Finite Group Databasebeta

← C5×#86710 #14483051

Subgroups — C5×#86710 #14483051

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×#41C211yesmaximal, characteristic, complemented
2C22×C5×#239C211yesmaximal, characteristic, complemented
3C3×C5×#548C211yesmaximal, characteristic, complemented
4C5×#5834C211yesmaximal, characteristic, complemented
5C5×Q8×#67C211yesmaximal, characteristic, complemented
6C5×#5676C213yesmaximal, complemented
7C5×#5668C213yesmaximal, complemented
8C5×#5631C213yesmaximal, complemented
9C5×#5627C213yesmaximal, complemented
10C5×#5609C213yesmaximal, complemented
11C5×#5606C213yesmaximal, complemented
12C5×#5576C211yesmaximal, characteristic, complemented
13C4×C5×#239C211yesmaximal, characteristic, complemented
14C5×#5550C213yesmaximal, complemented
15C4×C5×D3×D4C213yesmaximal, complemented
16C5×D4×#41—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C5×D3×#41—28no—
20C2×C5×#239—28no—
21C2×C5×#239C2211yescharacteristic
22C2×C5×#239C2213yescomplemented
23C2×C5×#239C2213yescomplemented
24C2×C5×#239C2211yescharacteristic, complemented
25C2×C5×D3×Q8C2211yescharacteristic, complemented
26C2×C5×#237C2213yescomplemented
27C2×C5×D3×D4C2213yes—
28C2×C5×D3×D4C2213yescomplemented
29C2×C5×#235C2213yescomplemented
30C22×C5×D12C2213yescomplemented
31C22×C4×C5×D3C2213yescomplemented
32C22×C4×C5×D3C2213yescomplemented
33C3×C5×#124C2213yescomplemented
34C3×C5×C22⋊Q8C2213yescomplemented
35C3×C5×#121C2213yescomplemented
36C3×C4×C5×Q8C2211yescharacteristic, complemented
37C3×C4×C5×D4C2213yescomplemented
38C5×#946C2213yescomplemented
39C5×Q8×Dic3C2211yescharacteristic, complemented
40C5×#944C2213yescomplemented
41C5×#940C2213yescomplemented
42C5×#938C2213yescomplemented
43C5×#937C2216yescomplemented
44C5×D4×Dic3C2213yescomplemented
45C5×#930C2213yescomplemented
46C4×C5×#67C2213yes—
47C4×C5×#67C2213yescomplemented
48C5×#924C2213yescomplemented
49C5×#897C2213yescomplemented
50C5×#895C2213yescomplemented
51C5×#894C2216yescomplemented
52C5×#893C2213yescomplemented
53C5×#893C2213yescomplemented
54C5×#892C2213yescomplemented
55C5×D3×C4⋊C4C2213yescomplemented
56C5×#884C2216yescomplemented
57C5×#884C2216yescomplemented
58C5×#883C2216yescomplemented
59C5×#882C2216yescomplemented
60C5×#67⋊C4C2211yescharacteristic
61C5×#67⋊C4C2213yescomplemented
62C5×#67⋊C4C2216yescomplemented
63C5×D3×C22⋊C4C2213yescomplemented
64C5×D3×C22⋊C4C2213yescomplemented
65C5×#875C2213yescomplemented
66C4×C5×D12C2213yescomplemented
67C4×C5×D12C2213yescomplemented
68C42×C5×D3C2213yescomplemented
69#86710C511yesmaximal, characteristic, direct product factor, Hall
70C22×C5×#41—31no—
71C22×C5×#41—31no—
72C5×#550—31no—
73C5×D4×Q8—31no—
74C5×#548—31no—
75C5×#548D311yescharacteristic, complemented
76C5×#547—33no—
77C5×#546—33no—
78C5×#546—33no—
79C5×D42—33no—
80C5×#532—33no—
81C5×#525—33no—
82C5×#525—33no—
83C4×C5×#41—31no—
84C2×C4×C5×D4—33no—
85C23×C5×D3C2313yes—
86C23×C5×D3C2313yes—
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×#67C2316yes—
97C2×C5×#67C2316yes—
