Finite Group Databasebeta

← #14458613

Subgroups — #14458613

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#546C211yesmaximal, characteristic
2#11756300C211yesmaximal, characteristic, complemented
3#11751340C211yesmaximal, characteristic, complemented
4#11751334C211yesmaximal, characteristic, complemented
5#11751319C211yesmaximal, characteristic, complemented
6C2×#91116C211yesmaximal, characteristic, complemented
7#11751157C211yesmaximal, characteristic, complemented
8#11751155C211yesmaximal, characteristic, complemented
9#11751152C211yesmaximal, characteristic, complemented
10#11751144C211yesmaximal, characteristic, complemented
11#11751142C211yesmaximal, characteristic, complemented
12#11751136C211yesmaximal, characteristic, complemented
13C4×#6716C211yesmaximal, characteristic, complemented
14D4×C3⋊#168C211yesmaximal, characteristic, complemented
15#11751110C211yesmaximal, characteristic, complemented
16#10615225—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C3×C5×#124C2211yescharacteristic
20C3×C5×#123—21no—
21C3×C5×C22⋊Q8C2211yescharacteristic
22C3×C5×#121—21no—
23C3×C5×#121C2211yescharacteristic
24C3×C5×#120—21no—
25C3×C4×C5×D4C2211yescharacteristic
26C3×C4×C5×D4C2211yescharacteristic
27C2×C3×C5×C22⋊C4—21no—
28C2×#6718C2211yescharacteristic, complemented
29#91824—21no—
30C2×#6716C2211yescharacteristic
31C2×#6716C2211yescharacteristic
32#91815C2211yescharacteristic, complemented
33C2×C4⋊Dic15C2211yescharacteristic
34#91813C2211yescharacteristic
35#91813C2211yescharacteristic, complemented
36C22×C3⋊#168C2211yescharacteristic
37C22×C3⋊#168C2211yescharacteristic, complemented
38#91778—21no—
39#91768—21no—
40#91766—21no—
41#91759C2211yescharacteristic, complemented
42C4×Dic30C2211yescharacteristic, complemented
43#91119C2211yescharacteristic, complemented
44#91119C2211yescharacteristic, complemented
45#91119C2211yescharacteristic, complemented
46#91116C2211yescharacteristic
47#91116C2211yescharacteristic
48#91116C2211yescharacteristic
49#91116C2211yescharacteristic
50#91116C2211yescharacteristic
51#91116C2211yescharacteristic
52#91114C2211yescharacteristic
53#91114C2211yescharacteristic, complemented
54#91094C2211yescharacteristic, complemented
55#91092C2211yescharacteristic, complemented
56#91092C2211yescharacteristic, complemented
57#91091C2211yescharacteristic, complemented
58C4⋊(C3⋊#168)C2211yescharacteristic, complemented
59C4×C3⋊#168C2211yescharacteristic, complemented
60#83494—51nomaximal, Hall
61C5×#546D311yescharacteristic
62#65875—31no—
63#65528—31no—
64#65522—31no—
65#65507—31no—
66C2×#3964—31no—
67#65345—31no—
68#65343—31no—
69#65340—31no—
70#65332—31no—
71#65330—31no—
72#65324—31no—
73C4×#687—31no—
74D4×#168—31no—
75#65298—31no—
76C24×C3×C5—21no—
77C3×C5×#41—22no—
78C3×C5×#41—41no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—22no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—41no—
85C2×C3×C5×D4D411yescharacteristic
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C5×D4C2311yescharacteristic
88C22×C3×C4×C5—21no—
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×Dic15—21no—
93C2×Dic30C2311yescharacteristic
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4D411yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C22⋊C4—21no—
98C3×C5×C22⋊C4—21no—
99C3×C5×C22⋊C4—21no—
