Finite Group Databasebeta

← C5×#84019 #14457798

Subgroups — C5×#84019 #14457798

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×#578C211yesmaximal, characteristic, complemented
2C5×#5838C211yesmaximal, characteristic, complemented
3C5×#5837C211yesmaximal, characteristic, complemented
4C5×#5770C211yesmaximal, characteristic, complemented
5C5×#5246C211yesmaximal, characteristic, complemented
6C5×#5245C211yesmaximal, characteristic, complemented
7C5×#5205C211yesmaximal, characteristic, complemented
8C5×#5204C211yesmaximal, characteristic, complemented
9C5×#5203C211yesmaximal, characteristic, complemented
10C5×#5202C211yesmaximal, characteristic, complemented
11C5×#5197C211yesmaximal, characteristic, complemented
12C5×#5192C211yesmaximal, characteristic, complemented
13C5×#5190C211yesmaximal, characteristic, complemented
14C5×#5145C211yesmaximal, characteristic, complemented
15C5×#5141C211yesmaximal, characteristic, complemented
16C5×#3289—31nomaximal, Hall
17C3×C5×2−1+4C2211yescharacteristic
18C3×C5×2−1+4C2211yescharacteristic, complemented
19C5×#1010C2211yescharacteristic
20C5×#1009C2211yescharacteristic
21C3×C5×#137—21no—
22C3×C5×#137—21no—
23C3×C5×#137C2211yescharacteristic
24C3×C5×#137C2211yescharacteristic, complemented
25C3×C5×#135—21no—
26C3×C5×#135C2211yescharacteristic
27C2×C3×C5×Q16—21no—
28C2×C3×C5×Q16C2211yescharacteristic, complemented
29C3×C5×#131C2211yescharacteristic, complemented
30C5×#951—21no—
31C5×#951C2211yescharacteristic
32C5×#951C2211yescharacteristic, complemented
33C5×#950—21no—
34C5×#950—21no—
35C5×#950C2211yescharacteristic
36C5×#949—21no—
37C5×#949C2211yescharacteristic
38C5×#949C2211yescharacteristic
39C5×#948C2211yescharacteristic
40C5×#948C2211yescharacteristic, complemented
41C5×#947C2211yescharacteristic
42C5×#944C2211yescharacteristic, complemented
43C2×C5×#216—21no—
44C2×C5×#216C2211yescharacteristic, complemented
45C5×#942—21no—
46C5×#942—21no—
47C5×#942C2211yescharacteristic
48C5×#942C2211yescharacteristic
49C2×C5×#215—21no—
50C2×C5×#215C2211yescharacteristic
51C5×#918—21no—
52C5×#916—21no—
53C5×D3×SD16—21no—
54C5×#911—21no—
55C2×C5×#204C2211yescharacteristic
56C5×#901C2211yescharacteristic
57C5×#837C2211yescharacteristic
58C5×#837C2211yescharacteristic, complemented
59C5×#837C2211yescharacteristic, complemented
60C5×#836C2211yescharacteristic, complemented
61C5×#836C2211yescharacteristic, complemented
62C5×#825C2211yescharacteristic
63C5×#824C2211yescharacteristic, complemented
64C5×#823C2211yescharacteristic
65C5×#822C2211yescharacteristic, complemented
66C5×#819C2211yescharacteristic, complemented
67C5×#815C2211yescharacteristic, complemented
68#84019C511yesmaximal, characteristic, direct product factor, Hall
69C5×#578—31no—
70C5×#578D311yescharacteristic, complemented
71C5×#577—31no—
72C5×#577—31no—
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×#41—41no—
90C3×C5×#41C2311yescharacteristic
91C3×C5×#41C2311yescharacteristic
92C3×C5×#41C2311yescharacteristic
93C2×C3×C5×Q8—21no—
94C2×C3×C5×Q8—21no—
95C2×C3×C5×Q8—21no—
96C2×C3×C5×Q8—21no—
