Finite Group Databasebeta

← #14418965

Subgroups — #14418965

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×#6819C211yesmaximal, characteristic
2C3×C5×#435C211yesmaximal, characteristic, complemented
3#11751229C211yesmaximal, characteristic, complemented
4M16×Dic15C211yesmaximal, characteristic, complemented
5#11751212C211yesmaximal, characteristic, complemented
6C2×C8×Dic15C211yesmaximal, characteristic, complemented
7#11751112C211yesmaximal, characteristic, complemented
8#11750934C211yesmaximal, characteristic, complemented
9#11750929C211yesmaximal, characteristic, complemented
10#11750831C211yesmaximal, characteristic, complemented
11#11750830C211yesmaximal, characteristic, complemented
12#11750819C211yesmaximal, characteristic, complemented
13#11750819C211yesmaximal, characteristic, complemented
14#11750808C211yesmaximal, characteristic, complemented
15#11750802C211yesmaximal, characteristic, complemented
16#10611184—31nomaximal, Hall
17C2×#6819C411yescharacteristic
18C2×C3×C5×M16C2211yescharacteristic
19C22×C3×C5×C8C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21D4×Dic15C411yescharacteristic
22C4×#1220C2211yescharacteristic
23C4×#1220C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26C2×#6710C2211yescharacteristic
27C22×C3⋊#168C2211yescharacteristic
28C2×#6705C2211yescharacteristic
29C2×#6705C2211yescharacteristic
30#91781C411yescharacteristic
31#91776C411yescharacteristic
32#91770C411yescharacteristic
33#91770C411yescharacteristic
34#91766C411yescharacteristic
35#91766C411yescharacteristic
36C42×D15C2211yescharacteristic
37C4×Dic30C2211yescharacteristic
38C3×C5×C4⋊C8C2211yescharacteristic
39C3×C5×C22⋊C8C2211yescharacteristic
40C3×C5×C22⋊C8C2211yescharacteristic
41C3×C5×#97C2211yescharacteristic
42#91114C2211yescharacteristic
43#91114C2211yescharacteristic
44#91104C2211yescharacteristic
45#91104C2211yescharacteristic
46#91099C2211yescharacteristic
47#91099C2211yescharacteristic
48#91098C2211yescharacteristic
49#91098C2211yescharacteristic
50#91098C2211yescharacteristic
51#91098C2211yescharacteristic
52C8×Dic15C2211yescharacteristic
53C8×Dic15C2211yescharacteristic
54C8×Dic15C2211yescharacteristic
55C8×Dic15C2211yescharacteristic
56C8×Dic15C2211yescharacteristic
57C8×Dic15C2211yescharacteristic
58C4⋊(C3⋊#168)C2211yescharacteristic
59#91087C2211yescharacteristic
60#79453—51nomaximal, Hall
61C4×#711—31no—
62C5×#435D311yescharacteristic, complemented
63#65417—31no—
64M16×Dic5—31no—
65#65400—31no—
66C2×C8×Dic5—31no—
67#65300—31no—
68#65122—31no—
69#65117—31no—
70#65019—31no—
71#65018—31no—
72#65007—31no—
73#65007—31no—
74#64996—31no—
75#64990—31no—
76C2×C3×C5×D4C2×C411yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220C2×C411yescharacteristic
80C2×#1220C2×C411yescharacteristic
