Finite Group Databasebeta

← D3×#65908 #14479112

Subgroups — D3×#65908 #14479112

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#713C211yesmaximal, characteristic
2#11756333C211yesmaximal, characteristic, complemented
3C4×C5×D3×Q8C211yesmaximal, characteristic, complemented
4C3×#65908C211yesmaximal, characteristic, complemented
5#11755217C211yesmaximal, characteristic, complemented
6D3×Q8×Dic5C211yesmaximal, characteristic, complemented
7#11755149C211yesmaximal, characteristic, complemented
8D3×#4039C213yesmaximal, complemented
9D3×D5×C4⋊C4C213yesmaximal, complemented
10#11753401C213yesmaximal, complemented
11#11753336C213yesmaximal, complemented
12C4×D3×D20C213yesmaximal, complemented
13D3×#4018C213yesmaximal, complemented
14#11752521C213yesmaximal, complemented
15#11752520C213yesmaximal, complemented
16C2×#65908—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic
20D3×#713C4116yescomplemented
21C2×D3×D20C2213yes—
22C2×C4×D3×D5C2216yes—
23C2×C4×D3×D5C2213yes—
24C2×#6773C2213yes—
25C2×#6766C2213yes—
26C3×C4×C5×Q8C2211yescharacteristic, complemented
27Q8×Dic15C2211yescharacteristic, complemented
28#91782C2213yescomplemented
29C4⋊C4×D15C2213yescomplemented
30C4×D60C2213yescomplemented
31#91761C2213yescomplemented
32C5×Q8×Dic3C2211yescharacteristic, complemented
33C5×D3×C4⋊C4C2213yes—
34C5×#887C2213yescomplemented
35C42×C5×D3C2213yes—
36C4×C5×Dic6C2213yescomplemented
37C3×Q8×Dic5C2211yescharacteristic, complemented
38C3×#4039C2213yescomplemented
39C3×D5×C4⋊C4C2213yescomplemented
40C3×C4×D20C2213yescomplemented
41C3×#4018C2213yescomplemented
42D3×#685C2213yes—
43D3×#685C2213yes—
44#91444C2216yescomplemented
45C4×#1202C2216yescomplemented
46#91437C2213yescomplemented
47#91434C2213yescomplemented
48#91428C2213yescomplemented
49D3×C4⋊Dic5C2213yes—
50Dic3×D20C2213yescomplemented
51#91418C2213yescomplemented
52D5×C4⋊Dic3C2213yescomplemented
53#91404C2216yescomplemented
54#91403C2213yescomplemented
55#91403C2213yescomplemented
56D3×#683C2211yescharacteristic
57D3×#683C2213yes—
58C4×D3×Dic5C2213yes—
59#91396C2216yescomplemented
60#91395C2216yescomplemented
61#91393C2213yescomplemented
62#91393C2213yescomplemented
63D5×Dic3⋊C4C2216yescomplemented
64#91386C2213yescomplemented
65#91357C2213yescomplemented
66#91344C2213yescomplemented
67Dic5×Dic6C2213yescomplemented
68D3×#520—51nomaximal, Hall
69C22×#713—31no—
70C2×C4×C5×Q8—31no—
71C2×Q8×Dic5—31no—
72#65908—31no—
73#65908—33no—
74#65908—33no—
75#65908—33no—
76#65908—33no—
77#65908—31no—
78#65908—31no—
79#65908D311yescharacteristic, direct product factor
80C2×#4039—33no—
81C2×D5×C4⋊C4—33no—
82C2×C4×D20—33no—
83C2×#4018—33no—
84C22×D3×D5C2313yes—
85C2×C3×C5×Q8C2311yescharacteristic
86#6821C2×C418yescomplemented