97C2×C3×C5×Q8C2311yescharacteristic
98C2×C3×C5×Q8C2311yescharacteristic
99C5×#239—21no—
100C5×D3×Q8—21no—
101C5×#237—21no—
102C5×#237—41no—
103C5×D3×D4—21no—
104C5×D3×D4—41no—
105C5×#235—21no—
106C5×#235—21no—
107C5×#235C2311yescharacteristic
108C2×C5×D12—21no—
109C2×C5×D12C2311yescharacteristic
110C2×C5×Dic6—21no—
111C2×C5×Dic6C2311yescharacteristic
112C3×C5×Q16—21no—
113C3×C5×Q16—21no—
114C3×C5×Q16—21no—
115C3×C5×Q16—21no—
116C3×C5×Q16D411yescharacteristic
117C3×C5×SD16—21no—
118C3×C5×SD16—21no—
119C3×C5×SD16D411yescharacteristic
120C3×C5×SD16D411yescharacteristic
121C3×C5×D8D411yescharacteristic
122C3×C5×M16—21no—
123C3×C5×M16C2311yescharacteristic
124C2×C3×C5×C8—21no—
125C2×C3×C5×C8C2311yescharacteristic
126C5×#216—21no—
127C5×#216—21no—
128C5×#216—21no—
129C5×#216—21no—
130C5×#216—21no—
131C5×#216—21no—
132C5×#216D411yescharacteristic
133C5×#215—21no—
134C5×#215—21no—
135C5×#215—21no—
136C5×#215—21no—
137C5×#215—21no—
138C5×#215—21no—
139C5×#215D411yescharacteristic
140C5×#214—21no—
141C5×#214—21no—
142C5×#214D411yescharacteristic
143C5×#213—21no—
144C5×#213—21no—
145C5×#213D411yescharacteristic
146C5×(C2×D3)⋊C4—41no—
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×#204—21no—
158C5×#204—21no—
159C5×ΓL(1,𝔽25)—21no—
160C5×D3×C8—21no—
161C3×#578C2×C511yescharacteristic, complemented
162#5838C2×C511yescharacteristic, complemented
163#5837C2×C511yescharacteristic, complemented
164#5770C2×C511yescharacteristic, complemented
165#5246C2×C511yescharacteristic, complemented
166#5245C2×C511yescharacteristic, complemented
167#5205C2×C511yescharacteristic, complemented
168#5204C2×C511yescharacteristic, complemented
169#5203C2×C511yescharacteristic, complemented
170#5202C2×C511yescharacteristic, complemented
171#5197C2×C511yescharacteristic, complemented
172#5192C2×C511yescharacteristic, complemented
173#5190C2×C511yescharacteristic, complemented
174#5145C2×C511yescharacteristic, complemented
175#5141C2×C511yescharacteristic, complemented
176C5×2−1+4—31no—
177C5×2−1+4C2×D311yescharacteristic
178C5×2−1+4C2×D311yescharacteristic, complemented
179C5×H(5,𝔽2)—31no—
180C5×#137—21no—
181C5×#137—21no—
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×#137C2×D311yescharacteristic
191C5×#137C2×D311yescharacteristic, complemented
192C5×AGL(1,ℤ/8)—31no—
193C5×AGL(1,ℤ/8)—31no—
194C5×AGL(1,ℤ/8)—61no—
195C5×AGL(1,ℤ/8)—61no—
196C5×#135—21no—
197C5×#135—31no—
198C5×#135—61no—
199C5×#135—61no—
200C5×#135—61no—
201C5×#135C2×D311yescharacteristic
202C2×C5×Q16—21no—
203C2×C5×Q16—31no—
204C2×C5×Q16—61no—
205C2×C5×Q16C2×D311yescharacteristic, complemented
206C2×C5×SD16—31no—
207C2×C5×SD16—31no—
208C2×C5×SD16—61no—
209C2×C5×SD16—61no—
210C5×#131—31no—
211C5×#131—31no—
212C5×#131—31no—
213C5×#131C2×D311yescharacteristic, complemented
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
228C22×C5×D3—21no—
229C22×C5×D3—41no—
230C3×C5×Q8—21no—
231C3×C5×Q8—21no—
232C3×C5×Q8—21no—
233C3×C5×Q8—21no—
234C3×C5×Q8—41no—
235C3×C5×Q8—41no—
236C3×C5×Q8C2×D411yescharacteristic
237C3×C5×Q8C2×D411yescharacteristic
