Finite Group Databasebeta

← C5×#84013 #14457804

Subgroups — C5×#84013 #14457804

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#577C211yesmaximal, characteristic, complemented
2C5×#5838C211yesmaximal, characteristic, complemented
3C5×#5836C211yesmaximal, characteristic, complemented
4C5×#5771C211yesmaximal, characteristic, complemented
5C5×#5246C211yesmaximal, characteristic, complemented
6C5×#5242C211yesmaximal, characteristic, complemented
7C5×#5205C211yesmaximal, characteristic, complemented
8C5×#5204C211yesmaximal, characteristic, complemented
9C5×#5201C211yesmaximal, characteristic, complemented
10C5×#5200C211yesmaximal, characteristic, complemented
11C5×#5197C211yesmaximal, characteristic, complemented
12C5×#5177C211yesmaximal, characteristic, complemented
13C5×#5167C211yesmaximal, characteristic, complemented
14C5×#5145C211yesmaximal, characteristic, complemented
15C5×#5143C211yesmaximal, characteristic, complemented
16C5×#3289—31nomaximal, Hall
17C3×C5×2−1+4C2211yescharacteristic
18C3×C5×H(5,𝔽2)C2211yescharacteristic
19C5×#1010C2211yescharacteristic
20C5×#1010C2211yescharacteristic, complemented
21C3×C5×#137—21no—
22C3×C5×#137C2211yescharacteristic
23C3×C5×AGL(1,ℤ/8)—21no—
24C3×C5×AGL(1,ℤ/8)C2211yescharacteristic
25C3×C5×#135—21no—
26C3×C5×#135C2211yescharacteristic
27C2×C3×C5×SD16—21no—
28C2×C3×C5×SD16C2211yescharacteristic
29C3×C5×#131C2211yescharacteristic
30C5×#951—21no—
31C5×#951—21no—
32C5×#951C2211yescharacteristic
33C5×#951C2211yescharacteristic
34C5×#951C2211yescharacteristic
35C5×#951C2211yescharacteristic, complemented
36C5×#950—21no—
37C5×#950—21no—
38C5×#950C2211yescharacteristic
39C5×#948C2211yescharacteristic
40C5×#948C2211yescharacteristic, complemented
41C5×#944C2211yescharacteristic, complemented
42C2×C5×#216—21no—
43C2×C5×#216C2211yescharacteristic, complemented
44C5×#942—21no—
45C5×#942C2211yescharacteristic, complemented
46C5×#936C2211yescharacteristic
47C2×C5×#214—21no—
48C2×C5×#214C2211yescharacteristic
49C5×#932—21no—
50C5×#932C2211yescharacteristic
51C5×D3×Q16—21no—
52C5×#915—21no—
53C5×#915—21no—
54C5×#912—21no—
55C2×C5×Dic12C2211yescharacteristic, complemented
56C5×#901C2211yescharacteristic, complemented
57C5×#837C2211yescharacteristic
58C5×#837C2211yescharacteristic
59C5×#837C2211yescharacteristic, complemented
60C5×#836C2211yescharacteristic, complemented
61C5×#833C2211yescharacteristic
62C5×#825C2211yescharacteristic, complemented
63C5×#824C2211yescharacteristic, complemented
64C5×#824C2211yescharacteristic, complemented
65C5×#822C2211yescharacteristic, complemented
66C5×#819C2211yescharacteristic, complemented
67C5×#815C2211yescharacteristic, complemented
68#84013C511yesmaximal, characteristic, direct product factor, Hall
69C5×#578—31no—
70C5×#578—31no—
71C5×#577—31no—
