Finite Group Databasebeta

← C2×C3×D5×#104 #14412789

Subgroups — C2×C3×D5×#104 #14412789

Order 1920.

1712 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C2×C3×D5×M16C211yesmaximal, characteristic, complemented
3C2×C3×C42×D5C211yesmaximal, characteristic, complemented
4C2×C3×C5×#104C211yesmaximal, characteristic, complemented
5C2×C3×#3969C211yesmaximal, characteristic, complemented
6C2×C3×#3957C211yesmaximal, characteristic, complemented
7C2×C3×#3937C211yesmaximal, characteristic, complemented
8C3×D5×#104C218yesmaximal, direct product factor
9C2×D5×#104C311yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C3×D5×#41—22no—
12C3×D5×#41—22no—
13C3×D5×#41C414yescomplemented
14C3×D5×#41C2214yes—
15C2×C3×#713C411yescharacteristic, complemented
16C2×C3×Q8×D5C411yescharacteristic, complemented
17C2×C3×#711—21no—
18C2×C3×#711C411yescharacteristic, complemented
19C2×C3×D4×D5—21no—
20C2×C3×D4×D5C411yescharacteristic, complemented
21C2×C3×#709—21no—
22C2×C3×#709C2211yescharacteristic
23C22×C3×C4×D5—21no—
24C22×C3×C4×D5—21no—
25C22×C3×C4×D5C2211yescharacteristic
26C2×C3×C5×M16C2211yescharacteristic, complemented
27C2×C3×C42×C5C2211yescharacteristic, complemented
28C2×C3×C4×Dic5—21no—
29C2×C3×C4×Dic5C2211yescharacteristic, complemented
30C2×C3×#681C2211yescharacteristic, complemented
31C3×D5×M16—22no—
32C3×D5×M16C2214yescomplemented
33C2×C3×#676—21no—
34C2×C3×C8×D5—21no—
35C3×C42×D5—22no—
36C3×C42×D5C2214yescomplemented
37C3×C5×#104C2214yescomplemented
38C3×#3969C2214yescomplemented
39C3×#3957C2214yescomplemented
40C3×#3937C2214yescomplemented
41C22×C3×#104—51nomaximal, Hall
42C2×D5×#41C2×C311yescharacteristic
43C2×D5×M16C2×C311yescharacteristic, complemented
44C2×C42×D5C2×C311yescharacteristic, complemented
45C2×C5×#104C2×C311yescharacteristic, complemented
46C2×#3969C2×C311yescharacteristic, complemented
47C2×#3957C2×C311yescharacteristic, complemented
48C2×#3937C2×C311yescharacteristic, complemented
49D5×#104C2×C318yesdirect product factor
50C23×C3×D5—21no—
51C23×C3×D5D411yescharacteristic
52C3×C5×#41—21no—
53C3×C5×#41—21no—
54C3×C5×#41C2×C412yescomplemented
55C3×C5×#41C2312yes—
56C2×C3×C5×Q8C2×C411yescharacteristic, complemented
57C2×C3×C5×D4—21no—
58C2×C3×C5×D4C2×C411yescharacteristic, complemented
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×C3×C22⋊D5—21no—
63C2×C3×C22⋊D5—21no—
64C2×C3×C22⋊D5—21no—
65C22×C3×Dic5—21no—
66C22×C3×Dic5—21no—
67C22×C3×Dic5D411yescharacteristic
68C3×#713—22no—
69C3×#713C2×C414yescomplemented
70C3×Q8×D5—22no—
71C3×Q8×D5C2×C414yescomplemented
72C3×#711—24no—
73C3×#711—24no—
74C3×#711—22no—
75C3×#711C2×C414yescomplemented
76C3×D4×D5—24no—
77C3×D4×D5—24no—
78C3×D4×D5—22no—
79C3×D4×D5C2×C414yescomplemented
80C3×#709—21no—
81C3×#709—21no—
82C3×#709—24no—
83C3×#709—24no—
84C3×#709C2×C412yescomplemented
85C3×#709C2312yes—
86C2×C3×D20—21no—