81C22×Dic15C2×C411yescharacteristic
82C22×Dic15C2×C411yescharacteristic
83C22×Dic15C2×C411yescharacteristic
84C22×Dic15C2×C411yescharacteristic
85#6819—24no—
86C2×C4×D15C2×C411yescharacteristic
87C2×C4×D15C2×C411yescharacteristic
88C2×C4×D15C2311yescharacteristic
89C2×Dic30C2×C411yescharacteristic
90C3×C5×M16—22no—
91C2×C3×C5×C8—22no—
92C2×C3×C5×C8C2311yescharacteristic
93C2×C3×C5×C8C2311yescharacteristic
94C2×C3×C5×C8C2311yescharacteristic
95C2×C3×C5×C8C2311yescharacteristic
96C3×C5×C4⋊C4C2×C411yescharacteristic
97C3×C5×C22⋊C4C2×C411yescharacteristic
98C3×C5×C22⋊C4C2×C411yescharacteristic
99C3×C42×C5C2311yescharacteristic
100#6719C2×C411yescharacteristic
101#6719C2×C411yescharacteristic
102#6714C2×C411yescharacteristic
103#6714C2×C411yescharacteristic
104C4⋊Dic15C2×C411yescharacteristic
105#6712C2×C411yescharacteristic
106#6712C2×C411yescharacteristic
107#6712C2×C411yescharacteristic
108#6712C2×C411yescharacteristic
109C4×Dic15C2×C411yescharacteristic
110C4×Dic15C2×C411yescharacteristic
111C4×Dic15C2×C411yescharacteristic
112C4×Dic15C2×C411yescharacteristic
113C4×Dic15C2×C411yescharacteristic
114C4×Dic15C2×C411yescharacteristic
115C4×Dic15C2311yescharacteristic
116C4×Dic15C2311yescharacteristic
117C4×Dic15C2311yescharacteristic
118#6710—22no—
119C2×C3⋊#168—22no—
120C2×C3⋊#168C2311yescharacteristic
121C2×C3⋊#168C2311yescharacteristic
122C2×C3⋊#168C2311yescharacteristic
123C2×C3⋊#168C2311yescharacteristic
124#6705—22no—
125#6705—22no—
126C4×#237—51no—
127C3×#435D511yescharacteristic, complemented
128#5128—51no—
129Dic3×M16—51no—
130#5111—51no—
131C2×C8×Dic3—51no—
132#5011—51no—
133#4833—51no—
134#4828—51no—
135#4730—51no—
136#4729—51no—
137#4718—51no—
138#4718—51no—
139#4707—51no—
140#4701—51no—
141C2×#711—31no—
142C2×C5×M16C2×D311yescharacteristic
143C22×C5×C8C2×D311yescharacteristic
144C4×C5×D4C2×D311yescharacteristic
145D4×Dic5—31no—
146C4×C22⋊D5—31no—
147C4×C22⋊D5—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×#681—31no—
151C22×#168—31no—
152C2×#676—31no—
153C2×#676—31no—
154#4038—31no—
155#4033—31no—
156#4027—31no—
157#4027—31no—
158#4023—31no—
159#4023—31no—
160C42×D5—31no—
161C4×Dic10—31no—
162C5×C4⋊C8C2×D311yescharacteristic
163C5×C22⋊C8C2×D311yescharacteristic
164C5×C22⋊C8C2×D311yescharacteristic
165C5×#97C2×D311yescharacteristic
166C22⋊#168—31no—
167C22⋊#168—31no—
168#3952—31no—
169#3952—31no—
170#3947—31no—
171#3947—31no—
172#3946—31no—
173#3946—31no—
174#3946—31no—
175#3946—31no—
176C8×Dic5—31no—
177C8×Dic5—31no—
178C8×Dic5—31no—
179C8×Dic5—31no—
180C8×Dic5—31no—
181C8×Dic5—31no—
182C4⋊#168—31no—
183#3935—31no—
184#2965—151noSylow
185C23×C3×C5C22×C411yescharacteristic
186C23×C3×C5C22×C411yescharacteristic
187C22×D15C22×C411yescharacteristic
