Finite Group Databasebeta

← #14459147

Subgroups — #14459147

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5507C211yesmaximal, characteristic
2#67×Dic10C211yesmaximal, characteristic, complemented
3#11751072C211yesmaximal, characteristic, complemented
4C2×C3×#3942C211yesmaximal, characteristic, complemented
5#11748533C211yesmaximal, characteristic, complemented
6#11748529C211yesmaximal, characteristic, complemented
7#67×#168C211yesmaximal, characteristic, complemented
8#11747494C211yesmaximal, characteristic, complemented
9D3×#3942C211yesmaximal, characteristic, complemented
10#11747422C211yesmaximal, characteristic, complemented
11#11747420C211yesmaximal, characteristic, complemented
12#11747352C211yesmaximal, characteristic, complemented
13#11747348C211yesmaximal, characteristic, complemented
14#11747293C211yesmaximal, characteristic, complemented
15#11747264C211yesmaximal, characteristic, complemented
16#10615262—31nomaximal, Hall
17C2×C5×#235—21no—
18C22×C3×Dic10C2211yescharacteristic
19C2×D3×Dic10C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21#91813C2211yescharacteristic
22C5×#930C2211yescharacteristic
23C5×#929—21no—
24C4×C5×#67C2211yescharacteristic
25C5×#896—21no—
26C5×#895C2211yescharacteristic
27C5×#894—21no—
28C5×#893C2211yescharacteristic
29C5×D3×C4⋊C4C2211yescharacteristic
30C5×#888C2211yescharacteristic
31C22×C3×#168C2211yescharacteristic
32#91574—21no—
33Dic5×#67—21no—
34#91410—21no—
35#91389C2211yescharacteristic
36#91369C2211yescharacteristic
37Dic3×Dic10C2211yescharacteristic
38#91327—21no—
39C2×#6659C2211yescharacteristic
40C2×#6656C2211yescharacteristic
41C2×#6656C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic
43#91114C2211yescharacteristic
44#91094C2211yescharacteristic
45#91094C2211yescharacteristic
46#91092C2211yescharacteristic
47#91092C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49C3×#3942C2211yescharacteristic
50C3×#3942C2211yescharacteristic
51C3×#3942C2211yescharacteristic
52#90985C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90975C2211yescharacteristic
55#90970C2211yescharacteristic
56#90970C2211yescharacteristic
57#90967C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#78805—51nomaximal, Hall
61C5×#547—31no—
62D4×Dic10—31no—
63#65383—31no—
64#65382—31no—
65#65330—31no—
66#65330—31no—
67#65329—31no—
68#65329—31no—
69#65308—31no—
70C4×#687—31no—
71D4×#168—31no—
72#65260—31no—
73#65260—31no—
74C2×#3942—31no—
75C2×#3942D311yescharacteristic, complemented
76C22×C3×C4×C5—21no—
77C22×C3×C4×C5C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×#67—21no—
80C2×C5×#67D411yescharacteristic
81C5×#235—44no—
82C2×C5×D12—21no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3C2311yescharacteristic
87C2×C5×Dic6—21no—
88C22×C3×Dic5—21no—
89C2×C3×Dic10—22no—
90C2×C3×Dic10—21no—
91C2×C3×Dic10—41no—
92C2×C3×Dic10C2311yescharacteristic
93C2×C3×Dic10C2311yescharacteristic
94C2×#1204—21no—
95C2×D3×Dic5—21no—
96D3×Dic10—22no—
97D3×Dic10—41no—
98C3×C5×C4⋊C4—21no—
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101#6719—21no—
102C4⋊Dic15C2311yescharacteristic
103#6712—21no—
104C2×C3⋊#168C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C5×#217D411yescharacteristic
