Finite Group Databasebeta

← C3×D4×#685 #14325896

Subgroups — C3×D4×#685 #14325896

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
1C22×C3×D4×D5C211yesmaximal, characteristic
2C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
4C22×C3×#685C212yesmaximal, complemented
5C3×#65502C212yesmaximal, complemented
6C3×#65277C211yesmaximal, characteristic, complemented
7C3×#65276C211yesmaximal, characteristic, complemented
8C3×#65247C212yesmaximal, complemented
9C3×#65244C212yesmaximal, complemented
10C3×#65228C211yesmaximal, characteristic, complemented
11C3×C4×#685C211yesmaximal, characteristic, complemented
12D4×#685C311yesmaximal, characteristic, direct product factor, Hall
13C24×C3×D5C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2212yescomplemented
16C22×C3×C22⋊D5C2212yes—
17C23×C3×Dic5C2212yescomplemented
18C2×C3×D4×D5—24no—
19C2×C3×D4×D5—24no—
20C2×C3×D4×D5C418yescomplemented
21C22×C3×D20C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C3×C4×C5×D4—24no—
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
25C2×C3×C5×C22⋊C4C2212yescomplemented
26C2×C3×C42×C5C2211yescharacteristic, complemented
27C2×C3×C22⋊Dic5C2212yescomplemented
28C3×D4×Dic5—24no—
29C2×C3×#685—28no—
30C2×C3×#685C2212yes—
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2212yescomplemented
34C2×C3×#685C2212yescomplemented
35C2×C3×#685C2212yescomplemented
36C2×C3×#685C2212yescomplemented
37C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
38C2×C3×C4×Dic5C2211yescharacteristic, complemented
39C3×#3963C2211yescharacteristic, complemented
40C3×#3963C2211yescharacteristic, complemented
41C3×#3963C2212yescomplemented
42C3×D4×C22⋊C4—51nomaximal, Hall
43C22×D4×D5C2×C311yescharacteristic
44C2×C4×C5×D4C2×C311yescharacteristic, complemented
45C2×D4×Dic5C2×C311yescharacteristic, complemented
46C22×#685C2×C312yescomplemented
47#65502C2×C312yescomplemented
48#65277C2×C311yescharacteristic, complemented
49#65276C2×C311yescharacteristic, complemented
50#65247C2×C312yescomplemented
51#65244C2×C312yescomplemented
52#65228C2×C311yescharacteristic, complemented
53C4×#685C2×C311yescharacteristic, complemented
54C24×C3×C5C2312yes—
55C23×C3×D5—24no—
56C23×C3×D5—24no—
57C23×C3×D5—24no—
58C23×C3×D5—24no—
59C23×C3×D5—42no—
60C23×C3×D5—42no—
61C23×C3×D5C2×C418yescomplemented
62C23×C3×D5C2312yes—
63C23×C3×D5C2311yescharacteristic
64C2×C3×C5×D4C2×C414yes—
65C2×C3×C5×D4D414yes—
66C2×C3×C5×D4D414yes—
67C22×C3×C4×C5—24no—
68C22×C3×C4×C5—24no—
69C22×C3×C4×C5—42no—
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2312yes—
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C2×C3×C22⋊D5—24no—
75C2×C3×C22⋊D5—24no—
76C2×C3×C22⋊D5C2×C418yescomplemented
77C22×C3×Dic5—24no—
78C22×C3×Dic5—24no—
79C22×C3×Dic5—42no—
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2312yes—
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C3×D4×D5—232no—
85C2×C3×D20—22no—
86C2×C3×D20—22no—
87C2×C3×D20C2×C414yescomplemented
88C2×C3×C4×D5—22no—
89C2×C3×C4×D5—22no—
