Finite Group Databasebeta

← C2×#11754697 #14509992

Subgroups — C2×#11754697 #14509992

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1004C211yesmaximal, characteristic, complemented
2C2×#92017C211yesmaximal, characteristic, complemented
3C2×#91821C211yesmaximal, characteristic, complemented
4C22×C3×#686C211yesmaximal, characteristic, complemented
5C2×#91494C212yesmaximal, complemented
6C2×#91493C212yesmaximal, complemented
7#11754697C2116yesmaximal, direct product factor
8C2×#91480C212yesmaximal, complemented
9C2×D3×#686C212yesmaximal, complemented
10C2×#91303C211yesmaximal, characteristic, complemented
11C2×#91298C211yesmaximal, characteristic, complemented
12C2×#91286C211yesmaximal, characteristic, complemented
13C2×#66169—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic, complemented
15C2×#6817C2211yescharacteristic, complemented
16C22×C5×#67—22no—
17C5×#1004—24no—
18C5×#1004C2218yescomplemented
19C2×C5×#237—21no—
20C2×C5×#237C2212yescomplemented
21C2×C5×D3×D4—21no—
22C2×C5×D3×D4C2212yescomplemented
23C2×C5×#235C2211yescharacteristic
24C2×C5×#235C2211yescharacteristic, complemented
25C22×C3×D20C2211yescharacteristic, complemented
26C2×D5×#67—22no—
27#92017—24no—
28#92017C2218yescomplemented
29C2×#6777—21no—
30C2×D3×D20C2212yescomplemented
31C2×#6766—21no—
32C2×#6765C2212yescomplemented
33C2×#6716C2212yescomplemented
34#91821C2218yescomplemented
35C2×#6715C2212yescomplemented
36C2×#6710C2211yescharacteristic, complemented
37C2×C3×#686C2212yescomplemented
38C2×C3×#686C2212yescomplemented
39C2×C3×#686C2218yescomplemented
40C22×C3×#168C2211yescharacteristic, complemented
41#91494C22116yescomplemented
42#91493C22116yescomplemented
43#91480C22116yescomplemented
44D3×#686C22116yescomplemented
45C2×#6663C2211yescharacteristic, complemented
46C2×#6660C2211yescharacteristic, complemented
47C2×#6659C2211yescharacteristic, complemented
48C2×#6655C2212yescomplemented
49#91303C2218yescomplemented
50C2×#6654C2211yescharacteristic, complemented
51#91298C2218yescomplemented
52C2×#6652C2212yescomplemented
53C2×#6650C2212yescomplemented
54#91286C2218yescomplemented
55C2×D3×#168C2212yescomplemented
56C2×#5757—51nomaximal, Hall
57C2×C5×H(5,𝔽2)—31no—
58C2×#4149—31no—
59#66169—316no—
60C2×#4096—32no—
61C2×#4096—31no—
62C2×#4095—32no—
63C2×#4095—31no—
64C2×#4094—31no—
65C2×#4078—32no—
66C2×#4078—31no—
67C22×#686—32no—
68C22×#686D311yescharacteristic, complemented
69C24×C3×C5—21no—
70C23×C5×D3—22no—
71C23×C3×D5—21no—
72C22×D3×D5—22no—
73C2×C3×C5×D4—21no—
74C2×C3×C5×D4—22no—
75C2×C3×C5×D4C2312yes—
76C2×C3×C5×D4C2314yescomplemented
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—21no—
79#6817—22no—
80#6817C2314yescomplemented
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×Dic30C2311yescharacteristic
84C2×C5×#67—21no—
85C2×C5×#67—22no—
86C2×C5×#67—216no—
87C2×C5×#67—22no—
