Finite Group Databasebeta

← C5×#34294 #11957014

Subgroups — C5×#34294 #11957014

Order 1280.

3112 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#548C211yesmaximal, characteristic
2C2×C5×#520C211yesmaximal, characteristic, complemented
3C22×C4×C5×Q8C211yesmaximal, characteristic, complemented
4C5×#2367C213yesmaximal, complemented
5C5×#2361C213yesmaximal, complemented
6C5×#2360C213yesmaximal, complemented
7C5×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
8C5×D4×C4⋊C4C213yesmaximal, complemented
9C5×#2341C211yesmaximal, characteristic, complemented
10C5×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
11C5×#2326C213yesmaximal, complemented
12C5×#2323C213yesmaximal, complemented
13C4×C5×#121C213yesmaximal, complemented
14C5×#2290C213yesmaximal, complemented
15C5×#2276C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C23×C5×Q8C2211yescharacteristic
18C5×#548C4116yescomplemented
19C2×C5×#124C2213yes—
20C2×C5×C22⋊Q8C2213yes—
21C2×C5×#121C2213yes—
22C5×#520—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×D4C2216yes—
34C2×C4×C5×D4C2213yes—
35C2×C5×#117C2213yes—
36C22×C5×C4⋊C4C2213yes—
37C22×C5×C4⋊C4C2213yes—
38C22×C42×C5C2213yes—
39C5×#391C2213yes—
40C5×#391C2213yes—
41C5×#390C2213yes—
42C5×#390C2213yes—
43C5×#389C2213yes—
44C5×#389C2216yes—
45C5×#389C2213yes—
46C5×#388C2213yes—
47C5×#388C2213yes—
48C5×#388C2216yes—
49C5×#388C2216yes—
50C5×#387C2213yes—
51C5×#387C2213yes—
52C5×#386C2213yes—
53C5×#386C2213yes—
54C5×#385C2211yescharacteristic
55C5×#385C2213yes—
56C5×#385C2216yes—
57C5×#385C2216yes—
58C5×#384C2213yes—
59C5×#380C2213yes—
60C5×#380C2213yes—
61C4×C5×C4⋊C4C2213yes—
62C4×C5×C4⋊C4C2213yes—
63C4×C5×C4⋊C4C2213yes—
64C4×C5×C4⋊C4C2213yes—
65C4×C5×C22⋊C4C2213yes—
66C4×C5×C22⋊C4C2213yes—
67C4×C5×C22⋊C4C2216yes—
68C5×#376C2213yes—
69#34294C511yesmaximal, 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×C5C2311yescharacteristic
81C23×C4×C5C2313yes—
82C23×C4×C5C2313yes—
83C23×C4×C5C2313yes—
84C23×C4×C5C2316yes—
85C5×#124C2×C4124yescomplemented
86C5×C22⋊Q8C2×C4124yescomplemented
87C5×#121C2×C4124yescomplemented
88C4×C5×Q8—24no—
89C4×C5×Q8—24no—
90C4×C5×Q8—24no—
91C4×C5×Q8—212no—
92C4×C5×Q8—212no—
93C4×C5×Q8C2×C418yescomplemented
94C4×C5×Q8D418yescomplemented
95C4×C5×D4—212no—
96C4×C5×D4—212no—
97C4×C5×D4—412no—
98C4×C5×D4C2×C4124yescomplemented
99C5×#117—212no—
100C2×C5×C4⋊C4—212no—
101C2×C5×C4⋊C4—212no—
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2313yes—
104C2×C5×C4⋊C4C2313yes—
105C2×C5×C4⋊C4C2313yes—
106C2×C5×C4⋊C4C2316yes—
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2313yes—
109C2×C5×C4⋊C4C2313yes—
110C2×C5×C4⋊C4C2316yes—
111C2×C5×C4⋊C4C2313yes—
