Finite Group Databasebeta

← C5×#70415 #14297372

Subgroups — C5×#70415 #14297372

Order 1920.

1072 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1010C211yesmaximal, characteristic
2C3×C5×#421C211yesmaximal, characteristic, complemented
3C5×#5236C211yesmaximal, characteristic, complemented
4C5×#5132C211yesmaximal, characteristic, complemented
5C5×#5120C211yesmaximal, characteristic, complemented
6C5×#5006C211yesmaximal, characteristic, complemented
7C5×#5004C211yesmaximal, characteristic, complemented
8C5×#1796—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C5×#1010—22no—
11C5×#1010—22no—
12C5×#1010—22no—
13C5×#1010—22no—
14C2×C5×D3×Q8C412yescomplemented
15C2×C5×#237—22no—
16C2×C5×#237C412yescomplemented
17C2×C5×#235—21no—
18C2×C5×#235C2211yescharacteristic
19C22×C5×Dic6—21no—
20C22×C5×Dic6C2211yescharacteristic
21C2×C3×C5×M16C2211yescharacteristic
22C3×C5×#117C2211yescharacteristic
23C5×#926C2211yescharacteristic
24C2×C5×#208C2211yescharacteristic
25C3×C5×#104—22no—
26C5×#837—22no—
27C5×#824—21no—
28C5×#823—21no—
29C5×#816—22no—
30C5×#810—22no—
31C5×#806—22no—
32#70415C511yesmaximal, characteristic, direct product factor, Hall
33C2×C5×2−1+4—31no—
34C5×#421—31no—
35C5×#421D311yescharacteristic, complemented
36C5×#419—31no—
37C5×#419—31no—
38C5×#413—31no—
39C5×#410—31no—
40C3×C5×#41—21no—
41C3×C5×#41—21no—
42C3×C5×#41D412yes—
43C3×C5×#41D412yes—
44C2×C3×C5×Q8C2×C411yescharacteristic
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4C2×C411yescharacteristic
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5C2311yescharacteristic
49C2×C5×#67—22no—
50C2×C5×#67D412yes—
51C22×C5×Dic3—21no—
52C22×C5×Dic3—22no—
53C5×D3×Q8—24no—
54C5×D3×Q8—24no—
55C5×#237—28no—
56C5×#237—28no—
57C5×#237—24no—
58C5×#237—24no—
59C5×#235—24no—
60C5×#235—24no—
61C5×#235—21no—
62C5×#235—21no—
63C5×#235—21no—
64C5×#235—21no—
65C2×C5×D12D411yescharacteristic
66C2×C4×C5×D3—22no—
67C2×C4×C5×D3C2×C412yes—
68C2×C5×Dic6—24no—
69C2×C5×Dic6—24no—
70C2×C5×Dic6—21no—
71C2×C5×Dic6—21no—
72C2×C5×Dic6—21no—
73C2×C5×Dic6—22no—
74C2×C5×Dic6C2×C412yes—
75C2×C5×Dic6D411yescharacteristic
76C2×C5×Dic6D412yes—
77C2×C5×Dic6D412yes—
78C3×C5×M16—21no—
79C3×C5×M16—21no—
80C2×C3×C5×C8—21no—
81C3×C5×C4⋊C4—21no—
82C3×C5×C22⋊C4—21no—
83C3×C42×C5—21no—
84C5×#217—21no—
85C5×C4⋊Dic3—21no—
86C4×C5×Dic3—21no—
87C5×#208—21no—
88C5×#208—21no—
89C2×C5×C3⋊C8—21no—
90C2×#1010C2×C511yescharacteristic
91C3×#421C2×C511yescharacteristic, complemented
92#5236C2×C511yescharacteristic, complemented
93#5132C2×C511yescharacteristic, complemented
94#5120C2×C511yescharacteristic, complemented
95#5006C2×C511yescharacteristic, complemented
96#5004C2×C511yescharacteristic, complemented
