Finite Group Databasebeta

← #14331007

Subgroups — #14331007

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91421C211yesmaximal, characteristic
2#11751077C211yesmaximal, characteristic, complemented
3C5×#4973C211yesmaximal, characteristic, complemented
4C3×#65279C211yesmaximal, characteristic
5#11748885C211yesmaximal, characteristic
6#11748871C211yesmaximal, characteristic
7#11748847C211yesmaximal, characteristic, complemented
8#11748814C211yesmaximal, characteristic, complemented
9#11748811C211yesmaximal, characteristic, complemented
10#11748802C211yesmaximal, characteristic, complemented
11#11748770C211yesmaximal, characteristic
12#11748710C211yesmaximal, characteristic
13#11748707C211yesmaximal, characteristic
14#11748692C211yesmaximal, characteristic, complemented
15#11748650C211yesmaximal, characteristic, complemented
16#10608348—31nomaximal, Hall
17C22×C5×Dic6C2211yescharacteristic
18C22×D5×Dic3C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×#6712C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×#6712C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×#685C2211yescharacteristic
26C2×C3×#685C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×Dic3⋊Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×#6669C2211yescharacteristic
32C2×#6668C2211yescharacteristic
33C2×#6668C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×#6665C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38#91421C418yescomplemented
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41C5×C3⋊#95C2211yescharacteristic
42C5×C3⋊#95C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#75491—51nomaximal, Hall
54C2×#4092—31no—
55C5×#391—31no—
56#65519—31no—
57#65279D311yescharacteristic
58#65261—31no—
59#65229—31no—
60#65222—31no—
61#64959—31no—
62#64958—31no—
63#64956—31no—
64#64953—31no—
65#64943—31no—
66#64942—31no—
67#64941—31no—
68#64936—31no—
69C23×C3×D5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C2×C5×Dic6—41no—
82C2×C5×Dic6—41no—
83C2×C5×Dic6C2×C414yes—
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×D5×Dic3—41no—
88C2×D5×Dic3—41no—
89C2×D5×Dic3C2×C414yes—
90C3×C5×C4⋊C4—41no—
91#6712—41no—
92#6712—41no—
93#6712C2×C414yes—
94C4×Dic15—41no—
95C4×C5×Dic3—41no—
96C3×#685—41no—
97C3×#685—41no—
98C3×#685C2×C414yes—
99C3×C4×Dic5—41no—
100Dic3⋊Dic5—41no—
101Dic3⋊Dic5C2×C414yes—
102#6669—41no—
103#6668—41no—
104#6668C2×C414yes—
105#6665—41no—
106#6665—41no—
107#6665C2×C414yes—
108Dic3×Dic5—41no—
109C2×#878—51no—
110C3×#388—51no—
111#4976—51no—
112#4973D511yescharacteristic, complemented
113#4951—51no—
114#4944—51no—
115#4944—51no—
116#4943—51no—
117#4942—51no—
118#4933—51no—
119#4928—51no—
120#4655—51no—
121#4654—51no—
122#4652—51no—
123#4646—51no—
124C22×C5×Q8—31no—
125C22×C4×D5—31no—
126C2×C5×C4⋊C4C2×D311yescharacteristic
127C2×C42×C5—31no—
128#4092—38no—
129C2×#685—31no—
130C2×#685—31no—
131C2×#685—31no—
132C2×#685C2×D311yescharacteristic
133C2×#685C2×D311yescharacteristic
134C2×#685C2×D311yescharacteristic
135C2×C4⋊Dic5—31no—
136C2×C4⋊Dic5—31no—
137C2×#683—31no—
138C2×#683—31no—
139C2×#683—31no—
140C2×#683—31no—
141C2×#683—31no—
142C2×#683—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5—31no—
145C2×C4×Dic5C2×D311yescharacteristic
146C5×#95—31no—
147C5×#95—31no—
148C5×#95—31no—
149C5×#95—31no—
150#3963—31no—
151#3963—31no—
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963C2×D311yescharacteristic
159#3963C2×D311yescharacteristic
160#2378—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×C3×D5—21no—
163C22×C3×D5—21no—
