Finite Group Databasebeta

← C5×#85842 #14484792

Subgroups — C5×#85842 #14484792

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
2C5×#5834C211yesmaximal, characteristic, complemented
3C5×#5831C211yesmaximal, characteristic, complemented
4C5×#5576C211yesmaximal, characteristic, complemented
5C4×C5×#239C211yesmaximal, characteristic, complemented
6C4×C5×D3×Q8C211yesmaximal, characteristic, complemented
7C5×#5569C211yesmaximal, characteristic, complemented
8C5×#5559C213yesmaximal, complemented
9C5×#5558C213yesmaximal, complemented
10C5×#5557C213yesmaximal, complemented
11C5×#5548C213yesmaximal, complemented
12C5×#5533C213yesmaximal, complemented
13C5×#5530C213yesmaximal, complemented
14C5×#5479C213yesmaximal, complemented
15C4×C5×#235C213yesmaximal, complemented
16C5×#3480—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic
19C2×C5×D3×Q8C2211yescharacteristic
20C2×C5×#235C2213yes—
21C3×C4×C5×Q8C2211yescharacteristic
22C3×C4×C5×Q8C2211yescharacteristic
23C3×C4×C5×D4C2213yes—
24C3×C4×C5×D4C2213yes—
25C3×C5×#117C2213yes—
26C2×C3×C42×C5C2213yes—
27C5×Q8×Dic3C2211yescharacteristic
28C5×Q8×Dic3C2211yescharacteristic
29C5×#940C2213yes—
30C5×#938C2213yes—
31C5×#938C2213yes—
32C5×#936C2213yes—
33C5×#930C2213yes—
34C5×#929C2216yes—
35C4×C5×#67C2213yes—
36C4×C5×#67C2213yes—
37C4×C5×#67C2213yes—
38C4×C5×#67C2213yes—
39C4×C5×#67C2216yes—
40C5×#926C2213yes—
41C5×#924C2213yes—
42C5×#897C2213yes—
43C5×#895C2213yes—
44C5×#893C2213yes—
45C5×#892C2213yes—
46C5×D3×C4⋊C4C2213yes—
47C5×#890C2213yes—
48C5×#888C2213yes—
49C5×#887C2213yes—
50C5×#885C2216yes—
51C5×#884C2216yes—
52C5×#883C2216yes—
53C5×#879C2216yes—
54C5×#876C2216yes—
55C5×#875C2213yes—
56C4×C5×D12C2213yes—
57C4×C5×D12C2213yes—
58C4×C5×D12C2213yes—
59C5×#872C2211yescharacteristic
60C5×#872C2213yes—
61C42×C5×D3C2213yes—
62C42×C5×D3C2213yes—
63C5×#870C2213yes—
64C4×C5×Dic6C2213yes—
65C4×C5×Dic6C2213yes—
66C4×C5×Dic6C2213yes—
67#85842C511yesmaximal, characteristic, direct product factor, Hall
68C5×#559—33no—
69C5×#557—31no—
70C5×#556—33no—
71C5×#553—33no—
72C5×#553—33no—
73C5×#550—31no—
74C5×#548—31no—
75C5×#548—31no—
76C5×#532—33no—
77C5×#529—33no—
78C5×#529—33no—
79C4×C5×#41—31no—
80C4×C5×#41—33no—
81C4×C5×#41D311yescharacteristic, complemented
82C2×C4×C5×Q8—31no—
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×C5×#67C2313yes—
90C2×C5×#67C2313yes—
91C2×C5×#67C2316yes—
92C5×#239—24no—
93C5×D3×Q8—24no—
94C5×#235—212no—
95C2×C5×D12C2313yes—
