Finite Group Databasebeta

← #14418145

Subgroups — #14418145

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
1#11756509C211yesmaximal, characteristic, complemented
2#11755329C211yesmaximal, characteristic
3#11753953C211yesmaximal, characteristic, complemented
4C5×#5145C211yesmaximal, characteristic, complemented
5C3×#65433C211yesmaximal, characteristic, complemented
6#11749442C211yesmaximal, characteristic, complemented
7#11749441C211yesmaximal, characteristic, complemented
8#11749430C211yesmaximal, characteristic, complemented
9#11748236C211yesmaximal, characteristic, complemented
10#11748177C211yesmaximal, characteristic, complemented
11#11748174C211yesmaximal, characteristic, complemented
12#11748173C211yesmaximal, characteristic, complemented
13#11748078C211yesmaximal, characteristic, complemented
14#11748077C211yesmaximal, characteristic, complemented
15#11747592C211yesmaximal, characteristic, complemented
16#10611629—31nomaximal, Hall
17#41×D15C2211yescharacteristic
18#92016C2211yescharacteristic
19C3×C5×#131C2211yescharacteristic, complemented
20#91837C2211yescharacteristic, complemented
21#91796—21no—
22#91796C2211yescharacteristic, complemented
23M16×D15—21no—
24M16×D15C2211yescharacteristic
25#91790—21no—
26#91790C2211yescharacteristic, complemented
27C2×#6705—21no—
28C2×#6705C2211yescharacteristic
29C5×#950C2211yescharacteristic
30C5×#901C2211yescharacteristic, complemented
31C3×#4096C2211yescharacteristic
32C3×#4047C2211yescharacteristic, complemented
33#91524C411yescharacteristic, complemented
34#91522C411yescharacteristic, complemented
35#91512C411yescharacteristic, complemented
36#91506C411yescharacteristic, complemented
37#91500C411yescharacteristic, complemented
38#91498C411yescharacteristic, complemented
39#91488C411yescharacteristic, complemented
40#91482C411yescharacteristic, complemented
41C4×#1200C2211yescharacteristic
42#91311C2211yescharacteristic
43#91303C2211yescharacteristic
44C2×#6651C2211yescharacteristic
45#91292C2211yescharacteristic
46#91288C2211yescharacteristic, complemented
47#91284C2211yescharacteristic, complemented
48#91267—21no—
49#91266—21no—
50D3×#676—21no—
51D5×ΓL(1,𝔽25)—21no—
52C5×#837C2211yescharacteristic, complemented
53C5×#825C2211yescharacteristic, complemented
54C5×#822C2211yescharacteristic, complemented
55C5×#815C2211yescharacteristic, complemented
56C3×#3969C2211yescharacteristic, complemented
57C3×#3957C2211yescharacteristic, complemented
58C3×#3954C2211yescharacteristic, complemented
59C3×C8×Dic5C2211yescharacteristic, complemented
60#90993C2211yescharacteristic, complemented
61#90991C2211yescharacteristic, complemented
62#90981C2211yescharacteristic, complemented
63#90980C2211yescharacteristic, complemented
64#90979C2211yescharacteristic, complemented
65#90977C2211yescharacteristic, complemented