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5C22×C412yes—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5C22×C412yes—
178C2×Dic15—21no—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15—21no—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15C22×C412yes—
189C2×Dic15C22×C412yes—
190C2×C5×Dic3—21no—
191C2×C5×Dic3—21no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3C22×C412yes—
201C2×C5×Dic3C22×C412yes—
202C5×Dic6—44no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5C22×C412yes—
212D5×Dic3—44no—
213C23×Dic3—51no—
214C22×Dic6C2×D511yescharacteristic
215C2×C3×C4⋊C4C2×D511yescharacteristic
216C2×C3×C22⋊C4—51no—
217C2×C3×C22⋊C4—51no—
218C2×C3×C22⋊C4—51no—
219C2×C3×C42—51no—
220C2×#217—51no—
221C2×#217—51no—
222C2×#217—51no—
223C2×C4⋊Dic3—51no—
224C2×C4⋊Dic3—51no—
225C2×Dic3⋊C4—51no—
226C2×Dic3⋊C4—51no—
227C2×Dic3⋊C4—51no—
228C2×Dic3⋊C4—51no—
229C2×Dic3⋊C4—51no—
230C2×Dic3⋊C4—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×C4×Dic3C2×D511yescharacteristic
234#878—58no—
235C3×#95—51no—
236C3×#95—51no—
237C3⋊#95—51no—
238C3⋊#95—51no—
239C3⋊#95—51no—
240C3⋊#95—51no—
241C3⋊#95—51no—
242C3⋊#95—51no—
243C3⋊#95—51no—
244C3⋊#95—51no—
245C3⋊#95C2×D511yescharacteristic
246C3⋊#95C2×D511yescharacteristic
247C3⋊#95C2×D511yescharacteristic
248C3⋊#95C2×D511yescharacteristic
249C23×D5C22×D311yescharacteristic
250C2×C5×Q8—34no—
251C2×C5×Q8—121no—
252C2×C5×Q8—121no—
253C22×C4×C5—31no—
254C22×C4×C5—31no—
255C22×C4×C5—31no—
256C22×C4×C5—31no—
257C22×C4×C5C22×D311yescharacteristic
258C22×C4×C5C22×D311yescharacteristic
259C22×C4×C5C22×D311yescharacteristic
260C22×Dic5—31no—
261C22×Dic5—31no—
262C22×Dic5—31no—
263C22×Dic5—31no—
264C22×Dic5C22×D311yescharacteristic
265C22×Dic5C22×D311yescharacteristic
266C22×Dic5C22×D311yescharacteristic
267C2×C4×D5—34no—
268C2×C4×D5—121no—
269C2×C4×D5—121no—
270C5×C4⋊C4—41no—
271C42×C5—121no—
272#685—34no—
273#685—41no—
274#685—41no—
275#685—121no—
276#685—121no—
277#685C4×D314yes—
278C4⋊Dic5—34no—
279C4⋊Dic5—121no—
280#683—34no—
281#683—34no—
282#683—121no—
283#683—121no—
284#683—121no—
285#683—121no—
286C4×Dic5—41no—
287C4×Dic5—121no—
288C4×Dic5—121no—
289C2×C22⋊Q8—151no—
290#391—31no—
291#391—151no—
292#389—151no—
293#389—151no—
294#388—51no—
295#388—151no—
296#388—151no—
297#388—151no—
298#387—151no—
299#387—151no—
300#387—151no—
301#387—151no—
302#381—151no—
303#380—151no—
304C22×C3×C5C23×C411yescharacteristic
305C22×C3×C5H(5,𝔽2)11yescharacteristic
306C22×C3×C5H(5,𝔽2)11yescharacteristic
307C22×C3×C5H(5,𝔽2)11yescharacteristic
308C22×C3×C52−1+411yescharacteristic
309C22×C3×C52−1+411yescharacteristic
310C22×C3×C52−1+411yescharacteristic
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—22no—
314C2×C3×D5—41no—
315C2×C3×D5—41no—
316C2×C3×D5—41no—
317C2×C3×D5—41no—
318C3×C4×C5—22no—
319C3×C4×C5—41no—
320C3×C4×C5—41no—
321Dic15—22no—
322Dic15—22no—
323Dic15—41no—
324Dic15—41no—
325C3×Dic5—22no—
326C3×Dic5—41no—
327C3×Dic5—41no—
328C5×Dic3—22no—
329C5×Dic3—22no—
330C5×Dic3—41no—
331C5×Dic3—41no—
332C24×C3—51no—
333C22×C3×C4—51no—
334C22×C3×C4—51no—
335C22×C3×C4—51no—
336C22×C3×C4C22×D511yescharacteristic
337C22×C3×C4C22×D511yescharacteristic
338C22×C3×C4C22×D511yescharacteristic
339C22×Dic3—51no—
340C22×Dic3—51no—
341C22×Dic3—54no—
342C22×Dic3—51no—
343C22×Dic3—51no—
344C22×Dic3—201no—
345C22×Dic3—201no—
346C22×Dic3C22×D511yescharacteristic
347C22×Dic3C22×D511yescharacteristic
348C22×Dic3C22×D511yescharacteristic
349C22×Dic3C22×D511yescharacteristic
350C2×Dic6—41no—
351C2×Dic6—41no—
352C2×Dic6C4×D514yes—
353C3×C4⋊C4—41no—
