Finite Group Databasebeta

← C3×C22⋊C4×C22⋊D5 #14325902

Subgroups — C3×C22⋊C4×C22⋊D5 #14325902

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C22⋊D5C211yesmaximal, characteristic
2C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊D5C212yesmaximal, complemented
4C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#65536C211yesmaximal, characteristic, complemented
6C3×#65502C212yesmaximal, complemented
7C3×#65246C212yesmaximal, complemented
8C3×#65245C212yesmaximal, complemented
9C3×#65244C211yesmaximal, characteristic, complemented
10C3×#65231C211yesmaximal, characteristic, complemented
11C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12C22⋊C4×C22⋊D5C311yesmaximal, characteristic, direct product factor, Hall
13C25×C3×C5C2211yescharacteristic
14C24×C3×D5C2211yescharacteristic
15C23×C3×C4×C5C2212yescomplemented
16C22×C3×C22⋊D5—28no—
17C22×C3×C22⋊D5C418yescomplemented
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×C3×C4×D5C2212yescomplemented
24C2×C3×C5×C22⋊C4—24no—
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2212yescomplemented
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2212yescomplemented
31C2×C3×C22⋊Dic5C2212yescomplemented
32C3×C4×C22⋊D5—28no—
33C2×C3×#685C2212yescomplemented
34C2×C3×#685C2212yescomplemented
35C2×C3×#685C2212yescomplemented
36C2×C3×#683C2212yescomplemented
37C2×C3×C4×Dic5C2212yescomplemented
38C3×D5×C22⋊C4—24no—
39C3×#3963C2212yescomplemented
40C3×#3963C2212yescomplemented
41C3×D4×C22⋊C4—51nomaximal, Hall
42C23×C22⋊D5C2×C311yescharacteristic
43C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
44C2×C4×C22⋊D5C2×C312yescomplemented
45C2×D5×C22⋊C4C2×C311yescharacteristic, complemented
46#65536C2×C311yescharacteristic, complemented
47#65502C2×C312yescomplemented
48#65246C2×C312yescomplemented
49#65245C2×C312yescomplemented
50#65244C2×C311yescharacteristic, complemented
51#65231C2×C311yescharacteristic, complemented
52C22⋊C4×Dic5C2×C311yescharacteristic, complemented
53C24×C3×C5—24no—
54C24×C3×C5—22no—
55C24×C3×C5—22no—
56C24×C3×C5—42no—
57C24×C3×C5C2×C414yescomplemented
58C24×C3×C5C2311yescharacteristic
59C24×C3×C5C2311yescharacteristic
60C24×C3×C5C2311yescharacteristic
61C23×C3×D5—22no—
62C23×C3×D5—22no—
63C23×C3×D5—24no—
64C23×C3×D5—42no—
65C23×C3×D5C2×C414yescomplemented
66C23×C3×D5C2311yescharacteristic
67C23×C3×D5C2311yescharacteristic
68C22×C3×C4×C5—24no—
69C22×C3×C4×C5—24no—
70C22×C3×C4×C5—42no—
71C22×C3×C4×C5C2312yes—
72C22×C3×C4×C5C2312yes—
73C2×C3×C22⋊D5—24no—
74C2×C3×C22⋊D5—24no—
75C2×C3×C22⋊D5—232no—
