Finite Group Databasebeta

← C3×#10607031 #14324442

Subgroups — C3×#10607031 #14324442

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×#4043C211yesmaximal, characteristic
2C3×C5×#387C211yesmaximal, characteristic, complemented
3C3×#65278C211yesmaximal, characteristic
4C3×#65270C211yesmaximal, characteristic, complemented
5C3×#65262C211yesmaximal, characteristic, complemented
6C3×C4×#685C211yesmaximal, characteristic
7C3×#65217C211yesmaximal, characteristic, complemented
8C3×#64957C211yesmaximal, characteristic
9C3×#64956C211yesmaximal, characteristic
10C3×#64955C211yesmaximal, characteristic
11C3×D5×#95C211yesmaximal, characteristic
12C3×#64943C211yesmaximal, characteristic, complemented
13C3×#64942C211yesmaximal, characteristic, complemented
14C3×#64935C211yesmaximal, characteristic, complemented
15C3×#64935C211yesmaximal, characteristic, complemented
16#10607031C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×C3×#685C2211yescharacteristic
25C2×C3×#685C2211yescharacteristic
26C2×C3×#685C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C3×#4043C418yescomplemented
39C3×C5×#95C2211yescharacteristic
40C3×C5×#95C2211yescharacteristic
41C3×C5×#95C2211yescharacteristic
42C3×C5×#95C2211yescharacteristic
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×#4043C2×C311yescharacteristic
55C5×#387C2×C311yescharacteristic, complemented
56#65278C2×C311yescharacteristic
57#65270C2×C311yescharacteristic, complemented
58#65262C2×C311yescharacteristic, complemented
59C4×#685C2×C311yescharacteristic
60#65217C2×C311yescharacteristic, complemented
61#64957C2×C311yescharacteristic
62#64956C2×C311yescharacteristic
63#64955C2×C311yescharacteristic
64D5×#95C2×C311yescharacteristic
65#64943C2×C311yescharacteristic, complemented
66#64942C2×C311yescharacteristic, complemented
67#64935C2×C311yescharacteristic, complemented
68#64935C2×C311yescharacteristic, complemented
69C23×C3×D5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×C3×C4×D5—22no—
85C2×C3×C4×D5—41no—
86C2×C3×C4×D5—41no—
87C2×C3×C4×D5—41no—
88C2×C3×C4×D5—41no—
89C2×C3×C4×D5—41no—
90C2×C3×C4×D5—41no—
91C2×C3×C4×D5C2×C414yes—
92C2×C3×C4×D5Q814yescomplemented
93C2×C3×Dic10—41no—
94C2×C3×Dic10—41no—
95C2×C3×Dic10C2×C414yescomplemented
96C3×C5×C4⋊C4—41no—
97C3×C5×C4⋊C4C2×C414yescomplemented
98C3×C42×C5—41no—
99C3×#685—22no—
100C3×#685—22no—
101C3×#685C2×C414yes—
102C3×#685C2×C414yes—
103C3×C4⋊Dic5—41no—
104C3×C4⋊Dic5C2×C414yescomplemented
105C3×C4⋊Dic5C2×C414yescomplemented
106C3×#683—41no—
107C3×#683—41no—
108C3×#683—41no—
109C3×#683—41no—
110C3×C4×Dic5—41no—
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×#387D511yescharacteristic, complemented
122C3×#385—51no—
123C3×#385—51no—
124C3×#380—51no—
125C3×C4×C22⋊C4—51no—
126C3×C4×C22⋊C4—51no—
127C2×C3×#95—51no—
128C22×C4×D5C22×C311yescharacteristic
129C22×C4×D5C22×C311yescharacteristic
130C22×C4×D5C22×C311yescharacteristic
