Finite Group Databasebeta

← #14418138

Subgroups — #14418138

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#11755315C211yesmaximal, characteristic
2#11755296C211yesmaximal, characteristic, complemented
3#11754014C211yesmaximal, characteristic, complemented
4#11750924C211yesmaximal, characteristic, complemented
5C5×#4823C211yesmaximal, characteristic, complemented
6C3×D5×#104C211yesmaximal, characteristic, complemented
7#11749442C211yesmaximal, characteristic, complemented
8#11749438C211yesmaximal, characteristic, complemented
9#11748204C211yesmaximal, characteristic, complemented
10#11748174C211yesmaximal, characteristic, complemented
11#11748171C211yesmaximal, characteristic, complemented
12D5×#805C211yesmaximal, characteristic, complemented
13#11747107C211yesmaximal, characteristic, complemented
14#11747017C211yesmaximal, characteristic, complemented
15#11747003C211yesmaximal, characteristic, complemented
16#10611629—31nomaximal, Hall
17C3×D5×#41C2211yescharacteristic
18D5×#235C2211yescharacteristic
19#91839C2211yescharacteristic
20#91837C2211yescharacteristic, complemented
21#91796C2211yescharacteristic, complemented
22C5×#950C2211yescharacteristic
23C5×#948C2211yescharacteristic, complemented
24C5×#907C2211yescharacteristic, complemented
25C3×D5×M16C2211yescharacteristic
26C3×C42×D5C2211yescharacteristic
27#91515C411yescharacteristic, complemented
28#91513C411yescharacteristic, complemented
29#91508C411yescharacteristic, complemented
30#91502C411yescharacteristic, complemented
31#91491C411yescharacteristic, complemented
32#91489C411yescharacteristic, complemented
33#91484C411yescharacteristic, complemented
34#91478C411yescharacteristic, complemented
35#91311C2211yescharacteristic
36#91297C2211yescharacteristic
37C2×#6649—21no—
38C2×#6649C2211yescharacteristic
39C2×#6649C2211yescharacteristic
40#91291C2211yescharacteristic, complemented
41#91288C2211yescharacteristic, complemented
42#91284—21no—
43#91284C2211yescharacteristic, complemented
44#91283—21no—
45#91283C2211yescharacteristic, complemented
46D5×#208—21no—
47D5×#208C2211yescharacteristic
48#91266—21no—
49#91265—21no—
50#91246—21no—
51D3×#676—21no—
52C3×C5×#104C2211yescharacteristic, complemented
53#91106C2211yescharacteristic, complemented
54#91089C2211yescharacteristic, complemented
55#91087C2211yescharacteristic, complemented
56C5×#822C2211yescharacteristic, complemented
57C5×#805C2211yescharacteristic, complemented
58C5×#803C2211yescharacteristic, complemented
59C3×#3969C2211yescharacteristic, complemented
60C3×#3957C2211yescharacteristic, complemented
61C3×#3937C2211yescharacteristic, complemented
62#90993C2211yescharacteristic, complemented
63#90992C2211yescharacteristic, complemented
64#90981C2211yescharacteristic, complemented
65#90979C2211yescharacteristic, complemented
66Dic5×C3⋊C8C2211yescharacteristic, complemented
67Dic5×C3⋊C8C2211yescharacteristic, complemented
68#78980—51nomaximal, Hall
69#66102—31no—
70#66084—31no—
71#66084—31no—
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×#104D311yescharacteristic, complemented
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×D5—21no—
97C2×C3×C4×D5C2311yescharacteristic
98D5×#67—21no—
99#6782—21no—
100D5×D12C2×C411yescharacteristic
101C4×D3×D5—21no—
102#6773C2×C411yescharacteristic
103#6772C2×C411yescharacteristic
104#6771—21no—
105D5×Dic6C2×C411yescharacteristic
106C3×C5×M16C2311yescharacteristic
