Finite Group Databasebeta

← #14415476

Subgroups — #14415476

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756306C211yesmaximal, characteristic
2C22×#6651C211yesmaximal, characteristic, complemented
3C2×#91291C211yesmaximal, characteristic, complemented
4C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
5C3×#65300C211yesmaximal, characteristic, complemented
6#11748506C211yesmaximal, characteristic, complemented
7#11748506C211yesmaximal, characteristic, complemented
8#11748498C211yesmaximal, characteristic, complemented
9#11748497C211yesmaximal, characteristic, complemented
10#11748485C211yesmaximal, characteristic, complemented
11#11748312C211yesmaximal, characteristic, complemented
12#11747012C211yesmaximal, characteristic, complemented
13#11747001C211yesmaximal, characteristic, complemented
14#11746989C211yesmaximal, characteristic, complemented
15#11746982C211yesmaximal, characteristic, complemented
16#10611154—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20#91828C411yescharacteristic
21#91826C411yescharacteristic
22C4×#1220C2211yescharacteristic
23C4×#1220C2211yescharacteristic
24#91785C411yescharacteristic
25#91783C411yescharacteristic
26#91773C411yescharacteristic
27#91772C411yescharacteristic
28#91771C411yescharacteristic
29#91767C411yescharacteristic
30C4×D60C2211yescharacteristic
31#91761C2211yescharacteristic
32C22×C5×C3⋊C8C2211yescharacteristic
33C22×C5×C3⋊C8C2211yescharacteristic, complemented
34C2×C3×#681C2211yescharacteristic, complemented
35C22×C3×#168C2211yescharacteristic
36C2×#6651—24no—
37C2×#6651C2211yescharacteristic
38C2×#6651C2211yescharacteristic
39C2×#6651C2211yescharacteristic
40C2×#6651C2211yescharacteristic
41C2×#6651C2211yescharacteristic, complemented
42#91291—24no—
43C2×#6648C2211yescharacteristic
44C2×#6648C2211yescharacteristic
45C2×#6648C2211yescharacteristic, complemented
46C5×#830C2211yescharacteristic
47C5×#830C2211yescharacteristic, complemented
48C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
49C4×C5×C3⋊C8C2211yescharacteristic, complemented
50C3×C22⋊#168C2211yescharacteristic
51C3×C22⋊#168C2211yescharacteristic, complemented
52C3×C4⋊#168C2211yescharacteristic, complemented
53C3×#3935C2211yescharacteristic, complemented
54#90983C2211yescharacteristic, complemented
55#90983C2211yescharacteristic, complemented
56#90957C2211yescharacteristic
57#90957C2211yescharacteristic
58#90957C2211yescharacteristic, complemented
59#90957C2211yescharacteristic, complemented
60#90954C2211yescharacteristic, complemented
61#90951C2211yescharacteristic, complemented
62#79481—51nomaximal, Hall
63C2×#4047—31no—
64C22×#676—31no—
65#65881—31no—
66C5×C8×D4—31no—
67#65400—31no—
68#65400—31no—
69#65300D311yescharacteristic, complemented
70#65128—31no—
71#65125—31no—
