Finite Group Databasebeta

← #14418146

Subgroups — #14418146

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
1C3×#66084C211yesmaximal, characteristic, complemented
2#11755315C211yesmaximal, characteristic
3#11753949C211yesmaximal, characteristic, complemented
4#11751245C211yesmaximal, characteristic, complemented
5C5×#5145C211yesmaximal, characteristic, complemented
6#11749435C211yesmaximal, characteristic, complemented
7#11749432C211yesmaximal, characteristic, complemented
8D5×#837C211yesmaximal, characteristic, complemented
9D5×#825C211yesmaximal, characteristic, complemented
10#11748207C211yesmaximal, characteristic, complemented
11#11748202C211yesmaximal, characteristic, complemented
12#11748171C211yesmaximal, characteristic, complemented
13#11748077C211yesmaximal, characteristic, complemented
14#11748074C211yesmaximal, characteristic, complemented
15#11747601C211yesmaximal, characteristic, complemented
16#10611629—31nomaximal, Hall
17C3×D5×#41C2211yescharacteristic
18D5×#235C2211yescharacteristic
19C3×C5×#131C2211yescharacteristic, complemented
20#91839C2211yescharacteristic
21#91790C2211yescharacteristic, complemented
22C5×#950C2211yescharacteristic
23C5×#901C2211yescharacteristic, complemented
24C3×#4094C2211yescharacteristic, complemented
25C3×#4053—21no—
26C3×#4053C2211yescharacteristic, complemented
27C3×D5×M16—21no—
28C3×D5×M16C2211yescharacteristic
29C3×#4047—21no—
30C3×#4047C2211yescharacteristic, complemented
31C2×C3×#676—21no—
32C2×C3×#676C2211yescharacteristic
33#91515C411yescharacteristic, complemented
34#91513C411yescharacteristic, complemented
35#91508C411yescharacteristic, complemented
36#91502C411yescharacteristic, complemented
37#91491C411yescharacteristic, complemented
38#91489C411yescharacteristic, complemented
39#91484C411yescharacteristic, complemented
40#91478C411yescharacteristic, complemented
41C4×D5×Dic3C2211yescharacteristic
42#91311C2211yescharacteristic
43#91297C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45#91290C2211yescharacteristic, complemented
46#91286C2211yescharacteristic, complemented
47D5×#208C2211yescharacteristic
48#91268—21no—
49#91267—21no—
50#91246—21no—
51D3×#676—21no—
52#91121C2211yescharacteristic, complemented
53#91109C2211yescharacteristic, complemented
54#91106C2211yescharacteristic, complemented
55C8×Dic15C2211yescharacteristic, complemented
56C5×#837C2211yescharacteristic, complemented
57C5×#825C2211yescharacteristic, complemented
58C5×#822C2211yescharacteristic, complemented
59C5×#815C2211yescharacteristic, complemented
60#90993C2211yescharacteristic, complemented
61#90992C2211yescharacteristic, complemented
62#90980C2211yescharacteristic, complemented
63#90978C2211yescharacteristic, complemented
64#90977C2211yescharacteristic, complemented
65#90976C2211yescharacteristic, complemented
