Finite Group Databasebeta

← C4×C5×#548 #11956878

Subgroups — C4×C5×#548 #11956878

Order 1280.

3232 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#548C211yesmaximal, characteristic
2C2×C4×C5×#41C211yesmaximal, characteristic, complemented
3C22×C4×C5×Q8C211yesmaximal, characteristic, complemented
4C5×#2367C213yesmaximal, complemented
5C5×#2362C213yesmaximal, complemented
6C5×#2361C213yesmaximal, complemented
7C5×#2352C213yesmaximal, complemented
8C5×#2351C211yesmaximal, characteristic, complemented
9C5×#2341C211yesmaximal, characteristic, complemented
10C5×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
11C4×C5×#124C213yesmaximal, complemented
12C4×C5×C22⋊Q8C213yesmaximal, complemented
13C4×C5×#121C213yesmaximal, complemented
14C42×C5×Q8C211yesmaximal, characteristic, complemented
15C42×C5×D4C213yesmaximal, complemented
16C22×C5×#41C2211yescharacteristic
17C23×C5×Q8C2211yescharacteristic
18C5×#548C4116yesdirect product factor
19C2×C5×#124C2213yes—
20C2×C5×C22⋊Q8C2213yes—
21C2×C5×#121C2213yes—
22C4×C5×#41—28no—
23C2×C4×C5×Q8—28no—
24C2×C4×C5×Q8C2211yescharacteristic
25C2×C4×C5×Q8C2213yes—
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×Q8C2213yes—
28C2×C4×C5×Q8C2211yescharacteristic
29C2×C4×C5×Q8C2211yescharacteristic
30C2×C4×C5×Q8C2211yescharacteristic
31C2×C4×C5×D4C2213yes—
32C2×C4×C5×D4C2213yes—
33C2×C4×C5×D4C2213yes—
34C2×C4×C5×D4C2213yes—
35C2×C4×C5×D4C2213yes—
36C2×C5×#117C2213yes—
37C22×C5×C4⋊C4C2213yes—
38C22×C42×C5C2213yes—
39C22×C42×C5C2213yes—
40C5×#391C2213yes—
41C5×#391C2213yes—
42C5×#390C2213yes—
43C5×#390C2213yes—
44C5×#389C2213yes—
45C5×#389C2213yes—
46C5×#388C2216yes—
47C5×#388C2216yes—
48C5×#388C2216yes—
49C5×#387C2216yes—
50C5×#386C2216yes—
51C5×#385C2216yes—
52C5×#382C2213yes—
53C5×#380C2213yes—
54C5×#380C2213yes—
55C4×C5×C4⋊C4C2213yes—
56C4×C5×C4⋊C4C2213yes—
57C4×C5×C4⋊C4C2213yes—
58C4×C5×C4⋊C4C2213yes—
59C4×C5×C4⋊C4C2213yes—
60C4×C5×C4⋊C4C2213yes—
61C4×C5×C22⋊C4C2211yescharacteristic
62C4×C5×C22⋊C4C2213yes—
63C4×C5×C22⋊C4C2213yes—
64C4×C5×C22⋊C4C2213yes—
65C4×C5×C22⋊C4C2213yes—
66C4×C5×C22⋊C4C2213yes—
67C4×C5×C22⋊C4C2216yes—
68C43×C5C2213yes—
69C4×#548C511yesmaximal, characteristic, direct product factor, Sylow
70C2×C5×#41—24no—
71C2×C5×#41—24no—
72C2×C5×#41C2×C418yescomplemented
73C22×C5×Q8—24no—
74C22×C5×Q8—24no—
75C22×C5×Q8C2×C418yescomplemented
76C22×C5×Q8C2313yes—
77C22×C5×Q8C2311yescharacteristic
78C22×C5×D4C2313yes—
79C22×C5×D4C2313yes—
80C23×C4×C5C2313yes—
