Finite Group Databasebeta

← #14458956

Subgroups — #14458956

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5565C211yesmaximal, characteristic, complemented
2C3×#65884C211yesmaximal, characteristic, complemented
3D4×C3⋊#168C211yesmaximal, characteristic, complemented
4#11748547C211yesmaximal, characteristic, complemented
5#11748522C211yesmaximal, characteristic, complemented
6#11748511C211yesmaximal, characteristic, complemented
7#11748510C211yesmaximal, characteristic, complemented
8#11748461C211yesmaximal, characteristic, complemented
9#11748371C211yesmaximal, characteristic, complemented
10#11748364C211yesmaximal, characteristic, complemented
11C2×#90964C211yesmaximal, characteristic, complemented
12#11747034C211yesmaximal, characteristic, complemented
13C4×#6652C211yesmaximal, characteristic, complemented
14#11746896C211yesmaximal, characteristic, complemented
15#11746887C211yesmaximal, characteristic, complemented
16#10615345—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic, complemented
22C5×#939—21no—
23C5×#930C2211yescharacteristic
24C5×#930C2211yescharacteristic, complemented
25C5×#926C2211yescharacteristic, complemented
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C5×#898—21no—
28C5×#883—21no—
29C5×#67⋊C4—21no—
30C4×C5×D12C2211yescharacteristic, complemented
31C5×#870C2211yescharacteristic, complemented
32C3×#4083—21no—
33C3×#4076C2211yescharacteristic
34C3×#4070C2211yescharacteristic
35C3×#4040—21no—
36C3×#4030—21no—
37C3×D5×C22⋊C4—21no—
38C3×#4021C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C2×#6656C2211yescharacteristic, complemented
41C2×#6652C2211yescharacteristic
42C2×#6652C2211yescharacteristic
43#91114C2211yescharacteristic
44#91114C2211yescharacteristic, complemented
45C4⋊(C3⋊#168)C2211yescharacteristic, complemented
46C4×C3⋊#168C2211yescharacteristic, complemented
47#90989C2211yescharacteristic, complemented
48#90989C2211yescharacteristic, complemented
49#90986C2211yescharacteristic, complemented
50#90970C2211yescharacteristic, complemented
51#90970C2211yescharacteristic, complemented
52#90970C2211yescharacteristic, complemented
53#90966C2211yescharacteristic, complemented
54#90964C2211yescharacteristic
55#90964C2211yescharacteristic
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic
58#90964C2211yescharacteristic
59#90964C2211yescharacteristic
60#83495—51nomaximal, Hall
61C5×#553—31no—
62#65884D311yescharacteristic, complemented
63#65357—31no—
64#65355—31no—
65#65330—31no—
66#65327—31no—
67#65326—31no—
68#65325—31no—
69#65305—31no—
70C4×#686—31no—
71D4×#168—31no—
72#65292—31no—
73#65291—31no—
74#65259—31no—
75C2×#3941—31no—
76C23×C3×D5—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×C5×#67—21no—
81C2×C5×#67—21no—
82C22×C5×Dic3—21no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C3×#709—22no—
88C3×#709—41no—
89C2×C3×D20—22no—
90C2×C3×D20—21no—
91C2×C3×D20—41no—
92C2×C3×D20C2311yescharacteristic
93C2×C3×D20C2311yescharacteristic
94C2×C3×C4×D5—21no—
95C2×C3×C4×D5—21no—
96C2×C3×Dic10C2311yescharacteristic
97C3×C5×C4⋊C4D411yescharacteristic
98C3×C5×C22⋊C4D411yescharacteristic
99C3×C5×C22⋊C4D411yescharacteristic
100C3×C42×C5C2311yescharacteristic
101C2×C3⋊#168—41no—
102C2×C3⋊#168—41no—