98C2×C5×#67C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2313yes—
101C5×#239—24no—
102C5×#239—212no—
103C5×#239—212no—
104C5×#239D418yescomplemented
105C5×D3×Q8—24no—
106C5×#237—212no—
107C5×D3×D4—212no—
108C5×D3×D4—212no—
109C5×#235—212no—
110C2×C5×D12—212no—
111C2×C5×D12C2313yes—
112C2×C5×D12C2313yes—
113C2×C5×D12C2316yes—
114C2×C5×D12C2313yes—
115C2×C4×C5×D3—212no—
116C2×C4×C5×D3—212no—
117C2×C4×C5×D3C2313yes—
118C2×C4×C5×D3C2313yes—
119C2×C4×C5×D3C2313yes—
120C2×C4×C5×D3C2313yes—
121C2×C4×C5×D3C2313yes—
122C2×C4×C5×D3C2311yescharacteristic
123C2×C4×C5×D3C2313yes—
124C2×C4×C5×D3C2313yes—
125C2×C4×C5×D3C2313yes—
126C2×C5×Dic6C2313yes—
127C3×C5×C4⋊C4C2313yes—
128C3×C5×C4⋊C4C2313yes—
129C3×C5×C22⋊C4C2311yescharacteristic
130C3×C5×C22⋊C4C2313yes—
131C3×C5×C22⋊C4C2316yes—
132C3×C42×C5C2313yes—
133C5×#217C2313yes—
134C5×#217C2313yes—
135C5×(C2×D3)⋊C4C2311yescharacteristic
136C5×(C2×D3)⋊C4C2313yes—
137C5×(C2×D3)⋊C4C2316yes—
138C5×(C2×D3)⋊C4C2316yes—
139C5×(C2×D3)⋊C4C2313yes—
140C5×(C2×D3)⋊C4C2313yes—
141C5×C4⋊Dic3C2313yes—
142C5×C4⋊Dic3C2313yes—
143C5×Dic3⋊C4C2311yescharacteristic
144C5×Dic3⋊C4C2316yes—
145C5×Dic3⋊C4C2313yes—
146C4×C5×Dic3C2311yescharacteristic
147C4×C5×Dic3C2313yes—
148C4×C5×Dic3C2313yes—
149C2×D3×#41C2×C511yescharacteristic, complemented
150C22×#239C2×C511yescharacteristic, complemented
151C3×#548C2×C511yescharacteristic, complemented
152#5834C2×C511yescharacteristic, complemented
153Q8×#67C2×C511yescharacteristic, complemented
154#5676C2×C513yescomplemented
155#5668C2×C513yescomplemented
156#5631C2×C513yescomplemented
157#5627C2×C513yescomplemented
158#5609C2×C513yescomplemented
159#5606C2×C513yescomplemented
160#5576C2×C511yescharacteristic, complemented
161C4×#239C2×C511yescharacteristic, complemented
162#5550C2×C513yescomplemented
163C4×D3×D4C2×C513yescomplemented
164C2×C5×#41—31no—
165C2×C5×#41—33no—
166C2×C5×#41—33no—
167C2×C5×#41—31no—
168C2×C5×#41—33no—
169C2×C5×#41—33no—
170C2×C5×#41—68no—
171C2×C5×#41—68no—
172C2×C5×#41C2×D311yescharacteristic, complemented
173C22×C5×Q8—31no—
174C22×C5×Q8C2×D311yescharacteristic, complemented
175C22×C5×D4—33no—
176C22×C5×D4—33no—
177C22×C5×D4—33no—
178C23×C4×C5—33no—
179C23×C4×C5—33no—
180C5×C4⋊Q8—33no—
181C5×#127—33no—
182C5×#124—33no—
183C5×#124C2×D313yescomplemented
184C5×#123—36no—
185C5×#123—36no—
186C5×C22⋊Q8—33no—
187C5×C22⋊Q8—33no—
188C5×C22⋊Q8—33no—
189C5×C22⋊Q8C2×D313yescomplemented
190C5×#121—33no—
191C5×#121—33no—
192C5×#121—33no—
193C5×#121—36no—
194C5×#121—36no—
195C5×#121C2×D313yescomplemented
196C5×#120—36no—
197C5×#120—36no—
198C4×C5×Q8—31no—
199C4×C5×Q8C2×D311yescharacteristic, complemented
200C4×C5×D4—33no—
201C4×C5×D4—33no—
202C4×C5×D4—33no—
203C4×C5×D4—33no—
204C4×C5×D4—33no—
205C4×C5×D4—31no—
206C4×C5×D4—33no—
207C4×C5×D4—36no—
208C4×C5×D4—33no—
209C4×C5×D4—33no—
210C4×C5×D4C2×D313yescomplemented
211C5×#117—33no—
212C2×C5×C4⋊C4—33no—
213C2×C5×C22⋊C4—33no—
214C2×C5×C22⋊C4—33no—
215C2×C42×C5—33no—
216D4×#41—31noSylow
217C23×C3×C5C2413yes—
218C23×C3×C5C2411yescharacteristic
