Finite Group Databasebeta

← C2×#11756538 #14510132

Subgroups — C2×#11756538 #14510132

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92101C211yesmaximal, characteristic, complemented
2C2×#92098C211yesmaximal, characteristic, complemented
3C2×C3×C5×#137C211yesmaximal, characteristic, complemented
4C2×#91839C211yesmaximal, characteristic, complemented
5C22×#6718C211yesmaximal, characteristic, complemented
6#11756538C2116yesmaximal, direct product factor
7C2×#91807C212yesmaximal, complemented
8C2×Q16×D15C212yesmaximal, complemented
9C2×#91805C212yesmaximal, complemented
10C2×#91804C212yesmaximal, complemented
11C2×#91798C211yesmaximal, characteristic, complemented
12C2×#91796C211yesmaximal, characteristic, complemented
13C2×#66113—31nomaximal, Hall
14C2×C3×C5×#41C2211yescharacteristic
15C22×C3×C5×Q8C2211yescharacteristic
16#92101—24no—
17#92101C2218yescomplemented
18#92098—24no—
19#92098C2218yescomplemented
20C2×#6821—21no—
21C2×#6821C2212yes—
22C2×Q8×D15—21no—
23C2×Q8×D15C2212yes—
24C2×Q8×D15C2212yes—
25C2×#6819—22no—
26C2×#6819C2212yes—
27C2×#6817—22no—
28C2×#6817—21no—
29C2×#6817C2211yescharacteristic
30C2×#6817C2211yescharacteristic
31C22×Dic30—21no—
32C22×Dic30C2211yescharacteristic
33C3×C5×#137C2218yescomplemented
34C2×C3×C5×Q16C2212yes—
35C2×C3×C5×SD16C2212yes—
36C2×C3×C5×M16C2211yescharacteristic
37#91839C2218yescomplemented
38C2×#6718C2212yes—
39C2×#6718C2212yes—
40C2×#6718C2211yescharacteristic
41C2×#6718C2218yescomplemented
42C2×#6717C2211yescharacteristic
43C2×#6716C2211yescharacteristic
44C2×#6715C2211yescharacteristic
45C22×C3⋊#168C2211yescharacteristic
46#91807C22116yescomplemented
47Q16×D15C22116yescomplemented
48#91805C22116yescomplemented
49#91804C22116yescomplemented
50#91798C2218yescomplemented
51#91796C2218yescomplemented
52C2×Dic60C2212yes—
53C2×#6706C2212yes—
54C2×#6705C2212yes—
55C2×C8×D15C2212yes—
56C2×#5779—51nomaximal, Hall
57C2×#4150—31no—
58C2×#4147—31no—
59C2×C5×#137D311yescharacteristic, complemented
60C2×#4096—31no—
61C22×#689—31no—
62#66113—316no—
63C2×#4064—32no—
64C2×D5×Q16—32no—
65C2×#4062—32no—
66C2×#4061—32no—
67C2×#4055—31no—
68C2×#4053—31no—
69C3×C5×#41—22no—
70C3×C5×#41C2314yes—
71C2×C3×C5×Q8—21no—
72C2×C3×C5×Q8—22no—
73C2×C3×C5×Q8C2311yescharacteristic
74C2×C3×C5×Q8C2312yes—
75C2×C3×C5×Q8C2314yes—
76C2×C3×C5×D4—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C22×C3×C4×C5—21no—
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—21no—
82C2×#1220—22no—
83C2×#1220D412yes—
84C22×Dic15—21no—
85C22×Dic15—22no—
86#6821—28no—
87#6821—24no—
88#6821C2318yes—
89Q8×D15—24no—
90Q8×D15—24no—
91Q8×D15—28no—
92Q8×D15C2318yes—
93Q8×D15C2318yes—
94#6819—216no—
95#6819—24no—
96#6819C2318yes—
97#6817—22no—
98#6817—216no—
99#6817—28no—
100#6817D414yes—
101#6817C2314yes—
102#6817C2314yes—
103C2×D60—22no—
