Finite Group Databasebeta

← #14419052

Subgroups — #14419052

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6765C211yesmaximal, characteristic
2#11750929C211yesmaximal, characteristic, complemented
3C5×#4833C211yesmaximal, characteristic, complemented
4C3×#65125C211yesmaximal, characteristic, complemented
5#11747723C211yesmaximal, characteristic, complemented
6#11747722C211yesmaximal, characteristic, complemented
7#11747704C211yesmaximal, characteristic, complemented
8#11747702C211yesmaximal, characteristic, complemented
9Dic3×#676C211yesmaximal, characteristic, complemented
10#11747576C211yesmaximal, characteristic, complemented
11#11747576C211yesmaximal, characteristic, complemented
12C8×D5×Dic3C211yesmaximal, characteristic, complemented
13#11747005C211yesmaximal, characteristic, complemented
14#11746997C211yesmaximal, characteristic, complemented
15#11746852C211yesmaximal, characteristic, complemented
16#10611009—31nomaximal, Hall
17C2×#6765C411yescharacteristic
18C4×Dic30C2211yescharacteristic
19C42×C5×D3C2211yescharacteristic
20C2×C3×#676C2211yescharacteristic
21C2×C3×C8×D5C2211yescharacteristic
22C3×C4×D20C2211yescharacteristic
23#91441C411yescharacteristic
24#91441C411yescharacteristic
25C4×#1201C2211yescharacteristic
26C4×#1201C2211yescharacteristic
27Dic3×D20C411yescharacteristic
28#91393C411yescharacteristic
29#91393C411yescharacteristic
30C4×D5×Dic3C2211yescharacteristic
31C4×D5×Dic3C2211yescharacteristic
32#91340C411yescharacteristic
33#91338C411yescharacteristic
34C2×#6650C2211yescharacteristic
35C2×#6650C2211yescharacteristic
36C2×#6649C2211yescharacteristic
37C2×D5×C3⋊C8C2211yescharacteristic
38C3×C5×C4⋊C8C2211yescharacteristic
39#91099C2211yescharacteristic
40#91098C2211yescharacteristic
41#91098C2211yescharacteristic
42C8×Dic15C2211yescharacteristic
43#91087C2211yescharacteristic
44C5×(C2×D3)⋊C8C2211yescharacteristic
45C5×(C2×D3)⋊C8C2211yescharacteristic
46C5×C8×Dic3C2211yescharacteristic
47C5×C8×Dic3C2211yescharacteristic
48C5×C4⋊(C3⋊C8)C2211yescharacteristic
49C3×#3952C2211yescharacteristic
50C3×#3952C2211yescharacteristic
51C3×#3935C2211yescharacteristic
52#90983C2211yescharacteristic
53#90983C2211yescharacteristic
54#90955C2211yescharacteristic
55#90955C2211yescharacteristic
56#90954C2211yescharacteristic
57#90951C2211yescharacteristic
58Dic3×#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#79453—51nomaximal, Hall
61C4×#709—31no—
62C5×#431—31no—
63C4×#681—31no—
64#65125—31no—
65#65125D311yescharacteristic, complemented
66#65117—31no—
67#65117—31no—
68#65018—31no—
69#65018—31no—
70#65017—31no—
71#65017—31no—
72C4×#676—31no—
73#64974—31no—
74#64974—31no—
75C4×C8×D5—31no—
76C2×Dic30C2×C411yescharacteristic
77C2×C4×C5×D3C2×C411yescharacteristic
78C2×C4×C5×D3C2×C411yescharacteristic
79C2×C4×C5×D3C2311yescharacteristic
