Finite Group Databasebeta

← C2×#11754698 #14509993

Subgroups — C2×#11754698 #14509993

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×#92019C211yesmaximal, characteristic, complemented
3C22×#6715C211yesmaximal, characteristic, complemented
4C2×C3×#4078C211yesmaximal, characteristic, complemented
5C2×#91496C212yesmaximal, complemented
6C2×#91495C212yesmaximal, complemented
7#11754698C2116yesmaximal, direct product factor
8C2×#91480C212yesmaximal, complemented
9C2×D3×#686C212yesmaximal, complemented
10C2×#91305C211yesmaximal, characteristic, complemented
11C2×#91297C211yesmaximal, characteristic, complemented
12C2×#91288C211yesmaximal, characteristic, complemented
13C2×#66169—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic, complemented
15C22×D60C2211yescharacteristic, 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
25C2×C3×#709C2211yescharacteristic, complemented
26C2×#6790—22no—
27#92019—24no—
28#92019C2218yescomplemented
29C2×D3×D20C2212yescomplemented
30C2×D5×D12—21no—
31C2×#6773—21no—
32C2×#6769C2212yescomplemented
33C2×#6715C2212yescomplemented
34C2×#6715C2212yescomplemented
35C2×#6715C2218yescomplemented
36C22×C3⋊#168C2211yescharacteristic, complemented
37C2×C3×#687C2212yescomplemented
38C3×#4078C2218yescomplemented
39C2×C3×#686C2212yescomplemented
40C2×C3×#681C2211yescharacteristic, complemented
41#91496C22116yescomplemented
42#91495C22116yescomplemented
43#91480C22116yescomplemented
44D3×#686C22116yescomplemented
45C2×#6661C2211yescharacteristic, complemented
46C2×#6660C2212yescomplemented
47C2×#6656C2211yescharacteristic, complemented
48C2×#6655C2211yescharacteristic, complemented
49#91305C2218yescomplemented
50C2×#6654C2212yescomplemented
51#91297C2218yescomplemented
52C2×#6652C2211yescharacteristic, complemented
53C2×#6650C2212yescomplemented
54#91288C2218yescomplemented
55C2×D3×#168C2212yescomplemented
56C2×#5774—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×#4078D311yescharacteristic, complemented
67C22×#686—32no—
68C22×#686—31no—
69C24×C3×C5—21no—
70C23×D15—21no—
71C23×C5×D3—22no—
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×D60—21no—
79C2×D60—22no—
80C2×D60C2312yes—
81C2×D60C2314yescomplemented
82C2×C5×#67—21no—
83C2×C5×#67—22no—
84C2×C5×#67—216no—
85C2×C5×#67—22no—
86C2×C5×#67D412yes—
87C22×C5×Dic3—22no—
88C5×#237—24no—
89C5×#237—28no—
90C5×#237C2318yescomplemented
91C5×D3×D4—28no—
92C5×D3×D4—24no—
93C5×D3×D4C2318yescomplemented
94C5×#235—22no—
95C5×#235D414yes—
96C5×#235C2314yes—
97C5×#235C2314yescomplemented
98C2×C5×D12D411yescharacteristic
99C2×C5×D12C2311yescharacteristic
100C2×C4×C5×D3—21no—
101C2×C4×C5×D3C2312yes—
102C2×C5×Dic6D411yescharacteristic
103C2×C5×Dic6C2311yescharacteristic
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#6715C2318yescomplemented
