Finite Group Databasebeta

← #14415203

Subgroups — #14415203

Order 1920.

984 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
1C2×#91929C211yesmaximal, characteristic, complemented
2C2×D3×#700C211yesmaximal, characteristic, complemented
3#11753244C211yesmaximal, characteristic
4#11752352C211yesmaximal, characteristic, complemented
5C3×#65695C211yesmaximal, characteristic, complemented
6#11752054C211yesmaximal, characteristic, complemented
7#11752038C211yesmaximal, characteristic, complemented
8#11751987C211yesmaximal, characteristic, complemented
9#11751919C211yesmaximal, characteristic, complemented
10#11751914C211yesmaximal, characteristic, complemented
11#11751905C211yesmaximal, characteristic, complemented
12#11751903C211yesmaximal, characteristic, complemented
13#11751898C211yesmaximal, characteristic, complemented
14#11751868C211yesmaximal, characteristic, complemented
15#11751763C211yesmaximal, characteristic, complemented
16#10617290—31nomaximal, Hall
17C2×#6782C2211yescharacteristic
18C2×C4×D3×D5C2211yescharacteristic
19C22×C3⋊#170C2211yescharacteristic, complemented
20C2×#6758C2211yescharacteristic
21C2×C3×#704C2211yescharacteristic, complemented
22C2×C3×#700C2211yescharacteristic
23C2×#6740C2211yescharacteristic
24C2×#6740C2211yescharacteristic
25C2×#6740C2211yescharacteristic, complemented
26C2×#6739C2211yescharacteristic
27C2×#6739C2211yescharacteristic
28C2×#6738C2211yescharacteristic, complemented
29#91929—24no—
30C2×D3×#170C2211yescharacteristic
31C2×D3×#170C2211yescharacteristic
32D3×#700—24no—
33#91773C411yescharacteristic
34C5×#883C411yescharacteristic
35C3×#4027C2211yescharacteristic
36#91577C411yescharacteristic
37#91552C2211yescharacteristic
38#91550C411yescharacteristic
39#91476C411yescharacteristic
40#91444C2211yescharacteristic
41#91430C411yescharacteristic
42#91418C2211yescharacteristic
43#91398C2211yescharacteristic
44#91377C411yescharacteristic
45#91351C411yescharacteristic
46#91241C2211yescharacteristic, complemented
47#91232C2211yescharacteristic
48#91231C2211yescharacteristic, complemented
49C4⋊(C3⋊#170)C2211yescharacteristic, complemented
50C3×C22⋊#170C2211yescharacteristic, complemented
51C3×#4004C2211yescharacteristic, complemented
52C3×#4003C2211yescharacteristic
53C3×C4×#170C2211yescharacteristic, complemented
54#91177C2211yescharacteristic, complemented
55Dic3⋊#170C2211yescharacteristic, complemented
56#91171C2211yescharacteristic
57#91171C2211yescharacteristic
58#91171C2211yescharacteristic, complemented
59#91171C2211yescharacteristic, complemented
60#91169C2211yescharacteristic, complemented
61Dic3×#170C2211yescharacteristic, complemented
62#79537—51nomaximal, Hall
63C2×#4131—31no—
64C22×#700—31no—
65#65990—31no—
66#65775—31no—
67#65755—31no—
68#65705—31no—
69#65705—31no—
70#65704—31no—
71#65704—31no—
72#65696—31no—
73#65695—31no—
74#65695D311yescharacteristic, complemented
75#65693—31no—
76#65693—31no—
77#65691—31no—
78C22×D3×D5C2×C411yescharacteristic
79C2×#1220C2×C411yescharacteristic
80C2×#1220C2×C411yescharacteristic
81C2×D60C2×C411yescharacteristic
82C2×C4×D15C2×C411yescharacteristic
