Finite Group Databasebeta

← D3×#65737 #14417983

Subgroups — D3×#65737 #14417983

Order 1920.

928 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
1D3×#4133C211yesmaximal, characteristic, complemented
2D3×#4131C211yesmaximal, characteristic, complemented
3D3×#4062C211yesmaximal, characteristic
4#11752396C211yesmaximal, characteristic, complemented
5C3×#65737C211yesmaximal, characteristic, complemented
6#11751980C211yesmaximal, characteristic, complemented
7#11751976C211yesmaximal, characteristic, complemented
8D3×#4010C211yesmaximal, characteristic, complemented
9#11751958C211yesmaximal, characteristic, complemented
10#11751954C211yesmaximal, characteristic, complemented
11D3×#4008C211yesmaximal, characteristic, complemented
12#11751688C211yesmaximal, characteristic, complemented
13#11751681C211yesmaximal, characteristic, complemented
14D3×#3996C211yesmaximal, characteristic, complemented
15D3×#3992C211yesmaximal, characteristic, complemented
16C2×#65737—31nomaximal, Hall
17D3×#713C2211yescharacteristic
18D3×#711C2211yescharacteristic
19#91992C2211yescharacteristic, complemented
20#91990C2211yescharacteristic, complemented
21C3×#4133C2211yescharacteristic, complemented
22C3×#4131C2211yescharacteristic, complemented
23#91929—21no—
24D3×#704—21no—
25#91927—21no—
26C2×D3×#170—21no—
27C4×D3×AGL(1,𝔽5)C2211yescharacteristic
28#91916—21no—
29#91916C2211yescharacteristic, complemented
30#91914—21no—
31#91914C2211yescharacteristic, complemented
32#91913C2211yescharacteristic, complemented
33D3×#700—21no—
34D3×#700C2211yescharacteristic
35D3×#700C2211yescharacteristic
36#91911C2211yescharacteristic, complemented
37D3×D5⋊C8—21no—
38D3×D5⋊C8C2211yescharacteristic
39#91805C411yescharacteristic, complemented
40C5×D3×SD16C411yescharacteristic, complemented
41C3×#4062C2211yescharacteristic
42#91523C411yescharacteristic, complemented
43#91514C2211yescharacteristic
44D3×#689C411yescharacteristic, complemented
45#91497C411yescharacteristic, complemented
46#91492C2211yescharacteristic
47D3×#686C411yescharacteristic, complemented
48#91276C411yescharacteristic, complemented
49#91269C2211yescharacteristic
50D3×#677C411yescharacteristic, complemented
51D3×C8×D5C2211yescharacteristic
52#91239C2211yescharacteristic, complemented
53#91237C2211yescharacteristic, complemented
54#91225C2211yescharacteristic, complemented
55#91221C2211yescharacteristic, complemented
56C3×#4010C2211yescharacteristic, complemented
57C3×#4008C2211yescharacteristic, complemented
58C3×#3996C2211yescharacteristic, complemented
59C3×#3992C2211yescharacteristic, complemented
60#91162C2211yescharacteristic, complemented
61#91162C2211yescharacteristic, complemented
