Finite Group Databasebeta

← #14418031

Subgroups — #14418031

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755329C211yesmaximal, characteristic
2#11755299C211yesmaximal, characteristic, complemented
3#11754017C211yesmaximal, characteristic, complemented
4#11750922C211yesmaximal, characteristic, complemented
5C5×#4824C211yesmaximal, characteristic, complemented
6C3×#65112C211yesmaximal, characteristic, complemented
7#11749436C211yesmaximal, characteristic, complemented
8#11749433C211yesmaximal, characteristic, complemented
9#11748208C211yesmaximal, characteristic, complemented
10#11748206C211yesmaximal, characteristic, complemented
11#11748173C211yesmaximal, characteristic, complemented
12#11747113C211yesmaximal, characteristic, complemented
13#11747019C211yesmaximal, characteristic, complemented
14#11747016C211yesmaximal, characteristic, complemented
15#11746982C211yesmaximal, characteristic, complemented
16#10611619—31nomaximal, Hall
17#41×D15C2211yescharacteristic
18#92016C2211yescharacteristic
19M16×D15C2211yescharacteristic
20#91761C2211yescharacteristic
21C5×#950C2211yescharacteristic
22C5×#948C2211yescharacteristic, complemented
23C5×#907C2211yescharacteristic, complemented
24C3×#4096C2211yescharacteristic
25C3×#4094C2211yescharacteristic, complemented
26C3×#4053C2211yescharacteristic, complemented
27#91524C411yescharacteristic, complemented
28#91522C411yescharacteristic, complemented
29#91512C411yescharacteristic, complemented
30#91506C411yescharacteristic, complemented
31#91500C411yescharacteristic, complemented
32#91498C411yescharacteristic, complemented
33#91488C411yescharacteristic, complemented
34#91482C411yescharacteristic, complemented
35#91311C2211yescharacteristic
36#91303C2211yescharacteristic
37C2×#6651C2211yescharacteristic
38#91292—21no—
39#91292C2211yescharacteristic
40#91291—21no—
41#91291C2211yescharacteristic, complemented
42#91290—21no—
43#91290C2211yescharacteristic, complemented
44C2×#6648—21no—
45C2×#6648C2211yescharacteristic
46#91286C2211yescharacteristic, complemented
47#91283C2211yescharacteristic, complemented
48#91267—21no—
49#91266—21no—
50#91246—21no—
51D3×C8×D5—21no—
52C3×C5×#104C2211yescharacteristic, complemented
53#91121C2211yescharacteristic, complemented
54#91109C2211yescharacteristic, complemented
55#91089C2211yescharacteristic, complemented
56C5×#822C2211yescharacteristic, complemented
57C5×#805C2211yescharacteristic, complemented
58C4×C5×C3⋊C8C2211yescharacteristic, complemented
59C3×#3954C2211yescharacteristic, complemented
60C3×#3937C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62#90993C2211yescharacteristic, complemented
63#90991C2211yescharacteristic, complemented
64#90978C2211yescharacteristic, complemented
65#90976C2211yescharacteristic, complemented
66#90954C2211yescharacteristic, complemented
67#90951C2211yescharacteristic, complemented
68#79897—51nomaximal, Hall
