Finite Group Databasebeta

← D3×#65101 #14427971

Subgroups — D3×#65101 #14427971

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4092C211yesmaximal, characteristic, complemented
2C2×D3×#688C211yesmaximal, characteristic, complemented
3C2×D3×#676C211yesmaximal, characteristic, complemented
4D3×#4041C211yesmaximal, characteristic
5#11750913C211yesmaximal, characteristic, complemented
6C5×D3×#103C211yesmaximal, characteristic, complemented
7C3×#65101C211yesmaximal, characteristic, complemented
8#11749276C211yesmaximal, characteristic, complemented
9#11749273C211yesmaximal, characteristic, complemented
10D3×#3953C211yesmaximal, characteristic, complemented
11#11747941C211yesmaximal, characteristic, complemented
12#11747927C211yesmaximal, characteristic, complemented
13D3×#3939C211yesmaximal, characteristic, complemented
14#11747346C211yesmaximal, characteristic, complemented
15#11747345C211yesmaximal, characteristic, complemented
16C2×#65101—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18C2×D3×D20—21no—
19C2×D3×D20C2211yescharacteristic
20C2×C4×D3×D5C2211yescharacteristic
21#91835C2211yescharacteristic, complemented
22C2×#6717C2211yescharacteristic, complemented
23C2×#6705C2211yescharacteristic, complemented
24#91784C2211yescharacteristic
25C2×C5×D3×C8C2211yescharacteristic
26C5×D3×C4⋊C4C2211yescharacteristic
27C3×#4092C2211yescharacteristic, complemented
28C2×C3×#688C2211yescharacteristic, complemented
29C2×C3×#676C2211yescharacteristic, complemented
30C3×#4041C2211yescharacteristic
31D3×#688—24no—
32D3×#685—21no—
33D3×#685—21no—
34#91465C2211yescharacteristic
35#91459—21no—
36#91450C2211yescharacteristic
37D3×C4⋊Dic5C2211yescharacteristic
38#91424—21no—
39#91421—21no—
40#91409—21no—
41D3×#683—21no—
42#91383C2211yescharacteristic, complemented
43#91359C2211yescharacteristic, complemented
44C2×#6660C2211yescharacteristic, complemented
45C2×#6655C2211yescharacteristic, complemented
46C2×#6651C2211yescharacteristic, complemented
47C2×#6649C2211yescharacteristic, complemented
48C2×D3×#168C2211yescharacteristic
49D3×#676—24no—
50C3×C5×#103C2211yescharacteristic, complemented
51#91105C2211yescharacteristic, complemented
52#91091C2211yescharacteristic, complemented
53C5×#835C2211yescharacteristic, complemented
54C5×#816C2211yescharacteristic, complemented
55C5×#810C2211yescharacteristic, complemented
56C3×#3953C2211yescharacteristic, complemented
57C3×#3939C2211yescharacteristic, complemented
58#90989C2211yescharacteristic, complemented
59#90988C2211yescharacteristic, complemented
60#90968C2211yescharacteristic, complemented
61#90965C2211yescharacteristic, complemented
62D3×#468—51nomaximal, Hall
63C2×#4092—31no—
64C22×#688—31no—
65C22×#676—31no—
66C2×#4041—31no—
67C2×C5×#103—31no—
68C2×#3953—31no—
69C2×#3939—31no—