62#91158C2211yescharacteristic, complemented
63#91157C2211yescharacteristic, complemented
64#91156C2211yescharacteristic, complemented
65#91155C2211yescharacteristic, complemented
66#91150C2211yescharacteristic, complemented
67#91149C2211yescharacteristic, complemented
68D3×#444—51nomaximal, Hall
69C2×#4133—31no—
70C2×#4131—31no—
71C2×#4062—31no—
72C2×#4010—31no—
73C2×#4008—31no—
74#65737—31no—
75#65737—31no—
76#65737—31no—
77#65737—31no—
78#65737—31no—
79#65737—31no—
80#65737—31no—
81#65737D311yescharacteristic, direct product factor
82C2×#3996—31no—
83C2×#3992—31no—
84C2×D3×AGL(1,𝔽5)—21no—
85#6821C2×C411yescharacteristic
86#6819C2×C411yescharacteristic
87C5×D3×Q8C2×C411yescharacteristic
88C5×D3×D4C2×C411yescharacteristic
89C3×#713C2311yescharacteristic
90C3×#711C2311yescharacteristic
91D3×C22⋊D5—21no—
92#6782—21no—
93C2×D3×Dic5—21no—
94#6780—21no—
95D3×D20—21no—
96D3×D20C2×C411yescharacteristic
97C4×D3×D5—21no—
98C4×D3×D5C2311yescharacteristic
99#6773—21no—
100#6773C2311yescharacteristic
101#6772C2311yescharacteristic
102#6768C2×C411yescharacteristic
103D3×Dic10C2×C411yescharacteristic
104#6766—21no—
105#6766C2×C411yescharacteristic
106#6762—21no—
107C2×C3⋊#170—21no—
108C4×ΓL(1,𝔽16)C2311yescharacteristic
109#6758—21no—
110#6758C2311yescharacteristic
111#6758C2311yescharacteristic
112D5⋊(C3⋊C8)—21no—
113D5⋊(C3⋊C8)C2311yescharacteristic
114C3×#704—21no—
115C2×C3×#170—21no—
116C3×C4×AGL(1,𝔽5)C2311yescharacteristic
117C3×#700—21no—
118C3×#700C2311yescharacteristic
119C3×#700C2311yescharacteristic
120C3×D5⋊C8—21no—
121C3×D5⋊C8C2311yescharacteristic
122#6740—21no—
123#6740—21no—
124#6740—21no—
125#6740—21no—
126#6739—21no—
127#6739—21no—
128#6738—21no—
129#6738—21no—
130#6738D411yescharacteristic
131#6738D411yescharacteristic
132D3×#170—21no—
133D3×#170—21no—
134D3×#170—21no—
135D3×#170—21no—
136D3×#170D411yescharacteristic
137D3×#170D411yescharacteristic
138Dic3×AGL(1,𝔽5)—21no—
139C3×C5×SD16C2×C411yescharacteristic, complemented
140#6718C2×C411yescharacteristic, complemented
141#6715C2×C411yescharacteristic, complemented
142#6706C2×C411yescharacteristic, complemented
143C8×D15C2×C411yescharacteristic
144C5×#215C2×C411yescharacteristic, complemented
145C5×#214C2×C411yescharacteristic, complemented
146C5×#204C2×C411yescharacteristic, complemented
147C5×D3×C8C2×C411yescharacteristic
148C3×#689C2×C411yescharacteristic, complemented
149C3×#686C2×C411yescharacteristic, complemented
150C3×#677C2×C411yescharacteristic, complemented
151C3×C8×D5C2311yescharacteristic
152#6663C2×C411yescharacteristic, complemented
153#6661C2×C411yescharacteristic, complemented
154#6658C2×C411yescharacteristic, complemented
155#6657C2×C411yescharacteristic, complemented
