Finite Group Databasebeta

← C3×#10613827 #14323361

Subgroups — C3×#10613827 #14323361

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#4099C211yesmaximal, characteristic
3C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C3×#65536C211yesmaximal, characteristic, complemented
5C3×#65502C211yesmaximal, characteristic, complemented
6C3×#65499C211yesmaximal, characteristic, complemented
7C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
8C3×#65246C212yesmaximal, complemented
9C3×#65245C212yesmaximal, complemented
10C3×#65234C212yesmaximal, complemented
11C3×#65233C212yesmaximal, complemented
12#10613827C311yesmaximal, characteristic, direct product factor, Hall
13C25×C3×C5C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C22×C3×C22⋊D5C2211yescharacteristic
17C22×C3×C22⋊D5C2212yes—
18C22×C3×C4×D5C2211yescharacteristic, complemented
19C2×C3×C5×C22⋊C4—24no—
20C2×C3×C5×C22⋊C4C2212yes—
21C2×C3×C5×C22⋊C4C2212yes—
22C3×#4099C418yescomplemented
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×C22⋊Dic5C2212yes—
26C2×C3×C22⋊Dic5C2212yes—
27C2×C3×C22⋊Dic5C2212yes—
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C3×C4×C22⋊D5—24no—
30C2×C3×#685C2211yescharacteristic, complemented
31C2×C3×#685C2212yescomplemented
32C2×C3×#683C2211yescharacteristic, complemented
33C2×C3×#683C2212yescomplemented
34C2×C3×C4×Dic5C2211yescharacteristic, complemented
35C2×C3×C4×Dic5C2212yescomplemented
36C3×#3963C2212yescomplemented
37C3×#3963C2212yescomplemented
38C3×#3963C2212yescomplemented
39C3×#2321—51nomaximal, Hall
40C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
41C2×#4099C2×C311yescharacteristic
42C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
43#65536C2×C311yescharacteristic, complemented
44#65502C2×C311yescharacteristic, complemented
45#65499C2×C311yescharacteristic, complemented
46C4×C22⋊Dic5C2×C311yescharacteristic, complemented
47#65246C2×C312yescomplemented
48#65245C2×C312yescomplemented
49#65234C2×C312yescomplemented
50#65233C2×C312yescomplemented
51C24×C3×C5—22no—
52C24×C3×C5—22no—
53C24×C3×C5—42no—
54C24×C3×C5—42no—
55C24×C3×C5C2×C414yescomplemented
56C24×C3×C5C2312yes—
57C24×C3×C5C2311yescharacteristic
58C23×C3×D5C2311yescharacteristic
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—42no—
61C22×C3×C4×C5—42no—
62C22×C3×C4×C5D414yescomplemented
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C2×C3×C22⋊D5—22no—
67C2×C3×C22⋊D5—22no—
68C2×C3×C22⋊D5—42no—
69C2×C3×C22⋊D5—42no—
70C2×C3×C22⋊D5C2×C414yes—
71C2×C3×C22⋊D5C2×C418yescomplemented
72C22×C3×Dic5C2311yescharacteristic
73C22×C3×Dic5C2312yes—
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2312yes—
77C2×C3×C4×D5—22no—
78C2×C3×C4×D5—42no—
79C3×C5×C22⋊C4—24no—
80C3×C5×C22⋊C4—24no—
81C3×C22⋊Dic5—22no—
