Finite Group Databasebeta

← #14458685

Subgroups — #14458685

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
1C5×#5554C211yesmaximal, characteristic
2#11752613C211yesmaximal, characteristic, complemented
3C4×#6716C211yesmaximal, characteristic, complemented
4C3×#65298C211yesmaximal, characteristic, complemented
5#11749056C211yesmaximal, characteristic, complemented
6#11749054C211yesmaximal, characteristic, complemented
7#11748965C211yesmaximal, characteristic, complemented
8D3×#3964C211yesmaximal, characteristic, complemented
9#11747448C211yesmaximal, characteristic, complemented
10#11747447C211yesmaximal, characteristic, complemented
11#11747210C211yesmaximal, characteristic, complemented
12#11747197C211yesmaximal, characteristic, complemented
13#11746998C211yesmaximal, characteristic, complemented
14#11746903C211yesmaximal, characteristic, complemented
15#11746884C211yesmaximal, characteristic, complemented
16#10615225—31nomaximal, Hall
17C2×C5×#237C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C2×#6716C2211yescharacteristic
21C4×Dic30C2211yescharacteristic, complemented
22C5×#930—21no—
23C2×C5×(C2×D3)⋊C4—21no—
24C5×#897C2211yescharacteristic
25C5×#895C2211yescharacteristic
26C5×#886—21no—
27C5×#882—21no—
28C5×#875C2211yescharacteristic
29C4×C5×D12C2211yescharacteristic
30C3×#4016C2211yescharacteristic, complemented
31D3×C4⋊Dic5C2211yescharacteristic
32#91423—21no—
33#91400—21no—
34#91367—21no—
35#91365C2211yescharacteristic
36#91365C2211yescharacteristic, complemented
37#91338C2211yescharacteristic, complemented
38#91335—21no—
39C2×#6663C2211yescharacteristic, complemented
40C2×#6659C2211yescharacteristic
41C2×D3×#168C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic, complemented
43#91116C2211yescharacteristic
44#91094C2211yescharacteristic, complemented
45#91092C2211yescharacteristic, complemented
46C4×C3⋊#168C2211yescharacteristic, complemented
47C3×#3964C2211yescharacteristic
48C3×#3964C2211yescharacteristic
49C3×#3940C2211yescharacteristic, complemented
50C3×#3939C2211yescharacteristic, complemented
51C3×C4⋊#168C2211yescharacteristic, complemented
52#90973C2211yescharacteristic, complemented
53#90972C2211yescharacteristic, complemented
54#90972C2211yescharacteristic, complemented
55#90967C2211yescharacteristic
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic, complemented
60#81186—51nomaximal, Hall
61C5×#546—31no—
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#65298D311yescharacteristic, complemented
76C23×C5×D3—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C2×Dic30C2311yescharacteristic
80C2×C5×#67—21no—
81C2×C5×#67—21no—
82C22×C5×Dic3—21no—
83C5×#237—22no—
84C5×#237—41no—
85C5×D3×D4—22no—
86C5×D3×D4—41no—
87C2×C5×D12—21no—
88C2×C5×D12D411yescharacteristic
89C2×C5×D12C2311yescharacteristic
90C2×C4×C5×D3C2311yescharacteristic
91C2×C4×C5×D3C2311yescharacteristic
92C2×C5×Dic6C2311yescharacteristic
93C2×D3×Dic5—21no—
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C22⋊C4—21no—
96C3×C42×C5C2311yescharacteristic
97#6716—22no—
98C4⋊Dic15C2311yescharacteristic
99#6712—21no—
100C4×Dic15—21no—
101C2×C3⋊#168C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×(C2×D3)⋊C4—21no—
104C5×(C2×D3)⋊C4—21no—
