Finite Group Databasebeta

← C3×#10618612 #14484769

Subgroups — C3×#10618612 #14484769

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#548C211yesmaximal, characteristic, complemented
2C3×#66168C211yesmaximal, characteristic, complemented
3C3×#41×Dic5C211yesmaximal, characteristic, complemented
4C3×#66151C211yesmaximal, characteristic, complemented
5C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
6C3×#66015C213yesmaximal, complemented
7C3×#66014C213yesmaximal, complemented
8C3×#65975C213yesmaximal, complemented
9C3×#65958C213yesmaximal, complemented
10C3×#65952C213yesmaximal, complemented
11C3×#65930C213yesmaximal, complemented
12C3×C4×#713C211yesmaximal, characteristic, complemented
13C3×#65903C211yesmaximal, characteristic, complemented
14C3×#65899C213yesmaximal, complemented
15C3×C4×#711C213yesmaximal, complemented
16#10618612C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×Q8C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic
20C2×C3×#711C2213yes—
21C3×C5×#124C2213yes—
22C3×C5×C22⋊Q8C2213yes—
23C3×C5×#121C2213yes—
24C3×C4×C5×Q8C2211yescharacteristic
25C3×C4×C5×D4C2213yes—
26C3×#4093C2213yes—
27C3×#4092C2213yes—
28C3×Q8×Dic5C2211yescharacteristic
29C3×Q8×Dic5C2211yescharacteristic
30C3×Q8×Dic5C2213yes—
31C3×Q8×Dic5C2213yes—
32C3×Q8×Dic5C2211yescharacteristic
33C3×#4086C2213yes—
34C3×#4085C2216yes—
35C3×#4084C2213yes—
36C3×D4×Dic5C2213yes—
37C3×D4×Dic5C2213yes—
38C3×D4×Dic5C2213yes—
39C3×#4076C2213yes—
40C3×#4076C2213yes—
41C3×C4×C22⋊D5C2213yes—
42C3×C4×C22⋊D5C2213yes—
43C3×#4072C2213yes—
44C2×C3×C4⋊Dic5C2213yes—
45C2×C3×C4×Dic5C2213yes—
46C2×C3×C4×Dic5C2213yes—
47C3×#4044C2216yes—
48C3×#4039C2213yes—
49C3×#4038C2213yes—
50C3×#4038C2213yes—
51C3×#4036C2213yes—
52C3×#4034C2213yes—
53C3×#4033C2213yes—
54C3×#4032C2216yes—
55C3×#4031C2216yes—
56C3×#4029C2216yes—
57C3×#4027C2213yes—
58C3×#4027C2213yes—
59C3×#4027C2216yes—
60C3×#4025C2216yes—
61C3×#4023C2211yescharacteristic
62C3×#4023C2213yes—
63C3×C4×D20C2213yes—
64C3×C42×D5C2213yes—
65C3×#4016C2213yes—
66C3×C4×Dic10C2213yes—
67C3×#3480—51nomaximal, Hall
68C5×#548C2×C311yescharacteristic, complemented
69#66168C2×C311yescharacteristic, complemented
70#41×Dic5C2×C311yescharacteristic, complemented
71#66151C2×C311yescharacteristic, complemented
72C2×Q8×Dic5C2×C311yescharacteristic, complemented
73#66015C2×C313yescomplemented
74#66014C2×C313yescomplemented
75#65975C2×C313yescomplemented
76#65958C2×C313yescomplemented
77#65952C2×C313yescomplemented
78#65930C2×C313yescomplemented
79C4×#713C2×C311yescharacteristic, complemented
