Finite Group Databasebeta

← D3×#65056 #14426201

Subgroups — D3×#65056 #14426201

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4082C211yesmaximal, characteristic
2C2×D3×#687C211yesmaximal, characteristic
3C2×D3×Dic20C211yesmaximal, characteristic, complemented
4D3×#4033C211yesmaximal, characteristic, complemented
5#11750868C211yesmaximal, characteristic, complemented
6C5×D3×#102C211yesmaximal, characteristic
7C3×#65056C211yesmaximal, characteristic, complemented
8#11749007C211yesmaximal, characteristic, complemented
9#11749002C211yesmaximal, characteristic, complemented
10#11747853C211yesmaximal, characteristic, complemented
11#11747837C211yesmaximal, characteristic, complemented
12D3×#3946C211yesmaximal, characteristic, complemented
13D3×#3942C211yesmaximal, characteristic, complemented
14#11747385C211yesmaximal, characteristic, complemented
15#11747370C211yesmaximal, characteristic, complemented
16C2×#65056—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C2×D3×Dic10C2211yescharacteristic
19C2×D3×Dic10C2211yescharacteristic
20#91825C2211yescharacteristic
21C2×#6716C2211yescharacteristic
22C2×Dic60C2211yescharacteristic, complemented
23#91776C2211yescharacteristic, complemented
24C2×C5×D3×C8C2211yescharacteristic
25C5×D3×C4⋊C4C2211yescharacteristic
26C3×#4082C2211yescharacteristic
27C2×C3×#687C2211yescharacteristic
28C2×C3×Dic20C2211yescharacteristic, complemented
29C3×#4033C2211yescharacteristic, complemented
30D3×C22⋊Dic5—21no—
31D3×C22⋊Dic5—21no—
32#91525—21no—
33#91525—21no—
34D3×#687—24no—
35D3×#683—21no—
36C4×D3×Dic5—21no—
37C4×D3×Dic5C2211yescharacteristic
38#91373C2211yescharacteristic
39#91370C2211yescharacteristic
40#91333C2211yescharacteristic, complemented
41#91331C2211yescharacteristic, complemented
42#91325—21no—
43#91323—21no—
44C2×#6662C2211yescharacteristic, complemented
45C2×#6662C2211yescharacteristic, complemented
46C2×#6659C2211yescharacteristic
47C2×#6656C2211yescharacteristic
48C2×D3×#168C2211yescharacteristic
49D3×Dic20—24no—
50C3×C5×#102C2211yescharacteristic
51#91098C2211yescharacteristic, complemented
52#91094C2211yescharacteristic, complemented
53C5×#832C2211yescharacteristic
54C5×#821C2211yescharacteristic
55C5×#809C2211yescharacteristic
56C3×#3946C2211yescharacteristic, complemented
57C3×#3942C2211yescharacteristic, complemented
58#90983C2211yescharacteristic, complemented
59#90982C2211yescharacteristic, complemented
60#90975C2211yescharacteristic, complemented
61#90970C2211yescharacteristic, complemented
62D3×#464—51nomaximal, Hall
63C2×#4082—31no—
64C22×#687—31no—
65C22×Dic20—31no—
66C2×#4033—31no—
67C2×C5×#102—31no—
68C2×#3946—31no—
69C2×#3942—31no—
70#65056—31no—
71#65056—31no—
72#65056—31no—
73#65056—31no—
74#65056—31no—
75#65056—31no—
76#65056—31no—
77#65056D311yescharacteristic, direct product factor
78C23×C5×D3—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C2×Dic30C2311yescharacteristic
81C2×Dic30C2311yescharacteristic
82C2×C5×#67—21no—
