Finite Group Databasebeta

← #14458704

Subgroups — #14458704

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
1#11756300C211yesmaximal, characteristic, complemented
2C5×#5550C211yesmaximal, characteristic
3C3×D4×#168C211yesmaximal, characteristic, complemented
4#11748557C211yesmaximal, characteristic, complemented
5#11748543C211yesmaximal, characteristic, complemented
6#11748533C211yesmaximal, characteristic, complemented
7#11748447C211yesmaximal, characteristic, complemented
8#11748388C211yesmaximal, characteristic, complemented
9C2×#90967C211yesmaximal, characteristic, complemented
10#11748378C211yesmaximal, characteristic, complemented
11#11748361C211yesmaximal, characteristic, complemented
12C4×#6659C211yesmaximal, characteristic, complemented
13#11746907C211yesmaximal, characteristic, complemented
14#11746894C211yesmaximal, characteristic, complemented
15#11746884C211yesmaximal, characteristic, complemented
16#10615225—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20#91824—21no—
21#91815C2211yescharacteristic, complemented
22C2×C4⋊Dic15C2211yescharacteristic
23#91813C2211yescharacteristic
24#91813C2211yescharacteristic, complemented
25#91778—21no—
26#91768—21no—
27#91766—21no—
28#91759C2211yescharacteristic, complemented
29C4×Dic30C2211yescharacteristic, complemented
30C5×#937—21no—
31C5×#930C2211yescharacteristic
32C5×#924C2211yescharacteristic
33C5×#894—21no—
34C5×#884—21no—
35C5×D3×C22⋊C4—21no—
36C5×#875C2211yescharacteristic
37C4×C5×D12C2211yescharacteristic
38C22×C3×#168C2211yescharacteristic
39C22×C3×#168C2211yescharacteristic, complemented
40C2×#6663C2211yescharacteristic, complemented
41C2×#6659C2211yescharacteristic
42C2×#6659C2211yescharacteristic
43C3×C22⋊#168C2211yescharacteristic
44C3×C22⋊#168C2211yescharacteristic, complemented
45C3×C4⋊#168C2211yescharacteristic, complemented
46C3×C4×#168C2211yescharacteristic, complemented
47#90988C2211yescharacteristic, complemented
48#90985C2211yescharacteristic, complemented
49#90985C2211yescharacteristic, complemented
50#90975C2211yescharacteristic, complemented
51#90973C2211yescharacteristic, complemented
52#90973C2211yescharacteristic, complemented
53#90973C2211yescharacteristic, complemented
54#90967C2211yescharacteristic
55#90967C2211yescharacteristic
56#90967C2211yescharacteristic
57#90967C2211yescharacteristic
58#90967C2211yescharacteristic
59#90967C2211yescharacteristic
60#79440—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×#168D311yescharacteristic, complemented
75#65298—31no—
76C23×C5×D3—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×Dic15—21no—
81C2×Dic30C2311yescharacteristic
82C2×C5×#67—21no—
83C2×C5×#67—21no—
84C5×#235—22no—
85C5×#235—41no—
86C2×C5×D12—22no—
87C2×C5×D12—21no—
88C2×C5×D12—41no—
89C2×C5×D12C2311yescharacteristic
90C2×C5×D12C2311yescharacteristic
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3—21no—
93C2×C5×Dic6C2311yescharacteristic
94C3×C5×C4⋊C4D411yescharacteristic
95C3×C5×C22⋊C4D411yescharacteristic
96C3×C5×C22⋊C4D411yescharacteristic
97C3×C42×C5C2311yescharacteristic
98#6719—21no—
99#6719—21no—
100#6719—21no—
101C4⋊Dic15—21no—
102C4⋊Dic15C2311yescharacteristic
103C4⋊Dic15C2311yescharacteristic
104C4⋊Dic15C2311yescharacteristic
105#6712—21no—
106#6712—21no—
107#6712—21no—
108#6712—21no—
109#6712—21no—
110C4×Dic15—21no—
111C4×Dic15—21no—
112C5×#217—21no—
113C5×(C2×D3)⋊C4—21no—
114C5×(C2×D3)⋊C4—21no—
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4—21no—
117C5×C4⋊Dic3C2311yescharacteristic
118C5×Dic3⋊C4—21no—
119C2×C3×#168—41no—
120C2×C3×#168—41no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125#6663—41no—
126#6659—22no—
127#6659—41no—
128#5550D511yescharacteristic
