Finite Group Databasebeta

← C2×#11754691 #14509990

Subgroups — C2×#11754691 #14509990

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×C3×#4144C211yesmaximal, characteristic, complemented
2C2×#92018C211yesmaximal, characteristic, complemented
3C2×#91821C211yesmaximal, characteristic, complemented
4C22×C5×#213C211yesmaximal, characteristic, complemented
5C2×#91490C212yesmaximal, complemented
6C2×#91489C212yesmaximal, complemented
7#11754691C2116yesmaximal, direct product factor
8C2×#91478C212yesmaximal, complemented
9C2×D5×#213C212yesmaximal, complemented
10C2×#91311C211yesmaximal, characteristic, complemented
11C2×#91299C211yesmaximal, characteristic, complemented
12C2×#91283C211yesmaximal, characteristic, complemented
13C2×#66091—31nomaximal, Hall
14C22×C3×C5×D4C2211yescharacteristic, complemented
15C2×#6817C2211yescharacteristic, complemented
16C22×C5×D12C2211yescharacteristic, complemented
17C22×C3×C22⋊D5—22no—
18C3×#4144—24no—
19C3×#4144C2218yescomplemented
20C2×C3×#711—21no—
21C2×C3×#711C2212yescomplemented
22C2×C3×D4×D5—21no—
23C2×C3×D4×D5C2212yescomplemented
24C2×C3×#709C2211yescharacteristic
25C2×C3×#709C2211yescharacteristic, complemented
26C2×D3×C22⋊D5—22no—
27#92018—24no—
28#92018C2218yescomplemented
29C2×#6777—21no—
30C2×D5×D12C2212yescomplemented
31C2×#6772C2212yescomplemented
32C2×#6768—21no—
33C2×#6716C2212yescomplemented
34#91821C2218yescomplemented
35C2×#6715C2212yescomplemented
36C2×#6710C2211yescharacteristic, complemented
37C2×C5×#213C2212yescomplemented
38C2×C5×#213C2212yescomplemented
39C2×C5×#213C2218yescomplemented
40C22×C5×C3⋊C8C2211yescharacteristic, complemented
41#91490C22116yescomplemented
42#91489C22116yescomplemented
43#91478C22116yescomplemented
44D5×#213C22116yescomplemented
45C2×#6662C2211yescharacteristic, complemented
46C2×#6658C2211yescharacteristic, complemented
47#91311C2218yescomplemented
48C2×#6657C2211yescharacteristic, complemented
49C2×#6656C2212yescomplemented
50C2×#6653C2211yescharacteristic, complemented
51#91299C2218yescomplemented
52C2×#6652C2212yescomplemented
53C2×#6649C2212yescomplemented
54#91283C2218yescomplemented
55C2×D5×C3⋊C8C2212yescomplemented
56C2×#5835—51nomaximal, Hall
57C2×#4144—31no—
58C2×#4144D311yescharacteristic, complemented
59C22×C5×D8—31no—
60C2×#4078—31no—
61C2×#4078—31no—
62#66091—316no—
63C2×#4058—32no—
64C2×#4057—32no—
65C2×#4057—32no—
66C2×D5×D8—32no—
67C2×#4050—31no—
68C2×#4047—31no—
69C24×C3×C5—21no—
70C23×C5×D3—21no—
71C23×C3×D5—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×#1220—21no—
79#6817—22no—
80#6817C2314yescomplemented
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×Dic30C2311yescharacteristic
84C2×C5×D12—21no—
85C2×C5×D12—22no—