81C23×C4×C5C2313yes—
82C23×C4×C5C2313yes—
83C23×C4×C5C2313yes—
84C23×C4×C5C2313yes—
85C23×C4×C5C2311yescharacteristic
86C5×#124C2×C4124yescomplemented
87C5×C22⋊Q8C2×C4124yescomplemented
88C5×#121C2×C4124yescomplemented
89C4×C5×Q8—24no—
90C4×C5×Q8—24no—
91C4×C5×Q8—24no—
92C4×C5×Q8—212no—
93C4×C5×Q8—212no—
94C4×C5×Q8C2×C418yescomplemented
95C4×C5×Q8D418yescomplemented
96C4×C5×D4—212no—
97C4×C5×D4—212no—
98C4×C5×D4—212no—
99C4×C5×D4—212no—
100C4×C5×D4C2×C4124yescomplemented
101C5×#117—212no—
102C2×C5×C4⋊C4—212no—
103C2×C5×C4⋊C4C2313yes—
104C2×C5×C4⋊C4C2313yes—
105C2×C5×C4⋊C4C2313yes—
106C2×C5×C4⋊C4C2313yes—
107C2×C5×C4⋊C4C2313yes—
108C2×C5×C4⋊C4C2316yes—
109C2×C5×C4⋊C4C2313yes—
110C2×C5×C4⋊C4C2313yes—
111C2×C5×C4⋊C4C2313yes—
112C2×C5×C22⋊C4C2313yes—
113C2×C5×C22⋊C4C2313yes—
114C2×C5×C22⋊C4C2313yes—
115C2×C5×C22⋊C4C2316yes—
116C2×C5×C22⋊C4C2316yes—
117C2×C5×C22⋊C4C2311yescharacteristic
118C2×C5×C22⋊C4C2313yes—
119C2×C5×C22⋊C4C2316yes—
120C2×C5×C22⋊C4C2311yescharacteristic
121C2×C42×C5—212no—
122C2×C42×C5—212no—
123C2×C42×C5C2313yes—
124C2×C42×C5C2313yes—
125C2×C42×C5C2313yes—
126C2×C42×C5C2313yes—
127C2×C42×C5C2313yes—
128C2×C42×C5C2313yes—
129C2×C42×C5C2311yescharacteristic
130C2×C42×C5C2313yes—
131C2×C42×C5C2313yes—
132C2×C42×C5C2311yescharacteristic
133C2×C42×C5C2313yes—
134C2×C42×C5C2313yes—
135C2×C42×C5C2313yes—
136C5×#95C2311yescharacteristic
137C5×#95C2311yescharacteristic
138C5×#95C2313yes—
139C5×#95C2313yes—
140C5×#95C2313yes—
141C5×#95C2313yes—
142C5×#95C2316yes—
143C5×#95C2316yes—
144C5×#95C2316yes—
145C2×#548C2×C511yescharacteristic
146C2×C4×#41C2×C511yescharacteristic, complemented
147C22×C4×Q8C2×C511yescharacteristic, complemented
148#2367C2×C513yescomplemented
149#2362C2×C513yescomplemented
150#2361C2×C513yescomplemented
151#2352C2×C513yescomplemented
152#2351C2×C511yescharacteristic, complemented
153#2341C2×C511yescharacteristic, complemented
154Q8×C22⋊C4C2×C511yescharacteristic, complemented
155C4×#124C2×C513yescomplemented
156C4×C22⋊Q8C2×C513yescomplemented
157C4×#121C2×C513yescomplemented
158C42×Q8C2×C511yescharacteristic, complemented
159C42×D4C2×C513yescomplemented
160C24×C5C2413yes—
161C24×C5C2411yescharacteristic
162C5×#41—232no—
163C2×C5×Q8—232no—
164C2×C5×Q8—26no—
165C2×C5×Q8—26no—
166C2×C5×Q8C22×C4112yes—
167C2×C5×Q8C22×C414yes—
168C2×C5×Q8C2×D414yes—
169C2×C5×Q8#4114yes—
170C2×C5×D4—26no—
171C2×C5×D4—26no—
172C2×C5×D4—26no—
173C2×C5×D4—26no—
174C2×C5×D4C22×C4112yes—
