Finite Group Databasebeta

← D3×#65051 #14426060

Subgroups — D3×#65051 #14426060

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4086C211yesmaximal, characteristic
2C2×D3×#687C211yesmaximal, characteristic, complemented
3C2×D3×#677C211yesmaximal, characteristic, complemented
4D3×#4033C211yesmaximal, characteristic, complemented
5#11750863C211yesmaximal, characteristic, complemented
6C5×D3×#102C211yesmaximal, characteristic, complemented
7C3×#65051C211yesmaximal, characteristic, complemented
8#11749008C211yesmaximal, characteristic, complemented
9#11749000C211yesmaximal, characteristic, complemented
10#11747993C211yesmaximal, characteristic, complemented
11#11747843C211yesmaximal, characteristic, complemented
12D3×#3946C211yesmaximal, characteristic, complemented
13D3×#3941C211yesmaximal, characteristic, complemented
14#11747408C211yesmaximal, characteristic, complemented
15#11747400C211yesmaximal, characteristic, complemented
16C2×#65051—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C2×D3×C22⋊D5—21no—
19C2×D3×C22⋊D5—21no—
20C2×D3×D20C2211yescharacteristic
21C2×D3×Dic10C2211yescharacteristic
22#91829C2211yescharacteristic
23C2×#6716C2211yescharacteristic, complemented
24C2×#6706C2211yescharacteristic, complemented
25#91776C2211yescharacteristic, complemented
26C2×C5×D3×C8C2211yescharacteristic
27C5×D3×C4⋊C4C2211yescharacteristic
28C3×#4086C2211yescharacteristic
29C2×C3×#687C2211yescharacteristic, complemented
30C2×C3×#677C2211yescharacteristic, complemented
31C3×#4033C2211yescharacteristic, complemented
32#91567—21no—
33#91567—21no—
34D3×#687—24no—
35#91463C2211yescharacteristic
36#91451C2211yescharacteristic
37D3×#683—21no—
38C4×D3×Dic5—21no—
39C4×D3×Dic5C2211yescharacteristic
40#91333C2211yescharacteristic, complemented
41#91331C2211yescharacteristic, complemented
42#91325—21no—
43#91323—21no—
44C2×#6659C2211yescharacteristic, complemented
45C2×#6658C2211yescharacteristic, complemented
46C2×#6657C2211yescharacteristic, complemented
47C2×#6656C2211yescharacteristic, complemented
48C2×D3×#168C2211yescharacteristic
49D3×#677—24no—
50C3×C5×#102C2211yescharacteristic, complemented
51#91098C2211yescharacteristic, complemented
52#91093C2211yescharacteristic, complemented
53C5×#832C2211yescharacteristic, complemented
54C5×#821C2211yescharacteristic, complemented
55C5×#809C2211yescharacteristic, complemented
56C3×#3946C2211yescharacteristic, complemented
57C3×#3941C2211yescharacteristic, complemented
58#90983C2211yescharacteristic, complemented
59#90982C2211yescharacteristic, complemented
60#90969C2211yescharacteristic, complemented
61#90964C2211yescharacteristic, complemented
62D3×#460—51nomaximal, Hall
63C2×#4086—31no—
64C22×#687—31no—
65C22×#677—31no—
66C2×#4033—31no—
67C2×C5×#102—31no—
68C2×#3946—31no—
69C2×#3941—31no—
70#65051—31no—
71#65051—31no—
72#65051—31no—
73#65051—31no—
