Finite Group Databasebeta

← C5×#34262 #11956982

Subgroups — C5×#34262 #11956982

Order 1280.

2198 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#519C211yesmaximal, characteristic
2C5×#2356C213yesmaximal, complemented
3C5×#2355C213yesmaximal, complemented
4C5×#2351C211yesmaximal, characteristic, complemented
5C5×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
6C5×#2347C213yesmaximal
7C5×#2346C213yesmaximal
8C5×Q8×C22⋊C4C211yesmaximal, characteristic
9C5×Q8×C22⋊C4C211yesmaximal, characteristic
10C5×#2320C213yesmaximal, complemented
11C5×#2314C213yesmaximal
12C5×#2298C213yesmaximal
13C5×#2295C213yesmaximal, complemented
14C5×#2276C211yesmaximal, characteristic, complemented
15C42×C5×Q8C211yesmaximal, characteristic, complemented
16C23×C5×Q8C2211yescharacteristic
17C5×#519C4116yescomplemented
18C2×C4×C5×Q8C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C4×C5×Q8C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C4×C5×Q8C2213yes—
24C2×C4×C5×Q8C2211yescharacteristic
25C2×C4×C5×Q8C2213yes—
26C2×C5×#117C2213yes—
27C2×C5×#117C2213yes—
28C5×#391C2213yes—
29C5×#391C2213yes—
30C5×#391C2213yes—
31C5×#391C2213yes—
32C5×#389C2213yes—
33C5×#389C2213yes—
34C5×#389C2213yes—
35C5×#389C2213yes—
36C5×#388C2211yescharacteristic
37C5×#388C2213yes—
38C5×#388C2213yes—
39C5×#388C2213yes—
40C5×#388C2216yes—
41C5×#387C2213yes—
42C5×#387C2216yes—
43C5×#387C2213yes—
44C5×#387C2213yes—
45C5×#387C2213yes—
46C5×#387C2216yes—
47C5×#384C2213yes—
48C5×#383C2216yes—
49C5×#382C2213yes—
50C5×#382C2216yes—
51C5×#380C2213yes—
52C5×#380C2213yes—
53C4×C5×C4⋊C4C2213yes—
54C4×C5×C4⋊C4C2213yes—
55C4×C5×C4⋊C4C2213yes—
56C4×C5×C4⋊C4C2213yes—
57C4×C5×C4⋊C4C2213yes—
58C4×C5×C4⋊C4C2213yes—
59C4×C5×C4⋊C4C2216yes—
60C4×C5×C4⋊C4C2213yes—
61C4×C5×C4⋊C4C2213yes—
62C4×C5×C22⋊C4C2213yes—
63C4×C5×C22⋊C4C2213yes—
64C5×#376C2213yes—
65C5×#376C2216yes—
66C43×C5C2213yes—
67#34262C511yesmaximal, characteristic, direct product factor, Sylow
68C22×C5×Q8—24no—
69C22×C5×Q8—24no—
70C22×C5×Q8C2×C418yes—
71C22×C5×Q8C2313yes—
72C22×C5×Q8C2311yescharacteristic
73C23×C4×C5C2313yes—
74C4×C5×Q8—24no—
75C4×C5×Q8—24no—
76C4×C5×Q8—24no—
77C4×C5×Q8—24no—
78C4×C5×Q8C2×C4124yes—
79C4×C5×Q8C2×C4124yes—
80C4×C5×Q8C2×C418yes—
81C4×C5×Q8C2×C418yes—
82C5×#117C2×C4124yes—
83C5×#117C2×C4124yes—
84C2×C5×C4⋊C4C2311yescharacteristic
85C2×C5×C4⋊C4C2313yes—
86C2×C5×C4⋊C4C2313yes—
87C2×C5×C4⋊C4C2313yes—
88C2×C5×C4⋊C4C2313yes—
89C2×C5×C4⋊C4C2313yes—
90C2×C5×C4⋊C4C2313yes—
91C2×C5×C4⋊C4C2316yes—
92C2×C5×C4⋊C4C2313yes—
93C2×C5×C4⋊C4C2313yes—
94C2×C5×C4⋊C4C2313yes—
95C2×C5×C4⋊C4C2313yes—
96C2×C5×C4⋊C4C2313yes—
97C2×C5×C22⋊C4C2311yescharacteristic
98C2×C5×C22⋊C4C2311yescharacteristic
99C2×C5×C22⋊C4C2313yes—
