Finite Group Databasebeta

← C5×#86711 #14484768

Subgroups — C5×#86711 #14484768

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
2C5×#5834C211yesmaximal, characteristic, complemented
3C5×Dic3×#41C211yesmaximal, characteristic, complemented
4C5×#5817C211yesmaximal, characteristic, complemented
5C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
6C5×#5681C213yesmaximal, complemented
7C5×#5680C213yesmaximal, complemented
8C5×#5641C213yesmaximal, complemented
9C5×#5624C213yesmaximal, complemented
10C5×#5618C213yesmaximal, complemented
11C5×#5596C213yesmaximal, complemented
12C4×C5×#239C211yesmaximal, characteristic, complemented
13C5×#5569C211yesmaximal, characteristic, complemented
14C5×#5565C213yesmaximal, complemented
15C4×C5×#237C213yesmaximal, complemented
16C5×#3480—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×Q8C2211yescharacteristic
19C2×C5×#239C2211yescharacteristic
20C2×C5×#237C2213yes—
21C3×C5×#124C2213yes—
22C3×C5×C22⋊Q8C2213yes—
23C3×C5×#121C2213yes—
24C3×C4×C5×Q8C2211yescharacteristic
25C3×C4×C5×D4C2213yes—
26C5×#947C2213yes—
27C5×#946C2213yes—
28C5×Q8×Dic3C2213yes—
29C5×Q8×Dic3C2213yes—
30C5×Q8×Dic3C2211yescharacteristic
31C5×Q8×Dic3C2211yescharacteristic
32C5×Q8×Dic3C2211yescharacteristic
33C5×#940C2213yes—
34C5×#939C2216yes—
35C5×#938C2213yes—
36C5×D4×Dic3C2213yes—
37C5×D4×Dic3C2213yes—
38C5×D4×Dic3C2213yes—
39C5×#930C2213yes—
40C5×#930C2213yes—
41C4×C5×#67C2213yes—
42C4×C5×#67C2213yes—
43C5×#926C2213yes—
44C2×C5×C4⋊Dic3C2213yes—
45C2×C4×C5×Dic3C2213yes—
46C2×C4×C5×Dic3C2213yes—
47C5×#898C2216yes—
48C5×#893C2213yes—
49C5×#892C2213yes—
50C5×#892C2213yes—
51C5×#890C2213yes—
52C5×#888C2213yes—
53C5×#887C2213yes—
54C5×#886C2216yes—
55C5×#885C2216yes—
56C5×#883C2216yes—
57C5×#67⋊C4C2216yes—
58C5×#67⋊C4C2213yes—
59C5×#67⋊C4C2213yes—
60C5×#879C2216yes—
61C5×#877C2213yes—
62C5×#877C2211yescharacteristic
63C4×C5×D12C2213yes—
64C42×C5×D3C2213yes—
65C5×#870C2213yes—
66C4×C5×Dic6C2213yes—
67#86711C511yesmaximal, 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×#548D311yescharacteristic, complemented
76C5×#532—33no—
77C5×#529—33no—
78C5×#529—33no—
79C4×C5×#41—31no—
80C4×C5×#41—31no—
81C4×C5×#41—33no—
82C2×C4×C5×Q8—31no—
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×C5×#67C2313yes—
92C2×C5×#67C2313yes—
93C2×C5×#67C2316yes—
94C22×C5×Dic3C2313yes—
95C22×C5×Dic3C2313yes—
96C22×C5×Dic3C2313yes—
97C22×C5×Dic3C2311yescharacteristic
98C5×#239—24no—
99C5×#237—212no—
100C2×C5×D12C2313yes—
101C2×C4×C5×D3C2313yes—
102C2×C4×C5×D3C2313yes—
103C2×C4×C5×D3C2313yes—
104C2×C5×Dic6C2313yes—
105C3×C5×C4⋊C4C2313yes—
106C3×C5×C4⋊C4C2313yes—
107C3×C5×C22⋊C4C2311yescharacteristic
108C3×C5×C22⋊C4C2313yes—
109C3×C5×C22⋊C4C2316yes—
110C3×C42×C5C2313yes—
111C5×#217C2313yes—
112C5×#217C2311yescharacteristic