354C3×C22⋊C4—54no—
355C3×C22⋊C4—201no—
356C3×C22⋊C4—201no—
357C3×C42—201no—
358#217—54no—
359#217—201no—
360#217—201no—
361C4⋊Dic3—54no—
362C4⋊Dic3—201no—
363Dic3⋊C4—54no—
364Dic3⋊C4—54no—
365Dic3⋊C4—201no—
366Dic3⋊C4—201no—
367Dic3⋊C4—201no—
368Dic3⋊C4—201no—
369C4×Dic3—41no—
370C4×Dic3—201no—
371C4×Dic3—201no—
372C23×C5C23×D311yescharacteristic
373C22×D5—21no—
374C22×D5—21no—
375C22×D5—21no—
376C22×D5—21no—
377C22×D5—21no—
378C22×D5—21no—
379C22×D5C2×C4×D312yes—
380C5×Q8—124no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5—32no—
390C2×C4×C5—32no—
391C2×C4×C5—61no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5—61no—
396C2×C4×C5—61no—
397C2×C4×C5—61no—
398C2×C4×C5—61no—
399C2×C4×C5—61no—
400C2×C4×C5—61no—
401C2×C4×C5C2×C4×D312yes—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—21no—
409C2×Dic5—21no—
410C2×Dic5—32no—
411C2×Dic5—32no—
412C2×Dic5—61no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—61no—
418C2×Dic5—61no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421C2×Dic5—61no—
422C2×Dic5C2×C4×D312yes—
423C4×D5—124no—
424C22×Q8—31no—
425C23×C4—151no—
426C22⋊Q8—158no—
427C2×C4⋊C4—151no—
428C2×C4⋊C4—151no—
429C2×C4⋊C4—151no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4—151no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4D3×D511yescharacteristic
436C2×C22⋊C4—51no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4—51no—
439C2×C22⋊C4—151no—
440C2×C22⋊C4—151no—
441C2×C22⋊C4—151no—
442C2×C42—31no—
443C2×C42—51no—
444C2×C42—151no—
445C2×C42—151no—
446#95—31no—
447#95—31no—
448#95—31no—
449#95—31no—
450#95—51no—
451#95—51no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95—151no—
458#95—151no—
459#95—151no—
460C2×C3×C5#51811yescharacteristic
461C2×C3×C5#51911yescharacteristic
462C2×C3×C5#52011yescharacteristic
463C2×C3×C5#56211yescharacteristic
464C2×C3×C5#56211yescharacteristic
465C2×C3×C5#56311yescharacteristic
466C2×C3×C5#56311yescharacteristic
467C3×D5—42no—
468C23×C3—52no—
469C23×C3—101no—
470C23×C3—101no—
471C23×C3—101no—
472C23×C3—101no—
473C23×C3—101no—
474C23×C3—101no—
475C23×C3C23×D511yescharacteristic
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—52no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4—101no—
493C2×C3×C4C2×C4×D512yes—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—52no—
505C2×Dic3—52no—
506C2×Dic3—101no—
507C2×Dic3—101no—
508C2×Dic3—101no—
509C2×Dic3—101no—
510C2×Dic3—101no—
511C2×Dic3—101no—
512C2×Dic3—101no—
513C2×Dic3—101no—
514C2×Dic3—101no—
515C2×Dic3—101no—
516C2×Dic3—204no—
517C2×Dic3C2×C4×D512yes—
518C2×Dic3C2×C4×D512yes—
519Dic6—44no—
520C22×C5C22×C4×D311yescharacteristic
521C22×C5#100411yescharacteristic
522C22×C5#100411yescharacteristic
523C22×C5#100911yescharacteristic
524C22×C5#101011yescharacteristic
525C22×C5#101011yescharacteristic
526C22×C5#101011yescharacteristic
527C2×D5—22no—
528C2×D5—22no—
529C2×D5—22no—
530C2×D5—41no—
531C2×D5—41no—
532C2×D5—41no—
533C2×D5—41no—
534C4×C5—22no—
535C4×C5—41no—
536C4×C5—41no—
537C4×C5—62no—
538C4×C5—62no—
539C4×C5—121no—
540C4×C5—121no—
541Dic5—22no—
542Dic5—41no—
543Dic5—41no—
544Dic5—62no—
545Dic5—62no—
546Dic5—121no—
547Dic5—121no—
548C24—51no—
549C2×Q8—34no—
550C2×Q8—121no—
551C2×Q8—121no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—154no—
560C22×C4—151no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—601no—
565C22×C4—601no—
566C22×C4C2×D3×D511yescharacteristic
567C22×C4C2×D3×D511yescharacteristic
568C22×C4C2×D3×D511yescharacteristic
569C4⋊C4—41no—
570C4⋊C4—154no—
571C4⋊C4—154no—
572C4⋊C4—154no—
573C4⋊C4—601no—
