Finite Group Databasebeta

← C3×#10614309 #14323370

Subgroups — C3×#10614309 #14323370

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
1C2×C3×C5×#120C211yesmaximal, characteristic
2C22×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
4C3×#65536C211yesmaximal, characteristic, complemented
5C3×#65510C212yesmaximal, complemented
6C3×#65509C212yesmaximal, complemented
7C3×#65509C211yesmaximal, characteristic, complemented
8C3×#65240C212yesmaximal, complemented
9C3×#65240C212yesmaximal, complemented
10C3×#65239C211yesmaximal, characteristic, complemented
11C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12#10614309C311yesmaximal, characteristic, direct product factor, Hall
13C25×C3×C5C2211yescharacteristic
14C22×C3×C5×D4C2211yescharacteristic
15C22×C3×C5×D4C2212yes—
16C23×C3×Dic5C2211yescharacteristic
17C23×C3×Dic5C2211yescharacteristic
18C23×C3×Dic5C2211yescharacteristic, complemented
19C3×C5×#120C418yescomplemented
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2212yes—
22C2×C3×C22⋊Dic5—24no—
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×C22⋊Dic5C2212yes—
26C2×C3×C22⋊Dic5C2212yes—
27C2×C3×C22⋊Dic5C2212yes—
28C2×C3×C22⋊Dic5C2212yes—
29C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
30C2×C3×C22⋊Dic5C2212yescomplemented
31C3×D4×Dic5—24no—
32C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
33C2×C3×C4⋊Dic5C2212yescomplemented
34C2×C3×C4×Dic5C2211yescharacteristic, complemented
35C2×C3×C4×Dic5C2212yescomplemented
36C3×#3963C2212yescomplemented
37C3×#3963C2212yescomplemented
38C3×#3963C2212yescomplemented
39C3×#2321—51nomaximal, Hall
40C2×C5×#120C2×C311yescharacteristic
41C22×C22⋊Dic5C2×C311yescharacteristic, complemented
42C2×D4×Dic5C2×C311yescharacteristic, complemented
43#65536C2×C311yescharacteristic, complemented
44#65510C2×C312yescomplemented
45#65509C2×C312yescomplemented
46#65509C2×C311yescharacteristic, complemented
47#65240C2×C312yescomplemented
48#65240C2×C312yescomplemented
49#65239C2×C311yescharacteristic, complemented
50C22⋊C4×Dic5C2×C311yescharacteristic, complemented
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
58C24×C3×C5C2311yescharacteristic
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4—22no—
61C2×C3×C5×D4—42no—
62C2×C3×C5×D4—42no—
63C2×C3×C5×D4C2×C414yes—
64C2×C3×C5×D4C2×C418yescomplemented
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C3×Dic5—22no—
68C22×C3×Dic5—22no—
69C22×C3×Dic5—42no—
70C22×C3×Dic5—42no—
71C22×C3×Dic5—42no—
72C22×C3×Dic5D414yescomplemented
73C22×C3×Dic5C2312yes—
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C3×C5×C22⋊C4C2×C418yescomplemented
80C3×C5×C22⋊C4C2×C414yescomplemented
81C3×C22⋊Dic5—22no—
82C3×C22⋊Dic5—22no—
83C3×C22⋊Dic5—22no—
84C3×C22⋊Dic5—24no—
85C3×C22⋊Dic5—24no—
86C3×C22⋊Dic5—42no—
87C3×C22⋊Dic5—42no—
88C3×C22⋊Dic5—42no—
89C3×C4⋊Dic5—22no—
90C3×C4⋊Dic5—42no—
91C3×C4×Dic5—22no—
92C3×C4×Dic5—42no—
93C2×C3×#120D511yescharacteristic
94C2×C3×C4×D4—51no—
95C22×C3×C22⋊C4—51no—
96C3×#390—52no—
97C3×#388—52no—
98C3×#388—52no—
99C3×#386—52no—
100C3×#386—51no—
101C3×#385—51no—
102C3×#379—51no—
103C3×C4×C22⋊C4—51no—
104C25×C5C22×C311yescharacteristic
105C22×C5×D4C22×C311yescharacteristic
106C22×C5×D4C22×C312yes—
107C23×Dic5C22×C311yescharacteristic