80#65903C2×C311yescharacteristic, complemented
81#65899C2×C313yescomplemented
82C4×#711C2×C313yescomplemented
83C3×C5×#41—24no—
84C2×C3×C5×Q8—24no—
85C2×C3×C5×Q8C2313yes—
86C2×C3×C5×Q8C2311yescharacteristic
87C2×C3×C5×D4C2313yes—
88C2×C3×C5×D4C2313yes—
89C22×C3×C4×C5C2313yes—
90C22×C3×C4×C5C2313yes—
91C2×C3×C22⋊D5C2313yes—
92C2×C3×C22⋊D5C2313yes—
93C2×C3×C22⋊D5C2316yes—
94C22×C3×Dic5C2313yes—
95C22×C3×Dic5C2313yes—
96C22×C3×Dic5C2313yes—
97C22×C3×Dic5C2311yescharacteristic
98C3×#713—24no—
99C3×#711—212no—
100C2×C3×D20C2313yes—
101C2×C3×C4×D5C2313yes—
102C2×C3×C4×D5C2313yes—
103C2×C3×C4×D5C2313yes—
104C2×C3×Dic10C2313yes—
105C3×C5×C4⋊C4C2313yes—
106C3×C5×C4⋊C4C2313yes—
107C3×C5×C22⋊C4C2311yescharacteristic
108C3×C5×C22⋊C4C2313yes—
109C3×C5×C22⋊C4C2316yes—
110C3×C42×C5C2313yes—
111C3×C22⋊Dic5C2311yescharacteristic
112C3×C22⋊Dic5C2316yes—
113C3×C22⋊Dic5C2313yes—
114C3×#685C2316yes—
115C3×#685C2316yes—
116C3×#685C2313yes—
117C3×#685C2313yes—
118C3×C4⋊Dic5C2313yes—
119C3×C4⋊Dic5C2313yes—
120C3×C4⋊Dic5C2313yes—
121C3×C4⋊Dic5C2313yes—
122C3×C4⋊Dic5C2316yes—
123C3×#683C2316yes—
124C3×#683C2313yes—
125C3×#683C2311yescharacteristic
126C3×#683C2313yes—
127C3×#683C2311yescharacteristic
128C3×C4×Dic5C2313yes—
129C3×C4×Dic5C2313yes—
130C3×C4×Dic5C2313yes—
131C3×C4×Dic5C2313yes—
132C3×C4×Dic5C2313yes—
133C3×C4×Dic5C2313yes—
134C3×C4×Dic5C2311yescharacteristic
135C3×C4×Dic5C2311yescharacteristic
136C3×C4×Dic5C2313yes—
137C3×#559—53no—
138C3×#557—51no—
139C3×#556—53no—
140C3×#553—53no—
141C3×#553—53no—
142C3×#550—51no—
143C3×#548—51no—
144C3×#548D511yescharacteristic, complemented
145C3×#532—53no—
146C3×#529—53no—
147C3×#529—53no—
148C3×C4×#41—51no—
149C3×C4×#41—51no—
150C3×C4×#41—53no—
151C2×C3×C4×Q8—51no—
152C2×C5×#41C22×C311yescharacteristic
153C22×C5×Q8C22×C311yescharacteristic
154C2×#713C22×C311yescharacteristic
155C2×#711C22×C313yes—
156C5×#124C22×C313yes—
157C5×C22⋊Q8C22×C313yes—
158C5×#121C22×C313yes—
159C4×C5×Q8C22×C311yescharacteristic
160C4×C5×D4C22×C313yes—
161#4093C22×C313yes—
162#4092C22×C313yes—
163Q8×Dic5C22×C311yescharacteristic
164Q8×Dic5C22×C311yescharacteristic
165Q8×Dic5C22×C313yes—
166Q8×Dic5C22×C313yes—
167Q8×Dic5C22×C311yescharacteristic
168#4086C22×C313yes—
169#4085C22×C316yes—
170#4084C22×C313yes—
171D4×Dic5C22×C313yes—
172D4×Dic5C22×C313yes—
173D4×Dic5C22×C313yes—
174#4076C22×C313yes—
175#4076C22×C313yes—
176C4×C22⋊D5C22×C313yes—
177C4×C22⋊D5C22×C313yes—
178#4072C22×C313yes—
179C2×C4⋊Dic5C22×C313yes—
180C2×C4×Dic5C22×C313yes—
181C2×C4×Dic5C22×C313yes—