74#65051—31no—
75#65051—31no—
76#65051—31no—
77#65051D311yescharacteristic, direct product factor
78C23×C5×D3—21no—
79C22×D3×D5—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C2×#1220—21no—
82C2×#1220—21no—
83C2×D60C2311yescharacteristic
84C2×Dic30C2311yescharacteristic
85C2×C5×#67—21no—
86C5×D3×D4—22no—
87C5×D3×D4—22no—
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3—21no—
90C2×C4×C5×D3C2311yescharacteristic
91C2×C3×C22⋊D5—21no—
92C2×C3×C22⋊D5—21no—
93C2×C3×D20C2311yescharacteristic
94C2×C3×Dic10C2311yescharacteristic
95D3×C22⋊D5—44no—
96D3×C22⋊D5—44no—
97C2×#1204—21no—
98C2×#1203—21no—
99C2×#1203—21no—
100C2×#1202—21no—
101C2×#1201—21no—
102C2×#1201—21no—
103C2×D3×Dic5—21no—
104C2×D3×Dic5D411yescharacteristic
105C2×D3×Dic5D411yescharacteristic
106D3×D20—22no—
107D3×D20—22no—
108D3×Dic10—22no—
109D3×Dic10D414yescomplemented
110C2×C3×C5×C8C2311yescharacteristic
111C3×C5×C4⋊C4C2311yescharacteristic
112#6716—22no—
113#6712—21no—
114C4×Dic15—21no—
115C4×Dic15C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117#6706—22no—
118C5×C4⋊Dic3C2311yescharacteristic
119C5×Dic3⋊C4—21no—
120C2×C5×C3⋊C8C2311yescharacteristic
121C5×D3×C8—22no—
122C3×#687—22no—
123C3×#683—21no—
124C3×C4×Dic5—21no—
125C3×C4×Dic5C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C3×#677—22no—
128#6669—21no—
129#6668—21no—
130Dic3×Dic5—21no—
131Dic3×Dic5—21no—
132Dic3×Dic5D411yescharacteristic
133Dic3×Dic5D411yescharacteristic
134#6659—22no—
135#6658—22no—
136#6657—22no—
137#6656—22no—
138D3×#168—22no—
139C2×D3×SD16—51no—
140C2×D3×SD16—51no—
141D3×#127—51no—
142C4×D3×Q8—51no—
143C3×#460—51no—
144#5163—51no—
145#5163—51no—
146#5075—51no—
147#5027—51no—
148#4848—51no—
149D3×C4⋊C8—51no—
150D3×#102—51no—
151D3×#102D511yescharacteristic, complemented
152#4762—51no—
153#4762—51no—
154C22×C5×D4—31no—
155C22×C22⋊D5—61no—
156C22×C22⋊D5—61no—
157C22×D20—31no—
158C22×Dic10—31no—
159C22×C5×C8—31no—
160C2×C5×C4⋊C4—31no—
161#4086—31no—
162#4086—31no—
163#4086—31no—
164#4086—61no—
165#4086—61no—
166#4086C2×D311yescharacteristic
167C2×#687—31no—
168C2×#687—31no—
169C2×#687—31no—
170C2×#687—64no—
171C2×#687C2×D311yescharacteristic, complemented
172C2×#683—61no—
173C2×C4×Dic5—31no—
174C2×C4×Dic5—61no—
175C22×#168—31no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—31no—
179C2×#677—64no—
180C2×#677C2×D311yescharacteristic, complemented
181#4033—31no—
182#4033—31no—
183#4033—31no—
184#4033—61no—
185#4033—61no—
186#4033C2×D311yescharacteristic, complemented
187C5×#102—31no—
188C5×#102—31no—
189C5×#102—31no—
190C5×#102C2×D311yescharacteristic, complemented
191#3946—31no—
192#3946—31no—
193#3946—31no—
194#3946C2×D311yescharacteristic, complemented
195#3941—31no—
196#3941—31no—
197#3941—31no—
198#3941C2×D311yescharacteristic, complemented
199C2×#460—151noSylow
200C23×C3×C5—21no—
201C22×D15—21no—
202C22×C5×D3—21no—