66#90953C2211yescharacteristic, complemented
67#90951C2211yescharacteristic, complemented
68#83811—51nomaximal, Hall
69#66102—31no—
70#66084—31no—
71#66084D311yescharacteristic, complemented
72C5×#444—31no—
73#65485—31no—
74#65433—31no—
75#65433—31no—
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#6817C2311yescharacteristic
86C5×#235C2311yescharacteristic
87C3×#713C2×C411yescharacteristic
88C3×Q8×D5C2×C411yescharacteristic
89C3×#711—21no—
90C3×#711C2×C411yescharacteristic
91C3×D4×D5—21no—
92C3×D4×D5C2×C411yescharacteristic
93C3×#709—21no—
94C3×#709C2311yescharacteristic
95C2×C3×C4×D5—21no—
96C2×C3×C4×D5C2311yescharacteristic
97D5×#67—21no—
98#6782—21no—
99C2×D5×Dic3—21no—
100D5×D12C2×C411yescharacteristic
101C4×D3×D5—21no—
102#6773C2×C411yescharacteristic
103#6772C2×C411yescharacteristic
104#6771—21no—
105D5×Dic6C2×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×#216C2×C411yescharacteristic, complemented
120C5×#215C2×C411yescharacteristic, complemented
121C5×#214C2×C411yescharacteristic, complemented
122C5×#213C2×C411yescharacteristic, complemented
123C4×C5×Dic3C2311yescharacteristic
124C5×#208C2311yescharacteristic
125C2×C5×C3⋊C8C2311yescharacteristic
126C5×ΓL(1,𝔽25)—21no—
127C5×D3×C8—21no—
128C3×#681—21no—
129C3×#681C2311yescharacteristic
130C2×C3×#168—21no—
131C2×C3×#168C2311yescharacteristic
132C3×#676—21no—
133C3×#676—21no—
134C3×#676—21no—
135C3×#676D411yescharacteristic
136C3×#676D411yescharacteristic
137C3×#676D411yescharacteristic
138C3×#676D411yescharacteristic
139C3×C8×D5—21no—
140C3×C8×D5—21no—
141C3×C8×D5—21no—
142Dic3×Dic5—21no—
143#6662C2×C411yescharacteristic, complemented
144#6661C2×C411yescharacteristic, complemented
145#6658C2×C411yescharacteristic, complemented
146#6657C2×C411yescharacteristic, complemented
147#6656C2×C411yescharacteristic, complemented
148#6655C2×C411yescharacteristic, complemented
149#6653C2×C411yescharacteristic, complemented
150#6652C2×C411yescharacteristic, complemented
151#6651—21no—
152#6650—21no—
153#6649—21no—
154#6649C2×C411yescharacteristic
155#6649C2×C411yescharacteristic
156#6649C2×C411yescharacteristic
157#6649C2×C411yescharacteristic
158#6648—21no—
159D3×#168—21no—
160D5×C3⋊C8—21no—
161C3×#568—51no—
162#5822—51no—
163#5745—51no—
164C2×#837—51no—
165#5145—51no—
166#5145—51no—
167#5145—51no—
168#5145D511yescharacteristic, complemented
169#5144—51no—
170#5144—51no—
171#5144—51no—
172#5144—51no—
173C2×#825—51no—
174#5124—51no—
175Dic3×M16—51no—
176D5×#41—31no—
177D5×#41C2×D311yescharacteristic
178C5×#135—31no—
179C5×#131—31no—
180C5×#131C2×D311yescharacteristic, complemented
181#4096—31no—
182#4096—31no—
183#4094—31no—
184#4094C2×D311yescharacteristic, complemented
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—21no—
194#4053—31no—
195#4053—61no—
196#4053C2×D311yescharacteristic, complemented
197D5×M16—21no—
