Finite Group Databasebeta

← C5×#82335 #14327339

Subgroups — C5×#82335 #14327339

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×C5×#926C211yesmaximal, characteristic, complemented
3C22×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C5×#5220C212yesmaximal
5C5×#5212C211yesmaximal, characteristic, complemented
6C5×#5212C211yesmaximal, characteristic, complemented
7C5×#4980C212yesmaximal, complemented
8C5×#4951C212yesmaximal, complemented
9C5×Dic3×C22⋊C4C212yesmaximal, complemented
10C5×#4936C211yesmaximal, characteristic, complemented
11C4×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
12C5×#2352—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C5×Dic3C2212yes—
17C3×C4×C5×D4C418yescomplemented
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×C5×#217C2212yes—
23C2×C5×#217C2212yes—
24C2×C5×#217C2212yes—
25C5×#926—24no—
26C2×C5×C4⋊Dic3—24no—
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C5×C4⋊Dic3C2212yes—
31C2×C5×C4⋊Dic3C2211yescharacteristic
32C2×C4×C5×Dic3C2212yes—
33C2×C4×C5×Dic3C2212yes—
34C5×C3⋊#95C2212yes—
35C5×C3⋊#95C2212yes—
36C5×C3⋊#95C2212yes—
37C5×C3⋊#95C2212yes—
38C5×C3⋊#95C2212yes—
39#82335C511yesmaximal, characteristic, direct product factor, Hall
40C2×C4×C5×D4D311yescharacteristic
41C2×C5×#117—31no—
42C22×C5×C4⋊C4—31no—
43C5×#388—32no—
44C5×#387—32no—
45C5×#386—32no—
46C5×#382—31no—
47C5×#380—31no—
48C5×#380—31no—
49C4×C5×C4⋊C4—31no—
50C4×C5×C22⋊C4—32no—
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4C2×C414yes—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5C2×C414yes—
61C22×C3×C4×C5C2×C414yescomplemented
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×C5×Dic3—24no—
68C22×C5×Dic3—24no—
69C22×C5×Dic3—42no—
70C22×C5×Dic3C2312yes—
71C22×C5×Dic3C2312yes—
72C22×C5×Dic3C2312yes—
73C22×C5×Dic3C2312yes—
74C3×C5×C4⋊C4C2×C414yescomplemented
75C3×C5×C22⋊C4C2×C414yes—
76C3×C5×C22⋊C4C2×C414yescomplemented
77C3×C42×C5C2×C414yescomplemented
78C5×#217—24no—
79C5×#217—24no—
80C5×#217—42no—
81C5×C4⋊Dic3—22no—
82C5×C4⋊Dic3—22no—
83C5×C4⋊Dic3—22no—
84C5×C4⋊Dic3—24no—
85C5×C4⋊Dic3D414yescomplemented
86C4×C5×Dic3—24no—
87C4×C5×Dic3—42no—
88C2×C3×C4×D4C2×C511yescharacteristic
89C2×#926C2×C511yescharacteristic, complemented
90C22×C4⋊Dic3C2×C511yescharacteristic, complemented
91#5220C2×C512yes—
92#5212C2×C511yescharacteristic, complemented
93#5212C2×C511yescharacteristic, complemented
94#4980C2×C512yescomplemented
95#4951C2×C512yescomplemented
96Dic3×C22⋊C4C2×C512yescomplemented
97#4936C2×C511yescharacteristic, complemented
98C4×C4⋊Dic3C2×C511yescharacteristic, complemented
99C22×C5×D4C2×D311yescharacteristic
100C23×C4×C5—32no—
101C23×C4×C5C2×D311yescharacteristic
102C23×C4×C5C2×D311yescharacteristic
103C4×C5×D4Dic318yescomplemented
104C5×#117—64no—
105C2×C5×C4⋊C4—31no—
106C2×C5×C4⋊C4—31no—
107C2×C5×C4⋊C4—31no—
108C2×C5×C4⋊C4—31no—
109C2×C5×C4⋊C4—32no—
110C2×C5×C4⋊C4—64no—
111C2×C5×C4⋊C4C2×D311yescharacteristic
112C2×C5×C22⋊C4—32no—
113C2×C5×C22⋊C4—32no—
