Finite Group Databasebeta

← #14453642

Subgroups — #14453642

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5609C211yesmaximal, characteristic, complemented
2C2×D3×#687C211yesmaximal, characteristic, complemented
3#11754528C211yesmaximal, characteristic, complemented
4C2×#91299C211yesmaximal, characteristic, complemented
5#11751143C211yesmaximal, characteristic, complemented
6C3×#65326C211yesmaximal, characteristic, complemented
7#11749071C211yesmaximal, characteristic, complemented
8#11749032C211yesmaximal, characteristic, complemented
9#11749005C211yesmaximal, characteristic, complemented
10#11748543C211yesmaximal, characteristic, complemented
11#11748496C211yesmaximal, characteristic, complemented
12#11747494C211yesmaximal, characteristic, complemented
13#11747375C211yesmaximal, characteristic, complemented
14#11747319C211yesmaximal, characteristic, complemented
15#11747265C211yesmaximal, characteristic, complemented
16#10615222—31nomaximal, Hall
17C2×C5×D3×D4—21no—
18C2×C5×D3×D4C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C2×C3×#709C2211yescharacteristic, complemented
21C2×D3×Dic10C2211yescharacteristic, complemented
22C3×C5×#121C2211yescharacteristic
23C2×#6716C2211yescharacteristic, complemented
24#91813C2211yescharacteristic, complemented
25C2×#6710C2211yescharacteristic, complemented
26C5×#940C2211yescharacteristic
27C5×#937—21no—
28C4×C5×#67C2211yescharacteristic
29C5×#895C2211yescharacteristic
30C5×#893C2211yescharacteristic
31C5×#884—21no—
32C5×#882—21no—
33C2×C3×#687C2211yescharacteristic, complemented
34C2×C3×#686C2211yescharacteristic, complemented
35#91565—21no—
36#91534—21no—
37D3×#687—24no—
38#91456C2211yescharacteristic, complemented
39#91440—21no—
40#91364C2211yescharacteristic, complemented
41#91349—21no—
42Dic3×Dic10C2211yescharacteristic, complemented
43C2×#6659C2211yescharacteristic
44C2×#6659C2211yescharacteristic, complemented
45C2×#6656C2211yescharacteristic
46C2×#6656C2211yescharacteristic, complemented
47#91299—24no—
48C2×#6652C2211yescharacteristic
49C2×#6652C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91094C2211yescharacteristic, complemented
53#91091C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic, complemented
55C3×#3942C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic, complemented
57Dic3⋊#168C2211yescharacteristic, complemented
58#90967C2211yescharacteristic
59#90967C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#80121—51nomaximal, Hall
63C5×D42—31no—
64C22×#687—31no—
65C2×#4078—31no—
66#65886—31no—
67#65507—31no—
68#65506—31no—
69#65364—31no—
70#65363—31no—
71#65331—31no—
72#65329—31no—
73#65327—31no—
74#65326D311yescharacteristic, complemented
75#65307—31no—
76#65305—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C23×C5×D3—21no—
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×Dic30C2311yescharacteristic
84C2×C5×#67—21no—
85C2×C5×#67—21no—
86C2×C5×#67—21no—
87C2×C5×#67D411yescharacteristic
88C5×D3×D4—22no—
89C5×D3×D4—41no—
90C5×D3×D4—44no—
91C2×C5×D12—22no—
92C2×C5×D12—21no—
93C2×C5×D12—21no—
94C2×C5×D12—41no—
95C2×C5×D12C2311yescharacteristic
96C2×C5×D12C2311yescharacteristic