76C2×C3×C22⋊D5—24no—
77C2×C3×C22⋊D5C2×C414yes—
78C2×C3×C22⋊D5C2×C414yescomplemented
79C2×C3×C22⋊D5C2×C414yescomplemented
80C2×C3×C22⋊D5C2×C414yescomplemented
81C2×C3×C22⋊D5D418yes—
82C22×C3×Dic5—24no—
83C22×C3×Dic5C2×C414yescomplemented
84C22×C3×Dic5C2312yes—
85C22×C3×Dic5C2312yes—
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C2×C3×C4×D5—24no—
89C2×C3×C4×D5—24no—
90C2×C3×C4×D5—42no—
91C3×C5×C22⋊C4—22no—
92C3×C5×C22⋊C4—24no—
93C3×C5×C22⋊C4D414yescomplemented
94C3×C22⋊Dic5—22no—
95C3×C22⋊Dic5—24no—
96C3×C22⋊Dic5—22no—
97C3×C22⋊Dic5—42no—
98C3×#685—24no—
99C3×#685—24no—
100C3×#685—42no—
101C3×#683—24no—
102C3×C4×Dic5—24no—
103C23×C3×D4—51no—
104C2×C3×C4×D4—52no—
105C22×C3×C22⋊C4—51no—
106C22×C3×C22⋊C4D511yescharacteristic, complemented
107C3×#390—52no—
108C3×#386—52no—
109C3×#386—52no—
110C3×#380—51no—
111C3×#379—51no—
112C3×#379—51no—
113C3×C4×C22⋊C4—51no—
114C25×C5C22×C311yescharacteristic
115C24×D5C22×C311yescharacteristic
116C23×C4×C5C22×C312yescomplemented
117C22×C22⋊D5—28no—
118C22×C22⋊D5C3×C418yescomplemented
119C22×C22⋊D5C22×C311yescharacteristic
120C22×C22⋊D5C22×C311yescharacteristic
121C22×C22⋊D5C22×C311yescharacteristic
122C22×C22⋊D5C22×C311yescharacteristic
123C23×Dic5C22×C311yescharacteristic
124C22×C4×D5C22×C312yescomplemented
125C2×C5×C22⋊C4—24no—
126C2×C5×C22⋊C4C22×C311yescharacteristic
127C2×C5×C22⋊C4C22×C311yescharacteristic
128C2×C5×C22⋊C4C22×C312yescomplemented
129C2×C22⋊Dic5C22×C311yescharacteristic
130C2×C22⋊Dic5C22×C311yescharacteristic
131C2×C22⋊Dic5C22×C312yescomplemented
132C2×C22⋊Dic5C22×C312yescomplemented
133C4×C22⋊D5—28no—
134C2×#685C22×C312yescomplemented
135C2×#685C22×C312yescomplemented
136C2×#685C22×C312yescomplemented
137C2×#683C22×C312yescomplemented
138C2×C4×Dic5C22×C312yescomplemented
139D5×C22⋊C4—24no—
140#3963C22×C312yescomplemented
141#3963C22×C312yescomplemented
142D4×C22⋊C4—51noSylow
143C23×C3×C5—22no—
144C23×C3×C5—21no—
145C23×C3×C5—21no—
146C23×C3×C5—22no—
147C23×C3×C5—22no—
148C23×C3×C5—28no—
149C23×C3×C5—28no—
150C23×C3×C5—21no—
151C23×C3×C5—22no—
152C23×C3×C5—21no—
153C23×C3×C5—22no—
154C23×C3×C5—44no—
155C23×C3×C5—48no—
156C23×C3×C5—48no—
157C23×C3×C5C22×C412yes—
158C23×C3×C5C22×C412yes—
159C23×C3×C5C22×C412yes—
160C23×C3×C5C2×D414yes—
161C23×C3×C5C2×D412yes—
162C23×C3×C5#4112yes—
163C23×C3×C5C2411yescharacteristic
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—22no—
167C22×C3×D5—28no—
168C22×C3×D5—21no—
169C22×C3×D5—22no—
170C22×C3×D5—21no—
171C22×C3×D5—22no—
172C22×C3×D5—28no—
173C22×C3×D5—44no—
174C22×C3×D5—48no—
