Finite Group Databasebeta

← C5×#82541 #14435583

Subgroups — C5×#82541 #14435583

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#518C211yesmaximal, characteristic, complemented
2C5×#5534C211yesmaximal, characteristic, complemented
3C5×#5218C211yesmaximal, characteristic, complemented
4C5×#5217C211yesmaximal, characteristic
5C5×#5018C211yesmaximal, characteristic, complemented
6C4×C5×#214C211yesmaximal, characteristic, complemented
7C5×#5016C211yesmaximal, characteristic, complemented
8C5×#5016C211yesmaximal, characteristic, complemented
9C5×#5014C211yesmaximal, characteristic, complemented
10C4×C5×#213C211yesmaximal, characteristic, complemented
11C5×#5008C211yesmaximal, characteristic, complemented
12C5×#5007C211yesmaximal, characteristic, complemented
13C5×#5003C211yesmaximal, characteristic, complemented
14C5×#5000C211yesmaximal, characteristic, complemented
15C5×#4996C211yesmaximal, characteristic, complemented
16C5×#3118—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C3×C4×C5×D4—21no—
19C3×C4×C5×D4—21no—
20C3×C4×C5×D4C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22C3×C4×C5×D4C2211yescharacteristic
23C3×C4×C5×D4C2211yescharacteristic
24C3×C5×#117C2211yescharacteristic
25C3×C5×#117C2211yescharacteristic
26C2×C3×C5×C22⋊C4—21no—
27C2×C3×C5×C22⋊C4—21no—
28C2×C5×#214C2211yescharacteristic
29C2×C5×#214C2211yescharacteristic
30C2×C5×#213C2211yescharacteristic
31C2×C5×#213C2211yescharacteristic
32C5×#930C2211yescharacteristic
33C5×#924C2211yescharacteristic
34C5×#898—21no—
35C5×#896—21no—
36C5×#885—21no—
37C5×#883—21no—
38C5×#875C2211yescharacteristic, complemented
39C4×C5×D12C2211yescharacteristic, complemented
40C5×#869C2211yescharacteristic, complemented
41C4×C5×Dic6C2211yescharacteristic, complemented
42C5×#832C2211yescharacteristic
43C5×#832C2211yescharacteristic
44C5×#832C2211yescharacteristic
45C5×#832C2211yescharacteristic
46C5×#830C2211yescharacteristic
47C5×#830C2211yescharacteristic
48C5×#810C2211yescharacteristic, complemented
49C5×#810C2211yescharacteristic, complemented
50C5×#809C2211yescharacteristic, complemented
51C5×#809C2211yescharacteristic, complemented
52C5×#808C2211yescharacteristic, complemented
53C5×#808C2211yescharacteristic, complemented
54C5×#807C2211yescharacteristic, complemented
55C5×#807C2211yescharacteristic, complemented
56C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
58C5×#803C2211yescharacteristic, complemented
59C4×C5×C3⋊C8C2211yescharacteristic, complemented
60#82541C511yesmaximal, characteristic, direct product factor, Hall
61C5×#542—31no—
62C5×#518D311yescharacteristic, complemented
63C5×#485—31no—
64C5×#482—31no—
65C5×#476—31no—
66C5×#474—31no—
67C5×#463—31no—
68C5×#463—31no—
69C5×#450—31no—
70C5×#447—31no—
71C5×#442—31no—
72C5×#440—31no—
73C4×C5×SD16—31no—
74C4×C5×D8—31no—
75C5×#433—31no—
76C24×C3×C5—21no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5—21no—
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5—21no—
85C22×C3×C4×C5—21no—
86C22×C3×C4×C5C2311yescharacteristic
87C2×C5×#67—21no—
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3—21no—
90C2×C5×Dic6—21no—
91C2×C5×Dic6C2311yescharacteristic