203C22×C5×D3—42no—
204C22×C5×D3—42no—
205C22×C5×D3—42no—
206C22×C5×D3C2×D411yescharacteristic
207C22×C3×D5—21no—
208C2×D3×D5—42no—
209C2×D3×D5—42no—
210C2×D3×D5—42no—
211C3×C5×D4—21no—
212C3×C5×D4—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C2411yescharacteristic
215#1220—42no—
216#1220—42no—
217C2×Dic15—21no—
218C2×Dic15C2×D411yescharacteristic
219C2×Dic15C2×D411yescharacteristic
220D60—21no—
221D60—21no—
222Dic30—21no—
223Dic30C2×D412yescomplemented
224C5×#67—42no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3C2×D411yescharacteristic
227C5×D12—21no—
228C5×D12—21no—
229C4×C5×D3—42no—
230C4×C5×D3C2×D412yes—
231C4×C5×D3#4112yes—
232C3×C22⋊D5—42no—
233C3×C22⋊D5—42no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5C2×D411yescharacteristic
236C2×C3×Dic5C2×D411yescharacteristic
237C3×D20—21no—
238C3×D20—21no—
239C3×Dic10—21no—
240C3×Dic10C2×D412yescomplemented
241#1204—24no—
242#1203—42no—
243#1203—42no—
244#1202—42no—
245#1201—42no—
246#1201—42no—
247D3×Dic5—24no—
248D3×Dic5—22no—
249D3×Dic5SD1614yescomplemented
250C3×C5×C8—21no—
251C3⋊#168—21no—
252C3×#168—21no—
253C5×C3⋊C8—21no—
254C2×D3×Q8—51no—
255C2×D3×D4—51no—
256C2×D3×D4—101no—
257C2×D3×D4—101no—
258C2×D3×D4C2×D511yescharacteristic
259C2×C3×SD16—51no—
260C2×C3×SD16—51no—
261C3×#127—51no—
262C3×C4×Q8—51no—
263Q8×Dic3—51no—
264C2×#215—51no—
265C2×#215—51no—
266#940—51no—
267#940—51no—
268#940—101no—
269#940—101no—
270C2×#214—51no—
271C2×#214—51no—
272D3×SD16—104no—
273D3×SD16—104no—
274C2×#204—51no—
275C2×#204—51no—
276C2×D3×C8—51no—
277C2×D3×C8C2×D511yescharacteristic
278D3×C4⋊C4—101no—
279D3×C4⋊C4C2×D511yescharacteristic
280#887—51no—
281#887—101no—
282#874—51no—
283C42×D3—51no—
284C42×D3—101no—
285C4×Dic6—51no—
286C4×Dic6—101no—
287C3×C4⋊C8—51no—
288C3×#102—51no—
289C3×#102C2×D511yescharacteristic, complemented
290#832—51no—
291#832C2×D511yescharacteristic, complemented
292#821—51no—
293#821C2×D511yescharacteristic, complemented
294Dic3⋊C8—51no—
295Dic3⋊C8—51no—
296#809—51no—
297#809C2×D511yescharacteristic, complemented
298C4⋊(C3⋊C8)—51no—
299C24×C5—61no—
300C23×D5—61no—
301C2×C5×D4—31no—
302C2×C5×D4—62no—
303C2×C5×D4—62no—
304C2×C5×D4—61no—
305C2×C5×D4C22×D311yescharacteristic
306C22×C4×C5—31no—
307C22×C4×C5—61no—
308C2×C22⋊D5—21no—
309C2×C22⋊D5—21no—
310C2×C22⋊D5—61no—
311C2×C22⋊D5—61no—
312C2×C22⋊D5—61no—
313C2×C22⋊D5—61no—
314C2×C22⋊D5—61no—
315C2×C22⋊D5—61no—
316C2×C22⋊D5—124no—
317C2×C22⋊D5—124no—
318C22×Dic5—31no—
319C22×Dic5—31no—
320C22×Dic5—61no—
321C2×D20—31no—
322C2×D20—62no—
323C2×D20—62no—
324C2×D20—61no—
325C2×D20C22×D311yescharacteristic
326C2×Dic10—31no—
327C2×Dic10—34no—
328C2×Dic10—62no—
329C2×Dic10—61no—
330C2×Dic10C22×D311yescharacteristic
331C2×C5×C8—31no—
332C2×C5×C8—62no—
333C2×C5×C8C22×D311yescharacteristic
334C5×C4⋊C4—31no—
335C5×C4⋊C4—61no—
336C5×C4⋊C4C22×D311yescharacteristic