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4D411yescharacteristic
103C3×C5×C22⋊C4D411yescharacteristic
104C3×C42×C5C2311yescharacteristic
105#6719—21no—
106#6719—21no—
107#6719—21no—
108#6718—41no—
109#6716—22no—
110#6716—41no—
111C4⋊Dic15—21no—
112C4⋊Dic15C2311yescharacteristic
113C4⋊Dic15C2311yescharacteristic
114C4⋊Dic15C2311yescharacteristic
115#6712—21no—
116#6712—21no—
117#6712—21no—
118#6712—21no—
119#6712—21no—
120C4×Dic15—21no—
121C4×Dic15—21no—
122C2×C3⋊#168—41no—
123C2×C3⋊#168—41no—
124C2×C3⋊#168C2311yescharacteristic
125C2×C3⋊#168C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C2×C3⋊#168C2311yescharacteristic
128C3×#546D511yescharacteristic
129#5541—51no—
130#5239—51no—
131#5233—51no—
132#5218—51no—
133C2×#832—51no—
134#5056—51no—
135#5054—51no—
136#5051—51no—
137#5043—51no—
138#5041—51no—
139#5035—51no—
140C4×#214—51no—
141D4×C3⋊C8—51no—
142#5009—51no—
143C2×C5×#41C2×D311yescharacteristic
144C22×C5×D4C2×D311yescharacteristic
145C5×#124C2×D311yescharacteristic
146C5×#123—21no—
147C5×C22⋊Q8C2×D311yescharacteristic
148C5×#121—21no—
149C5×#121C2×D311yescharacteristic
150C5×#120—21no—
151C4×C5×D4C2×D311yescharacteristic
152C4×C5×D4C2×D311yescharacteristic
153C2×C5×C22⋊C4—21no—
154C2×#689—31no—
155#4081—61no—
156C2×#687—31no—
157C2×#687—31no—
158#4072—31no—
159C2×C4⋊Dic5—31no—
160#4070—31no—
161#4070—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4035—61no—
165#4025—61no—
166#4023—61no—
167#4016—31no—
168C4×Dic10—31no—
169#3967—31no—
170#3967—31no—
171#3967—31no—
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964—31no—
178C22⋊#168—31no—
179C22⋊#168—31no—
180#3942—31no—
181#3940—31no—
182#3940—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3296—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—42no—
190C23×C3×C5—42no—
191C23×C3×C5—81no—
192C23×C3×C5C2×D411yescharacteristic
193C23×C3×C5C2×D411yescharacteristic
194C3×C5×Q8—21no—
195C3×C5×Q8—21no—
196C3×C5×D4—22no—
197C3×C5×D4—21no—
198C3×C5×D4—21no—
199C3×C5×D4—21no—
200C3×C5×D4—42no—
201C3×C5×D4—42no—
202C3×C5×D4—81no—
203C3×C5×D4#4112yes—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—42no—
211C2×C3×C4×C5—81no—
212C2×C3×C4×C5C2×D411yescharacteristic
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2411yescharacteristic
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—42no—
222Dic30—21no—
223Dic30—21no—
224C3⋊#168—21no—
225C3⋊#168—21no—
226C3⋊#168—21no—
227C3⋊#168—21no—
228C2×C3×#41C2×D511yescharacteristic
229C22×C3×D4C2×D511yescharacteristic
230C3×#124C2×D511yescharacteristic
231C3×#123—21no—
232C3×C22⋊Q8C2×D511yescharacteristic
233C3×#121—21no—
234C3×#121C2×D511yescharacteristic
235C3×#120—21no—
236C3×C4×D4C2×D511yescharacteristic
237C3×C4×D4C2×D511yescharacteristic
238C2×C3×C22⋊C4—21no—
239C2×#216—51no—
240#935—101no—
241C2×#214—51no—
242C2×#214—51no—
243#926—51no—
244C2×C4⋊Dic3—51no—
245#924—51no—
246#924—51no—
247C22×C3⋊C8—51no—
248C22×C3⋊C8—51no—
249#889—101no—
250#879—101no—
251#877—101no—
252#870—51no—
253C4×Dic6—51no—
254#835—51no—
255#835—51no—
256#835—51no—
257#832—51no—
258#832—51no—
259#832—51no—
260#832—51no—
261#832—51no—
262#832—51no—
263#830—51no—
264#830—51no—
265#810—51no—
266#808—51no—
267#808—51no—
268#807—51no—
269C4⋊(C3⋊C8)—51no—
270C4×C3⋊C8—51no—
271C24×C5—21no—
272C5×#41—22no—
273C5×#41—41no—