92C3×C5×C4⋊C4D411yescharacteristic
93C3×C5×C4⋊C4D411yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C22⋊C4—21no—
97C3×C5×C22⋊C4—21no—
98C3×C5×C22⋊C4—21no—
99C3×C5×C22⋊C4—21no—
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4D411yescharacteristic
102C3×C5×C22⋊C4D411yescharacteristic
103C3×C42×C5—21no—
104C3×C42×C5C2311yescharacteristic
105C3×C42×C5C2311yescharacteristic
106C5×#217—21no—
107C5×#214—22no—
108C5×#214—22no—
109C5×#213—22no—
110C5×#213—22no—
111C5×(C2×D3)⋊C4—21no—
112C5×(C2×D3)⋊C4—21no—
113C5×(C2×D3)⋊C4—21no—
114C5×(C2×D3)⋊C4—21no—
115C5×C4⋊Dic3—21no—
116C5×C4⋊Dic3C2311yescharacteristic
117C5×C4⋊Dic3C2311yescharacteristic
118C5×Dic3⋊C4—21no—
119C5×Dic3⋊C4—21no—
120C4×C5×Dic3—21no—
121C2×C5×C3⋊C8C2311yescharacteristic
122C2×C5×C3⋊C8C2311yescharacteristic
123C2×C5×C3⋊C8C2311yescharacteristic
124C2×C5×C3⋊C8C2311yescharacteristic
125C3×#518C2×C511yescharacteristic, complemented
126#5534C2×C511yescharacteristic, complemented
127#5218C2×C511yescharacteristic, complemented
128#5217C2×C511yescharacteristic
129#5018C2×C511yescharacteristic, complemented
130C4×#214C2×C511yescharacteristic, complemented
131#5016C2×C511yescharacteristic, complemented
132#5016C2×C511yescharacteristic, complemented
133#5014C2×C511yescharacteristic, complemented
134C4×#213C2×C511yescharacteristic, complemented
135#5008C2×C511yescharacteristic, complemented
136#5007C2×C511yescharacteristic, complemented
137#5003C2×C511yescharacteristic, complemented
138#5000C2×C511yescharacteristic, complemented
139#4996C2×C511yescharacteristic, complemented
140C22×C5×D4C2×D311yescharacteristic
141C2×C5×SD16—31no—
142C2×C5×SD16—31no—
143C2×C5×D8—31no—
144C2×C5×D8—31no—
145C5×C4⋊Q8—31no—
146C5×#126—61no—
147C5×#124—31no—
148C5×#124—61no—
149C5×#123—61no—
150C5×C22⋊Q8—31no—
151C5×C22⋊Q8—61no—
152C5×#121—31no—
153C4×C5×Q8—31no—
154C4×C5×D4—21no—
155C4×C5×D4—21no—
156C4×C5×D4—31no—
157C4×C5×D4C2×D311yescharacteristic
158C4×C5×D4C2×D311yescharacteristic
159C4×C5×D4C2×D311yescharacteristic
160C4×C5×D4C2×D311yescharacteristic
161C5×#117C2×D311yescharacteristic
162C5×#117C2×D311yescharacteristic
163C2×C5×C22⋊C4—21no—
164C2×C5×C22⋊C4—21no—
165C5×#107—31no—
166C5×#107—31no—
167C5×#106—31no—
168C5×#106—31no—
169C5×C4⋊C8—31no—
170C5×C4⋊C8—31no—
171C5×#103—31no—
172C5×#103—31no—
173C5×#102—31no—
174C5×#102—31no—
175C5×#102—31no—
176C5×#102—31no—
177C5×#102—31no—
178C5×#102—31no—
179C5×C22⋊C8—31no—
180C5×C22⋊C8—31no—
181C5×#97—31no—
182C4×C5×C8—31no—
183#3118—31noSylow
184C23×C3×C5—24no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—81no—
188C23×C3×C5—81no—
189C23×C3×C5C2×D411yescharacteristic
190C22×C5×D3—21no—
191C3×C5×D4—24no—
192C3×C5×D4—21no—
193C3×C5×D4—21no—
194C3×C5×D4#4112yes—
195C3×C5×D4#4112yes—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—81no—
201C2×C3×C4×C5—81no—
202C2×C3×C4×C5—81no—
203C2×C3×C4×C5—81no—
204C2×C3×C4×C5C2×D411yescharacteristic
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2411yescharacteristic
210C5×#67—81no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C5×D12—21no—
215C5×D12—21no—
216C4×C5×D3—81no—
217C5×Dic6—21no—
218C5×Dic6—21no—
219C5×Dic6—81no—