80C2×C3×D20C2×C411yescharacteristic
81C2×C3×C4×D5C2311yescharacteristic
82C2×C3×C4×D5C2311yescharacteristic
83C2×#1201C2×C411yescharacteristic
84C2×#1201C2×C411yescharacteristic
85C2×D5×Dic3C2×C411yescharacteristic
86C2×D5×Dic3C2×C411yescharacteristic
87C2×D5×Dic3C2×C411yescharacteristic
88C2×D5×Dic3C2×C411yescharacteristic
89#6765—24no—
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C42×C5C2311yescharacteristic
93C4⋊Dic15C2×C411yescharacteristic
94#6712C2×C411yescharacteristic
95#6712C2×C411yescharacteristic
96C4×Dic15C2311yescharacteristic
97C4×Dic15C2311yescharacteristic
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C4×C5×Dic3C2×C411yescharacteristic
101C4×C5×Dic3C2×C411yescharacteristic
102C4×C5×Dic3C2311yescharacteristic
103C2×C5×C3⋊C8C2311yescharacteristic
104C2×C5×C3⋊C8C2311yescharacteristic
105C3×#685C2×C411yescharacteristic
106C3×#685C2×C411yescharacteristic
107C3×C4⋊Dic5C2×C411yescharacteristic
108C2×C3×#168C2311yescharacteristic
109C2×C3×#168C2311yescharacteristic
110C3×#676—22no—
111C3×C8×D5—22no—
112#6669C2×C411yescharacteristic
113#6669C2×C411yescharacteristic
114(C2×D3)⋊Dic5C2×C411yescharacteristic
115(C2×D3)⋊Dic5C2×C411yescharacteristic
116#6665C2×C411yescharacteristic
117#6665C2×C411yescharacteristic
118Dic3×Dic5C2×C411yescharacteristic
119Dic3×Dic5C2×C411yescharacteristic
120Dic3×Dic5C2×C411yescharacteristic
121Dic3×Dic5C2×C411yescharacteristic
122#6650—22no—
123#6650—22no—
124#6649—22no—
125D5×C3⋊C8—22no—
126C4×#237—51no—
127C3×#435—51no—
128#5128—51no—
129Dic3×M16—51no—
130#5111—51no—
131C2×C8×Dic3—51no—
132#5011—51no—
133#4833D511yescharacteristic, complemented
134#4828—51no—
135#4730—51no—
136#4729—51no—
137#4718—51no—
138#4718—51no—
139#4707—51no—
140#4701—51no—
141C2×#709—31no—
142C2×C42×C5—31no—
143C4×C22⋊D5—31no—
144C4×C22⋊D5—31no—
145C4×C22⋊D5—31no—
146C4×C22⋊D5—31no—
147#4072—31no—
148C2×#681—31no—
149C2×#681—31no—
150C2×#676—31no—
151C2×#676C2×D311yescharacteristic
152C2×C8×D5—31no—
153C2×C8×D5C2×D311yescharacteristic
154C4×D20—31no—
155C4×D20C2×D311yescharacteristic
156#4018—31no—
157#4018—31no—
158C42×D5—31no—
159C42×D5—31no—
160C4×Dic10—31no—
161C4×Dic10—31no—
162C5×C4⋊C8—31no—
163C5×C4⋊C8C2×D311yescharacteristic
164C5×C22⋊C8—31no—
165C5×C22⋊C8—31no—
166C4×C5×C8—31no—
167C4×C5×C8—31no—
168#3952—31no—
169#3952—31no—
170#3952C2×D311yescharacteristic
171#3952C2×D311yescharacteristic
172#3947—31no—
173#3947—31no—
174#3946—31no—
175#3946—31no—
176#3946—31no—
177#3946—31no—
178C8×Dic5—31no—
179C8×Dic5—31no—
180#3935—31no—
181#3935C2×D311yescharacteristic
182C4×#168—31no—
183C4×#168—31no—
184#2965—151noSylow
185C22×C5×D3C22×C411yescharacteristic
186C22×C3×D5C22×C411yescharacteristic
187C22×C3×D5C22×C411yescharacteristic
188C2×C3×C4×C5C22×C411yescharacteristic
