Finite Group Databasebeta

← #14418143

Subgroups — #14418143

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5750C211yesmaximal, characteristic, complemented
2#11755322C211yesmaximal, characteristic
3#11753951C211yesmaximal, characteristic, complemented
4#11751246C211yesmaximal, characteristic, complemented
5C3×#65433C211yesmaximal, characteristic, complemented
6#11749438C211yesmaximal, characteristic, complemented
7#11749437C211yesmaximal, characteristic, complemented
8D3×#3969C211yesmaximal, characteristic, complemented
9D3×#3957C211yesmaximal, characteristic, complemented
10#11748209C211yesmaximal, characteristic, complemented
11#11748204C211yesmaximal, characteristic, complemented
12#11748172C211yesmaximal, characteristic, complemented
13#11748078C211yesmaximal, characteristic, complemented
14#11748075C211yesmaximal, characteristic, complemented
15Dic5×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16#10615542—31nomaximal, Hall
17C5×D3×#41C2211yescharacteristic
18D3×#709C2211yescharacteristic
19C3×C5×#131C2211yescharacteristic, complemented
20#91839C2211yescharacteristic
21#91790C2211yescharacteristic, complemented
22C5×#948C2211yescharacteristic, complemented
23C5×#907—21no—
24C5×#907C2211yescharacteristic, complemented
25C5×D3×M16—21no—
26C5×D3×M16C2211yescharacteristic
27C5×#901—21no—
28C5×#901C2211yescharacteristic, complemented
29C2×C5×ΓL(1,𝔽25)—21no—
30C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
31C3×#4096C2211yescharacteristic
32C3×#4047C2211yescharacteristic, complemented
33#91520C411yescharacteristic, complemented
34#91518C411yescharacteristic, complemented
35#91510C411yescharacteristic, complemented
36#91504C411yescharacteristic, complemented
37#91496C411yescharacteristic, complemented
38#91494C411yescharacteristic, complemented
39#91486C411yescharacteristic, complemented
40#91480C411yescharacteristic, complemented
41C4×D3×Dic5C2211yescharacteristic
42#91303C2211yescharacteristic
43#91297C2211yescharacteristic
44C2×#6650C2211yescharacteristic
45#91291C2211yescharacteristic, complemented
46D3×#681C2211yescharacteristic
47#91283C2211yescharacteristic, complemented
48#91268—21no—
49#91266—21no—
50#91246—21no—
51D5×ΓL(1,𝔽25)—21no—
52#91121C2211yescharacteristic, complemented
53#91109C2211yescharacteristic, complemented
54#91106C2211yescharacteristic, complemented
55#91099C2211yescharacteristic, complemented
56C3×#3969C2211yescharacteristic, complemented
57C3×#3957C2211yescharacteristic, complemented
58C3×#3954C2211yescharacteristic, complemented
59C3×C8×Dic5C2211yescharacteristic, complemented
60#90992C2211yescharacteristic, complemented
61#90991C2211yescharacteristic, complemented
62#90981C2211yescharacteristic, complemented
63#90979C2211yescharacteristic, complemented
64#90978C2211yescharacteristic, complemented
