Finite Group Databasebeta

← C3×#10617743 #14484793

Subgroups — C3×#10617743 #14484793

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×C4×C5×#41C211yesmaximal, characteristic, complemented
2C3×#66168C211yesmaximal, characteristic, complemented
3C3×#66165C211yesmaximal, characteristic, complemented
4C3×#65910C211yesmaximal, characteristic, complemented
5C3×C4×#713C211yesmaximal, characteristic, complemented
6C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
7C3×#65903C211yesmaximal, characteristic, complemented
8C3×#65893C213yesmaximal, complemented
9C3×#65892C213yesmaximal, complemented
10C3×#65891C213yesmaximal, complemented
11C3×#65882C213yesmaximal, complemented
12C3×#65867C213yesmaximal, complemented
13C3×#65864C213yesmaximal, complemented
14C3×#65813C213yesmaximal, complemented
15C3×C4×#709C213yesmaximal, complemented
16#10617743C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×#713C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic
20C2×C3×#709C2213yes—
21C3×C4×C5×Q8C2211yescharacteristic
22C3×C4×C5×Q8C2211yescharacteristic
23C3×C4×C5×D4C2213yes—
24C3×C4×C5×D4C2213yes—
25C3×C5×#117C2213yes—
26C2×C3×C42×C5C2213yes—
27C3×Q8×Dic5C2211yescharacteristic
28C3×Q8×Dic5C2211yescharacteristic
29C3×#4086C2213yes—
30C3×#4084C2213yes—
31C3×#4084C2213yes—
32C3×#4082C2213yes—
33C3×#4076C2213yes—
34C3×#4075C2216yes—
35C3×C4×C22⋊D5C2213yes—
36C3×C4×C22⋊D5C2213yes—
37C3×C4×C22⋊D5C2216yes—
38C3×C4×C22⋊D5C2213yes—
39C3×C4×C22⋊D5C2213yes—
40C3×#4072C2213yes—
41C3×#4070C2213yes—
42C3×#4043C2213yes—
43C3×#4041C2213yes—
44C3×#4039C2213yes—
45C3×#4038C2213yes—
46C3×D5×C4⋊C4C2213yes—
47C3×#4036C2213yes—
48C3×#4034C2213yes—
49C3×#4033C2213yes—
50C3×#4031C2216yes—
51C3×#4030C2216yes—
52C3×#4029C2216yes—
53C3×#4025C2216yes—
54C3×#4022C2216yes—
55C3×#4021C2213yes—
56C3×C4×D20C2213yes—
57C3×C4×D20C2213yes—
58C3×C4×D20C2213yes—
59C3×#4018C2211yescharacteristic
60C3×#4018C2213yes—
61C3×C42×D5C2213yes—
62C3×C42×D5C2213yes—
63C3×#4016C2213yes—
64C3×C4×Dic10C2213yes—
65C3×C4×Dic10C2213yes—
66C3×C4×Dic10C2213yes—
67C3×#3480—51nomaximal, Hall
68C4×C5×#41C2×C311yescharacteristic, complemented
69#66168C2×C311yescharacteristic, complemented
70#66165C2×C311yescharacteristic, complemented
71#65910C2×C311yescharacteristic, complemented
72C4×#713C2×C311yescharacteristic, complemented
73C4×Q8×D5C2×C311yescharacteristic, complemented
74#65903C2×C311yescharacteristic, complemented
75#65893C2×C313yescomplemented