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4—21no—
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4D411yescharacteristic
111C5×C4⋊Dic3C2311yescharacteristic
112C5×Dic3⋊C4—21no—
113C5×Dic3⋊C4—21no—
114C5×Dic3⋊C4D411yescharacteristic
115C4×C5×Dic3C2311yescharacteristic
116C2×C3×#168—41no—
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119Dic3⋊Dic5—21no—
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6668—21no—
123(C2×D3)⋊Dic5—21no—
124Dic3×Dic5—21no—
125#6659—41no—
126#6656—22no—
127#6656—41no—
128D3×#168—41no—
129Q8×#67—51no—
130#5507D511yescharacteristic
131C2×C3×#103—51no—
132#5227—51no—
133#5114—51no—
134C8×#67—51no—
135#4971—51no—
136#4818—51no—
137#4807—51no—
138#4806—51no—
139#4805—51no—
140D3×#103—51no—
141#4792—51no—
142#4791—51no—
143#4788—51no—
144C2×C5×#41—61no—
145C22×Dic10—31no—
146C22×Dic10C2×D311yescharacteristic
147C5×C4⋊Q8—31no—
148C5×#123—61no—
149C5×#123—61no—
150C5×C22⋊Q8—61no—
151C5×#121—31no—
152C5×#121—31no—
153C4×C5×D4—31no—
154C4×C5×D4—31no—
155C2×C5×C4⋊C4—31no—
156C2×C5×C4⋊C4C2×D311yescharacteristic
157D4×Dic5—61no—
158C2×#687—31no—
159C2×#687—31no—
160C2×#687—31no—
161#4070—31no—
162#4070—31no—
163C22×#168—31no—
164C22×#168C2×D311yescharacteristic
165#4034—61no—
166#4024—61no—
167#4024—61no—
168#4015—31no—
169C4×Dic10—31no—
170#3964—31no—
171C22⋊#168—31no—
172C22⋊#168—31no—
173#3942—31no—
174#3942—31no—
175#3942—31no—
176#3942—31no—
177#3942—31no—
178#3942C2×D311yescharacteristic
179#3942C2×D311yescharacteristic
180#3942C2×D311yescharacteristic
181#3942C2×D311yescharacteristic
182#3940—31no—
183#3940—31no—
184#3940—31no—
185C4⋊#168—31no—
186C4×#168—31no—
187#3298—151noSylow
188C23×C3×C5C2×D411yescharacteristic
189C22×C5×D3—21no—
190C22×C5×D3C2×D411yescharacteristic
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—42no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2411yescharacteristic
198C2×Dic15—21no—
199C2×Dic15—21no—
200Dic30—21no—
201Dic30—21no—
202C5×#67—42no—
203C5×#67SD1614yescomplemented
204C2×C5×Dic3—21no—
205C2×C5×Dic3C2×D411yescharacteristic
206C2×C5×Dic3C2×D411yescharacteristic
207C2×C5×Dic3C2×D411yescharacteristic
208C5×D12—21no—
209C5×D12—21no—
210C5×D12—42no—
211C4×C5×D3—21no—
212C4×C5×D3—21no—
213C4×C5×D3—42no—
214C4×C5×D3—42no—
215C5×Dic6—42no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—42no—
219C3×Dic10—21no—
220C3×Dic10—21no—
221C3×Dic10—21no—
222C3×Dic10—42no—
223C3×Dic10#4112yescomplemented
224#1204—42no—
225D3×Dic5—42no—
226C3⋊#168—21no—
227C3⋊#168—21no—
228C3×#168—21no—
229C3×#168—21no—
230C22×C3×Q8—51no—
231C2×D3×Q8—51no—
232C2×#235—21no—
233C22×C3×C8—51no—
234C2×C3×C4⋊C4C2×D511yescharacteristic
235#946—51no—
236#946—101no—
237Q8×Dic3—51no—
238#944—51no—
239#944—101no—
240C2×#215—51no—
241C2×#215—51no—
242#930C2×D511yescharacteristic
243#929—21no—
244C4×#67—101no—
245C4×#67C2×D511yescharacteristic
246#924—51no—
247#924—101no—
248C2×#204—51no—
249C2×D3×C8—51no—
250#896—21no—
251#895C2×D511yescharacteristic
252#894—21no—
253#893C2×D511yescharacteristic
254D3×C4⋊C4C2×D511yescharacteristic
255#888C2×D511yescharacteristic
256C3×#103—51no—
257C3×#103—51no—
258C3×#103—51no—
259C3×#103—51no—
260#835—51no—