337#687—22no—
338#687—62no—
339#687—62no—
340#687—62no—
341#683—21no—
342#683—61no—
343#683—61no—
344#683—61no—
345C4×Dic5—21no—
346C4×Dic5—31no—
347C4×Dic5—31no—
348C4×Dic5—31no—
349C4×Dic5—61no—
350C4×Dic5—61no—
351C4×Dic5—61no—
352C4×Dic5C22×D311yescharacteristic
353C2×#168—31no—
354C2×#168—62no—
355C2×#168C22×D311yescharacteristic
356#677—22no—
357#677—62no—
358#677—62no—
359#677—62no—
360C22×SD16—151no—
361C22×SD16—151no—
362C2×#127—151no—
363C2×C4×Q8—151no—
364#460—51no—
365#460—151no—
366#460—151no—
367#460—151no—
368#460—151no—
369#460—151no—
370#460—151no—
371#460—151no—
372C2×C4⋊C8—151no—
373C2×#102—31no—
374C2×#102—151no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5C22×D411yescharacteristic
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C2×C5×D3—41no—
383C2×C5×D3—41no—
384C2×C5×D3—41no—
385C2×C5×D3—84no—
386C2×C5×D3#12112yes—
387C2×C5×D3C2×SD1612yes—
388C2×C5×D3AGL(1,ℤ/8)12yes—
389C2×C3×D5—41no—
390C2×C3×D5—41no—
391C2×C3×D5—41no—
392D3×D5—84no—
393C3×C4×C5—41no—
394C3×C4×C5C22×D411yescharacteristic
395C3×C4×C5C2×#4111yescharacteristic
396Dic15—22no—
397Dic15—21no—
398Dic15C2×SD1612yescomplemented
399C3×Dic5—22no—
400C3×Dic5—21no—
401C3×Dic5C2×SD1612yescomplemented
402C5×Dic3—41no—
403C5×Dic3#12112yes—
404C23×D3—21no—
405C23×D3—101no—
406C2×C3×Q8—51no—
407C2×C3×D4—51no—
408C2×C3×D4—101no—
409C2×C3×D4—101no—
410C2×C3×D4C22×D511yescharacteristic
411C2×#67—21no—
412C2×#67—101no—
413C2×#67—101no—
414C2×#67—101no—
415C2×#67—101no—
416C2×#67—101no—
417D3×Q8—54no—
418D3×Q8—102no—
419D3×D4—22no—
420D3×D4—22no—
421D3×D4—102no—
422D3×D4—102no—
423D3×D4—204no—
424D3×D4—204no—
425C2×D12—51no—
426C2×D12—101no—
427C2×D12—101no—
428C2×D12C22×D511yescharacteristic
429C2×C4×D3—21no—
430C2×C4×D3—51no—
431C2×C4×D3—51no—
432C2×C4×D3—101no—
433C2×C4×D3C22×D511yescharacteristic
434C2×Dic6—51no—
435C2×Dic6—101no—
436C3×SD16—102no—
437C3×SD16—102no—
438C2×C3×C8—51no—
439C2×C3×C8C22×D511yescharacteristic
440C3×C4⋊C4—101no—
441C3×C4⋊C4C22×D511yescharacteristic
442C3×C42—51no—
443C3×C42—101no—
444#215—102no—
445#215—102no—
446#214—102no—
447#214—102no—
448C4⋊Dic3—101no—
449C4⋊Dic3C22×D511yescharacteristic
450Dic3⋊C4—21no—
451Dic3⋊C4—101no—
452Dic3⋊C4—101no—
453C4×Dic3—51no—
454C4×Dic3—51no—
455C4×Dic3—51no—
456C4×Dic3—101no—
457C4×Dic3—101no—
458C4×Dic3—101no—
459C2×C3⋊C8—51no—
460C2×C3⋊C8C22×D511yescharacteristic
461#204—102no—
462#204—102no—
463D3×C8—22no—
464D3×C8—102no—
465C23×C5—21no—
466C23×C5—31no—
467C23×C5—61no—
468C23×C5—122no—
469C23×C5—122no—
470C23×C5—122no—
471C22×D5—21no—
472C22×D5—61no—
473C22×D5—122no—
474C22×D5—122no—
475C22×D5—122no—
476C5×D4—21no—
477C5×D4—21no—
478C5×D4—61no—
479C5×D4—61no—
480C5×D4—122no—
481C2×C4×C5—21no—
482C2×C4×C5—31no—
483C2×C4×C5—32no—
484C2×C4×C5—32no—
485C2×C4×C5—61no—
486C2×C4×C5—122no—
487C2×C4×C5C23×D311yescharacteristic
488C22⋊D5—42no—