107C3×C42×C5C2311yescharacteristic
108#6718C2×C411yescharacteristic, complemented
109#6717C2×C411yescharacteristic, complemented
110#6716C2×C411yescharacteristic, complemented
111#6715C2×C411yescharacteristic, complemented
112#6710—21no—
113#6710C2311yescharacteristic
114C2×C3⋊#168—21no—
115C2×C3⋊#168C2311yescharacteristic
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
123C5×#208—21no—
124C5×#208C2311yescharacteristic
125C2×C5×C3⋊C8—21no—
126C2×C5×C3⋊C8C2311yescharacteristic
127C2×C5×C3⋊C8C2311yescharacteristic
128C5×ΓL(1,𝔽25)—21no—
129C5×D3×C8—21no—
130C3×C4×Dic5—21no—
131C3×C4×Dic5C2311yescharacteristic
132C3×#681C2311yescharacteristic
133C3×#676—21no—
134C3×C8×D5—21no—
135#6662C2×C411yescharacteristic, complemented
136#6661C2×C411yescharacteristic, complemented
137#6658C2×C411yescharacteristic, complemented
138#6657C2×C411yescharacteristic, complemented
139#6656C2×C411yescharacteristic, complemented
140#6655C2×C411yescharacteristic, complemented
141#6653C2×C411yescharacteristic, complemented
142#6652C2×C411yescharacteristic, complemented
143#6651—21no—
144#6650—21no—
145#6649—21no—
146#6649—21no—
147#6649—21no—
148#6649C2×C411yescharacteristic
149#6649C2×C411yescharacteristic
150#6649C2×C411yescharacteristic
151#6649C2×C411yescharacteristic
152#6649D411yescharacteristic
153#6649D411yescharacteristic
154#6649D411yescharacteristic
155#6649D411yescharacteristic
156#6648—21no—
157D3×#168—21no—
158D5×C3⋊C8—21no—
159D5×C3⋊C8—21no—
160D5×C3⋊C8—21no—
161#5822—51no—
162#5819—51no—
163#5745—51no—
164C2×C3×#104—51no—
165#5124—51no—
166C2×#805—51no—
167C4×#208—51no—
168#4824—51no—
169#4824—51no—
170#4824—51no—
171#4824—51no—
172#4823—51no—
173#4823—51no—
174#4823—51no—
175#4823D511yescharacteristic, complemented
176D5×#41—31no—
177D5×#41C2×D311yescharacteristic
178C5×#135—31no—
179C5×#131—31no—
180C5×#131—31no—
181#4096—31no—
182#4096—31no—
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—61no—
199D5×M16—61no—
200D5×M16C2×D311yescharacteristic
201#4050—31no—
202#4047—31no—
203#4047—31no—
204#4047—61no—
205#4047—61no—
206C2×#676—31no—
207C2×#676—31no—
208C2×#676—61no—
209C2×#676—61no—
210C42×D5C2×D311yescharacteristic
211C5×#108—31no—
212C5×#104—31no—
213C5×#104C2×D311yescharacteristic, complemented
214C5×#97—31no—
215#3969—31no—
216#3969C2×D311yescharacteristic, complemented
217#3957—31no—
218#3957C2×D311yescharacteristic, complemented
219#3954—31no—
220#3954—31no—
221#3951—31no—
222C8×Dic5—31no—
223C8×Dic5—31no—
224#3937—31no—
225#3937C2×D311yescharacteristic, complemented
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×C5—21no—
236C2×C3×C4×C5C2411yescharacteristic
237#1220—21no—
238D60C22×C411yescharacteristic
239C4×D15—21no—
240Dic30C22×C411yescharacteristic
241C5×#67—21no—
242C5×D12C22×C411yescharacteristic
243C4×C5×D3—21no—
244C5×Dic6C22×C411yescharacteristic
245C3×C22⋊D5—21no—
246C3×C22⋊D5—21no—
247C3×C22⋊D5—21no—
248C2×C3×Dic5—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×D5—42no—
257C3×C4×D5C22×C411yescharacteristic
258C3×C4×D5C22×C411yescharacteristic
259C3×C4×D5C2×D411yescharacteristic
260C3×C4×D5C2×D411yescharacteristic
261C3×Dic10—21no—
262C3×Dic10C22×C411yescharacteristic
263#1204—21no—
264#1203—21no—
265#1202—21no—
266#1201—21no—
267#1200—21no—
268D3×Dic5—21no—
269D5×Dic3—21no—
270C3×C5×C8—21no—
271C3⋊#168—21no—
272C3⋊#168C22×C411yescharacteristic
273C3⋊#168C22×C411yescharacteristic
274C3⋊#168C2×D411yescharacteristic
