Finite Group Databasebeta

← C3×D5×#537 #14480558

Subgroups — C3×D5×#537 #14480558

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C212yesmaximal, complemented
2C3×C5×#537C211yesmaximal, characteristic, complemented
3C3×#66167C212yesmaximal, complemented
4C3×#65963C214yesmaximal, complemented
5C3×D5×C22⋊Q8C214yesmaximal, complemented
6C3×#65942C214yesmaximal, complemented
7C3×D5×#121C214yesmaximal, complemented
8C3×D5×#121C214yesmaximal, complemented
9C3×#65931C214yesmaximal, complemented
10C3×#65844C211yesmaximal, characteristic, complemented
11C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
12D5×#537C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C5×#41C2212yescomplemented
14C3×D5×#41—216no—
15C2×C3×#713C2212yescomplemented
16C2×C3×Q8×D5C2212yes—
17C2×C3×#711C2214yescomplemented
18C2×C3×#711C2212yescomplemented
19C2×C3×D4×D5C2214yes—
20C2×C3×D4×D5C2212yes—
21C2×C3×D4×D5C2214yes—
22C2×C3×#709C2212yescomplemented
23C2×C3×#709C2214yescomplemented
24C22×C3×C4×D5C2214yes—
25C22×C3×C4×D5C2212yes—
26C22×C3×C4×D5C2211yescharacteristic
27C3×C5×C22⋊Q8C2214yescomplemented
28C3×C5×#121C2214yescomplemented
29C3×C5×#121C2214yescomplemented
30C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
31C3×#4092C2214yescomplemented
32C3×#4085C2218yescomplemented
33C3×#4085C2218yescomplemented
34C3×#4084C2214yescomplemented
35C3×#4084C2214yescomplemented
36C3×#4076C2214yescomplemented
37C3×#4076C2214yescomplemented
38C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
39C3×#4070C2214yescomplemented
40C2×C3×#683C2212yescomplemented
41C3×#4043C2214yescomplemented
42C3×#4042C2218yescomplemented
43C3×#4041C2214yescomplemented
44C3×#4041C2214yescomplemented
45C3×D5×C4⋊C4C2214yes—
46C3×D5×C4⋊C4C2214yes—
47C3×D5×C4⋊C4C2214yescomplemented
48C3×#4030C2218yescomplemented
49C3×#4030C2218yescomplemented
50C3×D5×C22⋊C4C2218yes—
51C3×#4024C2218yescomplemented
52C2×C3×#537—51nomaximal, Hall
53C2×D5×#41C2×C312yescomplemented
54C5×#537C2×C311yescharacteristic, complemented
55#66167C2×C312yescomplemented
56#65963C2×C314yescomplemented
57D5×C22⋊Q8C2×C314yescomplemented
58#65942C2×C314yescomplemented
59D5×#121C2×C314yescomplemented
60D5×#121C2×C314yescomplemented
61#65931C2×C314yescomplemented
62#65844C2×C311yescharacteristic, complemented
63C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
64C23×C3×D5C2314yes—
65C23×C3×D5C2311yescharacteristic
66C3×C5×#41—28no—
67C2×C3×C5×Q8C2312yes—
68C2×C3×C5×D4C2312yes—
69C2×C3×C5×D4C2314yes—
70C2×C3×C5×D4C2314yes—
71C22×C3×C4×C5C2314yes—
72C22×C3×C4×C5C2312yes—
73C22×C3×C4×C5C2311yescharacteristic
74C2×C3×C22⋊D5C2314yes—
75C2×C3×C22⋊D5C2314yes—
76C2×C3×C22⋊D5C2314yes—
77C2×C3×C22⋊D5C2318yes—
78C22×C3×Dic5C2314yes—
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2311yescharacteristic
