Finite Group Databasebeta

← C4×D3×Q8×D5 #14478851

Subgroups — C4×D3×Q8×D5 #14478851

Order 1920.

3328 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Q8×D5C211yesmaximal, characteristic
2C4×Q8×D15C211yesmaximal, characteristic, complemented
3C4×C5×D3×Q8C211yesmaximal, characteristic, complemented
4C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
5Q8×#1200C211yesmaximal, characteristic, complemented
6D3×Q8×Dic5C211yesmaximal, characteristic, complemented
7Q8×D5×Dic3C211yesmaximal, characteristic, complemented
8D3×D5×C4⋊C4C213yesmaximal
9#11753409C213yesmaximal, complemented
10D3×#4033C213yesmaximal, complemented
11D5×#887C213yesmaximal, complemented
12C42×D3×D5C213yesmaximal
13C4×D15⋊Q8C213yesmaximal, complemented
14C4×D3×Dic10C213yesmaximal, complemented
15C4×D5×Dic6C213yesmaximal, complemented
16C2×C4×Q8×D5—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic
20D3×Q8×D5C4116yesdirect product factor
21C2×C4×D3×D5C2213yes—
22C2×C4×D3×D5C2213yes—
23C2×C4×D3×D5C2211yescharacteristic
24C2×D15⋊Q8C2213yes—
25C2×D3×Dic10C2213yes—
26C2×D5×Dic6C2213yes—
27C3×C4×C5×Q8C2211yescharacteristic, complemented
28Q8×Dic15C2211yescharacteristic, complemented
29C4⋊C4×D15C2213yes—
30#91776C2213yescomplemented
31C42×D15C2213yes—
32C4×Dic30C2213yescomplemented
33C5×Q8×Dic3C2211yescharacteristic, complemented
34C5×D3×C4⋊C4C2213yes—
35C5×#887C2213yescomplemented
36C42×C5×D3C2213yes—
37C4×C5×Dic6C2213yescomplemented
38C3×Q8×Dic5C2211yescharacteristic, complemented
39C3×D5×C4⋊C4C2213yes—
40C3×#4033C2213yescomplemented
41C3×C42×D5C2213yes—
42C3×C4×Dic10C2213yescomplemented
43C4×#1204C2216yescomplemented
44#91437C2213yes—
45D3×C4⋊Dic5C2213yes—
46D5×C4⋊Dic3C2213yes—
47#91404C2216yes—
48C4×#1200C2213yes—
49C4×#1200C2213yes—
50C4×#1200C2213yes—
51D3×#683C2216yes—
52C4×D3×Dic5C2213yes—
53C4×D3×Dic5C2213yes—
54C4×D3×Dic5C2213yes—
55D5×Dic3⋊C4C2216yes—
56C4×D5×Dic3C2213yes—
57C4×D5×Dic3C2213yes—
58C4×D5×Dic3C2213yes—
59#91344C2213yescomplemented
60#91340C2213yescomplemented
61#91333C2213yescomplemented
62Dic5×Dic6C2213yescomplemented
63#91331C2213yescomplemented
64Dic3×Dic10C2213yescomplemented
65#91325C2216yescomplemented
66#91324C2216yescomplemented
67#91323C2216yescomplemented
68C2×C4×D3×Q8—51nomaximal, Hall
69C22×Q8×D5—31no—
70C2×C4×C5×Q8—31no—
71C2×Q8×Dic5—31no—
72C4×Q8×D5—31no—
73C4×Q8×D5—33no—
74C4×Q8×D5—33no—
75C4×Q8×D5—33no—
76C4×Q8×D5—33no—
77C4×Q8×D5—31no—
78C4×Q8×D5—31no—
79C4×Q8×D5D311yescharacteristic, direct product factor
80C2×D5×C4⋊C4—33no—
