Finite Group Databasebeta

← D3×#66168 #14482989

Subgroups — D3×#66168 #14482989

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×#41C211yesmaximal, characteristic, complemented
2C2×D3×#713C211yesmaximal, characteristic, complemented
3#11756593C211yesmaximal, characteristic, complemented
4C3×#66168C211yesmaximal, characteristic, complemented
5#11755254C211yesmaximal, characteristic, complemented
6#11755245C211yesmaximal, characteristic, complemented
7D3×Q8×Dic5C211yesmaximal, characteristic, complemented
8D3×#4086C213yesmaximal, complemented
9D3×#4084C213yesmaximal, complemented
10#11754948C213yesmaximal, complemented
11#11754807C213yesmaximal, complemented
12D3×#4076C213yesmaximal, complemented
13C4×D3×C22⋊D5C213yesmaximal, complemented
14#11754545C213yesmaximal, complemented
15#11754535C213yesmaximal, complemented
16C2×#66168—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C2×#6821C2211yescharacteristic, complemented
19C5×D3×#41—28no—
20C2×C5×#239C2211yescharacteristic, complemented
21C2×C5×D3×Q8C2211yescharacteristic
22C2×C5×#237C2213yescomplemented
23C2×C5×D3×D4C2213yes—
24C2×C5×#235C2213yescomplemented
25C22×C4×C5×D3C2213yes—
26C2×C3×#713C2211yescharacteristic, complemented
27C2×D3×C22⋊D5C2213yes—
28C2×D3×C22⋊D5C2216yes—
29D3×#713—28no—
30C2×D3×D20C2213yes—
31C2×C4×D3×D5C2213yes—
32C2×#6773C2213yescomplemented
33C2×#6766C2213yescomplemented
34Q8×Dic15C2211yescharacteristic, complemented
35#91829C2213yescomplemented
36#91827C2213yescomplemented
37#91819C2213yescomplemented
38C4×#1220C2213yescomplemented
39C3×Q8×Dic5C2211yescharacteristic, complemented
40C3×#4086C2213yescomplemented
41C3×#4084C2213yescomplemented
42C3×#4076C2213yescomplemented
43C3×C4×C22⋊D5C2213yescomplemented
44#91569C2216yescomplemented
45#91567C2216yescomplemented
46#91567C2216yescomplemented
47#91557C2216yescomplemented
48#91556C2213yescomplemented
49D3×C22⋊Dic5C2213yes—
50Dic3×C22⋊D5C2213yescomplemented
51#91549C2216yescomplemented
52D3×#685C2213yes—
53#91466C2213yescomplemented
54#91463C2213yescomplemented
55#91460C2213yescomplemented
56#91456C2213yescomplemented
57#91454C2216yescomplemented
58#91451C2213yescomplemented
59#91449C2213yescomplemented
60#91446C2213yescomplemented
61C4×#1203C2213yescomplemented
62#91441C2213yescomplemented
63C4×#1201C2213yescomplemented
64D3×C4⋊Dic5C2213yes—
65D3×#683C2211yescharacteristic
66C4×D3×Dic5C2213yes—
67#91344C2213yescomplemented
68Dic5×Dic6C2213yescomplemented
69D3×#550—51nomaximal, Hall
70C22×C5×#41—31no—
71C22×#713—31no—
72#66168—31no—
73#66168—33no—
74#66168—33no—
75#66168—33no—
76#66168—33no—
77#66168—31no—
78#66168—31no—
79#66168D311yescharacteristic, direct product factor
80C2×Q8×Dic5—31no—
81C2×#4086—33no—
82C2×#4084—33no—
83C2×#4076—33no—
84C2×C4×C22⋊D5—33no—
85C23×C5×D3C2313yes—
86C22×D3×D5C2313yes—
87C3×C5×#41—24no—
88C2×C3×C5×Q8C2311yescharacteristic
89C2×C3×C5×D4C2313yes—
90C22×C3×C4×C5C2313yes—
91C2×#1220C2313yes—
92C2×#1220C2316yes—
93#6821—24no—
94C2×D60C2313yes—
95C2×C4×D15C2313yes—
96C2×C5×#67C2316yes—
97C22×C5×Dic3C2313yes—
98C5×#239—24no—
99C5×D3×Q8D418yescomplemented
100C5×#237—212no—
101C5×D3×D4—212no—
102C5×#235—212no—
103C2×C5×D12C2313yes—
104C2×C4×C5×D3—212no—
105C2×C4×C5×D3C2311yescharacteristic
106C2×C4×C5×D3C2313yes—
107C2×C4×C5×D3C2313yes—
108C2×C4×C5×D3C2313yes—
109C2×C5×Dic6C2313yes—
110C2×C3×C22⋊D5C2313yes—
111C2×C3×C22⋊D5C2316yes—
112C3×#713—24no—
113C2×C3×D20C2313yes—
114C2×C3×C4×D5C2313yes—
115D3×C22⋊D5—212no—
116D3×C22⋊D5—412no—
117C2×#1203C2313yes—
118C2×#1203C2316yes—
119C2×#1202C2316yes—
120C2×#1201C2313yes—
121C2×#1201C2316yes—
122C2×#1200C2313yes—
123C2×D3×Dic5C2313yes—
124C2×D3×Dic5C2311yescharacteristic
125C2×D3×Dic5C2311yescharacteristic
