Finite Group Databasebeta

← C3×#10606329 #14330708

Subgroups — C3×#10606329 #14330708

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4029C211yesmaximal, characteristic
2C3×C5×#385C211yesmaximal, characteristic, complemented
3C3×#65502C211yesmaximal, characteristic
4C3×#65499C211yesmaximal, characteristic, complemented
5C3×#65279C211yesmaximal, characteristic, complemented
6C3×#65276C211yesmaximal, characteristic, complemented
7C3×#65262C211yesmaximal, characteristic, complemented
8C3×#65261C211yesmaximal, characteristic, complemented
9C3×#65246C211yesmaximal, characteristic
10C3×#65240C211yesmaximal, characteristic, complemented
11C3×#65233C211yesmaximal, characteristic, complemented
12C3×#64958C211yesmaximal, characteristic, complemented
13C3×#64956C211yesmaximal, characteristic, complemented
14C3×#64944C211yesmaximal, characteristic, complemented
15C3×#64942C211yesmaximal, characteristic, complemented
16#10606329C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C3×#4029C418yescomplemented
43C3×C5×#95C2211yescharacteristic
44C3×C5×#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#2376—51nomaximal, Hall
54C2×#4029C2×C311yescharacteristic
55C5×#385C2×C311yescharacteristic, complemented
56#65502C2×C311yescharacteristic
57#65499C2×C311yescharacteristic, complemented
58#65279C2×C311yescharacteristic, complemented
59#65276C2×C311yescharacteristic, complemented
60#65262C2×C311yescharacteristic, complemented
61#65261C2×C311yescharacteristic, complemented
62#65246C2×C311yescharacteristic
63#65240C2×C311yescharacteristic, complemented
64#65233C2×C311yescharacteristic, complemented
65#64958C2×C311yescharacteristic, complemented
66#64956C2×C311yescharacteristic, complemented
67#64944C2×C311yescharacteristic, complemented
68#64942C2×C311yescharacteristic, complemented
69C24×C3×C5C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C22×C3×C4×C5—41no—
72C22×C3×C4×C5—41no—
73C22×C3×C4×C5—41no—
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×C3×C22⋊D5—41no—
81C2×C3×C22⋊D5—41no—
82C2×C3×C22⋊D5C2×C414yes—
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C2×C3×C4×D5—41no—
91C2×C3×C4×D5—41no—
92C2×C3×C4×D5C2×C414yescomplemented
93C3×C5×C4⋊C4—41no—
94C3×C5×C4⋊C4—41no—
95C3×C5×C22⋊C4—41no—
96C3×C5×C22⋊C4C2×C414yes—
97C3×C22⋊Dic5—41no—
98C3×C22⋊Dic5—41no—
99C3×C22⋊Dic5C2×C414yes—
100C3×#685—41no—
101C3×#685—41no—
102C3×#685—41no—
103C3×#685—41no—
104C3×#685C2×C414yescomplemented
105C3×C4⋊Dic5—41no—
106C3×C4⋊Dic5C2×C414yescomplemented
107C3×#683—41no—
108C3×#683—41no—
109C3×#683—41no—
110C3×#683—41no—
111C3×#683C2×C414yescomplemented
112C3×C4×Dic5—41no—
113C3×C4×Dic5—41no—
114C3×C4×Dic5—41no—
115C2×C3×#123—51no—
116C3×#390—51no—
117C3×#389—51no—
118C3×#389—51no—
119C3×#388—51no—
120C3×#388—51no—
121C3×#388—51no—
122C3×#388—51no—
123C3×#387—51no—
124C3×#387—51no—
125C3×#386—51no—
126C3×#385—51no—
127C3×#385D511yescharacteristic, complemented
128C3×#380—51no—
129C3×#380—51no—
130C23×C4×C5C22×C311yescharacteristic
131C22×C22⋊D5C22×C311yescharacteristic
132C22×C4×D5C22×C311yescharacteristic
133C2×C5×C4⋊C4C22×C311yescharacteristic
134C2×C5×C4⋊C4C22×C311yescharacteristic
135C2×C5×C22⋊C4C22×C311yescharacteristic
136C2×C5×C22⋊C4C22×C311yescharacteristic
137C2×C22⋊Dic5C22×C311yescharacteristic
138C2×C22⋊Dic5C22×C311yescharacteristic
139C2×C22⋊Dic5C22×C311yescharacteristic