219C22×C5×D3—26no—
220C22×C5×D3—26no—
221C22×C5×D3—26no—
222C22×C5×D3—26no—
223C22×C5×D3—43no—
224C22×C5×D3—43no—
225C22×C5×D3C2413yes—
226C22×C5×D3C2413yes—
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×C5C2413yes—
235C2×C3×C4×C5C2411yescharacteristic
236C2×C3×C4×C5C2413yes—
237C2×C3×C4×C5C2411yescharacteristic
238C2×C3×C4×C5C2413yes—
239C5×#67—212no—
240C5×#67—26no—
241C5×#67—46no—
242C5×#67#4114yescomplemented
243C2×C5×Dic3—22no—
244C2×C5×Dic3—26no—
245C2×C5×Dic3C2413yes—
246C2×C5×Dic3C2413yes—
247C2×C5×Dic3C2411yescharacteristic
248C2×C5×Dic3C2411yescharacteristic
249C2×C5×Dic3C2411yescharacteristic
250C5×D12—212no—
251C5×D12—26no—
252C5×D12—26no—
253C5×D12C2×D4112yescomplemented
254C4×C5×D3—26no—
255C4×C5×D3—26no—
256C4×C5×D3—26no—
257C4×C5×D3—26no—
258C4×C5×D3—22no—
259C4×C5×D3—26no—
260C4×C5×D3—26no—
261C4×C5×D3—43no—
262C4×C5×D3C2×D4112yescomplemented
263C5×Dic6—26no—
264C2×C3×#41C22×C511yescharacteristic, complemented
265C22×C3×Q8C22×C511yescharacteristic, complemented
266D3×#41—28no—
267C2×#239—28no—
268C2×#239C22×C511yescharacteristic
269C2×#239C22×C513yescomplemented
270C2×#239C22×C513yescomplemented
271C2×#239C22×C511yescharacteristic, complemented
272C2×D3×Q8C22×C511yescharacteristic, complemented
273C2×#237C22×C513yescomplemented
274C2×D3×D4C22×C513yes—
275C2×D3×D4C22×C513yescomplemented
276C2×#235C22×C513yescomplemented
277C22×D12C22×C513yescomplemented
278C22×C4×D3C22×C513yescomplemented
279C22×C4×D3C22×C513yescomplemented
280C3×#124C22×C513yescomplemented
281C3×C22⋊Q8C22×C513yescomplemented
282C3×#121C22×C513yescomplemented
283C3×C4×Q8C22×C511yescharacteristic, complemented
284C3×C4×D4C22×C513yescomplemented
285#946C22×C513yescomplemented
286Q8×Dic3C22×C511yescharacteristic, complemented
287#944C22×C513yescomplemented
288#940C22×C513yescomplemented
289#938C22×C513yescomplemented
290#937C22×C516yescomplemented
291D4×Dic3C22×C513yescomplemented
292#930C22×C513yescomplemented
293C4×#67C22×C513yes—
294C4×#67C22×C513yescomplemented
295#924C22×C513yescomplemented
296#897C22×C513yescomplemented
297#895C22×C513yescomplemented
298#894C22×C516yescomplemented
299#893C22×C513yescomplemented
300#893C22×C513yescomplemented
301#892C22×C513yescomplemented
302D3×C4⋊C4C22×C513yescomplemented
303#884C22×C516yescomplemented
304#884C22×C516yescomplemented
305#883C22×C516yescomplemented
306#882C22×C516yescomplemented
307#67⋊C4C22×C511yescharacteristic
308#67⋊C4C22×C513yescomplemented
309#67⋊C4C22×C516yescomplemented
310D3×C22⋊C4C22×C513yescomplemented
311D3×C22⋊C4C22×C513yescomplemented
312#875C22×C513yescomplemented
313C4×D12C22×C513yescomplemented
314C4×D12C22×C513yescomplemented
315C42×D3C22×C513yescomplemented
316C24×C5—33no—
317C24×C5—33no—
318C5×#41—24no—
319C5×#41—38no—
320C5×#41—612no—
321C5×#41—612no—
322C5×#41—612no—
323C5×#41—612no—
324C5×#41—64no—
325C2×C5×Q8—24no—
326C2×C5×Q8—33no—
327C2×C5×Q8—64no—
328C2×C5×Q8C22×D313yes—
329C2×C5×Q8C22×D311yescharacteristic
330C2×C5×D4—31no—
331C2×C5×D4—33no—
332C2×C5×D4—36no—
333C2×C5×D4—36no—
334C2×C5×D4—33no—