81C3×#713—28no—
82C3×Q8×D5—28no—
83C3×#711—216no—
84C3×#711—28no—
85C3×D4×D5—216no—
86C3×D4×D5—28no—
87C3×D4×D5—48no—
88C3×#709—28no—
89C3×#709—216no—
90C2×C3×D20C2314yes—
91C2×C3×D20C2312yes—
92C2×C3×D20C2314yes—
93C2×C3×C4×D5—216no—
94C2×C3×C4×D5—44no—
95C2×C3×C4×D5D418yescomplemented
96C2×C3×C4×D5C2314yes—
97C2×C3×C4×D5C2314yes—
98C2×C3×C4×D5C2314yes—
99C2×C3×C4×D5C2314yes—
100C2×C3×C4×D5C2314yes—
101C2×C3×C4×D5C2312yes—
102C2×C3×C4×D5C2312yes—
103C2×C3×Dic10C2314yes—
104C2×C3×Dic10C2312yes—
105C3×C5×C4⋊C4C2314yes—
106C3×C5×C4⋊C4C2314yes—
107C3×C5×C22⋊C4C2318yes—
108C3×C22⋊Dic5C2318yes—
109C3×#685C2318yes—
110C3×#685C2318yes—
111C3×C4⋊Dic5C2314yes—
112C3×C4⋊Dic5C2314yes—
113C3×#683C2318yes—
114C3×#683C2318yes—
115C22×C3×#41—52no—
116C3×#537—52no—
117C3×#537—54no—
118C3×#537—54no—
119C3×#537—54no—
120C3×#537—51no—
121C3×#537D511yescharacteristic, direct product factor
122C2×C3×C22⋊Q8—54no—
123C2×C3×#121—54no—
124C2×C3×#121—54no—
125C22×C3×C4⋊C4—51no—
126C2×C5×#41C22×C312yescomplemented
127D5×#41—216no—
128C2×#713C22×C312yescomplemented
129C2×Q8×D5C22×C312yes—
130C2×#711C22×C314yescomplemented
131C2×#711C22×C312yescomplemented
132C2×D4×D5C22×C314yes—
133C2×D4×D5C22×C312yes—
134C2×D4×D5C22×C314yes—
135C2×#709C22×C312yescomplemented
136C2×#709C22×C314yescomplemented
137C22×C4×D5C22×C314yes—
138C22×C4×D5C22×C312yes—
139C22×C4×D5C22×C311yescharacteristic
140C5×C22⋊Q8C22×C314yescomplemented
141C5×#121C22×C314yescomplemented
142C5×#121C22×C314yescomplemented
143C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
144#4092C22×C314yescomplemented
145#4085C22×C318yescomplemented
146#4085C22×C318yescomplemented
147#4084C22×C314yescomplemented
148#4084C22×C314yescomplemented
149#4076C22×C314yescomplemented
150#4076C22×C314yescomplemented
151C2×C4⋊Dic5C22×C311yescharacteristic, complemented
152#4070C22×C314yescomplemented
153C2×#683C22×C312yescomplemented
154#4043C22×C314yescomplemented
155#4042C22×C318yescomplemented
156#4041C22×C314yescomplemented
157#4041C22×C314yescomplemented
158D5×C4⋊C4C22×C314yes—
159D5×C4⋊C4C22×C314yes—
160D5×C4⋊C4C22×C314yescomplemented
161#4030C22×C318yescomplemented
162#4030C22×C318yescomplemented
163D5×C22⋊C4C22×C318yes—
164#4024C22×C318yescomplemented
165C2×#537—51noSylow
166C23×C3×C5C2414yes—
167C23×C3×C5C2411yescharacteristic
168C22×C3×D5—22no—
169C22×C3×D5—22no—
170C22×C3×D5—28no—
171C22×C3×D5—28no—
172C22×C3×D5—28no—
173C22×C3×D5C2×D414yes—
174C22×C3×D5C2414yes—
175C22×C3×D5C2411yescharacteristic
176C22×C3×D5C2411yescharacteristic
177C3×C5×Q8—24no—
178C3×C5×D4—28no—
179C3×C5×D4—24no—
180C3×C5×D4—44no—
181C2×C3×C4×C5—28no—
182C2×C3×C4×C5—42no—
183C2×C3×C4×C5C2×D414yescomplemented
184C2×C3×C4×C5C2414yes—
185C2×C3×C4×C5C2414yes—