76#65892C2×C313yescomplemented
77#65891C2×C313yescomplemented
78#65882C2×C313yescomplemented
79#65867C2×C313yescomplemented
80#65864C2×C313yescomplemented
81#65813C2×C313yescomplemented
82C4×#709C2×C313yescomplemented
83C3×C5×#41—24no—
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×D4C2313yes—
86C22×C3×C4×C5C2313yes—
87C22×C3×C4×C5C2313yes—
88C22×C3×C4×C5C2313yes—
89C2×C3×C22⋊D5C2313yes—
90C2×C3×C22⋊D5C2313yes—
91C2×C3×C22⋊D5C2316yes—
92C3×#713—24no—
93C3×Q8×D5—24no—
94C3×#709—212no—
95C2×C3×D20C2313yes—
96C2×C3×D20C2313yes—
97C2×C3×C4×D5C2313yes—
98C2×C3×C4×D5C2313yes—
99C2×C3×C4×D5C2313yes—
100C2×C3×C4×D5C2313yes—
101C2×C3×C4×D5C2313yes—
102C2×C3×C4×D5C2311yescharacteristic
103C2×C3×Dic10C2313yes—
104C2×C3×Dic10C2313yes—
105C3×C5×C4⋊C4C2313yes—
106C3×C5×C4⋊C4C2313yes—
107C3×C5×C22⋊C4C2316yes—
108C3×C42×C5C2313yes—
109C3×C42×C5C2313yes—
110C3×C42×C5C2313yes—
111C3×C42×C5C2311yescharacteristic
112C3×C22⋊Dic5C2313yes—
113C3×C22⋊Dic5C2316yes—
114C3×C22⋊Dic5C2313yes—
115C3×#685C2311yescharacteristic
116C3×#685C2311yescharacteristic
117C3×#685C2313yes—
118C3×#685C2313yes—
119C3×#685C2316yes—
120C3×#685C2316yes—
121C3×C4⋊Dic5C2313yes—
122C3×C4⋊Dic5C2313yes—
123C3×C4⋊Dic5C2313yes—
124C3×C4⋊Dic5C2313yes—
125C3×#683C2311yescharacteristic
126C3×#683C2311yescharacteristic
127C3×#683C2313yes—
128C3×#683C2313yes—
129C3×#683C2316yes—
130C3×#683C2316yes—
131C3×C4×Dic5C2313yes—
132C3×C4×Dic5C2313yes—
133C3×C4×Dic5C2313yes—
134C3×C4×Dic5C2313yes—
135C3×C4×Dic5C2313yes—
136C3×C4×Dic5C2311yescharacteristic
137C3×#559—53no—
138C3×#557—51no—
139C3×#556—53no—
140C3×#553—53no—
141C3×#553—53no—
142C3×#550—51no—
143C3×#548—51no—
144C3×#548—51no—
145C3×#532—53no—
146C3×#529—53no—
147C3×#529—53no—
148C3×C4×#41—51no—
149C3×C4×#41—53no—
150C3×C4×#41D511yescharacteristic, complemented
151C2×C3×C4×Q8—51no—
152C2×C5×#41C22×C311yescharacteristic
153C2×#713C22×C311yescharacteristic
154C2×Q8×D5C22×C311yescharacteristic
155C2×#709C22×C313yes—
156C4×C5×Q8C22×C311yescharacteristic
157C4×C5×Q8C22×C311yescharacteristic
158C4×C5×D4C22×C313yes—
159C4×C5×D4C22×C313yes—
160C5×#117C22×C313yes—
161C2×C42×C5C22×C313yes—
162Q8×Dic5C22×C311yescharacteristic
163Q8×Dic5C22×C311yescharacteristic
164#4086C22×C313yes—
165#4084C22×C313yes—
166#4084C22×C313yes—
167#4082C22×C313yes—
168#4076C22×C313yes—
169#4075C22×C316yes—
170C4×C22⋊D5C22×C313yes—
171C4×C22⋊D5C22×C313yes—
172C4×C22⋊D5C22×C313yes—
173C4×C22⋊D5C22×C313yes—