72C5×#577D311yescharacteristic, complemented
73C5×#497—31no—
74C5×#473—31no—
75C5×#473—31no—
76C5×#471—31no—
77C5×#471—31no—
78C5×#456—31no—
79C5×#456—31no—
80C5×#455—31no—
81C5×#454—31no—
82C5×#444—31no—
83C5×#444—31no—
84C3×C5×#41—21no—
85C3×C5×#41—21no—
86C3×C5×#41—21no—
87C3×C5×#41—21no—
88C3×C5×#41—41no—
89C3×C5×#41C2311yescharacteristic
90C3×C5×#41C2311yescharacteristic
91C3×C5×#41C2311yescharacteristic
92C2×C3×C5×Q8—21no—
93C2×C3×C5×Q8—21no—
94C2×C3×C5×Q8C2311yescharacteristic
95C2×C3×C5×D4—21no—
96C2×C3×C5×D4—21no—
97C2×C3×C5×D4—41no—
98C2×C3×C5×D4C2311yescharacteristic
99C5×D3×Q8—21no—
100C5×D3×Q8—21no—
101C5×#237—21no—
102C5×#237—21no—
103C5×#237—41no—
104C5×#237—41no—
105C5×#235—21no—
106C5×#235—21no—
107C5×#235C2311yescharacteristic
108C2×C5×Dic6—21no—
109C2×C5×Dic6—21no—
110C2×C5×Dic6C2311yescharacteristic
111C2×C5×Dic6C2311yescharacteristic
112C3×C5×Q16—21no—
113C3×C5×Q16D411yescharacteristic
114C3×C5×SD16—21no—
115C3×C5×SD16—21no—
116C3×C5×SD16—21no—
117C3×C5×SD16—21no—
118C3×C5×SD16D411yescharacteristic
119C3×C5×SD16D411yescharacteristic
120C3×C5×D8—21no—
121C3×C5×D8D411yescharacteristic
122C3×C5×M16—21no—
123C3×C5×M16C2311yescharacteristic
124C2×C3×C5×C8—21no—
125C2×C3×C5×C8C2311yescharacteristic
126C5×#217—41no—
127C5×#216—21no—
128C5×#216—21no—
129C5×#216—21no—
130C5×#216—21no—
131C5×#216—21no—
132C5×#216—21no—
133C5×#216—21no—
134C5×#216D411yescharacteristic
135C5×#215—21no—
136C5×#215D411yescharacteristic
137C5×#214—21no—
138C5×#214—21no—
139C5×#214—21no—
140C5×#214—21no—
141C5×#214—21no—
142C5×#214—21no—
143C5×#214—21no—
144C5×#214D411yescharacteristic
145C5×#213—21no—
146C5×#213D411yescharacteristic
147C5×Dic3⋊C4—41no—
148C4×C5×Dic3C2311yescharacteristic
149C5×#208—21no—
150C5×#208—21no—
151C5×#208C2311yescharacteristic
152C5×#208C2311yescharacteristic
153C5×#208C2311yescharacteristic
154C2×C5×C3⋊C8—21no—
155C2×C5×C3⋊C8—21no—
156C2×C5×C3⋊C8C2311yescharacteristic
157C5×Dic12—21no—
158C5×Dic12—21no—
159C5×ΓL(1,𝔽25)—21no—
160C5×D3×C8—21no—
161C3×#577C2×C511yescharacteristic, complemented
162#5838C2×C511yescharacteristic, complemented
163#5836C2×C511yescharacteristic, complemented
164#5771C2×C511yescharacteristic, complemented
165#5246C2×C511yescharacteristic, complemented
166#5242C2×C511yescharacteristic, complemented
167#5205C2×C511yescharacteristic, complemented
168#5204C2×C511yescharacteristic, complemented
169#5201C2×C511yescharacteristic, complemented
170#5200C2×C511yescharacteristic, complemented
171#5197C2×C511yescharacteristic, complemented
172#5177C2×C511yescharacteristic, complemented
173#5167C2×C511yescharacteristic, complemented
174#5145C2×C511yescharacteristic, complemented
175#5143C2×C511yescharacteristic, complemented
176C5×2−1+4—31no—
177C5×2−1+4—31no—