198D5×M16—31no—
199D5×M16—61no—
200D5×M16C2×D311yescharacteristic
201#4050—31no—
202#4047—21no—
203#4047—31no—
204#4047—61no—
205#4047C2×D311yescharacteristic, complemented
206C2×#676—21no—
207C2×#676—31no—
208C2×#676—61no—
209C2×#676C2×D311yescharacteristic
210C42×D5—31no—
211C5×#108—31no—
212C5×#104—31no—
213C5×#104—31no—
214C5×#97—31no—
215#3969—31no—
216#3969—31no—
217#3957—31no—
218#3957—31no—
219#3954—31no—
220#3954—31no—
221#3951—31no—
222C8×Dic5—31no—
223C8×Dic5—31no—
224#3937—31no—
225#3937—31no—
226#3935—31no—
227#2956—151noSylow
228C22×C3×D5—21no—
229C22×C3×D5#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—
242C2×C5×Dic3—21no—
243C5×D12C22×C411yescharacteristic
244C4×C5×D3—21no—
245C5×Dic6C22×C411yescharacteristic
246C3×C22⋊D5—21no—
247C3×C22⋊D5—21no—
248C3×C22⋊D5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5#4111yescharacteristic
251C3×D20—21no—
252C3×D20C22×C411yescharacteristic
253C3×C4×D5—21no—
254C3×C4×D5—21no—
255C3×C4×D5—21no—
256C3×C4×D5C22×C411yescharacteristic
257C3×C4×D5C22×C411yescharacteristic
258C3×C4×D5C2×D411yescharacteristic
259C3×C4×D5C2×D411yescharacteristic
260C3×Dic10—21no—
261C3×Dic10C22×C411yescharacteristic
262#1204—21no—
263#1203—21no—
264#1202—21no—
265#1201—21no—
266#1200—21no—
267D3×Dic5—21no—
268D5×Dic3—21no—
269D5×Dic3—42no—
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×#168C2×D411yescharacteristic
278C3×#168C2×D411yescharacteristic
279C5×C3⋊C8—21no—
280C5×C3⋊C8C22×C411yescharacteristic
281C5×C3⋊C8C22×C411yescharacteristic
282C2×C3×#41—51no—
283C2×#235—51no—
284C3×#131—51no—
285C3×#131—51no—
286C3×#131—51no—
287C3×#131—101no—
288C3×#131—101no—
289C3×#131C2×D511yescharacteristic, complemented
290C2×C3×M16—51no—
291C2×C3×M16—51no—
292C2×C3×M16—101no—
293C2×C3×M16—101no—
294#951—51no—
295#951—51no—
296#950—51no—
297#950—51no—
298#950—51no—
299#950C2×D511yescharacteristic
300#949—51no—
301#949—51no—
302#942—51no—
303#942—51no—
304#932—51no—
305#932—51no—
306C2×C4×Dic3—51no—
307C2×#208—51no—
308C2×#208—51no—
309#907—101no—
310#907—101no—
311D3×M16—101no—
312D3×M16—101no—
313#901—51no—
314#901—51no—
315#901—51no—
316#901C2×D511yescharacteristic, complemented
317#837—51no—
318#837—51no—
319#837—51no—
320#837C2×D511yescharacteristic, complemented
321#825—51no—
322#825—51no—
323#825—51no—
324#825C2×D511yescharacteristic, complemented
325#822—51no—
326#822—51no—
327#822—51no—
328#822C2×D511yescharacteristic, complemented
329#815—51no—
330#815C2×D511yescharacteristic, complemented
331C8×Dic3—51no—
332C8×Dic3—51no—
333C5×#41—31no—
334C5×#41C22×D311yescharacteristic
335#713—31no—
336#713C4×D311yescharacteristic
337Q8×D5—31no—
338Q8×D5C4×D311yescharacteristic
339#711—21no—
340#711—31no—
341#711—61no—
342#711C4×D311yescharacteristic
343D4×D5—21no—
344D4×D5—31no—
345D4×D5—61no—
346D4×D5C4×D311yescharacteristic
347#709—21no—