81C2×#4033—33no—
82C2×C42×D5—33no—
83C2×C4×Dic10—33no—
84C22×D3×D5C2311yescharacteristic
85C2×C3×C5×Q8C2311yescharacteristic
86Q8×D15C2×C418yescomplemented
87C2×C4×D15C2313yes—
88C2×C4×D15C2313yes—
89C2×C4×D15C2311yescharacteristic
90C2×Dic30C2313yes—
91C5×D3×Q8C2×C418yescomplemented
92C2×C4×C5×D3C2313yes—
93C2×C4×C5×D3C2313yes—
94C2×C4×C5×D3C2311yescharacteristic
95C2×C5×Dic6C2313yes—
96C3×Q8×D5C2×C418yescomplemented
97C2×C3×C4×D5C2313yes—
98C2×C3×C4×D5C2313yes—
99C2×C3×C4×D5C2311yescharacteristic
100C2×C3×Dic10C2313yes—
101C2×#1204C2316yes—
102C2×#1200C2313yes—
103C2×#1200C2313yes—
104C2×#1200C2311yescharacteristic
105C2×D3×Dic5C2313yes—
106C2×D3×Dic5C2313yes—
107C2×D3×Dic5C2311yescharacteristic
108C2×D5×Dic3C2313yes—
109C2×D5×Dic3C2313yes—
110C2×D5×Dic3C2311yescharacteristic
111C4×D3×D5—212no—
112C4×D3×D5C2×C4124yes—
113C4×D3×D5Q818yesdirect product factor
114D15⋊Q8C2×C4124yescomplemented
115D3×Dic10C2×C4124yescomplemented
116D5×Dic6C2×C4124yescomplemented
117C3×C5×C4⋊C4C2313yes—
118C3×C42×C5C2313yes—
119C4⋊Dic15C2313yes—
120#6712C2316yes—
121C4×Dic15C2313yes—
122C4×Dic15C2313yes—
123C4×Dic15C2313yes—
124C5×C4⋊Dic3C2313yes—
125C5×Dic3⋊C4C2316yes—
126C4×C5×Dic3C2313yes—
127C4×C5×Dic3C2313yes—
128C4×C5×Dic3C2313yes—
129C3×C4⋊Dic5C2313yes—
130C3×#683C2316yes—
131C3×C4×Dic5C2313yes—
132C3×C4×Dic5C2313yes—
133C3×C4×Dic5C2313yes—
134Dic3⋊Dic5C2316yes—
135#6669C2316yes—
136#6668C2316yes—
137Dic3×Dic5C2313yes—
138Dic3×Dic5C2313yes—
139Dic3×Dic5C2313yes—
140Dic3×Dic5C2313yes—
141Dic3×Dic5C2313yes—
142Dic3×Dic5C2313yes—
143C22×D3×Q8—51no—
144C2×C3×C4×Q8—51no—
145C2×Q8×Dic3—51no—
146C4×D3×Q8—51no—
147C4×D3×Q8—51no—
148C4×D3×Q8—51no—
149C4×D3×Q8—53no—
150C4×D3×Q8—53no—
151C4×D3×Q8—53no—
152C4×D3×Q8—53no—
153C4×D3×Q8D511yescharacteristic, direct product factor
154C2×D3×C4⋊C4—53no—
155C2×#887—53no—
156C2×C42×D3—53no—
157C2×C4×Dic6—53no—
158C22×C5×Q8—31no—
159C2×Q8×D5—31no—
160C2×Q8×D5—316no—
161C2×Q8×D5—33no—
162C2×Q8×D5—33no—
163C2×Q8×D5C2×D311yescharacteristic
164C22×C4×D5—31no—
165C22×C4×D5—33no—
166C22×C4×D5—33no—
167C22×Dic10—33no—
168C4×C5×Q8—31no—
169C4×C5×Q8—33no—
170C4×C5×Q8—33no—
171C4×C5×Q8C2×D311yescharacteristic, complemented
172C2×C5×C4⋊C4—33no—
173C2×C42×C5—33no—
174Q8×Dic5—31no—
175Q8×Dic5—33no—
176Q8×Dic5—33no—
177Q8×Dic5C2×D311yescharacteristic, complemented
178C2×C4⋊Dic5—33no—
179C2×#683—36no—
180C2×C4×Dic5—33no—
181C2×C4×Dic5—33no—
182C2×C4×Dic5—33no—
183D5×C4⋊C4—36no—
184D5×C4⋊C4—33no—
185D5×C4⋊C4—33no—
186D5×C4⋊C4—33no—
187D5×C4⋊C4—36no—