274C2×C5×Q8C22×D311yescharacteristic
275C2×C5×D4—22no—
276C2×C5×D4—21no—
277C2×C5×D4—21no—
278C2×C5×D4—21no—
279C2×C5×D4—41no—
280C2×C5×D4#6711yescharacteristic
281C2×C5×D4C22×D311yescharacteristic
282C2×C5×D4C22×D311yescharacteristic
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5C22×D311yescharacteristic
286C22×C4×C5C22×D311yescharacteristic
287C22×Dic5—61no—
288C2×Dic10—31no—
289C5×C4⋊C4—21no—
290C5×C4⋊C4#6711yescharacteristic
291C5×C4⋊C4C22×D311yescharacteristic
292C5×C22⋊C4—21no—
293C5×C22⋊C4—21no—
294C5×C22⋊C4—21no—
295C5×C22⋊C4—21no—
296C5×C22⋊C4—21no—
297C5×C22⋊C4#6711yescharacteristic
298C5×C22⋊C4#6711yescharacteristic
299C42×C5C22×D311yescharacteristic
300C22⋊Dic5—61no—
301C22⋊Dic5—61no—
302C22⋊Dic5—61no—
303#689—121no—
304#687—62no—
305#687—121no—
306C4⋊Dic5—31no—
307C4⋊Dic5—31no—
308C4⋊Dic5—31no—
309C4⋊Dic5—61no—
310#683—61no—
311#683—61no—
312#683—61no—
313#683—61no—
314#683—61no—
315C4×Dic5—61no—
316C4×Dic5—61no—
317C2×#168—31no—
318C2×#168—31no—
319C2×#168—31no—
320C2×#168—31no—
321C2×#168—121no—
322C2×#168—121no—
323#552—151no—
324#546D1511yescharacteristic
325#488—151no—
326#483—151no—
327#482—151no—
328#478—151no—
329#467—151no—
330#465—151no—
331#464—151no—
332#452—151no—
333#450—151no—
334C4×SD16—151no—
335C8×D4—151no—
336#416—151no—
337C2×#102—151no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5—22no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—41no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—84no—
350C22×C3×C5#13512yes—
351C22×C3×C5C22×D411yescharacteristic
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—21no—
356C3×C4×C5—41no—
357C3×C4×C5—41no—
358C3×C4×C5C2×#4111yescharacteristic
359C3×C4×C5H(5,𝔽2)11yescharacteristic
360Dic15—41no—
361Dic15—41no—
362Dic15—41no—
363Dic15—41no—
364C24×C3—21no—
365C3×#41—22no—
366C3×#41—41no—
367C2×C3×Q8C22×D511yescharacteristic
368C2×C3×D4—22no—
369C2×C3×D4—21no—
370C2×C3×D4—21no—
371C2×C3×D4—21no—
372C2×C3×D4—41no—
373C2×C3×D4C22⋊D511yescharacteristic
374C2×C3×D4C22×D511yescharacteristic
375C2×C3×D4C22×D511yescharacteristic
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4C22×D511yescharacteristic
379C22×C3×C4C22×D511yescharacteristic
380C22×Dic3—101no—
381C2×Dic6—51no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4C22⋊D511yescharacteristic
384C3×C4⋊C4C22×D511yescharacteristic
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4C22⋊D511yescharacteristic
391C3×C22⋊C4C22⋊D511yescharacteristic
392C3×C42C22×D511yescharacteristic
393#217—101no—
394#217—101no—
395#217—101no—
396#216—201no—
397#214—102no—
398#214—201no—
399C4⋊Dic3—51no—
400C4⋊Dic3—51no—
401C4⋊Dic3—51no—
402C4⋊Dic3—101no—
403Dic3⋊C4—101no—
404Dic3⋊C4—101no—
405Dic3⋊C4—101no—
406Dic3⋊C4—101no—
407Dic3⋊C4—101no—
408C4×Dic3—101no—
409C4×Dic3—101no—
410C2×C3⋊C8—51no—
411C2×C3⋊C8—51no—
412C2×C3⋊C8—51no—
413C2×C3⋊C8—51no—
414C2×C3⋊C8—201no—
415C2×C3⋊C8—201no—
416C23×C5—21no—
417C23×C5—21no—
418C23×C5—42no—
419C23×C5—42no—
420C23×C5—81no—
421C23×C5C2×#6711yescharacteristic
422C23×C5C2×#6711yescharacteristic
423C5×Q8—21no—
424C5×Q8—21no—
425C5×D4—22no—
426C5×D4—21no—
427C5×D4—21no—
428C5×D4—21no—
429C5×D4—42no—
430C5×D4—42no—
431C5×D4—81no—
432C5×D4#23712yes—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—42no—
440C2×C4×C5—81no—
441C2×C4×C5C2×#6711yescharacteristic