65#90976C2211yescharacteristic, complemented
66#90954C2211yescharacteristic, complemented
67Dic5×C3⋊C8C2211yescharacteristic, complemented
68#79889—51nomaximal, Hall
69C5×#568—31no—
70#66156—31no—
71#66079—31no—
72C2×#3969—31no—
73#65434—31no—
74#65434—31no—
75#65434—31no—
76#65434—31no—
77#65433—31no—
78#65433—31no—
79#65433—31no—
80#65433D311yescharacteristic, complemented
81C2×#3957—31no—
82#65413—31no—
83M16×Dic5—31no—
84C3×C5×#41C2311yescharacteristic
85#6817C2311yescharacteristic
86C5×#239C2×C411yescharacteristic
87C5×D3×Q8C2×C411yescharacteristic
88C5×#237—21no—
89C5×#237C2×C411yescharacteristic
90C5×D3×D4—21no—
91C5×D3×D4C2×C411yescharacteristic
92C5×#235—21no—
93C5×#235C2311yescharacteristic
94C2×C4×C5×D3—21no—
95C2×C4×C5×D3C2311yescharacteristic
96C3×#709C2311yescharacteristic
97D3×C22⋊D5—21no—
98C2×D3×Dic5—21no—
99#6779—21no—
100D3×D20C2×C411yescharacteristic
101C4×D3×D5—21no—
102#6771—21no—
103#6769C2×C411yescharacteristic
104D3×Dic10C2×C411yescharacteristic
105#6765C2×C411yescharacteristic
106C3×C5×M16—21no—
107C3×C5×M16C2311yescharacteristic
108C2×C3×C5×C8—21no—
109C2×C3×C5×C8C2311yescharacteristic
110#6718C2×C411yescharacteristic, complemented
111#6717C2×C411yescharacteristic, complemented
112#6716C2×C411yescharacteristic, complemented
113#6715C2×C411yescharacteristic, complemented
114C4×Dic15C2311yescharacteristic
115#6710C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117#6705—21no—
118C8×D15—21no—
119C5×#208—21no—
120C5×#208C2311yescharacteristic
121C2×C5×C3⋊C8—21no—
122C2×C5×C3⋊C8C2311yescharacteristic
123C5×ΓL(1,𝔽25)—21no—
124C5×ΓL(1,𝔽25)—21no—
125C5×ΓL(1,𝔽25)—21no—
126C5×ΓL(1,𝔽25)D411yescharacteristic
127C5×ΓL(1,𝔽25)D411yescharacteristic
128C5×ΓL(1,𝔽25)D411yescharacteristic
129C5×ΓL(1,𝔽25)D411yescharacteristic
130C5×D3×C8—21no—
131C5×D3×C8—21no—
132C5×D3×C8—21no—
133C3×#689C2×C411yescharacteristic, complemented
134C3×#688C2×C411yescharacteristic, complemented
135C3×#687C2×C411yescharacteristic, complemented
136C3×#686C2×C411yescharacteristic, complemented
137C3×C4×Dic5C2311yescharacteristic
138C3×#681C2311yescharacteristic
139C2×C3×#168C2311yescharacteristic
140C3×#676—21no—
141C3×C8×D5—21no—
142Dic3×Dic5—21no—
143#6663C2×C411yescharacteristic, complemented
144#6661C2×C411yescharacteristic, complemented
145#6660C2×C411yescharacteristic, complemented
146#6659C2×C411yescharacteristic, complemented
147#6656C2×C411yescharacteristic, complemented
148#6655C2×C411yescharacteristic, complemented
149#6654C2×C411yescharacteristic, complemented
150#6652C2×C411yescharacteristic, complemented
151#6651—21no—
152#6650—21no—
153#6650C2×C411yescharacteristic
154#6650C2×C411yescharacteristic
155#6650C2×C411yescharacteristic
156#6650C2×C411yescharacteristic
157#6649—21no—
158#6648—21no—
159D3×#168—21no—