121#6715C2318yescomplemented
122C2×C3⋊#168C2311yescharacteristic
123C2×C3⋊#168C2311yescharacteristic
124C2×C3⋊#168C2314yescomplemented
125C3×#687C2318yescomplemented
126C3×#686C2318yescomplemented
127C3×#681C2314yescomplemented
128C2×C3×#168C2312yes—
129#6661C2314yescomplemented
130#6660C2318yescomplemented
131#6656C2314yescomplemented
132#6655C2314yescomplemented
133#6654C2318yescomplemented
134#6652C2314yescomplemented
135#6650C2318yescomplemented
136D3×#168C2318yescomplemented
137C2×#1009—51no—
138C2×#1004D511yescharacteristic, complemented
139C2×C3×AGL(1,ℤ/8)—51no—
140C2×#950—51no—
141C22×#213—51no—
142#5774—516no—
143C2×#916—52no—
144C2×#914—52no—
145C2×#911—52no—
146C2×D3×D8—52no—
147C2×#908—51no—
148C2×#907—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—32no—
165C2×#709C2×D311yescharacteristic, complemented
166C22×D20—31no—
167C22×D20—32no—
168#4096—38no—
169#4096—316no—
170#4095—316no—
171#4095—38no—
172#4094—38no—
173C2×#689—31no—
174C2×#688—31no—
175C2×#688—32no—
176C2×#687—31no—
177C2×#687C2×D312yescomplemented
178#4078—316no—
179#4078C2×D318yescomplemented
180C2×#686—32no—
181C2×#686—32no—
182C2×#686—38no—
183C2×#686—31no—
184C2×#686—316no—
185C2×#686—32no—
186C2×#686C2×D312yescomplemented
187C2×#681—32no—
188C2×#681C2×D311yescharacteristic, complemented
189C22×#168—31no—
190C22×#168—32no—
191C2×#576—151noSylow
192C23×C3×C5—22no—
193C23×C3×C5—24no—
194C23×C3×C5—82no—
195C23×C3×C5C2×D411yescharacteristic
196C22×D15—22no—
197C22×D15—24no—
198C22×D15—82no—
199C22×C5×D3—21no—
200C22×C5×D3—28no—
201C22×C5×D3—84no—
202C22×C5×D3C2×D412yes—
203C22×C3×D5—21no—
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—
213D60—22no—
214D60—24no—
215D60C2414yes—
216C5×#67—24no—
217C5×#67—28no—
218C5×#67—28no—
219C5×#67C2×D418yes—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—28no—
222C2×C5×Dic3C2×D412yes—
223C5×D12—21no—
224C5×D12C2×D414yes—
225C5×D12C2412yes—
226C4×C5×D3—24no—
227C4×C5×D3C2×D414yes—
228C4×C5×D3C2414yes—
229C5×Dic6—21no—
230C5×Dic6C2×D414yes—
231C5×Dic6C2412yes—
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⋊#168C2412yes—
243C3⋊#168C2412yes—
244C3×#168C2414yes—
245C2×C3×#41—51no—
246C22×C3×D4C2×D511yescharacteristic, complemented
247C22×#67—22no—
248#1009—58no—
249#1009—104no—
250C2×#239—52no—
251#1004—24no—
252#1004C2×D518yescomplemented
253C2×#237—21no—
254C2×#237C2×D512yescomplemented
255C2×D3×D4—21no—
256C2×D3×D4—52no—
257C2×D3×D4—102no—
258C2×D3×D4C2×D512yescomplemented
259C2×#235—101no—
260C2×#235C2×D511yescharacteristic
261C2×#235C2×D511yescharacteristic, complemented
262C22×D12—51no—
263C22×D12—101no—
264C3×AGL(1,ℤ/8)—58no—
265C2×C3×SD16—52no—
266C2×C3×D8—52no—
267C2×C3×M16—51no—
268#950—58no—
269C2×#216—51no—
270C2×#215—51no—