87C2×C3×D20C2×C411yescharacteristic, complemented
88C2×C3×C4×D5—28no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—24no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5—24no—
94C2×C3×C4×D5—24no—
95C2×C3×C4×D5C2×C411yescharacteristic
96C2×C3×C4×D5C2×C411yescharacteristic
97C2×C3×C4×D5C2×C412yes—
98C2×C3×C4×D5D412yes—
99C2×C3×C4×D5D411yescharacteristic
100C2×C3×C4×D5D411yescharacteristic
101C2×C3×C4×D5D412yes—
102C2×C3×C4×D5C2312yes—
103C2×C3×Dic10—21no—
104C2×C3×Dic10C2×C411yescharacteristic, complemented
105C3×C5×M16—21no—
106C3×C5×M16C2312yescomplemented
107C2×C3×C5×C8—21no—
108C3×C42×C5—21no—
109C3×C42×C5C2312yescomplemented
110C3×C4×Dic5—21no—
111C3×C4×Dic5—24no—
112C3×C4×Dic5C2312yescomplemented
113C3×#681—21no—
114C3×#681C2312yescomplemented
115C2×C3×#168—21no—
116C3×#676—24no—
117C3×C8×D5—24no—
118C22×C3×#41—51no—
119C22×C3×M16—51no—
120C22×C3×C42—51no—
121C2×C3×#104—51no—
122C2×C3×#104—51no—
123C2×C3×#104—51no—
124C2×C3×#104—58no—
125C2×C3×#104D511yescharacteristic, direct product factor
126C2×C5×#41C22×C311yescharacteristic
127D5×#41—22no—
128D5×#41—22no—
129D5×#41C3×C414yescomplemented
130D5×#41C22×C314yes—
131C2×#713C3×C411yescharacteristic, complemented
132C2×Q8×D5C3×C411yescharacteristic, complemented
133C2×#711—21no—
134C2×#711C3×C411yescharacteristic, complemented
135C2×D4×D5—21no—
136C2×D4×D5C3×C411yescharacteristic, complemented
137C2×#709—21no—
138C2×#709C22×C311yescharacteristic
139C22×C4×D5—21no—
140C22×C4×D5—21no—
141C22×C4×D5C22×C311yescharacteristic
142C2×C5×M16C22×C311yescharacteristic, complemented
143C2×C42×C5C22×C311yescharacteristic, complemented
144C2×C4×Dic5—21no—
145C2×C4×Dic5C22×C311yescharacteristic, complemented
146C2×#681C22×C311yescharacteristic, complemented
147D5×M16—22no—
148D5×M16C22×C314yescomplemented
149C2×#676—21no—
150C2×C8×D5—21no—
151C42×D5—22no—
152C42×D5C22×C314yescomplemented
153C5×#104C22×C314yescomplemented
154#3969C22×C314yescomplemented
155#3957C22×C314yescomplemented
156#3937C22×C314yescomplemented
157C22×#104—51noSylow
158C23×C3×C5—21no—
159C23×C3×C5C2×D411yescharacteristic
160C22×C3×D5—24no—
161C22×C3×D5—21no—
162C22×C3×D5—24no—
163C22×C3×D5—44no—
164C22×C3×D5C22⋊C411yescharacteristic
165C22×C3×D5C22⋊C412yes—
166C22×C3×D5C22⋊C411yescharacteristic
167C22×C3×D5C2×D412yes—
168C3×C5×Q8—21no—
169C3×C5×Q8C22×C412yescomplemented
170C3×C5×D4—22no—
171C3×C5×D4—22no—
172C3×C5×D4—21no—
173C3×C5×D4C22×C412yescomplemented
174C2×C3×C4×C5—24no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—22no—
177C2×C3×C4×C5—22no—
178C2×C3×C4×C5—22no—
179C2×C3×C4×C5C22×C411yescharacteristic
180C2×C3×C4×C5C22×C411yescharacteristic
181C2×C3×C4×C5C2×D411yescharacteristic
182C2×C3×C4×C5C2×D411yescharacteristic
183C2×C3×C4×C5C2×D411yescharacteristic
184C2×C3×C4×C5C2411yescharacteristic
185C3×C22⋊D5—22no—
186C3×C22⋊D5—22no—
187C3×C22⋊D5—24no—