238C3×C5×Q8C2×D411yescharacteristic
239C3×C5×D4—21no—
240C3×C5×D4—21no—
241C3×C5×D4—21no—
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—21no—
252C2×C3×C4×C5—41no—
253C2×C3×C4×C5—41no—
254C2×C3×C4×C5—41no—
255C2×C3×C4×C5—41no—
256C2×C3×C4×C5C2411yescharacteristic
257C5×#67—21no—
258C5×#67—41no—
259C5×#67—41no—
260C2×C5×Dic3—21no—
261C2×C5×Dic3—21no—
262C2×C5×Dic3—41no—
263C5×D12—21no—
264C5×D12—21no—
265C5×D12—41no—
266C5×D12C2×D411yescharacteristic
267C4×C5×D3—21no—
268C4×C5×D3—41no—
269C4×C5×D3—41no—
270C5×Dic6—21no—
271C5×Dic6—21no—
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
283C3×2−1+4C22×C511yescharacteristic, complemented
284#1010C22×C511yescharacteristic
285#1009C22×C511yescharacteristic
286C3×#137—21no—
287C3×#137—21no—
288C3×#137C22×C511yescharacteristic
289C3×#137C22×C511yescharacteristic, complemented
290C3×#135—21no—
291C3×#135C22×C511yescharacteristic
292C2×C3×Q16—21no—
293C2×C3×Q16C22×C511yescharacteristic, complemented
294C3×#131C22×C511yescharacteristic, complemented
295#951—21no—
296#951C22×C511yescharacteristic
297#951C22×C511yescharacteristic, complemented
298#950—21no—
299#950—21no—
300#950C22×C511yescharacteristic
301#949—21no—
302#949C22×C511yescharacteristic
303#949C22×C511yescharacteristic
304#948C22×C511yescharacteristic
305#948C22×C511yescharacteristic, complemented
306#947C22×C511yescharacteristic
307#944C22×C511yescharacteristic, complemented
308C2×#216—21no—
309C2×#216C22×C511yescharacteristic, complemented
310#942—21no—
311#942—21no—
312#942C22×C511yescharacteristic
313#942C22×C511yescharacteristic
314C2×#215—21no—
315C2×#215C22×C511yescharacteristic
316#918—21no—
317#916—21no—
318D3×SD16—21no—
319#911—21no—
320C2×#204C22×C511yescharacteristic
321#901C22×C511yescharacteristic
322#837C22×C511yescharacteristic
323#837C22×C511yescharacteristic, complemented
324#837C22×C511yescharacteristic, complemented
325#836C22×C511yescharacteristic, complemented
326#836C22×C511yescharacteristic, complemented
327#825C22×C511yescharacteristic
328#824C22×C511yescharacteristic, complemented
329#823C22×C511yescharacteristic
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—41no—
340C5×#41—61no—
341C5×#41—61no—
342C5×#41—61no—
343C5×#41—61no—
344C5×#41—121no—
345C5×#41C22×D311yescharacteristic
346C5×#41C22×D311yescharacteristic
347C5×#41C22×D311yescharacteristic
348C2×C5×Q8—21no—
349C2×C5×Q8—21no—
350C2×C5×Q8—21no—
351C2×C5×Q8—21no—
352C2×C5×Q8—31no—
353C2×C5×Q8—61no—
354C2×C5×Q8—61no—
355C2×C5×Q8C22×D311yescharacteristic
356C2×C5×Q8C22×D311yescharacteristic
357C2×C5×D4—31no—
358C2×C5×D4—61no—
359C2×C5×D4—61no—
360C2×C5×D4—121no—
361C5×Q16—21no—
362C5×Q16—21no—
363C5×Q16—21no—
364C5×Q16—21no—
365C5×Q16—31no—
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—31no—
376C5×SD16—31no—
377C5×SD16—61no—
378C5×SD16—61no—
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—31no—
390C5×D8—61no—
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#578C5×D311yescharacteristic, complemented
412#577—31no—
413#577—31no—