86C2×C5×D12C2312yes—
87C2×C5×D12C2314yescomplemented
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5—22no—
90C2×C3×C22⋊D5—216no—
91C2×C3×C22⋊D5—22no—
92C2×C3×C22⋊D5D412yes—
93C22×C3×Dic5—22no—
94C3×#711—24no—
95C3×#711—28no—
96C3×#711C2318yescomplemented
97C3×D4×D5—28no—
98C3×D4×D5—24no—
99C3×D4×D5C2318yescomplemented
100C3×#709—22no—
101C3×#709D414yes—
102C3×#709C2314yes—
103C3×#709C2314yescomplemented
104C2×C3×D20D411yescharacteristic
105C2×C3×D20C2311yescharacteristic
106C2×C3×C4×D5—21no—
107C2×C3×C4×D5C2312yes—
108C2×C3×Dic10D411yescharacteristic
109C2×C3×Dic10C2311yescharacteristic
110D3×C22⋊D5—216no—
111C2×#1203—22no—
112C2×#1201—22no—
113C2×D3×Dic5—22no—
114#6777—28no—
115D5×D12—24no—
116D5×D12C2318yescomplemented
117#6772—24no—
118#6772C2318yescomplemented
119#6768—28no—
120#6716C2318yescomplemented
121#6715C2318yescomplemented
122#6710C2314yescomplemented
123C2×C3⋊#168C2312yes—
124C5×#213C2318yescomplemented
125C5×#213C2318yescomplemented
126C2×C5×C3⋊C8C2311yescharacteristic
127C2×C5×C3⋊C8C2311yescharacteristic
128C2×C5×C3⋊C8C2314yescomplemented
129#6662C2314yescomplemented
130#6658C2314yescomplemented
131#6657C2314yescomplemented
132#6656C2318yescomplemented
133#6653C2314yescomplemented
134#6652C2318yescomplemented
135#6649C2318yescomplemented
136D5×C3⋊C8C2318yescomplemented
137C2×C3×H(5,𝔽2)—51no—
138C2×#1009—51no—
139#5835—516no—
140C2×#950—52no—
141C2×#950—51no—
142C2×#949—51no—
143C2×#949—52no—
144C2×#948—51no—
145C2×#932—51no—
146C2×#932—52no—
147C22×#213—52no—
148C22×#213D511yescharacteristic, complemented
149C22×C5×D4—31no—
150C22×C5×D4C2×D311yescharacteristic, complemented
151C22×C22⋊D5—22no—
152C22×C22⋊D5—62no—
153#4144—24no—
154#4144—38no—
155#4144—64no—
156#4144C2×D318yescomplemented
157C2×#711—21no—
158C2×#711—32no—
159C2×#711—61no—
160C2×#711C2×D312yescomplemented
161C2×D4×D5—21no—
162C2×D4×D5—32no—
163C2×D4×D5—61no—
164C2×D4×D5C2×D312yescomplemented
165C2×#709—31no—
166C2×#709C2×D311yescharacteristic
167C2×#709C2×D311yescharacteristic, complemented
168C2×C5×D8—32no—
169C2×C5×D8—32no—
170C2×C5×D8—38no—
171C22×C5×C8—31no—
172C2×#687—32no—
173C2×#687—32no—
174#4078—38no—
175#4078—38no—
176C2×#686—32no—
177C2×#686—32no—
178C2×#681—31no—
179#4058—316no—
180#4057—316no—
181#4057—316no—
182D5×D8—316no—
183C2×Dic20—31no—
184#4050—38no—
185C2×D40—31no—
186C2×#677—31no—
187C2×#677—31no—
188#4047—38no—
189C2×#676—32no—
190C2×C8×D5—32no—
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—22no—
198C22×C5×D3—24no—
199C22×C5×D3—82no—
200C22×C3×D5—21no—
201C22×C3×D5—28no—
202C22×C3×D5—84no—
203C22×C3×D5C2×D412yes—
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×D12—24no—
221C5×D12—22no—
222C5×D12C2414yes—