175C22×C3×D5—48no—
176C22×C3×D5C22×C412yes—
177C22×C3×D5C22×C412yes—
178C22×C3×D5C2×D414yes—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5—22no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5—22no—
184C2×C3×C4×C5—48no—
185C2×C3×C4×C5C2×D414yescomplemented
186C3×C22⋊D5—28no—
187C3×C22⋊D5—28no—
188C3×C22⋊D5—28no—
189C3×C22⋊D5C22⋊C4116yesdirect product factor
190C2×C3×Dic5—22no—
191C2×C3×Dic5—28no—
192C2×C3×Dic5—22no—
193C2×C3×Dic5—22no—
194C2×C3×Dic5—22no—
195C2×C3×Dic5—22no—
196C2×C3×Dic5—22no—
197C2×C3×Dic5—22no—
198C2×C3×Dic5C22×C412yes—
199C2×C3×Dic5C22×C412yes—
200C2×C3×Dic5C2×D414yes—
201C3×C4×D5—48no—
202C25×C3—51no—
203C25×C3C2×D511yescharacteristic
204C22×C3×D4—51no—
205C22×C3×D4—58no—
206C22×C3×D4—51no—
207C22×C3×D4—51no—
208C22×C3×D4—51no—
209C22×C3×D4—108no—
210C23×C3×C4—51no—
211C23×C3×C4—52no—
212C23×C3×C4C2×D512yescomplemented
213C3×C4×D4—108no—
214C2×C3×C4⋊C4—52no—
215C2×C3×C22⋊C4—24no—
216C2×C3×C22⋊C4—51no—
217C2×C3×C22⋊C4—51no—
218C2×C3×C22⋊C4—52no—
219C2×C3×C22⋊C4—52no—
220C2×C3×C22⋊C4—52no—
221C2×C3×C22⋊C4—52no—
222C2×C3×C22⋊C4—52no—
223C2×C3×C22⋊C4—104no—
224C2×C3×C22⋊C4C2×D511yescharacteristic
225C2×C3×C22⋊C4C2×D511yescharacteristic
226C2×C3×C22⋊C4C2×D512yescomplemented
227C2×C3×C42—52no—
228C3×#95—52no—
229C3×#95—52no—
230C24×C5—22no—
231C24×C5—24no—
232C24×C5—22no—
233C24×C5—42no—
234C24×C5C2×C3×C414yescomplemented
235C24×C5C23×C311yescharacteristic
236C24×C5C23×C311yescharacteristic
237C24×C5C23×C311yescharacteristic
238C23×D5—22no—
239C23×D5—22no—
240C23×D5—24no—
241C23×D5—42no—
242C23×D5C2×C3×C414yescomplemented
243C23×D5C23×C311yescharacteristic
244C23×D5C23×C311yescharacteristic
245C22×C4×C5—24no—
246C22×C4×C5—24no—
247C22×C4×C5—42no—
248C22×C4×C5C23×C312yes—
249C22×C4×C5C23×C312yes—
250C2×C22⋊D5—24no—
251C2×C22⋊D5—24no—
252C2×C22⋊D5—232no—
253C2×C22⋊D5—24no—
254C2×C22⋊D5C2×C3×C414yes—
255C2×C22⋊D5C2×C3×C414yescomplemented
256C2×C22⋊D5C2×C3×C414yescomplemented
257C2×C22⋊D5C2×C3×C414yescomplemented
258C2×C22⋊D5C3×D418yes—
259C22×Dic5—24no—
260C22×Dic5C2×C3×C414yescomplemented
261C22×Dic5C23×C312yes—
262C22×Dic5C23×C312yes—
263C22×Dic5C23×C311yescharacteristic
264C22×Dic5C23×C311yescharacteristic
265C2×C4×D5—24no—
266C2×C4×D5—24no—
267C2×C4×D5—42no—
268C5×C22⋊C4—22no—
269C5×C22⋊C4—24no—
270C5×C22⋊C4C3×D414yescomplemented
271C22⋊Dic5—22no—
272C22⋊Dic5—24no—
273C22⋊Dic5—22no—
274C22⋊Dic5—42no—
275#685—24no—
276#685—24no—
277#685—42no—
278#683—24no—
279C4×Dic5—24no—
280C23×D4—51no—
281C2×C4×D4—52no—
282C22×C22⋊C4—51no—
283C22×C22⋊C4C3×D511yescharacteristic, complemented