275C3⋊#168C2×D411yescharacteristic
276C3×#168—21no—
277C5×C3⋊C8—21no—
278C5×C3⋊C8C22×C411yescharacteristic
279C5×C3⋊C8C22×C411yescharacteristic
280C5×C3⋊C8C2×D411yescharacteristic
281C5×C3⋊C8C2×D411yescharacteristic
282C2×C3×#41—51no—
283C2×#235—51no—
284C2×C3×M16—51no—
285C2×C3×C42—51no—
286#951—51no—
287#951—51no—
288#950—51no—
289#950—51no—
290#950—51no—
291#950C2×D511yescharacteristic
292#949—51no—
293#949—51no—
294#948—51no—
295#948—51no—
296#948—51no—
297#948—101no—
298#948—101no—
299#948C2×D511yescharacteristic, complemented
300#942—51no—
301#942—51no—
302#932—51no—
303#932—51no—
304C2×#208—51no—
305C2×#208—51no—
306C2×#208—51no—
307C2×#208—101no—
308C2×#208—101no—
309#907—51no—
310#907—51no—
311#907—51no—
312#907C2×D511yescharacteristic, complemented
313D3×M16—101no—
314D3×M16—101no—
315#901—101no—
316#901—101no—
317C3×#104—51no—
318C3×#104—51no—
319C3×#104—51no—
320C3×#104C2×D511yescharacteristic, complemented
321#822—51no—
322#822—51no—
323#822—51no—
324#822C2×D511yescharacteristic, complemented
325#805—51no—
326#805—51no—
327#805—51no—
328#805C2×D511yescharacteristic, complemented
329#803—51no—
330#803C2×D511yescharacteristic, complemented
331C4×C3⋊C8—51no—
332C4×C3⋊C8—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—21no—
353C2×C4×D5—61no—
354C2×C4×D5C22×D311yescharacteristic
355C5×Q16—31no—
356C5×SD16—31no—
357C5×SD16—31no—
358C5×D8—31no—
359C5×M16—31no—
360C5×M16—61no—
361C5×M16—61no—
362C5×M16C22×D311yescharacteristic
363C2×C5×C8—31no—
364C2×C5×C8—31no—
365C2×C5×C8—61no—
366C2×C5×C8—61no—
367C42×C5C22×D311yescharacteristic
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—21no—
377C4×Dic5C22×D311yescharacteristic
378#681—31no—
379#681—61no—
380#681—61no—
381#681C22×D311yescharacteristic
382C2×#168—31no—
383C2×#168—31no—
384C2×#168—61no—
385C2×#168—61no—
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—151no—
418#443—151no—
419#443—151no—
420#443—151no—
421#430—151no—
422C2×#104—51no—
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×C5—41no—
437C3×C4×C5C23×C411yescharacteristic
438C3×C4×C5C22×D411yescharacteristic
439Dic15—21no—
440C3×Dic5—22no—
441C3×Dic5—21no—
442C3×Dic5C4×D411yescharacteristic
443C3×Dic5C4×D411yescharacteristic
444C5×Dic3—21no—
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—
456C22×C3×C4—101no—
457C2×#67—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—51no—
468C3×M16—101no—
469C3×M16C22×D511yescharacteristic
470C2×C3×C8—101no—
471C3×C42—51no—
472C3×C42—101no—
473C3×C42C22×D511yescharacteristic
474#216—51no—
475#216—51no—
476#216—51no—
477#216C4×D511yescharacteristic, complemented
478#215—51no—
479#215—51no—
480#215—51no—
481#215C4×D511yescharacteristic, complemented
482#214—51no—
483#214—51no—
484#214—51no—
485#214C4×D511yescharacteristic, complemented
486#213—51no—
487#213—51no—
488#213—51no—
489#213C4×D511yescharacteristic, complemented
490#208—21no—
491#208—51no—
492#208—51no—
493#208—51no—
494#208—51no—
495#208—51no—
496#208—51no—
497#208—51no—
498#208—51no—
499#208—51no—
500#208—101no—
501#208—101no—
502#208—101no—
503#208—101no—
504#208C22×D511yescharacteristic
505C2×C3⋊C8—21no—
506C2×C3⋊C8—51no—
507C2×C3⋊C8—51no—
508C2×C3⋊C8—101no—
509C2×C3⋊C8—101no—
510C2×C3⋊C8—101no—
511C2×C3⋊C8—101no—
512C2×C3⋊C8C22×D511yescharacteristic
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#23711yescharacteristic
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—21no—