97C2×C4×C5×D3—21no—
98C2×C4×C5×D3C2311yescharacteristic
99C2×C3×C22⋊D5—21no—
100C3×#709—22no—
101C3×#709—41no—
102C2×C3×D20C2311yescharacteristic
103C2×C3×C4×D5—21no—
104C2×C3×Dic10C2311yescharacteristic
105C2×#1204—21no—
106C2×#1201—21no—
107C2×D3×Dic5—21no—
108D3×Dic10—22no—
109D3×Dic10—41no—
110C3×C5×C4⋊C4C2311yescharacteristic
111C3×C5×C22⋊C4—21no—
112#6719—21no—
113#6716—22no—
114C4⋊Dic15C2311yescharacteristic
115#6712—21no—
116#6710—22no—
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C5×#217D411yescharacteristic
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4D411yescharacteristic
123C5×Dic3⋊C4D411yescharacteristic
124C4×C5×Dic3C2311yescharacteristic
125C3×#687—22no—
126C3×#686—41no—
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129#6668—21no—
130#6665—21no—
131#6665—21no—
132#6665—21no—
133Dic3×Dic5—21no—
134#6659—22no—
135#6659—41no—
136#6656—22no—
137#6656D414yescomplemented
138#6652—22no—
139#6652—22no—
140D3×#168—22no—
141#5831—51no—
142C2×#949—51no—
143C2×D3×SD16—51no—
144#5609D511yescharacteristic, complemented
145C3×#449—51no—
146#5163—51no—
147#5156—51no—
148#5154—51no—
149#5042—51no—
150#4817—51no—
151#4806—51no—
152#4787—51no—
153#4775—51no—
154#4731—51no—
155#4728—51no—
156C22×C5×D4—31no—
157C22×C5×D4—31no—
158C22×C5×D4—61no—
159C2×#709C2×D311yescharacteristic, complemented
160C22×Dic10—31no—
161C5×#127—31no—
162C5×#121—31no—
163C5×#121—61no—
164C5×#121C2×D311yescharacteristic
165C5×#120—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4—31no—
169#4085—61no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#687—31no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—64no—
176C2×#687C2×D311yescharacteristic, complemented
177#4078—64no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686C2×D311yescharacteristic, complemented
181#4076—31no—
182#4070—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4042—61no—
186#4031—61no—
187#4027—61no—
188#4021—31no—
189C4×Dic10—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168C2×D311yescharacteristic, complemented
195#3942—31no—
196#3942C2×D311yescharacteristic, complemented
197#3941C2×D311yescharacteristic, complemented
198#3939—31no—
199C4⋊#168—31no—
200#3935—31no—
201#3265—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—42no—
207C22×C5×D3—42no—
208C22×C5×D3—42no—
209C22×C5×D3—42no—
210C22×C5×D3—81no—
211C22×C5×D3—81no—
212C22×C5×D3C2×D411yescharacteristic
213C22×C3×D5—21no—
214C3×C5×D4—21no—
215C3×C5×D4—21no—
216C3×C5×D4—42no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2411yescharacteristic
222C2×Dic15—21no—
223C2×Dic15—21no—
224Dic30—21no—
225Dic30—21no—
226C5×#67—22no—
227C5×#67—42no—
228C5×#67—42no—
229C5×#67—81no—
230C2×C5×Dic3C2×D411yescharacteristic
231C2×C5×Dic3C2×D411yescharacteristic
232C2×C5×Dic3C2×D411yescharacteristic
233C5×D12—21no—
234C5×D12—21no—
235C5×D12—21no—
236C5×D12—42no—
237C5×D12—42no—
238C5×D12C2×D412yes—
239C4×C5×D3—21no—
240C4×C5×D3—21no—
241C4×C5×D3—42no—
242C3×C22⋊D5—42no—
243C2×C3×Dic5—21no—
244C3×D20—21no—
245C3×D20—21no—
246C3×C4×D5—42no—
247C3×Dic10—21no—
248C3×Dic10C2×D412yescomplemented
249#1204—42no—
250#1201—42no—