223C3×C22⋊D5—24no—
224C3×C22⋊D5—28no—
225C3×C22⋊D5—28no—
226C3×C22⋊D5C2×D418yes—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—28no—
229C2×C3×Dic5C2×D412yes—
230C3×D20—21no—
231C3×D20C2×D414yes—
232C3×D20C2412yes—
233C3×C4×D5—24no—
234C3×C4×D5C2×D414yes—
235C3×C4×D5C2414yes—
236C3×Dic10—21no—
237C3×Dic10C2×D414yes—
238C3×Dic10C2412yes—
239#1203—28no—
240#1201—28no—
241D3×Dic5—28no—
242C3⋊#168C2414yes—
243C5×C3⋊C8C2412yes—
244C5×C3⋊C8C2412yes—
245C3×H(5,𝔽2)—58no—
246C3×H(5,𝔽2)—104no—
247C2×C3×#41—51no—
248C2×C3×#41—52no—
249C2×C3×#41—51no—
250C2×C3×#41—101no—
251C22×C3×D4—52no—
252C22×C3×D4—101no—
253C22×C3×D4—102no—
254C22×C3×D4C2×D511yescharacteristic, complemented
255#1009—58no—
256#1009—104no—
257C2×#239—101no—
258C2×D3×D4—101no—
259C2×D3×D4—102no—
260C2×#235—51no—
261C2×#235—52no—
262C22×D12—52no—
263C22×D12C2×D511yescharacteristic, complemented
264#950—516no—
265#950—58no—
266#949—58no—
267#949—516no—
268#948—58no—
269C2×#216—51no—
270C2×#215—52no—
271C2×#215—51no—
272C2×#214—52no—
273C2×#214—51no—
274#932—58no—
275#932—516no—
276C2×#213—52no—
277C2×#213—52no—
278C2×#213—516no—
279C2×#213—51no—
280C2×#213C2×D512yescomplemented
281C2×#213C2×D512yescomplemented
282C2×#213C2×D518yescomplemented
283C2×#208—51no—
284C2×#208—52no—
285C22×C3⋊C8—52no—
286C22×C3⋊C8C2×D511yescharacteristic, complemented
287C24×C5—21no—
288C24×C5—61no—
289C23×D5—22no—
290C23×D5—62no—
291C2×C5×D4—21no—
292C2×C5×D4—22no—
293C2×C5×D4—32no—
294C2×C5×D4—34no—
295C2×C5×D4—61no—
296C2×C5×D4—62no—
297C2×C5×D4C22×D312yes—
298C2×C5×D4C22×D314yescomplemented
299C22×C4×C5C22×D311yescharacteristic
300C2×C22⋊D5—21no—
301C2×C22⋊D5—22no—
302C2×C22⋊D5—216no—
303C2×C22⋊D5—22no—
304C2×C22⋊D5—61no—
305C2×C22⋊D5—62no—
306C2×C22⋊D5—616no—
307C2×C22⋊D5—62no—
308C2×C22⋊D5#6712yes—
309C22×Dic5—22no—
310C22×Dic5—62no—
311#711—24no—
312#711—28no—
313#711—38no—
314#711—64no—
315#711—68no—
316#711C22×D318yescomplemented
317D4×D5—28no—
318D4×D5—24no—
319D4×D5—38no—
320D4×D5—68no—
321D4×D5—64no—
322D4×D5C22×D318yescomplemented
323#709—22no—
324#709—34no—
325#709—62no—
326#709#6714yes—
327#709C22×D314yes—
328#709C22×D314yescomplemented
329C2×D20—31no—
330C2×D20#6711yescharacteristic
331C2×D20C22×D311yescharacteristic
332C2×C4×D5—21no—
333C2×C4×D5—61no—
334C2×C4×D5C22×D312yes—
335C2×Dic10—31no—
336C2×Dic10#6711yescharacteristic
337C2×Dic10C22×D311yescharacteristic
338C5×D8—38no—
339C5×D8—38no—
340C2×C5×C8—31no—
341C2×C5×C8—31no—
342C2×C5×C8—34no—
343#687—38no—
344#687—38no—
345#686—38no—
346#686—38no—
347#681—34no—
348C2×#168—32no—
349Dic20—34no—
350D40—34no—
351#677—34no—
352#677—34no—
353#676—38no—
354C8×D5—38no—
355C2×H(5,𝔽2)—51no—
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—31no—