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—21no—
543C2×Dic5—61no—
544C2×Dic5#23711yescharacteristic
545D20—21no—
546D20—31no—
547D20—61no—
548D20C2×C4×D311yescharacteristic
549C4×D5—21no—
550C4×D5—21no—
551C4×D5—21no—
552C4×D5—42no—
553C4×D5—61no—
554C4×D5—61no—
555C4×D5—61no—
556C4×D5C2×C4×D311yescharacteristic
557C4×D5C2×C4×D311yescharacteristic
558C4×D5D3×D411yescharacteristic
559C4×D5D3×D411yescharacteristic
560Dic10—21no—
561Dic10—31no—
562Dic10—61no—
563Dic10C2×C4×D311yescharacteristic
564C5×C8—21no—
565C5×C8—31no—
566C5×C8—31no—
567C5×C8—31no—
568C5×C8—31no—
569C5×C8—61no—
570#168—21no—
571#168—31no—
572#168—31no—
573#168—31no—
574#168—31no—
575#168—61no—
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—31no—
592#131—151no—
593#131—151no—
594#131—151no—
595#131—151no—
596#131—151no—
597#131—151no—
598#131—301no—
599#131—301no—
600#131—301no—
601#131—301no—
602C2×M16—51no—
603C2×M16—151no—
604C2×M16—151no—
605C2×M16—151no—
606C2×M16—301no—
607C2×M16—301no—
608C2×M16—301no—
609C2×M16—301no—
610C2×C42—51no—
611#108—31no—
612#108—151no—
613#108—151no—
614#108—151no—
615#104—31no—
616#104—51no—
617#104—51no—
618#104—51no—
619#104—151no—
620#104—151no—
621#104—151no—
622#104D3×D511yescharacteristic, complemented
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—21no—
650C2×C3×C4—51no—
651C2×C3×C4—51no—
652C2×C3×C4—51no—
653C2×C3×C4—51no—
654C2×C3×C4—51no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—101no—
660C2×C3×C4—202no—
661C2×C3×C4C23×D511yescharacteristic
662#67—21no—
663#67—101no—
664#67—101no—
665#67—101no—
666C2×Dic3—101no—
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—101no—
679C3⋊C8—21no—
680C3⋊C8—51no—
681C3⋊C8—51no—
682C3⋊C8—51no—
683C3⋊C8—51no—
684C3⋊C8—101no—
685C3⋊C8C2×C4×D511yescharacteristic
686C3⋊C8C2×C4×D511yescharacteristic
687C3⋊C8D4×D511yescharacteristic
688C3⋊C8D4×D511yescharacteristic
689C22×C5—21no—
690C22×C5—61no—
691C22×C5C2×#23711yescharacteristic
692C2×D5—21no—
693C2×D5—41no—
694C2×D5—61no—
695C2×D5—81no—
696C2×D5—241no—
697C2×D5#67⋊C411yescharacteristic
698C2×D5#67⋊C411yescharacteristic
699C4×C5—21no—
700C4×C5—41no—
701C4×C5—61no—
702C4×C5C22×C4×D311yescharacteristic
703C4×C5C2×D3×D411yescharacteristic
704Dic5—22no—
705Dic5—21no—
706Dic5—61no—
707Dic5#67⋊C411yescharacteristic
708Dic5#67⋊C411yescharacteristic
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—101no—
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—31no—
748M16—51no—
749M16—61no—
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—31no—
770C2×C8—31no—
771C2×C8—61no—
772C2×C8—61no—
773C2×C8—101no—
774C2×C8—151no—
775C2×C8—151no—
776C2×C8—301no—
777C2×C8—301no—
778C2×C8—301no—
779C2×C8—301no—
780C2×C8—301no—
781C2×C8—301no—
782C2×C8—301no—
783C42—51no—
784C42—101no—
785C42C2×D3×D511yescharacteristic
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—41no—
799C3×C4—51no—
800C3×C4—51no—
801C3×C4—102no—
802C3×C4—101no—
803C3×C4C22×C4×D511yescharacteristic
804C3×C4C2×D4×D511yescharacteristic
805Dic3—21no—
806Dic3—101no—
807C2×C5—21no—
808C2×C5—41no—
809C2×C5—121no—
810C2×C5C2×#67⋊C411yescharacteristic
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—21no—
840C2×C4—51no—
841C2×C4—51no—
842C2×C4—51no—
843C2×C4—51no—
844C2×C4—51no—
845C2×C4—61no—
846C2×C4—101no—
847C2×C4—101no—
848C2×C4—101no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—202no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4C22×D3×D511yescharacteristic