188C3×C22⋊D5—24no—
189C2×C3×Dic5—24no—
190C2×C3×Dic5—21no—
191C2×C3×Dic5—22no—
192C2×C3×Dic5—24no—
193C2×C3×Dic5C22⋊C411yescharacteristic
194C2×C3×Dic5C22⋊C411yescharacteristic
195C2×C3×Dic5C22⋊C412yes—
196C2×C3×Dic5C2×D412yes—
197C3×D20—24no—
198C3×D20—21no—
199C3×D20C22×C412yescomplemented
200C3×C4×D5—216no—
201C3×C4×D5—24no—
202C3×C4×D5—22no—
203C3×C4×D5—22no—
204C3×C4×D5—24no—
205C3×C4×D5C22⋊C412yes—
206C3×C4×D5C22⋊C412yes—
207C3×C4×D5C22⋊C412yes—
208C3×C4×D5C22⋊C412yes—
209C3×C4×D5C22×C412yes—
210C3×C4×D5C22×C412yes—
211C3×C4×D5C2×D412yes—
212C3×C4×D5C2×D412yes—
213C3×Dic10—21no—
214C3×Dic10—24no—
215C3×Dic10C22×C412yescomplemented
216C3×C5×C8—22no—
217C3×#168—22no—
218C2×C3×#41—54no—
219C2×C3×#41—54no—
220C2×C3×#41—51no—
221C2×C3×#41—51no—
222C2×C3×#41—51no—
223C2×C3×#41—101no—
224C2×C3×#41—101no—
225C2×C3×#41—102no—
226C2×C3×#41—102no—
227C2×C3×#41C2×D511yescharacteristic
228C22×C3×Q8—51no—
229C22×C3×D4—51no—
230C22×C3×D4—101no—
231C23×C3×C4—51no—
232C23×C3×C4—101no—
233C23×C3×C4—101no—
234C2×C3×M16—51no—
235C2×C3×M16—54no—
236C2×C3×M16—101no—
237C2×C3×M16—102no—
238C2×C3×M16C2×D511yescharacteristic, complemented
239C22×C3×C8—101no—
240C2×C3×C42—51no—
241C2×C3×C42—54no—
242C2×C3×C42—102no—
243C2×C3×C42—101no—
244C2×C3×C42C2×D511yescharacteristic, complemented
245C3×#104—54no—
246C3×#104—54no—
247C3×#104—54no—
248C3×#104C2×D514yesdirect product factor
249C23×D5—21no—
250C23×D5C3×D411yescharacteristic
251C5×#41—21no—
252C5×#41—21no—
253C5×#41C2×C3×C412yescomplemented
254C5×#41C23×C312yes—
255C2×C5×Q8C2×C3×C411yescharacteristic, complemented
256C2×C5×D4—21no—
257C2×C5×D4C2×C3×C411yescharacteristic, complemented
258C22×C4×C5—21no—
259C22×C4×C5—21no—
260C22×C4×C5C23×C311yescharacteristic
261C2×C22⋊D5—21no—
262C2×C22⋊D5—21no—
263C2×C22⋊D5—21no—
264C22×Dic5—21no—
265C22×Dic5—21no—
266C22×Dic5C3×D411yescharacteristic
267#713—22no—
268#713C2×C3×C414yescomplemented
269Q8×D5—22no—
270Q8×D5C2×C3×C414yescomplemented
271#711—24no—
272#711—24no—
273#711—22no—
274#711C2×C3×C414yescomplemented
275D4×D5—24no—
276D4×D5—24no—
277D4×D5—22no—
278D4×D5C2×C3×C414yescomplemented
279#709—21no—
280#709—21no—
281#709—24no—
282#709—24no—
283#709C2×C3×C412yescomplemented
284#709C23×C312yes—
285C2×D20—21no—
286C2×D20C2×C3×C411yescharacteristic, complemented
287C2×C4×D5—28no—
288C2×C4×D5—21no—
289C2×C4×D5—24no—
290C2×C4×D5—21no—
291C2×C4×D5—21no—
292C2×C4×D5—24no—
293C2×C4×D5—24no—
294C2×C4×D5C2×C3×C411yescharacteristic
295C2×C4×D5C2×C3×C411yescharacteristic
296C2×C4×D5C2×C3×C412yes—
297C2×C4×D5C3×D412yes—
298C2×C4×D5C3×D411yescharacteristic
299C2×C4×D5C3×D411yescharacteristic
300C2×C4×D5C3×D412yes—
301C2×C4×D5C23×C312yes—
302C2×Dic10—21no—
303C2×Dic10C2×C3×C411yescharacteristic, complemented
304C5×M16—21no—
305C5×M16C23×C312yescomplemented
306C2×C5×C8—21no—
307C42×C5—21no—
308C42×C5C23×C312yescomplemented