188C3×C5×D4—22no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5C22×C411yescharacteristic
194C2×C3×C4×C5C22×C411yescharacteristic
195C2×C3×C4×C5C22×C411yescharacteristic
196C2×C3×C4×C5C22×C411yescharacteristic
197C2×C3×C4×C5C2411yescharacteristic
198#1220—22no—
199#1220—22no—
200C2×Dic15—22no—
201C2×Dic15—22no—
202C2×Dic15—22no—
203C2×Dic15M1614yescomplemented
204C2×Dic15C22×C411yescharacteristic
205C2×Dic15C22×C411yescharacteristic
206C2×Dic15C22×C411yescharacteristic
207C2×Dic15C22×C411yescharacteristic
208C2×Dic15C22×C411yescharacteristic
209C2×Dic15C22×C411yescharacteristic
210C2×Dic15C22×C411yescharacteristic
211C4×D15—21no—
212C4×D15—21no—
213C4×D15—22no—
214C4×D15—22no—
215Dic30—22no—
216C3×C5×C8—21no—
217C3×C5×C8—21no—
218C3×C5×C8—21no—
219C3×C5×C8#4112yescomplemented
220C3⋊#168—21no—
221C3⋊#168—21no—
222C3⋊#168—21no—
223C3⋊#168#4112yescomplemented
224C2×#237—51no—
225C2×C3×M16C2×D511yescharacteristic
226C22×C3×C8C2×D511yescharacteristic
227C3×C4×D4C2×D511yescharacteristic
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×D3—51no—
244C4×Dic6—51no—
245C3×C4⋊C8C2×D511yescharacteristic
246C3×C22⋊C8C2×D511yescharacteristic
247C3×C22⋊C8C2×D511yescharacteristic
248C3×#97C2×D511yescharacteristic
249#830—51no—
250#830—51no—
251(C2×D3)⋊C8—51no—
252(C2×D3)⋊C8—51no—
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×Dic3—51no—
264C8×Dic3—51no—
265C4⋊(C3⋊C8)—51no—
266#803—51no—
267C2×C5×D4C4×D311yescharacteristic
268C22×C4×C5C22×D311yescharacteristic
269C22×C4×C5C22×D311yescharacteristic
270C2×C22⋊D5—31no—
271C2×C22⋊D5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—31no—
276#711—64no—
277C2×C4×D5—31no—
278C2×C4×D5—31no—
279C2×C4×D5—31no—
280C2×Dic10—31no—
281C5×M16—22no—
282C2×C5×C8—22no—
283C2×C5×C8C22×D311yescharacteristic
284C2×C5×C8C22×D311yescharacteristic
285C2×C5×C8C22×D311yescharacteristic
286C2×C5×C8C22×D311yescharacteristic
287C5×C4⋊C4C4×D311yescharacteristic
288C5×C22⋊C4C4×D311yescharacteristic
289C5×C22⋊C4C4×D311yescharacteristic
290C42×C5C22×D311yescharacteristic
291C22⋊Dic5—31no—
292C22⋊Dic5—31no—
293#685—31no—
294#685—31no—
295C4⋊Dic5—31no—
296#683—31no—
297#683—31no—
298#683—31no—
299#683—31no—
300C4×Dic5—31no—
301C4×Dic5—31no—
302C4×Dic5—31no—
303C4×Dic5—31no—
304C4×Dic5—31no—
305C4×Dic5—31no—
306C4×Dic5—31no—
307C4×Dic5—31no—
308C4×Dic5—31no—
309#681—62no—
310C2×#168—31no—
311C2×#168—31no—
312C2×#168—31no—
313C2×#168—31no—
314C2×#168—62no—
315#676—62no—
316#676—62no—
317C4×#41—151no—
318#446—151no—
319#446—151no—
320#436—151no—
321#436—151no—
322#435—151no—
323#435—151no—
324#435—151no—
325#435D1511yescharacteristic, complemented
326#431—151no—
327#431—151no—
328#431—151no—
329C4×M16—151no—
330C4×M16—151no—
331C2×C4×C8—151no—
332C22×C3×C5—21no—
333C22×C3×C5—21no—
334C22×C3×C5—21no—
335C22×C3×C5—21no—