90C2×C3×C4×D5C2×C414yescomplemented
91C3×C5×C4⋊C4—22no—
92C3×C5×C22⋊C4—24no—
93C3×C42×C5—22no—
94C3×C22⋊Dic5—24no—
95C3×#685—24no—
96C3×#685—22no—
97C3×#685—24no—
98C3×#685—24no—
99C3×#685—42no—
100C3×#685—42no—
101C3×#685D414yesdirect product factor
102C3×C4⋊Dic5—22no—
103C3×C4×Dic5—22no—
104C23×C3×D4—51no—
105C2×C3×C4×D4—51no—
106C2×C3×C4×D4D511yescharacteristic, complemented
107C22×C3×C22⋊C4—52no—
108C3×#390—51no—
109C3×#390—51no—
110C3×#386—52no—
111C3×#386—52no—
112C3×#380—51no—
113C3×#379—52no—
114C3×C4×C22⋊C4—51no—
115C24×D5C22×C312yes—
116C22×C5×D4C22×C311yescharacteristic
117C23×C4×C5C22×C312yescomplemented
118C22×C22⋊D5C22×C312yes—
119C23×Dic5C22×C312yescomplemented
120C2×D4×D5—24no—
121C2×D4×D5—24no—
122C2×D4×D5C3×C418yescomplemented
123C22×D20C22×C311yescharacteristic
124C22×C4×D5C22×C311yescharacteristic
125C4×C5×D4—24no—
126C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
127C2×C5×C22⋊C4C22×C312yescomplemented
128C2×C42×C5C22×C311yescharacteristic, complemented
129C2×C22⋊Dic5C22×C312yescomplemented
130D4×Dic5—24no—
131C2×#685—28no—
132C2×#685C22×C312yes—
133C2×#685C22×C311yescharacteristic
134C2×#685C22×C311yescharacteristic
135C2×#685C22×C312yescomplemented
136C2×#685C22×C312yescomplemented
137C2×#685C22×C312yescomplemented
138C2×#685C22×C312yescomplemented
139C2×C4⋊Dic5C22×C311yescharacteristic, complemented
140C2×C4×Dic5C22×C311yescharacteristic, complemented
141#3963C22×C311yescharacteristic, complemented
142#3963C22×C311yescharacteristic, complemented
143#3963C22×C312yescomplemented
144D4×C22⋊C4—51noSylow
145C23×C3×C5—22no—
146C23×C3×C5—22no—
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5C22×C414yes—
150C23×C3×C5C2×D414yes—
151C23×C3×C5C2×D414yes—
152C23×C3×C5C2411yescharacteristic
153C22×C3×D5—21no—
154C22×C3×D5—21no—
155C22×C3×D5—21no—
156C22×C3×D5—21no—
157C22×C3×D5—216no—
158C22×C3×D5—22no—
159C22×C3×D5—22no—
160C22×C3×D5—22no—
161C22×C3×D5—22no—
162C22×C3×D5—22no—
163C22×C3×D5—22no—
164C22×C3×D5—216no—
165C22×C3×D5—48no—
166C22×C3×D5—48no—
167C22×C3×D5—48no—
168C22×C3×D5—48no—
169C22×C3×D5—48no—
170C22×C3×D5C22×C414yes—
171C22×C3×D5C22×C412yes—
172C22×C3×D5C2×D412yes—
173C22×C3×D5#4112yes—
174C3×C5×D4C22⋊C4116yescomplemented
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—22no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5—48no—
184C2×C3×C4×C5C22×C412yes—
185C2×C3×C4×C5C2×D412yes—
186C2×C3×C4×C5C2×D412yes—
187C2×C3×C4×C5C2×D412yescomplemented
188C3×C22⋊D5—216no—
189C2×C3×Dic5—21no—
190C2×C3×Dic5—21no—
191C2×C3×Dic5—21no—
192C2×C3×Dic5—21no—
193C2×C3×Dic5—21no—
194C2×C3×Dic5—22no—
195C2×C3×Dic5—22no—
196C2×C3×Dic5—21no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—22no—
199C2×C3×Dic5—48no—
200C2×C3×Dic5C22×C412yes—
201C2×C3×Dic5C2×D412yescomplemented
202C3×D20—28no—
203C3×C4×D5—28no—
204C25×C3—52no—
205C22×C3×D4—52no—
206C22×C3×D4—58no—
207C22×C3×D4—51no—
208C22×C3×D4—104no—
209C22×C3×D4—104no—
210C22×C3×D4C2×D511yescharacteristic
211C23×C3×C4—51no—
