Finite Group Databasebeta

← #14418140

Subgroups — #14418140

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#11755322C211yesmaximal, characteristic
2#11755298C211yesmaximal, characteristic, complemented
3#11754016C211yesmaximal, characteristic, complemented
4#11750924C211yesmaximal, characteristic, complemented
5C5×D3×#104C211yesmaximal, characteristic, complemented
6C3×#65112C211yesmaximal, characteristic, complemented
7#11749440C211yesmaximal, characteristic, complemented
8#11749434C211yesmaximal, characteristic, complemented
9#11748203C211yesmaximal, characteristic, complemented
10#11748176C211yesmaximal, characteristic, complemented
11#11748172C211yesmaximal, characteristic, complemented
12D3×#3937C211yesmaximal, characteristic, complemented
13#11747107C211yesmaximal, characteristic, complemented
14#11747019C211yesmaximal, characteristic, complemented
15#11747005C211yesmaximal, characteristic, complemented
16#10610711—31nomaximal, Hall
17C5×D3×#41C2211yescharacteristic
18D3×#709C2211yescharacteristic
19#91839C2211yescharacteristic
20#91837C2211yescharacteristic, complemented
21#91796C2211yescharacteristic, complemented
22C5×D3×M16C2211yescharacteristic
23C42×C5×D3C2211yescharacteristic
24C3×#4096C2211yescharacteristic
25C3×#4094C2211yescharacteristic, complemented
26C3×#4053C2211yescharacteristic, complemented
27#91520C411yescharacteristic, complemented
28#91518C411yescharacteristic, complemented
29#91510C411yescharacteristic, complemented
30#91504C411yescharacteristic, complemented
31#91496C411yescharacteristic, complemented
32#91494C411yescharacteristic, complemented
33#91486C411yescharacteristic, complemented
34#91480C411yescharacteristic, complemented
35#91303C2211yescharacteristic
36#91297C2211yescharacteristic
37C2×#6650—21no—
38C2×#6650C2211yescharacteristic
39C2×#6650C2211yescharacteristic
40#91290C2211yescharacteristic, complemented
41#91288—21no—
42#91288C2211yescharacteristic, complemented
43D3×#681—21no—
44D3×#681C2211yescharacteristic
45#91286—21no—
46#91286C2211yescharacteristic, complemented
47#91284C2211yescharacteristic, complemented
48#91267—21no—
49#91265—21no—
50#91246—21no—
51D5×ΓL(1,𝔽25)—21no—
52C3×C5×#104C2211yescharacteristic, complemented
53#91106C2211yescharacteristic, complemented
54#91089C2211yescharacteristic, complemented
55#91087C2211yescharacteristic, complemented
56C5×#837C2211yescharacteristic, complemented
57C5×#825C2211yescharacteristic, complemented
58C5×#805C2211yescharacteristic, complemented
59C3×#3954C2211yescharacteristic, complemented
60C3×#3937C2211yescharacteristic, complemented
61C3×#3935C2211yescharacteristic, complemented
62#90992C2211yescharacteristic, complemented
63#90991C2211yescharacteristic, complemented
64#90980C2211yescharacteristic, complemented
65#90977C2211yescharacteristic, complemented
66Dic3×#168C2211yescharacteristic, complemented
67Dic3×#168C2211yescharacteristic, complemented
68#79898—51nomaximal, Hall
69#66156—31no—
70#66153—31no—
71#66079—31no—
72C2×C5×#104—31no—
73#65413—31no—
74C2×#3937—31no—
75C4×#681—31no—
76#65113—31no—
77#65113—31no—
78#65113—31no—
79#65113—31no—
80#65112—31no—
81#65112—31no—
82#65112—31no—
83#65112D311yescharacteristic, complemented
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×D3—21no—