87C2×D60C2313yes—
88C2×C4×D15C2316yes—
89C2×C4×D15C2313yes—
90C5×D3×Q8C2×C418yescomplemented
91C2×C4×C5×D3C2311yescharacteristic
92C2×C4×C5×D3C2313yes—
93C2×C4×C5×D3C2313yes—
94C2×C5×Dic6C2313yes—
95C3×#713C2×C418yescomplemented
96C2×C3×D20C2313yes—
97C2×C3×C4×D5C2316yes—
98C2×C3×C4×D5C2313yes—
99C2×#1202C2316yes—
100C2×#1200C2316yes—
101C2×#1200C2313yes—
102C2×D3×Dic5C2311yescharacteristic
103C2×D3×Dic5C2313yes—
104C2×D3×Dic5C2311yescharacteristic
105C2×D5×Dic3C2316yes—
106C2×D5×Dic3C2313yes—
107D3×D20C2×C4124yescomplemented
108C4×D3×D5—412no—
109C4×D3×D5C2×C4124yescomplemented
110#6773C2×C4124yescomplemented
111#6766C2×C4124yescomplemented
112C3×C5×C4⋊C4C2313yes—
113C3×C42×C5C2313yes—
114#6714C2313yes—
115#6714C2313yes—
116C4⋊Dic15C2313yes—
117#6712C2313yes—
118#6712C2311yescharacteristic
119C4×Dic15C2313yes—
120C5×C4⋊Dic3C2313yes—
121C5×Dic3⋊C4C2316yes—
122C4×C5×Dic3C2313yes—
123C4×C5×Dic3C2313yes—
124C4×C5×Dic3C2313yes—
125C3×#685C2313yes—
126C3×#685C2313yes—
127C3×C4⋊Dic5C2313yes—
128C3×#683C2311yescharacteristic
129C3×#683C2313yes—
130C3×C4×Dic5C2313yes—
131Dic3⋊Dic5C2316yes—
132#6669C2313yes—
133#6669C2311yescharacteristic
134#6668C2311yescharacteristic
135#6668C2313yes—
136#6667C2313yes—
137#6667C2313yes—
138#6665C2313yes—
139#6665C2313yes—
140Dic3×Dic5C2313yes—
141Dic3×Dic5C2313yes—
142C2×D3×#41—51no—
143C3×#520—51no—
144#5827—51no—
145#5574—51no—
146#5574—51no—
147C4×D3×Q8—51no—
148C4×D3×Q8D511yescharacteristic, complemented
149#5546—53no—
150#5546—53no—
151C4×D3×D4—53no—
152C4×D3×D4—53no—
153#5523—53no—
154D3×#117—53no—
155#5504—53no—
156C2×D3×C4⋊C4—53no—
157C22×C5×Q8—31no—
158C2×#713—31no—
159C2×#713—316no—
160C2×#713—33no—
161C2×#713—33no—
162C2×#713C2×D311yescharacteristic
163C22×D20—33no—
164C22×C4×D5—33no—
165C22×C4×D5—36no—
166C4×C5×Q8—31no—
167C4×C5×Q8—33no—
168C4×C5×Q8—33no—
169C4×C5×Q8C2×D311yescharacteristic, complemented
170C2×C5×C4⋊C4—33no—
171C2×C42×C5—33no—
172Q8×Dic5—31no—
173Q8×Dic5—33no—
174Q8×Dic5—33no—
175Q8×Dic5C2×D311yescharacteristic, complemented
176C2×#685—33no—
177C2×#685—33no—
178C2×C4⋊Dic5—33no—
179C2×#683—31no—
180C2×#683—33no—
181C2×C4×Dic5—33no—
182#4039—33no—
183#4039—36no—
184#4039—33no—
185#4039—36no—
186#4039—33no—
187#4039C2×D313yescomplemented
188D5×C4⋊C4—36no—
189D5×C4⋊C4—33no—
190D5×C4⋊C4—33no—
191D5×C4⋊C4—33no—
192D5×C4⋊C4—36no—
193D5×C4⋊C4C2×D313yescomplemented
194C4×D20—33no—
195C4×D20—36no—
196C4×D20—33no—
197C4×D20—36no—
198C4×D20—33no—
199C4×D20C2×D313yescomplemented
200#4018—33no—
201#4018—33no—
202#4018—33no—
203#4018—33no—
204#4018—33no—
205#4018—33no—
206#4018—33no—
207#4018C2×D313yescomplemented
208C2×#520—151noSylow
209C22×D15C2413yes—
210C22×C5×D3C2411yescharacteristic
211C22×C3×D5C2413yes—