112C2×C5×C4⋊C4C2313yes—
113C2×C5×C4⋊C4C2313yes—
114C2×C5×C22⋊C4C2311yescharacteristic
115C2×C5×C22⋊C4C2313yes—
116C2×C5×C22⋊C4C2313yes—
117C2×C5×C22⋊C4C2313yes—
118C2×C5×C22⋊C4C2313yes—
119C2×C5×C22⋊C4C2313yes—
120C2×C5×C22⋊C4C2316yes—
121C2×C5×C22⋊C4C2316yes—
122C2×C5×C22⋊C4C2311yescharacteristic
123C2×C5×C22⋊C4C2313yes—
124C2×C42×C5—212no—
125C2×C42×C5C2313yes—
126C2×C42×C5C2313yes—
127C2×C42×C5C2313yes—
128C2×C42×C5C2313yes—
129C2×C42×C5C2313yes—
130C2×C42×C5C2316yes—
131C2×C42×C5C2313yes—
132C2×C42×C5C2313yes—
133C5×#95C2311yescharacteristic
134C5×#95C2313yes—
135C5×#95C2313yes—
136C5×#95C2313yes—
137C5×#95C2311yescharacteristic
138C5×#95C2313yes—
139C5×#95C2313yes—
140C5×#95C2316yes—
141C5×#95C2313yes—
142C5×#95C2313yes—
143C5×#95C2313yes—
144C2×#548C2×C511yescharacteristic
145C2×#520C2×C511yescharacteristic, complemented
146C22×C4×Q8C2×C511yescharacteristic, complemented
147#2367C2×C513yescomplemented
148#2361C2×C513yescomplemented
149#2360C2×C513yescomplemented
150Q8×C4⋊C4C2×C511yescharacteristic, complemented
151D4×C4⋊C4C2×C513yescomplemented
152#2341C2×C511yescharacteristic, complemented
153Q8×C22⋊C4C2×C511yescharacteristic, complemented
154#2326C2×C513yescomplemented
155#2323C2×C513yescomplemented
156C4×#121C2×C513yescomplemented
157#2290C2×C513yescomplemented
158#2276C2×C511yescharacteristic, complemented
159C24×C5C2413yes—
160C24×C5C2411yescharacteristic
161C5×#41—232no—
162C2×C5×Q8—232no—
163C2×C5×Q8—26no—
164C2×C5×Q8—26no—
165C2×C5×Q8C22×C4112yes—
166C2×C5×Q8C22×C414yes—
167C2×C5×Q8C2×D414yes—
168C2×C5×Q8#4114yes—
169C2×C5×D4—26no—
170C2×C5×D4—26no—
171C2×C5×D4—26no—
172C2×C5×D4—26no—
173C2×C5×D4C22×C4112yes—
174C2×C5×D4C22×C4112yes—
175C22×C4×C5—22no—
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—212no—
185C22×C4×C5—43no—
186C22×C4×C5—46no—
187C22×C4×C5—46no—
188C22×C4×C5C22×C4112yes—
189C22×C4×C5C22×C4112yes—
190C22×C4×C5C2411yescharacteristic
191C22×C4×C5C2413yes—
192C22×C4×C5C2411yescharacteristic
193C22×C4×C5C2413yes—
194C22×C4×C5C2413yes—
195C22×C4×C5C2411yescharacteristic
196C22×C4×C5C2413yes—
197C22×C4×C5C2413yes—
198C22×C4×C5C2411yescharacteristic
199C22×C4×C5C2411yescharacteristic
200C22×C4×C5C2413yes—
201C22×C4×C5C2411yescharacteristic
202C22×C4×C5C2413yes—
203C5×C4⋊C4—26no—
204C5×C4⋊C4—26no—
205C5×C4⋊C4—212no—
206C5×C4⋊C4—26no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—26no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—43no—
211C5×C4⋊C4—46no—
212C5×C4⋊C4C22×C4112yes—
213C5×C4⋊C4C22×C4112yes—
214C5×C4⋊C4C2×D4112yes—
215C5×C22⋊C4—26no—
216C5×C22⋊C4—22no—
217C5×C22⋊C4—26no—
218C5×C22⋊C4—26no—
219C5×C22⋊C4—26no—
220C5×C22⋊C4—43no—