82C3×C22⋊Dic5—22no—
83C3×C22⋊Dic5—42no—
84C3×C22⋊Dic5—42no—
85C3×C22⋊Dic5C2×C418yescomplemented
86C3×C22⋊Dic5C2×C414yescomplemented
87C3×#685—22no—
88C3×#685—42no—
89C3×#683—22no—
90C3×#683—42no—
91C3×C4×Dic5—22no—
92C3×C4×Dic5—42no—
93C2×C3×#120—51no—
94C2×C3×C4×D4—51no—
95C22×C3×C22⋊C4D511yescharacteristic, complemented
96C3×#390—52no—
97C3×#388—52no—
98C3×#388—52no—
99C3×#386—51no—
100C3×#386—52no—
101C3×#385—51no—
102C3×#379—51no—
103C3×C4×C22⋊C4—51no—
104C25×C5C22×C311yescharacteristic
105C23×C4×C5C22×C311yescharacteristic
106C23×C4×C5C22×C311yescharacteristic
107C22×C22⋊D5C22×C311yescharacteristic
108C22×C22⋊D5C22×C312yes—
109C22×C4×D5C22×C311yescharacteristic, complemented
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4C22×C312yes—
112C2×C5×C22⋊C4C22×C312yes—
113#4099C3×C418yescomplemented
114C2×C22⋊Dic5C22×C311yescharacteristic
115C2×C22⋊Dic5C22×C311yescharacteristic
116C2×C22⋊Dic5C22×C312yes—
117C2×C22⋊Dic5C22×C312yes—
118C2×C22⋊Dic5C22×C312yes—
119C2×C22⋊Dic5C22×C311yescharacteristic
120C4×C22⋊D5—24no—
121C2×#685C22×C311yescharacteristic, complemented
122C2×#685C22×C312yescomplemented
123C2×#683C22×C311yescharacteristic, complemented
124C2×#683C22×C312yescomplemented
125C2×C4×Dic5C22×C311yescharacteristic, complemented
126C2×C4×Dic5C22×C312yescomplemented
127#3963C22×C312yescomplemented
128#3963C22×C312yescomplemented
129#3963C22×C312yescomplemented
130#2321—51noSylow
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—28no—
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5—48no—
141C23×C3×C5—44no—
142C23×C3×C5—44no—
143C23×C3×C5—48no—
144C23×C3×C5C22×C414yes—
145C23×C3×C5C22×C412yes—
146C23×C3×C5C2×D412yes—
147C23×C3×C5#4112yes—
148C23×C3×C5C2411yescharacteristic
149C22×C3×D5—21no—
150C22×C3×D5—21no—
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5C22×C412yes—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—44no—
160C2×C3×C4×C5—44no—
161C2×C3×C4×C5C2×D412yes—
162C2×C3×C4×C5C2×D412yes—
163C3×C22⋊D5—28no—
164C3×C22⋊D5—48no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C22×C412yes—
177C2×C3×Dic5C22×C414yes—
178C3×C4×D5—44no—
179C25×C3C2×D511yescharacteristic
180C22×C3×D4—51no—
181C22×C3×D4—52no—
182C23×C3×C4—51no—
183C23×C3×C4C2×D511yescharacteristic
184C23×C3×C4C2×D511yescharacteristic
185C3×#120—58no—
186C3×C4×D4—104no—
187C2×C3×C4⋊C4—51no—
188C2×C3×C4⋊C4—52no—
189C2×C3×C22⋊C4—24no—
190C2×C3×C22⋊C4—51no—
191C2×C3×C22⋊C4—52no—
192C2×C3×C22⋊C4—51no—
193C2×C3×C22⋊C4—51no—
194C2×C3×C22⋊C4—51no—
195C2×C3×C22⋊C4—52no—
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—52no—
198C2×C3×C22⋊C4C2×D512yes—
199C2×C3×C22⋊C4C2×D512yes—
200C2×C3×C42—51no—
201C2×C3×C42—52no—
202C3×#95—52no—
203C3×#95—52no—
204C3×#95—52no—
205C24×C5—22no—
206C24×C5—22no—
207C24×C5—42no—