188D5×C4⋊C4C2×D313yes—
189#4033—33no—
190#4033—33no—
191#4033—36no—
192#4033—36no—
193#4033—33no—
194#4033C2×D313yescomplemented
195C42×D5—33no—
196C42×D5—33no—
197C42×D5—33no—
198C42×D5—33no—
199C42×D5—33no—
200C42×D5—33no—
201C42×D5—33no—
202C42×D5C2×D313yes—
203C4×Dic10—33no—
204C4×Dic10—33no—
205C4×Dic10—33no—
206C4×Dic10—36no—
207C4×Dic10—36no—
208C4×Dic10C2×D313yescomplemented
209C22×C4×Q8—151noSylow
210C22×D15C2411yescharacteristic
211C22×C5×D3C2411yescharacteristic
212C22×C3×D5C2411yescharacteristic
213C2×D3×D5C22×C414yes—
214C2×D3×D5C2×Q814yes—
215C2×D3×D5#4114yes—
216C3×C5×Q8C22×C414yescomplemented
217C2×C3×C4×C5C2413yes—
218C2×C3×C4×C5C2413yes—
219C2×C3×C4×C5C2411yescharacteristic
220C2×Dic15C2413yes—
221C2×Dic15C2413yes—
222C2×Dic15C2411yescharacteristic
223C4×D15—26no—
224C4×D15C22×C4112yes—
225C4×D15C2×Q814yescomplemented
226Dic30C22×C4112yescomplemented
227C2×C5×Dic3C2413yes—
228C2×C5×Dic3C2413yes—
229C2×C5×Dic3C2411yescharacteristic
230C4×C5×D3—26no—
231C4×C5×D3C22×C4112yes—
232C4×C5×D3C2×Q814yescomplemented
233C5×Dic6C22×C4112yescomplemented
234C2×C3×Dic5C2413yes—
235C2×C3×Dic5C2413yes—
236C2×C3×Dic5C2411yescharacteristic
237C3×C4×D5—26no—
238C3×C4×D5C22×C4112yes—
239C3×C4×D5C2×Q814yescomplemented
240C3×Dic10C22×C4112yescomplemented
241#1204C22×C4124yescomplemented
242#1200—26no—
243#1200C22×C4112yes—
244#1200C2×Q814yescomplemented
245D3×Dic5—26no—
246D3×Dic5C22×C4112yes—
247D3×Dic5C2×Q814yescomplemented
248D5×Dic3—26no—
249D5×Dic3C22×C4112yes—
250D5×Dic3C2×Q814yescomplemented
251C22×C3×Q8—51no—
252C2×D3×Q8—51no—
253C2×D3×Q8—516no—
254C2×D3×Q8—53no—
255C2×D3×Q8—53no—
256C2×D3×Q8C2×D511yescharacteristic
257C22×C4×D3—53no—
258C22×C4×D3—51no—
259C22×C4×D3—53no—
260C22×Dic6—53no—
261C3×C4×Q8—51no—
262C3×C4×Q8—53no—
263C3×C4×Q8—53no—
264C3×C4×Q8C2×D511yescharacteristic, complemented
265C2×C3×C4⋊C4—53no—
266C2×C3×C42—53no—
267Q8×Dic3—51no—
268Q8×Dic3—53no—
269Q8×Dic3—53no—
270Q8×Dic3C2×D511yescharacteristic, complemented
271C2×C4⋊Dic3—53no—
272C2×Dic3⋊C4—56no—
273C2×C4×Dic3—53no—
274C2×C4×Dic3—53no—
275C2×C4×Dic3—53no—
276D3×C4⋊C4—56no—
277D3×C4⋊C4—53no—
278D3×C4⋊C4—53no—
279D3×C4⋊C4—53no—
280D3×C4⋊C4—56no—
281D3×C4⋊C4C2×D513yes—
282#887—53no—
283#887—53no—
284#887—56no—
285#887—56no—
286#887—53no—
287#887C2×D513yescomplemented
288C42×D3—53no—
289C42×D3—53no—
290C42×D3—53no—
291C42×D3—53no—
292C42×D3—53no—
293C42×D3—53no—
294C42×D3—53no—
295C42×D3C2×D513yes—
296C4×Dic6—53no—
297C4×Dic6—53no—
298C4×Dic6—53no—
299C4×Dic6—56no—
300C4×Dic6—56no—