113C5×#217C2316yes—
114C5×(C2×D3)⋊C4C2316yes—
115C5×(C2×D3)⋊C4C2316yes—
116C5×(C2×D3)⋊C4C2313yes—
117C5×(C2×D3)⋊C4C2313yes—
118C5×C4⋊Dic3C2313yes—
119C5×C4⋊Dic3C2313yes—
120C5×C4⋊Dic3C2313yes—
121C5×C4⋊Dic3C2313yes—
122C5×C4⋊Dic3C2316yes—
123C5×Dic3⋊C4C2311yescharacteristic
124C5×Dic3⋊C4C2313yes—
125C5×Dic3⋊C4C2316yes—
126C5×Dic3⋊C4C2313yes—
127C5×Dic3⋊C4C2311yescharacteristic
128C4×C5×Dic3C2313yes—
129C4×C5×Dic3C2313yes—
130C4×C5×Dic3C2311yescharacteristic
131C4×C5×Dic3C2313yes—
132C4×C5×Dic3C2313yes—
133C4×C5×Dic3C2313yes—
134C4×C5×Dic3C2311yescharacteristic
135C4×C5×Dic3C2313yes—
136C4×C5×Dic3C2313yes—
137C3×#548C2×C511yescharacteristic, complemented
138#5834C2×C511yescharacteristic, complemented
139Dic3×#41C2×C511yescharacteristic, complemented
140#5817C2×C511yescharacteristic, complemented
141C2×Q8×Dic3C2×C511yescharacteristic, complemented
142#5681C2×C513yescomplemented
143#5680C2×C513yescomplemented
144#5641C2×C513yescomplemented
145#5624C2×C513yescomplemented
146#5618C2×C513yescomplemented
147#5596C2×C513yescomplemented
148C4×#239C2×C511yescharacteristic, complemented
149#5569C2×C511yescharacteristic, complemented
150#5565C2×C513yescomplemented
151C4×#237C2×C513yescomplemented
152C2×C5×#41—31no—
153C2×C5×#41—33no—
154C2×C5×#41C2×D311yescharacteristic
155C22×C5×Q8C2×D311yescharacteristic
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×#124C2×D313yes—
165C5×#123—36no—
166C5×#123—36no—
167C5×C22⋊Q8—33no—
168C5×C22⋊Q8C2×D313yes—
169C5×#121—33no—
170C5×#121—36no—
171C5×#121—33no—
172C5×#121—33no—
173C5×#121C2×D313yes—
174C4×C5×Q8—31no—
175C4×C5×Q8—33no—
176C4×C5×Q8—31no—
177C4×C5×Q8—33no—
178C4×C5×Q8—31no—
179C4×C5×Q8—33no—
180C4×C5×Q8—33no—
181C4×C5×Q8C2×D311yescharacteristic
182C4×C5×D4—33no—
183C4×C5×D4—33no—
184C4×C5×D4—33no—
185C4×C5×D4—33no—
186C4×C5×D4—33no—
187C4×C5×D4—33no—
188C4×C5×D4—33no—
189C4×C5×D4—33no—
190C4×C5×D4—36no—
191C4×C5×D4—33no—
192C4×C5×D4C2×D313yes—
193C5×#117—33no—
194C5×#117—33no—
195C5×#117—33no—
196C5×#117—31no—
197C5×#117—33no—
198C2×C5×C4⋊C4—33no—
199C2×C42×C5—33no—
200C2×C42×C5—33no—
201C2×C42×C5—33no—
202#3480—31noSylow
203C23×C3×C5C2413yes—
204C23×C3×C5C2411yescharacteristic
205C22×C5×D3C2413yes—
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—
217C5×#67—26no—
218C5×#67—26no—
219C5×#67—46no—
220C2×C5×Dic3—26no—
221C2×C5×Dic3—43no—
222C2×C5×Dic3—43no—
223C2×C5×Dic3#4114yescomplemented
224C2×C5×Dic3C2411yescharacteristic
225C2×C5×Dic3C2411yescharacteristic
226C2×C5×Dic3C2413yes—
227C2×C5×Dic3C2413yes—
228C2×C5×Dic3C2413yes—
229C2×C5×Dic3C2411yescharacteristic
230C2×C5×Dic3C2411yescharacteristic
231C5×D12—26no—
232C4×C5×D3—26no—
233C4×C5×D3—26no—
234C4×C5×D3—43no—
235C5×Dic6—26no—
236C2×C3×#41C22×C511yescharacteristic
237C22×C3×Q8C22×C511yescharacteristic
