Finite Group Databasebeta

← C2×#11755325 #14510005

Subgroups — C2×#11755325 #14510005

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×#1009C211yesmaximal, characteristic, complemented
2C2×#92019C211yesmaximal, characteristic, complemented
3C2×#91838C211yesmaximal, characteristic, complemented
4C2×C3×#4096C211yesmaximal, characteristic, complemented
5#11755325C2116yesmaximal, direct product factor
6C2×#91519C212yesmaximal, complemented
7C2×#91504C212yesmaximal, complemented
8C2×#91496C212yesmaximal, complemented
9C2×D3×#686C212yesmaximal, complemented
10C22×#6654C211yesmaximal, characteristic, complemented
11C2×#91299C211yesmaximal, characteristic, complemented
12C2×#91286C211yesmaximal, characteristic, complemented
13C2×#66169—31nomaximal, Hall
14C2×C3×C5×#41C2211yescharacteristic, complemented
15C22×D60C2211yescharacteristic, complemented
16C5×#1009—24no—
17C5×#1009C2218yescomplemented
18C2×C5×#239C2212yescomplemented
19C2×C5×D3×D4—22no—
20C2×C5×D3×D4C2212yescomplemented
21C2×C5×#235—21no—
22C2×C5×#235C2211yescharacteristic
23C22×C5×D12—21no—
24C22×C5×D12C2211yescharacteristic, complemented
25C2×C3×#709C2211yescharacteristic, complemented
26C2×#6790—22no—
27#92019—24no—
28#92019C2218yescomplemented
29C2×D3×D20C2212yescomplemented
30C2×D5×D12—21no—
31C2×#6773—21no—
32C2×#6769C2212yescomplemented
33#91838C2218yescomplemented
34C2×#6717C2212yescomplemented
35C2×#6715C2212yescomplemented
36C2×#6710C2211yescharacteristic, complemented
37C3×#4096C2218yescomplemented
38C2×C3×#689C2211yescharacteristic, complemented
39C2×C3×#688C2211yescharacteristic, complemented
40C2×C3×#687C2211yescharacteristic, complemented
41C2×C3×#686C2211yescharacteristic, complemented
42C22×C3×#168C2211yescharacteristic, complemented
43#91519C22116yescomplemented
44#91504C22116yescomplemented
45#91496C22116yescomplemented
46D3×#686C22116yescomplemented
47C2×#6656C2212yescomplemented
48C2×#6654C2212yescomplemented
49C2×#6654C2212yescomplemented
50C2×#6654C2218yescomplemented
51#91299C2218yescomplemented
52C2×#6652C2212yescomplemented
53C2×#6650C2212yescomplemented
54#91286C2218yescomplemented
55C2×D3×#168C2212yescomplemented
56C2×#5769—51nomaximal, Hall
57C2×C5×H(5,𝔽2)—31no—
58C2×#4149—31no—
59#66169—316no—
60C2×#4096—32no—
61C2×#4096D311yescharacteristic, complemented
62C2×#4095—32no—
63C2×#4095—31no—
64C2×#4094—31no—
65C2×#4078—32no—
66C2×#4078—31no—
67C22×#686—32no—
68C22×#686—31no—
69C23×D15—21no—
70C23×C5×D3—21no—
71C23×C5×D3—22no—
72C22×D3×D5—22no—
73C3×C5×#41—22no—
74C3×C5×#41C2314yescomplemented
75C2×C3×C5×Q8C2311yescharacteristic
76C2×C3×C5×D4—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C22×C3×C4×C5C2311yescharacteristic
80C2×D60—21no—
81C2×D60—22no—
82C2×D60C2312yes—
83C2×D60C2314yescomplemented
84C2×C5×#67—22no—