336C22×C3×C5—21no—
337C22×C3×C5C2×M1612yes—
338C22×C3×C5C23×C411yescharacteristic
339C2×D15—21no—
340C2×D15—21no—
341C2×D15—21no—
342C3×C4×C5—21no—
343C3×C4×C5—21no—
344C3×C4×C5—21no—
345C3×C4×C5—21no—
346C3×C4×C5C2×#4111yescharacteristic
347C3×C4×C5C2×#4111yescharacteristic
348Dic15—21no—
349Dic15—21no—
350Dic15—21no—
351Dic15—21no—
352Dic15C2×M1612yes—
353Dic15C2×M1612yes—
354Dic15#13112yes—
355C2×C3×D4C4×D511yescharacteristic
356C22×C3×C4C22×D511yescharacteristic
357C22×C3×C4C22×D511yescharacteristic
358C2×#67—51no—
359C2×#67—51no—
360C22×Dic3—51no—
361C22×Dic3—51no—
362C22×Dic3—51no—
363C22×Dic3—51no—
364#237—104no—
365C2×C4×D3—51no—
366C2×C4×D3—51no—
367C2×C4×D3—51no—
368C2×Dic6—51no—
369C3×M16—22no—
370C2×C3×C8—22no—
371C2×C3×C8C22×D511yescharacteristic
372C2×C3×C8C22×D511yescharacteristic
373C2×C3×C8C22×D511yescharacteristic
374C2×C3×C8C22×D511yescharacteristic
375C3×C4⋊C4C4×D511yescharacteristic
376C3×C22⋊C4C4×D511yescharacteristic
377C3×C22⋊C4C4×D511yescharacteristic
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×Dic3—51no—
395C4×Dic3—51no—
396C4×Dic3—51no—
397#208—102no—
398C2×C3⋊C8—51no—
399C2×C3⋊C8—51no—
400C2×C3⋊C8—51no—
401C2×C3⋊C8—51no—
402C2×C3⋊C8—102no—
403ΓL(1,𝔽25)—102no—
404ΓL(1,𝔽25)—102no—
405C23×C5C2×C4×D311yescharacteristic
406C23×C5C2×C4×D311yescharacteristic
407C22×D5—31no—
408C5×D4—22no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5—21no—
412C2×C4×C5—21no—
413C2×C4×C5C2×C4×D311yescharacteristic
414C2×C4×C5C2×C4×D311yescharacteristic
415C2×C4×C5C2×C4×D311yescharacteristic
416C2×C4×C5C2×C4×D311yescharacteristic
417C2×C4×C5C23×D311yescharacteristic
418C22⋊D5—62no—
419C22⋊D5—62no—
420C2×Dic5—34no—
421C2×Dic5—31no—
422C2×Dic5—31no—
423C2×Dic5—31no—
424C2×Dic5—31no—
425C2×Dic5—31no—
426C2×Dic5—31no—
427C2×Dic5—31no—
428C2×Dic5—62no—
429C2×Dic5—62no—
430C2×Dic5—62no—
431C4×D5—62no—
432C4×D5—62no—
433C4×D5—61no—
434C4×D5—61no—
435Dic10—62no—
436C5×C8—21no—
437C5×C8—21no—
438C5×C8—21no—
439C5×C8#23712yescomplemented
440#168—32no—
441#168—61no—
442#168—61no—
443#168—61no—
444C2×#41—151no—
445C2×M16—151no—
446C2×M16—151no—
447C2×M16—151no—
448C2×M16C2×D1511yescharacteristic
449C22×C8—151no—
450C22×C8C2×D1511yescharacteristic
451C4×Q8—151no—
452C4×Q8—151no—
453C4×D4—151no—
454C4×D4—151no—
455C4×D4—151no—
456C4×D4—151no—
457C4×D4—151no—
458C4×D4C2×D1511yescharacteristic
459#117—151no—
460#117—151no—
461#117—151no—
462C2×C42—151no—
463C2×C42—151no—
464C2×C42—151no—
465C4⋊C8—151no—
466C4⋊C8—151no—
467C4⋊C8—151no—
468C4⋊C8—151no—
469C4⋊C8—151no—
470C4⋊C8C2×D1511yescharacteristic
471C22⋊C8—151no—
472C22⋊C8—151no—
473C22⋊C8—151no—
474C22⋊C8—151no—
475C22⋊C8C2×D1511yescharacteristic
476C22⋊C8C2×D1511yescharacteristic
477#97—151no—
478#97—151no—
479#97—151no—
480#97C2×D1511yescharacteristic