348#709—31no—
349#709—61no—
350#709C22×D311yescharacteristic
351C2×C4×D5—21no—
352C2×C4×D5—61no—
353C2×C4×D5—61no—
354C2×C4×D5C22×D311yescharacteristic
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#689—31no—
370#688—31no—
371#688—31no—
372#687—31no—
373#687—31no—
374#686—31no—
375#686—31no—
376C4×Dic5—31no—
377C4×Dic5—61no—
378#681—21no—
379#681—31no—
380#681—61no—
381#681C22×D311yescharacteristic
382C2×#168—21no—
383C2×#168—31no—
384C2×#168—61no—
385C2×#168C22×D311yescharacteristic
386Dic20—31no—
387D40—31no—
388#677—31no—
389#677—31no—
390#676—21no—
391#676—21no—
392#676—21no—
393#676—31no—
394#676—31no—
395#676—31no—
396#676—31no—
397#676—61no—
398#676—61no—
399#676—61no—
400#676#6711yescharacteristic
401#676#6711yescharacteristic
402#676#6711yescharacteristic
403#676#6711yescharacteristic
404C8×D5—21no—
405C8×D5—21no—
406C8×D5—21no—
407C8×D5—61no—
408C8×D5—61no—
409C8×D5—61no—
410#575—151no—
411#568—51no—
412#568—151no—
413#444—31no—
414#444—151no—
415#444—151no—
416#444—151no—
417#443—151no—
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×C3×D5—21no—
430C2×C3×D5—41no—
431C2×C3×D5—81no—
432C2×C3×D5C4×D411yescharacteristic
433C2×C3×D5C4×D411yescharacteristic
434D3×D5—81no—
435C3×C4×C5—21no—
436C3×C4×C5C23×C411yescharacteristic
437C3×C4×C5C22×D411yescharacteristic
438Dic15—22no—
439Dic15—21no—
440C3×Dic5—21no—
441C3×Dic5C4×D411yescharacteristic
442C3×Dic5C4×D411yescharacteristic
443C5×Dic3—21no—
444C5×Dic3—41no—
445C3×#41—51no—
446C3×#41—51no—
447C3×#41—51no—
448C3×#41—101no—
449C3×#41—101no—
450C3×#41C22×D511yescharacteristic
451C2×C3×Q8—51no—
452C2×C3×D4—51no—
453C2×C3×D4—101no—
454C22×C3×C4—51no—
455C22×C3×C4—101no—
456C2×#67—101no—
457C22×Dic3—101no—
458#235—51no—
459#235—51no—
460#235—51no—
461#235—101no—
462#235—101no—
463#235C22×D511yescharacteristic
464C2×D12—51no—
465C2×C4×D3—101no—
466C2×Dic6—51no—
467C3×M16—21no—
468C3×M16—51no—
469C3×M16—51no—
470C3×M16—51no—
471C3×M16—51no—
472C3×M16—51no—
473C3×M16—101no—
474C3×M16—101no—
475C3×M16—101no—
476C3×M16—101no—
477C3×M16C22×D511yescharacteristic
478C2×C3×C8—21no—
479C2×C3×C8—51no—
480C2×C3×C8—101no—
481C2×C3×C8—101no—
482C2×C3×C8—101no—
483C2×C3×C8—101no—
484C2×C3×C8C22×D511yescharacteristic
485#216—51no—
486#216—51no—
487#216—51no—
488#216C4×D511yescharacteristic, complemented
489#215—51no—
490#215—51no—
491#215—51no—
492#215C4×D511yescharacteristic, complemented
493#214—51no—
494#214—51no—
495#214—51no—
496#214C4×D511yescharacteristic, complemented
497#213—51no—
498#213—51no—
499#213—51no—
500#213C4×D511yescharacteristic, complemented
501C4×Dic3—51no—
502C4×Dic3—101no—
503C4×Dic3C22×D511yescharacteristic
504#208—51no—
505#208—51no—
506#208—51no—
507#208—51no—
508#208—51no—
509#208—101no—
510#208C22×D511yescharacteristic
511C2×C3⋊C8—51no—
512C2×C3⋊C8—101no—
513C2×C3⋊C8C22×D511yescharacteristic
