Finite Group Databasebeta

← #14415400

Subgroups — #14415400

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91268C211yesmaximal, characteristic, complemented
2C2×#91266C211yesmaximal, characteristic, complemented
3#11752675C211yesmaximal, characteristic
4#11750937C211yesmaximal, characteristic, complemented
5C5×#4837C211yesmaximal, characteristic, complemented
6C3×#65125C211yesmaximal, characteristic, complemented
7#11748140C211yesmaximal, characteristic, complemented
8#11748140C211yesmaximal, characteristic, complemented
9#11748047C211yesmaximal, characteristic, complemented
10#11747727C211yesmaximal, characteristic, complemented
11#11747726C211yesmaximal, characteristic, complemented
12#11747706C211yesmaximal, characteristic, complemented
13#11746997C211yesmaximal, characteristic, complemented
14#11746989C211yesmaximal, characteristic, complemented
15D3×#3935C211yesmaximal, characteristic, complemented
16#10610773—31nomaximal, Hall
17C2×#6771C2211yescharacteristic
18C2×#6771C2211yescharacteristic
19C2×#6705C2211yescharacteristic
20C2×C8×D15C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
23C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
24C42×C5×D3C2211yescharacteristic
25C2×C3×#676C2211yescharacteristic
26C2×C3×C8×D5C2211yescharacteristic
27C3×C4×D20C2211yescharacteristic
28#91469C411yescharacteristic
29#91460C411yescharacteristic
30#91458C411yescharacteristic
31#91456C411yescharacteristic
32#91454C411yescharacteristic
33#91454C411yescharacteristic
34C4×#1202C2211yescharacteristic
35C4×#1202C2211yescharacteristic
36#91353C411yescharacteristic
37#91353C411yescharacteristic
38C2×#6651C2211yescharacteristic
39C2×#6649C2211yescharacteristic
40C2×#6648C2211yescharacteristic
41C2×D3×#168C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic
43C2×D5×C3⋊C8C2211yescharacteristic
44#91268—24no—
45#91266—24no—
46C3×C5×C4⋊C8C2211yescharacteristic
47#91104C2211yescharacteristic
48#91104C2211yescharacteristic
49#91087C2211yescharacteristic
50C5×Dic3⋊C8C2211yescharacteristic
51C5×Dic3⋊C8C2211yescharacteristic
52C5×C4⋊(C3⋊C8)C2211yescharacteristic
53C3×#3952C2211yescharacteristic
54C3×#3952C2211yescharacteristic
55C3×#3935C2211yescharacteristic
56#90957C2211yescharacteristic
57#90957C2211yescharacteristic
58#90955C2211yescharacteristic
59#90955C2211yescharacteristic
60#90953C2211yescharacteristic
61#90953C2211yescharacteristic
62#79480—51nomaximal, Hall
63C2×#4053—31no—
64C2×#4053—31no—
65#65811—31no—
66C5×#423—31no—
67#65418—31no—
68#65418—31no—
69C2×#3935—31no—
70#65125—31no—
71#65125—31no—
72#65125—31no—
73#65125—31no—
74#65125—31no—
75#65125—31no—
76#65125—31no—
77#65125D311yescharacteristic, complemented
78C2×D60C2×C411yescharacteristic
79C2×C4×D15C2311yescharacteristic
80C2×C4×D15C2311yescharacteristic
81C2×C4×C5×D3C2×C411yescharacteristic
82C2×C4×C5×D3C2×C411yescharacteristic
83C2×C4×C5×D3C2311yescharacteristic
84C2×C3×D20C2×C411yescharacteristic
85C2×C3×C4×D5C2311yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1204C2×C411yescharacteristic