335C2×C5×D4—33no—
336C2×C5×D4—36no—
337C2×C5×D4—33no—
338C2×C5×D4—612no—
339C2×C5×D4—612no—
340C2×C5×D4—612no—
341C2×C5×D4C22×D313yes—
342C2×C5×D4C22×D313yes—
343C22×C4×C5—33no—
344C22×C4×C5—31no—
345C22×C4×C5—33no—
346C22×C4×C5—33no—
347C22×C4×C5—33no—
348C22×C4×C5—33no—
349C22×C4×C5—31no—
350C22×C4×C5—33no—
351C22×C4×C5—33no—
352C22×C4×C5—33no—
353C22×C4×C5—33no—
354C22×C4×C5—612no—
355C22×C4×C5—612no—
356C22×C4×C5C22×D313yes—
357C22×C4×C5C22×D313yes—
358C5×C4⋊C4—31no—
359C5×C4⋊C4—33no—
360C5×C4⋊C4—33no—
361C5×C4⋊C4—33no—
362C5×C4⋊C4—36no—
363C5×C4⋊C4C22×D313yes—
364C5×C4⋊C4C22×D313yes—
365C5×C22⋊C4—33no—
366C5×C22⋊C4—33no—
367C5×C22⋊C4—31no—
368C5×C22⋊C4—33no—
369C5×C22⋊C4—33no—
370C5×C22⋊C4—33no—
371C5×C22⋊C4—36no—
372C5×C22⋊C4—36no—
373C5×C22⋊C4C22×D311yescharacteristic
374C5×C22⋊C4C22×D313yes—
375C5×C22⋊C4C22×D316yes—
376C42×C5—31no—
377C42×C5—33no—
378C42×C5—33no—
379C42×C5C22×D313yes—
380C22×#41—31no—
381C22×#41—31no—
382#550—31no—
383D4×Q8—31no—
384#548—31no—
385#548C5×D311yescharacteristic, complemented
386#547—33no—
387#546—33no—
388#546—33no—
389D42—33no—
390#532—33no—
391#525—33no—
392#525—33no—
393C4×#41—31no—
394C2×C4×D4—33no—
395C22×C3×C5—21no—
396C22×C3×C5—21no—
397C22×C3×C5—23no—
398C22×C3×C5—23no—
399C22×C3×C5—23no—
400C22×C3×C5C2×#4112yescomplemented
401C22×C3×C5C2511yescharacteristic
402C2×C5×D3—21no—
403C2×C5×D3—23no—
404C2×C5×D3—23no—
405C2×C5×D3—21no—
406C2×C5×D3—23no—
407C2×C5×D3—23no—
408C2×C5×D3—23no—
409C2×C5×D3—412no—
410C2×C5×D3—412no—
411C2×C5×D3C22×D416yes—
412C2×C5×D3C2×#4112yescomplemented
413C3×C4×C5—21no—
414C3×C4×C5—23no—
415C3×C4×C5—23no—
416C3×C4×C5—21no—
417C3×C4×C5C22×D416yes—
418C5×Dic3—23no—
419C5×Dic3—21no—
420C5×Dic3—23no—
421C5×Dic3C22×D412yes—
422C5×Dic3C2×#4112yescomplemented
423C23×D3C23×C513yes—
424C23×D3C23×C513yes—
425C3×#41—24no—
426C2×C3×Q8—24no—
427C2×C3×Q8C23×C513yes—
428C2×C3×Q8C23×C511yescharacteristic
429C2×C3×D4C23×C513yes—
430C2×C3×D4C23×C513yes—
431C22×C3×C4C23×C513yes—
432C22×C3×C4C23×C513yes—
433C2×#67C23×C513yes—
434C2×#67C23×C516yes—
435C2×#67C23×C516yes—
436C2×#67C23×C511yescharacteristic
437C22×Dic3C23×C511yescharacteristic
438C22×Dic3C23×C513yes—
439#239—24no—
440#239—212no—
441#239—212no—
442#239C5×D418yescomplemented
443D3×Q8—24no—
444#237—212no—
445D3×D4—212no—
446D3×D4—212no—
447#235—212no—
448C2×D12—212no—
449C2×D12C23×C513yes—
450C2×D12C23×C513yes—
451C2×D12C23×C516yes—
452C2×D12C23×C513yes—
453C2×C4×D3—212no—
454C2×C4×D3—212no—
455C2×C4×D3C23×C513yes—
456C2×C4×D3C23×C513yes—
457C2×C4×D3C23×C513yes—
458C2×C4×D3C23×C513yes—
459C2×C4×D3C23×C513yes—
460C2×C4×D3C23×C511yescharacteristic
461C2×C4×D3C23×C513yes—
462C2×C4×D3C23×C513yes—
463C2×C4×D3C23×C513yes—
464C2×Dic6C23×C513yes—
465C3×C4⋊C4C23×C513yes—
466C3×C4⋊C4C23×C513yes—
467C3×C22⋊C4C23×C511yescharacteristic
468C3×C22⋊C4C23×C513yes—
469C3×C22⋊C4C23×C516yes—
470C3×C42C23×C513yes—
471#217C23×C513yes—
472#217C23×C513yes—
473(C2×D3)⋊C4C23×C511yescharacteristic
474(C2×D3)⋊C4C23×C513yes—
475(C2×D3)⋊C4C23×C516yes—
476(C2×D3)⋊C4C23×C516yes—
