Finite Group Databasebeta

← C3×#10605178 #14324439

Subgroups — C3×#10605178 #14324439

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4024C211yesmaximal, characteristic
2C3×C4×C5×C22⋊C4C211yesmaximal, characteristic
3C3×C4×C22⋊Dic5C211yesmaximal, characteristic
4C2×C3×#3963C211yesmaximal, characteristic
5C3×#65239C211yesmaximal, characteristic
6C3×#65235C211yesmaximal, characteristic
7C3×#65231C211yesmaximal, characteristic
8C3×#65222C211yesmaximal, characteristic, complemented
9C3×#65222C211yesmaximal, characteristic, complemented
10C3×#65218C211yesmaximal, characteristic, complemented
11C3×#65217C211yesmaximal, characteristic, complemented
12C3×#64944C211yesmaximal, characteristic, complemented
13C3×#64943C211yesmaximal, characteristic, complemented
14C3×#64936C211yesmaximal, characteristic, complemented
15C3×#64935C211yesmaximal, characteristic, complemented
16#10605178C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C23×C3×Dic5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×C3×C42×C5C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C3×#4024C418yescomplemented
39C3×C5×#95C2211yescharacteristic
40C3×C5×#95C2211yescharacteristic
41C3×#3963C2211yescharacteristic
42C3×#3963C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#2329—51nomaximal, Hall
54C2×#4024C2×C311yescharacteristic
55C4×C5×C22⋊C4C2×C311yescharacteristic
56C4×C22⋊Dic5C2×C311yescharacteristic
57C2×#3963C2×C311yescharacteristic
58#65239C2×C311yescharacteristic
59#65235C2×C311yescharacteristic
60#65231C2×C311yescharacteristic
61#65222C2×C311yescharacteristic, complemented
62#65222C2×C311yescharacteristic, complemented
63#65218C2×C311yescharacteristic, complemented
64#65217C2×C311yescharacteristic, complemented
65#64944C2×C311yescharacteristic, complemented
66#64943C2×C311yescharacteristic, complemented
67#64936C2×C311yescharacteristic, complemented
68#64935C2×C311yescharacteristic, complemented
69C24×C3×C5C2311yescharacteristic
70C22×C3×C4×C5—41no—
71C22×C3×C4×C5—41no—
72C22×C3×C4×C5Q814yescomplemented
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×Dic5—22no—
80C22×C3×Dic5—41no—
81C22×C3×Dic5—41no—
82C22×C3×Dic5—41no—
83C22×C3×Dic5—41no—
84C22×C3×Dic5C2×C414yes—
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C2×C3×Dic10—41no—
94C2×C3×Dic10—41no—
95C2×C3×Dic10C2×C414yescomplemented
96C3×C5×C22⋊C4—22no—
97C3×C5×C22⋊C4C2×C414yes—
98C3×C42×C5—41no—
99C3×C42×C5—41no—
100C3×C22⋊Dic5—22no—
101C3×C22⋊Dic5C2×C414yes—
102C3×C4⋊Dic5—41no—
103C3×C4⋊Dic5—41no—
104C3×C4⋊Dic5C2×C414yescomplemented
105C3×#683—41no—
106C3×#683—41no—
107C3×#683—41no—
108C3×#683—41no—
109C3×#683C2×C414yescomplemented
110C3×#683C2×C414yescomplemented
111C3×C4×Dic5—41no—
112C3×C4×Dic5—41no—
113C2×C3×C22⋊Q8—51no—