69#66102—31no—
70D5×#131—31no—
71D5×#131—31no—
72C5×#443—31no—
73#65486—31no—
74#65433—31no—
75#65433—31no—
76#65183—31no—
77#65182—31no—
78#65112—31no—
79#65112D311yescharacteristic, complemented
80#65110—31no—
81#65110—31no—
82#64989—31no—
83#64978—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—
98#6780—21no—
99#6777C2×C411yescharacteristic
100C4×D3×D5—21no—
101#6771—21no—
102D15⋊Q8C2×C411yescharacteristic
103#6768C2×C411yescharacteristic
104#6766C2×C411yescharacteristic
105C3×C5×M16C2311yescharacteristic
106C3×C42×C5C2311yescharacteristic
107#6714—21no—
108#6712—21no—
109C4×Dic15C2311yescharacteristic
110#6710C2311yescharacteristic
111#6705—21no—
112C8×D15—21no—
113C5×#216C2×C411yescharacteristic
114C5×#215C2×C411yescharacteristic
115C5×#214C2×C411yescharacteristic
116C5×#213C2×C411yescharacteristic
117C5×#208—21no—
118C5×#208C2311yescharacteristic
119C2×C5×C3⋊C8—21no—
120C2×C5×C3⋊C8C2311yescharacteristic
121C2×C5×C3⋊C8C2311yescharacteristic
122C5×ΓL(1,𝔽25)—21no—
123C5×D3×C8—21no—
124C3×#689C2×C411yescharacteristic
125C3×#688C2×C411yescharacteristic
126C3×#687C2×C411yescharacteristic
127C3×#686C2×C411yescharacteristic
128C3×#681—21no—
129C3×#681C2311yescharacteristic
130C2×C3×#168—21no—
131C2×C3×#168C2311yescharacteristic
132C2×C3×#168C2311yescharacteristic
133C3×#676—21no—
134C3×C8×D5—21no—
135#6663C2×C411yescharacteristic
136#6662C2×C411yescharacteristic
137#6660C2×C411yescharacteristic
138#6659C2×C411yescharacteristic
139#6658C2×C411yescharacteristic
140#6657C2×C411yescharacteristic
141#6654C2×C411yescharacteristic
142#6653C2×C411yescharacteristic
143#6651—21no—
144#6651—21no—
145#6651—21no—
146#6651C2×C411yescharacteristic
147#6651C2×C411yescharacteristic
148#6651C2×C411yescharacteristic
149#6651C2×C411yescharacteristic
150#6650—21no—
151#6649—21no—
152#6648—21no—
153#6648—21no—
154#6648—21no—
155#6648D411yescharacteristic
156#6648D411yescharacteristic
157#6648D411yescharacteristic
158#6648D411yescharacteristic
159D3×#168—21no—
160D5×C3⋊C8—21no—
161#5768—51no—
162D3×#131—51no—
163D3×#131—51no—
164C3×#444—51no—
165#5196—51no—
166#5145—51no—
167#5145—51no—
168#4895—51no—
169#4893—51no—
170#4824—51no—
171#4824D511yescharacteristic, complemented
172#4821—51no—
173#4821—51no—
174#4717—51no—
175#4708—51no—
176D5×#41—31no—
177D5×#41—31no—
178C5×#135—31no—
179C5×#131—31no—
180C5×#131—31no—
181#4096—31no—
182#4096C2×D311yescharacteristic
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—31no—
194#4053—61no—
195#4053—61no—
196#4053C2×D311yescharacteristic, complemented
197D5×M16—31no—
198D5×M16—31no—
199D5×M16—61no—
200D5×M16—61no—
201#4050—31no—
202#4047—31no—
203#4047—31no—
204#4047—61no—
205#4047—61no—
206C2×#676—31no—
207C2×C8×D5—31no—
208C2×C8×D5—61no—
209C2×C8×D5—61no—
210#4018—31no—
211C5×#108—31no—
212C5×#104—31no—
213C5×#104C2×D311yescharacteristic, complemented
214C4×C5×C8—31no—
215#3969—31no—
216#3969—31no—
217#3957—31no—
