Finite Group Databasebeta

← C5×D3×#548 #14482793

Subgroups — C5×D3×#548 #14482793

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×#41C211yesmaximal, characteristic, complemented
2C22×C5×D3×Q8C211yesmaximal, characteristic, complemented
3C3×C5×#548C211yesmaximal, characteristic, complemented
4C5×#5831C211yesmaximal, characteristic, complemented
5C5×#5817C211yesmaximal, characteristic, complemented
6C5×#5677C213yesmaximal, complemented
7C5×D3×#124C213yesmaximal, complemented
8C5×#5633C213yesmaximal, complemented
9C5×D3×C22⋊Q8C213yesmaximal, complemented
10C5×D3×#121C213yesmaximal, complemented
11C5×#5598C213yesmaximal, complemented
12C5×#5576C211yesmaximal, characteristic, complemented
13C4×C5×D3×Q8C211yesmaximal, characteristic, complemented
14C5×#5552C213yesmaximal, complemented
15C4×C5×D3×D4C213yesmaximal, complemented
16C2×C5×#548—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C5×D3×#41—28no—
20C2×C5×#239C2211yescharacteristic, complemented
21C2×C5×D3×Q8—28no—
22C2×C5×D3×Q8C2213yes—
23C2×C5×D3×Q8C2211yescharacteristic
24C2×C5×D3×Q8C2213yescomplemented
25C2×C5×D3×Q8C2211yescharacteristic, complemented
26C2×C5×#237C2213yescomplemented
27C2×C5×D3×D4C2213yes—
28C2×C5×D3×D4C2213yes—
29C2×C5×#235C2213yescomplemented
30C22×C4×C5×D3C2213yes—
31C22×C4×C5×D3C2213yes—
32C22×C5×Dic6C2213yescomplemented
33C3×C5×#124C2213yescomplemented
34C3×C5×C22⋊Q8C2213yescomplemented
35C3×C5×#121C2213yescomplemented
36C3×C4×C5×Q8C2211yescharacteristic, complemented
37C3×C4×C5×D4C2213yescomplemented
38C5×#947C2213yescomplemented
39C5×#946C2213yescomplemented
40C5×Q8×Dic3C2211yescharacteristic, complemented
41C5×#939C2216yescomplemented
42C5×#938C2213yescomplemented
43C5×#936C2213yescomplemented
44C5×D4×Dic3C2213yescomplemented
45C5×#930C2213yescomplemented
46C4×C5×#67C2213yescomplemented
47C4×C5×#67C2213yescomplemented
48C5×#924C2213yescomplemented
49C5×#897C2213yescomplemented
50C5×#896C2216yescomplemented
51C5×#895C2213yescomplemented
52C5×#893C2213yescomplemented
53C5×D3×C4⋊C4C2213yes—
54C5×D3×C4⋊C4C2213yes—
55C5×#887C2213yescomplemented
56C5×#885C2216yescomplemented
57C5×#885C2216yescomplemented
58C5×#884C2216yescomplemented
59C5×#67⋊C4C2213yescomplemented
60C5×#67⋊C4C2213yescomplemented
61C5×D3×C22⋊C4C2213yes—
62C5×D3×C22⋊C4C2216yes—
63C5×D3×C22⋊C4C2211yescharacteristic
64C5×#878C2216yescomplemented
65C5×#875C2213yescomplemented
66C4×C5×D12C2213yescomplemented
67C42×C5×D3C2213yes—
68C4×C5×Dic6C2213yescomplemented
69D3×#548C511yesmaximal, characteristic, direct product factor, Hall
70C22×C5×#41—31no—
71C23×C5×Q8—31no—
72C5×#548—31no—
73C5×#548—31no—
74C5×#548—33no—
75C5×#548—33no—
76C5×#548—33no—
77C5×#548—31no—
78C5×#548—33no—
79C5×#548D311yescharacteristic, direct product factor
80C2×C5×#124—33no—
81C2×C5×C22⋊Q8—33no—
82C2×C5×#121—33no—
83C2×C4×C5×Q8—31no—
84C2×C4×C5×D4—33no—
85C23×C5×D3C2313yes—
86C23×C5×D3C2311yescharacteristic
87C3×C5×#41—24no—
88C2×C3×C5×Q8—24no—
89C2×C3×C5×Q8C2313yes—
90C2×C3×C5×Q8C2311yescharacteristic
91C2×C3×C5×D4C2313yes—
92C2×C3×C5×D4C2313yes—