83C5×D3×D4—22no—
84C5×D3×D4—22no—
85C2×C5×D12C2311yescharacteristic
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3C2311yescharacteristic
88C2×C3×Dic10C2311yescharacteristic
89C2×C3×Dic10C2311yescharacteristic
90C2×#1204—21no—
91C2×#1204—21no—
92C2×D3×Dic5—21no—
93C2×D3×Dic5—21no—
94C2×D3×Dic5D411yescharacteristic
95C2×D3×Dic5D411yescharacteristic
96D3×Dic10—22no—
97D3×Dic10—22no—
98D3×Dic10—22no—
99D3×Dic10D414yes—
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102#6719—21no—
103#6719—21no—
104#6716—22no—
105#6712—21no—
106C4×Dic15—21no—
107C4×Dic15C2311yescharacteristic
108C2×C3⋊#168C2311yescharacteristic
109Dic60—22no—
110C5×C4⋊Dic3C2311yescharacteristic
111C5×Dic3⋊C4—21no—
112C2×C5×C3⋊C8C2311yescharacteristic
113C5×D3×C8—22no—
114C3×C22⋊Dic5—21no—
115C3×C22⋊Dic5—21no—
116C3×#687—22no—
117C3×#683—21no—
118C3×C4×Dic5—21no—
119C3×C4×Dic5C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C3×Dic20—22no—
122#6669—21no—
123#6668—21no—
124(C2×D3)⋊Dic5—21no—
125(C2×D3)⋊Dic5—21no—
126(C2×D3)⋊Dic5—21no—
127(C2×D3)⋊Dic5—21no—
128Dic3×Dic5—21no—
129Dic3×Dic5—21no—
130Dic3×Dic5D411yescharacteristic
131Dic3×Dic5D411yescharacteristic
132#6662—22no—
133#6662—22no—
134#6659—22no—
135#6656—22no—
136D3×#168—22no—
137C2×D3×Q16—51no—
138C2×D3×SD16—51no—
139D3×#124—51no—
140C4×D3×Q8—51no—
141C3×#464—51no—
142#5185—51no—
143#5166—51no—
144#5054—51no—
145#5028—51no—
146#4845—51no—
147D3×C4⋊C8—51no—
148D3×#103—51no—
149#4798—51no—
150D3×#102D511yescharacteristic
151#4767—51no—
152C22×C5×D4—31no—
153C22×Dic10—31no—
154C22×Dic10—31no—
155C22×C5×C8—31no—
156C2×C5×C4⋊C4—31no—
157C2×C22⋊Dic5—61no—
158C2×C22⋊Dic5—61no—
159#4082—31no—
160#4082—31no—
161#4082—31no—
162#4082—61no—
163#4082—61no—
164#4082C2×D311yescharacteristic
165C2×#687—31no—
166C2×#687—31no—
167C2×#687—31no—
168C2×#687—64no—
169C2×#687C2×D311yescharacteristic
170C2×#683—61no—
171C2×C4×Dic5—31no—
172C2×C4×Dic5—61no—
173C22×#168—31no—
174C2×Dic20—31no—
175C2×Dic20—31no—
176C2×Dic20—31no—
177C2×Dic20—64no—
178C2×Dic20C2×D311yescharacteristic, complemented
179#4033—31no—
180#4033—31no—
181#4033—31no—
182#4033—61no—
183#4033—61no—
184#4033C2×D311yescharacteristic, complemented
185C5×#102—31no—
186C5×#102—31no—
187C5×#102—31no—
188C5×#102C2×D311yescharacteristic
189#3946—31no—
190#3946—31no—
191#3946—31no—
192#3946C2×D311yescharacteristic, complemented
193#3942—31no—
194#3942—31no—
195#3942—31no—
196#3942C2×D311yescharacteristic, complemented
197C2×#464—151noSylow
198C23×C3×C5—21no—
199C22×C5×D3—21no—
200C22×C5×D3—42no—
201C22×C5×D3—42no—
202C22×C5×D3—42no—
203C22×C5×D3C2×D411yescharacteristic
204C3×C5×D4—21no—
205C3×C5×D4—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5C2411yescharacteristic
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15C2×D411yescharacteristic
211C2×Dic15C2×D411yescharacteristic
212Dic30—21no—
213Dic30—21no—
214Dic30—21no—
215Dic30C2×D412yes—
216C5×#67—42no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3C2×D411yescharacteristic