104C2×D60D411yescharacteristic
105C2×D60C2311yescharacteristic
106C2×C4×D15—22no—
107C2×C4×D15—22no—
108C2×C4×D15—21no—
109C2×C4×D15—22no—
110C2×C4×D15C2312yes—
111C2×Dic30—21no—
112C2×Dic30—22no—
113C2×Dic30—22no—
114C2×Dic30—22no—
115C2×Dic30—28no—
116C2×Dic30D411yescharacteristic
117C2×Dic30C2312yes—
118C2×Dic30C2311yescharacteristic
119C2×Dic30C2314yes—
120C3×C5×Q16C2318yes—
121C3×C5×SD16C2318yes—
122C3×C5×M16C2314yes—
123C2×C3×C5×C8C2312yes—
124#6718C2318yes—
125#6718C2318yes—
126#6718C2314yes—
127#6717C2314yes—
128#6716C2314yes—
129#6715C2314yes—
130C2×C3⋊#168C2311yescharacteristic
131C2×C3⋊#168C2311yescharacteristic
132C2×C3⋊#168C2314yes—
133Dic60C2318yes—
134#6706C2318yes—
135#6705C2318yes—
136C8×D15C2318yes—
137C2×#1010—51no—
138C2×#1007—51no—
139C2×C3×#137D511yescharacteristic, complemented
140C2×#950—51no—
141C22×#216—51no—
142#5779—516no—
143C2×#918—52no—
144C2×D3×Q16—52no—
145C2×#916—52no—
146C2×#915—52no—
147C2×#909—51no—
148C2×#907—51no—
149C2×C5×#41C2×D311yescharacteristic
150C22×C5×Q8C2×D311yescharacteristic
151#4150—38no—
152#4150—64no—
153#4147—38no—
154#4147—64no—
155C2×#713—32no—
156C2×#713—61no—
157C2×Q8×D5—32no—
158C2×Q8×D5—32no—
159C2×Q8×D5—61no—
160C2×#711—32no—
161C2×#711—62no—
162C2×#709—31no—
163C2×#709—31no—
164C2×#709—61no—
165C2×#709—62no—
166C22×Dic10—31no—
167C22×Dic10—61no—
168C5×#137C2×D318yescomplemented
169C2×C5×Q16C2×D312yes—
170C2×C5×SD16C2×D312yes—
171C2×C5×M16C2×D311yescharacteristic
172#4096—38no—
173C2×#689—32no—
174C2×#689—32no—
175C2×#689—31no—
176C2×#689—38no—
177C2×#688—31no—
178C2×#687—31no—
179C2×#686—31no—
180C22×#168—31no—
181#4064—316no—
182D5×Q16—316no—
183#4062—316no—
184#4061—316no—
185#4055—38no—
186#4053—38no—
187C2×Dic20—32no—
188C2×#677—32no—
189C2×#676—32no—
190C2×C8×D5—32no—
191C2×#578—151noSylow
192C23×C3×C5—21no—
193C23×C3×C5C2×D411yescharacteristic
194C22×D15—21no—
195C22×D15C2×D412yes—
196C3×C5×Q8—21no—
197C3×C5×Q8—22no—
198C3×C5×Q8—24no—
199C3×C5×Q8C2412yes—
200C3×C5×Q8C2414yes—
201C3×C5×D4—24no—
202C3×C5×D4—21no—
203C3×C5×D4C2412yes—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—22no—
206C2×C3×C4×C5—24no—
207C2×C3×C4×C5—24no—
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2×D412yes—
210C2×C3×C4×C5C2411yescharacteristic
211C2×C3×C4×C5C2412yes—
212#1220—24no—
213#1220—28no—
214#1220C2×D418yes—
215C2×Dic15—21no—
216C2×Dic15—22no—
217C2×Dic15—24no—
218C2×Dic15—28no—
219C2×Dic15C2×D412yes—
220D60—28no—
221D60—21no—
222D60C2×D414yes—
223D60C2412yes—
224C4×D15—28no—
225C4×D15—28no—
226C4×D15—24no—
227C4×D15—28no—
228C4×D15C2×D414yes—
229C4×D15C2414yes—
230Dic30—24no—
231Dic30—22no—
232Dic30—21no—
233Dic30—28no—
234Dic30—28no—
235Dic30C2×D414yes—
236Dic30C2414yes—
237Dic30C2412yes—
238C3×C5×C8C2414yes—
239C3⋊#168C2412yes—
240C3⋊#168C2412yes—
241C2×C3×#41C2×D511yescharacteristic