131C22×Dic10C22×C311yescharacteristic
132C2×C5×C4⋊C4C22×C311yescharacteristic
133C2×C5×C4⋊C4C22×C311yescharacteristic
134C2×C42×C5C22×C311yescharacteristic
135C2×#685C22×C311yescharacteristic
136C2×#685C22×C311yescharacteristic
137C2×#685C22×C311yescharacteristic
138C2×#685C22×C311yescharacteristic
139C2×C4⋊Dic5C22×C311yescharacteristic
140C2×C4⋊Dic5C22×C311yescharacteristic
141C2×C4⋊Dic5C22×C311yescharacteristic
142C2×#683C22×C311yescharacteristic
143C2×#683C22×C311yescharacteristic
144C2×#683C22×C311yescharacteristic
145C2×#683C22×C311yescharacteristic
146C2×C4×Dic5C22×C311yescharacteristic
147C2×C4×Dic5C22×C311yescharacteristic
148C2×C4×Dic5C22×C311yescharacteristic
149#4043C3×C418yescomplemented
150C5×#95C22×C311yescharacteristic
151C5×#95C22×C311yescharacteristic
152C5×#95C22×C311yescharacteristic
153C5×#95C22×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×C5C2411yescharacteristic
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5—21no—
169C22×C3×D5—21no—
170C22×C3×D5C22×C412yes—
171C22×C3×D5C2×Q812yes—
172C22×C3×D5#4112yes—
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—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C22×C412yes—
191C2×C3×C4×C5C22×C412yes—
192C2×C3×C4×C5C22×C412yes—
193C2×C3×C4×C5C2×Q812yes—
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×Dic5C22×C412yes—
212C2×C3×Dic5C22×C412yes—
213C2×C3×Dic5C22×C412yes—
214C2×C3×Dic5C2×Q812yes—
215C3×C4×D5—44no—
216C3×C4×D5—44no—
217C3×C4×D5—44no—
218C3×Dic10—44no—
219C22×C3×Q8—51no—
220C23×C3×C4—51no—
221C23×C3×C4—51no—
222C23×C3×C4—51no—
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⋊C4C2×D511yescharacteristic
232C2×C3×C4⋊C4C2×D511yescharacteristic
233C2×C3×C22⋊C4—51no—
234C2×C3×C22⋊C4—51no—
235C2×C3×C22⋊C4—51no—
236C2×C3×C22⋊C4—51no—
237C2×C3×C42—51no—
238C2×C3×C42—51no—
239C2×C3×C42—51no—
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×#95C2×D511yescharacteristic
252C3×#95C2×D511yescharacteristic
253C3×#95C2×D511yescharacteristic
254C3×#95C2×D511yescharacteristic
255C23×D5C23×C311yescharacteristic
256C22×C4×C5C23×C311yescharacteristic
257C22×C4×C5C23×C311yescharacteristic
258C22×C4×C5C23×C311yescharacteristic
259C22×C4×C5C23×C311yescharacteristic
260C22×C4×C5C23×C311yescharacteristic
261C22×C4×C5C23×C311yescharacteristic
262C22×C4×C5C23×C311yescharacteristic
263C22×Dic5C23×C311yescharacteristic
264C22×Dic5C23×C311yescharacteristic
265C22×Dic5C23×C311yescharacteristic
266C22×Dic5C23×C311yescharacteristic
267C22×Dic5C23×C311yescharacteristic
268C22×Dic5C23×C311yescharacteristic
269C22×Dic5C23×C311yescharacteristic
270C2×C4×D5—22no—
271C2×C4×D5—41no—
272C2×C4×D5—41no—
273C2×C4×D5—41no—
274C2×C4×D5—41no—
275C2×C4×D5—41no—
276C2×C4×D5—41no—
277C2×C4×D5C2×C3×C414yes—
278C2×C4×D5C3×Q814yescomplemented
279C2×Dic10—41no—
280C2×Dic10—41no—
281C2×Dic10C2×C3×C414yescomplemented
282C5×C4⋊C4—41no—
283C5×C4⋊C4C2×C3×C414yescomplemented
284C42×C5—41no—
