Finite Group Databasebeta

← #14426283

Subgroups — #14426283

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5832C211yesmaximal, characteristic, complemented
2C2×C3×#4096C211yesmaximal, characteristic, complemented
3Dic3×#709C211yesmaximal, characteristic, complemented
4C2×#91297C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11749252C211yesmaximal, characteristic, complemented
7#11749251C211yesmaximal, characteristic, complemented
8#11749228C211yesmaximal, characteristic, complemented
9#11749227C211yesmaximal, characteristic, complemented
10#11749006C211yesmaximal, characteristic, complemented
11#11749005C211yesmaximal, characteristic, complemented
12#11748982C211yesmaximal, characteristic, complemented
13#11748981C211yesmaximal, characteristic, complemented
14C2×Dic3⋊#168C211yesmaximal, characteristic, complemented
15#11748388C211yesmaximal, characteristic, complemented
16#10615027—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C5×#235C2211yescharacteristic
19C2×C3×#709C2211yescharacteristic
20#91815C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C5×#947C2211yescharacteristic
23C5×#944C2211yescharacteristic
24C5×#940C2211yescharacteristic
25C5×#939—21no—
26C5×#939—21no—
27C5×#936C2211yescharacteristic
28C4×C5×#67—21no—
29C4×C5×#67—21no—
30C2×C4×C5×Dic3C2211yescharacteristic
31C3×#4096—24no—
32C2×C3×#689C2211yescharacteristic
33C2×C3×#688C2211yescharacteristic
34C2×C3×#687C2211yescharacteristic
35C2×C3×#686C2211yescharacteristic
36C22×C3×#168C2211yescharacteristic
37Dic3×C22⋊D5—21no—
38Dic3×C22⋊D5—21no—
39Dic3×D20C2211yescharacteristic
40Dic3×D20C2211yescharacteristic
41C4×D5×Dic3—21no—
42#91357—21no—
43Dic3×Dic10C2211yescharacteristic
44Dic3×Dic10C2211yescharacteristic
45C2×#6661C2211yescharacteristic
46C2×#6656C2211yescharacteristic
47C2×#6655C2211yescharacteristic
48#91297—24no—
49C2×#6652C2211yescharacteristic
50#91119C2211yescharacteristic
51#91119C2211yescharacteristic
52#91116C2211yescharacteristic
53#91116C2211yescharacteristic
54Dic3⋊#168C2211yescharacteristic
55Dic3⋊#168C2211yescharacteristic
56Dic3⋊#168C2211yescharacteristic
57Dic3⋊#168C2211yescharacteristic
58#90973C2211yescharacteristic
59#90973C2211yescharacteristic
60#90967C2211yescharacteristic
61#90967C2211yescharacteristic
62#83900—51nomaximal, Hall
63C5×#532—31no—
64C2×#4096—31no—
65C2×#4096D311yescharacteristic, complemented
66C4×#709—31no—
67#65522—31no—
68#65522—31no—
69#65379—31no—
70#65372—31no—
71#65364—31no—
72#65361—31no—
73#65346—31no—
74#65346—31no—
75#65343—31no—
76#65343—31no—
77C2×C4⋊#168—31no—
78C3×C5×#41—22no—
79C3×C5×#41—22no—
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5C2311yescharacteristic
85C2×C5×#67—21no—
86C2×C5×#67—21no—
87C2×C5×#67—21no—
88C22×C5×Dic3D411yescharacteristic
89C22×C5×Dic3D411yescharacteristic
90C5×#235—22no—
91C5×#235—22no—
92C2×C5×D12C2311yescharacteristic