85C2×C5×#67D412yes—
86C5×#239—24no—
87C5×#239C2318yescomplemented
88C5×D3×D4—216no—
89C5×D3×D4—24no—
90C5×D3×D4C2318yescomplemented
91C5×#235—28no—
92C5×#235D414yes—
93C5×#235C2314yes—
94C2×C5×D12—22no—
95C2×C5×D12—21no—
96C2×C5×D12—22no—
97C2×C5×D12—28no—
98C2×C5×D12D411yescharacteristic
99C2×C5×D12C2312yes—
100C2×C5×D12C2314yescomplemented
101C2×C4×C5×D3—22no—
102C2×C4×C5×D3C2312yes—
103C2×C5×Dic6D411yescharacteristic
104C2×C3×C22⋊D5—21no—
105C3×#709—22no—
106C3×#709C2314yescomplemented
107C2×C3×D20C2311yescharacteristic
108C2×C3×C4×D5—21no—
109C2×C3×Dic10C2311yescharacteristic
110#6790—216no—
111C2×#1203—22no—
112C2×#1202—22no—
113C2×#1200—22no—
114D3×D20—24no—
115D3×D20C2318yescomplemented
116D5×D12—28no—
117#6773—28no—
118#6769—24no—
119#6769C2318yescomplemented
120#6717C2318yescomplemented
121#6715C2318yescomplemented
122#6710C2314yescomplemented
123C2×C3⋊#168C2312yes—
124C3×#689C2314yescomplemented
125C3×#688C2314yescomplemented
126C3×#687C2314yescomplemented
127C3×#686C2314yescomplemented
128C2×C3×#168C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2314yescomplemented
131#6656C2318yescomplemented
132#6654C2318yescomplemented
133#6654C2318yescomplemented
134#6652C2318yescomplemented
135#6650C2318yescomplemented
136D3×#168C2318yescomplemented
137C2×#1009—51no—
138C2×#1009D511yescharacteristic, complemented
139C2×C3×#135—51no—
140C2×#949—51no—
141C2×#949—51no—
142#5769—516no—
143C2×#919—52no—
144C2×#914—52no—
145C2×#914—52no—
146C2×D3×D8—52no—
147C22×D24—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—61no—
154C2×C5×#41C2×D311yescharacteristic, complemented
155C22×C5×D4—32no—
156C22×C5×D4—31no—
157C22×C5×D4—61no—
158C22×C5×D4—62no—
159#4149—38no—
160#4149—64no—
161C2×#713—61no—
162C2×D4×D5—61no—
163C2×D4×D5—62no—
164C2×#709—32no—
165C2×#709C2×D311yescharacteristic, complemented
166C22×D20—31no—
167C22×D20—32no—
168#4096—316no—
169#4096C2×D318yescomplemented
170#4095—38no—
171#4095—316no—
172#4094—38no—
173C2×#689C2×D311yescharacteristic, complemented
174C2×#688—32no—
175C2×#688C2×D311yescharacteristic, complemented
176C2×#687—32no—
177C2×#687C2×D311yescharacteristic, complemented
178#4078—38no—
179#4078—316no—
180C2×#686—32no—
181C2×#686—32no—
182C2×#686—316no—
183C2×#686—32no—
184C2×#686—32no—
185C2×#686—38no—
186C2×#686C2×D311yescharacteristic, complemented
187C2×#681—31no—
188C2×#681—32no—
189C22×#168—32no—
190C22×#168C2×D311yescharacteristic, complemented
191C2×#576—151noSylow
192C23×C3×C5—21no—
193C23×C3×C5C2×D411yescharacteristic
194C22×D15—22no—
195C22×D15—24no—
196C22×D15—82no—
197C22×C5×D3—22no—
198C22×C5×D3—24no—
199C22×C5×D3—28no—
200C22×C5×D3—84no—
201C22×C5×D3—82no—
202C22×C5×D3C2×D412yes—
203C22×C3×D5—21no—
204C2×D3×D5—28no—
205C2×D3×D5—84no—
206C3×C5×Q8—21no—