219C5×D12—21no—
220C5×D12—21no—
221C4×C5×D3—42no—
222C4×C5×D3C2×D412yes—
223C4×C5×D3#4112yes—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5C2×D411yescharacteristic
227C2×C3×Dic5C2×D411yescharacteristic
228C3×Dic10—21no—
229C3×Dic10—21no—
230C3×Dic10—21no—
231C3×Dic10C2×D412yes—
232#1204—24no—
233#1204—42no—
234D3×Dic5—24no—
235D3×Dic5—22no—
236D3×Dic5—22no—
237D3×Dic5—42no—
238C3×C5×C8—21no—
239C3⋊#168—21no—
240C3×#168—21no—
241C5×C3⋊C8—21no—
242C2×D3×Q8—51no—
243C2×D3×Q8—51no—
244C2×D3×D4C2×D511yescharacteristic
245C2×C3×Q16—51no—
246C2×C3×SD16—51no—
247C3×#124—51no—
248C3×C4×Q8—51no—
249#947—51no—
250Q8×Dic3—51no—
251C2×#216—51no—
252C2×#216—51no—
253C2×#215—51no—
254#936—51no—
255C2×#214—51no—
256D3×Q16—104no—
257D3×SD16—104no—
258C2×Dic12—51no—
259C2×#204—51no—
260C2×D3×C8—51no—
261C2×D3×C8C2×D511yescharacteristic
262D3×C4⋊C4—101no—
263D3×C4⋊C4C2×D511yescharacteristic
264#887—51no—
265#887—101no—
266#885—101no—
267#885—101no—
268D3×C22⋊C4—101no—
269D3×C22⋊C4—101no—
270#875—51no—
271C42×D3—51no—
272C42×D3—101no—
273C4×Dic6—51no—
274C4×Dic6—101no—
275C3×C4⋊C8—51no—
276C3×#103—51no—
277C3×#102C2×D511yescharacteristic
278#835—51no—
279#832C2×D511yescharacteristic
280#821C2×D511yescharacteristic
281#816—51no—
282Dic3⋊C8—51no—
283Dic3⋊C8—51no—
284#810—51no—
285#809C2×D511yescharacteristic
286C4⋊(C3⋊C8)—51no—
287C24×C5—61no—
288C2×C5×D4—31no—
289C2×C5×D4—62no—
290C2×C5×D4—62no—
291C2×C5×D4—61no—
292C2×C5×D4C22×D311yescharacteristic
293C22×C4×C5—31no—
294C22×C4×C5—61no—
295C22×Dic5—31no—
296C22×Dic5—31no—
297C22×Dic5—61no—
298C22×Dic5—61no—
299C2×Dic10—31no—
300C2×Dic10—34no—
301C2×Dic10—31no—
302C2×Dic10—62no—
303C2×Dic10—62no—
304C2×Dic10—62no—
305C2×Dic10—61no—
306C2×Dic10—61no—
307C2×Dic10C22×D311yescharacteristic
308C2×Dic10C22×D311yescharacteristic
309C2×C5×C8—31no—
310C2×C5×C8—62no—
311C2×C5×C8C22×D311yescharacteristic
312C5×C4⋊C4—31no—
313C5×C4⋊C4—61no—
314C5×C4⋊C4C22×D311yescharacteristic
315C22⋊Dic5—21no—
316C22⋊Dic5—21no—
317C22⋊Dic5—61no—
318C22⋊Dic5—61no—
319C22⋊Dic5—61no—
320C22⋊Dic5—61no—
321C22⋊Dic5—61no—
322C22⋊Dic5—61no—
323#687—22no—
324#687—62no—
325#687—62no—
326#687—62no—
327#683—21no—
328#683—61no—
329#683—61no—
330#683—61no—
331C4×Dic5—21no—
332C4×Dic5—31no—
333C4×Dic5—31no—
334C4×Dic5—31no—
335C4×Dic5—61no—
336C4×Dic5—61no—
337C4×Dic5—61no—
338C4×Dic5C22×D311yescharacteristic
339C2×#168—31no—
340C2×#168—62no—
341C2×#168C22×D311yescharacteristic
342Dic20—22no—
343Dic20—62no—
344Dic20—62no—
345Dic20—62no—
346C22×Q16—151no—
347C22×SD16—151no—
348C2×#124—151no—
349C2×C4×Q8—151no—
350#464—51no—
351#464—151no—
352#464—151no—
353#464—151no—
354#464—151no—
355#464—151no—
356#464—151no—
357#464—151no—
358C2×C4⋊C8—151no—
359C2×#103—151no—
360C2×#102—31no—
361C22×C3×C5—41no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5C22×D411yescharacteristic
365C2×C5×D3—41no—
366C2×C5×D3—41no—
367C2×C5×D3—41no—
368C2×C5×D3—84no—
369C2×C5×D3#12112yes—