70#65101—31no—
71#65101—31no—
72#65101—31no—
73#65101—31no—
74#65101—31no—
75#65101—31no—
76#65101—31no—
77#65101D311yescharacteristic, direct product factor
78C22×D3×D5—21no—
79C22×D3×D5D411yescharacteristic
80C2×C3×C5×Q8C2311yescharacteristic
81C2×D60—21no—
82C2×D60C2311yescharacteristic
83C2×C4×D15C2311yescharacteristic
84C5×D3×Q8—22no—
85C5×D3×Q8—22no—
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3—21no—
88C2×C4×C5×D3C2311yescharacteristic
89C2×C5×Dic6—21no—
90C2×C5×Dic6C2311yescharacteristic
91C2×C3×D20—21no—
92C2×C3×D20C2311yescharacteristic
93C2×C3×C4×D5C2311yescharacteristic
94C2×#1202—21no—
95C2×#1202—21no—
96C2×#1202—21no—
97C2×#1200D411yescharacteristic
98C2×D3×Dic5—21no—
99C2×D3×Dic5D411yescharacteristic
100C2×D5×Dic3D411yescharacteristic
101D3×D20—22no—
102D3×D20—22no—
103D3×D20—44no—
104C4×D3×D5—22no—
105C4×D3×D5—22no—
106C2×C3×C5×C8C2311yescharacteristic
107C3×C5×C4⋊C4C2311yescharacteristic
108#6717—22no—
109#6714—21no—
110#6714—21no—
111C4⋊Dic15C2311yescharacteristic
112#6712—21no—
113C2×C3⋊#168C2311yescharacteristic
114#6705—22no—
115C5×C4⋊Dic3C2311yescharacteristic
116C5×Dic3⋊C4—21no—
117C2×C5×C3⋊C8C2311yescharacteristic
118C5×D3×C8—22no—
119C3×#688—22no—
120C3×#685—21no—
121C3×#685—21no—
122C3×C4⋊Dic5C2311yescharacteristic
123C3×#683—21no—
124C2×C3×#168C2311yescharacteristic
125C3×#676—22no—
126Dic3⋊Dic5—21no—
127#6669—21no—
128#6668—21no—
129#6667—21no—
130#6667—21no—
131#6665—21no—
132#6665—21no—
133#6660—22no—
134#6655—22no—
135#6651—22no—
136#6649—22no—
137D3×#168D414yescomplemented
138C2×D3×SD16—51no—
139C2×D3×M16—51no—
140D3×C22⋊Q8—51no—
141D3×#121—51no—
142C3×#468—51no—
143#5174—51no—
144#5134—51no—
145#5049—51no—
146#5042—51no—
147#4886—51no—
148D3×#107—51no—
149#4812—51no—
150D3×#103D511yescharacteristic, complemented
151#4780—51no—
152D3×#102—51no—
153C22×C5×Q8—31no—
154C22×D20—31no—
155C22×D20—61no—
156C22×C4×D5—31no—
157C22×C5×C8—31no—
158C2×C5×C4⋊C4—31no—
159#4092—31no—
160#4092—31no—
161#4092—31no—
162#4092—61no—
163#4092—61no—
164#4092C2×D311yescharacteristic, complemented
165C2×#688—31no—
166C2×#688—31no—
167C2×#688—31no—
168C2×#688—64no—
169C2×#688C2×D311yescharacteristic, complemented
170C2×#685—61no—
171C2×#685—61no—
172C2×C4⋊Dic5—31no—
173C2×#683—61no—
174C22×#168—31no—
175C2×#676—31no—
176C2×#676—31no—
177C2×#676—31no—
178C2×#676—64no—
179C2×#676C2×D311yescharacteristic, complemented
180#4041—31no—
181#4041—31no—
182#4041—31no—
183#4041—61no—
184#4041—61no—
185#4041C2×D311yescharacteristic
186C5×#103—31no—
187C5×#103—31no—
188C5×#103—31no—
189C5×#103C2×D311yescharacteristic, complemented
190#3953—31no—
191#3953—31no—
192#3953—31no—
193#3953C2×D311yescharacteristic, complemented
194#3939—31no—
195#3939—31no—
196#3939—31no—
197#3939C2×D311yescharacteristic, complemented