489C22⋊D5—42no—
490C22⋊D5—122no—
491C22⋊D5—122no—
492C22⋊D5—122no—
493C22⋊D5—122no—
494C22⋊D5—122no—
495C22⋊D5—122no—
496C2×Dic5—21no—
497C2×Dic5—31no—
498C2×Dic5—34no—
499C2×Dic5—31no—
500C2×Dic5—64no—
501C2×Dic5—62no—
502C2×Dic5—61no—
503C2×Dic5D3×D411yescharacteristic
504C2×Dic5D3×D411yescharacteristic
505D20—21no—
506D20—21no—
507D20—61no—
508D20—61no—
509D20—122no—
510Dic10—21no—
511Dic10—32no—
512Dic10—64no—
513Dic10—61no—
514Dic10D3×D412yescomplemented
515C5×C8—21no—
516C5×C8—61no—
517#168—21no—
518#168—61no—
519C22×Q8—151no—
520C22×D4—31no—
521C22×D4—151no—
522C22×D4—301no—
523C22×D4—301no—
524C2×SD16—51no—
525C2×SD16—51no—
526C2×SD16—151no—
527C2×SD16—151no—
528C2×SD16—151no—
529C2×SD16—151no—
530C2×SD16—151no—
531C2×SD16—151no—
532C2×SD16—304no—
533C2×SD16—304no—
534C22×C8—31no—
535C22×C8—151no—
536#127—51no—
537#127—151no—
538#127—151no—
539#127—151no—
540#127—301no—
541#127—301no—
542C4×Q8—51no—
543C4×Q8—151no—
544C4×Q8—151no—
545C4×Q8—151no—
546C4×Q8—301no—
547C4×Q8—301no—
548C2×C4⋊C4—31no—
549C2×C4⋊C4—301no—
550C2×C42—151no—
551C2×C42—301no—
552C4⋊C8—51no—
553C4⋊C8—151no—
554C4⋊C8—151no—
555C4⋊C8—151no—
556#102—31no—
557#102—31no—
558#102—31no—
559#102—51no—
560#102—151no—
561#102—151no—
562#102—151no—
563#102D3×D511yescharacteristic, complemented
564C2×C3×C5—81no—
565C2×C3×C5C2×#12111yescharacteristic
566C2×C3×C5C22×SD1611yescharacteristic
567C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
568D15—81no—
569C3×D5—81no—
570C5×D3—81no—
571C5×D3#46014yescomplemented
572C23×C3—21no—
573C23×C3—101no—
574C22×D3—21no—
575C22×D3—42no—
576C22×D3—42no—
577C22×D3—42no—
578C22×D3—101no—
579C22×D3—202no—
580C22×D3—202no—
581C22×D3—202no—
582C22×D3D4×D511yescharacteristic
583C3×Q8—52no—
584C3×Q8—101no—
585C3×D4—21no—
586C3×D4—21no—
587C3×D4—101no—
588C3×D4—101no—
589C3×D4—202no—
590C3×D4—202no—
591C2×C3×C4—21no—
592C2×C3×C4—51no—
593C2×C3×C4—51no—
594C2×C3×C4—101no—
595C2×C3×C4C23×D511yescharacteristic
596#67—42no—
597#67—202no—
598#67—202no—
599#67—202no—
600#67—202no—
601#67—202no—
602C2×Dic3—21no—
603C2×Dic3—51no—
604C2×Dic3—51no—
605C2×Dic3—101no—
606C2×Dic3D4×D511yescharacteristic
607D12—21no—
608D12—21no—
609D12—101no—
610D12—101no—
611D12—202no—
612D12—202no—
613C4×D3—42no—
614C4×D3—54no—
615C4×D3—104no—
616C4×D3—102no—
617C4×D3#70912yes—
618C4×D3D4×D512yes—
619Dic6—52no—
620Dic6—101no—
621Dic6—104no—
622C3×C8—21no—
623C3×C8—101no—
624C3⋊C8—21no—
625C3⋊C8—101no—
626C22×C5—32no—
627C22×C5—32no—
628C22×C5—32no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5—41no—
632C22×C5—121no—
633C22×C5—121no—
634C22×C5—121no—
635C22×C5—244no—
636C22×C5C2×D3×D411yescharacteristic
637C2×D5—41no—
638C2×D5—41no—
639C2×D5—41no—
640C2×D5—121no—
641C2×D5—121no—
642C2×D5—121no—
643C2×D5—244no—
644C4×C5—32no—
645C4×C5—41no—
646C4×C5—121no—
647C4×C5C2×D3×D411yescharacteristic
648C4×C5D3×#4111yescharacteristic