140C2×#685C22×C311yescharacteristic
141C2×#685C22×C311yescharacteristic
142C2×#685C22×C311yescharacteristic
143C2×#685C22×C311yescharacteristic
144C2×#685C22×C311yescharacteristic
145C2×C4⋊Dic5C22×C311yescharacteristic
146C2×C4⋊Dic5C22×C311yescharacteristic
147C2×#683C22×C311yescharacteristic
148C2×#683C22×C311yescharacteristic
149C2×#683C22×C311yescharacteristic
150C2×#683C22×C311yescharacteristic
151C2×#683C22×C311yescharacteristic
152C2×C4×Dic5C22×C311yescharacteristic
153C2×C4×Dic5C22×C311yescharacteristic
154C2×C4×Dic5C22×C311yescharacteristic
155#4029C3×C418yescomplemented
156C5×#95C22×C311yescharacteristic
157C5×#95C22×C311yescharacteristic
158#3963C22×C311yescharacteristic
159#3963C22×C311yescharacteristic
160#3963C22×C311yescharacteristic
161#3963C22×C311yescharacteristic
162#3963C22×C311yescharacteristic
163#3963C22×C311yescharacteristic
164#3963C22×C311yescharacteristic
165#3963C22×C311yescharacteristic
166#2376—51noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5C22×C412yes—
174C23×C3×C5C2411yescharacteristic
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5—21no—
180C22×C3×D5—21no—
181C22×C3×D5C22×C412yes—
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×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—44no—
199C2×C3×C4×C5C22×C412yes—
200C2×C3×C4×C5C22×C412yes—
201C3×C22⋊D5—44no—
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—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5C22×C412yes—
221C2×C3×Dic5C22×C412yes—
222C2×C3×Dic5C22×C412yes—
223C3×C4×D5—44no—
224C22×C3×D4—51no—
225C23×C3×C4—51no—
226C23×C3×C4C2×D511yescharacteristic
227C3×#123—58no—
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×C4⋊C4—51no—
234C2×C3×C4⋊C4—51no—
235C2×C3×C4⋊C4C2×D511yescharacteristic
236C2×C3×C4⋊C4C2×D511yescharacteristic
237C2×C3×C22⋊C4—51no—
238C2×C3×C22⋊C4—51no—
239C2×C3×C22⋊C4—51no—
240C2×C3×C22⋊C4—51no—
241C2×C3×C22⋊C4—51no—
242C2×C3×C22⋊C4—51no—
243C2×C3×C22⋊C4—51no—
244C2×C3×C22⋊C4—51no—
245C2×C3×C22⋊C4C2×D511yescharacteristic
246C2×C3×C22⋊C4C2×D511yescharacteristic
247C2×C3×C42—51no—
248C2×C3×C42—51no—
249C2×C3×C42—51no—
250C3×#95—51no—
251C3×#95—51no—
252C3×#95—51no—
253C3×#95—51no—
254C3×#95—51no—
255C3×#95—51no—
256C3×#95—51no—
257C3×#95—51no—
258C3×#95C2×D511yescharacteristic
259C3×#95C2×D511yescharacteristic
260C24×C5C23×C311yescharacteristic
261C23×D5C23×C311yescharacteristic
262C22×C4×C5—41no—
263C22×C4×C5—41no—
264C22×C4×C5—41no—
265C22×C4×C5C23×C311yescharacteristic
266C22×C4×C5C23×C311yescharacteristic
267C22×C4×C5C23×C311yescharacteristic
268C22×C4×C5C23×C311yescharacteristic
269C22×C4×C5C23×C311yescharacteristic
270C22×C4×C5C23×C311yescharacteristic
271C2×C22⋊D5—41no—
272C2×C22⋊D5—41no—
273C2×C22⋊D5C2×C3×C414yes—
274C22×Dic5C23×C311yescharacteristic
275C22×Dic5C23×C311yescharacteristic
276C22×Dic5C23×C311yescharacteristic
277C22×Dic5C23×C311yescharacteristic
278C22×Dic5C23×C311yescharacteristic
279C22×Dic5C23×C311yescharacteristic
280C22×Dic5C23×C311yescharacteristic
281C2×C4×D5—41no—
282C2×C4×D5—41no—
283C2×C4×D5C2×C3×C414yescomplemented
284C5×C4⋊C4—41no—
285C5×C4⋊C4—41no—
286C5×C22⋊C4—41no—
287C5×C22⋊C4C2×C3×C414yes—
288C22⋊Dic5—41no—
289C22⋊Dic5—41no—
290C22⋊Dic5C2×C3×C414yes—
291#685—41no—
292#685—41no—
293#685—41no—
294#685—41no—
295#685C2×C3×C414yescomplemented
296C4⋊Dic5—41no—