108C23×Dic5C22×C311yescharacteristic
109C23×Dic5C22×C311yescharacteristic, complemented
110C5×#120C3×C418yescomplemented
111C2×C5×C22⋊C4C22×C311yescharacteristic
112C2×C5×C22⋊C4C22×C312yes—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5C22×C311yescharacteristic
115C2×C22⋊Dic5C22×C311yescharacteristic
116C2×C22⋊Dic5C22×C312yes—
117C2×C22⋊Dic5C22×C312yes—
118C2×C22⋊Dic5C22×C312yes—
119C2×C22⋊Dic5C22×C312yes—
120C2×C22⋊Dic5C22×C311yescharacteristic, complemented
121C2×C22⋊Dic5C22×C312yescomplemented
122D4×Dic5—24no—
123C2×C4⋊Dic5C22×C311yescharacteristic, complemented
124C2×C4⋊Dic5C22×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—21no—
136C23×C3×C5—21no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5—22no—
141C23×C3×C5—22no—
142C23×C3×C5—22no—
143C23×C3×C5—22no—
144C23×C3×C5—48no—
145C23×C3×C5—44no—
146C23×C3×C5—44no—
147C23×C3×C5—48no—
148C23×C3×C5C22×C414yes—
149C23×C3×C5C22×C412yes—
150C23×C3×C5C22×C412yes—
151C23×C3×C5C2×D412yes—
152C23×C3×C5#4112yes—
153C23×C3×C5C2411yescharacteristic
154C3×C5×D4—28no—
155C3×C5×D4—48no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5C22×C412yes—
161C2×C3×C4×C5C22×C414yes—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—21no—
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—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—44no—
175C2×C3×Dic5—44no—
176C2×C3×Dic5—44no—
177C2×C3×Dic5C2×D412yes—
178C2×C3×Dic5C2×D412yes—
179C25×C3C2×D511yescharacteristic
180C22×C3×D4C2×D511yescharacteristic
181C22×C3×D4C2×D512yes—
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×C3×C4—51no—
185C3×#120Dic518yescomplemented
186C3×C4×D4—104no—
187C2×C3×C4⋊C4—51no—
188C2×C3×C4⋊C4—52no—
189C2×C3×C22⋊C4—51no—
190C2×C3×C22⋊C4—51no—
191C2×C3×C22⋊C4—52no—
192C2×C3×C22⋊C4—52no—
193C2×C3×C22⋊C4—51no—
194C2×C3×C22⋊C4—52no—
195C2×C3×C22⋊C4—52no—
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—104no—
198C2×C3×C22⋊C4C2×D511yescharacteristic
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
212C24×C5C23×C311yescharacteristic
213C2×C5×D4—22no—
214C2×C5×D4—22no—
215C2×C5×D4—42no—
216C2×C5×D4—42no—
217C2×C5×D4C2×C3×C414yes—
218C2×C5×D4C2×C3×C418yescomplemented
219C22×C4×C5C23×C311yescharacteristic
220C22×C4×C5C23×C312yes—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—42no—
224C22×Dic5—42no—
225C22×Dic5—42no—
226C22×Dic5C3×D414yescomplemented
227C22×Dic5C23×C312yes—
228C22×Dic5C23×C311yescharacteristic
229C22×Dic5C23×C311yescharacteristic
230C22×Dic5C23×C312yes—
231C22×Dic5C23×C311yescharacteristic
232C22×Dic5C23×C311yescharacteristic
233C5×C22⋊C4C2×C3×C418yescomplemented
234C5×C22⋊C4C2×C3×C414yescomplemented
235C22⋊Dic5—22no—
236C22⋊Dic5—22no—
237C22⋊Dic5—24no—
238C22⋊Dic5—24no—
239C22⋊Dic5—22no—
240C22⋊Dic5—42no—
241C22⋊Dic5—42no—
242C22⋊Dic5—42no—
243C4⋊Dic5—22no—
244C4⋊Dic5—42no—
245C4×Dic5—22no—
246C4×Dic5—42no—
247C2×#120C3×D511yescharacteristic
248C2×C4×D4—51no—
249C22×C22⋊C4—51no—
250#390—52no—
251#388—52no—
252#388—52no—
253#386—52no—
254#386—51no—
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—22no—
263C22×C3×C5—24no—
264C22×C3×C5—24no—
265C22×C3×C5—24no—
266C22×C3×C5—24no—
267C22×C3×C5—416no—
268C22×C3×C5—41no—
269C22×C3×C5—42no—
270C22×C3×C5—41no—
271C22×C3×C5—42no—