514ΓL(1,𝔽25)—21no—
515ΓL(1,𝔽25)—101no—
516ΓL(1,𝔽25)—101no—
517ΓL(1,𝔽25)—101no—
518D3×C8—21no—
519D3×C8—101no—
520D3×C8—101no—
521D3×C8—101no—
522C22×D5—21no—
523C22×D5—61no—
524C22×D5#23511yescharacteristic
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—21no—
537C22⋊D5—21no—
538C22⋊D5—61no—
539C22⋊D5—61no—
540C22⋊D5—61no—
541C2×Dic5—21no—
542C2×Dic5—61no—
543C2×Dic5—61no—
544C2×Dic5#23511yescharacteristic
545D20—21no—
546D20—31no—
547D20—61no—
548D20C2×C4×D311yescharacteristic
549C4×D5—21no—
550C4×D5—21no—
551C4×D5—21no—
552C4×D5—61no—
553C4×D5—61no—
554C4×D5—61no—
555C4×D5—122no—
556C4×D5C2×C4×D311yescharacteristic
557C4×D5C2×C4×D311yescharacteristic
558C4×D5C2×#6711yescharacteristic
559C4×D5C2×#6711yescharacteristic
560Dic10—21no—
561Dic10—31no—
562Dic10—61no—
563Dic10C2×C4×D311yescharacteristic
564C5×C8—21no—
565C5×C8—31no—
566C5×C8—31no—
567C5×C8—61no—
568C5×C8C2×#6711yescharacteristic
569C5×C8C2×#6711yescharacteristic
570#168—21no—
571#168—31no—
572#168—31no—
573#168—61no—
574#168C2×#6711yescharacteristic
575#168C2×#6711yescharacteristic
576C2×#41—51no—
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—151no—
588#135—151no—
589#135—151no—
590#131—31no—
591#131—51no—
592#131—51no—
593#131—51no—
594#131—101no—
595#131—101no—
596#131—151no—
597#131—151no—
598#131—151no—
599#131—301no—
600#131—301no—
601#131D3×D511yescharacteristic, complemented
602C2×M16—51no—
603C2×M16—51no—
604C2×M16—101no—
605C2×M16—101no—
606C2×M16—151no—
607C2×M16—151no—
608C2×M16—301no—
609C2×M16—301no—
610C2×C42—151no—
611#108—31no—
612#108—151no—
613#108—151no—
614#108—151no—
615#104—31no—
616#104—31no—
617#104—151no—
618#104—151no—
619#104—151no—
620#104—151no—
621#104—151no—
622#104—151no—
623#97—31no—
624#97—151no—
625C4×C8—151no—
626C4×C8—151no—
627C2×C3×C5—21no—
628C2×C3×C5—41no—
629C2×C3×C5C2×C4×D411yescharacteristic
630D15—41no—
631C3×D5—21no—
632C3×D5—21no—
633C3×D5—41no—
634C5×D3—41no—
635C23×C3—51no—
636C23×C3—101no—
637C22×D3—101no—
638C3×Q8—51no—
639C3×Q8—101no—
640C3×Q8C2×C4×D511yescharacteristic
641C3×D4—21no—
642C3×D4—51no—
643C3×D4—101no—
644C3×D4—101no—
645C3×D4—101no—
646C3×D4—101no—
647C3×D4C2×C4×D511yescharacteristic
648C2×C3×C4—21no—
649C2×C3×C4—51no—
650C2×C3×C4—51no—
651C2×C3×C4—51no—
652C2×C3×C4—51no—
653C2×C3×C4—51no—
654C2×C3×C4—101no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4C23×D511yescharacteristic
659#67—21no—
660#67—101no—
661#67—101no—
662#67—101no—
663C2×Dic3—21no—
664C2×Dic3—101no—
665C2×Dic3—101no—
666C2×Dic3—202no—
667D12—51no—
668D12—101no—
669D12C2×C4×D511yescharacteristic
670C4×D3—21no—
671C4×D3—101no—
672C4×D3—101no—
673C4×D3—101no—
674Dic6—51no—
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×C5C2×#23511yescharacteristic
692C2×D5—21no—
693C2×D5—41no—
694C2×D5—61no—
695C2×D5—81no—
696C2×D5—241no—
697C2×D5C4×#6711yescharacteristic