218#3957—31no—
219#3954—31no—
220#3954C2×D311yescharacteristic, complemented
221#3951—31no—
222#3947—31no—
223C8×Dic5—31no—
224#3937—31no—
225#3937C2×D311yescharacteristic, complemented
226#3935C2×D311yescharacteristic, complemented
227#2955—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×C5—21no—
236C2×C3×C4×C5C2411yescharacteristic
237#1220—21no—
238#1220—21no—
239#1220—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15#4111yescharacteristic
243D60—21no—
244D60C22×C411yescharacteristic
245C4×D15—21no—
246C4×D15—21no—
247C4×D15—21no—
248C4×D15C22×C411yescharacteristic
249C4×D15C22×C411yescharacteristic
250C4×D15C2×D411yescharacteristic
251C4×D15C2×D411yescharacteristic
252Dic30—21no—
253Dic30C22×C411yescharacteristic
254C5×#67—21no—
255C5×D12C22×C411yescharacteristic
256C4×C5×D3—21no—
257C5×Dic6C22×C411yescharacteristic
258C3×C22⋊D5—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—
268D5×Dic3—21no—
269C3×C5×C8—21no—
270C3⋊#168—21no—
271C3×#168—21no—
272C3×#168C22×C411yescharacteristic
273C3×#168C22×C411yescharacteristic
274C3×#168C2×D411yescharacteristic
275C3×#168C2×D411yescharacteristic
276C5×C3⋊C8—21no—
277C5×C3⋊C8C22×C411yescharacteristic
278C5×C3⋊C8C22×C411yescharacteristic
279C5×C3⋊C8C2×D411yescharacteristic
280C5×C3⋊C8C2×D411yescharacteristic
281D3×#41—51no—
282D3×#41—51no—
283C3×#135—51no—
284C3×#131—51no—
285C3×#131—51no—
286#950—51no—
287#950C2×D511yescharacteristic
288#948—51no—
289#948C2×D511yescharacteristic, complemented
290#918—51no—
291#918—51no—
292#915—51no—
293#915—51no—
294#914—51no—
295#914—51no—
296#911—51no—
297#911—51no—
298#907—51no—
299#907—101no—
300#907—101no—
301#907C2×D511yescharacteristic, complemented
302D3×M16—51no—
303D3×M16—51no—
304D3×M16—101no—
305D3×M16—101no—
306#904—51no—
307#901—51no—
308#901—51no—
309#901—101no—
310#901—101no—
311C2×ΓL(1,𝔽25)—51no—
312C2×D3×C8—51no—
313C2×D3×C8—101no—
314C2×D3×C8—101no—
315#872—51no—
316C3×#108—51no—
317C3×#104—51no—
318C3×#104C2×D511yescharacteristic, complemented
319C3×#97—51no—
320#837—51no—
321#837—51no—
322#825—51no—
323#825—51no—
324#822—51no—
325#822C2×D511yescharacteristic, complemented
326#819—51no—
327#815—51no—
328C8×Dic3—51no—
329#805—51no—
330#805C2×D511yescharacteristic, complemented
331C4×C3⋊C8C2×D511yescharacteristic, complemented
332C5×#41—31no—
333C5×#41C22×D311yescharacteristic
334#713—31no—
335#713—31no—
336Q8×D5—31no—
337Q8×D5—31no—
338#711—31no—
339#711—31no—
340#711—61no—
341#711—61no—
342D4×D5—31no—
343D4×D5—31no—
344D4×D5—61no—
345D4×D5—61no—
346#709—31no—
347#709—61no—
348#709—61no—
349#709C22×D311yescharacteristic
350C2×C4×D5—31no—
351C2×C4×D5—61no—
352C2×C4×D5—61no—
353C5×Q16—31no—
354C5×SD16—31no—
355C5×SD16—31no—
356C5×D8—31no—
357C5×M16—31no—
358C5×M16—61no—
359C5×M16—61no—
360C5×M16C22×D311yescharacteristic
361C2×C5×C8—31no—
362C2×C5×C8—31no—
363C2×C5×C8—61no—
364C2×C5×C8—61no—
365C42×C5C22×D311yescharacteristic
366#689—31no—