301C4×Dic6C2×D513yescomplemented
302C23×D5—31no—
303C2×C5×Q8—38no—
304C2×C5×Q8—33no—
305C2×C5×Q8C22×D311yescharacteristic
306C22×C4×C5—31no—
307C22×C4×C5—33no—
308C22×C4×C5—33no—
309C22×Dic5—33no—
310C22×Dic5—31no—
311C22×Dic5—33no—
312Q8×D5—38no—
313Q8×D5—324no—
314Q8×D5—324no—
315Q8×D5C4×D318yesdirect product factor
316C2×C4×D5—33no—
317C2×C4×D5—31no—
318C2×C4×D5—33no—
319C2×C4×D5—31no—
320C2×C4×D5—33no—
321C2×C4×D5—31no—
322C2×C4×D5—324no—
323C2×C4×D5—38no—
324C2×C4×D5—33no—
325C2×C4×D5—33no—
326C2×C4×D5—33no—
327C2×C4×D5—612no—
328C2×C4×D5C22×D313yes—
329C2×C4×D5C22×D313yes—
330C2×C4×D5C22×D311yescharacteristic
331C2×Dic10—33no—
332C2×Dic10—36no—
333C2×Dic10—324no—
334C2×Dic10C22×D313yes—
335C5×C4⋊C4—36no—
336C5×C4⋊C4—33no—
337C5×C4⋊C4C22×D313yes—
338C42×C5—33no—
339C42×C5—33no—
340C42×C5—33no—
341C42×C5C22×D313yes—
342C4⋊Dic5—33no—
343C4⋊Dic5—36no—
344C4⋊Dic5C22×D313yes—
345#683—36no—
346#683—36no—
347#683—36no—
348#683C22×D316yes—
349C4×Dic5—33no—
350C4×Dic5—33no—
351C4×Dic5—33no—
352C4×Dic5—33no—
353C4×Dic5—33no—
354C4×Dic5—33no—
355C4×Dic5—33no—
356C4×Dic5—33no—
357C4×Dic5—33no—
358C4×Dic5C22×D313yes—
359C4×Dic5C22×D313yes—
360C4×Dic5C22×D313yes—
361C23×Q8—151no—
362C2×C4×Q8—31no—
363C2×C4×Q8—51no—
364C2×C4×Q8—153no—
365C2×C4×Q8—153no—
366C2×C4×Q8—153no—
367C2×C4×Q8—153no—
368C2×C4×Q8—151no—
369C2×C4×Q8—153no—
370C2×C4×Q8—153no—
371C2×C4×Q8—151no—
372C2×C4×Q8—151no—
373C2×C4×Q8—151no—
374C22×C4⋊C4—153no—
375C22×C42—153no—
376C22×C3×C5C2511yescharacteristic
377C2×D15C23×C412yes—
378C2×D15C22×Q812yes—
379C2×D15C2×#4112yes—
380C2×C5×D3C23×C412yes—
381C2×C5×D3C22×Q812yes—
382C2×C5×D3C2×#4112yes—
383C2×C3×D5C23×C412yes—
384C2×C3×D5C22×Q812yes—
385C2×C3×D5C2×#4112yes—
386D3×D5C4×Q8116yesdirect product factor
387C3×C4×C5—23no—
388C3×C4×C5C23×C416yes—
389C3×C4×C5C22×Q812yescomplemented
390Dic15—23no—
391Dic15C23×C416yes—
392Dic15C22×Q812yescomplemented
393C3×Dic5—23no—
394C3×Dic5C23×C416yes—
395C3×Dic5C22×Q812yescomplemented
396C5×Dic3—23no—
397C5×Dic3C23×C416yes—
398C5×Dic3C22×Q812yescomplemented
399C23×D3—51no—
400C2×C3×Q8—58no—
401C2×C3×Q8—53no—
402C2×C3×Q8C22×D511yescharacteristic
403C22×C3×C4—51no—
404C22×C3×C4—53no—
405C22×C3×C4—53no—
406C22×Dic3—51no—
407C22×Dic3—53no—
408C22×Dic3—53no—
409D3×Q8—58no—
410D3×Q8—524no—
411D3×Q8—524no—
412D3×Q8C4×D518yesdirect product factor
413C2×C4×D3—51no—
414C2×C4×D3—53no—
415C2×C4×D3—51no—
416C2×C4×D3—53no—
417C2×C4×D3—51no—
418C2×C4×D3—53no—
419C2×C4×D3—524no—
420C2×C4×D3—58no—
421C2×C4×D3—53no—