93C2×C4×C5×D3—21no—
94C2×C5×Dic6C2311yescharacteristic
95C2×C3×C22⋊D5—21no—
96C3×#709—22no—
97C3×#709D414yescomplemented
98C2×C3×D20C2311yescharacteristic
99C2×C3×C4×D5—21no—
100C2×C3×Dic10C2311yescharacteristic
101C2×D5×Dic3—21no—
102C2×D5×Dic3—21no—
103#6719—21no—
104C4⋊Dic15C2311yescharacteristic
105C4⋊Dic15C2311yescharacteristic
106C4×Dic15—21no—
107C2×C3⋊#168—22no—
108C2×C3⋊#168C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C5×#217—21no—
111C5×#217—21no—
112C5×(C2×D3)⋊C4—21no—
113C5×(C2×D3)⋊C4—21no—
114C5×Dic3⋊C4—21no—
115C5×Dic3⋊C4—21no—
116C4×C5×Dic3D411yescharacteristic
117C4×C5×Dic3D411yescharacteristic
118C4×C5×Dic3C2311yescharacteristic
119C4×C5×Dic3C2311yescharacteristic
120C3×#689—22no—
121C3×#688—22no—
122C3×#687—22no—
123C3×#686—22no—
124C2×C3×#168—22no—
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127#6668—21no—
128#6668—21no—
129#6665—21no—
130#6665—21no—
131Dic3×Dic5—21no—
132Dic3×Dic5—21no—
133#6661—22no—
134#6656—22no—
135#6655—22no—
136#6652—22no—
137C2×C3×#135—51no—
138#5832D511yescharacteristic, complemented
139Dic3×#41—51no—
140C2×#950—51no—
141#5233—51no—
142#5185—51no—
143#5182—51no—
144#5166—51no—
145#5165—51no—
146#5163—51no—
147#5162—51no—
148#5153—51no—
149#5150—51no—
150#5113—51no—
151C2×Dic3⋊C8—51no—
152C2×C5×#41—31no—
153C2×C5×#41C2×D311yescharacteristic
154C2×#709C2×D311yescharacteristic
155C5×C4⋊Q8—31no—
156C5×#127—31no—
157C5×#124—31no—
158C5×#124—31no—
159C5×#121—61no—
160C5×#121—61no—
161C4×C5×D4—61no—
162C4×C5×D4—61no—
163C2×C42×C5—31no—
164#4096—24no—
165#4096—64no—
166C2×#689—31no—
167C2×#689C2×D311yescharacteristic
168C2×#688—31no—
169C2×#688C2×D311yescharacteristic
170C2×#687—31no—
171C2×#687C2×D311yescharacteristic
172C2×#686—31no—
173C2×#686C2×D311yescharacteristic
174C4×C22⋊D5—61no—
175C4×C22⋊D5—61no—
176#4072—31no—
177C22×#168—31no—
178C22×#168C2×D311yescharacteristic
179C4×D20—31no—
180C4×D20—31no—
181#4018—61no—
182C42×D5—61no—
183C4×Dic10—31no—
184C4×Dic10—31no—
185#3967—31no—
186#3967—31no—
187#3967—31no—
188#3967—31no—
189#3964—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C4⋊#168—31no—
194C4⋊#168—31no—
195C4⋊#168—31no—
196C4⋊#168—31no—
197#3035—151noSylow
198C23×C3×C5—21no—
199C23×C3×C5C2×D411yescharacteristic
200C22×C5×D3—21no—
201C22×C3×D5—21no—
202C3×C5×Q8—21no—
203C3×C5×Q8—21no—
204C3×C5×D4—21no—
205C3×C5×D4—21no—
206C3×C5×D4—42no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—42no—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2×D412yes—
211C2×C3×C4×C5#4112yes—
212C2×C3×C4×C5C2411yescharacteristic
213C2×Dic15—21no—
214C2×Dic15—21no—
215C5×#67—42no—
216C5×#67—42no—
217C5×#67—42no—
218C2×C5×Dic3—22no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—41no—
221C2×C5×Dic3C2×D411yescharacteristic
222C2×C5×Dic3C2×D411yescharacteristic
223C2×C5×Dic3C2×D411yescharacteristic
224C2×C5×Dic3C2×D411yescharacteristic
225C5×D12—21no—