220C5×C3⋊C8—21no—
221C5×C3⋊C8—21no—
222C5×C3⋊C8—21no—
223C5×C3⋊C8—21no—
224C22×C3×D4C22×C511yescharacteristic
225C3×C4×D4—21no—
226C3×C4×D4—21no—
227C3×C4×D4C22×C511yescharacteristic
228C3×C4×D4C22×C511yescharacteristic
229C3×C4×D4C22×C511yescharacteristic
230C3×C4×D4C22×C511yescharacteristic
231C3×#117C22×C511yescharacteristic
232C3×#117C22×C511yescharacteristic
233C2×C3×C22⋊C4—21no—
234C2×C3×C22⋊C4—21no—
235C2×#214C22×C511yescharacteristic
236C2×#214C22×C511yescharacteristic
237C2×#213C22×C511yescharacteristic
238C2×#213C22×C511yescharacteristic
239#930C22×C511yescharacteristic
240#924C22×C511yescharacteristic
241#898—21no—
242#896—21no—
243#885—21no—
244#883—21no—
245#875C22×C511yescharacteristic, complemented
246C4×D12C22×C511yescharacteristic, complemented
247#869C22×C511yescharacteristic, complemented
248C4×Dic6C22×C511yescharacteristic, complemented
249#832C22×C511yescharacteristic
250#832C22×C511yescharacteristic
251#832C22×C511yescharacteristic
252#832C22×C511yescharacteristic
253#830C22×C511yescharacteristic
254#830C22×C511yescharacteristic
255#810C22×C511yescharacteristic, complemented
256#810C22×C511yescharacteristic, complemented
257#809C22×C511yescharacteristic, complemented
258#809C22×C511yescharacteristic, complemented
259#808C22×C511yescharacteristic, complemented
260#808C22×C511yescharacteristic, complemented
261#807C22×C511yescharacteristic, complemented
262#807C22×C511yescharacteristic, complemented
263C4⋊(C3⋊C8)C22×C511yescharacteristic, complemented
264C4⋊(C3⋊C8)C22×C511yescharacteristic, complemented
265#803C22×C511yescharacteristic, complemented
266C4×C3⋊C8C22×C511yescharacteristic, complemented
267C24×C5—21no—
268C2×C5×Q8—31no—
269C2×C5×Q8—61no—
270C2×C5×D4—22no—
271C2×C5×D4—22no—
272C2×C5×D4—21no—
273C2×C5×D4—31no—
274C2×C5×D4—61no—
275C2×C5×D4C22×D311yescharacteristic
276C2×C5×D4C22×D311yescharacteristic
277C22×C4×C5—21no—
278C22×C4×C5—21no—
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C22×C4×C5—61no—
282C22×C4×C5C22×D311yescharacteristic
283C5×SD16—62no—
284C5×SD16—62no—
285C5×D8—62no—
286C5×D8—62no—
287C2×C5×C8—31no—
288C2×C5×C8—31no—
289C2×C5×C8—31no—
290C2×C5×C8—31no—
291C5×C4⋊C4—31no—
292C5×C4⋊C4—31no—
293C5×C4⋊C4—61no—
294C5×C4⋊C4—61no—
295C5×C4⋊C4—61no—
296C5×C4⋊C4#6711yescharacteristic
297C5×C4⋊C4#6711yescharacteristic
298C5×C4⋊C4C22×D311yescharacteristic
299C5×C4⋊C4C22×D311yescharacteristic
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4—21no—
303C5×C22⋊C4—21no—
304C5×C22⋊C4—21no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4—61no—
307C5×C22⋊C4—61no—
308C5×C22⋊C4—61no—
309C5×C22⋊C4—61no—
310C5×C22⋊C4#6711yescharacteristic
311C5×C22⋊C4#6711yescharacteristic
312C42×C5—21no—
313C42×C5—61no—
314C42×C5C22×D311yescharacteristic
315C42×C5C22×D311yescharacteristic
316#542—31no—
317#518C5×D311yescharacteristic, complemented
318#485—31no—
319#482—31no—
320#476—31no—
321#474—31no—
322#463—31no—
323#463—31no—
324#450—31no—
325#447—31no—
326#442—31no—
327#440—31no—
328C4×SD16—31no—
329C4×D8—31no—
330#433—31no—
331C22×C3×C5—21no—
332C22×C3×C5—22no—
333C22×C3×C5—22no—
334C22×C3×C5—21no—
335C22×C3×C5—21no—
336C22×C3×C5—41no—