198C2×#468—151noSylow
199C22×D15—21no—
200C22×D15C2×D411yescharacteristic
201C22×C5×D3C2×D411yescharacteristic
202C22×C3×D5—21no—
203C22×C3×D5C2×D411yescharacteristic
204C2×D3×D5—22no—
205C2×D3×D5—22no—
206C2×D3×D5—22no—
207C2×D3×D5—42no—
208C2×D3×D5—42no—
209C2×D3×D5—42no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C2411yescharacteristic
215C2×Dic15—21no—
216C2×Dic15C2×D411yescharacteristic
217D60—21no—
218D60—21no—
219D60—42no—
220C4×D15—21no—
221C4×D15—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3C2×D411yescharacteristic
225C4×C5×D3—42no—
226C4×C5×D3—42no—
227C4×C5×D3C2×D412yes—
228C4×C5×D3#4112yes—
229C5×Dic6—21no—
230C5×Dic6—21no—
231C5×Dic6—42no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5C2×D411yescharacteristic
234C3×D20—21no—
235C3×D20—21no—
236C3×D20—42no—
237C3×C4×D5—21no—
238C3×C4×D5—21no—
239#1202—42no—
240#1202—42no—
241#1202—42no—
242#1200—22no—
243D3×Dic5—22no—
244D3×Dic5—42no—
245D5×Dic3—22no—
246C3×C5×C8—21no—
247C3⋊#168C2×D412yescomplemented
248C3×#168C2×D412yescomplemented
249C5×C3⋊C8—21no—
250C2×D3×Q8C2×D511yescharacteristic
251C2×D3×D4—51no—
252C2×D3×D4—101no—
253C22×C4×D3—51no—
254C2×C3×SD16—51no—
255C2×C3×M16—51no—
256C3×C22⋊Q8—51no—
257C3×#121—51no—
258#946—51no—
259C2×#215—51no—
260#939—101no—
261#938—51no—
262C2×#214—51no—
263#930—51no—
264#924—51no—
265C2×#208—51no—
266D3×SD16—104no—
267D3×M16—104no—
268C2×#204—51no—
269C2×ΓL(1,𝔽25)—51no—
270C2×ΓL(1,𝔽25)—51no—
271C2×D3×C8—51no—
272C2×D3×C8C2×D511yescharacteristic
273#897—51no—
274#896—101no—
275#895—51no—
276D3×C4⋊C4—51no—
277D3×C4⋊C4—101no—
278D3×C4⋊C4C2×D511yescharacteristic
279#884—101no—
280D3×C22⋊C4—101no—
281D3×C22⋊C4—101no—
282#878—101no—
283C3×#107—51no—
284C3×#103C2×D511yescharacteristic, complemented
285C3×#102—51no—
286#835C2×D511yescharacteristic, complemented
287#832—51no—
288#821—51no—
289#818—51no—
290#816C2×D511yescharacteristic, complemented
291#810C2×D511yescharacteristic, complemented
292#809—51no—
293#807—51no—
294#807—51no—
295C23×D5—31no—
296C23×D5—61no—
297C2×C5×Q8—31no—
298C2×C5×Q8—61no—
299C2×C5×Q8—62no—
300C2×C5×Q8—62no—
301C2×C5×Q8C22×D311yescharacteristic
302C22×C4×C5—31no—
303C22×C4×C5—61no—
304C22×C4×C5—61no—
305C22×Dic5—31no—
306C22×Dic5—61no—
307C2×D20—21no—
308C2×D20—31no—
309C2×D20—62no—
310C2×D20—62no—
311C2×D20—61no—
312C2×D20—61no—
313C2×D20—61no—
314C2×D20—61no—
315C2×D20—124no—
316C2×D20C22×D311yescharacteristic
317C2×C4×D5—31no—
318C2×C4×D5—31no—
319C2×C4×D5—31no—
320C2×C4×D5—62no—
321C2×C4×D5—62no—
322C2×C4×D5C22×D311yescharacteristic
323C2×C5×C8—31no—
324C2×C5×C8—62no—
325C2×C5×C8C22×D311yescharacteristic
326C5×C4⋊C4—31no—
327C5×C4⋊C4—61no—
328C5×C4⋊C4C22×D311yescharacteristic
329#688—22no—
330#688—62no—
331#688—62no—
332#688—62no—
333#685—21no—
334#685—21no—
335#685—61no—
336#685—61no—
