Finite Group Databasebeta

← #14415204

Subgroups — #14415204

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×#91915C211yesmaximal, characteristic, complemented
3#11753249C211yesmaximal, characteristic
4#11752352C211yesmaximal, characteristic, complemented
5C3×#65695C211yesmaximal, characteristic, complemented
6#11752053C211yesmaximal, characteristic, complemented
7#11752045C211yesmaximal, characteristic, complemented
8#11752040C211yesmaximal, characteristic, complemented
9#11751913C211yesmaximal, characteristic, complemented
10#11751910C211yesmaximal, characteristic, complemented
11#11751902C211yesmaximal, characteristic, complemented
12#11751899C211yesmaximal, characteristic, complemented
13#11751897C211yesmaximal, characteristic, complemented
14#11751872C211yesmaximal, characteristic, complemented
15#11751802C211yesmaximal, characteristic, complemented
16#10617226—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×#6739C2211yescharacteristic
26C2×#6739C2211yescharacteristic
27C2×#6739C2211yescharacteristic, complemented
28C2×#6738C2211yescharacteristic
29C2×#6738C2211yescharacteristic
30#91929—24no—
31C2×D3×#170C2211yescharacteristic, complemented
32#91915—24no—
33#91772C411yescharacteristic
34C5×#884C411yescharacteristic
35C3×#4027C2211yescharacteristic
36#91577C411yescharacteristic
37Dic5×#67C2211yescharacteristic
38#91549C411yescharacteristic
39#91475C411yescharacteristic
40#91440C2211yescharacteristic
41#91422C411yescharacteristic
42Dic5×D12C2211yescharacteristic
43#91402C2211yescharacteristic
44#91355C411yescharacteristic
45#91352C411yescharacteristic
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(C2×D3)⋊#170C2211yescharacteristic
57(C2×D3)⋊#170C2211yescharacteristic
58(C2×D3)⋊#170C2211yescharacteristic, complemented
59(C2×D3)⋊#170C2211yescharacteristic, complemented
60#91169C2211yescharacteristic, complemented
61Dic3×#170C2211yescharacteristic, complemented
62#79537—51nomaximal, Hall
63C2×#4131—31no—
64C2×D5⋊M16—31no—
65#65940—31no—
66#65776—31no—
67#65774—31no—
68#65774—31no—
69#65773—31no—
70#65773—31no—
71#65756—31no—
72#65708—31no—
73#65701—31no—
74#65695—31no—
75#65695D311yescharacteristic, complemented
76#65693—31no—
77#65693—31no—
78C22×D3×D5C2×C411yescharacteristic
79C2×#1220C2×C411yescharacteristic
80C2×C4×D15C2×C411yescharacteristic
81C2×C5×#67C2×C411yescharacteristic
82C2×C5×#67C2×C411yescharacteristic
83C2×C5×D12C2×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×#1201C2×C411yescharacteristic
91C2×#1200C2311yescharacteristic
92#6782—22no—
93#6782—22no—
94C2×D3×Dic5C2311yescharacteristic
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#6739—22no—
114#6739—22no—
115#6739—22no—
116#6738—22no—
117#6738D414yescomplemented
118D3×#170—22no—
119C3×C5×C22⋊C4C2×C411yescharacteristic
120#6719C2×C411yescharacteristic
121#6714C2×C411yescharacteristic
122C4⋊Dic15C2×C411yescharacteristic
123#6712C2×C411yescharacteristic
124C5×(C2×D3)⋊C4C2×C411yescharacteristic
125C5×Dic3⋊C4C2×C411yescharacteristic
126C3×#685C2×C411yescharacteristic
127C3×#683C2×C411yescharacteristic
128C3×C4×Dic5C2311yescharacteristic
129Dic3⋊Dic5C2×C411yescharacteristic
130Dic3⋊Dic5C2×C411yescharacteristic
131#6667C2×C411yescharacteristic
132(C2×D3)⋊Dic5C2×C411yescharacteristic
133(C2×D3)⋊Dic5C2×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×#704—31no—
157C2×#704C2×D311yescharacteristic, complemented
158C22×#170—31no—
159C22×#170—31no—
160#4131—64no—
161D5⋊M16—64no—
162C2×#700—31no—
163C2×#700—31no—
164C2×#700—31no—
165C2×#700C2×D311yescharacteristic
166C2×D5⋊C8—31no—
167C2×D5⋊C8—31no—
168C5×#121—31no—
169#4084—31no—
170#4083—31no—
171#4083—31no—
172D4×Dic5—31no—
173D4×Dic5—31no—
174#4070—31no—
175#4043—31no—
176#4038—31no—
177#4029—31no—
178#4029—31no—
179#4027—31no—
180#4027C2×D311yescharacteristic
181C22⋊#170—31no—
182C22⋊#170—31no—
183C22⋊#170—31no—
184C22⋊#170—31no—
185C22⋊#170—31no—
186C22⋊#170C2×D311yescharacteristic, complemented
187#4004—31no—