857C8—21no—
858C8—31no—
859C8—31no—
860C8—31no—
861C8—31no—
862C8—61no—
863C8—101no—
864C8—151no—
865C8—151no—
866C8—151no—
867C8—151no—
868C8—301no—
869C2×C3—21no—
870C2×C3—41no—
871C2×C3—101no—
872C2×C3—101no—
873C2×C3—201no—
874C2×C3C4×D4×D511yescharacteristic
875D3—41no—
876D3—201no—
877C5#7898011yescharacteristic, complemented, Sylow
878C22—21no—
879C22—51no—
880C22—51no—
881C22—61no—
882C22—101no—
883C22—201no—
884C22—301no—
885C22—401no—
886C22—1201no—
887C22D5×#23711yescharacteristic
888C4—21no—
889C4—41no—
890C4—51no—
891C4—51no—
892C4—61no—
893C4—102no—
894C4—101no—
895C4—301no—
896C4C2×C4×D3×D511yescharacteristic
897C4D3×D4×D511yescharacteristic
898C3#1061162911yescharacteristic, complemented, Sylow
899C2—21no—
900C2—41no—
901C2—101no—
902C2—101no—
903C2—121no—
904C2—201no—
905C2—601no—
906C2D5×#67⋊C411yescharacteristic
subgroupG/H
centerC4D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#104C22
socleC2×C3×C5C2×C4×D4
prime radical#11755315C2
cosocleC2×C3×C4×C5C24
hypercenter#104D3×D5
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #11755296C2semidirect
3. #11754014C2semidirect
4. #11750924C2semidirect
5. C5×#4823C2semidirect
6. C3×D5×#104C2semidirect
7. #11749442C2semidirect
8. #11749438C2semidirect
9. #11748204C2semidirect
10. #11748174C2semidirect
11. #11748171C2semidirect
12. D5×#805C2semidirect
13. #11747107C2semidirect
14. #11747017C2semidirect
15. #11747003C2semidirect
20. #91837C22semidirect
21. #91796C22semidirect
23. C5×#948C22semidirect
24. C5×#907C22semidirect
27. #91515C4semidirect
28. #91513C4semidirect
29. #91508C4semidirect
30. #91502C4semidirect
31. #91491C4semidirect
32. #91489C4semidirect
33. #91484C4semidirect
34. #91478C4semidirect
40. #91291C22semidirect
41. #91288C22semidirect
43. #91284C22semidirect
45. #91283C22semidirect
52. C3×C5×#104C22semidirect
53. #91106C22semidirect
54. #91089C22semidirect
55. #91087C22semidirect
56. C5×#822C22semidirect
57. C5×#805C22semidirect
58. C5×#803C22semidirect
59. C3×#3969C22semidirect
60. C3×#3957C22semidirect
61. C3×#3937C22semidirect
62. #90993C22semidirect
63. #90992C22semidirect
64. #90981C22semidirect
65. #90979C22semidirect
66. Dic5×C3⋊C8C22semidirect
67. Dic5×C3⋊C8C22semidirect
81. D5×#104D3semidirect
108. #6718C2×C4semidirect
109. #6717C2×C4semidirect
110. #6716C2×C4semidirect
111. #6715C2×C4semidirect
119. C5×#216C2×C4semidirect
120. C5×#215C2×C4semidirect
121. C5×#214C2×C4semidirect
122. C5×#213C2×C4semidirect
135. #6662C2×C4semidirect
136. #6661C2×C4semidirect
137. #6658C2×C4semidirect
138. #6657C2×C4semidirect
139. #6656C2×C4semidirect
140. #6655C2×C4semidirect
141. #6653C2×C4semidirect
142. #6652C2×C4semidirect
175. #4823D5semidirect
213. C5×#104C2×D3semidirect
216. #3969C2×D3semidirect
218. #3957C2×D3semidirect
225. #3937C2×D3semidirect
299. #948C2×D5semidirect
312. #907C2×D5semidirect
320. C3×#104C2×D5semidirect
324. #822C2×D5semidirect
328. #805C2×D5semidirect
330. #803C2×D5semidirect
477. #216C4×D5semidirect
481. #215C4×D5semidirect
485. #214C4×D5semidirect
489. #213C4×D5semidirect
622. #104D3×D5semidirect
786. C3×C5#2956semidirect
877. C5#78980semidirect
898. C3#10611629semidirect

Maximal subgroups

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

subgroupindex
#117553152
#117552962
#117540142
#117509242
C5×#48232
C3×D5×#1042
#117494422
#117494382
#117482042
#117481742
#117481712
D5×#8052
#117471072
#117470172
#117470032
#106116293
#789805