442C2×C4×C5C2×#6711yescharacteristic
443C2×C4×C5C2×#6711yescharacteristic
444C2×C4×C5C2×#6711yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—122no—
451Dic10—61no—
452Dic10—61no—
453#168—61no—
454#168—61no—
455#168—61no—
456#168—61no—
457C2×#41C2×D1511yescharacteristic
458C22×D4C2×D1511yescharacteristic
459C2×Q16—151no—
460C2×SD16—151no—
461C2×SD16—151no—
462C22×C8—151no—
463C22×C8—151no—
464#126—301no—
465#125—151no—
466#125—301no—
467#124C2×D1511yescharacteristic
468#123—21no—
469#123—301no—
470C22⋊Q8—151no—
471C22⋊Q8—151no—
472C22⋊Q8C2×D1511yescharacteristic
473#121—21no—
474#121C2×D1511yescharacteristic
475#120—21no—
476C4×Q8—151no—
477C4×D4C2×D1511yescharacteristic
478C4×D4C2×D1511yescharacteristic
479#117—151no—
480#117—301no—
481C2×C4⋊C4—151no—
482C2×C22⋊C4—21no—
483#107—151no—
484#106—151no—
485#106—151no—
486C4⋊C8—151no—
487#103—151no—
488#103—151no—
489#103—151no—
490#103—151no—
491#102—151no—
492#102—151no—
493#102—151no—
494#102—151no—
495#102—151no—
496#102—151no—
497C22⋊C8—151no—
498C22⋊C8—151no—
499C4×C8—151no—
500C2×C3×C5—22no—
501C2×C3×C5—41no—
502C2×C3×C5—42no—
503C2×C3×C5—81no—
504C2×C3×C5#54611yescharacteristic
505C2×C3×C5C2×#13511yescharacteristic
506C2×C3×C5#57711yescharacteristic
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—42no—
510C23×C3—42no—
511C23×C3—81no—
512C23×C3C2×C22⋊D511yescharacteristic
513C23×C3C2×C22⋊D511yescharacteristic
514C3×Q8—21no—
515C3×Q8—21no—
516C3×D4—22no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—42no—
521C3×D4—42no—
522C3×D4—81no—
523C3×D4#71112yes—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—42no—
531C2×C3×C4—81no—
532C2×C3×C4C2×C22⋊D511yescharacteristic
533C2×C3×C4C2×C22⋊D511yescharacteristic
534C2×C3×C4C2×C22⋊D511yescharacteristic
535C2×C3×C4C2×C22⋊D511yescharacteristic
536C2×C3×C4C23×D511yescharacteristic
537C2×Dic3—101no—
538C2×Dic3—101no—
539C2×Dic3—101no—
540C2×Dic3—101no—
541C2×Dic3—202no—
542Dic6—101no—
543Dic6—101no—
544C3⋊C8—101no—
545C3⋊C8—101no—
546C3⋊C8—101no—
547C3⋊C8—101no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5—21no—
551C22×C5—22no—
552C22×C5—21no—
553C22×C5—21no—
554C22×C5—41no—
555C22×C5—41no—
556C22×C5—41no—
557C22×C5—41no—
558C22×C5—41no—
559C22×C5—84no—
560C22×C5#95012yes—
561C22×C5C22×#6711yescharacteristic
562C4×C5—21no—
563C4×C5—21no—
564C4×C5—21no—
565C4×C5—21no—
566C4×C5—41no—
567C4×C5—41no—
568C4×C5C2×#23711yescharacteristic
569C4×C5#100411yescharacteristic
570Dic5—121no—
571Dic5—121no—
572Dic5—121no—
573Dic5—121no—
574C24—21no—
575#41—22no—
576#41—41no—
577C2×Q8—151no—
578C2×Q8C22×D1511yescharacteristic
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4#122011yescharacteristic
585C2×D4C22×D1511yescharacteristic
586C2×D4C22×D1511yescharacteristic
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—301no—
590C22×C4C22×D1511yescharacteristic
591C22×C4C22×D1511yescharacteristic
592Q16—601no—
593SD16—302no—
594SD16—601no—
595C2×C8—151no—
596C2×C8—151no—
597C2×C8—151no—
598C2×C8—151no—
599C2×C8—601no—
600C2×C8—601no—
601C4⋊C4—21no—
602C4⋊C4—151no—
603C4⋊C4—151no—
604C4⋊C4—151no—
605C4⋊C4—301no—
606C4⋊C4—301no—
607C4⋊C4—301no—
608C4⋊C4—301no—
609C4⋊C4—301no—
610C4⋊C4—301no—
611C4⋊C4#122011yescharacteristic
612C4⋊C4C22×D1511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—301no—