367#689C4×D311yescharacteristic
368#688—31no—
369#688C4×D311yescharacteristic
370#687—31no—
371#687C4×D311yescharacteristic
372#686—31no—
373#686C4×D311yescharacteristic
374#685—61no—
375#683—61no—
376C4×Dic5—31no—
377#681—21no—
378#681—31no—
379#681—61no—
380#681C22×D311yescharacteristic
381C2×#168—21no—
382C2×#168—61no—
383C2×#168C22×D311yescharacteristic
384C2×#168C22×D311yescharacteristic
385Dic20—31no—
386D40—31no—
387#677—31no—
388#677—31no—
389#676—21no—
390#676—31no—
391#676—31no—
392#676—31no—
393#676—31no—
394#676—61no—
395#676—61no—
396#676—61no—
397#676—61no—
398#676—61no—
399C8×D5—21no—
400C8×D5—31no—
401C8×D5—31no—
402C8×D5—31no—
403C8×D5—31no—
404C8×D5—61no—
405C8×D5—61no—
406C8×D5—61no—
407C8×D5—61no—
408C8×D5—61no—
409#575—151no—
410C2×#131—151no—
411C2×#131—151no—
412#444—51no—
413#444—151no—
414#444—151no—
415#444—151no—
416#443—31no—
417#443—151no—
418#443—151no—
419#443—151no—
420#430—151no—
421#421—151no—
422#421—151no—
423#405—151no—
424C22×C3×C5—21no—
425C22×C3×C5C2×#4111yescharacteristic
426C2×D15—21no—
427C2×D15—41no—
428C2×D15—42no—
429C2×D15C4×D411yescharacteristic
430C2×D15C4×D411yescharacteristic
431C2×C5×D3—21no—
432C2×C3×D5—21no—
433D3×D5—42no—
434C3×C4×C5—21no—
435C3×C4×C5—41no—
436C3×C4×C5C23×C411yescharacteristic
437C3×C4×C5C22×D411yescharacteristic
438Dic15—21no—
439Dic15—41no—
440Dic15C4×D411yescharacteristic
441Dic15C4×D411yescharacteristic
442C3×Dic5—21no—
443C5×Dic3—21no—
444C3×#41—51no—
445C3×#41C22×D511yescharacteristic
446#239—51no—
447#239—51no—
448D3×Q8—51no—
449D3×Q8—51no—
450#237—51no—
451#237—51no—
452#237—101no—
453#237—101no—
454D3×D4—51no—
455D3×D4—51no—
456D3×D4—101no—
457D3×D4—101no—
458#235—51no—
459#235—101no—
460#235—101no—
461#235C22×D511yescharacteristic
462C2×C4×D3—51no—
463C2×C4×D3—101no—
464C2×C4×D3—101no—
465C3×Q16—51no—
466C3×SD16—51no—
467C3×SD16—51no—
468C3×D8—51no—
469C3×M16—51no—
470C3×M16—101no—
471C3×M16—101no—
472C3×M16C22×D511yescharacteristic
473C2×C3×C8—51no—
474C2×C3×C8—51no—
475C2×C3×C8—101no—
476C2×C3×C8—101no—
477C3×C42C22×D511yescharacteristic
478#216—51no—
479#216C4×D511yescharacteristic
480#215—51no—
481#215C4×D511yescharacteristic
482#214—51no—
483#214C4×D511yescharacteristic
484#213—51no—
485#213C4×D511yescharacteristic
486(C2×D3)⋊C4—101no—
487Dic3⋊C4—101no—
488C4×Dic3—51no—
489#208—21no—
490#208—51no—
491#208—101no—
492#208C22×D511yescharacteristic
493C2×C3⋊C8—21no—
494C2×C3⋊C8—101no—
495C2×C3⋊C8C22×D511yescharacteristic
496C2×C3⋊C8C22×D511yescharacteristic
497Dic12—51no—
498D24—51no—
499#204—51no—
500#204—51no—
501ΓL(1,𝔽25)—21no—
502ΓL(1,𝔽25)—51no—
503ΓL(1,𝔽25)—51no—
504ΓL(1,𝔽25)—51no—
505ΓL(1,𝔽25)—51no—
506ΓL(1,𝔽25)—101no—
507ΓL(1,𝔽25)—101no—
508ΓL(1,𝔽25)—101no—
509ΓL(1,𝔽25)—101no—
510ΓL(1,𝔽25)—101no—
511D3×C8—21no—
512D3×C8—51no—
513D3×C8—51no—
514D3×C8—51no—
515D3×C8—51no—
516D3×C8—101no—
517D3×C8—101no—
518D3×C8—101no—
519D3×C8—101no—
520D3×C8—101no—