105C5×(C2×D3)⋊C4—21no—
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4D411yescharacteristic
108C5×(C2×D3)⋊C4D411yescharacteristic
109C5×C4⋊Dic3—21no—
110C5×C4⋊Dic3D411yescharacteristic
111C3×C4⋊Dic5C2311yescharacteristic
112C3×C4⋊Dic5C2311yescharacteristic
113C3×#683—21no—
114C3×#683—21no—
115C2×C3×#168C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117Dic3⋊Dic5—21no—
118#6668—21no—
119#6668—21no—
120(C2×D3)⋊Dic5—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123Dic3×Dic5—21no—
124#6663—41no—
125#6659—41no—
126D3×#168—41no—
127D3×#168—41no—
128#5694—51no—
129#5554D511yescharacteristic
130C3×#478—51no—
131#5068—51no—
132C4×#214—51no—
133#4887—51no—
134#4885—51no—
135#4864—51no—
136#4862—51no—
137#4845—51no—
138#4834—51no—
139#4783—51no—
140#4776—51no—
141#4772—51no—
142D3×#102—51no—
143C2×C5×#41—31no—
144C22×C5×D4—31no—
145C5×#124—31no—
146C5×#123—61no—
147C5×C22⋊Q8—31no—
148C5×#121—31no—
149C5×#121—61no—
150C5×#120—61no—
151C4×C5×D4—31no—
152C4×C5×D4C2×D311yescharacteristic
153C2×C5×C22⋊C4—61no—
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#4016C2×D311yescharacteristic, complemented
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#3964C2×D311yescharacteristic
177#3964C2×D311yescharacteristic
178C22⋊#168—31no—
179C22⋊#168—31no—
180#3942—31no—
181#3940—31no—
182#3940C2×D311yescharacteristic, complemented
183#3939C2×D311yescharacteristic, complemented
184C4⋊#168C2×D311yescharacteristic, complemented
185C4×#168—31no—
186#3296—151noSylow
187C23×C3×C5—21no—
188C22×C5×D3—21no—
189C22×C5×D3—42no—
190C22×C5×D3—42no—
191C22×C5×D3—81no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C5×D3C2×D411yescharacteristic
194C3×C5×D4—21no—
195C3×C5×D4#4112yes—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—81no—
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2411yescharacteristic
201C2×Dic15—21no—
202C2×Dic15—21no—
203Dic30—21no—
204Dic30—21no—
205C5×#67—42no—
206C5×#67—42no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—42no—
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C5×D12—22no—
212C5×D12—21no—
213C5×D12—21no—
214C5×D12—81no—
215C4×C5×D3—21no—
216C4×C5×D3—21no—
217C4×C5×D3—21no—
218C4×C5×D3—21no—
219C5×Dic6—21no—
220C5×Dic6—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223D3×Dic5—42no—
224C3⋊#168—21no—
225C3⋊#168—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×#237C2×D511yescharacteristic
229C2×D3×D4C2×D511yescharacteristic
230C3×#125—51no—
231C3×C4×D4C2×D511yescharacteristic
232C2×#214—51no—
233#930—21no—
234C2×(C2×D3)⋊C4—21no—
235C2×Dic12—51no—
236C2×#204—51no—
237C2×D3×C8—51no—
238C2×D3×C8—51no—
239#898—101no—
240#897—51no—
241#897—51no—
242#897C2×D511yescharacteristic
243#895C2×D511yescharacteristic
244#894—101no—
245#892—51no—
246#892—101no—
247D3×C4⋊C4—51no—
248#890—101no—
249#886—21no—
250#882—21no—
251#875C2×D511yescharacteristic
252C4×D12C2×D511yescharacteristic
253C4×Dic6—51no—
254C3×#107—51no—
255C3×#106—51no—
256C3×C4⋊C8—51no—
257C3×#102—51no—
258C3×#102—51no—
259#832—51no—
260#821—51no—
261(C2×D3)⋊C8—51no—
262(C2×D3)⋊C8—51no—
263#816—51no—
264#810—51no—
265#810—51no—
266#810—51no—
267#809—51no—
268#809—51no—
269#808—51no—
270C4×C3⋊C8—51no—
271C24×C5—61no—
