Finite Group Databasebeta

← #14415249

Subgroups — #14415249

Order 1920.

1000 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
1#11754539C211yesmaximal, characteristic
2C2×#91288C211yesmaximal, characteristic, complemented
3C2×#91268C211yesmaximal, characteristic, complemented
4#11750826C211yesmaximal, characteristic, complemented
5C5×#4727C211yesmaximal, characteristic, complemented
6C3×#65018C211yesmaximal, characteristic, complemented
7#11748493C211yesmaximal, characteristic, complemented
8#11748312C211yesmaximal, characteristic, complemented
9#11748139C211yesmaximal, characteristic, complemented
10#11748045C211yesmaximal, characteristic, complemented
11#11747723C211yesmaximal, characteristic, complemented
12#11747708C211yesmaximal, characteristic, complemented
13#11747696C211yesmaximal, characteristic, complemented
14#11747590C211yesmaximal, characteristic, complemented
15D3×C8×Dic5C211yesmaximal, characteristic, complemented
16#10610388—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
18C2×#6771C2211yescharacteristic
19C4×#1220C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C2×C8×D15C2211yescharacteristic
22C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
23C2×C5×D3×C8C2211yescharacteristic
24C3×C4×C22⋊D5C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26C2×C3×#676C2211yescharacteristic
27#91567C411yescharacteristic
28#91565C411yescharacteristic
29#91558C411yescharacteristic
30#91525C411yescharacteristic
31#91455C411yescharacteristic
32#91453C411yescharacteristic
33C4×#1203C2211yescharacteristic
34C4×#1201C2211yescharacteristic
35#91416C411yescharacteristic
36C4×D3×Dic5C2211yescharacteristic
37#91329C411yescharacteristic
38C2×#6651C2211yescharacteristic
39C2×#6650C2211yescharacteristic
40C2×#6650C2211yescharacteristic
41#91288—24no—
42C2×D3×#168C2211yescharacteristic
43C2×D3×#168C2211yescharacteristic
44C2×D5×C3⋊C8C2211yescharacteristic
45#91268—24no—
46C3×C5×C22⋊C8C2211yescharacteristic
47#91104C2211yescharacteristic
48#91098C2211yescharacteristic
49C8×Dic15C2211yescharacteristic
50C5×#830C2211yescharacteristic
51C5×(C2×D3)⋊C8C2211yescharacteristic
52C5×(C2×D3)⋊C8C2211yescharacteristic
53C3×#3952C2211yescharacteristic
54C3×#3946C2211yescharacteristic
55C3×C8×Dic5C2211yescharacteristic
56#90983C2211yescharacteristic
57#90982C2211yescharacteristic
58#90957C2211yescharacteristic
59#90955C2211yescharacteristic
60#90951C2211yescharacteristic
61Dic5×C3⋊C8C2211yescharacteristic
62#79538—51nomaximal, Hall
63#66166—31no—
64C2×#4094—31no—
65C2×#4053—31no—
66C5×#408—31no—
67#65407—31no—
68#65399—31no—
69C2×C8×Dic5—31no—
70#65018—31no—
71#65018—31no—
72#65018—31no—
73#65018D311yescharacteristic, complemented
74#65014—31no—
75#65014—31no—
76#65014—31no—
77#65014—31no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220C2×C411yescharacteristic
80C2×C4×D15C2311yescharacteristic
81C2×C5×#67C2×C411yescharacteristic
