Finite Group Databasebeta

← C2×#11756537 #14510029

Subgroups — C2×#11756537 #14510029

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92100C211yesmaximal, characteristic, complemented
2C2×#92098C211yesmaximal, characteristic, complemented
3C2×C3×C5×#137C211yesmaximal, characteristic, complemented
4C2×#91839C211yesmaximal, characteristic, complemented
5C22×#6717C211yesmaximal, characteristic, complemented
6#11756537C2116yesmaximal, direct product factor
7C2×#91808C212yesmaximal, complemented
8C2×#91807C212yesmaximal, complemented
9C2×#91803C212yesmaximal, complemented
10C2×SD16×D15C212yesmaximal, complemented
11C2×#91797C211yesmaximal, characteristic, complemented
12C2×#91796C211yesmaximal, characteristic, complemented
13C2×#66112—31nomaximal, Hall
14C2×C3×C5×#41C2211yescharacteristic
15C22×C3×C5×Q8C2211yescharacteristic, complemented
16#92100—24no—
17#92100C2218yescomplemented
18#92098—24no—
19#92098C2218yescomplemented
20C2×#6821—21no—
21C2×#6821C2212yes—
22C2×#6821C2212yescomplemented
23C2×Q8×D15—21no—
24C2×Q8×D15C2212yescomplemented
25C2×D4×D15—22no—
26C2×D4×D15C2212yes—
27C2×#6817—22no—
28C2×#6817—21no—
29C2×#6817C2211yescharacteristic
30C2×#6817C2211yescharacteristic, complemented
31C22×D60—21no—
32C22×D60C2211yescharacteristic
33C3×C5×#137C2218yescomplemented
34C2×C3×C5×Q16C2212yescomplemented
35C2×C3×C5×SD16C2212yescomplemented
36C2×C3×C5×M16C2211yescharacteristic, complemented
37#91839C2218yescomplemented
38C2×#6718C2211yescharacteristic, complemented
39C2×#6717C2212yescomplemented
40C2×#6717C2212yescomplemented
41C2×#6717C2211yescharacteristic, complemented
42C2×#6717C2218yescomplemented
43C2×#6716C2211yescharacteristic, complemented
44C2×#6715C2211yescharacteristic, complemented
45C22×C3⋊#168C2211yescharacteristic, complemented
46#91808C22116yescomplemented
47#91807C22116yescomplemented
48#91803C22116yescomplemented
49SD16×D15C22116yescomplemented
50#91797C2218yescomplemented
51#91796C2218yescomplemented
52C2×D120C2212yescomplemented
53C2×#6706C2212yescomplemented
54C2×#6705C2212yescomplemented
55C2×C8×D15C2212yescomplemented
56C2×#5778—51nomaximal, Hall
57C2×#4149—31no—
58C2×#4147—31no—
59C2×C5×#137D311yescharacteristic, complemented
60C2×#4096—31no—
61C22×#688—31no—
62#66112—316no—
63C2×#4065—32no—
64C2×#4064—32no—
65C2×#4060—32no—
66C2×D5×SD16—32no—
67C2×#4054—31no—
68C2×#4053—31no—
69C23×D15—21no—
70C23×D15—22no—
71C3×C5×#41—22no—
72C3×C5×#41C2314yes—
73C2×C3×C5×Q8—21no—
74C2×C3×C5×Q8—22no—
75C2×C3×C5×Q8C2312yes—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×Q8C2314yescomplemented
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5C2311yescharacteristic
83C2×#1220—21no—
84C2×#1220—22no—
85C2×#1220D412yes—
86#6821—28no—
87#6821—24no—
88#6821—24no—
89#6821C2318yes—
90#6821C2318yescomplemented