272C22×C3×C5—42no—
273C22×C3×C5—42no—
274C22×C3×C5—42no—
275C22×C3×C5C4×D414yes—
276C22×C3×C5C23×C411yescharacteristic
277C22×C3×C5C22×D411yescharacteristic
278C22×C3×C5C2×#4111yescharacteristic
279C22×C3×C5H(5,𝔽2)12yes—
280C22×C3×C5H(5,𝔽2)12yes—
281C3×C4×C5—22no—
282C3×C4×C5—24no—
283C3×Dic5—22no—
284C3×Dic5—22no—
285C3×Dic5—41no—
286C3×Dic5—41no—
287C3×Dic5—42no—
288C3×Dic5—42no—
289C24×C3—22no—
290C24×C3—22no—
291C24×C3—42no—
292C24×C3—42no—
293C24×C3C2×Dic514yescomplemented
294C24×C3C22×D512yes—
295C24×C3C22×D511yescharacteristic
296C24×C3C22×D511yescharacteristic
297C2×C3×D4—22no—
298C2×C3×D4—22no—
299C2×C3×D4—42no—
300C2×C3×D4—42no—
301C2×C3×D4C2×Dic514yes—
302C2×C3×D4C2×Dic518yescomplemented
303C22×C3×C4—51no—
304C22×C3×C4—51no—
305C22×C3×C4—54no—
306C22×C3×C4—52no—
307C22×C3×C4—52no—
308C22×C3×C4—51no—
309C22×C3×C4—51no—
310C22×C3×C4—102no—
311C22×C3×C4—102no—
312C22×C3×C4—202no—
313C22×C3×C4—202no—
314C22×C3×C4—202no—
315C22×C3×C4C22×D511yescharacteristic
316C22×C3×C4C22×D512yes—
317C3×C4⋊C4—102no—
318C3×C4⋊C4—202no—
319C3×C22⋊C4—104no—
320C3×C22⋊C4—104no—
321C3×C22⋊C4—102no—
322C3×C22⋊C4—102no—
323C3×C22⋊C4—102no—
324C3×C22⋊C4—202no—
325C3×C22⋊C4—202no—
326C3×C22⋊C4—202no—
327C3×C22⋊C4C2×Dic518yescomplemented
328C3×C22⋊C4C2×Dic514yescomplemented
329C3×C42—102no—
330C3×C42—202no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—28no—
334C23×C5—22no—
335C23×C5—21no—
336C23×C5—21no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—48no—
345C23×C5—44no—
346C23×C5—44no—
347C23×C5—48no—
348C23×C5C22×C3×C414yes—
349C23×C5C22×C3×C412yes—
350C23×C5C22×C3×C412yes—
351C23×C5C2×C3×D412yes—
352C23×C5C3×#4112yes—
353C23×C5C24×C311yescharacteristic
354C5×D4—28no—
355C5×D4—48no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5C22×C3×C412yes—
361C2×C4×C5C22×C3×C414yes—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—21no—
365C2×Dic5—21no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—44no—
375C2×Dic5—44no—
376C2×Dic5—44no—
377C2×Dic5C2×C3×D412yes—
378C2×Dic5C2×C3×D412yes—
379C25C2×C3×D511yescharacteristic
380C22×D4C2×C3×D511yescharacteristic
381C22×D4C2×C3×D512yes—
382C23×C4—51no—
383C23×C4—51no—
384C23×C4—51no—
385#120C3×Dic518yescomplemented
386C4×D4—104no—
387C2×C4⋊C4—51no—
388C2×C4⋊C4—52no—
389C2×C22⋊C4—52no—
390C2×C22⋊C4—52no—
391C2×C22⋊C4—51no—
392C2×C22⋊C4—51no—
393C2×C22⋊C4—51no—
394C2×C22⋊C4—52no—
395C2×C22⋊C4—52no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—104no—
398C2×C22⋊C4C2×C3×D511yescharacteristic
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—42no—
407C2×C3×C5—44no—
408C2×C3×C5C2×C4×D411yescharacteristic
409C2×C3×C5#51812yes—
410C2×C3×C5#53411yescharacteristic
411C2×C3×C5#53511yescharacteristic
412C2×C3×C5#53812yes—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—28no—
426C23×C3—48no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—48no—
430C23×C3D4×D512yes—
431C23×C3#71112yes—
432C23×C3C22×Dic514yes—
433C23×C3C22×Dic512yes—
434C23×C3C22×Dic512yes—
435C23×C3C23×D511yescharacteristic
436C3×D4—28no—
437C3×D4—48no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—52no—
443C2×C3×C4—52no—
444C2×C3×C4—102no—
445C2×C3×C4—102no—
446C2×C3×C4—101no—
447C2×C3×C4—102no—
448C2×C3×C4—101no—