93C22×C3×C4×C5C2313yes—
94C22×C3×C4×C5C2313yes—
95C2×C5×#67C2313yes—
96C2×C5×#67C2313yes—
97C2×C5×#67C2316yes—
98C22×C5×Dic3C2313yes—
99C22×C5×Dic3C2313yes—
100C5×#239—24no—
101C5×D3×Q8—24no—
102C5×D3×Q8—212no—
103C5×D3×Q8—212no—
104C5×D3×Q8D418yescomplemented
105C5×#237—212no—
106C5×D3×D4—212no—
107C5×D3×D4—212no—
108C5×#235—212no—
109C2×C5×D12C2313yes—
110C2×C5×D12C2313yes—
111C2×C4×C5×D3—212no—
112C2×C4×C5×D3—212no—
113C2×C4×C5×D3C2311yescharacteristic
114C2×C4×C5×D3C2313yes—
115C2×C4×C5×D3C2313yes—
116C2×C4×C5×D3C2313yes—
117C2×C4×C5×D3C2313yes—
118C2×C4×C5×D3C2311yescharacteristic
119C2×C4×C5×D3C2313yes—
120C2×C4×C5×D3C2313yes—
121C2×C4×C5×D3C2313yes—
122C2×C5×Dic6—212no—
123C2×C5×Dic6C2313yes—
124C2×C5×Dic6C2316yes—
125C2×C5×Dic6C2313yes—
126C3×C5×C4⋊C4C2313yes—
127C3×C5×C4⋊C4C2313yes—
128C3×C5×C22⋊C4C2316yes—
129C3×C5×C22⋊C4C2311yescharacteristic
130C3×C5×C22⋊C4C2313yes—
131C3×C42×C5C2313yes—
132C5×#217C2316yes—
133C5×#217C2313yes—
134C5×#217C2311yescharacteristic
135C5×(C2×D3)⋊C4C2311yescharacteristic
136C5×(C2×D3)⋊C4C2313yes—
137C5×(C2×D3)⋊C4C2316yes—
138C5×(C2×D3)⋊C4C2316yes—
139C5×(C2×D3)⋊C4C2313yes—
140C5×(C2×D3)⋊C4C2311yescharacteristic
141C5×C4⋊Dic3C2313yes—
142C5×C4⋊Dic3C2313yes—
143C5×Dic3⋊C4C2316yes—
144C5×Dic3⋊C4C2313yes—
145C5×Dic3⋊C4C2313yes—
146C4×C5×Dic3C2313yes—
147C4×C5×Dic3C2313yes—
148C4×C5×Dic3C2313yes—
149C2×D3×#41C2×C511yescharacteristic, complemented
150C22×D3×Q8C2×C511yescharacteristic, complemented
151C3×#548C2×C511yescharacteristic, complemented
152#5831C2×C511yescharacteristic, complemented
153#5817C2×C511yescharacteristic, complemented
154#5677C2×C513yescomplemented
155D3×#124C2×C513yescomplemented
156#5633C2×C513yescomplemented
157D3×C22⋊Q8C2×C513yescomplemented
158D3×#121C2×C513yescomplemented
159#5598C2×C513yescomplemented
160#5576C2×C511yescharacteristic, complemented
161C4×D3×Q8C2×C511yescharacteristic, complemented
162#5552C2×C513yescomplemented
163C4×D3×D4C2×C513yescomplemented
164C2×C5×#41—31no—
165C2×C5×#41—33no—
166C2×C5×#41—33no—
167C2×C5×#41—68no—
168C2×C5×#41C2×D311yescharacteristic, complemented
169C22×C5×Q8—31no—
170C22×C5×Q8—33no—
171C22×C5×Q8—33no—
172C22×C5×Q8—31no—
173C22×C5×Q8—33no—
174C22×C5×Q8—68no—
175C22×C5×Q8C2×D311yescharacteristic, complemented
176C22×C5×D4—33no—
177C22×C5×D4—33no—
178C23×C4×C5—33no—
179C23×C4×C5—33no—
180C5×#124—33no—
181C5×#124—33no—
182C5×#124—36no—
183C5×#124—36no—
184C5×#124—33no—
185C5×#124C2×D313yescomplemented
186C5×C22⋊Q8—33no—
187C5×C22⋊Q8—33no—
188C5×C22⋊Q8—36no—
189C5×C22⋊Q8—33no—
190C5×C22⋊Q8—36no—
191C5×C22⋊Q8C2×D313yescomplemented
192C5×#121—33no—
193C5×#121—36no—
194C5×#121—33no—
195C5×#121—33no—
196C5×#121—36no—
197C5×#121C2×D313yescomplemented
198C4×C5×Q8—31no—
199C4×C5×Q8—33no—
200C4×C5×Q8—33no—
201C4×C5×Q8C2×D311yescharacteristic, complemented
202C4×C5×D4—33no—
203C4×C5×D4—33no—
204C4×C5×D4—33no—
205C4×C5×D4—33no—
206C4×C5×D4—33no—
207C4×C5×D4—33no—
208C4×C5×D4—33no—
209C4×C5×D4C2×D313yescomplemented
210C2×C5×C4⋊C4—33no—
211C2×C5×C4⋊C4—33no—
212C2×C5×C22⋊C4—31no—