370C2×C5×D3#13512yes—
371C2×C5×D3#13712yes—
372C3×C4×C5—41no—
373C3×C4×C5C22×D411yescharacteristic
374C3×C4×C5C2×#4111yescharacteristic
375Dic15—22no—
376Dic15—21no—
377Dic15—21no—
378Dic15—41no—
379C3×Dic5—22no—
380C3×Dic5—21no—
381C3×Dic5—21no—
382C3×Dic5—41no—
383C5×Dic3—41no—
384C5×Dic3#12112yes—
385C23×D3—21no—
386C2×C3×Q8—51no—
387C2×C3×Q8—51no—
388C2×C3×D4C22×D511yescharacteristic
389C2×#67—21no—
390D3×Q8—54no—
391D3×Q8—102no—
392D3×Q8—102no—
393D3×Q8—102no—
394D3×D4—22no—
395D3×D4—22no—
396C2×D12C22×D511yescharacteristic
397C2×C4×D3—21no—
398C2×C4×D3—51no—
399C2×C4×D3—51no—
400C2×C4×D3—101no—
401C2×C4×D3—101no—
402C2×C4×D3C22×D511yescharacteristic
403C2×Dic6—51no—
404C2×Dic6—51no—
405C2×Dic6—101no—
406C2×Dic6—101no—
407C3×Q16—102no—
408C3×SD16—102no—
409C2×C3×C8—51no—
410C2×C3×C8C22×D511yescharacteristic
411C3×C4⋊C4—101no—
412C3×C4⋊C4C22×D511yescharacteristic
413C3×C22⋊C4—101no—
414C3×C22⋊C4—101no—
415C3×C42—51no—
416C3×C42—101no—
417#217—101no—
418#217—101no—
419#216—102no—
420#216—102no—
421#215—102no—
422#214—102no—
423(C2×D3)⋊C4—101no—
424(C2×D3)⋊C4—101no—
425(C2×D3)⋊C4—101no—
426(C2×D3)⋊C4—101no—
427C4⋊Dic3—101no—
428C4⋊Dic3C22×D511yescharacteristic
429Dic3⋊C4—21no—
430Dic3⋊C4—101no—
431Dic3⋊C4—101no—
432C4×Dic3—51no—
433C4×Dic3—51no—
434C4×Dic3—51no—
435C4×Dic3—101no—
436C4×Dic3—101no—
437C4×Dic3—101no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8C22×D511yescharacteristic
440Dic12—102no—
441#204—102no—
442D3×C8—22no—
443D3×C8—102no—
444C23×C5—21no—
445C23×C5—31no—
446C23×C5—61no—
447C23×C5—122no—
448C23×C5—122no—
449C23×C5—122no—
450C5×D4—21no—
451C5×D4—21no—
452C5×D4—61no—
453C5×D4—61no—
454C5×D4—122no—
455C2×C4×C5—21no—
456C2×C4×C5—31no—
457C2×C4×C5—32no—
458C2×C4×C5—32no—
459C2×C4×C5—61no—
460C2×C4×C5—122no—
461C2×C4×C5C23×D311yescharacteristic
462C2×Dic5—21no—
463C2×Dic5—21no—
464C2×Dic5—31no—
465C2×Dic5—31no—
466C2×Dic5—64no—
467C2×Dic5—62no—
468C2×Dic5—62no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5—122no—
472C2×Dic5D3×D411yescharacteristic
473C2×Dic5D3×D411yescharacteristic
474Dic10—21no—
475Dic10—21no—
476Dic10—21no—
477Dic10—32no—
478Dic10—64no—
479Dic10—61no—
480Dic10—61no—
481Dic10—61no—
482Dic10—122no—
483Dic10D3×D412yes—
484C5×C8—21no—
485C5×C8—61no—
486#168—21no—
487#168—61no—
488C22×Q8—151no—
489C22×Q8—151no—
490C22×D4—31no—
491C2×Q16—51no—
492C2×Q16—151no—
493C2×Q16—151no—
494C2×Q16—151no—
495C2×Q16—304no—
496C2×SD16—51no—
497C2×SD16—151no—
498C2×SD16—151no—
499C2×SD16—151no—
500C2×SD16—304no—
501C22×C8—31no—
502C22×C8—151no—
503#124—51no—
504#124—151no—
505#124—151no—
506#124—151no—
507#124—301no—
508#124—301no—
509C4×Q8—51no—
510C4×Q8—151no—
511C4×Q8—151no—
512C4×Q8—151no—
513C4×Q8—301no—
514C4×Q8—301no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—301no—
517C2×C22⋊C4—301no—
518C2×C22⋊C4—301no—
519C2×C42—151no—
520C2×C42—301no—
521C4⋊C8—51no—
522C4⋊C8—151no—
523C4⋊C8—151no—
524C4⋊C8—151no—
525#103—51no—
526#103—151no—
527#103—151no—