337#685—61no—
338#685—61no—
339#685—61no—
340#685—61no—
341C4⋊Dic5—31no—
342C4⋊Dic5—61no—
343C4⋊Dic5C22×D311yescharacteristic
344#683—21no—
345#683—61no—
346#683—61no—
347#683—61no—
348C2×#168—31no—
349C2×#168—34no—
350C2×#168C22×D311yescharacteristic
351#676—22no—
352#676—62no—
353#676—62no—
354#676—62no—
355C22×SD16—151no—
356C22×M16—151no—
357C2×C22⋊Q8—151no—
358C2×#121—151no—
359#468—51no—
360#468—151no—
361#468—151no—
362#468—151no—
363#468—151no—
364#468—151no—
365#468—151no—
366#468—151no—
367C2×#107—151no—
368C2×#103—31no—
369C2×#102—151no—
370C22×C3×C5C22×D411yescharacteristic
371C2×D15—21no—
372C2×D15—21no—
373C2×D15—21no—
374C2×D15—41no—
375C2×D15—41no—
376C2×D15—41no—
377C2×C5×D3#12112yes—
378C2×C5×D3AGL(1,ℤ/8)12yes—
379C2×C5×D3#13712yes—
380C2×C3×D5—21no—
381C2×C3×D5—21no—
382C2×C3×D5—21no—
383C2×C3×D5—41no—
384C2×C3×D5—41no—
385C2×C3×D5—41no—
386D3×D5—44no—
387D3×D5—84no—
388C3×C4×C5—41no—
389C3×C4×C5—41no—
390C3×C4×C5C22×D411yescharacteristic
391C3×C4×C5C2×#4111yescharacteristic
392Dic15—21no—
393Dic15—41no—
394C3×Dic5—21no—
395C3×Dic5—41no—
396C5×Dic3—41no—
397C5×Dic3—41no—
398C5×Dic3#12112yes—
399C23×D3—51no—
400C23×D3—101no—
401C2×C3×Q8C22×D511yescharacteristic
402C2×C3×D4—51no—
403C2×C3×D4—101no—
404C22×C3×C4—51no—
405C2×#67—101no—
406C2×#67—101no—
407C2×#67—101no—
408C22×Dic3—51no—
409D3×Q8—22no—
410D3×Q8—22no—
411D3×D4—102no—
412D3×D4—102no—
413D3×D4—204no—
414C2×D12—51no—
415C2×D12—101no—
416C2×C4×D3—21no—
417C2×C4×D3—21no—
418C2×C4×D3—51no—
419C2×C4×D3—51no—
420C2×C4×D3—51no—
421C2×C4×D3—102no—
422C2×C4×D3—102no—
423C2×C4×D3—101no—
424C2×C4×D3C22×D511yescharacteristic
425C2×Dic6—21no—
426C2×Dic6C22×D511yescharacteristic
427C3×SD16—102no—
428C3×M16—102no—
429C2×C3×C8—51no—
430C2×C3×C8C22×D511yescharacteristic
431C3×C4⋊C4—51no—
432C3×C4⋊C4—101no—
433C3×C4⋊C4C22×D511yescharacteristic
434C3×C22⋊C4—101no—
435C3×C22⋊C4—101no—
436#217—101no—
437#217—101no—
438#215—102no—
439#214—102no—
440(C2×D3)⋊C4—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444C4⋊Dic3—51no—
445C4⋊Dic3—101no—
446C4⋊Dic3C22×D511yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4—101no—
449Dic3⋊C4—101no—
450Dic3⋊C4—101no—
451#208—102no—
452C2×C3⋊C8—51no—
453C2×C3⋊C8C22×D511yescharacteristic
454#204—102no—
455ΓL(1,𝔽25)—102no—
456ΓL(1,𝔽25)—102no—
457D3×C8—22no—
458D3×C8—54no—
459C23×C5—31no—
460C22×D5—21no—
461C22×D5—31no—
462C22×D5—62no—
463C22×D5—62no—
464C22×D5—62no—
465C22×D5—61no—
466C22×D5—122no—
467C22×D5—122no—
468C22×D5—122no—
469C22×D5D3×D411yescharacteristic
470C5×Q8—21no—
471C5×Q8—21no—
472C5×Q8—61no—
473C5×Q8—61no—
474C5×Q8—122no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—31no—
478C2×C4×C5—32no—
479C2×C4×C5—32no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—122no—
483C2×C4×C5—122no—
484C2×C4×C5C23×D311yescharacteristic