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—44no—
377C2×C5×D3—84no—
378C2×C3×D5—24no—
379C2×C3×D5—22no—
380C2×C3×D5—42no—
381C2×C3×D5—88no—
382C2×C3×D5C22×D414yes—
383D3×D5—88no—
384C3×C4×C5C22×D411yescharacteristic
385C3×C4×C5C22×D412yes—
386C3×C4×C5C2511yescharacteristic
387Dic15—22no—
388C3×Dic5—22no—
389C3×Dic5C22×D414yes—
390C24×C3—21no—
391C24×C3—102no—
392C23×D3—21no—
393C23×D3—102no—
394C3×#41—54no—
395C3×#41—54no—
396C3×#41—58no—
397C3×#41—54no—
398C3×#41—104no—
399C3×#41—108no—
400C3×#41—102no—
401C2×C3×Q8—51no—
402C2×C3×Q8—51no—
403C2×C3×D4—21no—
404C2×C3×D4—22no—
405C2×C3×D4—52no—
406C2×C3×D4—58no—
407C2×C3×D4—51no—
408C2×C3×D4—51no—
409C2×C3×D4—104no—
410C2×C3×D4—102no—
411C2×C3×D4—108no—
412C2×C3×D4—1016no—
413C2×C3×D4—102no—
414C2×C3×D4—101no—
415C2×C3×D4C22×D512yes—
416C2×C3×D4C22×D514yescomplemented
417C22×C3×C4—52no—
418C22×C3×C4—102no—
419C22×C3×C4—101no—
420C22×C3×C4C22×D511yescharacteristic
421C2×#67—102no—
422C2×#67—101no—
423#239—108no—
424D3×D4—108no—
425D3×D4—1016no—
426#235—54no—
427#235—58no—
428#235—104no—
429#235—102no—
430C2×D12—21no—
431C2×D12—22no—
432C2×D12—51no—
433C2×D12—58no—
434C2×D12—104no—
435C2×D12—102no—
436C2×D12C22×D512yes—
437C2×D12C22×D514yescomplemented
438C2×C4×D3—102no—
439C2×C4×D3—101no—
440C2×Dic6—51no—
441#216—54no—
442#215—58no—
443#215—54no—
444#214—58no—
445#214—54no—
446#213—58no—
447#213—58no—
448#213—54no—
449#213C22×D518yescomplemented
450#213C22×D518yescomplemented
451#208—54no—
452#208—58no—
453C2×C3⋊C8—52no—
454C2×C3⋊C8—58no—
455C2×C3⋊C8C22×D511yescharacteristic
456C2×C3⋊C8C22×D511yescharacteristic
457C2×C3⋊C8C22×D514yescomplemented
458C23×C5—22no—
459C23×C5—24no—
460C23×C5—62no—
461C23×C5—64no—
462C23×C5—82no—
463C23×C5—242no—
464C23×C5C2×#6711yescharacteristic
465C22×D5—21no—
466C22×D5—28no—
467C22×D5—61no—
468C22×D5—68no—
469C22×D5—84no—
470C22×D5—244no—
471C22×D5C2×#6712yes—
472C5×D4—22no—
473C5×D4—24no—
474C5×D4—34no—
475C5×D4—62no—
476C5×D4—64no—
477C5×D4C23×D314yes—
478C2×C4×C5C2×#6711yescharacteristic
479C2×C4×C5C2×#6712yes—
480C2×C4×C5C23×D311yescharacteristic
481C2×C4×C5C23×D312yes—
482C22⋊D5—24no—
483C22⋊D5—28no—
484C22⋊D5—28no—
485C22⋊D5—64no—
486C22⋊D5—68no—
487C22⋊D5—68no—
488C22⋊D5C2×#6718yes—
489C2×Dic5—21no—
490C2×Dic5—28no—
491C2×Dic5—61no—
492C2×Dic5—68no—
493C2×Dic5C2×#6712yes—
494D20—21no—
495D20—32no—
496D20—61no—
497D20C2×#6714yes—
498D20C23×D312yes—
499C4×D5—24no—
500C4×D5—64no—
501C4×D5C2×#6714yes—
502C4×D5C23×D314yes—
503Dic10—21no—
504Dic10—32no—
505Dic10—61no—
506Dic10C2×#6714yes—
507Dic10C23×D312yes—
508C5×C8—32no—
509C5×C8—32no—
510#168—34no—
511H(5,𝔽2)—58no—
512H(5,𝔽2)—104no—
513H(5,𝔽2)—158no—