207C3×C5×Q8C2412yes—
208C3×C5×D4—24no—
209C3×C5×D4—21no—
210C3×C5×D4C2412yes—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—24no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D412yes—
215C2×C3×C4×C5C2411yescharacteristic
216C2×C3×C4×C5C2412yes—
217D60—22no—
218D60—24no—
219D60C2414yes—
220C5×#67—28no—
221C5×#67C2×D418yes—
222C2×C5×Dic3C2×D412yes—
223C5×D12—28no—
224C5×D12—24no—
225C5×D12—22no—
226C5×D12C2×D414yes—
227C5×D12C2414yes—
228C4×C5×D3—28no—
229C4×C5×D3C2×D414yes—
230C4×C5×D3C2414yes—
231C5×Dic6C2×D414yes—
232C3×C22⋊D5—24no—
233C2×C3×Dic5—21no—
234C3×D20—21no—
235C3×D20C2412yes—
236C3×C4×D5—24no—
237C3×Dic10—21no—
238C3×Dic10C2412yes—
239#1203—28no—
240#1202—28no—
241#1200—28no—
242C3⋊#168C2414yes—
243C3×#168C2412yes—
244C3×#168C2412yes—
245C2×C3×#41—51no—
246C2×C3×#41C2×D511yescharacteristic, complemented
247#1009—24no—
248#1009—58no—
249#1009—104no—
250#1009C2×D518yescomplemented
251C2×#239—52no—
252C2×#239C2×D512yescomplemented
253C2×D3×D4—22no—
254C2×D3×D4—52no—
255C2×D3×D4—102no—
256C2×D3×D4C2×D512yescomplemented
257C2×#235—21no—
258C2×#235—101no—
259C2×#235C2×D511yescharacteristic
260C22×D12—21no—
261C22×D12—51no—
262C22×D12—101no—
263C22×D12C2×D511yescharacteristic, complemented
264C3×#135—58no—
265C2×C3×Q16—51no—
266C2×C3×SD16—51no—
267C2×C3×SD16—51no—
268C2×C3×D8—51no—
269C22×C3×C8—51no—
270#949—58no—
271#949—58no—
272C2×#215—52no—
273C2×#215—52no—
274C2×#213—52no—
275C2×#213—52no—
276C2×#208—51no—
277#919—516no—
278#914—516no—
279#914—516no—
280D3×D8—516no—
281C2×D24—52no—
282C2×D24—52no—
283C2×D24—58no—
284#901—58no—
285C2×ΓL(1,𝔽25)—52no—
286C2×D3×C8—52no—
287C24×C5—62no—
288C24×C5—61no—
289C23×D5—62no—
290C23×D5—61no—
291C5×#41—22no—
292C5×#41—34no—
293C5×#41—34no—
294C5×#41—38no—
295C5×#41—68no—
296C5×#41—64no—
297C5×#41C22×D314yescomplemented
298C2×C5×Q8—31no—
299C2×C5×Q8C22×D311yescharacteristic
300C2×C5×D4—21no—
301C2×C5×D4—32no—
302C2×C5×D4—38no—
303C2×C5×D4—31no—
304C2×C5×D4—32no—
305C2×C5×D4—34no—
306C2×C5×D4—68no—
307C2×C5×D4—62no—
308C2×C5×D4—64no—
309C2×C5×D4—62no—
310C2×C5×D4—616no—
311C2×C5×D4—61no—
312C2×C5×D4—62no—
313C2×C5×D4C22×D311yescharacteristic
314C22×C4×C5—21no—
315C22×C4×C5—32no—
316C22×C4×C5—62no—
317C22×C4×C5C22×D311yescharacteristic
318C2×C22⋊D5—21no—
319C2×C22⋊D5—62no—
320#713—68no—
321D4×D5—68no—
322D4×D5—616no—
323#709—22no—
324#709—38no—
325#709—64no—
326#709C22×D314yescomplemented
327C2×D20—32no—
328C2×D20—34no—
329C2×D20—38no—
330C2×D20—64no—
331C2×D20—62no—
332C2×D20—61no—
333C2×D20—62no—
334C2×D20C22×D311yescharacteristic
335C2×C4×D5—21no—
336C2×C4×D5—62no—
337C2×Dic10C22×D311yescharacteristic
338#689C22×D314yescomplemented
339#688—38no—
340#688C22×D314yescomplemented
341#687—38no—
342#687C22×D314yescomplemented
343#686—38no—
344#686—38no—