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C5×#217—21no—
108C5×(C2×D3)⋊C4—21no—
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4—21no—
111C5×C4⋊Dic3—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×C4⋊Dic3C2311yescharacteristic
114C5×C4⋊Dic3C2311yescharacteristic
115C5×Dic3⋊C4—21no—
116C5×Dic3⋊C4—21no—
117C4×C5×Dic3—21no—
118C3×C22⋊Dic5—21no—
119C3×#685—21no—
120C3×#685—21no—
121C3×#685—21no—
122C3×#685—21no—
123C3×C4⋊Dic5C2311yescharacteristic
124C3×#683—21no—
125#6656—41no—
126#6652—22no—
127#6652—41no—
128C3×#546—51no—
129#5565D511yescharacteristic, complemented
130#5238—51no—
131#5233—51no—
132#5217—51no—
133C2×#832—51no—
134#5057—51no—
135#5056—51no—
136#5048—51no—
137#5044—51no—
138#5038—51no—
139#5035—51no—
140C4×#213—51no—
141D4×C3⋊C8—51no—
142#5009—51no—
143C2×#709C2×D311yescharacteristic
144C22×D20C2×D311yescharacteristic
145C5×#126—61no—
146C5×#125—31no—
147C5×#123—61no—
148C5×#121—31no—
149C5×#121—31no—
150C5×#121—61no—
151C4×C5×D4—31no—
152C4×C5×D4—61no—
153C4×C5×D4C2×D311yescharacteristic
154C5×#117—31no—
155C2×C5×C4⋊C4—31no—
156#4083—21no—
157C2×#687—31no—
158C2×#686—31no—
159C2×#686—31no—
160#4076C2×D311yescharacteristic
161#4070C2×D311yescharacteristic
162C22×#168—31no—
163C22×#168—31no—
164#4040—21no—
165#4030—21no—
166D5×C22⋊C4—21no—
167#4021C2×D311yescharacteristic
168C4×D20C2×D311yescharacteristic
169#3964—31no—
170C22⋊#168—31no—
171C22⋊#168—31no—
172#3942—31no—
173#3942—31no—
174#3942—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941—31no—
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×C5×D3—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—42no—
193C22×C3×D5—42no—
194C22×C3×D5—81no—
195C3×C5×D4—22no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205C5×#67—42no—
206C5×#67—81no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—81no—
211C5×D12—21no—
212C5×D12—21no—
213C4×C5×D3—81no—
214C3×C22⋊D5—42no—
215C3×C22⋊D5—81no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C3×D20—21no—
219C3×D20—21no—
220C3×D20—21no—
221C3×D20—42no—
222C3×D20#4112yes—
223C3×C4×D5—42no—
224C3×C4×D5—81no—
225C3×Dic10—21no—
226C3×Dic10—21no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3⋊#168—21no—
230C3⋊#168—21no—
231C2×C3×#41—51no—
232C22×C3×D4—51no—
233C3×#124—51no—
234C3×#123—101no—
235C3×C22⋊Q8—51no—
236C3×#121—51no—
237C3×#121—101no—
238C3×#120—101no—
239C3×C4×D4—51no—
240C3×C4×D4C2×D511yescharacteristic
241C2×C3×C22⋊C4—101no—
242C2×#215—51no—
243#939—21no—
244C2×#213—51no—
245C2×#213—51no—
246#930C2×D511yescharacteristic
247#930C2×D511yescharacteristic, complemented
248#926C2×D511yescharacteristic, complemented
249C2×C4⋊Dic3C2×D511yescharacteristic
250C22×C3⋊C8—51no—
251C22×C3⋊C8—51no—
252#898—21no—
253#883—21no—
254#67⋊C4—21no—
255C4×D12C2×D511yescharacteristic, complemented
256#870C2×D511yescharacteristic, complemented
257#835—51no—
258#835—51no—
259#835—51no—
260#832—51no—
261#832—51no—
262#832—51no—
263#832—51no—
264#832—51no—
265#832—51no—
266#830—51no—
267#830—51no—
268#809—51no—
269#808—51no—
270#807—51no—
271#807—51no—
272C4⋊(C3⋊C8)—51no—
273C4×C3⋊C8—51no—
274C23×D5—21no—
275C2×C5×D4—31no—
276C2×C5×D4—61no—
277C2×C5×D4—61no—
278C2×C5×D4#6711yescharacteristic