285#685—22no—
286#685—22no—
287#685C2×C3×C414yes—
288#685C2×C3×C414yes—
289C4⋊Dic5—41no—
290C4⋊Dic5C2×C3×C414yescomplemented
291C4⋊Dic5C2×C3×C414yescomplemented
292#683—41no—
293#683—41no—
294#683—41no—
295#683—41no—
296C4×Dic5—41no—
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#387C3×D511yescharacteristic, complemented
308#385—51no—
309#385—51no—
310#380—51no—
311C4×C22⋊C4—51no—
312C4×C22⋊C4—51no—
313C2×#95—51no—
314C22×C3×C5C23×C411yescharacteristic
315C22×C3×C5C22×Q811yescharacteristic
316C22×C3×C5C2×#4111yescharacteristic
317C22×C3×C5H(5,𝔽2)11yescharacteristic
318C22×C3×C5H(5,𝔽2)11yescharacteristic
319C22×C3×C5H(5,𝔽2)11yescharacteristic
320C22×C3×C52−1+411yescharacteristic
321C2×C3×D5—22no—
322C2×C3×D5—22no—
323C2×C3×D5—22no—
324C2×C3×D5—22no—
325C2×C3×D5—22no—
326C2×C3×D5—22no—
327C2×C3×D5C4×Q814yes—
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×C4×C5—41no—
335C3×Dic5—22no—
336C3×Dic5—22no—
337C3×Dic5—22no—
338C3×Dic5—22no—
339C3×Dic5—41no—
340C3×Dic5—41no—
341C3×Dic5—41no—
342C24×C3—51no—
343C2×C3×Q8—54no—
344C2×C3×Q8—201no—
345C2×C3×Q8—201no—
346C22×C3×C4—51no—
347C22×C3×C4—51no—
348C22×C3×C4—51no—
349C22×C3×C4—51no—
350C22×C3×C4—54no—
351C22×C3×C4—54no—
352C22×C3×C4—51no—
353C22×C3×C4—51no—
354C22×C3×C4—51no—
355C22×C3×C4—102no—
356C22×C3×C4—201no—
357C22×C3×C4—201no—
358C22×C3×C4—201no—
359C22×C3×C4—201no—
360C22×C3×C4—201no—
361C22×C3×C4—201no—
362C22×C3×C4C22×D511yescharacteristic
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—41no—
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⋊C4C4×D514yescomplemented
378C3×C22⋊C4—54no—
379C3×C22⋊C4—54no—
380C3×C22⋊C4—102no—
381C3×C22⋊C4—102no—
382C3×C42—41no—
383C3×C42—201no—
384C3×C42—201no—
385C3×C42—201no—
386C23×C5C24×C311yescharacteristic
387C22×D5—21no—
388C22×D5—21no—
389C22×D5—21no—
390C22×D5—21no—
391C22×D5C22×C3×C412yes—
392C22×D5C2×C3×Q812yes—
393C22×D5C3×#4112yes—
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—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5C22×C3×C412yes—
412C2×C4×C5C22×C3×C412yes—
413C2×C4×C5C22×C3×C412yes—
414C2×C4×C5C2×C3×Q812yes—
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×Dic5C22×C3×C412yes—
433C2×Dic5C22×C3×C412yes—
434C2×Dic5C22×C3×C412yes—
435C2×Dic5C2×C3×Q812yes—
436C4×D5—44no—
437C4×D5—44no—
438C4×D5—44no—
439Dic10—44no—
440C22×Q8—51no—
441C23×C4—51no—
442C23×C4—51no—
443C23×C4—51no—
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⋊C4C2×C3×D511yescharacteristic
453C2×C4⋊C4C2×C3×D511yescharacteristic
454C2×C22⋊C4—51no—
455C2×C22⋊C4—51no—
456C2×C22⋊C4—51no—
457C2×C22⋊C4—51no—
458C2×C42—51no—
459C2×C42—51no—
460C2×C42—51no—
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#95C2×C3×D511yescharacteristic
473#95C2×C3×D511yescharacteristic
474#95C2×C3×D511yescharacteristic
475#95C2×C3×D511yescharacteristic
476C2×C3×C5C2×C4×Q811yescharacteristic
477C2×C3×C5#51811yescharacteristic