72#65018—31no—
73#65016—31no—
74#65014—31no—
75D5×C22⋊C8—31no—
76#64978—31no—
77#64977—31no—
78C23×D15C2×C411yescharacteristic
79C2×C3×C5×D4C2×C411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220C2×C411yescharacteristic
83C2×#1220C2×C411yescharacteristic
84C2×#1220C2×C411yescharacteristic
85C2×#1220C2×C411yescharacteristic
86C22×Dic15C2×C411yescharacteristic
87#6817—22no—
88#6817—22no—
89C2×D60C2×C411yescharacteristic
90C2×D60C2×C411yescharacteristic
91C2×C4×D15—22no—
92C2×C4×D15—22no—
93C2×C4×D15C2×C411yescharacteristic
94C2×C4×D15C2×C411yescharacteristic
95C2×C4×D15C2311yescharacteristic
96C2×C4×D15C2311yescharacteristic
97C2×C4×D15C2311yescharacteristic
98C2×Dic30C2×C411yescharacteristic
99C3×C5×C4⋊C4C2×C411yescharacteristic
100C3×C5×C22⋊C4C2×C411yescharacteristic
101C3×C5×C22⋊C4C2×C411yescharacteristic
102C3×C42×C5C2311yescharacteristic
103#6719C2×C411yescharacteristic
104#6719C2×C411yescharacteristic
105#6714C2×C411yescharacteristic
106#6714C2×C411yescharacteristic
107#6714C2×C411yescharacteristic
108#6714C2×C411yescharacteristic
109#6714C2×C411yescharacteristic
110#6714C2×C411yescharacteristic
111C4⋊Dic15C2×C411yescharacteristic
112#6712C2×C411yescharacteristic
113#6712C2×C411yescharacteristic
114#6712C2×C411yescharacteristic
115#6712C2×C411yescharacteristic
116C4×Dic15C2311yescharacteristic
117C2×C5×C3⋊C8—22no—
118C2×C5×C3⋊C8—22no—
119C2×C5×C3⋊C8C2311yescharacteristic
120C2×C5×C3⋊C8C2311yescharacteristic
121C2×C5×C3⋊C8C2311yescharacteristic
122C2×C5×C3⋊C8C2311yescharacteristic
123C3×#681—22no—
124C2×C3×#168—22no—
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129#6651—22no—
130#6651—22no—
131#6651—22no—
132#6651—22no—
133#6651D414yescomplemented
134#6648—22no—
135#6648—22no—
136#6648—22no—
137C2×#907—51no—
138C22×ΓL(1,𝔽25)—51no—
139#5547—51no—
140C3×#435—51no—
141#5128—51no—
142C8×#67—51no—
143D4×C3⋊C8D511yescharacteristic, complemented
144#4839—51no—
145#4838—51no—
146#4730—51no—
147#4730—51no—
148#4727—51no—
149D3×C22⋊C8—51no—
150#4708—51no—
151#4706—51no—
152C2×#709—31no—
153C22×C4×D5—31no—
154C22×C5×C8—31no—
155C22×C5×C8—31no—
156C4×C5×D4C2×D311yescharacteristic
157#4085—31no—
158#4083—31no—
159C4×C22⋊D5—31no—
160C4×C22⋊D5—31no—
161C2×#681C2×D311yescharacteristic, complemented
162C22×#168C2×D311yescharacteristic
163#4047—64no—
164C2×#676—31no—
165C2×#676—31no—
166C2×#676—31no—
167C2×#676—31no—
168C2×#676—31no—
169C2×#676—64no—
170C2×C8×D5—31no—
171C2×C8×D5—31no—
172C2×C8×D5—31no—
173#4042—31no—
174#4040—31no—
175#4030—31no—
176#4029—31no—
177#4028—31no—
178#4024—31no—
179C4×D20—31no—
180#4018—31no—
181C5×C4⋊C8—31no—
182C5×C22⋊C8—31no—
183C5×C22⋊C8—31no—
184C4×C5×C8—31no—
185C22⋊#168C2×D311yescharacteristic
186C22⋊#168C2×D311yescharacteristic, complemented
187#3952—31no—
188#3952—31no—