213C2×C5×C22⋊C4—33no—
214C2×C5×C22⋊C4—36no—
215C2×C42×C5—33no—
216C2×#548—31noSylow
217C23×C3×C5C2413yes—
218C23×C3×C5C2411yescharacteristic
219C22×C5×D3—22no—
220C22×C5×D3—22no—
221C22×C5×D3—26no—
222C22×C5×D3—26no—
223C22×C5×D3—26no—
224C22×C5×D3#4114yescomplemented
225C22×C5×D3C2413yes—
226C22×C5×D3C2411yescharacteristic
227C22×C5×D3C2411yescharacteristic
228C3×C5×Q8—26no—
229C3×C5×Q8C2×D414yescomplemented
230C3×C5×D4—26no—
231C3×C5×D4—26no—
232C2×C3×C4×C5—26no—
233C2×C3×C4×C5—26no—
234C2×C3×C4×C5C2411yescharacteristic
235C2×C3×C4×C5C2413yes—
236C2×C3×C4×C5C2411yescharacteristic
237C2×C3×C4×C5C2413yes—
238C2×C3×C4×C5C2413yes—
239C5×#67—26no—
240C5×#67—26no—
241C5×#67—212no—
242C2×C5×Dic3—26no—
243C2×C5×Dic3—26no—
244C2×C5×Dic3C2411yescharacteristic
245C2×C5×Dic3C2413yes—
246C2×C5×Dic3C2411yescharacteristic
247C2×C5×Dic3C2413yes—
248C2×C5×Dic3C2413yes—
249C5×D12—26no—
250C5×D12—26no—
251C4×C5×D3—22no—
252C4×C5×D3—26no—
253C4×C5×D3—26no—
254C4×C5×D3—22no—
255C4×C5×D3—26no—
256C4×C5×D3—26no—
257C4×C5×D3—26no—
258C4×C5×D3—26no—
259C4×C5×D3C2×D4112yes—
260C5×Dic6—26no—
261C5×Dic6—212no—
262C5×Dic6C2×D4112yescomplemented
263C2×C3×#41C22×C511yescharacteristic, complemented
264C22×C3×Q8C22×C511yescharacteristic, complemented
265D3×#41—28no—
266C2×#239C22×C511yescharacteristic, complemented
267C2×D3×Q8—28no—
268C2×D3×Q8C22×C513yes—
269C2×D3×Q8C22×C511yescharacteristic
270C2×D3×Q8C22×C513yescomplemented
271C2×D3×Q8C22×C511yescharacteristic, complemented
272C2×#237C22×C513yescomplemented
273C2×D3×D4C22×C513yes—
274C2×D3×D4C22×C513yes—
275C2×#235C22×C513yescomplemented
276C22×C4×D3C22×C513yes—
277C22×C4×D3C22×C513yes—
278C22×Dic6C22×C513yescomplemented
279C3×#124C22×C513yescomplemented
280C3×C22⋊Q8C22×C513yescomplemented
281C3×#121C22×C513yescomplemented
282C3×C4×Q8C22×C511yescharacteristic, complemented
283C3×C4×D4C22×C513yescomplemented
284#947C22×C513yescomplemented
285#946C22×C513yescomplemented
286Q8×Dic3C22×C511yescharacteristic, complemented
287#939C22×C516yescomplemented
288#938C22×C513yescomplemented
289#936C22×C513yescomplemented
290D4×Dic3C22×C513yescomplemented
291#930C22×C513yescomplemented
292C4×#67C22×C513yescomplemented
293C4×#67C22×C513yescomplemented
294#924C22×C513yescomplemented
295#897C22×C513yescomplemented
296#896C22×C516yescomplemented
297#895C22×C513yescomplemented
298#893C22×C513yescomplemented
299D3×C4⋊C4C22×C513yes—
300D3×C4⋊C4C22×C513yes—
301#887C22×C513yescomplemented
302#885C22×C516yescomplemented
303#885C22×C516yescomplemented
304#884C22×C516yescomplemented
305#67⋊C4C22×C513yescomplemented
306#67⋊C4C22×C513yescomplemented
307D3×C22⋊C4C22×C513yes—
308D3×C22⋊C4C22×C516yes—
309D3×C22⋊C4C22×C511yescharacteristic
310#878C22×C516yescomplemented
311#875C22×C513yescomplemented
312C4×D12C22×C513yescomplemented
313C42×D3C22×C513yes—
314C4×Dic6C22×C513yescomplemented
315C24×C5—31no—
316C24×C5—33no—
317C5×#41—24no—
318C5×#41—612no—
319C5×#41—612no—
320C5×#41—64no—
321C2×C5×Q8—24no—
322C2×C5×Q8—38no—
323C2×C5×Q8—33no—
324C2×C5×Q8—36no—
325C2×C5×Q8—33no—