272C5×#41—62no—
273C5×#41—121no—
274C2×C5×Q8—31no—
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4—61no—
279C2×C5×D4—62no—
280C2×C5×D4—61no—
281C2×C5×D4—121no—
282C2×C5×D4C22×D311yescharacteristic
283C22×C4×C5—21no—
284C22×C4×C5—31no—
285C22×C4×C5—31no—
286C22×C4×C5—61no—
287C22×Dic5—61no—
288C2×Dic10—31no—
289C5×C4⋊C4—31no—
290C5×C4⋊C4—61no—
291C5×C4⋊C4C22×D311yescharacteristic
292C5×C22⋊C4—21no—
293C5×C22⋊C4—31no—
294C5×C22⋊C4—31no—
295C5×C22⋊C4—61no—
296C5×C22⋊C4—61no—
297C5×C22⋊C4—61no—
298C5×C22⋊C4—61no—
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—61no—
308C4⋊Dic5C22×D311yescharacteristic
309C4⋊Dic5C22×D311yescharacteristic
310#683—21no—
311#683—21no—
312#683—61no—
313#683—61no—
314#683—61no—
315C4×Dic5—61no—
316C4×Dic5—61no—
317C2×#168—31no—
318C2×#168—31no—
319C2×#168—121no—
320C2×#168—121no—
321C2×#168C22×D311yescharacteristic
322C2×#168C22×D311yescharacteristic
323#552—151no—
324#546—31no—
325#488—151no—
326#483—151no—
327#482—151no—
328#478—51no—
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—22no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5C22×D411yescharacteristic
342C2×C5×D3—21no—
343C2×C5×D3—21no—
344C2×C5×D3—21no—
345C2×C5×D3—21no—
346C2×C5×D3—21no—
347C2×C5×D3—41no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—84no—
351C2×C5×D3#13512yes—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—41no—
355C3×C4×C5C2×#4111yescharacteristic
356C3×C4×C5H(5,𝔽2)11yescharacteristic
357Dic15—41no—
358Dic15—41no—
359C3×Dic5—41no—
360C3×Dic5—41no—
361C5×Dic3—21no—
362C5×Dic3—21no—
363C5×Dic3—41no—
364C23×D3—21no—
365C2×C3×D4C22×D511yescharacteristic
366C22×C3×C4—21no—
367C2×#67—21no—
368C2×#67—21no—
369C22×Dic3—21no—
370#237—22no—
371#237—41no—
372D3×D4—22no—
373D3×D4—41no—
374C2×D12—21no—
375C2×D12C22⋊D511yescharacteristic
376C2×D12C22×D511yescharacteristic
377C2×C4×D3—101no—
378C2×C4×D3C22×D511yescharacteristic
379C2×C4×D3C22×D511yescharacteristic
380C2×Dic6—51no—
381C2×Dic6C22×D511yescharacteristic
382C2×C3×C8—51no—
383C2×C3×C8—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—101no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4C22×D511yescharacteristic
389C3×C22⋊C4—21no—
390C3×C42C22×D511yescharacteristic
391#214—102no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—101no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4—101no—
399(C2×D3)⋊C4C22⋊D511yescharacteristic
400(C2×D3)⋊C4C22⋊D511yescharacteristic
401C4⋊Dic3—21no—
402C4⋊Dic3—51no—
403C4⋊Dic3—101no—
404C4⋊Dic3—101no—
405C4⋊Dic3C22⋊D511yescharacteristic
406Dic3⋊C4—101no—
407Dic3⋊C4—101no—
408C4×Dic3—101no—
409C4×Dic3—101no—
410C2×C3⋊C8—51no—
411C2×C3⋊C8—51no—
412Dic12—201no—
413#204—201no—
414D3×C8—201no—
415D3×C8—201no—
416C23×C5—21no—
417C23×C5—31no—
418C23×C5—31no—
419C23×C5—61no—
420C23×C5—122no—
421C23×C5—122no—
422C23×C5—241no—
423C5×Q8—61no—
424C5×Q8—61no—
425C5×D4—21no—
426C5×D4—62no—
427C5×D4—61no—
428C5×D4—61no—
429C5×D4—122no—
430C5×D4—122no—
431C5×D4—241no—
432C5×D4#23912yes—
433C2×C4×C5—21no—
434C2×C4×C5—31no—
435C2×C4×C5—31no—
436C2×C4×C5—61no—
437C2×C4×C5—61no—
438C2×C4×C5—61no—
439C2×C4×C5—61no—
440C2×C4×C5—61no—
441C2×C4×C5—81no—
442C2×C4×C5—122no—
443C2×C4×C5D3×D411yescharacteristic