129#5541—51no—
130C3×C8×D4—51no—
131#5116—51no—
132#5114—51no—
133#5113—51no—
134C2×#821—51no—
135#4847—51no—
136#4845—51no—
137#4737—51no—
138#4733—51no—
139#4731—51no—
140#4721—51no—
141#4697—51no—
142C4×#204—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×#168C2×D311yescharacteristic
163C22×#168C2×D311yescharacteristic, complemented
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⋊#168C2×D311yescharacteristic
179C22⋊#168C2×D311yescharacteristic, complemented
180#3942—31no—
181#3940—31no—
182#3940—31no—
183#3939—31no—
184C4⋊#168C2×D311yescharacteristic, complemented
185C4×#168C2×D311yescharacteristic, complemented
186#3296—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—42no—
192C22×C5×D3—42no—
193C22×C5×D3—81no—
194C3×C5×D4—22no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—21no—
208C2×Dic15—42no—
209Dic30—21no—
210Dic30—21no—
211C5×#67—42no—
212C5×#67—81no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C5×D12—21no—
216C5×D12—21no—
217C5×D12—21no—
218C5×D12—42no—
219C5×D12#4112yes—
220C4×C5×D3—42no—
221C4×C5×D3—81no—
222C5×Dic6—21no—
223C5×Dic6—21no—
224C3×#168—21no—
225C3×#168—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×#235C2×D511yescharacteristic
229C22×D12C2×D511yescharacteristic
230C22×C3×C8—51no—
231C22×C3×C8—51no—
232C3×C4×D4C2×D511yescharacteristic
233#937—21no—
234#935—101no—
235#930C2×D511yescharacteristic
236#926—51no—
237C2×C4⋊Dic3—51no—
238#924—51no—
239#924—51no—
240#924C2×D511yescharacteristic
241C2×Dic12—51no—
242C2×#204—51no—
243C2×#204—51no—
244#894—21no—
245#889—101no—
246#884—21no—
247D3×C22⋊C4—21no—
248#879—101no—
249#877—101no—
250#875C2×D511yescharacteristic
251C4×D12C2×D511yescharacteristic
252#870—51no—
253C4×Dic6—51no—
254C3×C4⋊C8—51no—
255C3×C22⋊C8—51no—
256C3×C22⋊C8—51no—
257C3×C4×C8—51no—
258#821—51no—
259#821—51no—
260#821—51no—
261#821—51no—
262#821—51no—
263#821—51no—
264#818—51no—
265#817—51no—
266#817—51no—
267#816—51no—
268#816—51no—
269#816—51no—
270#816—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—62no—
278C2×C5×D4—61no—
279C2×C5×D4—61no—
280C2×C5×D4—61no—
281C2×C5×D4—121no—
282C2×C5×D4D1211yescharacteristic
283C22×C4×C5—61no—
284C22×C4×C5—61no—
285C22×C4×C5C22×D311yescharacteristic
286C22×C4×C5C22×D311yescharacteristic
287C22×Dic5—61no—
288C2×Dic10—31no—
289C5×C4⋊C4—31no—
290C5×C4⋊C4—61no—
291C5×C4⋊C4D1211yescharacteristic
292C5×C22⋊C4—61no—
293C5×C22⋊C4—61no—
294C5×C22⋊C4—61no—
295C5×C22⋊C4—61no—
296C5×C22⋊C4—61no—
297C5×C22⋊C4D1211yescharacteristic
298C5×C22⋊C4D1211yescharacteristic
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—41no—
318C2×#168—41no—
319C2×#168C22×D311yescharacteristic
320C2×#168C22×D311yescharacteristic
321C2×#168C22×D311yescharacteristic
322C2×#168C22×D311yescharacteristic
323#552—151no—
324#546—31no—
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—51no—
336#416—151no—
337C2×#102—151no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5#13512yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×C5×D3—22no—
346C2×C5×D3—41no—
347C2×C5×D3—41no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C5×D3—84no—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—21no—
355C3×C4×C5—21no—
356C3×C4×C5C2×#4111yescharacteristic
357C3×C4×C5H(5,𝔽2)11yescharacteristic
358Dic15—41no—
359Dic15—41no—
360Dic15—41no—
361Dic15—41no—
362C5×Dic3—41no—
363C5×Dic3—41no—
364C23×D3—21no—
365C2×C3×D4C22⋊D511yescharacteristic
366C22×C3×C4C22×D511yescharacteristic
367C22×C3×C4C22×D511yescharacteristic
368C2×#67—21no—
369C2×#67—21no—
370C22×Dic3—101no—
371#235—22no—
372#235—41no—
373C2×D12—22no—
374C2×D12—21no—
375C2×D12—41no—
376C2×D12C22×D511yescharacteristic
377C2×D12C22×D511yescharacteristic
378C2×C4×D3—21no—