345#686—38no—
346#686—38no—
347#686C22×D314yescomplemented
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—51no—
363C2×#135—152no—
364C22×D8—151no—
365C22×D8—152no—
366C2×#131—151no—
367C22×C3×C5—22no—
368C22×C3×C5—22no—
369C22×C3×C5—42no—
370C22×C3×C5C22×D412yes—
371C22×C3×C5C22×D411yescharacteristic
372C2×D15—24no—
373C2×D15—44no—
374C2×D15—84no—
375C2×C5×D3—24no—
376C2×C5×D3—24no—
377C2×C5×D3—44no—
378C2×C5×D3—88no—
379C2×C5×D3—84no—
380C2×C5×D3C22×D414yes—
381C2×C3×D5—22no—
382C2×C3×D5—42no—
383D3×D5—88no—
384C3×C4×C5—22no—
385C3×C4×C5C22×D411yescharacteristic
386C3×C4×C5C22×D412yes—
387C3×C4×C5C2511yescharacteristic
388C3×Dic5—22no—
389C5×Dic3C22×D414yes—
390C23×D3—21no—
391C23×D3—22no—
392C23×D3—101no—
393C23×D3—102no—
394C3×#41—22no—
395C3×#41—54no—
396C3×#41—102no—
397C3×#41C22×D514yescomplemented
398C2×C3×Q8—51no—
399C2×C3×Q8C22×D511yescharacteristic
400C2×C3×D4—21no—
401C2×C3×D4—51no—
402C2×C3×D4—101no—
403C2×C3×D4C22×D511yescharacteristic
404C22×C3×C4—21no—
405C22×C3×C4—101no—
406C22×C3×C4C22×D511yescharacteristic
407C2×#67—22no—
408C2×#67—102no—
409C2×#67C22⋊D512yes—
410#239—24no—
411#239—58no—
412#239—104no—
413#239C22×D518yescomplemented
414D3×D4—216no—
415D3×D4—24no—
416D3×D4—58no—
417D3×D4—1016no—
418D3×D4—104no—
419D3×D4C22×D518yescomplemented
420#235—28no—
421#235—108no—
422#235C22⋊D514yes—
423#235C22×D514yes—
424C2×D12—22no—
425C2×D12—21no—
426C2×D12—22no—
427C2×D12—28no—
428C2×D12—52no—
429C2×D12—54no—
430C2×D12—102no—
431C2×D12—101no—
432C2×D12—102no—
433C2×D12—108no—
434C2×D12C22⋊D511yescharacteristic
435C2×D12C22×D512yes—
436C2×D12C22×D514yescomplemented
437C2×C4×D3—22no—
438C2×C4×D3—102no—
439C2×C4×D3C22×D512yes—
440C2×Dic6C22⋊D511yescharacteristic
441C3×Q16—54no—
442C3×SD16—54no—
443C3×SD16—54no—
444C3×D8—54no—
445C2×C3×C8—51no—
446C2×C3×C8—51no—
447C2×C3×C8—54no—
448#215—58no—
449#215—58no—
450#213—58no—
451#213—58no—
452#208—54no—
453C2×C3⋊C8—52no—
454D24—58no—
455D24—58no—
456ΓL(1,𝔽25)—58no—
457D3×C8—58no—
458C23×C5—21no—
459C23×C5—32no—
460C23×C5—68no—
461C23×C5—62no—
462C23×C5—64no—
463C23×C5—242no—
464C23×C5—244no—
465C23×C5D3×D411yescharacteristic
466C22×D5—21no—
467C22×D5—68no—
468C22×D5—62no—
469C22×D5—64no—
470C22×D5—244no—
471C22×D5—242no—
472C5×Q8—21no—
473C5×Q8—34no—
474C5×Q8C23×D312yes—
475C5×D4—24no—
476C5×D4—21no—
477C5×D4—38no—
478C5×D4—34no—
479C5×D4—34no—
480C5×D4—68no—
481C5×D4—68no—
482C5×D4—62no—
483C5×D4—64no—
484C5×D4C23×D312yes—
485C2×C4×C5—21no—
486C2×C4×C5—24no—
487C2×C4×C5—32no—
488C2×C4×C5—34no—
489C2×C4×C5—34no—
490C2×C4×C5—68no—
491C2×C4×C5D3×D411yescharacteristic
492C2×C4×C5D3×D412yes—
493C2×C4×C5C23×D311yescharacteristic
494C2×C4×C5C23×D312yes—
495C22⋊D5—24no—
496C22⋊D5—68no—
497C2×Dic5—21no—
498D20—21no—
499D20—34no—
500D20—68no—
501D20—62no—