189#3952—31no—
190#3952—31no—
191#3947—31no—
192#3946—31no—
193#3946—31no—
194C8×Dic5—31no—
195C4⋊#168C2×D311yescharacteristic, complemented
196#3935C2×D311yescharacteristic, complemented
197#2933—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C23×C3×C5C22×C411yescharacteristic
200C22×D15—22no—
201C22×D15—22no—
202C22×D15—41no—
203C22×D15C22×C411yescharacteristic
204C22×D15C22×C411yescharacteristic
205C22×D15C22×C411yescharacteristic
206C3×C5×D4—22no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5C22×C411yescharacteristic
212C2×C3×C4×C5C22×C411yescharacteristic
213C2×C3×C4×C5C22×C411yescharacteristic
214C2×C3×C4×C5C22×C411yescharacteristic
215C2×C3×C4×C5C2411yescharacteristic
216#1220—22no—
217#1220—22no—
218#1220—22no—
219#1220—41no—
220C2×Dic15—22no—
221C2×Dic15C22×C411yescharacteristic
222C2×Dic15C22×C411yescharacteristic
223C2×Dic15C22×C411yescharacteristic
224C2×Dic15C22×C411yescharacteristic
225C2×Dic15C22×C411yescharacteristic
226D60—22no—
227D60—41no—
228C4×D15—22no—
229C4×D15—21no—
230C4×D15—21no—
231C4×D15—21no—
232C4×D15—21no—
233C4×D15—22no—
234C4×D15C2×D412yes—
235C4×D15#4112yes—
236Dic30—22no—
237C3×#168—21no—
238C3×#168—21no—
239C3×#168—21no—
240C3×#168C2×D412yes—
241C5×C3⋊C8—21no—
242C5×C3⋊C8—21no—
243C5×C3⋊C8—21no—
244C5×C3⋊C8C2×D412yes—
245C2×#235—51no—
246C22×C4×D3—51no—
247C2×C3×M16—51no—
248C22×C3×C8—51no—
249C3×C4×D4C2×D511yescharacteristic
250#939—51no—
251#937—51no—
252C4×#67—51no—
253C4×#67—51no—
254C22×C3⋊C8C2×D511yescharacteristic
255C22×C3⋊C8C2×D511yescharacteristic, complemented
256#907—104no—
257C2×ΓL(1,𝔽25)—51no—
258C2×ΓL(1,𝔽25)—51no—
259C2×ΓL(1,𝔽25)—51no—
260C2×ΓL(1,𝔽25)—51no—
261C2×ΓL(1,𝔽25)—51no—
262C2×ΓL(1,𝔽25)—104no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—51no—
266#896—51no—
267#894—51no—
268#884—51no—
269#883—51no—
270#882—51no—
271#878—51no—
272C4×D12—51no—
273#872—51no—
274C3×C4⋊C8—51no—
275C3×C22⋊C8—51no—
276C3×C22⋊C8—51no—
277C3×#97—51no—
278#830C2×D511yescharacteristic
279#830C2×D511yescharacteristic, complemented
280(C2×D3)⋊C8—51no—
281(C2×D3)⋊C8—51no—
282(C2×D3)⋊C8—51no—
283(C2×D3)⋊C8—51no—
284#815—51no—
285Dic3⋊C8—51no—
286Dic3⋊C8—51no—
287C8×Dic3—51no—
288C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
289C4×C3⋊C8C2×D511yescharacteristic, complemented
290C23×D5—31no—
291C2×C5×D4C4×D311yescharacteristic
292C22×C4×C5C22×D311yescharacteristic
293C22×C4×C5C22×D311yescharacteristic
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5—31no—
297C2×C22⋊D5—31no—
298C22×Dic5—31no—
299#709—62no—
300#709—62no—
301C2×D20—31no—
302C2×D20—31no—
303C2×C4×D5—31no—
304C2×C4×D5—31no—
305C2×C4×D5—31no—
306C2×C4×D5—31no—
307C2×C4×D5—31no—
308C2×C4×D5—62no—
309C2×C4×D5—62no—
310C2×Dic10—31no—
311C2×C5×C8—31no—
312C2×C5×C8—31no—
313C2×C5×C8—31no—