574C4⋊C4—601no—
575C4⋊C4—601no—
576C4⋊C4—601no—
577C4⋊C4—601no—
578C22⋊C4—54no—
579C22⋊C4—154no—
580C22⋊C4—201no—
581C22⋊C4—201no—
582C22⋊C4—601no—
583C22⋊C4—601no—
584C42—121no—
585C42—201no—
586C42—601no—
587C42—601no—
588C3×C5#237811yescharacteristic, complemented, Hall
589C22×C3—102no—
590C22×C3—102no—
591C22×C3—102no—
592C22×C3—201no—
593C22×C3—201no—
594C22×C3—201no—
595C22×C3—201no—
596C22×C3C22×C4×D511yescharacteristic
597C22×C3#414411yescharacteristic
598C22×C3#414411yescharacteristic
599C22×C3#414711yescharacteristic
600C22×C3#414711yescharacteristic
601C22×C3#414911yescharacteristic
602C22×C3#415011yescharacteristic
603C3×C4—22no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—102no—
607C3×C4—201no—
608C3×C4—201no—
609Dic3—22no—
610Dic3—22no—
611Dic3—41no—
612Dic3—41no—
613Dic3—102no—
614Dic3—102no—
615Dic3—201no—
616Dic3—201no—
617C2×C5#551611yescharacteristic
618C2×C5#554511yescharacteristic
619C2×C5#554611yescharacteristic
620C2×C5#562111yescharacteristic
621C2×C5#566711yescharacteristic
622C2×C5#567211yescharacteristic
623C2×C5#571211yescharacteristic
624D5—42no—
625C23—52no—
626C23—101no—
627C23—101no—
628C23—101no—
629C23—101no—
630C23—101no—
631C23—101no—
632C23C22×D3×D511yescharacteristic
633Q8—124no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—32no—
643C2×C4—32no—
644C2×C4—52no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—101no—
656C2×C4—101no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—101no—
662C2×C4—101no—
663C2×C4—152no—
664C2×C4—152no—
665C2×C4—301no—
666C2×C4—301no—
667C2×C4—301no—
668C2×C4—301no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—301no—
672C2×C4—301no—
673C2×C4—301no—
674C2×C4—301no—
675C2×C4—604no—
676C2×C4C4×D3×D512yes—
677C2×C3—202no—
678C2×C3#6582011yescharacteristic
679C2×C3#6590611yescharacteristic
680C2×C3#6590811yescharacteristic
681C2×C3#6598011yescharacteristic
682C2×C3#6598111yescharacteristic
683C2×C3#6601811yescharacteristic
684C2×C3#6606911yescharacteristic
685C5#7549111yescharacteristic, complemented, Sylow
686C22—102no—
687C22—102no—
688C22—102no—
689C22—201no—
690C22—201no—
691C22—201no—
692C22—201no—
693C22C2×C4×D3×D511yescharacteristic
694C22#9201811yescharacteristic
695C22#9202011yescharacteristic
696C22#9202611yescharacteristic
697C22#9202811yescharacteristic
698C22#9202811yescharacteristic
699C22#9204911yescharacteristic
700C4—22no—
701C4—41no—
702C4—41no—
703C4—62no—
704C4—62no—
705C4—102no—
706C4—121no—
707C4—121no—
708C4—201no—
709C4—201no—
710C4—302no—
711C4—302no—
712C4—601no—
713C4—601no—
714C3#1060834811yescharacteristic, complemented, Sylow
715C2—202no—
716C2#1175339711yescharacteristic
717C2#1175340111yescharacteristic
718C2#1175365211yescharacteristic
719C2#1175381711yescharacteristic
720C2#1175462711yescharacteristic
721C2#1175490811yescharacteristic
722C2#1175521511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2378
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751077C2semidirect
3. C5×#4973C2semidirect
7. #11748847C2semidirect
8. #11748814C2semidirect
9. #11748811C2semidirect
10. #11748802C2semidirect
14. #11748692C2semidirect
15. #11748650C2semidirect
38. #91421C4semidirect
112. #4973D5semidirect
588. C3×C5#2378semidirect
685. C5#75491semidirect
714. C3#10608348semidirect

Maximal subgroups

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

subgroupindex
C2×#914212
#117510772
C5×#49732
C3×#652792
#117488852
#117488712
#117488472
#117488142
#117488112
#117488022
#117487702
#117487102
#117487072
#117486922
#117486502
#106083483
#754915