186C2×C3×C4×C5C2412yes—
187C3×C22⋊D5—28no—
188C3×C22⋊D5—28no—
189C3×C22⋊D5—28no—
190C3×C22⋊D5—48no—
191C2×C3×Dic5—28no—
192C2×C3×Dic5—42no—
193C2×C3×Dic5C2×D414yescomplemented
194C2×C3×Dic5C2414yes—
195C2×C3×Dic5C2414yes—
196C2×C3×Dic5C2412yes—
197C3×D20—28no—
198C3×D20—24no—
199C3×D20—44no—
200C3×C4×D5—28no—
201C3×C4×D5—28no—
202C3×C4×D5—28no—
203C3×C4×D5—28no—
204C3×C4×D5—44no—
205C3×C4×D5C2×D418yes—
206C3×C4×D5C2×D418yescomplemented
207C3×Dic10—24no—
208C3×Dic10—28no—
209C2×C3×#41—52no—
210C2×C3×#41—54no—
211C2×C3×#41—52no—
212C2×C3×#41—54no—
213C2×C3×#41—52no—
214C2×C3×#41—1016no—
215C2×C3×#41C2×D512yescomplemented
216C22×C3×Q8—52no—
217C22×C3×D4—52no—
218C22×C3×D4—54no—
219C22×C3×D4—54no—
220C23×C3×C4—51no—
221C23×C3×C4—54no—
222C23×C3×C4—52no—
223C3×C22⋊Q8—54no—
224C3×C22⋊Q8—54no—
225C3×C22⋊Q8—58no—
226C3×C22⋊Q8—54no—
227C3×C22⋊Q8—58no—
228C3×C22⋊Q8C2×D514yescomplemented
229C3×#121—54no—
230C3×#121—54no—
231C3×#121—58no—
232C3×#121—58no—
233C3×#121—54no—
234C3×#121—54no—
235C3×#121—54no—
236C3×#121—54no—
237C3×#121—58no—
238C3×#121—58no—
239C3×#121C2×D514yescomplemented
240C3×#121C2×D514yescomplemented
241C2×C3×C4⋊C4—52no—
242C2×C3×C4⋊C4—51no—
243C2×C3×C4⋊C4—54no—
244C2×C3×C4⋊C4—54no—
245C2×C3×C4⋊C4—54no—
246C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
247C2×C3×C22⋊C4—58no—
248C23×D5C23×C314yes—
249C23×D5C23×C311yescharacteristic
250C5×#41—28no—
251C2×C5×Q8C23×C312yes—
252C2×C5×D4C23×C312yes—
253C2×C5×D4C23×C314yes—
254C2×C5×D4C23×C314yes—
255C22×C4×C5C23×C314yes—
256C22×C4×C5C23×C312yes—
257C22×C4×C5C23×C311yescharacteristic
258C2×C22⋊D5C23×C314yes—
259C2×C22⋊D5C23×C314yes—
260C2×C22⋊D5C23×C314yes—
261C2×C22⋊D5C23×C318yes—
262C22×Dic5C23×C314yes—
263C22×Dic5C23×C312yes—
264C22×Dic5C23×C311yescharacteristic
265#713—28no—
266Q8×D5—28no—
267#711—216no—
268#711—28no—
269D4×D5—216no—
270D4×D5—28no—
271D4×D5—48no—
272#709—28no—
273#709—216no—
274C2×D20C23×C314yes—
275C2×D20C23×C312yes—
276C2×D20C23×C314yes—
277C2×C4×D5—216no—
278C2×C4×D5—44no—
279C2×C4×D5C3×D418yescomplemented
280C2×C4×D5C23×C314yes—
281C2×C4×D5C23×C314yes—
282C2×C4×D5C23×C314yes—
283C2×C4×D5C23×C314yes—
284C2×C4×D5C23×C314yes—
285C2×C4×D5C23×C312yes—
286C2×C4×D5C23×C312yes—
287C2×Dic10C23×C314yes—
288C2×Dic10C23×C312yes—
289C5×C4⋊C4C23×C314yes—
290C5×C4⋊C4C23×C314yes—
291C5×C22⋊C4C23×C318yes—
292C22⋊Dic5C23×C318yes—
293#685C23×C318yes—
294#685C23×C318yes—
295C4⋊Dic5C23×C314yes—
296C4⋊Dic5C23×C314yes—
297#683C23×C318yes—
298#683C23×C318yes—
299C22×#41—52no—
300#537—52no—
301#537—54no—
302#537—54no—
303#537—54no—
304#537—51no—
305#537C3×D511yescharacteristic, direct product factor
306C2×C22⋊Q8—54no—
307C2×#121—54no—
308C2×#121—54no—
309C22×C4⋊C4—51no—
310C22×C3×C5—21no—
311C22×C3×C5—21no—
312C22×C3×C5—24no—
313C22×C3×C5—24no—