175C2×C5×D4C22×C4112yes—
176C22×C4×C5—22no—
177C22×C4×C5—26no—
178C22×C4×C5—26no—
179C22×C4×C5—26no—
180C22×C4×C5—26no—
181C22×C4×C5—22no—
182C22×C4×C5—26no—
183C22×C4×C5—26no—
184C22×C4×C5—26no—
185C22×C4×C5—26no—
186C22×C4×C5—26no—
187C22×C4×C5—26no—
188C22×C4×C5—26no—
189C22×C4×C5—43no—
190C22×C4×C5—43no—
191C22×C4×C5C22×C4112yes—
192C22×C4×C5C22×C4112yes—
193C22×C4×C5#4114yescomplemented
194C22×C4×C5C2413yes—
195C22×C4×C5C2413yes—
196C22×C4×C5C2413yes—
197C22×C4×C5C2411yescharacteristic
198C22×C4×C5C2411yescharacteristic
199C22×C4×C5C2413yes—
200C22×C4×C5C2413yes—
201C22×C4×C5C2413yes—
202C22×C4×C5C2411yescharacteristic
203C22×C4×C5C2411yescharacteristic
204C22×C4×C5C2411yescharacteristic
205C22×C4×C5C2413yes—
206C22×C4×C5C2411yescharacteristic
207C5×C4⋊C4—212no—
208C5×C4⋊C4—26no—
209C5×C4⋊C4—26no—
210C5×C4⋊C4—26no—
211C5×C4⋊C4—26no—
212C5×C4⋊C4—26no—
213C5×C4⋊C4C22×C4112yes—
214C5×C4⋊C4C22×C4112yes—
215C5×C4⋊C4C2×D4112yes—
216C5×C22⋊C4—26no—
217C5×C22⋊C4—212no—
218C5×C22⋊C4—26no—
219C5×C22⋊C4—26no—
220C5×C22⋊C4—46no—
221C5×C22⋊C4C22×C414yes—
222C5×C22⋊C4C22×C4112yes—
223C5×C22⋊C4C22×C4124yes—
224C5×C22⋊C4#4114yescomplemented
225C42×C5—22no—
226C42×C5—26no—
227C42×C5—26no—
228C42×C5—26no—
229C42×C5—26no—
230C42×C5—26no—
231C42×C5—26no—
232C42×C5—26no—
233C42×C5—26no—
234C42×C5—22no—
235C42×C5—43no—
236C42×C5C22×C4112yes—
237C42×C5C2×D4112yes—
238C22×#41C22×C511yescharacteristic
239C23×Q8C22×C511yescharacteristic
240#548C4×C5116yesdirect product factor
241C2×#124C22×C513yes—
242C2×C22⋊Q8C22×C513yes—
243C2×#121C22×C513yes—
244C4×#41—28no—
245C2×C4×Q8—28no—
246C2×C4×Q8C22×C511yescharacteristic
247C2×C4×Q8C22×C511yescharacteristic
248C2×C4×Q8C22×C511yescharacteristic
249C2×C4×Q8C22×C513yes—
250C2×C4×Q8C22×C513yes—
251C2×C4×Q8C22×C511yescharacteristic
252C2×C4×Q8C22×C511yescharacteristic
253C2×C4×D4C22×C513yes—
254C2×C4×D4C22×C513yes—
255C2×C4×D4C22×C513yes—
256C2×C4×D4C22×C513yes—
257C2×C4×D4C22×C513yes—
258C2×#117C22×C513yes—
259C22×C4⋊C4C22×C513yes—
260C22×C42C22×C513yes—
261C22×C42C22×C513yes—
262#391C22×C513yes—
263#391C22×C513yes—
264#390C22×C513yes—
265#390C22×C513yes—
266#389C22×C513yes—
267#389C22×C513yes—
268#388C22×C516yes—
269#388C22×C516yes—
270#388C22×C516yes—
271#387C22×C516yes—
272#386C22×C516yes—
273#385C22×C516yes—
274#382C22×C513yes—
275#380C22×C513yes—
276#380C22×C513yes—
277C4×C4⋊C4C22×C513yes—
278C4×C4⋊C4C22×C513yes—
279C4×C4⋊C4C22×C513yes—
280C4×C4⋊C4C22×C513yes—
281C4×C4⋊C4C22×C513yes—
