Finite Group Databasebeta

← C3×#10613828 #14326240

Subgroups — C3×#10613828 #14326240

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×C3×C22⋊Dic5C211yesmaximal, characteristic
3C2×C3×#4072C211yesmaximal, characteristic, complemented
4C3×#65536C211yesmaximal, characteristic
5C3×#65501C211yesmaximal, characteristic, complemented
6C3×#65500C211yesmaximal, characteristic, complemented
7C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
8C3×#65240C212yesmaximal, complemented
9C3×#65240C212yesmaximal, complemented
10C3×#65239C212yesmaximal, complemented
11C3×C22⋊C4×Dic5C212yesmaximal, complemented
12#10613828C311yesmaximal, characteristic, direct product factor, Hall
13C25×C3×C5C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×Dic5C2212yes—
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×C3×C22⋊Dic5—24no—
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×C3×C22⋊Dic5C2212yes—
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2212yes—
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×C22⋊Dic5C2212yes—
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C3×#4072—24no—
31C2×C3×C4⋊Dic5C2212yescomplemented
32C2×C3×C4⋊Dic5C2212yescomplemented
33C2×C3×C4×Dic5C2212yescomplemented
34C2×C3×C4×Dic5C2212yescomplemented
35C3×#3963C2212yescomplemented
36C3×#3963C2212yescomplemented
37C3×#3963C2212yescomplemented
38C3×#3963C2212yescomplemented
39C3×#2342—51nomaximal, Hall
40C22×C5×C22⋊C4C2×C311yescharacteristic
41C22×C22⋊Dic5C2×C311yescharacteristic
42C2×#4072C2×C311yescharacteristic, complemented
43#65536C2×C311yescharacteristic
44#65501C2×C311yescharacteristic, complemented
45#65500C2×C311yescharacteristic, complemented
46C4×C22⋊Dic5C2×C311yescharacteristic, complemented
47#65240C2×C312yescomplemented
48#65240C2×C312yescomplemented
49#65239C2×C312yescomplemented
50C22⋊C4×Dic5C2×C312yescomplemented
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×C3×Dic5—24no—
69C22×C3×Dic5—24no—
70C22×C3×Dic5—42no—
71C22×C3×Dic5C2312yes—
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2312yes—
74C22×C3×Dic5C2312yes—
75C3×C5×C22⋊C4C2×C414yes—
76C3×C5×C22⋊C4C2×C414yes—
77C3×C5×C22⋊C4C2×C414yescomplemented
78C3×C5×C22⋊C4C2×C414yescomplemented
79C3×C22⋊Dic5—22no—
80C3×C22⋊Dic5—22no—
81C3×C22⋊Dic5—24no—
82C3×C22⋊Dic5—22no—
83C3×C22⋊Dic5—24no—
84C3×C22⋊Dic5—42no—
85C3×C22⋊Dic5D414yes—
86C3×C4⋊Dic5—24no—
87C3×C4⋊Dic5—42no—
88C3×C4×Dic5—24no—
89C3×C4×Dic5—42no—
90C2×C3×#117—51no—
91C22×C3×C22⋊C4—51no—
92C22×C3×C22⋊C4D511yescharacteristic
93C3×#388—52no—
94C3×#388—52no—
95C3×#385—52no—
96C3×#381—51no—
97C3×#380—51no—
98C3×#379—51no—
99C3×C4×C22⋊C4—51no—
100C3×C4×C22⋊C4—52no—
101C25×C5C22×C311yescharacteristic
102C23×C4×C5C22×C311yescharacteristic
103C23×C4×C5C22×C311yescharacteristic
104C23×Dic5C22×C312yes—
105C2×C5×C22⋊C4C3×C418yescomplemented
106C2×C5×C22⋊C4C22×C311yescharacteristic
107C2×C5×C22⋊C4C22×C311yescharacteristic
108C2×C5×C22⋊C4C22×C311yescharacteristic
