Finite Group Databasebeta

← D3×#65071 #14428028

Subgroups — D3×#65071 #14428028

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4084C211yesmaximal, characteristic, complemented
2C2×D3×#686C211yesmaximal, characteristic, complemented
3C2×D3×#676C211yesmaximal, characteristic, complemented
4D3×#4041C211yesmaximal, characteristic, complemented
5#11750883C211yesmaximal, characteristic, complemented
6C5×D3×#102C211yesmaximal, characteristic, complemented
7C3×#65071C211yesmaximal, characteristic, complemented
8#11749030C211yesmaximal, characteristic, complemented
9#11749027C211yesmaximal, characteristic, complemented
10D3×#3953C211yesmaximal, characteristic, complemented
11#11747925C211yesmaximal, characteristic, complemented
12#11747894C211yesmaximal, characteristic, complemented
13D3×#3940C211yesmaximal, characteristic, complemented
14#11747317C211yesmaximal, characteristic, complemented
15#11747312C211yesmaximal, characteristic, complemented
16C2×#65071—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C2×D3×C22⋊D5—21no—
19C2×D3×D20—21no—
20C2×D3×D20C2211yescharacteristic
21C2×C4×D3×D5C2211yescharacteristic
22#91827C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic, complemented
24C2×#6705C2211yescharacteristic, complemented
25#91784C2211yescharacteristic, complemented
26C2×C5×D3×C8C2211yescharacteristic
27C5×D3×C4⋊C4C2211yescharacteristic
28C3×#4084C2211yescharacteristic, complemented
29C2×C3×#686C2211yescharacteristic, complemented
30C2×C3×#676C2211yescharacteristic, complemented
31C3×#4041C2211yescharacteristic, complemented
32#91557—21no—
33D3×C22⋊Dic5—21no—
34#91549—21no—
35D3×#686—24no—
36D3×#685—21no—
37#91466C2211yescharacteristic, complemented
38#91465C2211yescharacteristic, complemented
39#91459—21no—
40#91450C2211yescharacteristic, complemented
41#91449C2211yescharacteristic, complemented
42D3×C4⋊Dic5C2211yescharacteristic
43#91409—21no—
44C2×#6654C2211yescharacteristic, complemented
45C2×#6652C2211yescharacteristic, complemented
46C2×#6651C2211yescharacteristic, complemented
47C2×#6649C2211yescharacteristic, complemented
48C2×D3×#168C2211yescharacteristic
49D3×#676—24no—
50C3×C5×#102C2211yescharacteristic, complemented
51#91105C2211yescharacteristic, complemented
52#91092C2211yescharacteristic, complemented
53C5×#832C2211yescharacteristic, complemented
54C5×#821C2211yescharacteristic, complemented
55C5×#809C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic, complemented
57C3×#3940C2211yescharacteristic, complemented
58#90986C2211yescharacteristic, complemented
59#90985C2211yescharacteristic, complemented
60#90968C2211yescharacteristic, complemented
61#90965C2211yescharacteristic, complemented
62D3×#469—51nomaximal, Hall
63C2×#4084—31no—
64C22×#686—31no—
65C22×#676—31no—
66C2×#4041—31no—
67C2×C5×#102—31no—
68C2×#3953—31no—
69C2×#3940—31no—
70#65071—31no—
71#65071—31no—
72#65071—31no—
73#65071—31no—
74#65071—31no—
75#65071—31no—
76#65071—31no—