88C2×C5×#67D412yes—
89C22×C5×Dic3—22no—
90C5×#237—24no—
91C5×#237—28no—
92C5×#237C2318yescomplemented
93C5×D3×D4—28no—
94C5×D3×D4—24no—
95C5×D3×D4C2318yescomplemented
96C5×#235—22no—
97C5×#235D414yes—
98C5×#235C2314yes—
99C5×#235C2314yescomplemented
100C2×C5×D12D411yescharacteristic
101C2×C5×D12C2311yescharacteristic
102C2×C4×C5×D3—21no—
103C2×C4×C5×D3C2312yes—
104C2×C5×Dic6D411yescharacteristic
105C2×C5×Dic6C2311yescharacteristic
106C2×C3×D20—21no—
107C2×C3×D20—22no—
108C2×C3×D20C2312yes—
109C2×C3×D20C2314yescomplemented
110D5×#67—216no—
111C2×#1202—22no—
112C2×#1201—22no—
113C2×D5×Dic3—22no—
114#6777—28no—
115D3×D20—24no—
116D3×D20C2318yescomplemented
117#6766—28no—
118#6765—24no—
119#6765C2318yescomplemented
120#6716C2318yescomplemented
121#6715C2318yescomplemented
122#6710C2314yescomplemented
123C2×C3⋊#168C2312yes—
124C3×#686C2318yescomplemented
125C3×#686C2318yescomplemented
126C2×C3×#168C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2314yescomplemented
129#6663C2314yescomplemented
130#6660C2314yescomplemented
131#6659C2314yescomplemented
132#6655C2318yescomplemented
133#6654C2314yescomplemented
134#6652C2318yescomplemented
135#6650C2318yescomplemented
136D3×#168C2318yescomplemented
137C2×#1004—51no—
138C2×#1004D511yescharacteristic, complemented
139C22×C3×D8—51no—
140C2×#932—51no—
141C2×#932—51no—
142#5757—516no—
143C2×#912—52no—
144C2×#911—52no—
145C2×#911—52no—
146C2×D3×D8—52no—
147C2×#904—51no—
148C2×#901—51no—
149C5×H(5,𝔽2)—38no—
150C5×H(5,𝔽2)—64no—
151C2×C5×#41—31no—
152C2×C5×#41—32no—
153C2×C5×#41—31no—
154C2×C5×#41—61no—
155C22×C5×D4—32no—
156C22×C5×D4—61no—
157C22×C5×D4—62no—
158C22×C5×D4C2×D311yescharacteristic, complemented
159#4149—38no—
160#4149—64no—
161C2×#713—61no—
162C2×D4×D5—61no—
163C2×D4×D5—62no—
164C2×#709—31no—
165C2×#709—32no—
166C22×D20—32no—
167C22×D20C2×D311yescharacteristic, complemented
168#4096—316no—
169#4096—38no—
170#4095—38no—
171#4095—316no—
172#4094—38no—
173C2×#689—31no—
174C2×#688—32no—
175C2×#688—31no—
176C2×#687—32no—
177C2×#687—31no—
178#4078—38no—
179#4078—316no—
180C2×#686—32no—
181C2×#686—32no—
182C2×#686—316no—
183C2×#686—31no—
184C2×#686C2×D312yescomplemented
185C2×#686C2×D312yescomplemented
186C2×#686C2×D318yescomplemented
187C2×#681—31no—
188C2×#681—32no—
189C22×#168—32no—
190C22×#168C2×D311yescharacteristic, complemented
191C2×#576—151noSylow
192C23×C3×C5—22no—
193C23×C3×C5—24no—
194C23×C3×C5—82no—
195C23×C3×C5C2×D411yescharacteristic
196C22×D15—21no—
197C22×C5×D3—21no—
198C22×C5×D3—28no—
199C22×C5×D3—84no—
200C22×C5×D3C2×D412yes—
201C22×C3×D5—22no—
202C22×C3×D5—24no—
203C22×C3×D5—82no—
204C2×D3×D5—28no—
205C2×D3×D5—84no—
206C3×C5×D4—22no—
207C3×C5×D4—24no—
208C3×C5×D4C2414yes—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2×D412yes—
211C2×C3×C4×C5C2411yescharacteristic
212C2×C3×C4×C5C2412yes—
213#1220—24no—