379C2×C4×D3—21no—
380C2×Dic6—51no—
381C2×Dic6C22×D511yescharacteristic
382C2×C3×C8—51no—
383C2×C3×C8—51no—
384C2×C3×C8—51no—
385C2×C3×C8—51no—
386C2×C3×C8—201no—
387C2×C3×C8—201no—
388C3×C4⋊C4C22⋊D511yescharacteristic
389C3×C22⋊C4C22⋊D511yescharacteristic
390C3×C22⋊C4C22⋊D511yescharacteristic
391C3×C42C22×D511yescharacteristic
392#217—21no—
393#217—101no—
394#217—101no—
395#217—101no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400C4⋊Dic3—51no—
401C4⋊Dic3—51no—
402C4⋊Dic3—51no—
403C4⋊Dic3—101no—
404C4⋊Dic3C22×D511yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—101no—
407Dic3⋊C4—101no—
408Dic3⋊C4—101no—
409Dic3⋊C4—101no—
410Dic3⋊C4—101no—
411C4×Dic3—101no—
412C4×Dic3—101no—
413Dic12—201no—
414#204—102no—
415#204—201no—
416C23×C5—61no—
417C23×C5—61no—
418C23×C5—122no—
419C23×C5—122no—
420C23×C5—241no—
421C23×C5C2×D1211yescharacteristic
422C23×C5C2×D1211yescharacteristic
423C5×Q8—61no—
424C5×Q8—61no—
425C5×D4—22no—
426C5×D4—32no—
427C5×D4—61no—
428C5×D4—61no—
429C5×D4—61no—
430C5×D4—122no—
431C5×D4—122no—
432C5×D4—241no—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—61no—
438C2×C4×C5—61no—
439C2×C4×C5—122no—
440C2×C4×C5—241no—
441C2×C4×C5C2×D1211yescharacteristic
442C2×C4×C5C2×D1211yescharacteristic
443C2×C4×C5C2×D1211yescharacteristic
444C2×C4×C5C2×D1211yescharacteristic
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—21no—
454#168—21no—
455#168—21no—
456#168—21no—
457C2×#41—31no—
458C22×D4—31no—
459C2×Q16—151no—
460C2×SD16—151no—
461C2×SD16—151no—
462C22×C8—51no—
463C22×C8—51no—
464#126—301no—
465#125—151no—
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—151no—
484#106—151no—
485#106—151no—
486C4⋊C8—51no—
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—51no—
498C22⋊C8—51no—
499C4×C8—51no—
500C2×C3×C5—22no—
501C2×C3×C5—41no—
502C2×C3×C5#54611yescharacteristic
503C2×C3×C5C2×#13511yescharacteristic
504C2×C3×C5#57711yescharacteristic
505C5×D3—42no—
506C5×D3—81no—
507C23×C3C2×C22⋊D511yescharacteristic
508C23×C3C2×C22⋊D511yescharacteristic
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—42no—
512C22×D3—42no—
513C22×D3—81no—
514C3×D4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4C2×C22⋊D511yescharacteristic
520C2×C3×C4C2×C22⋊D511yescharacteristic
521C2×C3×C4C2×C22⋊D511yescharacteristic
522C2×C3×C4C2×C22⋊D511yescharacteristic
523C2×C3×C4C23×D511yescharacteristic
524#67—42no—
525#67—81no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—202no—
533D12—21no—
534D12—21no—
535D12—21no—
536D12—42no—
537D12#71112yes—
538C4×D3—42no—
539C4×D3—81no—
540Dic6—21no—
541Dic6—21no—
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—21no—
552C22×C5—21no—
553C22×C5—62no—
554C22×C5—121no—
555C22×C5—121no—
556C22×C5—121no—
557C22×C5—121no—
558C22×C5—121no—
559C22×C5—244no—
560C22×C5#90412yes—
561C22×C5C22×D1211yescharacteristic
562C4×C5—21no—
563C4×C5—21no—
564C4×C5—21no—
565C4×C5—21no—
566C4×C5—121no—
567C4×C5—121no—
568C4×C5#100411yescharacteristic
569C4×C5D3×#4111yescharacteristic
570Dic5—121no—
571Dic5—121no—
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—62no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—121no—
586C2×D4#120311yescharacteristic
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—301no—
590C22×C4C2×D3×D511yescharacteristic
591C22×C4C2×D3×D511yescharacteristic
592Q16—601no—
593SD16—302no—
594SD16—601no—
595C2×C8—51no—
596C2×C8—51no—
597C2×C8—51no—
598C2×C8—51no—
599C2×C8—201no—
600C2×C8—201no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—151no—
604C4⋊C4—151no—
605C4⋊C4—151no—
606C4⋊C4—301no—
607C4⋊C4—301no—
608C4⋊C4—301no—
609C4⋊C4—301no—
610C4⋊C4—301no—
611C4⋊C4—301no—
612C4⋊C4#120311yescharacteristic