96C2×C5×D12C2313yes—
97C2×C4×C5×D3C2313yes—
98C2×C4×C5×D3C2313yes—
99C2×C4×C5×D3C2313yes—
100C2×C4×C5×D3C2313yes—
101C2×C4×C5×D3C2313yes—
102C2×C4×C5×D3C2311yescharacteristic
103C2×C5×Dic6C2313yes—
104C2×C5×Dic6C2313yes—
105C3×C5×C4⋊C4C2313yes—
106C3×C5×C4⋊C4C2313yes—
107C3×C5×C22⋊C4C2316yes—
108C3×C42×C5C2313yes—
109C3×C42×C5C2313yes—
110C3×C42×C5C2313yes—
111C3×C42×C5C2311yescharacteristic
112C5×#217C2313yes—
113C5×#217C2316yes—
114C5×#217C2313yes—
115C5×(C2×D3)⋊C4C2311yescharacteristic
116C5×(C2×D3)⋊C4C2311yescharacteristic
117C5×(C2×D3)⋊C4C2313yes—
118C5×(C2×D3)⋊C4C2313yes—
119C5×(C2×D3)⋊C4C2316yes—
120C5×(C2×D3)⋊C4C2316yes—
121C5×C4⋊Dic3C2313yes—
122C5×C4⋊Dic3C2313yes—
123C5×C4⋊Dic3C2313yes—
124C5×C4⋊Dic3C2313yes—
125C5×Dic3⋊C4C2311yescharacteristic
126C5×Dic3⋊C4C2311yescharacteristic
127C5×Dic3⋊C4C2313yes—
128C5×Dic3⋊C4C2313yes—
129C5×Dic3⋊C4C2316yes—
130C5×Dic3⋊C4C2316yes—
131C4×C5×Dic3C2313yes—
132C4×C5×Dic3C2313yes—
133C4×C5×Dic3C2313yes—
134C4×C5×Dic3C2313yes—
135C4×C5×Dic3C2313yes—
136C4×C5×Dic3C2311yescharacteristic
137C3×C4×#41C2×C511yescharacteristic, complemented
138#5834C2×C511yescharacteristic, complemented
139#5831C2×C511yescharacteristic, complemented
140#5576C2×C511yescharacteristic, complemented
141C4×#239C2×C511yescharacteristic, complemented
142C4×D3×Q8C2×C511yescharacteristic, complemented
143#5569C2×C511yescharacteristic, complemented
144#5559C2×C513yescomplemented
145#5558C2×C513yescomplemented
146#5557C2×C513yescomplemented
147#5548C2×C513yescomplemented
148#5533C2×C513yescomplemented
149#5530C2×C513yescomplemented
150#5479C2×C513yescomplemented
151C4×#235C2×C513yescomplemented
152C2×C5×#41—31no—
153C2×C5×#41—33no—
154C2×C5×#41C2×D311yescharacteristic
155C22×C5×Q8—31no—
156C5×C4⋊Q8—33no—
157C5×#127—33no—
158C5×#126—36no—
159C5×#126—36no—
160C5×#125—33no—
161C5×#125—33no—
162C5×#124—33no—
163C5×#124—36no—
164C5×#124—33no—
165C5×#123—36no—
166C5×#123—36no—
167C5×C22⋊Q8—33no—
168C5×C22⋊Q8—33no—
169C5×#121—33no—
170C5×#121—33no—
171C5×#121—33no—
172C5×#121—33no—
173C5×#121—36no—
174C4×C5×Q8—31no—
175C4×C5×Q8—31no—
176C4×C5×Q8—33no—
177C4×C5×Q8—33no—
178C4×C5×Q8—33no—
179C4×C5×Q8—33no—
180C4×C5×Q8C2×D311yescharacteristic
181C4×C5×Q8C2×D311yescharacteristic
182C4×C5×D4—33no—
183C4×C5×D4—33no—
184C4×C5×D4—33no—
185C4×C5×D4—33no—
186C4×C5×D4—36no—
187C4×C5×D4—33no—
188C4×C5×D4—33no—
189C4×C5×D4—33no—
190C4×C5×D4—33no—
191C4×C5×D4C2×D313yes—
192C4×C5×D4C2×D313yes—