284#390—52no—
285#386—52no—
286#386—52no—
287#380—51no—
288#379—51no—
289#379—51no—
290C4×C22⋊C4—51no—
291C22×C3×C5—22no—
292C22×C3×C5—22no—
293C22×C3×C5—22no—
294C22×C3×C5—22no—
295C22×C3×C5—24no—
296C22×C3×C5—24no—
297C22×C3×C5—24no—
298C22×C3×C5—24no—
299C22×C3×C5—22no—
300C22×C3×C5—22no—
301C22×C3×C5—22no—
302C22×C3×C5—416no—
303C22×C3×C5—42no—
304C22×C3×C5—42no—
305C22×C3×C5C2×C22⋊C414yescomplemented
306C22×C3×C5C4×D414yescomplemented
307C22×C3×C5C23×C411yescharacteristic
308C22×C3×C5C22×D412yes—
309C22×C3×C5C22×D411yescharacteristic
310C22×C3×C5C2×#4111yescharacteristic
311C22×C3×C5H(5,𝔽2)12yes—
312C2×C3×D5—22no—
313C2×C3×D5—22no—
314C2×C3×D5—24no—
315C2×C3×D5—24no—
316C2×C3×D5—22no—
317C2×C3×D5—22no—
318C2×C3×D5—22no—
319C2×C3×D5—416no—
320C2×C3×D5—42no—
321C2×C3×D5—42no—
322C2×C3×D5C2×C22⋊C414yescomplemented
323C3×C4×C5—24no—
324C3×C4×C5—42no—
325C3×Dic5—22no—
326C3×Dic5—42no—
327C3×Dic5—42no—
328C3×Dic5C2×C22⋊C414yescomplemented
329C24×C3—22no—
330C24×C3—24no—
331C24×C3—22no—
332C24×C3—42no—
333C24×C3—51no—
334C24×C3—51no—
335C24×C3—54no—
336C24×C3—104no—
337C24×C3—102no—
338C24×C3—102no—
339C24×C3—202no—
340C24×C3C4×D514yescomplemented
341C24×C3C22×D511yescharacteristic
342C24×C3C22×D511yescharacteristic
343C24×C3C22×D511yescharacteristic
344C2×C3×D4—54no—
345C2×C3×D4—58no—
346C2×C3×D4—54no—
347C2×C3×D4—54no—
348C2×C3×D4—54no—
349C2×C3×D4—104no—
350C2×C3×D4—1032no—
351C2×C3×D4—104no—
352C2×C3×D4—104no—
353C22×C3×C4—24no—
354C22×C3×C4—24no—
355C22×C3×C4—42no—
356C22×C3×C4—51no—
357C22×C3×C4—54no—
358C22×C3×C4—51no—
359C22×C3×C4—52no—
360C22×C3×C4—52no—
361C22×C3×C4—104no—
362C22×C3×C4—104no—
363C22×C3×C4—104no—
364C22×C3×C4—202no—
365C22×C3×C4C22×D512yes—
366C22×C3×C4C22×D512yes—
367C3×C4⋊C4—104no—
368C3×C22⋊C4—22no—
369C3×C22⋊C4—24no—
370C3×C22⋊C4—104no—
371C3×C22⋊C4—102no—
372C3×C22⋊C4—104no—
373C3×C22⋊C4—102no—
374C3×C22⋊C4—104no—
375C3×C22⋊C4—202no—
376C3×C22⋊C4—202no—
377C3×C22⋊C4C22⋊D514yesdirect product factor
378C3×C42—104no—
379C23×C5—22no—
380C23×C5—21no—
381C23×C5—21no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—28no—
385C23×C5—28no—
386C23×C5—21no—
387C23×C5—22no—
388C23×C5—21no—
389C23×C5—22no—
390C23×C5—44no—
391C23×C5—48no—
392C23×C5—48no—
393C23×C5C22×C3×C412yes—
394C23×C5C22×C3×C412yes—
395C23×C5C22×C3×C412yes—
396C23×C5C2×C3×D414yes—
397C23×C5C2×C3×D412yes—
398C23×C5C3×#4112yes—
399C23×C5C24×C311yescharacteristic
400C22×D5—21no—
401C22×D5—21no—
402C22×D5—22no—
403C22×D5—28no—
404C22×D5—21no—
405C22×D5—22no—
406C22×D5—21no—