82C2×C5×#67C2×C411yescharacteristic
83C5×#235—22no—
84C5×#235—22no—
85C2×C5×D12C2×C411yescharacteristic
86C2×C4×C5×D3C2311yescharacteristic
87C2×C4×C5×D3C2311yescharacteristic
88C2×C5×Dic6C2×C411yescharacteristic
89C2×C3×C22⋊D5C2×C411yescharacteristic
90C2×C3×C4×D5C2311yescharacteristic
91C2×#1204C2×C411yescharacteristic
92C2×#1203C2×C411yescharacteristic
93C2×#1203C2×C411yescharacteristic
94C2×#1202C2×C411yescharacteristic
95C2×#1201C2×C411yescharacteristic
96C2×#1201C2×C411yescharacteristic
97C2×D3×Dic5C2×C411yescharacteristic
98C2×D3×Dic5C2×C411yescharacteristic
99#6771—22no—
100#6771—22no—
101C2×C3×C5×C8C2311yescharacteristic
102C2×C3×C5×C8C2311yescharacteristic
103#6719C2×C411yescharacteristic
104#6714C2×C411yescharacteristic
105#6712C2×C411yescharacteristic
106C4×Dic15C2311yescharacteristic
107C2×C3⋊#168—22no—
108C2×C3⋊#168C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C8×D15—22no—
111C2×C5×C3⋊C8C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C5×ΓL(1,𝔽25)—22no—
114C5×D3×C8—22no—
115C3×C22⋊Dic5C2×C411yescharacteristic
116C3×#685C2×C411yescharacteristic
117C3×#683C2×C411yescharacteristic
118C3×C4×Dic5C2311yescharacteristic
119C3×#681—22no—
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122C3×#676—22no—
123#6669C2×C411yescharacteristic
124#6668C2×C411yescharacteristic
125#6667C2×C411yescharacteristic
126(C2×D3)⋊Dic5C2×C411yescharacteristic
127(C2×D3)⋊Dic5C2×C411yescharacteristic
128#6665C2×C411yescharacteristic
129Dic3×Dic5C2×C411yescharacteristic
130Dic3×Dic5C2×C411yescharacteristic
131#6651—22no—
132#6650—22no—
133#6650—22no—
134D3×#168—22no—
135D3×#168D414yescomplemented
136D5×C3⋊C8—22no—
137C2×#907—51no—
138C2×#907—51no—
139#5548—51no—
140C3×#436—51no—
141#5128—51no—
142#5128—51no—
143D4×C3⋊C8—51no—
144#4837—51no—
145#4834—51no—
146#4727—51no—
147#4727D511yescharacteristic, complemented
148#67⋊C8—51no—
149#67⋊C8—51no—
150#4688—51no—
151C4×D3×C8—51no—
152C2×C5×#41—31no—
153C2×#709—31no—
154C2×C5×M16—31no—
155C22×C5×C8—31no—
156#4094—64no—
157#4093—31no—
158#4090—31no—
159#4086—31no—
160#4085—31no—
161#4085—31no—
162#4085—31no—
163#4085—31no—
164#4082—31no—
165C4×C22⋊D5—31no—
166C4×C22⋊D5—31no—
167C4×C22⋊D5—31no—
168C4×C22⋊D5C2×D311yescharacteristic
169C2×C4×Dic5—31no—
170C2×#681—31no—
171C2×#681—31no—
172C2×#681C2×D311yescharacteristic
173C22×#168—31no—
174C22×#168—31no—
175C22×#168—31no—
176#4053—64no—
177C2×#676—31no—
178C2×#676C2×D311yescharacteristic
179C2×C8×D5—31no—
180C2×C8×D5—31no—
181C5×C22⋊C8—31no—
182C5×C22⋊C8—31no—
183C5×C22⋊C8—31no—
184C5×C22⋊C8C2×D311yescharacteristic
185#3952—31no—
186#3952—31no—
187#3952—31no—
188#3952C2×D311yescharacteristic
189#3946—31no—
190#3946—31no—
191#3946—31no—
192#3946C2×D311yescharacteristic
193C8×Dic5—31no—
194C8×Dic5—31no—
195C8×Dic5—31no—
196C8×Dic5C2×D311yescharacteristic
197#2931—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C22×D15C22×C411yescharacteristic