242C22×C3×Q8C2×D511yescharacteristic
243#1010—58no—
244#1010—104no—
245#1007—58no—
246#1007—104no—
247C2×#239—52no—
248C2×#239—101no—
249C2×D3×Q8—52no—
250C2×D3×Q8—52no—
251C2×D3×Q8—101no—
252C2×#237—52no—
253C2×#237—102no—
254C2×#235—51no—
255C2×#235—51no—
256C2×#235—101no—
257C2×#235—102no—
258C22×Dic6—51no—
259C22×Dic6—101no—
260C3×#137C2×D518yescomplemented
261C2×C3×Q16C2×D512yes—
262C2×C3×SD16C2×D512yes—
263C2×C3×M16C2×D511yescharacteristic
264#950—58no—
265C2×#216—52no—
266C2×#216—52no—
267C2×#216—51no—
268C2×#216—58no—
269C2×#215—51no—
270C2×#214—51no—
271C2×#213—51no—
272C22×C3⋊C8—51no—
273#918—516no—
274D3×Q16—516no—
275#916—516no—
276#915—516no—
277#909—58no—
278#907—58no—
279C2×Dic12—52no—
280C2×#204—52no—
281C2×ΓL(1,𝔽25)—52no—
282C2×D3×C8—52no—
283C5×#41—22no—
284C5×#41C22×D314yes—
285C2×C5×Q8—21no—
286C2×C5×Q8—22no—
287C2×C5×Q8C22×D312yes—
288C2×C5×Q8C22×D311yescharacteristic
289C2×C5×Q8C22×D314yes—
290C2×C5×D4—21no—
291C2×C5×D4C22×D311yescharacteristic
292C22×C4×C5—21no—
293C22×C4×C5—21no—
294C22×C4×C5C22×D311yescharacteristic
295C2×C22⋊D5—32no—
296C2×C22⋊D5—62no—
297C2×C22⋊D5—61no—
298C22×Dic5—62no—
299C22×Dic5—61no—
300#713—38no—
301#713—64no—
302#713—68no—
303Q8×D5—38no—
304Q8×D5—38no—
305Q8×D5—68no—
306Q8×D5—64no—
307Q8×D5—64no—
308#711—38no—
309#711—64no—
310#711—616no—
311#709—34no—
312#709—34no—
313#709—34no—
314#709—68no—
315#709—616no—
316#709—62no—
317C2×D20—31no—
318C2×D20—31no—
319C2×D20—62no—
320C2×C4×D5—32no—
321C2×C4×D5—62no—
322C2×C4×D5—62no—
323C2×C4×D5—62no—
324C2×C4×D5—61no—
325C2×Dic10—31no—
326C2×Dic10—32no—
327C2×Dic10—34no—
328C2×Dic10—31no—
329C2×Dic10—68no—
330C2×Dic10—62no—
331C2×Dic10—62no—
332C2×Dic10—61no—
333C2×Dic10—62no—
334C5×Q16C22×D318yes—
335C5×SD16C22×D318yes—
336C5×M16C22×D314yes—
337C2×C5×C8C22×D312yes—
338#689—34no—
339#689—38no—
340#689—38no—
341#688—34no—
342#687—34no—
343#686—34no—
344C2×#168—34no—
345C2×#168—31no—
346C2×#168—31no—
347Dic20—38no—
348#677—38no—
349#676—38no—
350C8×D5—38no—
351C2×2−1+4—151no—
352C2×2−1+4—151no—
353#578—1516no—
354C2×#137—152no—
355C2×#137—152no—
356C2×#137—151no—
357C2×#137D1511yescharacteristic, complemented
358C2×#135—151no—
359C2×#135—152no—
360C22×Q16—151no—
361C22×Q16—152no—
362C2×#131—151no—
363C22×C3×C5—22no—
364C22×C3×C5—22no—
365C22×C3×C5—42no—
366C22×C3×C5C22×D412yes—
367C22×C3×C5C22×D411yescharacteristic
368C2×D15—24no—
369C2×D15—22no—
370C2×D15—42no—
371C2×D15C22×D414yes—
372C3×C4×C5—22no—
373C3×C4×C5—24no—
374C3×C4×C5C22×D411yescharacteristic
375C3×C4×C5C22×D412yes—
376C3×C4×C5C2511yescharacteristic
377Dic15—22no—
378Dic15—24no—
379Dic15C22×D414yes—
380C3×#41—22no—
381C3×#41C22×D514yes—
382C2×C3×Q8—21no—
383C2×C3×Q8—22no—
384C2×C3×Q8C22×D511yescharacteristic
385C2×C3×Q8C22×D512yes—
386C2×C3×Q8C22×D514yes—
387C2×C3×D4—21no—