100C2×C5×C22⋊C4C2313yes—
101C2×C5×C22⋊C4C2311yescharacteristic
102C2×C5×C22⋊C4C2313yes—
103C2×C42×C5C2311yescharacteristic
104C2×C42×C5C2313yes—
105C2×C42×C5C2313yes—
106C2×C42×C5C2313yes—
107C2×C42×C5C2313yes—
108C2×C42×C5C2313yes—
109C2×C42×C5C2313yes—
110C2×C42×C5C2313yes—
111C2×C42×C5C2316yes—
112C2×C42×C5C2313yes—
113C2×C42×C5C2316yes—
114C2×C42×C5C2313yes—
115C5×#95C2311yescharacteristic
116C5×#95C2313yes—
117C5×#95C2313yes—
118C5×#95C2313yes—
119C5×#95C2313yes—
120C5×#95C2313yes—
121C5×#95C2316yes—
122C5×#95C2316yes—
123C5×#95C2313yes—
124C5×#95C2313yes—
125C5×#95C2313yes—
126C5×#95C2316yes—
127C5×#95C2311yescharacteristic
128C5×#95C2316yes—
129C5×#95C2313yes—
130C5×#95C2313yes—
131C2×#519C2×C511yescharacteristic
132#2356C2×C513yescomplemented
133#2355C2×C513yescomplemented
134#2351C2×C511yescharacteristic, complemented
135Q8×C4⋊C4C2×C511yescharacteristic, complemented
136#2347C2×C513yes—
137#2346C2×C513yes—
138Q8×C22⋊C4C2×C511yescharacteristic
139Q8×C22⋊C4C2×C511yescharacteristic
140#2320C2×C513yescomplemented
141#2314C2×C513yes—
142#2298C2×C513yes—
143#2295C2×C513yescomplemented
144#2276C2×C511yescharacteristic, complemented
145C42×Q8C2×C511yescharacteristic, complemented
146C24×C5C2411yescharacteristic
147C2×C5×Q8—232no—
148C2×C5×Q8—26no—
149C2×C5×Q8—26no—
150C2×C5×Q8C22×C4112yes—
151C2×C5×Q8C22×C414yes—
152C2×C5×Q8#4114yes—
153C2×C5×Q8#4114yes—
154C22×C4×C5—26no—
155C22×C4×C5—26no—
156C22×C4×C5C22×C4112yes—
157C22×C4×C5C2413yes—
158C22×C4×C5C2413yes—
159C22×C4×C5C2411yescharacteristic
160C22×C4×C5C2413yes—
161C22×C4×C5C2413yes—
162C22×C4×C5C2411yescharacteristic
163C22×C4×C5C2411yescharacteristic
164C22×C4×C5C2413yes—
165C22×C4×C5C2413yes—
166C22×C4×C5C2411yescharacteristic
167C22×C4×C5C2413yes—
168C22×C4×C5C2411yescharacteristic
169C22×C4×C5C2411yescharacteristic
170C22×C4×C5C2413yes—
171C5×C4⋊C4—26no—
172C5×C4⋊C4—26no—
173C5×C4⋊C4—26no—
174C5×C4⋊C4—26no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—26no—
177C5×C4⋊C4—43no—
178C5×C4⋊C4—43no—
179C5×C4⋊C4—46no—
180C5×C4⋊C4C22×C4112yes—
181C5×C4⋊C4C22×C4112yes—
182C5×C4⋊C4C22×C4112yes—
183C5×C4⋊C4C22×C4112yes—
184C5×C22⋊C4—22no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4—43no—
187C5×C22⋊C4—43no—
188C5×C22⋊C4C22×C414yes—
189C5×C22⋊C4C22×C4112yes—
190C42×C5—26no—
191C42×C5—26no—
192C42×C5—26no—
193C42×C5—26no—
194C42×C5—22no—
195C42×C5—26no—
196C42×C5—43no—
197C42×C5—46no—
198C42×C5—43no—
199C42×C5C22×C4124yes—
200C42×C5C22×C4112yes—
201C42×C5C22×C4112yes—
202C23×Q8C22×C511yescharacteristic
203#519C4×C5116yescomplemented
204C2×C4×Q8C22×C511yescharacteristic
205C2×C4×Q8C22×C511yescharacteristic
206C2×C4×Q8C22×C511yescharacteristic
207C2×C4×Q8C22×C511yescharacteristic