193C5×#117—33no—
194C5×#117—33no—
195C5×#117—31no—
196C5×#117—33no—
197C5×#117C2×D313yes—
198C2×C5×C4⋊C4—33no—
199C2×C42×C5—33no—
200C2×C42×C5—33no—
201C2×C42×C5C2×D313yes—
202#3480—31noSylow
203C23×C3×C5C2413yes—
204C22×C5×D3C2413yes—
205C22×C5×D3C2411yescharacteristic
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
217C5×#67—26no—
218C5×#67—26no—
219C5×#67—46no—
220C2×C5×Dic3C2411yescharacteristic
221C2×C5×Dic3C2411yescharacteristic
222C2×C5×Dic3C2413yes—
223C2×C5×Dic3C2413yes—
224C2×C5×Dic3C2413yes—
225C2×C5×Dic3C2411yescharacteristic
226C5×D12—26no—
227C5×D12—26no—
228C4×C5×D3—26no—
229C4×C5×D3—26no—
230C4×C5×D3—26no—
231C4×C5×D3—43no—
232C4×C5×D3—43no—
233C4×C5×D3#4114yescomplemented
234C5×Dic6—26no—
235C5×Dic6—26no—
236C2×C3×#41C22×C511yescharacteristic
237C2×#239C22×C511yescharacteristic
238C2×D3×Q8C22×C511yescharacteristic
239C2×#235C22×C513yes—
240C3×C4×Q8C22×C511yescharacteristic
241C3×C4×Q8C22×C511yescharacteristic
242C3×C4×D4C22×C513yes—
243C3×C4×D4C22×C513yes—
244C3×#117C22×C513yes—
245C2×C3×C42C22×C513yes—
246Q8×Dic3C22×C511yescharacteristic
247Q8×Dic3C22×C511yescharacteristic
248#940C22×C513yes—
249#938C22×C513yes—
250#938C22×C513yes—
251#936C22×C513yes—
252#930C22×C513yes—
253#929C22×C516yes—
254C4×#67C22×C513yes—
255C4×#67C22×C513yes—
256C4×#67C22×C513yes—
257C4×#67C22×C513yes—
258C4×#67C22×C516yes—
259#926C22×C513yes—
260#924C22×C513yes—
261#897C22×C513yes—
262#895C22×C513yes—
263#893C22×C513yes—
264#892C22×C513yes—
265D3×C4⋊C4C22×C513yes—
266#890C22×C513yes—
267#888C22×C513yes—
268#887C22×C513yes—
269#885C22×C516yes—
270#884C22×C516yes—
271#883C22×C516yes—
272#879C22×C516yes—
273#876C22×C516yes—
274#875C22×C513yes—
275C4×D12C22×C513yes—
276C4×D12C22×C513yes—
277C4×D12C22×C513yes—
278#872C22×C511yescharacteristic
279#872C22×C513yes—
280C42×D3C22×C513yes—
281C42×D3C22×C513yes—
282#870C22×C513yes—
283C4×Dic6C22×C513yes—
284C4×Dic6C22×C513yes—
285C4×Dic6C22×C513yes—
286C5×#41—24no—
287C5×#41—612no—
288C5×#41—64no—
289C2×C5×Q8—33no—
290C2×C5×Q8—33no—
291C2×C5×Q8—64no—
292C2×C5×Q8C22×D311yescharacteristic
293C2×C5×D4—33no—
294C2×C5×D4—33no—
295C2×C5×D4—36no—
296C2×C5×D4—33no—
297C2×C5×D4—33no—
298C2×C5×D4C22×D313yes—
299C22×C4×C5—31no—
300C22×C4×C5—33no—
301C22×C4×C5—33no—
302C22×C4×C5—33no—
303C22×C4×C5—33no—
304C22×C4×C5—33no—
305C22×C4×C5C22×D313yes—
306C22×C4×C5C22×D313yes—
307C22×C4×C5C22×D313yes—
308C5×C4⋊C4—33no—
309C5×C4⋊C4—36no—
310C5×C4⋊C4—31no—
311C5×C4⋊C4—31no—