444C2×C4×C5D3×D411yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—122no—
451Dic10—61no—
452Dic10—61no—
453#168—21no—
454#168—21no—
455#168—61no—
456#168—61no—
457C2×#41—31no—
458C22×D4—31no—
459C2×Q16—151no—
460C2×SD16—151no—
461C2×SD16—151no—
462C22×C8—151no—
463C22×C8—151no—
464#126—301no—
465#125—51no—
466#125—301no—
467#124—31no—
468#123—61no—
469#123—301no—
470C22⋊Q8—31no—
471C22⋊Q8—151no—
472C22⋊Q8—151no—
473#121—31no—
474#121—61no—
475#120—61no—
476C4×Q8—151no—
477C4×D4—31no—
478C4×D4D3×D511yescharacteristic
479#117—151no—
480#117—301no—
481C2×C4⋊C4—151no—
482C2×C22⋊C4—61no—
483#107—51no—
484#106—51no—
485#106—151no—
486C4⋊C8—51no—
487#103—151no—
488#103—151no—
489#103—151no—
490#103—151no—
491#102—51no—
492#102—51no—
493#102—151no—
494#102—151no—
495#102—151no—
496#102—151no—
497C22⋊C8—151no—
498C22⋊C8—151no—
499C4×C8—151no—
500C2×C3×C5—42no—
501C2×C3×C5#54611yescharacteristic
502C2×C3×C5C2×#13511yescharacteristic
503C2×C3×C5#57711yescharacteristic
504C5×D3—22no—
505C5×D3—41no—
506C5×D3—81no—
507C23×C3—21no—
508C22×D3—21no—
509C22×D3—42no—
510C22×D3—42no—
511C22×D3—81no—
512C22×D3C2×C22⋊D511yescharacteristic
513C22×D3C2×C22⋊D511yescharacteristic
514C3×D4—21no—
515C3×D4#71112yes—
516C2×C3×C4—21no—
517C2×C3×C4—81no—
518C2×C3×C4—101no—
519C2×C3×C4—101no—
520C2×C3×C4C2×C22⋊D511yescharacteristic
521C2×C3×C4C2×C22⋊D511yescharacteristic
522C2×C3×C4C23×D511yescharacteristic
523#67—42no—
524#67—42no—
525C2×Dic3—21no—
526C2×Dic3—42no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3C2×C22⋊D511yescharacteristic
530C2×Dic3C2×C22⋊D511yescharacteristic
531D12—22no—
532D12—21no—
533D12—21no—
534D12—81no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—202no—
540Dic6—21no—
541Dic6—21no—
542Dic6—101no—
543Dic6—101no—
544C3×C8—101no—
545C3×C8—101no—
546C3⋊C8—101no—
547C3⋊C8—101no—
548C22×C5—22no—
549C22×C5—32no—
550C22×C5—41no—
551C22×C5—41no—
552C22×C5—61no—
553C22×C5—61no—
554C22×C5—61no—
555C22×C5—61no—
556C22×C5—61no—
557C22×C5—121no—
558C22×C5—121no—
559C22×C5—121no—
560C22×C5—244no—
561C22×C5C2×D3×D411yescharacteristic
562C4×C5—21no—
563C4×C5—21no—
564C4×C5—41no—
565C4×C5—61no—
566C4×C5—61no—
567C4×C5—121no—
568C4×C5C2×#23911yescharacteristic
569C4×C5#100911yescharacteristic
570Dic5—41no—
571Dic5—41no—
572Dic5—121no—
573Dic5—121no—
574C24—61no—
575#41—62no—
576#41—121no—
577C2×Q8—31no—
578C2×Q8—151no—
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—62no—
584C2×D4—61no—
585C2×D4—121no—
586C2×D4C2×D3×D511yescharacteristic
587C22×C4—21no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—301no—
592Q16—601no—
593SD16—302no—
594SD16—601no—
595C2×C8—51no—
596C2×C8—51no—
597C2×C8—151no—
598C2×C8—151no—
599C2×C8—601no—
600C2×C8—601no—
601C4⋊C4—31no—
602C4⋊C4—51no—
603C4⋊C4—51no—
604C4⋊C4—61no—
605C4⋊C4—101no—
606C4⋊C4—101no—
607C4⋊C4—151no—
608C4⋊C4—301no—
609C4⋊C4—301no—
610C4⋊C4—301no—
611C4⋊C4—301no—
612C4⋊C4C2×D3×D511yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—301no—
621C22⋊C4—301no—
622C22⋊C4—301no—
623C42—301no—
624C42—301no—
625C42C2×D3×D511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—22no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3C22×C22⋊D511yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—84no—