83C2×C5×#67C2×C411yescharacteristic
84C2×C4×C5×D3C2×C411yescharacteristic
85C2×C3×C22⋊D5C2×C411yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×C3×C4×D5C2311yescharacteristic
88C2×#1204C2×C411yescharacteristic
89C2×#1203C2×C411yescharacteristic
90C2×#1202C2×C411yescharacteristic
91C2×#1200C2311yescharacteristic
92C2×#1200C2311yescharacteristic
93#6782—22no—
94#6782—22no—
95C2×D3×Dic5C2311yescharacteristic
96C2×D5×Dic3C2×C411yescharacteristic
97C4×D3×D5—22no—
98C4×D3×D5—22no—
99C2×C3⋊#170—22no—
100C2×C3⋊#170C2311yescharacteristic
101C2×C3⋊#170C2311yescharacteristic
102C2×C3⋊#170C2311yescharacteristic
103C2×C3⋊#170C2311yescharacteristic
104#6758—22no—
105C3×#704—22no—
106C2×C3×#170C2311yescharacteristic
107C2×C3×#170C2311yescharacteristic
108C2×C3×#170C2311yescharacteristic
109C2×C3×#170C2311yescharacteristic
110C3×#700—22no—
111#6740—22no—
112#6740—22no—
113#6740—22no—
114#6739—22no—
115#6739—22no—
116#6738—22no—
117D3×#170—22no—
118D3×#170D414yescomplemented
119C3×C5×C22⋊C4C2×C411yescharacteristic
120#6714C2×C411yescharacteristic
121#6712C2×C411yescharacteristic
122C5×#217C2×C411yescharacteristic
123C5×(C2×D3)⋊C4C2×C411yescharacteristic
124C5×C4⋊Dic3C2×C411yescharacteristic
125C5×Dic3⋊C4C2×C411yescharacteristic
126C3×#685C2×C411yescharacteristic
127C3×#683C2×C411yescharacteristic
128C3×C4×Dic5C2311yescharacteristic
129#6669C2×C411yescharacteristic
130#6669C2×C411yescharacteristic
131#6667C2×C411yescharacteristic
132#6667C2×C411yescharacteristic
133#6667C2×C411yescharacteristic
134(C2×D3)⋊Dic5C2×C411yescharacteristic
135#6665C2×C411yescharacteristic
136Dic3×Dic5C2311yescharacteristic
137C2×#907—51no—
138C2×D3×M16—51no—
139#5547—51no—
140C3×#436—51no—
141#5128—51no—
142#5128—51no—
143#5011—51no—
144#4839—51no—
145#4836—51no—
146#4730—51no—
147#4728—51no—
148#4727—51no—
149#4726—51no—
150#4689—51no—
151#4688—51no—
152C2×#711—31no—
153C22×C4×D5—31no—
154C2×#704—31no—
155C2×#704—31no—
156C2×#704C2×D311yescharacteristic, complemented
157C22×#170—31no—
158C22×#170—31no—
159C22×#170—31no—
160#4131—64no—
161C2×#700—31no—
162C2×#700—31no—
163C2×#700—31no—
164C2×#700—31no—
165C2×#700—64no—
166C2×#700C2×D311yescharacteristic
167C2×D5⋊C8—31no—
168C5×#123—31no—
169#4083—31no—
170#4075—31no—
171#4042—31no—
172#4042—31no—
173#4039—31no—
174#4039—31no—
175#4030—31no—
176#4030—31no—
177#4028—31no—
178#4027—31no—
179#4027C2×D311yescharacteristic
180#4023—31no—
181C22⋊#170—31no—
182C22⋊#170C2×D311yescharacteristic, complemented
183#4004—31no—
184#4004C2×D311yescharacteristic, complemented
185#4003—31no—
186#4003—31no—
187#4003—31no—
188#4003—31no—
189#4003—31no—
190#4003C2×D311yescharacteristic
191#4002—31no—
192#4002—31no—
193C4⋊#170—31no—
194C4⋊#170—31no—
195C4×#170—31no—
196C4×#170C2×D311yescharacteristic, complemented
197#2930—151noSylow
198C23×C3×C5C22×C411yescharacteristic
199C22×D15C22×C411yescharacteristic
200C22×D15C22×C411yescharacteristic
201C22×C5×D3C22×C411yescharacteristic
202C22×C3×D5C22×C411yescharacteristic
203C2×D3×D5—22no—
204C2×D3×D5—41no—
205C2×D3×D5—41no—
206C2×C3×C4×C5C22×C411yescharacteristic