91Q8×D15—24no—
92Q8×D15—28no—
93Q8×D15C2318yescomplemented
94D4×D15—216no—
95D4×D15—24no—
96D4×D15C2318yes—
97#6817—22no—
98#6817—216no—
99#6817—28no—
100#6817D414yes—
101#6817C2314yes—
102#6817C2314yescomplemented
103C2×D60—22no—
104C2×D60—22no—
105C2×D60—21no—
106C2×D60—22no—
107C2×D60—28no—
108C2×D60D411yescharacteristic
109C2×D60C2312yes—
110C2×D60C2311yescharacteristic
111C2×D60C2314yes—
112C2×C4×D15—22no—
113C2×C4×D15—21no—
114C2×C4×D15—22no—
115C2×C4×D15—22no—
116C2×C4×D15C2312yes—
117C2×Dic30—22no—
118C2×Dic30D411yescharacteristic
119C2×Dic30C2311yescharacteristic
120C3×C5×Q16C2318yescomplemented
121C3×C5×SD16C2318yescomplemented
122C3×C5×M16C2314yescomplemented
123C2×C3×C5×C8C2312yes—
124#6718C2314yescomplemented
125#6717C2318yescomplemented
126#6717C2318yescomplemented
127#6717C2314yescomplemented
128#6716C2314yescomplemented
129#6715C2314yescomplemented
130C2×C3⋊#168C2311yescharacteristic
131C2×C3⋊#168C2311yescharacteristic
132C2×C3⋊#168C2314yescomplemented
133D120C2318yescomplemented
134#6706C2318yescomplemented
135#6705C2318yescomplemented
136C8×D15C2318yescomplemented
137C2×#1009—51no—
138C2×#1007—51no—
139C2×C3×#137D511yescharacteristic, complemented
140C2×#950—51no—
141C22×#215—51no—
142#5778—516no—
143C2×#919—52no—
144C2×#918—52no—
145C2×#914—52no—
146C2×D3×SD16—52no—
147C2×#908—51no—
148C2×#907—51no—
149C2×C5×#41C2×D311yescharacteristic
150C22×C5×Q8C2×D311yescharacteristic, complemented
151#4149—38no—
152#4149—64no—
153#4147—38no—
154#4147—64no—
155C2×#713—32no—
156C2×#713—32no—
157C2×#713—61no—
158C2×Q8×D5—32no—
159C2×Q8×D5—61no—
160C2×D4×D5—32no—
161C2×D4×D5—62no—
162C2×#709—31no—
163C2×#709—31no—
164C2×#709—61no—
165C2×#709—62no—
166C22×D20—31no—
167C22×D20—61no—
168C5×#137C2×D318yescomplemented
169C2×C5×Q16C2×D312yescomplemented
170C2×C5×SD16C2×D312yescomplemented
171C2×C5×M16C2×D311yescharacteristic, complemented
172#4096—38no—
173C2×#689—31no—
174C2×#688—32no—
175C2×#688—32no—
176C2×#688—31no—
177C2×#688—38no—
178C2×#687—31no—
179C2×#686—31no—
180C22×#168—31no—
181#4065—316no—
182#4064—316no—
183#4060—316no—
184D5×SD16—316no—
185#4054—38no—
186#4053—38no—
187C2×D40—32no—
188C2×#677—32no—
189C2×#676—32no—
190C2×C8×D5—32no—
191C2×#577—151noSylow
192C23×C3×C5—21no—
193C23×C3×C5C2×D411yescharacteristic
194C22×D15—21no—
195C22×D15—22no—
196C22×D15—24no—
197C22×D15—28no—
198C22×D15—84no—
199C22×D15—82no—
200C22×D15C2×D412yes—
201C3×C5×Q8—22no—
202C3×C5×Q8—24no—
203C3×C5×Q8—21no—
204C3×C5×Q8C2414yes—
205C3×C5×Q8C2412yes—
206C3×C5×D4—24no—
207C3×C5×D4—21no—
208C3×C5×D4C2412yes—
209C2×C3×C4×C5—22no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—24no—
212C2×C3×C4×C5—24no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D412yes—
215C2×C3×C4×C5C2411yescharacteristic
216C2×C3×C4×C5C2412yes—
217#1220—24no—
218#1220—28no—