212C23×C3×C4—52no—
213C23×C3×C4C2×D512yescomplemented
214C3×C4×D4—24no—
215C3×C4×D4—104no—
216C2×C3×C4⋊C4—51no—
217C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
218C2×C3×C22⋊C4—51no—
219C2×C3×C22⋊C4—52no—
220C2×C3×C22⋊C4—51no—
221C2×C3×C22⋊C4—52no—
222C2×C3×C22⋊C4—52no—
223C2×C3×C22⋊C4—52no—
224C2×C3×C22⋊C4—52no—
225C2×C3×C22⋊C4—52no—
226C2×C3×C22⋊C4—108no—
227C2×C3×C22⋊C4C2×D512yescomplemented
228C2×C3×C42—51no—
229C2×C3×C42C2×D511yescharacteristic, complemented
230C3×#95—51no—
231C3×#95—51no—
232C3×#95—52no—
233C24×C5C23×C312yes—
234C23×D5—24no—
235C23×D5—24no—
236C23×D5—24no—
237C23×D5—24no—
238C23×D5—42no—
239C23×D5—42no—
240C23×D5C2×C3×C418yescomplemented
241C23×D5C23×C312yes—
242C23×D5C23×C311yescharacteristic
243C2×C5×D4C2×C3×C414yes—
244C2×C5×D4C3×D414yes—
245C2×C5×D4C3×D414yes—
246C22×C4×C5—24no—
247C22×C4×C5—24no—
248C22×C4×C5—42no—
249C22×C4×C5C23×C311yescharacteristic
250C22×C4×C5C23×C312yes—
251C22×C4×C5C23×C311yescharacteristic
252C22×C4×C5C23×C311yescharacteristic
253C2×C22⋊D5—24no—
254C2×C22⋊D5—24no—
255C2×C22⋊D5C2×C3×C418yescomplemented
256C22×Dic5—24no—
257C22×Dic5—24no—
258C22×Dic5—42no—
259C22×Dic5C23×C311yescharacteristic
260C22×Dic5C23×C312yes—
261C22×Dic5C23×C311yescharacteristic
262C22×Dic5C23×C311yescharacteristic
263D4×D5—232no—
264C2×D20—22no—
265C2×D20—22no—
266C2×D20C2×C3×C414yescomplemented
267C2×C4×D5—22no—
268C2×C4×D5—22no—
269C2×C4×D5C2×C3×C414yescomplemented
270C5×C4⋊C4—22no—
271C5×C22⋊C4—24no—
272C42×C5—22no—
273C22⋊Dic5—24no—
274#685—24no—
275#685—22no—
276#685—24no—
277#685—24no—
278#685—42no—
279#685—42no—
280#685C3×D414yesdirect product factor
281C4⋊Dic5—22no—
282C4×Dic5—22no—
283C23×D4—51no—
284C2×C4×D4—51no—
285C2×C4×D4C3×D511yescharacteristic, complemented
286C22×C22⋊C4—52no—
287#390—51no—
288#390—51no—
289#386—52no—
290#386—52no—
291#380—51no—
292#379—52no—
293C4×C22⋊C4—51no—
294C22×C3×C5—24no—
295C22×C3×C5—24no—
296C22×C3×C5—24no—
297C22×C3×C5—24no—
298C22×C3×C5—24no—
299C22×C3×C5—24no—
300C22×C3×C5C2×C22⋊C418yescomplemented
301C22×C3×C5C23×C411yescharacteristic
302C22×C3×C5C22×D411yescharacteristic
303C22×C3×C5C22×D411yescharacteristic
304C22×C3×C5C22×D411yescharacteristic
305C22×C3×C5C2×#4111yescharacteristic
306C22×C3×C5H(5,𝔽2)11yescharacteristic
307C22×C3×C5H(5,𝔽2)11yescharacteristic
308C2×C3×D5—22no—
309C2×C3×D5—22no—
310C2×C3×D5—22no—
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—22no—
314C2×C3×D5—24no—
315C2×C3×D5—24no—
316C2×C3×D5—24no—
317C2×C3×D5—432no—
318C2×C3×D5—42no—
319C2×C3×D5—42no—
320C2×C3×D5—42no—
321C2×C3×D5—42no—
322C2×C3×D5C4×D414yescomplemented
323C3×C4×C5—22no—
324C3×C4×C5—42no—
325C3×C4×C5—41no—
326C3×C4×C5C2×C22⋊C414yescomplemented
327C3×Dic5—22no—
328C3×Dic5—22no—
329C3×Dic5—42no—
330C3×Dic5—41no—
331C24×C3—51no—
332C24×C3—52no—
333C24×C3—58no—
334C24×C3—104no—
335C24×C3—104no—
336C24×C3—104no—
337C24×C3—104no—
338C24×C3—202no—
339C24×C3—202no—
340C24×C3C22×D512yes—
341C2×C3×D4—58no—
342C2×C3×D4—54no—