502D20—64no—
503D20C23×D312yes—
504C4×D5—24no—
505C4×D5—68no—
506Dic10—21no—
507Dic10C23×D312yes—
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—51no—
518C2×#41—61no—
519C2×#41—152no—
520C2×#41—301no—
521C2×#41D3×D511yescharacteristic, complemented
522C22×D4—32no—
523C22×D4—31no—
524C22×D4—61no—
525C22×D4—62no—
526C22×D4—152no—
527C22×D4—151no—
528C22×D4—301no—
529C22×D4—302no—
530AGL(1,ℤ/8)—1516no—
531AGL(1,ℤ/8)—1516no—
532AGL(1,ℤ/8)—158no—
533AGL(1,ℤ/8)—158no—
534#135—58no—
535#135—1516no—
536C2×Q16—51no—
537C2×SD16—51no—
538C2×SD16—51no—
539C2×SD16—152no—
540C2×SD16—152no—
541C2×D8—51no—
542C2×D8—152no—
543C2×D8—152no—
544C2×D8—158no—
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—42no—
555C2×C3×C5#57612yescomplemented
556C2×C3×C5C23×D411yescharacteristic
557D15—44no—
558C3×D5—42no—
559C5×D3—24no—
560C5×D3—44no—
561C23×C3—21no—
562C23×C3—101no—
563C23×C3C2×C22⋊D511yescharacteristic
564C22×D3—22no—
565C22×D3—24no—
566C22×D3—28no—
567C22×D3—84no—
568C22×D3—82no—
569C22×D3—102no—
570C22×D3—104no—
571C22×D3—108no—
572C22×D3—404no—
573C22×D3—402no—
574C22×D3C2×C22⋊D512yes—
575C3×Q8—21no—
576C3×Q8—52no—
577C3×Q8—101no—
578C3×Q8C23×D512yes—
579C3×D4—24no—
580C3×D4—21no—
581C3×D4—52no—
582C3×D4—104no—
583C3×D4—101no—
584C3×D4C23×D512yes—
585C2×C3×C4—21no—
586C2×C3×C4—24no—
587C2×C3×C4—101no—
588C2×C3×C4—104no—
589C2×C3×C4C2×C22⋊D511yescharacteristic
590C2×C3×C4C2×C22⋊D512yes—
591C2×C3×C4C23×D511yescharacteristic
592C2×C3×C4C23×D512yes—
593#67—28no—
594#67—108no—
595#67C2×C22⋊D518yes—
596C2×Dic3C2×C22⋊D512yes—
597D12—28no—
598D12—24no—
599D12—22no—
600D12—54no—
601D12—108no—
602D12—104no—
603D12—102no—
604D12C2×C22⋊D514yes—
605D12C23×D514yes—
606C4×D3—28no—
607C4×D3—108no—
608C4×D3C2×C22⋊D514yes—
609C4×D3C23×D514yes—
610Dic6C2×C22⋊D514yes—
611C3×C8—52no—
612C3×C8—52no—
613C3⋊C8—54no—
614C22×C5—22no—
615C22×C5—22no—
616C22×C5—34no—
617C22×C5—42no—
618C22×C5—64no—
619C22×C5—64no—
620C22×C5—124no—
621C22×C5—244no—
622C22×C5—248no—
623C22×C5C2×D3×D412yes—
624C22×C5C2×D3×D411yescharacteristic
625C2×D5—22no—
626C2×D5—42no—
627C2×D5—64no—
628C2×D5—124no—
629C2×D5—248no—
630C2×D5—244no—
631C4×C5—22no—
632C4×C5—34no—
633C4×C5C2×D3×D411yescharacteristic
634C4×C5C2×D3×D412yes—
635C4×C5C24×D311yescharacteristic
636Dic5—22no—
637C24—62no—
638C24—61no—
639C24—302no—
640C24—301no—
641#41—22no—
642#41—34no—
643#41—34no—
644#41—38no—
645#41—54no—
646#41—68no—
647#41—64no—
648#41—102no—
649#41—158no—
650#41—304no—
651#41—308no—
652#41C2×D3×D514yescomplemented
653C2×Q8—31no—
654C2×Q8—51no—
655C2×Q8C2×D3×D511yescharacteristic
656C2×D4—21no—
657C2×D4—32no—
658C2×D4—38no—
659C2×D4—31no—
660C2×D4—32no—
661C2×D4—34no—
662C2×D4—51no—
663C2×D4—68no—
664C2×D4—62no—
665C2×D4—64no—
666C2×D4—62no—
667C2×D4—616no—
668C2×D4—61no—