178C5×2−1+4C2×D311yescharacteristic
179C5×H(5,𝔽2)C2×D311yescharacteristic
180C5×#137—21no—
181C5×#137—31no—
182C5×#137—31no—
183C5×#137—31no—
184C5×#137—31no—
185C5×#137—31no—
186C5×#137—61no—
187C5×#137—61no—
188C5×#137—61no—
189C5×#137—61no—
190C5×#137—61no—
191C5×#137C2×D311yescharacteristic
192C5×AGL(1,ℤ/8)—21no—
193C5×AGL(1,ℤ/8)—31no—
194C5×AGL(1,ℤ/8)—61no—
195C5×AGL(1,ℤ/8)C2×D311yescharacteristic
196C5×#135—21no—
197C5×#135—31no—
198C5×#135—61no—
199C5×#135—61no—
200C5×#135—61no—
201C5×#135C2×D311yescharacteristic
202C2×C5×Q16—31no—
203C2×C5×Q16—31no—
204C2×C5×Q16—61no—
205C2×C5×Q16—61no—
206C2×C5×SD16—21no—
207C2×C5×SD16—31no—
208C2×C5×SD16—61no—
209C2×C5×SD16C2×D311yescharacteristic
210C5×#131—31no—
211C5×#131—31no—
212C5×#131—31no—
213C5×#131C2×D311yescharacteristic
214C5×C4⋊Q8—31no—
215C5×#124—31no—
216C5×#108—31no—
217C5×#108—31no—
218C5×#104—31no—
219C5×#104—31no—
220C5×#104—31no—
221C5×#104—31no—
222C5×#101—31no—
223C5×#101—31no—
224C5×#101—31no—
225C5×#100—31no—
226C5×#97—31no—
227#3289—31noSylow
228C23×C3×C5—21no—
229C23×C3×C5—41no—
230C3×C5×Q8—21no—
231C3×C5×Q8—21no—
232C3×C5×Q8—41no—
233C3×C5×Q8C2×D411yescharacteristic
234C3×C5×Q8C2×D411yescharacteristic
235C3×C5×Q8C2×D411yescharacteristic
236C3×C5×D4—21no—
237C3×C5×D4—21no—
238C3×C5×D4—21no—
239C3×C5×D4—21no—
240C3×C5×D4—21no—
241C3×C5×D4—41no—
242C3×C5×D4—41no—
243C3×C5×D4—41no—
244C3×C5×D4C2×D411yescharacteristic
245C3×C5×D4C2×D411yescharacteristic
246C3×C5×D4C2×D411yescharacteristic
247C2×C3×C4×C5—21no—
248C2×C3×C4×C5—21no—
249C2×C3×C4×C5—21no—
250C2×C3×C4×C5—21no—
251C2×C3×C4×C5—41no—
252C2×C3×C4×C5—41no—
253C2×C3×C4×C5—41no—
254C2×C3×C4×C5C2411yescharacteristic
255C5×#67—21no—
256C5×#67—41no—
257C5×#67—41no—
258C2×C5×Dic3—21no—
259C2×C5×Dic3—21no—
260C2×C5×Dic3—21no—
261C2×C5×Dic3—41no—
262C2×C5×Dic3—41no—
263C5×D12C2×D411yescharacteristic
264C4×C5×D3—21no—
265C4×C5×D3—41no—
266C4×C5×D3—41no—
267C5×Dic6—21no—
268C5×Dic6—21no—
269C5×Dic6—21no—
270C5×Dic6—21no—
271C5×Dic6—41no—
272C5×Dic6—41no—
273C5×Dic6C2×D411yescharacteristic
274C3×C5×C8—21no—
275C3×C5×C8C2×D411yescharacteristic
276C3×C5×C8C2×D411yescharacteristic
277C5×C3⋊C8—21no—
278C5×C3⋊C8—21no—
279C5×C3⋊C8—21no—
280C5×C3⋊C8C2×D411yescharacteristic
281C5×C3⋊C8C2×D411yescharacteristic
282C3×2−1+4C22×C511yescharacteristic
283C3×H(5,𝔽2)C22×C511yescharacteristic
284#1010C22×C511yescharacteristic
285#1010C22×C511yescharacteristic, complemented
286C3×#137—21no—
287C3×#137C22×C511yescharacteristic
288C3×AGL(1,ℤ/8)—21no—
289C3×AGL(1,ℤ/8)C22×C511yescharacteristic
290C3×#135—21no—
291C3×#135C22×C511yescharacteristic
292C2×C3×SD16—21no—
293C2×C3×SD16C22×C511yescharacteristic
294C3×#131C22×C511yescharacteristic
295#951—21no—
296#951—21no—
297#951C22×C511yescharacteristic
298#951C22×C511yescharacteristic