96C2×C4×C5×D3C2311yescharacteristic
97C3×#709C2311yescharacteristic
98D3×C22⋊D5—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×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—
119C4×C5×Dic3—21no—
120C4×C5×Dic3C2311yescharacteristic
121C5×#208C2311yescharacteristic
122C5×ΓL(1,𝔽25)—21no—
123C5×D3×C8—21no—
124C3×#689C2×C411yescharacteristic, complemented
125C3×#688C2×C411yescharacteristic, complemented
126C3×#687C2×C411yescharacteristic, complemented
127C3×#686C2×C411yescharacteristic, complemented
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, complemented
136#6661C2×C411yescharacteristic, complemented
137#6660C2×C411yescharacteristic, complemented
138#6659C2×C411yescharacteristic, complemented
139#6656C2×C411yescharacteristic, complemented
140#6655C2×C411yescharacteristic, complemented
141#6654C2×C411yescharacteristic, complemented
142#6652C2×C411yescharacteristic, complemented
143#6651—21no—
144#6650—21no—
145#6650—21no—
146#6650—21no—
147#6650C2×C411yescharacteristic
148#6650C2×C411yescharacteristic
149#6650C2×C411yescharacteristic
150#6650C2×C411yescharacteristic
151#6650D411yescharacteristic
152#6650D411yescharacteristic
153#6650D411yescharacteristic
154#6650D411yescharacteristic
155#6649—21no—
156#6648—21no—
157D3×#168—21no—
158D3×#168—21no—
159D3×#168—21no—
160D5×C3⋊C8—21no—
161#5768—51no—
162#5750—51no—
163#5750—51no—
164C3×#444—51no—
165#5196—51no—
166#5144—51no—
167#5144—51no—
168#4895—51no—
169#4893—51no—
170#4823—51no—
171#4823—51no—
172D3×#104—51no—
173D3×#104D511yescharacteristic, complemented
174#4717—51no—
175#4707—51no—
176C2×C5×#41—31no—
177C2×#709—31no—
178C2×C5×M16—31no—
179C2×C42×C5—31no—
180#4097—31no—
181#4097—31no—
182#4096—31no—
183#4096—31no—
184#4096—31no—
185#4096C2×D311yescharacteristic
186#4095—31no—
187#4095—31no—
188#4094—31no—
189#4094—31no—
190#4094—31no—
191#4094—61no—
192#4094—61no—
193#4094C2×D311yescharacteristic, complemented
194#4088—31no—
195#4088—31no—
196#4078—31no—
197#4078—31no—
198C2×#681—31no—
199C2×#681—31no—
200C2×#681—31no—
201C2×#681—61no—
202C2×#681—61no—
203#4053—31no—
204#4053—31no—
205#4053—31no—
206#4053C2×D311yescharacteristic, complemented
207D5×M16—61no—
208D5×M16—61no—
209#4047—61no—
210#4047—61no—
211C5×#104—31no—
212C5×#104—31no—
213C5×#104—31no—
214C5×#104C2×D311yescharacteristic, complemented
215#3954—31no—
216#3954—31no—
217#3954—31no—
218#3954C2×D311yescharacteristic, complemented
219#3937—31no—
220#3937—31no—
221#3937—31no—
222#3937C2×D311yescharacteristic, complemented
223#3935—31no—
224#3935C2×D311yescharacteristic, complemented
225C4×#168—31no—
226C4×#168—31no—
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×C5—21no—
236C2×C3×C4×C5C2411yescharacteristic
237#1220—21no—
238D60C22×C411yescharacteristic
239C4×D15—21no—
240Dic30C22×C411yescharacteristic
241C5×#67—21no—
242C5×#67—21no—
243C5×#67—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3#4111yescharacteristic
247C5×D12—21no—
248C5×D12C22×C411yescharacteristic
249C4×C5×D3—21no—
250C4×C5×D3—21no—
251C4×C5×D3—21no—
252C4×C5×D3—42no—
253C4×C5×D3C22×C411yescharacteristic
254C4×C5×D3C22×C411yescharacteristic
255C4×C5×D3C2×D411yescharacteristic
256C4×C5×D3C2×D411yescharacteristic
257C5×Dic6—21no—
258C5×Dic6C22×C411yescharacteristic
259C3×C22⋊D5—21no—