219#1220C2×D418yes—
220C2×Dic15—21no—
221C2×Dic15C2×D412yes—
222D60—28no—
223D60—28no—
224D60—24no—
225D60—22no—
226D60—21no—
227D60C2×D414yes—
228D60C2414yes—
229D60C2412yes—
230C4×D15—28no—
231C4×D15—24no—
232C4×D15—28no—
233C4×D15—28no—
234C4×D15C2×D414yes—
235C4×D15C2414yes—
236Dic30—21no—
237Dic30—28no—
238Dic30C2×D414yes—
239Dic30C2412yes—
240C3×C5×C8C2414yes—
241C3⋊#168C2412yes—
242C3⋊#168C2412yes—
243C2×C3×#41C2×D511yescharacteristic
244C22×C3×Q8C2×D511yescharacteristic, complemented
245#1009—58no—
246#1009—104no—
247#1007—58no—
248#1007—104no—
249C2×#239—52no—
250C2×#239—52no—
251C2×#239—101no—
252C2×D3×Q8—52no—
253C2×D3×Q8—101no—
254C2×D3×D4—52no—
255C2×D3×D4—102no—
256C2×#235—51no—
257C2×#235—51no—
258C2×#235—101no—
259C2×#235—102no—
260C22×D12—51no—
261C22×D12—101no—
262C3×#137C2×D518yescomplemented
263C2×C3×Q16C2×D512yescomplemented
264C2×C3×SD16C2×D512yescomplemented
265C2×C3×M16C2×D511yescharacteristic, complemented
266#950—58no—
267C2×#216—51no—
268C2×#215—52no—
269C2×#215—52no—
270C2×#215—51no—
271C2×#215—58no—
272C2×#214—51no—
273C2×#213—51no—
274C22×C3⋊C8—51no—
275#919—516no—
276#918—516no—
277#914—516no—
278D3×SD16—516no—
279#908—58no—
280#907—58no—
281C2×D24—52no—
282C2×#204—52no—
283C2×ΓL(1,𝔽25)—52no—
284C2×D3×C8—52no—
285C23×D5—62no—
286C23×D5—61no—
287C5×#41—22no—
288C5×#41C22×D314yes—
289C2×C5×Q8—21no—
290C2×C5×Q8—22no—
291C2×C5×Q8C22×D312yes—
292C2×C5×Q8C22×D311yescharacteristic
293C2×C5×Q8C22×D314yescomplemented
294C2×C5×D4—21no—
295C2×C5×D4C22×D311yescharacteristic
296C22×C4×C5—21no—
297C22×C4×C5—21no—
298C22×C4×C5C22×D311yescharacteristic
299C2×C22⋊D5—32no—
300C2×C22⋊D5—62no—
301C2×C22⋊D5—61no—
302#713—38no—
303#713—38no—
304#713—64no—
305#713—64no—
306#713—68no—
307Q8×D5—38no—
308Q8×D5—68no—
309Q8×D5—64no—
310D4×D5—38no—
311D4×D5—64no—
312D4×D5—616no—
313#709—34no—
314#709—34no—
315#709—34no—
316#709—68no—
317#709—616no—
318#709—62no—
319C2×D20—31no—
320C2×D20—32no—
321C2×D20—34no—
322C2×D20—31no—
323C2×D20—68no—
324C2×D20—62no—
325C2×D20—62no—
326C2×D20—61no—
327C2×D20—62no—
328C2×C4×D5—32no—
329C2×C4×D5—62no—
330C2×C4×D5—62no—
331C2×C4×D5—62no—
332C2×C4×D5—61no—
333C2×Dic10—31no—
334C2×Dic10—31no—
335C2×Dic10—62no—
336C5×Q16C22×D318yescomplemented
337C5×SD16C22×D318yescomplemented
338C5×M16C22×D314yescomplemented
339C2×C5×C8C22×D312yes—
340#689—34no—
341#688—34no—
342#688—38no—
343#688—38no—
344#687—34no—
345#686—34no—
346C2×#168—34no—
347C2×#168—31no—
348C2×#168—31no—
349D40—38no—
350#677—38no—
351#676—38no—
352C8×D5—38no—
353C2×2−1+4—151no—
354C2×H(5,𝔽2)—151no—
355#577—1516no—
356C2×#137—152no—
357C2×#137D1511yescharacteristic, complemented
358C2×AGL(1,ℤ/8)—152no—
359C2×AGL(1,ℤ/8)—151no—
360C2×#135—151no—
361C2×#135—152no—
362C22×SD16—151no—
363C22×SD16—152no—
364C2×#131—151no—
365C22×C3×C5—22no—