261#835—51no—
262#830—51no—
263#821—51no—
264(C2×D3)⋊C8—51no—
265#817—51no—
266#816—51no—
267Dic3⋊C8—51no—
268C8×Dic3—51no—
269#810—51no—
270#810—51no—
271#808—51no—
272#808—51no—
273C5×#41—124no—
274C2×C5×Q8—61no—
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4—61no—
279C22×C4×C5—21no—
280C22×C4×C5—31no—
281C22×C4×C5—61no—
282C22×C4×C5—61no—
283C22×C4×C5C22×D311yescharacteristic
284C22×Dic5—21no—
285C22×Dic5—61no—
286C2×Dic10—22no—
287C2×Dic10—21no—
288C2×Dic10—31no—
289C2×Dic10—41no—
290C2×Dic10—62no—
291C2×Dic10—61no—
292C2×Dic10—121no—
293C2×Dic10C22×D311yescharacteristic
294C2×Dic10C22×D311yescharacteristic
295C5×C4⋊C4—21no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—61no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—31no—
303C5×C22⋊C4—31no—
304C5×C22⋊C4—61no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4—61no—
307C42×C5—31no—
308C22⋊Dic5—61no—
309C22⋊Dic5—61no—
310#687—62no—
311#687—121no—
312#687—121no—
313C4⋊Dic5—31no—
314C4⋊Dic5—61no—
315C4⋊Dic5—61no—
316#683—61no—
317#683—61no—
318#683—61no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—41no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326D4×Q8—151no—
327#547—31no—
328#487—151no—
329#483—151no—
330#483—151no—
331#475—151no—
332#465—151no—
333#465—151no—
334#461—151no—
335#448—151no—
336#448—151no—
337C4×SD16—151no—
338C8×D4—151no—
339C2×#103—51no—
340C2×#103—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5C2×SD1612yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×C5×D3—21no—
346C2×C5×D3—21no—
347C2×C5×D3—41no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3C2×SD1612yes—
351C3×C4×C5—21no—
352C3×C4×C5—41no—
353C3×C4×C5—41no—
354C3×C4×C5C2×#4111yescharacteristic
355C3×C4×C5H(5,𝔽2)11yescharacteristic
356Dic15—41no—
357Dic15—41no—
358C3×Dic5—22no—
359C3×Dic5—41no—
360C5×Dic3—21no—
361C5×Dic3—21no—
362C5×Dic3—41no—
363C5×Dic3C2×SD1612yes—
364C2×C3×Q8—51no—
365C2×C3×Q8—51no—
366C2×C3×Q8—102no—
367C2×C3×Q8—101no—
368C2×C3×Q8—201no—
369C22×C3×C4—21no—
370C22×C3×C4—101no—
371C22×C3×C4C22×D511yescharacteristic
372C2×#67—21no—
373C2×#67C22⋊D511yescharacteristic
374D3×Q8—102no—
375D3×Q8—201no—
376#235—44no—
377C2×D12—21no—
378C2×D12C22×D511yescharacteristic
379C2×C4×D3—21no—
380C2×C4×D3—21no—
381C2×C4×D3—101no—
382C2×C4×D3C22×D511yescharacteristic
383C2×Dic6—21no—
384C2×Dic6—51no—
385C2×Dic6—101no—
386C2×C3×C8—51no—
387C2×C3×C8—51no—
388C2×C3×C8—201no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4C22×D511yescharacteristic
391C3×C4⋊C4C22×D511yescharacteristic
392#217—101no—
393#217C22⋊D511yescharacteristic
394#215—102no—
395#215—201no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—101no—
400(C2×D3)⋊C4C22⋊D511yescharacteristic
401C4⋊Dic3—51no—
402C4⋊Dic3—101no—
403C4⋊Dic3C22×D511yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4—101no—
407Dic3⋊C4—101no—
408Dic3⋊C4—101no—
409Dic3⋊C4—101no—
410Dic3⋊C4C22⋊D511yescharacteristic
411C4×Dic3—101no—
412C4×Dic3C22×D511yescharacteristic
413C2×C3⋊C8—51no—
414C2×C3⋊C8—51no—
415#204—201no—
416D3×C8—201no—
417C23×C5—31no—
418C23×C5—61no—
419C23×C5D3×D411yescharacteristic
420C5×Q8—122no—
421C5×D4—34no—
422C5×D4—61no—
423C5×D4—61no—
424C5×D4—122no—