299#951C22×C511yescharacteristic
300#951C22×C511yescharacteristic, complemented
301#950—21no—
302#950—21no—
303#950C22×C511yescharacteristic
304#948C22×C511yescharacteristic
305#948C22×C511yescharacteristic, complemented
306#944C22×C511yescharacteristic, complemented
307C2×#216—21no—
308C2×#216C22×C511yescharacteristic, complemented
309#942—21no—
310#942C22×C511yescharacteristic, complemented
311#936C22×C511yescharacteristic
312C2×#214—21no—
313C2×#214C22×C511yescharacteristic
314#932—21no—
315#932C22×C511yescharacteristic
316D3×Q16—21no—
317#915—21no—
318#915—21no—
319#912—21no—
320C2×Dic12C22×C511yescharacteristic, complemented
321#901C22×C511yescharacteristic, complemented
322#837C22×C511yescharacteristic
323#837C22×C511yescharacteristic
324#837C22×C511yescharacteristic, complemented
325#836C22×C511yescharacteristic, complemented
326#833C22×C511yescharacteristic
327#825C22×C511yescharacteristic, complemented
328#824C22×C511yescharacteristic, complemented
329#824C22×C511yescharacteristic, complemented
330#822C22×C511yescharacteristic, complemented
331#819C22×C511yescharacteristic, complemented
332#815C22×C511yescharacteristic, complemented
333C5×#41—21no—
334C5×#41—21no—
335C5×#41—21no—
336C5×#41—21no—
337C5×#41—31no—
338C5×#41—41no—
339C5×#41—61no—
340C5×#41—61no—
341C5×#41—61no—
342C5×#41—61no—
343C5×#41—121no—
344C5×#41—121no—
345C5×#41C22×D311yescharacteristic
346C5×#41C22×D311yescharacteristic
347C5×#41C22×D311yescharacteristic
348C2×C5×Q8—21no—
349C2×C5×Q8—21no—
350C2×C5×Q8—31no—
351C2×C5×Q8—31no—
352C2×C5×Q8—61no—
353C2×C5×Q8—61no—
354C2×C5×Q8—61no—
355C2×C5×Q8—61no—
356C2×C5×Q8C22×D311yescharacteristic
357C2×C5×D4—21no—
358C2×C5×D4—21no—
359C2×C5×D4—41no—
360C2×C5×D4C22×D311yescharacteristic
361C5×Q16—21no—
362C5×Q16—31no—
363C5×Q16—61no—
364C5×Q16—61no—
365C5×Q16—61no—
366C5×Q16—61no—
367C5×Q16—61no—
368C5×Q16—61no—
369C5×Q16—61no—
370C5×Q16—61no—
371C5×Q16—61no—
372C5×Q16#6711yescharacteristic
373C5×SD16—21no—
374C5×SD16—21no—
375C5×SD16—21no—
376C5×SD16—21no—
377C5×SD16—31no—
378C5×SD16—31no—
379C5×SD16—61no—
380C5×SD16—61no—
381C5×SD16—61no—
382C5×SD16—61no—
383C5×SD16—61no—
384C5×SD16—61no—
385C5×SD16—61no—
386C5×SD16—61no—
387C5×SD16#6711yescharacteristic
388C5×SD16#6711yescharacteristic
389C5×D8—21no—
390C5×D8—31no—
391C5×D8—61no—
392C5×D8#6711yescharacteristic
393C5×M16—21no—
394C5×M16—31no—
395C5×M16—31no—
396C5×M16—31no—
397C5×M16—61no—
398C5×M16—61no—
399C5×M16—61no—
400C5×M16C22×D311yescharacteristic
401C2×C5×C8—21no—
402C2×C5×C8—31no—
403C2×C5×C8—61no—
404C2×C5×C8—61no—
405C2×C5×C8—61no—
406C2×C5×C8C22×D311yescharacteristic
407C5×C4⋊C4—121no—
408C5×C22⋊C4—121no—
409C42×C5—31no—
410#578—31no—
411#578—31no—
412#577—31no—
413#577C5×D311yescharacteristic, complemented
414#497—31no—
415#473—31no—