208C2×C4×Q8C22×C513yes—
209C2×C4×Q8C22×C511yescharacteristic
210C2×C4×Q8C22×C513yes—
211C2×C4×Q8C22×C511yescharacteristic
212C2×#117C22×C513yes—
213C2×#117C22×C513yes—
214#391C22×C513yes—
215#391C22×C513yes—
216#391C22×C513yes—
217#391C22×C513yes—
218#389C22×C513yes—
219#389C22×C513yes—
220#389C22×C513yes—
221#389C22×C513yes—
222#388C22×C513yes—
223#388C22×C516yes—
224#388C22×C513yes—
225#388C22×C513yes—
226#388C22×C511yescharacteristic
227#387C22×C516yes—
228#387C22×C516yes—
229#387C22×C513yes—
230#387C22×C513yes—
231#387C22×C513yes—
232#387C22×C513yes—
233#384C22×C513yes—
234#383C22×C516yes—
235#382C22×C513yes—
236#382C22×C516yes—
237#380C22×C513yes—
238#380C22×C513yes—
239C4×C4⋊C4C22×C513yes—
240C4×C4⋊C4C22×C513yes—
241C4×C4⋊C4C22×C513yes—
242C4×C4⋊C4C22×C513yes—
243C4×C4⋊C4C22×C513yes—
244C4×C4⋊C4C22×C516yes—
245C4×C4⋊C4C22×C513yes—
246C4×C4⋊C4C22×C513yes—
247C4×C4⋊C4C22×C513yes—
248C4×C22⋊C4C22×C513yes—
249C4×C22⋊C4C22×C513yes—
250#376C22×C513yes—
251#376C22×C516yes—
252C43C22×C513yes—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5—21no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5C23×C412yes—
260C23×C5C2511yescharacteristic
261C5×Q8—224no—
262C5×Q8#117116yes—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—23no—
266C2×C4×C5—23no—
267C2×C4×C5—21no—
268C2×C4×C5—23no—
269C2×C4×C5—21no—
270C2×C4×C5—23no—
271C2×C4×C5—21no—
272C2×C4×C5—23no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—23no—
277C2×C4×C5—224no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—23no—
281C2×C4×C5—23no—
282C2×C4×C5—23no—
283C2×C4×C5—23no—
284C2×C4×C5—23no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—23no—
288C2×C4×C5—21no—
289C2×C4×C5—23no—
290C2×C4×C5—23no—
291C2×C4×C5—23no—
292C2×C4×C5—23no—
293C2×C4×C5—23no—
294C2×C4×C5—23no—
295C2×C4×C5—21no—
296C2×C4×C5C23×C416yes—
297C2×C4×C5C23×C412yes—
298C2×C4×C5C23×C416yes—
299C2×C4×C5C23×C412yes—
300C2×C4×C5C23×C416yes—
301C2×C4×C5C23×C416yes—
302C2×C4×C5C2×#4116yes—
303C2×C4×C5C2×#4116yes—
304C2×C4×C52−1+412yes—
305C2×C4×C52−1+412yes—
306C22×Q8—24no—
307C22×Q8—24no—
308C22×Q8C2×C4×C518yes—
309C22×Q8C23×C513yes—
310C22×Q8C23×C511yescharacteristic
311C23×C4C23×C513yes—
312C4×Q8—24no—
313C4×Q8—24no—
314C4×Q8—24no—
315C4×Q8—24no—
316C4×Q8C2×C4×C5124yes—
317C4×Q8C2×C4×C5124yes—
318C4×Q8C2×C4×C518yes—
319C4×Q8C2×C4×C518yes—
320#117C2×C4×C5124yes—
321#117C2×C4×C5124yes—
322C2×C4⋊C4C23×C513yes—
323C2×C4⋊C4C23×C513yes—
324C2×C4⋊C4C23×C513yes—
325C2×C4⋊C4C23×C513yes—
326C2×C4⋊C4C23×C511yescharacteristic
327C2×C4⋊C4C23×C513yes—
328C2×C4⋊C4C23×C513yes—
329C2×C4⋊C4C23×C516yes—
330C2×C4⋊C4C23×C513yes—
331C2×C4⋊C4C23×C513yes—
332C2×C4⋊C4C23×C513yes—
333C2×C4⋊C4C23×C513yes—