182#4044C22×C316yes—
183#4039C22×C313yes—
184#4038C22×C313yes—
185#4038C22×C313yes—
186#4036C22×C313yes—
187#4034C22×C313yes—
188#4033C22×C313yes—
189#4032C22×C316yes—
190#4031C22×C316yes—
191#4029C22×C316yes—
192#4027C22×C313yes—
193#4027C22×C313yes—
194#4027C22×C316yes—
195#4025C22×C316yes—
196#4023C22×C311yescharacteristic
197#4023C22×C313yes—
198C4×D20C22×C313yes—
199C42×D5C22×C313yes—
200#4016C22×C313yes—
201C4×Dic10C22×C313yes—
202#3480—51noSylow
203C23×C3×C5C2413yes—
204C23×C3×C5C2411yescharacteristic
205C22×C3×D5C2413yes—
206C3×C5×Q8—26no—
207C3×C5×Q8#4114yescomplemented
208C3×C5×D4—26no—
209C3×C5×D4—26no—
210C2×C3×C4×C5—26no—
211C2×C3×C4×C5—26no—
212C2×C3×C4×C5C2411yescharacteristic
213C2×C3×C4×C5C2413yes—
214C2×C3×C4×C5C2411yescharacteristic
215C2×C3×C4×C5C2413yes—
216C2×C3×C4×C5C2413yes—
217C3×C22⋊D5—26no—
218C3×C22⋊D5—26no—
219C3×C22⋊D5—46no—
220C2×C3×Dic5—26no—
221C2×C3×Dic5—43no—
222C2×C3×Dic5—43no—
223C2×C3×Dic5#4114yescomplemented
224C2×C3×Dic5C2411yescharacteristic
225C2×C3×Dic5C2411yescharacteristic
226C2×C3×Dic5C2413yes—
227C2×C3×Dic5C2413yes—
228C2×C3×Dic5C2413yes—
229C2×C3×Dic5C2411yescharacteristic
230C2×C3×Dic5C2411yescharacteristic
231C3×D20—26no—
232C3×C4×D5—26no—
233C3×C4×D5—26no—
234C3×C4×D5—43no—
235C3×Dic10—26no—
236C2×C3×#41—51no—
237C2×C3×#41—53no—
238C2×C3×#41C2×D511yescharacteristic
239C22×C3×Q8C2×D511yescharacteristic
240C3×C4⋊Q8—53no—
241C3×#127—53no—
242C3×#126—56no—
243C3×#126—56no—
244C3×#125—53no—
245C3×#125—53no—
246C3×#124—53no—
247C3×#124—56no—
248C3×#124C2×D513yes—
249C3×#123—56no—
250C3×#123—56no—
251C3×C22⋊Q8—53no—
252C3×C22⋊Q8C2×D513yes—
253C3×#121—53no—
254C3×#121—56no—
255C3×#121—53no—
256C3×#121—53no—
257C3×#121C2×D513yes—
258C3×C4×Q8—53no—
259C3×C4×Q8—51no—
260C3×C4×Q8—53no—
261C3×C4×Q8—51no—
262C3×C4×Q8—51no—
263C3×C4×Q8—53no—
264C3×C4×Q8—53no—
265C3×C4×Q8C2×D511yescharacteristic
266C3×C4×D4—53no—
267C3×C4×D4—53no—
268C3×C4×D4—53no—
269C3×C4×D4—53no—
270C3×C4×D4—53no—
271C3×C4×D4—53no—
272C3×C4×D4—53no—
273C3×C4×D4—53no—
274C3×C4×D4—56no—
275C3×C4×D4—53no—
276C3×C4×D4C2×D513yes—
277C3×#117—53no—
278C3×#117—53no—
279C3×#117—53no—
280C3×#117—51no—
281C3×#117—53no—
282C2×C3×C4⋊C4—53no—
283C2×C3×C42—53no—
284C2×C3×C42—53no—
285C2×C3×C42—53no—
286C5×#41—24no—
287C2×C5×Q8—24no—
288C2×C5×Q8C23×C313yes—
289C2×C5×Q8C23×C311yescharacteristic
290C2×C5×D4C23×C313yes—
291C2×C5×D4C23×C313yes—
292C22×C4×C5C23×C313yes—
293C22×C4×C5C23×C313yes—
294C2×C22⋊D5C23×C313yes—
295C2×C22⋊D5C23×C313yes—
296C2×C22⋊D5C23×C316yes—
297C22×Dic5C23×C313yes—