109C2×C5×C22⋊C4C22×C311yescharacteristic
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5C22×C311yescharacteristic
112C2×C22⋊Dic5C22×C312yes—
113C2×C22⋊Dic5C22×C311yescharacteristic
114C2×C22⋊Dic5C22×C312yes—
115C2×C22⋊Dic5C22×C311yescharacteristic
116C2×C22⋊Dic5C22×C312yes—
117C2×C22⋊Dic5C22×C311yescharacteristic
118#4072—24no—
119C2×C4⋊Dic5C22×C312yescomplemented
120C2×C4⋊Dic5C22×C312yescomplemented
121C2×C4×Dic5C22×C312yescomplemented
122C2×C4×Dic5C22×C312yescomplemented
123#3963C22×C312yescomplemented
124#3963C22×C312yescomplemented
125#3963C22×C312yescomplemented
126#3963C22×C312yescomplemented
127#2342—51noSylow
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×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—48no—
173C2×C3×Dic5C2×D414yes—
174C25×C3C2×D511yescharacteristic
175C23×C3×C4—52no—
176C23×C3×C4C2×D511yescharacteristic
177C23×C3×C4C2×D511yescharacteristic
178C3×#117—104no—
179C2×C3×C4⋊C4—52no—
180C2×C3×C4⋊C4—52no—
181C2×C3×C22⋊C4—51no—
182C2×C3×C22⋊C4—51no—
183C2×C3×C22⋊C4—52no—
184C2×C3×C22⋊C4—51no—
185C2×C3×C22⋊C4—51no—
186C2×C3×C22⋊C4—52no—
187C2×C3×C22⋊C4—52no—
188C2×C3×C22⋊C4—104no—
189C2×C3×C22⋊C4Dic518yescomplemented
190C2×C3×C22⋊C4C2×D511yescharacteristic
191C2×C3×C22⋊C4C2×D511yescharacteristic
192C2×C3×C22⋊C4C2×D511yescharacteristic
193C2×C3×C22⋊C4C2×D511yescharacteristic
194C2×C3×C42—52no—
195C2×C3×C42—52no—
196C3×#95—52no—
197C3×#95—52no—
198C3×#95—52no—
199C3×#95—52no—
200C24×C5—22no—
201C24×C5—24no—
202C24×C5—22no—
203C24×C5—42no—
204C24×C5C2×C3×C414yes—
205C24×C5C23×C311yescharacteristic
206C24×C5C23×C311yescharacteristic
207C24×C5C23×C311yescharacteristic
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—42no—
211C22×C4×C5C2×C3×C414yescomplemented
212C22×C4×C5C2×C3×C414yescomplemented
213C22×C4×C5C23×C311yescharacteristic
214C22×C4×C5C23×C311yescharacteristic
215C22×C4×C5C23×C311yescharacteristic
216C22×C4×C5C23×C311yescharacteristic
217C22×Dic5—24no—
218C22×Dic5—24no—
219C22×Dic5—42no—
220C22×Dic5C23×C312yes—
221C22×Dic5C23×C312yes—
222C22×Dic5C23×C312yes—
223C22×Dic5C23×C312yes—
224C5×C22⋊C4C2×C3×C414yes—
225C5×C22⋊C4C2×C3×C414yes—
226C5×C22⋊C4C2×C3×C414yescomplemented
227C5×C22⋊C4C2×C3×C414yescomplemented
228C22⋊Dic5—22no—
229C22⋊Dic5—22no—
230C22⋊Dic5—24no—
231C22⋊Dic5—22no—
232C22⋊Dic5—24no—
233C22⋊Dic5—42no—
234C22⋊Dic5C3×D414yes—
235C4⋊Dic5—24no—
236C4⋊Dic5—42no—
237C4×Dic5—24no—
238C4×Dic5—42no—
239C2×#117—51no—
240C22×C22⋊C4—51no—
241C22×C22⋊C4C3×D511yescharacteristic
242#388—52no—
243#388—52no—
244#385—52no—
245#381—51no—
246#380—51no—
247#379—51no—
248C4×C22⋊C4—51no—
249C4×C22⋊C4—52no—
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—
275C3×Dic5—24no—
276C3×Dic5—42no—
277C3×Dic5—42no—
278C3×Dic5—42no—
279C24×C3—24no—
280C24×C3—22no—
281C24×C3—22no—
282C24×C3—42no—
283C24×C3C2×Dic514yes—
284C24×C3C22×D511yescharacteristic
285C24×C3C22×D511yescharacteristic