337C22×C3×C5—41no—
338C22×C3×C5—41no—
339C22×C3×C5—41no—
340C22×C3×C5—84no—
341C22×C3×C5C22×D411yescharacteristic
342C2×C5×D3—41no—
343C2×C5×D3—41no—
344C2×C5×D3—41no—
345C3×C4×C5—21no—
346C3×C4×C5—21no—
347C3×C4×C5—21no—
348C3×C4×C5—21no—
349C3×C4×C5—21no—
350C3×C4×C5—41no—
351C3×C4×C5—41no—
352C3×C4×C5C2×#4111yescharacteristic
353C3×C4×C5C2×#4111yescharacteristic
354C5×Dic3—41no—
355C5×Dic3—41no—
356C5×Dic3—41no—
357C24×C3—21no—
358C2×C3×D4—22no—
359C2×C3×D4—22no—
360C2×C3×D4—21no—
361C2×C3×D4C23×C511yescharacteristic
362C2×C3×D4C23×C511yescharacteristic
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4C23×C511yescharacteristic
368C2×#67—21no—
369C2×D12C23×C511yescharacteristic
370C2×C4×D3—21no—
371C2×Dic6—21no—
372C2×Dic6C23×C511yescharacteristic
373C3×C4⋊C4C5×D411yescharacteristic
374C3×C4⋊C4C5×D411yescharacteristic
375C3×C4⋊C4C23×C511yescharacteristic
376C3×C4⋊C4C23×C511yescharacteristic
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4C5×D411yescharacteristic
383C3×C22⋊C4C5×D411yescharacteristic
384C3×C42—21no—
385C3×C42C23×C511yescharacteristic
386C3×C42C23×C511yescharacteristic
387#217—21no—
388#214—22no—
389#214—22no—
390#213—22no—
391#213—22no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3C23×C511yescharacteristic
398C4⋊Dic3C23×C511yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401C4×Dic3—21no—
402C2×C3⋊C8C23×C511yescharacteristic
403C2×C3⋊C8C23×C511yescharacteristic
404C2×C3⋊C8C23×C511yescharacteristic
405C2×C3⋊C8C23×C511yescharacteristic
406C23×C5—24no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—61no—
410C23×C5—81no—
411C23×C5—81no—
412C23×C5C2×#6711yescharacteristic
413C5×Q8—61no—
414C5×Q8—61no—
415C5×Q8—241no—
416C5×D4—24no—
417C5×D4—21no—
418C5×D4—21no—
419C5×D4—61no—
420C5×D4—61no—
421C5×D4—241no—
422C5×D4#23512yes—
423C5×D4#23512yes—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—81no—
432C2×C4×C5—81no—
433C2×C4×C5—81no—
434C2×C4×C5—81no—
435C2×C4×C5—241no—
436C2×C4×C5C2×#6711yescharacteristic
437C2×C4×C5C2×#6711yescharacteristic
438C2×C4×C5C2×#6711yescharacteristic
439C2×C4×C5C2×#6711yescharacteristic
440C2×C4×C5C2×#6711yescharacteristic
441C2×C4×C5C23×D311yescharacteristic
442C5×C8—61no—
443C5×C8—61no—
444C5×C8—61no—
445C5×C8—61no—
446C22×D4C2×C5×D311yescharacteristic
447C2×SD16—31no—
448C2×SD16—31no—
449C2×D8—31no—
450C2×D8—31no—
451C4⋊Q8—31no—
452#126—61no—
453#124—31no—
454#124—61no—
455#123—61no—
456C22⋊Q8—31no—
457C22⋊Q8—61no—
458#121—31no—
459C4×Q8—31no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—31no—
463C4×D4C2×C5×D311yescharacteristic
464C4×D4C2×C5×D311yescharacteristic
465C4×D4C2×C5×D311yescharacteristic
466C4×D4C2×C5×D311yescharacteristic
467#117C2×C5×D311yescharacteristic
468#117C2×C5×D311yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471#107—31no—
472#107—31no—
473#106—31no—
474#106—31no—
475C4⋊C8—31no—
476C4⋊C8—31no—
477#103—31no—
478#103—31no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485C22⋊C8—31no—
486C22⋊C8—31no—
487#97—31no—
488C4×C8—31no—
489C2×C3×C5—41no—
490C2×C3×C5—42no—
491C2×C3×C5—42no—
492C2×C3×C5#52511yescharacteristic
493C2×C3×C5#57611yescharacteristic