343C2×C3×D4—104no—
344C2×C3×D4—104no—
345C2×C3×D4—1032no—
346C2×C3×D4—102no—
347C2×C3×D4—102no—
348C2×C3×D4C4×D514yes—
349C2×C3×D4D2014yes—
350C2×C3×D4C22⋊D514yes—
351C22×C3×C4—24no—
352C22×C3×C4—24no—
353C22×C3×C4—42no—
354C22×C3×C4—51no—
355C22×C3×C4—51no—
356C22×C3×C4—54no—
357C22×C3×C4—51no—
358C22×C3×C4—52no—
359C22×C3×C4—104no—
360C22×C3×C4—102no—
361C22×C3×C4—102no—
362C22×C3×C4—104no—
363C22×C3×C4—202no—
364C22×C3×C4C22×D511yescharacteristic
365C22×C3×C4C22×D512yes—
366C22×C3×C4C22×D511yescharacteristic
367C22×C3×C4C22×D511yescharacteristic
368C3×C4⋊C4—22no—
369C3×C4⋊C4—102no—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—54no—
372C3×C22⋊C4—104no—
373C3×C22⋊C4—102no—
374C3×C22⋊C4—104no—
375C3×C22⋊C4—104no—
376C3×C22⋊C4—104no—
377C3×C22⋊C4—202no—
378C3×C22⋊C4—202no—
379C3×C42—22no—
380C3×C42—102no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5C22×C3×C414yes—
386C23×C5C2×C3×D414yes—
387C23×C5C2×C3×D414yes—
388C23×C5C24×C311yescharacteristic
389C22×D5—21no—
390C22×D5—21no—
391C22×D5—21no—
392C22×D5—21no—
393C22×D5—216no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—216no—
401C22×D5—48no—
402C22×D5—48no—
403C22×D5—48no—
404C22×D5—48no—
405C22×D5—48no—
406C22×D5C22×C3×C414yes—
407C22×D5C22×C3×C412yes—
408C22×D5C2×C3×D412yes—
409C22×D5C3×#4112yes—
410C5×D4C3×C22⋊C4116yescomplemented
411C2×C4×C5—21no—
412C2×C4×C5—21no—
413C2×C4×C5—22no—
414C2×C4×C5—21no—
415C2×C4×C5—22no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—22no—
419C2×C4×C5—48no—
420C2×C4×C5C22×C3×C412yes—
421C2×C4×C5C2×C3×D412yes—
422C2×C4×C5C2×C3×D412yes—
423C2×C4×C5C2×C3×D412yescomplemented
424C22⋊D5—216no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—21no—
429C2×Dic5—21no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5—22no—
435C2×Dic5—48no—
436C2×Dic5C22×C3×C412yes—
437C2×Dic5C2×C3×D412yescomplemented
438D20—28no—
439C4×D5—28no—
440C25—52no—
441C22×D4—52no—
442C22×D4—58no—
443C22×D4—51no—
444C22×D4—104no—
445C22×D4—104no—
446C22×D4C2×C3×D511yescharacteristic
447C23×C4—51no—
448C23×C4—52no—
449C23×C4C2×C3×D512yescomplemented
450C4×D4—24no—
451C4×D4—104no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
454C2×C22⋊C4—51no—
455C2×C22⋊C4—52no—
456C2×C22⋊C4—52no—
457C2×C22⋊C4—52no—
458C2×C22⋊C4—52no—
459C2×C22⋊C4—51no—
460C2×C22⋊C4—52no—
461C2×C22⋊C4—52no—
462C2×C22⋊C4—108no—
463C2×C22⋊C4C2×C3×D512yescomplemented
464C2×C42—51no—
465C2×C42C2×C3×D511yescharacteristic, complemented
466#95—51no—
467#95—51no—
468#95—52no—
469C2×C3×C5—28no—
470C2×C3×C5C22×C22⋊C411yescharacteristic
471C2×C3×C5C2×C4×D411yescharacteristic
472C2×C3×C5#51811yescharacteristic
473C2×C3×C5D4211yescharacteristic
474C2×C3×C5D4211yescharacteristic
475C2×C3×C5#54611yescharacteristic
476C2×C3×C5#54611yescharacteristic
477C3×D5—24no—
478C3×D5—44no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—52no—
484C23×C3—52no—
485C23×C3—52no—
486C23×C3—54no—
487C23×C3—1016no—
488C23×C3—101no—
489C23×C3—101no—
490C23×C3—101no—
491C23×C3—101no—