208C24×C5—42no—
209C24×C5C2×C3×C414yescomplemented
210C24×C5C23×C312yes—
211C24×C5C23×C311yescharacteristic
212C23×D5C23×C311yescharacteristic
213C22×C4×C5—22no—
214C22×C4×C5—42no—
215C22×C4×C5—42no—
216C22×C4×C5C3×D414yescomplemented
217C22×C4×C5C23×C312yes—
218C22×C4×C5C23×C311yescharacteristic
219C22×C4×C5C23×C311yescharacteristic
220C2×C22⋊D5—22no—
221C2×C22⋊D5—22no—
222C2×C22⋊D5—42no—
223C2×C22⋊D5—42no—
224C2×C22⋊D5C2×C3×C414yes—
225C2×C22⋊D5C2×C3×C418yescomplemented
226C22×Dic5C23×C311yescharacteristic
227C22×Dic5C23×C312yes—
228C22×Dic5C23×C311yescharacteristic
229C22×Dic5C23×C311yescharacteristic
230C22×Dic5C23×C312yes—
231C2×C4×D5—22no—
232C2×C4×D5—42no—
233C5×C22⋊C4—24no—
234C5×C22⋊C4—24no—
235C22⋊Dic5—22no—
236C22⋊Dic5—22no—
237C22⋊Dic5—42no—
238C22⋊Dic5—42no—
239C22⋊Dic5C2×C3×C418yescomplemented
240C22⋊Dic5C2×C3×C414yescomplemented
241#685—22no—
242#685—42no—
243#683—22no—
244#683—42no—
245C4×Dic5—22no—
246C4×Dic5—42no—
247C2×#120—51no—
248C2×C4×D4—51no—
249C22×C22⋊C4C3×D511yescharacteristic, complemented
250#390—52no—
251#388—52no—
252#388—52no—
253#386—51no—
254#386—52no—
255#385—51no—
256#379—51no—
257C4×C22⋊C4—51no—
258C22×C3×C5—24no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—24no—
262C22×C3×C5—24no—
263C22×C3×C5—24no—
264C22×C3×C5—24no—
265C22×C3×C5—416no—
266C22×C3×C5—42no—
267C22×C3×C5—42no—
268C22×C3×C5—42no—
269C22×C3×C5—42no—
270C22×C3×C5C4×D414yes—
271C22×C3×C5C23×C411yescharacteristic
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C2×#4111yescharacteristic
274C22×C3×C5H(5,𝔽2)12yes—
275C22×C3×C5H(5,𝔽2)12yes—
276C2×C3×D5—22no—
277C2×C3×D5—24no—
278C2×C3×D5—41no—
279C2×C3×D5—41no—
280C2×C3×D5—42no—
281C3×C4×C5—22no—
282C3×C4×C5—22no—
283C3×C4×C5—42no—
284C3×Dic5—22no—
285C3×Dic5—24no—
286C3×Dic5—41no—
287C3×Dic5—41no—
288C3×Dic5—42no—
289C24×C3—22no—
290C24×C3—22no—
291C24×C3—42no—
292C24×C3—42no—
293C24×C3—51no—
294C24×C3C4×D514yescomplemented
295C24×C3C22×D512yes—
296C24×C3C22×D511yescharacteristic
297C2×C3×D4—54no—
298C2×C3×D4—58no—
299C2×C3×D4—102no—
300C2×C3×D4—102no—
301C2×C3×D4—202no—
302C2×C3×D4—202no—
303C22×C3×C4—22no—
304C22×C3×C4—42no—
305C22×C3×C4—42no—
306C22×C3×C4—51no—
307C22×C3×C4—52no—
308C22×C3×C4—52no—
309C22×C3×C4—51no—
310C22×C3×C4—51no—
311C22×C3×C4—102no—
312C22×C3×C4—202no—
313C22×C3×C4C22⋊D514yescomplemented
314C22×C3×C4C22×D512yes—
315C22×C3×C4C22×D511yescharacteristic
316C22×C3×C4C22×D511yescharacteristic
317C3×C4⋊C4—102no—
318C3×C4⋊C4—202no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—24no—
321C3×C22⋊C4—58no—
322C3×C22⋊C4—54no—
323C3×C22⋊C4—102no—
324C3×C22⋊C4—102no—
325C3×C22⋊C4—102no—
326C3×C22⋊C4—202no—
327C3×C22⋊C4—202no—
328C3×C22⋊C4—202no—
329C3×C42—102no—
330C3×C42—202no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—28no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—48no—