66#90953C2211yescharacteristic, complemented
67Dic5×C3⋊C8C2211yescharacteristic, complemented
68#79889—51nomaximal, Hall
69#66102—31no—
70#66084—31no—
71#66084—31no—
72C5×#444—31no—
73#65485—31no—
74#65433—31no—
75#65433D311yescharacteristic, complemented
76#65184—31no—
77#65182—31no—
78#65112—31no—
79#65112—31no—
80D5×#104—31no—
81D5×#104—31no—
82#65006—31no—
83#64996—31no—
84C3×C5×#41C2311yescharacteristic
85#6821C2×C411yescharacteristic
86Q8×D15C2×C411yescharacteristic
87#6819—21no—
88#6819C2×C411yescharacteristic
89D4×D15—21no—
90D4×D15C2×C411yescharacteristic
91#6817—21no—
92#6817C2311yescharacteristic
93C2×C4×D15—21no—
94C2×C4×D15C2311yescharacteristic
95C5×#235C2311yescharacteristic
96C3×#709C2311yescharacteristic
97#6790—21no—
98C2×#1200—21no—
99#6780—21no—
100#6777C2×C411yescharacteristic
101C4×D3×D5—21no—
102#6771—21no—
103D15⋊Q8C2×C411yescharacteristic
104#6768C2×C411yescharacteristic
105#6766C2×C411yescharacteristic
106C3×C5×M16—21no—
107C3×C5×M16C2311yescharacteristic
108C2×C3×C5×C8—21no—
109C2×C3×C5×C8C2311yescharacteristic
110#6710—21no—
111#6710C2311yescharacteristic
112C2×C3⋊#168—21no—
113C2×C3⋊#168C2311yescharacteristic
114#6705—21no—
115#6705—21no—
116#6705—21no—
117#6705D411yescharacteristic
118#6705D411yescharacteristic
119#6705D411yescharacteristic
120#6705D411yescharacteristic
121C8×D15—21no—
122C8×D15—21no—
123C8×D15—21no—
124C5×#216C2×C411yescharacteristic, complemented
125C5×#215C2×C411yescharacteristic, complemented
126C5×#214C2×C411yescharacteristic, complemented
127C5×#213C2×C411yescharacteristic, complemented
128C4×C5×Dic3C2311yescharacteristic
129C5×#208C2311yescharacteristic
130C2×C5×C3⋊C8C2311yescharacteristic
131C5×ΓL(1,𝔽25)—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#6662C2×C411yescharacteristic, complemented
145#6660C2×C411yescharacteristic, complemented
146#6659C2×C411yescharacteristic, complemented
147#6658C2×C411yescharacteristic, complemented
148#6657C2×C411yescharacteristic, complemented
149#6654C2×C411yescharacteristic, complemented
150#6653C2×C411yescharacteristic, complemented
151#6651—21no—
152#6651C2×C411yescharacteristic
153#6651C2×C411yescharacteristic
154#6651C2×C411yescharacteristic
155#6651C2×C411yescharacteristic
156#6650—21no—
157#6649—21no—
158#6648—21no—
159D3×#168—21no—
160D5×C3⋊C8—21no—
161#5768—51no—
162#5750—51no—
163#5750—51no—
164C3×#443—51no—
165#5197—51no—
166#5145—51no—
167#5145D511yescharacteristic, complemented
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—
176D5×#41—31no—
177D5×#41—31no—
178C5×#135—31no—
179C5×#131—31no—
180C5×#131C2×D311yescharacteristic, complemented
181#4096—31no—
182#4096C2×D311yescharacteristic
183#4094—31no—
184#4094—31no—
185#4064—31no—
186#4064—31no—
187#4061—31no—
188#4061—31no—
189#4060—31no—
190#4060—31no—
191#4057—31no—
192#4057—31no—
193#4053—31no—
194#4053—31no—
195#4053—61no—
196#4053—61no—