207C2×C3×C4×C5C22×C411yescharacteristic
208#1220—22no—
209#1220—41no—
210C2×Dic15C22×C411yescharacteristic
211C2×Dic15C22×C411yescharacteristic
212D60—41no—
213C4×D15—22no—
214C5×#67—22no—
215C2×C5×Dic3C22×C411yescharacteristic
216C2×C5×Dic3C22×C411yescharacteristic
217C2×C5×Dic3C22×C411yescharacteristic
218C4×C5×D3—22no—
219C3×C22⋊D5—41no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5C22×C411yescharacteristic
223C2×C3×Dic5C22×C411yescharacteristic
224C2×C3×Dic5C2411yescharacteristic
225C3×C4×D5—21no—
226C3×C4×D5—21no—
227#1204—22no—
228#1203—22no—
229#1202—41no—
230#1200—21no—
231#1200—21no—
232#1200—21no—
233#1200—21no—
234D3×Dic5C2×D412yes—
235D3×Dic5#4112yes—
236D5×Dic3—22no—
237C3⋊#170—21no—
238C3⋊#170—21no—
239C3⋊#170—21no—
240C3⋊#170C2×D412yes—
241C3×#170—21no—
242C3×#170—21no—
243C3×#170—21no—
244C3×#170C2×D412yes—
245C2×#235—51no—
246C22×C4×D3—51no—
247C2×C3×M16—51no—
248C2×C3×M16—51no—
249C3×C4×D4—51no—
250#939—51no—
251#937—51no—
252C4×#67—51no—
253C4×#67—51no—
254C2×#208—51no—
255C22×C3⋊C8—51no—
256#907—104no—
257D3×M16—104no—
258C2×ΓL(1,𝔽25)—51no—
259C2×ΓL(1,𝔽25)—51no—
260C2×ΓL(1,𝔽25)—51no—
261C2×ΓL(1,𝔽25)—51no—
262C2×ΓL(1,𝔽25)—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—51no—
266#896—51no—
267#894—51no—
268#884—51no—
269#883AGL(1,𝔽5)11yescharacteristic
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×C4×C8—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—
285Dic3⋊C8—51no—
286Dic3⋊C8—51no—
287C8×Dic3—51no—
288C4⋊(C3⋊C8)—51no—
289#803—51no—
290C23×D5—31no—
291C2×C5×D4—31no—
292C22×C4×C5—31no—
293C2×C22⋊D5—31no—
294C2×C22⋊D5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5C4×D311yescharacteristic
297C22×Dic5—31no—
298C22×Dic5C22×D311yescharacteristic
299#711—62no—
300#711—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—62no—
308C2×C4×D5—62no—
309C2×C4×D5C22×D311yescharacteristic
310C2×Dic10—31no—
311#704—22no—
312#704—62no—
313#704—62no—
314C2×#170—31no—
315C2×#170—34no—
316C2×#170—31no—
317C2×#170—31no—
318C2×#170—31no—
319C2×#170—62no—
320C2×#170—62no—
321C2×#170C22×D311yescharacteristic
322C2×#170C22×D311yescharacteristic
323C2×#170C22×D311yescharacteristic
324C2×#170C22×D311yescharacteristic
325#700—22no—
326#700—62no—
327#700—62no—
328#700—62no—
329#700—62no—
330D5⋊C8—62no—
331C5×C4⋊C4—31no—
332C5×C4⋊C4—31no—
333C5×C22⋊C4—31no—
334C5×C22⋊C4—31no—
335C5×C22⋊C4C4×D311yescharacteristic
336C22⋊Dic5—31no—
337#685—31no—
338#685—31no—
339#685—31no—
340#685—31no—
341#685—31no—
342#685C4×D311yescharacteristic
343#683—31no—
344#683—31no—
345#683—31no—
346#683C4×D311yescharacteristic
347C4×Dic5—31no—
348C4×Dic5C22×D311yescharacteristic
349C2×#131—151no—
350C22×M16—151no—
351#525—151no—
352#436—51no—
353#436—151no—
354#436—151no—
355#436—151no—
356#435—151no—
357#435—151no—
358#435—151no—
359#435—151no—
360#424—151no—
361#408—151no—
362#407—151no—
363#405—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×D15—21no—
372C2×D15—21no—
373C2×D15—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—
380D3×D5—44no—
381C3×C4×C5—21no—
382C3×C4×C5—21no—
383Dic15—21no—
384Dic15C4×D412yes—