314C2×C5×C8—31no—
315C2×C5×C8—62no—
316C2×C5×C8—62no—
317C5×C4⋊C4C4×D311yescharacteristic
318C5×C22⋊C4C4×D311yescharacteristic
319C5×C22⋊C4C4×D311yescharacteristic
320C42×C5C22×D311yescharacteristic
321C22⋊Dic5—31no—
322C22⋊Dic5—31no—
323#685—31no—
324#685—31no—
325#685—31no—
326#685—31no—
327#685—31no—
328#685—31no—
329C4⋊Dic5—31no—
330#683—31no—
331#683—31no—
332#683—31no—
333#683—31no—
334C4×Dic5—31no—
335#681—22no—
336C2×#168—22no—
337C2×#168C22×D311yescharacteristic
338C2×#168C22×D311yescharacteristic
339C2×#168C22×D311yescharacteristic
340C2×#168C22×D311yescharacteristic
341#676—34no—
342#676—62no—
343#676—62no—
344#676—62no—
345#676—62no—
346C8×D5—62no—
347C8×D5—62no—
348C8×D5—62no—
349C2×#131—151no—
350C22×M16—151no—
351#525—151no—
352#436—151no—
353#436—151no—
354#435—51no—
355#435—151no—
356#435—151no—
357#435—151no—
358C8×D4—31no—
359C8×D4—151no—
360#424—151no—
361#408—151no—
362C2×C22⋊C8—151no—
363#405—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5—21no—
367C22×C3×C5—21no—
368C22×C3×C5—21no—
369C22×C3×C5#13112yescomplemented
370C22×C3×C5C23×C411yescharacteristic
371C2×D15—21no—
372C2×D15—21no—
373C2×D15—21no—
374C2×D15—21no—
375C2×D15—21no—
376C2×D15—21no—
377C2×D15—21no—
378C2×D15—21no—
379C2×D15—44no—
380C2×D15C4×D412yes—
381C3×C4×C5—21no—
382C3×C4×C5—21no—
383C3×C4×C5—21no—
384C3×C4×C5—21no—
385C3×C4×C5C22×D411yescharacteristic
386C3×C4×C5C2×#4111yescharacteristic
387Dic15—21no—
388Dic15—21no—
389Dic15—21no—
390Dic15—21no—
391Dic15C4×D412yes—
392C23×D3—51no—
393C2×C3×D4C4×D511yescharacteristic
394C22×C3×C4C22×D511yescharacteristic
395C22×C3×C4C22×D511yescharacteristic
396C2×#67—51no—
397C2×#67—51no—
398C2×#67—51no—
399C2×#67—51no—
400C22×Dic3—51no—
401#235—102no—
402#235—102no—
403C2×D12—51no—
404C2×D12—51no—
405C2×C4×D3—51no—
406C2×C4×D3—51no—
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3—51no—
410C2×C4×D3—102no—
411C2×C4×D3—102no—
412C2×Dic6—51no—
413C3×M16—102no—
414C2×C3×C8—51no—
415C2×C3×C8—51no—
416C2×C3×C8—51no—
417C2×C3×C8—51no—
418C2×C3×C8—102no—
419C3×C4⋊C4C4×D511yescharacteristic
420C3×C22⋊C4C4×D511yescharacteristic
421C3×C22⋊C4C4×D511yescharacteristic
422C3×C42C22×D511yescharacteristic
423#217—51no—
424#217—51no—
425(C2×D3)⋊C4—51no—
426(C2×D3)⋊C4—51no—
427(C2×D3)⋊C4—51no—
428(C2×D3)⋊C4—51no—
429(C2×D3)⋊C4—51no—
430(C2×D3)⋊C4—51no—
431C4⋊Dic3—51no—
432Dic3⋊C4—51no—
433Dic3⋊C4—51no—
434Dic3⋊C4—51no—
435Dic3⋊C4—51no—
436C4×Dic3—51no—
437C2×C3⋊C8—22no—
438C2×C3⋊C8—22no—
439C2×C3⋊C8C22×D511yescharacteristic
440C2×C3⋊C8C22×D511yescharacteristic
441C2×C3⋊C8C22×D511yescharacteristic
442C2×C3⋊C8C22×D511yescharacteristic
443ΓL(1,𝔽25)—54no—
444ΓL(1,𝔽25)—102no—
445ΓL(1,𝔽25)—102no—
446ΓL(1,𝔽25)—102no—
447ΓL(1,𝔽25)—102no—
448D3×C8—102no—
449D3×C8—102no—
450D3×C8—102no—