314C22×C3×C5—24no—
315C22×C3×C5C22×D412yes—
316C22×C3×C5C2511yescharacteristic
317C2×C3×D5—21no—
318C2×C3×D5—21no—
319C2×C3×D5—28no—
320C2×C3×D5—24no—
321C2×C3×D5—24no—
322C2×C3×D5—24no—
323C2×C3×D5—416no—
324C2×C3×D5C22×D412yes—
325C2×C3×D5C22×D412yes—
326C2×C3×D5H(5,𝔽2)12yes—
327C2×C3×D52−1+412yes—
328C3×C4×C5—24no—
329C3×C4×C5—24no—
330C3×C4×C5C22×D414yes—
331C3×Dic5—24no—
332C3×Dic5—24no—
333C3×Dic5C22×D414yes—
334C24×C3—51no—
335C24×C3—54no—
336C3×#41—28no—
337C3×#41—1016no—
338C3×#41—1016no—
339C3×#41—108no—
340C3×#41—108no—
341C3×#41—108no—
342C2×C3×Q8—54no—
343C2×C3×Q8—52no—
344C2×C3×Q8—108no—
345C2×C3×Q8C22×D512yes—
346C2×C3×D4—54no—
347C2×C3×D4—54no—
348C2×C3×D4—54no—
349C2×C3×D4—58no—
350C2×C3×D4—54no—
351C2×C3×D4—52no—
352C2×C3×D4—54no—
353C2×C3×D4—108no—
354C2×C3×D4—1016no—
355C2×C3×D4—208no—
356C2×C3×D4C22×D514yes—
357C2×C3×D4C22×D512yes—
358C2×C3×D4C22×D514yes—
359C22×C3×C4—51no—
360C22×C3×C4—58no—
361C22×C3×C4—52no—
362C22×C3×C4—52no—
363C22×C3×C4—54no—
364C22×C3×C4—52no—
365C22×C3×C4—54no—
366C22×C3×C4—54no—
367C22×C3×C4—54no—
368C22×C3×C4—54no—
369C22×C3×C4—54no—
370C22×C3×C4—1016no—
371C22×C3×C4—204no—
372C22×C3×C4C22×D514yes—
373C22×C3×C4C22×D512yes—
374C22×C3×C4C22×D511yescharacteristic
375C3×C4⋊C4—58no—
376C3×C4⋊C4—58no—
377C3×C4⋊C4—54no—
378C3×C4⋊C4—54no—
379C3×C4⋊C4C22×D514yes—
380C3×C4⋊C4C22×D514yes—
381C3×C22⋊C4—58no—
382C3×C22⋊C4—58no—
383C3×C22⋊C4—58no—
384C3×C22⋊C4C22×D518yes—
385C23×C5C24×C314yes—
386C23×C5C24×C311yescharacteristic
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—28no—
390C22×D5—28no—
391C22×D5—28no—
392C22×D5C2×C3×D414yes—
393C22×D5C24×C314yes—
394C22×D5C24×C311yescharacteristic
395C22×D5C24×C311yescharacteristic
396C5×Q8—24no—
397C5×D4—28no—
398C5×D4—24no—
399C5×D4—44no—
400C2×C4×C5—28no—
401C2×C4×C5—42no—
402C2×C4×C5C2×C3×D414yescomplemented
403C2×C4×C5C24×C314yes—
404C2×C4×C5C24×C314yes—
405C2×C4×C5C24×C312yes—
406C22⋊D5—28no—
407C22⋊D5—28no—
408C22⋊D5—28no—
409C22⋊D5—48no—
410C2×Dic5—28no—
411C2×Dic5—42no—
412C2×Dic5C2×C3×D414yescomplemented
413C2×Dic5C24×C314yes—
414C2×Dic5C24×C314yes—
415C2×Dic5C24×C312yes—
416D20—28no—
417D20—24no—
418D20—44no—
419C4×D5—28no—
420C4×D5—28no—
421C4×D5—28no—
422C4×D5—28no—
423C4×D5—44no—
424C4×D5C2×C3×D418yes—
425C4×D5C2×C3×D418yescomplemented
426Dic10—24no—
427Dic10—28no—
428C2×#41—52no—
429C2×#41—54no—
430C2×#41—52no—
431C2×#41—54no—
432C2×#41—52no—
433C2×#41—1016no—
434C2×#41C2×C3×D512yescomplemented
435C22×Q8—52no—
436C22×D4—52no—
437C22×D4—54no—
438C22×D4—54no—
439C23×C4—51no—
440C23×C4—54no—
441C23×C4—52no—
442C22⋊Q8—54no—
443C22⋊Q8—54no—
444C22⋊Q8—58no—
445C22⋊Q8—54no—
446C22⋊Q8—58no—
447C22⋊Q8C2×C3×D514yescomplemented
448#121—54no—
449#121—54no—
450#121—58no—
451#121—58no—
452#121—54no—