174C4×C22⋊D5C22×C316yes—
175#4072C22×C313yes—
176#4070C22×C313yes—
177#4043C22×C313yes—
178#4041C22×C313yes—
179#4039C22×C313yes—
180#4038C22×C313yes—
181D5×C4⋊C4C22×C313yes—
182#4036C22×C313yes—
183#4034C22×C313yes—
184#4033C22×C313yes—
185#4031C22×C316yes—
186#4030C22×C316yes—
187#4029C22×C316yes—
188#4025C22×C316yes—
189#4022C22×C316yes—
190#4021C22×C313yes—
191C4×D20C22×C313yes—
192C4×D20C22×C313yes—
193C4×D20C22×C313yes—
194#4018C22×C311yescharacteristic
195#4018C22×C313yes—
196C42×D5C22×C313yes—
197C42×D5C22×C313yes—
198#4016C22×C313yes—
199C4×Dic10C22×C313yes—
200C4×Dic10C22×C313yes—
201C4×Dic10C22×C313yes—
202#3480—51noSylow
203C23×C3×C5C2413yes—
204C22×C3×D5C2413yes—
205C22×C3×D5C2411yescharacteristic
206C3×C5×Q8#4114yescomplemented
207C3×C5×D4—26no—
208C2×C3×C4×C5—26no—
209C2×C3×C4×C5—26no—
210C2×C3×C4×C5—43no—
211C2×C3×C4×C5C2413yes—
212C2×C3×C4×C5C2411yescharacteristic
213C2×C3×C4×C5C2411yescharacteristic
214C2×C3×C4×C5C2413yes—
215C2×C3×C4×C5C2413yes—
216C2×C3×C4×C5C2411yescharacteristic
217C3×C22⋊D5—26no—
218C3×C22⋊D5—26no—
219C3×C22⋊D5—46no—
220C2×C3×Dic5C2411yescharacteristic
221C2×C3×Dic5C2411yescharacteristic
222C2×C3×Dic5C2413yes—
223C2×C3×Dic5C2413yes—
224C2×C3×Dic5C2413yes—
225C2×C3×Dic5C2411yescharacteristic
226C3×D20—26no—
227C3×D20—26no—
228C3×C4×D5—26no—
229C3×C4×D5—26no—
230C3×C4×D5—26no—
231C3×C4×D5—43no—
232C3×C4×D5—43no—
233C3×C4×D5#4114yescomplemented
234C3×Dic10—26no—
235C3×Dic10—26no—
236C2×C3×#41—51no—
237C2×C3×#41—53no—
238C2×C3×#41C2×D511yescharacteristic
239C22×C3×Q8—51no—
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×#124—53no—
249C3×#123—56no—
250C3×#123—56no—
251C3×C22⋊Q8—53no—
252C3×C22⋊Q8—53no—
253C3×#121—53no—
254C3×#121—53no—
255C3×#121—53no—
256C3×#121—53no—
257C3×#121—56no—
258C3×C4×Q8—51no—
259C3×C4×Q8—51no—
260C3×C4×Q8—53no—
261C3×C4×Q8—53no—
262C3×C4×Q8—53no—
263C3×C4×Q8—53no—
264C3×C4×Q8C2×D511yescharacteristic
265C3×C4×Q8C2×D511yescharacteristic
266C3×C4×D4—53no—
267C3×C4×D4—53no—
268C3×C4×D4—53no—
269C3×C4×D4—53no—
270C3×C4×D4—56no—
271C3×C4×D4—53no—
272C3×C4×D4—53no—
273C3×C4×D4—53no—
274C3×C4×D4—53no—
275C3×C4×D4C2×D513yes—
276C3×C4×D4C2×D513yes—
277C3×#117—53no—
278C3×#117—53no—
279C3×#117—51no—
280C3×#117—53no—
281C3×#117C2×D513yes—
282C2×C3×C4⋊C4—53no—
283C2×C3×C42—53no—
284C2×C3×C42—53no—
285C2×C3×C42C2×D513yes—
286C5×#41—24no—
287C2×C5×Q8C23×C311yescharacteristic
288C2×C5×D4C23×C313yes—
289C22×C4×C5C23×C313yes—