451C23×C5C2×C4×D311yescharacteristic
452C23×C5C2×C4×D311yescharacteristic
453C22×D5—31no—
454C22×D5—31no—
455C22×D5—31no—
456C22×D5—62no—
457C22×D5—62no—
458C22×D5—121no—
459C5×D4—22no—
460C2×C4×C5—21no—
461C2×C4×C5—21no—
462C2×C4×C5—21no—
463C2×C4×C5—21no—
464C2×C4×C5C2×C4×D311yescharacteristic
465C2×C4×C5C2×C4×D311yescharacteristic
466C2×C4×C5C2×C4×D311yescharacteristic
467C2×C4×C5C2×C4×D311yescharacteristic
468C2×C4×C5C23×D311yescharacteristic
469C22⋊D5—62no—
470C22⋊D5—62no—
471C22⋊D5—62no—
472C22⋊D5—121no—
473C2×Dic5—31no—
474C2×Dic5—31no—
475C2×Dic5—31no—
476C2×Dic5—31no—
477C2×Dic5—31no—
478C2×Dic5—62no—
479D20—62no—
480D20—121no—
481C4×D5—32no—
482C4×D5—32no—
483C4×D5—62no—
484C4×D5—62no—
485C4×D5—61no—
486C4×D5—61no—
487C4×D5—61no—
488C4×D5—61no—
489Dic10—62no—
490C5×C8—32no—
491C5×C8—61no—
492C5×C8—61no—
493C5×C8—61no—
494#168—21no—
495#168—21no—
496#168—21no—
497#168D3×D412yes—
498C2×#41—151no—
499C23×C4—151no—
500#131—304no—
501C2×M16—51no—
502C2×M16—151no—
503C2×M16—151no—
504C2×M16—151no—
505C2×M16—151no—
506C2×M16—151no—
507C2×M16—304no—
508C22×C8—31no—
509C22×C8—31no—
510C22×C8—51no—
511C22×C8—151no—
512C22×C8—151no—
513C22×C8—151no—
514#123—151no—
515#123—151no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518#121—151no—
519#121—151no—
520#120—151no—
521#120—151no—
522C4×D4—151no—
523C4×D4—151no—
524C4×D4—151no—
525C4×D4D3×D511yescharacteristic
526#117—151no—
527C4⋊C8—31no—
528C4⋊C8—51no—
529C4⋊C8—151no—
530C4⋊C8—151no—
531C22⋊C8—31no—
532C22⋊C8—31no—
533C22⋊C8—51no—
534C22⋊C8—51no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8—151no—
538C22⋊C8—151no—
539#97—51no—
540#97—151no—
541C4×C8—31no—
542C4×C8—151no—
543C2×C3×C5—22no—
544C2×C3×C5—41no—
545C2×C3×C5C2×C4×D411yescharacteristic
546C2×C3×C5C2×#13111yescharacteristic
547C2×C3×C5#56811yescharacteristic
548D15—22no—
549D15—41no—
550D15—41no—
551C23×C3C2×C4×D511yescharacteristic
552C23×C3C2×C4×D511yescharacteristic
553C22×D3—51no—
554C22×D3—51no—
555C22×D3—51no—
556C22×D3—102no—
557C22×D3—102no—
558C22×D3—201no—
559C3×D4—22no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4C2×C4×D511yescharacteristic
565C2×C3×C4C2×C4×D511yescharacteristic
566C2×C3×C4C2×C4×D511yescharacteristic
567C2×C3×C4C2×C4×D511yescharacteristic
568C2×C3×C4C23×D511yescharacteristic
569#67—102no—
570#67—102no—
571#67—102no—
572#67—201no—
573C2×Dic3—51no—
574C2×Dic3—51no—
575C2×Dic3—51no—
576C2×Dic3—51no—
577C2×Dic3—51no—
578C2×Dic3—102no—
579D12—102no—
580D12—201no—
581C4×D3—52no—
582C4×D3—52no—
583C4×D3—102no—
584C4×D3—102no—
585C4×D3—101no—
586C4×D3—101no—
587C4×D3—101no—
588C4×D3—101no—
589Dic6—102no—
590C3×C8—52no—
591C3×C8—101no—
592C3×C8—101no—
593C3×C8—101no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C3⋊C8D4×D512yes—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—21no—
