Finite Group Databasebeta

← #14326802

Subgroups — #14326802

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91403C211yesmaximal, characteristic
2#11750770C211yesmaximal, characteristic
3C5×#4650C211yesmaximal, characteristic, complemented
4C3×#64938C211yesmaximal, characteristic, complemented
5#11748876C211yesmaximal, characteristic
6#11748875C211yesmaximal, characteristic
7#11748829C211yesmaximal, characteristic
8#11748801C211yesmaximal, characteristic, complemented
9#11748727C211yesmaximal, characteristic
10#11748669C211yesmaximal, characteristic
11#11748644C211yesmaximal, characteristic, complemented
12#11748637C211yesmaximal, characteristic, complemented
13#11748635C211yesmaximal, characteristic, complemented
14#11748629C211yesmaximal, characteristic, complemented
15#11748611C211yesmaximal, characteristic, complemented
16#10605887—31nomaximal, Hall
17C22×#1200C2211yescharacteristic
18C2×#6714C2211yescharacteristic
19C2×#6714C2211yescharacteristic
20C2×#6714C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×Dic3⋊C4C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×#6669C2211yescharacteristic
32C2×#6668C2211yescharacteristic
33C2×#6668C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×#6667C2211yescharacteristic
36C2×#6667C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40#91403C418yescomplemented
41C3×C5×#95C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#73633—51nomaximal, Hall
54C2×#4018—31no—
55C5×#382—31no—
56#65279—31no—
57#65279—31no—
58#65261—31no—
59#65261—31no—
60#65221—31no—
61#64958—31no—
62#64958—31no—
63#64956—31no—
64#64955—31no—
65#64939—31no—
66#64938—31no—
67#64938D311yescharacteristic, complemented
68#64937—31no—
69C23×D15C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×C5×Dic3C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×#1200—22no—
85C2×#1200—22no—
86C2×#1200C2×C414yes—
87#6714—22no—
88#6714—41no—
89#6714C2×C414yes—
90#6712—41no—
91C4×Dic15—22no—
92C5×Dic3⋊C4—41no—
93C5×Dic3⋊C4—41no—
94C4×C5×Dic3C2×C414yes—
95C3×#683—22no—
96C3×#683C2×C414yes—
97C3×C4×Dic5—22no—
98C3×C4×Dic5—22no—
99C3×C4×Dic5—22no—
100#6669—41no—
101#6668—22no—
102#6668C2×C414yes—
103#6667—22no—
104#6667—41no—
105#6667C2×C414yes—
106Dic3×Dic5—22no—
107Dic3×Dic5—22no—
108Dic3×Dic5C2×C414yes—
109C2×#892—51no—
110C3×C4×C4⋊C4—51no—
111#4987—51no—
112Dic3×C4⋊C4—51no—
113#4972—51no—
114#4940—51no—
115#4940—51no—
116C4×(C2×D3)⋊C4—51no—
117#4932—51no—
118#4932—51no—
119#4928—51no—
120#4669—51no—
121#4669—51no—
122#4650—51no—
123#4650D511yescharacteristic, complemented
124C22×C4×D5—31no—
125C2×C5×C4⋊C4—31no—
126C2×C5×C4⋊C4—31no—
127C2×C42×C5—31no—
128C2×#685—31no—
129C2×#685—31no—
130C2×#685—31no—
131C2×#685—31no—
132C2×#685—31no—
133C2×#685—31no—
134C2×#683—31no—
135C2×#683—31no—
136C2×#683—31no—
137C2×#683—31no—
138C2×#683C2×D311yescharacteristic
139C2×#683C2×D311yescharacteristic
140C2×C4×Dic5—31no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—31no—
143C2×C4×Dic5—31no—
144C2×C4×Dic5C2×D311yescharacteristic
145C2×C4×Dic5C2×D311yescharacteristic
146C2×C4×Dic5C2×D311yescharacteristic
147#4018—38no—
148C5×#95—31no—
149C5×#95—31no—
150C5×#95—31no—
151C5×#95C2×D311yescharacteristic
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963C2×D311yescharacteristic
160#2346—151noSylow
161C23×C3×C5C2411yescharacteristic
162C22×D15—21no—
163C22×D15—21no—
164C22×D15—21no—
165C22×D15—21no—
166C22×D15—21no—