214C2×Dic15—21no—
215D60—21no—
216D60C2412yes—
217C4×D15—24no—
218Dic30—21no—
219Dic30C2412yes—
220C5×#67—24no—
221C5×#67—28no—
222C5×#67—28no—
223C5×#67C2×D418yes—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—28no—
226C2×C5×Dic3C2×D412yes—
227C5×D12—21no—
228C5×D12C2×D414yes—
229C5×D12C2412yes—
230C4×C5×D3—24no—
231C4×C5×D3C2×D414yes—
232C4×C5×D3C2414yes—
233C5×Dic6—21no—
234C5×Dic6C2×D414yes—
235C5×Dic6C2412yes—
236C3×D20—22no—
237C3×D20—24no—
238C3×D20C2414yes—
239#1202—28no—
240#1201—28no—
241D5×Dic3—28no—
242C3⋊#168C2414yes—
243C3×#168C2412yes—
244C3×#168C2412yes—
245C22×C3×D4—51no—
246C22×C3×D4C2×D511yescharacteristic, complemented
247C22×#67—22no—
248C22×#67—102no—
249#1004—24no—
250#1004—58no—
251#1004—104no—
252#1004C2×D518yescomplemented
253C2×#237—21no—
254C2×#237—52no—
255C2×#237—101no—
256C2×#237C2×D512yescomplemented
257C2×D3×D4—21no—
258C2×D3×D4—52no—
259C2×D3×D4—101no—
260C2×D3×D4C2×D512yescomplemented
261C2×#235—51no—
262C2×#235C2×D511yescharacteristic
263C2×#235C2×D511yescharacteristic, complemented
264C2×C3×D8—52no—
265C2×C3×D8—52no—
266C2×C3×D8—58no—
267C22×C3×C8—51no—
268C2×#214—52no—
269C2×#214—52no—
270#932—58no—
271#932—58no—
272C2×#213—52no—
273C2×#213—52no—
274C2×#208—51no—
275#912—516no—
276#911—516no—
277#911—516no—
278D3×D8—516no—
279C2×Dic12—51no—
280#904—58no—
281C2×D24—51no—
282C2×#204—51no—
283C2×#204—51no—
284#901—58no—
285C2×ΓL(1,𝔽25)—52no—
286C2×D3×C8—52no—
287C24×C5—21no—
288C24×C5—62no—
289C23×D5—21no—
290C23×D5—62no—
291C5×#41—34no—
292C5×#41—34no—
293C5×#41—38no—
294C5×#41—34no—
295C5×#41—64no—
296C5×#41—68no—
297C5×#41—62no—
298C2×C5×Q8—31no—
299C2×C5×Q8—31no—
300C2×C5×D4—21no—
301C2×C5×D4—22no—
302C2×C5×D4—32no—
303C2×C5×D4—38no—
304C2×C5×D4—31no—
305C2×C5×D4—31no—
306C2×C5×D4—64no—
307C2×C5×D4—62no—
308C2×C5×D4—68no—
309C2×C5×D4—616no—
310C2×C5×D4—62no—
311C2×C5×D4—61no—
312C2×C5×D4C22×D312yes—
313C2×C5×D4C22×D314yescomplemented
314C22×C4×C5—32no—
315C22×C4×C5—62no—
316C22×C4×C5—61no—
317C22×C4×C5C22×D311yescharacteristic
318C2×C22⋊D5—62no—
319C2×C22⋊D5—61no—
320#713—68no—
321D4×D5—68no—
322D4×D5—616no—
323#709—34no—
324#709—38no—
325#709—64no—
326#709—62no—
327C2×D20—21no—
328C2×D20—22no—
329C2×D20—31no—
330C2×D20—38no—
331C2×D20—64no—
332C2×D20—62no—
333C2×D20C22×D312yes—
334C2×D20C22×D314yescomplemented
335C2×C4×D5—62no—
336C2×C4×D5—61no—
337C2×Dic10—31no—
338#689—34no—
339#688—38no—
340#688—34no—
341#687—38no—
342#687—34no—
343#686—38no—
344#686—38no—
345#686—34no—
346#686C22×D318yescomplemented
347#686C22×D318yescomplemented
348#681—34no—
349#681—38no—
350C2×#168—32no—
351C2×#168—38no—
352C2×#168C22×D311yescharacteristic
353C2×#168C22×D311yescharacteristic
354C2×#168C22×D314yescomplemented
355C2×H(5,𝔽2)—31no—
356C2×H(5,𝔽2)—151no—
357#576—1516no—
358C2×AGL(1,ℤ/8)—152no—
359C2×AGL(1,ℤ/8)—152no—
360C2×AGL(1,ℤ/8)—151no—
