Finite Group Databasebeta

← C5×#82097 #14326239

Subgroups — C5×#82097 #14326239

Order 1920.

1584 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
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
2C22×C5×#217C211yesmaximal, characteristic
3C2×C5×#926C211yesmaximal, characteristic, complemented
4C5×#5247C211yesmaximal, characteristic
5C5×#5212C211yesmaximal, characteristic, complemented
6C5×#5211C211yesmaximal, characteristic, complemented
7C4×C5×#217C211yesmaximal, characteristic, complemented
8C5×#4951C212yesmaximal, complemented
9C5×#4951C212yesmaximal, complemented
10C5×#4950C212yesmaximal, complemented
11C5×Dic3×C22⋊C4C212yesmaximal, complemented
12C5×#2342—31nomaximal, Hall
13C25×C3×C5C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C5×Dic3C2212yes—
17C2×C3×C5×C22⋊C4C418yescomplemented
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C5×#217—24no—
23C2×C5×#217C2212yes—
24C2×C5×#217C2212yes—
25C2×C5×#217C2211yescharacteristic
26C2×C5×#217C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C2×C5×#217C2212yes—
29C2×C5×#217C2211yescharacteristic
30C5×#926—24no—
31C2×C5×C4⋊Dic3C2212yescomplemented
32C2×C5×C4⋊Dic3C2212yescomplemented
33C2×C4×C5×Dic3C2212yescomplemented
34C2×C4×C5×Dic3C2212yescomplemented
35C5×C3⋊#95C2212yescomplemented
36C5×C3⋊#95C2212yescomplemented
37C5×C3⋊#95C2212yescomplemented
38C5×C3⋊#95C2212yescomplemented
39#82097C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#117—31no—
41C22×C5×C22⋊C4—31no—
42C22×C5×C22⋊C4D311yescharacteristic
43C5×#388—32no—
44C5×#388—32no—
45C5×#385—32no—
46C5×#381—31no—
47C5×#380—31no—
48C5×#379—31no—
49C4×C5×C22⋊C4—31no—
50C4×C5×C22⋊C4—32no—
51C24×C3×C5—22no—
52C24×C3×C5—24no—
53C24×C3×C5—22no—
54C24×C3×C5—42no—
55C24×C3×C5C2×C414yes—
56C24×C3×C5C2311yescharacteristic
57C24×C3×C5C2311yescharacteristic
58C24×C3×C5C2311yescharacteristic
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—42no—
62C22×C3×C4×C5C2×C414yescomplemented
63C22×C3×C4×C5C2×C414yescomplemented
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C5×Dic3—24no—
69C22×C5×Dic3—24no—
70C22×C5×Dic3—42no—
71C22×C5×Dic3C2312yes—
72C22×C5×Dic3C2312yes—
73C22×C5×Dic3C2312yes—
74C22×C5×Dic3C2312yes—
75C3×C5×C22⋊C4C2×C414yes—
76C3×C5×C22⋊C4C2×C414yes—
77C3×C5×C22⋊C4C2×C414yescomplemented
78C3×C5×C22⋊C4C2×C414yescomplemented
79C5×#217—22no—
80C5×#217—22no—
81C5×#217—24no—
82C5×#217—22no—
83C5×#217—24no—
84C5×#217—42no—
85C5×#217D414yes—
86C5×C4⋊Dic3—24no—
87C5×C4⋊Dic3—42no—
88C4×C5×Dic3—24no—
89C4×C5×Dic3—42no—
90C22×C3×C22⋊C4C2×C511yescharacteristic
91C22×#217C2×C511yescharacteristic
92C2×#926C2×C511yescharacteristic, complemented
93#5247C2×C511yescharacteristic
94#5212C2×C511yescharacteristic, complemented
95#5211C2×C511yescharacteristic, complemented
96C4×#217C2×C511yescharacteristic, complemented
97#4951C2×C512yescomplemented
98#4951C2×C512yescomplemented
99#4950C2×C512yescomplemented
100Dic3×C22⋊C4C2×C512yescomplemented
101C25×C5C2×D311yescharacteristic
102C23×C4×C5—32no—
103C23×C4×C5C2×D311yescharacteristic
104C23×C4×C5C2×D311yescharacteristic
105C5×#117—64no—
106C2×C5×C4⋊C4—32no—
107C2×C5×C4⋊C4—32no—
108C2×C5×C22⋊C4—31no—
109C2×C5×C22⋊C4—31no—
110C2×C5×C22⋊C4—32no—
111C2×C5×C22⋊C4—31no—