407C22×D5—22no—
408C22×D5—28no—
409C22×D5—44no—
410C22×D5—48no—
411C22×D5—48no—
412C22×D5C22×C3×C412yes—
413C22×D5C22×C3×C412yes—
414C22×D5C2×C3×D414yes—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—48no—
421C2×C4×C5C2×C3×D414yescomplemented
422C22⋊D5—28no—
423C22⋊D5—28no—
424C22⋊D5—28no—
425C22⋊D5C3×C22⋊C4116yesdirect product factor
426C2×Dic5—22no—
427C2×Dic5—28no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5C22×C3×C412yes—
435C2×Dic5C22×C3×C412yes—
436C2×Dic5C2×C3×D414yes—
437C4×D5—48no—
438C25—51no—
439C25C2×C3×D511yescharacteristic
440C22×D4—51no—
441C22×D4—58no—
442C22×D4—51no—
443C22×D4—51no—
444C22×D4—51no—
445C22×D4—108no—
446C23×C4—51no—
447C23×C4—52no—
448C23×C4C2×C3×D512yescomplemented
449C4×D4—108no—
450C2×C4⋊C4—52no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—51no—
453C2×C22⋊C4—51no—
454C2×C22⋊C4—52no—
455C2×C22⋊C4—52no—
456C2×C22⋊C4—52no—
457C2×C22⋊C4—52no—
458C2×C22⋊C4—52no—
459C2×C22⋊C4—104no—
460C2×C22⋊C4C2×C3×D511yescharacteristic
461C2×C22⋊C4C2×C3×D511yescharacteristic
462C2×C22⋊C4C2×C3×D512yescomplemented
463C2×C42—52no—
464#95—52no—
465#95—52no—
466C2×C3×C5—24no—
467C2×C3×C5—24no—
468C2×C3×C5—42no—
469C2×C3×C5C22×C22⋊C411yescharacteristic
470C2×C3×C5C2×C4×D411yescharacteristic
471C2×C3×C5#51811yescharacteristic
472C2×C3×C5D4212yes—
473C2×C3×C5#54612yes—
474C3×D5—24no—
475C3×D5—42no—
476C23×C3—21no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—21no—
485C23×C3—28no—
486C23×C3—28no—
487C23×C3—44no—
488C23×C3—48no—
489C23×C3—48no—
490C23×C3—52no—
491C23×C3—54no—
492C23×C3—52no—
493C23×C3—108no—
494C23×C3—101no—
495C23×C3—102no—
496C23×C3—101no—
497C23×C3—101no—
498C23×C3—102no—
499C23×C3—102no—
500C23×C3—101no—
501C23×C3—108no—
502C23×C3—204no—
503C23×C3—208no—
504C23×C3—208no—
505C23×C3C2×C4×D512yes—
506C23×C3C2×C4×D512yes—
507C23×C3C2×C4×D512yes—
508C23×C3#70912yes—
509C23×C3D4×D514yes—
510C23×C3C2×C22⋊D512yes—
511C23×C3C23×D511yescharacteristic
512C3×D4—516no—
513C3×D4—108no—
514C3×D4—108no—
515C3×D4—108no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—48no—
522C2×C3×C4—52no—
523C2×C3×C4—54no—
524C2×C3×C4—52no—
525C2×C3×C4—108no—
526C2×C3×C4—102no—
527C2×C3×C4—102no—
528C2×C3×C4—102no—
529C2×C3×C4—102no—
530C2×C3×C4—102no—
531C2×C3×C4—102no—
532C2×C3×C4—102no—
533C2×C3×C4—208no—
534C2×C3×C4C2×C22⋊D514yescomplemented
535C22×C5—22no—
536C22×C5—22no—
537C22×C5—22no—
538C22×C5—22no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—24no—
542C22×C5—24no—
543C22×C5—22no—
544C22×C5—22no—
545C22×C5—22no—