449C2×C3×C4—102no—
450C2×C3×C4—102no—
451C2×C3×C4—102no—
452C2×C3×C4—102no—
453C2×C3×C4—102no—
454C2×C3×C4—102no—
455C2×C3×C4—102no—
456C2×C3×C4—204no—
457C2×C3×C4—204no—
458C2×C3×C4—204no—
459C2×C3×C4C22×Dic512yes—
460C2×C3×C4C22×Dic514yes—
461C22×C5—24no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—24no—
465C22×C5—22no—
466C22×C5—24no—
467C22×C5—24no—
468C22×C5—24no—
469C22×C5—24no—
470C22×C5—416no—
471C22×C5—41no—
472C22×C5—42no—
473C22×C5—41no—
474C22×C5—42no—
475C22×C5—42no—
476C22×C5—42no—
477C22×C5—42no—
478C22×C5C3×C4×D414yes—
479C22×C5C23×C3×C411yescharacteristic
480C22×C5C22×C3×D411yescharacteristic
481C22×C5C2×C3×#4111yescharacteristic
482C22×C5C3×H(5,𝔽2)12yes—
483C22×C5C3×H(5,𝔽2)12yes—
484C4×C5—22no—
485C4×C5—24no—
486Dic5—22no—
487Dic5—22no—
488Dic5—41no—
489Dic5—41no—
490Dic5—42no—
491Dic5—42no—
492C24—22no—
493C24—22no—
494C24—42no—
495C24—42no—
496C24C2×C3×Dic514yescomplemented
497C24C22×C3×D512yes—
498C24C22×C3×D511yescharacteristic
499C24C22×C3×D511yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4C2×C3×Dic514yes—
505C2×D4C2×C3×Dic518yescomplemented
506C22×C4—51no—
507C22×C4—51no—
508C22×C4—54no—
509C22×C4—52no—
510C22×C4—52no—
511C22×C4—51no—
512C22×C4—51no—
513C22×C4—102no—
514C22×C4—102no—
515C22×C4—202no—
516C22×C4—202no—
517C22×C4—202no—
518C22×C4C22×C3×D511yescharacteristic
519C22×C4C22×C3×D512yes—
520C4⋊C4—102no—
521C4⋊C4—202no—
522C22⋊C4—104no—
523C22⋊C4—104no—
524C22⋊C4—102no—
525C22⋊C4—102no—
526C22⋊C4—102no—
527C22⋊C4—202no—
528C22⋊C4—202no—
529C22⋊C4—202no—
530C22⋊C4C2×C3×Dic518yescomplemented
531C22⋊C4C2×C3×Dic514yescomplemented
532C42—102no—
533C42—202no—
534C3×C5#232111yescharacteristic, complemented, Hall
535C22×C3—24no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—24no—
539C22×C3—22no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—416no—
545C22×C3—41no—
546C22×C3—42no—
547C22×C3—41no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3D4×Dic514yes—
553C22×C3C2×D4×D511yescharacteristic
554C22×C3C2×#71111yescharacteristic
555C22×C3#414412yes—
556C22×C3#414412yes—
557C22×C3C23×Dic511yescharacteristic
558C3×C4—22no—
559C3×C4—24no—
560C3×C4—102no—
561C3×C4—102no—
562C3×C4—201no—
563C3×C4—201no—
564C3×C4—202no—
565C3×C4—202no—
566C2×C5—24no—
567C2×C5—44no—
568C2×C5—42no—
569C2×C5C2×C3×C4×D411yescharacteristic
570C2×C5C3×#51812yes—
571C2×C5C3×#53411yescharacteristic
572C2×C5C3×#53511yescharacteristic
573C2×C5C3×#53812yes—
574C23—22no—
575C23—22no—
576C23—28no—
577C23—22no—
578C23—21no—
579C23—21no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—48no—
588C23—44no—
589C23—44no—
590C23—48no—
591C23C3×D4×D512yes—
592C23C3×#71112yes—
593C23C22×C3×Dic514yes—
594C23C22×C3×Dic512yes—
595C23C22×C3×Dic512yes—
596C23C23×C3×D511yescharacteristic
597D4—28no—
598D4—48no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—52no—
604C2×C4—52no—
605C2×C4—102no—
606C2×C4—102no—
607C2×C4—101no—
608C2×C4—102no—
609C2×C4—101no—
610C2×C4—102no—
611C2×C4—102no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—204no—
618C2×C4—204no—
619C2×C4—204no—
620C2×C4C22×C3×Dic512yes—
621C2×C4C22×C3×Dic514yes—
622C2×C3—24no—
623C2×C3—44no—
624C2×C3—42no—
625C2×C3#6592311yescharacteristic
626C2×C3#6592611yescharacteristic