221C5×C22⋊C4—46no—
222C5×C22⋊C4C22×C414yes—
223C5×C22⋊C4C22×C4112yes—
224C5×C22⋊C4C22×C4124yes—
225C42×C5—26no—
226C42×C5—26no—
227C42×C5—26no—
228C42×C5—26no—
229C42×C5—26no—
230C42×C5—46no—
231C42×C5C22×C4112yes—
232C42×C5C2×D4112yes—
233C22×#41C22×C511yescharacteristic
234C23×Q8C22×C511yescharacteristic
235#548C4×C5116yescomplemented
236C2×#124C22×C513yes—
237C2×C22⋊Q8C22×C513yes—
238C2×#121C22×C513yes—
239#520—28no—
240C2×C4×Q8—28no—
241C2×C4×Q8C22×C513yes—
242C2×C4×Q8C22×C511yescharacteristic
243C2×C4×Q8C22×C511yescharacteristic
244C2×C4×Q8C22×C511yescharacteristic
245C2×C4×Q8C22×C513yes—
246C2×C4×Q8C22×C511yescharacteristic
247C2×C4×Q8C22×C511yescharacteristic
248C2×C4×D4C22×C513yes—
249C2×C4×D4C22×C513yes—
250C2×C4×D4C22×C516yes—
251C2×C4×D4C22×C513yes—
252C2×#117C22×C513yes—
253C22×C4⋊C4C22×C513yes—
254C22×C4⋊C4C22×C513yes—
255C22×C42C22×C513yes—
256#391C22×C513yes—
257#391C22×C513yes—
258#390C22×C513yes—
259#390C22×C513yes—
260#389C22×C516yes—
261#389C22×C513yes—
262#389C22×C513yes—
263#388C22×C516yes—
264#388C22×C516yes—
265#388C22×C513yes—
266#388C22×C513yes—
267#387C22×C513yes—
268#387C22×C513yes—
269#386C22×C513yes—
270#386C22×C513yes—
271#385C22×C516yes—
272#385C22×C516yes—
273#385C22×C513yes—
274#385C22×C511yescharacteristic
275#384C22×C513yes—
276#380C22×C513yes—
277#380C22×C513yes—
278C4×C4⋊C4C22×C513yes—
279C4×C4⋊C4C22×C513yes—
280C4×C4⋊C4C22×C513yes—
281C4×C4⋊C4C22×C513yes—
282C4×C22⋊C4C22×C513yes—
283C4×C22⋊C4C22×C513yes—
284C4×C22⋊C4C22×C516yes—
285#376C22×C513yes—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—23no—
291C23×C5—23no—
292C23×C5—23no—
293C23×C5—23no—
294C23×C5—23no—
295C23×C5—23no—
296C23×C5C23×C416yes—
297C23×C5C23×C412yes—
298C23×C5H(5,𝔽2)12yes—
299C23×C52−1+412yes—
300C23×C5C2511yescharacteristic
301C5×Q8—224no—
302C5×Q8C4×D4116yescomplemented
303C5×D4—224no—
304C5×D4—224no—
305C2×C4×C5—28no—
306C2×C4×C5—21no—
307C2×C4×C5—23no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—23no—
311C2×C4×C5—23no—
312C2×C4×C5—23no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—23no—
318C2×C4×C5—21no—
319C2×C4×C5—23no—
320C2×C4×C5—224no—
321C2×C4×C5—224no—
322C2×C4×C5—21no—
323C2×C4×C5—23no—
324C2×C4×C5—23no—
325C2×C4×C5—21no—
326C2×C4×C5—23no—
327C2×C4×C5—23no—
328C2×C4×C5—23no—
329C2×C4×C5—23no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—23no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—23no—
336C2×C4×C5—23no—
337C2×C4×C5—412no—
338C2×C4×C5—812no—
339C2×C4×C5C23×C412yes—
340C2×C4×C5C23×C416yes—
341C2×C4×C5C23×C416yes—
342C2×C4×C5C23×C412yes—
343C2×C4×C5C23×C416yes—
344C2×C4×C5C22×D412yes—
345C2×C4×C5C22×D416yes—
346C2×C4×C5C22×D416yes—