514H(5,𝔽2)—304no—
515C2×#41—51no—
516C2×#41—52no—
517C2×#41—51no—
518C2×#41—101no—
519C2×#41—152no—
520C2×#41—151no—
521C2×#41—301no—
522C22×D4—31no—
523C22×D4—52no—
524C22×D4—101no—
525C22×D4—102no—
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—32no—
542C2×D8—32no—
543C2×D8—38no—
544C2×D8—151no—
545C2×D8—1516no—
546C2×D8—152no—
547C2×D8—152no—
548#131—158no—
549C2×M16—152no—
550C2×M16—151no—
551C22×C8—31no—
552C22×C8—152no—
553C2×C3×C5—22no—
554C2×C3×C5—44no—
555C2×C3×C5#57612yescomplemented
556C2×C3×C5C23×D411yescharacteristic
557D15—42no—
558C3×D5—24no—
559C3×D5—42no—
560C5×D3—44no—
561C23×C3—22no—
562C23×C3—24no—
563C23×C3—52no—
564C23×C3—82no—
565C23×C3—108no—
566C23×C3—101no—
567C23×C3—404no—
568C23×C3D4×D511yescharacteristic
569C22×D3—22no—
570C22×D3—24no—
571C22×D3—82no—
572C22×D3—108no—
573C22×D3—101no—
574C22×D3—404no—
575C3×Q8—54no—
576C3×Q8—52no—
577C3×Q8—101no—
578C3×D4—22no—
579C3×D4—24no—
580C3×D4—58no—
581C3×D4—54no—
582C3×D4—52no—
583C3×D4—108no—
584C3×D4—108no—
585C3×D4—104no—
586C3×D4—101no—
587C3×D4C23×D514yes—
588C2×C3×C4—52no—
589C2×C3×C4—54no—
590C2×C3×C4—54no—
591C2×C3×C4—108no—
592C2×C3×C4—101no—
593C2×C3×C4—104no—
594C2×C3×C4D4×D511yescharacteristic
595C2×C3×C4D4×D512yes—
596C2×C3×C4C23×D511yescharacteristic
597C2×C3×C4C23×D512yes—
598#67—108no—
599#67—104no—
600C2×Dic3—101no—
601D12—22no—
602D12—24no—
603D12—52no—
604D12—108no—
605D12—101no—
606D12C23×D514yes—
607C4×D3—108no—
608C4×D3—104no—
609Dic6—52no—
610Dic6—101no—
611C3⋊C8—54no—
612C3⋊C8C23×D512yes—
613C3⋊C8C23×D512yes—
614C22×C5—22no—
615C22×C5—24no—
616C22×C5—44no—
617C22×C5—64no—
618C22×C5—84no—
619C22×C5—124no—
620C22×C5—244no—
621C22×C5C22×#6712yes—
622C22×C5C22×#6711yescharacteristic
623C2×D5—24no—
624C2×D5—22no—
625C2×D5—42no—
626C2×D5—62no—
627C2×D5—88no—
628C2×D5—122no—
629C2×D5—248no—
630C2×D5C22×#6714yes—
631C4×C5C22×#6711yescharacteristic
632C4×C5C22×#6712yes—
633C4×C5C24×D311yescharacteristic
634Dic5—22no—
635Dic5—62no—
636Dic5C22×#6714yes—
637C24—21no—
638C24—61no—
639C24—102no—
640C24—302no—
641#41—54no—
642#41—54no—
643#41—58no—
644#41—54no—
645#41—104no—
646#41—108no—
647#41—102no—
648#41—158no—
649#41—154no—
650#41—304no—
651#41—308no—
652#41—302no—
653C2×Q8—51no—
654C2×Q8—51no—
655C2×Q8—151no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—32no—
659C2×D4—34no—
660C2×D4—52no—
661C2×D4—58no—
662C2×D4—51no—
663C2×D4—51no—
664C2×D4—61no—
665C2×D4—62no—
666C2×D4—104no—
667C2×D4—102no—
668C2×D4—108no—
669C2×D4—1016no—
670C2×D4—102no—
671C2×D4—101no—
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—52no—
683C22×C4—102no—
684C22×C4—101no—
685C22×C4—302no—
686C22×C4—301no—
687C22×C4C2×D3×D511yescharacteristic
688Q16—154no—