290C22×C4×C5C23×C313yes—
291C22×C4×C5C23×C313yes—
292C2×C22⋊D5C23×C313yes—
293C2×C22⋊D5C23×C313yes—
294C2×C22⋊D5C23×C316yes—
295#713—24no—
296Q8×D5—24no—
297#709—212no—
298C2×D20C23×C313yes—
299C2×D20C23×C313yes—
300C2×C4×D5C23×C313yes—
301C2×C4×D5C23×C313yes—
302C2×C4×D5C23×C313yes—
303C2×C4×D5C23×C313yes—
304C2×C4×D5C23×C313yes—
305C2×C4×D5C23×C311yescharacteristic
306C2×Dic10C23×C313yes—
307C2×Dic10C23×C313yes—
308C5×C4⋊C4C23×C313yes—
309C5×C4⋊C4C23×C313yes—
310C5×C22⋊C4C23×C316yes—
311C42×C5C23×C311yescharacteristic
312C42×C5C23×C313yes—
313C42×C5C23×C313yes—
314C42×C5C23×C313yes—
315C22⋊Dic5C23×C313yes—
316C22⋊Dic5C23×C316yes—
317C22⋊Dic5C23×C313yes—
318#685C23×C311yescharacteristic
319#685C23×C311yescharacteristic
320#685C23×C313yes—
321#685C23×C313yes—
322#685C23×C316yes—
323#685C23×C316yes—
324C4⋊Dic5C23×C313yes—
325C4⋊Dic5C23×C313yes—
326C4⋊Dic5C23×C313yes—
327C4⋊Dic5C23×C313yes—
328#683C23×C311yescharacteristic
329#683C23×C311yescharacteristic
330#683C23×C313yes—
331#683C23×C313yes—
332#683C23×C316yes—
333#683C23×C316yes—
334C4×Dic5C23×C313yes—
335C4×Dic5C23×C313yes—
336C4×Dic5C23×C313yes—
337C4×Dic5C23×C313yes—
338C4×Dic5C23×C313yes—
339C4×Dic5C23×C311yescharacteristic
340#559—53no—
341#557—51no—
342#556—53no—
343#553—53no—
344#553—53no—
345#550—51no—
346#548—51no—
347#548—51no—
348#532—53no—
349#529—53no—
350#529—53no—
351C4×#41—51no—
352C4×#41—53no—
353C4×#41C3×D511yescharacteristic, complemented
354C2×C4×Q8—51no—
355C22×C3×C5—23no—
356C22×C3×C5—23no—
357C22×C3×C5—23no—
358C22×C3×C5C2511yescharacteristic
359C2×C3×D5—21no—
360C2×C3×D5—21no—
361C2×C3×D5—23no—
362C2×C3×D5—23no—
363C2×C3×D5—23no—
364C2×C3×D5C2×#4112yes—
365C3×C4×C5—23no—
366C3×C4×C5—21no—
367C3×C4×C5—23no—
368C3×C4×C5—21no—
369C3×C4×C5C2×#4116yes—
370C3×C4×C5C2×#4112yes—
371C3×Dic5—23no—
372C3×Dic5—23no—
373C3×Dic5—21no—
374C3×Dic5—21no—
375C3×Dic5—23no—
376C3×Dic5C2×#4112yes—
377C3×#41—24no—
378C3×#41—1012no—
379C3×#41—104no—
380C2×C3×Q8—53no—
381C2×C3×Q8—53no—
382C2×C3×Q8—104no—
383C2×C3×Q8C22×D511yescharacteristic
384C2×C3×D4—53no—
385C2×C3×D4—53no—
386C2×C3×D4—56no—
387C2×C3×D4—53no—
388C2×C3×D4—53no—
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×C4C22×D513yes—
397C22×C3×C4C22×D513yes—
398C22×C3×C4C22×D513yes—
399C3×C4⋊C4—56no—
400C3×C4⋊C4—51no—
401C3×C4⋊C4—51no—
402C3×C4⋊C4—53no—
403C3×C4⋊C4—53no—
404C3×C4⋊C4—56no—
405C3×C4⋊C4—53no—
406C3×C4⋊C4—53no—
407C3×C4⋊C4—53no—
408C3×C4⋊C4—53no—