282C4×C4⋊C4C22×C513yes—
283C4×C22⋊C4C22×C513yes—
284C4×C22⋊C4C22×C513yes—
285C4×C22⋊C4C22×C513yes—
286C4×C22⋊C4C22×C513yes—
287C4×C22⋊C4C22×C511yescharacteristic
288C4×C22⋊C4C22×C513yes—
289C4×C22⋊C4C22×C516yes—
290C43C22×C513yes—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—21no—
295C23×C5—23no—
296C23×C5—23no—
297C23×C5—23no—
298C23×C5—23no—
299C23×C5—23no—
300C23×C5—23no—
301C23×C5C23×C416yes—
302C23×C5C23×C412yes—
303C23×C5C2×#4112yes—
304C23×C5C2×#4112yes—
305C23×C5C2511yescharacteristic
306C5×Q8—224no—
307C5×Q8C4×D4116yescomplemented
308C5×D4—224no—
309C5×D4—224no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—23no—
314C2×C4×C5—21no—
315C2×C4×C5—23no—
316C2×C4×C5—23no—
317C2×C4×C5—23no—
318C2×C4×C5—21no—
319C2×C4×C5—23no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—23no—
325C2×C4×C5—21no—
326C2×C4×C5—224no—
327C2×C4×C5—224no—
328C2×C4×C5—28no—
329C2×C4×C5—23no—
330C2×C4×C5—23no—
331C2×C4×C5—23no—
332C2×C4×C5—23no—
333C2×C4×C5—23no—
334C2×C4×C5—23no—
335C2×C4×C5—23no—
336C2×C4×C5—23no—
337C2×C4×C5—23no—
338C2×C4×C5—412no—
339C2×C4×C5—412no—
340C2×C4×C5—412no—
341C2×C4×C5C23×C412yes—
342C2×C4×C5C23×C416yes—
343C2×C4×C5C23×C416yes—
344C2×C4×C5C23×C412yes—
345C2×C4×C5C23×C416yes—
346C2×C4×C5C22×D416yes—
347C2×C4×C5C22×D416yes—
348C2×C4×C5C22×D412yes—
349C2×C4×C5C2×#4112yes—
350C2×C4×C5C2×#4112yes—
351C2×C4×C5C2×#4112yes—
352C2×C4×C5C2×#4116yes—
353C2×C4×C5C2×#4112yes—
354C2×C4×C52−1+412yes—
355C2×#41—24no—
356C2×#41—24no—
357C2×#41C2×C4×C518yescomplemented
358C22×Q8—24no—
359C22×Q8—24no—
360C22×Q8C2×C4×C518yescomplemented
361C22×Q8C23×C513yes—
362C22×Q8C23×C511yescharacteristic
363C22×D4C23×C513yes—
364C22×D4C23×C513yes—
365C23×C4C23×C513yes—
366C23×C4C23×C513yes—
367C23×C4C23×C513yes—
368C23×C4C23×C513yes—
369C23×C4C23×C513yes—
370C23×C4C23×C511yescharacteristic
371#124C2×C4×C5124yescomplemented
372C22⋊Q8C2×C4×C5124yescomplemented
373#121C2×C4×C5124yescomplemented
374C4×Q8—24no—
375C4×Q8—24no—
376C4×Q8—24no—
377C4×Q8—212no—
378C4×Q8—212no—
379C4×Q8C2×C4×C518yescomplemented
380C4×Q8C5×D418yescomplemented
381C4×D4—212no—
382C4×D4—212no—
383C4×D4—212no—
384C4×D4—212no—
385C4×D4C2×C4×C5124yescomplemented
386#117—212no—
387C2×C4⋊C4—212no—
388C2×C4⋊C4C23×C513yes—
389C2×C4⋊C4C23×C516yes—
390C2×C4⋊C4C23×C513yes—
391C2×C4⋊C4C23×C513yes—
392C2×C4⋊C4C23×C513yes—
393C2×C4⋊C4C23×C513yes—
394C2×C4⋊C4C23×C513yes—
395C2×C4⋊C4C23×C513yes—
396C2×C4⋊C4C23×C513yes—
397C2×C22⋊C4C23×C516yes—