279C22×C4×C5—61no—
280C22×C4×C5—61no—
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—21no—
284C2×C22⋊D5—21no—
285#709—22no—
286#709—41no—
287C2×D20—22no—
288C2×D20—21no—
289C2×D20—41no—
290C2×D20C22×D311yescharacteristic
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—21no—
294C2×Dic10C22×D311yescharacteristic
295C5×C4⋊C4—31no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—61no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4—61no—
301C5×C4⋊C4#6711yescharacteristic
302C5×C22⋊C4—61no—
303C5×C22⋊C4—61no—
304C5×C22⋊C4—61no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4#6711yescharacteristic
307C5×C22⋊C4#6711yescharacteristic
308C42×C5—61no—
309C42×C5C22×D311yescharacteristic
310C22⋊Dic5—21no—
311#687—121no—
312#686—62no—
313#686—121no—
314#685—21no—
315#685—21no—
316#685—21no—
317#685—21no—
318C4⋊Dic5C22×D311yescharacteristic
319#683—21no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—31no—
323C2×#168—31no—
324C2×#168—121no—
325C2×#168—121no—
326#553—31no—
327#546—51no—
328#488—151no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—151no—
334#463—151no—
335#449—151no—
336#447—151no—
337C4×D8—151no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—21no—
345C22×C3×C5—21no—
346C22×C3×C5#13512yes—
347C22×C3×C5C22×D411yescharacteristic
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C3×D5—22no—
352C2×C3×D5—41no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—21no—
362C3×C4×C5C2×#4111yescharacteristic
363C3×C4×C5H(5,𝔽2)11yescharacteristic
364C3×Dic5—41no—
365C3×Dic5—41no—
366C5×Dic3—41no—
367C5×Dic3—41no—
368C5×Dic3—41no—
369C24×C3—101no—
370C3×#41—102no—
371C3×#41—201no—
372C2×C3×Q8—51no—
373C2×C3×D4—51no—
374C2×C3×D4—51no—
375C2×C3×D4—102no—
376C2×C3×D4—101no—
377C2×C3×D4—101no—
378C2×C3×D4—101no—
379C2×C3×D4—201no—
380C2×C3×D4C22⋊D511yescharacteristic
381C22×C3×C4—101no—
382C22×C3×C4—101no—
383C22×C3×C4C22×D511yescharacteristic
384C22×C3×C4C22×D511yescharacteristic
385C2×#67—21no—
386C2×#67—21no—
387C22×Dic3—21no—
388C2×D12C22×D511yescharacteristic
389C2×C4×D3—21no—
390C3×C4⋊C4—51no—
391C3×C4⋊C4—101no—
392C3×C4⋊C4C22⋊D511yescharacteristic
393C3×C22⋊C4—101no—
394C3×C22⋊C4—101no—
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4C22⋊D511yescharacteristic
399C3×C22⋊C4C22⋊D511yescharacteristic
400C3×C42C22×D511yescharacteristic
401#217—21no—
402#215—201no—
403#213—102no—
404#213—201no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408C4⋊Dic3—21no—
409C4⋊Dic3C22×D511yescharacteristic
410C4⋊Dic3C22×D511yescharacteristic
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—21no—
413Dic3⋊C4—21no—
414C4×Dic3—21no—
415C2×C3⋊C8—51no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—51no—
418C2×C3⋊C8—51no—
419C2×C3⋊C8—201no—
420C2×C3⋊C8—201no—
421C23×C5—61no—
422C23×C5C2×#6711yescharacteristic
423C23×C5C2×#6711yescharacteristic
424C22×D5—21no—
425C22×D5—21no—
426C22×D5—42no—
427C22×D5—42no—
428C22×D5—81no—
429C5×D4—22no—
430C5×D4—61no—
431C5×D4—61no—
432C5×D4—122no—
433C5×D4—241no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—61no—
439C2×C4×C5—61no—
440C2×C4×C5—61no—
441C2×C4×C5—241no—
442C2×C4×C5—241no—
443C2×C4×C5C2×#6711yescharacteristic
444C2×C4×C5C2×#6711yescharacteristic