156#6654C2×C411yescharacteristic, complemented
157#6652C2×C411yescharacteristic, complemented
158#6648C2×C411yescharacteristic
159D3×#168C2×C411yescharacteristic
160D5×C3⋊C8C2311yescharacteristic
161D3×#135—51no—
162D3×#131—51no—
163D3×#131—51no—
164C3×#444—51no—
165#5197—51no—
166#5145—51no—
167#5145—51no—
168#4894—51no—
169D3×#108—51no—
170#4823—51no—
171#4823—51no—
172D3×#104—51no—
173D3×#104—51no—
174#4717—51no—
175D3×#97—51no—
176C2×#713—31no—
177C2×#711—31no—
178C2×#704—61no—
179C22×#170—61no—
180#4133—31no—
181#4133—31no—
182#4133—31no—
183#4133—61no—
184#4133—61no—
185#4133C2×D311yescharacteristic, complemented
186#4131—31no—
187#4131—31no—
188#4131—31no—
189#4131—61no—
190#4131—61no—
191#4131C2×D311yescharacteristic, complemented
192C2×C4×AGL(1,𝔽5)—31no—
193C2×#700—31no—
194C2×#700—31no—
195C2×#700—61no—
196C2×D5⋊C8—31no—
197C2×D5⋊C8—61no—
198C2×C5×SD16—31no—
199C2×#689—31no—
200C2×#686—31no—
201#4062—31no—
202#4062—31no—
203#4062—31no—
204#4062—31no—
205#4062—31no—
206#4062—31no—
207#4062—31no—
208#4062C2×D311yescharacteristic
209C2×#677—31no—
210C2×C8×D5—31no—
211#4010—31no—
212#4010—31no—
213#4010—31no—
214#4010C2×D311yescharacteristic, complemented
215#4008—31no—
216#4008—31no—
217#4008—31no—
218#4008C2×D311yescharacteristic, complemented
219#3996—31no—
220#3996—31no—
221#3996—31no—
222#3996C2×D311yescharacteristic, complemented
223#3992—31no—
224#3992—31no—
225#3992—31no—
226#3992C2×D311yescharacteristic, complemented
227C2×#444—151noSylow
228C22×C5×D3—21no—
229C2×D3×D5—21no—
230C2×D3×D5#4111yescharacteristic
231C2×ΓL(1,𝔽16)—21no—
232C2×C3×AGL(1,𝔽5)—21no—
233D3×AGL(1,𝔽5)—42no—
234C3×C5×Q8C22×C411yescharacteristic
235C3×C5×D4C22×C411yescharacteristic
236#1220—21no—
237C2×Dic15—21no—
238D60—21no—
239D60C22×C411yescharacteristic
240C4×D15—21no—
241C4×D15C22×C411yescharacteristic
242Dic30C22×C411yescharacteristic
243C5×#67—21no—
244C5×D12C22×C411yescharacteristic
245C4×C5×D3—21no—
246C4×C5×D3C22×C411yescharacteristic
247C5×Dic6—21no—
248C5×Dic6C22×C411yescharacteristic
249C3×C22⋊D5—21no—
250C2×C3×Dic5—21no—
251C3×D20—21no—
252C3×D20C22×C411yescharacteristic
253C3×C4×D5—21no—
254C3×C4×D5C2411yescharacteristic
255C3×Dic10C22×C411yescharacteristic
256#1204—21no—
257#1203—21no—
258#1202—21no—
259#1202—21no—
260#1202—21no—
261#1201—21no—
262#1200—21no—
263#1200C2×D411yescharacteristic
264D3×Dic5—21no—
265D3×Dic5—21no—
266D3×Dic5—21no—
267D3×Dic5C2×D411yescharacteristic
268D5×Dic3—21no—
269D5×Dic3#4111yescharacteristic
270C3⋊#170—21no—
271C3⋊#170—21no—
272C3⋊#170C2×D411yescharacteristic
273C3⋊#170C2×D411yescharacteristic
274C3×#170—21no—
275C3×#170—21no—
276C3×#170C2×D411yescharacteristic
277C3×#170C2×D411yescharacteristic
278C3×C5×C8C22×C411yescharacteristic