521C22×D5—31no—
522C22×D5—61no—
523C22×D5—61no—
524C5×Q8—31no—
525C5×Q8C2×C4×D311yescharacteristic
526C5×D4—21no—
527C5×D4—31no—
528C5×D4—61no—
529C5×D4C2×C4×D311yescharacteristic
530C2×C4×C5—21no—
531C2×C4×C5—21no—
532C2×C4×C5—61no—
533C2×C4×C5C23×D311yescharacteristic
534C22⋊D5—21no—
535C22⋊D5—61no—
536C22⋊D5—61no—
537C22⋊D5—61no—
538C22⋊D5—61no—
539C22⋊D5—61no—
540C2×Dic5—31no—
541C2×Dic5—61no—
542C2×Dic5—61no—
543C2×Dic5—61no—
544D20—31no—
545D20—61no—
546D20—61no—
547D20C2×C4×D311yescharacteristic
548C4×D5—21no—
549C4×D5—31no—
550C4×D5—31no—
551C4×D5—31no—
552C4×D5—31no—
553C4×D5—61no—
554C4×D5—61no—
555C4×D5—61no—
556C4×D5—61no—
557C4×D5—61no—
558Dic10—31no—
559Dic10—61no—
560Dic10—61no—
561Dic10C2×C4×D311yescharacteristic
562C5×C8—21no—
563C5×C8—31no—
564C5×C8—31no—
565C5×C8—31no—
566C5×C8—31no—
567C5×C8—61no—
568#168—21no—
569#168—61no—
570#168C2×C4×D311yescharacteristic
571#168C2×C4×D311yescharacteristic
572#168D3×D411yescharacteristic
573#168D3×D411yescharacteristic
574C2×#41—151no—
575C2×#41—151no—
576#137—151no—
577#137—151no—
578#137—151no—
579#137—151no—
580AGL(1,ℤ/8)—151no—
581AGL(1,ℤ/8)—151no—
582AGL(1,ℤ/8)—151no—
583AGL(1,ℤ/8)—151no—
584#135—31no—
585#135—51no—
586#135—151no—
587#135—151no—
588#131—31no—
589#131—31no—
590#131—51no—
591#131—51no—
592#131—151no—
593#131—151no—
594#131—151no—
595#131—151no—
596#131—301no—
597#131—301no—
598#131—301no—
599#131—301no—
600C2×M16—151no—
601C2×M16—151no—
602C2×M16—151no—
603C2×M16—301no—
604C2×M16—301no—
605C22×C8—151no—
606C22×C8—301no—
607C22×C8—301no—
608#117—151no—
609#108—31no—
610#108—51no—
611#108—151no—
612#108—151no—
613#104—31no—
614#104—51no—
615#104—151no—
616#104—151no—
617#104—151no—
618#104—151no—
619#104—151no—
620#104D3×D511yescharacteristic, complemented
621#97—51no—
622#97—151no—
623C4×C8—31no—
624C4×C8—151no—
625C2×C3×C5—21no—
626C2×C3×C5—41no—
627C2×C3×C5C2×C4×D411yescharacteristic
628D15—21no—
629D15—21no—
630D15—41no—
631C3×D5—41no—
632C5×D3—41no—
633C22×D3—51no—
634C22×D3—101no—
635C22×D3—101no—
636C3×Q8—51no—
637C3×Q8C2×C4×D511yescharacteristic
638C3×D4—21no—
639C3×D4—51no—
640C3×D4—101no—
641C3×D4C2×C4×D511yescharacteristic
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—101no—
645C2×C3×C4C23×D511yescharacteristic
646#67—21no—
647#67—101no—
648#67—101no—
649#67—101no—
650#67—101no—
651#67—101no—
652C2×Dic3—51no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656D12—51no—
657D12—101no—
658D12—101no—
659D12C2×C4×D511yescharacteristic
660C4×D3—21no—
661C4×D3—51no—
662C4×D3—51no—
663C4×D3—51no—
664C4×D3—51no—
665C4×D3—101no—
666C4×D3—101no—
667C4×D3—101no—
668C4×D3—101no—
669C4×D3—101no—
670Dic6—51no—
671Dic6—101no—
672Dic6—101no—
673Dic6C2×C4×D511yescharacteristic
674C3×C8—21no—
675C3×C8—51no—
676C3×C8—51no—
677C3×C8—51no—
678C3×C8—51no—
679C3×C8—101no—
680C3⋊C8—21no—
681C3⋊C8—101no—
682C3⋊C8C2×C4×D511yescharacteristic
683C3⋊C8C2×C4×D511yescharacteristic