416#473—31no—
417#471—31no—
418#471—31no—
419#456—31no—
420#456—31no—
421#455—31no—
422#454—31no—
423#444—31no—
424#444—31no—
425C22×C3×C5—21no—
426C22×C3×C5—21no—
427C22×C3×C5—21no—
428C22×C3×C5—41no—
429C22×C3×C5—81no—
430C22×C3×C5—161no—
431C22×C3×C5H(5,𝔽2)11yescharacteristic
432C2×C5×D3—21no—
433C3×C4×C5—21no—
434C3×C4×C5—21no—
435C3×C4×C5—21no—
436C3×C4×C5—41no—
437C3×C4×C5C22×D411yescharacteristic
438C3×C4×C5C22×D411yescharacteristic
439C5×Dic3—21no—
440C5×Dic3—41no—
441C5×Dic3—41no—
442C5×Dic3—41no—
443C3×#41—21no—
444C3×#41—21no—
445C3×#41—21no—
446C3×#41—21no—
447C3×#41—41no—
448C3×#41C23×C511yescharacteristic
449C3×#41C23×C511yescharacteristic
450C3×#41C23×C511yescharacteristic
451C2×C3×Q8—21no—
452C2×C3×Q8—21no—
453C2×C3×Q8C23×C511yescharacteristic
454C2×C3×D4—21no—
455C2×C3×D4—21no—
456C2×C3×D4—41no—
457C2×C3×D4C23×C511yescharacteristic
458D3×Q8—21no—
459D3×Q8—21no—
460#237—21no—
461#237—21no—
462#237—41no—
463#237—41no—
464#235—21no—
465#235—21no—
466#235C23×C511yescharacteristic
467C2×Dic6—21no—
468C2×Dic6—21no—
469C2×Dic6C23×C511yescharacteristic
470C2×Dic6C23×C511yescharacteristic
471C3×Q16—21no—
472C3×Q16C5×D411yescharacteristic
473C3×SD16—21no—
474C3×SD16—21no—
475C3×SD16—21no—
476C3×SD16—21no—
477C3×SD16C5×D411yescharacteristic
478C3×SD16C5×D411yescharacteristic
479C3×D8—21no—
480C3×D8C5×D411yescharacteristic
481C3×M16—21no—
482C3×M16C23×C511yescharacteristic
483C2×C3×C8—21no—
484C2×C3×C8C23×C511yescharacteristic
485#217—41no—
486#216—21no—
487#216—21no—
488#216—21no—
489#216—21no—
490#216—21no—
491#216—21no—
492#216—21no—
493#216C5×D411yescharacteristic
494#215—21no—
495#215C5×D411yescharacteristic
496#214—21no—
497#214—21no—
498#214—21no—
499#214—21no—
500#214—21no—
501#214—21no—
502#214—21no—
503#214C5×D411yescharacteristic
504#213—21no—
505#213C5×D411yescharacteristic
506Dic3⋊C4—41no—
507C4×Dic3C23×C511yescharacteristic
508#208—21no—
509#208—21no—
510#208C23×C511yescharacteristic
511#208C23×C511yescharacteristic
512#208C23×C511yescharacteristic
513C2×C3⋊C8—21no—
514C2×C3⋊C8—21no—
515C2×C3⋊C8C23×C511yescharacteristic
516Dic12—21no—
517Dic12—21no—
518ΓL(1,𝔽25)—21no—
519D3×C8—21no—
520C23×C5—21no—
521C23×C5—41no—
522C5×Q8—21no—
523C5×Q8—21no—
524C5×Q8—31no—
525C5×Q8—41no—
526C5×Q8—61no—
527C5×Q8—61no—
528C5×Q8—61no—
529C5×Q8—61no—
530C5×Q8—121no—
531C5×Q8—121no—
532C5×Q8D3×D411yescharacteristic
533C5×Q8C2×#6711yescharacteristic
534C5×Q8C2×#6711yescharacteristic
535C5×D4—21no—
536C5×D4—21no—
537C5×D4—21no—
538C5×D4—21no—
539C5×D4—21no—
540C5×D4—31no—
541C5×D4—41no—
542C5×D4—41no—
543C5×D4—41no—
544C5×D4—61no—
545C5×D4—121no—
546C5×D4—121no—
547C5×D4D3×D411yescharacteristic
548C5×D4C2×#6711yescharacteristic
549C5×D4C2×#6711yescharacteristic
550C2×C4×C5—21no—
551C2×C4×C5—21no—
552C2×C4×C5—21no—