189C2×C3×C4×C5C22×C411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15C22×C411yescharacteristic
192C2×Dic15C22×C411yescharacteristic
193C2×Dic15C22×C411yescharacteristic
194C2×Dic15C22×C411yescharacteristic
195Dic30—22no—
196C2×C5×Dic3C22×C411yescharacteristic
197C2×C5×Dic3C22×C411yescharacteristic
198C2×C5×Dic3C22×C411yescharacteristic
199C4×C5×D3—21no—
200C4×C5×D3—21no—
201C4×C5×D3—22no—
202C4×C5×D3—22no—
203C2×C3×Dic5C22×C411yescharacteristic
204C2×C3×Dic5C22×C411yescharacteristic
205C3×D20—22no—
206C3×C4×D5—21no—
207C3×C4×D5—21no—
208C3×C4×D5—21no—
209C3×C4×D5—21no—
210#1201—22no—
211#1201—22no—
212D5×Dic3—22no—
213D5×Dic3—22no—
214D5×Dic3—22no—
215D5×Dic3M1614yescomplemented
216C3×C5×C8—21no—
217C3×C5×C8—21no—
218C3⋊#168—21no—
219C3⋊#168#4112yescomplemented
220C3×#168—21no—
221C3×#168#4112yescomplemented
222C5×C3⋊C8—21no—
223C5×C3⋊C8—21no—
224C2×#237—51no—
225C2×C3×M16—51no—
226C22×C3×C8—51no—
227C3×C4×D4—51no—
228D4×Dic3—51no—
229C4×#67—51no—
230C4×#67—51no—
231C2×C4×Dic3—51no—
232C2×C4×Dic3—51no—
233C2×#208—51no—
234C22×C3⋊C8—51no—
235C2×ΓL(1,𝔽25)—51no—
236C2×ΓL(1,𝔽25)—51no—
237#892—51no—
238#887—51no—
239#67⋊C4—51no—
240#67⋊C4—51no—
241#877—51no—
242#877—51no—
243C42×D3C2×D511yescharacteristic
244C4×Dic6—51no—
245C3×C4⋊C8C2×D511yescharacteristic
246C3×C22⋊C8—51no—
247C3×C22⋊C8—51no—
248C3×#97—51no—
249#830—51no—
250#830—51no—
251(C2×D3)⋊C8C2×D511yescharacteristic
252(C2×D3)⋊C8C2×D511yescharacteristic
253#815—51no—
254#815—51no—
255Dic3⋊C8—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258Dic3⋊C8—51no—
259C8×Dic3—51no—
260C8×Dic3—51no—
261C8×Dic3—51no—
262C8×Dic3—51no—
263C8×Dic3C2×D511yescharacteristic
264C8×Dic3C2×D511yescharacteristic
265C4⋊(C3⋊C8)C2×D511yescharacteristic
266#803—51no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C2×C22⋊D5—31no—
271C2×C22⋊D5—31no—
272#709—64no—
273C2×D20C4×D311yescharacteristic
274C2×C4×D5—31no—
275C2×C4×D5—31no—
276C2×C4×D5—31no—
277C2×C4×D5—31no—
278C2×C4×D5C22×D311yescharacteristic
279C2×C4×D5C22×D311yescharacteristic
280C2×Dic10—31no—
281C2×C5×C8—31no—
282C2×C5×C8—31no—
283C2×C5×C8C22×D311yescharacteristic
284C2×C5×C8C22×D311yescharacteristic
285C42×C5—31no—
286C42×C5—31no—
287C42×C5—31no—
288C42×C5C22×D311yescharacteristic
289C22⋊Dic5—31no—
290C22⋊Dic5—31no—
291#685—31no—
292#685—31no—
293#685C4×D311yescharacteristic
294#685C4×D311yescharacteristic
295C4⋊Dic5—31no—
296C4⋊Dic5C4×D311yescharacteristic
297#683—31no—
298#683—31no—
299#683—31no—
300#683—31no—
301C4×Dic5—31no—
302C4×Dic5—31no—
303C4×Dic5—31no—
304C4×Dic5—31no—
305C4×Dic5—31no—
306C4×Dic5—31no—
307#681—62no—
308#681—62no—
309C2×#168—31no—
310C2×#168—31no—
311C2×#168C22×D311yescharacteristic
312C2×#168C22×D311yescharacteristic
313#676—22no—
314#676—62no—
315C8×D5—22no—
316C8×D5—62no—
317C4×#41—151no—
318#446—151no—
319#446—151no—
320#436—151no—
321#436—151no—