698C2×D5C4×#6711yescharacteristic
699C4×C5—21no—
700C4×C5—61no—
701C4×C5—121no—
702C4×C5C22×C4×D311yescharacteristic
703C4×C5C22×#6711yescharacteristic
704Dic5—21no—
705Dic5—62no—
706Dic5—61no—
707Dic5C4×#6711yescharacteristic
708Dic5C4×#6711yescharacteristic
709#41—31no—
710#41—51no—
711#41—51no—
712#41—51no—
713#41—101no—
714#41—101no—
715#41—151no—
716#41—151no—
717#41—151no—
718#41—301no—
719#41—301no—
720#41C2×D3×D511yescharacteristic
721C2×Q8—51no—
722C2×Q8—151no—
723C2×D4—51no—
724C2×D4—101no—
725C2×D4—151no—
726C2×D4—301no—
727C22×C4—51no—
728C22×C4—101no—
729C22×C4—301no—
730C22×C4—301no—
731Q16—31no—
732Q16—151no—
733Q16—151no—
734Q16—151no—
735SD16—31no—
736SD16—31no—
737SD16—151no—
738SD16—151no—
739SD16—151no—
740SD16—151no—
741SD16—151no—
742SD16—151no—
743D8—31no—
744D8—151no—
745D8—151no—
746D8—151no—
747M16—21no—
748M16—31no—
749M16—51no—
750M16—51no—
751M16—51no—
752M16—51no—
753M16—51no—
754M16—61no—
755M16—101no—
756M16—101no—
757M16—101no—
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—101no—
774C2×C8—101no—
775C2×C8—101no—
776C2×C8—101no—
777C2×C8—151no—
778C2×C8—301no—
779C2×C8—301no—
780C2×C8—301no—
781C2×C8—301no—
782C2×C8C2×D3×D511yescharacteristic
783C42—31no—
784C42—151no—
785C42—301no—
786C3×C5#295611yescharacteristic, complemented, Hall
787C22×C3—21no—
788C22×C3—51no—
789C22×C3—51no—
790C22×C3—101no—
791C22×C3—201no—
792C22×C3—401no—
793C22×C3D5×#4111yescharacteristic
794C2×D3—21no—
795C2×D3—101no—
796C2×D3—401no—
797C3×C4—21no—
798C3×C4—51no—
799C3×C4—51no—
800C3×C4—101no—
801C3×C4C22×C4×D511yescharacteristic
802C3×C4C2×D4×D511yescharacteristic
803Dic3—21no—
804Dic3—41no—
805Dic3—102no—
806Dic3—101no—
807C2×C5—21no—
808C2×C5—41no—
809C2×C5—121no—
810C2×C5C2×C4×#6711yescharacteristic
811D5—21no—
812D5—21no—
813D5—41no—
814D5—121no—
815C23—51no—
816C23—101no—
817C23—301no—
818Q8—31no—
819Q8—51no—
820Q8—101no—
821Q8—151no—
822Q8—301no—
823Q8C4×D3×D511yescharacteristic
824D4—21no—
825D4—31no—
826D4—51no—
827D4—61no—
828D4—101no—
829D4—101no—
830D4—101no—
831D4—101no—
832D4—151no—
833D4—301no—
834D4—301no—
835D4—301no—
836D4—301no—
837D4C4×D3×D511yescharacteristic
838C2×C4—21no—
839C2×C4—51no—
840C2×C4—51no—
841C2×C4—51no—
842C2×C4—51no—
843C2×C4—51no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—101no—
847C2×C4—101no—
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—
867C8D5×#6711yescharacteristic
868C8D5×#6711yescharacteristic
869C2×C3—21no—
870C2×C3—41no—
871C2×C3—101no—
872C2×C3—101no—
873C2×C3—201no—
874C2×C3C4×D4×D511yescharacteristic
875D3—41no—
876D3—201no—
877C5#8381111yescharacteristic, complemented, Sylow
878C22—21no—
879C22—51no—
880C22—51no—
881C22—61no—
882C22—101no—
883C22—201no—
884C22—301no—
885C22—401no—
886C22—1201no—
887C22D5×#23511yescharacteristic
888C4—21no—
889C4—51no—
890C4—51no—