212C2×D3×D5—26no—
213C2×D3×D5—26no—
214C2×D3×D5C22×C4112yes—
215C3×C5×Q8C22×C414yescomplemented
216C2×C3×C4×C5C2411yescharacteristic
217C2×C3×C4×C5C2413yes—
218C2×C3×C4×C5C2413yes—
219C2×Dic15C2411yescharacteristic
220C2×Dic15C2413yes—
221C2×Dic15C2411yescharacteristic
222D60C22×C4112yescomplemented
223C4×D15—46no—
224C4×D15C22×C4112yescomplemented
225C2×C5×Dic3C2411yescharacteristic
226C2×C5×Dic3C2413yes—
227C2×C5×Dic3C2413yes—
228C4×C5×D3—26no—
229C4×C5×D3—22no—
230C4×C5×D3C22×C4112yes—
231C5×Dic6C22×C4112yescomplemented
232C2×C3×Dic5C2411yescharacteristic
233C2×C3×Dic5C2413yes—
234C2×C3×Dic5C2411yescharacteristic
235C3×D20C22×C4112yescomplemented
236C3×C4×D5—46no—
237C3×C4×D5C22×C4112yescomplemented
238#1202C22×C4124yescomplemented
239#1200—46no—
240#1200C22×C4112yescomplemented
241D3×Dic5—26no—
242D3×Dic5—22no—
243D3×Dic5C22×C414yes—
244D5×Dic3—46no—
245D5×Dic3C22×C4112yescomplemented
246C2×C3×#41—51no—
247D3×#41—516no—
248C2×#239—51no—
249C2×D3×Q8C2×D511yescharacteristic
250C2×#237—53no—
251C2×D3×D4—53no—
252C2×#235—53no—
253C22×C4×D3—53no—
254C22×C4×D3—56no—
255C3×C4×Q8—51no—
256C3×C4×Q8C2×D511yescharacteristic, complemented
257C3×C4×D4—53no—
258C3×C4×D4—53no—
259C3×#117—53no—
260C2×C3×C4⋊C4—53no—
261Q8×Dic3—51no—
262Q8×Dic3C2×D511yescharacteristic, complemented
263D4×Dic3—53no—
264D4×Dic3—53no—
265C4×#67—56no—
266C4×#67—56no—
267#926—53no—
268C2×C4⋊Dic3—53no—
269C2×Dic3⋊C4—56no—
270#893—53no—
271#893—53no—
272#892—53no—
273#892—53no—
274D3×C4⋊C4—53no—
275D3×C4⋊C4—51no—
276D3×C4⋊C4—53no—
277D3×C4⋊C4—53no—
278D3×C4⋊C4—53no—
279D3×C4⋊C4—56no—
280D3×C4⋊C4C2×D513yes—
281#887—53no—
282#887C2×D513yescomplemented
283#67⋊C4—56no—
284#67⋊C4—56no—
285D3×C22⋊C4—53no—
286D3×C22⋊C4—53no—
287#877—53no—
288#877—53no—
289C4×D12—53no—
290C4×D12—53no—
291#872—53no—
292#872—53no—
293C42×D3—53no—
294C42×D3C2×D513yes—
295C4×Dic6—53no—
296C4×Dic6C2×D513yescomplemented
297C23×D5—33no—
298C2×C5×Q8—38no—
299C2×C5×Q8—33no—
300C2×C5×Q8C22×D311yescharacteristic
301C22×C4×C5—33no—
302C22×C4×C5—31no—
303C22×C4×C5—33no—
304C22×Dic5—31no—
305C22×Dic5—33no—
306C22×Dic5—31no—
307#713—38no—
308#713—324no—
309#713—324no—
310#713C4×D318yescomplemented
311C2×D20—36no—
312C2×D20—33no—
313C2×D20—324no—
314C2×D20C22×D313yes—
315C2×C4×D5—33no—
316C2×C4×D5—33no—
317C2×C4×D5—33no—
318C2×C4×D5—324no—
319C2×C4×D5—36no—
320C2×C4×D5—36no—
321C2×C4×D5—36no—
322C2×C4×D5—1212no—
323C2×C4×D5C22×D316yes—
324C2×C4×D5C22×D313yes—
325C5×C4⋊C4—36no—
326C5×C4⋊C4—33no—
327C5×C4⋊C4C22×D313yes—
328C42×C5—33no—
329C42×C5—33no—
330C42×C5—33no—
331C42×C5C22×D313yes—
332#685—33no—
333#685—33no—
334#685—33no—
335#685—33no—
336#685—33no—
337#685—33no—
338#685C22×D313yes—
339#685C22×D313yes—
340C4⋊Dic5—33no—