619C22⋊C4—301no—
620C22⋊C4—301no—
621C22⋊C4#122011yescharacteristic
622C22⋊C4#122011yescharacteristic
623C42—301no—
624C42—301no—
625C42C22×D1511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—84no—
639C22×C3#409612yes—
640C22×C3C22×C22⋊D511yescharacteristic
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4C2×#71111yescharacteristic
648C3×C4#414411yescharacteristic
649Dic3—201no—
650Dic3—201no—
651Dic3—201no—
652Dic3—201no—
653C2×C5—22no—
654C2×C5—41no—
655C2×C5—42no—
656C2×C5—81no—
657C2×C5#580611yescharacteristic
658C2×C5C2×#95011yescharacteristic
659C2×C5#583611yescharacteristic
660C23—21no—
661C23—21no—
662C23—42no—
663C23—42no—
664C23—81no—
665C23C2×#122011yescharacteristic
666C23C2×#122011yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—301no—
670Q8—301no—
671D4—22no—
672D4—21no—
673D4—21no—
674D4—21no—
675D4—42no—
676D4—42no—
677D4—81no—
678D4#681912yes—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—42no—
686C2×C4—81no—
687C2×C4—301no—
688C2×C4—301no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—602no—
692C2×C4C2×#122011yescharacteristic
693C2×C4C2×#122011yescharacteristic
694C2×C4C2×#122011yescharacteristic
695C2×C4C2×#122011yescharacteristic
696C2×C4C23×D1511yescharacteristic
697C8—301no—
698C8—301no—
699C8—301no—
700C8—301no—
701C2×C3—22no—
702C2×C3—41no—
703C2×C3—42no—
704C2×C3—81no—
705C2×C3#6614011yescharacteristic
706C2×C3C2×#409611yescharacteristic
707C2×C3#6617011yescharacteristic
708C5#8349411yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—21no—
714C22—21no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—84no—
721C22#9183912yes—
722C22C22×#122011yescharacteristic
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—41no—
728C4—41no—
729C4—601no—
730C4—601no—
731C4—601no—
732C4—601no—
733C4C2×#681911yescharacteristic
734C4#9209511yescharacteristic
735C3#1061522511yescharacteristic, complemented, Sylow
736C2—22no—
737C2—41no—
738C2—42no—
739C2—81no—
740C2#1175656511yescharacteristic
741C2C2×#9183911yescharacteristic
742C2#1175659511yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
Fitting, prime radicalC3×C5×#546C2
socleC22×C3×C5C22×D4
hypercenter#546D15
hypocenterC3×C5#3296
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
2. #11756300C2semidirect
3. #11751340C2semidirect
4. #11751334C2semidirect
5. #11751319C2semidirect
6. C2×#91116C2semidirect
7. #11751157C2semidirect
8. #11751155C2semidirect
9. #11751152C2semidirect
10. #11751144C2semidirect
11. #11751142C2semidirect
12. #11751136C2semidirect
13. C4×#6716C2semidirect
14. D4×C3⋊#168C2semidirect
15. #11751110C2semidirect
28. C2×#6718C22semidirect
32. #91815C22semidirect
35. #91813C22semidirect
37. C22×C3⋊#168C22semidirect
41. #91759C22semidirect
42. C4×Dic30C22semidirect
43. #91119C22semidirect
44. #91119C22semidirect
45. #91119C22semidirect
53. #91114C22semidirect
54. #91094C22semidirect
55. #91092C22semidirect
56. #91092C22semidirect
57. #91091C22semidirect
58. C4⋊(C3⋊#168)C22semidirect
59. C4×C3⋊#168C22semidirect
626. C3×C5#3296semidirect
708. C5#83494semidirect
735. C3#10615225semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5462
#117563002
#117513402
#117513342
#117513192
C2×#911162
#117511572
#117511552
#117511522
#117511442
#117511422
#117511362
C4×#67162
D4×C3⋊#1682
#117511102
#106152253
#834945