494C2×C3×C5#57711yescharacteristic
495C5×D3—81no—
496C23×C3—24no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—81no—
500C23×C3—81no—
501C23×C3C2×C5×D411yescharacteristic
502C22×D3—21no—
503C3×D4—24no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4C5×#4112yes—
507C3×D4C5×#4112yes—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—81no—
513C2×C3×C4—81no—
514C2×C3×C4—81no—
515C2×C3×C4—81no—
516C2×C3×C4C2×C5×D411yescharacteristic
517C2×C3×C4C2×C5×D411yescharacteristic
518C2×C3×C4C2×C5×D411yescharacteristic
519C2×C3×C4C2×C5×D411yescharacteristic
520C2×C3×C4C2×C5×D411yescharacteristic
521C2×C3×C4C24×C511yescharacteristic
522#67—81no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526D12—21no—
527D12—21no—
528C4×D3—81no—
529Dic6—21no—
530Dic6—21no—
531Dic6—81no—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C3⋊C8—21no—
535C3⋊C8—21no—
536C22×C5—21no—
537C22×C5—22no—
538C22×C5—22no—
539C22×C5—21no—
540C22×C5—21no—
541C22×C5—41no—
542C22×C5—41no—
543C22×C5—41no—
544C22×C5—41no—
545C22×C5—84no—
546C22×C5—121no—
547C22×C5—121no—
548C22×C5—121no—
549C22×C5C22×#6711yescharacteristic
550C4×C5—21no—
551C4×C5—21no—
552C4×C5—21no—
553C4×C5—21no—
554C4×C5—21no—
555C4×C5—41no—
556C4×C5—41no—
557C4×C5—121no—
558C4×C5—121no—
559C4×C5—121no—
560C4×C5C2×#23511yescharacteristic
561C4×C5C2×#23511yescharacteristic
562C24—21no—
563C2×Q8—31no—
564C2×Q8—61no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—31no—
569C2×D4—61no—
570C2×D4C22×C5×D311yescharacteristic
571C2×D4C22×C5×D311yescharacteristic
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—61no—
577C22×C4C22×C5×D311yescharacteristic
578SD16—62no—
579SD16—62no—
580D8—62no—
581D8—62no—
582C2×C8—31no—
583C2×C8—31no—
584C2×C8—31no—
585C2×C8—31no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4C5×#6711yescharacteristic
592C4⋊C4C5×#6711yescharacteristic
593C4⋊C4C22×C5×D311yescharacteristic
594C4⋊C4C22×C5×D311yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—61no—
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4C5×#6711yescharacteristic
606C22⋊C4C5×#6711yescharacteristic
607C42—21no—
608C42—61no—
609C42C22×C5×D311yescharacteristic
610C42C22×C5×D311yescharacteristic
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—84no—
622C22×C3C22×C5×D411yescharacteristic
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4C2×C5×#4111yescharacteristic
634C3×C4C2×C5×#4111yescharacteristic
635Dic3—41no—
636Dic3—41no—
637Dic3—41no—
638C2×C5—41no—
639C2×C5—42no—
640C2×C5—42no—
641C2×C5—241no—
642C2×C5#579111yescharacteristic
643C2×C5#583511yescharacteristic
644C2×C5#583611yescharacteristic
645C23—24no—
646C23—21no—
647C23—21no—
648C23—61no—
649C23—81no—
650C23—81no—
651C23C2×C5×#6711yescharacteristic
652Q8—61no—
653Q8—61no—
654Q8—241no—
655D4—24no—
656D4—21no—
657D4—21no—
658D4—61no—
659D4—61no—
660D4—241no—
661D4C5×#23512yes—
662D4C5×#23512yes—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—241no—
675C2×C4C2×C5×#6711yescharacteristic
676C2×C4C2×C5×#6711yescharacteristic
677C2×C4C2×C5×#6711yescharacteristic
678C2×C4C2×C5×#6711yescharacteristic
679C2×C4C2×C5×#6711yescharacteristic
680C2×C4C23×C5×D311yescharacteristic