341C4⋊Dic5—36no—
342C4⋊Dic5C22×D313yes—
343#683—31no—
344#683—33no—
345#683—31no—
346#683—33no—
347#683—31no—
348#683—33no—
349#683C22×D311yescharacteristic
350#683C22×D313yes—
351C4×Dic5—33no—
352C4×Dic5—33no—
353C4×Dic5—33no—
354C4×Dic5C22×D313yes—
355C22×#41—151no—
356#520—51no—
357#520—153no—
358#520—153no—
359#520—153no—
360#520—153no—
361#520—151no—
362#520—151no—
363#520—151no—
364C2×C4×Q8—31no—
365C2×C4×Q8—151no—
366C2×C4×D4—153no—
367C2×C4×D4—153no—
368C2×#117—153no—
369C22×C4⋊C4—153no—
370C22×C3×C5C2511yescharacteristic
371C2×D15—23no—
372C2×D15—23no—
373C2×D15C23×C416yes—
374C2×C5×D3C23×C412yes—
375C2×C5×D3H(5,𝔽2)12yes—
376C2×C5×D32−1+412yes—
377C2×C3×D5—23no—
378C2×C3×D5—23no—
379C2×C3×D5C23×C416yes—
380D3×D5—224no—
381C3×C4×C5—23no—
382C3×C4×C5—21no—
383C3×C4×C5C23×C416yes—
384Dic15—23no—
385Dic15—21no—
386Dic15C23×C412yes—
387C3×Dic5—23no—
388C3×Dic5—21no—
389C3×Dic5C23×C412yes—
390C5×Dic3—23no—
391C5×Dic3—21no—
392C5×Dic3C23×C416yes—
393C23×D3—53no—
394C3×#41—58no—
395C2×C3×Q8C22×D511yescharacteristic
396C2×C3×D4—53no—
397C22×C3×C4—53no—
398C22×C3×C4—56no—
399C2×#67—56no—
400C22×Dic3—53no—
401C22×Dic3—56no—
402#239—58no—
403D3×Q8C4×D518yescomplemented
404#237—524no—
405D3×D4—524no—
406#235—524no—
407C2×D12—53no—
408C2×C4×D3—51no—
409C2×C4×D3—53no—
410C2×C4×D3—53no—
411C2×C4×D3—524no—
412C2×C4×D3—51no—
413C2×C4×D3—53no—
414C2×C4×D3—56no—
415C2×C4×D3—56no—
416C2×C4×D3—2012no—
417C2×C4×D3C22×D511yescharacteristic
418C2×C4×D3C22×D513yes—
419C2×C4×D3C22×D513yes—
420C2×Dic6C22×D513yes—
421C3×C4⋊C4—53no—
422C3×C4⋊C4—51no—
423C3×C4⋊C4—53no—
424C3×C4⋊C4C22×D513yes—
425C3×C22⋊C4—53no—
426C3×C22⋊C4—53no—
427C3×C42—53no—
428C3×C42C22×D513yes—
429#217—53no—
430#217—53no—
431(C2×D3)⋊C4—53no—
432(C2×D3)⋊C4—53no—
433(C2×D3)⋊C4—53no—
434(C2×D3)⋊C4—53no—
435C4⋊Dic3—53no—
436C4⋊Dic3—53no—
437C4⋊Dic3—51no—
438C4⋊Dic3C22×D513yes—
439Dic3⋊C4—51no—
440Dic3⋊C4—53no—
441Dic3⋊C4—51no—
442Dic3⋊C4—53no—
443Dic3⋊C4—56no—
444Dic3⋊C4C22×D516yes—
445C4×Dic3—53no—
446C4×Dic3—53no—
447C4×Dic3—53no—
448C4×Dic3C22×D513yes—
449C4×Dic3C22×D513yes—
450C4×Dic3C22×D513yes—
451C23×C5—31no—
452C22×D5—33no—
453C22×D5—312no—
454C22×D5—66no—
455C22×D5—66no—
456C22×D5C23×D313yes—
457C5×Q8—312no—
458C5×Q8C2×C4×D314yescomplemented
459C2×C4×C5—33no—
460C2×C4×C5—312no—
461C2×C4×C5—31no—
462C2×C4×C5—33no—
463C2×C4×C5—66no—
464C2×C4×C5—62no—
465C2×C4×C5C23×D311yescharacteristic
466C2×C4×C5C23×D313yes—
467C2×C4×C5C23×D313yes—
468C2×Dic5—31no—
469C2×Dic5—34no—
470C2×Dic5—31no—
471C2×Dic5—33no—
472C2×Dic5—66no—
473C2×Dic5—62no—
474C2×Dic5C23×D311yescharacteristic
475C2×Dic5C23×D313yes—
476C2×Dic5C23×D311yescharacteristic
477D20—324no—
478D20—312no—
479D20C2×C4×D3112yescomplemented
480C4×D5—312no—