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—301no—
619C22⋊C4—301no—
620C22⋊C4—301no—
621C22⋊C4#120311yescharacteristic
622C22⋊C4#120311yescharacteristic
623C42—301no—
624C42—301no—
625C42C2×D3×D511yescharacteristic
626C3×C5#329611yescharacteristic, complemented, Hall
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3#409612yes—
633C22×C3C22×C22⋊D511yescharacteristic
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—84no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4C2×#71111yescharacteristic
646C3×C4#414411yescharacteristic
647Dic3—41no—
648Dic3—41no—
649Dic3—201no—
650Dic3—201no—
651Dic3—201no—
652Dic3—201no—
653C2×C5—22no—
654C2×C5—41no—
655C2×C5—122no—
656C2×C5—241no—
657C2×C5#555411yescharacteristic
658C2×C5C2×#90411yescharacteristic
659C2×C5#575111yescharacteristic
660C23—61no—
661C23—61no—
662C23—122no—
663C23—122no—
664C23—241no—
665C23C2×#120311yescharacteristic
666C23C2×#120311yescharacteristic
667Q8—61no—
668Q8—61no—
669Q8—301no—
670Q8—301no—
671D4—22no—
672D4—32no—
673D4—61no—
674D4—61no—
675D4—61no—
676D4—122no—
677D4—122no—
678D4—241no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—122no—
686C2×C4—241no—
687C2×C4—301no—
688C2×C4—301no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—602no—
692C2×C4C2×#120311yescharacteristic
693C2×C4C2×#120311yescharacteristic
694C2×C4C2×#120311yescharacteristic
695C2×C4C2×#120311yescharacteristic
696C2×C4C22×D3×D511yescharacteristic
697C8—101no—
698C8—101no—
699C8—101no—
700C8—101no—
701C2×C3—22no—
702C2×C3—41no—
703C2×C3#6614011yescharacteristic
704C2×C3C2×#409611yescharacteristic
705C2×C3#6617011yescharacteristic
706D3—42no—
707D3—81no—
708C5#7944011yescharacteristic, complemented, Sylow
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—62no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22—121no—
720C22—244no—
721C22#9130312yes—
722C22C22×#120311yescharacteristic
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—121no—
728C4—121no—
729C4—601no—
730C4—601no—
731C4—601no—
732C4—601no—
733C4D3×#71111yescharacteristic
734C4#9202511yescharacteristic
735C3#1061522511yescharacteristic, complemented, Sylow
736C2—22no—
737C2—41no—
738C2—122no—
739C2—241no—
740C2C2×#9130311yescharacteristic
741C2#1175497511yescharacteristic
742C2#1175530711yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5550C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3296
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. #11756300C2semidirect
3. C3×D4×#168C2semidirect
4. #11748557C2semidirect
5. #11748543C2semidirect
6. #11748533C2semidirect
7. #11748447C2semidirect
8. #11748388C2semidirect
9. C2×#90967C2semidirect
10. #11748378C2semidirect
11. #11748361C2semidirect
12. C4×#6659C2semidirect
13. #11746907C2semidirect
14. #11746894C2semidirect
15. #11746884C2semidirect
21. #91815C22semidirect
24. #91813C22semidirect
28. #91759C22semidirect
29. C4×Dic30C22semidirect
39. C22×C3×#168C22semidirect
40. C2×#6663C22semidirect
44. C3×C22⋊#168C22semidirect
45. C3×C4⋊#168C22semidirect
46. C3×C4×#168C22semidirect
47. #90988C22semidirect
48. #90985C22semidirect
49. #90985C22semidirect
50. #90975C22semidirect
51. #90973C22semidirect
52. #90973C22semidirect
53. #90973C22semidirect
74. D4×#168D3semidirect
163. C22×#168C2×D3semidirect
179. C22⋊#168C2×D3semidirect
184. C4⋊#168C2×D3semidirect
185. C4×#168C2×D3semidirect
626. C3×C5#3296semidirect
708. C5#79440semidirect
735. C3#10615225semidirect

Maximal subgroups

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

subgroupindex
#117563002
C5×#55502
C3×D4×#1682
#117485572
#117485432
#117485332
#117484472
#117483882
C2×#909672
#117483782
#117483612
C4×#66592
#117469072
#117468942
#117468842
#106152253
#794405