322#435—51no—
323#435—151no—
324#435—151no—
325#435—151no—
326#431—31no—
327#431—151no—
328#431—151no—
329C4×M16—151no—
330C4×M16—151no—
331C2×C4×C8—151no—
332C22×C3×C5C23×C411yescharacteristic
333C2×C5×D3—21no—
334C2×C5×D3—21no—
335C2×C5×D3—21no—
336C2×C3×D5—21no—
337C2×C3×D5—21no—
338C2×C3×D5—21no—
339C2×C3×D5—21no—
340C2×C3×D5—21no—
341C2×C3×D5C2×M1612yes—
342C3×C4×C5—21no—
343C3×C4×C5—21no—
344C3×C4×C5C2×#4111yescharacteristic
345C3×C4×C5C2×#4111yescharacteristic
346Dic15—21no—
347Dic15—21no—
348Dic15—21no—
349Dic15C2×M1612yes—
350C3×Dic5—21no—
351C3×Dic5—21no—
352C5×Dic3—21no—
353C5×Dic3C2×M1612yes—
354C5×Dic3#13112yes—
355C2×C3×D4—51no—
356C22×C3×C4—51no—
357C22×C3×C4—51no—
358C2×#67—51no—
359C2×#67—51no—
360C22×Dic3—51no—
361C22×Dic3—51no—
362C22×Dic3—51no—
363C22×Dic3—51no—
364#237—104no—
365C2×C4×D3C4×D511yescharacteristic
366C2×C4×D3C4×D511yescharacteristic
367C2×C4×D3C22×D511yescharacteristic
368C2×Dic6—51no—
369C3×M16—102no—
370C2×C3×C8—51no—
371C2×C3×C8—51no—
372C2×C3×C8—102no—
373C2×C3×C8C22×D511yescharacteristic
374C2×C3×C8C22×D511yescharacteristic
375C3×C4⋊C4—51no—
376C3×C22⋊C4—51no—
377C3×C22⋊C4—51no—
378C3×C42C22×D511yescharacteristic
379#217—51no—
380#217—51no—
381(C2×D3)⋊C4—51no—
382(C2×D3)⋊C4—51no—
383C4⋊Dic3—51no—
384Dic3⋊C4—51no—
385Dic3⋊C4—51no—
386Dic3⋊C4—51no—
387Dic3⋊C4—51no—
388C4×Dic3—51no—
389C4×Dic3—51no—
390C4×Dic3—51no—
391C4×Dic3—51no—
392C4×Dic3—51no—
393C4×Dic3—51no—
394C4×Dic3C4×D511yescharacteristic
395C4×Dic3C4×D511yescharacteristic
396C4×Dic3C22×D511yescharacteristic
397#208—102no—
398C2×C3⋊C8—51no—
399C2×C3⋊C8—51no—
400C2×C3⋊C8—102no—
401C2×C3⋊C8C22×D511yescharacteristic
402C2×C3⋊C8C22×D511yescharacteristic
403ΓL(1,𝔽25)—102no—
404ΓL(1,𝔽25)—102no—
405C23×C5—31no—
406C22×D5C2×C4×D311yescharacteristic
407C22×D5C2×C4×D311yescharacteristic
408C2×C4×C5—31no—
409C2×C4×C5—31no—
410C2×C4×C5—31no—
411C2×C4×C5—62no—
412C2×C4×C5—62no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5C2×C4×D311yescharacteristic
416C2×C4×C5C2×C4×D311yescharacteristic
417C2×C4×C5C23×D311yescharacteristic
418C22⋊D5—62no—
419C22⋊D5—62no—
420C2×Dic5—31no—
421C2×Dic5—31no—
422C2×Dic5—31no—
423C2×Dic5—31no—
424C2×Dic5C2×C4×D311yescharacteristic
425C2×Dic5C2×C4×D311yescharacteristic
426D20—22no—
427C4×D5—21no—
428C4×D5—21no—
429C4×D5—21no—
430C4×D5—21no—
431C4×D5—34no—
432C4×D5—62no—
433C4×D5—62no—
434C4×D5—62no—
435Dic10—62no—
436C5×C8—21no—
437C5×C8—21no—
438C5×C8—61no—
439C5×C8—61no—
440#168—21no—
441#168—32no—
442#168—61no—
443#168#23712yescomplemented
444C2×#41—151no—
445C2×M16—51no—
446C2×M16—151no—
447C2×M16—151no—
448C2×M16—151no—
449C22×C8—51no—
450C22×C8—151no—
451C4×Q8—151no—
452C4×Q8—151no—
453C4×D4—51no—
454C4×D4—151no—
455C4×D4—151no—
456C4×D4—151no—
457C4×D4—151no—
458C4×D4—151no—
459#117—151no—
460#117—151no—
461#117—151no—