481C4×D5—312no—
482C4×D5—312no—
483C4×D5—46no—
484C4×D5—126no—
485C4×D5—126no—
486C4×D5—126no—
487C4×D5C2×C4×D3112yescomplemented
488C2×#41—51no—
489C2×#41—153no—
490C2×#41—153no—
491C2×#41—1516no—
492C2×#41—151no—
493C22×Q8—31no—
494C22×D4—153no—
495C23×C4—153no—
496C23×C4—156no—
497C4×Q8—31no—
498C4×Q8—33no—
499C4×Q8—33no—
500C4×Q8—51no—
501C4×Q8—153no—
502C4×Q8—153no—
503C4×Q8—151no—
504C4×Q8D3×D511yescharacteristic, complemented
505C4×D4—53no—
506C4×D4—53no—
507C4×D4—156no—
508C4×D4—153no—
509C4×D4—156no—
510C4×D4—153no—
511C4×D4—153no—
512C4×D4—156no—
513C4×D4—156no—
514C4×D4—153no—
515C4×D4—153no—
516C4×D4—153no—
517#117—53no—
518#117—153no—
519#117—153no—
520#117—153no—
521#117—153no—
522#117—153no—
523#117—153no—
524#117—153no—
525C2×C4⋊C4—33no—
526C2×C4⋊C4—53no—
527C2×C4⋊C4—156no—
528C2×C4⋊C4—153no—
529C2×C4⋊C4—156no—
530C2×C4⋊C4—153no—
531C2×C4⋊C4—153no—
532C2×C4⋊C4—153no—
533C2×C4⋊C4—151no—
534C2×C4⋊C4—153no—
535C2×C22⋊C4—153no—
536C2×C22⋊C4—153no—
537C2×C42—33no—
538C2×C42—153no—
539C2×C3×C5C24×C411yescharacteristic
540C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
541C2×C3×C5C2×2−1+411yescharacteristic
542D15—26no—
543C3×D5—26no—
544C5×D3#52014yescomplemented
545C23×C3—53no—
546C22×D3—53no—
547C22×D3—512no—
548C22×D3—106no—
549C22×D3—106no—
550C22×D3C23×D511yescharacteristic
551C3×Q8C2×C4×D514yescomplemented
552C3×D4—512no—
553C2×C3×C4—51no—
554C2×C3×C4—512no—
555C2×C3×C4—51no—
556C2×C3×C4—53no—
557C2×C3×C4—206no—
558C2×C3×C4C23×D511yescharacteristic
559C2×C3×C4C23×D513yes—
560C2×C3×C4C23×D513yes—
561#67—524no—
562C2×Dic3—51no—
563C2×Dic3—512no—
564C2×Dic3—51no—
565C2×Dic3—53no—
566C2×Dic3—206no—
567C2×Dic3C23×D511yescharacteristic
568C2×Dic3C23×D513yes—
569C2×Dic3C23×D513yes—
570D12—512no—
571C4×D3—22no—
572C4×D3—26no—
573C4×D3—54no—
574C4×D3—512no—
575C4×D3—512no—
576C4×D3—102no—
577C4×D3—106no—
578C4×D3—206no—
579C4×D3—206no—
580C4×D3C2×C4×D5112yes—
581Dic6C2×C4×D5112yescomplemented
582C22×C5—32no—
583C22×C5—32no—
584C22×C5—32no—
585C22×C5C24×D311yescharacteristic
586C2×D5—23no—
587C2×D5—23no—
588C2×D5—36no—
589C2×D5—624no—
590C2×D5—63no—
591C2×D5—63no—
592C2×D5C22×C4×D316yes—
593C4×C5—23no—
594C4×C5—21no—
595C4×C5—36no—
596C4×C5—63no—
597C4×C5—61no—
598C4×C5C22×C4×D316yes—
599Dic5—23no—
600Dic5—21no—
601Dic5—32no—
602Dic5—63no—
603Dic5—61no—
604Dic5C22×C4×D312yes—
605C24—153no—
606#41—58no—
607#41—1524no—
608#41—1524no—
609#41—158no—
610C2×Q8—38no—
611C2×Q8—33no—
612C2×Q8C2×D3×D511yescharacteristic
613C2×D4—53no—
614C2×D4—1524no—
615C2×D4—156no—
616C2×D4—153no—
617C22×C4—33no—
618C22×C4—31no—
619C22×C4—33no—
620C22×C4—53no—
621C22×C4—56no—
622C22×C4—153no—
623C22×C4—1524no—
624C22×C4—156no—
625C22×C4—153no—
626C22×C4—156no—