112C2×C5×C22⋊C4—31no—
113C2×C5×C22⋊C4—32no—
114C2×C5×C22⋊C4—32no—
115C2×C5×C22⋊C4—64no—
116C2×C5×C22⋊C4Dic318yescomplemented
117C2×C5×C22⋊C4C2×D311yescharacteristic
118C2×C5×C22⋊C4C2×D311yescharacteristic
119C2×C5×C22⋊C4C2×D311yescharacteristic
120C2×C5×C22⋊C4C2×D311yescharacteristic
121C2×C42×C5—32no—
122C2×C42×C5—32no—
123C5×#95—32no—
124C5×#95—32no—
125C5×#95—32no—
126C5×#95—32no—
127#2342—31noSylow
128C23×C3×C5—21no—
129C23×C3×C5—22no—
130C23×C3×C5—21no—
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—28no—
134C23×C3×C5—28no—
135C23×C3×C5—21no—
136C23×C3×C5—22no—
137C23×C3×C5—21no—
138C23×C3×C5—22no—
139C23×C3×C5—44no—
140C23×C3×C5—48no—
141C23×C3×C5—48no—
142C23×C3×C5C22×C412yes—
143C23×C3×C5C22×C412yes—
144C23×C3×C5C22×C412yes—
145C23×C3×C5C2×D412yes—
146C23×C3×C5#4114yes—
147C23×C3×C5#4112yes—
148C23×C3×C5C2411yescharacteristic
149C2×C3×C4×C5—28no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—44no—
157C2×C3×C4×C5C22×C412yes—
158C2×C3×C4×C5C22×C412yes—
159C2×C3×C4×C5C22×C412yes—
160C2×C3×C4×C5C22×C412yes—
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—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—48no—
173C2×C5×Dic3C2×D414yes—
174C25×C3C22×C511yescharacteristic
175C23×C3×C4C22×C511yescharacteristic
176C23×C3×C4C22×C511yescharacteristic
177C23×Dic3C22×C512yes—
178C2×C3×C22⋊C4C4×C518yescomplemented
179C2×C3×C22⋊C4C22×C511yescharacteristic
180C2×C3×C22⋊C4C22×C511yescharacteristic
181C2×C3×C22⋊C4C22×C511yescharacteristic
182C2×C3×C22⋊C4C22×C511yescharacteristic
183C2×#217—24no—
184C2×#217C22×C512yes—
185C2×#217C22×C512yes—
186C2×#217C22×C511yescharacteristic
187C2×#217C22×C511yescharacteristic
188C2×#217C22×C511yescharacteristic
189C2×#217C22×C512yes—
190C2×#217C22×C511yescharacteristic
191#926—24no—
192C2×C4⋊Dic3C22×C512yescomplemented
193C2×C4⋊Dic3C22×C512yescomplemented
194C2×C4×Dic3C22×C512yescomplemented
195C2×C4×Dic3C22×C512yescomplemented
196C3⋊#95C22×C512yescomplemented
197C3⋊#95C22×C512yescomplemented
198C3⋊#95C22×C512yescomplemented
199C3⋊#95C22×C512yescomplemented
200C24×C5—24no—
201C24×C5—22no—
202C24×C5—22no—
203C24×C5—42no—
204C24×C5C2×Dic314yes—
205C24×C5C22×D311yescharacteristic
206C24×C5C22×D311yescharacteristic
207C24×C5C22×D311yescharacteristic
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—32no—
211C22×C4×C5—32no—
212C22×C4×C5—32no—
213C22×C4×C5—32no—
214C22×C4×C5—42no—
215C22×C4×C5—64no—
216C22×C4×C5—64no—
217C22×C4×C5—122no—
218C22×C4×C5C2×Dic314yescomplemented
219C22×C4×C5C2×Dic314yescomplemented
220C22×C4×C5C22×D311yescharacteristic
221C22×C4×C5C22×D311yescharacteristic
222C22×C4×C5C22×D311yescharacteristic
223C22×C4×C5C22×D311yescharacteristic
224C5×C4⋊C4—64no—
225C5×C4⋊C4—122no—
226C5×C22⋊C4—34no—
227C5×C22⋊C4—64no—
228C5×C22⋊C4—64no—
229C5×C22⋊C4—62no—
230C5×C22⋊C4—62no—
231C5×C22⋊C4—62no—
232C5×C22⋊C4—122no—
233C5×C22⋊C4C2×Dic314yes—
234C5×C22⋊C4C2×Dic314yes—
235C5×C22⋊C4C2×Dic314yescomplemented
236C5×C22⋊C4C2×Dic314yescomplemented
237C42×C5—64no—
238C42×C5—122no—
239C2×#117—31no—
240C22×C22⋊C4—31no—
241C22×C22⋊C4C5×D311yescharacteristic
242#388—32no—
243#388—32no—
244#385—32no—
245#381—31no—
246#380—31no—
247#379—31no—
248C4×C22⋊C4—31no—