347C2×C4×C5C2×#4116yes—
348C2×C4×C52−1+412yes—
349C2×#41—24no—
350C2×#41—24no—
351C2×#41C2×C4×C518yescomplemented
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8C2×C4×C518yescomplemented
355C22×Q8C23×C513yes—
356C22×Q8C23×C511yescharacteristic
357C22×D4C23×C513yes—
358C22×D4C23×C513yes—
359C23×C4C23×C511yescharacteristic
360C23×C4C23×C513yes—
361C23×C4C23×C513yes—
362C23×C4C23×C513yes—
363C23×C4C23×C516yes—
364#124C2×C4×C5124yescomplemented
365C22⋊Q8C2×C4×C5124yescomplemented
366#121C2×C4×C5124yescomplemented
367C4×Q8—24no—
368C4×Q8—24no—
369C4×Q8—24no—
370C4×Q8—212no—
371C4×Q8—212no—
372C4×Q8C2×C4×C518yescomplemented
373C4×Q8C5×D418yescomplemented
374C4×D4—212no—
375C4×D4—212no—
376C4×D4—412no—
377C4×D4C2×C4×C5124yescomplemented
378#117—212no—
379C2×C4⋊C4—212no—
380C2×C4⋊C4—212no—
381C2×C4⋊C4C23×C513yes—
382C2×C4⋊C4C23×C513yes—
383C2×C4⋊C4C23×C513yes—
384C2×C4⋊C4C23×C516yes—
385C2×C4⋊C4C23×C511yescharacteristic
386C2×C4⋊C4C23×C513yes—
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C4⋊C4C23×C516yes—
389C2×C4⋊C4C23×C513yes—
390C2×C4⋊C4C23×C513yes—
391C2×C4⋊C4C23×C513yes—
392C2×C4⋊C4C23×C513yes—
393C2×C22⋊C4C23×C513yes—
394C2×C22⋊C4C23×C513yes—
395C2×C22⋊C4C23×C513yes—
396C2×C22⋊C4C23×C511yescharacteristic
397C2×C22⋊C4C23×C513yes—
398C2×C22⋊C4C23×C516yes—
399C2×C22⋊C4C23×C513yes—
400C2×C22⋊C4C23×C511yescharacteristic
401C2×C22⋊C4C23×C513yes—
402C2×C22⋊C4C23×C516yes—
403C2×C42—212no—
404C2×C42C23×C513yes—
405C2×C42C23×C513yes—
406C2×C42C23×C513yes—
407C2×C42C23×C513yes—
408C2×C42C23×C513yes—
409C2×C42C23×C516yes—
410C2×C42C23×C513yes—
411C2×C42C23×C513yes—
412#95C23×C511yescharacteristic
413#95C23×C513yes—
414#95C23×C513yes—
415#95C23×C513yes—
416#95C23×C511yescharacteristic
417#95C23×C513yes—
418#95C23×C513yes—
419#95C23×C516yes—
420#95C23×C513yes—
421#95C23×C513yes—
422#95C23×C513yes—
423C22×C5—22no—
424C22×C5—22no—
425C22×C5—22no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—26no—
430C22×C5—26no—
431C22×C5—26no—
432C22×C5—43no—
433C22×C5—43no—
434C22×C5—43no—
435C22×C5—43no—
436C22×C5#52014yescomplemented
437C22×C5C24×C411yescharacteristic
438C22×C5C23×D411yescharacteristic
439C22×C5C22×#4111yescharacteristic
440C22×C5C2×H(5,𝔽2)11yescharacteristic
441C22×C5C2×2−1+411yescharacteristic
442C22×C5C2×2−1+411yescharacteristic
443C22×C5#58511yescharacteristic
444C4×C5—22no—
445C4×C5—26no—
446C4×C5—26no—
447C4×C5—22no—
448C4×C5—22no—
449C4×C5—22no—
450C4×C5—26no—
451C4×C5—41no—
452C4×C5—43no—
453C4×C5—43no—
454C4×C5—41no—
455C4×C5—43no—
456C4×C5C2×C4×D4112yes—
457C24C24×C513yes—
458C24C24×C511yescharacteristic
459#41—232no—
460C2×Q8—232no—
461C2×Q8—26no—
462C2×Q8—26no—