481C4×C8—151no—
482C4×C8—151no—
483C4×C8—151no—
484C4×C8—151no—
485C4×C8—151no—
486C4×C8—151no—
487C2×C3×C5—22no—
488C2×C3×C5—41no—
489C2×C3×C5C4×#4111yescharacteristic
490C2×C3×C5C22×M1611yescharacteristic
491C2×C3×C5C2×#13111yescharacteristic
492D15—41no—
493C23×C3C2×C4×D511yescharacteristic
494C23×C3C2×C4×D511yescharacteristic
495C22×D3—51no—
496C3×D4—22no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4C2×C4×D511yescharacteristic
502C2×C3×C4C2×C4×D511yescharacteristic
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—51no—
510C2×Dic3—51no—
511C2×Dic3—54no—
512C2×Dic3—51no—
513C2×Dic3—51no—
514C2×Dic3—51no—
515C2×Dic3—51no—
516C2×Dic3—102no—
517C2×Dic3—102no—
518C2×Dic3—102no—
519C4×D3—102no—
520C4×D3—102no—
521C4×D3—101no—
522C4×D3—101no—
523Dic6—102no—
524C3×C8—21no—
525C3×C8—21no—
526C3×C8—21no—
527C3×C8#71112yescomplemented
528C3⋊C8—52no—
529C3⋊C8—101no—
530C3⋊C8—101no—
531C3⋊C8—101no—
532C22×C5—21no—
533C22×C5—21no—
534C22×C5—21no—
535C22×C5—21no—
536C22×C5—21no—
537C22×C5D3×M1612yes—
538C22×C5C22×C4×D311yescharacteristic
539C2×D5—61no—
540C2×D5—61no—
541C2×D5—61no—
542C4×C5—21no—
543C4×C5—21no—
544C4×C5—21no—
545C4×C5—21no—
546C4×C5C2×#23711yescharacteristic
547C4×C5D3×#4111yescharacteristic
548Dic5—32no—
549Dic5—32no—
550Dic5—32no—
551Dic5—61no—
552Dic5—61no—
553Dic5—61no—
554Dic5—61no—
555#41—304no—
556C2×Q8—151no—
557C2×D4—151no—
558C2×D4—151no—
559C2×D4C4×D1511yescharacteristic
560C22×C4—151no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—151no—
565C22×C4—151no—
566C22×C4—151no—
567C22×C4C22×D1511yescharacteristic
568C22×C4C22×D1511yescharacteristic
569M16—22no—
570M16—302no—
571M16—302no—
572M16—302no—
573C2×C8—22no—
574C2×C8—151no—
575C2×C8—151no—
576C2×C8—151no—
577C2×C8—151no—
578C2×C8—302no—
579C2×C8C22×D1511yescharacteristic
580C2×C8C22×D1511yescharacteristic
581C2×C8C22×D1511yescharacteristic
582C2×C8C22×D1511yescharacteristic
583C4⋊C4—151no—
584C4⋊C4—151no—
585C4⋊C4—151no—
586C4⋊C4—151no—
587C4⋊C4—151no—
588C4⋊C4C4×D1511yescharacteristic
589C22⋊C4—151no—
590C22⋊C4—151no—
591C22⋊C4—151no—
592C22⋊C4—151no—
593C22⋊C4C4×D1511yescharacteristic
594C22⋊C4C4×D1511yescharacteristic
595C42—151no—
596C42—151no—
597C42—151no—
598C42—151no—
599C42—151no—
600C42—151no—
601C42—151no—
602C42—151no—
603C42—151no—
604C42C22×D1511yescharacteristic
605C3×C5#296511yescharacteristic, complemented, Hall
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3D5×M1612yes—
612C22×C3C22×C4×D511yescharacteristic
613C2×D3—101no—
614C2×D3—101no—
615C2×D3—101no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4C2×#71111yescharacteristic
621C3×C4D5×#4111yescharacteristic
622Dic3—52no—
623Dic3—52no—
624Dic3—52no—
625Dic3—101no—
626Dic3—101no—
627Dic3—101no—
628Dic3—101no—
629C2×C5—22no—