279C3⋊#168C22×C411yescharacteristic
280C3×#168C22×C411yescharacteristic
281C5×C3⋊C8C22×C411yescharacteristic
282D3×#41—51no—
283D3×#41—51no—
284C3×#135—51no—
285C3×#131—51no—
286C3×#131—51no—
287#950—51no—
288#950—51no—
289#948—51no—
290#948—51no—
291#919—51no—
292D3×Q16—51no—
293#916—51no—
294#916—51no—
295D3×SD16—51no—
296D3×SD16AGL(1,𝔽5)11yescharacteristic, complemented
297#912—51no—
298D3×D8—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—51no—
310#901—101no—
311#901—101no—
312C2×D3×C8—51no—
313C2×D3×C8—51no—
314C2×D3×C8—101no—
315C2×D3×C8—101no—
316C42×D3—51no—
317C3×#108—51no—
318C3×#104—51no—
319C3×#104—51no—
320C3×#97—51no—
321#837—51no—
322#837—51no—
323#825—51no—
324#825—51no—
325#822—51no—
326#822—51no—
327#819—51no—
328#815—51no—
329#815—51no—
330#805—51no—
331#805—51no—
332#803—51no—
333C22×AGL(1,𝔽5)—61no—
334C2×C5×Q8—31no—
335C2×C5×D4—31no—
336C2×C22⋊D5—61no—
337C22×Dic5—61no—
338#713—31no—
339#713—31no—
340#713—31no—
341#713—61no—
342#713—61no—
343#713C22×D311yescharacteristic
344#711—31no—
345#711—31no—
346#711—31no—
347#711—61no—
348#711—61no—
349#711C22×D311yescharacteristic
350C2×D20—31no—
351C2×D20—61no—
352C2×C4×D5—31no—
353C2×C4×D5—61no—
354C2×Dic10—31no—
355#704—21no—
356#704—61no—
357#704—61no—
358#704—61no—
359C2×#170—21no—
360C2×#170—31no—
361C2×#170—31no—
362C2×#170—61no—
363C2×#170—61no—
364C2×#170—61no—
365C2×#170—61no—
366C2×#170—61no—
367C4×AGL(1,𝔽5)—31no—
368C4×AGL(1,𝔽5)—61no—
369C4×AGL(1,𝔽5)C22×D311yescharacteristic
370#700—21no—
371#700—31no—
372#700—31no—
373#700—61no—
374#700—61no—
375#700—61no—
376#700—61no—
377#700—61no—
378#700C22×D311yescharacteristic
379#700C22×D311yescharacteristic
380D5⋊C8—21no—
381D5⋊C8—31no—
382D5⋊C8—31no—
383D5⋊C8—31no—
384D5⋊C8—61no—
385D5⋊C8—61no—
386D5⋊C8—61no—
387D5⋊C8C22×D311yescharacteristic
388C5×SD16—31no—
389C5×SD16—31no—
390C5×SD16—31no—
391C5×SD16C4×D311yescharacteristic, complemented
392C2×C5×C8—31no—
393#689—31no—
394#689—31no—
395#689—31no—
396#689C4×D311yescharacteristic, complemented
397#686—31no—
398#686—31no—
399#686—31no—
400#686C4×D311yescharacteristic, complemented
401C2×#168—31no—
402#677—31no—
403#677—31no—
404#677—31no—
405#677C4×D311yescharacteristic, complemented
406C8×D5—31no—
407C8×D5—31no—
408C8×D5—31no—
409C8×D5C22×D311yescharacteristic
410C2×#135—151no—
411C2×#131—151no—
412C2×#131—151no—
413#444—51no—
414#444—151no—
415#444—151no—
416#444—151no—
417#444—151no—
418#444—151no—
419#444—151no—
420#444—151no—
421C2×#108—151no—
422C2×#104—151no—
423C2×#104—151no—
424C2×#97—151no—
425C22×C3×C5—21no—
426C2×D15—21no—
427C2×D15C4×D411yescharacteristic
428C2×C5×D3—21no—
429C2×C5×D3—42no—
430C2×C5×D3C4×D411yescharacteristic
431C2×C3×D5—21no—