167C22×D15—21no—
168C22×D15C22×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×Dic15C22×C412yes—
186C2×Dic15#4112yes—
187C2×C5×Dic3—21no—
188C2×C5×Dic3—21no—
189C2×C5×Dic3—21no—
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×Dic3C22×C412yes—
198C2×C5×Dic3C22×C412yes—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5C22×C412yes—
207C2×C3×Dic5C22×C412yes—
208C2×C3×Dic5#4112yes—
209C2×C3×Dic5#4112yes—
210C2×C3×Dic5#4112yes—
211#1200—28no—
212C22×C4×D3—51no—
213C2×C3×C4⋊C4—51no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C42—51no—
216C2×C3×C42—51no—
217C2×C3×C42—51no—
218C2×(C2×D3)⋊C4—51no—
219C2×(C2×D3)⋊C4—51no—
220C2×(C2×D3)⋊C4—51no—
221C2×(C2×D3)⋊C4—51no—
222C2×(C2×D3)⋊C4—51no—
223C2×(C2×D3)⋊C4—51no—
224C2×C4⋊Dic3—51no—
225C2×C4⋊Dic3—51no—
226C2×Dic3⋊C4—51no—
227C2×Dic3⋊C4—51no—
228C2×Dic3⋊C4C2×D511yescharacteristic
229C2×Dic3⋊C4C2×D511yescharacteristic
230C2×C4×Dic3—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×C4×Dic3—51no—
234C2×C4×Dic3C2×D511yescharacteristic
235#892—58no—
236C3×#95—51no—
237C3×#95C2×D511yescharacteristic
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
248C23×D5—31no—
249C22×C4×C5—31no—
250C22×C4×C5—31no—
251C22×C4×C5—31no—
252C22×C4×C5—31no—
253C22×C4×C5C22×D311yescharacteristic
254C22×C4×C5C22×D311yescharacteristic
255C22×C4×C5C22×D311yescharacteristic
256C22×Dic5—31no—
257C22×Dic5—31no—
258C22×Dic5—31no—
259C22×Dic5C22×D311yescharacteristic
260C22×Dic5C22×D311yescharacteristic
261C22×Dic5C22×D311yescharacteristic
262C22×Dic5C22×D311yescharacteristic
263C2×C4×D5—34no—
264C2×C4×D5—62no—
265C2×C4×D5—62no—
266C5×C4⋊C4—121no—
267C5×C4⋊C4—121no—
268C42×C5—34no—
269#685—34no—
270#685—34no—
271#685—62no—
272#685—62no—
273#685—121no—
274#685—121no—
275#683—22no—
276#683—34no—
277#683—62no—
278#683—121no—
279#683—121no—
280#683C4×D314yes—
281C4×Dic5—22no—
282C4×Dic5—22no—
283C4×Dic5—22no—
284C4×Dic5—34no—
285C4×Dic5—62no—
286C4×Dic5—62no—
287C4×Dic5—62no—
288C2×#117—151no—
289#389—151no—
290#389—151no—
291#388—151no—
292#388—151no—
293#388—151no—
294#388—151no—
295#382—31no—
296#382—151no—
297#380—151no—
298C4×C4⋊C4—51no—
299C4×C4⋊C4—151no—
300C4×C22⋊C4—151no—
301#376—151no—
302#376—151no—
303C22×C3×C5C23×C411yescharacteristic
304C22×C3×C5C2×#4111yescharacteristic
305C22×C3×C5C2×#4111yescharacteristic
306C22×C3×C5C2×#4111yescharacteristic
307C22×C3×C5C2×#4111yescharacteristic
308C22×C3×C5H(5,𝔽2)11yescharacteristic
309C22×C3×C52−1+411yescharacteristic
310C2×D15—22no—
311C2×D15—22no—
312C2×D15—22no—
313C2×D15—41no—
314C2×D15—41no—
315C2×D15—41no—
316C2×D15—41no—
317C3×C4×C5—22no—
318C3×C4×C5—41no—
319C3×C4×C5—41no—
320Dic15—22no—
321Dic15—22no—
322Dic15—41no—
323C3×Dic5—22no—
324C3×Dic5—22no—
325C3×Dic5—41no—
326C3×Dic5#11714yes—
327C5×Dic3—22no—
328C5×Dic3—22no—
329C5×Dic3—41no—
330C5×Dic3—41no—
331C23×D3—51no—
332C22×C3×C4—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—51no—
342C22×Dic3C22×D511yescharacteristic
343C22×Dic3C22×D511yescharacteristic
344C22×Dic3C22×D511yescharacteristic
345C22×Dic3C22×D511yescharacteristic
346C2×C4×D3—54no—
347C2×C4×D3—102no—
348C2×C4×D3—102no—
349C3×C4⋊C4—54no—
350C3×C4⋊C4—102no—
351C3×C42—102no—
352C3×C42—102no—
353C3×C42—102no—
354(C2×D3)⋊C4—54no—
355(C2×D3)⋊C4—54no—
356(C2×D3)⋊C4—102no—
357(C2×D3)⋊C4—102no—
358(C2×D3)⋊C4—201no—
359(C2×D3)⋊C4—201no—
360C4⋊Dic3—54no—
361C4⋊Dic3—102no—
362Dic3⋊C4—41no—
363Dic3⋊C4—41no—
364Dic3⋊C4—201no—
365Dic3⋊C4—201no—