891C4—61no—
892C4—101no—
893C4—121no—
894C4—302no—
895C4—301no—
896C4C2×C4×D3×D511yescharacteristic
897C4C2×D5×#6711yescharacteristic
898C3#1061162911yescharacteristic, complemented, Sylow
899C2—21no—
900C2—41no—
901C2—101no—
902C2—101no—
903C2—121no—
904C2—201no—
905C2—601no—
906C2C4×D5×#6711yescharacteristic
subgroupG/H
centerC4C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#131C22
socleC2×C3×C5C2×C4×D4
prime radical#11755315C2
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. C3×#66084C2semidirect
3. #11753949C2semidirect
4. #11751245C2semidirect
5. C5×#5145C2semidirect
6. #11749435C2semidirect
7. #11749432C2semidirect
8. D5×#837C2semidirect
9. D5×#825C2semidirect
10. #11748207C2semidirect
11. #11748202C2semidirect
12. #11748171C2semidirect
13. #11748077C2semidirect
14. #11748074C2semidirect
15. #11747601C2semidirect
19. C3×C5×#131C22semidirect
21. #91790C22semidirect
23. C5×#901C22semidirect
24. C3×#4094C22semidirect
26. C3×#4053C22semidirect
30. C3×#4047C22semidirect
33. #91515C4semidirect
34. #91513C4semidirect
35. #91508C4semidirect
36. #91502C4semidirect
37. #91491C4semidirect
38. #91489C4semidirect
39. #91484C4semidirect
40. #91478C4semidirect
45. #91290C22semidirect
46. #91286C22semidirect
52. #91121C22semidirect
53. #91109C22semidirect
54. #91106C22semidirect
55. C8×Dic15C22semidirect
56. C5×#837C22semidirect
57. C5×#825C22semidirect
58. C5×#822C22semidirect
59. C5×#815C22semidirect
60. #90993C22semidirect
61. #90992C22semidirect
62. #90980C22semidirect
63. #90978C22semidirect
64. #90977C22semidirect
65. #90976C22semidirect
66. #90953C22semidirect
67. #90951C22semidirect
71. #66084D3semidirect
110. #6718C2×C4semidirect
111. #6717C2×C4semidirect
112. #6716C2×C4semidirect
113. #6715C2×C4semidirect
119. C5×#216C2×C4semidirect
120. C5×#215C2×C4semidirect
121. C5×#214C2×C4semidirect
122. C5×#213C2×C4semidirect
143. #6662C2×C4semidirect
144. #6661C2×C4semidirect
145. #6658C2×C4semidirect
146. #6657C2×C4semidirect
147. #6656C2×C4semidirect
148. #6655C2×C4semidirect
149. #6653C2×C4semidirect
150. #6652C2×C4semidirect
168. #5145D5semidirect
180. C5×#131C2×D3semidirect
184. #4094C2×D3semidirect
196. #4053C2×D3semidirect
205. #4047C2×D3semidirect
289. C3×#131C2×D5semidirect
316. #901C2×D5semidirect
320. #837C2×D5semidirect
324. #825C2×D5semidirect
328. #822C2×D5semidirect
330. #815C2×D5semidirect
488. #216C4×D5semidirect
492. #215C4×D5semidirect
496. #214C4×D5semidirect
500. #213C4×D5semidirect
601. #131D3×D5semidirect
786. C3×C5#2956semidirect
877. C5#83811semidirect
898. C3#10611629semidirect

Maximal subgroups

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

subgroupindex
C3×#660842
#117553152
#117539492
#117512452
C5×#51452
#117494352
#117494322
D5×#8372
D5×#8252
#117482072
#117482022
#117481712
#117480772
#117480742
#117476012
#106116293
#838115