188#4004C2×D311yescharacteristic, complemented
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×C5×D3C22×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—
209C2×Dic15C22×C411yescharacteristic
210C2×Dic15C22×C411yescharacteristic
211C2×Dic15C22×C411yescharacteristic
212C4×D15—22no—
213C5×#67—22no—
214C5×#67—41no—
215C2×C5×Dic3C22×C411yescharacteristic
216C2×C5×Dic3C22×C411yescharacteristic
217C5×D12—41no—
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#1201—41no—
230#1200C2×D412yes—
231#1200#4112yes—
232D3×Dic5—21no—
233D3×Dic5—21no—
234D3×Dic5—21no—
235D3×Dic5—21no—
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#884AGL(1,𝔽5)11yescharacteristic
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×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—
292C2×C5×D4—31no—
293C2×C5×D4—31no—
294C22×C4×C5—31no—
295C2×C22⋊D5—31no—
296C2×C22⋊D5—31no—
297C2×C22⋊D5—31no—
298C2×C22⋊D5C4×D311yescharacteristic
299C22×Dic5—31no—
300C22×Dic5—31no—
301C22×Dic5C22×D311yescharacteristic
302#711—62no—
303#711—62no—
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—
314#704—62no—
315C2×#170—31no—
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—
329D5⋊C8—34no—
330D5⋊C8—62no—
331C5×C4⋊C4—31no—
332C5×C22⋊C4—31no—
333C5×C22⋊C4C4×D311yescharacteristic
334C22⋊Dic5—31no—
335C22⋊Dic5—31no—
336C22⋊Dic5—31no—
337C22⋊Dic5—31no—
338#685—31no—
339#685—31no—
340#685—31no—
341#685C4×D311yescharacteristic
342C4⋊Dic5—31no—
343C4⋊Dic5—31no—
344C4⋊Dic5—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×D15C4×D412yes—
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3—21no—
374C2×C5×D3—21no—
375C2×C5×D3—21no—
376C2×C5×D3—21no—
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—
384Dic15—21no—
385Dic15—21no—
386C3×Dic5—21no—
387C3×Dic5—21no—
388C3×Dic5C22×D411yescharacteristic
389C3×Dic5C2×#4111yescharacteristic
390C5×Dic3—21no—
391C5×Dic3C4×D412yes—
392C23×D3—51no—
393C2×C3×D4—51no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C2×#67—51no—
397C2×#67—51no—
398C2×#67C2×AGL(1,𝔽5)11yescharacteristic
399C2×#67C2×AGL(1,𝔽5)11yescharacteristic
400C22×Dic3—51no—
401#235—102no—
402#235—102no—
403C2×D12—51no—
404C2×D12C2×AGL(1,𝔽5)11yescharacteristic
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#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)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
431C4⋊Dic3—51no—
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×C5—31no—
453C23×C5C2×C4×D311yescharacteristic
454C22×D5—31no—
455C22×D5—62no—
456C22×D5—121no—
457C22×D5—121no—
458C22×D5C2×C4×D311yescharacteristic
459C5×D4—62no—
460C5×D4—121no—
461C5×D4—121no—
462C2×C4×C5—31no—
463C2×C4×C5—31no—
464C2×C4×C5—62no—
465C2×C4×C5C2×C4×D311yescharacteristic
466C2×C4×C5C2×C4×D311yescharacteristic
467C22⋊D5—41no—
468C22⋊D5—62no—
469C22⋊D5—62no—
470C22⋊D5—121no—
471C2×Dic5—21no—
472C2×Dic5—21no—
473C2×Dic5—31no—
474C2×Dic5—31no—
475C2×Dic5—31no—
476C2×Dic5—61no—
477C2×Dic5—61no—
478C2×Dic5—61no—
479C2×Dic5—61no—
480C2×Dic5C2×C4×D311yescharacteristic
481C2×Dic5C2×C4×D311yescharacteristic
482C2×Dic5C23×D311yescharacteristic
483C4×D5—21no—
484C4×D5—21no—
485C4×D5—32no—
486C4×D5—32no—
487C4×D5—62no—
488C4×D5—62no—
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—151no—
515#123—151no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518#121—31no—
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—22no—
548C3×D5—41no—
549C5×D3—41no—
550C5×D3—41no—
551C23×C3—51no—
552C23×C3C22×AGL(1,𝔽5)11yescharacteristic
553C22×D3—51no—
554C22×D3—102no—
555C22×D3—201no—
556C22×D3—201no—
557C22×D3C22×AGL(1,𝔽5)11yescharacteristic
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—41no—
571#67—102no—
572#67—201no—
573C2×Dic3—51no—
574C2×Dic3—51no—
575C2×Dic3—51no—
576C2×Dic3—102no—
577C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
578C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
579D12—41no—
580D12—102no—
581C4×D3—22no—
582C4×D3—52no—
583C4×D3—52no—
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—52no—