298C22×Dic5C23×C313yes—
299C22×Dic5C23×C313yes—
300C22×Dic5C23×C311yescharacteristic
301#713—24no—
302#711—212no—
303C2×D20C23×C313yes—
304C2×C4×D5C23×C313yes—
305C2×C4×D5C23×C313yes—
306C2×C4×D5C23×C313yes—
307C2×Dic10C23×C313yes—
308C5×C4⋊C4C23×C313yes—
309C5×C4⋊C4C23×C313yes—
310C5×C22⋊C4C23×C311yescharacteristic
311C5×C22⋊C4C23×C313yes—
312C5×C22⋊C4C23×C316yes—
313C42×C5C23×C313yes—
314C22⋊Dic5C23×C313yes—
315C22⋊Dic5C23×C311yescharacteristic
316C22⋊Dic5C23×C316yes—
317#685C23×C316yes—
318#685C23×C316yes—
319#685C23×C313yes—
320#685C23×C313yes—
321C4⋊Dic5C23×C313yes—
322C4⋊Dic5C23×C313yes—
323C4⋊Dic5C23×C313yes—
324C4⋊Dic5C23×C313yes—
325C4⋊Dic5C23×C316yes—
326#683C23×C311yescharacteristic
327#683C23×C313yes—
328#683C23×C316yes—
329#683C23×C313yes—
330#683C23×C311yescharacteristic
331C4×Dic5C23×C313yes—
332C4×Dic5C23×C313yes—
333C4×Dic5C23×C311yescharacteristic
334C4×Dic5C23×C313yes—
335C4×Dic5C23×C313yes—
336C4×Dic5C23×C313yes—
337C4×Dic5C23×C311yescharacteristic
338C4×Dic5C23×C313yes—
339C4×Dic5C23×C313yes—
340#559—53no—
341#557—51no—
342#556—53no—
343#553—53no—
344#553—53no—
345#550—51no—
346#548—51no—
347#548C3×D511yescharacteristic, complemented
348#532—53no—
349#529—53no—
350#529—53no—
351C4×#41—51no—
352C4×#41—51no—
353C4×#41—53no—
354C2×C4×Q8—51no—
355C22×C3×C5—21no—
356C22×C3×C5—21no—
357C22×C3×C5—23no—
358C22×C3×C5—23no—
359C22×C3×C5—23no—
360C22×C3×C5C2×#4112yes—
361C22×C3×C5C2511yescharacteristic
362C2×C3×D5—23no—
363C2×C3×D5—23no—
364C2×C3×D5—23no—
365C3×C4×C5—23no—
366C3×C4×C5—21no—
367C3×C4×C5—23no—
368C3×C4×C5—21no—
369C3×C4×C5C2×#4116yes—
370C3×Dic5—23no—
371C3×Dic5—21no—
372C3×Dic5—23no—
373C3×Dic5—21no—
374C3×Dic5—23no—
375C3×Dic5C2×#4112yes—
376C3×Dic5C2×#4112yes—
377C3×#41—24no—
378C3×#41—1012no—
379C3×#41—104no—
380C2×C3×Q8—24no—
381C2×C3×Q8—53no—
382C2×C3×Q8C22×D513yes—
383C2×C3×Q8C22×D511yescharacteristic
384C2×C3×D4—53no—
385C2×C3×D4—53no—
386C2×C3×D4—56no—
387C2×C3×D4—53no—
388C2×C3×D4C22×D513yes—
389C2×C3×D4C22×D513yes—
390C22×C3×C4—51no—
391C22×C3×C4—53no—
392C22×C3×C4—53no—
393C22×C3×C4—53no—
394C22×C3×C4—53no—
395C22×C3×C4—53no—
396C22×C3×C4—53no—
397C22×C3×C4C22×D513yes—
398C22×C3×C4C22×D513yes—
399C3×C4⋊C4—51no—
400C3×C4⋊C4—51no—
401C3×C4⋊C4—53no—
402C3×C4⋊C4—53no—
403C3×C4⋊C4—56no—
404C3×C4⋊C4—53no—
405C3×C4⋊C4—53no—
406C3×C4⋊C4—56no—
407C3×C4⋊C4—53no—
408C3×C4⋊C4—53no—
409C3×C4⋊C4C22×D513yes—
410C3×C4⋊C4C22×D513yes—
411C3×C22⋊C4—51no—
412C3×C22⋊C4—53no—
413C3×C22⋊C4—56no—
414C3×C22⋊C4—53no—
415C3×C22⋊C4—56no—
416C3×C22⋊C4—53no—
417C3×C22⋊C4—56no—