238C2×#239C22×C511yescharacteristic
239C2×#237C22×C513yes—
240C3×#124C22×C513yes—
241C3×C22⋊Q8C22×C513yes—
242C3×#121C22×C513yes—
243C3×C4×Q8C22×C511yescharacteristic
244C3×C4×D4C22×C513yes—
245#947C22×C513yes—
246#946C22×C513yes—
247Q8×Dic3C22×C513yes—
248Q8×Dic3C22×C513yes—
249Q8×Dic3C22×C511yescharacteristic
250Q8×Dic3C22×C511yescharacteristic
251Q8×Dic3C22×C511yescharacteristic
252#940C22×C513yes—
253#939C22×C516yes—
254#938C22×C513yes—
255D4×Dic3C22×C513yes—
256D4×Dic3C22×C513yes—
257D4×Dic3C22×C513yes—
258#930C22×C513yes—
259#930C22×C513yes—
260C4×#67C22×C513yes—
261C4×#67C22×C513yes—
262#926C22×C513yes—
263C2×C4⋊Dic3C22×C513yes—
264C2×C4×Dic3C22×C513yes—
265C2×C4×Dic3C22×C513yes—
266#898C22×C516yes—
267#893C22×C513yes—
268#892C22×C513yes—
269#892C22×C513yes—
270#890C22×C513yes—
271#888C22×C513yes—
272#887C22×C513yes—
273#886C22×C516yes—
274#885C22×C516yes—
275#883C22×C516yes—
276#67⋊C4C22×C516yes—
277#67⋊C4C22×C513yes—
278#67⋊C4C22×C513yes—
279#879C22×C516yes—
280#877C22×C513yes—
281#877C22×C511yescharacteristic
282C4×D12C22×C513yes—
283C42×D3C22×C513yes—
284#870C22×C513yes—
285C4×Dic6C22×C513yes—
286C5×#41—24no—
287C5×#41—612no—
288C5×#41—64no—
289C2×C5×Q8—24no—
290C2×C5×Q8—33no—
291C2×C5×Q8C22×D313yes—
292C2×C5×Q8C22×D311yescharacteristic
293C2×C5×D4—33no—
294C2×C5×D4—33no—
295C2×C5×D4—36no—
296C2×C5×D4—33no—
297C2×C5×D4C22×D313yes—
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×C5—33no—
306C22×C4×C5C22×D313yes—
307C22×C4×C5C22×D313yes—
308C5×C4⋊C4—33no—
309C5×C4⋊C4—33no—
310C5×C4⋊C4—36no—
311C5×C4⋊C4—31no—
312C5×C4⋊C4—31no—
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—31no—
321C5×C22⋊C4—33no—
322C5×C22⋊C4—36no—
323C5×C22⋊C4—33no—
324C5×C22⋊C4—36no—
325C5×C22⋊C4—33no—
326C5×C22⋊C4—36no—
327C5×C22⋊C4C22×D311yescharacteristic
328C5×C22⋊C4C22×D313yes—
329C5×C22⋊C4C22×D316yes—
330C42×C5—31no—
331C42×C5—31no—
332C42×C5—33no—
333C42×C5—33no—
334C42×C5—33no—
335C42×C5—33no—
336C42×C5—33no—
337C42×C5—33no—
338C42×C5—33no—
339C42×C5C22×D313yes—
340#559—33no—
341#557—31no—
342#556—33no—
343#553—33no—
344#553—33no—
345#550—31no—
346#548—31no—
347#548C5×D311yescharacteristic, complemented
348#532—33no—
349#529—33no—
350#529—33no—
351C4×#41—31no—
352C4×#41—31no—
353C4×#41—33no—
354C2×C4×Q8—31no—
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×C5×D3—23no—
363C2×C5×D3—23no—
364C2×C5×D3—23no—
365C3×C4×C5—23no—
366C3×C4×C5—21no—
367C3×C4×C5—23no—
368C3×C4×C5—21no—
369C3×C4×C5C2×#4116yes—
370C5×Dic3—23no—
371C5×Dic3—21no—
372C5×Dic3—23no—
373C5×Dic3—21no—
374C5×Dic3—23no—
375C5×Dic3C2×#4112yes—
376C5×Dic3C2×#4112yes—
377C3×#41—24no—
378C2×C3×Q8—24no—
379C2×C3×Q8C23×C513yes—
380C2×C3×Q8C23×C511yescharacteristic
381C2×C3×D4C23×C513yes—
382C2×C3×D4C23×C513yes—
383C22×C3×C4C23×C513yes—