160D5×C3⋊C8—21no—
161#5768—51no—
162#5750—51no—
163#5750D511yescharacteristic, complemented
164C3×#443—51no—
165#5197—51no—
166#5145—51no—
167#5145—51no—
168#4894—51no—
169#4893—51no—
170#4824—51no—
171#4824—51no—
172D3×#104—51no—
173D3×#104—51no—
174#4700—51no—
175C4×ΓL(1,𝔽25)—51no—
176C2×C5×#41—31no—
177C2×#709—31no—
178C5×#131—31no—
179C5×#131—31no—
180C5×#131—31no—
181C5×#131—61no—
182C5×#131—61no—
183C5×#131C2×D311yescharacteristic, complemented
184C2×C5×M16—31no—
185C2×C5×M16—31no—
186C2×C5×M16—61no—
187C2×C5×M16—61no—
188#4097—31no—
189#4097—31no—
190#4096—31no—
191#4096—31no—
192#4096—31no—
193#4096C2×D311yescharacteristic
194#4095—31no—
195#4095—31no—
196#4088—31no—
197#4088—31no—
198#4078—31no—
199#4078—31no—
200C2×C4×Dic5—31no—
201C2×#681—31no—
202C2×#681—31no—
203#4053—61no—
204#4053—61no—
205D5×M16—61no—
206D5×M16—61no—
207#4047—31no—
208#4047—31no—
209#4047—31no—
210#4047C2×D311yescharacteristic, complemented
211#3969—31no—
212#3969—31no—
213#3969—31no—
214#3969C2×D311yescharacteristic, complemented
215#3957—31no—
216#3957—31no—
217#3957—31no—
218#3957C2×D311yescharacteristic, complemented
219#3954—31no—
220#3954—31no—
221#3954—31no—
222#3954C2×D311yescharacteristic, complemented
223#3947—31no—
224#3947—31no—
225C8×Dic5—31no—
226C8×Dic5C2×D311yescharacteristic, complemented
227#2956—151noSylow
228C22×C5×D3—21no—
229C22×C5×D3#4111yescharacteristic
230C2×D3×D5—21no—
231C3×C5×Q8C22×C411yescharacteristic
232C3×C5×D4—21no—
233C3×C5×D4C22×C411yescharacteristic
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5C2411yescharacteristic
236#1220—21no—
237C2×Dic15—21no—
238D60C22×C411yescharacteristic
239C4×D15—21no—
240Dic30C22×C411yescharacteristic
241C5×#67—21no—
242C5×#67—21no—
243C5×#67—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3#4111yescharacteristic
246C5×D12—21no—
247C5×D12C22×C411yescharacteristic
248C4×C5×D3—21no—
249C4×C5×D3—21no—
250C4×C5×D3—21no—
251C4×C5×D3C22×C411yescharacteristic
252C4×C5×D3C22×C411yescharacteristic
253C4×C5×D3C2×D411yescharacteristic
254C4×C5×D3C2×D411yescharacteristic
255C5×Dic6—21no—
256C5×Dic6C22×C411yescharacteristic
257C3×C22⋊D5—21no—
258C2×C3×Dic5—21no—
259C3×D20C22×C411yescharacteristic
260C3×C4×D5—21no—
261C3×Dic10C22×C411yescharacteristic
262#1204—21no—
263#1203—21no—
264#1202—21no—
265#1201—21no—
266#1200—21no—
267D3×Dic5—21no—
268D3×Dic5—42no—
269D5×Dic3—21no—
270C3×C5×C8—21no—
271C3×C5×C8C2×D411yescharacteristic
272C3×C5×C8C2×D411yescharacteristic
273C3⋊#168—21no—
274C3⋊#168C22×C411yescharacteristic
275C3⋊#168C22×C411yescharacteristic
276C3×#168—21no—
277C3×#168C22×C411yescharacteristic
278C3×#168C22×C411yescharacteristic
279C5×C3⋊C8—21no—
280C5×C3⋊C8C2×D411yescharacteristic
281C5×C3⋊C8C2×D411yescharacteristic
282D3×#41—51no—
283D3×#41C2×D511yescharacteristic
284C3×#135—51no—