260C3×D20C22×C411yescharacteristic
261C3×C4×D5—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—
277C3×#168C22×C411yescharacteristic
278C3×#168C22×C411yescharacteristic
279C3×#168C2×D411yescharacteristic
280C3×#168C2×D411yescharacteristic
281C5×C3⋊C8—21no—
282D3×#41—51no—
283D3×#41C2×D511yescharacteristic
284C3×#135—51no—
285C3×#131—51no—
286C3×#131—51no—
287#950—51no—
288#950—51no—
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—101no—
305D3×M16—101no—
306D3×M16C2×D511yescharacteristic
307#904—51no—
308#901—51no—
309#901—51no—
310#901—101no—
311#901—101no—
312C2×ΓL(1,𝔽25)—51no—
313C2×ΓL(1,𝔽25)—51no—
314C2×ΓL(1,𝔽25)—101no—
315C2×ΓL(1,𝔽25)—101no—
316C42×D3C2×D511yescharacteristic
317C3×#108—51no—
318C3×#104—51no—
319C3×#104C2×D511yescharacteristic, complemented
320C3×#97—51no—
321#837—51no—
322#837C2×D511yescharacteristic, complemented
323#825—51no—
324#825C2×D511yescharacteristic, complemented
325#822—51no—
326#822—51no—
327#819—51no—
328C8×Dic3—51no—
329C8×Dic3—51no—
330#805—51no—
331#805C2×D511yescharacteristic, complemented
332#803—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—
344C22×C4×C5—61no—
345C2×C22⋊D5—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—31no—
356C5×M16—61no—
357C5×M16C22×D311yescharacteristic
358C2×C5×C8—61no—
359C42×C5—31no—
360C42×C5—61no—
361C42×C5C22×D311yescharacteristic
362#689—31no—
363#689—31no—
364#689—31no—
365#689C4×D311yescharacteristic, complemented
366#688—31no—
367#688—31no—
368#688—31no—
369#688C4×D311yescharacteristic, complemented
370#687—31no—
371#687—31no—
372#687—31no—
373#687C4×D311yescharacteristic, complemented
374#686—31no—
375#686—31no—
376#686—31no—
377#686C4×D311yescharacteristic, complemented
378#681—21no—
379#681—31no—
380#681—31no—
381#681—31no—
382#681—31no—
383#681—31no—
384#681—31no—
385#681—31no—
386#681—31no—
387#681—31no—
388#681—61no—
389#681—61no—
390#681—61no—
391#681—61no—
392#681C22×D311yescharacteristic
393C2×#168—21no—
394C2×#168—31no—
395C2×#168—31no—
396C2×#168—61no—
397C2×#168—61no—
398C2×#168—61no—
399C2×#168—61no—
400C2×#168C22×D311yescharacteristic
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—151no—
412#568—151no—
413#444—51no—
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—31no—
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×C5—41no—
437C3×C4×C5C23×C411yescharacteristic
438C3×C4×C5C22×D411yescharacteristic
439Dic15—21no—
440C3×Dic5—21no—
441C5×Dic3—22no—
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—21no—
465C2×C4×D3—101no—
466C2×C4×D3C22×D511yescharacteristic
467C3×Q16—51no—
468C3×SD16—51no—
469C3×SD16—51no—
470C3×D8—51no—
471C3×M16—51no—
472C3×M16—101no—
473C3×M16—101no—
474C3×M16C22×D511yescharacteristic
475C2×C3×C8—51no—
476C2×C3×C8—51no—
477C2×C3×C8—101no—
478C2×C3×C8—101no—
479C3×C42C22×D511yescharacteristic
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—21no—
489C4×Dic3C22×D511yescharacteristic
490#208—51no—
491#208—101no—
492#208—101no—
493#208C22×D511yescharacteristic
494C2×C3⋊C8—51no—
495C2×C3⋊C8—51no—
496C2×C3⋊C8—101no—
497C2×C3⋊C8—101no—
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—
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—21no—
537C2×C4×C5—31no—
538C2×C4×C5—31no—
539C2×C4×C5—31no—
540C2×C4×C5—31no—
541C2×C4×C5—31no—
542C2×C4×C5—61no—