88C2×#1204C2×C411yescharacteristic
89C2×#1203C2×C411yescharacteristic
90C2×#1203C2×C411yescharacteristic
91C2×#1202C2×C411yescharacteristic
92C2×#1202C2×C411yescharacteristic
93C2×#1202C2×C411yescharacteristic
94C2×#1202C2×C411yescharacteristic
95C2×#1201C2×C411yescharacteristic
96C2×#1201C2×C411yescharacteristic
97#6771—22no—
98#6771—22no—
99#6771—22no—
100#6771—22no—
101C2×C3×C5×C8C2311yescharacteristic
102C2×C3×C5×C8C2311yescharacteristic
103C3×C42×C5C2311yescharacteristic
104#6714C2×C411yescharacteristic
105#6714C2×C411yescharacteristic
106C4⋊Dic15C2×C411yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108C2×C3⋊#168C2311yescharacteristic
109#6705—22no—
110C8×D15—22no—
111C4×C5×Dic3C2×C411yescharacteristic
112C4×C5×Dic3C2×C411yescharacteristic
113C4×C5×Dic3C2311yescharacteristic
114C2×C5×C3⋊C8C2311yescharacteristic
115C2×C5×C3⋊C8C2311yescharacteristic
116C5×ΓL(1,𝔽25)—22no—
117C5×ΓL(1,𝔽25)—22no—
118C3×#685C2×C411yescharacteristic
119C3×#685C2×C411yescharacteristic
120C3×C4⋊Dic5C2×C411yescharacteristic
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C3×#676—22no—
124C3×C8×D5—22no—
125Dic3⋊Dic5C2×C411yescharacteristic
126Dic3⋊Dic5C2×C411yescharacteristic
127#6667C2×C411yescharacteristic
128#6667C2×C411yescharacteristic
129#6665C2×C411yescharacteristic
130#6665C2×C411yescharacteristic
131#6651—22no—
132#6649—22no—
133#6648—22no—
134D3×#168—22no—
135D3×#168D414yescomplemented
136D5×C3⋊C8—22no—
137C2×#907—51no—
138C2×#901—51no—
139#5548—51no—
140C3×#435—51no—
141#5127—51no—
142#5111—51no—
143#5011—51no—
144#4837D511yescharacteristic, complemented
145#4836—51no—
146#4730—51no—
147#4728—51no—
148#4727—51no—
149#4727—51no—
150#4706—51no—
151D3×#97—51no—
152C2×#709—31no—
153C2×#709—31no—
154C2×C5×M16—31no—
155C2×C5×M16—31no—
156C2×C42×C5—31no—
157#4076—31no—
158#4076—31no—
159#4076—31no—
160#4076—31no—
161C22×#168—31no—
162C22×#168—31no—
163#4053—64no—
164#4053—64no—
165C2×#676—31no—
166C2×#676—31no—
167C2×#676—31no—
168C2×#676C2×D311yescharacteristic
169C2×C8×D5—31no—
170C2×C8×D5—31no—
171C2×C8×D5—31no—
172C2×C8×D5C2×D311yescharacteristic
173#4021—31no—
174#4021—31no—
175#4020—31no—
176C4×D20—31no—
177C4×D20—31no—
178C4×D20—31no—
179C4×D20C2×D311yescharacteristic
180#4015—31no—
181C5×C4⋊C8—31no—
182C5×C4⋊C8—31no—
183C5×C4⋊C8—31no—
184C5×C4⋊C8C2×D311yescharacteristic
185#3952—31no—
186#3952—31no—
187#3952—31no—
188#3952—31no—
189#3952—31no—
190#3952—31no—
191#3952C2×D311yescharacteristic
192#3952C2×D311yescharacteristic
193#3935—31no—
194#3935—31no—
195#3935—31no—
196#3935C2×D311yescharacteristic
197#2932—151noSylow
198C22×D15C22×C411yescharacteristic
199C22×D15C22×C411yescharacteristic
200C22×C5×D3C22×C411yescharacteristic
201C22×C3×D5C22×C411yescharacteristic
202C22×C3×D5C22×C411yescharacteristic
203C2×C3×C4×C5C22×C411yescharacteristic
204C2×C3×C4×C5C22×C411yescharacteristic
205C2×C3×C4×C5C2411yescharacteristic
206C2×Dic15C22×C411yescharacteristic
207C2×Dic15C22×C411yescharacteristic
208D60—41no—
209C4×D15—21no—
210C4×D15—21no—
211C4×D15—21no—
212C4×D15—21no—