97C5×2−1+4—62no—
98C5×2−1+4—62no—
99C5×2−1+4—62no—
100C5×2−1+4—62no—
101C2×C5×#41—31no—
102C2×C5×#41—32no—
103C2×C5×#41—61no—
104C2×C5×#41—62no—
105C2×C5×#41C2×D311yescharacteristic
106C22×C5×Q8—32no—
107C22×C5×Q8—31no—
108C22×C5×Q8—61no—
109C2×C5×M16—31no—
110C2×C5×M16C2×D311yescharacteristic
111C5×#117—31no—
112C5×#117C2×D311yescharacteristic
113C5×#104—22no—
114C5×#104—62no—
115C5×#103—62no—
116C5×#103—62no—
117C5×#101—61no—
118C5×#100—61no—
119C5×#99—62no—
120#1796—31noSylow
121C23×C3×C5—21no—
122C23×C3×C5C2×D411yescharacteristic
123C22×C5×D3C22⋊C412yes—
124C3×C5×Q8—21no—
125C3×C5×Q8C22⋊C412yes—
126C3×C5×D4—22no—
127C3×C5×D4—22no—
128C3×C5×D4—21no—
129C3×C5×D4C22⋊C412yes—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5C22×C411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C5×#67—28no—
141C5×#67—22no—
142C5×#67—22no—
143C2×C5×Dic3—28no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—41no—
148C2×C5×Dic3C22⋊C412yes—
149C5×D12—21no—
150C5×D12—21no—
151C4×C5×D3—28no—
152C4×C5×D3—22no—
153C4×C5×D3—22no—
154C5×Dic6—28no—
155C5×Dic6—22no—
156C5×Dic6—21no—
157C5×Dic6—21no—
158C5×Dic6—22no—
159C5×Dic6—22no—
160C5×Dic6C22⋊C414yes—
161C3×C5×C8—41no—
162C5×C3⋊C8—41no—
163C2×C3×#41C22×C511yescharacteristic
164#1010—22no—
165#1010—22no—
166#1010—22no—
167#1010—22no—
168C2×D3×Q8C4×C512yescomplemented
169C2×#237—22no—
170C2×#237C4×C512yescomplemented
171C2×#235—21no—
172C2×#235C22×C511yescharacteristic
173C22×Dic6—21no—
174C22×Dic6C22×C511yescharacteristic
175C2×C3×M16C22×C511yescharacteristic
176C3×#117C22×C511yescharacteristic
177#926C22×C511yescharacteristic
178C2×#208C22×C511yescharacteristic
179C3×#104—22no—
180#837—22no—
181#824—21no—
182#823—21no—
183#816—22no—
184#810—22no—
185#806—22no—
186C5×#41—21no—
187C5×#41—21no—
188C5×#41—64no—
189C5×#41—64no—
190C5×#41—64no—
191C5×#41—68no—
192C5×#41—68no—
193C5×#41—64no—
194C5×#41—61no—
195C5×#41—61no—
196C5×#41—61no—
197C5×#41—61no—
198C5×#41D1212yes—
199C5×#41#6712yes—
200C2×C5×Q8—31no—
201C2×C5×Q8—32no—
202C2×C5×Q8—32no—
203C2×C5×Q8—32no—
204C2×C5×Q8—62no—
205C2×C5×Q8—64no—
206C2×C5×Q8—64no—
207C2×C5×Q8—64no—
208C2×C5×Q8—64no—
209C2×C5×Q8—61no—
210C2×C5×Q8—61no—
211C2×C5×Q8—61no—
212C2×C5×Q8C4×D311yescharacteristic
213C2×C5×D4—21no—
214C2×C5×D4—32no—
215C2×C5×D4—31no—
216C2×C5×D4—62no—
217C2×C5×D4C4×D311yescharacteristic
218C22×C4×C5—21no—
219C22×C4×C5—32no—
220C22×C4×C5—62no—
221C22×C4×C5—62no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C5×M16—21no—
225C5×M16—21no—
226C5×M16—61no—
227C5×M16—61no—
228C2×C5×C8—21no—
229C2×C5×C8—61no—
230C5×C4⋊C4—21no—
231C5×C4⋊C4—61no—
232C5×C22⋊C4—21no—
233C5×C22⋊C4—61no—
234C42×C5—21no—
235C42×C5—61no—