251D3×Dic5—42no—
252C3⋊#168—21no—
253C3⋊#168C2×D412yescomplemented
254C3×#168—21no—
255C3×#168—21no—
256C2×C3×#41—51no—
257C2×D3×Q8—51no—
258C2×D3×D4—21no—
259C2×D3×D4C2×D511yescharacteristic
260C22×D12C2×D511yescharacteristic
261C2×C3×SD16—51no—
262C2×C3×D8—51no—
263C3×#121C2×D511yescharacteristic
264#949—104no—
265Q8×Dic3—51no—
266C2×#215—51no—
267C2×#215—51no—
268#940C2×D511yescharacteristic
269#938—51no—
270#938—101no—
271#937—21no—
272#936—51no—
273#936—101no—
274C2×#214—51no—
275C2×#213—51no—
276C2×#213—51no—
277C4×#67—101no—
278C4×#67C2×D511yescharacteristic
279#924—51no—
280#924—101no—
281C2×#208—51no—
282D3×SD16—104no—
283C2×#204—51no—
284C2×#204—51no—
285C2×D3×C8—51no—
286#895C2×D511yescharacteristic
287#893C2×D511yescharacteristic
288#884—21no—
289#882—21no—
290C3×#103—51no—
291C3×#102—51no—
292C3×C22⋊C8—51no—
293#832—51no—
294#821—51no—
295#821—51no—
296(C2×D3)⋊C8—51no—
297#815—51no—
298Dic3⋊C8—51no—
299#810—51no—
300#807—51no—
301C24×C5—61no—
302C24×C5—61no—
303C2×C5×D4—21no—
304C2×C5×D4—31no—
305C2×C5×D4—31no—
306C2×C5×D4—31no—
307C2×C5×D4—62no—
308C2×C5×D4—61no—
309C2×C5×D4—61no—
310C2×C5×D4—61no—
311C2×C5×D4—61no—
312C2×C5×D4—62no—
313C2×C5×D4—61no—
314C2×C5×D4—121no—
315C2×C5×D4—121no—
316C2×C5×D4—124no—
317C2×C5×D4C22×D311yescharacteristic
318C22×C4×C5—31no—
319C22×C4×C5—61no—
320C22×C4×C5C22×D311yescharacteristic
321C2×C22⋊D5—21no—
322C2×C22⋊D5—61no—
323C22×Dic5—61no—
324#709—22no—
325#709—41no—
326C2×D20C22×D311yescharacteristic
327C2×C4×D5—21no—
328C2×Dic10—31no—
329C2×Dic10—62no—
330C2×Dic10—61no—
331C2×Dic10—121no—
332C2×Dic10C22×D311yescharacteristic
333C5×C4⋊C4—31no—
334C5×C4⋊C4C22×D311yescharacteristic
335C5×C22⋊C4—21no—
336C5×C22⋊C4—31no—
337C5×C22⋊C4—31no—
338C5×C22⋊C4—61no—
339C5×C22⋊C4—61no—
340C42×C5—31no—
341C22⋊Dic5—61no—
342#687—22no—
343#687—34no—
344#687—62no—
345#687—62no—
346#687—62no—
347#687—121no—
348#686—41no—
349#686—62no—
350#686—62no—
351#685—61no—
352#685—61no—
353#685—61no—
354C4⋊Dic5—31no—
355#683—61no—
356#683—61no—
357C4×Dic5—61no—
358#681—62no—
359C2×#168—31no—
360C2×#168—31no—
361C2×#168—62no—
362C2×#168C22×D311yescharacteristic
363C2×#168C22×D311yescharacteristic
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—151no—
367D42—31no—
368#496—151no—
369#468—151no—
370#466—151no—
371#463—151no—
372#460—151no—
373#450—151no—
374#449—51no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5C22×D411yescharacteristic
386C2×C5×D3—21no—
387C2×C5×D3—21no—
388C2×C5×D3—22no—
389C2×C5×D3—41no—
390C2×C5×D3—41no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—84no—
395C2×C5×D3—84no—
396C2×C5×D3AGL(1,ℤ/8)12yescomplemented
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C3×C4×C5—21no—
401C3×C4×C5—41no—
402C3×C4×C5C22×D411yescharacteristic
403C3×C4×C5H(5,𝔽2)11yescharacteristic
404Dic15—41no—
405Dic15—41no—
406C3×Dic5—22no—
407C5×Dic3—21no—
408C5×Dic3—21no—
409C5×Dic3—21no—
410C23×D3—21no—
411C23×D3—21no—
412C3×#41—102no—
413C3×#41—201no—
414C2×C3×Q8—51no—
415C2×C3×D4—21no—
416C2×C3×D4—51no—
417C2×C3×D4—101no—
418C2×C3×D4C22×D511yescharacteristic
419C22×C3×C4—101no—
420C22×C3×C4C22×D511yescharacteristic
421C2×#67—21no—
422C2×#67—21no—