271C2×#214—51no—
272C2×#213—52no—
273C2×#213—52no—
274C2×#213—58no—
275C2×#213—51no—
276C22×C3⋊C8—51no—
277#916—516no—
278#914—516no—
279#911—516no—
280D3×D8—516no—
281#908—58no—
282#907—58no—
283C2×D24—52no—
284C2×#204—52no—
285C2×ΓL(1,𝔽25)—52no—
286C2×D3×C8—52no—
287C24×C5—21no—
288C24×C5—62no—
289C23×D5—62no—
290C23×D5—61no—
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—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#689—34no—
339#688—34no—
340#688—38no—
341#687—34no—
342#687C22×D318yescomplemented
343#686—38no—
344#686—38no—
345#686—34no—
346#686—38no—
347#686C22×D318yescomplemented
348#681—38no—
349#681C22×D314yescomplemented
350C2×#168—34no—
351C2×#168—31no—
352C2×#168—31no—
353C2×#168—38no—
354C2×#168C22×D312yes—
355C2×H(5,𝔽2)—31no—
356C2×H(5,𝔽2)—151no—
357#576—1516no—
358C2×AGL(1,ℤ/8)—51no—
359C2×AGL(1,ℤ/8)—151no—
360C2×AGL(1,ℤ/8)—152no—
361C2×AGL(1,ℤ/8)—152no—
362C2×#135—152no—
363C2×#135—151no—
364C22×D8—152no—
365C22×D8—151no—
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—24no—
374C2×D15—44no—
375C2×D15—84no—
376C2×C5×D3—24no—
377C2×C5×D3—22no—
378C2×C5×D3—42no—
379C2×C5×D3—88no—
380C2×C5×D3C22×D414yes—
381C2×C3×D5—22no—
382C2×C3×D5—42no—
383D3×D5—88no—
384C3×C4×C5C22×D411yescharacteristic
385C3×C4×C5C22×D412yes—
386C3×C4×C5C2511yescharacteristic
387C3×Dic5—22no—
388C5×Dic3—22no—
389C5×Dic3C22×D414yes—
390C24×C3—21no—
391C23×D3—22no—
392C23×D3—101no—
393C23×D3—102no—
394C3×#41—54no—
395C3×#41—102no—
396C2×C3×Q8—51no—
397C2×C3×D4—21no—
398C2×C3×D4—22no—
399C2×C3×D4—51no—
400C2×C3×D4—101no—
401C2×C3×D4C22×D512yes—
402C2×C3×D4C22×D514yescomplemented
403C22×C3×C4—101no—
404C22×C3×C4C22×D511yescharacteristic
405C2×#67—21no—
406C2×#67—22no—
407C2×#67—216no—
408C2×#67—22no—
409C2×#67—102no—
410C2×#67C22⋊D512yes—
411C22×Dic3—22no—
412#239—58no—
413#239—104no—
414#237—24no—
415#237—28no—
416#237C22×D518yescomplemented
417D3×D4—28no—
418D3×D4—24no—
419D3×D4—58no—
420D3×D4—1016no—
421D3×D4—104no—
422D3×D4C22×D518yescomplemented
423#235—22no—
424#235—108no—
425#235C22⋊D514yes—
426#235C22×D514yes—
427#235C22×D514yescomplemented
428C2×D12—52no—
429C2×D12—54no—
430C2×D12—102no—
431C2×D12—101no—
432C2×D12—102no—
433C2×D12—108no—
434C2×D12C22⋊D511yescharacteristic
435C2×D12C22×D511yescharacteristic
436C2×C4×D3—21no—
437C2×C4×D3—102no—
438C2×C4×D3C22×D512yes—
439C2×Dic6C22⋊D511yescharacteristic
440C2×Dic6C22×D511yescharacteristic
441C3×SD16—58no—
442C3×D8—58no—
443C3×M16—54no—
444C2×C3×C8—52no—
445#216—54no—
446#215—54no—
447#214—54no—
448#213—58no—
449#213—58no—
450#213—54no—
451C2×C3⋊C8—51no—
452C2×C3⋊C8—51no—
453C2×C3⋊C8—54no—
454D24—58no—
455#204—58no—
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—21no—
467C22×D5—68no—
468C22×D5—62no—
469C22×D5—64no—
470C22×D5—244no—