543C2×C4×C5—61no—
544C2×C4×C5—61no—
545C2×C4×C5—61no—
546C2×C4×C5—61no—
547C2×C4×C5—122no—
548C2×C4×C5C23×D311yescharacteristic
549C22⋊D5—21no—
550C22⋊D5—61no—
551C22⋊D5—61no—
552C22⋊D5—61no—
553C2×Dic5—61no—
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—61no—
566#168—21no—
567#168—31no—
568#168—31no—
569#168—31no—
570#168—31no—
571#168—61no—
572#168C2×C4×D311yescharacteristic
573#168C2×C4×D311yescharacteristic
574#168D3×D411yescharacteristic
575#168D3×D411yescharacteristic
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—51no—
591#131—51no—
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—31no—
603C2×M16—151no—
604C2×M16—151no—
605C2×M16—151no—
606C2×M16—301no—
607C2×M16—301no—
608C2×M16—301no—
609C2×M16—301no—
610C2×C42—31no—
611#108—51no—
612#108—151no—
613#108—151no—
614#108—151no—
615#104—31no—
616#104—31no—
617#104—31no—
618#104—51no—
619#104—151no—
620#104—151no—
621#104—151no—
622#104D3×D511yescharacteristic, complemented
623#97—51no—
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—41no—
632C5×D3—21no—
633C5×D3—21no—
634C5×D3—41no—
635C22×D3—21no—
636C22×D3—101no—
637C22×D3#71111yescharacteristic
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—21no—
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—21no—
656C2×Dic3—101no—
657C2×Dic3#71111yescharacteristic
658D12—21no—
659D12—51no—
660D12—101no—
661D12C2×C4×D511yescharacteristic
662C4×D3—21no—
663C4×D3—21no—
664C4×D3—21no—
665C4×D3—42no—
666C4×D3—101no—
667C4×D3—101no—
668C4×D3—101no—
669C4×D3C2×C4×D511yescharacteristic
670C4×D3C2×C4×D511yescharacteristic
671C4×D3D4×D511yescharacteristic
672C4×D3D4×D511yescharacteristic
673Dic6—21no—
674Dic6—51no—
675Dic6—101no—
676Dic6C2×C4×D511yescharacteristic
677C3×C8—21no—
678C3×C8—51no—
679C3×C8—51no—
680C3×C8—51no—
681C3×C8—51no—
682C3×C8—101no—
683C3⋊C8—21no—
684C3⋊C8—51no—
685C3⋊C8—51no—
686C3⋊C8—51no—
687C3⋊C8—51no—
688C3⋊C8—101no—
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—41no—
703C4×C5—62no—
704C4×C5—61no—
705C4×C5C22×C4×D311yescharacteristic
706C4×C5C2×D3×D411yescharacteristic
707Dic5—21no—
708Dic5—61no—
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—61no—
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—31no—
748M16—51no—
749M16—61no—
750M16—101no—
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—51no—
770C2×C8—51no—
771C2×C8—61no—
772C2×C8—101no—
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—31no—
784C42—61no—
785C42C2×D3×D511yescharacteristic
786C3×C5#295611yescharacteristic, complemented, Hall
787C22×C3—21no—
788C22×C3—101no—
789C22×C3C2×#71111yescharacteristic
790C2×D3—21no—
791C2×D3—41no—
792C2×D3—81no—
793C2×D3—101no—
794C2×D3—401no—
795C2×D3#402711yescharacteristic
796C2×D3#402711yescharacteristic
797C3×C4—21no—
798C3×C4—41no—
799C3×C4—101no—
800C3×C4C22×C4×D511yescharacteristic
801C3×C4C2×D4×D511yescharacteristic
802Dic3—22no—
803Dic3—21no—
804Dic3—101no—
805Dic3#402711yescharacteristic
806Dic3#402711yescharacteristic
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—21no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—101no—
851C2×C4—122no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4C22×D3×D511yescharacteristic
857C8—21no—
858C8—51no—
859C8—51no—
860C8—51no—
861C8—51no—
862C8—61no—
863C8—101no—
864C8—151no—