226C5×D12—21no—
227C4×C5×D3—42no—
228C5×Dic6—21no—
229C5×Dic6—21no—
230C3×C22⋊D5—24no—
231C2×C3×Dic5—21no—
232C3×D20—21no—
233C3×D20C2×D412yes—
234C3×C4×D5—24no—
235C3×Dic10—21no—
236C3×Dic10C2×D412yes—
237D5×Dic3—42no—
238D5×Dic3—42no—
239C3⋊#168—21no—
240C3⋊#168—21no—
241C3×#168—21no—
242C3×#168—21no—
243C2×C3×#41—51no—
244C2×C3×#41C2×D511yescharacteristic
245C2×#235C2×D511yescharacteristic
246C3×#135—104no—
247C2×C3×Q16—51no—
248C2×C3×SD16—51no—
249C2×C3×SD16—51no—
250C2×C3×D8—51no—
251C22×C3×C8—51no—
252#950—104no—
253#947C2×D511yescharacteristic
254Q8×Dic3—51no—
255Q8×Dic3—51no—
256#944C2×D511yescharacteristic
257C2×#216—51no—
258C2×#215—51no—
259#940C2×D511yescharacteristic
260#939—21no—
261#939—21no—
262#936C2×D511yescharacteristic
263D4×Dic3—51no—
264D4×Dic3—51no—
265D4×Dic3—101no—
266D4×Dic3—101no—
267C2×#214—51no—
268C2×#213—51no—
269C4×#67—21no—
270C4×#67—21no—
271#926—51no—
272#926—101no—
273C2×C4×Dic3—101no—
274C2×C4×Dic3C2×D511yescharacteristic
275C22×C3⋊C8—51no—
276#835—51no—
277#835—51no—
278#832—51no—
279#832—51no—
280#821—51no—
281#821—51no—
282#816—51no—
283#816—51no—
284Dic3⋊C8—51no—
285Dic3⋊C8—51no—
286Dic3⋊C8—51no—
287Dic3⋊C8—51no—
288C5×#41—22no—
289C5×#41—22no—
290C5×#41—62no—
291C5×#41—62no—
292C2×C5×Q8—31no—
293C2×C5×Q8C22×D311yescharacteristic
294C2×C5×D4—21no—
295C2×C5×D4—31no—
296C2×C5×D4—61no—
297C2×C5×D4—61no—
298C2×C5×D4—61no—
299C2×C5×D4C22×D311yescharacteristic
300C22×C4×C5—21no—
301C22×C4×C5—31no—
302C22×C4×C5—31no—
303C22×C4×C5—61no—
304C22×C4×C5C22×D311yescharacteristic
305C2×C22⋊D5—21no—
306#709—22no—
307#709#6714yescomplemented
308C2×D20C22×D311yescharacteristic
309C2×C4×D5—21no—
310C2×C4×D5—61no—
311C2×C4×D5—61no—
312C2×Dic10C22×D311yescharacteristic
313C5×C4⋊C4—61no—
314C5×C4⋊C4—61no—
315C5×C22⋊C4—61no—
316C5×C22⋊C4—61no—
317C5×C22⋊C4—61no—
318C5×C22⋊C4—61no—
319C42×C5—31no—
320C42×C5—31no—
321C42×C5—31no—
322C42×C5—31no—
323C22⋊Dic5—61no—
324#689—22no—
325#689—62no—
326#688—22no—
327#688—62no—
328#687—22no—
329#687—62no—
330#686—22no—
331#686—62no—
332#685—61no—
333#685—61no—
334C4⋊Dic5—31no—
335C4⋊Dic5—31no—
336#683—61no—
337#683—61no—
338C4×Dic5—61no—
339C4×Dic5—61no—
340C4×Dic5—61no—
341C2×#168—22no—
342C2×#168—31no—
343C2×#168—31no—
344C2×#168—62no—
345C2×#168C22×D311yescharacteristic
346C2×#168C22×D311yescharacteristic
347C2×#135—51no—
348C2×#135—151no—
349#532—31no—
350C4×#41—151no—
351#464—151no—
352#464—151no—
353#463—151no—
354#463—151no—
355#462—151no—
356#461—151no—
357#460—151no—
358#459—151no—
359C2×C4⋊C8—151no—
360#416—151no—
361#416—151no—
362C22×C3×C5—21no—
363C22×C3×C5—21no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5#12112yes—
368C22×C3×C5C22×D411yescharacteristic
369C2×C5×D3—41no—
370C2×C5×D3—41no—
371C2×C5×D3—41no—
372C2×C3×D5—22no—
373C2×C3×D5—41no—
374C2×C3×D5—41no—
375C3×C4×C5—41no—
376C3×C4×C5#12112yes—
377C3×C4×C5C22×D411yescharacteristic