546C22×C5—416no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5C2×C3×C22⋊C414yescomplemented
550C22×C5C3×C4×D414yescomplemented
551C22×C5C23×C3×C411yescharacteristic
552C22×C5C22×C3×D412yes—
553C22×C5C22×C3×D411yescharacteristic
554C22×C5C2×C3×#4111yescharacteristic
555C22×C5C3×H(5,𝔽2)12yes—
556C2×D5—22no—
557C2×D5—22no—
558C2×D5—24no—
559C2×D5—24no—
560C2×D5—22no—
561C2×D5—22no—
562C2×D5—22no—
563C2×D5—416no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5C2×C3×C22⋊C414yescomplemented
567C4×C5—24no—
568C4×C5—42no—
569Dic5—22no—
570Dic5—42no—
571Dic5—42no—
572Dic5C2×C3×C22⋊C414yescomplemented
573C24—22no—
574C24—24no—
575C24—22no—
576C24—42no—
577C24—51no—
578C24—51no—
579C24—54no—
580C24—104no—
581C24—102no—
582C24—102no—
583C24—202no—
584C24C3×C4×D514yescomplemented
585C24C22×C3×D511yescharacteristic
586C24C22×C3×D511yescharacteristic
587C24C22×C3×D511yescharacteristic
588C2×D4—54no—
589C2×D4—58no—
590C2×D4—54no—
591C2×D4—54no—
592C2×D4—54no—
593C2×D4—104no—
594C2×D4—1032no—
595C2×D4—104no—
596C2×D4—104no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—42no—
600C22×C4—51no—
601C22×C4—54no—
602C22×C4—51no—
603C22×C4—52no—
604C22×C4—52no—
605C22×C4—104no—
606C22×C4—104no—
607C22×C4—104no—
608C22×C4—202no—
609C22×C4C22×C3×D512yes—
610C22×C4C22×C3×D512yes—
611C4⋊C4—104no—
612C22⋊C4—22no—
613C22⋊C4—24no—
614C22⋊C4—104no—
615C22⋊C4—102no—
616C22⋊C4—104no—
617C22⋊C4—102no—
618C22⋊C4—104no—
619C22⋊C4—202no—
620C22⋊C4—202no—
621C22⋊C4C3×C22⋊D514yesdirect product factor
622C42—104no—
623C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—22no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—416no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—54no—
639C22×C3—102no—
640C22×C3—104no—
641C22×C3—102no—
642C22×C3—104no—
643C22×C3—102no—
644C22×C3—102no—
645C22×C3—102no—
646C22×C3—2016no—
647C22×C3—202no—
648C22×C3—202no—
649C22×C3D5×C22⋊C414yescomplemented
650C22×C3C4×C22⋊D514yescomplemented
651C22×C3C22×C4×D511yescharacteristic
652C22×C3C2×#70911yescharacteristic
653C22×C3C2×D4×D512yes—
654C22×C3#414412yes—
655C22×C3C22×C22⋊D511yescharacteristic
656C3×C4—24no—
657C3×C4—42no—
658C3×C4—54no—
659C3×C4—102no—
660C3×C4—202no—
661C3×C4—202no—
662C2×C5—24no—
663C2×C5—24no—
664C2×C5—42no—
665C2×C5C22×C3×C22⋊C411yescharacteristic
666C2×C5C2×C3×C4×D411yescharacteristic
667C2×C5C3×#51811yescharacteristic
668C2×C5C3×D4212yes—
669C2×C5C3×#54612yes—
670D5—24no—
671D5—42no—
672C23—21no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—28no—
682C23—28no—
683C23—44no—
684C23—48no—
685C23—48no—
686C23—52no—