361C2×AGL(1,ℤ/8)—151no—
362C2×#135—151no—
363C2×#135—152no—
364C22×D8—51no—
365C22×D8—152no—
366C2×#131—151no—
367C22×C3×C5—22no—
368C22×C3×C5—24no—
369C22×C3×C5—44no—
370C22×C3×C5—84no—
371C22×C3×C5C22×D412yes—
372C22×C3×C5C22×D411yescharacteristic
373C2×D15—22no—
374C2×D15—42no—
375C2×C5×D3—24no—
376C2×C5×D3—22no—
377C2×C5×D3—42no—
378C2×C5×D3—88no—
379C2×C5×D3C22×D414yes—
380C2×C3×D5—24no—
381C2×C3×D5—44no—
382C2×C3×D5—84no—
383D3×D5—88no—
384C3×C4×C5C22×D411yescharacteristic
385C3×C4×C5C22×D412yes—
386C3×C4×C5C2511yescharacteristic
387Dic15—22no—
388C5×Dic3—22no—
389C5×Dic3C22×D414yes—
390C24×C3—21no—
391C24×C3—101no—
392C23×D3—22no—
393C23×D3—102no—
394C2×C3×D4—21no—
395C2×C3×D4—22no—
396C2×C3×D4—52no—
397C2×C3×D4—54no—
398C2×C3×D4—101no—
399C2×C3×D4—102no—
400C2×C3×D4C22×D512yes—
401C2×C3×D4C22×D514yescomplemented
402C22×C3×C4C22×D511yescharacteristic
403C2×#67—21no—
404C2×#67—22no—
405C2×#67—216no—
406C2×#67—22no—
407C2×#67—101no—
408C2×#67—102no—
409C2×#67—1016no—
410C2×#67—102no—
411C2×#67C22⋊D512yes—
412C22×Dic3—22no—
413C22×Dic3—102no—
414#237—24no—
415#237—28no—
416#237—58no—
417#237—104no—
418#237—108no—
419#237C22×D518yescomplemented
420D3×D4—28no—
421D3×D4—24no—
422D3×D4—58no—
423D3×D4—108no—
424D3×D4—104no—
425D3×D4C22×D518yescomplemented
426#235—22no—
427#235—54no—
428#235—102no—
429#235C22⋊D514yes—
430#235C22×D514yes—
431#235C22×D514yescomplemented
432C2×D12—51no—
433C2×D12C22⋊D511yescharacteristic
434C2×D12C22×D511yescharacteristic
435C2×C4×D3—21no—
436C2×C4×D3—101no—
437C2×C4×D3C22×D512yes—
438C2×Dic6—51no—
439C2×Dic6C22⋊D511yescharacteristic
440C2×Dic6C22×D511yescharacteristic
441C3×D8—58no—
442C3×D8—58no—
443C2×C3×C8—51no—
444C2×C3×C8—51no—
445C2×C3×C8—54no—
446#214—58no—
447#214—58no—
448#213—58no—
449#213—58no—
450#208—54no—
451C2×C3⋊C8—52no—
452Dic12—54no—
453D24—54no—
454#204—54no—
455#204—54no—
456ΓL(1,𝔽25)—58no—
457D3×C8—58no—
458C23×C5—22no—
459C23×C5—24no—
460C23×C5—32no—
461C23×C5—68no—
462C23×C5—61no—
463C23×C5—82no—
464C23×C5—244no—
465C23×C5D3×D411yescharacteristic
466C22×D5—22no—
467C22×D5—24no—
468C22×D5—68no—
469C22×D5—61no—
470C22×D5—82no—
471C22×D5—244no—
472C5×Q8—34no—
473C5×Q8—32no—
474C5×Q8—61no—
475C5×D4—22no—
476C5×D4—24no—
477C5×D4—38no—
478C5×D4—34no—
479C5×D4—32no—
480C5×D4—68no—
481C5×D4—68no—
482C5×D4—64no—
483C5×D4—61no—
484C5×D4C23×D314yes—
485C2×C4×C5—32no—
486C2×C4×C5—34no—
487C2×C4×C5—34no—
488C2×C4×C5—68no—
489C2×C4×C5—61no—
490C2×C4×C5—64no—
491C2×C4×C5D3×D411yescharacteristic
492C2×C4×C5D3×D412yes—
493C2×C4×C5C23×D311yescharacteristic
494C2×C4×C5C23×D312yes—
495C22⋊D5—68no—
496C22⋊D5—64no—
497C2×Dic5—61no—
498D20—22no—
499D20—24no—
500D20—32no—
501D20—68no—
502D20—61no—
503D20C23×D314yes—
504C4×D5—68no—
505C4×D5—64no—
506Dic10—32no—
507Dic10—61no—
508#168—34no—
509#168C23×D312yes—
510#168C23×D312yes—
511H(5,𝔽2)—38no—