341C23×C5—44no—
342C23×C5—44no—
343C23×C5—48no—
344C23×C5C22×C3×C414yes—
345C23×C5C22×C3×C412yes—
346C23×C5C2×C3×D412yes—
347C23×C5C3×#4112yes—
348C23×C5C24×C311yescharacteristic
349C22×D5—21no—
350C22×D5—21no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5C22×C3×C412yes—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—44no—
360C2×C4×C5—44no—
361C2×C4×C5C2×C3×D412yes—
362C2×C4×C5C2×C3×D412yes—
363C22⋊D5—28no—
364C22⋊D5—48no—
365C2×Dic5—21no—
366C2×Dic5—21no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—21no—
370C2×Dic5—21no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5C22×C3×C412yes—
377C2×Dic5C22×C3×C414yes—
378C4×D5—44no—
379C25C2×C3×D511yescharacteristic
380C22×D4—51no—
381C22×D4—52no—
382C23×C4—51no—
383C23×C4C2×C3×D511yescharacteristic
384C23×C4C2×C3×D511yescharacteristic
385#120—58no—
386C4×D4—104no—
387C2×C4⋊C4—51no—
388C2×C4⋊C4—52no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—51no—
391C2×C22⋊C4—52no—
392C2×C22⋊C4—51no—
393C2×C22⋊C4—51no—
394C2×C22⋊C4—51no—
395C2×C22⋊C4—52no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—52no—
398C2×C22⋊C4C2×C3×D512yes—
399C2×C22⋊C4C2×C3×D512yes—
400C2×C42—51no—
401C2×C42—52no—
402#95—52no—
403#95—52no—
404#95—52no—
405C2×C3×C5—24no—
406C2×C3×C5—44no—
407C2×C3×C5C2×C4×D411yescharacteristic
408C2×C3×C5#51812yes—
409C2×C3×C5#53411yescharacteristic
410C2×C3×C5#53511yescharacteristic
411C2×C3×C5#53812yes—
412C3×D5—42no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—28no—
422C23×C3—48no—
423C23×C3—48no—
424C23×C3—44no—
425C23×C3—44no—
426C23×C3—52no—
427C23×C3—101no—
428C23×C3—102no—
429C23×C3—102no—
430C23×C3—101no—
431C23×C3C2×C4×D514yes—
432C23×C3C2×C4×D512yes—
433C23×C3#70912yes—
434C23×C3C2×C22⋊D512yes—
435C23×C3C23×D511yescharacteristic
436C3×D4—108no—
437C3×D4—208no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—44no—
444C2×C3×C4—44no—
445C2×C3×C4—54no—
446C2×C3×C4—52no—
447C2×C3×C4—101no—
448C2×C3×C4—102no—
449C2×C3×C4—102no—
450C2×C3×C4—101no—
451C2×C3×C4—102no—
452C2×C3×C4—102no—
453C2×C3×C4—102no—
454C2×C3×C4—102no—
455C2×C3×C4—102no—
456C2×C3×C4—101no—
457C2×C3×C4—101no—
458C2×C3×C4—204no—
459C2×C3×C4C2×C22⋊D512yes—
460C2×C3×C4C2×C22⋊D512yes—
461C22×C5—24no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—24no—
465C22×C5—24no—
466C22×C5—24no—
467C22×C5—24no—
468C22×C5—416no—
469C22×C5—42no—
470C22×C5—42no—
471C22×C5—42no—
472C22×C5—42no—
473C22×C5C3×C4×D414yes—
474C22×C5C23×C3×C411yescharacteristic
475C22×C5C22×C3×D411yescharacteristic
476C22×C5C2×C3×#4111yescharacteristic
477C22×C5C3×H(5,𝔽2)12yes—
478C22×C5C3×H(5,𝔽2)12yes—
479C2×D5—22no—
480C2×D5—24no—
481C2×D5—41no—
482C2×D5—41no—
483C2×D5—42no—
484C4×C5—22no—
485C4×C5—22no—