309C4×Dic5—21no—
310C4×Dic5—24no—
311C4×Dic5C23×C312yescomplemented
312#681—21no—
313#681C23×C312yescomplemented
314C2×#168—21no—
315#676—24no—
316C8×D5—24no—
317C22×#41—51no—
318C22×M16—51no—
319C22×C42—51no—
320C2×#104—51no—
321C2×#104—51no—
322C2×#104—51no—
323C2×#104—58no—
324C2×#104C3×D511yescharacteristic, direct product factor
325C22×C3×C5—22no—
326C22×C3×C5—22no—
327C22×C3×C5—42no—
328C22×C3×C5C2×C22⋊C411yescharacteristic
329C22×C3×C5C2×C22⋊C411yescharacteristic
330C22×C3×C5C22×D411yescharacteristic
331C2×C3×D5—22no—
332C2×C3×D5—24no—
333C2×C3×D5—24no—
334C2×C3×D5—22no—
335C2×C3×D5—42no—
336C2×C3×D5—48no—
337C2×C3×D5#10414yesdirect product factor
338C2×C3×D5C2×C22⋊C412yes—
339C2×C3×D5C2×C22⋊C412yes—
340C3×C4×C5—24no—
341C3×C4×C5—22no—
342C3×C4×C5C2×C22⋊C411yescharacteristic
343C3×C4×C5C2×C22⋊C411yescharacteristic
344C3×C4×C5C23×C411yescharacteristic
345C3×C4×C5C22×D411yescharacteristic
346C3×Dic5—24no—
347C3×Dic5—22no—
348C3×Dic5C2×C22⋊C412yes—
349C3×Dic5C2×C22⋊C412yes—
350C24×C3—51no—
351C24×C3—101no—
352C3×#41—21no—
353C3×#41—21no—
354C3×#41—54no—
355C3×#41—54no—
356C3×#41—52no—
357C3×#41—52no—
358C3×#41—104no—
359C3×#41—104no—
360C3×#41—104no—
361C3×#41—104no—
362C3×#41—102no—
363C3×#41—102no—
364C3×#41—101no—
365C3×#41—101no—
366C3×#41C4×D512yescomplemented
367C3×#41C22×D512yes—
368C2×C3×Q8—54no—
369C2×C3×Q8—51no—
370C2×C3×Q8—101no—
371C2×C3×Q8—102no—
372C2×C3×Q8C4×D511yescharacteristic, complemented
373C2×C3×D4—21no—
374C2×C3×D4—54no—
375C2×C3×D4—51no—
376C2×C3×D4—101no—
377C2×C3×D4—102no—
378C2×C3×D4—101no—
379C2×C3×D4—104no—
380C2×C3×D4—104no—
381C2×C3×D4—101no—
382C2×C3×D4—101no—
383C2×C3×D4C4×D511yescharacteristic, complemented
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—51no—
387C22×C3×C4—51no—
388C22×C3×C4—51no—
389C22×C3×C4—52no—
390C22×C3×C4—52no—
391C22×C3×C4—52no—
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C22×C3×C4—52no—
395C22×C3×C4—101no—
396C22×C3×C4—104no—
397C22×C3×C4—104no—
398C22×C3×C4—104no—
399C22×C3×C4—101no—
400C22×C3×C4—108no—
401C22×C3×C4—101no—
402C22×C3×C4—101no—
403C22×C3×C4—101no—
404C22×C3×C4C22×D511yescharacteristic
405C3×M16—21no—
406C3×M16—52no—
407C3×M16—104no—
408C3×M16—101no—
409C3×M16C22×D512yescomplemented
410C2×C3×C8—21no—
411C2×C3×C8—104no—
412C2×C3×C8—101no—
413C3×C42—21no—
414C3×C42—52no—
415C3×C42—104no—
416C3×C42—101no—
417C3×C42C22×D512yescomplemented
418C23×C5—21no—
419C23×C5C2×C3×D411yescharacteristic
420C22×D5—24no—
421C22×D5—21no—
422C22×D5—24no—
423C22×D5—44no—
424C22×D5C3×C22⋊C411yescharacteristic
425C22×D5C3×C22⋊C412yes—
426C22×D5C3×C22⋊C411yescharacteristic
427C22×D5C2×C3×D412yes—
428C5×Q8—21no—
429C5×Q8C22×C3×C412yescomplemented
430C5×D4—22no—
431C5×D4—22no—
432C5×D4—21no—
433C5×D4C22×C3×C412yescomplemented
434C2×C4×C5—24no—
435C2×C4×C5—21no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5C22×C3×C411yescharacteristic