213C2×C5×Dic3C22×C411yescharacteristic
214C2×C5×Dic3C22×C411yescharacteristic
215C2×C5×Dic3C22×C411yescharacteristic
216C4×C5×D3—41no—
217C4×C5×D3—41no—
218C4×C5×D3C2×D412yes—
219C4×C5×D3#4112yes—
220C2×C3×Dic5C22×C411yescharacteristic
221C2×C3×Dic5C22×C411yescharacteristic
222C3×D20—41no—
223C3×C4×D5—21no—
224C3×C4×D5—21no—
225C3×C4×D5—21no—
226C3×C4×D5—21no—
227#1204—22no—
228#1204—22no—
229#1203—22no—
230#1203—22no—
231#1202—22no—
232#1202—22no—
233#1202—41no—
234#1202—41no—
235#1201—22no—
236#1201—22no—
237C3×C5×C8—21no—
238C3×C5×C8—21no—
239C3⋊#168—21no—
240C3⋊#168C2×D412yes—
241C3×#168—21no—
242C3×#168C2×D412yes—
243C5×C3⋊C8—21no—
244C5×C3⋊C8—21no—
245C2×#235—51no—
246C2×#235—51no—
247C2×C3×M16—51no—
248C22×C3×C8—51no—
249C3×C4×D4—51no—
250#940—51no—
251#938—51no—
252C4×#67—51no—
253C4×#67—51no—
254C2×#208—51no—
255C22×C3⋊C8—51no—
256#907—104no—
257#901—104no—
258C2×ΓL(1,𝔽25)—51no—
259C2×ΓL(1,𝔽25)—51no—
260C2×ΓL(1,𝔽25)C2×D511yescharacteristic
261C2×ΓL(1,𝔽25)C2×D511yescharacteristic
262C2×D3×C8—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—51no—
266#895—51no—
267#888—51no—
268#885—51no—
269#885—51no—
270#884—51no—
271#884—51no—
272C4×D12—51no—
273C42×D3C2×D511yescharacteristic
274C3×C4⋊C8C2×D511yescharacteristic
275C3×C22⋊C8—51no—
276C3×C22⋊C8—51no—
277C3×#97—51no—
278#830—51no—
279#830—51no—
280(C2×D3)⋊C8—51no—
281(C2×D3)⋊C8—51no—
282(C2×D3)⋊C8—51no—
283(C2×D3)⋊C8—51no—
284#815—51no—
285#815—51no—
286Dic3⋊C8C2×D511yescharacteristic
287Dic3⋊C8C2×D511yescharacteristic
288C4⋊(C3⋊C8)C2×D511yescharacteristic
289#803—51no—
290C22×C4×C5—31no—
291C22×C4×C5—31no—
292C22×C4×C5—31no—
293C2×C22⋊D5—31no—
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5—31no—
297#709—62no—
298#709—62no—
299#709—62no—
300#709—62no—
301C2×D20—31no—
302C2×D20—31no—
303C2×D20—31no—
304C2×D20—31no—
305C2×D20—31no—
306C2×D20C4×D311yescharacteristic
307C2×C4×D5—31no—
308C2×C4×D5—31no—
309C2×C4×D5C22×D311yescharacteristic
310C2×C4×D5C22×D311yescharacteristic
311C2×Dic10—31no—
312C2×Dic10—31no—
313C5×M16—62no—
314C5×M16—62no—
315C2×C5×C8—31no—
316C2×C5×C8—31no—
317C2×C5×C8C22×D311yescharacteristic
318C2×C5×C8C22×D311yescharacteristic
319C42×C5—31no—
320C42×C5—31no—
321C42×C5—31no—
322C42×C5C22×D311yescharacteristic
323#685—31no—
324#685—31no—
325#685—31no—
326#685—31no—
327#685—31no—
328#685—31no—
329#685C4×D311yescharacteristic
330#685C4×D311yescharacteristic
331C4⋊Dic5—31no—
332C4⋊Dic5—31no—
333C4⋊Dic5—31no—
334C4⋊Dic5C4×D311yescharacteristic
335C2×#168—31no—
336C2×#168—34no—
337C2×#168—31no—
338C2×#168—62no—
339C2×#168C22×D311yescharacteristic
340C2×#168C22×D311yescharacteristic
341#676—22no—
342#676—62no—
343#676—62no—
344#676—62no—
345C8×D5—22no—
346C8×D5—62no—
347C8×D5—62no—
348C8×D5—62no—
349C2×#131—151no—
350C2×#131—151no—
351#532—151no—
352#435—51no—
353#435—151no—
354#435—151no—
355#435—151no—
356#435—151no—
357#435—151no—
358#435—151no—
359#435—151no—
360#423—31no—
361#408—151no—
362#408—151no—
363C2×#97—151no—
364C22×C3×C5C23×C411yescharacteristic
365C2×D15—21no—
366C2×D15—21no—
367C2×D15—21no—