463C2×Q8C22×C4×C5112yes—
464C2×Q8C22×C4×C514yes—
465C2×Q8C2×C5×D414yes—
466C2×Q8C5×#4114yes—
467C2×D4—26no—
468C2×D4—26no—
469C2×D4—26no—
470C2×D4—26no—
471C2×D4C22×C4×C5112yes—
472C2×D4C22×C4×C5112yes—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—26no—
476C22×C4—26no—
477C22×C4—26no—
478C22×C4—26no—
479C22×C4—22no—
480C22×C4—26no—
481C22×C4—26no—
482C22×C4—212no—
483C22×C4—43no—
484C22×C4—46no—
485C22×C4—46no—
486C22×C4C22×C4×C5112yes—
487C22×C4C22×C4×C5112yes—
488C22×C4C24×C511yescharacteristic
489C22×C4C24×C511yescharacteristic
490C22×C4C24×C513yes—
491C22×C4C24×C513yes—
492C22×C4C24×C513yes—
493C22×C4C24×C511yescharacteristic
494C22×C4C24×C513yes—
495C22×C4C24×C513yes—
496C22×C4C24×C511yescharacteristic
497C22×C4C24×C511yescharacteristic
498C22×C4C24×C513yes—
499C22×C4C24×C511yescharacteristic
500C22×C4C24×C513yes—
501C4⋊C4—26no—
502C4⋊C4—26no—
503C4⋊C4—212no—
504C4⋊C4—26no—
505C4⋊C4—22no—
506C4⋊C4—26no—
507C4⋊C4—22no—
508C4⋊C4—46no—
509C4⋊C4—43no—
510C4⋊C4C22×C4×C5112yes—
511C4⋊C4C22×C4×C5112yes—
512C4⋊C4C2×C5×D4112yes—
513C22⋊C4—26no—
514C22⋊C4—22no—
515C22⋊C4—26no—
516C22⋊C4—26no—
517C22⋊C4—26no—
518C22⋊C4—46no—
519C22⋊C4—43no—
520C22⋊C4C22×C4×C514yes—
521C22⋊C4C22×C4×C5112yes—
522C22⋊C4C22×C4×C5124yes—
523C42—26no—
524C42—26no—
525C42—26no—
526C42—26no—
527C42—26no—
528C42—46no—
529C42C22×C4×C5112yes—
530C42C2×C5×D4112yes—
531C2×C5—24no—
532C2×C5—46no—
533C2×C5C22×C4×D411yescharacteristic
534C2×C5C2×#52011yescharacteristic
535C2×C5C4×2−1+411yescharacteristic
536C2×C5#348611yescharacteristic
537C2×C5#348811yescharacteristic
538C2×C5#351611yescharacteristic
539C2×C5#352211yescharacteristic
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—23no—
545C23—23no—
546C23—23no—
547C23—23no—
548C23—23no—
549C23—23no—
550C23C23×C4×C516yes—
551C23C23×C4×C512yes—
552C23C5×H(5,𝔽2)12yes—
553C23C5×2−1+412yes—
554C23C25×C511yescharacteristic
555Q8—224no—
556Q8C4×C5×D4116yescomplemented
557D4—224no—
558D4—224no—
559C2×C4—28no—
560C2×C4—21no—
561C2×C4—23no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—23no—
572C2×C4—21no—
573C2×C4—23no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—21no—
577C2×C4—23no—
578C2×C4—23no—
579C2×C4—21no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—23no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—23no—
590C2×C4—23no—
591C2×C4—412no—
592C2×C4—812no—
593C2×C4C23×C4×C512yes—
594C2×C4C23×C4×C516yes—
595C2×C4C23×C4×C516yes—
596C2×C4C23×C4×C512yes—
597C2×C4C23×C4×C516yes—
598C2×C4C22×C5×D412yes—
599C2×C4C22×C5×D416yes—
600C2×C4C22×C5×D416yes—
601C2×C4C2×C5×#4116yes—
602C2×C4C5×2−1+412yes—
603C5#3429411yescharacteristic, direct product factor, Sylow