197D5×M16—31no—
198D5×M16—31no—
199D5×M16—61no—
200D5×M16—61no—
201#4050—31no—
202#4047—31no—
203#4047—61no—
204#4047—61no—
205#4047C2×D311yescharacteristic, complemented
206C2×#676—31no—
207C2×#676—31no—
208C2×#676—61no—
209C2×#676—61no—
210C42×D5—31no—
211C5×#108—31no—
212C5×#104—31no—
213C5×#104—31no—
214C5×#97—31no—
215#3969—31no—
216#3969C2×D311yescharacteristic, complemented
217#3957—31no—
218#3957C2×D311yescharacteristic, complemented
219#3954—31no—
220#3954C2×D311yescharacteristic, complemented
221#3951—31no—
222C8×Dic5—31no—
223C8×Dic5C2×D311yescharacteristic, complemented
224#3937—31no—
225#3937—31no—
226#3935—31no—
227#2956—151noSylow
228C22×D15—21no—
229C22×D15#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—
237#1220—21no—
238#1220—21no—
239C2×Dic15—21no—
240C2×Dic15#4111yescharacteristic
241D60—21no—
242D60C22×C411yescharacteristic
243C4×D15—21no—
244C4×D15—21no—
245C4×D15—21no—
246C4×D15C22×C411yescharacteristic
247C4×D15C22×C411yescharacteristic
248C4×D15C2×D411yescharacteristic
249C4×D15C2×D411yescharacteristic
250Dic30—21no—
251Dic30C22×C411yescharacteristic
252C5×#67—21no—
253C2×C5×Dic3—21no—
254C5×D12C22×C411yescharacteristic
255C4×C5×D3—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—
267#1200—42no—
268D3×Dic5—21no—
269D5×Dic3—21no—
270C3×C5×C8—21no—
271C3×C5×C8C2×D411yescharacteristic
272C3×C5×C8C2×D411yescharacteristic
273C3⋊#168—21no—
274C3⋊#168C2×D411yescharacteristic
275C3⋊#168C2×D411yescharacteristic
276C3×#168—21no—
277C3×#168C22×C411yescharacteristic
278C3×#168C22×C411yescharacteristic
279C5×C3⋊C8—21no—
280C5×C3⋊C8C22×C411yescharacteristic
281C5×C3⋊C8C22×C411yescharacteristic
282D3×#41—51no—
283D3×#41—51no—
284C3×#135—51no—
285C3×#131—51no—
286C3×#131C2×D511yescharacteristic, complemented
287#950—51no—
288#950C2×D511yescharacteristic
289#948—51no—
290#948—51no—
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—51no—
300#907—51no—
301#907—101no—
302#907—101no—
303D3×M16—51no—
304D3×M16—51no—
305D3×M16—101no—
306D3×M16—101no—
307#904—51no—
308#901—51no—
309#901—101no—
310#901—101no—
311#901C2×D511yescharacteristic, complemented
312C2×ΓL(1,𝔽25)—51no—
313C2×ΓL(1,𝔽25)—51no—
314C2×ΓL(1,𝔽25)—101no—
315C2×ΓL(1,𝔽25)—101no—
316C42×D3—51no—
317C3×#108—51no—
318C3×#104—51no—
319C3×#104—51no—
320C3×C4×C8—51no—
321#837—51no—
322#837C2×D511yescharacteristic, complemented
323#825—51no—
324#825C2×D511yescharacteristic, complemented
325#822—51no—
326#822C2×D511yescharacteristic, complemented
327#819—51no—
328#815—51no—
329#815C2×D511yescharacteristic, complemented
330#805—51no—
331#805—51no—
332C4×C3⋊C8—51no—
333C5×#41—31no—
334C5×#41C22×D311yescharacteristic
335#713—31no—
336#713—31no—
337Q8×D5—31no—
338Q8×D5—31no—
339#711—31no—
340#711—31no—
341#711—61no—
342#711—61no—
343D4×D5—31no—
344D4×D5—31no—
345D4×D5—61no—
346D4×D5—61no—
347#709—31no—