409C3×C4⋊C4C22×D513yes—
410C3×C4⋊C4C22×D513yes—
411C3×C22⋊C4—53no—
412C3×C22⋊C4—53no—
413C3×C22⋊C4—56no—
414C3×C22⋊C4—51no—
415C3×C22⋊C4—51no—
416C3×C22⋊C4—53no—
417C3×C22⋊C4—56no—
418C3×C22⋊C4—53no—
419C3×C22⋊C4—56no—
420C3×C22⋊C4C22×D516yes—
421C3×C42—53no—
422C3×C42—53no—
423C3×C42—53no—
424C3×C42—53no—
425C3×C42—51no—
426C3×C42—53no—
427C3×C42C22×D513yes—
428C3×C42C22×D513yes—
429C3×C42C22×D513yes—
430C3×C42C22×D511yescharacteristic
431C23×C5C24×C313yes—
432C22×D5C24×C313yes—
433C22×D5C24×C311yescharacteristic
434C5×Q8C3×#4114yescomplemented
435C5×D4—26no—
436C2×C4×C5—26no—
437C2×C4×C5—26no—
438C2×C4×C5—43no—
439C2×C4×C5C24×C313yes—
440C2×C4×C5C24×C311yescharacteristic
441C2×C4×C5C24×C311yescharacteristic
442C2×C4×C5C24×C313yes—
443C2×C4×C5C24×C311yescharacteristic
444C2×C4×C5C24×C313yes—
445C22⋊D5—26no—
446C22⋊D5—26no—
447C22⋊D5—46no—
448C2×Dic5C24×C311yescharacteristic
449C2×Dic5C24×C311yescharacteristic
450C2×Dic5C24×C313yes—
451C2×Dic5C24×C313yes—
452C2×Dic5C24×C313yes—
453C2×Dic5C24×C311yescharacteristic
454D20—26no—
455D20—26no—
456C4×D5—26no—
457C4×D5—26no—
458C4×D5—26no—
459C4×D5—43no—
460C4×D5—43no—
461C4×D5C3×#4114yescomplemented
462Dic10—26no—
463Dic10—26no—
464C2×#41—51no—
465C2×#41—53no—
466C2×#41C2×C3×D511yescharacteristic
467C22×Q8—51no—
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#124—53no—
477#123—56no—
478#123—56no—
479C22⋊Q8—53no—
480C22⋊Q8—53no—
481#121—53no—
482#121—53no—
483#121—53no—
484#121—53no—
485#121—56no—
486C4×Q8—51no—
487C4×Q8—51no—
488C4×Q8—53no—
489C4×Q8—53no—
490C4×Q8—53no—
491C4×Q8—53no—
492C4×Q8C2×C3×D511yescharacteristic
493C4×Q8C2×C3×D511yescharacteristic
494C4×D4—53no—
495C4×D4—53no—
496C4×D4—53no—
497C4×D4—53no—
498C4×D4—56no—
499C4×D4—53no—
500C4×D4—53no—
501C4×D4—53no—
502C4×D4—53no—
503C4×D4C2×C3×D513yes—
504C4×D4C2×C3×D513yes—
505#117—53no—
506#117—53no—
507#117—51no—
508#117—53no—
509#117C2×C3×D513yes—
510C2×C4⋊C4—53no—
511C2×C42—53no—
512C2×C42—53no—
513C2×C42C2×C3×D513yes—
514C2×C3×C5—43no—
515C2×C3×C5C22×#4111yescharacteristic
516C2×C3×C5C22×#4111yescharacteristic
517C2×C3×C5#58511yescharacteristic
518C3×D5—22no—
519C3×D5—43no—
520C23×C3—51no—
521C23×C3—53no—
522C23×C3C23×D513yes—
523C3×Q8—106no—
524C3×Q8—106no—
525C3×Q8#70914yescomplemented
526C3×D4—26no—
527C3×D4—106no—
528C3×D4—106no—
529C3×D4—106no—
530C3×D4—106no—
531C3×D4—206no—
532C2×C3×C4—26no—
533C2×C3×C4—26no—
534C2×C3×C4—43no—
535C2×C3×C4—51no—
536C2×C3×C4—54no—