423C2×#67—21no—
424C2×#67—101no—
425C2×#67C22⋊D511yescharacteristic
426D3×Q8—102no—
427D3×Q8—201no—
428D3×D4—22no—
429D3×D4—41no—
430D3×D4—44no—
431C2×D12—22no—
432C2×D12—21no—
433C2×D12—21no—
434C2×D12—41no—
435C2×D12C22×D511yescharacteristic
436C2×D12C22×D511yescharacteristic
437C2×C4×D3—21no—
438C2×C4×D3—101no—
439C2×C4×D3C22×D511yescharacteristic
440C2×Dic6—51no—
441C2×Dic6—101no—
442C3×SD16—102no—
443C3×D8—201no—
444C2×C3×C8—51no—
445C2×C3×C8—51no—
446C3×C4⋊C4C22×D511yescharacteristic
447C3×C22⋊C4—21no—
448#217—101no—
449#217—101no—
450#217—101no—
451#217—101no—
452#217C22⋊D511yescharacteristic
453#215—54no—
454#215—102no—
455#214—102no—
456#213—102no—
457#213—102no—
458(C2×D3)⋊C4—21no—
459(C2×D3)⋊C4—21no—
460(C2×D3)⋊C4C22⋊D511yescharacteristic
461C4⋊Dic3—51no—
462C4⋊Dic3—101no—
463Dic3⋊C4—101no—
464Dic3⋊C4C22⋊D511yescharacteristic
465C4×Dic3—101no—
466C4×Dic3C22×D511yescharacteristic
467#208—102no—
468C2×C3⋊C8—51no—
469C2×C3⋊C8—51no—
470#204—102no—
471#204—201no—
472D3×C8—102no—
473C23×C5—21no—
474C23×C5—31no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5—122no—
478C23×C5—122no—
479C23×C5—122no—
480C23×C5—122no—
481C23×C5—241no—
482C23×C5—241no—
483C23×C5D3×D411yescharacteristic
484C22×D5—21no—
485C5×D4—21no—
486C5×D4—21no—
487C5×D4—32no—
488C5×D4—42no—
489C5×D4—62no—
490C5×D4—61no—
491C5×D4—61no—
492C5×D4—61no—
493C5×D4—122no—
494C5×D4—122no—
495C5×D4—122no—
496C5×D4—122no—
497C5×D4—241no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—31no—
502C2×C4×C5—31no—
503C2×C4×C5—31no—
504C2×C4×C5—61no—
505C2×C4×C5—61no—
506C2×C4×C5—122no—
507C2×C4×C5D3×D411yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—42no—
510C22⋊D5—122no—
511C2×Dic5—21no—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—122no—
515D20—21no—
516D20—21no—
517C4×D5—42no—
518Dic10—21no—
519Dic10—61no—
520Dic10—61no—
521Dic10—122no—
522Dic10D3×D412yescomplemented
523#168—21no—
524#168—21no—
525#168—32no—
526#168—61no—
527C2×#41—51no—
528C22×Q8—151no—
529C22×D4—31no—
530C22×D4—31no—
531C22×D4—61no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—51no—
534C2×SD16—151no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—51no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—151no—
544C22×C8—151no—
545#127—31no—
546#124—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—31no—
551#121—61no—
552#121—151no—
553#121—301no—
554#121D3×D511yescharacteristic
555#120—61no—
556#120—61no—
557C4×Q8—151no—
558C4×D4—31no—
559C4×D4—31no—
560C4×D4—301no—
561#107—151no—
562C4⋊C8—151no—
563#103—51no—
564#103—151no—
565#102—51no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—51no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—41no—
573C2×C3×C5—81no—
574C2×C3×C5D4211yescharacteristic
575C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
576C2×C3×C5#57711yescharacteristic
577C3×D5—81no—
578C5×D3—22no—
579C5×D3—42no—
580C5×D3—81no—
581C23×C3—21no—
582C23×C3—101no—
583C23×C3C2×C22⋊D511yescharacteristic
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—42no—
587C22×D3—42no—
588C22×D3—42no—
589C22×D3—42no—
590C22×D3—81no—
591C22×D3—81no—
592C22×D3C2×C22⋊D511yescharacteristic