630C2×C5—41no—
631C2×C5C4×#23711yescharacteristic
632C2×C5C2×D3×M1611yescharacteristic
633C2×C5D3×#13111yescharacteristic
634D5—121no—
635C23—151no—
636C23C2×C4×D1511yescharacteristic
637C23C2×C4×D1511yescharacteristic
638Q8—302no—
639D4—22no—
640D4—302no—
641D4—302no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—154no—
647C2×C4—151no—
648C2×C4—151no—
649C2×C4—151no—
650C2×C4—151no—
651C2×C4—151no—
652C2×C4—151no—
653C2×C4—151no—
654C2×C4—302no—
655C2×C4—302no—
656C2×C4—302no—
657C2×C4—302no—
658C2×C4—302no—
659C2×C4—301no—
660C2×C4—301no—
661C2×C4C2×C4×D1511yescharacteristic
662C2×C4C2×C4×D1511yescharacteristic
663C2×C4C2×C4×D1511yescharacteristic
664C2×C4C2×C4×D1511yescharacteristic
665C2×C4C23×D1511yescharacteristic
666C8—21no—
667C8—21no—
668C8—21no—
669C8—152no—
670C8—301no—
671C8—301no—
672C8—301no—
673C8#681912yescomplemented
674C2×C3—22no—
675C2×C3—41no—
676C2×C3C4×#71111yescharacteristic
677C2×C3C2×D5×M1611yescharacteristic
678C2×C3D5×#13111yescharacteristic
679D3—201no—
680C5#7945311yescharacteristic, complemented, Sylow
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—301no—
687C22—301no—
688C22—301no—
689C22M16×D1512yes—
690C22C22×C4×D1511yescharacteristic
691C4—21no—
692C4—21no—
693C4—21no—
694C4—21no—
695C4—152no—
696C4—152no—
697C4—152no—
698C4—301no—
699C4—301no—
700C4—301no—
701C4—301no—
702C4C2×#681911yescharacteristic
703C4#41×D1511yescharacteristic
704C3#1061118411yescharacteristic, complemented, Sylow
705C2—22no—
706C2—41no—
707C2—601no—
708C2C4×#681911yescharacteristic
709C2C2×M16×D1511yescharacteristic
710C2D15×#13111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D15
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×#435C2
prime radicalC2×#6819C4
cosocleC2×C3×C4×C5C24
hypercenter#435D15
hypocenterC3×C5#2965
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. C3×C5×#435C2semidirect
3. #11751229C2semidirect
4. M16×Dic15C2semidirect
5. #11751212C2semidirect
6. C2×C8×Dic15C2semidirect
7. #11751112C2semidirect
8. #11750934C2semidirect
9. #11750929C2semidirect
10. #11750831C2semidirect
11. #11750830C2semidirect
12. #11750819C2semidirect
13. #11750819C2semidirect
14. #11750808C2semidirect
15. #11750802C2semidirect
62. C5×#435D3semidirect
127. C3×#435D5semidirect
203. C2×Dic15M16semidirect
219. C3×C5×C8#41semidirect
223. C3⋊#168#41semidirect
325. #435D15semidirect
439. C5×C8#237semidirect
527. C3×C8#711semidirect
605. C3×C5#2965semidirect
673. C8#6819semidirect
680. C5#79453semidirect
704. C3#10611184semidirect

Maximal subgroups

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

subgroupindex
C4×#68192
C3×C5×#4352
#117512292
M16×Dic152
#117512122
C2×C8×Dic152
#117511122
#117509342
#117509292
#117508312
#117508302
#117508192
#117508082
#117508022
#106111843
#794535