77#65071D311yescharacteristic, direct product factor
78C23×C5×D3—21no—
79C22×D3×D5—21no—
80C22×D3×D5D411yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C2×#1220—21no—
83C2×D60—21no—
84C2×D60C2311yescharacteristic
85C2×C4×D15C2311yescharacteristic
86C2×C5×#67—21no—
87C5×D3×D4—22no—
88C5×D3×D4—22no—
89C2×C5×D12C2311yescharacteristic
90C2×C4×C5×D3—21no—
91C2×C4×C5×D3C2311yescharacteristic
92C2×C3×C22⋊D5—21no—
93C2×C3×D20—21no—
94C2×C3×D20C2311yescharacteristic
95C2×C3×C4×D5C2311yescharacteristic
96D3×C22⋊D5—44no—
97C2×#1203—21no—
98C2×#1202—21no—
99C2×#1202—21no—
100C2×#1202—21no—
101C2×#1201—21no—
102C2×#1200D411yescharacteristic
103C2×D3×Dic5—21no—
104C2×D3×Dic5D411yescharacteristic
105C2×D5×Dic3D411yescharacteristic
106D3×D20—22no—
107D3×D20—22no—
108D3×D20—44no—
109C4×D3×D5—22no—
110C4×D3×D5—22no—
111C2×C3×C5×C8C2311yescharacteristic
112C3×C5×C4⋊C4C2311yescharacteristic
113#6719—21no—
114#6715—22no—
115#6714—21no—
116C4⋊Dic15C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118#6705—22no—
119C5×C4⋊Dic3C2311yescharacteristic
120C5×Dic3⋊C4—21no—
121C2×C5×C3⋊C8C2311yescharacteristic
122C5×D3×C8—22no—
123C3×C22⋊Dic5—21no—
124C3×#686—22no—
125C3×#685—21no—
126C3×C4⋊Dic5C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C3×#676—22no—
129Dic3⋊Dic5—21no—
130#6667—21no—
131(C2×D3)⋊Dic5—21no—
132(C2×D3)⋊Dic5—21no—
133#6665—21no—
134#6654—22no—
135#6652—22no—
136#6651—22no—
137#6649—22no—
138D3×#168D414yescomplemented
139C2×D3×D8—51no—
140C2×D3×M16—51no—
141D3×#121—51no—
142D3×#121—51no—
143C3×#469—51no—
144#5159—51no—
145#5135—51no—
146#5039—51no—
147#5039—51no—
148#4865—51no—
149D3×#106—51no—
150#4782—51no—
151#4782—51no—
152D3×#102—51no—
153D3×#102D511yescharacteristic, complemented
154C22×C5×D4—31no—
155C22×C22⋊D5—61no—
156C22×D20—31no—
157C22×D20—61no—
158C22×C4×D5—31no—
159C22×C5×C8—31no—
160C2×C5×C4⋊C4—31no—
161C2×C22⋊Dic5—61no—
162#4084—31no—
163#4084—31no—
164#4084—31no—
165#4084—61no—
166#4084—61no—
167#4084C2×D311yescharacteristic, complemented
168C2×#686—31no—
169C2×#686—31no—
170C2×#686—31no—
171C2×#686—64no—
172C2×#686C2×D311yescharacteristic, complemented
173C2×#685—61no—
174C2×C4⋊Dic5—31no—
175C22×#168—31no—
176C2×#676—31no—
177C2×#676—31no—
178C2×#676—31no—
179C2×#676—64no—
180C2×#676C2×D311yescharacteristic, complemented
181#4041—31no—
182#4041—31no—
183#4041—31no—
184#4041—61no—
185#4041—61no—
186#4041C2×D311yescharacteristic, complemented
187C5×#102—31no—
188C5×#102—31no—
189C5×#102—31no—
190C5×#102C2×D311yescharacteristic, complemented
191#3953—31no—
192#3953—31no—
193#3953—31no—
194#3953C2×D311yescharacteristic, complemented
195#3940—31no—
196#3940—31no—
197#3940—31no—
198#3940C2×D311yescharacteristic, complemented
199C2×#469—151noSylow
200C23×C3×C5—21no—
201C22×D15—21no—
202C22×D15C2×D411yescharacteristic
203C22×C5×D3—21no—
204C22×C5×D3—42no—
205C22×C5×D3—42no—
206C22×C5×D3—42no—
207C22×C5×D3C2×D411yescharacteristic
208C22×C3×D5—21no—