627C22×C4—151no—
628C22×C4—151no—
629C22×C4—153no—
630C22×C4—153no—
631C22×C4—156no—
632C22×C4—6012no—
633C4⋊C4—36no—
634C4⋊C4—33no—
635C4⋊C4—53no—
636C4⋊C4—53no—
637C4⋊C4—51no—
638C4⋊C4—153no—
639C4⋊C4—153no—
640C4⋊C4—156no—
641C4⋊C4—151no—
642C4⋊C4—151no—
643C4⋊C4—153no—
644C4⋊C4—153no—
645C4⋊C4—151no—
646C4⋊C4C2×D3×D513yes—
647C22⋊C4—53no—
648C22⋊C4—53no—
649C22⋊C4—153no—
650C22⋊C4—153no—
651C22⋊C4—153no—
652C22⋊C4—153no—
653C22⋊C4—153no—
654C22⋊C4—153no—
655C42—33no—
656C42—33no—
657C42—33no—
658C42—53no—
659C42—153no—
660C42—153no—
661C42—153no—
662C42C2×D3×D513yes—
663C3×C5C2×#52011yescharacteristic, complemented, Hall
664C22×C3—56no—
665C22×C3—103no—
666C22×C3—103no—
667C22×C3C24×D511yescharacteristic
668C2×D3—56no—
669C2×D3—103no—
670C2×D3—103no—
671C2×D3—1024no—
672C2×D3C22×C4×D512yes—
673C2×D3#414712yes—
674C2×D3#414912yes—
675C3×C4—21no—
676C3×C4—23no—
677C3×C4—52no—
678C3×C4—101no—
679C3×C4—103no—
680C3×C4C22×C4×D516yes—
681Dic3—21no—
682Dic3—23no—
683Dic3—52no—
684Dic3—101no—
685Dic3—103no—
686Dic3C22×C4×D516yes—
687C2×C5—34no—
688C2×C5C23×C4×D311yescharacteristic
689C2×C5D3×H(5,𝔽2)11yescharacteristic
690C2×C5D3×2−1+411yescharacteristic
691D5—26no—
692D5—66no—
693C23—31no—
694C23—53no—
695C23—1512no—
696C23—153no—
697C23—306no—
698C23—306no—
699Q8—312no—
700Q8C4×D3×D514yescomplemented
701D4—512no—
702D4—1524no—
703D4—1512no—
704C2×C4—33no—
705C2×C4—312no—
706C2×C4—31no—
707C2×C4—33no—
708C2×C4—51no—
709C2×C4—512no—
710C2×C4—51no—
711C2×C4—53no—
712C2×C4—66no—
713C2×C4—62no—
714C2×C4—1512no—
715C2×C4—1512no—
716C2×C4—154no—
717C2×C4—151no—
718C2×C4—1512no—
719C2×C4—151no—
720C2×C4—153no—
721C2×C4—206no—
722C2×C4—306no—
723C2×C4—302no—
724C2×C4—606no—
725C2×C4—606no—
726C2×C4—606no—
727C2×C4C22×D3×D511yescharacteristic
728C2×C4C22×D3×D513yes—
729C2×C4C22×D3×D513yes—
730C2×C3—106no—
731C2×C3C23×C4×D511yescharacteristic
732C2×C3C2×#414711yescharacteristic
733C2×C3C2×#414911yescharacteristic
734D3—106no—
735D3#6590814yesdirect product factor
736C5D3×#52011yescharacteristic, complemented, Sylow
737C22—32no—
738C22—32no—
739C22—32no—
740C22—56no—
741C22—103no—
742C22—103no—
743C22—156no—
744C22—3024no—
745C22—303no—
746C22—303no—
747C22C23×D3×D511yescharacteristic
748C4—21no—
749C4—23no—
750C4—36no—
751C4—52no—
752C4—61no—
753C4—63no—
754C4—101no—
755C4—103no—
756C4—152no—
757C4—301no—
758C4—303no—
759C4C2×C4×D3×D516yes—
760C3C2×#6590811yescharacteristic, complemented, Sylow
761C2—34no—
762C2—106no—
763C2—306no—
764C2C22×C4×D3×D511yescharacteristic
765C2D3×#414711yescharacteristic
766C2D3×#414911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC3×C4×C5×Q8C22
socle, cosocleC22×C3×C5C25
prime radicalC2×D3×#713C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#520