378C3×C4×C5C2×#4111yescharacteristic
379Dic15—41no—
380Dic15—41no—
381C3×Dic5—22no—
382C5×Dic3—21no—
383C5×Dic3—21no—
384C5×Dic3—21no—
385C5×Dic3—41no—
386C5×Dic3#13512yescomplemented
387C3×#41—22no—
388C3×#41—22no—
389C3×#41—54no—
390C3×#41—102no—
391C2×C3×Q8—51no—
392C2×C3×Q8C22×D511yescharacteristic
393C2×C3×D4—21no—
394C2×C3×D4—51no—
395C2×C3×D4—101no—
396C2×C3×D4C22×D511yescharacteristic
397C22×C3×C4—21no—
398C22×C3×C4—101no—
399C22×C3×C4C22×D511yescharacteristic
400C2×#67—21no—
401C2×#67—21no—
402C2×#67—21no—
403C22×Dic3—101no—
404C22×Dic3—101no—
405C22×Dic3C22⋊D511yescharacteristic
406C22×Dic3C22⋊D511yescharacteristic
407#235—22no—
408#235—22no—
409C2×D12C22×D511yescharacteristic
410C2×C4×D3—21no—
411C2×Dic6C22×D511yescharacteristic
412C3×Q16—102no—
413C3×SD16—102no—
414C3×SD16—102no—
415C3×D8—102no—
416C2×C3×C8—51no—
417C2×C3×C8—51no—
418C2×C3×C8—102no—
419#217—21no—
420#217—21no—
421#217—101no—
422#217—101no—
423#217—101no—
424#216—102no—
425#215—102no—
426#214—102no—
427#213—102no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430C4⋊Dic3—51no—
431C4⋊Dic3—51no—
432C4⋊Dic3—101no—
433C4⋊Dic3—101no—
434Dic3⋊C4—21no—
435Dic3⋊C4—21no—
436C4×Dic3—101no—
437C4×Dic3—101no—
438C4×Dic3—101no—
439C4×Dic3C22⋊D511yescharacteristic
440C4×Dic3C22⋊D511yescharacteristic
441C4×Dic3C22×D511yescharacteristic
442C4×Dic3C22×D511yescharacteristic
443C2×C3⋊C8—51no—
444C2×C3⋊C8—51no—
445C2×C3⋊C8—102no—
446C23×C5—21no—
447C23×C5—61no—
448C23×C5D3×D411yescharacteristic
449C22×D5—21no—
450C5×Q8—21no—
451C5×Q8—21no—
452C5×Q8—61no—
453C5×Q8—61no—
454C5×D4—21no—
455C5×D4—21no—
456C5×D4—42no—
457C5×D4—61no—
458C5×D4—61no—
459C5×D4—122no—
460C5×D4—122no—
461C5×D4—122no—
462C2×C4×C5—21no—
463C2×C4×C5—31no—
464C2×C4×C5—31no—
465C2×C4×C5—31no—
466C2×C4×C5—31no—
467C2×C4×C5—42no—
468C2×C4×C5—62no—
469C2×C4×C5—61no—
470C2×C4×C5—121no—
471C2×C4×C5—122no—
472C2×C4×C5D3×D411yescharacteristic
473C2×C4×C5#23712yes—
474C2×C4×C5C2×#6712yes—
475C2×C4×C5C23×D311yescharacteristic
476C22⋊D5—24no—
477C2×Dic5—21no—
478C2×Dic5—61no—
479C2×Dic5—61no—
480D20—21no—
481D20C2×#6712yes—
482C4×D5—24no—
483C4×D5—122no—
484C4×D5—122no—
485Dic10—21no—
486Dic10C2×#6712yes—
487#168—21no—
488#168—21no—
489#168—61no—
490#168—61no—
491C2×#41—31no—
492C2×#41—51no—
493C2×#41D3×D511yescharacteristic
494#135—104no—
495#135—304no—
496C2×Q16—51no—
497C2×Q16—151no—
498C2×SD16—51no—
499C2×SD16—51no—
500C2×SD16—151no—
501C2×SD16—151no—
502C2×D8—51no—
503C2×D8—151no—
504C22×C8—51no—
505C22×C8—151no—
506C4⋊Q8—31no—
507#127—31no—
508#124—31no—
509#124—31no—
510#121—61no—
511#121—61no—
512C4×Q8—151no—
513C4×Q8—151no—
514C4×D4—61no—
515C4×D4—61no—
516C4×D4—151no—
517C4×D4—151no—
518C4×D4—301no—
519C4×D4—301no—
520#117—151no—
521#117—301no—
522C2×C42—31no—
523C2×C42—301no—
524C4⋊C8—151no—
525C4⋊C8—151no—
526C4⋊C8—151no—
527C4⋊C8—151no—
528#103—151no—
529#103—151no—