326C2×C5×Q8—612no—
327C2×C5×Q8—612no—
328C2×C5×Q8—612no—
329C2×C5×Q8—64no—
330C2×C5×Q8C22×D313yes—
331C2×C5×Q8C22×D311yescharacteristic
332C2×C5×D4—33no—
333C2×C5×D4—33no—
334C2×C5×D4—36no—
335C2×C5×D4—33no—
336C2×C5×D4—33no—
337C2×C5×D4—612no—
338C2×C5×D4—612no—
339C2×C5×D4C22×D313yes—
340C2×C5×D4C22×D313yes—
341C22×C4×C5—33no—
342C22×C4×C5—33no—
343C22×C4×C5—33no—
344C22×C4×C5—31no—
345C22×C4×C5—33no—
346C22×C4×C5—33no—
347C22×C4×C5—31no—
348C22×C4×C5—33no—
349C22×C4×C5—33no—
350C22×C4×C5—33no—
351C22×C4×C5—33no—
352C22×C4×C5—612no—
353C22×C4×C5—612no—
354C22×C4×C5C22×D313yes—
355C22×C4×C5C22×D313yes—
356C5×C4⋊C4—33no—
357C5×C4⋊C4—33no—
358C5×C4⋊C4—33no—
359C5×C4⋊C4—36no—
360C5×C4⋊C4—33no—
361C5×C4⋊C4C22×D313yes—
362C5×C4⋊C4C22×D313yes—
363C5×C22⋊C4—31no—
364C5×C22⋊C4—33no—
365C5×C22⋊C4—36no—
366C5×C22⋊C4—31no—
367C5×C22⋊C4—31no—
368C5×C22⋊C4—33no—
369C5×C22⋊C4—33no—
370C5×C22⋊C4—36no—
371C5×C22⋊C4—36no—
372C5×C22⋊C4C22×D311yescharacteristic
373C5×C22⋊C4C22×D313yes—
374C5×C22⋊C4C22×D316yes—
375C42×C5—33no—
376C42×C5—33no—
377C42×C5—33no—
378C42×C5C22×D313yes—
379C22×#41—31no—
380C23×Q8—31no—
381#548—31no—
382#548—31no—
383#548—33no—
384#548—33no—
385#548—33no—
386#548—31no—
387#548—33no—
388#548C5×D311yescharacteristic, direct product factor
389C2×#124—33no—
390C2×C22⋊Q8—33no—
391C2×#121—33no—
392C2×C4×Q8—31no—
393C2×C4×D4—33no—
394C22×C3×C5—21no—
395C22×C3×C5—21no—
396C22×C3×C5—23no—
397C22×C3×C5—23no—
398C22×C3×C5—23no—
399C22×C3×C5C2×#4112yescomplemented
400C22×C3×C5C2511yescharacteristic
401C2×C5×D3—21no—
402C2×C5×D3—21no—
403C2×C5×D3—28no—
404C2×C5×D3—23no—
405C2×C5×D3—23no—
406C2×C5×D3—23no—
407C2×C5×D3—412no—
408C2×C5×D3C22×D412yes—
409C2×C5×D3C2×#4112yes—
410C2×C5×D3C2×#4112yescomplemented
411C2×C5×D32−1+412yes—
412C3×C4×C5—23no—
413C3×C4×C5—21no—
414C3×C4×C5—23no—
415C3×C4×C5—21no—
416C3×C4×C5C22×D416yes—
417C5×Dic3—23no—
418C5×Dic3—21no—
419C5×Dic3—23no—
420C5×Dic3—21no—
421C5×Dic3C22×D416yes—
422C23×D3C23×C513yes—
423C23×D3C23×C511yescharacteristic
424C3×#41—24no—
425C2×C3×Q8—24no—
426C2×C3×Q8C23×C513yes—
427C2×C3×Q8C23×C511yescharacteristic
428C2×C3×D4C23×C513yes—
429C2×C3×D4C23×C513yes—
430C22×C3×C4C23×C513yes—
431C22×C3×C4C23×C513yes—
432C2×#67C23×C513yes—
433C2×#67C23×C513yes—
434C2×#67C23×C516yes—
435C22×Dic3C23×C513yes—
436C22×Dic3C23×C513yes—
437#239—24no—
438D3×Q8—24no—
439D3×Q8—212no—
440D3×Q8—212no—
441D3×Q8C5×D418yescomplemented
442#237—212no—
443D3×D4—212no—
444D3×D4—212no—
445#235—212no—
446C2×D12C23×C513yes—
447C2×D12C23×C513yes—
448C2×C4×D3—212no—
449C2×C4×D3—212no—
450C2×C4×D3C23×C511yescharacteristic
451C2×C4×D3C23×C513yes—
452C2×C4×D3C23×C513yes—
453C2×C4×D3C23×C513yes—
454C2×C4×D3C23×C513yes—
455C2×C4×D3C23×C511yescharacteristic
456C2×C4×D3C23×C513yes—
457C2×C4×D3C23×C513yes—
458C2×C4×D3C23×C513yes—
459C2×Dic6—212no—
460C2×Dic6C23×C513yes—
461C2×Dic6C23×C516yes—
462C2×Dic6C23×C513yes—
463C3×C4⋊C4C23×C513yes—
464C3×C4⋊C4C23×C513yes—
465C3×C22⋊C4C23×C516yes—
466C3×C22⋊C4C23×C511yescharacteristic
467C3×C22⋊C4C23×C513yes—
468C3×C42C23×C513yes—