512H(5,𝔽2)—64no—
513H(5,𝔽2)—158no—
514H(5,𝔽2)—304no—
515C2×#41—31no—
516C2×#41—32no—
517C2×#41—31no—
518C2×#41—61no—
519C2×#41—152no—
520C2×#41—151no—
521C2×#41—301no—
522C22×D4—32no—
523C22×D4—51no—
524C22×D4—61no—
525C22×D4—62no—
526C22×D4—152no—
527C22×D4—301no—
528C22×D4—302no—
529C22×D4D3×D511yescharacteristic, complemented
530AGL(1,ℤ/8)—1516no—
531AGL(1,ℤ/8)—1516no—
532AGL(1,ℤ/8)—158no—
533AGL(1,ℤ/8)—158no—
534#135—158no—
535#135—1516no—
536C2×Q16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—152no—
540C2×SD16—152no—
541C2×D8—52no—
542C2×D8—52no—
543C2×D8—58no—
544C2×D8—151no—
545C2×D8—1516no—
546C2×D8—152no—
547C2×D8—152no—
548#131—158no—
549C2×M16—152no—
550C2×M16—151no—
551C22×C8—51no—
552C22×C8—152no—
553C2×C3×C5—22no—
554C2×C3×C5—44no—
555C2×C3×C5#57612yescomplemented
556C2×C3×C5C23×D411yescharacteristic
557D15—42no—
558C3×D5—44no—
559C5×D3—24no—
560C5×D3—42no—
561C23×C3—22no—
562C23×C3—24no—
563C23×C3—82no—
564C23×C3—102no—
565C23×C3—104no—
566C23×C3—402no—
567C23×C3C2×C22⋊D511yescharacteristic
568C22×D3—21no—
569C22×D3—28no—
570C22×D3—84no—
571C22×D3—101no—
572C22×D3—108no—
573C22×D3—404no—
574C22×D3C2×C22⋊D512yes—
575C3×D4—22no—
576C3×D4—24no—
577C3×D4—54no—
578C3×D4—102no—
579C3×D4—104no—
580C3×D4C23×D514yes—
581C2×C3×C4C2×C22⋊D511yescharacteristic
582C2×C3×C4C2×C22⋊D512yes—
583C2×C3×C4C23×D511yescharacteristic
584C2×C3×C4C23×D512yes—
585#67—24no—
586#67—28no—
587#67—28no—
588#67—104no—
589#67—108no—
590#67—108no—
591#67C2×C22⋊D518yes—
592C2×Dic3—21no—
593C2×Dic3—28no—
594C2×Dic3—101no—
595C2×Dic3—108no—
596C2×Dic3C2×C22⋊D512yes—
597D12—21no—
598D12—52no—
599D12—101no—
600D12C2×C22⋊D514yes—
601D12C23×D512yes—
602C4×D3—24no—
603C4×D3—104no—
604C4×D3C2×C22⋊D514yes—
605C4×D3C23×D514yes—
606Dic6—21no—
607Dic6—52no—
608Dic6—101no—
609Dic6C2×C22⋊D514yes—
610Dic6C23×D512yes—
611C3×C8—52no—
612C3×C8—52no—
613C3⋊C8—54no—
614C22×C5—22no—
615C22×C5—24no—
616C22×C5—34no—
617C22×C5—44no—
618C22×C5—64no—
619C22×C5—62no—
620C22×C5—84no—
621C22×C5—122no—
622C22×C5—248no—
623C22×C5C2×D3×D412yes—
624C22×C5C2×D3×D411yescharacteristic
625C2×D5—24no—
626C2×D5—44no—
627C2×D5—62no—
628C2×D5—84no—
629C2×D5—122no—
630C2×D5—248no—
631C4×C5—34no—
632C4×C5—62no—
633C4×C5C2×D3×D411yescharacteristic
634C4×C5C2×D3×D412yes—
635C4×C5C24×D311yescharacteristic
636Dic5—62no—
637C24—21no—
638C24—62no—
639C24—101no—
640C24—302no—
641#41—34no—
642#41—34no—
643#41—38no—
644#41—34no—
645#41—64no—
646#41—68no—
647#41—62no—
648#41—158no—
649#41—154no—
650#41—304no—
651#41—308no—
652#41—302no—
653C2×Q8—31no—
654C2×Q8—31no—
655C2×Q8—151no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—32no—
659C2×D4—38no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—52no—
663C2×D4—54no—
664C2×D4—64no—
665C2×D4—62no—
666C2×D4—68no—
667C2×D4—616no—
668C2×D4—62no—
669C2×D4—61no—
670C2×D4—101no—