422C2×C4×D3—53no—
423C2×C4×D3—53no—
424C2×C4×D3—1012no—
425C2×C4×D3C22×D513yes—
426C2×C4×D3C22×D513yes—
427C2×C4×D3C22×D511yescharacteristic
428C2×Dic6—53no—
429C2×Dic6—56no—
430C2×Dic6—524no—
431C2×Dic6C22×D513yes—
432C3×C4⋊C4—56no—
433C3×C4⋊C4—53no—
434C3×C4⋊C4C22×D513yes—
435C3×C42—53no—
436C3×C42—53no—
437C3×C42—53no—
438C3×C42C22×D513yes—
439C4⋊Dic3—53no—
440C4⋊Dic3—56no—
441C4⋊Dic3C22×D513yes—
442Dic3⋊C4—56no—
443Dic3⋊C4—56no—
444Dic3⋊C4—56no—
445Dic3⋊C4C22×D516yes—
446C4×Dic3—53no—
447C4×Dic3—53no—
448C4×Dic3—53no—
449C4×Dic3—53no—
450C4×Dic3—53no—
451C4×Dic3—53no—
452C4×Dic3—53no—
453C4×Dic3—53no—
454C4×Dic3—53no—
455C4×Dic3C22×D513yes—
456C4×Dic3C22×D513yes—
457C4×Dic3C22×D513yes—
458C23×C5—31no—
459C22×D5—31no—
460C22×D5—34no—
461C22×D5—34no—
462C22×D5—34no—
463C22×D5C23×D311yescharacteristic
464C5×Q8—312no—
465C5×Q8C2×C4×D314yescomplemented
466C2×C4×C5—31no—
467C2×C4×C5—33no—
468C2×C4×C5—312no—
469C2×C4×C5—34no—
470C2×C4×C5—33no—
471C2×C4×C5—66no—
472C2×C4×C5C23×D313yes—
473C2×C4×C5C23×D313yes—
474C2×C4×C5C23×D311yescharacteristic
475C2×Dic5—31no—
476C2×Dic5—33no—
477C2×Dic5—312no—
478C2×Dic5—34no—
479C2×Dic5—33no—
480C2×Dic5—66no—
481C2×Dic5C23×D313yes—
482C2×Dic5C23×D313yes—
483C2×Dic5C23×D311yescharacteristic
484C4×D5—26no—
485C4×D5—312no—
486C4×D5—34no—
487C4×D5—312no—
488C4×D5—34no—
489C4×D5—312no—
490C4×D5—34no—
491C4×D5—66no—
492C4×D5—66no—
493C4×D5—66no—
494C4×D5C2×C4×D3112yes—
495C4×D5D3×Q814yesdirect product factor
496Dic10—312no—
497Dic10—324no—
498Dic10C2×C4×D3112yescomplemented
499C22×Q8—31no—
500C22×Q8—51no—
501C22×Q8—153no—
502C22×Q8—153no—
503C22×Q8—153no—
504C22×Q8—1516no—
505C22×Q8—151no—
506C23×C4—153no—
507C23×C4—151no—
508C23×C4—153no—
509C4×Q8—31no—
510C4×Q8—33no—
511C4×Q8—33no—
512C4×Q8—51no—
513C4×Q8—53no—
514C4×Q8—53no—
515C4×Q8—156no—
516C4×Q8—156no—
517C4×Q8—153no—
518C4×Q8—153no—
519C4×Q8—156no—
520C4×Q8—153no—
521C4×Q8—153no—
522C4×Q8—156no—
523C4×Q8—153no—
524C4×Q8—153no—
525C4×Q8—151no—
526C4×Q8—153no—
527C4×Q8—153no—
528C4×Q8D3×D511yescharacteristic, direct product factor
529C2×C4⋊C4—33no—
530C2×C4⋊C4—53no—
531C2×C4⋊C4—156no—
532C2×C4⋊C4—153no—
533C2×C4⋊C4—156no—
534C2×C4⋊C4—153no—
535C2×C4⋊C4—156no—
536C2×C4⋊C4—153no—
537C2×C4⋊C4—153no—
538C2×C42—33no—
539C2×C42—53no—
540C2×C42—153no—
541C2×C42—153no—
542C2×C42—153no—
543C2×C42—153no—
544C2×C42—153no—
545C2×C42—153no—
546C2×C42—153no—
547C2×C42—153no—
548C2×C42—153no—
549C2×C42—153no—
550C2×C3×C5C24×C411yescharacteristic
551C2×C3×C5C23×Q811yescharacteristic