485C2×Dic5—21no—
486C2×Dic5—31no—
487C2×Dic5—62no—
488C2×Dic5—61no—
489C2×Dic5—122no—
490C2×Dic5D3×D411yescharacteristic
491D20—21no—
492D20—21no—
493D20—42no—
494D20—61no—
495D20—61no—
496D20—122no—
497D20—122no—
498D20—122no—
499D20—122no—
500C4×D5—21no—
501C4×D5—21no—
502C4×D5—62no—
503C4×D5—62no—
504C4×D5—61no—
505C4×D5—61no—
506C5×C8—21no—
507C5×C8—61no—
508#168—32no—
509#168D3×D412yescomplemented
510C22×Q8—31no—
511C22×D4—151no—
512C22×D4—301no—
513C23×C4—151no—
514C2×SD16—51no—
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—304no—
519C2×M16—51no—
520C2×M16—151no—
521C2×M16—151no—
522C2×M16—151no—
523C2×M16—304no—
524C22×C8—31no—
525C22×C8—151no—
526C22⋊Q8—51no—
527C22⋊Q8—151no—
528C22⋊Q8—151no—
529C22⋊Q8—151no—
530C22⋊Q8—301no—
531C22⋊Q8—301no—
532#121—51no—
533#121—151no—
534#121—151no—
535#121—151no—
536#121—301no—
537#121—301no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—151no—
540C2×C4⋊C4—301no—
541C2×C22⋊C4—301no—
542C2×C22⋊C4—301no—
543#107—51no—
544#107—151no—
545#107—151no—
546#107—151no—
547#103—31no—
548#103—31no—
549#103—31no—
550#103D3×D511yescharacteristic, complemented
551#102—51no—
552#102—151no—
553#102—151no—
554#102—151no—
555C2×C3×C5C2×#12111yescharacteristic
556C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
557C2×C3×C5C2×#13711yescharacteristic
558D15—41no—
559D15—81no—
560C3×D5—41no—
561C3×D5—81no—
562C5×D3#46814yescomplemented
563C23×C3—51no—
564C23×C3—101no—
565C22×D3—51no—
566C22×D3—102no—
567C22×D3—102no—
568C22×D3—102no—
569C22×D3—101no—
570C22×D3—202no—
571C22×D3—202no—
572C22×D3—202no—
573C22×D3D4×D511yescharacteristic
574C3×Q8—21no—
575C3×Q8—21no—
576C3×D4—101no—
577C3×D4—101no—
578C3×D4—202no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—51no—
582C2×C3×C4—101no—
583C2×C3×C4—101no—
584C2×C3×C4—101no—
585C2×C3×C4C23×D511yescharacteristic
586#67—202no—
587#67—202no—
588#67—202no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—51no—
592C2×Dic3—102no—
593C2×Dic3—101no—
594C2×Dic3D4×D511yescharacteristic
595D12—101no—
596D12—101no—
597D12—202no—
598C4×D3—42no—
599C4×D3—42no—
600C4×D3—102no—
601C4×D3—101no—
602C4×D3—101no—
603C4×D3—102no—
604C4×D3—202no—
605C4×D3#70912yes—
606C4×D3D4×D512yes—
607Dic6—21no—
608Dic6—21no—
609Dic6—42no—
610C3×C8—21no—
611C3×C8—52no—
612C3⋊C8—21no—
613C3⋊C8—52no—
614C22×C5—32no—
615C22×C5—32no—
616C22×C5—32no—
617C22×C5C2×D3×D411yescharacteristic
618C2×D5—21no—
619C2×D5—21no—
620C2×D5—21no—
621C2×D5—41no—
622C2×D5—41no—
623C2×D5—41no—
624C2×D5—61no—
625C2×D5—61no—
626C2×D5—61no—
627C2×D5—124no—
628C2×D5—121no—
629C2×D5—121no—
630C2×D5—121no—
631C2×D5—244no—
632C4×C5—32no—
633C4×C5—41no—
634C4×C5—41no—
635C4×C5—121no—
636C4×C5—121no—
637C4×C5C2×D3×D411yescharacteristic
638C4×C5D3×#4111yescharacteristic
639Dic5—21no—