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11756333C2semidirect
3. C4×C5×D3×Q8C2semidirect
4. C3×#65908C2semidirect
5. #11755217C2semidirect
6. D3×Q8×Dic5C2semidirect
7. #11755149C2semidirect
8. D3×#4039C2semidirect
9. D3×D5×C4⋊C4C2semidirect
10. #11753401C2semidirect
11. #11753336C2semidirect
12. C4×D3×D20C2semidirect
13. D3×#4018C2semidirect
14. #11752521C2semidirect
15. #11752520C2semidirect
20. D3×#713C4semidirect
26. C3×C4×C5×Q8C22semidirect
27. Q8×Dic15C22semidirect
28. #91782C22semidirect
29. C4⋊C4×D15C22semidirect
30. C4×D60C22semidirect
31. #91761C22semidirect
32. C5×Q8×Dic3C22semidirect
34. C5×#887C22semidirect
36. C4×C5×Dic6C22semidirect
37. C3×Q8×Dic5C22semidirect
38. C3×#4039C22semidirect
39. C3×D5×C4⋊C4C22semidirect
40. C3×C4×D20C22semidirect
41. C3×#4018C22semidirect
44. #91444C22semidirect
45. C4×#1202C22semidirect
46. #91437C22semidirect
47. #91434C22semidirect
48. #91428C22semidirect
50. Dic3×D20C22semidirect
51. #91418C22semidirect
52. D5×C4⋊Dic3C22semidirect
53. #91404C22semidirect
54. #91403C22semidirect
55. #91403C22semidirect
59. #91396C22semidirect
60. #91395C22semidirect
61. #91393C22semidirect
62. #91393C22semidirect
63. D5×Dic3⋊C4C22semidirect
64. #91386C22semidirect
65. #91357C22semidirect
66. #91344C22semidirect
67. Dic5×Dic6C22semidirect
79. #65908D3direct (N × H)
86. #6821C2×C4semidirect
90. C5×D3×Q8C2×C4semidirect
95. C3×#713C2×C4semidirect
107. D3×D20C2×C4semidirect
109. C4×D3×D5C2×C4semidirect
110. #6773C2×C4semidirect
111. #6766C2×C4semidirect
148. C4×D3×Q8D5semidirect
169. C4×C5×Q8C2×D3semidirect
175. Q8×Dic5C2×D3semidirect
187. #4039C2×D3semidirect
193. D5×C4⋊C4C2×D3semidirect
199. C4×D20C2×D3semidirect
207. #4018C2×D3semidirect
215. C3×C5×Q8C22×C4semidirect
222. D60C22×C4semidirect
224. C4×D15C22×C4semidirect
231. C5×Dic6C22×C4semidirect
235. C3×D20C22×C4semidirect
237. C3×C4×D5C22×C4semidirect
238. #1202C22×C4semidirect
240. #1200C22×C4semidirect
245. D5×Dic3C22×C4semidirect
256. C3×C4×Q8C2×D5semidirect
262. Q8×Dic3C2×D5semidirect
282. #887C2×D5semidirect
296. C4×Dic6C2×D5semidirect
310. #713C4×D3semidirect
403. D3×Q8C4×D5semidirect
458. C5×Q8C2×C4×D3semidirect
479. D20C2×C4×D3semidirect
487. C4×D5C2×C4×D3semidirect
504. C4×Q8D3×D5semidirect
544. C5×D3#520semidirect
551. C3×Q8C2×C4×D5semidirect
581. Dic6C2×C4×D5semidirect
663. C3×C5C2×#520semidirect
700. Q8C4×D3×D5semidirect
735. D3#65908direct (N × H)
736. C5D3×#520semidirect
760. C3C2×#65908semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7132
#117563332
C4×C5×D3×Q82
C3×#659082
#117552172
D3×Q8×Dic52
#117551492
D3×#40392
D3×D5×C4⋊C42
#117534012
#117533362
C4×D3×D202
D3×#40182
#117525212
#117525202
C2×#659083
D3×#5205