114C3×#391—51no—
115C3×#391—51no—
116C3×#389—51no—
117C3×#389—51no—
118C3×#387—51no—
119C3×#387—51no—
120C3×#387—51no—
121C3×#387—51no—
122C3×#385—51no—
123C3×#385—51no—
124C3×#380—51no—
125C3×C4×C22⋊C4—51no—
126C3×C4×C22⋊C4D511yescharacteristic
127C2×C3×#95—51no—
128C23×C4×C5C22×C311yescharacteristic
129C23×Dic5C22×C311yescharacteristic
130C23×Dic5C22×C311yescharacteristic
131C22×Dic10C22×C311yescharacteristic
132C2×C5×C22⋊C4C22×C311yescharacteristic
133C2×C5×C22⋊C4C22×C311yescharacteristic
134C2×C42×C5C22×C311yescharacteristic
135C2×C42×C5C22×C311yescharacteristic
136C2×C22⋊Dic5C22×C311yescharacteristic
137C2×C22⋊Dic5C22×C311yescharacteristic
138C2×C4⋊Dic5C22×C311yescharacteristic
139C2×C4⋊Dic5C22×C311yescharacteristic
140C2×C4⋊Dic5C22×C311yescharacteristic
141C2×#683C22×C311yescharacteristic
142C2×#683C22×C311yescharacteristic
143C2×#683C22×C311yescharacteristic
144C2×#683C22×C311yescharacteristic
145C2×#683C22×C311yescharacteristic
146C2×#683C22×C311yescharacteristic
147C2×C4×Dic5C22×C311yescharacteristic
148C2×C4×Dic5C22×C311yescharacteristic
149#4024C3×C418yescomplemented
150C5×#95C22×C311yescharacteristic
151C5×#95C22×C311yescharacteristic
152#3963C22×C311yescharacteristic
153#3963C22×C311yescharacteristic
154#3963C22×C311yescharacteristic
155#3963C22×C311yescharacteristic
156#3963C22×C311yescharacteristic
157#3963C22×C311yescharacteristic
158#3963C22×C311yescharacteristic
159#3963C22×C311yescharacteristic
160#3963C22×C311yescharacteristic
161#3963C22×C311yescharacteristic
162#3963C22×C311yescharacteristic
163#3963C22×C311yescharacteristic
164#2329—51noSylow
165C23×C3×C5—21no—
166C23×C3×C5—21no—
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5C22×C412yes—
170C23×C3×C5C2×Q812yes—
171C23×C3×C5#4112yes—
172C23×C3×C5C2411yescharacteristic
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—44no—
188C2×C3×C4×C5C22×C412yes—
189C2×C3×C4×C5C22×C412yes—
190C2×C3×C4×C5C2×Q812yes—
191C2×C3×C4×C5C2×Q812yes—
192C2×C3×Dic5—21no—
193C2×C3×Dic5—21no—
194C2×C3×Dic5—21no—
195C2×C3×Dic5—21no—
196C2×C3×Dic5—21no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—44no—
213C2×C3×Dic5—44no—
214C2×C3×Dic5C22×C412yes—
215C2×C3×Dic5C22×C412yes—
216C2×C3×Dic5C22×C412yes—
217C2×C3×Dic5C22×C412yes—
218C3×Dic10—44no—
219C22×C3×Q8—51no—
220C23×C3×C4—51no—
221C23×C3×C4—51no—
222C23×C3×C4C2×D511yescharacteristic
223C3×C22⋊Q8—58no—
224C2×C3×C4⋊C4—51no—
225C2×C3×C4⋊C4—51no—
226C2×C3×C4⋊C4—51no—
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—51no—
229C2×C3×C4⋊C4—51no—
230C2×C3×C4⋊C4—51no—
231C2×C3×C4⋊C4—51no—
232C2×C3×C4⋊C4—51no—
233C2×C3×C22⋊C4—51no—
234C2×C3×C22⋊C4—51no—
235C2×C3×C22⋊C4C2×D511yescharacteristic
236C2×C3×C22⋊C4C2×D511yescharacteristic
237C2×C3×C42—51no—
238C2×C3×C42—51no—