649Dic5—21no—
650Dic5—22no—
651Dic5—32no—
652Dic5—61no—
653Dic5—62no—
654Dic5D3×SD1612yescomplemented
655C24—61no—
656C24—301no—
657C2×Q8—51no—
658C2×Q8—154no—
659C2×Q8—151no—
660C2×Q8—301no—
661C2×Q8—302no—
662C2×D4—31no—
663C2×D4—51no—
664C2×D4—62no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—101no—
668C2×D4—101no—
669C2×D4—151no—
670C2×D4—302no—
671C2×D4—302no—
672C2×D4—301no—
673C2×D4—301no—
674C2×D4—301no—
675C2×D4—301no—
676C2×D4—301no—
677C2×D4—301no—
678C2×D4—301no—
679C2×D4—604no—
680C2×D4—604no—
681C2×D4C2×D3×D511yescharacteristic
682C22×C4—31no—
683C22×C4—61no—
684C22×C4—151no—
685C22×C4—151no—
686C22×C4—301no—
687SD16—102no—
688SD16—102no—
689SD16—302no—
690SD16—302no—
691SD16—302no—
692SD16—302no—
693SD16—302no—
694SD16—302no—
695C2×C8—31no—
696C2×C8—51no—
697C2×C8—62no—
698C2×C8—151no—
699C2×C8—302no—
700C2×C8C2×D3×D511yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—61no—
703C4⋊C4—101no—
704C4⋊C4—301no—
705C4⋊C4—301no—
706C4⋊C4—301no—
707C4⋊C4C2×D3×D511yescharacteristic
708C42—51no—
709C42—101no—
710C42—151no—
711C42—151no—
712C42—151no—
713C42—301no—
714C42—301no—
715C42—301no—
716C3×C5C2×#46011yescharacteristic, complemented, Hall
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—201no—
721C22×C3—201no—
722C22×C3—201no—
723C22×C3C2×D4×D511yescharacteristic
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—41no—
727C2×D3—84no—
728C2×D3—201no—
729C2×D3—201no—
730C2×D3—201no—
731C2×D3—404no—
732C2×D3#403012yes—
733C2×D3#405712yes—
734C2×D3D5×SD1612yes—
735C3×C4—41no—
736C3×C4—52no—
737C3×C4—102no—
738C3×C4—101no—
739C3×C4C2×#70911yescharacteristic
740C3×C4C2×D4×D511yescharacteristic
741Dic3—41no—
742Dic3—52no—
743Dic3—102no—
744Dic3—101no—
745Dic3#403012yes—
746C2×C5—34no—
747C2×C5—81no—
748C2×C5—241no—
749C2×C5D3×#12111yescharacteristic
750C2×C5C2×D3×SD1611yescharacteristic
751C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
752D5—81no—
753D5—241no—
754C23—21no—
755C23—31no—
756C23—61no—
757C23—101no—
758C23—122no—
759C23—122no—
760C23—122no—
761C23—301no—
762C23—602no—
763C23—602no—
764C23—602no—
765Q8—52no—
766Q8—101no—
767Q8—152no—
768Q8—304no—
769Q8—301no—
770D4—21no—
771D4—21no—
772D4—61no—
773D4—61no—
774D4—101no—
775D4—101no—
776D4—122no—
777D4—202no—
778D4—202no—
779D4—301no—
780D4—301no—
781D4—602no—
782D4—602no—
783D4—602no—
784D4—602no—
785D4—602no—
786D4—602no—
787D4—602no—
788C2×C4—21no—
789C2×C4—31no—
790C2×C4—32no—
791C2×C4—32no—
792C2×C4—51no—
793C2×C4—51no—
794C2×C4—61no—
795C2×C4—101no—
796C2×C4—122no—
797C2×C4—154no—
798C2×C4—151no—
799C2×C4—151no—
800C2×C4—302no—
801C2×C4—304no—
802C2×C4—301no—
803C2×C4C22×D3×D511yescharacteristic
804C8—21no—
805C8—61no—
806C8—101no—
807C8—301no—
808C2×C3—81no—
809C2×C3—401no—
810C2×C3C2×#403011yescharacteristic
811C2×C3C2×#405711yescharacteristic
812C2×C3C2×D5×SD1611yescharacteristic