368C2×D15—21no—
369C2×D15—21no—
370C2×D15—21no—
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3C4×D412yes—
374C2×C3×D5—21no—
375C2×C3×D5—21no—
376C2×C3×D5—21no—
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5—21no—
380C3×C4×C5—21no—
381C3×C4×C5—21no—
382C3×C4×C5C22×D411yescharacteristic
383C3×C4×C5C2×#4111yescharacteristic
384Dic15—21no—
385Dic15—21no—
386C3×Dic5—21no—
387C3×Dic5—21no—
388C5×Dic3—21no—
389C5×Dic3—21no—
390C5×Dic3C4×D412yes—
391C2×C3×D4—51no—
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C2×#67—51no—
395C2×#67—51no—
396C2×#67—51no—
397C2×#67—51no—
398C2×#67—51no—
399C2×#67—51no—
400#235—102no—
401#235—102no—
402#235—102no—
403#235—102no—
404C2×D12—51no—
405C2×D12—51no—
406C2×D12—51no—
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3C4×D511yescharacteristic
410C2×C4×D3C4×D511yescharacteristic
411C2×C4×D3C22×D511yescharacteristic
412C2×Dic6—51no—
413C2×Dic6—51no—
414C3×M16—102no—
415C2×C3×C8—51no—
416C2×C3×C8—51no—
417C2×C3×C8—102no—
418C2×C3×C8C22×D511yescharacteristic
419C2×C3×C8C22×D511yescharacteristic
420C3×C4⋊C4—51no—
421C3×C22⋊C4—51no—
422C3×C22⋊C4—51no—
423C3×C42C22×D511yescharacteristic
424#217—51no—
425#217—51no—
426(C2×D3)⋊C4—51no—
427(C2×D3)⋊C4—51no—
428(C2×D3)⋊C4—51no—
429(C2×D3)⋊C4—51no—
430C4⋊Dic3—51no—
431Dic3⋊C4—51no—
432Dic3⋊C4—51no—
433C4×Dic3C4×D511yescharacteristic
434C4×Dic3C4×D511yescharacteristic
435C4×Dic3C22×D511yescharacteristic
436#208—102no—
437C2×C3⋊C8—51no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—102no—
440C2×C3⋊C8C22×D511yescharacteristic
441C2×C3⋊C8C22×D511yescharacteristic
442ΓL(1,𝔽25)—22no—
443ΓL(1,𝔽25)—22no—
444ΓL(1,𝔽25)—102no—
445ΓL(1,𝔽25)—102no—
446D3×C8—54no—
447D3×C8—102no—
448D3×C8—102no—
449D3×C8—102no—
450C23×C5—31no—
451C22×D5—31no—
452C22×D5—31no—
453C22×D5C2×C4×D311yescharacteristic
454C22×D5C2×C4×D311yescharacteristic
455C2×C4×C5—31no—
456C2×C4×C5—32no—
457C2×C4×C5—32no—
458C2×C4×C5—31no—
459C2×C4×C5—31no—
460C2×C4×C5—121no—
461C2×C4×C5—121no—
462C2×C4×C5C2×C4×D311yescharacteristic
463C2×C4×C5C2×C4×D311yescharacteristic
464C2×C4×C5C23×D311yescharacteristic
465C22⋊D5—62no—
466C22⋊D5—62no—
467C22⋊D5—62no—
468C22⋊D5—62no—
469C2×Dic5—31no—
470C2×Dic5—31no—
471C2×Dic5C2×C4×D311yescharacteristic
472C2×Dic5C2×C4×D311yescharacteristic
473D20—41no—
474D20—62no—
475D20—62no—
476D20—121no—
477D20—121no—
478D20—121no—
479C4×D5—21no—
480C4×D5—21no—
481C4×D5—21no—
482C4×D5—21no—
483C4×D5—61no—
484C4×D5—61no—
485C4×D5—61no—
486C4×D5—61no—
487Dic10—62no—
488Dic10—62no—
489C5×C8—21no—
490C5×C8—21no—
491C5×C8—61no—
492C5×C8—61no—
493#168—21no—
494#168—32no—
495#168—61no—
496#168D3×D412yes—
497C2×#41—151no—
498C2×#41—151no—
499#131—304no—
500#131—304no—
501C2×M16—31no—
502C2×M16—31no—
503C2×M16—51no—
504C2×M16—151no—
505C2×M16—151no—
506C2×M16—151no—
507C22×C8—51no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—151no—
513C4⋊Q8—151no—
514#127—151no—
515#124—151no—
516#124—151no—
517#121—151no—
518#121—151no—
519#121—151no—
520#121—151no—
521C4×D4—51no—
522C4×D4—151no—
523C4×D4—151no—
524C4×D4—151no—