366C22×C3×C5—22no—
367C22×C3×C5—42no—
368C22×C3×C5C22×D412yes—
369C22×C3×C5C22×D411yescharacteristic
370C2×D15—24no—
371C2×D15—22no—
372C2×D15—24no—
373C2×D15—42no—
374C2×D15—44no—
375C2×D15—88no—
376C2×D15—84no—
377C2×D15C22×D414yes—
378C3×C4×C5—24no—
379C3×C4×C5—22no—
380C3×C4×C5C22×D411yescharacteristic
381C3×C4×C5C22×D412yes—
382C3×C4×C5C2511yescharacteristic
383Dic15—22no—
384Dic15C22×D414yes—
385C23×D3—102no—
386C23×D3—101no—
387C3×#41—22no—
388C3×#41C22×D514yes—
389C2×C3×Q8—21no—
390C2×C3×Q8—22no—
391C2×C3×Q8C22×D512yes—
392C2×C3×Q8C22×D511yescharacteristic
393C2×C3×Q8C22×D514yescomplemented
394C2×C3×D4—21no—
395C2×C3×D4C22×D511yescharacteristic
396C22×C3×C4—21no—
397C22×C3×C4—21no—
398C22×C3×C4C22×D511yescharacteristic
399C2×#67—52no—
400C2×#67—102no—
401C2×#67—101no—
402#239—58no—
403#239—58no—
404#239—104no—
405#239—104no—
406#239—108no—
407D3×Q8—58no—
408D3×Q8—108no—
409D3×Q8—104no—
410D3×D4—58no—
411D3×D4—104no—
412D3×D4—1016no—
413#235—54no—
414#235—54no—
415#235—54no—
416#235—108no—
417#235—1016no—
418#235—102no—
419C2×D12—51no—
420C2×D12—52no—
421C2×D12—51no—
422C2×D12—54no—
423C2×D12—108no—
424C2×D12—102no—
425C2×D12—102no—
426C2×D12—101no—
427C2×D12—102no—
428C2×C4×D3—52no—
429C2×C4×D3—102no—
430C2×C4×D3—102no—
431C2×C4×D3—102no—
432C2×C4×D3—101no—
433C2×Dic6—51no—
434C2×Dic6—51no—
435C2×Dic6—102no—
436C3×Q16C22×D518yescomplemented
437C3×SD16C22×D518yescomplemented
438C3×M16C22×D514yescomplemented
439C2×C3×C8C22×D512yes—
440#216—54no—
441#215—58no—
442#215—58no—
443#215—54no—
444#214—54no—
445#213—54no—
446C2×C3⋊C8—51no—
447C2×C3⋊C8—51no—
448C2×C3⋊C8—54no—
449D24—58no—
450#204—58no—
451ΓL(1,𝔽25)—58no—
452D3×C8—58no—
453C23×C5—21no—
454C23×C5D3×D411yescharacteristic
455C22×D5—32no—
456C22×D5—68no—
457C22×D5—61no—
458C22×D5—62no—
459C22×D5—64no—
460C22×D5—244no—
461C22×D5—242no—
462C5×Q8—22no—
463C5×Q8—24no—
464C5×Q8—21no—
465C5×Q8C23×D314yes—
466C5×Q8C23×D312yes—
467C5×D4—24no—
468C5×D4—21no—
469C5×D4C23×D312yes—
470C2×C4×C5—22no—
471C2×C4×C5—21no—
472C2×C4×C5—24no—
473C2×C4×C5—24no—
474C2×C4×C5D3×D411yescharacteristic
475C2×C4×C5D3×D412yes—
476C2×C4×C5C23×D311yescharacteristic
477C2×C4×C5C23×D312yes—
478C22⋊D5—38no—
479C22⋊D5—68no—
480C22⋊D5—64no—
481C2×Dic5—32no—
482C2×Dic5—61no—
483D20—34no—
484D20—34no—
485D20—32no—
486D20—68no—
487D20—68no—
488D20—64no—
489D20—62no—
490D20—61no—
491C4×D5—34no—
492C4×D5—34no—
493C4×D5—68no—
494C4×D5—68no—
495C4×D5—68no—
496C4×D5—64no—
497Dic10—34no—
498Dic10—32no—
499Dic10—68no—
500Dic10—61no—
501C5×C8C23×D314yes—
502#168—32no—
503#168—32no—
5042−1+4—158no—
5052−1+4—304no—
506H(5,𝔽2)—158no—
507H(5,𝔽2)—304no—
508C2×#41—151no—
509C2×#41—152no—
510C2×#41—152no—
511C2×#41—151no—
512C2×#41—302no—
513C2×#41—301no—
514C2×#41—301no—
515C2×#41C2×D1511yescharacteristic