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×C5H(5,𝔽2)11yescharacteristic
429C2×C5×D3—21no—
430C2×C5×D3—41no—
431C2×C5×D3—81no—
432C2×C5×D3—161no—
433C3×C4×C5—21no—
434C3×C4×C5—21no—
435C3×C4×C5—21no—
436C3×C4×C5—41no—
437C3×C4×C5—41no—
438C3×C4×C5C22×D411yescharacteristic
439C3×C4×C5C22×D411yescharacteristic
440C5×Dic3—21no—
441C5×Dic3—41no—
442C5×Dic3—41no—
443C3×#41—21no—
444C3×#41—21no—
445C3×#41—21no—
446C3×#41—21no—
447C3×#41—41no—
448C3×#41—41no—
449C3×#41C23×C511yescharacteristic
450C3×#41C23×C511yescharacteristic
451C3×#41C23×C511yescharacteristic
452C2×C3×Q8—21no—
453C2×C3×Q8—21no—
454C2×C3×Q8—21no—
455C2×C3×Q8—21no—
456C2×C3×Q8C23×C511yescharacteristic
457C2×C3×Q8C23×C511yescharacteristic
458#239—21no—
459D3×Q8—21no—
460#237—21no—
461#237—41no—
462D3×D4—21no—
463D3×D4—41no—
464#235—21no—
465#235—21no—
466#235C23×C511yescharacteristic
467C2×D12—21no—
468C2×D12C23×C511yescharacteristic
469C2×Dic6—21no—
470C2×Dic6C23×C511yescharacteristic
471C3×Q16—21no—
472C3×Q16—21no—
473C3×Q16—21no—
474C3×Q16—21no—
475C3×Q16C5×D411yescharacteristic
476C3×SD16—21no—
477C3×SD16—21no—
478C3×SD16C5×D411yescharacteristic
479C3×SD16C5×D411yescharacteristic
480C3×D8C5×D411yescharacteristic
481C3×M16—21no—
482C3×M16C23×C511yescharacteristic
483C2×C3×C8—21no—
484C2×C3×C8C23×C511yescharacteristic
485#216—21no—
486#216—21no—
487#216—21no—
488#216—21no—
489#216—21no—
490#216—21no—
491#216C5×D411yescharacteristic
492#215—21no—
493#215—21no—
494#215—21no—
495#215—21no—
496#215—21no—
497#215—21no—
498#215C5×D411yescharacteristic
499#214—21no—
500#214—21no—
501#214C5×D411yescharacteristic
502#213—21no—
503#213—21no—
504#213C5×D411yescharacteristic
505(C2×D3)⋊C4—41no—
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
516#204—21no—
517#204—21no—
518ΓL(1,𝔽25)—21no—
519D3×C8—21no—
520C23×C5—61no—
521C23×C5—121no—
522C5×Q8—21no—
523C5×Q8—21no—
524C5×Q8—21no—
525C5×Q8—21no—
526C5×Q8—31no—
527C5×Q8—41no—
528C5×Q8—41no—
529C5×Q8—61no—
530C5×Q8—61no—
531C5×Q8—121no—
532C5×Q8D3×D411yescharacteristic
533C5×Q8C2×#6711yescharacteristic
534C5×Q8C2×#6711yescharacteristic
535C5×D4—21no—
536C5×D4—21no—
537C5×D4—21no—
538C5×D4—31no—
539C5×D4—41no—
540C5×D4—41no—
541C5×D4—61no—
542C5×D4—61no—
543C5×D4—61no—
544C5×D4—121no—
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—21no—
555C2×C4×C5—41no—
556C2×C4×C5—41no—
557C2×C4×C5—41no—
558C2×C4×C5—41no—
559C2×C4×C5—61no—
560C2×C4×C5—61no—
561C2×C4×C5—61no—
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+4C2×C5×D311yescharacteristic
5762−1+4C2×C5×D311yescharacteristic, complemented
577H(5,𝔽2)—31no—
578#137—21no—
579#137—21no—
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#137C2×C5×D311yescharacteristic
589#137C2×C5×D311yescharacteristic, complemented
590AGL(1,ℤ/8)—31no—
591AGL(1,ℤ/8)—31no—
592AGL(1,ℤ/8)—61no—
593AGL(1,ℤ/8)—61no—
594#135—21no—
595#135—31no—
596#135—61no—
597#135—61no—
598#135—61no—
599#135C2×C5×D311yescharacteristic
600C2×Q16—21no—
601C2×Q16—31no—
602C2×Q16—61no—
603C2×Q16C2×C5×D311yescharacteristic, complemented
604C2×SD16—31no—
605C2×SD16—31no—
606C2×SD16—61no—