681C8—61no—
682C8—61no—
683C8—61no—
684C8—61no—
685C2×C3—41no—
686C2×C3—42no—
687C2×C3—42no—
688C2×C3C5×#52511yescharacteristic
689C2×C3C5×#57611yescharacteristic
690C2×C3C5×#57711yescharacteristic
691D3—81no—
692C5#8254111yescharacteristic, direct product factor, Sylow
693C22—21no—
694C22—22no—
695C22—22no—
696C22—21no—
697C22—21no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—84no—
703C22—121no—
704C22—121no—
705C22—121no—
706C22C22×C5×#6711yescharacteristic
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—41no—
713C4—41no—
714C4—121no—
715C4—121no—
716C4—121no—
717C4C2×C5×#23511yescharacteristic
718C4C2×C5×#23511yescharacteristic
719C3C5×#311811yescharacteristic, complemented, Sylow
720C2—41no—
721C2—42no—
722C2—42no—
723C2—241no—
724C2C5×#579111yescharacteristic
725C2C5×#583511yescharacteristic
726C2C5×#583611yescharacteristic
subgroupG/H
centerC22×C5C22×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#518C2
socleC22×C3×C5C22×D4
prime radicalC5×#5217C2
hypercenterC5×#518D3
hypocenterC3C5×#3118
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#117 ◁ C5×#518

Complements

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

NH ≅ G/Ntype
1. C3×C5×#518C2semidirect
2. C5×#5534C2semidirect
3. C5×#5218C2semidirect
5. C5×#5018C2semidirect
6. C4×C5×#214C2semidirect
7. C5×#5016C2semidirect
8. C5×#5016C2semidirect
9. C5×#5014C2semidirect
10. C4×C5×#213C2semidirect
11. C5×#5008C2semidirect
12. C5×#5007C2semidirect
13. C5×#5003C2semidirect
14. C5×#5000C2semidirect
15. C5×#4996C2semidirect
38. C5×#875C22semidirect
39. C4×C5×D12C22semidirect
40. C5×#869C22semidirect
41. C4×C5×Dic6C22semidirect
48. C5×#810C22semidirect
49. C5×#810C22semidirect
50. C5×#809C22semidirect
51. C5×#809C22semidirect
52. C5×#808C22semidirect
53. C5×#808C22semidirect
54. C5×#807C22semidirect
55. C5×#807C22semidirect
56. C5×C4⋊(C3⋊C8)C22semidirect
57. C5×C4⋊(C3⋊C8)C22semidirect
58. C5×#803C22semidirect
59. C4×C5×C3⋊C8C22semidirect
60. #82541C5direct (N × H)
62. C5×#518D3semidirect
125. C3×#518C2×C5semidirect
126. #5534C2×C5semidirect
127. #5218C2×C5semidirect
129. #5018C2×C5semidirect
130. C4×#214C2×C5semidirect
131. #5016C2×C5semidirect
132. #5016C2×C5semidirect
133. #5014C2×C5semidirect
134. C4×#213C2×C5semidirect
135. #5008C2×C5semidirect
136. #5007C2×C5semidirect
137. #5003C2×C5semidirect
138. #5000C2×C5semidirect
139. #4996C2×C5semidirect
245. #875C22×C5semidirect
246. C4×D12C22×C5semidirect
247. #869C22×C5semidirect
248. C4×Dic6C22×C5semidirect
255. #810C22×C5semidirect
256. #810C22×C5semidirect
257. #809C22×C5semidirect
258. #809C22×C5semidirect
259. #808C22×C5semidirect
260. #808C22×C5semidirect
261. #807C22×C5semidirect
262. #807C22×C5semidirect
263. C4⋊(C3⋊C8)C22×C5semidirect
264. C4⋊(C3⋊C8)C22×C5semidirect
265. #803C22×C5semidirect
266. C4×C3⋊C8C22×C5semidirect
317. #518C5×D3semidirect
611. C3×C5#3118semidirect
692. C5#82541direct (N × H)
719. C3C5×#3118semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5182
C5×#55342
C5×#52182
C5×#52172
C5×#50182
C4×C5×#2142
C5×#50162
C5×#50142
C4×C5×#2132
C5×#50082
C5×#50072
C5×#50032
C5×#50002
C5×#49962
C5×#31183
#825415