627C2×C3#6592712yes—
628C2×C3C2×D4×Dic511yescharacteristic
629C2×C3#6613212yes—
630C5C3×#232111yescharacteristic, complemented, Sylow
631C22—24no—
632C22—22no—
633C22—22no—
634C22—24no—
635C22—22no—
636C22—24no—
637C22—24no—
638C22—24no—
639C22—24no—
640C22—416no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—41no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22C3×D4×Dic514yes—
649C22C2×C3×D4×D511yescharacteristic
650C22C2×C3×#71111yescharacteristic
651C22C3×#414412yes—
652C22C3×#414412yes—
653C22C23×C3×Dic511yescharacteristic
654C4—22no—
655C4—24no—
656C4—102no—
657C4—102no—
658C4—201no—
659C4—202no—
660C4—201no—
661C4—202no—
662C3#1061430911yescharacteristic, direct product factor, Sylow
663C2—24no—
664C2—44no—
665C2—42no—
666C2C3×#6592311yescharacteristic
667C2C3×#6592611yescharacteristic
668C2C3×#6592712yes—
669C2C2×C3×D4×Dic511yescharacteristic
670C2C3×#6613212yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
Fitting, prime radicalC2×C3×C5×#120C2
socleC23×C3×C5C24
cosocleC23×C5C24×C3
hypercenterC2×C3×#120D5
hypocenterC5C3×#2321
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
2. C22×C3×C22⋊Dic5C2semidirect
3. C2×C3×D4×Dic5C2semidirect
4. C3×#65536C2semidirect
5. C3×#65510C2semidirect
6. C3×#65509C2semidirect
7. C3×#65509C2semidirect
8. C3×#65240C2semidirect
9. C3×#65240C2semidirect
10. C3×#65239C2semidirect
11. C3×C22⋊C4×Dic5C2semidirect
12. #10614309C3direct (N × H)
18. C23×C3×Dic5C22semidirect
19. C3×C5×#120C4semidirect
29. C2×C3×C22⋊Dic5C22semidirect
30. C2×C3×C22⋊Dic5C22semidirect
32. C2×C3×C4⋊Dic5C22semidirect
33. C2×C3×C4⋊Dic5C22semidirect
34. C2×C3×C4×Dic5C22semidirect
35. C2×C3×C4×Dic5C22semidirect
36. C3×#3963C22semidirect
37. C3×#3963C22semidirect
38. C3×#3963C22semidirect
41. C22×C22⋊Dic5C2×C3semidirect
42. C2×D4×Dic5C2×C3semidirect
43. #65536C2×C3semidirect
44. #65510C2×C3semidirect
45. #65509C2×C3semidirect
46. #65509C2×C3semidirect
47. #65240C2×C3semidirect
48. #65240C2×C3semidirect
49. #65239C2×C3semidirect
50. C22⋊C4×Dic5C2×C3semidirect
55. C24×C3×C5C2×C4semidirect
64. C2×C3×C5×D4C2×C4semidirect
72. C22×C3×Dic5D4semidirect
79. C3×C5×C22⋊C4C2×C4semidirect
80. C3×C5×C22⋊C4C2×C4semidirect
109. C23×Dic5C22×C3semidirect
110. C5×#120C3×C4semidirect
120. C2×C22⋊Dic5C22×C3semidirect
121. C2×C22⋊Dic5C22×C3semidirect
123. C2×C4⋊Dic5C22×C3semidirect
124. C2×C4⋊Dic5C22×C3semidirect
125. C2×C4×Dic5C22×C3semidirect
126. C2×C4×Dic5C22×C3semidirect
127. #3963C22×C3semidirect
128. #3963C22×C3semidirect
129. #3963C22×C3semidirect
185. C3×#120Dic5semidirect
209. C24×C5C2×C3×C4semidirect
218. C2×C5×D4C2×C3×C4semidirect
226. C22×Dic5C3×D4semidirect
233. C5×C22⋊C4C2×C3×C4semidirect
234. C5×C22⋊C4C2×C3×C4semidirect
293. C24×C3C2×Dic5semidirect
302. C2×C3×D4C2×Dic5semidirect
327. C3×C22⋊C4C2×Dic5semidirect
328. C3×C22⋊C4C2×Dic5semidirect
385. #120C3×Dic5semidirect
496. C24C2×C3×Dic5semidirect
505. C2×D4C2×C3×Dic5semidirect
530. C22⋊C4C2×C3×Dic5semidirect
531. C22⋊C4C2×C3×Dic5semidirect
534. C3×C5#2321semidirect
630. C5C3×#2321semidirect
662. C3#10614309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1202
C22×C3×C22⋊Dic52
C2×C3×D4×Dic52
C3×#655362
C3×#655102
C3×#655092
C3×#652402
C3×#652392
C3×C22⋊C4×Dic52
#106143093
C3×#23215