453#121—54no—
454#121—54no—
455#121—54no—
456#121—58no—
457#121—58no—
458#121C2×C3×D514yescomplemented
459#121C2×C3×D514yescomplemented
460C2×C4⋊C4—52no—
461C2×C4⋊C4—51no—
462C2×C4⋊C4—54no—
463C2×C4⋊C4—54no—
464C2×C4⋊C4—54no—
465C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
466C2×C22⋊C4—58no—
467C2×C3×C5—22no—
468C2×C3×C5—44no—
469C2×C3×C5C23×D411yescharacteristic
470C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
471C2×C3×C5C2×2−1+411yescharacteristic
472C3×D5—22no—
473C3×D5—44no—
474C3×D5#53714yesdirect product factor
475C23×C3—51no—
476C23×C3—54no—
477C23×C3—51no—
478C23×C3—54no—
479C23×C3—102no—
480C23×C3—102no—
481C23×C3—108no—
482C23×C3—108no—
483C23×C3—108no—
484C23×C3C23×D514yes—
485C23×C3C23×D511yescharacteristic
486C3×Q8—24no—
487C3×Q8—108no—
488C3×Q8—104no—
489C3×D4—28no—
490C3×D4—24no—
491C3×D4—44no—
492C3×D4—108no—
493C3×D4—108no—
494C3×D4—108no—
495C3×D4—108no—
496C3×D4—104no—
497C3×D4—204no—
498C3×D4—208no—
499C2×C3×C4—28no—
500C2×C3×C4—42no—
501C2×C3×C4—54no—
502C2×C3×C4—52no—
503C2×C3×C4—58no—
504C2×C3×C4—58no—
505C2×C3×C4—54no—
506C2×C3×C4—54no—
507C2×C3×C4—108no—
508C2×C3×C4—108no—
509C2×C3×C4—108no—
510C2×C3×C4—108no—
511C2×C3×C4—108no—
512C2×C3×C4—204no—
513C2×C3×C4—202no—
514C2×C3×C4D4×D514yescomplemented
515C2×C3×C4C23×D514yes—
516C2×C3×C4C23×D514yes—
517C2×C3×C4C23×D512yes—
518C22×C5—21no—
519C22×C5—21no—
520C22×C5—24no—
521C22×C5—24no—
522C22×C5—24no—
523C22×C5C22×C3×D412yes—
524C22×C5C25×C311yescharacteristic
525C2×D5—21no—
526C2×D5—21no—
527C2×D5—28no—
528C2×D5—24no—
529C2×D5—24no—
530C2×D5—24no—
531C2×D5—416no—
532C2×D5C22×C3×D412yes—
533C2×D5C22×C3×D412yes—
534C2×D5C3×H(5,𝔽2)12yes—
535C2×D5C3×2−1+412yes—
536C4×C5—24no—
537C4×C5—24no—
538C4×C5C22×C3×D414yes—
539Dic5—24no—
540Dic5—24no—
541Dic5C22×C3×D414yes—
542C24—51no—
543C24—54no—
544#41—28no—
545#41—1016no—
546#41—1016no—
547#41—108no—
548#41—108no—
549#41—108no—
550C2×Q8—54no—
551C2×Q8—52no—
552C2×Q8—108no—
553C2×Q8C22×C3×D512yes—
554C2×D4—54no—
555C2×D4—54no—
556C2×D4—54no—
557C2×D4—58no—
558C2×D4—54no—
559C2×D4—52no—
560C2×D4—54no—
561C2×D4—108no—
562C2×D4—1016no—
563C2×D4—208no—
564C2×D4C22×C3×D514yes—
565C2×D4C22×C3×D512yes—
566C2×D4C22×C3×D514yes—
567C22×C4—51no—
568C22×C4—58no—
569C22×C4—52no—
570C22×C4—52no—
571C22×C4—54no—
572C22×C4—52no—
573C22×C4—54no—
574C22×C4—54no—
575C22×C4—54no—
576C22×C4—54no—
577C22×C4—54no—
578C22×C4—1016no—
579C22×C4—204no—
580C22×C4C22×C3×D514yes—
581C22×C4C22×C3×D512yes—
582C22×C4C22×C3×D511yescharacteristic
583C4⋊C4—58no—
584C4⋊C4—54no—
585C4⋊C4—58no—
586C4⋊C4—54no—
587C4⋊C4C22×C3×D514yes—
588C4⋊C4C22×C3×D514yes—
589C22⋊C4—58no—
590C22⋊C4—58no—
591C22⋊C4—58no—
592C22⋊C4C22×C3×D518yes—
593C3×C5C2×#53711yescharacteristic, complemented, Hall