528#103—151no—
529#102—31no—
530#102—31no—
531#102—31no—
532#102D3×D511yescharacteristic
533C2×C3×C5—81no—
534C2×C3×C5C2×#12111yescharacteristic
535C2×C3×C5C2×#13511yescharacteristic
536C2×C3×C5C2×#13711yescharacteristic
537C5×D3—81no—
538C5×D3#46414yescomplemented
539C23×C3—21no—
540C22×D3—21no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3D4×D511yescharacteristic
545C3×Q8—52no—
546C3×Q8—101no—
547C3×Q8—101no—
548C3×Q8—101no—
549C3×D4—21no—
550C3×D4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—51no—
553C2×C3×C4—51no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4C23×D511yescharacteristic
557#67—42no—
558C2×Dic3—21no—
559C2×Dic3—51no—
560C2×Dic3—51no—
561C2×Dic3—101no—
562C2×Dic3—101no—
563C2×Dic3D4×D511yescharacteristic
564D12—21no—
565D12—21no—
566C4×D3—42no—
567C4×D3—104no—
568C4×D3—102no—
569C4×D3—102no—
570C4×D3—202no—
571C4×D3#70912yes—
572C4×D3D4×D512yes—
573Dic6—52no—
574Dic6—101no—
575Dic6—104no—
576Dic6—101no—
577Dic6—101no—
578Dic6—202no—
579C3×C8—21no—
580C3×C8—101no—
581C3⋊C8—21no—
582C3⋊C8—101no—
583C22×C5—32no—
584C22×C5—32no—
585C22×C5—32no—
586C22×C5—41no—
587C22×C5—41no—
588C22×C5—41no—
589C22×C5—121no—
590C22×C5—121no—
591C22×C5—121no—
592C22×C5—244no—
593C22×C5C2×D3×D411yescharacteristic
594C4×C5—32no—
595C4×C5—41no—
596C4×C5—121no—
597C4×C5C2×D3×D411yescharacteristic
598C4×C5D3×#4111yescharacteristic
599Dic5—21no—
600Dic5—21no—
601Dic5—22no—
602Dic5—41no—
603Dic5—61no—
604Dic5—61no—
605Dic5—62no—
606Dic5—121no—
607C24—61no—
608C2×Q8—51no—
609C2×Q8—51no—
610C2×Q8—154no—
611C2×Q8—151no—
612C2×Q8—151no—
613C2×Q8—301no—
614C2×Q8—301no—
615C2×Q8—302no—
616C2×Q8—302no—
617C2×Q8—302no—
618C2×D4—31no—
619C2×D4—62no—
620C2×D4—62no—
621C2×D4—61no—
622C2×D4C2×D3×D511yescharacteristic
623C22×C4—31no—
624C22×C4—61no—
625C22×C4—151no—
626C22×C4—151no—
627C22×C4—301no—
628C22×C4—301no—
629Q16—102no—
630Q16—302no—
631Q16—302no—
632Q16—302no—
633SD16—102no—
634SD16—302no—
635SD16—302no—
636SD16—302no—
637C2×C8—31no—
638C2×C8—51no—
639C2×C8—62no—
640C2×C8—151no—
641C2×C8—302no—
642C2×C8C2×D3×D511yescharacteristic
643C4⋊C4—31no—
644C4⋊C4—61no—
645C4⋊C4—101no—
646C4⋊C4—301no—
647C4⋊C4—301no—
648C4⋊C4—301no—
649C4⋊C4C2×D3×D511yescharacteristic
650C22⋊C4—101no—
651C22⋊C4—101no—
652C22⋊C4—301no—
653C22⋊C4—301no—
654C22⋊C4—301no—
655C22⋊C4—301no—
656C22⋊C4—301no—
657C22⋊C4—301no—
658C42—51no—
659C42—101no—
660C42—151no—
661C42—151no—
662C42—151no—
663C42—301no—
664C42—301no—
665C42—301no—
666C3×C5C2×#46411yescharacteristic, complemented, Hall
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3C2×D4×D511yescharacteristic
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—84no—
675C2×D3#403012yes—
676C2×D3#405812yes—
677C2×D3#406112yes—
678C3×C4—41no—
679C3×C4—102no—
680C3×C4—101no—
681C3×C4—101no—
682C3×C4—201no—
683C3×C4C2×#70911yescharacteristic
684C3×C4C2×D4×D511yescharacteristic
685Dic3—41no—
686Dic3—102no—
687Dic3—101no—
688Dic3—101no—
689Dic3—201no—
690Dic3#403012yes—