445C2×C4×C5C2×#6711yescharacteristic
446C2×C4×C5C2×#6711yescharacteristic
447C2×C4×C5C23×D311yescharacteristic
448C22⋊D5—42no—
449C22⋊D5—81no—
450C2×Dic5—21no—
451C2×Dic5—21no—
452D20—21no—
453D20—21no—
454D20—21no—
455D20—42no—
456D20#23712yes—
457C4×D5—42no—
458C4×D5—81no—
459Dic10—21no—
460Dic10—21no—
461#168—61no—
462#168—61no—
463#168—61no—
464#168—61no—
465C2×#41—51no—
466C22×D4—51no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—151no—
471C22×C8—151no—
472#126—61no—
473#125—31no—
474#124—51no—
475#123—61no—
476#123—101no—
477C22⋊Q8—51no—
478#121—31no—
479#121—31no—
480#121—51no—
481#121—61no—
482#121—101no—
483#120—101no—
484C4×D4—31no—
485C4×D4—51no—
486C4×D4—61no—
487C4×D4D3×D511yescharacteristic
488#117—31no—
489C2×C4⋊C4—31no—
490C2×C22⋊C4—101no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—151no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C4×C8—151no—
508C2×C3×C5—22no—
509C2×C3×C5—41no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513C3×D5—42no—
514C3×D5—81no—
515C5×D3—81no—
516C23×C3—101no—
517C23×C3—101no—
518C23×C3—202no—
519C23×C3—202no—
520C23×C3—401no—
521C23×C3C2×C22⋊D511yescharacteristic
522C23×C3C2×C22⋊D511yescharacteristic
523C22×D3—21no—
524C3×Q8—101no—
525C3×Q8—101no—
526C3×D4—22no—
527C3×D4—52no—
528C3×D4—101no—
529C3×D4—101no—
530C3×D4—101no—
531C3×D4—202no—
532C3×D4—202no—
533C3×D4—401no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—101no—
539C2×C3×C4—101no—
540C2×C3×C4—202no—
541C2×C3×C4—401no—
542C2×C3×C4C2×C22⋊D511yescharacteristic
543C2×C3×C4C2×C22⋊D511yescharacteristic
544C2×C3×C4C2×C22⋊D511yescharacteristic
545C2×C3×C4C2×C22⋊D511yescharacteristic
546C2×C3×C4C23×D511yescharacteristic
547#67—42no—
548#67—81no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—81no—
553D12—21no—
554D12—21no—
555C4×D3—81no—
556C3⋊C8—101no—
557C3⋊C8—101no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5—121no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5#95012yes—
569C22×C5C22×#6711yescharacteristic
570C2×D5—22no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—84no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5—121no—
582C4×C5—121no—
583C4×C5—121no—
584C4×C5C2×#23711yescharacteristic
585C4×C5#100411yescharacteristic
586Dic5—41no—
587Dic5—41no—
588C24—101no—
589#41—102no—
590#41—201no—
591C2×Q8—51no—
592C2×D4—31no—
593C2×D4—51no—
594C2×D4—51no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—102no—
598C2×D4—101no—
599C2×D4—101no—
600C2×D4—101no—
601C2×D4—201no—
602C2×D4#120111yescharacteristic
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4C2×D3×D511yescharacteristic
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—151no—
613C2×C8—151no—
614C2×C8—151no—
615C2×C8—151no—
616C2×C8—601no—
617C2×C8—601no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—51no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—101no—
626C4⋊C4#120111yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—101no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4#120111yescharacteristic
637C22⋊C4#120111yescharacteristic
638C42—61no—
639C42C2×D3×D511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—102no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3—201no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—404no—