398C2×C22⋊C4C23×C513yes—
399C2×C22⋊C4C23×C513yes—
400C2×C22⋊C4C23×C513yes—
401C2×C22⋊C4C23×C516yes—
402C2×C22⋊C4C23×C511yescharacteristic
403C2×C22⋊C4C23×C513yes—
404C2×C22⋊C4C23×C516yes—
405C2×C22⋊C4C23×C511yescharacteristic
406C2×C42—212no—
407C2×C42—212no—
408C2×C42C23×C513yes—
409C2×C42C23×C513yes—
410C2×C42C23×C513yes—
411C2×C42C23×C513yes—
412C2×C42C23×C513yes—
413C2×C42C23×C513yes—
414C2×C42C23×C513yes—
415C2×C42C23×C513yes—
416C2×C42C23×C511yescharacteristic
417C2×C42C23×C511yescharacteristic
418C2×C42C23×C513yes—
419C2×C42C23×C513yes—
420C2×C42C23×C513yes—
421#95C23×C511yescharacteristic
422#95C23×C511yescharacteristic
423#95C23×C513yes—
424#95C23×C513yes—
425#95C23×C513yes—
426#95C23×C513yes—
427#95C23×C516yes—
428#95C23×C516yes—
429#95C23×C516yes—
430C22×C5—22no—
431C22×C5—22no—
432C22×C5—22no—
433C22×C5—22no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—26no—
437C22×C5—26no—
438C22×C5—26no—
439C22×C5—43no—
440C22×C5—43no—
441C22×C5—43no—
442C22×C5—43no—
443C22×C5C4×#4114yescomplemented
444C22×C5C24×C411yescharacteristic
445C22×C5C23×D411yescharacteristic
446C22×C5C22×#4111yescharacteristic
447C22×C5C22×#4111yescharacteristic
448C22×C5C22×#4111yescharacteristic
449C22×C5C2×2−1+411yescharacteristic
450C22×C5#58511yescharacteristic
451C4×C5—22no—
452C4×C5—26no—
453C4×C5—26no—
454C4×C5—22no—
455C4×C5—22no—
456C4×C5—22no—
457C4×C5—26no—
458C4×C5—22no—
459C4×C5—43no—
460C4×C5—43no—
461C4×C5—43no—
462C4×C5C2×C4×D4112yes—
463C4×C5#54814yesdirect product factor
464C24C24×C513yes—
465C24C24×C511yescharacteristic
466#41—232no—
467C2×Q8—232no—
468C2×Q8—26no—
469C2×Q8—26no—
470C2×Q8C22×C4×C5112yes—
471C2×Q8C22×C4×C514yes—
472C2×Q8C2×C5×D414yes—
473C2×Q8C5×#4114yes—
474C2×D4—26no—
475C2×D4—26no—
476C2×D4—26no—
477C2×D4—26no—
478C2×D4C22×C4×C5112yes—
479C2×D4C22×C4×C5112yes—
480C22×C4—22no—
481C22×C4—26no—
482C22×C4—26no—
483C22×C4—26no—
484C22×C4—26no—
485C22×C4—22no—
486C22×C4—26no—
487C22×C4—26no—
488C22×C4—26no—
489C22×C4—26no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—43no—
494C22×C4—43no—
495C22×C4C22×C4×C5112yes—
496C22×C4C22×C4×C5112yes—
497C22×C4C5×#4114yescomplemented
498C22×C4C24×C513yes—
499C22×C4C24×C513yes—
500C22×C4C24×C513yes—
501C22×C4C24×C511yescharacteristic
502C22×C4C24×C511yescharacteristic
503C22×C4C24×C513yes—
504C22×C4C24×C513yes—
505C22×C4C24×C513yes—
506C22×C4C24×C511yescharacteristic
507C22×C4C24×C511yescharacteristic
508C22×C4C24×C511yescharacteristic