669C2×D4—62no—
670C2×D4—101no—
671C2×D4—158no—
672C2×D4—152no—
673C2×D4—154no—
674C2×D4—304no—
675C2×D4—302no—
676C2×D4—308no—
677C2×D4—302no—
678C2×D4—3016no—
679C2×D4—301no—
680C2×D4—302no—
681C2×D4C2×D3×D511yescharacteristic
682C22×C4—21no—
683C22×C4—32no—
684C22×C4—62no—
685C22×C4—101no—
686C22×C4—302no—
687C22×C4C2×D3×D511yescharacteristic
688Q16—54no—
689SD16—54no—
690SD16—54no—
691SD16—158no—
692SD16—158no—
693D8—54no—
694D8—158no—
695D8—158no—
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—22no—
708C22×C3—42no—
709C22×C3—102no—
710C22×C3—202no—
711C22×C3C22×C22⋊D512yes—
712C22×C3C22×C22⋊D511yescharacteristic
713C2×D3—24no—
714C2×D3—24no—
715C2×D3—44no—
716C2×D3—88no—
717C2×D3—84no—
718C2×D3—104no—
719C2×D3—204no—
720C2×D3—408no—
721C2×D3—404no—
722C2×D3C22×C22⋊D514yes—
723C3×C4—22no—
724C3×C4—102no—
725C3×C4C22×C22⋊D512yes—
726C3×C4C22×C22⋊D511yescharacteristic
727C3×C4C24×D511yescharacteristic
728Dic3C22×C22⋊D514yes—
729C2×C5—22no—
730C2×C5—42no—
731C2×C5—64no—
732C2×C5—124no—
733C2×C5#576912yescomplemented
734C2×C5C22×D3×D411yescharacteristic
735D5—42no—
736D5—124no—
737C23—21no—
738C23—32no—
739C23—68no—
740C23—62no—
741C23—64no—
742C23—101no—
743C23—242no—
744C23—244no—
745C23—308no—
746C23—302no—
747C23—304no—
748C23—1202no—
749C23—1204no—
750C23D3×C22⋊D511yescharacteristic
751Q8—21no—
752Q8—34no—
753Q8—52no—
754Q8—101no—
755Q8C22×D3×D512yes—
756D4—24no—
757D4—21no—
758D4—38no—
759D4—34no—
760D4—34no—
761D4—52no—
762D4—68no—
763D4—68no—
764D4—64no—
765D4—62no—
766D4—104no—
767D4—101no—
768D4—154no—
769D4—308no—
770D4—308no—
771D4—304no—
772D4—302no—
773D4C22×D3×D512yes—
774C2×C4—21no—
775C2×C4—24no—
776C2×C4—32no—
777C2×C4—34no—
778C2×C4—34no—
779C2×C4—68no—
780C2×C4—101no—
781C2×C4—104no—
782C2×C4—308no—
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—42no—
792C2×C3—202no—
793C2×C3#6616912yescomplemented
794C2×C3C23×C22⋊D511yescharacteristic
795D3—24no—
796D3—44no—
797D3—204no—
798C5C2×#576911yescharacteristic, complemented, Sylow
799C22—22no—
800C22—22no—
801C22—34no—
802C22—42no—
803C22—64no—
804C22—64no—
805C22—102no—
806C22—124no—
807C22—202no—
808C22—244no—
809C22—248no—
810C22—304no—
811C22—604no—
812C22—1204no—
813C22—1208no—
814C22C2×D3×C22⋊D512yes—
815C22C2×D3×C22⋊D511yescharacteristic
816C4—22no—
817C4—34no—
818C4—102no—
819C4C2×D3×C22⋊D512yes—
820C4C2×D3×C22⋊D511yescharacteristic
821C4C23×D3×D511yescharacteristic
822C3C2×#6616911yescharacteristic, complemented, Sylow
823C2—22no—
824C2—42no—
825C2—64no—
826C2—124no—
827C2—202no—
828C2—604no—
829C2#1175532512yesdirect product factor
830C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1009C2semidirect
2. C2×#92019C2semidirect
3. C2×#91838C2semidirect
4. C2×C3×#4096C2semidirect
5. #11755325C2direct (N × H)