312C5×C4⋊C4—33no—
313C5×C4⋊C4—33no—
314C5×C4⋊C4—33no—
315C5×C4⋊C4—33no—
316C5×C4⋊C4—33no—
317C5×C4⋊C4—36no—
318C5×C4⋊C4C22×D313yes—
319C5×C4⋊C4C22×D313yes—
320C5×C22⋊C4—33no—
321C5×C22⋊C4—33no—
322C5×C22⋊C4—36no—
323C5×C22⋊C4—31no—
324C5×C22⋊C4—31no—
325C5×C22⋊C4—33no—
326C5×C22⋊C4—36no—
327C5×C22⋊C4—33no—
328C5×C22⋊C4—36no—
329C5×C22⋊C4C22×D316yes—
330C42×C5—33no—
331C42×C5—33no—
332C42×C5—33no—
333C42×C5—33no—
334C42×C5—31no—
335C42×C5—33no—
336C42×C5C22×D313yes—
337C42×C5C22×D313yes—
338C42×C5C22×D313yes—
339C42×C5C22×D311yescharacteristic
340#559—33no—
341#557—31no—
342#556—33no—
343#553—33no—
344#553—33no—
345#550—31no—
346#548—31no—
347#548—31no—
348#532—33no—
349#529—33no—
350#529—33no—
351C4×#41—31no—
352C4×#41—33no—
353C4×#41C5×D311yescharacteristic, complemented
354C2×C4×Q8—31no—
355C22×C3×C5—23no—
356C22×C3×C5—23no—
357C22×C3×C5—23no—
358C22×C3×C5C2511yescharacteristic
359C2×C5×D3—21no—
360C2×C5×D3—21no—
361C2×C5×D3—23no—
362C2×C5×D3—23no—
363C2×C5×D3—23no—
364C2×C5×D3C2×#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—
371C5×Dic3—23no—
372C5×Dic3—23no—
373C5×Dic3—21no—
374C5×Dic3—21no—
375C5×Dic3—23no—
376C5×Dic3C2×#4112yes—
377C3×#41—24no—
378C2×C3×Q8C23×C511yescharacteristic
379C2×C3×D4C23×C513yes—
380C22×C3×C4C23×C513yes—
381C22×C3×C4C23×C513yes—
382C22×C3×C4C23×C513yes—
383C2×#67C23×C513yes—
384C2×#67C23×C513yes—
385C2×#67C23×C516yes—
386#239—24no—
387D3×Q8—24no—
388#235—212no—
389C2×D12C23×C513yes—
390C2×D12C23×C513yes—
391C2×C4×D3C23×C513yes—
392C2×C4×D3C23×C513yes—
393C2×C4×D3C23×C513yes—
394C2×C4×D3C23×C513yes—
395C2×C4×D3C23×C513yes—
396C2×C4×D3C23×C511yescharacteristic
397C2×Dic6C23×C513yes—
398C2×Dic6C23×C513yes—
399C3×C4⋊C4C23×C513yes—
400C3×C4⋊C4C23×C513yes—
401C3×C22⋊C4C23×C516yes—
402C3×C42C23×C513yes—
403C3×C42C23×C513yes—
404C3×C42C23×C513yes—
405C3×C42C23×C511yescharacteristic
406#217C23×C513yes—
407#217C23×C516yes—
408#217C23×C513yes—
409(C2×D3)⋊C4C23×C511yescharacteristic
410(C2×D3)⋊C4C23×C511yescharacteristic
411(C2×D3)⋊C4C23×C513yes—
412(C2×D3)⋊C4C23×C513yes—
413(C2×D3)⋊C4C23×C516yes—
414(C2×D3)⋊C4C23×C516yes—
415C4⋊Dic3C23×C513yes—
416C4⋊Dic3C23×C513yes—
417C4⋊Dic3C23×C513yes—
418C4⋊Dic3C23×C513yes—
419Dic3⋊C4C23×C511yescharacteristic
420Dic3⋊C4C23×C511yescharacteristic
421Dic3⋊C4C23×C513yes—
422Dic3⋊C4C23×C513yes—
423Dic3⋊C4C23×C516yes—
424Dic3⋊C4C23×C516yes—
425C4×Dic3C23×C513yes—
426C4×Dic3C23×C513yes—
427C4×Dic3C23×C513yes—
428C4×Dic3C23×C513yes—