595C3⋊C8—101no—
596C3⋊C8—101no—
597C3⋊C8—101no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—21no—
601C22×C5—61no—
602C22×C5—61no—
603C22×C5—61no—
604C22×C5—61no—
605C22×C5—61no—
606C22×C5—61no—
607C22×C5C22×C4×D311yescharacteristic
608C2×D5—21no—
609C2×D5—21no—
610C2×D5—21no—
611C2×D5—32no—
612C2×D5—61no—
613C2×D5—61no—
614C2×D5—124no—
615C4×C5—21no—
616C4×C5—21no—
617C4×C5—32no—
618C4×C5—61no—
619Dic5—21no—
620Dic5—21no—
621Dic5—61no—
622Dic5—61no—
623Dic5—61no—
624Dic5C2×D3×D411yescharacteristic
625Dic5D3×#4111yescharacteristic
626C24—151no—
627#41—302no—
628#41—302no—
629C2×Q8—151no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—51no—
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—51no—
669C4⋊C4—151no—
670C4⋊C4—151no—
671C4⋊C4—151no—
672C4⋊C4—151no—
673C22⋊C4—31no—
674C22⋊C4—51no—
675C22⋊C4—151no—
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—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—52no—
700C2×D3—101no—
701C2×D3—101no—
702C2×D3—204no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—51no—
706C3×C4—51no—
707C3×C4—101no—
708C3×C4—101no—
709Dic3—21no—
710Dic3—101no—
711Dic3—101no—
712Dic3—101no—
713Dic3D4×AGL(1,𝔽5)12yes—
714C2×C5—41no—
715C2×C5—121no—
716C2×C5—121no—
717C2×C5C4×D3×D411yescharacteristic
718C2×C5#574511yescharacteristic
719C2×C5#575011yescharacteristic
720D5—41no—
721D5—62no—
722C23—31no—
723C23—31no—
724C23—51no—
725C23—151no—
726C23—302no—
727C23—601no—
728C23—601no—
729C23C2×D3×AGL(1,𝔽5)11yescharacteristic
730Q8—302no—
731D4—62no—
732D4—121no—
733D4—121no—
734D4—201no—
735D4—302no—
736D4—302no—
737D4—601no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—51no—
741C2×C4—51no—
742C2×C4—51no—
743C2×C4—62no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—152no—
749C2×C4—152no—
750C2×C4—151no—
751C2×C4—151no—
752C2×C4—151no—
753C2×C4—302no—
754C2×C4—302no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
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×C3#6625611yescharacteristic
772C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
773C2×C3#6626411yescharacteristic
774D3—41no—
775D3—41no—
776D3—102no—
777C5#7953711yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—21no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—101no—
788C22—101no—
789C22—101no—
790C22—152no—
791C22—301no—
792C22—301no—
793C22—604no—
794C22C22×D3×AGL(1,𝔽5)11yescharacteristic
795C4—21no—
796C4—21no—
797C4—32no—
798C4—51no—
799C4—51no—
800C4—61no—
801C4—101no—
802C4—101no—
803C4—301no—
804C4—301no—
805C4—301no—
806C3#1061722611yescharacteristic, complemented, Sylow
807C2—41no—
808C2—121no—
809C2—121no—
810C2—201no—
811C2—302no—
812C2#1175682311yescharacteristic
813C2#1175684111yescharacteristic
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#11753249C2
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×#91915C2semidirect
4. #11752352C2semidirect
5. C3×#65695C2semidirect
6. #11752053C2semidirect
7. #11752045C2semidirect
8. #11752040C2semidirect
9. #11751913C2semidirect
10. #11751910C2semidirect
11. #11751902C2semidirect
12. #11751899C2semidirect
13. #11751897C2semidirect
14. #11751872C2semidirect
15. #11751802C2semidirect
19. C22×C3⋊#170C22semidirect
21. C2×C3×#704C22semidirect
27. C2×#6739C22semidirect
31. C2×D3×#170C22semidirect
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. (C2×D3)⋊#170C22semidirect
59. (C2×D3)⋊#170C22semidirect
60. #91169C22semidirect
61. Dic3×#170C22semidirect
75. #65695D3semidirect
117. #6738D4semidirect
157. C2×#704C2×D3semidirect
186. C22⋊#170C2×D3semidirect
188. #4004C2×D3semidirect
196. C4×#170C2×D3semidirect
685. C3×C5#2930semidirect
777. C5#79537semidirect
806. C3#10617226semidirect

Maximal subgroups

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

subgroupindex
C2×#919292
C2×#919152
#117532492
#117523522
C3×#656952
#117520532
#117520452
#117520402
#117519132
#117519102
#117519022
#117518992
#117518972
#117518722
#117518022
#106172263
#795375