478C2×C3×C5#52011yescharacteristic
479C2×C3×C5#53811yescharacteristic
480C2×C3×C5#53911yescharacteristic
481C2×C3×C5#54311yescharacteristic
482C2×C3×C5#54411yescharacteristic
483C3×D5—24no—
484C23×C3—52no—
485C23×C3—52no—
486C23×C3—52no—
487C23×C3—101no—
488C23×C3—101no—
489C23×C3—101no—
490C23×C3—101no—
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—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—52no—
511C2×C3×C4—52no—
512C2×C3×C4—52no—
513C2×C3×C4—52no—
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—204no—
532C2×C3×C4—204no—
533C2×C3×C4—204no—
534C2×C3×C4C2×C4×D512yes—
535C2×C3×C4C2×C4×D512yes—
536C2×C3×C4C2×C4×D512yes—
537C2×C3×C4Q8×D512yes—
538C22×C5C23×C3×C411yescharacteristic
539C22×C5C22×C3×Q811yescharacteristic
540C22×C5C2×C3×#4111yescharacteristic
541C22×C5C3×H(5,𝔽2)11yescharacteristic
542C22×C5C3×H(5,𝔽2)11yescharacteristic
543C22×C5C3×H(5,𝔽2)11yescharacteristic
544C22×C5C3×2−1+411yescharacteristic
545C2×D5—22no—
546C2×D5—22no—
547C2×D5—22no—
548C2×D5—22no—
549C2×D5—22no—
550C2×D5—22no—
551C2×D5C3×C4×Q814yes—
552C4×C5—22no—
553C4×C5—22no—
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—41no—
557C4×C5—41no—
558C4×C5—41no—
559Dic5—22no—
560Dic5—22no—
561Dic5—22no—
562Dic5—22no—
563Dic5—41no—
564Dic5—41no—
565Dic5—41no—
566C24—51no—
567C2×Q8—54no—
568C2×Q8—201no—
569C2×Q8—201no—
570C22×C4—51no—
571C22×C4—51no—
572C22×C4—51no—
573C22×C4—51no—
574C22×C4—54no—
575C22×C4—54no—
576C22×C4—51no—
577C22×C4—51no—
578C22×C4—51no—
579C22×C4—102no—
580C22×C4—201no—
581C22×C4—201no—
582C22×C4—201no—
583C22×C4—201no—
584C22×C4—201no—
585C22×C4—201no—
586C22×C4C22×C3×D511yescharacteristic
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—41no—
594C4⋊C4—54no—
595C4⋊C4—54no—
596C4⋊C4—201no—
597C4⋊C4—201no—
598C4⋊C4—201no—
599C4⋊C4—201no—
600C4⋊C4—201no—
601C4⋊C4C3×C4×D514yescomplemented
602C22⋊C4—54no—
603C22⋊C4—54no—
604C22⋊C4—102no—
605C22⋊C4—102no—
606C42—41no—
607C42—201no—
608C42—201no—
609C42—201no—
610C3×C5#232911yescharacteristic, complemented, Hall
611C22×C3—54no—
612C22×C3—102no—
613C22×C3—102no—
614C22×C3—102no—
615C22×C3—102no—
616C22×C3—102no—
617C22×C3—102no—
618C22×C3C22×C4×D511yescharacteristic
619C22×C3#414411yescharacteristic
620C22×C3C2×Q8×D511yescharacteristic
621C22×C3D5×#4111yescharacteristic
622C22×C3#414911yescharacteristic
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—41no—
632C3×C4—102no—
633C3×C4—102no—
634C3×C4—102no—
635C3×C4—102no—
636C3×C4—201no—
637C3×C4—201no—
638C3×C4—201no—
639C2×C5C2×C3×C4×Q811yescharacteristic
640C2×C5C3×#51811yescharacteristic
641C2×C5C3×#52011yescharacteristic
642C2×C5C3×#53811yescharacteristic
643C2×C5C3×#53911yescharacteristic
644C2×C5C3×#54311yescharacteristic
645C2×C5C3×#54411yescharacteristic
646D5—24no—
647C23—52no—
648C23—52no—
649C23—52no—
650C23—101no—
651C23—101no—
652C23—101no—
653C23—101no—
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—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—52no—