200C22×C5×D3C22×C411yescharacteristic
201C22×C5×D3C22×C411yescharacteristic
202C22×C3×D5C22×C411yescharacteristic
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5C22×C411yescharacteristic
206C2×C3×C4×C5C2411yescharacteristic
207#1220—22no—
208C2×Dic15C22×C411yescharacteristic
209C2×Dic15C22×C411yescharacteristic
210C2×Dic15C22×C411yescharacteristic
211C4×D15—21no—
212C4×D15—21no—
213C5×#67—22no—
214C5×#67—22no—
215C2×C5×Dic3C22×C411yescharacteristic
216C2×C5×Dic3C22×C411yescharacteristic
217C5×D12—22no—
218C4×C5×D3—21no—
219C4×C5×D3—21no—
220C4×C5×D3C2×D412yes—
221C4×C5×D3#4112yes—
222C5×Dic6—22no—
223C3×C22⋊D5—22no—
224C2×C3×Dic5C22×C411yescharacteristic
225C2×C3×Dic5C22×C411yescharacteristic
226C2×C3×Dic5C22×C411yescharacteristic
227C3×C4×D5—21no—
228C3×C4×D5—21no—
229#1204—22no—
230#1203—22no—
231#1203—22no—
232#1202—22no—
233#1201—22no—
234#1201—22no—
235D3×Dic5—22no—
236D3×Dic5—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×#235C2×D511yescharacteristic
247C2×C3×M16—51no—
248C2×C3×M16—51no—
249C3×C4×D4—51no—
250#940—51no—
251#938—51no—
252C4×#67—51no—
253C4×#67—51no—
254C22×C3⋊C8—51no—
255C22×C3⋊C8—51no—
256#907—104no—
257#907—104no—
258C2×ΓL(1,𝔽25)—51no—
259C2×ΓL(1,𝔽25)—51no—
260C2×ΓL(1,𝔽25)—51no—
261C2×ΓL(1,𝔽25)C2×D511yescharacteristic
262C2×D3×C8—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8C2×D511yescharacteristic
266#895—51no—
267#888—51no—
268#885—51no—
269#885—51no—
270#884—51no—
271#884—51no—
272C4×D12—51no—
273C42×D3—51no—
274C3×C4⋊C8—51no—
275C3×C22⋊C8—51no—
276C3×C22⋊C8C2×D511yescharacteristic
277C3×C4×C8—51no—
278#830—51no—
279#830C2×D511yescharacteristic
280(C2×D3)⋊C8—51no—
281(C2×D3)⋊C8—51no—
282(C2×D3)⋊C8C2×D511yescharacteristic
283(C2×D3)⋊C8C2×D511yescharacteristic
284Dic3⋊C8—51no—
285Dic3⋊C8—51no—
286C8×Dic3—51no—
287C8×Dic3—51no—
288C4⋊(C3⋊C8)—51no—
289C4×C3⋊C8—51no—
290C5×#41—62no—
291C5×#41—62no—
292C2×C5×Q8—31no—
293C2×C5×D4—31no—
294C2×C5×D4—31no—
295C2×C5×D4—31no—
296C22×C4×C5—31no—
297C22×C4×C5—31no—
298C22×C4×C5C22×D311yescharacteristic
299C2×C22⋊D5—31no—
300C2×C22⋊D5—31no—
301C2×C22⋊D5—31no—
302C2×C22⋊D5—31no—
303C2×C22⋊D5—31no—
304C2×C22⋊D5C4×D311yescharacteristic
305C22×Dic5—31no—
306C22×Dic5—31no—
307#709—62no—
308#709—62no—
309C2×D20—31no—
310C2×C4×D5—31no—
311C2×C4×D5C22×D311yescharacteristic
312C2×Dic10—31no—
313C5×M16—62no—
314C2×C5×C8—31no—
315C2×C5×C8—31no—
316C2×C5×C8—62no—
317C2×C5×C8C22×D311yescharacteristic
318C2×C5×C8C22×D311yescharacteristic
319C22⋊Dic5—31no—
320C22⋊Dic5—31no—
321C22⋊Dic5—31no—
322C22⋊Dic5C4×D311yescharacteristic
323#685—31no—
324#685—31no—
325#685—31no—
326#685C4×D311yescharacteristic
327#683—31no—
328#683—31no—
329#683—31no—
330#683C4×D311yescharacteristic
331C4×Dic5—31no—
332C4×Dic5—31no—
333C4×Dic5—31no—
334C4×Dic5C22×D311yescharacteristic
335#681—22no—
336#681—62no—
337#681—62no—
338C2×#168—31no—
339C2×#168—34no—
340C2×#168—31no—