388C2×C3×D4C22×D511yescharacteristic
389C22×C3×C4—21no—
390C22×C3×C4—21no—
391C22×C3×C4C22×D511yescharacteristic
392C2×#67—52no—
393C2×#67—102no—
394C2×#67—101no—
395C22×Dic3—102no—
396C22×Dic3—101no—
397#239—58no—
398#239—104no—
399#239—108no—
400D3×Q8—58no—
401D3×Q8—58no—
402D3×Q8—108no—
403D3×Q8—104no—
404D3×Q8—104no—
405#237—58no—
406#237—104no—
407#237—1016no—
408#235—54no—
409#235—54no—
410#235—54no—
411#235—108no—
412#235—1016no—
413#235—102no—
414C2×D12—51no—
415C2×D12—51no—
416C2×D12—102no—
417C2×C4×D3—52no—
418C2×C4×D3—102no—
419C2×C4×D3—102no—
420C2×C4×D3—102no—
421C2×C4×D3—101no—
422C2×Dic6—51no—
423C2×Dic6—52no—
424C2×Dic6—51no—
425C2×Dic6—54no—
426C2×Dic6—108no—
427C2×Dic6—102no—
428C2×Dic6—102no—
429C2×Dic6—101no—
430C2×Dic6—102no—
431C3×Q16C22×D518yes—
432C3×SD16C22×D518yes—
433C3×M16C22×D514yes—
434C2×C3×C8C22×D512yes—
435#216—58no—
436#216—58no—
437#216—54no—
438#215—54no—
439#214—54no—
440#213—54no—
441C2×C3⋊C8—51no—
442C2×C3⋊C8—51no—
443C2×C3⋊C8—54no—
444Dic12—58no—
445#204—58no—
446ΓL(1,𝔽25)—58no—
447D3×C8—58no—
448C23×C5—21no—
449C23×C5D3×D411yescharacteristic
450C22×D5—32no—
451C22×D5—61no—
452C5×Q8—21no—
453C5×Q8—24no—
454C5×Q8—22no—
455C5×Q8C23×D312yes—
456C5×Q8C23×D314yes—
457C5×D4—24no—
458C5×D4—21no—
459C5×D4C23×D312yes—
460C2×C4×C5—21no—
461C2×C4×C5—22no—
462C2×C4×C5—24no—
463C2×C4×C5—24no—
464C2×C4×C5D3×D411yescharacteristic
465C2×C4×C5D3×D412yes—
466C2×C4×C5C23×D311yescharacteristic
467C2×C4×C5C23×D312yes—
468C22⋊D5—38no—
469C22⋊D5—68no—
470C22⋊D5—64no—
471C2×Dic5—32no—
472C2×Dic5—68no—
473C2×Dic5—61no—
474C2×Dic5—62no—
475C2×Dic5—64no—
476D20—34no—
477D20—32no—
478D20—68no—
479D20—61no—
480C4×D5—34no—
481C4×D5—34no—
482C4×D5—68no—
483C4×D5—68no—
484C4×D5—68no—
485C4×D5—64no—
486Dic10—34no—
487Dic10—34no—
488Dic10—32no—
489Dic10—68no—
490Dic10—68no—
491Dic10—64no—
492Dic10—62no—
493Dic10—61no—
494C5×C8C23×D314yes—
495#168—32no—
496#168—32no—
4972−1+4—158no—
4982−1+4—158no—
4992−1+4—304no—
5002−1+4—304no—
501C2×#41—151no—
502C2×#41—152no—
503C2×#41—152no—
504C2×#41—151no—
505C2×#41—302no—
506C2×#41—301no—
507C2×#41—302no—
508C2×#41—301no—
509C2×#41C2×D1511yescharacteristic
510C22×Q8—152no—
511C22×Q8—152no—
512C22×Q8—151no—
513C22×Q8—301no—
514C22×Q8—301no—
515C22×Q8C2×D1511yescharacteristic
516#137—1516no—
517#137—1516no—
518#137—158no—
519#137C2×D1518yescomplemented
520#135—158no—
521#135—1516no—
522C2×Q16—151no—
523C2×Q16—152no—
524C2×Q16—152no—
525C2×Q16—158no—
526C2×Q16—1516no—
527C2×Q16—152no—
528C2×Q16C2×D1512yes—
529C2×SD16—151no—
530C2×SD16—151no—
531C2×SD16—152no—
532C2×SD16C2×D1512yes—
533C2×D8—151no—
534#131—158no—
535C2×M16—152no—
536C2×M16C2×D1511yescharacteristic
537C22×C8—151no—
538C22×C8—152no—
539C2×C3×C5—22no—
540C2×C3×C5—42no—
541C2×C3×C5#57812yescomplemented
542C2×C3×C5C23×D411yescharacteristic