602C22×C5—21no—
603C22×C5#90712yescomplemented
604C22×C5C22×C4×D311yescharacteristic
605C2×D5—32no—
606C2×D5—61no—
607C2×D5—61no—
608C2×D5—61no—
609C2×D5—61no—
610C2×D5—61no—
611C2×D5—61no—
612C2×D5—61no—
613C2×D5—61no—
614C2×D5—124no—
615C4×C5—21no—
616C4×C5—21no—
617C4×C5—21no—
618C4×C5—21no—
619C4×C5C2×D3×D411yescharacteristic
620C4×C5D3×#4111yescharacteristic
621Dic5—32no—
622Dic5—61no—
623Dic5—61no—
624Dic5—61no—
625Dic5—61no—
626C24—151no—
627#41—302no—
628#41—302no—
629C2×Q8—151no—
630C2×D4—151no—
631C2×D4—151no—
632C2×D4—151no—
633C2×D4—151no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4#120011yescharacteristic
637C22×C4—151no—
638C22×C4—151no—
639C22×C4—151no—
640C22×C4—151no—
641C22×C4—151no—
642C22×C4—151no—
643C22×C4—302no—
644C22×C4—302no—
645C22×C4C2×D3×D511yescharacteristic
646C22×C4C2×D3×D511yescharacteristic
647M16—102no—
648M16—154no—
649M16—302no—
650M16—302no—
651M16—302no—
652M16—302no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—51no—
658C2×C8—51no—
659C2×C8—51no—
660C2×C8—51no—
661C2×C8—62no—
662C2×C8—62no—
663C2×C8—102no—
664C2×C8—302no—
665C2×C8—302no—
666C2×C8—302no—
667C4⋊C4—151no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C4⋊C4—151no—
672C4⋊C4#120011yescharacteristic
673C22⋊C4—151no—
674C22⋊C4—151no—
675C22⋊C4—151no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C22⋊C4—151no—
680C22⋊C4—151no—
681C22⋊C4#120011yescharacteristic
682C22⋊C4#120011yescharacteristic
683C42—151no—
684C42C2×D3×D511yescharacteristic
685C3×C5#293311yescharacteristic, complemented, Hall
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3#404712yescomplemented
692C22×C3C22×C4×D511yescharacteristic
693C2×D3—52no—
694C2×D3—101no—
695C2×D3—101no—
696C2×D3—101no—
697C2×D3—101no—
698C2×D3—101no—
699C2×D3—101no—
700C2×D3—101no—
701C2×D3—101no—
702C2×D3—204no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4C2×D4×D511yescharacteristic
708C3×C4D5×#4111yescharacteristic
709Dic3—52no—
710Dic3—101no—
711Dic3—101no—
712Dic3—101no—
713Dic3—101no—
714C2×C5—22no—
715C2×C5—41no—
716C2×C5C4×D3×D411yescharacteristic
717C2×C5C2×#90711yescharacteristic
718C2×C5#575011yescharacteristic
719D5—62no—
720D5—121no—
721D5—121no—
722C23—151no—
723C23—151no—
724C23—151no—
725C23—302no—
726C23—302no—
727C23—601no—
728C23C2×#120011yescharacteristic
729C23C2×#120011yescharacteristic
730Q8—302no—
731D4—22no—
732D4—302no—
733D4—302no—
734D4—302no—
735D4—302no—
736D4—601no—
737D4—601no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—151no—
743C2×C4—152no—
744C2×C4—152no—
745C2×C4—151no—
746C2×C4—151no—
747C2×C4—151no—
748C2×C4—151no—
749C2×C4—302no—
750C2×C4—302no—
751C2×C4—302no—
752C2×C4—301no—
753C2×C4—301no—
754C2×C4—301no—
755C2×C4—301no—
756C2×C4C2×#120011yescharacteristic