432C2×C3×D5C2×#4111yescharacteristic
433D3×D5—22no—
434D3×D5—42no—
435ΓL(1,𝔽16)—41no—
436C3×AGL(1,𝔽5)—41no—
437C3×C4×C5—21no—
438C3×C4×C5C23×C411yescharacteristic
439Dic15—21no—
440Dic15C4×D411yescharacteristic
441C3×Dic5—21no—
442C3×Dic5C22×D411yescharacteristic
443C5×Dic3—21no—
444C5×Dic3C4×D411yescharacteristic
445C3×#41—51no—
446C3×#41—51no—
447#239—51no—
448#239—51no—
449D3×Q8—51no—
450D3×Q8C2×AGL(1,𝔽5)11yescharacteristic
451#237—51no—
452#237—51no—
453#237—101no—
454#237—101no—
455D3×D4—51no—
456D3×D4—101no—
457D3×D4—101no—
458D3×D4C2×AGL(1,𝔽5)11yescharacteristic
459#235—51no—
460#235—51no—
461#235—101no—
462#235—101no—
463C2×C4×D3—51no—
464C2×C4×D3—101no—
465C2×C4×D3—101no—
466C2×C4×D3—101no—
467C3×Q16—51no—
468C3×SD16—51no—
469C3×SD16C2×AGL(1,𝔽5)11yescharacteristic, complemented
470C3×D8—51no—
471C3×M16—51no—
472C3×M16—51no—
473C3×M16—101no—
474C3×M16—101no—
475C2×C3×C8—51no—
476C2×C3×C8—51no—
477C2×C3×C8—101no—
478C2×C3×C8—101no—
479C3×C42—51no—
480#216—51no—
481#216—51no—
482#215—51no—
483#215C2×AGL(1,𝔽5)11yescharacteristic, complemented
484#214—51no—
485#214C2×AGL(1,𝔽5)11yescharacteristic, complemented
486#213—51no—
487#213—51no—
488C4×Dic3—51no—
489C4×Dic3—101no—
490#208—51no—
491#208—51no—
492#208—101no—
493#208—101no—
494C2×C3⋊C8—51no—
495C2×C3⋊C8—51no—
496C2×C3⋊C8—101no—
497C2×C3⋊C8—101no—
498Dic12—51no—
499D24—51no—
500#204—51no—
501#204C2×AGL(1,𝔽5)11yescharacteristic, complemented
502ΓL(1,𝔽25)—101no—
503ΓL(1,𝔽25)—101no—
504ΓL(1,𝔽25)—101no—
505ΓL(1,𝔽25)—101no—
506ΓL(1,𝔽25)—101no—
507ΓL(1,𝔽25)—101no—
508D3×C8—51no—
509D3×C8—51no—
510D3×C8—51no—
511D3×C8—51no—
512D3×C8—51no—
513D3×C8—51no—
514D3×C8—51no—
515D3×C8—101no—
516D3×C8—101no—
517D3×C8—101no—
518D3×C8—101no—
519D3×C8—101no—
520D3×C8—101no—
521D3×C8C2×AGL(1,𝔽5)11yescharacteristic
522C23×C5—61no—
523C22×D5—31no—
524C22×D5—61no—
525C2×AGL(1,𝔽5)—21no—
526C2×AGL(1,𝔽5)—61no—
527C2×AGL(1,𝔽5)—122no—
528C5×Q8—31no—
529C5×Q8—61no—
530C5×Q8C2×C4×D311yescharacteristic
531C5×D4—31no—
532C5×D4—61no—
533C5×D4C2×C4×D311yescharacteristic
534C2×C4×C5—31no—
535C2×C4×C5—61no—
536C22⋊D5—21no—
537C22⋊D5—61no—
538C22⋊D5—61no—
539C22⋊D5—61no—
540C2×Dic5—21no—
541C2×Dic5—31no—
542C2×Dic5—61no—
543C2×Dic5—61no—
544C2×Dic5—61no—
545C2×Dic5—61no—
546D20—21no—
547D20—31no—
548D20—61no—
549D20—61no—
550D20—61no—
551D20—61no—
552D20C2×C4×D311yescharacteristic
553C4×D5—21no—
554C4×D5—31no—
555C4×D5—31no—
556C4×D5—31no—
557C4×D5—61no—
558C4×D5—61no—
559C4×D5—61no—
560C4×D5C23×D311yescharacteristic
561Dic10—31no—
562Dic10—61no—
563Dic10C2×C4×D311yescharacteristic
564#170—21no—
565#170—21no—
566#170—31no—
567#170—31no—
568#170—61no—
569#170—61no—
570#170D3×D411yescharacteristic
571#170D3×D411yescharacteristic