209C22×C3×D5C2×D411yescharacteristic
210C2×D3×D5—22no—
211C2×D3×D5—22no—
212C2×D3×D5—22no—
213C2×D3×D5—42no—
214C2×D3×D5—42no—
215C2×D3×D5—42no—
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5C2411yescharacteristic
220#1220—42no—
221C2×Dic15—21no—
222C2×Dic15C2×D411yescharacteristic
223D60—21no—
224D60—21no—
225D60—42no—
226C4×D15—21no—
227C4×D15—21no—
228C5×#67—42no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3C2×D411yescharacteristic
231C5×D12—21no—
232C5×D12—21no—
233C4×C5×D3—42no—
234C4×C5×D3C2×D412yes—
235C4×C5×D3#4112yes—
236C3×C22⋊D5—42no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5C2×D411yescharacteristic
239C3×D20—21no—
240C3×D20—21no—
241C3×D20—42no—
242C3×C4×D5—21no—
243C3×C4×D5—21no—
244#1203—42no—
245#1202—42no—
246#1202—42no—
247#1202—42no—
248#1201—42no—
249#1200—22no—
250D3×Dic5—22no—
251D3×Dic5—42no—
252D5×Dic3—22no—
253C3×C5×C8—21no—
254C3⋊#168C2×D412yescomplemented
255C3×#168C2×D412yescomplemented
256C5×C3⋊C8—21no—
257C2×D3×D4—51no—
258C2×D3×D4—101no—
259C2×D3×D4—101no—
260C2×D3×D4C2×D511yescharacteristic
261C22×C4×D3—51no—
262C2×C3×D8—51no—
263C2×C3×M16—51no—
264C3×#121—51no—
265C3×#121—51no—
266#939—101no—
267#939—101no—
268#938—51no—
269#938—51no—
270C2×#213—51no—
271C2×#213—51no—
272#930—51no—
273#930—51no—
274C2×#208—51no—
275D3×D8—104no—
276D3×M16—104no—
277C2×D24—51no—
278C2×ΓL(1,𝔽25)—51no—
279C2×ΓL(1,𝔽25)—51no—
280C2×D3×C8—51no—
281C2×D3×C8C2×D511yescharacteristic
282#895—51no—
283#895—51no—
284D3×C4⋊C4—51no—
285D3×C4⋊C4C2×D511yescharacteristic
286#884—101no—
287#884—101no—
288D3×C22⋊C4—101no—
289D3×C22⋊C4—101no—
290C3×#106—51no—
291C3×#102—51no—
292C3×#102C2×D511yescharacteristic, complemented
293#832—51no—
294#832C2×D511yescharacteristic, complemented
295#821—51no—
296#821C2×D511yescharacteristic, complemented
297#817—51no—
298#809—51no—
299#809C2×D511yescharacteristic, complemented
300#808—51no—
301#808—51no—
302C24×C5—61no—
303C23×D5—31no—
304C23×D5—61no—
305C2×C5×D4—31no—
306C2×C5×D4—62no—
307C2×C5×D4—62no—
308C2×C5×D4—61no—
309C2×C5×D4C22×D311yescharacteristic
310C22×C4×C5—31no—
311C22×C4×C5—61no—
312C2×C22⋊D5—21no—
313C2×C22⋊D5—61no—
314C2×C22⋊D5—61no—
315C2×C22⋊D5—61no—
316C2×C22⋊D5—124no—
317C22×Dic5—31no—
318C22×Dic5—61no—
319C2×D20—21no—
320C2×D20—31no—
321C2×D20—62no—
322C2×D20—62no—
323C2×D20—61no—
324C2×D20—61no—
325C2×D20—61no—
326C2×D20—61no—
327C2×D20—124no—
328C2×D20C22×D311yescharacteristic
329C2×C4×D5—31no—
330C2×C4×D5—31no—
331C2×C4×D5—31no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C2×C4×D5C22×D311yescharacteristic
335C2×C5×C8—31no—
336C2×C5×C8—62no—
337C2×C5×C8C22×D311yescharacteristic
338C5×C4⋊C4—31no—
339C5×C4⋊C4—61no—
340C5×C4⋊C4C22×D311yescharacteristic
341C22⋊Dic5—21no—
342C22⋊Dic5—61no—
343C22⋊Dic5—61no—
344C22⋊Dic5—61no—
345#686—22no—
346#686—62no—
347#686—62no—
348#686—62no—
349#685—21no—
350#685—61no—
351#685—61no—
352#685—61no—
353C4⋊Dic5—31no—
354C4⋊Dic5—61no—
355C4⋊Dic5C22×D311yescharacteristic