348#709—61no—
349#709—61no—
350#709C22×D311yescharacteristic
351C2×C4×D5—31no—
352C2×C4×D5—61no—
353C2×C4×D5—61no—
354C2×C4×D5—61no—
355C5×Q16—31no—
356C5×SD16—31no—
357C5×SD16—31no—
358C5×D8—31no—
359C5×M16—21no—
360C5×M16—31no—
361C5×M16—61no—
362C5×M16C22×D311yescharacteristic
363C2×C5×C8—21no—
364C2×C5×C8—31no—
365C2×C5×C8—61no—
366C2×C5×C8C22×D311yescharacteristic
367C42×C5—31no—
368#689—31no—
369#689C4×D311yescharacteristic, complemented
370#688—31no—
371#688C4×D311yescharacteristic, complemented
372#687—31no—
373#687C4×D311yescharacteristic, complemented
374#686—31no—
375#686C4×D311yescharacteristic, complemented
376C4×Dic5—61no—
377C4×Dic5C22×D311yescharacteristic
378#681—31no—
379#681—61no—
380#681—61no—
381#681C22×D311yescharacteristic
382C2×#168—31no—
383C2×#168—61no—
384C2×#168—61no—
385C2×#168C22×D311yescharacteristic
386Dic20—31no—
387D40—31no—
388#677—31no—
389#677—31no—
390#676—21no—
391#676—31no—
392#676—31no—
393#676—31no—
394#676—31no—
395#676—31no—
396#676—31no—
397#676—31no—
398#676—31no—
399#676—61no—
400#676—61no—
401#676—61no—
402#676—61no—
403#676—61no—
404C8×D5—21no—
405C8×D5—61no—
406C8×D5—61no—
407C8×D5—61no—
408C8×D5—61no—
409C8×D5—61no—
410#575—151no—
411#568—151no—
412#568—151no—
413#444—31no—
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×D15—41no—
429C2×D15—81no—
430C2×D15C4×D411yescharacteristic
431C2×D15C4×D411yescharacteristic
432C2×C5×D3—21no—
433C2×C3×D5—21no—
434D3×D5—81no—
435C3×C4×C5—21no—
436C3×C4×C5C23×C411yescharacteristic
437C3×C4×C5C22×D411yescharacteristic
438Dic15—21no—
439Dic15C4×D411yescharacteristic
440Dic15C4×D411yescharacteristic
441C3×Dic5—22no—
442C3×Dic5—21no—
443C5×Dic3—21no—
444C5×Dic3—41no—
445C3×#41—51no—
446C3×#41C22×D511yescharacteristic
447#239—51no—
448#239—51no—
449D3×Q8—51no—
450D3×Q8—51no—
451#237—51no—
452#237—51no—
453#237—101no—
454#237—101no—
455D3×D4—51no—
456D3×D4—51no—
457D3×D4—101no—
458D3×D4—101no—
459#235—51no—
460#235—101no—
461#235—101no—
462#235C22×D511yescharacteristic
463C2×C4×D3—51no—
464C2×C4×D3—101no—
465C2×C4×D3—101no—
466C2×C4×D3—101no—
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#216C4×D511yescharacteristic, complemented
482#215—51no—
483#215C4×D511yescharacteristic, complemented
484#214—51no—
485#214C4×D511yescharacteristic, complemented
486#213—51no—
487#213C4×D511yescharacteristic, complemented
488C4×Dic3—101no—
489C4×Dic3C22×D511yescharacteristic
490#208—51no—
491#208—101no—
492#208—101no—
493#208C22×D511yescharacteristic
494C2×C3⋊C8—51no—
495C2×C3⋊C8—101no—
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)—51no—
504ΓL(1,𝔽25)—51no—
505ΓL(1,𝔽25)—51no—
506ΓL(1,𝔽25)—51no—
507ΓL(1,𝔽25)—51no—
508ΓL(1,𝔽25)—51no—
509ΓL(1,𝔽25)—51no—
510ΓL(1,𝔽25)—51no—
511ΓL(1,𝔽25)—101no—
512ΓL(1,𝔽25)—101no—
513ΓL(1,𝔽25)—101no—
514ΓL(1,𝔽25)—101no—
515ΓL(1,𝔽25)—101no—
516D3×C8—21no—
517D3×C8—101no—