516C22×Q8—152no—
517C22×Q8—301no—
518C22×Q8C2×D1511yescharacteristic, complemented
519C22×D4—152no—
520C22×D4—151no—
521C22×D4—301no—
522C22×D4—302no—
523#137—1516no—
524#137C2×D1518yescomplemented
525AGL(1,ℤ/8)—1516no—
526AGL(1,ℤ/8)—158no—
527#135—158no—
528#135—1516no—
529C2×Q16—151no—
530C2×Q16C2×D1512yescomplemented
531C2×SD16—152no—
532C2×SD16—152no—
533C2×SD16—151no—
534C2×SD16—158no—
535C2×SD16—151no—
536C2×SD16—1516no—
537C2×SD16—152no—
538C2×SD16C2×D1512yescomplemented
539C2×D8—151no—
540C2×D8—152no—
541#131—158no—
542C2×M16—152no—
543C2×M16C2×D1511yescharacteristic, complemented
544C22×C8—151no—
545C22×C8—152no—
546C2×C3×C5—22no—
547C2×C3×C5—42no—
548C2×C3×C5#57712yescomplemented
549C2×C3×C5C23×D411yescharacteristic
550D15—24no—
551D15—42no—
552D15—44no—
553C23×C3—21no—
554C23×C3D4×D511yescharacteristic
555C22×D3—52no—
556C22×D3—108no—
557C22×D3—101no—
558C22×D3—102no—
559C22×D3—104no—
560C22×D3—404no—
561C22×D3—402no—
562C3×Q8—22no—
563C3×Q8—24no—
564C3×Q8—21no—
565C3×Q8C23×D514yes—
566C3×Q8C23×D512yes—
567C3×D4—24no—
568C3×D4—21no—
569C3×D4C23×D512yes—
570C2×C3×C4—22no—
571C2×C3×C4—21no—
572C2×C3×C4—24no—
573C2×C3×C4—24no—
574C2×C3×C4D4×D511yescharacteristic
575C2×C3×C4D4×D512yes—
576C2×C3×C4C23×D511yescharacteristic
577C2×C3×C4C23×D512yes—
578#67—58no—
579#67—108no—
580#67—104no—
581C2×Dic3—52no—
582C2×Dic3—101no—
583D12—54no—
584D12—54no—
585D12—52no—
586D12—108no—
587D12—108no—
588D12—104no—
589D12—102no—
590D12—101no—
591C4×D3—54no—
592C4×D3—54no—
593C4×D3—108no—
594C4×D3—108no—
595C4×D3—108no—
596C4×D3—104no—
597Dic6—54no—
598Dic6—52no—
599Dic6—108no—
600Dic6—101no—
601C3×C8C23×D514yes—
602C3⋊C8—52no—
603C3⋊C8—52no—
604C22×C5—22no—
605C22×C5—22no—
606C22×C5—42no—
607C22×C5C2×D3×D412yes—
608C22×C5C2×D3×D411yescharacteristic
609C2×D5—34no—
610C2×D5—64no—
611C2×D5—62no—
612C2×D5—64no—
613C2×D5—122no—
614C2×D5—124no—
615C2×D5—248no—
616C2×D5—244no—
617C4×C5—24no—
618C4×C5—22no—
619C4×C5C2×D3×D412yes—
620C4×C5C2×D3×D411yescharacteristic
621C4×C5C24×D311yescharacteristic
622Dic5—34no—
623Dic5—62no—
624C24—302no—
625C24—301no—
626#41—22no—
627#41—154no—
628#41—154no—
629#41—158no—
630#41—158no—
631#41—154no—
632#41—3016no—
633#41—308no—
634#41—304no—
635#41—304no—
636#41—308no—
637#41—302no—
638#41C22×D1514yes—
639C2×Q8—21no—
640C2×Q8—22no—
641C2×Q8—151no—
642C2×Q8—158no—
643C2×Q8—151no—
644C2×Q8—302no—
645C2×Q8—304no—
646C2×Q8—308no—
647C2×Q8C22×D1512yes—
648C2×Q8C22×D1511yescharacteristic
649C2×Q8C22×D1514yescomplemented
650C2×D4—21no—
651C2×D4—152no—
652C2×D4—158no—
653C2×D4—151no—
654C2×D4—151no—
655C2×D4—152no—
656C2×D4—154no—
657C2×D4—308no—
658C2×D4—302no—
659C2×D4—302no—
660C2×D4—304no—
661C2×D4—302no—
662C2×D4—3016no—
663C2×D4—301no—
664C2×D4—301no—
665C2×D4—302no—
666C2×D4C22×D1511yescharacteristic