572C5×C8—31no—
573C5×C8C2×C4×D311yescharacteristic
574#168—31no—
575#168C2×C4×D311yescharacteristic
576C2×#41—151no—
577C2×#41—151no—
578#135—51no—
579#135—151no—
580#135—151no—
581#135—151no—
582#135—151no—
583#135—151no—
584#135—151no—
585#135—151no—
586C2×Q16—151no—
587C2×SD16—31no—
588C2×SD16—151no—
589C2×D8—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—151no—
603C2×M16—151no—
604C2×M16—301no—
605C2×M16—301no—
606C22×C8—151no—
607C22×C8—151no—
608C22×C8—301no—
609C22×C8—301no—
610C2×C42—151no—
611#108—51no—
612#108—151no—
613#108—151no—
614#108—151no—
615#104—51no—
616#104—51no—
617#104—151no—
618#104—151no—
619#104—151no—
620#104—151no—
621#104—151no—
622#104—151no—
623#97—51no—
624#97—151no—
625#97—151no—
626#97—151no—
627C2×C3×C5—41no—
628C2×C3×C5C2×C4×D411yescharacteristic
629D15—21no—
630D15—41no—
631C3×D5—21no—
632C3×D5—41no—
633C5×D3—41no—
634C5×D3#44412yescomplemented
635C22×D3—21no—
636C22×D3—51no—
637C22×D3—101no—
638C3×Q8—51no—
639C3×Q8C22×AGL(1,𝔽5)11yescharacteristic
640C3×D4—51no—
641C3×D4—101no—
642C3×D4—101no—
643C3×D4C22×AGL(1,𝔽5)11yescharacteristic
644C2×C3×C4—51no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4—101no—
648#67—21no—
649#67—101no—
650#67—101no—
651#67—101no—
652#67—101no—
653#67—101no—
654C2×Dic3—51no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658D12—51no—
659D12—101no—
660D12—101no—
661D12C22×AGL(1,𝔽5)11yescharacteristic
662C4×D3—21no—
663C4×D3—51no—
664C4×D3—51no—
665C4×D3—51no—
666C4×D3—101no—
667C4×D3—101no—
668C4×D3—101no—
669C4×D3—101no—
670C4×D3—101no—
671C4×D3—202no—
672C4×D3C22×AGL(1,𝔽5)11yescharacteristic
673Dic6—21no—
674Dic6—51no—
675Dic6—101no—
676Dic6C22×AGL(1,𝔽5)11yescharacteristic
677C3×C8—51no—
678C3×C8—51no—
679C3×C8—51no—
680C3×C8—101no—
681C3×C8—101no—
682C3×C8C22×AGL(1,𝔽5)11yescharacteristic
683C3⋊C8—51no—
684C3⋊C8—51no—
685C3⋊C8—51no—
686C3⋊C8—101no—
687C3⋊C8—101no—
688C3⋊C8C22×AGL(1,𝔽5)11yescharacteristic
689C22×C5—21no—
690C22×C5—31no—
691C22×C5—61no—
692C22×C5—122no—
693C2×D5—21no—
694C2×D5—31no—
695C2×D5—62no—
696C2×D5—61no—
697C2×D5—122no—
698C2×D5D3×#4111yescharacteristic
699AGL(1,𝔽5)—41no—
700AGL(1,𝔽5)—121no—
701C4×C5—21no—
702C4×C5—31no—
703C4×C5—61no—
704C4×C5C22×C4×D311yescharacteristic
705Dic5—21no—
706Dic5—31no—
707Dic5—61no—
708Dic5C2×D3×D411yescharacteristic
709#41—51no—
710#41—51no—
711#41—151no—
712#41—151no—
713#41—151no—
714#41—151no—
715#41—151no—
716#41—151no—
717#41—301no—
718#41—301no—
719#41—301no—
720#41—301no—
721C2×Q8—31no—
722C2×Q8—151no—
723C2×D4—31no—
724C2×D4—151no—
725C2×D4—301no—
726C2×D4—301no—
727C22×C4—151no—
728C22×C4—301no—
729C22×C4—301no—
730C22×C4—301no—
731Q16—51no—
732Q16—151no—
733Q16—151no—
734Q16—151no—