653C22×C3#409612yes—
654C22×C3C22×C22⋊D511yescharacteristic
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—201no—
663C3×C4—201no—
664C3×C4D5×#4111yescharacteristic
665C3×C4#414911yescharacteristic
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669C2×C5—22no—
670C2×C5—41no—
671C2×C5—241no—
672C2×C5#580611yescharacteristic
673C2×C5C2×#95011yescharacteristic
674C2×C5#583511yescharacteristic
675D5—42no—
676D5—81no—
677C23—61no—
678C23—101no—
679C23—101no—
680C23—202no—
681C23—202no—
682C23—401no—
683C23C2×#120111yescharacteristic
684C23C2×#120111yescharacteristic
685Q8—101no—
686Q8—101no—
687D4—22no—
688D4—52no—
689D4—61no—
690D4—61no—
691D4—101no—
692D4—101no—
693D4—101no—
694D4—122no—
695D4—202no—
696D4—202no—
697D4—241no—
698D4—401no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—202no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4—401no—
712C2×C4C2×#120111yescharacteristic
713C2×C4C2×#120111yescharacteristic
714C2×C4C2×#120111yescharacteristic
715C2×C4C2×#120111yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—301no—
718C8—301no—
719C8—301no—
720C8—301no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3—202no—
724C2×C3—401no—
725C2×C3C2×#409611yescharacteristic
726C2×C3#6616311yescharacteristic
727C2×C3#6616911yescharacteristic
728D3—81no—
729C5#8349511yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—102no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—201no—
743C22—201no—
744C22—404no—
745C22#9129712yes—
746C22C22×#120111yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—201no—
755C4—201no—
756C4D5×#23711yescharacteristic
757C4#9202611yescharacteristic
758C3#1061534511yescharacteristic, complemented, Sylow
759C2—22no—
760C2—41no—
761C2—202no—
762C2—241no—
763C2—401no—
764C2C2×#9129711yescharacteristic
765C2#1175496111yescharacteristic
766C2#1175530111yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5565C2semidirect
2. C3×#65884C2semidirect
3. D4×C3⋊#168C2semidirect
4. #11748547C2semidirect
5. #11748522C2semidirect
6. #11748511C2semidirect
7. #11748510C2semidirect
8. #11748461C2semidirect
9. #11748371C2semidirect
10. #11748364C2semidirect
11. C2×#90964C2semidirect
12. #11747034C2semidirect
13. C4×#6652C2semidirect
14. #11746896C2semidirect
15. #11746887C2semidirect
21. C22×C3⋊#168C22semidirect
24. C5×#930C22semidirect
25. C5×#926C22semidirect
30. C4×C5×D12C22semidirect
31. C5×#870C22semidirect
40. C2×#6656C22semidirect
44. #91114C22semidirect
45. C4⋊(C3⋊#168)C22semidirect
46. C4×C3⋊#168C22semidirect
47. #90989C22semidirect
48. #90989C22semidirect
49. #90986C22semidirect
50. #90970C22semidirect
51. #90970C22semidirect
52. #90970C22semidirect
53. #90966C22semidirect
62. #65884D3semidirect
129. #5565D5semidirect
247. #930C2×D5semidirect
248. #926C2×D5semidirect
255. C4×D12C2×D5semidirect
256. #870C2×D5semidirect
640. C3×C5#3297semidirect
729. C5#83495semidirect
758. C3#10615345semidirect

Maximal subgroups

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

subgroupindex
C5×#55652
C3×#658842
D4×C3⋊#1682
#117485472
#117485222
#117485112
#117485102
#117484612
#117483712
#117483642
C2×#909642
#117470342
C4×#66522
#117468962
#117468872
#106153453
#834955