418C3×C22⋊C4C22×D511yescharacteristic
419C3×C22⋊C4C22×D513yes—
420C3×C22⋊C4C22×D516yes—
421C3×C42—51no—
422C3×C42—51no—
423C3×C42—53no—
424C3×C42—53no—
425C3×C42—53no—
426C3×C42—53no—
427C3×C42—53no—
428C3×C42—53no—
429C3×C42—53no—
430C3×C42C22×D513yes—
431C23×C5C24×C313yes—
432C23×C5C24×C311yescharacteristic
433C22×D5C24×C313yes—
434C5×Q8—26no—
435C5×Q8C3×#4114yescomplemented
436C5×D4—26no—
437C5×D4—26no—
438C2×C4×C5—26no—
439C2×C4×C5—26no—
440C2×C4×C5C24×C311yescharacteristic
441C2×C4×C5C24×C313yes—
442C2×C4×C5C24×C311yescharacteristic
443C2×C4×C5C24×C313yes—
444C2×C4×C5C24×C313yes—
445C22⋊D5—26no—
446C22⋊D5—26no—
447C22⋊D5—46no—
448C2×Dic5—26no—
449C2×Dic5—43no—
450C2×Dic5—43no—
451C2×Dic5C3×#4114yescomplemented
452C2×Dic5C24×C311yescharacteristic
453C2×Dic5C24×C311yescharacteristic
454C2×Dic5C24×C313yes—
455C2×Dic5C24×C313yes—
456C2×Dic5C24×C313yes—
457C2×Dic5C24×C311yescharacteristic
458C2×Dic5C24×C311yescharacteristic
459D20—26no—
460C4×D5—26no—
461C4×D5—26no—
462C4×D5—43no—
463Dic10—26no—
464C2×#41—51no—
465C2×#41—53no—
466C2×#41C2×C3×D511yescharacteristic
467C22×Q8C2×C3×D511yescharacteristic
468C4⋊Q8—53no—
469#127—53no—
470#126—56no—
471#126—56no—
472#125—53no—
473#125—53no—
474#124—53no—
475#124—56no—
476#124C2×C3×D513yes—
477#123—56no—
478#123—56no—
479C22⋊Q8—53no—
480C22⋊Q8C2×C3×D513yes—
481#121—53no—
482#121—56no—
483#121—53no—
484#121—53no—
485#121C2×C3×D513yes—
486C4×Q8—51no—
487C4×Q8—53no—
488C4×Q8—51no—
489C4×Q8—53no—
490C4×Q8—51no—
491C4×Q8—53no—
492C4×Q8—53no—
493C4×Q8C2×C3×D511yescharacteristic
494C4×D4—53no—
495C4×D4—53no—
496C4×D4—53no—
497C4×D4—53no—
498C4×D4—53no—
499C4×D4—53no—
500C4×D4—53no—
501C4×D4—53no—
502C4×D4—56no—
503C4×D4—53no—
504C4×D4C2×C3×D513yes—
505#117—53no—
506#117—53no—
507#117—53no—
508#117—51no—
509#117—53no—
510C2×C4⋊C4—53no—
511C2×C42—53no—
512C2×C42—53no—
513C2×C42—53no—
514C2×C3×C5—22no—
515C2×C3×C5—43no—
516C2×C3×C5C22×#4111yescharacteristic
517C2×C3×C5C22×#4111yescharacteristic
518C2×C3×C5#58511yescharacteristic
519C3×D5—43no—
520C23×C3—53no—
521C23×C3C23×D513yes—
522C23×C3C23×D511yescharacteristic
523C3×Q8—26no—
524C3×Q8—106no—
525C3×Q8#71114yescomplemented
526C3×D4—26no—
527C3×D4—26no—
528C3×D4—106no—
529C3×D4—106no—
530C3×D4—106no—
531C3×D4—206no—
532C2×C3×C4—26no—
533C2×C3×C4—26no—
534C2×C3×C4—54no—
535C2×C3×C4—51no—
536C2×C3×C4—51no—
537C2×C3×C4—51no—
538C2×C3×C4—51no—
539C2×C3×C4—53no—
540C2×C3×C4—53no—
541C2×C3×C4—53no—
542C2×C3×C4—106no—
543C2×C3×C4—106no—
544C2×C3×C4—106no—
545C2×C3×C4—203no—
546C2×C3×C4—203no—