552C2×C3×C5C22×#4111yescharacteristic
553D15C2×C4×Q814yescomplemented
554C3×D5C2×C4×Q814yescomplemented
555C5×D3C2×C4×Q814yescomplemented
556C23×C3—51no—
557C22×D3—51no—
558C22×D3—54no—
559C22×D3—54no—
560C22×D3—54no—
561C22×D3C23×D511yescharacteristic
562C3×Q8—512no—
563C3×Q8C2×C4×D514yescomplemented
564C2×C3×C4—51no—
565C2×C3×C4—53no—
566C2×C3×C4—512no—
567C2×C3×C4—54no—
568C2×C3×C4—53no—
569C2×C3×C4—106no—
570C2×C3×C4C23×D513yes—
571C2×C3×C4C23×D513yes—
572C2×C3×C4C23×D511yescharacteristic
573C2×Dic3—51no—
574C2×Dic3—53no—
575C2×Dic3—512no—
576C2×Dic3—54no—
577C2×Dic3—53no—
578C2×Dic3—106no—
579C2×Dic3C23×D513yes—
580C2×Dic3C23×D513yes—
581C2×Dic3C23×D511yescharacteristic
582C4×D3—26no—
583C4×D3—512no—
584C4×D3—54no—
585C4×D3—512no—
586C4×D3—54no—
587C4×D3—512no—
588C4×D3—54no—
589C4×D3—106no—
590C4×D3—106no—
591C4×D3—106no—
592C4×D3C2×C4×D5112yes—
593C4×D3Q8×D514yesdirect product factor
594Dic6—512no—
595Dic6—524no—
596Dic6C2×C4×D5112yescomplemented
597C22×C5—32no—
598C22×C5—32no—
599C22×C5—32no—
600C22×C5C24×D311yescharacteristic
601C2×D5—32no—
602C2×D5—32no—
603C2×D5—32no—
604C2×D5—316no—
605C2×D5C22×C4×D312yes—
606C2×D5C2×D3×Q812yes—
607C2×D5D3×#4112yes—
608C4×C5—23no—
609C4×C5—36no—
610C4×C5—32no—
611C4×C5—63no—
612C4×C5C22×C4×D316yes—
613C4×C5C2×D3×Q812yescomplemented
614Dic5—23no—
615Dic5—36no—
616Dic5—32no—
617Dic5—63no—
618Dic5C22×C4×D316yes—
619Dic5C2×D3×Q812yescomplemented
620C24—151no—
621C2×Q8—38no—
622C2×Q8—33no—
623C2×Q8—58no—
624C2×Q8—53no—
625C2×Q8—156no—
626C2×Q8—1524no—
627C2×Q8—1524no—
628C2×Q8—1524no—
629C2×Q8—158no—
630C2×Q8—153no—
631C2×Q8C2×D3×D511yescharacteristic
632C22×C4—33no—
633C22×C4—31no—
634C22×C4—33no—
635C22×C4—53no—
636C22×C4—51no—
637C22×C4—53no—
638C22×C4—151no—
639C22×C4—153no—
640C22×C4—1524no—
641C22×C4—158no—
642C22×C4—153no—
643C22×C4—151no—
644C22×C4—153no—
645C22×C4—153no—
646C22×C4—151no—
647C22×C4—153no—
648C22×C4—153no—
649C22×C4—153no—
650C22×C4—151no—
651C22×C4—153no—
652C22×C4—3012no—
653C4⋊C4—36no—
654C4⋊C4—33no—
655C4⋊C4—56no—
656C4⋊C4—53no—
657C4⋊C4—156no—
658C4⋊C4—156no—
659C4⋊C4—156no—
660C4⋊C4—156no—
661C4⋊C4—153no—
662C4⋊C4C2×D3×D513yes—
663C42—33no—
664C42—33no—
665C42—33no—
666C42—53no—
667C42—53no—
668C42—53no—
669C42—153no—
670C42—153no—
671C42—153no—
672C42—153no—
673C42—153no—
674C42—153no—
675C42—153no—
676C42—153no—
677C42—153no—
678C42C2×D3×D513yes—
679C3×C5C22×C4×Q811yescharacteristic, complemented, Hall
680C22×C3—52no—
681C22×C3—52no—
682C22×C3—52no—
683C22×C3C24×D511yescharacteristic