440C2×C4×C5C22×C3×C411yescharacteristic
441C2×C4×C5C2×C3×D411yescharacteristic
442C2×C4×C5C2×C3×D411yescharacteristic
443C2×C4×C5C2×C3×D411yescharacteristic
444C2×C4×C5C24×C311yescharacteristic
445C22⋊D5—22no—
446C22⋊D5—22no—
447C22⋊D5—24no—
448C22⋊D5—24no—
449C2×Dic5—24no—
450C2×Dic5—21no—
451C2×Dic5—22no—
452C2×Dic5—24no—
453C2×Dic5C3×C22⋊C411yescharacteristic
454C2×Dic5C3×C22⋊C411yescharacteristic
455C2×Dic5C3×C22⋊C412yes—
456C2×Dic5C2×C3×D412yes—
457D20—24no—
458D20—21no—
459D20C22×C3×C412yescomplemented
460C4×D5—216no—
461C4×D5—24no—
462C4×D5—22no—
463C4×D5—22no—
464C4×D5—24no—
465C4×D5C3×C22⋊C412yes—
466C4×D5C3×C22⋊C412yes—
467C4×D5C3×C22⋊C412yes—
468C4×D5C3×C22⋊C412yes—
469C4×D5C22×C3×C412yes—
470C4×D5C22×C3×C412yes—
471C4×D5C2×C3×D412yes—
472C4×D5C2×C3×D412yes—
473Dic10—21no—
474Dic10—24no—
475Dic10C22×C3×C412yescomplemented
476C5×C8—22no—
477#168—22no—
478C2×#41—54no—
479C2×#41—54no—
480C2×#41—51no—
481C2×#41—51no—
482C2×#41—51no—
483C2×#41—101no—
484C2×#41—101no—
485C2×#41—102no—
486C2×#41—102no—
487C2×#41C2×C3×D511yescharacteristic
488C22×Q8—51no—
489C22×D4—51no—
490C22×D4—101no—
491C23×C4—51no—
492C23×C4—101no—
493C23×C4—101no—
494C2×M16—51no—
495C2×M16—54no—
496C2×M16—101no—
497C2×M16—102no—
498C2×M16C2×C3×D511yescharacteristic, complemented
499C22×C8—101no—
500C2×C42—51no—
501C2×C42—54no—
502C2×C42—102no—
503C2×C42—101no—
504C2×C42C2×C3×D511yescharacteristic, complemented
505#104—54no—
506#104—54no—
507#104—54no—
508#104C2×C3×D514yesdirect product factor
509C2×C3×C5—21no—
510C2×C3×C5—21no—
511C2×C3×C5—42no—
512C2×C3×C5C2×#10412yescomplemented
513C2×C3×C5C22×C22⋊C411yescharacteristic
514C3×D5—22no—
515C3×D5—42no—
516C3×D5C2×#10414yesdirect product factor
517C23×C3—21no—
518C23×C3—51no—
519C23×C3—52no—
520C23×C3—52no—
521C23×C3—51no—
522C23×C3—104no—
523C23×C3—104no—
524C23×C3—101no—
525C23×C3—204no—
526C23×C3D4×D511yescharacteristic
527C3×Q8—21no—
528C3×Q8—52no—
529C3×Q8—104no—
530C3×Q8—101no—
531C3×Q8C2×C4×D512yescomplemented
532C3×D4—22no—
533C3×D4—22no—
534C3×D4—21no—
535C3×D4—52no—
536C3×D4—104no—
537C3×D4—104no—
538C3×D4—104no—
539C3×D4—102no—
540C3×D4—102no—
541C3×D4—101no—
542C3×D4C2×C4×D512yescomplemented
543C2×C3×C4—24no—
544C2×C3×C4—22no—
545C2×C3×C4—21no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—52no—
549C2×C3×C4—51no—
550C2×C3×C4—51no—
551C2×C3×C4—52no—
552C2×C3×C4—52no—
553C2×C3×C4—52no—
554C2×C3×C4—52no—
555C2×C3×C4—52no—
556C2×C3×C4—52no—
557C2×C3×C4—52no—
558C2×C3×C4—52no—
559C2×C3×C4—52no—
560C2×C3×C4—104no—
561C2×C3×C4—104no—
562C2×C3×C4—1016no—
563C2×C3×C4—104no—
564C2×C3×C4—104no—
565C2×C3×C4—102no—
566C2×C3×C4—101no—
567C2×C3×C4—102no—
568C2×C3×C4—102no—
569C2×C3×C4C2×C4×D511yescharacteristic
570C2×C3×C4C2×C4×D511yescharacteristic
571C2×C3×C4D4×D511yescharacteristic
572C2×C3×C4D4×D511yescharacteristic