735SD16—31no—
736SD16—31no—
737SD16—31no—
738SD16—51no—
739SD16—151no—
740SD16—151no—
741SD16—151no—
742SD16D3×AGL(1,𝔽5)11yescharacteristic, complemented
743D8—51no—
744D8—151no—
745D8—151no—
746D8—151no—
747M16—51no—
748M16—51no—
749M16—101no—
750M16—101no—
751M16—151no—
752M16—151no—
753M16—301no—
754M16—301no—
755M16—301no—
756M16—301no—
757M16—301no—
758M16—301no—
759M16—301no—
760M16—301no—
761C2×C8—31no—
762C2×C8—51no—
763C2×C8—51no—
764C2×C8—101no—
765C2×C8—101no—
766C2×C8—151no—
767C2×C8—151no—
768C2×C8—151no—
769C2×C8—151no—
770C2×C8—151no—
771C2×C8—151no—
772C2×C8—151no—
773C2×C8—151no—
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×C8—301no—
783C42—51no—
784C42—151no—
785C42—301no—
786C3×C5C2×#44411yescharacteristic, complemented, Hall
787C22×C3—21no—
788C22×C3—51no—
789C22×C3—101no—
790C2×D3—21no—
791C2×D3—42no—
792C2×D3—51no—
793C2×D3—102no—
794C2×D3—101no—
795C2×D3—202no—
796C2×D3D4×AGL(1,𝔽5)11yescharacteristic
797C3×C4—21no—
798C3×C4—51no—
799C3×C4—101no—
800C3×C4—201no—
801C3×C4C23×AGL(1,𝔽5)11yescharacteristic
802Dic3—21no—
803Dic3—51no—
804Dic3—101no—
805Dic3—201no—
806Dic3D4×AGL(1,𝔽5)11yescharacteristic
807C2×C5—32no—
808C2×C5—41no—
809C2×C5—121no—
810C2×C5C4×D3×D411yescharacteristic
811D5—21no—
812D5—41no—
813D5—61no—
814D5—121no—
815C23—61no—
816C23—151no—
817C23—301no—
818Q8—31no—
819Q8—51no—
820Q8—61no—
821Q8—151no—
822Q8—301no—
823Q8C2×D3×AGL(1,𝔽5)11yescharacteristic
824D4—31no—
825D4—51no—
826D4—61no—
827D4—101no—
828D4—101no—
829D4—151no—
830D4—301no—
831D4—301no—
832D4—301no—
833D4—301no—
834D4—301no—
835D4—301no—
836D4—301no—
837D4C2×D3×AGL(1,𝔽5)11yescharacteristic
838C2×C4—31no—
839C2×C4—51no—
840C2×C4—61no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
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—301no—
856C2×C4—602no—
857C8—31no—
858C8—51no—
859C8—51no—
860C8—51no—
861C8—101no—
862C8—101no—
863C8—151no—
864C8—151no—
865C8—151no—
866C8—301no—
867C8—301no—
868C8C2×D3×AGL(1,𝔽5)11yescharacteristic
869C2×C3—41no—
870C2×C3—101no—
871C2×C3—201no—
872C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
873D3—41no—
874D3—101no—
875D3—201no—
876D3#6573712yesdirect product factor
877C5D3×#44411yescharacteristic, complemented, Sylow
878C22—21no—
879C22—31no—
880C22—51no—
881C22—61no—
882C22—101no—
883C22—122no—
884C22—151no—
885C22—302no—
886C22—301no—
887C22—602no—
888C4—21no—
889C4—31no—
890C4—51no—
891C4—61no—
892C4—101no—
893C4—151no—
894C4—201no—
895C4—301no—
896C4—601no—
897C4C22×D3×AGL(1,𝔽5)11yescharacteristic
898C3C2×#6573711yescharacteristic, complemented, Sylow
899C2—32no—
900C2—41no—
901C2—101no—
902C2—121no—
903C2—201no—
904C2—301no—
905C2—601no—