429C4×Dic3C23×C513yes—
430C4×Dic3C23×C511yescharacteristic
431C23×C5—31no—
432C23×C5—33no—
433C23×C5C23×D313yes—
434C5×Q8—66no—
435C5×Q8—66no—
436C5×Q8#23514yescomplemented
437C5×D4—26no—
438C5×D4—66no—
439C5×D4—66no—
440C5×D4—66no—
441C5×D4—66no—
442C5×D4—126no—
443C2×C4×C5—26no—
444C2×C4×C5—26no—
445C2×C4×C5—31no—
446C2×C4×C5—34no—
447C2×C4×C5—31no—
448C2×C4×C5—31no—
449C2×C4×C5—33no—
450C2×C4×C5—33no—
451C2×C4×C5—33no—
452C2×C4×C5—43no—
453C2×C4×C5—66no—
454C2×C4×C5—66no—
455C2×C4×C5—66no—
456C2×C4×C5—123no—
457C2×C4×C5—123no—
458C2×C4×C5C23×D313yes—
459C2×C4×C5C23×D311yescharacteristic
460C2×C4×C5C23×D311yescharacteristic
461C2×C4×C5C23×D313yes—
462C2×C4×C5C23×D313yes—
463C2×C4×C5C23×D311yescharacteristic
464C2×#41—31no—
465C2×#41—33no—
466C2×#41C2×C5×D311yescharacteristic
467C22×Q8—31no—
468C4⋊Q8—33no—
469#127—33no—
470#126—36no—
471#126—36no—
472#125—33no—
473#125—33no—
474#124—33no—
475#124—36no—
476#124—33no—
477#123—36no—
478#123—36no—
479C22⋊Q8—33no—
480C22⋊Q8—33no—
481#121—33no—
482#121—33no—
483#121—33no—
484#121—33no—
485#121—36no—
486C4×Q8—31no—
487C4×Q8—31no—
488C4×Q8—33no—
489C4×Q8—33no—
490C4×Q8—33no—
491C4×Q8—33no—
492C4×Q8C2×C5×D311yescharacteristic
493C4×Q8C2×C5×D311yescharacteristic
494C4×D4—33no—
495C4×D4—33no—
496C4×D4—33no—
497C4×D4—33no—
498C4×D4—36no—
499C4×D4—33no—
500C4×D4—33no—
501C4×D4—33no—
502C4×D4—33no—
503C4×D4C2×C5×D313yes—
504C4×D4C2×C5×D313yes—
505#117—33no—
506#117—33no—
507#117—31no—
508#117—33no—
509#117C2×C5×D313yes—
510C2×C4⋊C4—33no—
511C2×C42—33no—
512C2×C42—33no—
513C2×C42C2×C5×D313yes—
514C2×C3×C5—43no—
515C2×C3×C5C22×#4111yescharacteristic
516C2×C3×C5C22×#4111yescharacteristic
517C2×C3×C5#58511yescharacteristic
518C5×D3—22no—
519C5×D3—43no—
520C23×C3C24×C513yes—
521C22×D3C24×C513yes—
522C22×D3C24×C511yescharacteristic
523C3×Q8C5×#4114yescomplemented
524C3×D4—26no—
525C2×C3×C4—26no—
526C2×C3×C4—26no—
527C2×C3×C4—43no—
528C2×C3×C4C24×C513yes—
529C2×C3×C4C24×C511yescharacteristic
530C2×C3×C4C24×C511yescharacteristic
531C2×C3×C4C24×C513yes—
532C2×C3×C4C24×C511yescharacteristic
533C2×C3×C4C24×C513yes—
534#67—26no—
535#67—26no—
536#67—46no—
537C2×Dic3C24×C511yescharacteristic
538C2×Dic3C24×C511yescharacteristic
539C2×Dic3C24×C513yes—
540C2×Dic3C24×C513yes—
541C2×Dic3C24×C513yes—
542C2×Dic3C24×C511yescharacteristic
543D12—26no—
544D12—26no—
545C4×D3—26no—
546C4×D3—26no—
547C4×D3—26no—
548C4×D3—43no—
549C4×D3—43no—
550C4×D3C5×#4114yescomplemented
551Dic6—26no—