573C2×C3×C4D4×D511yescharacteristic
574C2×C3×C4C23×D511yescharacteristic
575C3×C8—22no—
576C3×C8—102no—
577C22×C5—22no—
578C22×C5—22no—
579C22×C5—42no—
580C22×C5C2×C3×C22⋊C411yescharacteristic
581C22×C5C2×C3×C22⋊C411yescharacteristic
582C22×C5C22×C3×D411yescharacteristic
583C2×D5—22no—
584C2×D5—24no—
585C2×D5—24no—
586C2×D5—22no—
587C2×D5—42no—
588C2×D5—48no—
589C2×D5C3×#10414yesdirect product factor
590C2×D5C2×C3×C22⋊C412yes—
591C2×D5C2×C3×C22⋊C412yes—
592C4×C5—24no—
593C4×C5—22no—
594C4×C5C2×C3×C22⋊C411yescharacteristic
595C4×C5C2×C3×C22⋊C411yescharacteristic
596C4×C5C23×C3×C411yescharacteristic
597C4×C5C22×C3×D411yescharacteristic
598Dic5—24no—
599Dic5—22no—
600Dic5C2×C3×C22⋊C412yes—
601Dic5C2×C3×C22⋊C412yes—
602C24—51no—
603C24—101no—
604#41—21no—
605#41—21no—
606#41—54no—
607#41—54no—
608#41—52no—
609#41—52no—
610#41—104no—
611#41—104no—
612#41—104no—
613#41—104no—
614#41—102no—
615#41—102no—
616#41—101no—
617#41—101no—
618#41C3×C4×D512yescomplemented
619#41C22×C3×D512yes—
620C2×Q8—54no—
621C2×Q8—51no—
622C2×Q8—101no—
623C2×Q8—102no—
624C2×Q8C3×C4×D511yescharacteristic, complemented
625C2×D4—21no—
626C2×D4—54no—
627C2×D4—51no—
628C2×D4—101no—
629C2×D4—102no—
630C2×D4—101no—
631C2×D4—104no—
632C2×D4—104no—
633C2×D4—101no—
634C2×D4—101no—
635C2×D4C3×C4×D511yescharacteristic, complemented
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—51no—
639C22×C4—51no—
640C22×C4—51no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—51no—
644C22×C4—51no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—101no—
648C22×C4—104no—
649C22×C4—104no—
650C22×C4—104no—
651C22×C4—101no—
652C22×C4—108no—
653C22×C4—101no—
654C22×C4—101no—
655C22×C4—101no—
656C22×C4C22×C3×D511yescharacteristic
657M16—21no—
658M16—52no—
659M16—104no—
660M16—101no—
661M16C22×C3×D512yescomplemented
662C2×C8—21no—
663C2×C8—104no—
664C2×C8—101no—
665C42—21no—
666C42—52no—
667C42—104no—
668C42—101no—
669C42C22×C3×D512yescomplemented
670C3×C5C22×#10411yescharacteristic, complemented, Hall
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—42no—
674C22×C3—52no—
675C22×C3—54no—
676C22×C3—52no—
677C22×C3—104no—
678C22×C3—104no—
679C22×C3—102no—
680C22×C3—102no—
681C22×C3—208no—
682C22×C3—202no—
683C22×C3D5×C22⋊C411yescharacteristic
684C22×C3D5×C22⋊C411yescharacteristic
685C22×C3C2×D4×D511yescharacteristic
686C3×C4—24no—
687C3×C4—22no—
688C3×C4—52no—
689C3×C4—52no—
690C3×C4—104no—
691C3×C4—102no—
692C3×C4D5×C22⋊C411yescharacteristic
693C3×C4D5×C22⋊C411yescharacteristic
694C3×C4C22×C4×D511yescharacteristic
695C3×C4C2×D4×D511yescharacteristic
696C2×C5—21no—
697C2×C5—21no—
698C2×C5—42no—
699C2×C5C2×C3×#10412yescomplemented
700C2×C5C22×C3×C22⋊C411yescharacteristic
701D5—22no—
702D5—42no—
703D5C2×C3×#10414yesdirect product factor
704C23—21no—
705C23—51no—
706C23—52no—
707C23—52no—
708C23—51no—
709C23—104no—