239C2×C3×C42C2×D511yescharacteristic
240C2×C3×C42C2×D511yescharacteristic
241C3×#95—51no—
242C3×#95—51no—
243C3×#95—51no—
244C3×#95—51no—
245C3×#95—51no—
246C3×#95—51no—
247C3×#95—51no—
248C3×#95—51no—
249C3×#95—51no—
250C3×#95—51no—
251C3×#95—51no—
252C3×#95—51no—
253C3×#95C2×D511yescharacteristic
254C3×#95C2×D511yescharacteristic
255C24×C5C23×C311yescharacteristic
256C22×C4×C5—41no—
257C22×C4×C5—41no—
258C22×C4×C5C3×Q814yescomplemented
259C22×C4×C5C23×C311yescharacteristic
260C22×C4×C5C23×C311yescharacteristic
261C22×C4×C5C23×C311yescharacteristic
262C22×C4×C5C23×C311yescharacteristic
263C22×C4×C5C23×C311yescharacteristic
264C22×C4×C5C23×C311yescharacteristic
265C22×Dic5—22no—
266C22×Dic5—41no—
267C22×Dic5—41no—
268C22×Dic5—41no—
269C22×Dic5—41no—
270C22×Dic5C2×C3×C414yes—
271C22×Dic5C23×C311yescharacteristic
272C22×Dic5C23×C311yescharacteristic
273C22×Dic5C23×C311yescharacteristic
274C22×Dic5C23×C311yescharacteristic
275C22×Dic5C23×C311yescharacteristic
276C22×Dic5C23×C311yescharacteristic
277C22×Dic5C23×C311yescharacteristic
278C22×Dic5C23×C311yescharacteristic
279C2×Dic10—41no—
280C2×Dic10—41no—
281C2×Dic10C2×C3×C414yescomplemented
282C5×C22⋊C4—22no—
283C5×C22⋊C4C2×C3×C414yes—
284C42×C5—41no—
285C42×C5—41no—
286C22⋊Dic5—22no—
287C22⋊Dic5C2×C3×C414yes—
288C4⋊Dic5—41no—
289C4⋊Dic5—41no—
290C4⋊Dic5C2×C3×C414yescomplemented
291#683—41no—
292#683—41no—
293#683—41no—
294#683—41no—
295#683C2×C3×C414yescomplemented
296#683C2×C3×C414yescomplemented
297C4×Dic5—41no—
298C4×Dic5—41no—
299C2×C22⋊Q8—51no—
300#391—51no—
301#391—51no—
302#389—51no—
303#389—51no—
304#387—51no—
305#387—51no—
306#387—51no—
307#387—51no—
308#385—51no—
309#385—51no—
310#380—51no—
311C4×C22⋊C4—51no—
312C4×C22⋊C4C3×D511yescharacteristic
313C2×#95—51no—
314C22×C3×C5—22no—
315C22×C3×C5—22no—
316C22×C3×C5—22no—
317C22×C3×C5—22no—
318C22×C3×C5—22no—
319C22×C3×C5—22no—
320C22×C3×C5C4×Q814yes—
321C22×C3×C5C23×C411yescharacteristic
322C22×C3×C5C22×Q811yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C5H(5,𝔽2)11yescharacteristic
325C22×C3×C5H(5,𝔽2)11yescharacteristic
326C22×C3×C5H(5,𝔽2)11yescharacteristic
327C22×C3×C52−1+411yescharacteristic
328C3×C4×C5—22no—
329C3×C4×C5—22no—
330C3×C4×C5—22no—
331C3×C4×C5—22no—
332C3×C4×C5—41no—
333C3×C4×C5—41no—
334C3×Dic5—22no—
335C3×Dic5—22no—
336C3×Dic5—22no—
337C3×Dic5—22no—
338C3×Dic5—41no—
339C3×Dic5—41no—
340C3×Dic5—41no—
341C3×Dic5—41no—
342C24×C3C22×D511yescharacteristic
343C2×C3×Q8—54no—
344C2×C3×Q8—201no—
345C2×C3×Q8—201no—
346C22×C3×C4—41no—
347C22×C3×C4—41no—
348C22×C3×C4—51no—
349C22×C3×C4—51no—
350C22×C3×C4—51no—
351C22×C3×C4—51no—
352C22×C3×C4—54no—
353C22×C3×C4—51no—
354C22×C3×C4—51no—
355C22×C3×C4—51no—
356C22×C3×C4—51no—
357C22×C3×C4—102no—
358C22×C3×C4—201no—
359C22×C3×C4—201no—