492C23×C3—102no—
493C23×C3—102no—
494C23×C3—102no—
495C23×C3—102no—
496C23×C3—102no—
497C23×C3—102no—
498C23×C3—1016no—
499C23×C3—208no—
500C23×C3—208no—
501C23×C3—208no—
502C23×C3—208no—
503C23×C3—208no—
504C23×C3C2×C4×D514yes—
505C23×C3C2×D2014yes—
506C23×C3C2×C22⋊D514yes—
507C23×C3C23×D511yescharacteristic
508C3×D4—1016no—
509C3×D4—108no—
510C3×D4#685116yesdirect product factor
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—22no—
519C2×C3×C4—48no—
520C2×C3×C4—52no—
521C2×C3×C4—52no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—108no—
527C2×C3×C4—101no—
528C2×C3×C4—102no—
529C2×C3×C4—102no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—102no—
533C2×C3×C4—208no—
534C2×C3×C4C2×C4×D512yes—
535C2×C3×C4C2×D2012yes—
536C2×C3×C4D4×D512yescomplemented
537C2×C3×C4C2×C22⋊D512yes—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—24no—
542C22×C5—24no—
543C22×C5—24no—
544C22×C5C2×C3×C22⋊C418yescomplemented
545C22×C5C23×C3×C411yescharacteristic
546C22×C5C22×C3×D411yescharacteristic
547C22×C5C22×C3×D411yescharacteristic
548C22×C5C22×C3×D411yescharacteristic
549C22×C5C2×C3×#4111yescharacteristic
550C22×C5C3×H(5,𝔽2)11yescharacteristic
551C22×C5C3×H(5,𝔽2)11yescharacteristic
552C2×D5—22no—
553C2×D5—22no—
554C2×D5—22no—
555C2×D5—22no—
556C2×D5—22no—
557C2×D5—22no—
558C2×D5—24no—
559C2×D5—24no—
560C2×D5—24no—
561C2×D5—432no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5C3×C4×D414yescomplemented
567C4×C5—22no—
568C4×C5—42no—
569C4×C5—41no—
570C4×C5C2×C3×C22⋊C414yescomplemented
571Dic5—22no—
572Dic5—22no—
573Dic5—42no—
574Dic5—41no—
575C24—51no—
576C24—52no—
577C24—58no—
578C24—104no—
579C24—104no—
580C24—104no—
581C24—104no—
582C24—202no—
583C24—202no—
584C24C22×C3×D512yes—
585C2×D4—58no—
586C2×D4—54no—
587C2×D4—104no—
588C2×D4—104no—
589C2×D4—1032no—
590C2×D4—102no—
591C2×D4—102no—
592C2×D4C3×C4×D514yes—
593C2×D4C3×D2014yes—
594C2×D4C3×C22⋊D514yes—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—42no—
598C22×C4—51no—
599C22×C4—51no—
600C22×C4—54no—
601C22×C4—51no—
602C22×C4—52no—
603C22×C4—104no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—104no—
607C22×C4—202no—
608C22×C4C22×C3×D511yescharacteristic
609C22×C4C22×C3×D512yes—
610C22×C4C22×C3×D511yescharacteristic
611C22×C4C22×C3×D511yescharacteristic
612C4⋊C4—22no—
613C4⋊C4—102no—
614C22⋊C4—24no—
615C22⋊C4—54no—
616C22⋊C4—104no—
617C22⋊C4—104no—
618C22⋊C4—102no—
619C22⋊C4—104no—
620C22⋊C4—104no—
621C22⋊C4—202no—
622C22⋊C4—202no—
623C42—22no—
624C42—102no—
625C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—54no—
633C22×C3—102no—
634C22×C3—102no—
635C22×C3—102no—
636C22×C3—102no—
637C22×C3—102no—
638C22×C3—102no—
639C22×C3—104no—
640C22×C3—104no—
641C22×C3—104no—
642C22×C3—2032no—
643C22×C3—202no—
644C22×C3—202no—
645C22×C3—202no—
646C22×C3—202no—
647C22×C3C2×#68518yescomplemented
648C22×C3C22×C4×D511yescharacteristic
649C22×C3C22×D2011yescharacteristic
650C22×C3C2×D4×D511yescharacteristic
651C22×C3#414411yescharacteristic