671C2×D4—102no—
672C2×D4—158no—
673C2×D4—151no—
674C2×D4—304no—
675C2×D4—302no—
676C2×D4—308no—
677C2×D4—3016no—
678C2×D4—302no—
679C2×D4—301no—
680C2×D4C2×D3×D512yes—
681C2×D4C2×D3×D514yescomplemented
682C22×C4—32no—
683C22×C4—62no—
684C22×C4—61no—
685C22×C4—302no—
686C22×C4—301no—
687C22×C4C2×D3×D511yescharacteristic
688Q16—154no—
689SD16—154no—
690SD16—154no—
691SD16—158no—
692SD16—158no—
693D8—58no—
694D8—58no—
695D8—154no—
696D8—158no—
697D8—158no—
698M16—158no—
699M16—154no—
700C2×C8—51no—
701C2×C8—51no—
702C2×C8—54no—
703C2×C8—158no—
704C2×C8—152no—
705C3×C5C2×#57611yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—24no—
708C22×C3—44no—
709C22×C3—84no—
710C22×C3—104no—
711C22×C3—204no—
712C22×C3—404no—
713C22×C3C22×C22⋊D512yes—
714C22×C3C22×C22⋊D511yescharacteristic
715C2×D3—24no—
716C2×D3—22no—
717C2×D3—42no—
718C2×D3—88no—
719C2×D3—102no—
720C2×D3—202no—
721C2×D3—408no—
722C2×D3C22×C22⋊D514yes—
723C3×C4C22×C22⋊D511yescharacteristic
724C3×C4C22×C22⋊D512yes—
725C3×C4C24×D511yescharacteristic
726Dic3—22no—
727Dic3—102no—
728Dic3C22×C22⋊D514yes—
729C2×C5—22no—
730C2×C5—44no—
731C2×C5—64no—
732C2×C5—122no—
733C2×C5#575712yescomplemented
734C2×C5C22×D3×D411yescharacteristic
735D5—44no—
736D5—122no—
737C23—22no—
738C23—24no—
739C23—32no—
740C23—68no—
741C23—61no—
742C23—82no—
743C23—102no—
744C23—104no—
745C23—244no—
746C23—308no—
747C23—301no—
748C23—402no—
749C23—1204no—
750C23D3×C22⋊D511yescharacteristic
751Q8—34no—
752Q8—32no—
753Q8—61no—
754Q8—152no—
755Q8—301no—
756D4—22no—
757D4—24no—
758D4—38no—
759D4—34no—
760D4—32no—
761D4—54no—
762D4—68no—
763D4—68no—
764D4—64no—
765D4—61no—
766D4—102no—
767D4—104no—
768D4—152no—
769D4—308no—
770D4—308no—
771D4—304no—
772D4—301no—
773D4C22×D3×D514yes—
774C2×C4—32no—
775C2×C4—34no—
776C2×C4—34no—
777C2×C4—68no—
778C2×C4—61no—
779C2×C4—64no—
780C2×C4—308no—
781C2×C4—301no—
782C2×C4—304no—
783C2×C4D3×C22⋊D512yes—
784C2×C4D3×C22⋊D511yescharacteristic
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D511yescharacteristic
787C8—52no—
788C8—52no—
789C8—154no—
790C2×C3—22no—
791C2×C3—44no—
792C2×C3—204no—
793C2×C3#6616912yescomplemented
794C2×C3C23×C22⋊D511yescharacteristic
795D3—24no—
796D3—42no—
797D3—202no—
798C5C2×#575711yescharacteristic, complemented, Sylow
799C22—22no—
800C22—24no—
801C22—34no—
802C22—44no—
803C22—64no—
804C22—62no—
805C22—84no—
806C22—104no—
807C22—122no—
808C22—204no—
809C22—248no—
810C22—302no—
811C22—404no—
812C22—602no—
813C22—1208no—
814C22C2×D3×C22⋊D512yes—
815C22C2×D3×C22⋊D511yescharacteristic
816C4—34no—
817C4—62no—
818C4—302no—
819C4C2×D3×C22⋊D511yescharacteristic
820C4C2×D3×C22⋊D512yes—
821C4C23×D3×D511yescharacteristic
822C3C2×#6616911yescharacteristic, complemented, Sylow
823C2—22no—
824C2—44no—
825C2—64no—
826C2—122no—
827C2—204no—
828C2—602no—
829C2#1175469712yesdirect product factor