462C2×C42—31no—
463C2×C42—151no—
464C2×C42—151no—
465C4⋊C8—31no—
466C4⋊C8—151no—
467C4⋊C8—151no—
468C4⋊C8—151no—
469C4⋊C8—151no—
470C4⋊C8D3×D511yescharacteristic
471C22⋊C8—31no—
472C22⋊C8—31no—
473C22⋊C8—51no—
474C22⋊C8—51no—
475C22⋊C8—151no—
476C22⋊C8—151no—
477#97—51no—
478#97—151no—
479#97—151no—
480#97—151no—
481C4×C8—31no—
482C4×C8—31no—
483C4×C8—151no—
484C4×C8—151no—
485C4×C8—151no—
486C4×C8—151no—
487C2×C3×C5C4×#4111yescharacteristic
488C2×C3×C5C22×M1611yescharacteristic
489C2×C3×C5C2×#13111yescharacteristic
490C3×D5—22no—
491C3×D5—41no—
492C5×D3—41no—
493C23×C3—51no—
494C23×C3—51no—
495C22×D3C2×C4×D511yescharacteristic
496C3×D4—102no—
497C2×C3×C4—51no—
498C2×C3×C4—51no—
499C2×C3×C4—101no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4C2×C4×D511yescharacteristic
504C2×C3×C4C2×C4×D511yescharacteristic
505C2×C3×C4C23×D511yescharacteristic
506#67—102no—
507#67—102no—
508C2×Dic3—51no—
509C2×Dic3—54no—
510C2×Dic3—51no—
511C2×Dic3—51no—
512C2×Dic3—51no—
513C2×Dic3—102no—
514C2×Dic3—102no—
515C2×Dic3—102no—
516C2×Dic3C2×C4×D511yescharacteristic
517C2×Dic3C2×C4×D511yescharacteristic
518C2×Dic3C2×C4×D511yescharacteristic
519C4×D3—21no—
520C4×D3—21no—
521C4×D3—22no—
522C4×D3—22no—
523Dic6—102no—
524C3×C8—21no—
525C3×C8—21no—
526C3×C8—52no—
527C3×C8—101no—
528C3⋊C8—21no—
529C3⋊C8—21no—
530C3⋊C8—52no—
531C3⋊C8—101no—
532C22×C5—61no—
533C22×C5—61no—
534C22×C5—61no—
535C22×C5C22×C4×D311yescharacteristic
536C2×D5—21no—
537C2×D5—21no—
538C2×D5—21no—
539C2×D5—21no—
540C2×D5—21no—
541C2×D5D3×M1612yes—
542C4×C5—21no—
543C4×C5—21no—
544C4×C5—32no—
545C4×C5—32no—
546C4×C5—61no—
547C4×C5C2×#23711yescharacteristic
548C4×C5D3×#4111yescharacteristic
549Dic5—21no—
550Dic5—21no—
551Dic5—32no—
552Dic5—61no—
553Dic5—61no—
554Dic5—61no—
555#41—304no—
556C2×Q8—151no—
557C2×D4—51no—
558C2×D4—151no—
559C2×D4—151no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—51no—
564C22×C4—51no—
565C22×C4—151no—
566C22×C4—151no—
567C22×C4—151no—
568C22×C4—151no—
569M16—102no—
570M16—302no—
571M16—302no—
572M16—302no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8—51no—
576C2×C8—51no—
577C2×C8—102no—
578C2×C8—151no—
579C2×C8—151no—
580C2×C8—302no—
581C2×C8C2×D3×D511yescharacteristic
582C2×C8C2×D3×D511yescharacteristic
583C4⋊C4—51no—
584C4⋊C4—151no—
585C4⋊C4—151no—
586C4⋊C4—151no—
587C4⋊C4—151no—
588C4⋊C4—151no—
589C22⋊C4—51no—
590C22⋊C4—51no—
591C22⋊C4—151no—
592C22⋊C4—151no—
593C22⋊C4—151no—
594C22⋊C4—151no—
595C42—31no—
596C42—31no—
597C42—31no—
598C42—151no—
599C42—151no—
600C42—151no—
601C42—151no—
602C42—151no—
603C42—151no—
604C42C2×D3×D511yescharacteristic
605C3×C5#296511yescharacteristic, complemented, Hall
606C22×C3—52no—
607C22×C3—101no—
608C22×C3—101no—
609C22×C3—101no—
610C22×C3—101no—
611C22×C3—101no—
612C22×C3C22×C4×D511yescharacteristic