684C2×D3—52no—
685C2×D3—52no—
686C2×D3—52no—
687C2×D3—516no—
688C2×D3C22×C4×D512yes—
689C2×D3C2×Q8×D512yes—
690C2×D3D5×#4112yes—
691C3×C4—23no—
692C3×C4—56no—
693C3×C4—52no—
694C3×C4—103no—
695C3×C4C22×C4×D516yes—
696C3×C4C2×Q8×D512yescomplemented
697Dic3—23no—
698Dic3—56no—
699Dic3—52no—
700Dic3—103no—
701Dic3C22×C4×D516yes—
702Dic3C2×Q8×D512yescomplemented
703C2×C5—34no—
704C2×C5C23×C4×D311yescharacteristic
705C2×C5C22×D3×Q811yescharacteristic
706C2×C5C2×D3×#4111yescharacteristic
707D5—34no—
708D5C4×D3×Q814yesdirect product factor
709C23—31no—
710C23—51no—
711C23—154no—
712C23—154no—
713C23—154no—
714C23—151no—
715Q8—312no—
716Q8—512no—
717Q8—1524no—
718Q8—1512no—
719Q8C4×D3×D514yesdirect product factor
720C2×C4—31no—
721C2×C4—33no—
722C2×C4—312no—
723C2×C4—34no—
724C2×C4—33no—
725C2×C4—51no—
726C2×C4—53no—
727C2×C4—512no—
728C2×C4—54no—
729C2×C4—53no—
730C2×C4—66no—
731C2×C4—106no—
732C2×C4—1512no—
733C2×C4—154no—
734C2×C4—1512no—
735C2×C4—154no—
736C2×C4—1512no—
737C2×C4—154no—
738C2×C4—151no—
739C2×C4—153no—
740C2×C4—1512no—
741C2×C4—154no—
742C2×C4—153no—
743C2×C4—306no—
744C2×C4—306no—
745C2×C4—306no—
746C2×C4—306no—
747C2×C4C22×D3×D513yes—
748C2×C4C22×D3×D513yes—
749C2×C4C22×D3×D511yescharacteristic
750C2×C3—54no—
751C2×C3C23×C4×D511yescharacteristic
752C2×C3C22×Q8×D511yescharacteristic
753C2×C3C2×D5×#4111yescharacteristic
754D3—54no—
755D3C4×Q8×D514yesdirect product factor
756C5C2×C4×D3×Q811yescharacteristic, complemented, Sylow
757C22—32no—
758C22—32no—
759C22—32no—
760C22—52no—
761C22—52no—
762C22—52no—
763C22—1516no—
764C22—152no—
765C22—152no—
766C22—152no—
767C22C23×D3×D511yescharacteristic
768C4—23no—
769C4—36no—
770C4—32no—
771C4—56no—
772C4—52no—
773C4—63no—
774C4—103no—
775C4—156no—
776C4—152no—
777C4—303no—
778C4C2×C4×D3×D516yes—
779C4D3×Q8×D512yesdirect product factor
780C3C2×C4×Q8×D511yescharacteristic, complemented, Sylow
781C2—34no—
782C2—54no—
783C2—154no—
784C2C22×C4×D3×D511yescharacteristic
785C2C2×D3×Q8×D511yescharacteristic
786C2D3×D5×#4111yescharacteristic
subgroupG/H
centerC2×C4C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC3×C4×C5×Q8C22
socle, cosocleC22×C3×C5C25
prime radicalC22×D3×D5C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5C22×C4×Q8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D15C2semidirect
3. C4×C5×D3×Q8C2semidirect
4. C3×C4×Q8×D5C2semidirect
5. Q8×#1200C2semidirect
6. D3×Q8×Dic5C2semidirect
7. Q8×D5×Dic3C2semidirect
9. #11753409C2semidirect
10. D3×#4033C2semidirect