552Dic6—26no—
553C22×C5—23no—
554C22×C5—23no—
555C22×C5—23no—
556C22×C5—32no—
557C22×C5—61no—
558C22×C5—61no—
559C22×C5—63no—
560C22×C5—63no—
561C22×C5—63no—
562C22×C5C24×D311yescharacteristic
563C4×C5—21no—
564C4×C5—23no—
565C4×C5—21no—
566C4×C5—23no—
567C4×C5—32no—
568C4×C5—61no—
569C4×C5—63no—
570C4×C5—63no—
571C4×C5—61no—
572C4×C5—63no—
573C4×C5C2×#23516yes—
574C4×C5D3×#4112yes—
575#41—24no—
576#41—612no—
577#41—64no—
578C2×Q8—33no—
579C2×Q8—33no—
580C2×Q8—64no—
581C2×Q8C22×C5×D311yescharacteristic
582C2×D4—33no—
583C2×D4—33no—
584C2×D4—36no—
585C2×D4—33no—
586C2×D4—33no—
587C2×D4C22×C5×D313yes—
588C22×C4—31no—
589C22×C4—33no—
590C22×C4—33no—
591C22×C4—33no—
592C22×C4—33no—
593C22×C4—33no—
594C22×C4C22×C5×D313yes—
595C22×C4C22×C5×D313yes—
596C22×C4C22×C5×D313yes—
597C4⋊C4—33no—
598C4⋊C4—36no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—33no—
602C4⋊C4—33no—
603C4⋊C4—33no—
604C4⋊C4—33no—
605C4⋊C4—33no—
606C4⋊C4—36no—
607C4⋊C4C22×C5×D313yes—
608C4⋊C4C22×C5×D313yes—
609C22⋊C4—33no—
610C22⋊C4—33no—
611C22⋊C4—36no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—33no—
615C22⋊C4—36no—
616C22⋊C4—33no—
617C22⋊C4—36no—
618C22⋊C4C22×C5×D316yes—
619C42—31no—
620C42—33no—
621C42—33no—
622C42—33no—
623C42—33no—
624C42—33no—
625C42C22×C5×D313yes—
626C42C22×C5×D311yescharacteristic
627C42C22×C5×D313yes—
628C42C22×C5×D313yes—
629C3×C5#348011yescharacteristic, complemented, Hall
630C22×C3—23no—
631C22×C3—23no—
632C22×C3—23no—
633C22×C3C25×C511yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—23no—
637C2×D3—23no—
638C2×D3—23no—
639C2×D3C2×C5×#4112yes—
640C3×C4—23no—
641C3×C4—21no—
642C3×C4—23no—
643C3×C4—21no—
644C3×C4C2×C5×#4116yes—
645C3×C4C2×C5×#4112yes—
646Dic3—23no—
647Dic3—23no—
648Dic3—21no—
649Dic3—21no—
650Dic3—23no—
651Dic3C2×C5×#4112yes—
652C2×C5—43no—
653C2×C5—62no—
654C2×C5—123no—
655C2×C5C22×#23511yescharacteristic
656C2×C5C2×D3×#4111yescharacteristic
657C2×C5#596411yescharacteristic
658C23—31no—
659C23—33no—
660C23C23×C5×D313yes—
661Q8—66no—
662Q8—66no—
663Q8C5×#23514yescomplemented
664D4—26no—
665D4—66no—
666D4—66no—
667D4—66no—
668D4—66no—
669D4—126no—
670C2×C4—26no—
671C2×C4—26no—
672C2×C4—31no—
673C2×C4—34no—
674C2×C4—31no—
675C2×C4—31no—
676C2×C4—33no—
677C2×C4—33no—
678C2×C4—33no—
679C2×C4—43no—
680C2×C4—66no—
681C2×C4—66no—
682C2×C4—66no—
683C2×C4—123no—
684C2×C4—123no—
685C2×C4C23×C5×D313yes—
686C2×C4C23×C5×D311yescharacteristic
687C2×C4C23×C5×D311yescharacteristic