469#217C23×C516yes—
470#217C23×C513yes—
471#217C23×C511yescharacteristic
472(C2×D3)⋊C4C23×C511yescharacteristic
473(C2×D3)⋊C4C23×C513yes—
474(C2×D3)⋊C4C23×C516yes—
475(C2×D3)⋊C4C23×C516yes—
476(C2×D3)⋊C4C23×C513yes—
477(C2×D3)⋊C4C23×C511yescharacteristic
478C4⋊Dic3C23×C513yes—
479C4⋊Dic3C23×C513yes—
480Dic3⋊C4C23×C516yes—
481Dic3⋊C4C23×C513yes—
482Dic3⋊C4C23×C513yes—
483C4×Dic3C23×C513yes—
484C4×Dic3C23×C513yes—
485C4×Dic3C23×C513yes—
486C23×C5—31no—
487C23×C5—34no—
488C23×C5—31no—
489C23×C5—33no—
490C23×C5—62no—
491C23×C5—62no—
492C23×C5—66no—
493C23×C5—66no—
494C23×C5—66no—
495C23×C5C23×D313yes—
496C23×C5C23×D311yescharacteristic
497C5×Q8—26no—
498C5×Q8—312no—
499C5×Q8—612no—
500C5×Q8—66no—
501C5×Q8D3×D414yescomplemented
502C5×D4—26no—
503C5×D4—26no—
504C5×D4—66no—
505C5×D4—612no—
506C5×D4—66no—
507C5×D4—66no—
508C5×D4—66no—
509C2×C4×C5—26no—
510C2×C4×C5—26no—
511C2×C4×C5—33no—
512C2×C4×C5—312no—
513C2×C4×C5—31no—
514C2×C4×C5—33no—
515C2×C4×C5—33no—
516C2×C4×C5—31no—
517C2×C4×C5—66no—
518C2×C4×C5—66no—
519C2×C4×C5—62no—
520C2×C4×C5—62no—
521C2×C4×C5—66no—
522C2×C4×C5—66no—
523C2×C4×C5—66no—
524C2×C4×C5—66no—
525C2×C4×C5—66no—
526C2×C4×C5—66no—
527C2×C4×C5C23×D311yescharacteristic
528C2×C4×C5C23×D313yes—
529C2×C4×C5C23×D313yes—
530C2×C4×C5C23×D311yescharacteristic
531C2×C4×C5C23×D313yes—
532C2×#41—31no—
533C2×#41—33no—
534C2×#41—33no—
535C2×#41—68no—
536C2×#41C2×C5×D311yescharacteristic, complemented
537C22×Q8—31no—
538C22×Q8—33no—
539C22×Q8—33no—
540C22×Q8—31no—
541C22×Q8—33no—
542C22×Q8—68no—
543C22×Q8C2×C5×D311yescharacteristic, complemented
544C22×D4—33no—
545C22×D4—33no—
546C23×C4—33no—
547C23×C4—33no—
548#124—33no—
549#124—33no—
550#124—36no—
551#124—36no—
552#124—33no—
553#124C2×C5×D313yescomplemented
554C22⋊Q8—33no—
555C22⋊Q8—33no—
556C22⋊Q8—36no—
557C22⋊Q8—33no—
558C22⋊Q8—36no—
559C22⋊Q8C2×C5×D313yescomplemented
560#121—33no—
561#121—36no—
562#121—33no—
563#121—33no—
564#121—36no—
565#121C2×C5×D313yescomplemented
566C4×Q8—31no—
567C4×Q8—33no—
568C4×Q8—33no—
569C4×Q8C2×C5×D311yescharacteristic, complemented
570C4×D4—33no—
571C4×D4—33no—
572C4×D4—33no—
573C4×D4—33no—
574C4×D4—33no—
575C4×D4—33no—
576C4×D4—33no—
577C4×D4C2×C5×D313yescomplemented
578C2×C4⋊C4—33no—
579C2×C4⋊C4—33no—
580C2×C22⋊C4—31no—
581C2×C22⋊C4—33no—
582C2×C22⋊C4—36no—
583C2×C42—33no—
584C2×C3×C5—22no—
585C2×C3×C5—43no—
586C2×C3×C5C23×D411yescharacteristic
587C2×C3×C5C22×#4111yescharacteristic
588C2×C3×C5C2×2−1+411yescharacteristic
589C5×D3—22no—
590C5×D3—43no—
591C5×D3#54814yesdirect product factor
592C23×C3C24×C513yes—
593C23×C3C24×C511yescharacteristic
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—26no—
597C22×D3—26no—
598C22×D3—26no—
599C22×D3C5×#4114yescomplemented
600C22×D3C24×C513yes—
601C22×D3C24×C511yescharacteristic
602C22×D3C24×C511yescharacteristic
603C3×Q8—26no—
604C3×Q8C2×C5×D414yescomplemented
605C3×D4—26no—
606C3×D4—26no—
607C2×C3×C4—26no—
608C2×C3×C4—26no—
609C2×C3×C4C24×C511yescharacteristic
610C2×C3×C4C24×C513yes—
611C2×C3×C4C24×C511yescharacteristic