356C2×#168—31no—
357C2×#168—34no—
358C2×#168C22×D311yescharacteristic
359#676—22no—
360#676—62no—
361#676—62no—
362#676—62no—
363C22×D8—151no—
364C22×M16—151no—
365C2×#121—151no—
366C2×#121—151no—
367#469—51no—
368#469—151no—
369#469—151no—
370#469—151no—
371#469—151no—
372#469—151no—
373#469—151no—
374#469—151no—
375C2×#106—151no—
376C2×#102—31no—
377C2×#102—151no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5C22×D411yescharacteristic
382C2×D15—21no—
383C2×D15—21no—
384C2×D15—21no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×C5×D3—41no—
389C2×C5×D3—41no—
390C2×C5×D3—41no—
391C2×C5×D3—84no—
392C2×C5×D3#12112yes—
393C2×C5×D3AGL(1,ℤ/8)12yes—
394C2×C5×D3AGL(1,ℤ/8)12yes—
395C2×C3×D5—21no—
396C2×C3×D5—21no—
397C2×C3×D5—21no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C2×C3×D5—41no—
401D3×D5—44no—
402D3×D5—84no—
403C3×C4×C5—41no—
404C3×C4×C5C22×D411yescharacteristic
405C3×C4×C5C2×#4111yescharacteristic
406Dic15—21no—
407Dic15—41no—
408C3×Dic5—21no—
409C3×Dic5—41no—
410C5×Dic3—41no—
411C5×Dic3#12112yes—
412C23×D3—21no—
413C23×D3—51no—
414C23×D3—101no—
415C2×C3×D4—51no—
416C2×C3×D4—101no—
417C2×C3×D4—101no—
418C2×C3×D4C22×D511yescharacteristic
419C22×C3×C4—51no—
420C2×#67—21no—
421C2×#67—101no—
422C2×#67—101no—
423C2×#67—101no—
424C2×#67—101no—
425C2×#67—101no—
426C22×Dic3—51no—
427D3×D4—22no—
428D3×D4—22no—
429D3×D4—102no—
430D3×D4—102no—
431D3×D4—204no—
432D3×D4—204no—
433C2×D12—51no—
434C2×D12—101no—
435C2×D12—101no—
436C2×D12C22×D511yescharacteristic
437C2×C4×D3—21no—
438C2×C4×D3—51no—
439C2×C4×D3—51no—
440C2×C4×D3—51no—
441C2×C4×D3—102no—
442C2×C4×D3—102no—
443C2×C4×D3—101no—
444C2×C4×D3C22×D511yescharacteristic
445C3×D8—102no—
446C3×M16—102no—
447C2×C3×C8—51no—
448C2×C3×C8C22×D511yescharacteristic
449C3×C4⋊C4—51no—
450C3×C4⋊C4C22×D511yescharacteristic
451C3×C22⋊C4—101no—
452C3×C22⋊C4—101no—
453#217—101no—
454#217—101no—
455#213—102no—
456#213—102no—
457(C2×D3)⋊C4—101no—
458(C2×D3)⋊C4—101no—
459(C2×D3)⋊C4—101no—
460(C2×D3)⋊C4—101no—
461C4⋊Dic3—51no—
462C4⋊Dic3C22×D511yescharacteristic
463Dic3⋊C4—21no—
464Dic3⋊C4—101no—
465#208—102no—
466C2×C3⋊C8—51no—
467C2×C3⋊C8C22×D511yescharacteristic
468D24—102no—
469ΓL(1,𝔽25)—102no—
470ΓL(1,𝔽25)—102no—
471D3×C8—22no—
472D3×C8—54no—
473C23×C5—21no—
474C23×C5—31no—
475C23×C5—61no—
476C23×C5—122no—
477C23×C5—122no—
478C23×C5—122no—
479C22×D5—21no—
480C22×D5—31no—
481C22×D5—62no—
482C22×D5—62no—
483C22×D5—62no—
484C22×D5—61no—
485C22×D5—122no—
486C22×D5—122no—
487C22×D5—122no—
488C22×D5D3×D411yescharacteristic
489C5×D4—21no—
490C5×D4—21no—
491C5×D4—61no—
492C5×D4—61no—
493C5×D4—122no—
494C2×C4×C5—21no—
495C2×C4×C5—31no—
496C2×C4×C5—32no—
497C2×C4×C5—32no—
498C2×C4×C5—61no—
499C2×C4×C5—122no—
500C2×C4×C5C23×D311yescharacteristic
501C22⋊D5—42no—
502C22⋊D5—122no—
503C22⋊D5—122no—
504C22⋊D5—122no—
505C2×Dic5—21no—
506C2×Dic5—31no—
507C2×Dic5—62no—
508C2×Dic5—61no—
509C2×Dic5—122no—
510C2×Dic5D3×D411yescharacteristic
511D20—21no—
