103no—
764#67—103no—
765#67—103no—
766C2×Dic3—101no—
767D12—23no—
768D12—53no—
769D12—103no—
770D12—106no—
771D12—103no—
772D12C23×D513yes—
773C4×D3—23no—
774C4×D3—103no—
775C4×D3—103no—
776C4×D3—103no—
777Dic6—51no—
778Dic6—101no—
779Dic6C23×D511yescharacteristic
780C3⋊C8—51no—
781C3⋊C8—53no—
782C3⋊C8C23×D511yescharacteristic
783C3⋊C8C23×D513yes—
784C22×C5—23no—
785C22×C5—63no—
786C22×C5—83no—
787C22×C5—243no—
788C22×C5C22×#6713yes—
789C2×D5—26no—
790C2×D5—23no—
791C2×D5—46no—
792C2×D5—63no—
793C2×D5—86no—
794C2×D5—83no—
795C2×D5—126no—
796C2×D5—246no—
797C2×D5—243no—
798C2×D5C22×#6713yes—
799C2×D5C22×#6711yescharacteristic
800C4×C5—21no—
801C4×C5—61no—
802C4×C5C22×#6713yes—
803C4×C5C24×D311yescharacteristic
804Dic5—21no—
805Dic5—61no—
806Dic5C22×#6711yescharacteristic
807Dic5C22×#6713yes—
808C24—103no—
809C24—303no—
810#41—21no—
811#41—33no—
812#41—51no—
813#41—53no—
814#41—53no—
815#41—53no—
816#41—53no—
817#41—53no—
818#41—61no—
819#41—103no—
820#41—103no—
821#41—103no—
822#41—103no—
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—51no—
835C2×Q8—51no—
836C2×Q8—151no—
837C2×D4—23no—
838C2×D4—33no—
839C2×D4—53no—
840C2×D4—53no—
841C2×D4—56no—
842C2×D4—53no—
843C2×D4—63no—
844C2×D4—103no—
845C2×D4—103no—
846C2×D4—103no—
847C2×D4—103no—
848C2×D4—106no—
849C2×D4—103no—
850C2×D4—103no—
851C2×D4—106no—
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—53no—
867C22×C4—103no—
868C22×C4—303no—
869Q16—31no—
870Q16—151no—
871Q16—151no—
872Q16—151no—
873SD16—33no—
874SD16—33no—
875SD16—153no—
876SD16—153no—
877SD16—153no—
878SD16—153no—
879SD16—153no—
880SD16—153no—
881D8—33no—
882D8—36no—
883D8—153no—
884D8—156no—
885D8—153no—
886D8—156no—
887D8—153no—
888D8—156no—
889M16—33no—
890M16—156no—
891M16—153no—
892C2×C8—33no—
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—51no—
901C22×C3—53no—
902C22×C3—83no—
903C22×C3—106no—
904C22×C3—103no—
905C22×C3—206no—
906C22×C3—403no—
907C22×C3—406no—
908C22×C3C2×D4×D513yes—
909C2×D3—23no—
910C2×D3—83no—
911C2×D3—103no—
912C2×D3—206no—
913C2×D3—406no—
914C2×D3—403no—
915C3×C4—21no—
916C3×C4—51no—
917C3×C4—53no—
918C3×C4—101no—
919C3×C4C2×D4×D513yes—
920C3×C4C24×D511yescharacteristic
921Dic3—21no—
922Dic3—101no—
923C2×C5—23no—
924C2×C5—43no—
925C2×C5—123no—
926C2×C5C23×#6711yescharacteristic
927D5—23no—
928D5—43no—
929D5—123no—
930D5#583512yesdirect product factor
931C23—23no—
932C23—53no—
933C23—63no—
934C23—103no—
935C23—106no—
936C23—103no—
937C23—303no—
938C23—306no—
939C23—303no—
940C23—406no—
941C23—1206no—
942Q8—31no—
943Q8—53no—
944Q8—51no—
945Q8—101no—
946Q8—151no—
947Q8—301no—
948Q8D5×#6711yescharacteristic
949Q8C22×D3×D511yescharacteristic
950D4—23no—
951D4—23no—
952D4—33no—
953D4—56no—
954D4—53no—
955D4—53no—