297C4⋊Dic5C2×C3×C414yescomplemented
298#683—41no—
299#683—41no—
300#683—41no—
301#683—41no—
302#683C2×C3×C414yescomplemented
303C4×Dic5—41no—
304C4×Dic5—41no—
305C4×Dic5—41no—
306C2×#123—51no—
307#390—51no—
308#389—51no—
309#389—51no—
310#388—51no—
311#388—51no—
312#388—51no—
313#388—51no—
314#387—51no—
315#387—51no—
316#386—51no—
317#385—51no—
318#385C3×D511yescharacteristic, complemented
319#380—51no—
320#380—51no—
321C22×C3×C5—22no—
322C22×C3×C5—22no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—41no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5C23×C411yescharacteristic
329C22×C3×C5H(5,𝔽2)11yescharacteristic
330C22×C3×C5H(5,𝔽2)11yescharacteristic
331C22×C3×C5H(5,𝔽2)11yescharacteristic
332C22×C3×C5H(5,𝔽2)11yescharacteristic
333C22×C3×C52−1+411yescharacteristic
334C22×C3×C52−1+411yescharacteristic
335C2×C3×D5—22no—
336C2×C3×D5—22no—
337C2×C3×D5—22no—
338C2×C3×D5—41no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C3×C4×C5—22no—
343C3×C4×C5—22no—
344C3×C4×C5—41no—
345C3×C4×C5—41no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348C3×Dic5—22no—
349C3×Dic5—22no—
350C3×Dic5—22no—
351C3×Dic5—41no—
352C3×Dic5—41no—
353C3×Dic5—41no—
354C3×Dic5—41no—
355C24×C3—51no—
356C24×C3C22×D511yescharacteristic
357C2×C3×D4—54no—
358C2×C3×D4—201no—
359C2×C3×D4—201no—
360C22×C3×C4—41no—
361C22×C3×C4—41no—
362C22×C3×C4—41no—
363C22×C3×C4—51no—
364C22×C3×C4—51no—
365C22×C3×C4—51no—
366C22×C3×C4—54no—
367C22×C3×C4—51no—
368C22×C3×C4—51no—
369C22×C3×C4—51no—
370C22×C3×C4—51no—
371C22×C3×C4—201no—
372C22×C3×C4—201no—
373C22×C3×C4C22×D511yescharacteristic
374C22×C3×C4C22×D511yescharacteristic
375C22×C3×C4C22×D511yescharacteristic
376C22×C3×C4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C22×C3×C4C22×D511yescharacteristic
379C3×C4⋊C4—41no—
380C3×C4⋊C4—41no—
381C3×C4⋊C4—54no—
382C3×C4⋊C4—54no—
383C3×C4⋊C4—201no—
384C3×C4⋊C4—201no—
385C3×C4⋊C4—201no—
386C3×C4⋊C4—201no—
387C3×C4⋊C4—201no—
388C3×C22⋊C4—41no—
389C3×C22⋊C4—54no—
390C3×C22⋊C4—54no—
391C3×C22⋊C4—201no—
392C3×C22⋊C4—201no—
393C3×C22⋊C4—201no—
394C3×C22⋊C4—201no—
395C3×C22⋊C4—201no—
396C3×C22⋊C4—201no—
397C3×C22⋊C4C4×D514yes—
398C3×C42—201no—
399C3×C42—201no—
400C3×C42—201no—
401C23×C5—21no—
402C23×C5—21no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5C22×C3×C412yes—
408C23×C5C24×C311yescharacteristic
409C22×D5—21no—
410C22×D5—21no—
411C22×D5—21no—
412C22×D5—21no—
413C22×D5—21no—
414C22×D5—21no—
415C22×D5C22×C3×C412yes—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—44no—
433C2×C4×C5C22×C3×C412yes—
434C2×C4×C5C22×C3×C412yes—
435C22⋊D5—44no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—21no—
449C2×Dic5—21no—
450C2×Dic5—21no—
451C2×Dic5—21no—
452C2×Dic5—21no—
453C2×Dic5—21no—
454C2×Dic5C22×C3×C412yes—
455C2×Dic5C22×C3×C412yes—
456C2×Dic5C22×C3×C412yes—
457C4×D5—44no—
458C22×D4—51no—
459C23×C4—51no—
460C23×C4C2×C3×D511yescharacteristic
461#123—58no—
462C2×C4⋊C4—51no—
463C2×C4⋊C4—51no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4C2×C3×D511yescharacteristic
470C2×C4⋊C4C2×C3×D511yescharacteristic
471C2×C22⋊C4—51no—
472C2×C22⋊C4—51no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—51no—
476C2×C22⋊C4—51no—
477C2×C22⋊C4—51no—
478C2×C22⋊C4—51no—
479C2×C22⋊C4C2×C3×D511yescharacteristic
480C2×C22⋊C4C2×C3×D511yescharacteristic
481C2×C42—51no—
482C2×C42—51no—
483C2×C42—51no—
484#95—51no—