512D20—21no—
513D20—42no—
514D20—61no—
515D20—61no—
516D20—122no—
517D20—122no—
518D20—122no—
519D20—122no—
520C4×D5—21no—
521C4×D5—21no—
522C4×D5—62no—
523C4×D5—62no—
524C4×D5—61no—
525C4×D5—61no—
526C5×C8—21no—
527C5×C8—61no—
528#168—32no—
529#168D3×D412yescomplemented
530C22×D4—31no—
531C22×D4—151no—
532C22×D4—301no—
533C22×D4—301no—
534C23×C4—151no—
535C2×D8—51no—
536C2×D8—151no—
537C2×D8—151no—
538C2×D8—151no—
539C2×D8—304no—
540C2×M16—51no—
541C2×M16—151no—
542C2×M16—151no—
543C2×M16—151no—
544C2×M16—304no—
545C22×C8—31no—
546C22×C8—151no—
547#121—51no—
548#121—51no—
549#121—151no—
550#121—151no—
551#121—151no—
552#121—151no—
553#121—151no—
554#121—151no—
555#121—301no—
556#121—301no—
557#121—301no—
558#121—301no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—151no—
561C2×C22⋊C4—301no—
562C2×C22⋊C4—301no—
563#106—51no—
564#106—151no—
565#106—151no—
566#106—151no—
567#102—31no—
568#102—31no—
569#102—31no—
570#102—51no—
571#102—151no—
572#102—151no—
573#102—151no—
574#102D3×D511yescharacteristic, complemented
575C2×C3×C5—81no—
576C2×C3×C5C2×#12111yescharacteristic
577C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
578C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
579D15—41no—
580D15—81no—
581C3×D5—41no—
582C3×D5—81no—
583C5×D3—81no—
584C5×D3#46914yescomplemented
585C23×C3—21no—
586C23×C3—51no—
587C23×C3—101no—
588C22×D3—21no—
589C22×D3—42no—
590C22×D3—42no—
591C22×D3—42no—
592C22×D3—51no—
593C22×D3—102no—
594C22×D3—102no—
595C22×D3—102no—
596C22×D3—101no—
597C22×D3—202no—
598C22×D3—202no—
599C22×D3—202no—
600C22×D3D4×D511yescharacteristic
601C3×D4—21no—
602C3×D4—21no—
603C3×D4—101no—
604C3×D4—101no—
605C3×D4—202no—
606C3×D4—202no—
607C2×C3×C4—21no—
608C2×C3×C4—51no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4C23×D511yescharacteristic
613#67—42no—
614#67—202no—
615#67—202no—
616#67—202no—
617#67—202no—
618#67—202no—
619C2×Dic3—21no—
620C2×Dic3—51no—
621C2×Dic3—102no—
622C2×Dic3—101no—
623C2×Dic3D4×D511yescharacteristic
624D12—21no—
625D12—21no—
626D12—101no—
627D12—101no—
628D12—202no—
629D12—202no—
630C4×D3—42no—
631C4×D3—102no—
632C4×D3—101no—
633C4×D3—101no—
634C4×D3—102no—
635C4×D3—202no—
636C4×D3#70912yes—
637C4×D3D4×D512yes—
638C3×C8—21no—
639C3×C8—52no—
640C3⋊C8—21no—
641C3⋊C8—52no—
642C22×C5—32no—
643C22×C5—32no—
644C22×C5—32no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—41no—
648C22×C5—121no—
649C22×C5—121no—
650C22×C5—121no—
651C22×C5—244no—
652C22×C5C2×D3×D411yescharacteristic
653C2×D5—21no—
654C2×D5—21no—
655C2×D5—21no—
656C2×D5—41no—
657C2×D5—41no—
658C2×D5—41no—
659C2×D5—61no—
660C2×D5—61no—
661C2×D5—61no—
662C2×D5—124no—
663C2×D5—121no—
664C2×D5—121no—
665C2×D5—121no—
666C2×D5—244no—
667C4×C5—32no—
668C4×C5—41no—
669C4×C5—121no—
670C4×C5C2×D3×D411yescharacteristic
671C4×C5D3×#4111yescharacteristic
672Dic5—21no—
673Dic5—41no—
674Dic5—61no—
675Dic5—121no—
676C24—61no—
677C24—151no—
678C24—301no—
679C2×D4—31no—