366C4×Dic3—54no—
367C4×Dic3—102no—
368C4×Dic3—102no—
369C4×Dic3—102no—
370C4×Dic3C4×D514yes—
371C23×C5C23×D311yescharacteristic
372C22×D5—32no—
373C22×D5—61no—
374C22×D5—61no—
375C22×D5—61no—
376C22×D5—61no—
377C22×D5—61no—
378C22×D5—61no—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
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—32no—
388C2×C4×C5—32no—
389C2×C4×C5—61no—
390C2×C4×C5—61no—
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×C5C2×C4×D312yes—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—32no—
408C2×Dic5—32no—
409C2×Dic5—61no—
410C2×Dic5—61no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5C2×C4×D312yes—
417C2×Dic5C2×C4×D312yes—
418C2×Dic5#23512yes—
419C2×Dic5#23512yes—
420C2×Dic5#23712yes—
421C4×D5—68no—
422C23×C4—151no—
423#117—158no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—51no—
427C2×C4⋊C4—51no—
428C2×C4⋊C4—151no—
429C2×C4⋊C4—151no—
430C2×C4⋊C4—151no—
431C2×C4⋊C4—151no—
432C2×C22⋊C4—151no—
433C2×C22⋊C4—151no—
434C2×C22⋊C4—151no—
435C2×C22⋊C4—151no—
436C2×C22⋊C4—151no—
437C2×C22⋊C4—151no—
438C2×C42—31no—
439C2×C42—51no—
440C2×C42—51no—
441C2×C42—51no—
442C2×C42—151no—
443C2×C42—151no—
444C2×C42—151no—
445C2×C42—151no—
446#95—31no—
447#95—31no—
448#95—31no—
449#95—51no—
450#95—151no—
451#95—151no—
452#95—151no—
453#95—151no—
454#95—151no—
455#95—151no—
456#95—151no—
457#95D3×D511yescharacteristic
458C2×C3×C5C2×#11711yescharacteristic
459C2×C3×C5C4×#4111yescharacteristic
460C2×C3×C5#52011yescharacteristic
461C2×C3×C5#55211yescharacteristic
462C2×C3×C5#55211yescharacteristic
463C2×C3×C5#55511yescharacteristic
464C2×C3×C5#55511yescharacteristic
465D15—42no—
466C23×C3C23×D511yescharacteristic
467C22×D3—52no—
468C22×D3—101no—
469C22×D3—101no—
470C22×D3—101no—
471C22×D3—101no—
472C22×D3—101no—
473C22×D3—101no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
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—52no—
483C2×C3×C4—52no—
484C2×C3×C4—52no—
485C2×C3×C4—52no—
486C2×C3×C4—52no—
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×C4—101no—
494C2×C3×C4C2×C4×D512yes—
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—21no—
505C2×Dic3—52no—
506C2×Dic3—52no—
507C2×Dic3—101no—
508C2×Dic3—101no—
509C2×Dic3—101no—
510C2×Dic3—101no—
511C2×Dic3—101no—
512C2×Dic3—101no—
513C2×Dic3—101no—
514C2×Dic3C2×C4×D512yes—
515C2×Dic3C2×C4×D512yes—
516C4×D3—108no—
517C22×C5C22×C4×D311yescharacteristic
518C22×C5C2×#23511yescharacteristic
519C22×C5C2×#23511yescharacteristic
520C22×C5C2×#23711yescharacteristic
521C22×C5#100711yescharacteristic
522C22×C5D3×#4111yescharacteristic
523C22×C5#100911yescharacteristic
524C2×D5—62no—
525C2×D5—62no—
526C2×D5—62no—
527C2×D5—121no—
528C2×D5—121no—
529C2×D5—121no—
530C2×D5—121no—
531C4×C5—22no—
532C4×C5—41no—
533C4×C5—41no—
534C4×C5—62no—
535C4×C5—62no—
536C4×C5—121no—
537C4×C5—121no—
538Dic5—22no—
539Dic5—22no—
540Dic5—41no—
541Dic5—62no—
542Dic5—62no—
543Dic5—121no—
544Dic5#87214yes—
545C24—151no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—51no—
553C22×C4—51no—
554C22×C4—154no—
555C22×C4—151no—
556C22×C4—151no—
557C22×C4—151no—
558C22×C4—302no—
559C22×C4—302no—
560C22×C4C2×D3×D511yescharacteristic
561C22×C4C2×D3×D511yescharacteristic
562C22×C4C2×D3×D511yescharacteristic
563C4⋊C4—54no—
564C4⋊C4—102no—
565C4⋊C4—121no—
566C4⋊C4—121no—
567C4⋊C4—154no—
568C4⋊C4—302no—
569C4⋊C4—601no—
570C4⋊C4—601no—
571C22⋊C4—154no—
572C22⋊C4—154no—
573C22⋊C4—302no—