640Dic5—41no—
641Dic5—61no—
642Dic5—121no—
643C24—151no—
644C24—301no—
645C2×Q8—31no—
646C2×Q8—61no—
647C2×Q8—62no—
648C2×Q8—62no—
649C2×Q8C2×D3×D511yescharacteristic
650C2×D4—51no—
651C2×D4—101no—
652C2×D4—151no—
653C2×D4—301no—
654C2×D4—302no—
655C2×D4—302no—
656C2×D4—301no—
657C2×D4—301no—
658C2×D4—301no—
659C2×D4—604no—
660C22×C4—31no—
661C22×C4—51no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—151no—
665C22×C4—151no—
666C22×C4—151no—
667C22×C4—151no—
668C22×C4—302no—
669C22×C4—302no—
670C22×C4—301no—
671SD16—102no—
672SD16—302no—
673SD16—302no—
674SD16—302no—
675M16—102no—
676M16—302no—
677M16—302no—
678M16—302no—
679C2×C8—31no—
680C2×C8—51no—
681C2×C8—62no—
682C2×C8—154no—
683C2×C8—151no—
684C2×C8C2×D3×D511yescharacteristic
685C4⋊C4—31no—
686C4⋊C4—51no—
687C4⋊C4—61no—
688C4⋊C4—101no—
689C4⋊C4—151no—
690C4⋊C4—301no—
691C4⋊C4—301no—
692C4⋊C4—301no—
693C4⋊C4—301no—
694C4⋊C4C2×D3×D511yescharacteristic
695C22⋊C4—101no—
696C22⋊C4—101no—
697C22⋊C4—301no—
698C22⋊C4—301no—
699C22⋊C4—301no—
700C22⋊C4—301no—
701C22⋊C4—301no—
702C22⋊C4—301no—
703C3×C5C2×#46811yescharacteristic, complemented, Hall
704C22×C3—101no—
705C22×C3—101no—
706C22×C3—101no—
707C22×C3—201no—
708C22×C3—201no—
709C22×C3—201no—
710C22×C3C2×D4×D511yescharacteristic
711C2×D3—101no—
712C2×D3—101no—
713C2×D3—101no—
714C2×D3—204no—
715C2×D3—201no—
716C2×D3—201no—
717C2×D3—201no—
718C2×D3—404no—
719C2×D3#403012yes—
720C2×D3#406012yes—
721C2×D3#406412yes—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—101no—
725C3×C4—201no—
726C3×C4C2×#70911yescharacteristic
727C3×C4C2×D4×D511yescharacteristic
728Dic3—41no—
729Dic3—41no—
730Dic3—101no—
731Dic3—201no—
732Dic3#403012yes—
733C2×C5—34no—
734C2×C5D3×#12111yescharacteristic
735C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
736C2×C5D3×#13711yescharacteristic
737D5—41no—
738D5—81no—
739D5—121no—
740D5—241no—
741C23—31no—
742C23—51no—
743C23—101no—
744C23—151no—
745C23—302no—
746C23—302no—
747C23—302no—
748C23—301no—
749C23—602no—
750C23—602no—
751C23—602no—
752Q8—21no—
753Q8—21no—
754Q8—61no—
755Q8—61no—
756Q8—122no—
757D4—101no—
758D4—101no—
759D4—202no—
760D4—301no—
761D4—301no—
762D4—602no—
763D4—602no—
764D4—602no—
765D4—602no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—31no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—51no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—101no—
775C2×C4—101no—
776C2×C4—101no—
777C2×C4—122no—
778C2×C4—122no—
779C2×C4—151no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—302no—
783C2×C4—301no—
784C2×C4—301no—
785C2×C4—301no—
786C2×C4—602no—
787C2×C4C22×D3×D511yescharacteristic
788C8—21no—
789C8—52no—
790C8—61no—
791C8—152no—
792C2×C3—201no—
793C2×C3—401no—
794C2×C3C2×#403011yescharacteristic
795C2×C3C2×#406011yescharacteristic