710C23—104no—
711C23—101no—
712C23—204no—
713C23C3×D4×D511yescharacteristic
714Q8—21no—
715Q8—52no—
716Q8—104no—
717Q8—101no—
718Q8C2×C3×C4×D512yescomplemented
719D4—22no—
720D4—22no—
721D4—21no—
722D4—52no—
723D4—104no—
724D4—104no—
725D4—104no—
726D4—102no—
727D4—102no—
728D4—101no—
729D4C2×C3×C4×D512yescomplemented
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—52no—
736C2×C4—51no—
737C2×C4—51no—
738C2×C4—52no—
739C2×C4—52no—
740C2×C4—52no—
741C2×C4—52no—
742C2×C4—52no—
743C2×C4—52no—
744C2×C4—52no—
745C2×C4—52no—
746C2×C4—52no—
747C2×C4—104no—
748C2×C4—104no—
749C2×C4—1016no—
750C2×C4—104no—
751C2×C4—104no—
752C2×C4—102no—
753C2×C4—101no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4C2×C3×C4×D511yescharacteristic
757C2×C4C2×C3×C4×D511yescharacteristic
758C2×C4C3×D4×D511yescharacteristic
759C2×C4C3×D4×D511yescharacteristic
760C2×C4C3×D4×D511yescharacteristic
761C2×C4C23×C3×D511yescharacteristic
762C8—22no—
763C8—102no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3—54no—
768C2×C3—102no—
769C2×C3—202no—
770C2×C3D5×#10412yesdirect product factor
771C2×C3C2×D5×C22⋊C411yescharacteristic
772C5C22×C3×#10411yescharacteristic, complemented, Sylow
773C22—22no—
774C22—22no—
775C22—42no—
776C22—54no—
777C22—52no—
778C22—52no—
779C22—104no—
780C22—104no—
781C22—102no—
782C22—102no—
783C22—208no—
784C22—202no—
785C22C3×D5×C22⋊C411yescharacteristic
786C22C3×D5×C22⋊C411yescharacteristic
787C22C2×C3×D4×D511yescharacteristic
788C4—24no—
789C4—22no—
790C4—52no—
791C4—52no—
792C4—104no—
793C4—102no—
794C4C3×D5×C22⋊C411yescharacteristic
795C4C3×D5×C22⋊C411yescharacteristic
796C4C22×C3×C4×D511yescharacteristic
797C4C2×C3×D4×D511yescharacteristic
798C3C2×D5×#10411yescharacteristic, direct product factor, Sylow
799C2—21no—
800C2—21no—
801C2—42no—
802C2—54no—
803C2—102no—
804C2—202no—
805C2C3×D5×#10412yesdirect product factor
806C2C2×C3×D5×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C3×C4D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#104C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D5×#41C2
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#104D5
hypocenterC5C22×C3×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×M16C2semidirect
3. C2×C3×C42×D5C2semidirect
4. C2×C3×C5×#104C2semidirect
5. C2×C3×#3969C2semidirect
6. C2×C3×#3957C2semidirect
7. C2×C3×#3937C2semidirect
8. C3×D5×#104C2direct (N × H)
9. C2×D5×#104C3direct (N × H)
13. C3×D5×#41C4semidirect
15. C2×C3×#713C4semidirect
16. C2×C3×Q8×D5C4semidirect
18. C2×C3×#711C4semidirect
20. C2×C3×D4×D5C4semidirect
26. C2×C3×C5×M16C22semidirect
27. C2×C3×C42×C5C22semidirect
29. C2×C3×C4×Dic5C22semidirect
30. C2×C3×#681C22semidirect
32. C3×D5×M16C22semidirect
36. C3×C42×D5C22semidirect
37. C3×C5×#104C22semidirect
38. C3×#3969C22semidirect
39. C3×#3957C22semidirect
40. C3×#3937C22semidirect