114C2×C5×C22⋊C4—32no—
115C2×C5×C22⋊C4C2×D311yescharacteristic
116C2×C5×C22⋊C4C2×D311yescharacteristic
117C2×C42×C5—32no—
118C2×C42×C5—32no—
119C2×C42×C5C2×D311yescharacteristic
120C5×#95—32no—
121C5×#95—32no—
122C5×#95—32no—
123C5×#95—32no—
124C5×#95—32no—
125#2352—31noSylow
126C23×C3×C5—21no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—21no—
130C23×C3×C5—21no—
131C23×C3×C5—21no—
132C23×C3×C5—21no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5C22×C412yes—
137C23×C3×C5C22×C412yes—
138C23×C3×C5#4112yes—
139C23×C3×C5#4112yes—
140C23×C3×C5C2411yescharacteristic
141C3×C5×D4—28no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—28no—
151C2×C3×C4×C5—28no—
152C2×C3×C4×C5C22×C412yes—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C22×C412yes—
155C2×C3×C4×C5C22×C412yes—
156C2×C3×C4×C5C22×C412yes—
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5#4112yes—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—48no—
171C2×C5×Dic3C2×D414yes—
172C22×C3×D4C22×C511yescharacteristic
173C23×C3×C4C22×C511yescharacteristic
174C23×C3×C4C22×C511yescharacteristic
175C23×Dic3C22×C512yes—
176C3×C4×D4C4×C518yescomplemented
177C2×C3×C4⋊C4C22×C511yescharacteristic
178C2×C3×C22⋊C4C22×C511yescharacteristic
179C2×C3×C22⋊C4C22×C511yescharacteristic
180C2×C3×C42C22×C511yescharacteristic
181C2×#217C22×C512yes—
182C2×#217C22×C512yes—
183C2×#217C22×C512yes—
184#926—24no—
185C2×C4⋊Dic3—24no—
186C2×C4⋊Dic3C22×C511yescharacteristic
187C2×C4⋊Dic3C22×C511yescharacteristic
188C2×C4⋊Dic3C22×C511yescharacteristic
189C2×C4⋊Dic3C22×C512yes—
190C2×C4⋊Dic3C22×C511yescharacteristic
191C2×C4×Dic3C22×C512yes—
192C2×C4×Dic3C22×C512yes—
193C3⋊#95C22×C512yes—
194C3⋊#95C22×C512yes—
195C3⋊#95C22×C512yes—
196C3⋊#95C22×C512yes—
197C3⋊#95C22×C512yes—
198C24×C5C22×D311yescharacteristic
199C24×C5C22×D311yescharacteristic
200C2×C5×D4—22no—
201C2×C5×D4—22no—
202C2×C5×D4C2×Dic314yes—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—32no—
208C22×C4×C5—32no—
209C22×C4×C5—32no—
210C22×C4×C5—32no—
211C22×C4×C5—64no—
212C22×C4×C5—64no—
213C22×C4×C5—122no—
214C22×C4×C5C2×Dic314yes—
215C22×C4×C5C2×Dic314yescomplemented
216C22×C4×C5C22×D311yescharacteristic
217C22×C4×C5C22×D311yescharacteristic
218C22×C4×C5C22×D311yescharacteristic
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C5×C4⋊C4—34no—
222C5×C4⋊C4—64no—
223C5×C4⋊C4—62no—
224C5×C4⋊C4—62no—
225C5×C4⋊C4—62no—
226C5×C4⋊C4C2×Dic314yescomplemented
227C5×C22⋊C4—64no—
228C5×C22⋊C4—64no—
229C5×C22⋊C4—122no—
230C5×C22⋊C4C2×Dic314yes—
231C5×C22⋊C4C2×Dic314yescomplemented
232C42×C5—64no—
233C42×C5—122no—
234C42×C5C2×Dic314yescomplemented
235C2×C4×D4C5×D311yescharacteristic
236C2×#117—31no—
237C22×C4⋊C4—31no—
238#388—32no—
239#387—32no—
240#386—32no—
241#382—31no—
242#380—31no—
243#380—31no—
244C4×C4⋊C4—31no—
245C4×C22⋊C4—32no—
246C22×C3×C5—22no—
247C22×C3×C5—22no—
248C22×C3×C5—22no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—22no—
255C22×C3×C5—41no—
256C22×C3×C5—41no—