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—26no—
611C22—26no—
612C22—26no—
613C22—43no—
614C22—43no—
615C22—43no—
616C22—43no—
617C22C5×#52014yescomplemented
618C22C24×C4×C511yescharacteristic
619C22C23×C5×D411yescharacteristic
620C22C22×C5×#4111yescharacteristic
621C22C2×C5×H(5,𝔽2)11yescharacteristic
622C22C2×C5×2−1+411yescharacteristic
623C22C2×C5×2−1+411yescharacteristic
624C22C5×#58511yescharacteristic
625C4—22no—
626C4—26no—
627C4—26no—
628C4—22no—
629C4—22no—
630C4—22no—
631C4—26no—
632C4—41no—
633C4—43no—
634C4—43no—
635C4—41no—
636C4—43no—
637C4C2×C4×C5×D4112yes—
638C2—24no—
639C2—46no—
640C2C22×C4×C5×D411yescharacteristic
641C2C2×C5×#52011yescharacteristic
642C2C4×C5×2−1+411yescharacteristic
643C2C5×#348611yescharacteristic
644C2C5×#348811yescharacteristic
645C2C5×#351611yescharacteristic
646C2C5×#352211yescharacteristic
subgroupG/H
center, socleC23×C5C25
commutatorC22C24×C4×C5
Frattini, cosocleC23C25×C5
prime radicalC2×C5×#548C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#520C2semidirect
3. C22×C4×C5×Q8C2semidirect
4. C5×#2367C2semidirect
5. C5×#2361C2semidirect
6. C5×#2360C2semidirect
7. C5×Q8×C4⋊C4C2semidirect
8. C5×D4×C4⋊C4C2semidirect
9. C5×#2341C2semidirect
10. C5×Q8×C22⋊C4C2semidirect
11. C5×#2326C2semidirect
12. C5×#2323C2semidirect
13. C4×C5×#121C2semidirect
14. C5×#2290C2semidirect
15. C5×#2276C2semidirect
18. C5×#548C4semidirect
69. #34294C5direct (N × H)
72. C2×C5×#41C2×C4semidirect
75. C22×C5×Q8C2×C4semidirect
85. C5×#124C2×C4semidirect
86. C5×C22⋊Q8C2×C4semidirect
87. C5×#121C2×C4semidirect
93. C4×C5×Q8C2×C4semidirect
94. C4×C5×Q8D4semidirect
98. C4×C5×D4C2×C4semidirect
145. C2×#520C2×C5semidirect
146. C22×C4×Q8C2×C5semidirect
147. #2367C2×C5semidirect
148. #2361C2×C5semidirect
149. #2360C2×C5semidirect
150. Q8×C4⋊C4C2×C5semidirect
151. D4×C4⋊C4C2×C5semidirect
152. #2341C2×C5semidirect
153. Q8×C22⋊C4C2×C5semidirect
154. #2326C2×C5semidirect
155. #2323C2×C5semidirect
156. C4×#121C2×C5semidirect
157. #2290C2×C5semidirect
158. #2276C2×C5semidirect
235. #548C4×C5semidirect
302. C5×Q8C4×D4semidirect
351. C2×#41C2×C4×C5semidirect
354. C22×Q8C2×C4×C5semidirect
364. #124C2×C4×C5semidirect
365. C22⋊Q8C2×C4×C5semidirect
366. #121C2×C4×C5semidirect
372. C4×Q8C2×C4×C5semidirect
373. C4×Q8C5×D4semidirect
377. C4×D4C2×C4×C5semidirect
436. C22×C5#520semidirect
556. Q8C4×C5×D4semidirect
603. C5#34294direct (N × H)
617. C22C5×#520semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5482
C2×C5×#5202
C22×C4×C5×Q82
C5×#23672
C5×#23612
C5×#23602
C5×Q8×C4⋊C42
C5×D4×C4⋊C42
C5×#23412
C5×Q8×C22⋊C42
C5×#23262
C5×#23232
C4×C5×#1212
C5×#22902
C5×#22762
#342945