525C2×C42—31no—
526C4⋊C8—31no—
527C4⋊C8—31no—
528C4⋊C8—31no—
529C4⋊C8D3×D511yescharacteristic
530C22⋊C8—51no—
531C22⋊C8—51no—
532C22⋊C8—151no—
533C22⋊C8—151no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8—151no—
538#97—51no—
539#97—151no—
540#97—151no—
541#97—151no—
542C2×C3×C5C2×C4×D411yescharacteristic
543C2×C3×C5#56811yescharacteristic
544C2×C3×C5#56811yescharacteristic
545D15—41no—
546D15—41no—
547C3×D5—41no—
548C3×D5—41no—
549C5×D3—22no—
550C23×C3—51no—
551C23×C3—51no—
552C22×D3—51no—
553C22×D3—51no—
554C22×D3C2×C4×D511yescharacteristic
555C3×D4—201no—
556C2×C3×C4—51no—
557C2×C3×C4—51no—
558C2×C3×C4—101no—
559C2×C3×C4—101no—
560C2×C3×C4—101no—
561C2×C3×C4—101no—
562C2×C3×C4C2×C4×D511yescharacteristic
563C2×C3×C4C2×C4×D511yescharacteristic
564C2×C3×C4C23×D511yescharacteristic
565#67—102no—
566#67—102no—
567#67—102no—
568#67—102no—
569#67—201no—
570#67—201no—
571C2×Dic3—51no—
572C2×Dic3—51no—
573C2×Dic3C2×C4×D511yescharacteristic
574C2×Dic3C2×C4×D511yescharacteristic
575C2×Dic3C2×C4×D511yescharacteristic
576D12—102no—
577D12—102no—
578D12—201no—
579C4×D3—41no—
580C4×D3—41no—
581C4×D3—101no—
582C4×D3—101no—
583C4×D3—101no—
584C4×D3—101no—
585C4×D3D4×D512yes—
586C4×D3#71312yes—
587Dic6—102no—
588Dic6—102no—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—52no—
592C3×C8—101no—
593C3⋊C8—21no—
594C3⋊C8—21no—
595C3⋊C8—52no—
596C3⋊C8—101no—
597C22×C5—32no—
598C22×C5—61no—
599C22×C5—61no—
600C22×C5C22×C4×D311yescharacteristic
601C2×D5—21no—
602C2×D5—21no—
603C2×D5—21no—
604C2×D5—21no—
605C2×D5—21no—
606C2×D5—21no—
607C2×D5—61no—
608C2×D5—61no—
609C2×D5—61no—
610C2×D5—61no—
611C2×D5—61no—
612C2×D5—61no—
613C4×C5—21no—
614C4×C5—21no—
615C4×C5—32no—
616C4×C5—61no—
617C4×C5—61no—
618C4×C5C2×D3×D411yescharacteristic
619C4×C5D3×#4111yescharacteristic
620Dic5—21no—
621Dic5—21no—
622Dic5—61no—
623Dic5—61no—
624#41—302no—
625#41—302no—
626#41—302no—
627#41—302no—
628C2×Q8—151no—
629C2×Q8—151no—
630C2×D4—51no—
631C2×D4—151no—
632C2×D4—151no—
633C2×D4—151no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C2×D4—151no—
638C2×D4—151no—
639C2×D4—151no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—51no—
644C22×C4—51no—
645C22×C4—151no—
646C22×C4—151no—
647M16—62no—
648M16—62no—
649M16—102no—
650M16—302no—
651M16—302no—
652M16—302no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—51no—
656C2×C8—51no—
657C2×C8—102no—
658C2×C8—154no—
659C2×C8—151no—
660C2×C8—151no—
661C2×C8—302no—
662C2×C8—302no—
663C2×C8—302no—
664C2×C8—302no—
665C2×C8C2×D3×D511yescharacteristic
666C2×C8C2×D3×D511yescharacteristic
667C4⋊C4—51no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C22⋊C4—51no—
672C22⋊C4—51no—
673C22⋊C4—151no—
674C22⋊C4—151no—
675C22⋊C4—151no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C42—31no—
680C42—31no—
681C42—31no—
682C42C2×D3×D511yescharacteristic
683C3×C5#293211yescharacteristic, complemented, Hall
684C22×C3—101no—
685C22×C3—101no—
686C22×C3—101no—
687C22×C3—101no—
688C22×C3—101no—
689C22×C3—101no—
690C22×C3C22×C4×D511yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—101no—