689SD16—154no—
690SD16—154no—
691SD16—158no—
692SD16—158no—
693D8—38no—
694D8—38no—
695D8—154no—
696D8—158no—
697D8—158no—
698M16—158no—
699M16—154no—
700C2×C8—31no—
701C2×C8—31no—
702C2×C8—34no—
703C2×C8—158no—
704C2×C8—152no—
705C3×C5C2×#57611yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—24no—
708C22×C3—44no—
709C22×C3—54no—
710C22×C3—84no—
711C22×C3—104no—
712C22×C3—102no—
713C22×C3—202no—
714C22×C3—408no—
715C22×C3C2×D4×D512yes—
716C22×C3C2×D4×D511yescharacteristic
717C2×D3—24no—
718C2×D3—44no—
719C2×D3—84no—
720C2×D3—102no—
721C2×D3—202no—
722C2×D3—408no—
723C3×C4—54no—
724C3×C4—102no—
725C3×C4C2×D4×D511yescharacteristic
726C3×C4C2×D4×D512yes—
727C3×C4C24×D511yescharacteristic
728Dic3—102no—
729C2×C5—22no—
730C2×C5—44no—
731C2×C5—124no—
732C2×C5#583512yescomplemented
733C2×C5C23×#6711yescharacteristic
734D5—24no—
735D5—42no—
736D5—122no—
737C23—22no—
738C23—24no—
739C23—52no—
740C23—62no—
741C23—64no—
742C23—82no—
743C23—108no—
744C23—101no—
745C23—242no—
746C23—308no—
747C23—301no—
748C23—404no—
749C23—1204no—
750C23D5×#6711yescharacteristic
751Q8—54no—
752Q8—52no—
753Q8—101no—
754Q8—152no—
755Q8—301no—
756D4—22no—
757D4—24no—
758D4—34no—
759D4—58no—
760D4—54no—
761D4—52no—
762D4—62no—
763D4—64no—
764D4—108no—
765D4—108no—
766D4—104no—
767D4—101no—
768D4—152no—
769D4—308no—
770D4—308no—
771D4—304no—
772D4—301no—
773D4C22×D3×D514yes—
774C2×C4—52no—
775C2×C4—54no—
776C2×C4—54no—
777C2×C4—108no—
778C2×C4—101no—
779C2×C4—104no—
780C2×C4—308no—
781C2×C4—301no—
782C2×C4—304no—
783C2×C4D5×#6712yes—
784C2×C4D5×#6711yescharacteristic
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D511yescharacteristic
787C8—32no—
788C8—32no—
789C8—154no—
790C2×C3—22no—
791C2×C3—44no—
792C2×C3—104no—
793C2×C3—202no—
794C2×C3#6609112yescomplemented
795C2×C3C22×D4×D511yescharacteristic
796D3—44no—
797D3—202no—
798C5C2×#583511yescharacteristic, complemented, Sylow
799C22—22no—
800C22—24no—
801C22—44no—
802C22—54no—
803C22—64no—
804C22—84no—
805C22—104no—
806C22—102no—
807C22—124no—
808C22—202no—
809C22—244no—
810C22—302no—
811C22—408no—
812C22—602no—
813C22—1208no—
814C22C2×D5×#6712yes—
815C22C2×D5×#6711yescharacteristic
816C4—54no—
817C4—102no—
818C4—302no—
819C4C2×D5×#6711yescharacteristic
820C4C2×D5×#6712yes—
821C4C23×D3×D511yescharacteristic
822C3C2×#6609111yescharacteristic, complemented, Sylow
823C2—22no—
824C2—44no—
825C2—104no—
826C2—124no—
827C2—202no—
828C2—602no—
829C2#1175469112yesdirect product factor
830C2C22×D5×#6711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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×C3×#4144C2semidirect
2. C2×#92018C2semidirect
3. C2×#91821C2semidirect
4. C22×C5×#213C2semidirect