385C3×Dic5—21no—
386C3×Dic5—21no—
387C3×Dic5C22×D411yescharacteristic
388C3×Dic5C2×#4111yescharacteristic
389C5×Dic3—21no—
390C5×Dic3—21no—
391C5×Dic3—21no—
392C23×D3—51no—
393C2×C3×D4—51no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C2×#67—51no—
397C2×#67—51no—
398C2×#67—51no—
399C2×#67C2×AGL(1,𝔽5)11yescharacteristic
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—102no—
410C2×C4×D3—102no—
411C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
412C2×Dic6—51no—
413C3×M16—102no—
414C3×M16—102no—
415C2×C3×C8—51no—
416C2×C3×C8—51no—
417C2×C3×C8—51no—
418C2×C3×C8—51no—
419C3×C4⋊C4—51no—
420C3×C22⋊C4—51no—
421C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
422C3×C42—51no—
423#217—51no—
424#217C2×AGL(1,𝔽5)11yescharacteristic
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)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
431C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
432Dic3⋊C4—51no—
433Dic3⋊C4—51no—
434Dic3⋊C4—51no—
435Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
436C4×Dic3—51no—
437#208—102no—
438C2×C3⋊C8—51no—
439C2×C3⋊C8—51no—
440C2×C3⋊C8—51no—
441C2×C3⋊C8—51no—
442C2×C3⋊C8—102no—
443ΓL(1,𝔽25)—102no—
444ΓL(1,𝔽25)—102no—
445ΓL(1,𝔽25)—102no—
446ΓL(1,𝔽25)—102no—
447ΓL(1,𝔽25)—102no—
448D3×C8—54no—
449D3×C8—102no—
450D3×C8—102no—
451C23×C5—31no—
452C23×C5C2×C4×D311yescharacteristic
453C22×D5—31no—
454C22×D5—31no—
455C22×D5—62no—
456C22×D5—121no—
457C22×D5—121no—
458C22×D5C2×C4×D311yescharacteristic
459C5×D4—62no—
460C2×C4×C5—31no—
461C2×C4×C5—31no—
462C2×C4×C5—31no—
463C2×C4×C5—62no—
464C2×C4×C5C2×C4×D311yescharacteristic
465C2×C4×C5C2×C4×D311yescharacteristic
466C22⋊D5—41no—
467C22⋊D5—62no—
468C22⋊D5—62no—
469C22⋊D5—121no—
470C2×Dic5—21no—
471C2×Dic5—21no—
472C2×Dic5—31no—
473C2×Dic5—32no—
474C2×Dic5—32no—
475C2×Dic5—31no—
476C2×Dic5C2×C4×D311yescharacteristic
477C2×Dic5C2×C4×D311yescharacteristic
478C2×Dic5C23×D311yescharacteristic
479D20—121no—
480D20—121no—
481C4×D5—21no—
482C4×D5—21no—
483C4×D5—62no—
484C4×D5—62no—
485C4×D5—61no—
486C4×D5—61no—
487C4×D5—61no—
488C4×D5—61no—
489Dic10—62no—
490#170—21no—
491#170—21no—
492#170—21no—
493#170—32no—
494#170—61no—
495#170—61no—
496#170—61no—
497#170D3×D412yes—
498C2×#41—151no—
499C23×C4—151no—
500#131—304no—
501C2×M16—51no—
502C2×M16—51no—
503C2×M16—151no—
504C2×M16—151no—
505C2×M16—151no—
506C2×M16—151no—
507C2×M16—151no—
508C2×M16—151no—
509C2×M16—304no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—151no—
513C22×C8—151no—
514#123—31no—
515#123—151no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518#121—151no—
519#121—151no—
520#120—151no—
521#120—151no—
522C4×D4—51no—
523C4×D4—151no—
524C4×D4—151no—
525C4×D4—151no—
526#117—151no—
527C4⋊C8—51no—
528C4⋊C8—151no—
529C4⋊C8—151no—
530C4⋊C8—151no—
531C22⋊C8—51no—
532C22⋊C8—51no—
533C22⋊C8—151no—
534C22⋊C8—151no—
535C22⋊C8—151no—
536C22⋊C8—151no—
537C22⋊C8—151no—
538C22⋊C8—151no—
539#97—151no—
540#97—151no—
541C4×C8—51no—
542C4×C8—151no—
543C2×C3×C5—41no—
544C2×C3×C5C2×C4×D411yescharacteristic
545C2×C3×C5#56811yescharacteristic
546C2×C3×C5#56811yescharacteristic
547D15—41no—