694C2×D3—101no—
695C2×D3—101no—
696C2×D3—101no—
697C2×D3—101no—
698C2×D3—101no—
699C2×D3#403912yes—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—101no—
703C3×C4—101no—
704C3×C4C2×D4×D511yescharacteristic
705C3×C4C2×#71311yescharacteristic
706Dic3—21no—
707Dic3—21no—
708Dic3—101no—
709Dic3—101no—
710Dic3#403912yes—
711C2×C5—62no—
712C2×C5C4×D3×D411yescharacteristic
713C2×C5#574511yescharacteristic
714C2×C5#575011yescharacteristic
715D5—41no—
716D5—41no—
717D5—121no—
718D5—121no—
719C23—31no—
720C23—51no—
721C23—51no—
722C23—151no—
723C23—151no—
724Q8—302no—
725Q8—302no—
726D4—201no—
727D4—302no—
728D4—302no—
729D4—302no—
730D4—302no—
731D4—302no—
732D4—302no—
733D4—601no—
734D4—601no—
735D4—601no—
736C2×C4—31no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—51no—
742C2×C4—51no—
743C2×C4—101no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—151no—
750C2×C4—151no—
751C2×C4—301no—
752C2×C4—301no—
753C2×C4—301no—
754C2×C4—301no—
755C2×C4C4×D3×D511yescharacteristic
756C2×C4C4×D3×D511yescharacteristic
757C2×C4C22×D3×D511yescharacteristic
758C8—21no—
759C8—21no—
760C8—52no—
761C8—61no—
762C8—61no—
763C8—101no—
764C8—152no—
765C8—301no—
766C2×C3—201no—
767C2×C3—201no—
768C2×C3C2×#403911yescharacteristic
769C2×C3#6607911yescharacteristic
770C2×C3#6607911yescharacteristic
771D3—22no—
772D3—201no—
773D3—201no—
774C5#7948011yescharacteristic, complemented, Sylow
775C22—32no—
776C22—61no—
777C22—61no—
778C22—101no—
779C22—101no—
780C22—101no—
781C22—101no—
782C22—101no—
783C22—101no—
784C22—301no—
785C22—301no—
786C22—301no—
787C22—301no—
788C22—301no—
789C22—301no—
790C22C2×C4×D3×D511yescharacteristic
791C4—21no—
792C4—21no—
793C4—32no—
794C4—61no—
795C4—61no—
796C4—101no—
797C4—101no—
798C4—301no—
799C4—301no—
800C4D3×D4×D511yescharacteristic
801C4D3×#71311yescharacteristic
802C3#1061077311yescharacteristic, complemented, Sylow
803C2—62no—
804C2—201no—
805C2—201no—
806C2—601no—
807C2—601no—
808C2D3×#403911yescharacteristic
809C2#1175395111yescharacteristic
810C2#1175404111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C8C22
prime radical#11752675C2
cosocleC2×C3×C4×C5C24
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#2932
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
1. C2×#91268C2semidirect
2. C2×#91266C2semidirect
4. #11750937C2semidirect
5. C5×#4837C2semidirect
6. C3×#65125C2semidirect
7. #11748140C2semidirect
8. #11748140C2semidirect
9. #11748047C2semidirect
10. #11747727C2semidirect
11. #11747726C2semidirect
12. #11747706C2semidirect
13. #11746997C2semidirect
14. #11746989C2semidirect
15. D3×#3935C2semidirect
77. #65125D3semidirect
135. D3×#168D4semidirect
144. #4837D5semidirect
683. C3×C5#2932semidirect
774. C5#79480semidirect
802. C3#10610773semidirect

Maximal subgroups

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

subgroupindex
C2×#912682
C2×#912662
#117526752
#117509372
C5×#48372
C3×#651252
#117481402
#117480472
#117477272
#117477262
#117477062
#117469972
#117469892
D3×#39352
#106107733
#794805