612C2×C3×C4C24×C513yes—
613C2×C3×C4C24×C513yes—
614#67—26no—
615#67—26no—
616#67—212no—
617C2×Dic3—26no—
618C2×Dic3—26no—
619C2×Dic3C24×C511yescharacteristic
620C2×Dic3C24×C513yes—
621C2×Dic3C24×C511yescharacteristic
622C2×Dic3C24×C513yes—
623C2×Dic3C24×C513yes—
624D12—26no—
625D12—26no—
626C4×D3—22no—
627C4×D3—26no—
628C4×D3—26no—
629C4×D3—22no—
630C4×D3—26no—
631C4×D3—26no—
632C4×D3—26no—
633C4×D3—26no—
634C4×D3C2×C5×D4112yes—
635Dic6—26no—
636Dic6—212no—
637Dic6C2×C5×D4112yescomplemented
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—23no—
641C22×C5—23no—
642C22×C5—23no—
643C22×C5—32no—
644C22×C5—32no—
645C22×C5—32no—
646C22×C5—32no—
647C22×C5—68no—
648C22×C5—61no—
649C22×C5—61no—
650C22×C5—63no—
651C22×C5—63no—
652C22×C5—63no—
653C22×C5—1212no—
654C22×C5D3×#4112yescomplemented
655C22×C5C24×D311yescharacteristic
656C4×C5—21no—
657C4×C5—23no—
658C4×C5—23no—
659C4×C5—21no—
660C4×C5—36no—
661C4×C5—61no—
662C4×C5—63no—
663C4×C5—63no—
664C4×C5—61no—
665C4×C5C2×D3×D416yes—
666C24—31no—
667C24—33no—
668#41—24no—
669#41—612no—
670#41—612no—
671#41—64no—
672C2×Q8—24no—
673C2×Q8—38no—
674C2×Q8—33no—
675C2×Q8—36no—
676C2×Q8—33no—
677C2×Q8—612no—
678C2×Q8—612no—
679C2×Q8—612no—
680C2×Q8—64no—
681C2×Q8C22×C5×D313yes—
682C2×Q8C22×C5×D311yescharacteristic
683C2×D4—33no—
684C2×D4—33no—
685C2×D4—36no—
686C2×D4—33no—
687C2×D4—33no—
688C2×D4—612no—
689C2×D4—612no—
690C2×D4C22×C5×D313yes—
691C2×D4C22×C5×D313yes—
692C22×C4—33no—
693C22×C4—33no—
694C22×C4—33no—
695C22×C4—31no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—31no—
699C22×C4—33no—
700C22×C4—33no—
701C22×C4—33no—
702C22×C4—33no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4C22×C5×D313yes—
706C22×C4C22×C5×D313yes—
707C4⋊C4—33no—
708C4⋊C4—33no—
709C4⋊C4—33no—
710C4⋊C4—36no—
711C4⋊C4—33no—
712C4⋊C4C22×C5×D313yes—
713C4⋊C4C22×C5×D313yes—
714C22⋊C4—31no—
715C22⋊C4—33no—
716C22⋊C4—36no—
717C22⋊C4—31no—
718C22⋊C4—31no—
719C22⋊C4—33no—
720C22⋊C4—33no—
721C22⋊C4—36no—
722C22⋊C4—36no—
723C22⋊C4C22×C5×D311yescharacteristic
724C22⋊C4C22×C5×D313yes—
725C22⋊C4C22×C5×D316yes—
726C42—33no—
727C42—33no—
728C42—33no—
729C42C22×C5×D313yes—
730C3×C5C2×#54811yescharacteristic, complemented, Hall
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—23no—
734C22×C3—23no—
735C22×C3—23no—
736C22×C3C2×C5×#4112yescomplemented
737C22×C3C25×C511yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—28no—
741C2×D3—23no—
742C2×D3—23no—
743C2×D3—23no—
744C2×D3—412no—
745C2×D3C22×C5×D412yes—
746C2×D3C2×C5×#4112yes—
747C2×D3C2×C5×#4112yescomplemented
748C2×D3C5×2−1+412yes—
749C3×C4—23no—
750C3×C4—21no—
751C3×C4—23no—
752C3×C4—21no—
753C3×C4C22×C5×D416yes—
754Dic3—23no—
755Dic3—21no—
756Dic3—23no—
757Dic3—21no—
758Dic3C22×C5×D416yes—
759C2×C5—22no—
760C2×C5—34no—
761C2×C5—43no—
762C2×C5—62no—
763C2×C5—123no—
764C2×C5C22×D3×D411yescharacteristic
765C2×C5C2×D3×#4111yescharacteristic
766C2×C5D3×2−1+411yescharacteristic
767C23—31no—
768C23—34no—
769C23—31no—
770C23—33no—
771C23—62no—
772C23—62no—
773C23—66no—
774C23—66no—
775C23—66no—
776C23C23×C5×D313yes—