543D15—24no—
544D15—42no—
545C23×C3—21no—
546C23×C3D4×D511yescharacteristic
547C22×D3—52no—
548C22×D3—101no—
549C3×Q8—21no—
550C3×Q8—24no—
551C3×Q8—22no—
552C3×Q8C23×D512yes—
553C3×Q8C23×D514yes—
554C3×D4—24no—
555C3×D4—21no—
556C3×D4C23×D512yes—
557C2×C3×C4—21no—
558C2×C3×C4—22no—
559C2×C3×C4—24no—
560C2×C3×C4—24no—
561C2×C3×C4D4×D511yescharacteristic
562C2×C3×C4D4×D512yes—
563C2×C3×C4C23×D511yescharacteristic
564C2×C3×C4C23×D512yes—
565#67—58no—
566#67—108no—
567#67—104no—
568C2×Dic3—52no—
569C2×Dic3—108no—
570C2×Dic3—101no—
571C2×Dic3—102no—
572C2×Dic3—104no—
573D12—54no—
574D12—52no—
575D12—108no—
576D12—101no—
577C4×D3—54no—
578C4×D3—54no—
579C4×D3—108no—
580C4×D3—108no—
581C4×D3—108no—
582C4×D3—104no—
583Dic6—54no—
584Dic6—54no—
585Dic6—52no—
586Dic6—108no—
587Dic6—108no—
588Dic6—104no—
589Dic6—102no—
590Dic6—101no—
591C3×C8C23×D514yes—
592C3⋊C8—52no—
593C3⋊C8—52no—
594C22×C5—22no—
595C22×C5—22no—
596C22×C5—42no—
597C22×C5C2×D3×D412yes—
598C22×C5C2×D3×D411yescharacteristic
599C2×D5—34no—
600C2×D5—64no—
601C2×D5—62no—
602C2×D5—122no—
603C4×C5—22no—
604C4×C5—24no—
605C4×C5C2×D3×D412yes—
606C4×C5C2×D3×D411yescharacteristic
607C4×C5C24×D311yescharacteristic
608Dic5—34no—
609Dic5—62no—
610Dic5—64no—
611#41—22no—
612#41—154no—
613#41—154no—
614#41—158no—
615#41—158no—
616#41—154no—
617#41—3016no—
618#41—308no—
619#41—304no—
620#41—304no—
621#41—3016no—
622#41—308no—
623#41—302no—
624#41C22×D1514yes—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—151no—
628C2×Q8—158no—
629C2×Q8—158no—
630C2×Q8—151no—
631C2×Q8—152no—
632C2×Q8—154no—
633C2×Q8—302no—
634C2×Q8—302no—
635C2×Q8—308no—
636C2×Q8—304no—
637C2×Q8—304no—
638C2×Q8—308no—
639C2×Q8—301no—
640C2×Q8—302no—
641C2×Q8C22×D1511yescharacteristic
642C2×Q8C22×D1512yes—
643C2×Q8C22×D1514yes—
644C2×D4—21no—
645C2×D4—152no—
646C2×D4—151no—
647C2×D4—151no—
648C2×D4—302no—
649C2×D4—302no—
650C2×D4—301no—
651C2×D4C22×D1511yescharacteristic
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—152no—
655C22×C4—302no—
656C22×C4—302no—
657C22×C4—302no—
658C22×C4—302no—
659C22×C4—301no—
660C22×C4—301no—
661C22×C4C22×D1511yescharacteristic
662Q16—154no—
663Q16—158no—
664Q16—158no—
665Q16—158no—
666Q16C22×D1518yes—
667SD16—154no—
668SD16—154no—
669SD16—158no—
670SD16C22×D1518yes—
671D8—154no—
672M16—158no—
673M16C22×D1514yes—
674C2×C8—151no—
675C2×C8—151no—
676C2×C8—154no—
677C2×C8—158no—
678C2×C8C22×D1512yes—
679C3×C5C2×#57811yescharacteristic, complemented, Hall
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—42no—
683C22×C3C2×D4×D512yes—
684C22×C3C2×D4×D511yescharacteristic
685C2×D3—54no—
686C2×D3—104no—
687C2×D3—102no—
688C2×D3—202no—
689C3×C4—22no—
690C3×C4—24no—
691C3×C4C2×D4×D512yes—
692C3×C4C2×D4×D511yescharacteristic
693C3×C4C24×D511yescharacteristic
694Dic3—54no—
695Dic3—102no—