425C5×D4—122no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—31no—
431C2×C4×C5—31no—
432C2×C4×C5—31no—
433C2×C4×C5—42no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—122no—
438C2×C4×C5—122no—
439C2×C4×C5D3×D411yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—42no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—122no—
447Dic10—21no—
448Dic10—21no—
449Dic10—21no—
450Dic10—42no—
451Dic10—61no—
452Dic10—61no—
453Dic10—122no—
454Dic10#23512yescomplemented
455#168—21no—
456#168—21no—
457#168—61no—
458#168—61no—
459C2×#41—61no—
460C22×Q8—51no—
461C22×Q8—151no—
462C2×SD16—151no—
463C2×SD16—151no—
464C2×SD16—151no—
465C22×C8—51no—
466C22×C8—151no—
467C4⋊Q8—31no—
468C4⋊Q8—151no—
469C4⋊Q8—301no—
470#123—61no—
471#123—61no—
472C22⋊Q8—61no—
473C22⋊Q8—151no—
474C22⋊Q8—151no—
475C22⋊Q8—301no—
476C22⋊Q8—301no—
477#121—31no—
478#121—31no—
479C4×Q8—151no—
480C4×D4—31no—
481C4×D4—31no—
482C4×D4—301no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4D3×D511yescharacteristic
485#106—151no—
486#106—151no—
487#106—151no—
488C4⋊C8—151no—
489#103—51no—
490#103—51no—
491#103—51no—
492#103—51no—
493#103—151no—
494#103—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—151no—
499C22⋊C8—151no—
500C22⋊C8—151no—
501C4×C8—151no—
502C2×C3×C5—22no—
503C2×C3×C5#54611yescharacteristic
504C2×C3×C5C22×SD1611yescharacteristic
505C2×C3×C5#57811yescharacteristic
506C5×D3—22no—
507C5×D3—81no—
508C23×C3C2×C22⋊D511yescharacteristic
509C22×D3—21no—
510C22×D3C2×C22⋊D511yescharacteristic
511C3×Q8—52no—
512C3×Q8—101no—
513C3×Q8—101no—
514C3×Q8—101no—
515C3×Q8—202no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—42no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—202no—
524C2×C3×C4C2×C22⋊D511yescharacteristic
525C2×C3×C4C23×D511yescharacteristic
526#67—42no—
527#67#68714yescomplemented
528C2×Dic3—21no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3C2×C22⋊D511yescharacteristic
532C2×Dic3C2×C22⋊D511yescharacteristic
533C2×Dic3C2×C22⋊D511yescharacteristic
534D12—21no—
535D12—21no—
536D12—42no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—42no—
540C4×D3—42no—
541C4×D3—202no—
542Dic6—42no—
543Dic6—101no—
544Dic6—101no—
545Dic6—202no—
546C3×C8—101no—
547C3×C8—101no—
548C3⋊C8—101no—
549C3⋊C8—101no—
550C22×C5—21no—
551C22×C5—21no—
552C22×C5—32no—
553C22×C5—61no—
554C22×C5—61no—
555C22×C5—121no—
556C22×C5—121no—
557C22×C5—121no—
558C22×C5D3×SD1612yes—
559C22×C5C2×D3×D411yescharacteristic
560C4×C5—21no—
561C4×C5—32no—
562C4×C5—41no—
563C4×C5—41no—
564C4×C5—61no—
565C4×C5—61no—
566C4×C5—121no—
567C4×C5C2×#23511yescharacteristic
568C4×C5#100411yescharacteristic
569Dic5—22no—
570Dic5—41no—
571Dic5—121no—
572Dic5—121no—
573#41—124no—
574C2×Q8—51no—
575C2×Q8—51no—
576C2×Q8—61no—
577C2×Q8—102no—
578C2×Q8—101no—
579C2×Q8—151no—
580C2×Q8—201no—
581C2×Q8—301no—
582C2×Q8—302no—
583C2×Q8—601no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C22×C4—21no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—101no—
593C22×C4—301no—
594C22×C4C2×D3×D511yescharacteristic
595SD16—302no—
596SD16—601no—
597SD16—601no—
598C2×C8—51no—
599C2×C8—51no—
600C2×C8—151no—
601C2×C8—151no—
602C2×C8—201no—
603C2×C8—601no—