777C23C23×C5×D311yescharacteristic
778Q8—26no—
779Q8—312no—
780Q8—612no—
781Q8—66no—
782Q8C5×D3×D414yescomplemented
783D4—26no—
784D4—26no—
785D4—66no—
786D4—612no—
787D4—66no—
788D4—66no—
789D4—66no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—33no—
793C2×C4—312no—
794C2×C4—31no—
795C2×C4—33no—
796C2×C4—33no—
797C2×C4—31no—
798C2×C4—66no—
799C2×C4—66no—
800C2×C4—62no—
801C2×C4—66no—
802C2×C4—66no—
803C2×C4—62no—
804C2×C4—66no—
805C2×C4—66no—
806C2×C4—66no—
807C2×C4—66no—
808C2×C4C23×C5×D311yescharacteristic
809C2×C4C23×C5×D313yes—
810C2×C4C23×C5×D313yes—
811C2×C4C23×C5×D311yescharacteristic
812C2×C4C23×C5×D313yes—
813C2×C3—22no—
814C2×C3—43no—
815C2×C3C23×C5×D411yescharacteristic
816C2×C3C22×C5×#4111yescharacteristic
817C2×C3C2×C5×2−1+411yescharacteristic
818D3—22no—
819D3—43no—
820D3C5×#54814yesdirect product factor
821C5D3×#54811yescharacteristic, direct product factor, Sylow
822C22—21no—
823C22—21no—
824C22—23no—
825C22—23no—
826C22—23no—
827C22—32no—
828C22—32no—
829C22—32no—
830C22—32no—
831C22—68no—
832C22—61no—
833C22—61no—
834C22—63no—
835C22—63no—
836C22—63no—
837C22—1212no—
838C22C5×D3×#4112yescomplemented
839C22C24×C5×D311yescharacteristic
840C4—21no—
841C4—23no—
842C4—23no—
843C4—21no—
844C4—36no—
845C4—61no—
846C4—63no—
847C4—63no—
848C4—61no—
849C4C2×C5×D3×D416yes—
850C3C2×C5×#54811yescharacteristic, complemented, Sylow
851C2—22no—
852C2—34no—
853C2—43no—
854C2—62no—
855C2—123no—
856C2C22×C5×D3×D411yescharacteristic
857C2C2×C5×D3×#4111yescharacteristic
858C2C5×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C5C24×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC3×C5×#548C2
socleC22×C3×C5C25
hypercenterC5×#548D3
hypocenterC3C2×C5×#548
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#548

Complements

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

NH ≅ G/Ntype
1. C2×C5×D3×#41C2semidirect
2. C22×C5×D3×Q8C2semidirect
3. C3×C5×#548C2semidirect
4. C5×#5831C2semidirect
5. C5×#5817C2semidirect
6. C5×#5677C2semidirect
7. C5×D3×#124C2semidirect
8. C5×#5633C2semidirect
9. C5×D3×C22⋊Q8C2semidirect
10. C5×D3×#121C2semidirect
11. C5×#5598C2semidirect
12. C5×#5576C2semidirect
13. C4×C5×D3×Q8C2semidirect
14. C5×#5552C2semidirect
15. C4×C5×D3×D4C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×Q8C22semidirect
20. C2×C5×#239C22semidirect
24. C2×C5×D3×Q8C22semidirect
25. C2×C5×D3×Q8C22semidirect
26. C2×C5×#237C22semidirect
29. C2×C5×#235C22semidirect
32. C22×C5×Dic6C22semidirect
33. C3×C5×#124C22semidirect
34. C3×C5×C22⋊Q8C22semidirect
35. C3×C5×#121C22semidirect
36. C3×C4×C5×Q8C22semidirect
37. C3×C4×C5×D4C22semidirect
38. C5×#947C22semidirect
39. C5×#946C22semidirect
40. C5×Q8×Dic3C22semidirect
41. C5×#939C22semidirect
42. C5×#938C22semidirect
43. C5×#936C22semidirect
44. C5×D4×Dic3C22semidirect
45. C5×#930C22semidirect
46. C4×C5×#67C22semidirect
47. C4×C5×#67C22semidirect
48. C5×#924C22semidirect
49. C5×#897C22semidirect
50. C5×#896C22semidirect
51. C5×#895C22semidirect
52. C5×#893C22semidirect
55. C5×#887C22semidirect