607C2×SD16—61no—
608#131—31no—
609#131—31no—
610#131—31no—
611#131C2×C5×D311yescharacteristic, complemented
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×C5D4211yescharacteristic
630C5×D3—41no—
631C5×D3—81no—
632C22×D3—21no—
633C22×D3—41no—
634C3×Q8—21no—
635C3×Q8—21no—
636C3×Q8—21no—
637C3×Q8—21no—
638C3×Q8—41no—
639C3×Q8—41no—
640C3×Q8C2×C5×D411yescharacteristic
641C3×Q8C2×C5×D411yescharacteristic
642C3×Q8C2×C5×D411yescharacteristic
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—21no—
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—21no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4C24×C511yescharacteristic
661#67—21no—
662#67—41no—
663#67—41no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—41no—
667D12—21no—
668D12—21no—
669D12—41no—
670D12C2×C5×D411yescharacteristic
671C4×D3—21no—
672C4×D3—41no—
673C4×D3—41no—
674Dic6—21no—
675Dic6—21no—
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—61no—
690C22×C5—121no—
691C22×C5—241no—
692C22×C5—481no—
693C22×C5#100411yescharacteristic
694C4×C5—21no—
695C4×C5—21no—
696C4×C5—21no—
697C4×C5—41no—
698C4×C5—41no—
699C4×C5—61no—
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—41no—
711#41—61no—
712#41—61no—
713#41—61no—
714#41—61no—
715#41—121no—
716#41C22×C5×D311yescharacteristic
717#41C22×C5×D311yescharacteristic
718#41C22×C5×D311yescharacteristic
719C2×Q8—21no—
720C2×Q8—21no—
721C2×Q8—21no—
722C2×Q8—21no—
723C2×Q8—31no—
724C2×Q8—61no—
725C2×Q8—61no—
726C2×Q8C22×C5×D311yescharacteristic
727C2×Q8C22×C5×D311yescharacteristic
728C2×D4—31no—
729C2×D4—61no—
730C2×D4—61no—
731C2×D4—121no—
732Q16—21no—
733Q16—21no—
734Q16—21no—
735Q16—21no—
736Q16—31no—
737Q16—61no—
738Q16—61no—
739Q16—61no—
740Q16—61no—
741Q16—61no—
742Q16—61no—
743Q16C5×#6711yescharacteristic
744SD16—21no—
745SD16—21no—
746SD16—31no—
747SD16—31no—
748SD16—61no—
749SD16—61no—
750SD16—61no—
751SD16—61no—
752SD16—61no—
753SD16—61no—
754SD16—61no—
755SD16—61no—
756SD16—61no—
757SD16—61no—
758SD16C5×#6711yescharacteristic
759SD16C5×#6711yescharacteristic
760D8—31no—
761D8—61no—
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×C3C5×H(5,𝔽2)11yescharacteristic
786C2×D3—21no—
787C2×D3—41no—
788C2×D3—81no—
789C2×D3—161no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4C22×C5×D411yescharacteristic
796C3×C4C22×C5×D411yescharacteristic
797Dic3—21no—
798Dic3—41no—
799Dic3—41no—
800C2×C5—21no—
801C2×C5—41no—
802C2×C5—41no—
803C2×C5—41no—
804C2×C5—121no—
805C2×C5—241no—
806C2×C5D4×#6711yescharacteristic
807C23—61no—
808C23—121no—
809Q8—21no—
810Q8—21no—
811Q8—21no—
812Q8—21no—
813Q8—31no—
814Q8—41no—
815Q8—41no—
816Q8—61no—
817Q8—61no—
818Q8—121no—
819Q8C5×D3×D411yescharacteristic
820Q8C2×C5×#6711yescharacteristic
821Q8C2×C5×#6711yescharacteristic
822D4—21no—
823D4—21no—
824D4—21no—
825D4—31no—
826D4—41no—
827D4—41no—
828D4—61no—
829D4—61no—
830D4—61no—
831D4—121no—
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—21no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
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×C3C5×D4211yescharacteristic