684C3⋊C8D4×D511yescharacteristic
685C3⋊C8D4×D511yescharacteristic
686C22×C5—21no—
687C22×C5—61no—
688C22×C5D3×#4111yescharacteristic
689C2×D5—21no—
690C2×D5—31no—
691C2×D5—31no—
692C2×D5—61no—
693C2×D5—122no—
694C2×D5—121no—
695C2×D5—122no—
696C4×C5—21no—
697C4×C5—41no—
698C4×C5—61no—
699C4×C5C22×C4×D311yescharacteristic
700C4×C5C2×D3×D411yescharacteristic
701Dic5—21no—
702Dic5—31no—
703Dic5—31no—
704Dic5—61no—
705Dic5—121no—
706#41—31no—
707#41—51no—
708#41—151no—
709#41—151no—
710#41—151no—
711#41—151no—
712#41—151no—
713#41—301no—
714#41—301no—
715#41—301no—
716#41—301no—
717#41C2×D3×D511yescharacteristic
718C2×Q8—151no—
719C2×Q8—151no—
720C2×D4—151no—
721C2×D4—151no—
722C2×D4—301no—
723C2×D4—301no—
724C22×C4—151no—
725C22×C4—301no—
726C22×C4—301no—
727Q16—31no—
728Q16—51no—
729Q16—151no—
730Q16—151no—
731SD16—31no—
732SD16—31no—
733SD16—51no—
734SD16—51no—
735SD16—151no—
736SD16—151no—
737SD16—151no—
738SD16—151no—
739D8—31no—
740D8—51no—
741D8—151no—
742D8—151no—
743M16—31no—
744M16—51no—
745M16—61no—
746M16—61no—
747M16—101no—
748M16—101no—
749M16—151no—
750M16—151no—
751M16—151no—
752M16—151no—
753M16—151no—
754M16—301no—
755M16—301no—
756M16—301no—
757M16—301no—
758M16—301no—
759M16—301no—
760M16C2×D3×D511yescharacteristic
761C2×C8—31no—
762C2×C8—31no—
763C2×C8—51no—
764C2×C8—51no—
765C2×C8—61no—
766C2×C8—61no—
767C2×C8—101no—
768C2×C8—101no—
769C2×C8—151no—
770C2×C8—151no—
771C2×C8—151no—
772C2×C8—151no—
773C2×C8—301no—
774C2×C8—301no—
775C2×C8—301no—
776C2×C8—301no—
777C2×C8—301no—
778C2×C8—301no—
779C4⋊C4—301no—
780C22⋊C4—301no—
781C42—151no—
782C42C2×D3×D511yescharacteristic
783C3×C5#295511yescharacteristic, complemented, Hall
784C22×C3—21no—
785C22×C3—101no—
786C22×C3D5×#4111yescharacteristic
787C2×D3—21no—
788C2×D3—51no—
789C2×D3—51no—
790C2×D3—101no—
791C2×D3—202no—
792C2×D3—201no—
793C2×D3—202no—
794C3×C4—21no—
795C3×C4—41no—
796C3×C4—101no—
797C3×C4C22×C4×D511yescharacteristic
798C3×C4C2×D4×D511yescharacteristic
799Dic3—21no—
800Dic3—51no—
801Dic3—51no—
802Dic3—101no—
803Dic3—201no—
804C2×C5—21no—
805C2×C5—41no—
806C2×C5—121no—
807C2×C5C4×D3×D411yescharacteristic
808D5—41no—
809D5—61no—
810D5—61no—
811D5—121no—
812C23—151no—
813C23—301no—
814C23—301no—
815Q8—31no—
816Q8—51no—
817Q8—151no—
818Q8—301no—
819Q8—301no—
820Q8C4×D3×D511yescharacteristic
821D4—21no—
822D4—31no—
823D4—51no—
824D4—61no—
825D4—101no—
826D4—151no—
827D4—301no—
828D4—301no—
829D4—301no—
830D4—301no—
831D4—301no—
832D4—301no—
833D4—301no—
834D4C4×D3×D511yescharacteristic
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—61no—
838C2×C4—101no—
839C2×C4—151no—
840C2×C4—151no—
841C2×C4—151no—
842C2×C4—151no—
843C2×C4—151no—
844C2×C4—301no—
845C2×C4—301no—
846C2×C4—301no—
847C2×C4—301no—
848C2×C4—301no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4C22×D3×D511yescharacteristic
853C8—21no—
854C8—31no—
855C8—31no—
856C8—31no—
857C8—31no—