384C22×C3×C4C23×C513yes—
385C2×#67C23×C513yes—
386C2×#67C23×C513yes—
387C2×#67C23×C516yes—
388C22×Dic3C23×C513yes—
389C22×Dic3C23×C513yes—
390C22×Dic3C23×C513yes—
391C22×Dic3C23×C511yescharacteristic
392#239—24no—
393#237—212no—
394C2×D12C23×C513yes—
395C2×C4×D3C23×C513yes—
396C2×C4×D3C23×C513yes—
397C2×C4×D3C23×C513yes—
398C2×Dic6C23×C513yes—
399C3×C4⋊C4C23×C513yes—
400C3×C4⋊C4C23×C513yes—
401C3×C22⋊C4C23×C511yescharacteristic
402C3×C22⋊C4C23×C513yes—
403C3×C22⋊C4C23×C516yes—
404C3×C42C23×C513yes—
405#217C23×C513yes—
406#217C23×C511yescharacteristic
407#217C23×C516yes—
408(C2×D3)⋊C4C23×C516yes—
409(C2×D3)⋊C4C23×C516yes—
410(C2×D3)⋊C4C23×C513yes—
411(C2×D3)⋊C4C23×C513yes—
412C4⋊Dic3C23×C513yes—
413C4⋊Dic3C23×C513yes—
414C4⋊Dic3C23×C513yes—
415C4⋊Dic3C23×C513yes—
416C4⋊Dic3C23×C516yes—
417Dic3⋊C4C23×C511yescharacteristic
418Dic3⋊C4C23×C513yes—
419Dic3⋊C4C23×C516yes—
420Dic3⋊C4C23×C513yes—
421Dic3⋊C4C23×C511yescharacteristic
422C4×Dic3C23×C513yes—
423C4×Dic3C23×C513yes—
424C4×Dic3C23×C511yescharacteristic
425C4×Dic3C23×C513yes—
426C4×Dic3C23×C513yes—
427C4×Dic3C23×C513yes—
428C4×Dic3C23×C511yescharacteristic
429C4×Dic3C23×C513yes—
430C4×Dic3C23×C513yes—
431C23×C5—33no—
432C23×C5C23×D313yes—
433C23×C5C23×D311yescharacteristic
434C5×Q8—26no—
435C5×Q8—66no—
436C5×Q8#23714yescomplemented
437C5×D4—26no—
438C5×D4—26no—
439C5×D4—66no—
440C5×D4—66no—
441C5×D4—66no—
442C5×D4—126no—
443C2×C4×C5—26no—
444C2×C4×C5—26no—
445C2×C4×C5—34no—
446C2×C4×C5—31no—
447C2×C4×C5—31no—
448C2×C4×C5—31no—
449C2×C4×C5—31no—
450C2×C4×C5—33no—
451C2×C4×C5—33no—
452C2×C4×C5—33no—
453C2×C4×C5—66no—
454C2×C4×C5—66no—
455C2×C4×C5—66no—
456C2×C4×C5—123no—
457C2×C4×C5—123no—
458C2×C4×C5—123no—
459C2×C4×C5C23×D311yescharacteristic
460C2×C4×C5C23×D313yes—
461C2×C4×C5C23×D311yescharacteristic
462C2×C4×C5C23×D313yes—
463C2×C4×C5C23×D313yes—
464C2×#41—31no—
465C2×#41—33no—
466C2×#41C2×C5×D311yescharacteristic
467C22×Q8C2×C5×D311yescharacteristic
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#124C2×C5×D313yes—
477#123—36no—
478#123—36no—
479C22⋊Q8—33no—
480C22⋊Q8C2×C5×D313yes—
481#121—33no—
482#121—36no—
483#121—33no—
484#121—33no—
485#121C2×C5×D313yes—
486C4×Q8—31no—
487C4×Q8—33no—
488C4×Q8—31no—
489C4×Q8—33no—
490C4×Q8—31no—
491C4×Q8—33no—
492C4×Q8—33no—
493C4×Q8C2×C5×D311yescharacteristic
494C4×D4—33no—
495C4×D4—33no—
496C4×D4—33no—
497C4×D4—33no—
498C4×D4—33no—
499C4×D4—33no—
500C4×D4—33no—
501C4×D4—33no—
502C4×D4—36no—
503C4×D4—33no—
504C4×D4C2×C5×D313yes—
505#117—33no—
506#117—33no—
507#117—33no—
508#117—31no—
509#117—33no—
510C2×C4⋊C4—33no—
511C2×C42—33no—
512C2×C42—33no—
513C2×C42—33no—
514C2×C3×C5—22no—
515C2×C3×C5—43no—
516C2×C3×C5C22×#4111yescharacteristic
517C2×C3×C5C22×#4111yescharacteristic
518C2×C3×C5#58511yescharacteristic