486C4×C5—42no—
487Dic5—22no—
488Dic5—24no—
489Dic5—41no—
490Dic5—41no—
491Dic5—42no—
492C24—22no—
493C24—22no—
494C24—42no—
495C24—42no—
496C24—51no—
497C24C3×C4×D514yescomplemented
498C24C22×C3×D512yes—
499C24C22×C3×D511yescharacteristic
500C2×D4—54no—
501C2×D4—58no—
502C2×D4—102no—
503C2×D4—102no—
504C2×D4—202no—
505C2×D4—202no—
506C22×C4—22no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—51no—
510C22×C4—52no—
511C22×C4—52no—
512C22×C4—51no—
513C22×C4—51no—
514C22×C4—102no—
515C22×C4—202no—
516C22×C4C3×C22⋊D514yescomplemented
517C22×C4C22×C3×D512yes—
518C22×C4C22×C3×D511yescharacteristic
519C22×C4C22×C3×D511yescharacteristic
520C4⋊C4—102no—
521C4⋊C4—202no—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—58no—
525C22⋊C4—54no—
526C22⋊C4—102no—
527C22⋊C4—102no—
528C22⋊C4—102no—
529C22⋊C4—202no—
530C22⋊C4—202no—
531C22⋊C4—202no—
532C42—102no—
533C42—202no—
534C3×C5#232111yescharacteristic, complemented, Hall
535C22×C3—24no—
536C22×C3—24no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—24no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—416no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—104no—
548C22×C3—102no—
549C22×C3—202no—
550C22×C3—201no—
551C22×C3—201no—
552C22×C3C4×C22⋊D514yes—
553C22×C3C22×C4×D511yescharacteristic
554C22×C3C2×#70911yescharacteristic
555C22×C3#414412yes—
556C22×C3#414412yes—
557C22×C3C22×C22⋊D511yescharacteristic
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—42no—
561C3×C4—104no—
562C3×C4—102no—
563C3×C4—202no—
564C3×C4—201no—
565C3×C4—201no—
566C2×C5—24no—
567C2×C5—44no—
568C2×C5C2×C3×C4×D411yescharacteristic
569C2×C5C3×#51812yes—
570C2×C5C3×#53411yescharacteristic
571C2×C5C3×#53511yescharacteristic
572C2×C5C3×#53812yes—
573D5—42no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—28no—
583C23—48no—
584C23—44no—
585C23—44no—
586C23—48no—
587C23—52no—
588C23—101no—
589C23—102no—
590C23—102no—
591C23—101no—
592C23C2×C3×C4×D514yes—
593C23C2×C3×C4×D512yes—
594C23C3×#70912yes—
595C23C2×C3×C22⋊D512yes—
596C23C23×C3×D511yescharacteristic
597D4—108no—
598D4—208no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—52no—
607C2×C4—54no—
608C2×C4—101no—
609C2×C4—102no—
610C2×C4—102no—
611C2×C4—101no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—101no—
618C2×C4—101no—
619C2×C4—204no—
620C2×C4C2×C3×C22⋊D512yes—
621C2×C4C2×C3×C22⋊D512yes—
622C2×C3—24no—
623C2×C3—44no—
624C2×C3—202no—
625C2×C3#6582012yes—
626C2×C3#6582812yes—
627C2×C3C2×C4×C22⋊D511yescharacteristic
628C2×C3#6613811yescharacteristic
629C2×C3#6613911yescharacteristic
630C5C3×#232111yescharacteristic, complemented, Sylow
631C22—22no—
632C22—22no—
633C22—24no—
634C22—24no—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—416no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—102no—