553C2×C4×C5—21no—
554C2×C4×C5—41no—
555C2×C4×C5—41no—
556C2×C4×C5—41no—
557C2×C4×C5—61no—
558C2×C4×C5—61no—
559C2×C4×C5—61no—
560C2×C4×C5—61no—
561C2×C4×C5—121no—
562C2×C4×C5—121no—
563C2×C4×C5—121no—
564C2×C4×C5—121no—
565C2×C4×C5C23×D311yescharacteristic
566C5×C8—21no—
567C5×C8—31no—
568C5×C8—31no—
569C5×C8—61no—
570C5×C8—61no—
571C5×C8—61no—
572C5×C8C2×#6711yescharacteristic
573C5×C8C2×#6711yescharacteristic
5742−1+4—31no—
5752−1+4—31no—
5762−1+4C2×C5×D311yescharacteristic
577H(5,𝔽2)C2×C5×D311yescharacteristic
578#137—21no—
579#137—31no—
580#137—31no—
581#137—31no—
582#137—31no—
583#137—31no—
584#137—61no—
585#137—61no—
586#137—61no—
587#137—61no—
588#137—61no—
589#137C2×C5×D311yescharacteristic
590AGL(1,ℤ/8)—21no—
591AGL(1,ℤ/8)—31no—
592AGL(1,ℤ/8)—61no—
593AGL(1,ℤ/8)C2×C5×D311yescharacteristic
594#135—21no—
595#135—31no—
596#135—61no—
597#135—61no—
598#135—61no—
599#135C2×C5×D311yescharacteristic
600C2×Q16—31no—
601C2×Q16—31no—
602C2×Q16—61no—
603C2×Q16—61no—
604C2×SD16—21no—
605C2×SD16—31no—
606C2×SD16—61no—
607C2×SD16C2×C5×D311yescharacteristic
608#131—31no—
609#131—31no—
610#131—31no—
611#131C2×C5×D311yescharacteristic
612C4⋊Q8—31no—
613#124—31no—
614#108—31no—
615#108—31no—
616#104—31no—
617#104—31no—
618#104—31no—
619#104—31no—
620#101—31no—
621#101—31no—
622#101—31no—
623#100—31no—
624#97—31no—
625C2×C3×C5—21no—
626C2×C3×C5—41no—
627C2×C3×C5—41no—
628C2×C3×C5—41no—
629C2×C3×C5—81no—
630C2×C3×C5D4211yescharacteristic
631C5×D3—41no—
632C23×C3—21no—
633C23×C3—41no—
634C3×Q8—21no—
635C3×Q8—21no—
636C3×Q8—41no—
637C3×Q8C2×C5×D411yescharacteristic
638C3×Q8C2×C5×D411yescharacteristic
639C3×Q8C2×C5×D411yescharacteristic
640C3×D4—21no—
641C3×D4—21no—
642C3×D4—21no—
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—41no—
646C3×D4—41no—
647C3×D4—41no—
648C3×D4C2×C5×D411yescharacteristic
649C3×D4C2×C5×D411yescharacteristic
650C3×D4C2×C5×D411yescharacteristic
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4C24×C511yescharacteristic
659#67—21no—
660#67—41no—
661#67—41no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667D12C2×C5×D411yescharacteristic
668C4×D3—21no—
669C4×D3—41no—
670C4×D3—41no—
671Dic6—21no—
672Dic6—21no—
673Dic6—21no—
674Dic6—21no—
675Dic6—41no—
676Dic6—41no—
677Dic6C2×C5×D411yescharacteristic
678C3×C8—21no—
679C3×C8C2×C5×D411yescharacteristic
680C3×C8C2×C5×D411yescharacteristic
681C3⋊C8—21no—
682C3⋊C8—21no—
683C3⋊C8—21no—
684C3⋊C8C2×C5×D411yescharacteristic
685C3⋊C8C2×C5×D411yescharacteristic
686C22×C5—21no—
687C22×C5—21no—
688C22×C5—21no—
689C22×C5—41no—
690C22×C5—61no—
691C22×C5—81no—
692C22×C5—161no—
693C22×C5#100411yescharacteristic
694C4×C5—21no—
695C4×C5—21no—
696C4×C5—21no—
697C4×C5—41no—
698C4×C5—61no—
699C4×C5—121no—
700C4×C5—121no—
701C4×C5—121no—
702C4×C5C2×D3×D411yescharacteristic