858C8—51no—
859C8—51no—
860C8—51no—
861C8—51no—
862C8—61no—
863C8—101no—
864C8—301no—
865C2×C3—21no—
866C2×C3—41no—
867C2×C3—201no—
868C2×C3C4×D4×D511yescharacteristic
869D3—41no—
870D3—101no—
871D3—101no—
872D3—201no—
873C5#7989711yescharacteristic, complemented, Sylow
874C22—21no—
875C22—61no—
876C22—101no—
877C22—151no—
878C22—151no—
879C22—301no—
880C22—601no—
881C22—602no—
882C22—602no—
883C22#9202411yescharacteristic
884C4—21no—
885C4—41no—
886C4—61no—
887C4—101no—
888C4—151no—
889C4—151no—
890C4—301no—
891C4—601no—
892C4C2×C4×D3×D511yescharacteristic
893C4D3×D4×D511yescharacteristic
894C3#1061161911yescharacteristic, complemented, Sylow
895C2—21no—
896C2—41no—
897C2—121no—
898C2—201no—
899C2—301no—
900C2—301no—
901C2—601no—
902C2#1175320311yescharacteristic
subgroupG/H
centerC4D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#104C22
socleC2×C3×C5C2×C4×D4
prime radical#11755329C2
cosocleC2×C3×C4×C5C24
hypercenter#104D3×D5
hypocenterC3×C5#2955
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. #11755299C2semidirect
3. #11754017C2semidirect
4. #11750922C2semidirect
5. C5×#4824C2semidirect
6. C3×#65112C2semidirect
7. #11749436C2semidirect
8. #11749433C2semidirect
9. #11748208C2semidirect
10. #11748206C2semidirect
11. #11748173C2semidirect
12. #11747113C2semidirect
13. #11747019C2semidirect
14. #11747016C2semidirect
15. #11746982C2semidirect
22. C5×#948C22semidirect
23. C5×#907C22semidirect
25. C3×#4094C22semidirect
26. C3×#4053C22semidirect
27. #91524C4semidirect
28. #91522C4semidirect
29. #91512C4semidirect
30. #91506C4semidirect
31. #91500C4semidirect
32. #91498C4semidirect
33. #91488C4semidirect
34. #91482C4semidirect
41. #91291C22semidirect
43. #91290C22semidirect
46. #91286C22semidirect
47. #91283C22semidirect
52. C3×C5×#104C22semidirect
53. #91121C22semidirect
54. #91109C22semidirect
55. #91089C22semidirect
56. C5×#822C22semidirect
57. C5×#805C22semidirect
58. C4×C5×C3⋊C8C22semidirect
59. C3×#3954C22semidirect
60. C3×#3937C22semidirect
61. C3×#3935C22semidirect
62. #90993C22semidirect
63. #90991C22semidirect
64. #90978C22semidirect
65. #90976C22semidirect
66. #90954C22semidirect
67. #90951C22semidirect
79. #65112D3semidirect
171. #4824D5semidirect
184. #4094C2×D3semidirect
196. #4053C2×D3semidirect
213. C5×#104C2×D3semidirect
220. #3954C2×D3semidirect
225. #3937C2×D3semidirect
226. #3935C2×D3semidirect
289. #948C2×D5semidirect
301. #907C2×D5semidirect
318. C3×#104C2×D5semidirect
325. #822C2×D5semidirect
330. #805C2×D5semidirect
331. C4×C3⋊C8C2×D5semidirect
620. #104D3×D5semidirect
783. C3×C5#2955semidirect
873. C5#79897semidirect
894. C3#10611619semidirect

Maximal subgroups

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

subgroupindex
#117553292
#117552992
#117540172
#117509222
C5×#48242
C3×#651122
#117494362
#117494332
#117482082
#117482062
#117481732
#117471132
#117470192
#117470162
#117469822
#106116193
#798975