471C22×D5—242no—
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—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—32no—
509#168—32no—
510#168C23×D314yes—
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—51no—
519C2×#41—61no—
520C2×#41—152no—
521C2×#41—301no—
522C22×D4—32no—
523C22×D4—61no—
524C22×D4—62no—
525C22×D4—152no—
526C22×D4—151no—
527C22×D4—301no—
528C22×D4—302no—
529C22×D4D3×D511yescharacteristic, complemented
530AGL(1,ℤ/8)—58no—
531AGL(1,ℤ/8)—158no—
532AGL(1,ℤ/8)—1516no—
533AGL(1,ℤ/8)—1516no—
534#135—1516no—
535#135—158no—
536C2×Q16—151no—
537C2×SD16—52no—
538C2×SD16—152no—
539C2×SD16—151no—
540C2×SD16—151no—
541C2×D8—52no—
542C2×D8—152no—
543C2×D8—1516no—
544C2×D8—151no—
545C2×D8—152no—
546C2×D8—152no—
547C2×D8—158no—
548#131—158no—
549C2×M16—51no—
550C2×M16—152no—
551C22×C8—152no—
552C22×C8—151no—
553C2×C3×C5—22no—
554C2×C3×C5—44no—
555C2×C3×C5#57612yescomplemented
556C2×C3×C5C23×D411yescharacteristic
557D15—44no—
558C3×D5—42no—
559C5×D3—24no—
560C5×D3—42no—
561C23×C3—22no—
562C23×C3—24no—
563C23×C3—82no—
564C23×C3—101no—
565C23×C3C2×C22⋊D511yescharacteristic
566C22×D3—21no—
567C22×D3—28no—
568C22×D3—84no—
569C22×D3—102no—
570C22×D3—104no—
571C22×D3—108no—
572C22×D3—404no—
573C22×D3—402no—
574C22×D3C2×C22⋊D512yes—
575C3×Q8—52no—
576C3×Q8—101no—
577C3×D4—22no—
578C3×D4—24no—
579C3×D4—52no—
580C3×D4—104no—
581C3×D4—101no—
582C3×D4C23×D514yes—
583C2×C3×C4—101no—
584C2×C3×C4—104no—
585C2×C3×C4C2×C22⋊D511yescharacteristic
586C2×C3×C4C2×C22⋊D512yes—
587C2×C3×C4C23×D511yescharacteristic
588C2×C3×C4C23×D512yes—
589#67—24no—
590#67—28no—
591#67—28no—
592#67—108no—
593#67C2×C22⋊D518yes—
594C2×Dic3—21no—
595C2×Dic3—28no—
596C2×Dic3C2×C22⋊D512yes—
597D12—21no—
598D12—54no—
599D12—108no—
600D12—104no—
601D12—102no—
602D12C2×C22⋊D514yes—
603D12C23×D512yes—
604C4×D3—24no—
605C4×D3—108no—
606C4×D3C2×C22⋊D514yes—
607C4×D3C23×D514yes—
608Dic6—21no—
609Dic6C2×C22⋊D514yes—
610Dic6C23×D512yes—
611C3×C8—54no—
612C3⋊C8—52no—
613C3⋊C8—52no—
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—22no—
626C2×D5—42no—
627C2×D5—64no—
628C2×D5—124no—
629C2×D5—248no—
630C2×D5—244no—
631C4×C5—34no—
632C4×C5—62no—
633C4×C5C2×D3×D411yescharacteristic
634C4×C5C2×D3×D412yes—
635C4×C5C24×D311yescharacteristic
636Dic5—22no—
637C24—21no—
638C24—62no—
639C24—302no—
640C24—301no—
641#41—34no—
642#41—34no—
643#41—38no—
644#41—34no—
645#41—54no—
646#41—64no—
647#41—68no—
648#41—62no—
649#41—102no—
650#41—158no—
651#41—304no—
652#41—308no—
653C2×Q8—31no—
654C2×Q8—31no—
655C2×Q8—51no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—32no—
659C2×D4—38no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—51no—
663C2×D4—64no—
664C2×D4—62no—
665C2×D4—68no—
666C2×D4—616no—
667C2×D4—62no—
668C2×D4—61no—
669C2×D4—101no—