796C2×C3C2×#406411yescharacteristic
797D3—201no—
798D3—401no—
799D3#6510114yesdirect product factor
800C5D3×#46811yescharacteristic, complemented, Sylow
801C22—32no—
802C22—32no—
803C22—32no—
804C22—101no—
805C22—101no—
806C22—101no—
807C22—201no—
808C22—201no—
809C22—201no—
810C22—301no—
811C22—301no—
812C22—301no—
813C22—604no—
814C22—601no—
815C22—601no—
816C22—601no—
817C22—1204no—
818C22D3×D4×D511yescharacteristic
819C4—32no—
820C4—41no—
821C4—41no—
822C4—101no—
823C4—121no—
824C4—121no—
825C4—201no—
826C4—301no—
827C4—601no—
828C4D3×#70911yescharacteristic
829C4D3×D4×D511yescharacteristic
830C3C2×#6510111yescharacteristic, complemented, Sylow
831C2—34no—
832C2—201no—
833C2—401no—
834C2—601no—
835C2—1201no—
836C2D3×#403011yescharacteristic
837C2D3×#406011yescharacteristic
838C2D3×#406411yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalD3×#4041C2
hypercenter#103D3×D5
hypocenterC3×C5C2×#468
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. D3×#4092C2semidirect
2. C2×D3×#688C2semidirect
3. C2×D3×#676C2semidirect
5. #11750913C2semidirect
6. C5×D3×#103C2semidirect
7. C3×#65101C2semidirect
8. #11749276C2semidirect
9. #11749273C2semidirect
10. D3×#3953C2semidirect
11. #11747941C2semidirect
12. #11747927C2semidirect
13. D3×#3939C2semidirect
14. #11747346C2semidirect
15. #11747345C2semidirect
21. #91835C22semidirect
22. C2×#6717C22semidirect
23. C2×#6705C22semidirect
27. C3×#4092C22semidirect
28. C2×C3×#688C22semidirect
29. C2×C3×#676C22semidirect
42. #91383C22semidirect
43. #91359C22semidirect
44. C2×#6660C22semidirect
45. C2×#6655C22semidirect
46. C2×#6651C22semidirect
47. C2×#6649C22semidirect
50. C3×C5×#103C22semidirect
51. #91105C22semidirect
52. #91091C22semidirect
53. C5×#835C22semidirect
54. C5×#816C22semidirect
55. C5×#810C22semidirect
56. C3×#3953C22semidirect
57. C3×#3939C22semidirect
58. #90989C22semidirect
59. #90988C22semidirect
60. #90968C22semidirect
61. #90965C22semidirect
77. #65101D3direct (N × H)
137. D3×#168D4semidirect
150. D3×#103D5semidirect
164. #4092C2×D3semidirect
169. C2×#688C2×D3semidirect
179. C2×#676C2×D3semidirect
189. C5×#103C2×D3semidirect
193. #3953C2×D3semidirect
197. #3939C2×D3semidirect
247. C3⋊#168C2×D4semidirect
248. C3×#168C2×D4semidirect
284. C3×#103C2×D5semidirect
286. #835C2×D5semidirect
290. #816C2×D5semidirect
291. #810C2×D5semidirect
509. #168D3×D4semidirect
550. #103D3×D5semidirect
562. C5×D3#468semidirect
703. C3×C5C2×#468semidirect
799. D3#65101direct (N × H)
800. C5D3×#468semidirect
830. C3C2×#65101semidirect

Maximal subgroups

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

subgroupindex
D3×#40922
C2×D3×#6882
C2×D3×#6762
D3×#40412
#117509132
C5×D3×#1032
C3×#651012
#117492762
#117492732
D3×#39532
#117479412
#117479272
D3×#39392
#117473462
#117473452
C2×#651013
D3×#4685