285C3×#131—51no—
286C3×#131C2×D511yescharacteristic, complemented
287#950—51no—
288#950—51no—
289#948—51no—
290#948C2×D511yescharacteristic, complemented
291#918—51no—
292#918—51no—
293#915—51no—
294#915—51no—
295#914—51no—
296#914—51no—
297#911—51no—
298#911—51no—
299#907—21no—
300#907—51no—
301#907—101no—
302#907C2×D511yescharacteristic, complemented
303D3×M16—21no—
304D3×M16—51no—
305D3×M16—101no—
306D3×M16C2×D511yescharacteristic
307#904—51no—
308#901—21no—
309#901—51no—
310#901—101no—
311#901C2×D511yescharacteristic, complemented
312C2×ΓL(1,𝔽25)—21no—
313C2×ΓL(1,𝔽25)—51no—
314C2×ΓL(1,𝔽25)—101no—
315C2×ΓL(1,𝔽25)C2×D511yescharacteristic
316C42×D3—51no—
317C3×#108—51no—
318C3×#104—51no—
319C3×#104—51no—
320C3×C4×C8—51no—
321#837—51no—
322#837—51no—
323#825—51no—
324#825—51no—
325#822—51no—
326#822—51no—
327#819—51no—
328#815—51no—
329#815—51no—
330#805—51no—
331#805—51no—
332C4×C3⋊C8—51no—
333C5×#41—31no—
334C5×#41—31no—
335C5×#41—31no—
336C5×#41—61no—
337C5×#41—61no—
338C5×#41C22×D311yescharacteristic
339C2×C5×Q8—31no—
340C2×C5×D4—31no—
341C2×C5×D4—61no—
342C22×C4×C5—31no—
343C22×C4×C5—61no—
344C2×C22⋊D5—61no—
345C22×Dic5—61no—
346#709—31no—
347#709—31no—
348#709—31no—
349#709—61no—
350#709—61no—
351#709C22×D311yescharacteristic
352C2×D20—31no—
353C2×C4×D5—61no—
354C2×Dic10—31no—
355C5×M16—21no—
356C5×M16—31no—
357C5×M16—31no—
358C5×M16—31no—
359C5×M16—31no—
360C5×M16—31no—
361C5×M16—61no—
362C5×M16—61no—
363C5×M16—61no—
364C5×M16—61no—
365C5×M16C22×D311yescharacteristic
366C2×C5×C8—21no—
367C2×C5×C8—31no—
368C2×C5×C8—61no—
369C2×C5×C8—61no—
370C2×C5×C8—61no—
371C2×C5×C8—61no—
372C2×C5×C8C22×D311yescharacteristic
373#689—31no—
374#689—31no—
375#689—31no—
376#689C4×D311yescharacteristic, complemented
377#688—31no—
378#688—31no—
379#688—31no—
380#688C4×D311yescharacteristic, complemented
381#687—31no—
382#687—31no—
383#687—31no—
384#687C4×D311yescharacteristic, complemented
385#686—31no—
386#686—31no—
387#686—31no—
388#686C4×D311yescharacteristic, complemented
389C4×Dic5—31no—
390C4×Dic5—61no—
391C4×Dic5C22×D311yescharacteristic
392#681—31no—
393#681—31no—
394#681—31no—
395#681—31no—
396#681—31no—
397#681—61no—
398#681C22×D311yescharacteristic
399C2×#168—31no—
400C2×#168—61no—
401C2×#168C22×D311yescharacteristic
402#676—21no—
403#676—61no—
404#676—61no—
405#676—61no—
406C8×D5—21no—
407C8×D5—61no—
408C8×D5—61no—
409C8×D5—61no—
410#575—151no—
411#568—31no—
412#568—151no—
413#444—151no—
414#444—151no—
415#444—151no—
416#444—151no—
417#443—51no—
418#443—151no—
419#443—151no—
420#443—151no—
421#430—151no—
422C2×#104—151no—
423C2×#104—151no—
424C4×M16—151no—
425C22×C3×C5—21no—
426C22×C3×C5C2×#4111yescharacteristic
427C2×D15—21no—
428C2×C5×D3—21no—
429C2×C5×D3—41no—
430C2×C5×D3—81no—
431C2×C5×D3C4×D411yescharacteristic