360C22×C3×C4—201no—
361C22×C3×C4—201no—
362C22×C3×C4Dic1014yescomplemented
363C22×C3×C4C22×D511yescharacteristic
364C22×C3×C4C22×D511yescharacteristic
365C22×C3×C4C22×D511yescharacteristic
366C22×C3×C4C22×D511yescharacteristic
367C22×C3×C4C22×D511yescharacteristic
368C22×C3×C4C22×D511yescharacteristic
369C3×C4⋊C4—54no—
370C3×C4⋊C4—54no—
371C3×C4⋊C4—54no—
372C3×C4⋊C4—201no—
373C3×C4⋊C4—201no—
374C3×C4⋊C4—201no—
375C3×C4⋊C4—201no—
376C3×C4⋊C4—201no—
377C3×C4⋊C4—201no—
378C3×C22⋊C4—22no—
379C3×C22⋊C4—54no—
380C3×C22⋊C4—102no—
381C3×C22⋊C4C4×D514yes—
382C3×C42—41no—
383C3×C42—41no—
384C3×C42—201no—
385C3×C42—201no—
386C23×C5—21no—
387C23×C5—21no—
388C23×C5—21no—
389C23×C5—21no—
390C23×C5C22×C3×C412yes—
391C23×C5C2×C3×Q812yes—
392C23×C5C3×#4112yes—
393C23×C5C24×C311yescharacteristic
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—44no—
409C2×C4×C5C22×C3×C412yes—
410C2×C4×C5C22×C3×C412yes—
411C2×C4×C5C2×C3×Q812yes—
412C2×C4×C5C2×C3×Q812yes—
413C2×Dic5—21no—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—21no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—21no—
429C2×Dic5—21no—
430C2×Dic5—21no—
431C2×Dic5—21no—
432C2×Dic5—21no—
433C2×Dic5—44no—
434C2×Dic5—44no—
435C2×Dic5C22×C3×C412yes—
436C2×Dic5C22×C3×C412yes—
437C2×Dic5C22×C3×C412yes—
438C2×Dic5C22×C3×C412yes—
439Dic10—44no—
440C22×Q8—51no—
441C23×C4—51no—
442C23×C4—51no—
443C23×C4C2×C3×D511yescharacteristic
444C22⋊Q8—58no—
445C2×C4⋊C4—51no—
446C2×C4⋊C4—51no—
447C2×C4⋊C4—51no—
448C2×C4⋊C4—51no—
449C2×C4⋊C4—51no—
450C2×C4⋊C4—51no—
451C2×C4⋊C4—51no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—51no—
454C2×C22⋊C4—51no—
455C2×C22⋊C4—51no—
456C2×C22⋊C4C2×C3×D511yescharacteristic
457C2×C22⋊C4C2×C3×D511yescharacteristic
458C2×C42—51no—
459C2×C42—51no—
460C2×C42C2×C3×D511yescharacteristic
461C2×C42C2×C3×D511yescharacteristic
462#95—51no—
463#95—51no—
464#95—51no—
465#95—51no—
466#95—51no—
467#95—51no—
468#95—51no—
469#95—51no—
470#95—51no—
471#95—51no—
472#95—51no—
473#95—51no—
474#95C2×C3×D511yescharacteristic
475#95C2×C3×D511yescharacteristic
476C2×C3×C5—24no—
477C2×C3×C5C2×C4×Q811yescharacteristic
478C2×C3×C5#51811yescharacteristic
479C2×C3×C5#52011yescharacteristic
480C2×C3×C5#53811yescharacteristic
481C2×C3×C5#53911yescharacteristic
482C2×C3×C5#54311yescharacteristic
483C2×C3×C5#54411yescharacteristic
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3C2×Dic1012yes—
489C23×C3C2×C4×D512yes—
490C23×C3#70912yes—
491C23×C3C23×D511yescharacteristic
492C3×Q8—204no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—44no—
508C2×C3×C4—52no—
509C2×C3×C4—52no—
510C2×C3×C4—52no—
511C2×C3×C4—52no—
512C2×C3×C4—101no—
513C2×C3×C4—101no—
514C2×C3×C4—101no—
515C2×C3×C4—101no—
516C2×C3×C4—101no—
517C2×C3×C4—101no—