485#95—51no—
486#95—51no—
487#95—51no—
488#95—51no—
489#95—51no—
490#95—51no—
491#95—51no—
492#95C2×C3×D511yescharacteristic
493#95C2×C3×D511yescharacteristic
494C2×C3×C5—42no—
495C2×C3×C5#51811yescharacteristic
496C2×C3×C5#52011yescharacteristic
497C2×C3×C5#52011yescharacteristic
498C2×C3×C5#56011yescharacteristic
499C2×C3×C5#56211yescharacteristic
500C2×C3×C5#56211yescharacteristic
501C2×C3×C5#56311yescharacteristic
502C3×D5—42no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—52no—
510C23×C3—101no—
511C23×C3—101no—
512C23×C3—101no—
513C23×C3—101no—
514C23×C3—101no—
515C23×C3—101no—
516C23×C3C2×C4×D512yes—
517C23×C3C23×D511yescharacteristic
518C3×D4—204no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—44no—
536C2×C3×C4—52no—
537C2×C3×C4—52no—
538C2×C3×C4—52no—
539C2×C3×C4—101no—
540C2×C3×C4—101no—
541C2×C3×C4—101no—
542C2×C3×C4—101no—
543C2×C3×C4—101no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—204no—
558C2×C3×C4C2×C4×D512yes—
559C2×C3×C4C2×C4×D512yes—
560C22×C5—22no—
561C22×C5—22no—
562C22×C5—22no—
563C22×C5—41no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5—41no—
567C22×C5C23×C3×C411yescharacteristic
568C22×C5C3×H(5,𝔽2)11yescharacteristic
569C22×C5C3×H(5,𝔽2)11yescharacteristic
570C22×C5C3×H(5,𝔽2)11yescharacteristic
571C22×C5C3×H(5,𝔽2)11yescharacteristic
572C22×C5C3×2−1+411yescharacteristic
573C22×C5C3×2−1+411yescharacteristic
574C2×D5—22no—
575C2×D5—22no—
576C2×D5—22no—
577C2×D5—41no—
578C2×D5—41no—
579C2×D5—41no—
580C2×D5—41no—
581C4×C5—22no—
582C4×C5—22no—
583C4×C5—41no—
584C4×C5—41no—
585C4×C5—41no—
586C4×C5—41no—
587Dic5—22no—
588Dic5—22no—
589Dic5—22no—
590Dic5—41no—
591Dic5—41no—
592Dic5—41no—
593Dic5—41no—
594C24—51no—
595C24C22×C3×D511yescharacteristic
596C2×D4—54no—
597C2×D4—201no—
598C2×D4—201no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—51no—
603C22×C4—51no—
604C22×C4—51no—
605C22×C4—54no—
606C22×C4—51no—
607C22×C4—51no—
608C22×C4—51no—
609C22×C4—51no—
610C22×C4—201no—
611C22×C4—201no—
612C22×C4C22×C3×D511yescharacteristic
613C22×C4C22×C3×D511yescharacteristic
614C22×C4C22×C3×D511yescharacteristic
615C22×C4C22×C3×D511yescharacteristic
616C22×C4C22×C3×D511yescharacteristic
617C22×C4C22×C3×D511yescharacteristic
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—54no—
621C4⋊C4—54no—
622C4⋊C4—201no—
623C4⋊C4—201no—
624C4⋊C4—201no—
625C4⋊C4—201no—
626C4⋊C4—201no—
627C22⋊C4—41no—
628C22⋊C4—54no—
629C22⋊C4—54no—
630C22⋊C4—201no—
631C22⋊C4—201no—
632C22⋊C4—201no—
633C22⋊C4—201no—
634C22⋊C4—201no—
635C22⋊C4—201no—
636C22⋊C4C3×C4×D514yes—
637C42—201no—
638C42—201no—
639C42—201no—
640C3×C5#237611yescharacteristic, complemented, Hall
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—102no—
649C22×C3—102no—
650C22×C3—102no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3—201no—
655C22×C3C22×C4×D511yescharacteristic
656C22×C3#414411yescharacteristic
657C22×C3#414411yescharacteristic
658C22×C3#414411yescharacteristic
659C22×C3#414711yescharacteristic
660C22×C3#414911yescharacteristic
661C22×C3#415011yescharacteristic
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—102no—
669C3×C4—102no—
670C3×C4—102no—
671C3×C4—201no—
672C3×C4—201no—
673C3×C4—201no—
674C3×C4—201no—
675C2×C5—42no—
676C2×C5C3×#51811yescharacteristic
677C2×C5C3×#52011yescharacteristic
678C2×C5C3×#52011yescharacteristic