519C5×D3—43no—
520C23×C3C24×C513yes—
521C23×C3C24×C511yescharacteristic
522C22×D3C24×C513yes—
523C3×Q8—26no—
524C3×Q8C5×#4114yescomplemented
525C3×D4—26no—
526C3×D4—26no—
527C2×C3×C4—26no—
528C2×C3×C4—26no—
529C2×C3×C4C24×C511yescharacteristic
530C2×C3×C4C24×C513yes—
531C2×C3×C4C24×C511yescharacteristic
532C2×C3×C4C24×C513yes—
533C2×C3×C4C24×C513yes—
534#67—26no—
535#67—26no—
536#67—46no—
537C2×Dic3—26no—
538C2×Dic3—43no—
539C2×Dic3—43no—
540C2×Dic3C5×#4114yescomplemented
541C2×Dic3C24×C511yescharacteristic
542C2×Dic3C24×C511yescharacteristic
543C2×Dic3C24×C513yes—
544C2×Dic3C24×C513yes—
545C2×Dic3C24×C513yes—
546C2×Dic3C24×C511yescharacteristic
547C2×Dic3C24×C511yescharacteristic
548D12—26no—
549C4×D3—26no—
550C4×D3—26no—
551C4×D3—43no—
552Dic6—26no—
553C22×C5—21no—
554C22×C5—21no—
555C22×C5—23no—
556C22×C5—23no—
557C22×C5—23no—
558C22×C5—63no—
559C22×C5—63no—
560C22×C5—63no—
561C22×C5D3×#4112yes—
562C22×C5C24×D311yescharacteristic
563C4×C5—21no—
564C4×C5—23no—
565C4×C5—23no—
566C4×C5—21no—
567C4×C5—32no—
568C4×C5—32no—
569C4×C5—61no—
570C4×C5—63no—
571C4×C5—63no—
572C4×C5—61no—
573C4×C5—63no—
574C4×C5C2×#23716yes—
575#41—24no—
576#41—612no—
577#41—64no—
578C2×Q8—24no—
579C2×Q8—33no—
580C2×Q8C22×C5×D313yes—
581C2×Q8C22×C5×D311yescharacteristic
582C2×D4—33no—
583C2×D4—33no—
584C2×D4—36no—
585C2×D4—33no—
586C2×D4C22×C5×D313yes—
587C2×D4C22×C5×D313yes—
588C22×C4—31no—
589C22×C4—33no—
590C22×C4—33no—
591C22×C4—33no—
592C22×C4—33no—
593C22×C4—33no—
594C22×C4—33no—
595C22×C4C22×C5×D313yes—
596C22×C4C22×C5×D313yes—
597C4⋊C4—33no—
598C4⋊C4—33no—
599C4⋊C4—36no—
600C4⋊C4—31no—
601C4⋊C4—31no—
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—31no—
610C22⋊C4—33no—
611C22⋊C4—36no—
612C22⋊C4—33no—
613C22⋊C4—36no—
614C22⋊C4—33no—
615C22⋊C4—36no—
616C22⋊C4C22×C5×D311yescharacteristic
617C22⋊C4C22×C5×D313yes—
618C22⋊C4C22×C5×D316yes—
619C42—31no—
620C42—31no—
621C42—33no—
622C42—33no—
623C42—33no—
624C42—33no—
625C42—33no—
626C42—33no—
627C42—33no—
628C42C22×C5×D313yes—
629C3×C5#348011yescharacteristic, complemented, Hall
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—23no—
633C22×C3—23no—
634C22×C3—23no—
635C22×C3C2×C5×#4112yes—
636C22×C3C25×C511yescharacteristic
637C2×D3—23no—
638C2×D3—23no—
639C2×D3—23no—
640C3×C4—23no—
641C3×C4—21no—
642C3×C4—23no—
643C3×C4—21no—
644C3×C4C2×C5×#4116yes—
645Dic3—23no—
646Dic3—21no—
647Dic3—23no—
648Dic3—21no—
649Dic3—23no—
650Dic3C2×C5×#4112yes—
651Dic3C2×C5×#4112yes—
652C2×C5—22no—
653C2×C5—43no—
654C2×C5—123no—
655C2×C5C22×#23711yescharacteristic
656C2×C5C2×D3×#4111yescharacteristic
657C2×C5#596811yescharacteristic
658C23—33no—
659C23C23×C5×D313yes—
660C23C23×C5×D311yescharacteristic
661Q8—26no—
662Q8—66no—
663Q8C5×#23714yescomplemented
664D4—26no—
665D4—26no—
666D4—66no—