757C2×C4C2×#120011yescharacteristic
758C2×C4C2×#120011yescharacteristic
759C2×C4C2×#120011yescharacteristic
760C2×C4C22×D3×D511yescharacteristic
761C8—32no—
762C8—52no—
763C8—61no—
764C8—61no—
765C8—61no—
766C8—101no—
767C8—101no—
768C8—101no—
769C2×C3—22no—
770C2×C3—41no—
771C2×C3C4×D4×D511yescharacteristic
772C2×C3C2×#404711yescharacteristic
773C2×C3#6608411yescharacteristic
774D3—102no—
775D3—201no—
776D3—201no—
777C5#7948111yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—152no—
784C22—301no—
785C22—301no—
786C22—301no—
787C22—301no—
788C22—301no—
789C22—301no—
790C22—301no—
791C22—301no—
792C22—604no—
793C22#9129112yescomplemented
794C22C22×#120011yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—152no—
800C4—301no—
801C4—301no—
802C4—301no—
803C4—301no—
804C4D3×D4×D511yescharacteristic
805C4#9202411yescharacteristic
806C3#1061115411yescharacteristic, complemented, Sylow
807C2—22no—
808C2—41no—
809C2—302no—
810C2—601no—
811C2—601no—
812C2C2×#9129111yescharacteristic
813C2D4×#120011yescharacteristic
814C2#1175530011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C4×C5×D4C22
prime radical#11756306C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5#2933
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#6651C2semidirect
3. C2×#91291C2semidirect
4. C5×D4×C3⋊C8C2semidirect
5. C3×#65300C2semidirect
6. #11748506C2semidirect
7. #11748506C2semidirect
8. #11748498C2semidirect
9. #11748497C2semidirect
10. #11748485C2semidirect
11. #11748312C2semidirect
12. #11747012C2semidirect
13. #11747001C2semidirect
14. #11746989C2semidirect
15. #11746982C2semidirect
33. C22×C5×C3⋊C8C22semidirect
34. C2×C3×#681C22semidirect
41. C2×#6651C22semidirect
45. C2×#6648C22semidirect
47. C5×#830C22semidirect
48. C5×C4⋊(C3⋊C8)C22semidirect
49. C4×C5×C3⋊C8C22semidirect
51. C3×C22⋊#168C22semidirect
52. C3×C4⋊#168C22semidirect
53. C3×#3935C22semidirect
54. #90983C22semidirect
55. #90983C22semidirect
58. #90957C22semidirect
59. #90957C22semidirect
60. #90954C22semidirect
61. #90951C22semidirect
69. #65300D3semidirect
133. #6651D4semidirect
143. D4×C3⋊C8D5semidirect
161. C2×#681C2×D3semidirect
186. C22⋊#168C2×D3semidirect
195. C4⋊#168C2×D3semidirect
196. #3935C2×D3semidirect
255. C22×C3⋊C8C2×D5semidirect
279. #830C2×D5semidirect
288. C4⋊(C3⋊C8)C2×D5semidirect
289. C4×C3⋊C8C2×D5semidirect
369. C22×C3×C5#131semidirect
603. C22×C5#907semidirect
685. C3×C5#2933semidirect
691. C22×C3#4047semidirect
777. C5#79481semidirect
793. C22#91291semidirect
806. C3#10611154semidirect

Maximal subgroups

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

subgroupindex
#117563062
C22×#66512
C2×#912912
C5×D4×C3⋊C82
C3×#653002
#117485062
#117484982
#117484972
#117484852
#117483122
#117470122
#117470012
#117469892
#117469822
#106111543
#794815