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—152no—
670C22×C4—302no—
671C22×C4—302no—
672C22×C4—302no—
673C22×C4—301no—
674C22×C4C22×D1511yescharacteristic
675Q16—154no—
676Q16C22×D1518yescomplemented
677SD16—158no—
678SD16—158no—
679SD16—154no—
680SD16—154no—
681SD16—158no—
682SD16C22×D1518yescomplemented
683D8—154no—
684D8—158no—
685M16—158no—
686M16C22×D1514yescomplemented
687C2×C8—151no—
688C2×C8—151no—
689C2×C8—154no—
690C2×C8—158no—
691C2×C8C22×D1512yes—
692C3×C5C2×#57711yescharacteristic, complemented, Hall
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—42no—
696C22×C3C2×D4×D512yes—
697C22×C3C2×D4×D511yescharacteristic
698C2×D3—54no—
699C2×D3—104no—
700C2×D3—102no—
701C2×D3—104no—
702C2×D3—202no—
703C2×D3—204no—
704C2×D3—408no—
705C2×D3—404no—
706C3×C4—24no—
707C3×C4—22no—
708C3×C4C2×D4×D512yes—
709C3×C4C2×D4×D511yescharacteristic
710C3×C4C24×D511yescharacteristic
711Dic3—54no—
712Dic3—102no—
713C2×C5—22no—
714C2×C5—42no—
715C2×C5#577812yescomplemented
716C2×C5C22×D3×D411yescharacteristic
717D5—64no—
718D5—124no—
719D5—122no—
720C23—21no—
721C23—152no—
722C23—308no—
723C23—301no—
724C23—302no—
725C23—304no—
726C23—1202no—
727C23—1204no—
728C23D4×D1511yescharacteristic
729Q8—22no—
730Q8—24no—
731Q8—21no—
732Q8—154no—
733Q8—152no—
734Q8—308no—
735Q8—301no—
736Q8C23×D1514yes—
737Q8C23×D1512yes—
738D4—24no—
739D4—21no—
740D4—158no—
741D4—154no—
742D4—152no—
743D4—154no—
744D4—308no—
745D4—308no—
746D4—308no—
747D4—304no—
748D4—304no—
749D4—302no—
750D4—301no—
751D4C23×D1512yes—
752C2×C4—24no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—152no—
757C2×C4—154no—
758C2×C4—154no—
759C2×C4—308no—
760C2×C4—308no—
761C2×C4—308no—
762C2×C4—301no—
763C2×C4—304no—
764C2×C4D4×D1512yes—
765C2×C4D4×D1511yescharacteristic
766C2×C4C23×D1512yes—
767C2×C4C23×D1511yescharacteristic
768C8—152no—
769C8—152no—
770C8C23×D1514yes—
771C2×C3—22no—
772C2×C3—42no—
773C2×C3#6611212yescomplemented
774C2×C3C22×D4×D511yescharacteristic
775D3—104no—
776D3—204no—
777D3—202no—
778C5C2×#577811yescharacteristic, complemented, Sylow
779C22—22no—
780C22—22no—
781C22—42no—
782C22—154no—
783C22—304no—
784C22—302no—
785C22—304no—
786C22—604no—
787C22—602no—
788C22—1204no—
789C22—1208no—
790C22C2×D4×D1512yes—
791C22C2×D4×D1511yescharacteristic
792C4—22no—
793C4—24no—
794C4—154no—
795C4—302no—
796C4C2×D4×D1512yes—
797C4C2×D4×D1511yescharacteristic
798C4C24×D1511yescharacteristic
799C3C2×#6611211yescharacteristic, complemented, Sylow
800C2—22no—
801C2—42no—
802C2—304no—
803C2—604no—
804C2—602no—
805C2#1175653712yesdirect product factor
806C2C22×D4×D1511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC3×C4×C5C25
FrattiniC4C24×D15
FittingC2×C3×C5×#137C2
socleC22×C3×C5C22×D4
hypercenterC2×#137D15
hypocenterC3×C5C2×#577
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#92100C2semidirect