432C2×C5×D3C4×D411yescharacteristic
433C2×C3×D5—21no—
434D3×D5—81no—
435C3×C4×C5—21no—
436C3×C4×C5C23×C411yescharacteristic
437C3×C4×C5C22×D411yescharacteristic
438Dic15—21no—
439Dic15—41no—
440C3×Dic5—22no—
441C3×Dic5—21no—
442C5×Dic3—21no—
443C5×Dic3C4×D411yescharacteristic
444C5×Dic3C4×D411yescharacteristic
445C3×#41—51no—
446C3×#41C22×D511yescharacteristic
447#239—51no—
448#239C4×D511yescharacteristic
449D3×Q8—51no—
450D3×Q8C4×D511yescharacteristic
451#237—21no—
452#237—51no—
453#237—101no—
454#237C4×D511yescharacteristic
455D3×D4—21no—
456D3×D4—51no—
457D3×D4—101no—
458D3×D4C4×D511yescharacteristic
459#235—21no—
460#235—51no—
461#235—101no—
462#235C22×D511yescharacteristic
463C2×C4×D3—21no—
464C2×C4×D3—101no—
465C2×C4×D3—101no—
466C2×C4×D3C22×D511yescharacteristic
467C3×Q16—51no—
468C3×SD16—51no—
469C3×SD16—51no—
470C3×D8—51no—
471C3×M16—21no—
472C3×M16—51no—
473C3×M16—101no—
474C3×M16C22×D511yescharacteristic
475C2×C3×C8—21no—
476C2×C3×C8—51no—
477C2×C3×C8—101no—
478C2×C3×C8C22×D511yescharacteristic
479C3×C42—51no—
480#216—51no—
481#216—51no—
482#215—51no—
483#215—51no—
484#214—51no—
485#214—51no—
486#213—51no—
487#213—51no—
488C4×Dic3—51no—
489C4×Dic3—101no—
490#208—21no—
491#208—51no—
492#208—101no—
493#208C22×D511yescharacteristic
494C2×C3⋊C8—21no—
495C2×C3⋊C8—51no—
496C2×C3⋊C8—101no—
497C2×C3⋊C8C22×D511yescharacteristic
498Dic12—51no—
499D24—51no—
500#204—51no—
501#204—51no—
502ΓL(1,𝔽25)—21no—
503ΓL(1,𝔽25)—21no—
504ΓL(1,𝔽25)—21no—
505ΓL(1,𝔽25)—51no—
506ΓL(1,𝔽25)—51no—
507ΓL(1,𝔽25)—51no—
508ΓL(1,𝔽25)—51no—
509ΓL(1,𝔽25)—101no—
510ΓL(1,𝔽25)—101no—
511ΓL(1,𝔽25)—101no—
512ΓL(1,𝔽25)C22⋊D511yescharacteristic
513ΓL(1,𝔽25)C22⋊D511yescharacteristic
514ΓL(1,𝔽25)C22⋊D511yescharacteristic
515ΓL(1,𝔽25)C22⋊D511yescharacteristic
516D3×C8—21no—
517D3×C8—21no—
518D3×C8—21no—
519D3×C8—101no—
520D3×C8—101no—
521D3×C8—101no—
522C23×C5—31no—
523C23×C5—61no—
524C22×D5—61no—
525C5×Q8—31no—
526C5×Q8—61no—
527C5×Q8C2×C4×D311yescharacteristic
528C5×D4—21no—
529C5×D4—31no—
530C5×D4—61no—
531C5×D4—61no—
532C5×D4—61no—
533C5×D4—61no—
534C5×D4C2×C4×D311yescharacteristic
535C2×C4×C5—21no—
536C2×C4×C5—31no—
537C2×C4×C5—31no—
538C2×C4×C5—31no—
539C2×C4×C5—31no—
540C2×C4×C5—31no—
541C2×C4×C5—61no—
542C2×C4×C5—61no—
543C2×C4×C5—61no—
544C2×C4×C5—61no—
545C2×C4×C5C23×D311yescharacteristic
546C22⋊D5—21no—
547C22⋊D5—61no—
548C22⋊D5—61no—
549C22⋊D5—61no—
550C2×Dic5—21no—
551C2×Dic5—61no—
552C2×Dic5—61no—
553C2×Dic5—122no—
554D20—31no—
555D20—61no—
556D20C2×C4×D311yescharacteristic
557C4×D5—21no—
558C4×D5—61no—
559C4×D5—61no—
560C4×D5—61no—
561Dic10—31no—
562Dic10—61no—
563Dic10C2×C4×D311yescharacteristic
564C5×C8—21no—
565C5×C8—31no—
566C5×C8—31no—
567C5×C8—61no—
568C5×C8D3×D411yescharacteristic
569C5×C8D3×D411yescharacteristic
570#168—21no—
571#168—31no—
572#168—31no—
573#168—61no—