680C2×D4—51no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—61no—
684C2×D4—101no—
685C2×D4—101no—
686C2×D4—151no—
687C2×D4—301no—
688C2×D4—302no—
689C2×D4—302no—
690C2×D4—301no—
691C2×D4—301no—
692C2×D4—301no—
693C2×D4—301no—
694C2×D4—301no—
695C2×D4—301no—
696C2×D4—604no—
697C2×D4—604no—
698C2×D4C2×D3×D511yescharacteristic
699C22×C4—31no—
700C22×C4—51no—
701C22×C4—61no—
702C22×C4—151no—
703C22×C4—151no—
704C22×C4—151no—
705C22×C4—151no—
706C22×C4—302no—
707C22×C4—302no—
708C22×C4—301no—
709D8—102no—
710D8—302no—
711D8—302no—
712D8—302no—
713M16—102no—
714M16—302no—
715M16—302no—
716M16—302no—
717C2×C8—31no—
718C2×C8—51no—
719C2×C8—62no—
720C2×C8—154no—
721C2×C8—151no—
722C2×C8C2×D3×D511yescharacteristic
723C4⋊C4—31no—
724C4⋊C4—51no—
725C4⋊C4—61no—
726C4⋊C4—151no—
727C4⋊C4—301no—
728C4⋊C4C2×D3×D511yescharacteristic
729C22⋊C4—101no—
730C22⋊C4—101no—
731C22⋊C4—301no—
732C22⋊C4—301no—
733C22⋊C4—301no—
734C22⋊C4—301no—
735C22⋊C4—301no—
736C22⋊C4—301no—
737C3×C5C2×#46911yescharacteristic, complemented, Hall
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—101no—
742C22×C3—101no—
743C22×C3—101no—
744C22×C3—201no—
745C22×C3—201no—
746C22×C3—201no—
747C22×C3C2×D4×D511yescharacteristic
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—84no—
752C2×D3—101no—
753C2×D3—101no—
754C2×D3—101no—
755C2×D3—204no—
756C2×D3—201no—
757C2×D3—201no—
758C2×D3—201no—
759C2×D3—404no—
760C2×D3#403012yes—
761C2×D3#405712yes—
762C2×D3#406012yes—
763C3×C4—41no—
764C3×C4—101no—
765C3×C4—201no—
766C3×C4C2×#70911yescharacteristic
767C3×C4C2×D4×D511yescharacteristic
768Dic3—41no—
769Dic3—101no—
770Dic3—201no—
771Dic3#403012yes—
772C2×C5—34no—
773C2×C5—81no—
774C2×C5—241no—
775C2×C5D3×#12111yescharacteristic
776C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
777C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
778D5—41no—
779D5—81no—
780D5—121no—
781D5—241no—
782C23—21no—
783C23—31no—
784C23—51no—
785C23—61no—
786C23—101no—
787C23—122no—
788C23—122no—
789C23—122no—
790C23—151no—
791C23—302no—
792C23—302no—
793C23—302no—
794C23—301no—
795C23—602no—
796C23—602no—
797C23—602no—
798D4—21no—
799D4—21no—
800D4—61no—
801D4—61no—
802D4—101no—
803D4—101no—
804D4—122no—
805D4—202no—
806D4—202no—
807D4—301no—
808D4—301no—
809D4—602no—
810D4—602no—
811D4—602no—
812D4—602no—
813D4—602no—
814D4—602no—
815D4—602no—
816C2×C4—21no—
817C2×C4—31no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—51no—
821C2×C4—61no—
822C2×C4—101no—
823C2×C4—101no—
824C2×C4—101no—
825C2×C4—122no—
826C2×C4—151no—
827C2×C4—302no—
828C2×C4—302no—
829C2×C4—302no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—602no—
834C2×C4C22×D3×D511yescharacteristic
835C8—21no—
836C8—52no—
837C8—61no—
838C8—152no—
839C2×C3—81no—
840C2×C3—201no—
841C2×C3—401no—
842C2×C3C2×#403011yescharacteristic
843C2×C3C2×#405711yescharacteristic
844C2×C3C2×#406011yescharacteristic
845D3—81no—
846D3—201no—
847D3—401no—
848D3#6507114yesdirect product factor