530#103—151no—
531#103—151no—
532#102—151no—
533#102—151no—
534#102—151no—
535#102—151no—
536C2×C3×C5—22no—
537C2×C3×C5—81no—
538C2×C3×C5C2×#12111yescharacteristic
539C2×C3×C5C2×#13511yescharacteristic
540C2×C3×C5#57511yescharacteristic
541C3×D5—42no—
542C5×D3—81no—
543C23×C3—21no—
544C23×C3—101no—
545C23×C3C2×C22⋊D511yescharacteristic
546C22×D3—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—52no—
550C3×Q8—101no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—42no—
554C3×D4—52no—
555C3×D4—104no—
556C3×D4—101no—
557C2×C3×C4—21no—
558C2×C3×C4—42no—
559C2×C3×C4—101no—
560C2×C3×C4—104no—
561C2×C3×C4D4×D512yes—
562C2×C3×C4#71112yes—
563C2×C3×C4C2×C22⋊D511yescharacteristic
564C2×C3×C4C23×D511yescharacteristic
565#67—42no—
566#67—42no—
567#67—42no—
568C2×Dic3—22no—
569C2×Dic3—21no—
570C2×Dic3—41no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—202no—
574C2×Dic3—202no—
575C2×Dic3C2×C22⋊D511yescharacteristic
576C2×Dic3C2×C22⋊D511yescharacteristic
577C2×Dic3C2×C22⋊D511yescharacteristic
578C2×Dic3C2×C22⋊D511yescharacteristic
579D12—21no—
580D12—21no—
581C4×D3—42no—
582Dic6—21no—
583Dic6—21no—
584C3×C8—101no—
585C3×C8—101no—
586C3⋊C8—101no—
587C3⋊C8—101no—
588C22×C5—21no—
589C22×C5—21no—
590C22×C5—41no—
591C22×C5—41no—
592C22×C5—41no—
593C22×C5—121no—
594C22×C5—121no—
595C22×C5—121no—
596C22×C5#93912yes—
597C22×C5C2×D3×D411yescharacteristic
598C2×D5—22no—
599C2×D5—41no—
600C2×D5—41no—
601C4×C5—32no—
602C4×C5—41no—
603C4×C5—61no—
604C4×C5—61no—
605C4×C5—61no—
606C4×C5—121no—
607C4×C5#93912yes—
608C4×C5C2×#23711yescharacteristic
609C4×C5C22×#6711yescharacteristic
610Dic5—22no—
611Dic5—121no—
612Dic5—121no—
613#41—22no—
614#41—22no—
615#41—54no—
616#41—62no—
617#41—62no—
618#41—102no—
619C2×Q8—31no—
620C2×Q8—51no—
621C2×Q8C2×D3×D511yescharacteristic
622C2×D4—21no—
623C2×D4—31no—
624C2×D4—51no—
625C2×D4—61no—
626C2×D4—61no—
627C2×D4—61no—
628C2×D4—101no—
629C2×D4C2×D3×D511yescharacteristic
630C22×C4—21no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—101no—
635C22×C4—301no—
636C22×C4—301no—
637C22×C4C2×D3×D511yescharacteristic
638Q16—102no—
639Q16—302no—
640SD16—102no—
641SD16—102no—
642SD16—302no—
643SD16—302no—
644D8—102no—
645D8—302no—
646C2×C8—51no—
647C2×C8—51no—
648C2×C8—102no—
649C2×C8—151no—
650C2×C8—151no—
651C2×C8—302no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4—151no—
655C4⋊C4—151no—
656C4⋊C4—301no—
657C4⋊C4—301no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—61no—
662C22⋊C4—301no—
663C22⋊C4—301no—
664C22⋊C4—301no—
665C42—31no—
666C42—31no—
667C42—31no—
668C42—31no—
669C42—301no—
670C42—301no—
671C42—301no—
672C3×C5#303511yescharacteristic, complemented, Hall
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—102no—
679C22×C3—201no—
680C22×C3—201no—
681C22×C3#408412yes—
682C22×C3C22×C22⋊D511yescharacteristic
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C3×C4—41no—