341C2×#168—62no—
342C2×#168—62no—
343C2×#168C22×D311yescharacteristic
344C2×#168C22×D311yescharacteristic
345#676—22no—
346#676—62no—
347C8×D5—62no—
348C8×D5—62no—
349C2×#131—151no—
350C2×#131—151no—
351#532—151no—
352#436—51no—
353#436—151no—
354#436—151no—
355#436—151no—
356C8×D4—151no—
357C8×D4—151no—
358C8×D4—151no—
359C8×D4—151no—
360#423—151no—
361#408—31no—
362#408—151no—
363C2×C4×C8—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5—21no—
367C22×C3×C5C23×C411yescharacteristic
368C2×D15—21no—
369C2×D15—21no—
370C2×D15—21no—
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3—21no—
374C2×C5×D3—21no—
375C2×C5×D3—21no—
376C2×C5×D3C4×D412yes—
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5—21no—
380C3×C4×C5—21no—
381C3×C4×C5C22×D411yescharacteristic
382C3×C4×C5C2×#4111yescharacteristic
383Dic15—21no—
384Dic15—21no—
385Dic15#13112yescomplemented
386C3×Dic5—21no—
387C3×Dic5—21no—
388C3×Dic5#13112yescomplemented
389C5×Dic3—21no—
390C5×Dic3C4×D412yes—
391C2×C3×D4—51no—
392C22×C3×C4—51no—
393C22×C3×C4C22×D511yescharacteristic
394C2×#67—51no—
395C2×#67—51no—
396C2×#67—51no—
397C2×#67—51no—
398C2×#67C4×D511yescharacteristic
399C2×#67C4×D511yescharacteristic
400#235—22no—
401#235—22no—
402#235—102no—
403#235—102no—
404C2×D12—51no—
405C2×D12—51no—
406C2×D12C4×D511yescharacteristic
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3—51no—
410C2×C4×D3C22×D511yescharacteristic
411C2×C4×D3C22×D511yescharacteristic
412C2×Dic6—51no—
413C2×Dic6C4×D511yescharacteristic
414C3×M16—102no—
415C3×M16—102no—
416C2×C3×C8—51no—
417C2×C3×C8—51no—
418C2×C3×C8C22×D511yescharacteristic
419C2×C3×C8C22×D511yescharacteristic
420C3×C4⋊C4—51no—
421C3×C22⋊C4—51no—
422C3×C22⋊C4—51no—
423C3×C42—51no—
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×Dic3—51no—
434C4×Dic3—51no—
435C4×Dic3—51no—
436C2×C3⋊C8—51no—
437C2×C3⋊C8—51no—
438C2×C3⋊C8—102no—
439C2×C3⋊C8—102no—
440C2×C3⋊C8C22×D511yescharacteristic
441C2×C3⋊C8C22×D511yescharacteristic
442ΓL(1,𝔽25)—22no—
443ΓL(1,𝔽25)—102no—
444ΓL(1,𝔽25)—102no—
445ΓL(1,𝔽25)—102no—
446D3×C8—22no—
447D3×C8—54no—
448D3×C8—102no—
449D3×C8—102no—
450C23×C5—31no—
451C23×C5—31no—
452C23×C5C2×C4×D311yescharacteristic
453C22×D5—31no—
454C22×D5C2×C4×D311yescharacteristic
455C5×Q8—62no—
456C5×D4—62no—
457C5×D4—62no—
458C5×D4—62no—
459C2×C4×C5—21no—
460C2×C4×C5—21no—
461C2×C4×C5—31no—
462C2×C4×C5—32no—
463C2×C4×C5—32no—
464C2×C4×C5—31no—
465C2×C4×C5—61no—
466C2×C4×C5—61no—
467C2×C4×C5C2×C4×D311yescharacteristic
468C2×C4×C5C23×D311yescharacteristic
469C22⋊D5—22no—
470C22⋊D5—62no—
471C22⋊D5—62no—
472C22⋊D5—62no—
473C22⋊D5—62no—
474C22⋊D5—62no—
475C2×Dic5—31no—
476C2×Dic5—31no—
477C2×Dic5—31no—
478C2×Dic5—62no—
479C2×Dic5—62no—
480C2×Dic5C2×C4×D311yescharacteristic
481C2×Dic5C2×C4×D311yescharacteristic
482C2×Dic5C2×C4×D311yescharacteristic
483D20—62no—
484C4×D5—21no—
485C4×D5—21no—
486C4×D5—61no—
487C4×D5—61no—