956D4—63no—
957D4—63no—
958D4—103no—
959D4—103no—
960D4—106no—
961D4—103no—
962D4—103no—
963D4—103no—
964D4—153no—
965D4—303no—
966D4—306no—
967D4—303no—
968D4—303no—
969D4—303no—
970D4—303no—
971D4D5×#6713yes—
972D4C22×D3×D513yes—
973C2×C4—23no—
974C2×C4—53no—
975C2×C4—53no—
976C2×C4—53no—
977C2×C4—51no—
978C2×C4—53no—
979C2×C4—63no—
980C2×C4—103no—
981C2×C4—101no—
982C2×C4—103no—
983C2×C4—103no—
984C2×C4—303no—
985C2×C4—303no—
986C2×C4—301no—
987C2×C4—303no—
988C2×C4C22×D3×D513yes—
989C8—31no—
990C8—33no—
991C8—151no—
992C8—153no—
993C2×C3—23no—
994C2×C3—43no—
995C2×C3—52no—
996C2×C3—103no—
997C2×C3—203no—
998C2×C3C22×D4×D511yescharacteristic
999D3—43no—
1000D3—203no—
1001C5C2×#583511yescharacteristic, complemented, Sylow
1002C22—23no—
1003C22—51no—
1004C22—53no—
1005C22—63no—
1006C22—83no—
1007C22—106no—
1008C22—103no—
1009C22—206no—
1010C22—243no—
1011C22—303no—
1012C22—403no—
1013C22—406no—
1014C22—606no—
1015C22—1203no—
1016C22—1206no—
1017C22C2×D5×#6713yes—
1018C4—21no—
1019C4—51no—
1020C4—53no—
1021C4—61no—
1022C4—101no—
1023C4—301no—
1024C4C2×D5×#6713yes—
1025C4C23×D3×D511yescharacteristic
1026C3D5×#57611yescharacteristic, complemented, Sylow
1027C2—23no—
1028C2—43no—
1029C2—52no—
1030C2—103no—
1031C2—123no—
1032C2—203no—
1033C2—603no—
1034C2C22×D5×#6711yescharacteristic
subgroupG/H
centerC2C22×D5×#67
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. C3×D5×H(5,𝔽2)C2semidirect
2. D5×#1009C2semidirect
3. #11756594C2semidirect
4. C5×#5835C2semidirect
5. #11755318C2semidirect
6. #11755316C2semidirect
7. D5×#950C2semidirect
8. D5×#949C2semidirect
9. #11755311C2semidirect
10. #11755301C2semidirect
11. D5×#948C2semidirect
12. #11754692C2semidirect
13. #11754691C2semidirect
14. D5×#932C2semidirect
15. C2×D5×#213C2semidirect
17. C3×C5×H(5,𝔽2)C22semidirect
18. #92100C22semidirect
19. C5×#1009C22semidirect
21. C3×#4149C22semidirect
22. C3×#4149C22semidirect
25. C3×D5×#41C22semidirect
27. C3×#4144C22semidirect
29. C2×C3×D4×D5C22semidirect
34. #92019C22semidirect
35. #92018C22semidirect
36. D5×#235C22semidirect
37. C2×D5×D12C22semidirect
38. #91839C22semidirect
39. #91838C22semidirect
40. #91837C22semidirect
41. #91821C22semidirect
42. C2×#6715C22semidirect
43. C5×#950C22semidirect
44. C5×#949C22semidirect
45. C5×#948C22semidirect
46. C5×#932C22semidirect
47. C2×C5×#213C22semidirect
48. #91516C22semidirect
49. #91514C22semidirect
50. D5×#216C22semidirect
51. #91502C22semidirect
52. D5×#215C22semidirect
53. #91492C22semidirect
54. #91491C22semidirect
55. #91490C22semidirect
56. #91489C22semidirect
57. D5×#214C22semidirect
58. #91478C22semidirect
59. D5×#213C22semidirect
60. D5×#213C22semidirect
61. D5×#213C22semidirect
62. D5×#213C22semidirect