286C24×C3C22×D511yescharacteristic
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—42no—
290C22×C3×C4—52no—
291C22×C3×C4—52no—
292C22×C3×C4—52no—
293C22×C3×C4—52no—
294C22×C3×C4—104no—
295C22×C3×C4—104no—
296C22×C3×C4—202no—
297C22×C3×C4C2×Dic514yescomplemented
298C22×C3×C4C2×Dic514yescomplemented
299C22×C3×C4C22×D511yescharacteristic
300C22×C3×C4C22×D511yescharacteristic
301C22×C3×C4C22×D511yescharacteristic
302C22×C3×C4C22×D511yescharacteristic
303C3×C4⋊C4—104no—
304C3×C4⋊C4—202no—
305C3×C22⋊C4—54no—
306C3×C22⋊C4—104no—
307C3×C22⋊C4—104no—
308C3×C22⋊C4—102no—
309C3×C22⋊C4—102no—
310C3×C22⋊C4—102no—
311C3×C22⋊C4—202no—
312C3×C22⋊C4C2×Dic514yes—
313C3×C22⋊C4C2×Dic514yes—
314C3×C22⋊C4C2×Dic514yescomplemented
315C3×C22⋊C4C2×Dic514yescomplemented
316C3×C42—104no—
317C3×C42—202no—
318C23×C5—21no—
319C23×C5—22no—
320C23×C5—21no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—28no—
324C23×C5—28no—
325C23×C5—21no—
326C23×C5—22no—
327C23×C5—21no—
328C23×C5—22no—
329C23×C5—44no—
330C23×C5—48no—
331C23×C5—48no—
332C23×C5C22×C3×C412yes—
333C23×C5C22×C3×C412yes—
334C23×C5C22×C3×C412yes—
335C23×C5C2×C3×D412yes—
336C23×C5C3×#4114yes—
337C23×C5C3×#4112yes—
338C23×C5C24×C311yescharacteristic
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—44no—
347C2×C4×C5C22×C3×C412yes—
348C2×C4×C5C22×C3×C412yes—
349C2×C4×C5C22×C3×C412yes—
350C2×C4×C5C22×C3×C412yes—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—48no—
363C2×Dic5C2×C3×D414yes—
364C25C2×C3×D511yescharacteristic
365C23×C4—52no—
366C23×C4C2×C3×D511yescharacteristic
367C23×C4C2×C3×D511yescharacteristic
368#117—104no—
369C2×C4⋊C4—52no—
370C2×C4⋊C4—52no—
371C2×C22⋊C4—51no—
372C2×C22⋊C4—51no—
373C2×C22⋊C4—52no—
374C2×C22⋊C4—51no—
375C2×C22⋊C4—51no—
376C2×C22⋊C4—52no—
377C2×C22⋊C4—52no—
378C2×C22⋊C4—104no—
379C2×C22⋊C4C3×Dic518yescomplemented
380C2×C22⋊C4C2×C3×D511yescharacteristic
381C2×C22⋊C4C2×C3×D511yescharacteristic
382C2×C22⋊C4C2×C3×D511yescharacteristic
383C2×C22⋊C4C2×C3×D511yescharacteristic
384C2×C42—52no—
385C2×C42—52no—
386#95—52no—
387#95—52no—
388#95—52no—
389#95—52no—
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—22no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—28no—
408C23×C3—28no—
409C23×C3—44no—
410C23×C3—48no—
411C23×C3—48no—
412C23×C3#70914yes—
413C23×C3D4×D512yes—
414C23×C3#71112yes—
415C23×C3C22×Dic512yes—
416C23×C3C22×Dic512yes—
417C23×C3C22×Dic512yes—
418C23×C3C23×D511yescharacteristic
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—28no—
426C2×C3×C4—44no—
427C2×C3×C4—54no—
428C2×C3×C4—102no—
429C2×C3×C4—102no—
430C2×C3×C4—102no—
431C2×C3×C4—102no—
432C2×C3×C4—102no—
433C2×C3×C4—102no—
434C2×C3×C4—102no—
435C2×C3×C4—102no—
436C2×C3×C4—102no—
437C2×C3×C4—102no—
438C2×C3×C4—102no—
439C2×C3×C4—208no—
440C2×C3×C4C22×Dic512yes—
441C2×C3×C4C22×Dic512yes—
442C2×C3×C4C22×Dic512yes—
443C2×C3×C4C22×Dic512yes—
444C22×C5—22no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—24no—