667D4—66no—
668D4—66no—
669D4—126no—
670C2×C4—26no—
671C2×C4—26no—
672C2×C4—34no—
673C2×C4—31no—
674C2×C4—31no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—33no—
678C2×C4—33no—
679C2×C4—33no—
680C2×C4—66no—
681C2×C4—66no—
682C2×C4—66no—
683C2×C4—123no—
684C2×C4—123no—
685C2×C4—123no—
686C2×C4C23×C5×D311yescharacteristic
687C2×C4C23×C5×D313yes—
688C2×C4C23×C5×D311yescharacteristic
689C2×C4C23×C5×D313yes—
690C2×C4C23×C5×D313yes—
691C2×C3—22no—
692C2×C3—43no—
693C2×C3C22×C5×#4111yescharacteristic
694C2×C3C22×C5×#4111yescharacteristic
695C2×C3C5×#58511yescharacteristic
696D3—43no—
697C5#8671111yescharacteristic, direct product factor, Sylow
698C22—21no—
699C22—21no—
700C22—23no—
701C22—23no—
702C22—23no—
703C22—63no—
704C22—63no—
705C22—63no—
706C22C5×D3×#4112yes—
707C22C24×C5×D311yescharacteristic
708C4—21no—
709C4—23no—
710C4—23no—
711C4—21no—
712C4—32no—
713C4—32no—
714C4—61no—
715C4—63no—
716C4—63no—
717C4—61no—
718C4—63no—
719C4C2×C5×#23716yes—
720C3C5×#348011yescharacteristic, complemented, Sylow
721C2—22no—
722C2—43no—
723C2—123no—
724C2C22×C5×#23711yescharacteristic
725C2C2×C5×D3×#4111yescharacteristic
726C2C5×#596811yescharacteristic
subgroupG/H
centerC22×C5C24×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC3×C5×#548C2
socleC22×C3×C5C25
hypercenterC5×#548D3
hypocenterC3C5×#3480
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#548

Complements

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

NH ≅ G/Ntype
1. C3×C5×#548C2semidirect
2. C5×#5834C2semidirect
3. C5×Dic3×#41C2semidirect
4. C5×#5817C2semidirect
5. C2×C5×Q8×Dic3C2semidirect
6. C5×#5681C2semidirect
7. C5×#5680C2semidirect
8. C5×#5641C2semidirect
9. C5×#5624C2semidirect
10. C5×#5618C2semidirect
11. C5×#5596C2semidirect
12. C4×C5×#239C2semidirect
13. C5×#5569C2semidirect
14. C5×#5565C2semidirect
15. C4×C5×#237C2semidirect
67. #86711C5direct (N × H)
75. C5×#548D3semidirect
137. C3×#548C2×C5semidirect
138. #5834C2×C5semidirect
139. Dic3×#41C2×C5semidirect
140. #5817C2×C5semidirect
141. C2×Q8×Dic3C2×C5semidirect
142. #5681C2×C5semidirect
143. #5680C2×C5semidirect
144. #5641C2×C5semidirect
145. #5624C2×C5semidirect
146. #5618C2×C5semidirect
147. #5596C2×C5semidirect
148. C4×#239C2×C5semidirect
149. #5569C2×C5semidirect
150. #5565C2×C5semidirect
151. C4×#237C2×C5semidirect
207. C3×C5×Q8#41semidirect
223. C2×C5×Dic3#41semidirect
347. #548C5×D3semidirect
436. C5×Q8#237semidirect
524. C3×Q8C5×#41semidirect
540. C2×Dic3C5×#41semidirect
629. C3×C5#3480semidirect
663. Q8C5×#237semidirect
697. C5#86711direct (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×C5×#5482
C5×#58342
C5×Dic3×#412
C5×#58172
C2×C5×Q8×Dic32
C5×#56812
C5×#56802
C5×#56412
C5×#56242
C5×#56182
C5×#55962
C4×C5×#2392
C5×#55692
C5×#55652
C4×C5×#2372
C5×#34803
#867115