696Dic3—104no—
697C2×C5—22no—
698C2×C5—42no—
699C2×C5#577912yescomplemented
700C2×C5C22×D3×D411yescharacteristic
701D5—64no—
702D5—122no—
703C23—21no—
704C23—152no—
705C23—301no—
706C23D4×D1511yescharacteristic
707Q8—24no—
708Q8—22no—
709Q8—21no—
710Q8—154no—
711Q8—152no—
712Q8—154no—
713Q8—308no—
714Q8—308no—
715Q8—304no—
716Q8—301no—
717Q8—302no—
718Q8C23×D1512yes—
719Q8C23×D1514yes—
720D4—24no—
721D4—21no—
722D4—158no—
723D4—154no—
724D4—152no—
725D4—308no—
726D4—308no—
727D4—304no—
728D4—301no—
729D4C23×D1512yes—
730C2×C4—24no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—152no—
735C2×C4—154no—
736C2×C4—154no—
737C2×C4—308no—
738C2×C4—308no—
739C2×C4—308no—
740C2×C4—308no—
741C2×C4—304no—
742C2×C4—301no—
743C2×C4—302no—
744C2×C4—304no—
745C2×C4D4×D1512yes—
746C2×C4D4×D1511yescharacteristic
747C2×C4C23×D1512yes—
748C2×C4C23×D1511yescharacteristic
749C8—152no—
750C8—152no—
751C8C23×D1514yes—
752C2×C3—22no—
753C2×C3—42no—
754C2×C3#6611312yescomplemented
755C2×C3C22×D4×D511yescharacteristic
756D3—104no—
757D3—202no—
758C5C2×#577911yescharacteristic, complemented, Sylow
759C22—22no—
760C22—22no—
761C22—42no—
762C22—154no—
763C22—304no—
764C22—302no—
765C22—602no—
766C22C2×D4×D1512yes—
767C22C2×D4×D1511yescharacteristic
768C4—22no—
769C4—24no—
770C4—154no—
771C4—302no—
772C4—304no—
773C4C2×D4×D1512yes—
774C4C2×D4×D1511yescharacteristic
775C4C24×D1511yescharacteristic
776C3C2×#6611311yescharacteristic, complemented, Sylow
777C2—22no—
778C2—42no—
779C2—304no—
780C2—602no—
781C2#1175653812yesdirect product factor
782C2C22×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×#578
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×#92101C2semidirect
2. C2×#92098C2semidirect
3. C2×C3×C5×#137C2semidirect
4. C2×#91839C2semidirect
5. C22×#6718C2semidirect
6. #11756538C2direct (N × H)
7. C2×#91807C2semidirect
8. C2×Q16×D15C2semidirect
9. C2×#91805C2semidirect
10. C2×#91804C2semidirect
11. C2×#91798C2semidirect
12. C2×#91796C2semidirect
17. #92101C22semidirect
19. #92098C22semidirect
33. C3×C5×#137C22semidirect
37. #91839C22semidirect
41. C2×#6718C22semidirect
46. #91807C22semidirect
47. Q16×D15C22semidirect
48. #91805C22semidirect
49. #91804C22semidirect
50. #91798C22semidirect
51. #91796C22semidirect
59. C2×C5×#137D3semidirect
139. C2×C3×#137D5semidirect
168. C5×#137C2×D3semidirect
260. C3×#137C2×D5semidirect
357. C2×#137D15semidirect
519. #137C2×D15semidirect
541. C2×C3×C5#578semidirect
679. C3×C5C2×#578semidirect
699. C2×C5#5779semidirect
754. C2×C3#66113semidirect
758. C5C2×#5779semidirect
776. C3C2×#66113semidirect
781. C2#11756538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#921012
C2×#920982
C2×C3×C5×#1372
C2×#918392
C22×#67182
#117565382
C2×#918072
C2×Q16×D152
C2×#918052
C2×#918042
C2×#917982
C2×#917962
C2×#661133
C2×#57795