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—52no—
600C22×C3—52no—
601C22×C3—52no—
602C22×C3—52no—
603C22×C3—108no—
604C22×C3—101no—
605C22×C3—101no—
606C22×C3—104no—
607C22×C3—104no—
608C22×C3—104no—
609C22×C3—2016no—
610C22×C3C2×D4×D512yes—
611C22×C3C24×D511yescharacteristic
612C3×C4—24no—
613C3×C4—24no—
614C3×C4—54no—
615C3×C4—104no—
616C3×C4—104no—
617C3×C4C2×D4×D514yes—
618C2×C5—22no—
619C2×C5—44no—
620C2×C5C23×C3×D411yescharacteristic
621C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
622C2×C5C2×C3×2−1+411yescharacteristic
623D5—22no—
624D5—44no—
625D5C3×#53714yesdirect product factor
626C23—51no—
627C23—54no—
628C23—51no—
629C23—54no—
630C23—102no—
631C23—102no—
632C23—108no—
633C23—108no—
634C23—108no—
635C23C23×C3×D514yes—
636C23C23×C3×D511yescharacteristic
637Q8—24no—
638Q8—108no—
639Q8—104no—
640D4—28no—
641D4—24no—
642D4—44no—
643D4—108no—
644D4—108no—
645D4—108no—
646D4—108no—
647D4—104no—
648D4—204no—
649D4—208no—
650C2×C4—28no—
651C2×C4—42no—
652C2×C4—54no—
653C2×C4—52no—
654C2×C4—58no—
655C2×C4—58no—
656C2×C4—54no—
657C2×C4—54no—
658C2×C4—108no—
659C2×C4—108no—
660C2×C4—108no—
661C2×C4—108no—
662C2×C4—108no—
663C2×C4—204no—
664C2×C4—202no—
665C2×C4C3×D4×D514yescomplemented
666C2×C4C23×C3×D514yes—
667C2×C4C23×C3×D514yes—
668C2×C4C23×C3×D512yes—
669C2×C3—22no—
670C2×C3—44no—
671C2×C3—54no—
672C2×C3—102no—
673C2×C3—204no—
674C2×C3C22×D4×D511yescharacteristic
675C2×C3D5×H(5,𝔽2)11yescharacteristic
676C2×C3D5×2−1+411yescharacteristic
677C5C2×C3×#53711yescharacteristic, complemented, Sylow
678C22—21no—
679C22—21no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—52no—
684C22—52no—
685C22—52no—
686C22—52no—
687C22—108no—
688C22—101no—
689C22—101no—
690C22—104no—
691C22—104no—
692C22—104no—
693C22—2016no—
694C22C2×C3×D4×D512yes—
695C22C24×C3×D511yescharacteristic
696C4—24no—
697C4—24no—
698C4—54no—
699C4—104no—
700C4—104no—
701C4C2×C3×D4×D514yes—
702C3D5×#53711yescharacteristic, direct product factor, Sylow
703C2—22no—
704C2—44no—
705C2—54no—
706C2—102no—
707C2—204no—
708C2C22×C3×D4×D511yescharacteristic
709C2C3×D5×H(5,𝔽2)11yescharacteristic
710C2C3×D5×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC3×C5×#537C2
socleC22×C3×C5C25
hypercenterC3×#537D5
hypocenterC5C2×C3×#537
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#537

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×#41C2semidirect
2. C3×C5×#537C2semidirect
3. C3×#66167C2semidirect
4. C3×#65963C2semidirect
5. C3×D5×C22⋊Q8C2semidirect
6. C3×#65942C2semidirect
7. C3×D5×#121C2semidirect
8. C3×D5×#121C2semidirect
9. C3×#65931C2semidirect
10. C3×#65844C2semidirect
11. C2×C3×D5×C4⋊C4C2semidirect
12. D5×#537C3direct (N × H)
13. C2×C3×C5×#41C22semidirect
15. C2×C3×#713C22semidirect
17. C2×C3×#711C22semidirect