249C4×C22⋊C4—32no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—24no—
255C22×C3×C5—24no—
256C22×C3×C5—24no—
257C22×C3×C5—24no—
258C22×C3×C5—22no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—416no—
262C22×C3×C5—42no—
263C22×C3×C5—42no—
264C22×C3×C5#11714yescomplemented
265C22×C3×C5C4×D414yes—
266C22×C3×C5C23×C411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C2×#4112yes—
269C22×C3×C5C2×#4111yescharacteristic
270C22×C3×C5H(5,𝔽2)12yes—
271C3×C4×C5—22no—
272C3×C4×C5—22no—
273C3×C4×C5—22no—
274C3×C4×C5—22no—
275C5×Dic3—24no—
276C5×Dic3—42no—
277C5×Dic3—42no—
278C5×Dic3—42no—
279C24×C3—22no—
280C24×C3—24no—
281C24×C3—22no—
282C24×C3—42no—
283C24×C3C2×C4×C514yes—
284C24×C3C23×C511yescharacteristic
285C24×C3C23×C511yescharacteristic
286C24×C3C23×C511yescharacteristic
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—42no—
290C22×C3×C4C2×C4×C514yescomplemented
291C22×C3×C4C2×C4×C514yescomplemented
292C22×C3×C4C23×C511yescharacteristic
293C22×C3×C4C23×C511yescharacteristic
294C22×C3×C4C23×C511yescharacteristic
295C22×C3×C4C23×C511yescharacteristic
296C22×Dic3—24no—
297C22×Dic3—24no—
298C22×Dic3—42no—
299C22×Dic3C23×C512yes—
300C22×Dic3C23×C512yes—
301C22×Dic3C23×C512yes—
302C22×Dic3C23×C512yes—
303C3×C22⋊C4C2×C4×C514yes—
304C3×C22⋊C4C2×C4×C514yes—
305C3×C22⋊C4C2×C4×C514yescomplemented
306C3×C22⋊C4C2×C4×C514yescomplemented
307#217—22no—
308#217—22no—
309#217—24no—
310#217—22no—
311#217—24no—
312#217—42no—
313#217C5×D414yes—
314C4⋊Dic3—24no—
315C4⋊Dic3—42no—
316C4×Dic3—24no—
317C4×Dic3—42no—
318C23×C5—22no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—28no—
324C23×C5—28no—
325C23×C5—22no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—22no—
329C23×C5—44no—
330C23×C5—48no—
331C23×C5—48no—
332C23×C5#23514yes—
333C23×C5D3×D412yes—
334C23×C5#23712yes—
335C23×C5C22×Dic312yes—
336C23×C5C22×Dic312yes—
337C23×C5C22×Dic312yes—
338C23×C5C23×D311yescharacteristic
339C2×C4×C5—28no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—34no—
347C2×C4×C5—44no—
348C2×C4×C5—62no—
349C2×C4×C5—62no—
350C2×C4×C5—62no—
351C2×C4×C5—62no—
352C2×C4×C5—62no—
353C2×C4×C5—62no—
354C2×C4×C5—62no—
355C2×C4×C5—62no—
356C2×C4×C5—62no—
357C2×C4×C5—62no—
358C2×C4×C5—62no—
359C2×C4×C5—128no—
360C2×C4×C5C22×Dic312yes—
361C2×C4×C5C22×Dic312yes—
362C2×C4×C5C22×Dic312yes—
363C2×C4×C5C22×Dic312yes—
364C25C2×C5×D311yescharacteristic
365C23×C4—32no—
366C23×C4C2×C5×D311yescharacteristic
367C23×C4C2×C5×D311yescharacteristic
368#117—64no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—32no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—31no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—64no—
379C2×C22⋊C4C5×Dic318yescomplemented
380C2×C22⋊C4C2×C5×D311yescharacteristic
381C2×C22⋊C4C2×C5×D311yescharacteristic
382C2×C22⋊C4C2×C5×D311yescharacteristic
383C2×C22⋊C4C2×C5×D311yescharacteristic
384C2×C42—32no—
385C2×C42—32no—
386#95—32no—
387#95—32no—
388#95—32no—
389#95—32no—
390C2×C3×C5—24no—
391C2×C3×C5—24no—
392C2×C3×C5—42no—
393C2×C3×C5C2×#11711yescharacteristic
394C2×C3×C5C2×C4×D411yescharacteristic
395C2×C3×C5#51811yescharacteristic
396C2×C3×C5#54612yes—
397C2×C3×C5#55112yes—
398C23×C3—21no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—28no—