703C4×C5C22×#6711yescharacteristic
704#41—21no—
705#41—21no—
706#41—21no—
707#41—21no—
708#41—31no—
709#41—41no—
710#41—61no—
711#41—61no—
712#41—61no—
713#41—61no—
714#41—121no—
715#41—121no—
716#41C22×C5×D311yescharacteristic
717#41C22×C5×D311yescharacteristic
718#41C22×C5×D311yescharacteristic
719C2×Q8—21no—
720C2×Q8—21no—
721C2×Q8—31no—
722C2×Q8—31no—
723C2×Q8—61no—
724C2×Q8—61no—
725C2×Q8—61no—
726C2×Q8—61no—
727C2×Q8C22×C5×D311yescharacteristic
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4C22×C5×D311yescharacteristic
732Q16—21no—
733Q16—31no—
734Q16—61no—
735Q16—61no—
736Q16—61no—
737Q16—61no—
738Q16—61no—
739Q16—61no—
740Q16—61no—
741Q16—61no—
742Q16—61no—
743Q16C5×#6711yescharacteristic
744SD16—21no—
745SD16—21no—
746SD16—21no—
747SD16—21no—
748SD16—31no—
749SD16—31no—
750SD16—61no—
751SD16—61no—
752SD16—61no—
753SD16—61no—
754SD16—61no—
755SD16—61no—
756SD16—61no—
757SD16—61no—
758SD16C5×#6711yescharacteristic
759SD16C5×#6711yescharacteristic
760D8—21no—
761D8—31no—
762D8—61no—
763D8C5×#6711yescharacteristic
764M16—21no—
765M16—31no—
766M16—31no—
767M16—31no—
768M16—61no—
769M16—61no—
770M16—61no—
771M16C22×C5×D311yescharacteristic
772C2×C8—21no—
773C2×C8—31no—
774C2×C8—61no—
775C2×C8—61no—
776C2×C8—61no—
777C2×C8C22×C5×D311yescharacteristic
778C4⋊C4—121no—
779C22⋊C4—121no—
780C42—31no—
781C3×C5#328911yescharacteristic, complemented, Hall
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—41no—
786C22×C3—81no—
787C22×C3—161no—
788C22×C3C5×H(5,𝔽2)11yescharacteristic
789C2×D3—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—41no—
794C3×C4C22×C5×D411yescharacteristic
795C3×C4C22×C5×D411yescharacteristic
796Dic3—21no—
797Dic3—41no—
798Dic3—41no—
799Dic3—41no—
800C2×C5—21no—
801C2×C5—41no—
802C2×C5—41no—
803C2×C5—41no—
804C2×C5—81no—
805C2×C5—121no—
806C2×C5D4×#6711yescharacteristic
807C23—21no—
808C23—41no—
809Q8—21no—
810Q8—21no—
811Q8—31no—
812Q8—41no—
813Q8—61no—
814Q8—61no—
815Q8—61no—
816Q8—61no—
817Q8—121no—
818Q8—121no—
819Q8C5×D3×D411yescharacteristic
820Q8C2×C5×#6711yescharacteristic
821Q8C2×C5×#6711yescharacteristic
822D4—21no—
823D4—21no—
824D4—21no—
825D4—21no—
826D4—21no—
827D4—31no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—61no—
832D4—121no—
833D4—121no—
834D4C5×D3×D411yescharacteristic
835D4C2×C5×#6711yescharacteristic
836D4C2×C5×#6711yescharacteristic
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—121no—
849C2×C4—121no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4C23×C5×D311yescharacteristic
853C8—21no—
854C8—31no—
855C8—31no—
856C8—61no—
857C8—61no—
858C8—61no—
859C8C2×C5×#6711yescharacteristic
860C8C2×C5×#6711yescharacteristic
861C2×C3—21no—
862C2×C3—41no—
863C2×C3—41no—
864C2×C3—41no—
865C2×C3—81no—
866C2×C3C5×D4211yescharacteristic
867D3—41no—