593C3×Q8—52no—
594C3×Q8—101no—
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—42no—
598C3×D4—101no—
599C3×D4—101no—
600C3×D4—202no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—101no—
605C2×C3×C4—202no—
606C2×C3×C4C2×C22⋊D511yescharacteristic
607C2×C3×C4C23×D511yescharacteristic
608#67—22no—
609#67—42no—
610#67—42no—
611#67—81no—
612#67—202no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3C2×C22⋊D511yescharacteristic
616C2×Dic3C2×C22⋊D511yescharacteristic
617C2×Dic3C2×C22⋊D511yescharacteristic
618D12—21no—
619D12—21no—
620D12—21no—
621D12—42no—
622D12—42no—
623D12D4×D512yes—
624C4×D3—21no—
625C4×D3—21no—
626C4×D3—42no—
627C4×D3—202no—
628Dic6—101no—
629Dic6—101no—
630Dic6—202no—
631C3×C8—101no—
632C3×C8—101no—
633C3⋊C8—52no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—32no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—61no—
643C22×C5—61no—
644C22×C5—62no—
645C22×C5—121no—
646C22×C5—121no—
647C22×C5—121no—
648C22×C5—121no—
649C22×C5—121no—
650C22×C5—244no—
651C22×C5—244no—
652C22×C5C2×D3×D411yescharacteristic
653C2×D5—41no—
654C2×D5—41no—
655C2×D5—41no—
656C4×C5—21no—
657C4×C5—41no—
658C4×C5—61no—
659C4×C5—61no—
660C4×C5—61no—
661C4×C5C2×D3×D411yescharacteristic
662C4×C5#100411yescharacteristic
663Dic5—22no—
664Dic5—121no—
665Dic5—121no—
666C24—61no—
667C24—61no—
668#41—102no—
669#41—201no—
670C2×Q8—51no—
671C2×Q8—151no—
672C2×Q8—301no—
673C2×Q8—302no—
674C2×Q8—601no—
675C2×D4—21no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—51no—
680C2×D4—62no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—62no—
686C2×D4—61no—
687C2×D4—101no—
688C2×D4—121no—
689C2×D4—121no—
690C2×D4—124no—
691C2×D4—301no—
692C2×D4C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—101no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—102no—
699SD16—154no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—201no—
705D8—302no—
706D8—302no—
707M16—302no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—31no—
714C4⋊C4—151no—
715C4⋊C4—301no—
716C4⋊C4—301no—
717C4⋊C4C2×D3×D511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—31no—
720C22⋊C4—31no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—31no—
728C42—301no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—201no—
737C22×C3—201no—
738C22×C3—201no—
739C22×C3C22×C22⋊D511yescharacteristic
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—22no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—84no—
749C2×D3—84no—
750C2×D3#407812yescomplemented
751C3×C4—21no—
752C3×C4—41no—
753C3×C4—102no—
754C3×C4C2×D4×D511yescharacteristic
755C3×C4#414411yescharacteristic
756Dic3—21no—
757Dic3—21no—
758Dic3—21no—
759Dic3—201no—
760Dic3—201no—
761C2×C5—41no—
762C2×C5—62no—
763C2×C5—81no—
764C2×C5—122no—
765C2×C5—241no—
766C2×C5#559011yescharacteristic
767C2×C5#577011yescharacteristic
768C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
769D5—81no—
770C23—21no—
771C23—31no—
772C23—61no—
773C23—61no—
774C23—101no—
775C23—122no—
776C23—122no—
777C23—122no—
778C23—122no—
779C23—241no—
780C23—241no—
781C23D3×C22⋊D511yescharacteristic
782Q8—52no—
783Q8—101no—
784Q8—301no—
785Q8—301no—
786Q8—602no—