687C23—54no—
688C23—52no—
689C23—108no—
690C23—101no—
691C23—102no—
692C23—101no—
693C23—101no—
694C23—102no—
695C23—102no—
696C23—101no—
697C23—108no—
698C23—204no—
699C23—208no—
700C23—208no—
701C23C2×C3×C4×D512yes—
702C23C2×C3×C4×D512yes—
703C23C2×C3×C4×D512yes—
704C23C3×#70912yes—
705C23C3×D4×D514yes—
706C23C2×C3×C22⋊D512yes—
707C23C23×C3×D511yescharacteristic
708D4—516no—
709D4—108no—
710D4—108no—
711D4—108no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—52no—
719C2×C4—54no—
720C2×C4—52no—
721C2×C4—108no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—208no—
730C2×C4C2×C3×C22⋊D514yescomplemented
731C2×C3—24no—
732C2×C3—24no—
733C2×C3—42no—
734C2×C3—104no—
735C2×C3—202no—
736C2×C3C2×D5×C22⋊C411yescharacteristic
737C2×C3#6582011yescharacteristic
738C2×C3#6582412yes—
739C2×C3C2×C4×C22⋊D511yescharacteristic
740C2×C3D4×C22⋊D512yes—
741C5C3×D4×C22⋊C411yescharacteristic, complemented, Sylow
742C22—22no—
743C22—24no—
744C22—24no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—24no—
749C22—24no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—416no—
754C22—42no—
755C22—42no—
756C22—54no—
757C22—102no—
758C22—104no—
759C22—102no—
760C22—104no—
761C22—102no—
762C22—102no—
763C22—102no—
764C22—2016no—
765C22—202no—
766C22—202no—
767C22C3×D5×C22⋊C414yescomplemented
768C22C3×C4×C22⋊D514yescomplemented
769C22C22×C3×C4×D511yescharacteristic
770C22C2×C3×#70911yescharacteristic
771C22C2×C3×D4×D512yes—
772C22C3×#414412yes—
773C22C22×C3×C22⋊D511yescharacteristic
774C4—24no—
775C4—42no—
776C4—54no—
777C4—102no—
778C4—202no—
779C4—202no—
780C3C22⋊C4×C22⋊D511yescharacteristic, direct product factor, Sylow
781C2—24no—
782C2—24no—
783C2—42no—
784C2—104no—
785C2—202no—
786C2C2×C3×D5×C22⋊C411yescharacteristic
787C2C3×#6582011yescharacteristic
788C2C3×#6582412yes—
789C2C2×C3×C4×C22⋊D511yescharacteristic
790C2C3×D4×C22⋊D512yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC23×C3×C22⋊D5C2
cosocleC23×C5C24×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C3×D4×C22⋊C4
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×C22⋊C4C2semidirect
3. C2×C3×C4×C22⋊D5C2semidirect
4. C2×C3×D5×C22⋊C4C2semidirect
5. C3×#65536C2semidirect
6. C3×#65502C2semidirect
7. C3×#65246C2semidirect
8. C3×#65245C2semidirect
9. C3×#65244C2semidirect
10. C3×#65231C2semidirect
11. C3×C22⋊C4×Dic5C2semidirect
12. C22⋊C4×C22⋊D5C3direct (N × H)
15. C23×C3×C4×C5C22semidirect
17. C22×C3×C22⋊D5C4semidirect
23. C22×C3×C4×D5C22semidirect
27. C2×C3×C5×C22⋊C4C22semidirect
30. C2×C3×C22⋊Dic5C22semidirect