518C2×C3×C4—101no—
519C2×C3×C4—101no—
520C2×C3×C4—101no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—204no—
533C2×C3×C4—204no—
534C2×C3×C4C2×Dic1012yes—
535C2×C3×C4C2×Dic1012yes—
536C2×C3×C4C2×C4×D512yes—
537C2×C3×C4C2×C4×D512yes—
538C22×C5—22no—
539C22×C5—22no—
540C22×C5—22no—
541C22×C5—22no—
542C22×C5—22no—
543C22×C5—22no—
544C22×C5C3×C4×Q814yes—
545C22×C5C23×C3×C411yescharacteristic
546C22×C5C22×C3×Q811yescharacteristic
547C22×C5C2×C3×#4111yescharacteristic
548C22×C5C3×H(5,𝔽2)11yescharacteristic
549C22×C5C3×H(5,𝔽2)11yescharacteristic
550C22×C5C3×H(5,𝔽2)11yescharacteristic
551C22×C5C3×2−1+411yescharacteristic
552C4×C5—22no—
553C4×C5—22no—
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—41no—
557C4×C5—41no—
558Dic5—22no—
559Dic5—22no—
560Dic5—22no—
561Dic5—22no—
562Dic5—41no—
563Dic5—41no—
564Dic5—41no—
565Dic5—41no—
566C24C22×C3×D511yescharacteristic
567C2×Q8—54no—
568C2×Q8—201no—
569C2×Q8—201no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—51no—
573C22×C4—51no—
574C22×C4—51no—
575C22×C4—51no—
576C22×C4—54no—
577C22×C4—51no—
578C22×C4—51no—
579C22×C4—51no—
580C22×C4—51no—
581C22×C4—102no—
582C22×C4—201no—
583C22×C4—201no—
584C22×C4—201no—
585C22×C4—201no—
586C22×C4C3×Dic1014yescomplemented
587C22×C4C22×C3×D511yescharacteristic
588C22×C4C22×C3×D511yescharacteristic
589C22×C4C22×C3×D511yescharacteristic
590C22×C4C22×C3×D511yescharacteristic
591C22×C4C22×C3×D511yescharacteristic
592C22×C4C22×C3×D511yescharacteristic
593C4⋊C4—54no—
594C4⋊C4—54no—
595C4⋊C4—54no—
596C4⋊C4—201no—
597C4⋊C4—201no—
598C4⋊C4—201no—
599C4⋊C4—201no—
600C4⋊C4—201no—
601C4⋊C4—201no—
602C22⋊C4—22no—
603C22⋊C4—54no—
604C22⋊C4—102no—
605C22⋊C4C3×C4×D514yes—
606C42—41no—
607C42—41no—
608C42—201no—
609C42—201no—
610C3×C5#232911yescharacteristic, complemented, Hall
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3C4×Dic1014yes—
618C22×C3C22×Dic1011yescharacteristic
619C22×C3C22×C4×D511yescharacteristic
620C22×C3C2×#70911yescharacteristic
621C22×C3#414411yescharacteristic
622C22×C3#414411yescharacteristic
623C22×C3#414911yescharacteristic
624C22×C3#415011yescharacteristic
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—102no—
632C3×C4—102no—
633C3×C4—102no—
634C3×C4—102no—
635C3×C4—201no—
636C3×C4—201no—
637C3×C4—201no—
638C3×C4—201no—
639C2×C5—24no—
640C2×C5C2×C3×C4×Q811yescharacteristic
641C2×C5C3×#51811yescharacteristic
642C2×C5C3×#52011yescharacteristic
643C2×C5C3×#53811yescharacteristic
644C2×C5C3×#53911yescharacteristic
645C2×C5C3×#54311yescharacteristic
646C2×C5C3×#54411yescharacteristic
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23C2×C3×Dic1012yes—
652C23C2×C3×C4×D512yes—
653C23C3×#70912yes—
654C23C23×C3×D511yescharacteristic
655Q8—204no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—44no—