574C22⋊C4—302no—
575C22⋊C4—601no—
576C22⋊C4—601no—
577C42—34no—
578C42—102no—
579C42—102no—
580C42—102no—
581C42—154no—
582C42—302no—
583C42—302no—
584C42—302no—
585C3×C5#234611yescharacteristic, complemented, Hall
586C22×C3C22×C4×D511yescharacteristic
587C22×C3#414411yescharacteristic
588C22×C3#414711yescharacteristic
589C22×C3D5×#4111yescharacteristic
590C22×C3D5×#4111yescharacteristic
591C22×C3D5×#4111yescharacteristic
592C22×C3D5×#4111yescharacteristic
593C2×D3—102no—
594C2×D3—102no—
595C2×D3—102no—
596C2×D3—201no—
597C2×D3—201no—
598C2×D3—201no—
599C2×D3—201no—
600C3×C4—22no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—54no—
604C3×C4—102no—
605C3×C4—102no—
606C3×C4—201no—
607Dic3—22no—
608Dic3—22no—
609Dic3—41no—
610Dic3—41no—
611Dic3—102no—
612Dic3—102no—
613Dic3—201no—
614C2×C5C2×#87211yescharacteristic
615C2×C5#551311yescharacteristic
616C2×C5#553211yescharacteristic
617C2×C5C4×#23711yescharacteristic
618C2×C5#556311yescharacteristic
619C2×C5#557411yescharacteristic
620C2×C5#558111yescharacteristic
621D5—122no—
622C23—152no—
623C23—301no—
624C23—301no—
625C23—301no—
626C23—301no—
627C23—301no—
628C23—301no—
629C23C22×D3×D511yescharacteristic
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—32no—
639C2×C4—32no—
640C2×C4—52no—
641C2×C4—52no—
642C2×C4—52no—
643C2×C4—52no—
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—152no—
663C2×C4—152no—
664C2×C4—308no—
665C2×C4—301no—
666C2×C4—301no—
667C2×C4—301no—
668C2×C4—301no—
669C2×C4—301no—
670C2×C4—301no—
671C2×C4—301no—
672C2×C4C4×D3×D512yes—
673C2×C3#6583811yescharacteristic
674C2×C3D5×#11711yescharacteristic
675C2×C3#6585611yescharacteristic
676C2×C3#6600411yescharacteristic
677C2×C3#6600411yescharacteristic
678C2×C3#6602711yescharacteristic
679C2×C3#6602711yescharacteristic
680D3—202no—
681C5#7363311yescharacteristic, complemented, Sylow
682C22—302no—
683C22—302no—
684C22—302no—
685C22—601no—
686C22—601no—
687C22—601no—
688C22—601no—
689C22C2×C4×D3×D511yescharacteristic
690C22D5×#23511yescharacteristic
691C22D5×#23511yescharacteristic
692C22D5×#23711yescharacteristic
693C22#9202411yescharacteristic
694C22#9202711yescharacteristic
695C22#9202911yescharacteristic
696C4—22no—
697C4—41no—
698C4—41no—
699C4—54no—
700C4—62no—
701C4—62no—
702C4—102no—
703C4—102no—
704C4—121no—
705C4—121no—
706C4—201no—
707C4—302no—
708C4—302no—
709C4—601no—
710C3#1060588711yescharacteristic, complemented, Sylow
711C2—602no—
712C2D5×#87211yescharacteristic
713C2#1175281811yescharacteristic
714C2#1175290711yescharacteristic
715C2#1175309211yescharacteristic
716C2#1175333711yescharacteristic
717C2#1175334511yescharacteristic
718C2#1175338311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenter#95D3×D5
hypocenterC3×C5#2346
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C5×#4650C2semidirect
4. C3×#64938C2semidirect
8. #11748801C2semidirect
11. #11748644C2semidirect
12. #11748637C2semidirect
13. #11748635C2semidirect
14. #11748629C2semidirect
15. #11748611C2semidirect
40. #91403C4semidirect
67. #64938D3semidirect
123. #4650D5semidirect
585. C3×C5#2346semidirect
681. C5#73633semidirect
710. C3#10605887semidirect

Maximal subgroups

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

subgroupindex
C2×#914032
#117507702
C5×#46502
C3×#649382
#117488762
#117488752
#117488292
#117488012
#117487272
#117486692
#117486442
#117486372
#117486352
#117486292
#117486112
#106058873
#736335