334C2×C4⋊C4C23×C513yes—
335C2×C22⋊C4C23×C511yescharacteristic
336C2×C22⋊C4C23×C511yescharacteristic
337C2×C22⋊C4C23×C513yes—
338C2×C22⋊C4C23×C513yes—
339C2×C22⋊C4C23×C511yescharacteristic
340C2×C22⋊C4C23×C513yes—
341C2×C42C23×C513yes—
342C2×C42C23×C513yes—
343C2×C42C23×C513yes—
344C2×C42C23×C513yes—
345C2×C42C23×C511yescharacteristic
346C2×C42C23×C513yes—
347C2×C42C23×C513yes—
348C2×C42C23×C513yes—
349C2×C42C23×C516yes—
350C2×C42C23×C513yes—
351C2×C42C23×C516yes—
352C2×C42C23×C513yes—
353#95C23×C511yescharacteristic
354#95C23×C513yes—
355#95C23×C513yes—
356#95C23×C513yes—
357#95C23×C513yes—
358#95C23×C513yes—
359#95C23×C516yes—
360#95C23×C516yes—
361#95C23×C513yes—
362#95C23×C513yes—
363#95C23×C513yes—
364#95C23×C516yes—
365#95C23×C511yescharacteristic
366#95C23×C516yes—
367#95C23×C513yes—
368#95C23×C513yes—
369C22×C5—22no—
370C22×C5—22no—
371C22×C5—22no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5—41no—
376C22×C5C24×C411yescharacteristic
377C22×C5C22×#4111yescharacteristic
378C22×C5C22×#4111yescharacteristic
379C22×C5C2×2−1+411yescharacteristic
380C22×C5C2×2−1+411yescharacteristic
381C22×C5#58511yescharacteristic
382C22×C5#58511yescharacteristic
383C4×C5—26no—
384C4×C5—22no—
385C4×C5—26no—
386C4×C5—26no—
387C4×C5—22no—
388C4×C5—22no—
389C4×C5—22no—
390C4×C5—43no—
391C4×C5—41no—
392C4×C5—43no—
393C4×C5—41no—
394C4×C5—43no—
395C4×C5—43no—
396C4×C5C2×#117112yes—
397C24C24×C511yescharacteristic
398C2×Q8—232no—
399C2×Q8—26no—
400C2×Q8—26no—
401C2×Q8C22×C4×C5112yes—
402C2×Q8C22×C4×C514yes—
403C2×Q8C5×#4114yes—
404C2×Q8C5×#4114yes—
405C22×C4—26no—
406C22×C4—26no—
407C22×C4C22×C4×C5112yes—
408C22×C4C24×C511yescharacteristic
409C22×C4C24×C511yescharacteristic
410C22×C4C24×C513yes—
411C22×C4C24×C513yes—
412C22×C4C24×C513yes—
413C22×C4C24×C513yes—
414C22×C4C24×C513yes—
415C22×C4C24×C511yescharacteristic
416C22×C4C24×C513yes—
417C22×C4C24×C513yes—
418C22×C4C24×C511yescharacteristic
419C22×C4C24×C511yescharacteristic
420C22×C4C24×C511yescharacteristic
421C22×C4C24×C513yes—
422C4⋊C4—26no—
423C4⋊C4—26no—
424C4⋊C4—26no—
425C4⋊C4—26no—
426C4⋊C4—22no—
427C4⋊C4—26no—
428C4⋊C4—43no—
429C4⋊C4—43no—
430C4⋊C4—46no—
431C4⋊C4C22×C4×C5112yes—
432C4⋊C4C22×C4×C5112yes—
433C4⋊C4C22×C4×C5112yes—
434C4⋊C4C22×C4×C5112yes—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—43no—
438C22⋊C4—43no—
439C22⋊C4C22×C4×C514yes—
440C22⋊C4C22×C4×C5112yes—
441C42—26no—
442C42—26no—
443C42—26no—
444C42—26no—
445C42—22no—
446C42—26no—
447C42—43no—
448C42—46no—
449C42—43no—
450C42C22×C4×C5124yes—
451C42C22×C4×C5112yes—
452C42C22×C4×C5112yes—
453C2×C5—42no—
454C2×C5C22×#11711yescharacteristic
455C2×C5C4×2−1+411yescharacteristic
456C2×C5C4×2−1+411yescharacteristic