518D3×C8—101no—
519D3×C8—101no—
520D3×C8—101no—
521D3×C8—101no—
522C22×D5—31no—
523C22×D5—61no—
524C22×D5—61no—
525C5×Q8—31no—
526C5×Q8C2×C4×D311yescharacteristic
527C5×D4—21no—
528C5×D4—31no—
529C5×D4—61no—
530C5×D4C2×C4×D311yescharacteristic
531C2×C4×C5—21no—
532C2×C4×C5—61no—
533C2×C4×C5—61no—
534C2×C4×C5C23×D311yescharacteristic
535C22⋊D5—21no—
536C22⋊D5—61no—
537C22⋊D5—61no—
538C22⋊D5—61no—
539C22⋊D5—61no—
540C22⋊D5—61no—
541C2×Dic5—21no—
542C2×Dic5—31no—
543C2×Dic5—61no—
544C2×Dic5—61no—
545D20—31no—
546D20—61no—
547D20—61no—
548D20C2×C4×D311yescharacteristic
549C4×D5—21no—
550C4×D5—31no—
551C4×D5—31no—
552C4×D5—31no—
553C4×D5—31no—
554C4×D5—61no—
555C4×D5—61no—
556C4×D5—61no—
557C4×D5—61no—
558C4×D5—61no—
559C4×D5—122no—
560Dic10—31no—
561Dic10—61no—
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—151no—
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—31no—
587#135—51no—
588#135—151no—
589#135—151no—
590#131—31no—
591#131—51no—
592#131—151no—
593#131—151no—
594#131—151no—
595#131—151no—
596#131—151no—
597#131—301no—
598#131—301no—
599#131—301no—
600#131—301no—
601#131D3×D511yescharacteristic, complemented
602C2×M16—151no—
603C2×M16—151no—
604C2×M16—151no—
605C2×M16—151no—
606C2×M16—301no—
607C2×M16—301no—
608C2×M16—301no—
609C2×M16—301no—
610C2×C42—151no—
611#108—31no—
612#108—51no—
613#108—151no—
614#108—151no—
615#104—31no—
616#104—31no—
617#104—51no—
618#104—51no—
619#104—151no—
620#104—151no—
621#104—151no—
622#104—151no—
623#97—31no—
624#97—151no—
625C4×C8—51no—
626C4×C8—151no—
627C2×C3×C5—21no—
628C2×C3×C5—41no—
629C2×C3×C5C2×C4×D411yescharacteristic
630D15—21no—
631D15—21no—
632D15—41no—
633C3×D5—41no—
634C5×D3—41no—
635C22×D3—51no—
636C22×D3—101no—
637C22×D3—101no—
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—101no—
650#67—101no—
651#67—101no—
652#67—101no—
653#67—101no—
654C2×Dic3—21no—
655C2×Dic3—51no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658D12—51no—
659D12—101no—
660D12—101no—
661D12C2×C4×D511yescharacteristic
662C4×D3—21no—
663C4×D3—51no—
664C4×D3—51no—
665C4×D3—51no—
666C4×D3—51no—
667C4×D3—101no—
668C4×D3—101no—
669C4×D3—101no—
670C4×D3—101no—
671C4×D3—101no—
672C4×D3—202no—
673Dic6—51no—
674Dic6—101no—
675Dic6—101no—
676Dic6C2×C4×D511yescharacteristic
677C3×C8—21no—
678C3×C8—51no—
679C3×C8—51no—
680C3×C8—101no—
681C3×C8D4×D511yescharacteristic
682C3×C8D4×D511yescharacteristic
683C3⋊C8—21no—
684C3⋊C8—51no—
685C3⋊C8—51no—
686C3⋊C8—101no—
687C3⋊C8C2×C4×D511yescharacteristic
688C3⋊C8C2×C4×D511yescharacteristic
689C22×C5—21no—
690C22×C5—61no—
691C22×C5D3×#4111yescharacteristic
692C2×D5—21no—
693C2×D5—31no—
694C2×D5—31no—
695C2×D5—61no—
696C2×D5—121no—
697C2×D5—241no—
698C2×D5—241no—
699C4×C5—21no—
700C4×C5—61no—
701C4×C5—121no—
702C4×C5C22×C4×D311yescharacteristic
703C4×C5C2×D3×D411yescharacteristic
704Dic5—22no—
705Dic5—21no—