43. C2×D5×M16C2×C3semidirect
44. C2×C42×D5C2×C3semidirect
45. C2×C5×#104C2×C3semidirect
46. C2×#3969C2×C3semidirect
47. C2×#3957C2×C3semidirect
48. C2×#3937C2×C3semidirect
49. D5×#104C2×C3direct (N × H)
54. C3×C5×#41C2×C4semidirect
56. C2×C3×C5×Q8C2×C4semidirect
58. C2×C3×C5×D4C2×C4semidirect
69. C3×#713C2×C4semidirect
71. C3×Q8×D5C2×C4semidirect
75. C3×#711C2×C4semidirect
79. C3×D4×D5C2×C4semidirect
84. C3×#709C2×C4semidirect
87. C2×C3×D20C2×C4semidirect
104. C2×C3×Dic10C2×C4semidirect
106. C3×C5×M16C23semidirect
109. C3×C42×C5C23semidirect
112. C3×C4×Dic5C23semidirect
114. C3×#681C23semidirect
125. C2×C3×#104D5direct (N × H)
129. D5×#41C3×C4semidirect
131. C2×#713C3×C4semidirect
132. C2×Q8×D5C3×C4semidirect
134. C2×#711C3×C4semidirect
136. C2×D4×D5C3×C4semidirect
142. C2×C5×M16C22×C3semidirect
143. C2×C42×C5C22×C3semidirect
145. C2×C4×Dic5C22×C3semidirect
146. C2×#681C22×C3semidirect
148. D5×M16C22×C3semidirect
152. C42×D5C22×C3semidirect
153. C5×#104C22×C3semidirect
154. #3969C22×C3semidirect
155. #3957C22×C3semidirect
156. #3937C22×C3semidirect
169. C3×C5×Q8C22×C4semidirect
173. C3×C5×D4C22×C4semidirect
199. C3×D20C22×C4semidirect
215. C3×Dic10C22×C4semidirect
238. C2×C3×M16C2×D5semidirect
244. C2×C3×C42C2×D5semidirect
248. C3×#104C2×D5direct (N × H)
253. C5×#41C2×C3×C4semidirect
255. C2×C5×Q8C2×C3×C4semidirect
257. C2×C5×D4C2×C3×C4semidirect
268. #713C2×C3×C4semidirect
270. Q8×D5C2×C3×C4semidirect
274. #711C2×C3×C4semidirect
278. D4×D5C2×C3×C4semidirect
283. #709C2×C3×C4semidirect
286. C2×D20C2×C3×C4semidirect
303. C2×Dic10C2×C3×C4semidirect
305. C5×M16C23×C3semidirect
308. C42×C5C23×C3semidirect
311. C4×Dic5C23×C3semidirect
313. #681C23×C3semidirect
324. C2×#104C3×D5direct (N × H)
337. C2×C3×D5#104direct (N × H)
366. C3×#41C4×D5semidirect
372. C2×C3×Q8C4×D5semidirect
383. C2×C3×D4C4×D5semidirect
409. C3×M16C22×D5semidirect
417. C3×C42C22×D5semidirect
429. C5×Q8C22×C3×C4semidirect
433. C5×D4C22×C3×C4semidirect
459. D20C22×C3×C4semidirect
475. Dic10C22×C3×C4semidirect
498. C2×M16C2×C3×D5semidirect
504. C2×C42C2×C3×D5semidirect
508. #104C2×C3×D5direct (N × H)
512. C2×C3×C5C2×#104semidirect
516. C3×D5C2×#104direct (N × H)
531. C3×Q8C2×C4×D5semidirect
542. C3×D4C2×C4×D5semidirect
589. C2×D5C3×#104direct (N × H)
618. #41C3×C4×D5semidirect
624. C2×Q8C3×C4×D5semidirect
635. C2×D4C3×C4×D5semidirect
661. M16C22×C3×D5semidirect
669. C42C22×C3×D5semidirect
670. C3×C5C22×#104semidirect
699. C2×C5C2×C3×#104semidirect
703. D5C2×C3×#104direct (N × H)
718. Q8C2×C3×C4×D5semidirect
729. D4C2×C3×C4×D5semidirect
770. C2×C3D5×#104direct (N × H)
772. C5C22×C3×#104semidirect
798. C3C2×D5×#104direct (N × H)
805. C2C3×D5×#104direct (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
C2×C3×D5×M162
C2×C3×C42×D52
C2×C3×C5×#1042
C2×C3×#39692
C2×C3×#39572
C2×C3×#39372
C3×D5×#1042
C2×D5×#1043
C22×C3×#1045