257C22×C3×C5—41no—
258C22×C3×C5—41no—
259C22×C3×C5#11714yescomplemented
260C22×C3×C5C23×C411yescharacteristic
261C22×C3×C5C22×D411yescharacteristic
262C22×C3×C5C2×#4111yescharacteristic
263C22×C3×C5C2×#4111yescharacteristic
264C22×C3×C5C2×#4111yescharacteristic
265C22×C3×C5H(5,𝔽2)11yescharacteristic
266C22×C3×C52−1+411yescharacteristic
267C3×C4×C5—22no—
268C3×C4×C5—22no—
269C3×C4×C5—22no—
270C3×C4×C5—22no—
271C3×C4×C5C4×D414yes—
272C5×Dic3—24no—
273C5×Dic3—42no—
274C5×Dic3—42no—
275C5×Dic3—42no—
276C24×C3C23×C511yescharacteristic
277C24×C3C23×C511yescharacteristic
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4C2×C4×C514yes—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4C2×C4×C514yes—
286C22×C3×C4C2×C4×C514yescomplemented
287C22×C3×C4C23×C511yescharacteristic
288C22×C3×C4C23×C511yescharacteristic
289C22×C3×C4C23×C511yescharacteristic
290C22×C3×C4C23×C511yescharacteristic
291C22×C3×C4C23×C511yescharacteristic
292C22×Dic3—24no—
293C22×Dic3—24no—
294C22×Dic3—42no—
295C22×Dic3C23×C512yes—
296C22×Dic3C23×C512yes—
297C22×Dic3C23×C512yes—
298C22×Dic3C23×C512yes—
299C3×C4⋊C4C2×C4×C514yescomplemented
300C3×C22⋊C4C2×C4×C514yes—
301C3×C22⋊C4C2×C4×C514yescomplemented
302C3×C42C2×C4×C514yescomplemented
303#217—24no—
304#217—24no—
305#217—42no—
306C4⋊Dic3—22no—
307C4⋊Dic3—22no—
308C4⋊Dic3—22no—
309C4⋊Dic3—24no—
310C4⋊Dic3C5×D414yescomplemented
311C4×Dic3—24no—
312C4×Dic3—42no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5#23512yes—
324C23×C5#23512yes—
325C23×C5C22×Dic312yes—
326C23×C5C22×Dic312yes—
327C23×C5C23×D311yescharacteristic
328C5×D4—28no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—28no—
338C2×C4×C5—28no—
339C2×C4×C5—34no—
340C2×C4×C5—62no—
341C2×C4×C5—62no—
342C2×C4×C5—62no—
343C2×C4×C5—62no—
344C2×C4×C5—62no—
345C2×C4×C5—62no—
346C2×C4×C5—62no—
347C2×C4×C5—62no—
348C2×C4×C5—62no—
349C2×C4×C5—62no—
350C2×C4×C5—62no—
351C2×C4×C5—128no—
352C2×C4×C5D3×D412yes—
353C2×C4×C5#23712yes—
354C2×C4×C5C22×Dic312yes—
355C2×C4×C5C22×Dic312yes—
356C2×C4×C5C22×Dic312yes—
357C2×C4×C5C22×Dic312yes—
358C2×C4×C5C22×Dic312yes—
359C22×D4C2×C5×D311yescharacteristic
360C23×C4—32no—
361C23×C4C2×C5×D311yescharacteristic
362C23×C4C2×C5×D311yescharacteristic
363C4×D4C5×Dic318yescomplemented
364#117—64no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—64no—
371C2×C4⋊C4C2×C5×D311yescharacteristic
372C2×C22⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4C2×C5×D311yescharacteristic
376C2×C22⋊C4C2×C5×D311yescharacteristic
377C2×C42—32no—
378C2×C42—32no—
379C2×C42C2×C5×D311yescharacteristic
380#95—32no—
381#95—32no—
382#95—32no—
383#95—32no—
384#95—32no—
385C2×C3×C5—24no—
386C2×C3×C5—42no—
387C2×C3×C5C2×#11711yescharacteristic
388C2×C3×C5C2×C4×D411yescharacteristic
389C2×C3×C5#52011yescharacteristic
390C2×C3×C5#54611yescharacteristic
391C2×C3×C5#54811yescharacteristic
392C2×C3×C5#55211yescharacteristic
393C2×C3×C5#55311yescharacteristic
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3C22×C4×C512yes—