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—31no—
498C2×#41—151no—
499#131—304no—
500#131—304no—
501C2×M16—31no—
502C2×M16—51no—
503C2×M16—51no—
504C2×M16—151no—
505C2×M16—151no—
506C2×M16—151no—
507C22×C8—31no—
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—151no—
526C4⋊C8—51no—
527C4⋊C8—151no—
528C4⋊C8—151no—
529C4⋊C8—151no—
530C22⋊C8—31no—
531C22⋊C8—31no—
532C22⋊C8—31no—
533C22⋊C8—51no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8D3×D511yescharacteristic
538C4×C8—51no—
539C4×C8—151no—
540C4×C8—151no—
541C4×C8—151no—
542C2×C3×C5—41no—
543C2×C3×C5C2×C4×D411yescharacteristic
544C2×C3×C5C2×#13111yescharacteristic
545C2×C3×C5C2×#13111yescharacteristic
546D15—41no—
547C3×D5—41no—
548C5×D3—22no—
549C5×D3—41no—
550C23×C3—51no—
551C23×C3C2×C4×D511yescharacteristic
552C22×D3—51no—
553C22×D3C2×C4×D511yescharacteristic
554C22×D3C2×C4×D511yescharacteristic
555C3×D4—102no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—51no—
559C2×C3×C4—51no—
560C2×C3×C4—51no—
561C2×C3×C4—101no—
562C2×C3×C4—101no—
563C2×C3×C4C2×C4×D511yescharacteristic
564C2×C3×C4C23×D511yescharacteristic
565#67—22no—
566#67—22no—
567#67—102no—
568#67—102no—
569#67—102no—
570#67—102no—
571C2×Dic3—51no—
572C2×Dic3—51no—
573C2×Dic3—51no—
574C2×Dic3C2×C4×D511yescharacteristic
575C2×Dic3C2×C4×D511yescharacteristic
576D12—22no—
577D12—102no—
578D12—102no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—102no—
582C4×D3—102no—
583C4×D3—101no—
584C4×D3—101no—
585C4×D3D4×D512yes—
586C4×D3#71112yes—
587Dic6—22no—
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—21no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—32no—
601C22×C5—61no—
602C22×C5—61no—
603C22×C5—61no—
604C22×C5—61no—
605C22×C5—61no—
606C22×C5C22×C4×D311yescharacteristic
607C2×D5—21no—
608C2×D5—21no—
609C2×D5—21no—
610C2×D5—61no—
611C2×D5—61no—
612C2×D5—61no—
613C4×C5—21no—
614C4×C5—32no—
615C4×C5—61no—
616C4×C5C2×D3×D411yescharacteristic
617C4×C5D3×#4111yescharacteristic
618Dic5—21no—
619Dic5—21no—
620Dic5—32no—
621Dic5—61no—
622Dic5—61no—
623Dic5#90712yescomplemented
624#41—62no—
625#41—62no—
626#41—302no—
627#41—302no—
628C2×Q8—31no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—51no—
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—51no—
643C22×C4—151no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4C2×D3×D511yescharacteristic
647M16—62no—
648M16—102no—
649M16—102no—
650M16—302no—
651M16—302no—
652M16—302no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—51no—
656C2×C8—51no—
657C2×C8—62no—
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—51no—
680C42—151no—
681C42—151no—
682C42—151no—
683C3×C5#293111yescharacteristic, complemented, Hall
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—101no—
688C22×C3—101no—
689C22×C3—101no—
690C22×C3C22×C4×D511yescharacteristic
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—101no—
697C2×D3—101no—
698C2×D3—101no—