18. C2×C3×#711C22semidirect
22. C2×C3×#709C22semidirect
23. C2×C3×#709C22semidirect
27. C3×C5×C22⋊Q8C22semidirect
28. C3×C5×#121C22semidirect
29. C3×C5×#121C22semidirect
30. C2×C3×C5×C4⋊C4C22semidirect
31. C3×#4092C22semidirect
32. C3×#4085C22semidirect
33. C3×#4085C22semidirect
34. C3×#4084C22semidirect
35. C3×#4084C22semidirect
36. C3×#4076C22semidirect
37. C3×#4076C22semidirect
38. C2×C3×C4⋊Dic5C22semidirect
39. C3×#4070C22semidirect
40. C2×C3×#683C22semidirect
41. C3×#4043C22semidirect
42. C3×#4042C22semidirect
43. C3×#4041C22semidirect
44. C3×#4041C22semidirect
47. C3×D5×C4⋊C4C22semidirect
48. C3×#4030C22semidirect
49. C3×#4030C22semidirect
51. C3×#4024C22semidirect
53. C2×D5×#41C2×C3semidirect
54. C5×#537C2×C3semidirect
55. #66167C2×C3semidirect
56. #65963C2×C3semidirect
57. D5×C22⋊Q8C2×C3semidirect
58. #65942C2×C3semidirect
59. D5×#121C2×C3semidirect
60. D5×#121C2×C3semidirect
61. #65931C2×C3semidirect
62. #65844C2×C3semidirect
63. C2×D5×C4⋊C4C2×C3semidirect
95. C2×C3×C4×D5D4semidirect
121. C3×#537D5direct (N × H)
126. C2×C5×#41C22×C3semidirect
128. C2×#713C22×C3semidirect
130. C2×#711C22×C3semidirect
131. C2×#711C22×C3semidirect
135. C2×#709C22×C3semidirect
136. C2×#709C22×C3semidirect
140. C5×C22⋊Q8C22×C3semidirect
141. C5×#121C22×C3semidirect
142. C5×#121C22×C3semidirect
143. C2×C5×C4⋊C4C22×C3semidirect
144. #4092C22×C3semidirect
145. #4085C22×C3semidirect
146. #4085C22×C3semidirect
147. #4084C22×C3semidirect
148. #4084C22×C3semidirect
149. #4076C22×C3semidirect
150. #4076C22×C3semidirect
151. C2×C4⋊Dic5C22×C3semidirect
152. #4070C22×C3semidirect
153. C2×#683C22×C3semidirect
154. #4043C22×C3semidirect
155. #4042C22×C3semidirect
156. #4041C22×C3semidirect
157. #4041C22×C3semidirect
160. D5×C4⋊C4C22×C3semidirect
161. #4030C22×C3semidirect
162. #4030C22×C3semidirect
164. #4024C22×C3semidirect
183. C2×C3×C4×C5C2×D4semidirect
193. C2×C3×Dic5C2×D4semidirect
206. C3×C4×D5C2×D4semidirect
215. C2×C3×#41C2×D5semidirect
228. C3×C22⋊Q8C2×D5semidirect
239. C3×#121C2×D5semidirect
240. C3×#121C2×D5semidirect
246. C2×C3×C4⋊C4C2×D5semidirect
279. C2×C4×D5C3×D4semidirect
305. #537C3×D5direct (N × H)
402. C2×C4×C5C2×C3×D4semidirect
412. C2×Dic5C2×C3×D4semidirect
425. C4×D5C2×C3×D4semidirect
434. C2×#41C2×C3×D5semidirect
447. C22⋊Q8C2×C3×D5semidirect
458. #121C2×C3×D5semidirect
459. #121C2×C3×D5semidirect
465. C2×C4⋊C4C2×C3×D5semidirect
474. C3×D5#537direct (N × H)
514. C2×C3×C4D4×D5semidirect
593. C3×C5C2×#537semidirect
625. D5C3×#537direct (N × H)
665. C2×C4C3×D4×D5semidirect
677. C5C2×C3×#537semidirect
702. C3D5×#537direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C3×C5×#5372
C3×#661672
C3×#659632
C3×D5×C22⋊Q82
C3×#659422
C3×D5×#1212
C3×#659312
C3×#658442
C2×C3×D5×C4⋊C42
D5×#5373
C2×C3×#5375