547C2×C3×C4—203no—
548C2×C3×C4C23×D511yescharacteristic
549C2×C3×C4C23×D513yes—
550C2×C3×C4C23×D511yescharacteristic
551C2×C3×C4C23×D513yes—
552C2×C3×C4C23×D513yes—
553C22×C5—21no—
554C22×C5—21no—
555C22×C5—23no—
556C22×C5—23no—
557C22×C5—23no—
558C22×C5C2×C3×#4112yes—
559C22×C5C25×C311yescharacteristic
560C2×D5—23no—
561C2×D5—23no—
562C2×D5—23no—
563C4×C5—23no—
564C4×C5—21no—
565C4×C5—23no—
566C4×C5—21no—
567C4×C5C2×C3×#4116yes—
568Dic5—23no—
569Dic5—21no—
570Dic5—23no—
571Dic5—21no—
572Dic5—23no—
573Dic5C2×C3×#4112yes—
574Dic5C2×C3×#4112yes—
575#41—24no—
576#41—1012no—
577#41—104no—
578C2×Q8—24no—
579C2×Q8—53no—
580C2×Q8C22×C3×D513yes—
581C2×Q8C22×C3×D511yescharacteristic
582C2×D4—53no—
583C2×D4—53no—
584C2×D4—56no—
585C2×D4—53no—
586C2×D4C22×C3×D513yes—
587C2×D4C22×C3×D513yes—
588C22×C4—51no—
589C22×C4—53no—
590C22×C4—53no—
591C22×C4—53no—
592C22×C4—53no—
593C22×C4—53no—
594C22×C4—53no—
595C22×C4C22×C3×D513yes—
596C22×C4C22×C3×D513yes—
597C4⋊C4—53no—
598C4⋊C4—53no—
599C4⋊C4—56no—
600C4⋊C4—51no—
601C4⋊C4—51no—
602C4⋊C4—53no—
603C4⋊C4—53no—
604C4⋊C4—53no—
605C4⋊C4—53no—
606C4⋊C4—56no—
607C4⋊C4C22×C3×D513yes—
608C4⋊C4C22×C3×D513yes—
609C22⋊C4—51no—
610C22⋊C4—53no—
611C22⋊C4—56no—
612C22⋊C4—53no—
613C22⋊C4—56no—
614C22⋊C4—53no—
615C22⋊C4—56no—
616C22⋊C4C22×C3×D511yescharacteristic
617C22⋊C4C22×C3×D513yes—
618C22⋊C4C22×C3×D516yes—
619C42—51no—
620C42—51no—
621C42—53no—
622C42—53no—
623C42—53no—
624C42—53no—
625C42—53no—
626C42—53no—
627C42—53no—
628C42C22×C3×D513yes—
629C3×C5#348011yescharacteristic, complemented, Hall
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—23no—
633C22×C3—23no—
634C22×C3—23no—
635C22×C3—103no—
636C22×C3—103no—
637C22×C3—103no—
638C22×C3D5×#4112yes—
639C22×C3C24×D511yescharacteristic
640C3×C4—21no—
641C3×C4—23no—
642C3×C4—23no—
643C3×C4—21no—
644C3×C4—52no—
645C3×C4—52no—
646C3×C4—101no—
647C3×C4—103no—
648C3×C4—103no—
649C3×C4—101no—
650C3×C4—103no—
651C3×C4C2×#71116yes—
652C2×C5—22no—
653C2×C5—43no—
654C2×C5C22×C3×#4111yescharacteristic
655C2×C5C22×C3×#4111yescharacteristic
656C2×C5C3×#58511yescharacteristic
657D5—43no—
658C23—53no—
659C23C23×C3×D513yes—
660C23C23×C3×D511yescharacteristic
661Q8—26no—
662Q8—106no—
663Q8C3×#71114yescomplemented
664D4—26no—
665D4—26no—
666D4—106no—
667D4—106no—
668D4—106no—
669D4—206no—
670C2×C4—26no—
671C2×C4—26no—
672C2×C4—54no—
673C2×C4—51no—
674C2×C4—51no—
675C2×C4—51no—
676C2×C4—51no—
677C2×C4—53no—
678C2×C4—53no—
679C2×C4—53no—
680C2×C4—106no—
681C2×C4—106no—
682C2×C4—106no—
683C2×C4—203no—
684C2×C4—203no—
685C2×C4—203no—