574#168C2×C4×D311yescharacteristic
575#168C2×C4×D311yescharacteristic
576C2×#41—31no—
577C2×#41—151no—
578#137—151no—
579#137—151no—
580#137—151no—
581#137—151no—
582AGL(1,ℤ/8)—151no—
583AGL(1,ℤ/8)—151no—
584AGL(1,ℤ/8)—151no—
585AGL(1,ℤ/8)—151no—
586#135—51no—
587#135—151no—
588#135—151no—
589#135—151no—
590#131—31no—
591#131—31no—
592#131—31no—
593#131—51no—
594#131—61no—
595#131—61no—
596#131—151no—
597#131—151no—
598#131—151no—
599#131—301no—
600#131—301no—
601#131D3×D511yescharacteristic, complemented
602C2×M16—31no—
603C2×M16—31no—
604C2×M16—61no—
605C2×M16—61no—
606C2×M16—151no—
607C2×M16—151no—
608C2×M16—301no—
609C2×M16—301no—
610C2×C42—151no—
611#108—51no—
612#108—151no—
613#108—151no—
614#108—151no—
615#104—51no—
616#104—51no—
617#104—151no—
618#104—151no—
619#104—151no—
620#104—151no—
621#104—151no—
622#104—151no—
623#97—151no—
624#97—151no—
625C4×C8—51no—
626C4×C8—151no—
627C2×C3×C5—21no—
628C2×C3×C5—41no—
629C2×C3×C5C2×C4×D411yescharacteristic
630D15—41no—
631C3×D5—41no—
632C5×D3—21no—
633C5×D3—21no—
634C5×D3—41no—
635C22×D3—21no—
636C22×D3—101no—
637C22×D3#70911yescharacteristic
638C3×Q8—51no—
639C3×Q8C2×C4×D511yescharacteristic
640C3×D4—21no—
641C3×D4—51no—
642C3×D4—101no—
643C3×D4C2×C4×D511yescharacteristic
644C2×C3×C4—21no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4C23×D511yescharacteristic
648#67—21no—
649#67—21no—
650#67—21no—
651#67—101no—
652#67—101no—
653#67—101no—
654C2×Dic3—21no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3#70911yescharacteristic
658D12—21no—
659D12—51no—
660D12—101no—
661D12C2×C4×D511yescharacteristic
662C4×D3—21no—
663C4×D3—21no—
664C4×D3—21no—
665C4×D3—101no—
666C4×D3—101no—
667C4×D3—101no—
668C4×D3—202no—
669C4×D3C2×C4×D511yescharacteristic
670C4×D3C2×C4×D511yescharacteristic
671C4×D3C2×C22⋊D511yescharacteristic
672C4×D3C2×C22⋊D511yescharacteristic
673Dic6—21no—
674Dic6—51no—
675Dic6—101no—
676Dic6C2×C4×D511yescharacteristic
677C3×C8—21no—
678C3×C8—51no—
679C3×C8—51no—
680C3×C8—101no—
681C3×C8C2×C22⋊D511yescharacteristic
682C3×C8C2×C22⋊D511yescharacteristic
683C3⋊C8—21no—
684C3⋊C8—51no—
685C3⋊C8—51no—
686C3⋊C8—101no—
687C3⋊C8C2×C22⋊D511yescharacteristic
688C3⋊C8C2×C22⋊D511yescharacteristic
689C22×C5—21no—
690C22×C5—31no—
691C22×C5—31no—
692C22×C5—61no—
693C22×C5—121no—
694C22×C5—241no—
695C22×C5D3×#4111yescharacteristic
696C2×D5—21no—
697C2×D5—61no—
698C2×D5—241no—
699C4×C5—21no—
700C4×C5—31no—
701C4×C5—31no—
702C4×C5—61no—
703C4×C5C22×C4×D311yescharacteristic
704C4×C5C2×D3×D411yescharacteristic
705Dic5—22no—
706Dic5—21no—
707Dic5—61no—
708Dic5—121no—
709#41—31no—
710#41—31no—
711#41—31no—
712#41—51no—
713#41—61no—
714#41—61no—
715#41—151no—
716#41—151no—
717#41—151no—
718#41—301no—
719#41—301no—
720#41C2×D3×D511yescharacteristic
721C2×Q8—31no—
722C2×Q8—151no—