670C2×D4—158no—
671C2×D4—152no—
672C2×D4—154no—
673C2×D4—304no—
674C2×D4—302no—
675C2×D4—308no—
676C2×D4—302no—
677C2×D4—3016no—
678C2×D4—301no—
679C2×D4—302no—
680C2×D4C2×D3×D512yes—
681C2×D4C2×D3×D514yescomplemented
682C22×C4—32no—
683C22×C4—62no—
684C22×C4—61no—
685C22×C4—101no—
686C22×C4—302no—
687C22×C4C2×D3×D511yescharacteristic
688Q16—154no—
689SD16—58no—
690SD16—158no—
691SD16—154no—
692SD16—154no—
693D8—58no—
694D8—158no—
695D8—154no—
696D8—158no—
697D8—158no—
698M16—54no—
699M16—158no—
700C2×C8—52no—
701C2×C8—158no—
702C2×C8—151no—
703C2×C8—151no—
704C2×C8—154no—
705C3×C5C2×#57611yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—24no—
708C22×C3—44no—
709C22×C3—84no—
710C22×C3—102no—
711C22×C3—202no—
712C22×C3C22×C22⋊D512yes—
713C22×C3C22×C22⋊D511yescharacteristic
714C2×D3—24no—
715C2×D3—22no—
716C2×D3—42no—
717C2×D3—88no—
718C2×D3—104no—
719C2×D3—204no—
720C2×D3—408no—
721C2×D3—404no—
722C2×D3C22×C22⋊D514yes—
723C3×C4—102no—
724C3×C4C22×C22⋊D511yescharacteristic
725C3×C4C22×C22⋊D512yes—
726C3×C4C24×D511yescharacteristic
727Dic3—22no—
728Dic3C22×C22⋊D514yes—
729C2×C5—22no—
730C2×C5—44no—
731C2×C5—64no—
732C2×C5—122no—
733C2×C5#577412yescomplemented
734C2×C5C22×D3×D411yescharacteristic
735D5—42no—
736D5—124no—
737C23—22no—
738C23—24no—
739C23—32no—
740C23—68no—
741C23—61no—
742C23—82no—
743C23—101no—
744C23—244no—
745C23—308no—
746C23—302no—
747C23—304no—
748C23—1202no—
749C23—1204no—
750C23D3×C22⋊D511yescharacteristic
751Q8—34no—
752Q8—32no—
753Q8—52no—
754Q8—61no—
755Q8—101no—
756D4—22no—
757D4—24no—
758D4—38no—
759D4—34no—
760D4—32no—
761D4—52no—
762D4—68no—
763D4—68no—
764D4—64no—
765D4—61no—
766D4—104no—
767D4—101no—
768D4—154no—
769D4—308no—
770D4—308no—
771D4—302no—
772D4—304no—
773D4C22×D3×D514yes—
774C2×C4—32no—
775C2×C4—34no—
776C2×C4—34no—
777C2×C4—68no—
778C2×C4—61no—
779C2×C4—64no—
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—54no—
788C8—152no—
789C8—152no—
790C2×C3—22no—
791C2×C3—44no—
792C2×C3—202no—
793C2×C3#6616912yescomplemented
794C2×C3C23×C22⋊D511yescharacteristic
795D3—24no—
796D3—42no—
797D3—204no—
798C5C2×#577411yescharacteristic, complemented, Sylow
799C22—22no—
800C22—24no—
801C22—34no—
802C22—44no—
803C22—64no—
804C22—62no—
805C22—84no—
806C22—102no—
807C22—122no—
808C22—202no—
809C22—248no—
810C22—304no—
811C22—604no—
812C22—1204no—
813C22—1208no—
814C22C2×D3×C22⋊D512yes—
815C22C2×D3×C22⋊D511yescharacteristic
816C4—34no—
817C4—62no—
818C4—102no—
819C4C2×D3×C22⋊D511yescharacteristic
820C4C2×D3×C22⋊D512yes—
821C4C23×D3×D511yescharacteristic
822C3C2×#6616911yescharacteristic, complemented, Sylow
823C2—22no—
824C2—44no—
825C2—64no—
826C2—122no—
827C2—202no—
828C2—604no—
829C2#1175469812yesdirect 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×#92019C2semidirect