865C8—151no—
866C8—151no—
867C8—151no—
868C8—301no—
869C2×C3—21no—
870C2×C3—41no—
871C2×C3—201no—
872C2×C3C2×#402711yescharacteristic
873D3—21no—
874D3—21no—
875D3—41no—
876D3—201no—
877C5#7989811yescharacteristic, complemented, Sylow
878C22—21no—
879C22—31no—
880C22—31no—
881C22—61no—
882C22—101no—
883C22—121no—
884C22—241no—
885C22—301no—
886C22—1201no—
887C22D3×#71111yescharacteristic
888C4—21no—
889C4—31no—
890C4—31no—
891C4—41no—
892C4—62no—
893C4—61no—
894C4—101no—
895C4—301no—
896C4C2×C4×D3×D511yescharacteristic
897C4D3×D4×D511yescharacteristic
898C3#1061071111yescharacteristic, complemented, Sylow
899C2—21no—
900C2—41no—
901C2—61no—
902C2—61no—
903C2—121no—
904C2—201no—
905C2—601no—
906C2D3×#402711yescharacteristic
subgroupG/H
centerC4D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#104C22
socleC2×C3×C5C2×C4×D4
prime radical#11755322C2
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. #11755298C2semidirect
3. #11754016C2semidirect
4. #11750924C2semidirect
5. C5×D3×#104C2semidirect
6. C3×#65112C2semidirect
7. #11749440C2semidirect
8. #11749434C2semidirect
9. #11748203C2semidirect
10. #11748176C2semidirect
11. #11748172C2semidirect
12. D3×#3937C2semidirect
13. #11747107C2semidirect
14. #11747019C2semidirect
15. #11747005C2semidirect
20. #91837C22semidirect
21. #91796C22semidirect
25. C3×#4094C22semidirect
26. C3×#4053C22semidirect
27. #91520C4semidirect
28. #91518C4semidirect
29. #91510C4semidirect
30. #91504C4semidirect
31. #91496C4semidirect
32. #91494C4semidirect
33. #91486C4semidirect
34. #91480C4semidirect
40. #91290C22semidirect
42. #91288C22semidirect
46. #91286C22semidirect
47. #91284C22semidirect
52. C3×C5×#104C22semidirect
53. #91106C22semidirect
54. #91089C22semidirect
55. #91087C22semidirect
56. C5×#837C22semidirect
57. C5×#825C22semidirect
58. C5×#805C22semidirect
59. C3×#3954C22semidirect
60. C3×#3937C22semidirect
61. C3×#3935C22semidirect
62. #90992C22semidirect
63. #90991C22semidirect
64. #90980C22semidirect
65. #90977C22semidirect
66. Dic3×#168C22semidirect
67. Dic3×#168C22semidirect
83. #65112D3semidirect
108. #6718C2×C4semidirect
109. #6717C2×C4semidirect
110. #6716C2×C4semidirect
111. #6715C2×C4semidirect
124. C3×#689C2×C4semidirect
125. C3×#688C2×C4semidirect
126. C3×#687C2×C4semidirect
127. C3×#686C2×C4semidirect
135. #6663C2×C4semidirect
136. #6661C2×C4semidirect
137. #6660C2×C4semidirect
138. #6659C2×C4semidirect
139. #6656C2×C4semidirect
140. #6655C2×C4semidirect
141. #6654C2×C4semidirect
142. #6652C2×C4semidirect
173. D3×#104D5semidirect
193. #4094C2×D3semidirect
206. #4053C2×D3semidirect
214. C5×#104C2×D3semidirect
218. #3954C2×D3semidirect
222. #3937C2×D3semidirect
224. #3935C2×D3semidirect
319. C3×#104C2×D5semidirect
322. #837C2×D5semidirect
324. #825C2×D5semidirect
331. #805C2×D5semidirect
365. #689C4×D3semidirect
369. #688C4×D3semidirect
373. #687C4×D3semidirect
377. #686C4×D3semidirect
622. #104D3×D5semidirect
786. C3×C5#2956semidirect
877. C5#79898semidirect
898. C3#10610711semidirect

Maximal subgroups

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

subgroupindex
#117553222
#117552982
#117540162
#117509242
C5×D3×#1042
C3×#651122
#117494402
#117494342
#117482032
#117481762
#117481722
D3×#39372
#117471072
#117470192
#117470052
#106107113
#798985