723C2×D4—31no—
724C2×D4—61no—
725C2×D4—151no—
726C2×D4—301no—
727C22×C4—31no—
728C22×C4—61no—
729C22×C4—301no—
730C22×C4—301no—
731Q16—51no—
732Q16—151no—
733Q16—151no—
734Q16—151no—
735SD16—51no—
736SD16—51no—
737SD16—151no—
738SD16—151no—
739SD16—151no—
740SD16—151no—
741SD16—151no—
742SD16—151no—
743D8—51no—
744D8—151no—
745D8—151no—
746D8—151no—
747M16—21no—
748M16—31no—
749M16—31no—
750M16—31no—
751M16—31no—
752M16—31no—
753M16—51no—
754M16—61no—
755M16—61no—
756M16—61no—
757M16—61no—
758M16—101no—
759M16—151no—
760M16—151no—
761M16—151no—
762M16—151no—
763M16—151no—
764M16—301no—
765M16—301no—
766M16—301no—
767M16—301no—
768M16C2×D3×D511yescharacteristic
769C2×C8—21no—
770C2×C8—31no—
771C2×C8—51no—
772C2×C8—61no—
773C2×C8—61no—
774C2×C8—61no—
775C2×C8—61no—
776C2×C8—101no—
777C2×C8—151no—
778C2×C8—301no—
779C2×C8—301no—
780C2×C8—301no—
781C2×C8—301no—
782C2×C8C2×D3×D511yescharacteristic
783C42—51no—
784C42—151no—
785C42—301no—
786C3×C5#295611yescharacteristic, complemented, Hall
787C22×C3—21no—
788C22×C3—101no—
789C22×C3C2×#70911yescharacteristic
790C2×D3—21no—
791C2×D3—41no—
792C2×D3—81no—
793C2×D3—101no—
794C2×D3—401no—
795C2×D3C4×C22⋊D511yescharacteristic
796C2×D3C4×C22⋊D511yescharacteristic
797C3×C4—21no—
798C3×C4—102no—
799C3×C4—101no—
800C3×C4C22×C4×D511yescharacteristic
801C3×C4C22×C22⋊D511yescharacteristic
802Dic3—21no—
803Dic3—101no—
804Dic3—201no—
805Dic3C4×C22⋊D511yescharacteristic
806Dic3C4×C22⋊D511yescharacteristic
807C2×C5—21no—
808C2×C5—41no—
809C2×C5—61no—
810C2×C5—61no—
811C2×C5—121no—
812C2×C5C4×D3×D411yescharacteristic
813D5—41no—
814D5—121no—
815C23—31no—
816C23—61no—
817C23—301no—
818Q8—31no—
819Q8—51no—
820Q8—61no—
821Q8—151no—
822Q8—301no—
823Q8C4×D3×D511yescharacteristic
824D4—21no—
825D4—31no—
826D4—51no—
827D4—61no—
828D4—61no—
829D4—61no—
830D4—61no—
831D4—101no—
832D4—151no—
833D4—301no—
834D4—301no—
835D4—301no—
836D4—301no—
837D4C4×D3×D511yescharacteristic
838C2×C4—21no—
839C2×C4—31no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—31no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—602no—
856C2×C4C22×D3×D511yescharacteristic
857C8—21no—
858C8—31no—
859C8—31no—
860C8—51no—
861C8—51no—
862C8—61no—
863C8—101no—
864C8—151no—
865C8—151no—
866C8—301no—
867C8D3×C22⋊D511yescharacteristic
868C8D3×C22⋊D511yescharacteristic
869C2×C3—21no—
870C2×C3—41no—
871C2×C3—201no—
872C2×C3C2×C4×C22⋊D511yescharacteristic
873D3—21no—
874D3—21no—
875D3—41no—
876D3—201no—
877C5#7988911yescharacteristic, complemented, Sylow
878C22—21no—
879C22—31no—
880C22—31no—
881C22—61no—
882C22—101no—
883C22—121no—
884C22—241no—
885C22—301no—
886C22—1201no—
887C22D3×#70911yescharacteristic
888C4—21no—
889C4—31no—
890C4—31no—
891C4—61no—
892C4—102no—
893C4—101no—
894C4—301no—
895C4—601no—
896C4C2×C4×D3×D511yescharacteristic