477(C2×D3)⋊C4C23×C513yes—
478(C2×D3)⋊C4C23×C513yes—
479C4⋊Dic3C23×C513yes—
480C4⋊Dic3C23×C513yes—
481Dic3⋊C4C23×C511yescharacteristic
482Dic3⋊C4C23×C516yes—
483Dic3⋊C4C23×C513yes—
484C4×Dic3C23×C511yescharacteristic
485C4×Dic3C23×C513yes—
486C4×Dic3C23×C513yes—
487C23×C5—31no—
488C23×C5—33no—
489C23×C5—33no—
490C23×C5—66no—
491C23×C5—66no—
492C23×C5—66no—
493C23×C5—66no—
494C23×C5—123no—
495C23×C5—123no—
496C23×C5C23×D313yes—
497C23×C5C23×D311yescharacteristic
498C5×Q8—26no—
499C5×Q8—66no—
500C5×Q8D3×D414yescomplemented
501C5×D4—26no—
502C5×D4—26no—
503C5×D4—34no—
504C5×D4—312no—
505C5×D4—66no—
506C5×D4—612no—
507C5×D4—66no—
508C5×D4—612no—
509C5×D4—66no—
510C5×D4—126no—
511C2×C4×C5—26no—
512C2×C4×C5—26no—
513C2×C4×C5—31no—
514C2×C4×C5—31no—
515C2×C4×C5—312no—
516C2×C4×C5—33no—
517C2×C4×C5—31no—
518C2×C4×C5—33no—
519C2×C4×C5—62no—
520C2×C4×C5—66no—
521C2×C4×C5—66no—
522C2×C4×C5—66no—
523C2×C4×C5—66no—
524C2×C4×C5—62no—
525C2×C4×C5—66no—
526C2×C4×C5—66no—
527C2×C4×C5—66no—
528C2×C4×C5—123no—
529C2×C4×C5C23×D311yescharacteristic
530C2×C4×C5C23×D313yes—
531C2×C4×C5C23×D311yescharacteristic
532C2×C4×C5C23×D313yes—
533C2×C4×C5C23×D313yes—
534C2×#41—31no—
535C2×#41—33no—
536C2×#41—33no—
537C2×#41—31no—
538C2×#41—33no—
539C2×#41—33no—
540C2×#41—68no—
541C2×#41—68no—
542C2×#41C2×C5×D311yescharacteristic, complemented
543C22×Q8—31no—
544C22×Q8C2×C5×D311yescharacteristic, complemented
545C22×D4—33no—
546C22×D4—33no—
547C22×D4—33no—
548C23×C4—33no—
549C23×C4—33no—
550C4⋊Q8—33no—
551#127—33no—
552#124—33no—
553#124C2×C5×D313yescomplemented
554#123—36no—
555#123—36no—
556C22⋊Q8—33no—
557C22⋊Q8—33no—
558C22⋊Q8—33no—
559C22⋊Q8C2×C5×D313yescomplemented
560#121—33no—
561#121—33no—
562#121—33no—
563#121—36no—
564#121—36no—
565#121C2×C5×D313yescomplemented
566#120—36no—
567#120—36no—
568C4×Q8—31no—
569C4×Q8C2×C5×D311yescharacteristic, complemented
570C4×D4—33no—
571C4×D4—33no—
572C4×D4—33no—
573C4×D4—33no—
574C4×D4—33no—
575C4×D4—31no—
576C4×D4—33no—
577C4×D4—36no—
578C4×D4—33no—
579C4×D4—33no—
580C4×D4C2×C5×D313yescomplemented
581#117—33no—
582C2×C4⋊C4—33no—
583C2×C22⋊C4—33no—
584C2×C22⋊C4—33no—
585C2×C42—33no—
586C2×C3×C5—22no—
587C2×C3×C5—43no—
588C2×C3×C5C23×D411yescharacteristic
589C2×C3×C5C22×#4111yescharacteristic
590C2×C3×C5#58511yescharacteristic
591C5×D3—22no—
592C5×D3—26no—
593C5×D3—43no—
594C23×C3C24×C513yes—
595C23×C3C24×C511yescharacteristic
596C22×D3—26no—
597C22×D3—26no—
598C22×D3—26no—
599C22×D3—26no—
600C22×D3—43no—
601C22×D3—43no—
602C22×D3C24×C513yes—
603C22×D3C24×C513yes—
604C22×D3C24×C511yescharacteristic
605C3×Q8—26no—
606C3×Q8C2×C5×D414yescomplemented
607C3×D4—26no—
608C3×D4—26no—
609C2×C3×C4—26no—
610C2×C3×C4—26no—
611C2×C3×C4C24×C513yes—
612C2×C3×C4C24×C511yescharacteristic
613C2×C3×C4C24×C513yes—
614C2×C3×C4C24×C511yescharacteristic
615C2×C3×C4C24×C513yes—
616#67—212no—
617#67—26no—
618#67—46no—
619#67C5×#4114yescomplemented
620C2×Dic3—22no—
621C2×Dic3—26no—
622C2×Dic3C24×C513yes—
623C2×Dic3C24×C513yes—
624C2×Dic3C24×C511yescharacteristic