687C3×C4—102no—
688C3×C4#408412yes—
689C3×C4C2×D4×D511yescharacteristic
690C3×C4C2×#71111yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—201no—
696Dic3—201no—
697Dic3#409612yescomplemented
698C2×C5—22no—
699C2×C5—81no—
700C2×C5—241no—
701C2×C5D3×#13511yescharacteristic
702C2×C5#576811yescharacteristic
703C2×C5C2×#93911yescharacteristic
704D5—42no—
705C23—21no—
706C23—61no—
707C23—101no—
708C23D3×C22⋊D511yescharacteristic
709Q8—21no—
710Q8—21no—
711Q8—52no—
712Q8—61no—
713Q8—61no—
714Q8—101no—
715D4—21no—
716D4—21no—
717D4—42no—
718D4—52no—
719D4—61no—
720D4—61no—
721D4—104no—
722D4—101no—
723D4—122no—
724D4—122no—
725D4—122no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—42no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—101no—
735C2×C4—104no—
736C2×C4—121no—
737C2×C4—122no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—602no—
741C2×C4—602no—
742C2×C4#678012yes—
743C2×C4D5×#6712yes—
744C2×C4D3×C22⋊D511yescharacteristic
745C2×C4C22×D3×D511yescharacteristic
746C8—101no—
747C8—101no—
748C8—301no—
749C8—301no—
750C2×C3—22no—
751C2×C3—81no—
752C2×C3—202no—
753C2×C3C2×#408411yescharacteristic
754C2×C3C2×#409611yescharacteristic
755C2×C3#6615611yescharacteristic
756D3—81no—
757C5#8390011yescharacteristic, complemented, Sylow
758C22—21no—
759C22—21no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—102no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—201no—
768C22—201no—
769C22#9154912yes—
770C22C2×D3×C22⋊D511yescharacteristic
771C4—32no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—102no—
777C4—121no—
778C4—601no—
779C4—601no—
780C4#9154912yes—
781C4C2×#678011yescharacteristic
782C4C2×D5×#6711yescharacteristic
783C3#1061502711yescharacteristic, complemented, Sylow
784C2—22no—
785C2—81no—
786C2—202no—
787C2—241no—
788C2D3×#409611yescharacteristic
789C2#1175532211yescharacteristic
790C2C2×#9154911yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3035
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C5×#5832C2semidirect
2. C2×C3×#4096C2semidirect
3. Dic3×#709C2semidirect
4. C2×#91297C2semidirect
5. #11751334C2semidirect
6. #11749252C2semidirect
7. #11749251C2semidirect
8. #11749228C2semidirect
9. #11749227C2semidirect
10. #11749006C2semidirect
11. #11749005C2semidirect
12. #11748982C2semidirect
13. #11748981C2semidirect
14. C2×Dic3⋊#168C2semidirect
15. #11748388C2semidirect
65. C2×#4096D3semidirect
97. C3×#709D4semidirect
138. #5832D5semidirect
307. #709#67semidirect
386. C5×Dic3#135semidirect
672. C3×C5#3035semidirect
697. Dic3#4096semidirect
757. C5#83900semidirect
783. C3#10615027semidirect

Maximal subgroups

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

subgroupindex
C5×#58322
C2×C3×#40962
Dic3×#7092
C2×#912972
#117513342
#117492522
#117492512
#117492282
#117492272
#117490062
#117490052
#117489822
#117489812
C2×Dic3⋊#1682
#117483882
#106150273
#839005