236C2×2−1+4—31no—
237#421—31no—
238#421C5×D311yescharacteristic, complemented
239#419—31no—
240#419—31no—
241#413—31no—
242#410—31no—
243C22×C3×C5—22no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5C2×C22⋊C411yescharacteristic
247C22×C3×C5#12011yescharacteristic
248C22×C3×C5#12011yescharacteristic
249C2×C5×D3—22no—
250C2×C5×D3—42no—
251C3×C4×C5—22no—
252C3×C4×C5—81no—
253C3×C4×C5C2×C22⋊C411yescharacteristic
254C3×C4×C5C2×C22⋊C411yescharacteristic
255C3×C4×C5#12011yescharacteristic
256C3×C4×C5#12011yescharacteristic
257C5×Dic3—22no—
258C5×Dic3—24no—
259C5×Dic3—81no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41C5×D412yes—
263C3×#41C5×D412yes—
264C2×C3×Q8C2×C4×C511yescharacteristic
265C2×C3×D4—21no—
266C2×C3×D4C2×C4×C511yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4C23×C511yescharacteristic
269C2×#67—22no—
270C2×#67C5×D412yes—
271C22×Dic3—21no—
272C22×Dic3—22no—
273D3×Q8—24no—
274D3×Q8—24no—
275#237—28no—
276#237—28no—
277#237—24no—
278#237—24no—
279#235—24no—
280#235—24no—
281#235—21no—
282#235—21no—
283#235—21no—
284#235—21no—
285C2×D12C5×D411yescharacteristic
286C2×C4×D3—22no—
287C2×C4×D3C2×C4×C512yes—
288C2×Dic6—24no—
289C2×Dic6—24no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6—22no—
294C2×Dic6C2×C4×C512yes—
295C2×Dic6C5×D411yescharacteristic
296C2×Dic6C5×D412yes—
297C2×Dic6C5×D412yes—
298C3×M16—21no—
299C3×M16—21no—
300C2×C3×C8—21no—
301C3×C4⋊C4—21no—
302C3×C22⋊C4—21no—
303C3×C42—21no—
304#217—21no—
305C4⋊Dic3—21no—
306C4×Dic3—21no—
307#208—21no—
308#208—21no—
309C2×C3⋊C8—21no—
310C23×C5—21no—
311C23×C5—32no—
312C23×C5D3×D411yescharacteristic
313C5×Q8—21no—
314C5×Q8—34no—
315C5×Q8—68no—
316C5×Q8—61no—
317C5×Q8—62no—
318C5×Q8—62no—
319C5×Q8—61no—
320C5×Q8—62no—
321C5×Q8(C2×D3)⋊C412yes—
322C5×D4—22no—
323C5×D4—22no—
324C5×D4—21no—
325C5×D4—68no—
326C5×D4—62no—
327C5×D4—62no—
328C5×D4—61no—
329C5×D4—61no—
330C5×D4(C2×D3)⋊C412yes—
331C2×C4×C5—21no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—32no—
335C2×C4×C5—41no—
336C2×C4×C5—68no—
337C2×C4×C5—68no—
338C2×C4×C5—62no—
339C2×C4×C5—62no—
340C2×C4×C5—62no—
341C2×C4×C5—62no—
342C2×C4×C5—62no—
343C2×C4×C5—121no—
344C2×C4×C5C2×C4×D311yescharacteristic
345C2×C4×C5C2×D1211yescharacteristic
346C2×C4×C5D3×D411yescharacteristic
347C2×C4×C5D3×D411yescharacteristic
348C2×C4×C5D3×D411yescharacteristic
349C2×C4×C5C2×#6711yescharacteristic
350C5×C8—41no—
351C5×C8—121no—
3522−1+4—62no—
3532−1+4—62no—
3542−1+4—62no—
3552−1+4—62no—
356C2×#41—31no—
357C2×#41—32no—
358C2×#41—61no—
359C2×#41—62no—
360C2×#41C2×C5×D311yescharacteristic
361C22×Q8—32no—
362C22×Q8—31no—
363C22×Q8—61no—
364C2×M16—31no—
365C2×M16C2×C5×D311yescharacteristic
366#117—31no—