652C22×C3D5×#4111yescharacteristic
653C22×C3#414911yescharacteristic
654C22×C3C22×C22⋊D511yescharacteristic
655C3×C4—22no—
656C3×C4—42no—
657C3×C4—41no—
658C3×C4—102no—
659C3×C4—102no—
660C3×C4—202no—
661C3×C4—201no—
662C3×C4C2×#68514yescomplemented
663C2×C5—28no—
664C2×C5C22×C3×C22⋊C411yescharacteristic
665C2×C5C2×C3×C4×D411yescharacteristic
666C2×C5C3×#51811yescharacteristic
667C2×C5C3×D4211yescharacteristic
668C2×C5C3×D4211yescharacteristic
669C2×C5C3×#54611yescharacteristic
670C2×C5C3×#54611yescharacteristic
671D5—24no—
672D5—44no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—52no—
678C23—52no—
679C23—52no—
680C23—54no—
681C23—1016no—
682C23—101no—
683C23—101no—
684C23—101no—
685C23—101no—
686C23—102no—
687C23—102no—
688C23—102no—
689C23—102no—
690C23—102no—
691C23—102no—
692C23—1016no—
693C23—208no—
694C23—208no—
695C23—208no—
696C23—208no—
697C23—208no—
698C23C2×C3×C4×D514yes—
699C23C2×C3×D2014yes—
700C23C2×C3×C22⋊D514yes—
701C23C23×C3×D511yescharacteristic
702D4—1016no—
703D4—108no—
704D4C3×#685116yesdirect product factor
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—52no—
715C2×C4—52no—
716C2×C4—101no—
717C2×C4—101no—
718C2×C4—101no—
719C2×C4—101no—
720C2×C4—108no—
721C2×C4—101no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—102no—
727C2×C4—208no—
728C2×C4C2×C3×C4×D512yes—
729C2×C4C2×C3×D2012yes—
730C2×C4C3×D4×D512yescomplemented
731C2×C4C2×C3×C22⋊D512yes—
732C2×C3—28no—
733C2×C3—104no—
734C2×C3—204no—
735C2×C3C4×D4×D511yescharacteristic
736C2×C3#6587911yescharacteristic
737C2×C3D4×D2011yescharacteristic
738C2×C3#6588811yescharacteristic
739C2×C3C22×#68511yescharacteristic
740C2×C3D4×C22⋊D511yescharacteristic
741C2×C3#6616311yescharacteristic
742C5C3×D4×C22⋊C411yescharacteristic, complemented, Sylow
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—54no—
750C22—102no—
751C22—102no—
752C22—102no—
753C22—102no—
754C22—102no—
755C22—102no—
756C22—104no—
757C22—104no—
758C22—104no—
759C22—2032no—
760C22—202no—
761C22—202no—
762C22—202no—
763C22—202no—
764C22C2×C3×#68518yescomplemented
765C22C22×C3×C4×D511yescharacteristic
766C22C22×C3×D2011yescharacteristic
767C22C2×C3×D4×D511yescharacteristic
768C22C3×#414411yescharacteristic
769C22C3×D5×#4111yescharacteristic
770C22C3×#414911yescharacteristic
771C22C22×C3×C22⋊D511yescharacteristic
772C4—22no—
773C4—42no—
774C4—41no—
775C4—102no—
776C4—102no—
777C4—202no—
778C4—201no—
779C4C2×C3×#68514yescomplemented
780C3D4×#68511yescharacteristic, direct product factor, Sylow
781C2—28no—
782C2—104no—
783C2—204no—
784C2C3×C4×D4×D511yescharacteristic
785C2C3×#6587911yescharacteristic
786C2C3×D4×D2011yescharacteristic
787C2C3×#6588811yescharacteristic
788C2C22×C3×#68511yescharacteristic
789C2C3×D4×C22⋊D511yescharacteristic
790C2C3×#6616311yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×D4×D5C2
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×D4×C22⋊C4
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C5×D4C2semidirect
3. C2×C3×D4×Dic5C2semidirect