906C2D3×D4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2D3×D4×AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×SD16C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD3×#4062C2
cosocleC3×C4×D5C24
hypercenterSD16D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. D3×#4133C2semidirect
2. D3×#4131C2semidirect
4. #11752396C2semidirect
5. C3×#65737C2semidirect
6. #11751980C2semidirect
7. #11751976C2semidirect
8. D3×#4010C2semidirect
9. #11751958C2semidirect
10. #11751954C2semidirect
11. D3×#4008C2semidirect
12. #11751688C2semidirect
13. #11751681C2semidirect
14. D3×#3996C2semidirect
15. D3×#3992C2semidirect
19. #91992C22semidirect
20. #91990C22semidirect
21. C3×#4133C22semidirect
22. C3×#4131C22semidirect
29. #91916C22semidirect
31. #91914C22semidirect
32. #91913C22semidirect
36. #91911C22semidirect
39. #91805C4semidirect
40. C5×D3×SD16C4semidirect
42. #91523C4semidirect
44. D3×#689C4semidirect
45. #91497C4semidirect
47. D3×#686C4semidirect
48. #91276C4semidirect
50. D3×#677C4semidirect
52. #91239C22semidirect
53. #91237C22semidirect
54. #91225C22semidirect
55. #91221C22semidirect
56. C3×#4010C22semidirect
57. C3×#4008C22semidirect
58. C3×#3996C22semidirect
59. C3×#3992C22semidirect
60. #91162C22semidirect
61. #91162C22semidirect
62. #91158C22semidirect
63. #91157C22semidirect
64. #91156C22semidirect
65. #91155C22semidirect
66. #91150C22semidirect
67. #91149C22semidirect
81. #65737D3direct (N × H)
139. C3×C5×SD16C2×C4semidirect
140. #6718C2×C4semidirect
141. #6715C2×C4semidirect
142. #6706C2×C4semidirect
144. C5×#215C2×C4semidirect
145. C5×#214C2×C4semidirect
146. C5×#204C2×C4semidirect
148. C3×#689C2×C4semidirect
149. C3×#686C2×C4semidirect
150. C3×#677C2×C4semidirect
152. #6663C2×C4semidirect
153. #6661C2×C4semidirect
154. #6658C2×C4semidirect
155. #6657C2×C4semidirect
156. #6654C2×C4semidirect
157. #6652C2×C4semidirect
185. #4133C2×D3semidirect
191. #4131C2×D3semidirect
214. #4010C2×D3semidirect
218. #4008C2×D3semidirect
222. #3996C2×D3semidirect
226. #3992C2×D3semidirect
296. D3×SD16AGL(1,𝔽5)semidirect
391. C5×SD16C4×D3semidirect
396. #689C4×D3semidirect
400. #686C4×D3semidirect
405. #677C4×D3semidirect
469. C3×SD16C2×AGL(1,𝔽5)semidirect
483. #215C2×AGL(1,𝔽5)semidirect
485. #214C2×AGL(1,𝔽5)semidirect
501. #204C2×AGL(1,𝔽5)semidirect
634. C5×D3#444semidirect
742. SD16D3×AGL(1,𝔽5)semidirect
786. C3×C5C2×#444semidirect
876. D3#65737direct (N × H)
877. C5D3×#444semidirect
898. C3C2×#65737semidirect

Maximal subgroups

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

subgroupindex
D3×#41332
D3×#41312
D3×#40622
#117523962
C3×#657372
#117519802
#117519762
D3×#40102
#117519582
#117519542
D3×#40082
#117516882
#117516812
D3×#39962
D3×#39922
C2×#657373
D3×#4445