866D3—41no—
867D3—81no—
868C5#8401911yescharacteristic, direct product factor, Sylow
869C22—21no—
870C22—21no—
871C22—21no—
872C22—61no—
873C22—121no—
874C22—241no—
875C22—481no—
876C22C5×#100411yescharacteristic
877C4—21no—
878C4—21no—
879C4—21no—
880C4—41no—
881C4—41no—
882C4—61no—
883C4—121no—
884C4—121no—
885C4C2×C5×D3×D411yescharacteristic
886C4C22×C5×#6711yescharacteristic
887C3C5×#328911yescharacteristic, complemented, Sylow
888C2—21no—
889C2—41no—
890C2—41no—
891C2—41no—
892C2—121no—
893C2—241no—
894C2C5×D4×#6711yescharacteristic
subgroupG/H
centerC2×C5D4×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#578C2
socleC2×C3×C5D42
hypercenterC5×#578D3
hypocenterC3C5×#3289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#578

Complements

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

NH ≅ G/Ntype
1. C3×C5×#578C2semidirect
2. C5×#5838C2semidirect
3. C5×#5837C2semidirect
4. C5×#5770C2semidirect
5. C5×#5246C2semidirect
6. C5×#5245C2semidirect
7. C5×#5205C2semidirect
8. C5×#5204C2semidirect
9. C5×#5203C2semidirect
10. C5×#5202C2semidirect
11. C5×#5197C2semidirect
12. C5×#5192C2semidirect
13. C5×#5190C2semidirect
14. C5×#5145C2semidirect
15. C5×#5141C2semidirect
18. C3×C5×2−1+4C22semidirect
24. C3×C5×#137C22semidirect
28. C2×C3×C5×Q16C22semidirect
29. C3×C5×#131C22semidirect
32. C5×#951C22semidirect
40. C5×#948C22semidirect
42. C5×#944C22semidirect
44. C2×C5×#216C22semidirect
58. C5×#837C22semidirect
59. C5×#837C22semidirect
60. C5×#836C22semidirect
61. C5×#836C22semidirect
63. C5×#824C22semidirect
65. C5×#822C22semidirect
66. C5×#819C22semidirect
67. C5×#815C22semidirect
68. #84019C5direct (N × H)
70. C5×#578D3semidirect
161. C3×#578C2×C5semidirect
162. #5838C2×C5semidirect
163. #5837C2×C5semidirect
164. #5770C2×C5semidirect
165. #5246C2×C5semidirect
166. #5245C2×C5semidirect
167. #5205C2×C5semidirect
168. #5204C2×C5semidirect
169. #5203C2×C5semidirect
170. #5202C2×C5semidirect
171. #5197C2×C5semidirect
172. #5192C2×C5semidirect
173. #5190C2×C5semidirect
174. #5145C2×C5semidirect
175. #5141C2×C5semidirect
178. C5×2−1+4C2×D3semidirect
191. C5×#137C2×D3semidirect
205. C2×C5×Q16C2×D3semidirect
213. C5×#131C2×D3semidirect
283. C3×2−1+4C22×C5semidirect
289. C3×#137C22×C5semidirect
293. C2×C3×Q16C22×C5semidirect
294. C3×#131C22×C5semidirect
297. #951C22×C5semidirect
305. #948C22×C5semidirect
307. #944C22×C5semidirect
309. C2×#216C22×C5semidirect
323. #837C22×C5semidirect
324. #837C22×C5semidirect
325. #836C22×C5semidirect
326. #836C22×C5semidirect
328. #824C22×C5semidirect
330. #822C22×C5semidirect
331. #819C22×C5semidirect
332. #815C22×C5semidirect
411. #578C5×D3semidirect
576. 2−1+4C2×C5×D3semidirect
589. #137C2×C5×D3semidirect
603. C2×Q16C2×C5×D3semidirect
611. #131C2×C5×D3semidirect
781. C3×C5#3289semidirect
868. C5#84019direct (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×#5782
C5×#58382
C5×#58372
C5×#57702
C5×#52462
C5×#52452
C5×#52052
C5×#52042
C5×#52032
C5×#52022
C5×#51972
C5×#51922
C5×#51902
C5×#51452
C5×#51412
C5×#32893
#840195