31. C2×C3×C22⋊Dic5C22semidirect
33. C2×C3×#685C22semidirect
34. C2×C3×#685C22semidirect
35. C2×C3×#685C22semidirect
36. C2×C3×#683C22semidirect
37. C2×C3×C4×Dic5C22semidirect
39. C3×#3963C22semidirect
40. C3×#3963C22semidirect
43. C22×C5×C22⋊C4C2×C3semidirect
44. C2×C4×C22⋊D5C2×C3semidirect
45. C2×D5×C22⋊C4C2×C3semidirect
46. #65536C2×C3semidirect
47. #65502C2×C3semidirect
48. #65246C2×C3semidirect
49. #65245C2×C3semidirect
50. #65244C2×C3semidirect
51. #65231C2×C3semidirect
52. C22⋊C4×Dic5C2×C3semidirect
57. C24×C3×C5C2×C4semidirect
65. C23×C3×D5C2×C4semidirect
78. C2×C3×C22⋊D5C2×C4semidirect
79. C2×C3×C22⋊D5C2×C4semidirect
80. C2×C3×C22⋊D5C2×C4semidirect
83. C22×C3×Dic5C2×C4semidirect
93. C3×C5×C22⋊C4D4semidirect
106. C22×C3×C22⋊C4D5semidirect
116. C23×C4×C5C22×C3semidirect
118. C22×C22⋊D5C3×C4semidirect
124. C22×C4×D5C22×C3semidirect
128. C2×C5×C22⋊C4C22×C3semidirect
131. C2×C22⋊Dic5C22×C3semidirect
132. C2×C22⋊Dic5C22×C3semidirect
134. C2×#685C22×C3semidirect
135. C2×#685C22×C3semidirect
136. C2×#685C22×C3semidirect
137. C2×#683C22×C3semidirect
138. C2×C4×Dic5C22×C3semidirect
140. #3963C22×C3semidirect
141. #3963C22×C3semidirect
185. C2×C3×C4×C5C2×D4semidirect
189. C3×C22⋊D5C22⋊C4direct (N × H)
212. C23×C3×C4C2×D5semidirect
226. C2×C3×C22⋊C4C2×D5semidirect
234. C24×C5C2×C3×C4semidirect
242. C23×D5C2×C3×C4semidirect
255. C2×C22⋊D5C2×C3×C4semidirect
256. C2×C22⋊D5C2×C3×C4semidirect
257. C2×C22⋊D5C2×C3×C4semidirect
260. C22×Dic5C2×C3×C4semidirect
270. C5×C22⋊C4C3×D4semidirect
283. C22×C22⋊C4C3×D5semidirect
305. C22×C3×C5C2×C22⋊C4semidirect
306. C22×C3×C5C4×D4semidirect
322. C2×C3×D5C2×C22⋊C4semidirect
328. C3×Dic5C2×C22⋊C4semidirect
340. C24×C3C4×D5semidirect
377. C3×C22⋊C4C22⋊D5direct (N × H)
421. C2×C4×C5C2×C3×D4semidirect
425. C22⋊D5C3×C22⋊C4direct (N × H)
448. C23×C4C2×C3×D5semidirect
462. C2×C22⋊C4C2×C3×D5semidirect
534. C2×C3×C4C2×C22⋊D5semidirect
549. C22×C5C2×C3×C22⋊C4semidirect
550. C22×C5C3×C4×D4semidirect
566. C2×D5C2×C3×C22⋊C4semidirect
572. Dic5C2×C3×C22⋊C4semidirect
584. C24C3×C4×D5semidirect
621. C22⋊C4C3×C22⋊D5direct (N × H)
623. C3×C5D4×C22⋊C4semidirect
649. C22×C3D5×C22⋊C4semidirect
650. C22×C3C4×C22⋊D5semidirect
730. C2×C4C2×C3×C22⋊D5semidirect
741. C5C3×D4×C22⋊C4semidirect
767. C22C3×D5×C22⋊C4semidirect
768. C22C3×C4×C22⋊D5semidirect
780. C3C22⋊C4×C22⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊D52
C22×C3×C5×C22⋊C42
C2×C3×C4×C22⋊D52
C2×C3×D5×C22⋊C42
C3×#655362
C3×#655022
C3×#652462
C3×#652452
C3×#652442
C3×#652312
C3×C22⋊C4×Dic52
C22⋊C4×C22⋊D53
C3×D4×C22⋊C45