457C2×C5#351611yescharacteristic
458C2×C5#351811yescharacteristic
459C2×C5#352311yescharacteristic
460C2×C5#352411yescharacteristic
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23C23×C4×C512yes—
468C23C25×C511yescharacteristic
469Q8—224no—
470Q8C5×#117116yes—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—23no—
474C2×C4—23no—
475C2×C4—21no—
476C2×C4—23no—
477C2×C4—21no—
478C2×C4—23no—
479C2×C4—21no—
480C2×C4—23no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—23no—
485C2×C4—224no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—23no—
489C2×C4—23no—
490C2×C4—23no—
491C2×C4—23no—
492C2×C4—23no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—23no—
496C2×C4—21no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—21no—
504C2×C4C23×C4×C516yes—
505C2×C4C23×C4×C512yes—
506C2×C4C23×C4×C516yes—
507C2×C4C23×C4×C512yes—
508C2×C4C23×C4×C516yes—
509C2×C4C23×C4×C516yes—
510C2×C4C2×C5×#4116yes—
511C2×C4C2×C5×#4116yes—
512C2×C4C5×2−1+412yes—
513C2×C4C5×2−1+412yes—
514C5#3426211yescharacteristic, direct product factor, Sylow
515C22—22no—
516C22—22no—
517C22—22no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22C24×C4×C511yescharacteristic
523C22C22×C5×#4111yescharacteristic
524C22C22×C5×#4111yescharacteristic
525C22C2×C5×2−1+411yescharacteristic
526C22C2×C5×2−1+411yescharacteristic
527C22C5×#58511yescharacteristic
528C22C5×#58511yescharacteristic
529C4—26no—
530C4—22no—
531C4—26no—
532C4—26no—
533C4—22no—
534C4—22no—
535C4—22no—
536C4—43no—
537C4—41no—
538C4—43no—
539C4—41no—
540C4—43no—
541C4—43no—
542C4C2×C5×#117112yes—
543C2—42no—
544C2C22×C5×#11711yescharacteristic
545C2C4×C5×2−1+411yescharacteristic
546C2C4×C5×2−1+411yescharacteristic
547C2C5×#351611yescharacteristic
548C2C5×#351811yescharacteristic
549C2C5×#352311yescharacteristic
550C2C5×#352411yescharacteristic
subgroupG/H
center, socleC23×C5C25
commutatorC22C24×C4×C5
Frattini, cosocleC23C25×C5
prime radicalC24×C5C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2356C2semidirect
3. C5×#2355C2semidirect
4. C5×#2351C2semidirect
5. C5×Q8×C4⋊C4C2semidirect
10. C5×#2320C2semidirect
13. C5×#2295C2semidirect
14. C5×#2276C2semidirect
15. C42×C5×Q8C2semidirect
17. C5×#519C4semidirect
67. #34262C5direct (N × H)
132. #2356C2×C5semidirect
133. #2355C2×C5semidirect
134. #2351C2×C5semidirect
135. Q8×C4⋊C4C2×C5semidirect
140. #2320C2×C5semidirect
143. #2295C2×C5semidirect
144. #2276C2×C5semidirect
145. C42×Q8C2×C5semidirect
203. #519C4×C5semidirect
514. C5#34262direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5192
C5×#23562
C5×#23552
C5×#23512
C5×Q8×C4⋊C42
C5×#23472
C5×#23462
C5×Q8×C22⋊C42
C5×#23202
C5×#23142
C5×#22982
C5×#22952
C5×#22762
C42×C5×Q82
#342625