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—101no—
619C3×C4—101no—
620C3×C4D5×#4111yescharacteristic
621C3×C4D5×#4111yescharacteristic
622Dic3—21no—
623Dic3—52no—
624Dic3—101no—
625Dic3—101no—
626Dic3—101no—
627Dic3#404712yes—
628Dic3D5×M1612yes—
629C2×C5—121no—
630C2×C5C4×#23711yescharacteristic
631C2×C5C2×D3×M1611yescharacteristic
632C2×C5D3×#13111yescharacteristic
633D5—22no—
634D5—41no—
635C23—31no—
636C23—51no—
637C23—51no—
638Q8—302no—
639D4—102no—
640D4—302no—
641D4—302no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—51no—
646C2×C4—51no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—101no—
652C2×C4—101no—
653C2×C4—101no—
654C2×C4—101no—
655C2×C4—154no—
656C2×C4—151no—
657C2×C4—151no—
658C2×C4—151no—
659C2×C4—151no—
660C2×C4—302no—
661C2×C4—302no—
662C2×C4—302no—
663C2×C4C4×D3×D511yescharacteristic
664C2×C4C4×D3×D511yescharacteristic
665C2×C4C22×D3×D511yescharacteristic
666C8—21no—
667C8—21no—
668C8—52no—
669C8—61no—
670C8—61no—
671C8—101no—
672C8—152no—
673C8—301no—
674C2×C3—102no—
675C2×C3—201no—
676C2×C3#6585611yescharacteristic
677C2×C3C2×#404711yescharacteristic
678C2×C3C2×D5×M1611yescharacteristic
679D3—41no—
680C5#7945311yescharacteristic, complemented, Sylow
681C22—52no—
682C22—61no—
683C22—61no—
684C22—61no—
685C22—101no—
686C22—101no—
687C22—101no—
688C22—101no—
689C22—101no—
690C22C2×C4×D3×D511yescharacteristic
691C4—21no—
692C4—21no—
693C4—32no—
694C4—32no—
695C4—61no—
696C4—101no—
697C4—101no—
698C4—152no—
699C4—301no—
700C4—301no—
701C4—301no—
702C4D5×#23711yescharacteristic
703C4#9203411yescharacteristic
704C3#1061100911yescharacteristic, complemented, Sylow
705C2—102no—
706C2—121no—
707C2—201no—
708C2#1175339811yescharacteristic
709C2D3×#404711yescharacteristic
710C2D3×D5×M1611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C8C22
prime radicalC2×#6765C4
cosocleC2×C3×C4×C5C24
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#2965
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750929C2semidirect
3. C5×#4833C2semidirect
4. C3×#65125C2semidirect
5. #11747723C2semidirect
6. #11747722C2semidirect
7. #11747704C2semidirect
8. #11747702C2semidirect
9. Dic3×#676C2semidirect
10. #11747576C2semidirect
11. #11747576C2semidirect
12. C8×D5×Dic3C2semidirect
13. #11747005C2semidirect
14. #11746997C2semidirect
15. #11746852C2semidirect
65. #65125D3semidirect
133. #4833D5semidirect
215. D5×Dic3M16semidirect
219. C3⋊#168#41semidirect
221. C3×#168#41semidirect
443. #168#237semidirect
605. C3×C5#2965semidirect
680. C5#79453semidirect
704. C3#10611009semidirect

Maximal subgroups

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

subgroupindex
C4×#67652
#117509292
C5×#48332
C3×#651252
#117477232
#117477222
#117477042
#117477022
Dic3×#6762
#117475762
C8×D5×Dic32
#117470052
#117469972
#117468522
#106110093
#794535