6. C2×#91519C2semidirect
7. C2×#91504C2semidirect
8. C2×#91496C2semidirect
9. C2×D3×#686C2semidirect
10. C22×#6654C2semidirect
11. C2×#91299C2semidirect
12. C2×#91286C2semidirect
14. C2×C3×C5×#41C22semidirect
15. C22×D60C22semidirect
17. C5×#1009C22semidirect
18. C2×C5×#239C22semidirect
20. C2×C5×D3×D4C22semidirect
24. C22×C5×D12C22semidirect
25. C2×C3×#709C22semidirect
28. #92019C22semidirect
29. C2×D3×D20C22semidirect
32. C2×#6769C22semidirect
33. #91838C22semidirect
34. C2×#6717C22semidirect
35. C2×#6715C22semidirect
36. C2×#6710C22semidirect
37. C3×#4096C22semidirect
38. C2×C3×#689C22semidirect
39. C2×C3×#688C22semidirect
40. C2×C3×#687C22semidirect
41. C2×C3×#686C22semidirect
42. C22×C3×#168C22semidirect
43. #91519C22semidirect
44. #91504C22semidirect
45. #91496C22semidirect
46. D3×#686C22semidirect
47. C2×#6656C22semidirect
48. C2×#6654C22semidirect
49. C2×#6654C22semidirect
50. C2×#6654C22semidirect
51. #91299C22semidirect
52. C2×#6652C22semidirect
53. C2×#6650C22semidirect
54. #91286C22semidirect
55. C2×D3×#168C22semidirect
61. C2×#4096D3semidirect
74. C3×C5×#41C23semidirect
83. C2×D60C23semidirect
87. C5×#239C23semidirect
90. C5×D3×D4C23semidirect
100. C2×C5×D12C23semidirect
106. C3×#709C23semidirect
115. D3×D20C23semidirect
119. #6769C23semidirect
120. #6717C23semidirect
121. #6715C23semidirect
122. #6710C23semidirect
124. C3×#689C23semidirect
125. C3×#688C23semidirect
126. C3×#687C23semidirect
127. C3×#686C23semidirect
130. C2×C3×#168C23semidirect
131. #6656C23semidirect
132. #6654C23semidirect
133. #6654C23semidirect
134. #6652C23semidirect
135. #6650C23semidirect
136. D3×#168C23semidirect
138. C2×#1009D5semidirect
154. C2×C5×#41C2×D3semidirect
165. C2×#709C2×D3semidirect
169. #4096C2×D3semidirect
173. C2×#689C2×D3semidirect
175. C2×#688C2×D3semidirect
177. C2×#687C2×D3semidirect
186. C2×#686C2×D3semidirect
190. C22×#168C2×D3semidirect
246. C2×C3×#41C2×D5semidirect
250. #1009C2×D5semidirect
252. C2×#239C2×D5semidirect
256. C2×D3×D4C2×D5semidirect
263. C22×D12C2×D5semidirect
297. C5×#41C22×D3semidirect
326. #709C22×D3semidirect
338. #689C22×D3semidirect
340. #688C22×D3semidirect
342. #687C22×D3semidirect
347. #686C22×D3semidirect
354. C2×#168C22×D3semidirect
397. C3×#41C22×D5semidirect
413. #239C22×D5semidirect
419. D3×D4C22×D5semidirect
436. C2×D12C22×D5semidirect
521. C2×#41D3×D5semidirect
555. C2×C3×C5#576semidirect
652. #41C2×D3×D5semidirect
705. C3×C5C2×#576semidirect
733. C2×C5#5769semidirect
793. C2×C3#66169semidirect
798. C5C2×#5769semidirect
822. C3C2×#66169semidirect
829. C2#11755325direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#10092
C2×#920192
C2×#918382
C2×C3×#40962
#117553252
C2×#915192
C2×#915042
C2×#914962
C2×D3×#6862
C22×#66542
C2×#912992
C2×#912862
C2×#661693
C2×#57695