691C2×C5—34no—
692C2×C5—81no—
693C2×C5—241no—
694C2×C5D3×#12111yescharacteristic
695C2×C5D3×#13511yescharacteristic
696C2×C5D3×#13711yescharacteristic
697C23—21no—
698C23—31no—
699C23—61no—
700C23—122no—
701C23—122no—
702C23—122no—
703Q8—52no—
704Q8—101no—
705Q8—101no—
706Q8—101no—
707Q8—152no—
708Q8—304no—
709Q8—301no—
710Q8—301no—
711Q8—301no—
712Q8—602no—
713D4—21no—
714D4—21no—
715D4—61no—
716D4—61no—
717D4—122no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—51no—
723C2×C4—51no—
724C2×C4—61no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—122no—
728C2×C4—151no—
729C2×C4—151no—
730C2×C4—302no—
731C2×C4—302no—
732C2×C4—304no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—602no—
736C2×C4C22×D3×D511yescharacteristic
737C8—21no—
738C8—61no—
739C8—101no—
740C8—301no—
741C2×C3—81no—
742C2×C3C2×#403011yescharacteristic
743C2×C3C2×#405811yescharacteristic
744C2×C3C2×#406111yescharacteristic
745D3—81no—
746D3#6505614yesdirect product factor
747C5D3×#46411yescharacteristic, complemented, Sylow
748C22—32no—
749C22—32no—
750C22—32no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—244no—
758C22D3×D4×D511yescharacteristic
759C4—32no—
760C4—41no—
761C4—102no—
762C4—101no—
763C4—101no—
764C4—121no—
765C4—201no—
766C4—302no—
767C4—301no—
768C4—301no—
769C4—601no—
770C4D3×#70911yescharacteristic
771C4D3×D4×D511yescharacteristic
772C3C2×#6505611yescharacteristic, complemented, Sylow
773C2—34no—
774C2—81no—
775C2—241no—
776C2D3×#403011yescharacteristic
777C2D3×#405811yescharacteristic
778C2D3×#406111yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D3×D4C22
hypercenter#102D3×D5
hypocenterC3×C5C2×#464
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
3. C2×D3×Dic20C2semidirect
4. D3×#4033C2semidirect
5. #11750868C2semidirect
7. C3×#65056C2semidirect
8. #11749007C2semidirect
9. #11749002C2semidirect
10. #11747853C2semidirect
11. #11747837C2semidirect
12. D3×#3946C2semidirect
13. D3×#3942C2semidirect
14. #11747385C2semidirect
15. #11747370C2semidirect
22. C2×Dic60C22semidirect
23. #91776C22semidirect
28. C2×C3×Dic20C22semidirect
29. C3×#4033C22semidirect
40. #91333C22semidirect
41. #91331C22semidirect
44. C2×#6662C22semidirect
45. C2×#6662C22semidirect
51. #91098C22semidirect
52. #91094C22semidirect
56. C3×#3946C22semidirect
57. C3×#3942C22semidirect
58. #90983C22semidirect
59. #90982C22semidirect
60. #90975C22semidirect
61. #90970C22semidirect
77. #65056D3direct (N × H)
178. C2×Dic20C2×D3semidirect
184. #4033C2×D3semidirect
192. #3946C2×D3semidirect
196. #3942C2×D3semidirect
538. C5×D3#464semidirect
666. C3×C5C2×#464semidirect
746. D3#65056direct (N × H)
747. C5D3×#464semidirect
772. C3C2×#65056semidirect

Maximal subgroups

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

subgroupindex
D3×#40822
C2×D3×#6872
C2×D3×Dic202
D3×#40332
#117508682
C5×D3×#1022
C3×#650562
#117490072
#117490022
#117478532
#117478372
D3×#39462
D3×#39422
#117473852
#117473702
C2×#650563
D3×#4645