404C23×C3—28no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—44no—
410C23×C3—48no—
411C23×C3—48no—
412C23×C3C22×C4×C512yes—
413C23×C3C22×C4×C512yes—
414C23×C3C22×C4×C512yes—
415C23×C3C2×C5×D412yes—
416C23×C3C5×#4114yes—
417C23×C3C5×#4112yes—
418C23×C3C24×C511yescharacteristic
419C2×C3×C4—28no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—44no—
427C2×C3×C4C22×C4×C512yes—
428C2×C3×C4C22×C4×C512yes—
429C2×C3×C4C22×C4×C512yes—
430C2×C3×C4C22×C4×C512yes—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—48no—
443C2×Dic3C2×C5×D414yes—
444C22×C5—24no—
445C22×C5—24no—
446C22×C5—24no—
447C22×C5—24no—
448C22×C5—22no—
449C22×C5—22no—
450C22×C5—22no—
451C22×C5—22no—
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—416no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5#92614yescomplemented
459C22×C5D4×Dic314yes—
460C22×C5C2×#23512yes—
461C22×C5C2×D3×D411yescharacteristic
462C22×C5C2×#23711yescharacteristic
463C22×C5#100412yes—
464C22×C5C23×Dic311yescharacteristic
465C4×C5—22no—
466C4×C5—22no—
467C4×C5—22no—
468C4×C5—22no—
469C4×C5—64no—
470C4×C5—122no—
471C4×C5—122no—
472C4×C5—122no—
473C24—24no—
474C24—22no—
475C24—22no—
476C24—42no—
477C24C2×C5×Dic314yes—
478C24C22×C5×D311yescharacteristic
479C24C22×C5×D311yescharacteristic
480C24C22×C5×D311yescharacteristic
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—32no—
484C22×C4—32no—
485C22×C4—32no—
486C22×C4—32no—
487C22×C4—42no—
488C22×C4—64no—
489C22×C4—64no—
490C22×C4—122no—
491C22×C4C2×C5×Dic314yescomplemented
492C22×C4C2×C5×Dic314yescomplemented
493C22×C4C22×C5×D311yescharacteristic
494C22×C4C22×C5×D311yescharacteristic
495C22×C4C22×C5×D311yescharacteristic
496C22×C4C22×C5×D311yescharacteristic
497C4⋊C4—64no—
498C4⋊C4—122no—
499C22⋊C4—34no—
500C22⋊C4—64no—
501C22⋊C4—64no—
502C22⋊C4—62no—
503C22⋊C4—62no—
504C22⋊C4—62no—
505C22⋊C4—122no—
506C22⋊C4C2×C5×Dic314yes—
507C22⋊C4C2×C5×Dic314yes—
508C22⋊C4C2×C5×Dic314yescomplemented
509C22⋊C4C2×C5×Dic314yescomplemented
510C42—64no—
511C42—122no—
512C3×C5#234211yescharacteristic, complemented, Hall
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—24no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—416no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3C5×#11714yescomplemented
528C22×C3C4×C5×D414yes—
529C22×C3C23×C4×C511yescharacteristic
530C22×C3C22×C5×D411yescharacteristic
531C22×C3C2×C5×#4112yes—
532C22×C3C2×C5×#4111yescharacteristic
533C22×C3C5×H(5,𝔽2)12yes—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—22no—
538Dic3—24no—
539Dic3—42no—
540Dic3—42no—
541Dic3—42no—
542C2×C5—24no—
543C2×C5—24no—
544C2×C5—42no—
545C2×C5#549012yes—
546C2×C5#549512yes—
547C2×C5C2×#92611yescharacteristic
548C2×C5C2×D4×Dic311yescharacteristic
549C2×C5#579811yescharacteristic
550C23—22no—
551C23—21no—
552C23—21no—
553C23—22no—
554C23—22no—
555C23—28no—
556C23—28no—
557C23—22no—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—44no—
562C23—48no—
563C23—48no—
564C23C5×#23514yes—
565C23C5×D3×D412yes—
566C23C5×#23712yes—
567C23C22×C5×Dic312yes—
568C23C22×C5×Dic312yes—
569C23C22×C5×Dic312yes—
570C23C23×C5×D311yescharacteristic
571C2×C4—28no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—34no—