674C2×C4—52no—
675C2×C4—52no—
676C2×C4—52no—
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—204no—
695C2×C4—204no—
696C2×C4—204no—
697C2×C4C2×C3×C4×D512yes—
698C2×C4C2×C3×C4×D512yes—
699C2×C4C2×C3×C4×D512yes—
700C2×C4C3×Q8×D512yes—
701C2×C3—104no—
702C2×C3#6585511yescharacteristic
703C2×C3#6588011yescharacteristic
704C2×C3C4×Q8×D511yescharacteristic
705C2×C3#6596811yescharacteristic
706C2×C3#6599111yescharacteristic
707C2×C3#6602311yescharacteristic
708C2×C3#6604111yescharacteristic
709C5C3×#232911yescharacteristic, complemented, Sylow
710C22—54no—
711C22—102no—
712C22—102no—
713C22—102no—
714C22—102no—
715C22—102no—
716C22—102no—
717C22C22×C3×C4×D511yescharacteristic
718C22C3×#414411yescharacteristic
719C22C2×C3×Q8×D511yescharacteristic
720C22C3×D5×#4111yescharacteristic
721C22C3×#414911yescharacteristic
722C22C3×#414911yescharacteristic
723C22C3×#415011yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—102no—
732C4—102no—
733C4—102no—
734C4—102no—
735C4—201no—
736C4—201no—
737C4—201no—
738C3#1060703111yescharacteristic, direct product factor, Sylow
739C2—104no—
740C2C3×#6585511yescharacteristic
741C2C3×#6588011yescharacteristic
742C2C3×C4×Q8×D511yescharacteristic
743C2C3×#6596811yescharacteristic
744C2C3×#6599111yescharacteristic
745C2C3×#6602311yescharacteristic
746C2C3×#6604111yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#387C2
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
cosocleC23×C5C24×C3
hypercenterC3×#387D5
hypocenterC5C3×#2329
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#387

Complements

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

NH ≅ G/Ntype
2. C3×C5×#387C2semidirect
4. C3×#65270C2semidirect
5. C3×#65262C2semidirect
7. C3×#65217C2semidirect
12. C3×#64943C2semidirect
13. C3×#64942C2semidirect
14. C3×#64935C2semidirect
15. C3×#64935C2semidirect
16. #10607031C3direct (N × H)
38. C3×#4043C4semidirect
55. C5×#387C2×C3semidirect
57. #65270C2×C3semidirect
58. #65262C2×C3semidirect
60. #65217C2×C3semidirect
65. #64943C2×C3semidirect
66. #64942C2×C3semidirect
67. #64935C2×C3semidirect
68. #64935C2×C3semidirect
92. C2×C3×C4×D5Q8semidirect
95. C2×C3×Dic10C2×C4semidirect
97. C3×C5×C4⋊C4C2×C4semidirect
104. C3×C4⋊Dic5C2×C4semidirect
105. C3×C4⋊Dic5C2×C4semidirect
121. C3×#387D5semidirect
149. #4043C3×C4semidirect
278. C2×C4×D5C3×Q8semidirect
281. C2×Dic10C2×C3×C4semidirect
283. C5×C4⋊C4C2×C3×C4semidirect
290. C4⋊Dic5C2×C3×C4semidirect
291. C4⋊Dic5C2×C3×C4semidirect
307. #387C3×D5semidirect
377. C3×C4⋊C4C4×D5semidirect
601. C4⋊C4C3×C4×D5semidirect
610. C3×C5#2329semidirect
709. C5C3×#2329semidirect
738. C3#10607031direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40432
C3×C5×#3872
C3×#652782
C3×#652702
C3×#652622
C3×C4×#6852
C3×#652172
C3×#649572
C3×#649562
C3×#649552
C3×D5×#952
C3×#649432
C3×#649422
C3×#649352
#106070313
C3×#23295