405C23×C3C22×C4×C512yes—
406C23×C3C5×#4112yes—
407C23×C3C5×#4112yes—
408C23×C3C24×C511yescharacteristic
409C3×D4—28no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—28no—
419C2×C3×C4—28no—
420C2×C3×C4C22×C4×C512yes—
421C2×C3×C4C22×C4×C512yes—
422C2×C3×C4C22×C4×C512yes—
423C2×C3×C4C22×C4×C512yes—
424C2×C3×C4C22×C4×C512yes—
425C2×C3×C4C2×C5×D412yes—
426C2×C3×C4C5×#4112yes—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—48no—
439C2×Dic3C2×C5×D414yes—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—22no—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5#92614yescomplemented
454C22×C5C2×#23511yescharacteristic
455C22×C5C2×#23511yescharacteristic
456C22×C5C2×D3×D411yescharacteristic
457C22×C5C2×#23711yescharacteristic
458C22×C5#100911yescharacteristic
459C22×C5#101011yescharacteristic
460C22×C5C23×Dic311yescharacteristic
461C4×C5—22no—
462C4×C5—22no—
463C4×C5—22no—
464C4×C5—22no—
465C4×C5—64no—
466C4×C5—122no—
467C4×C5—122no—
468C4×C5—122no—
469C4×C5D4×Dic314yes—
470C24C22×C5×D311yescharacteristic
471C24C22×C5×D311yescharacteristic
472C2×D4—22no—
473C2×D4—22no—
474C2×D4C2×C5×Dic314yes—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—32no—
480C22×C4—32no—
481C22×C4—32no—
482C22×C4—32no—
483C22×C4—64no—
484C22×C4—64no—
485C22×C4—122no—
486C22×C4C2×C5×Dic314yes—
487C22×C4C2×C5×Dic314yescomplemented
488C22×C4C22×C5×D311yescharacteristic
489C22×C4C22×C5×D311yescharacteristic
490C22×C4C22×C5×D311yescharacteristic
491C22×C4C22×C5×D311yescharacteristic
492C22×C4C22×C5×D311yescharacteristic
493C4⋊C4—34no—
494C4⋊C4—64no—
495C4⋊C4—62no—
496C4⋊C4—62no—
497C4⋊C4—62no—
498C4⋊C4C2×C5×Dic314yescomplemented
499C22⋊C4—64no—
500C22⋊C4—64no—
501C22⋊C4—122no—
502C22⋊C4C2×C5×Dic314yes—
503C22⋊C4C2×C5×Dic314yescomplemented
504C42—64no—
505C42—122no—
506C42C2×C5×Dic314yescomplemented
507C3×C5#235211yescharacteristic, complemented, Hall
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3C5×#11714yescomplemented
522C22×C3C23×C4×C511yescharacteristic
523C22×C3C22×C5×D411yescharacteristic
524C22×C3C2×C5×#4111yescharacteristic
525C22×C3C2×C5×#4111yescharacteristic
526C22×C3C2×C5×#4111yescharacteristic
527C22×C3C5×H(5,𝔽2)11yescharacteristic
528C22×C3C5×2−1+411yescharacteristic
529C3×C4—22no—
530C3×C4—22no—
531C3×C4—22no—
532C3×C4—22no—
533C3×C4C4×C5×D414yes—
534Dic3—24no—
535Dic3—42no—
536Dic3—42no—
537Dic3—42no—
538C2×C5—24no—
539C2×C5—42no—
540C2×C5#554111yescharacteristic
541C2×C5#555011yescharacteristic
542C2×C5#555211yescharacteristic
543C2×C5#556511yescharacteristic
544C2×C5C2×#92611yescharacteristic
545C2×C5C2×D4×Dic311yescharacteristic
546C2×C5#582711yescharacteristic
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23C5×#23512yes—
558C23C5×#23512yes—
559C23C22×C5×Dic312yes—
560C23C22×C5×Dic312yes—
561C23C23×C5×D311yescharacteristic
562D4—28no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—34no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—128no—