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×C4C23×D513yes—
548C2×C3×C4C23×D511yescharacteristic
549C2×C3×C4C23×D511yescharacteristic
550C2×C3×C4C23×D513yes—
551C2×C3×C4C23×D513yes—
552C2×C3×C4C23×D511yescharacteristic
553C22×C5—23no—
554C22×C5—23no—
555C22×C5—23no—
556C22×C5C25×C311yescharacteristic
557C2×D5—21no—
558C2×D5—21no—
559C2×D5—23no—
560C2×D5—23no—
561C2×D5—23no—
562C2×D5C2×C3×#4112yes—
563C4×C5—23no—
564C4×C5—21no—
565C4×C5—23no—
566C4×C5—21no—
567C4×C5C2×C3×#4116yes—
568C4×C5C2×C3×#4112yes—
569Dic5—23no—
570Dic5—23no—
571Dic5—21no—
572Dic5—21no—
573Dic5—23no—
574Dic5C2×C3×#4112yes—
575#41—24no—
576#41—1012no—
577#41—104no—
578C2×Q8—53no—
579C2×Q8—53no—
580C2×Q8—104no—
581C2×Q8C22×C3×D511yescharacteristic
582C2×D4—53no—
583C2×D4—53no—
584C2×D4—56no—
585C2×D4—53no—
586C2×D4—53no—
587C2×D4C22×C3×D513yes—
588C22×C4—51no—
589C22×C4—53no—
590C22×C4—53no—
591C22×C4—53no—
592C22×C4—53no—
593C22×C4—53no—
594C22×C4C22×C3×D513yes—
595C22×C4C22×C3×D513yes—
596C22×C4C22×C3×D513yes—
597C4⋊C4—53no—
598C4⋊C4—56no—
599C4⋊C4—51no—
600C4⋊C4—51no—
601C4⋊C4—53no—
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—53no—
610C22⋊C4—53no—
611C22⋊C4—56no—
612C22⋊C4—51no—
613C22⋊C4—51no—
614C22⋊C4—53no—
615C22⋊C4—56no—
616C22⋊C4—53no—
617C22⋊C4—56no—
618C22⋊C4C22×C3×D516yes—
619C42—51no—
620C42—53no—
621C42—53no—
622C42—53no—
623C42—53no—
624C42—53no—
625C42C22×C3×D513yes—
626C42C22×C3×D511yescharacteristic
627C42C22×C3×D513yes—
628C42C22×C3×D513yes—
629C3×C5#348011yescharacteristic, complemented, Hall
630C22×C3—23no—
631C22×C3—23no—
632C22×C3—23no—
633C22×C3—52no—
634C22×C3—101no—
635C22×C3—101no—
636C22×C3—103no—
637C22×C3—103no—
638C22×C3—103no—
639C22×C3C24×D511yescharacteristic
640C3×C4—21no—
641C3×C4—23no—
642C3×C4—21no—
643C3×C4—23no—
644C3×C4—52no—
645C3×C4—101no—
646C3×C4—103no—
647C3×C4—103no—
648C3×C4—101no—
649C3×C4—103no—
650C3×C4C2×#70916yes—
651C3×C4D5×#4112yes—
652C2×C5—43no—
653C2×C5C22×C3×#4111yescharacteristic
654C2×C5C22×C3×#4111yescharacteristic
655C2×C5C3×#58511yescharacteristic
656D5—22no—
657D5—43no—
658C23—51no—
659C23—53no—
660C23C23×C3×D513yes—
661Q8—106no—
662Q8—106no—
663Q8C3×#70914yescomplemented
664D4—26no—
665D4—106no—
666D4—106no—
667D4—106no—
668D4—106no—
669D4—206no—
670C2×C4—26no—
671C2×C4—26no—
672C2×C4—43no—
673C2×C4—51no—
674C2×C4—54no—
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×C4C23×C3×D513yes—
686C2×C4C23×C3×D511yescharacteristic