63. #91312C22semidirect
64. #91311C22semidirect
65. #91301C22semidirect
66. C2×#6653C22semidirect
67. #91299C22semidirect
68. #91298C22semidirect
69. #91297C22semidirect
70. C2×#6652C22semidirect
71. #91284C22semidirect
72. #91283C22semidirect
73. D5×#208C22semidirect
74. C2×D5×C3⋊C8C22semidirect
77. D5×H(5,𝔽2)D3semidirect
95. C3×C5×#41C23semidirect
97. C2×C3×C5×D4C23semidirect
100. #6817C23semidirect
101. C2×D60C23semidirect
104. C5×#235C23semidirect
105. C2×C5×D12C23semidirect
110. C3×#713C23semidirect
116. C3×#711C23semidirect
125. C3×D4×D5C23semidirect
129. C3×#709C23semidirect
131. C2×C3×D20C23semidirect
144. D5×D12C23semidirect
146. #6773C23semidirect
147. #6772C23semidirect
152. #6718C23semidirect
153. #6717C23semidirect
154. #6716C23semidirect
155. #6715C23semidirect
156. #6715C23semidirect
157. #6710C23semidirect
158. C2×C3⋊#168C23semidirect
159. C5×#216C23semidirect
160. C5×#215C23semidirect
161. C5×#214C23semidirect
162. C5×#213C23semidirect
163. C5×#213C23semidirect
164. C5×#208C23semidirect
165. C2×C5×C3⋊C8C23semidirect
166. #6662C23semidirect
167. #6661C23semidirect
168. #6658C23semidirect
169. #6657C23semidirect
170. #6656C23semidirect
171. #6655C23semidirect
172. #6653C23semidirect
173. #6653C23semidirect
174. #6652C23semidirect
175. #6652C23semidirect
176. #6649C23semidirect
179. D5×C3⋊C8C23semidirect
180. D5×C3⋊C8C23semidirect
190. #5835D5direct (N × H)
197. C5×H(5,𝔽2)C2×D3semidirect
202. #4149C2×D3semidirect
203. #4149C2×D3semidirect
208. D5×#41C2×D3semidirect
212. #4144C2×D3semidirect
216. C2×D4×D5C2×D3semidirect
322. C3×H(5,𝔽2)C2×D5semidirect
333. #1009C2×D5semidirect
345. #950C2×D5semidirect
351. #949C2×D5semidirect
355. #948C2×D5semidirect
364. #932C2×D5semidirect
372. C2×#213C2×D5semidirect
381. C5×#41C22×D3semidirect
385. C2×C5×D4C22×D3semidirect
394. #713C22×D3semidirect
404. #711C22×D3semidirect
421. D4×D5C22×D3semidirect
428. #709C22×D3semidirect
432. C2×D20C22×D3semidirect
519. C3×#41C22×D5semidirect
536. C2×C3×D4C22×D5semidirect
555. #235C22×D5semidirect
562. C2×D12C22×D5semidirect
568. #216C22×D5semidirect
572. #215C22×D5semidirect
576. #214C22×D5semidirect
583. #213C22×D5semidirect
584. #213C22×D5semidirect
587. #208C22×D5semidirect
593. C2×C3⋊C8C22×D5semidirect
667. H(5,𝔽2)D3×D5semidirect
720. C3×D5#576semidirect
833. #41C2×D3×D5semidirect
865. C2×D4C2×D3×D5semidirect
898. C3×C5C2×#576semidirect
930. D5#5835direct (N × H)
1001. C5C2×#5835semidirect
1026. C3D5×#576semidirect

Maximal subgroups

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

subgroupindex
C3×D5×H(5,𝔽2)2
D5×#10092
#117565942
C5×#58352
#117553182
#117553162
D5×#9502
D5×#9492
#117553112
#117553012
D5×#9482
#117546922
#117546912
D5×#9322
C2×D5×#2132
D5×#5763
C2×#58355