706Dic5—31no—
707Dic5—31no—
708Dic5—61no—
709#41—31no—
710#41—51no—
711#41—151no—
712#41—151no—
713#41—151no—
714#41—151no—
715#41—151no—
716#41—301no—
717#41—301no—
718#41—301no—
719#41—301no—
720#41C2×D3×D511yescharacteristic
721C2×Q8—151no—
722C2×Q8—151no—
723C2×D4—151no—
724C2×D4—151no—
725C2×D4—301no—
726C2×D4—301no—
727C22×C4—151no—
728C22×C4—301no—
729C22×C4—301no—
730C22×C4—301no—
731Q16—31no—
732Q16—51no—
733Q16—151no—
734Q16—151no—
735SD16—31no—
736SD16—31no—
737SD16—51no—
738SD16—51no—
739SD16—151no—
740SD16—151no—
741SD16—151no—
742SD16—151no—
743D8—31no—
744D8—51no—
745D8—151no—
746D8—151no—
747M16—21no—
748M16—31no—
749M16—51no—
750M16—61no—
751M16—101no—
752M16—151no—
753M16—151no—
754M16—151no—
755M16—151no—
756M16—151no—
757M16—151no—
758M16—151no—
759M16—151no—
760M16—151no—
761M16—301no—
762M16—301no—
763M16—301no—
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—101no—
774C2×C8—151no—
775C2×C8—301no—
776C2×C8—301no—
777C2×C8—301no—
778C2×C8—301no—
779C2×C8—301no—
780C2×C8—301no—
781C2×C8—301no—
782C2×C8C2×D3×D511yescharacteristic
783C42—31no—
784C42—51no—
785C42—301no—
786C3×C5#295611yescharacteristic, complemented, Hall
787C22×C3—21no—
788C22×C3—101no—
789C22×C3D5×#4111yescharacteristic
790C2×D3—21no—
791C2×D3—51no—
792C2×D3—51no—
793C2×D3—101no—
794C2×D3—201no—
795C2×D3—401no—
796C2×D3—401no—
797C3×C4—21no—
798C3×C4—102no—
799C3×C4—101no—
800C3×C4C22×C4×D511yescharacteristic
801C3×C4C2×D4×D511yescharacteristic
802Dic3—21no—
803Dic3—41no—
804Dic3—51no—
805Dic3—51no—
806Dic3—101no—
807C2×C5—21no—
808C2×C5—41no—
809C2×C5—121no—
810C2×C5C4×D3×D411yescharacteristic
811D5—41no—
812D5—61no—
813D5—61no—
814D5—121no—
815C23—151no—
816C23—301no—
817C23—301no—
818Q8—31no—
819Q8—51no—
820Q8—151no—
821Q8—301no—
822Q8—301no—
823Q8C4×D3×D511yescharacteristic
824D4—21no—
825D4—31no—
826D4—51no—
827D4—61no—
828D4—101no—
829D4—151no—
830D4—301no—
831D4—301no—
832D4—301no—
833D4—301no—
834D4—301no—
835D4—301no—
836D4—301no—
837D4C4×D3×D511yescharacteristic
838C2×C4—21no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—151no—
844C2×C4—151no—
845C2×C4—151no—
846C2×C4—151no—
847C2×C4—151no—
848C2×C4—301no—
849C2×C4—301no—
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—
867C8#679011yescharacteristic
868C8#679011yescharacteristic
869C2×C3—21no—
870C2×C3—41no—
871C2×C3—201no—
872C2×C3C4×D4×D511yescharacteristic
873D3—41no—
874D3—101no—
875D3—101no—
876D3—201no—
877C5#7988911yescharacteristic, complemented, Sylow
878C22—21no—
879C22—61no—
880C22—101no—
881C22—151no—
882C22—151no—
883C22—301no—
884C22—601no—
885C22—1201no—
886C22—1201no—
887C22#9201611yescharacteristic
888C4—21no—
889C4—61no—
890C4—102no—
891C4—101no—
892C4—121no—
893C4—151no—
894C4—151no—
895C4—301no—
896C4C2×C4×D3×D511yescharacteristic
897C4C2×#679011yescharacteristic
898C3#1061162911yescharacteristic, complemented, Sylow