787D4—21no—
788D4—21no—
789D4—32no—
790D4—42no—
791D4—62no—
792D4—61no—
793D4—61no—
794D4—61no—
795D4—101no—
796D4—101no—
797D4—122no—
798D4—122no—
799D4—122no—
800D4—122no—
801D4—202no—
802D4—241no—
803D4—602no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—101no—
813C2×C4—122no—
814C2×C4—202no—
815C2×C4—301no—
816C2×C4—301no—
817C2×C4—602no—
818C2×C4D3×C22⋊D511yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—101no—
821C8—101no—
822C8—152no—
823C8—301no—
824C2×C3—41no—
825C2×C3—81no—
826C2×C3—401no—
827C2×C3C2×#407811yescharacteristic
828C2×C3D4×C22⋊D511yescharacteristic
829C2×C3#6617011yescharacteristic
830D3—22no—
831D3—42no—
832D3—81no—
833C5#8012111yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—32no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—61no—
842C22—61no—
843C22—62no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—201no—
850C22—201no—
851C22—201no—
852C22—244no—
853C22—244no—
854C22C2×D3×C22⋊D511yescharacteristic
855C4—21no—
856C4—41no—
857C4—61no—
858C4—61no—
859C4—61no—
860C4—102no—
861C4—601no—
862C4—601no—
863C4D3×D4×D511yescharacteristic
864C4#9202511yescharacteristic
865C3#1061522211yescharacteristic, complemented, Sylow
866C2—41no—
867C2—62no—
868C2—81no—
869C2—122no—
870C2—241no—
871C2—401no—
872C2D3×#407811yescharacteristic
873C2#1175503211yescharacteristic
874C2#1175534711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C5×#5609C2semidirect
2. C2×D3×#687C2semidirect
3. #11754528C2semidirect
4. C2×#91299C2semidirect
5. #11751143C2semidirect
6. C3×#65326C2semidirect
7. #11749071C2semidirect
8. #11749032C2semidirect
9. #11749005C2semidirect
10. #11748543C2semidirect
11. #11748496C2semidirect
12. #11747494C2semidirect
13. #11747375C2semidirect
14. #11747319C2semidirect
15. #11747265C2semidirect
20. C2×C3×#709C22semidirect
21. C2×D3×Dic10C22semidirect
23. C2×#6716C22semidirect
24. #91813C22semidirect
25. C2×#6710C22semidirect
33. C2×C3×#687C22semidirect
34. C2×C3×#686C22semidirect
38. #91456C22semidirect
40. #91364C22semidirect
42. Dic3×Dic10C22semidirect
44. C2×#6659C22semidirect
46. C2×#6656C22semidirect
49. C2×#6652C22semidirect
50. C2×D3×#168C22semidirect
51. #91116C22semidirect
52. #91094C22semidirect
53. #91091C22semidirect
54. C3×C22⋊#168C22semidirect
55. C3×#3942C22semidirect
56. C3×#3941C22semidirect
57. Dic3⋊#168C22semidirect
59. #90967C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
74. #65326D3semidirect
137. #6656D4semidirect
144. #5609D5semidirect
159. C2×#709C2×D3semidirect
176. C2×#687C2×D3semidirect
180. C2×#686C2×D3semidirect
194. C22⋊#168C2×D3semidirect
196. #3942C2×D3semidirect
197. #3941C2×D3semidirect
248. C3×Dic10C2×D4semidirect
253. C3⋊#168C2×D4semidirect
396. C2×C5×D3AGL(1,ℤ/8)semidirect
522. Dic10D3×D4semidirect
729. C3×C5#3265semidirect
750. C2×D3#4078semidirect
833. C5#80121semidirect
865. C3#10615222semidirect

Maximal subgroups

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

subgroupindex
C5×#56092
C2×D3×#6872
#117545282
C2×#912992
#117511432
C3×#653262
#117490712
#117490322
#117490052
#117485432
#117484962
#117474942
#117473752
#117473192
#117472652
#106152223
#801215