625C2×Dic3C24×C511yescharacteristic
626C2×Dic3C24×C511yescharacteristic
627D12—212no—
628D12—26no—
629D12—26no—
630D12C2×C5×D4112yescomplemented
631C4×D3—26no—
632C4×D3—26no—
633C4×D3—26no—
634C4×D3—26no—
635C4×D3—22no—
636C4×D3—26no—
637C4×D3—26no—
638C4×D3—43no—
639C4×D3C2×C5×D4112yescomplemented
640Dic6—26no—
641C22×C5—21no—
642C22×C5—21no—
643C22×C5—23no—
644C22×C5—23no—
645C22×C5—23no—
646C22×C5—36no—
647C22×C5—32no—
648C22×C5—61no—
649C22×C5—63no—
650C22×C5—63no—
651C22×C5—61no—
652C22×C5—63no—
653C22×C5—63no—
654C22×C5—63no—
655C22×C5—1212no—
656C22×C5—1212no—
657C22×C5D3×#4112yescomplemented
658C22×C5C24×D311yescharacteristic
659C4×C5—21no—
660C4×C5—23no—
661C4×C5—23no—
662C4×C5—21no—
663C4×C5—32no—
664C4×C5—32no—
665C4×C5—61no—
666C4×C5—63no—
667C4×C5—63no—
668C4×C5C2×D3×D416yes—
669C24—33no—
670C24—33no—
671#41—24no—
672#41—38no—
673#41—612no—
674#41—612no—
675#41—612no—
676#41—612no—
677#41—64no—
678C2×Q8—24no—
679C2×Q8—33no—
680C2×Q8—64no—
681C2×Q8C22×C5×D313yes—
682C2×Q8C22×C5×D311yescharacteristic
683C2×D4—31no—
684C2×D4—33no—
685C2×D4—36no—
686C2×D4—36no—
687C2×D4—33no—
688C2×D4—33no—
689C2×D4—36no—
690C2×D4—33no—
691C2×D4—612no—
692C2×D4—612no—
693C2×D4—612no—
694C2×D4C22×C5×D313yes—
695C2×D4C22×C5×D313yes—
696C22×C4—33no—
697C22×C4—31no—
698C22×C4—33no—
699C22×C4—33no—
700C22×C4—33no—
701C22×C4—33no—
702C22×C4—31no—
703C22×C4—33no—
704C22×C4—33no—
705C22×C4—33no—
706C22×C4—33no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4C22×C5×D313yes—
710C22×C4C22×C5×D313yes—
711C4⋊C4—31no—
712C4⋊C4—33no—
713C4⋊C4—33no—
714C4⋊C4—33no—
715C4⋊C4—36no—
716C4⋊C4C22×C5×D313yes—
717C4⋊C4C22×C5×D313yes—
718C22⋊C4—33no—
719C22⋊C4—33no—
720C22⋊C4—31no—
721C22⋊C4—33no—
722C22⋊C4—33no—
723C22⋊C4—33no—
724C22⋊C4—36no—
725C22⋊C4—36no—
726C22⋊C4C22×C5×D311yescharacteristic
727C22⋊C4C22×C5×D313yes—
728C22⋊C4C22×C5×D316yes—
729C42—31no—
730C42—33no—
731C42—33no—
732C42C22×C5×D313yes—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—23no—
737C22×C3—23no—
738C22×C3—23no—
739C22×C3C2×C5×#4112yescomplemented
740C22×C3C25×C511yescharacteristic
741C2×D3—21no—
742C2×D3—23no—
743C2×D3—23no—
744C2×D3—21no—
745C2×D3—23no—
746C2×D3—23no—
747C2×D3—23no—
748C2×D3—412no—
749C2×D3—412no—
750C2×D3C22×C5×D416yes—
751C2×D3C2×C5×#4112yescomplemented
752C3×C4—21no—
753C3×C4—23no—
754C3×C4—23no—
755C3×C4—21no—
756C3×C4C22×C5×D416yes—
757Dic3—23no—
758Dic3—21no—
759Dic3—23no—
760Dic3C22×C5×D412yes—
761Dic3C2×C5×#4112yescomplemented
762C2×C5—22no—
763C2×C5—43no—
764C2×C5—62no—
765C2×C5—66no—
766C2×C5—123no—
767C2×C5C22×D3×D411yescharacteristic
768C2×C5C2×D3×#4111yescharacteristic
769C2×C5#596811yescharacteristic
770C23—31no—
771C23—33no—
772C23—33no—
773C23—66no—
774C23—66no—
775C23—66no—
776C23—66no—
777C23—123no—
778C23—123no—
779C23C23×C5×D313yes—
780C23C23×C5×D311yescharacteristic
781Q8—26no—
782Q8—66no—
783Q8C5×D3×D414yescomplemented
784D4—26no—
785D4—26no—
786D4—34no—
787D4—312no—
788D4—612no—
789D4—66no—
790D4—66no—
791D4—612no—
792D4—66no—
793D4—126no—
794C2×C4—26no—