449C22×C5—24no—
450C22×C5—24no—
451C22×C5—24no—
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—416no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5C3×#11714yescomplemented
459C22×C5C3×C4×D414yes—
460C22×C5C23×C3×C411yescharacteristic
461C22×C5C22×C3×D411yescharacteristic
462C22×C5C2×C3×#4112yes—
463C22×C5C2×C3×#4111yescharacteristic
464C22×C5C3×H(5,𝔽2)12yes—
465C4×C5—22no—
466C4×C5—22no—
467C4×C5—22no—
468C4×C5—22no—
469Dic5—24no—
470Dic5—42no—
471Dic5—42no—
472Dic5—42no—
473C24—24no—
474C24—22no—
475C24—22no—
476C24—42no—
477C24C2×C3×Dic514yes—
478C24C22×C3×D511yescharacteristic
479C24C22×C3×D511yescharacteristic
480C24C22×C3×D511yescharacteristic
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—42no—
484C22×C4—52no—
485C22×C4—52no—
486C22×C4—52no—
487C22×C4—52no—
488C22×C4—104no—
489C22×C4—104no—
490C22×C4—202no—
491C22×C4C2×C3×Dic514yescomplemented
492C22×C4C2×C3×Dic514yescomplemented
493C22×C4C22×C3×D511yescharacteristic
494C22×C4C22×C3×D511yescharacteristic
495C22×C4C22×C3×D511yescharacteristic
496C22×C4C22×C3×D511yescharacteristic
497C4⋊C4—104no—
498C4⋊C4—202no—
499C22⋊C4—54no—
500C22⋊C4—104no—
501C22⋊C4—104no—
502C22⋊C4—102no—
503C22⋊C4—102no—
504C22⋊C4—102no—
505C22⋊C4—202no—
506C22⋊C4C2×C3×Dic514yes—
507C22⋊C4C2×C3×Dic514yes—
508C22⋊C4C2×C3×Dic514yescomplemented
509C22⋊C4C2×C3×Dic514yescomplemented
510C42—104no—
511C42—202no—
512C3×C5#234211yescharacteristic, complemented, Hall
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—416no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3#407214yescomplemented
528C22×C3D4×Dic514yes—
529C22×C3C2×#70912yes—
530C22×C3C2×D4×D511yescharacteristic
531C22×C3C2×#71111yescharacteristic
532C22×C3#414412yes—
533C22×C3C23×Dic511yescharacteristic
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—22no—
538C3×C4—104no—
539C3×C4—202no—
540C3×C4—202no—
541C3×C4—202no—
542C2×C5—24no—
543C2×C5—24no—
544C2×C5—42no—
545C2×C5C2×C3×#11711yescharacteristic
546C2×C5C2×C3×C4×D411yescharacteristic
547C2×C5C3×#51811yescharacteristic
548C2×C5C3×#54612yes—
549C2×C5C3×#55112yes—
550C23—22no—
551C23—21no—
552C23—21no—
553C23—22no—
554C23—22no—
555C23—28no—
556C23—22no—
557C23—21no—
558C23—21no—
559C23—22no—
560C23—28no—
561C23—44no—
562C23—48no—
563C23—48no—
564C23C3×#70914yes—
565C23C3×D4×D512yes—
566C23C3×#71112yes—
567C23C22×C3×Dic512yes—
568C23C22×C3×Dic512yes—
569C23C22×C3×Dic512yes—
570C23C23×C3×D511yescharacteristic
571C2×C4—28no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—44no—
579C2×C4—54no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4—102no—
585C2×C4—102no—
586C2×C4—102no—
587C2×C4—102no—
588C2×C4—102no—
589C2×C4—102no—
590C2×C4—102no—
591C2×C4—208no—
592C2×C4C22×C3×Dic512yes—
593C2×C4C22×C3×Dic512yes—
594C2×C4C22×C3×Dic512yes—
595C2×C4C22×C3×Dic512yes—
596C2×C3—24no—
597C2×C3—24no—
598C2×C3—42no—
599C2×C3#6582412yes—
600C2×C3#6582912yes—
601C2×C3C2×#407211yescharacteristic