367#117C2×C5×D311yescharacteristic
368#104—22no—
369#104—62no—
370#103—62no—
371#103—62no—
372#101—61no—
373#100—61no—
374#99—62no—
375C2×C3×C5—21no—
376C2×C3×C5—21no—
377C2×C3×C5—21no—
378C2×C3×C5—42no—
379C2×C3×C5#37911yescharacteristic
380C5×D3—42no—
381C23×C3—21no—
382C23×C3C2×C5×D411yescharacteristic
383C22×D3C5×C22⋊C412yes—
384C3×Q8—21no—
385C3×Q8C5×C22⋊C412yes—
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—21no—
389C3×D4C5×C22⋊C412yes—
390C2×C3×C4—21no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—41no—
394C2×C3×C4C22×C4×C511yescharacteristic
395C2×C3×C4C2×C5×D411yescharacteristic
396C2×C3×C4C2×C5×D411yescharacteristic
397C2×C3×C4C2×C5×D411yescharacteristic
398C2×C3×C4C2×C5×D411yescharacteristic
399C2×C3×C4C2×C5×D411yescharacteristic
400#67—28no—
401#67—22no—
402#67—22no—
403C2×Dic3—28no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—41no—
408C2×Dic3C5×C22⋊C412yes—
409D12—21no—
410D12—21no—
411C4×D3—28no—
412C4×D3—22no—
413C4×D3—22no—
414Dic6—28no—
415Dic6—22no—
416Dic6—21no—
417Dic6—22no—
418Dic6—21no—
419Dic6—22no—
420Dic6C5×C22⋊C414yes—
421C3×C8—41no—
422C3⋊C8—41no—
423C22×C5—22no—
424C22×C5—41no—
425C22×C5—42no—
426C22×C5—62no—
427C22×C5—122no—
428C22×C5D3×C22⋊C411yescharacteristic
429C22×C5#88211yescharacteristic
430C22×C5#93711yescharacteristic
431C4×C5—22no—
432C4×C5—62no—
433C4×C5—64no—
434C4×C5—81no—
435C4×C5—241no—
436C4×C5D3×C22⋊C411yescharacteristic
437C4×C5#88211yescharacteristic
438C4×C5C2×(C2×D3)⋊C411yescharacteristic
439C4×C5#93711yescharacteristic
440#41—21no—
441#41—21no—
442#41—64no—
443#41—64no—
444#41—64no—
445#41—68no—
446#41—68no—
447#41—64no—
448#41—61no—
449#41—61no—
450#41—61no—
451#41—61no—
452#41C5×D1212yes—
453#41C5×#6712yes—
454C2×Q8—31no—
455C2×Q8—32no—
456C2×Q8—32no—
457C2×Q8—32no—
458C2×Q8—62no—
459C2×Q8—64no—
460C2×Q8—64no—
461C2×Q8—64no—
462C2×Q8—64no—
463C2×Q8—61no—
464C2×Q8—61no—
465C2×Q8—61no—
466C2×Q8C4×C5×D311yescharacteristic
467C2×D4—21no—
468C2×D4—32no—
469C2×D4—31no—
470C2×D4—62no—
471C2×D4C4×C5×D311yescharacteristic
472C22×C4—21no—
473C22×C4—32no—
474C22×C4—62no—
475C22×C4—62no—
476C22×C4—61no—
477C22×C4C22×C5×D311yescharacteristic
478M16—21no—
479M16—21no—
480M16—61no—
481M16—61no—
482C2×C8—21no—
483C2×C8—61no—
484C4⋊C4—21no—
485C4⋊C4—61no—
486C22⋊C4—21no—
487C22⋊C4—61no—
488C42—21no—
489C42—61no—
490C3×C5#179611yescharacteristic, complemented, Hall
491C22×C3—22no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3C2×C5×C22⋊C411yescharacteristic
495C22×C3C5×#12011yescharacteristic
496C22×C3C5×#12011yescharacteristic
497C2×D3—22no—
498C2×D3—42no—
499C3×C4—22no—
500C3×C4—81no—
501C3×C4C2×C5×C22⋊C411yescharacteristic
502C3×C4C2×C5×C22⋊C411yescharacteristic