699C2×D3#402712yes—
700C3×C4—21no—
701C3×C4—52no—
702C3×C4—101no—
703C3×C4—101no—
704C3×C4C2×D4×D511yescharacteristic
705C3×C4C2×#71111yescharacteristic
706Dic3—21no—
707Dic3—52no—
708Dic3—101no—
709Dic3—101no—
710Dic3#402712yes—
711C2×C5—41no—
712C2×C5—62no—
713C2×C5—121no—
714C2×C5C4×D3×D411yescharacteristic
715C2×C5C2×#90711yescharacteristic
716C2×C5D3×#13111yescharacteristic
717D5—41no—
718D5—121no—
719C23—31no—
720C23—31no—
721C23—51no—
722C23—151no—
723C23C4×D3×D511yescharacteristic
724Q8—62no—
725Q8—302no—
726D4—62no—
727D4—62no—
728D4—62no—
729D4—102no—
730D4—302no—
731D4—302no—
732D4—302no—
733D4—302no—
734D4—302no—
735D4—302no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—31no—
739C2×C4—32no—
740C2×C4—32no—
741C2×C4—31no—
742C2×C4—51no—
743C2×C4—51no—
744C2×C4—51no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—151no—
750C2×C4—151no—
751C2×C4—151no—
752C2×C4—302no—
753C2×C4—302no—
754C2×C4—301no—
755C2×C4—301no—
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—41no—
767C2×C3—201no—
768C2×C3C2×#402711yescharacteristic
769C2×C3D5×#13111yescharacteristic
770C2×C3D5×#13111yescharacteristic
771D3—22no—
772D3—41no—
773D3—201no—
774C5#7953811yescharacteristic, complemented, Sylow
775C22—21no—
776C22—21no—
777C22—21no—
778C22—32no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—101no—
785C22—101no—
786C22—101no—
787C22—301no—
788C22—301no—
789C22—301no—
790C22C2×C4×D3×D511yescharacteristic
791C4—21no—
792C4—32no—
793C4—52no—
794C4—61no—
795C4—101no—
796C4—101no—
797C4—152no—
798C4—301no—
799C4—301no—
800C4D3×D4×D511yescharacteristic
801C4D3×#71111yescharacteristic
802C3#1061038811yescharacteristic, complemented, Sylow
803C2—41no—
804C2—62no—
805C2—121no—
806C2—201no—
807C2—601no—
808C2D3×#402711yescharacteristic
809C2#1175395211yescharacteristic
810C2D5×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C8C22
prime radical#11754539C2
cosocleC2×C3×C4×C5C24
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#2931
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#91288C2semidirect
3. C2×#91268C2semidirect
4. #11750826C2semidirect
5. C5×#4727C2semidirect
6. C3×#65018C2semidirect
7. #11748493C2semidirect
8. #11748312C2semidirect
9. #11748139C2semidirect
10. #11748045C2semidirect
11. #11747723C2semidirect
12. #11747708C2semidirect
13. #11747696C2semidirect
14. #11747590C2semidirect
15. D3×C8×Dic5C2semidirect
73. #65018D3semidirect
135. D3×#168D4semidirect
147. #4727D5semidirect
385. Dic15#131semidirect
388. C3×Dic5#131semidirect
623. Dic5#907semidirect
683. C3×C5#2931semidirect
774. C5#79538semidirect
802. C3#10610388semidirect

Maximal subgroups

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

subgroupindex
#117545392
C2×#912882
C2×#912682
#117508262
C5×#47272
C3×#650182
#117484932
#117483122
#117481392
#117480452
#117477232
#117477082
#117476962
#117475902
D3×C8×Dic52
#106103883
#795385