5. C2×#91490C2semidirect
6. C2×#91489C2semidirect
7. #11754691C2direct (N × H)
8. C2×#91478C2semidirect
9. C2×D5×#213C2semidirect
10. C2×#91311C2semidirect
11. C2×#91299C2semidirect
12. C2×#91283C2semidirect
14. C22×C3×C5×D4C22semidirect
15. C2×#6817C22semidirect
16. C22×C5×D12C22semidirect
19. C3×#4144C22semidirect
21. C2×C3×#711C22semidirect
23. C2×C3×D4×D5C22semidirect
25. C2×C3×#709C22semidirect
28. #92018C22semidirect
30. C2×D5×D12C22semidirect
31. C2×#6772C22semidirect
33. C2×#6716C22semidirect
34. #91821C22semidirect
35. C2×#6715C22semidirect
36. C2×#6710C22semidirect
37. C2×C5×#213C22semidirect
38. C2×C5×#213C22semidirect
39. C2×C5×#213C22semidirect
40. C22×C5×C3⋊C8C22semidirect
41. #91490C22semidirect
42. #91489C22semidirect
43. #91478C22semidirect
44. D5×#213C22semidirect
45. C2×#6662C22semidirect
46. C2×#6658C22semidirect
47. #91311C22semidirect
48. C2×#6657C22semidirect
49. C2×#6656C22semidirect
50. C2×#6653C22semidirect
51. #91299C22semidirect
52. C2×#6652C22semidirect
53. C2×#6649C22semidirect
54. #91283C22semidirect
55. C2×D5×C3⋊C8C22semidirect
58. C2×#4144D3semidirect
76. C2×C3×C5×D4C23semidirect
80. #6817C23semidirect
87. C2×C5×D12C23semidirect
96. C3×#711C23semidirect
99. C3×D4×D5C23semidirect
103. C3×#709C23semidirect
116. D5×D12C23semidirect
118. #6772C23semidirect
120. #6716C23semidirect
121. #6715C23semidirect
122. #6710C23semidirect
124. C5×#213C23semidirect
125. C5×#213C23semidirect
128. C2×C5×C3⋊C8C23semidirect
129. #6662C23semidirect
130. #6658C23semidirect
131. #6657C23semidirect
132. #6656C23semidirect
133. #6653C23semidirect
134. #6652C23semidirect
135. #6649C23semidirect
136. D5×C3⋊C8C23semidirect
148. C22×#213D5semidirect
150. C22×C5×D4C2×D3semidirect
156. #4144C2×D3semidirect
160. C2×#711C2×D3semidirect
164. C2×D4×D5C2×D3semidirect
167. C2×#709C2×D3semidirect
254. C22×C3×D4C2×D5semidirect
263. C22×D12C2×D5semidirect
280. C2×#213C2×D5semidirect
281. C2×#213C2×D5semidirect
282. C2×#213C2×D5semidirect
286. C22×C3⋊C8C2×D5semidirect
298. C2×C5×D4C22×D3semidirect
316. #711C22×D3semidirect
322. D4×D5C22×D3semidirect
328. #709C22×D3semidirect
416. C2×C3×D4C22×D5semidirect
437. C2×D12C22×D5semidirect
449. #213C22×D5semidirect
450. #213C22×D5semidirect
457. C2×C3⋊C8C22×D5semidirect
529. C22×D4D3×D5semidirect
555. C2×C3×C5#576semidirect
681. C2×D4C2×D3×D5semidirect
705. C3×C5C2×#576semidirect
732. C2×C5#5835semidirect
794. C2×C3#66091semidirect
798. C5C2×#5835semidirect
822. C3C2×#66091semidirect
829. C2#11754691direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41442
C2×#920182
C2×#918212
C22×C5×#2132
C2×#914902
C2×#914892
#117546912
C2×#914782
C2×D5×#2132
C2×#913112
C2×#912992
C2×#912832
C2×#660913
C2×#58355