868C5#8401311yescharacteristic, direct product factor, Sylow
869C22—21no—
870C22—21no—
871C22—21no—
872C22—41no—
873C22—61no—
874C22—81no—
875C22—161no—
876C22C5×#100411yescharacteristic
877C4—21no—
878C4—21no—
879C4—21no—
880C4—41no—
881C4—61no—
882C4—121no—
883C4—121no—
884C4—121no—
885C4C2×C5×D3×D411yescharacteristic
886C4C22×C5×#6711yescharacteristic
887C3C5×#328911yescharacteristic, complemented, Sylow
888C2—21no—
889C2—41no—
890C2—41no—
891C2—41no—
892C2—81no—
893C2—121no—
894C2C5×D4×#6711yescharacteristic
subgroupG/H
centerC2×C5D4×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#577C2
socleC2×C3×C5D42
hypercenterC5×#577D3
hypocenterC3C5×#3289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#577

Complements

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

NH ≅ G/Ntype
1. C3×C5×#577C2semidirect
2. C5×#5838C2semidirect
3. C5×#5836C2semidirect
4. C5×#5771C2semidirect
5. C5×#5246C2semidirect
6. C5×#5242C2semidirect
7. C5×#5205C2semidirect
8. C5×#5204C2semidirect
9. C5×#5201C2semidirect
10. C5×#5200C2semidirect
11. C5×#5197C2semidirect
12. C5×#5177C2semidirect
13. C5×#5167C2semidirect
14. C5×#5145C2semidirect
15. C5×#5143C2semidirect
20. C5×#1010C22semidirect
35. C5×#951C22semidirect
40. C5×#948C22semidirect
41. C5×#944C22semidirect
43. C2×C5×#216C22semidirect
45. C5×#942C22semidirect
55. C2×C5×Dic12C22semidirect
56. C5×#901C22semidirect
59. C5×#837C22semidirect
60. C5×#836C22semidirect
62. C5×#825C22semidirect
63. C5×#824C22semidirect
64. C5×#824C22semidirect
65. C5×#822C22semidirect
66. C5×#819C22semidirect
67. C5×#815C22semidirect
68. #84013C5direct (N × H)
72. C5×#577D3semidirect
161. C3×#577C2×C5semidirect
162. #5838C2×C5semidirect
163. #5836C2×C5semidirect
164. #5771C2×C5semidirect
165. #5246C2×C5semidirect
166. #5242C2×C5semidirect
167. #5205C2×C5semidirect
168. #5204C2×C5semidirect
169. #5201C2×C5semidirect
170. #5200C2×C5semidirect
171. #5197C2×C5semidirect
172. #5177C2×C5semidirect
173. #5167C2×C5semidirect
174. #5145C2×C5semidirect
175. #5143C2×C5semidirect
285. #1010C22×C5semidirect
300. #951C22×C5semidirect
305. #948C22×C5semidirect
306. #944C22×C5semidirect
308. C2×#216C22×C5semidirect
310. #942C22×C5semidirect
320. C2×Dic12C22×C5semidirect
321. #901C22×C5semidirect
324. #837C22×C5semidirect
325. #836C22×C5semidirect
327. #825C22×C5semidirect
328. #824C22×C5semidirect
329. #824C22×C5semidirect
330. #822C22×C5semidirect
331. #819C22×C5semidirect
332. #815C22×C5semidirect
413. #577C5×D3semidirect
781. C3×C5#3289semidirect
868. C5#84013direct (N × H)
887. C3C5×#3289semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5772
C5×#58382
C5×#58362
C5×#57712
C5×#52462
C5×#52422
C5×#52052
C5×#52042
C5×#52012
C5×#52002
C5×#51972
C5×#51772
C5×#51672
C5×#51452
C5×#51432
C5×#32893
#840135