548D15—41no—
549C3×D5—41no—
550C5×D3—22no—
551C23×C3—51no—
552C23×C3C22×AGL(1,𝔽5)11yescharacteristic
553C22×D3—51no—
554C22×D3—51no—
555C22×D3—102no—
556C22×D3—201no—
557C22×D3—201no—
558C22×D3C22×AGL(1,𝔽5)11yescharacteristic
559C3×D4—201no—
560C2×C3×C4—51no—
561C2×C3×C4—51no—
562C2×C3×C4—51no—
563C2×C3×C4—101no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
568C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
569#67—22no—
570#67—102no—
571#67—201no—
572#67—201no—
573C2×Dic3—51no—
574C2×Dic3—51no—
575C2×Dic3—102no—
576C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
577C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
578C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
579D12—102no—
580D12—201no—
581C4×D3—22no—
582C4×D3—52no—
583C4×D3—52no—
584C4×D3—101no—
585C4×D3—101no—
586C4×D3—101no—
587C4×D3—101no—
588C4×D3—102no—
589Dic6—102no—
590C3×C8—52no—
591C3×C8—101no—
592C3×C8—101no—
593C3×C8—101no—
594C3⋊C8—52no—
595C3⋊C8—101no—
596C3⋊C8—101no—
597C3⋊C8—101no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—32no—
602C22×C5—61no—
603C22×C5—61no—
604C22×C5C22×C4×D311yescharacteristic
605C2×D5—21no—
606C2×D5—21no—
607C2×D5—21no—
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—61no—
618C4×C5—61no—
619C4×C5—61no—
620Dic5—21no—
621Dic5—21no—
622Dic5—32no—
623Dic5—61no—
624Dic5C2×D3×D411yescharacteristic
625Dic5D3×#4111yescharacteristic
626C24—151no—
627#41—302no—
628#41—302no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—51no—
632C2×D4—151no—
633C2×D4—151no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C22×C4—31no—
638C22×C4—51no—
639C22×C4—51no—
640C22×C4—151no—
641C22×C4—151no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—151no—
645C22×C4—302no—
646C22×C4—302no—
647M16—102no—
648M16—102no—
649M16—302no—
650M16—302no—
651M16—302no—
652M16—302no—
653M16—302no—
654M16—302no—
655C2×C8—51no—
656C2×C8—51no—
657C2×C8—51no—
658C2×C8—51no—
659C2×C8—154no—
660C2×C8—151no—
661C2×C8—151no—
662C2×C8—151no—
663C2×C8—151no—
664C2×C8—302no—
665C2×C8—302no—
666C2×C8—302no—
667C4⋊C4—31no—
668C4⋊C4—31no—
669C4⋊C4—51no—
670C4⋊C4—151no—
671C4⋊C4—151no—
672C4⋊C4—151no—
673C22⋊C4—31no—
674C22⋊C4—31no—
675C22⋊C4—51no—
676C22⋊C4—151no—
677C22⋊C4—151no—
678C22⋊C4—151no—
679C22⋊C4—151no—
680C22⋊C4—151no—
681C22⋊C4—151no—
682C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic
683C42—51no—
684C42—151no—
685C3×C5#293011yescharacteristic, complemented, Hall
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—101no—
690C22×C3—101no—
691C22×C3—101no—
692C22×C3C23×AGL(1,𝔽5)11yescharacteristic
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—101no—
696C2×D3—101no—
697C2×D3—101no—
698C2×D3—101no—
699C2×D3—101no—
700C2×D3—101no—
701C2×D3—204no—
702C2×D3D4×AGL(1,𝔽5)12yes—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—51no—
706C3×C4—51no—
707C3×C4—101no—
708C3×C4—101no—
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3—52no—
713Dic3—101no—
714C2×C5—41no—
715C2×C5—62no—
716C2×C5C4×D3×D411yescharacteristic
717C2×C5#574511yescharacteristic
718C2×C5#575011yescharacteristic
719D5—41no—
720D5—121no—