687C2×C4C23×C3×D511yescharacteristic
688C2×C4C23×C3×D513yes—
689C2×C4C23×C3×D513yes—
690C2×C4C23×C3×D511yescharacteristic
691C2×C3—43no—
692C2×C3—102no—
693C2×C3—203no—
694C2×C3C22×#70911yescharacteristic
695C2×C3C2×D5×#4111yescharacteristic
696C2×C3#6628311yescharacteristic
697C5C3×#348011yescharacteristic, complemented, Sylow
698C22—23no—
699C22—23no—
700C22—23no—
701C22—52no—
702C22—101no—
703C22—101no—
704C22—103no—
705C22—103no—
706C22—103no—
707C22C24×C3×D511yescharacteristic
708C4—21no—
709C4—23no—
710C4—21no—
711C4—23no—
712C4—52no—
713C4—101no—
714C4—103no—
715C4—103no—
716C4—101no—
717C4—103no—
718C4C2×C3×#70916yes—
719C4C3×D5×#4112yes—
720C3#1061774311yescharacteristic, direct product factor, Sylow
721C2—43no—
722C2—102no—
723C2—203no—
724C2C22×C3×#70911yescharacteristic
725C2C2×C3×D5×#4111yescharacteristic
726C2C3×#6628311yescharacteristic
subgroupG/H
centerC2×C3×C4C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC3×C4×C5×#41C2
socleC22×C3×C5C25
hypercenterC3×C4×#41D5
hypocenterC5C3×#3480
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
1. C3×C4×C5×#41C2semidirect
2. C3×#66168C2semidirect
3. C3×#66165C2semidirect
4. C3×#65910C2semidirect
5. C3×C4×#713C2semidirect
6. C3×C4×Q8×D5C2semidirect
7. C3×#65903C2semidirect
8. C3×#65893C2semidirect
9. C3×#65892C2semidirect
10. C3×#65891C2semidirect
11. C3×#65882C2semidirect
12. C3×#65867C2semidirect
13. C3×#65864C2semidirect
14. C3×#65813C2semidirect
15. C3×C4×#709C2semidirect
16. #10617743C3direct (N × H)
68. C4×C5×#41C2×C3semidirect
69. #66168C2×C3semidirect
70. #66165C2×C3semidirect
71. #65910C2×C3semidirect
72. C4×#713C2×C3semidirect
73. C4×Q8×D5C2×C3semidirect
74. #65903C2×C3semidirect
75. #65893C2×C3semidirect
76. #65892C2×C3semidirect
77. #65891C2×C3semidirect
78. #65882C2×C3semidirect
79. #65867C2×C3semidirect
80. #65864C2×C3semidirect
81. #65813C2×C3semidirect
82. C4×#709C2×C3semidirect
150. C3×C4×#41D5semidirect
206. C3×C5×Q8#41semidirect
233. C3×C4×D5#41semidirect
353. C4×#41C3×D5semidirect
434. C5×Q8C3×#41semidirect
461. C4×D5C3×#41semidirect
525. C3×Q8#709semidirect
629. C3×C5#3480semidirect
663. Q8C3×#709semidirect
697. C5C3×#3480semidirect
720. C3#10617743direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×C5×#412
C3×#661682
C3×#661652
C3×#659102
C3×C4×#7132
C3×C4×Q8×D52
C3×#659032
C3×#658932
C3×#658922
C3×#658912
C3×#658822
C3×#658672
C3×#658642
C3×#658132
C3×C4×#7092
#106177433
C3×#34805