897C4C2×D3×C22⋊D511yescharacteristic
898C3#1061554211yescharacteristic, complemented, Sylow
899C2—21no—
900C2—41no—
901C2—61no—
902C2—61no—
903C2—121no—
904C2—201no—
905C2—601no—
906C2C4×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC4C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#131C22
socleC2×C3×C5C2×C4×D4
prime radical#11755322C2
cosocleC2×C3×C4×C5C24
hypercenter#131D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C5×#5750C2semidirect
3. #11753951C2semidirect
4. #11751246C2semidirect
5. C3×#65433C2semidirect
6. #11749438C2semidirect
7. #11749437C2semidirect
8. D3×#3969C2semidirect
9. D3×#3957C2semidirect
10. #11748209C2semidirect
11. #11748204C2semidirect
12. #11748172C2semidirect
13. #11748078C2semidirect
14. #11748075C2semidirect
15. Dic5×ΓL(1,𝔽25)C2semidirect
19. C3×C5×#131C22semidirect
21. #91790C22semidirect
22. C5×#948C22semidirect
24. C5×#907C22semidirect
28. C5×#901C22semidirect
32. C3×#4047C22semidirect
33. #91520C4semidirect
34. #91518C4semidirect
35. #91510C4semidirect
36. #91504C4semidirect
37. #91496C4semidirect
38. #91494C4semidirect
39. #91486C4semidirect
40. #91480C4semidirect
45. #91291C22semidirect
47. #91283C22semidirect
52. #91121C22semidirect
53. #91109C22semidirect
54. #91106C22semidirect
55. #91099C22semidirect
56. C3×#3969C22semidirect
57. C3×#3957C22semidirect
58. C3×#3954C22semidirect
59. C3×C8×Dic5C22semidirect
60. #90992C22semidirect
61. #90991C22semidirect
62. #90981C22semidirect
63. #90979C22semidirect
64. #90978C22semidirect
65. #90976C22semidirect
66. #90954C22semidirect
67. Dic5×C3⋊C8C22semidirect
80. #65433D3semidirect
110. #6718C2×C4semidirect
111. #6717C2×C4semidirect
112. #6716C2×C4semidirect
113. #6715C2×C4semidirect
133. C3×#689C2×C4semidirect
134. C3×#688C2×C4semidirect
135. C3×#687C2×C4semidirect
136. C3×#686C2×C4semidirect
143. #6663C2×C4semidirect
144. #6661C2×C4semidirect
145. #6660C2×C4semidirect
146. #6659C2×C4semidirect
147. #6656C2×C4semidirect
148. #6655C2×C4semidirect
149. #6654C2×C4semidirect
150. #6652C2×C4semidirect
163. #5750D5semidirect
183. C5×#131C2×D3semidirect
210. #4047C2×D3semidirect
214. #3969C2×D3semidirect
218. #3957C2×D3semidirect
222. #3954C2×D3semidirect
226. C8×Dic5C2×D3semidirect
286. C3×#131C2×D5semidirect
290. #948C2×D5semidirect
302. #907C2×D5semidirect
311. #901C2×D5semidirect
376. #689C4×D3semidirect
380. #688C4×D3semidirect
384. #687C4×D3semidirect
388. #686C4×D3semidirect
601. #131D3×D5semidirect
786. C3×C5#2956semidirect
877. C5#79889semidirect
898. C3#10615542semidirect

Maximal subgroups

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

subgroupindex
C5×#57502
#117553222
#117539512
#117512462
C3×#654332
#117494382
#117494372
D3×#39692
D3×#39572
#117482092
#117482042
#117481722
#117480782
#117480752
Dic5×ΓL(1,𝔽25)2
#106155423
#798895