11. D5×#887C2semidirect
13. C4×D15⋊Q8C2semidirect
14. C4×D3×Dic10C2semidirect
15. C4×D5×Dic6C2semidirect
20. D3×Q8×D5C4direct (N × H)
27. C3×C4×C5×Q8C22semidirect
28. Q8×Dic15C22semidirect
30. #91776C22semidirect
32. C4×Dic30C22semidirect
33. C5×Q8×Dic3C22semidirect
35. C5×#887C22semidirect
37. C4×C5×Dic6C22semidirect
38. C3×Q8×Dic5C22semidirect
40. C3×#4033C22semidirect
42. C3×C4×Dic10C22semidirect
43. C4×#1204C22semidirect
59. #91344C22semidirect
60. #91340C22semidirect
61. #91333C22semidirect
62. Dic5×Dic6C22semidirect
63. #91331C22semidirect
64. Dic3×Dic10C22semidirect
65. #91325C22semidirect
66. #91324C22semidirect
67. #91323C22semidirect
79. C4×Q8×D5D3direct (N × H)
86. Q8×D15C2×C4semidirect
91. C5×D3×Q8C2×C4semidirect
96. C3×Q8×D5C2×C4semidirect
113. C4×D3×D5Q8direct (N × H)
114. D15⋊Q8C2×C4semidirect
115. D3×Dic10C2×C4semidirect
116. D5×Dic6C2×C4semidirect
153. C4×D3×Q8D5direct (N × H)
171. C4×C5×Q8C2×D3semidirect
177. Q8×Dic5C2×D3semidirect
194. #4033C2×D3semidirect
208. C4×Dic10C2×D3semidirect
216. C3×C5×Q8C22×C4semidirect
225. C4×D15C2×Q8semidirect
226. Dic30C22×C4semidirect
232. C4×C5×D3C2×Q8semidirect
233. C5×Dic6C22×C4semidirect
239. C3×C4×D5C2×Q8semidirect
240. C3×Dic10C22×C4semidirect
241. #1204C22×C4semidirect
244. #1200C2×Q8semidirect
247. D3×Dic5C2×Q8semidirect
250. D5×Dic3C2×Q8semidirect
264. C3×C4×Q8C2×D5semidirect
270. Q8×Dic3C2×D5semidirect
287. #887C2×D5semidirect
301. C4×Dic6C2×D5semidirect
315. Q8×D5C4×D3direct (N × H)
386. D3×D5C4×Q8direct (N × H)
389. C3×C4×C5C22×Q8semidirect
392. Dic15C22×Q8semidirect
395. C3×Dic5C22×Q8semidirect
398. C5×Dic3C22×Q8semidirect
412. D3×Q8C4×D5direct (N × H)
465. C5×Q8C2×C4×D3semidirect
495. C4×D5D3×Q8direct (N × H)
498. Dic10C2×C4×D3semidirect
528. C4×Q8D3×D5direct (N × H)
553. D15C2×C4×Q8semidirect
554. C3×D5C2×C4×Q8semidirect
555. C5×D3C2×C4×Q8semidirect
563. C3×Q8C2×C4×D5semidirect
593. C4×D3Q8×D5direct (N × H)
596. Dic6C2×C4×D5semidirect
613. C4×C5C2×D3×Q8semidirect
619. Dic5C2×D3×Q8semidirect
679. C3×C5C22×C4×Q8semidirect
696. C3×C4C2×Q8×D5semidirect
702. Dic3C2×Q8×D5semidirect
708. D5C4×D3×Q8direct (N × H)
719. Q8C4×D3×D5direct (N × H)
755. D3C4×Q8×D5direct (N × H)
756. C5C2×C4×D3×Q8semidirect
779. C4D3×Q8×D5direct (N × H)
780. C3C2×C4×Q8×D5semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Q8×D52
C4×Q8×D152
C4×C5×D3×Q82
C3×C4×Q8×D52
Q8×#12002
D3×Q8×Dic52
Q8×D5×Dic32
D3×D5×C4⋊C42
#117534092
D3×#40332
D5×#8872
C42×D3×D52
C4×D15⋊Q82
C4×D3×Dic102
C4×D5×Dic62
C2×C4×Q8×D53
C2×C4×D3×Q85