509C22×C4C24×C513yes—
510C22×C4C24×C511yescharacteristic
511C4⋊C4—212no—
512C4⋊C4—26no—
513C4⋊C4—26no—
514C4⋊C4—26no—
515C4⋊C4—26no—
516C4⋊C4—26no—
517C4⋊C4C22×C4×C5112yes—
518C4⋊C4C22×C4×C5112yes—
519C4⋊C4C2×C5×D4112yes—
520C22⋊C4—26no—
521C22⋊C4—212no—
522C22⋊C4—26no—
523C22⋊C4—26no—
524C22⋊C4—46no—
525C22⋊C4C22×C4×C514yes—
526C22⋊C4C22×C4×C5112yes—
527C22⋊C4C22×C4×C5124yes—
528C22⋊C4C5×#4114yescomplemented
529C42—22no—
530C42—26no—
531C42—26no—
532C42—26no—
533C42—26no—
534C42—26no—
535C42—26no—
536C42—26no—
537C42—26no—
538C42—22no—
539C42—43no—
540C42C22×C4×C5112yes—
541C42C2×C5×D4112yes—
542C2×C5—24no—
543C2×C5—46no—
544C2×C5C22×C4×D411yescharacteristic
545C2×C5C2×C4×#4111yescharacteristic
546C2×C5C4×2−1+411yescharacteristic
547C2×C5C2×#54811yescharacteristic
548C2×C5D4×#4111yescharacteristic
549C2×C5#348011yescharacteristic
550C2×C5#348211yescharacteristic
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—23no—
556C23—23no—
557C23—23no—
558C23—23no—
559C23—23no—
560C23—23no—
561C23C23×C4×C516yes—
562C23C23×C4×C512yes—
563C23C2×C5×#4112yes—
564C23C2×C5×#4112yes—
565C23C25×C511yescharacteristic
566Q8—224no—
567Q8C4×C5×D4116yescomplemented
568D4—224no—
569D4—224no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—23no—
576C2×C4—23no—
577C2×C4—23no—
578C2×C4—21no—
579C2×C4—23no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—23no—
585C2×C4—21no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—28no—
589C2×C4—23no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—23no—
593C2×C4—23no—
594C2×C4—23no—
595C2×C4—23no—
596C2×C4—23no—
597C2×C4—23no—
598C2×C4—412no—
599C2×C4—412no—
600C2×C4—412no—
601C2×C4C23×C4×C512yes—
602C2×C4C23×C4×C516yes—
603C2×C4C23×C4×C516yes—
604C2×C4C23×C4×C512yes—
605C2×C4C23×C4×C516yes—
606C2×C4C22×C5×D416yes—
607C2×C4C22×C5×D416yes—
608C2×C4C22×C5×D412yes—
609C2×C4C2×C5×#4112yes—
610C2×C4C2×C5×#4112yes—
611C2×C4C2×C5×#4112yes—
612C2×C4C2×C5×#4116yes—
613C2×C4C2×C5×#4112yes—
614C2×C4C5×2−1+412yes—
615C5C4×#54811yescharacteristic, direct product factor, Sylow
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—26no—
623C22—26no—
624C22—26no—
625C22—43no—
626C22—43no—
627C22—43no—
628C22—43no—
629C22C4×C5×#4114yescomplemented
630C22C24×C4×C511yescharacteristic
631C22C23×C5×D411yescharacteristic
632C22C22×C5×#4111yescharacteristic
633C22C22×C5×#4111yescharacteristic
634C22C22×C5×#4111yescharacteristic
635C22C2×C5×2−1+411yescharacteristic
636C22C5×#58511yescharacteristic