579C2×C4—44no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—128no—
592C2×C4C22×C5×Dic312yes—
593C2×C4C22×C5×Dic312yes—
594C2×C4C22×C5×Dic312yes—
595C2×C4C22×C5×Dic312yes—
596C2×C3—24no—
597C2×C3—24no—
598C2×C3—42no—
599C2×C3C2×C5×#11711yescharacteristic
600C2×C3C2×C4×C5×D411yescharacteristic
601C2×C3C5×#51811yescharacteristic
602C2×C3C5×#54612yes—
603C2×C3C5×#55112yes—
604C5#8209711yescharacteristic, direct product factor, Sylow
605C22—24no—
606C22—24no—
607C22—24no—
608C22—24no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—416no—
617C22—42no—
618C22—42no—
619C22C5×#92614yescomplemented
620C22C5×D4×Dic314yes—
621C22C2×C5×#23512yes—
622C22C2×C5×D3×D411yescharacteristic
623C22C2×C5×#23711yescharacteristic
624C22C5×#100412yes—
625C22C23×C5×Dic311yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—22no—
630C4—64no—
631C4—122no—
632C4—122no—
633C4—122no—
634C3C5×#234211yescharacteristic, complemented, Sylow
635C2—24no—
636C2—24no—
637C2—42no—
638C2C5×#549012yes—
639C2C5×#549512yes—
640C2C2×C5×#92611yescharacteristic
641C2C2×C5×D4×Dic311yescharacteristic
642C2C5×#579811yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC25×C3×C5C22
cosocleC23×C3C24×C5
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C5×#2342
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C5×#926C2semidirect
5. C5×#5212C2semidirect
6. C5×#5211C2semidirect
7. C4×C5×#217C2semidirect
8. C5×#4951C2semidirect
9. C5×#4951C2semidirect
10. C5×#4950C2semidirect
11. C5×Dic3×C22⋊C4C2semidirect
17. C2×C3×C5×C22⋊C4C4semidirect
31. C2×C5×C4⋊Dic3C22semidirect
32. C2×C5×C4⋊Dic3C22semidirect
33. C2×C4×C5×Dic3C22semidirect
34. C2×C4×C5×Dic3C22semidirect
35. C5×C3⋊#95C22semidirect
36. C5×C3⋊#95C22semidirect
37. C5×C3⋊#95C22semidirect
38. C5×C3⋊#95C22semidirect
39. #82097C5direct (N × H)
62. C22×C3×C4×C5C2×C4semidirect
63. C22×C3×C4×C5C2×C4semidirect
77. C3×C5×C22⋊C4C2×C4semidirect
78. C3×C5×C22⋊C4C2×C4semidirect
92. C2×#926C2×C5semidirect
94. #5212C2×C5semidirect
95. #5211C2×C5semidirect
96. C4×#217C2×C5semidirect
97. #4951C2×C5semidirect
98. #4951C2×C5semidirect
99. #4950C2×C5semidirect
100. Dic3×C22⋊C4C2×C5semidirect
116. C2×C5×C22⋊C4Dic3semidirect
178. C2×C3×C22⋊C4C4×C5semidirect
192. C2×C4⋊Dic3C22×C5semidirect
193. C2×C4⋊Dic3C22×C5semidirect
194. C2×C4×Dic3C22×C5semidirect
195. C2×C4×Dic3C22×C5semidirect
196. C3⋊#95C22×C5semidirect
197. C3⋊#95C22×C5semidirect
198. C3⋊#95C22×C5semidirect
199. C3⋊#95C22×C5semidirect
218. C22×C4×C5C2×Dic3semidirect
219. C22×C4×C5C2×Dic3semidirect
235. C5×C22⋊C4C2×Dic3semidirect
236. C5×C22⋊C4C2×Dic3semidirect
264. C22×C3×C5#117semidirect
290. C22×C3×C4C2×C4×C5semidirect
291. C22×C3×C4C2×C4×C5semidirect
305. C3×C22⋊C4C2×C4×C5semidirect
306. C3×C22⋊C4C2×C4×C5semidirect
379. C2×C22⋊C4C5×Dic3semidirect
458. C22×C5#926semidirect
491. C22×C4C2×C5×Dic3semidirect
492. C22×C4C2×C5×Dic3semidirect
508. C22⋊C4C2×C5×Dic3semidirect
509. C22⋊C4C2×C5×Dic3semidirect
512. C3×C5#2342semidirect
527. C22×C3C5×#117semidirect
604. C5#82097direct (N × H)
619. C22C5×#926semidirect
634. C3C5×#2342semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×C22⋊C42
C22×C5×#2172
C2×C5×#9262
C5×#52472
C5×#52122
C5×#52112
C4×C5×#2172
C5×#49512
C5×#49502
C5×Dic3×C22⋊C42
C5×#23423
#820975