4. C22×C3×#685C2semidirect
5. C3×#65502C2semidirect
6. C3×#65277C2semidirect
7. C3×#65276C2semidirect
8. C3×#65247C2semidirect
9. C3×#65244C2semidirect
10. C3×#65228C2semidirect
11. C3×C4×#685C2semidirect
12. D4×#685C3direct (N × H)
15. C23×C3×C4×C5C22semidirect
17. C23×C3×Dic5C22semidirect
20. C2×C3×D4×D5C4semidirect
24. C2×C3×C5×C4⋊C4C22semidirect
25. C2×C3×C5×C22⋊C4C22semidirect
26. C2×C3×C42×C5C22semidirect
27. C2×C3×C22⋊Dic5C22semidirect
33. C2×C3×#685C22semidirect
34. C2×C3×#685C22semidirect
35. C2×C3×#685C22semidirect
36. C2×C3×#685C22semidirect
37. C2×C3×C4⋊Dic5C22semidirect
38. C2×C3×C4×Dic5C22semidirect
39. C3×#3963C22semidirect
40. C3×#3963C22semidirect
41. C3×#3963C22semidirect
44. C2×C4×C5×D4C2×C3semidirect
45. C2×D4×Dic5C2×C3semidirect
46. C22×#685C2×C3semidirect
47. #65502C2×C3semidirect
48. #65277C2×C3semidirect
49. #65276C2×C3semidirect
50. #65247C2×C3semidirect
51. #65244C2×C3semidirect
52. #65228C2×C3semidirect
53. C4×#685C2×C3semidirect
61. C23×C3×D5C2×C4semidirect
76. C2×C3×C22⋊D5C2×C4semidirect
87. C2×C3×D20C2×C4semidirect
90. C2×C3×C4×D5C2×C4semidirect
101. C3×#685D4direct (N × H)
106. C2×C3×C4×D4D5semidirect
117. C23×C4×C5C22×C3semidirect
119. C23×Dic5C22×C3semidirect
122. C2×D4×D5C3×C4semidirect
126. C2×C5×C4⋊C4C22×C3semidirect
127. C2×C5×C22⋊C4C22×C3semidirect
128. C2×C42×C5C22×C3semidirect
129. C2×C22⋊Dic5C22×C3semidirect
135. C2×#685C22×C3semidirect
136. C2×#685C22×C3semidirect
137. C2×#685C22×C3semidirect
138. C2×#685C22×C3semidirect
139. C2×C4⋊Dic5C22×C3semidirect
140. C2×C4×Dic5C22×C3semidirect
141. #3963C22×C3semidirect
142. #3963C22×C3semidirect
143. #3963C22×C3semidirect
174. C3×C5×D4C22⋊C4semidirect
187. C2×C3×C4×C5C2×D4semidirect
201. C2×C3×Dic5C2×D4semidirect
213. C23×C3×C4C2×D5semidirect
217. C2×C3×C4⋊C4C2×D5semidirect
227. C2×C3×C22⋊C4C2×D5semidirect
229. C2×C3×C42C2×D5semidirect
240. C23×D5C2×C3×C4semidirect
255. C2×C22⋊D5C2×C3×C4semidirect
266. C2×D20C2×C3×C4semidirect
269. C2×C4×D5C2×C3×C4semidirect
280. #685C3×D4direct (N × H)
285. C2×C4×D4C3×D5semidirect
300. C22×C3×C5C2×C22⋊C4semidirect
322. C2×C3×D5C4×D4semidirect
326. C3×C4×C5C2×C22⋊C4semidirect
410. C5×D4C3×C22⋊C4semidirect
423. C2×C4×C5C2×C3×D4semidirect
437. C2×Dic5C2×C3×D4semidirect
449. C23×C4C2×C3×D5semidirect
453. C2×C4⋊C4C2×C3×D5semidirect
463. C2×C22⋊C4C2×C3×D5semidirect
465. C2×C42C2×C3×D5semidirect
510. C3×D4#685direct (N × H)
536. C2×C3×C4D4×D5semidirect
544. C22×C5C2×C3×C22⋊C4semidirect
566. C2×D5C3×C4×D4semidirect
570. C4×C5C2×C3×C22⋊C4semidirect
625. C3×C5D4×C22⋊C4semidirect
647. C22×C3C2×#685semidirect
662. C3×C4C2×#685semidirect
704. D4C3×#685direct (N × H)
730. C2×C4C3×D4×D5semidirect
742. C5C3×D4×C22⋊C4semidirect
764. C22C2×C3×#685semidirect
779. C4C2×C3×#685semidirect
780. C3D4×#685direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C2×C3×C4×C5×D42
C2×C3×D4×Dic52
C22×C3×#6852
C3×#655022
C3×#652772
C3×#652762
C3×#652472
C3×#652442
C3×#652282
C3×C4×#6852
D4×#6853
C3×D4×C22⋊C45