849C5D3×#46911yescharacteristic, complemented, Sylow
850C22—32no—
851C22—32no—
852C22—32no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—101no—
857C22—101no—
858C22—101no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—201no—
863C22—201no—
864C22—201no—
865C22—244no—
866C22—301no—
867C22—301no—
868C22—301no—
869C22—604no—
870C22—601no—
871C22—601no—
872C22—601no—
873C22—1204no—
874C22D3×D4×D511yescharacteristic
875C4—32no—
876C4—41no—
877C4—101no—
878C4—121no—
879C4—201no—
880C4—301no—
881C4—601no—
882C4D3×#70911yescharacteristic
883C4D3×D4×D511yescharacteristic
884C3C2×#6507111yescharacteristic, complemented, Sylow
885C2—34no—
886C2—81no—
887C2—201no—
888C2—241no—
889C2—401no—
890C2—601no—
891C2—1201no—
892C2D3×#403011yescharacteristic
893C2D3×#405711yescharacteristic
894C2D3×#406011yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
hypercenter#102D3×D5
hypocenterC3×C5C2×#469
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D3×#4084C2semidirect
2. C2×D3×#686C2semidirect
3. C2×D3×#676C2semidirect
4. D3×#4041C2semidirect
5. #11750883C2semidirect
6. C5×D3×#102C2semidirect
7. C3×#65071C2semidirect
8. #11749030C2semidirect
9. #11749027C2semidirect
10. D3×#3953C2semidirect
11. #11747925C2semidirect
12. #11747894C2semidirect
13. D3×#3940C2semidirect
14. #11747317C2semidirect
15. #11747312C2semidirect
22. #91827C22semidirect
23. C2×#6715C22semidirect
24. C2×#6705C22semidirect
25. #91784C22semidirect
28. C3×#4084C22semidirect
29. C2×C3×#686C22semidirect
30. C2×C3×#676C22semidirect
31. C3×#4041C22semidirect
37. #91466C22semidirect
38. #91465C22semidirect
40. #91450C22semidirect
41. #91449C22semidirect
44. C2×#6654C22semidirect
45. C2×#6652C22semidirect
46. C2×#6651C22semidirect
47. C2×#6649C22semidirect
50. C3×C5×#102C22semidirect
51. #91105C22semidirect
52. #91092C22semidirect
53. C5×#832C22semidirect
54. C5×#821C22semidirect
55. C5×#809C22semidirect
56. C3×#3953C22semidirect
57. C3×#3940C22semidirect
58. #90986C22semidirect
59. #90985C22semidirect
60. #90968C22semidirect
61. #90965C22semidirect
77. #65071D3direct (N × H)
138. D3×#168D4semidirect
153. D3×#102D5semidirect
167. #4084C2×D3semidirect
172. C2×#686C2×D3semidirect
180. C2×#676C2×D3semidirect
186. #4041C2×D3semidirect
190. C5×#102C2×D3semidirect
194. #3953C2×D3semidirect
198. #3940C2×D3semidirect
254. C3⋊#168C2×D4semidirect
255. C3×#168C2×D4semidirect
292. C3×#102C2×D5semidirect
294. #832C2×D5semidirect
296. #821C2×D5semidirect
299. #809C2×D5semidirect
529. #168D3×D4semidirect
574. #102D3×D5semidirect
584. C5×D3#469semidirect
737. C3×C5C2×#469semidirect
848. D3#65071direct (N × H)
849. C5D3×#469semidirect
884. C3C2×#65071semidirect

Maximal subgroups

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

subgroupindex
D3×#40842
C2×D3×#6862
C2×D3×#6762
D3×#40412
#117508832
C5×D3×#1022
C3×#650712
#117490302
#117490272
D3×#39532
#117479252
#117478942
D3×#39402
#117473172
#117473122
C2×#650713
D3×#4695