602C2×C3C2×D4×Dic511yescharacteristic
603C2×C3#6613211yescharacteristic
604C5C3×#234211yescharacteristic, complemented, Sylow
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—416no—
617C22—42no—
618C22—42no—
619C22C3×#407214yescomplemented
620C22C3×D4×Dic514yes—
621C22C2×C3×#70912yes—
622C22C2×C3×D4×D511yescharacteristic
623C22C2×C3×#71111yescharacteristic
624C22C3×#414412yes—
625C22C23×C3×Dic511yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—22no—
630C4—104no—
631C4—202no—
632C4—202no—
633C4—202no—
634C3#1061382811yescharacteristic, direct product factor, Sylow
635C2—24no—
636C2—24no—
637C2—42no—
638C2C3×#6582412yes—
639C2C3×#6582912yes—
640C2C2×C3×#407211yescharacteristic
641C2C2×C3×D4×Dic511yescharacteristic
642C2C3×#6613211yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC25×C3×C5C22
cosocleC23×C5C24×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C3×#2342
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
3. C2×C3×#4072C2semidirect
5. C3×#65501C2semidirect
6. C3×#65500C2semidirect
7. C3×C4×C22⋊Dic5C2semidirect
8. C3×#65240C2semidirect
9. C3×#65240C2semidirect
10. C3×#65239C2semidirect
11. C3×C22⋊C4×Dic5C2semidirect
12. #10613828C3direct (N × H)
17. C2×C3×C5×C22⋊C4C4semidirect
31. C2×C3×C4⋊Dic5C22semidirect
32. C2×C3×C4⋊Dic5C22semidirect
33. C2×C3×C4×Dic5C22semidirect
34. C2×C3×C4×Dic5C22semidirect
35. C3×#3963C22semidirect
36. C3×#3963C22semidirect
37. C3×#3963C22semidirect
38. C3×#3963C22semidirect
42. C2×#4072C2×C3semidirect
44. #65501C2×C3semidirect
45. #65500C2×C3semidirect
46. C4×C22⋊Dic5C2×C3semidirect
47. #65240C2×C3semidirect
48. #65240C2×C3semidirect
49. #65239C2×C3semidirect
50. C22⋊C4×Dic5C2×C3semidirect
62. C22×C3×C4×C5C2×C4semidirect
63. C22×C3×C4×C5C2×C4semidirect
77. C3×C5×C22⋊C4C2×C4semidirect
78. C3×C5×C22⋊C4C2×C4semidirect
105. C2×C5×C22⋊C4C3×C4semidirect
119. C2×C4⋊Dic5C22×C3semidirect
120. C2×C4⋊Dic5C22×C3semidirect
121. C2×C4×Dic5C22×C3semidirect
122. C2×C4×Dic5C22×C3semidirect
123. #3963C22×C3semidirect
124. #3963C22×C3semidirect
125. #3963C22×C3semidirect
126. #3963C22×C3semidirect
189. C2×C3×C22⋊C4Dic5semidirect
211. C22×C4×C5C2×C3×C4semidirect
212. C22×C4×C5C2×C3×C4semidirect
226. C5×C22⋊C4C2×C3×C4semidirect
227. C5×C22⋊C4C2×C3×C4semidirect
264. C22×C3×C5#117semidirect
297. C22×C3×C4C2×Dic5semidirect
298. C22×C3×C4C2×Dic5semidirect
314. C3×C22⋊C4C2×Dic5semidirect
315. C3×C22⋊C4C2×Dic5semidirect
379. C2×C22⋊C4C3×Dic5semidirect
458. C22×C5C3×#117semidirect
491. C22×C4C2×C3×Dic5semidirect
492. C22×C4C2×C3×Dic5semidirect
508. C22⋊C4C2×C3×Dic5semidirect
509. C22⋊C4C2×C3×Dic5semidirect
512. C3×C5#2342semidirect
527. C22×C3#4072semidirect
604. C5C3×#2342semidirect
619. C22C3×#4072semidirect
634. C3#10613828direct (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
C22×C3×C22⋊Dic52
C2×C3×#40722
C3×#655362
C3×#655012
C3×#655002
C3×C4×C22⋊Dic52
C3×#652402
C3×#652392
C3×C22⋊C4×Dic52
#106138283
C3×#23425