721D5—121no—
722C23—31no—
723C23—51no—
724C23—151no—
725C23—151no—
726C23—302no—
727C23—601no—
728C23—601no—
729C23C2×D3×AGL(1,𝔽5)11yescharacteristic
730Q8—302no—
731D4—62no—
732D4—201no—
733D4—302no—
734D4—302no—
735D4—601no—
736D4—601no—
737D4—601no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—51no—
742C2×C4—51no—
743C2×C4—51no—
744C2×C4—62no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—152no—
750C2×C4—152no—
751C2×C4—151no—
752C2×C4—151no—
753C2×C4—302no—
754C2×C4—301no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—302no—
759C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
760C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
761C8—52no—
762C8—101no—
763C8—101no—
764C8—101no—
765C8—152no—
766C8—301no—
767C8—301no—
768C8—301no—
769C2×C3—41no—
770C2×C3—201no—
771C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
772C2×C3#6626411yescharacteristic
773C2×C3#6626411yescharacteristic
774D3—22no—
775D3—201no—
776D3—201no—
777C5#7953711yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—21no—
781C22—32no—
782C22—61no—
783C22—61no—
784C22—101no—
785C22—101no—
786C22—101no—
787C22—301no—
788C22—301no—
789C22—301no—
790C22—301no—
791C22—301no—
792C22—301no—
793C22—604no—
794C22C22×D3×AGL(1,𝔽5)11yescharacteristic
795C4—21no—
796C4—21no—
797C4—51no—
798C4—51no—
799C4—61no—
800C4—61no—
801C4—61no—
802C4—101no—
803C4—101no—
804C4—152no—
805C4—301no—
806C3#1061729011yescharacteristic, complemented, Sylow
807C2—41no—
808C2—62no—
809C2—201no—
810C2—601no—
811C2—601no—
812C2#1175682311yescharacteristic
813C2#1175684211yescharacteristic
814C2D3×D4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radical#11753244C2
cosocleC2×C3×Dic5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2930
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91929C2semidirect
2. C2×D3×#700C2semidirect
4. #11752352C2semidirect
5. C3×#65695C2semidirect
6. #11752054C2semidirect
7. #11752038C2semidirect
8. #11751987C2semidirect
9. #11751919C2semidirect
10. #11751914C2semidirect
11. #11751905C2semidirect
12. #11751903C2semidirect
13. #11751898C2semidirect
14. #11751868C2semidirect
15. #11751763C2semidirect
19. C22×C3⋊#170C22semidirect
21. C2×C3×#704C22semidirect
25. C2×#6740C22semidirect
28. C2×#6738C22semidirect
46. #91241C22semidirect
48. #91231C22semidirect
49. C4⋊(C3⋊#170)C22semidirect
50. C3×C22⋊#170C22semidirect
51. C3×#4004C22semidirect
53. C3×C4×#170C22semidirect
54. #91177C22semidirect
55. Dic3⋊#170C22semidirect
58. #91171C22semidirect
59. #91171C22semidirect
60. #91169C22semidirect
61. Dic3×#170C22semidirect
74. #65695D3semidirect
118. D3×#170D4semidirect
156. C2×#704C2×D3semidirect
182. C22⋊#170C2×D3semidirect
184. #4004C2×D3semidirect
196. C4×#170C2×D3semidirect
685. C3×C5#2930semidirect
777. C5#79537semidirect
806. C3#10617290semidirect

Maximal subgroups

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

subgroupindex
C2×#919292
C2×D3×#7002
#117532442
#117523522
C3×#656952
#117520542
#117520382
#117519872
#117519192
#117519142
#117519052
#117519032
#117518982
#117518682
#117517632
#106172903
#795375