813D3—81no—
814D3—401no—
815D3#6505114yesdirect product factor
816C5D3×#46011yescharacteristic, complemented, Sylow
817C22—32no—
818C22—32no—
819C22—32no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—201no—
827C22—201no—
828C22—201no—
829C22—244no—
830C22—601no—
831C22—601no—
832C22—601no—
833C22—1204no—
834C22D3×D4×D511yescharacteristic
835C4—32no—
836C4—41no—
837C4—52no—
838C4—102no—
839C4—101no—
840C4—121no—
841C4—152no—
842C4—302no—
843C4—301no—
844C4D3×#70911yescharacteristic
845C4D3×D4×D511yescharacteristic
846C3C2×#6505111yescharacteristic, complemented, Sylow
847C2—34no—
848C2—81no—
849C2—241no—
850C2—401no—
851C2—1201no—
852C2D3×#403011yescharacteristic
853C2D3×#405711yescharacteristic
854C2D3×D5×SD1611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalD3×#4086C2
hypercenter#102D3×D5
hypocenterC3×C5C2×#460
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
2. C2×D3×#687C2semidirect
3. C2×D3×#677C2semidirect
4. D3×#4033C2semidirect
5. #11750863C2semidirect
6. C5×D3×#102C2semidirect
7. C3×#65051C2semidirect
8. #11749008C2semidirect
9. #11749000C2semidirect
10. #11747993C2semidirect
11. #11747843C2semidirect
12. D3×#3946C2semidirect
13. D3×#3941C2semidirect
14. #11747408C2semidirect
15. #11747400C2semidirect
23. C2×#6716C22semidirect
24. C2×#6706C22semidirect
25. #91776C22semidirect
29. C2×C3×#687C22semidirect
30. C2×C3×#677C22semidirect
31. C3×#4033C22semidirect
40. #91333C22semidirect
41. #91331C22semidirect
44. C2×#6659C22semidirect
45. C2×#6658C22semidirect
46. C2×#6657C22semidirect
47. C2×#6656C22semidirect
50. C3×C5×#102C22semidirect
51. #91098C22semidirect
52. #91093C22semidirect
53. C5×#832C22semidirect
54. C5×#821C22semidirect
55. C5×#809C22semidirect
56. C3×#3946C22semidirect
57. C3×#3941C22semidirect
58. #90983C22semidirect
59. #90982C22semidirect
60. #90969C22semidirect
61. #90964C22semidirect
77. #65051D3direct (N × H)
109. D3×Dic10D4semidirect
151. D3×#102D5semidirect
171. C2×#687C2×D3semidirect
180. C2×#677C2×D3semidirect
186. #4033C2×D3semidirect
190. C5×#102C2×D3semidirect
194. #3946C2×D3semidirect
198. #3941C2×D3semidirect
223. Dic30C2×D4semidirect
240. C3×Dic10C2×D4semidirect
249. D3×Dic5SD16semidirect
289. C3×#102C2×D5semidirect
291. #832C2×D5semidirect
293. #821C2×D5semidirect
297. #809C2×D5semidirect
398. Dic15C2×SD16semidirect
401. C3×Dic5C2×SD16semidirect
514. Dic10D3×D4semidirect
563. #102D3×D5semidirect
571. C5×D3#460semidirect
654. Dic5D3×SD16semidirect
716. C3×C5C2×#460semidirect
815. D3#65051direct (N × H)
816. C5D3×#460semidirect
846. C3C2×#65051semidirect

Maximal subgroups

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

subgroupindex
D3×#40862
C2×D3×#6872
C2×D3×#6772
D3×#40332
#117508632
C5×D3×#1022
C3×#650512
#117490082
#117490002
#117479932
#117478432
D3×#39462
D3×#39412
#117474082
#117474002
C2×#650513
D3×#4605