3. C22×#6715C2semidirect
4. C2×C3×#4078C2semidirect
5. C2×#91496C2semidirect
6. C2×#91495C2semidirect
7. #11754698C2direct (N × H)
8. C2×#91480C2semidirect
9. C2×D3×#686C2semidirect
10. C2×#91305C2semidirect
11. C2×#91297C2semidirect
12. C2×#91288C2semidirect
14. C22×C3×C5×D4C22semidirect
15. C22×D60C22semidirect
18. C5×#1004C22semidirect
20. C2×C5×#237C22semidirect
22. C2×C5×D3×D4C22semidirect
24. C2×C5×#235C22semidirect
25. C2×C3×#709C22semidirect
28. #92019C22semidirect
29. C2×D3×D20C22semidirect
32. C2×#6769C22semidirect
33. C2×#6715C22semidirect
34. C2×#6715C22semidirect
35. C2×#6715C22semidirect
36. C22×C3⋊#168C22semidirect
37. C2×C3×#687C22semidirect
38. C3×#4078C22semidirect
39. C2×C3×#686C22semidirect
40. C2×C3×#681C22semidirect
41. #91496C22semidirect
42. #91495C22semidirect
43. #91480C22semidirect
44. D3×#686C22semidirect
45. C2×#6661C22semidirect
46. C2×#6660C22semidirect
47. C2×#6656C22semidirect
48. C2×#6655C22semidirect
49. #91305C22semidirect
50. C2×#6654C22semidirect
51. #91297C22semidirect
52. C2×#6652C22semidirect
53. C2×#6650C22semidirect
54. #91288C22semidirect
55. C2×D3×#168C22semidirect
66. C2×#4078D3semidirect
76. C2×C3×C5×D4C23semidirect
81. C2×D60C23semidirect
90. C5×#237C23semidirect
93. C5×D3×D4C23semidirect
97. C5×#235C23semidirect
106. C3×#709C23semidirect
115. D3×D20C23semidirect
119. #6769C23semidirect
120. #6715C23semidirect
121. #6715C23semidirect
124. C2×C3⋊#168C23semidirect
125. C3×#687C23semidirect
126. C3×#686C23semidirect
127. C3×#681C23semidirect
129. #6661C23semidirect
130. #6660C23semidirect
131. #6656C23semidirect
132. #6655C23semidirect
133. #6654C23semidirect
134. #6652C23semidirect
135. #6650C23semidirect
136. D3×#168C23semidirect
138. C2×#1004D5semidirect
158. C22×C5×D4C2×D3semidirect
165. C2×#709C2×D3semidirect
177. C2×#687C2×D3semidirect
179. #4078C2×D3semidirect
186. C2×#686C2×D3semidirect
188. C2×#681C2×D3semidirect
246. C22×C3×D4C2×D5semidirect
252. #1004C2×D5semidirect
254. C2×#237C2×D5semidirect
258. C2×D3×D4C2×D5semidirect
261. C2×#235C2×D5semidirect
313. C2×C5×D4C22×D3semidirect
326. #709C22×D3semidirect
342. #687C22×D3semidirect
347. #686C22×D3semidirect
349. #681C22×D3semidirect
402. C2×C3×D4C22×D5semidirect
416. #237C22×D5semidirect
422. D3×D4C22×D5semidirect
427. #235C22×D5semidirect
529. C22×D4D3×D5semidirect
555. C2×C3×C5#576semidirect
681. C2×D4C2×D3×D5semidirect
705. C3×C5C2×#576semidirect
733. C2×C5#5774semidirect
793. C2×C3#66169semidirect
798. C5C2×#5774semidirect
822. C3C2×#66169semidirect
829. C2#11754698direct (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×#920192
C22×#67152
C2×C3×#40782
C2×#914962
C2×#914952
#117546982
C2×#914802
C2×D3×#6862
C2×#913052
C2×#912972
C2×#912882
C2×#661693
C2×#57745