604C4⋊C4—21no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—151no—
610C4⋊C4—301no—
611C4⋊C4—301no—
612C4⋊C4—301no—
613C4⋊C4—301no—
614C4⋊C4—301no—
615C4⋊C4C2×D3×D511yescharacteristic
616C4⋊C4C2×D3×D511yescharacteristic
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—301no—
623C22⋊C4—301no—
624C42—31no—
625C42—301no—
626C3×C5#329811yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3C2×#68712yes—
630C22×C3C22×C22⋊D511yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3C2×#68712yes—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—102no—
641C3×C4—201no—
642C3×C4D5×#4111yescharacteristic
643C3×C4#414911yescharacteristic
644Dic3—21no—
645Dic3—21no—
646Dic3—41no—
647Dic3—201no—
648Dic3—201no—
649Dic3C2×#68712yes—
650C2×C5—22no—
651C2×C5—62no—
652C2×C5—241no—
653C2×C5#549011yescharacteristic
654C2×C5C2×D3×SD1611yescharacteristic
655C2×C5#576611yescharacteristic
656C23—31no—
657C23—61no—
658C23D3×C22⋊D511yescharacteristic
659Q8—52no—
660Q8—101no—
661Q8—101no—
662Q8—101no—
663Q8—122no—
664Q8—202no—
665Q8—301no—
666Q8—301no—
667Q8—602no—
668D4—34no—
669D4—61no—
670D4—61no—
671D4—122no—
672D4—122no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—42no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—122no—
687C2×C4—122no—
688C2×C4—202no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—602no—
692C2×C4D3×C22⋊D511yescharacteristic
693C2×C4C22×D3×D511yescharacteristic
694C8—101no—
695C8—101no—
696C8—301no—
697C8—301no—
698C2×C3—22no—
699C2×C3C22×#68711yescharacteristic
700C2×C3#6616311yescharacteristic
701C2×C3#6617211yescharacteristic
702D3—22no—
703D3—81no—
704C5#7880511yescharacteristic, complemented, Sylow
705C22—21no—
706C22—21no—
707C22—32no—
708C22—61no—
709C22—61no—
710C22—121no—
711C22—121no—
712C22—121no—
713C22D3×#68712yes—
714C22C2×D3×C22⋊D511yescharacteristic
715C4—21no—
716C4—32no—
717C4—41no—
718C4—41no—
719C4—61no—
720C4—61no—
721C4—102no—
722C4—121no—
723C4—201no—
724C4—601no—
725C4—601no—
726C4D5×#23511yescharacteristic
727C4#9201711yescharacteristic
728C3#1061526211yescharacteristic, complemented, Sylow
729C2—22no—
730C2—62no—
731C2—241no—
732C2#1175465011yescharacteristic
733C2C2×D3×#68711yescharacteristic
734C2#1175510511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5507C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3298
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #67×Dic10C2semidirect
3. #11751072C2semidirect
4. C2×C3×#3942C2semidirect
5. #11748533C2semidirect
6. #11748529C2semidirect
7. #67×#168C2semidirect
8. #11747494C2semidirect
9. D3×#3942C2semidirect
10. #11747422C2semidirect
11. #11747420C2semidirect
12. #11747352C2semidirect
13. #11747348C2semidirect
14. #11747293C2semidirect
15. #11747264C2semidirect
75. C2×#3942D3semidirect
203. C5×#67SD16semidirect
223. C3×Dic10#41semidirect
454. Dic10#235semidirect
527. #67#687semidirect
626. C3×C5#3298semidirect
704. C5#78805semidirect
728. C3#10615262semidirect

Maximal subgroups

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

subgroupindex
C5×#55072
#67×Dic102
#117510722
C2×C3×#39422
#117485332
#117485292
#67×#1682
#117474942
D3×#39422
#117474222
#117474202
#117473522
#117473482
#117472932
#117472642
#106152623
#788055