586C2×C4C5×D3×D412yes—
587C2×C4C5×#23712yes—
588C2×C4C22×C5×Dic312yes—
589C2×C4C22×C5×Dic312yes—
590C2×C4C22×C5×Dic312yes—
591C2×C4C22×C5×Dic312yes—
592C2×C4C22×C5×Dic312yes—
593C2×C3—24no—
594C2×C3—42no—
595C2×C3C2×C5×#11711yescharacteristic
596C2×C3C2×C4×C5×D411yescharacteristic
597C2×C3C5×#52011yescharacteristic
598C2×C3C5×#54611yescharacteristic
599C2×C3C5×#54811yescharacteristic
600C2×C3C5×#55211yescharacteristic
601C2×C3C5×#55311yescharacteristic
602C5#8233511yescharacteristic, direct product factor, Sylow
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22C5×#92614yescomplemented
617C22C2×C5×#23511yescharacteristic
618C22C2×C5×#23511yescharacteristic
619C22C2×C5×D3×D411yescharacteristic
620C22C2×C5×#23711yescharacteristic
621C22C5×#100911yescharacteristic
622C22C5×#101011yescharacteristic
623C22C23×C5×Dic311yescharacteristic
624C4—22no—
625C4—22no—
626C4—22no—
627C4—22no—
628C4—64no—
629C4—122no—
630C4—122no—
631C4—122no—
632C4C5×D4×Dic314yes—
633C3C5×#235211yescharacteristic, complemented, Sylow
634C2—24no—
635C2—42no—
636C2C5×#554111yescharacteristic
637C2C5×#555011yescharacteristic
638C2C5×#555211yescharacteristic
639C2C5×#556511yescharacteristic
640C2C2×C5×#92611yescharacteristic
641C2C2×C5×D4×Dic311yescharacteristic
642C2C5×#582711yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C3C24×C5
hypercenterC2×C4×C5×D4D3
hypocenterC3C5×#2352
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#926C2semidirect
3. C22×C5×C4⋊Dic3C2semidirect
5. C5×#5212C2semidirect
6. C5×#5212C2semidirect
7. C5×#4980C2semidirect
8. C5×#4951C2semidirect
9. C5×Dic3×C22⋊C4C2semidirect
10. C5×#4936C2semidirect
11. C4×C5×C4⋊Dic3C2semidirect
17. C3×C4×C5×D4C4semidirect
39. #82335C5direct (N × H)
61. C22×C3×C4×C5C2×C4semidirect
74. C3×C5×C4⋊C4C2×C4semidirect
76. C3×C5×C22⋊C4C2×C4semidirect
77. C3×C42×C5C2×C4semidirect
85. C5×C4⋊Dic3D4semidirect
89. C2×#926C2×C5semidirect
90. C22×C4⋊Dic3C2×C5semidirect
92. #5212C2×C5semidirect
93. #5212C2×C5semidirect
94. #4980C2×C5semidirect
95. #4951C2×C5semidirect
96. Dic3×C22⋊C4C2×C5semidirect
97. #4936C2×C5semidirect
98. C4×C4⋊Dic3C2×C5semidirect
103. C4×C5×D4Dic3semidirect
176. C3×C4×D4C4×C5semidirect
215. C22×C4×C5C2×Dic3semidirect
226. C5×C4⋊C4C2×Dic3semidirect
231. C5×C22⋊C4C2×Dic3semidirect
234. C42×C5C2×Dic3semidirect
259. C22×C3×C5#117semidirect
286. C22×C3×C4C2×C4×C5semidirect
299. C3×C4⋊C4C2×C4×C5semidirect
301. C3×C22⋊C4C2×C4×C5semidirect
302. C3×C42C2×C4×C5semidirect
310. C4⋊Dic3C5×D4semidirect
363. C4×D4C5×Dic3semidirect
453. C22×C5#926semidirect
487. C22×C4C2×C5×Dic3semidirect
498. C4⋊C4C2×C5×Dic3semidirect
503. C22⋊C4C2×C5×Dic3semidirect
506. C42C2×C5×Dic3semidirect
507. C3×C5#2352semidirect
521. C22×C3C5×#117semidirect
602. C5#82335direct (N × H)
616. C22C5×#926semidirect
633. C3C5×#2352semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×C5×#9262
C22×C5×C4⋊Dic32
C5×#52202
C5×#52122
C5×#49802
C5×#49512
C5×Dic3×C22⋊C42
C5×#49362
C4×C5×C4⋊Dic32
C5×#23523
#823355