640C2×D3#409612yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—41no—
644C3×C4—201no—
645C3×C4—201no—
646C3×C4C2×#71111yescharacteristic
647C3×C4#414411yescharacteristic
648Dic3—21no—
649Dic3—21no—
650Dic3—41no—
651Dic3—201no—
652Dic3—201no—
653C2×C5—42no—
654C2×C5—62no—
655C2×C5—121no—
656C2×C5—241no—
657C2×C5#563011yescharacteristic
658C2×C5D3×#13511yescharacteristic
659C2×C5#577511yescharacteristic
660C23—21no—
661C23—31no—
662C23—31no—
663C23—61no—
664C23—122no—
665C23—122no—
666C23—241no—
667Q8—61no—
668Q8—61no—
669Q8—301no—
670Q8—301no—
671D4—21no—
672D4—62no—
673D4—61no—
674D4—61no—
675D4—122no—
676D4—122no—
677D4—241no—
678D4#676812yes—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—81no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—122no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—602no—
694C2×C4D3×C22⋊D511yescharacteristic
695C2×C4D3×C22⋊D511yescharacteristic
696C2×C4C22×D3×D511yescharacteristic
697C8—101no—
698C8—101no—
699C8—301no—
700C8—301no—
701C2×C3—42no—
702C2×C3#6614011yescharacteristic
703C2×C3C2×#409611yescharacteristic
704C2×C3#6617011yescharacteristic
705D3—22no—
706D3—41no—
707D3—81no—
708C5#8118611yescharacteristic, complemented, Sylow
709C22—22no—
710C22—32no—
711C22—41no—
712C22—41no—
713C22—61no—
714C22—61no—
715C22—61no—
716C22—61no—
717C22—61no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22—244no—
722C22C2×D3×C22⋊D511yescharacteristic
723C4—21no—
724C4—21no—
725C4—41no—
726C4—61no—
727C4—61no—
728C4—121no—
729C4—201no—
730C4—201no—
731C4—601no—
732C4—601no—
733C4C2×#676811yescharacteristic
734C4#9201811yescharacteristic
735C3#1061522511yescharacteristic, complemented, Sylow
736C2—42no—
737C2—62no—
738C2—121no—
739C2—241no—
740C2#1175434911yescharacteristic
741C2#1175472011yescharacteristic
742C2D3×#409611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5554C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3296
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752613C2semidirect
3. C4×#6716C2semidirect
4. C3×#65298C2semidirect
5. #11749056C2semidirect
6. #11749054C2semidirect
7. #11748965C2semidirect
8. D3×#3964C2semidirect
9. #11747448C2semidirect
10. #11747447C2semidirect
11. #11747210C2semidirect
12. #11747197C2semidirect
13. #11746998C2semidirect
14. #11746903C2semidirect
15. #11746884C2semidirect
21. C4×Dic30C22semidirect
30. C3×#4016C22semidirect
36. #91365C22semidirect
37. #91338C22semidirect
39. C2×#6663C22semidirect
42. C2×D3×#168C22semidirect
44. #91094C22semidirect
45. #91092C22semidirect
46. C4×C3⋊#168C22semidirect
49. C3×#3940C22semidirect
50. C3×#3939C22semidirect
51. C3×C4⋊#168C22semidirect
52. #90973C22semidirect
53. #90972C22semidirect
54. #90972C22semidirect
59. (C2×D3)⋊#168C22semidirect
75. #65298D3semidirect
167. #4016C2×D3semidirect
182. #3940C2×D3semidirect
183. #3939C2×D3semidirect
184. C4⋊#168C2×D3semidirect
626. C3×C5#3296semidirect
708. C5#81186semidirect
735. C3#10615225semidirect

Maximal subgroups

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

subgroupindex
C5×#55542
#117526132
C4×#67162
C3×#652982
#117490562
#117490542
#117489652
D3×#39642
#117474482
#117474472
#117472102
#117471972
#117469982
#117469032
#117468842
#106152253
#811865