686C2×C4C23×C3×D511yescharacteristic
687C2×C4C23×C3×D513yes—
688C2×C4C23×C3×D511yescharacteristic
689C2×C4C23×C3×D513yes—
690C2×C4C23×C3×D513yes—
691C2×C3—22no—
692C2×C3—43no—
693C2×C3—203no—
694C2×C3C22×#71111yescharacteristic
695C2×C3C2×D5×#4111yescharacteristic
696C2×C3#6628711yescharacteristic
697C5C3×#348011yescharacteristic, complemented, Sylow
698C22—21no—
699C22—21no—
700C22—23no—
701C22—23no—
702C22—23no—
703C22—103no—
704C22—103no—
705C22—103no—
706C22C3×D5×#4112yes—
707C22C24×C3×D511yescharacteristic
708C4—21no—
709C4—23no—
710C4—23no—
711C4—21no—
712C4—52no—
713C4—52no—
714C4—101no—
715C4—103no—
716C4—103no—
717C4—101no—
718C4—103no—
719C4C2×C3×#71116yes—
720C3#1061861211yescharacteristic, direct product factor, Sylow
721C2—22no—
722C2—43no—
723C2—203no—
724C2C22×C3×#71111yescharacteristic
725C2C2×C3×D5×#4111yescharacteristic
726C2C3×#6628711yescharacteristic
subgroupG/H
centerC22×C3C24×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC3×C5×#548C2
socleC22×C3×C5C25
hypercenterC3×#548D5
hypocenterC5C3×#3480
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#548

Complements

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

NH ≅ G/Ntype
1. C3×C5×#548C2semidirect
2. C3×#66168C2semidirect
3. C3×#41×Dic5C2semidirect
4. C3×#66151C2semidirect
5. C2×C3×Q8×Dic5C2semidirect
6. C3×#66015C2semidirect
7. C3×#66014C2semidirect
8. C3×#65975C2semidirect
9. C3×#65958C2semidirect
10. C3×#65952C2semidirect
11. C3×#65930C2semidirect
12. C3×C4×#713C2semidirect
13. C3×#65903C2semidirect
14. C3×#65899C2semidirect
15. C3×C4×#711C2semidirect
16. #10618612C3direct (N × H)
68. C5×#548C2×C3semidirect
69. #66168C2×C3semidirect
70. #41×Dic5C2×C3semidirect
71. #66151C2×C3semidirect
72. C2×Q8×Dic5C2×C3semidirect
73. #66015C2×C3semidirect
74. #66014C2×C3semidirect
75. #65975C2×C3semidirect
76. #65958C2×C3semidirect
77. #65952C2×C3semidirect
78. #65930C2×C3semidirect
79. C4×#713C2×C3semidirect
80. #65903C2×C3semidirect
81. #65899C2×C3semidirect
82. C4×#711C2×C3semidirect
144. C3×#548D5semidirect
207. C3×C5×Q8#41semidirect
223. C2×C3×Dic5#41semidirect
347. #548C3×D5semidirect
435. C5×Q8C3×#41semidirect
451. C2×Dic5C3×#41semidirect
525. C3×Q8#711semidirect
629. C3×C5#3480semidirect
663. Q8C3×#711semidirect
697. C5C3×#3480semidirect
720. C3#10618612direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5482
C3×#661682
C3×#41×Dic52
C3×#661512
C2×C3×Q8×Dic52
C3×#660152
C3×#660142
C3×#659752
C3×#659582
C3×#659522
C3×#659302
C3×C4×#7132
C3×#659032
C3×#658992
C3×C4×#7112
#106186123
C3×#34805