644C22—104no—
645C22—201no—
646C22—201no—
647C22—202no—
648C22C3×C4×C22⋊D514yes—
649C22C22×C3×C4×D511yescharacteristic
650C22C2×C3×#70911yescharacteristic
651C22C3×#414412yes—
652C22C3×#414412yes—
653C22C22×C3×C22⋊D511yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—102no—
658C4—104no—
659C4—201no—
660C4—201no—
661C4—202no—
662C3#1061382711yescharacteristic, direct product factor, Sylow
663C2—24no—
664C2—44no—
665C2—202no—
666C2C3×#6582012yes—
667C2C3×#6582812yes—
668C2C2×C3×C4×C22⋊D511yescharacteristic
669C2C3×#6613811yescharacteristic
670C2C3×#6613911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4099C2
cosocleC23×C5C24×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C3×#2321
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
1. C22×C3×C5×C22⋊C4C2semidirect
3. C2×C3×C4×C22⋊D5C2semidirect
4. C3×#65536C2semidirect
5. C3×#65502C2semidirect
6. C3×#65499C2semidirect
7. C3×C4×C22⋊Dic5C2semidirect
8. C3×#65246C2semidirect
9. C3×#65245C2semidirect
10. C3×#65234C2semidirect
11. C3×#65233C2semidirect
12. #10613827C3direct (N × H)
18. C22×C3×C4×D5C22semidirect
22. C3×#4099C4semidirect
30. C2×C3×#685C22semidirect
31. C2×C3×#685C22semidirect
32. C2×C3×#683C22semidirect
33. C2×C3×#683C22semidirect
34. C2×C3×C4×Dic5C22semidirect
35. C2×C3×C4×Dic5C22semidirect
36. C3×#3963C22semidirect
37. C3×#3963C22semidirect
38. C3×#3963C22semidirect
40. C22×C5×C22⋊C4C2×C3semidirect
42. C2×C4×C22⋊D5C2×C3semidirect
43. #65536C2×C3semidirect
44. #65502C2×C3semidirect
45. #65499C2×C3semidirect
46. C4×C22⋊Dic5C2×C3semidirect
47. #65246C2×C3semidirect
48. #65245C2×C3semidirect
49. #65234C2×C3semidirect
50. #65233C2×C3semidirect
55. C24×C3×C5C2×C4semidirect
62. C22×C3×C4×C5D4semidirect
71. C2×C3×C22⋊D5C2×C4semidirect
85. C3×C22⋊Dic5C2×C4semidirect
86. C3×C22⋊Dic5C2×C4semidirect
95. C22×C3×C22⋊C4D5semidirect
109. C22×C4×D5C22×C3semidirect
113. #4099C3×C4semidirect
121. C2×#685C22×C3semidirect
122. C2×#685C22×C3semidirect
123. C2×#683C22×C3semidirect
124. C2×#683C22×C3semidirect
125. C2×C4×Dic5C22×C3semidirect
126. C2×C4×Dic5C22×C3semidirect
127. #3963C22×C3semidirect
128. #3963C22×C3semidirect
129. #3963C22×C3semidirect
209. C24×C5C2×C3×C4semidirect
216. C22×C4×C5C3×D4semidirect
225. C2×C22⋊D5C2×C3×C4semidirect
239. C22⋊Dic5C2×C3×C4semidirect
240. C22⋊Dic5C2×C3×C4semidirect
249. C22×C22⋊C4C3×D5semidirect
294. C24×C3C4×D5semidirect
313. C22×C3×C4C22⋊D5semidirect
497. C24C3×C4×D5semidirect
516. C22×C4C3×C22⋊D5semidirect
534. C3×C5#2321semidirect
630. C5C3×#2321semidirect
662. C3#10613827direct (N × H)

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
C2×C3×#40992
C2×C3×C4×C22⋊D52
C3×#655362
C3×#655022
C3×#654992
C3×C4×C22⋊Dic52
C3×#652462
C3×#652452
C3×#652342
C3×#652332
#106138273
C3×#23215