679C2×C5C3×#56011yescharacteristic
680C2×C5C3×#56211yescharacteristic
681C2×C5C3×#56211yescharacteristic
682C2×C5C3×#56311yescharacteristic
683D5—42no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—52no—
691C23—101no—
692C23—101no—
693C23—101no—
694C23—101no—
695C23—101no—
696C23—101no—
697C23C2×C3×C4×D512yes—
698C23C23×C3×D511yescharacteristic
699D4—204no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—52no—
718C2×C4—52no—
719C2×C4—52no—
720C2×C4—101no—
721C2×C4—101no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—101no—
735C2×C4—101no—
736C2×C4—101no—
737C2×C4—101no—
738C2×C4—204no—
739C2×C4C2×C3×C4×D512yes—
740C2×C4C2×C3×C4×D512yes—
741C2×C3—42no—
742C2×C3—202no—
743C2×C3#6583811yescharacteristic
744C2×C3#6587911yescharacteristic
745C2×C3#6588011yescharacteristic
746C2×C3#6592911yescharacteristic
747C2×C3#6598011yescharacteristic
748C2×C3#6598111yescharacteristic
749C2×C3#6600111yescharacteristic
750C5C3×#237611yescharacteristic, complemented, Sylow
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—102no—
759C22—102no—
760C22—102no—
761C22—201no—
762C22—201no—
763C22—201no—
764C22—201no—
765C22C22×C3×C4×D511yescharacteristic
766C22C3×#414411yescharacteristic
767C22C3×#414411yescharacteristic
768C22C3×#414411yescharacteristic
769C22C3×#414711yescharacteristic
770C22C3×#414911yescharacteristic
771C22C3×#415011yescharacteristic
772C4—22no—
773C4—22no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—102no—
779C4—102no—
780C4—102no—
781C4—201no—
782C4—201no—
783C4—201no—
784C4—201no—
785C3#1060632911yescharacteristic, direct product factor, Sylow
786C2—42no—
787C2—202no—
788C2C3×#6583811yescharacteristic
789C2C3×#6587911yescharacteristic
790C2C3×#6588011yescharacteristic
791C2C3×#6592911yescharacteristic
792C2C3×#6598011yescharacteristic
793C2C3×#6598111yescharacteristic
794C2C3×#6600111yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#385C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×#385D5
hypocenterC5C3×#2376
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
2. C3×C5×#385C2semidirect
4. C3×#65499C2semidirect
5. C3×#65279C2semidirect
6. C3×#65276C2semidirect
7. C3×#65262C2semidirect
8. C3×#65261C2semidirect
10. C3×#65240C2semidirect
11. C3×#65233C2semidirect
12. C3×#64958C2semidirect
13. C3×#64956C2semidirect
14. C3×#64944C2semidirect
15. C3×#64942C2semidirect
16. #10606329C3direct (N × H)
42. C3×#4029C4semidirect
55. C5×#385C2×C3semidirect
57. #65499C2×C3semidirect
58. #65279C2×C3semidirect
59. #65276C2×C3semidirect
60. #65262C2×C3semidirect
61. #65261C2×C3semidirect
63. #65240C2×C3semidirect
64. #65233C2×C3semidirect
65. #64958C2×C3semidirect
66. #64956C2×C3semidirect
67. #64944C2×C3semidirect
68. #64942C2×C3semidirect
92. C2×C3×C4×D5C2×C4semidirect
104. C3×#685C2×C4semidirect
106. C3×C4⋊Dic5C2×C4semidirect
111. C3×#683C2×C4semidirect
127. C3×#385D5semidirect
155. #4029C3×C4semidirect
283. C2×C4×D5C2×C3×C4semidirect
295. #685C2×C3×C4semidirect
297. C4⋊Dic5C2×C3×C4semidirect
302. #683C2×C3×C4semidirect
318. #385C3×D5semidirect
640. C3×C5#2376semidirect
750. C5C3×#2376semidirect
785. C3#10606329direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40292
C3×C5×#3852
C3×#655022
C3×#654992
C3×#652792
C3×#652762
C3×#652622
C3×#652612
C3×#652462
C3×#652402
C3×#652332
C3×#649582
C3×#649562
C3×#649442
C3×#649422
#106063293
C3×#23765