688C2×C4C23×C5×D313yes—
689C2×C4C23×C5×D313yes—
690C2×C4C23×C5×D311yescharacteristic
691C2×C3—43no—
692C2×C3C22×C5×#4111yescharacteristic
693C2×C3C22×C5×#4111yescharacteristic
694C2×C3C5×#58511yescharacteristic
695D3—22no—
696D3—43no—
697C5#8584211yescharacteristic, direct product factor, Sylow
698C22—23no—
699C22—23no—
700C22—23no—
701C22—32no—
702C22—61no—
703C22—61no—
704C22—63no—
705C22—63no—
706C22—63no—
707C22C24×C5×D311yescharacteristic
708C4—21no—
709C4—23no—
710C4—21no—
711C4—23no—
712C4—32no—
713C4—61no—
714C4—63no—
715C4—63no—
716C4—61no—
717C4—63no—
718C4C2×C5×#23516yes—
719C4C5×D3×#4112yes—
720C3C5×#348011yescharacteristic, complemented, Sylow
721C2—43no—
722C2—62no—
723C2—123no—
724C2C22×C5×#23511yescharacteristic
725C2C2×C5×D3×#4111yescharacteristic
726C2C5×#596411yescharacteristic
subgroupG/H
centerC2×C4×C5C23×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC3×C4×C5×#41C2
socleC22×C3×C5C25
hypercenterC4×C5×#41D3
hypocenterC3C5×#3480
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C4×C5×#41

Complements

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

NH ≅ G/Ntype
1. C3×C4×C5×#41C2semidirect
2. C5×#5834C2semidirect
3. C5×#5831C2semidirect
4. C5×#5576C2semidirect
5. C4×C5×#239C2semidirect
6. C4×C5×D3×Q8C2semidirect
7. C5×#5569C2semidirect
8. C5×#5559C2semidirect
9. C5×#5558C2semidirect
10. C5×#5557C2semidirect
11. C5×#5548C2semidirect
12. C5×#5533C2semidirect
13. C5×#5530C2semidirect
14. C5×#5479C2semidirect
15. C4×C5×#235C2semidirect
67. #85842C5direct (N × H)
81. C4×C5×#41D3semidirect
137. C3×C4×#41C2×C5semidirect
138. #5834C2×C5semidirect
139. #5831C2×C5semidirect
140. #5576C2×C5semidirect
141. C4×#239C2×C5semidirect
142. C4×D3×Q8C2×C5semidirect
143. #5569C2×C5semidirect
144. #5559C2×C5semidirect
145. #5558C2×C5semidirect
146. #5557C2×C5semidirect
147. #5548C2×C5semidirect
148. #5533C2×C5semidirect
149. #5530C2×C5semidirect
150. #5479C2×C5semidirect
151. C4×#235C2×C5semidirect
206. C3×C5×Q8#41semidirect
233. C4×C5×D3#41semidirect
353. C4×#41C5×D3semidirect
436. C5×Q8#235semidirect
523. C3×Q8C5×#41semidirect
550. C4×D3C5×#41semidirect
629. C3×C5#3480semidirect
663. Q8C5×#235semidirect
697. C5#85842direct (N × H)
720. C3C5×#3480semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C5×#412
C5×#58342
C5×#58312
C5×#55762
C4×C5×#2392
C4×C5×D3×Q82
C5×#55692
C5×#55592
C5×#55582
C5×#55572
C5×#55482
C5×#55332
C5×#55302
C5×#54792
C4×C5×#2352
C5×#34803
#858425