56. C5×#885C22semidirect
57. C5×#885C22semidirect
58. C5×#884C22semidirect
59. C5×#67⋊C4C22semidirect
60. C5×#67⋊C4C22semidirect
64. C5×#878C22semidirect
65. C5×#875C22semidirect
66. C4×C5×D12C22semidirect
68. C4×C5×Dic6C22semidirect
69. D3×#548C5direct (N × H)
79. C5×#548D3direct (N × H)
104. C5×D3×Q8D4semidirect
149. C2×D3×#41C2×C5semidirect
150. C22×D3×Q8C2×C5semidirect
151. C3×#548C2×C5semidirect
152. #5831C2×C5semidirect
153. #5817C2×C5semidirect
154. #5677C2×C5semidirect
155. D3×#124C2×C5semidirect
156. #5633C2×C5semidirect
157. D3×C22⋊Q8C2×C5semidirect
158. D3×#121C2×C5semidirect
159. #5598C2×C5semidirect
160. #5576C2×C5semidirect
161. C4×D3×Q8C2×C5semidirect
162. #5552C2×C5semidirect
163. C4×D3×D4C2×C5semidirect
168. C2×C5×#41C2×D3semidirect
175. C22×C5×Q8C2×D3semidirect
185. C5×#124C2×D3semidirect
191. C5×C22⋊Q8C2×D3semidirect
197. C5×#121C2×D3semidirect
201. C4×C5×Q8C2×D3semidirect
209. C4×C5×D4C2×D3semidirect
224. C22×C5×D3#41semidirect
229. C3×C5×Q8C2×D4semidirect
262. C5×Dic6C2×D4semidirect
263. C2×C3×#41C22×C5semidirect
264. C22×C3×Q8C22×C5semidirect
266. C2×#239C22×C5semidirect
270. C2×D3×Q8C22×C5semidirect
271. C2×D3×Q8C22×C5semidirect
272. C2×#237C22×C5semidirect
275. C2×#235C22×C5semidirect
278. C22×Dic6C22×C5semidirect
279. C3×#124C22×C5semidirect
280. C3×C22⋊Q8C22×C5semidirect
281. C3×#121C22×C5semidirect
282. C3×C4×Q8C22×C5semidirect
283. C3×C4×D4C22×C5semidirect
284. #947C22×C5semidirect
285. #946C22×C5semidirect
286. Q8×Dic3C22×C5semidirect
287. #939C22×C5semidirect
288. #938C22×C5semidirect
289. #936C22×C5semidirect
290. D4×Dic3C22×C5semidirect
291. #930C22×C5semidirect
292. C4×#67C22×C5semidirect
293. C4×#67C22×C5semidirect
294. #924C22×C5semidirect
295. #897C22×C5semidirect
296. #896C22×C5semidirect
297. #895C22×C5semidirect
298. #893C22×C5semidirect
301. #887C22×C5semidirect
302. #885C22×C5semidirect
303. #885C22×C5semidirect
304. #884C22×C5semidirect
305. #67⋊C4C22×C5semidirect
306. #67⋊C4C22×C5semidirect
310. #878C22×C5semidirect
311. #875C22×C5semidirect
312. C4×D12C22×C5semidirect
314. C4×Dic6C22×C5semidirect
388. #548C5×D3direct (N × H)
399. C22×C3×C5C2×#41semidirect
410. C2×C5×D3C2×#41semidirect
441. D3×Q8C5×D4semidirect
501. C5×Q8D3×D4semidirect
536. C2×#41C2×C5×D3semidirect
543. C22×Q8C2×C5×D3semidirect
553. #124C2×C5×D3semidirect
559. C22⋊Q8C2×C5×D3semidirect
565. #121C2×C5×D3semidirect
569. C4×Q8C2×C5×D3semidirect
577. C4×D4C2×C5×D3semidirect
591. C5×D3#548direct (N × H)
599. C22×D3C5×#41semidirect
604. C3×Q8C2×C5×D4semidirect
637. Dic6C2×C5×D4semidirect
654. C22×C5D3×#41semidirect
730. C3×C5C2×#548semidirect
736. C22×C3C2×C5×#41semidirect
747. C2×D3C2×C5×#41semidirect
782. Q8C5×D3×D4semidirect
820. D3C5×#548direct (N × H)
821. C5D3×#548direct (N × H)
838. C22C5×D3×#41semidirect
850. C3C2×C5×#548semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×#412
C22×C5×D3×Q82
C3×C5×#5482
C5×#58312
C5×#58172
C5×#56772
C5×D3×#1242
C5×#56332
C5×D3×C22⋊Q82
C5×D3×#1212
C5×#55982
C5×#55762
C4×C5×D3×Q82
C5×#55522
C4×C5×D3×D42
C2×C5×#5483
D3×#5485