795C2×C4—26no—
796C2×C4—31no—
797C2×C4—31no—
798C2×C4—312no—
799C2×C4—33no—
800C2×C4—31no—
801C2×C4—33no—
802C2×C4—62no—
803C2×C4—66no—
804C2×C4—66no—
805C2×C4—66no—
806C2×C4—66no—
807C2×C4—62no—
808C2×C4—66no—
809C2×C4—66no—
810C2×C4—66no—
811C2×C4—123no—
812C2×C4C23×C5×D311yescharacteristic
813C2×C4C23×C5×D313yes—
814C2×C4C23×C5×D311yescharacteristic
815C2×C4C23×C5×D313yes—
816C2×C4C23×C5×D313yes—
817C2×C3—22no—
818C2×C3—43no—
819C2×C3C23×C5×D411yescharacteristic
820C2×C3C22×C5×#4111yescharacteristic
821C2×C3C5×#58511yescharacteristic
822D3—22no—
823D3—26no—
824D3—43no—
825C5#8671011yescharacteristic, direct product factor, Sylow
826C22—21no—
827C22—21no—
828C22—23no—
829C22—23no—
830C22—23no—
831C22—36no—
832C22—32no—
833C22—61no—
834C22—63no—
835C22—63no—
836C22—61no—
837C22—63no—
838C22—63no—
839C22—63no—
840C22—1212no—
841C22—1212no—
842C22C5×D3×#4112yescomplemented
843C22C24×C5×D311yescharacteristic
844C4—21no—
845C4—23no—
846C4—23no—
847C4—21no—
848C4—32no—
849C4—32no—
850C4—61no—
851C4—63no—
852C4—63no—
853C4C2×C5×D3×D416yes—
854C3C5×D4×#4111yescharacteristic, complemented, Sylow
855C2—22no—
856C2—43no—
857C2—62no—
858C2—66no—
859C2—123no—
860C2C22×C5×D3×D411yescharacteristic
861C2C2×C5×D3×#4111yescharacteristic
862C2C5×#596811yescharacteristic
subgroupG/H
centerC22×C5C24×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC3×C5×#548C2
socleC22×C3×C5C25
hypercenterC5×#548D3
hypocenterC3C5×D4×#41
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×#239C2semidirect
3. C3×C5×#548C2semidirect
4. C5×#5834C2semidirect
5. C5×Q8×#67C2semidirect
6. C5×#5676C2semidirect
7. C5×#5668C2semidirect
8. C5×#5631C2semidirect
9. C5×#5627C2semidirect
10. C5×#5609C2semidirect
11. C5×#5606C2semidirect
12. C5×#5576C2semidirect
13. C4×C5×#239C2semidirect
14. C5×#5550C2semidirect
15. C4×C5×D3×D4C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×Q8C22semidirect
22. C2×C5×#239C22semidirect
23. C2×C5×#239C22semidirect
24. C2×C5×#239C22semidirect
25. C2×C5×D3×Q8C22semidirect
26. C2×C5×#237C22semidirect
28. C2×C5×D3×D4C22semidirect
29. C2×C5×#235C22semidirect
30. C22×C5×D12C22semidirect
31. C22×C4×C5×D3C22semidirect
32. C22×C4×C5×D3C22semidirect
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×#946C22semidirect
39. C5×Q8×Dic3C22semidirect
40. C5×#944C22semidirect
41. C5×#940C22semidirect
42. C5×#938C22semidirect
43. C5×#937C22semidirect
44. C5×D4×Dic3C22semidirect
45. C5×#930C22semidirect
47. C4×C5×#67C22semidirect
48. C5×#924C22semidirect
49. C5×#897C22semidirect
50. C5×#895C22semidirect
51. C5×#894C22semidirect
52. C5×#893C22semidirect
53. C5×#893C22semidirect
54. C5×#892C22semidirect
55. C5×D3×C4⋊C4C22semidirect
56. C5×#884C22semidirect
57. C5×#884C22semidirect
58. C5×#883C22semidirect
59. C5×#882C22semidirect
61. C5×#67⋊C4C22semidirect
62. C5×#67⋊C4C22semidirect
63. C5×D3×C22⋊C4C22semidirect
64. C5×D3×C22⋊C4C22semidirect
65. C5×#875C22semidirect
66. C4×C5×D12C22semidirect
67. C4×C5×D12C22semidirect
68. C42×C5×D3C22semidirect
69. #86710C5direct (N × H)