671C2×C4—52no—
672C2×C4—52no—
673C2×C4—52no—
674C2×C4—52no—
675C2×C4—101no—
676C2×C4—101no—
677C2×C4—101no—
678C2×C4—101no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—101no—
691C2×C4—101no—
692C2×C4—101no—
693C2×C4—101no—
694C2×C4—101no—
695C2×C4—204no—
696C2×C4—204no—
697C2×C4C2×C3×Dic1012yes—
698C2×C4C2×C3×Dic1012yes—
699C2×C4C2×C3×C4×D512yes—
700C2×C4C2×C3×C4×D512yes—
701C2×C3—24no—
702C2×C3C2×C4×Dic1011yescharacteristic
703C2×C3#6581711yescharacteristic
704C2×C3#6585311yescharacteristic
705C2×C3#6587911yescharacteristic
706C2×C3#6588011yescharacteristic
707C2×C3#6589411yescharacteristic
708C2×C3#6589811yescharacteristic
709C5C3×#232911yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22C3×C4×Dic1014yes—
717C22C22×C3×Dic1011yescharacteristic
718C22C22×C3×C4×D511yescharacteristic
719C22C2×C3×#70911yescharacteristic
720C22C3×#414411yescharacteristic
721C22C3×#414411yescharacteristic
722C22C3×#414911yescharacteristic
723C22C3×#415011yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—41no—
729C4—41no—
730C4—102no—
731C4—102no—
732C4—102no—
733C4—102no—
734C4—201no—
735C4—201no—
736C4—201no—
737C4—201no—
738C3#1060517811yescharacteristic, direct product factor, Sylow
739C2—24no—
740C2C2×C3×C4×Dic1011yescharacteristic
741C2C3×#6581711yescharacteristic
742C2C3×#6585311yescharacteristic
743C2C3×#6587911yescharacteristic
744C2C3×#6588011yescharacteristic
745C2C3×#6589411yescharacteristic
746C2C3×#6589811yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#2329
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C3×#65222C2semidirect
9. C3×#65222C2semidirect
10. C3×#65218C2semidirect
11. C3×#65217C2semidirect
12. C3×#64944C2semidirect
13. C3×#64943C2semidirect
14. C3×#64936C2semidirect
15. C3×#64935C2semidirect
16. #10605178C3direct (N × H)
38. C3×#4024C4semidirect
61. #65222C2×C3semidirect
62. #65222C2×C3semidirect
63. #65218C2×C3semidirect
64. #65217C2×C3semidirect
65. #64944C2×C3semidirect
66. #64943C2×C3semidirect
67. #64936C2×C3semidirect
68. #64935C2×C3semidirect
72. C22×C3×C4×C5Q8semidirect
95. C2×C3×Dic10C2×C4semidirect
104. C3×C4⋊Dic5C2×C4semidirect
109. C3×#683C2×C4semidirect
110. C3×#683C2×C4semidirect
149. #4024C3×C4semidirect
258. C22×C4×C5C3×Q8semidirect
281. C2×Dic10C2×C3×C4semidirect
290. C4⋊Dic5C2×C3×C4semidirect
295. #683C2×C3×C4semidirect
296. #683C2×C3×C4semidirect
362. C22×C3×C4Dic10semidirect
586. C22×C4C3×Dic10semidirect
610. C3×C5#2329semidirect
709. C5C3×#2329semidirect
738. C3#10605178direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40242
C3×C4×C5×C22⋊C42
C3×C4×C22⋊Dic52
C2×C3×#39632
C3×#652392
C3×#652352
C3×#652312
C3×#652222
C3×#652182
C3×#652172
C3×#649442
C3×#649432
C3×#649362
C3×#649352
#106051783
C3×#23295