503C3×C4C5×#12011yescharacteristic
504C3×C4C5×#12011yescharacteristic
505Dic3—22no—
506Dic3—24no—
507Dic3—81no—
508C2×C5—21no—
509C2×C5—21no—
510C2×C5—21no—
511C2×C5—42no—
512C2×C5—122no—
513C2×C5#495511yescharacteristic
514C23—21no—
515C23—32no—
516C23C5×D3×D411yescharacteristic
517Q8—21no—
518Q8—34no—
519Q8—68no—
520Q8—61no—
521Q8—62no—
522Q8—62no—
523Q8—61no—
524Q8—62no—
525Q8C5×(C2×D3)⋊C412yes—
526D4—22no—
527D4—22no—
528D4—21no—
529D4—68no—
530D4—62no—
531D4—62no—
532D4—61no—
533D4—61no—
534D4C5×(C2×D3)⋊C412yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—32no—
539C2×C4—41no—
540C2×C4—68no—
541C2×C4—68no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—121no—
548C2×C4C2×C4×C5×D311yescharacteristic
549C2×C4C2×C5×D1211yescharacteristic
550C2×C4C5×D3×D411yescharacteristic
551C2×C4C5×D3×D411yescharacteristic
552C2×C4C5×D3×D411yescharacteristic
553C2×C4C2×C5×#6711yescharacteristic
554C8—41no—
555C8—121no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—42no—
560C2×C3C5×#37911yescharacteristic
561D3—42no—
562C5#7041511yescharacteristic, direct product factor, Sylow
563C22—22no—
564C22—41no—
565C22—42no—
566C22—62no—
567C22—122no—
568C22C5×D3×C22⋊C411yescharacteristic
569C22C5×#88211yescharacteristic
570C22C5×#93711yescharacteristic
571C4—22no—
572C4—62no—
573C4—64no—
574C4—81no—
575C4—241no—
576C4C5×D3×C22⋊C411yescharacteristic
577C4C5×#88211yescharacteristic
578C4C2×C5×(C2×D3)⋊C411yescharacteristic
579C4C5×#93711yescharacteristic
580C3C5×#179611yescharacteristic, complemented, Sylow
581C2—21no—
582C2—21no—
583C2—21no—
584C2—42no—
585C2—122no—
586C2C5×#495511yescharacteristic
subgroupG/H
centerC2×C5#4955
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#421C2
socleC2×C3×C5#379
prime radicalC2×C5×#1010C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#421D3
hypocenterC3C5×#1796
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#421

Complements

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

NH ≅ G/Ntype
2. C3×C5×#421C2semidirect
3. C5×#5236C2semidirect
4. C5×#5132C2semidirect
5. C5×#5120C2semidirect
6. C5×#5006C2semidirect
7. C5×#5004C2semidirect
14. C2×C5×D3×Q8C4semidirect
16. C2×C5×#237C4semidirect
32. #70415C5direct (N × H)
35. C5×#421D3semidirect
91. C3×#421C2×C5semidirect
92. #5236C2×C5semidirect
93. #5132C2×C5semidirect
94. #5120C2×C5semidirect
95. #5006C2×C5semidirect
96. #5004C2×C5semidirect
168. C2×D3×Q8C4×C5semidirect
170. C2×#237C4×C5semidirect
238. #421C5×D3semidirect
490. C3×C5#1796semidirect
562. C5#70415direct (N × H)
580. C3C5×#1796semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10102
C3×C5×#4212
C5×#52362
C5×#51322
C5×#51202
C5×#50062
C5×#50042
C5×#17963
#704155