75. C5×#548D3semidirect
104. C5×#239D4semidirect
149. C2×D3×#41C2×C5semidirect
150. C22×#239C2×C5semidirect
151. C3×#548C2×C5semidirect
152. #5834C2×C5semidirect
153. Q8×#67C2×C5semidirect
154. #5676C2×C5semidirect
155. #5668C2×C5semidirect
156. #5631C2×C5semidirect
157. #5627C2×C5semidirect
158. #5609C2×C5semidirect
159. #5606C2×C5semidirect
160. #5576C2×C5semidirect
161. C4×#239C2×C5semidirect
162. #5550C2×C5semidirect
163. C4×D3×D4C2×C5semidirect
172. C2×C5×#41C2×D3semidirect
174. C22×C5×Q8C2×D3semidirect
183. C5×#124C2×D3semidirect
189. C5×C22⋊Q8C2×D3semidirect
195. C5×#121C2×D3semidirect
199. C4×C5×Q8C2×D3semidirect
210. C4×C5×D4C2×D3semidirect
229. C3×C5×Q8C2×D4semidirect
242. C5×#67#41semidirect
253. C5×D12C2×D4semidirect
262. C4×C5×D3C2×D4semidirect
264. C2×C3×#41C22×C5semidirect
265. C22×C3×Q8C22×C5semidirect
269. C2×#239C22×C5semidirect
270. C2×#239C22×C5semidirect
271. C2×#239C22×C5semidirect
272. C2×D3×Q8C22×C5semidirect
273. C2×#237C22×C5semidirect
275. C2×D3×D4C22×C5semidirect
276. C2×#235C22×C5semidirect
277. C22×D12C22×C5semidirect
278. C22×C4×D3C22×C5semidirect
279. C22×C4×D3C22×C5semidirect
280. C3×#124C22×C5semidirect
281. C3×C22⋊Q8C22×C5semidirect
282. C3×#121C22×C5semidirect
283. C3×C4×Q8C22×C5semidirect
284. C3×C4×D4C22×C5semidirect
285. #946C22×C5semidirect
286. Q8×Dic3C22×C5semidirect
287. #944C22×C5semidirect
288. #940C22×C5semidirect
289. #938C22×C5semidirect
290. #937C22×C5semidirect
291. D4×Dic3C22×C5semidirect
292. #930C22×C5semidirect
294. C4×#67C22×C5semidirect
295. #924C22×C5semidirect
296. #897C22×C5semidirect
297. #895C22×C5semidirect
298. #894C22×C5semidirect
299. #893C22×C5semidirect
300. #893C22×C5semidirect
301. #892C22×C5semidirect
302. D3×C4⋊C4C22×C5semidirect
303. #884C22×C5semidirect
304. #884C22×C5semidirect
305. #883C22×C5semidirect
306. #882C22×C5semidirect
308. #67⋊C4C22×C5semidirect
309. #67⋊C4C22×C5semidirect
310. D3×C22⋊C4C22×C5semidirect
311. D3×C22⋊C4C22×C5semidirect
312. #875C22×C5semidirect
313. C4×D12C22×C5semidirect
314. C4×D12C22×C5semidirect
315. C42×D3C22×C5semidirect
385. #548C5×D3semidirect
400. C22×C3×C5C2×#41semidirect
412. C2×C5×D3C2×#41semidirect
422. C5×Dic3C2×#41semidirect
442. #239C5×D4semidirect
500. C5×Q8D3×D4semidirect
542. C2×#41C2×C5×D3semidirect
544. C22×Q8C2×C5×D3semidirect
553. #124C2×C5×D3semidirect
559. C22⋊Q8C2×C5×D3semidirect
565. #121C2×C5×D3semidirect
569. C4×Q8C2×C5×D3semidirect
580. C4×D4C2×C5×D3semidirect
606. C3×Q8C2×C5×D4semidirect
619. #67C5×#41semidirect
630. D12C2×C5×D4semidirect
639. C4×D3C2×C5×D4semidirect
657. C22×C5D3×#41semidirect
733. C3×C5D4×#41semidirect
739. C22×C3C2×C5×#41semidirect
751. C2×D3C2×C5×#41semidirect
761. Dic3C2×C5×#41semidirect
783. Q8C5×D3×D4semidirect
825. C5#86710direct (N × H)
842. C22C5×D3×#41semidirect
854. C3C5×D4×#41semidirect

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×#2392
C3×C5×#5482
C5×#58342
C5×Q8×#672
C5×#56762
C5×#56682
C5×#56312
C5×#56272
C5×#56092
C5×#56062
C5×#55762
C4×C5×#2392
C5×#55502
C4×C5×D3×D42
C5×D4×#413
#867105