2. C2×#92098C2semidirect
3. C2×C3×C5×#137C2semidirect
4. C2×#91839C2semidirect
5. C22×#6717C2semidirect
6. #11756537C2direct (N × H)
7. C2×#91808C2semidirect
8. C2×#91807C2semidirect
9. C2×#91803C2semidirect
10. C2×SD16×D15C2semidirect
11. C2×#91797C2semidirect
12. C2×#91796C2semidirect
15. C22×C3×C5×Q8C22semidirect
17. #92100C22semidirect
19. #92098C22semidirect
22. C2×#6821C22semidirect
24. C2×Q8×D15C22semidirect
30. C2×#6817C22semidirect
33. C3×C5×#137C22semidirect
34. C2×C3×C5×Q16C22semidirect
35. C2×C3×C5×SD16C22semidirect
36. C2×C3×C5×M16C22semidirect
37. #91839C22semidirect
38. C2×#6718C22semidirect
39. C2×#6717C22semidirect
40. C2×#6717C22semidirect
41. C2×#6717C22semidirect
42. C2×#6717C22semidirect
43. C2×#6716C22semidirect
44. C2×#6715C22semidirect
45. C22×C3⋊#168C22semidirect
46. #91808C22semidirect
47. #91807C22semidirect
48. #91803C22semidirect
49. SD16×D15C22semidirect
50. #91797C22semidirect
51. #91796C22semidirect
52. C2×D120C22semidirect
53. C2×#6706C22semidirect
54. C2×#6705C22semidirect
55. C2×C8×D15C22semidirect
59. C2×C5×#137D3semidirect
77. C2×C3×C5×Q8C23semidirect
90. #6821C23semidirect
93. Q8×D15C23semidirect
102. #6817C23semidirect
120. C3×C5×Q16C23semidirect
121. C3×C5×SD16C23semidirect
122. C3×C5×M16C23semidirect
124. #6718C23semidirect
125. #6717C23semidirect
126. #6717C23semidirect
127. #6717C23semidirect
128. #6716C23semidirect
129. #6715C23semidirect
132. C2×C3⋊#168C23semidirect
133. D120C23semidirect
134. #6706C23semidirect
135. #6705C23semidirect
136. C8×D15C23semidirect
139. C2×C3×#137D5semidirect
150. C22×C5×Q8C2×D3semidirect
168. C5×#137C2×D3semidirect
169. C2×C5×Q16C2×D3semidirect
170. C2×C5×SD16C2×D3semidirect
171. C2×C5×M16C2×D3semidirect
244. C22×C3×Q8C2×D5semidirect
262. C3×#137C2×D5semidirect
263. C2×C3×Q16C2×D5semidirect
264. C2×C3×SD16C2×D5semidirect
265. C2×C3×M16C2×D5semidirect
293. C2×C5×Q8C22×D3semidirect
336. C5×Q16C22×D3semidirect
337. C5×SD16C22×D3semidirect
338. C5×M16C22×D3semidirect
357. C2×#137D15semidirect
393. C2×C3×Q8C22×D5semidirect
436. C3×Q16C22×D5semidirect
437. C3×SD16C22×D5semidirect
438. C3×M16C22×D5semidirect
518. C22×Q8C2×D15semidirect
524. #137C2×D15semidirect
530. C2×Q16C2×D15semidirect
538. C2×SD16C2×D15semidirect
543. C2×M16C2×D15semidirect
548. C2×C3×C5#577semidirect
649. C2×Q8C22×D15semidirect
676. Q16C22×D15semidirect
682. SD16C22×D15semidirect
686. M16C22×D15semidirect
692. C3×C5C2×#577semidirect
715. C2×C5#5778semidirect
773. C2×C3#66112semidirect
778. C5C2×#5778semidirect
799. C3C2×#66112semidirect
805. C2#11756537direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#921002
C2×#920982
C2×C3×C5×#1372
C2×#918392
C22×#67172
#117565372
C2×#918082
C2×#918072
C2×#918032
C2×SD16×D152
C2×#917972
C2×#917962
C2×#661123
C2×#57785