899C2—21no—
900C2—41no—
901C2—121no—
902C2—201no—
903C2—301no—
904C2—301no—
905C2—601no—
906C2C4×#679011yescharacteristic
subgroupG/H
centerC4C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#131C22
socleC2×C3×C5C2×C4×D4
prime radical#11755329C2
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. #11756509C2semidirect
3. #11753953C2semidirect
4. C5×#5145C2semidirect
5. C3×#65433C2semidirect
6. #11749442C2semidirect
7. #11749441C2semidirect
8. #11749430C2semidirect
9. #11748236C2semidirect
10. #11748177C2semidirect
11. #11748174C2semidirect
12. #11748173C2semidirect
13. #11748078C2semidirect
14. #11748077C2semidirect
15. #11747592C2semidirect
19. C3×C5×#131C22semidirect
20. #91837C22semidirect
22. #91796C22semidirect
26. #91790C22semidirect
30. C5×#901C22semidirect
32. C3×#4047C22semidirect
33. #91524C4semidirect
34. #91522C4semidirect
35. #91512C4semidirect
36. #91506C4semidirect
37. #91500C4semidirect
38. #91498C4semidirect
39. #91488C4semidirect
40. #91482C4semidirect
46. #91288C22semidirect
47. #91284C22semidirect
52. C5×#837C22semidirect
53. C5×#825C22semidirect
54. C5×#822C22semidirect
55. C5×#815C22semidirect
56. C3×#3969C22semidirect
57. C3×#3957C22semidirect
58. C3×#3954C22semidirect
59. C3×C8×Dic5C22semidirect
60. #90993C22semidirect
61. #90991C22semidirect
62. #90981C22semidirect
63. #90980C22semidirect
64. #90979C22semidirect
65. #90977C22semidirect
66. #90953C22semidirect
67. Dic5×C3⋊C8C22semidirect
75. #65433D3semidirect
124. C5×#216C2×C4semidirect
125. C5×#215C2×C4semidirect
126. C5×#214C2×C4semidirect
127. C5×#213C2×C4semidirect
133. C3×#689C2×C4semidirect
134. C3×#688C2×C4semidirect
135. C3×#687C2×C4semidirect
136. C3×#686C2×C4semidirect
143. #6663C2×C4semidirect
144. #6662C2×C4semidirect
145. #6660C2×C4semidirect
146. #6659C2×C4semidirect
147. #6658C2×C4semidirect
148. #6657C2×C4semidirect
149. #6654C2×C4semidirect
150. #6653C2×C4semidirect
167. #5145D5semidirect
180. C5×#131C2×D3semidirect
205. #4047C2×D3semidirect
216. #3969C2×D3semidirect
218. #3957C2×D3semidirect
220. #3954C2×D3semidirect
223. C8×Dic5C2×D3semidirect
286. C3×#131C2×D5semidirect
311. #901C2×D5semidirect
322. #837C2×D5semidirect
324. #825C2×D5semidirect
326. #822C2×D5semidirect
329. #815C2×D5semidirect
369. #689C4×D3semidirect
371. #688C4×D3semidirect
373. #687C4×D3semidirect
375. #686C4×D3semidirect
481. #216C4×D5semidirect
483. #215C4×D5semidirect
485. #214C4×D5semidirect
487. #213C4×D5semidirect
601. #131D3×D5semidirect
786. C3×C5#2956semidirect
877. C5#79889semidirect
898. C3#10611629semidirect

Maximal subgroups

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

subgroupindex
#117565092
#117553292
#117539532
C5×#51452
C3×#654332
#117494422
#117494412
#117494302
#117482362
#117481772
#117481742
#117481732
#117480782
#117480772
#117475922
#106116293
#798895