637C4—22no—
638C4—26no—
639C4—26no—
640C4—22no—
641C4—22no—
642C4—22no—
643C4—26no—
644C4—22no—
645C4—43no—
646C4—43no—
647C4—43no—
648C4C2×C4×C5×D4112yes—
649C4C5×#54814yesdirect product factor
650C2—24no—
651C2—46no—
652C2C22×C4×C5×D411yescharacteristic
653C2C2×C4×C5×#4111yescharacteristic
654C2C4×C5×2−1+411yescharacteristic
655C2C2×C5×#54811yescharacteristic
656C2C5×D4×#4111yescharacteristic
657C2C5×#348011yescharacteristic
658C2C5×#348211yescharacteristic
subgroupG/H
centerC22×C4×C5C24
commutatorC22C24×C4×C5
Frattini, cosocleC23C25×C5
socleC23×C5C25
prime radicalC2×C5×#548C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×#41C2semidirect
3. C22×C4×C5×Q8C2semidirect
4. C5×#2367C2semidirect
5. C5×#2362C2semidirect
6. C5×#2361C2semidirect
7. C5×#2352C2semidirect
8. C5×#2351C2semidirect
9. C5×#2341C2semidirect
10. C5×Q8×C22⋊C4C2semidirect
11. C4×C5×#124C2semidirect
12. C4×C5×C22⋊Q8C2semidirect
13. C4×C5×#121C2semidirect
14. C42×C5×Q8C2semidirect
15. C42×C5×D4C2semidirect
18. C5×#548C4direct (N × H)
69. C4×#548C5direct (N × H)
72. C2×C5×#41C2×C4semidirect
75. C22×C5×Q8C2×C4semidirect
86. C5×#124C2×C4semidirect
87. C5×C22⋊Q8C2×C4semidirect
88. C5×#121C2×C4semidirect
94. C4×C5×Q8C2×C4semidirect
95. C4×C5×Q8D4semidirect
100. C4×C5×D4C2×C4semidirect
146. C2×C4×#41C2×C5semidirect
147. C22×C4×Q8C2×C5semidirect
148. #2367C2×C5semidirect
149. #2362C2×C5semidirect
150. #2361C2×C5semidirect
151. #2352C2×C5semidirect
152. #2351C2×C5semidirect
153. #2341C2×C5semidirect
154. Q8×C22⋊C4C2×C5semidirect
155. C4×#124C2×C5semidirect
156. C4×C22⋊Q8C2×C5semidirect
157. C4×#121C2×C5semidirect
158. C42×Q8C2×C5semidirect
159. C42×D4C2×C5semidirect
193. C22×C4×C5#41semidirect
224. C5×C22⋊C4#41semidirect
240. #548C4×C5direct (N × H)
307. C5×Q8C4×D4semidirect
357. C2×#41C2×C4×C5semidirect
360. C22×Q8C2×C4×C5semidirect
371. #124C2×C4×C5semidirect
372. C22⋊Q8C2×C4×C5semidirect
373. #121C2×C4×C5semidirect
379. C4×Q8C2×C4×C5semidirect
380. C4×Q8C5×D4semidirect
385. C4×D4C2×C4×C5semidirect
443. C22×C5C4×#41semidirect
463. C4×C5#548direct (N × H)
497. C22×C4C5×#41semidirect
528. C22⋊C4C5×#41semidirect
567. Q8C4×C5×D4semidirect
615. C5C4×#548direct (N × H)
629. C22C4×C5×#41semidirect
649. C4C5×#548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5482
C2×C4×C5×#412
C22×C4×C5×Q82
C5×#23672
C5×#23622
C5×#23612
C5×#23522
C5×#23512
C5×#23412
C5×Q8×C22⋊C42
C4×C5×#1242
C4×C5×C22⋊Q82
C4×C5×#1212
C42×C5×Q82
C42×C5×D42
C4×#5485