830C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1004C2semidirect
2. C2×#92017C2semidirect
3. C2×#91821C2semidirect
4. C22×C3×#686C2semidirect
5. C2×#91494C2semidirect
6. C2×#91493C2semidirect
7. #11754697C2direct (N × H)
8. C2×#91480C2semidirect
9. C2×D3×#686C2semidirect
10. C2×#91303C2semidirect
11. C2×#91298C2semidirect
12. C2×#91286C2semidirect
14. C22×C3×C5×D4C22semidirect
15. C2×#6817C22semidirect
18. C5×#1004C22semidirect
20. C2×C5×#237C22semidirect
22. C2×C5×D3×D4C22semidirect
24. C2×C5×#235C22semidirect
25. C22×C3×D20C22semidirect
28. #92017C22semidirect
30. C2×D3×D20C22semidirect
32. C2×#6765C22semidirect
33. C2×#6716C22semidirect
34. #91821C22semidirect
35. C2×#6715C22semidirect
36. C2×#6710C22semidirect
37. C2×C3×#686C22semidirect
38. C2×C3×#686C22semidirect
39. C2×C3×#686C22semidirect
40. C22×C3×#168C22semidirect
41. #91494C22semidirect
42. #91493C22semidirect
43. #91480C22semidirect
44. D3×#686C22semidirect
45. C2×#6663C22semidirect
46. C2×#6660C22semidirect
47. C2×#6659C22semidirect
48. C2×#6655C22semidirect
49. #91303C22semidirect
50. C2×#6654C22semidirect
51. #91298C22semidirect
52. C2×#6652C22semidirect
53. C2×#6650C22semidirect
54. #91286C22semidirect
55. C2×D3×#168C22semidirect
68. C22×#686D3semidirect
76. C2×C3×C5×D4C23semidirect
80. #6817C23semidirect
92. C5×#237C23semidirect
95. C5×D3×D4C23semidirect
99. C5×#235C23semidirect
109. C2×C3×D20C23semidirect
116. D3×D20C23semidirect
119. #6765C23semidirect
120. #6716C23semidirect
121. #6715C23semidirect
122. #6710C23semidirect
124. C3×#686C23semidirect
125. C3×#686C23semidirect
128. C2×C3×#168C23semidirect
129. #6663C23semidirect
130. #6660C23semidirect
131. #6659C23semidirect
132. #6655C23semidirect
133. #6654C23semidirect
134. #6652C23semidirect
135. #6650C23semidirect
136. D3×#168C23semidirect
138. C2×#1004D5semidirect
158. C22×C5×D4C2×D3semidirect
167. C22×D20C2×D3semidirect
184. C2×#686C2×D3semidirect
185. C2×#686C2×D3semidirect
186. C2×#686C2×D3semidirect
190. C22×#168C2×D3semidirect
246. C22×C3×D4C2×D5semidirect
252. #1004C2×D5semidirect
256. C2×#237C2×D5semidirect
260. C2×D3×D4C2×D5semidirect
263. C2×#235C2×D5semidirect
313. C2×C5×D4C22×D3semidirect
334. C2×D20C22×D3semidirect
346. #686C22×D3semidirect
347. #686C22×D3semidirect
354. C2×#168C22×D3semidirect
401. C2×C3×D4C22×D5semidirect
419. #237C22×D5semidirect
425. D3×D4C22×D5semidirect
431. #235C22×D5semidirect
529. C22×D4D3×D5semidirect
555. C2×C3×C5#576semidirect
681. C2×D4C2×D3×D5semidirect
705. C3×C5C2×#576semidirect
733. C2×C5#5757semidirect
793. C2×C3#66169semidirect
798. C5C2×#5757semidirect
822. C3C2×#66169semidirect
829. C2#11754697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#10042
C2×#920172
C2×#918212
C22×C3×#6862
C2×#914942
C2×#914932
#117546972
C2×#914802
C2×D3×#6862
C2×#913032
C2×#912982
C2×#912862
C2×#661693
C2×#57575