126C2×D5×Dic3C2313yes—
127D3×D20—212no—
128C4×D3×D5—212no—
129#6773—212no—
130#6766—212no—
131#6719C2313yes—
132#6714C2313yes—
133C4⋊Dic15C2313yes—
134#6712C2311yescharacteristic
135C4×Dic15C2313yes—
136C3×C22⋊Dic5C2313yes—
137C3×#685C2313yes—
138C3×C4⋊Dic5C2313yes—
139C3×#683C2311yescharacteristic
140C3×C4×Dic5C2313yes—
141Dic3⋊Dic5C2316yes—
142#6669C2311yescharacteristic
143#6668C2311yescharacteristic
144#6667C2313yes—
145(C2×D3)⋊Dic5C2313yes—
146(C2×D3)⋊Dic5C2313yes—
147#6665C2313yes—
148Dic3×Dic5C2313yes—
149Dic3×Dic5C2313yes—
150C2×D3×#41—51no—
151C2×D3×#41D511yescharacteristic, complemented
152C3×#550—51no—
153#5834—51no—
154#5834—51no—
155#5718—53no—
156D3×#127—53no—
157D3×#121—53no—
158D3×#121—53no—
159#5599—53no—
160#5599—53no—
161#5577—51no—
162C4×D3×Q8—51no—
163#5553—53no—
164C4×D3×D4—53no—
165C2×C5×#41—31no—
166C2×C5×#41—33no—
167C2×C5×#41—33no—
168C2×C5×#41—68no—
169C2×C5×#41C2×D311yescharacteristic, complemented
170C22×C5×Q8—31no—
171C22×C5×D4—33no—
172C23×C4×C5—33no—
173C22×C22⋊D5—33no—
174C22×C22⋊D5—36no—
175C2×#713—31no—
176C2×#713—33no—
177C2×#713—33no—
178C2×#713—68no—
179C2×#713C2×D311yescharacteristic, complemented
180C22×D20—33no—
181C22×C4×D5—33no—
182C2×C22⋊Dic5—33no—
183Q8×Dic5—31no—
184Q8×Dic5—33no—
185Q8×Dic5—33no—
186Q8×Dic5C2×D311yescharacteristic, complemented
187#4086—33no—
188#4086—36no—
189#4086—36no—
190#4086—33no—
191#4086—33no—
192#4086C2×D313yescomplemented
193#4084—33no—
194#4084—36no—
195#4084—33no—
196#4084—36no—
197#4084—33no—
198#4084C2×D313yescomplemented
199#4076—33no—
200#4076—36no—
201#4076—33no—
202#4076—36no—
203#4076—33no—
204#4076C2×D313yescomplemented
205C4×C22⋊D5—33no—
206C4×C22⋊D5—33no—
207C4×C22⋊D5—33no—
208C4×C22⋊D5—33no—
209C4×C22⋊D5—33no—
210C4×C22⋊D5—33no—
211C4×C22⋊D5—33no—
212C4×C22⋊D5C2×D313yescomplemented
213C2×#685—33no—
214C2×C4⋊Dic5—33no—
215C2×#683—31no—
216C2×C4×Dic5—33no—
217C2×#550—151noSylow
218C23×C3×C5C2413yes—
219C22×D15C2413yes—
220C22×C5×D3—26no—
221C22×C5×D3—26no—
222C22×C5×D3—26no—
223C22×C5×D3C2413yes—
224C22×C5×D3C2411yescharacteristic
225C22×C3×D5C2413yes—
226C2×D3×D5—26no—
227C2×D3×D5—26no—
228C2×D3×D5—26no—
229C3×C5×Q8C2×D414yescomplemented
230C3×C5×D4—26no—
231C2×C3×C4×C5—26no—
232C2×C3×C4×C5C2411yescharacteristic
233C2×C3×C4×C5C2413yes—
234#1220—26no—
235#1220—46no—
236C2×Dic15C2413yes—
237C2×Dic15C2411yescharacteristic
238C2×Dic15C2411yescharacteristic
239D60—26no—
240C4×D15—26no—
241C5×#67—212no—
242C2×C5×Dic3—26no—
243C2×C5×Dic3C2411yescharacteristic
244C2×C5×Dic3C2413yes—
245C5×D12—26no—
246C4×C5×D3—22no—
247C4×C5×D3—26no—
248C4×C5×D3—26no—
249C4×C5×D3C2×D4112yes—
250C5×Dic6C2×D4112yescomplemented
251C3×C22⋊D5—26no—
252C3×C22⋊D5—46no—
253C2×C3×Dic5C2413yes—
254C2×C3×Dic5C2411yescharacteristic
255C2×C3×Dic5C2411yescharacteristic
256C3×D20—26no—
257C3×C4×D5—26no—
258#1203—26no—
259#1203—46no—
260#1202—212no—
261#1201—26no—
262#1201—46no—
263#1200—26no—
264D3×Dic5—22no—
265D3×Dic5—26no—
266D3×Dic5#4114yescomplemented
267D5×Dic3—26no—
268C2×C3×#41—51no—
269C2×C3×#41C2×D511yescharacteristic, complemented
270D3×#41—28no—
271D3×#41—108no—
272C2×#239—51no—
273C2×#239C2×D511yescharacteristic, complemented
274C2×D3×Q8C2×D511yescharacteristic
275C2×#237—53no—
276C2×#237C2×D513yescomplemented
277C2×D3×D4—53no—
278C2×D3×D4—56no—
279C2×D3×D4—53no—
280C2×D3×D4C2×D513yes—
281C2×#235—53no—
282C2×#235C2×D513yescomplemented
283C22×C4×D3—53no—
284C22×C4×D3C2×D513yes—
285C3×#127—53no—
286C3×#121—53no—
287C3×#121—53no—
288C3×C4×Q8—51no—
289C3×C4×D4—53no—
290Q8×Dic3—51no—
291#940—53no—
292#940—56no—
293#940—56no—
294#940—53no—
295#939—56no—
296#939—56no—
297#938—53no—
298#938—53no—
299D4×Dic3—53no—
300#930—53no—
301#930—53no—
302C4×#67—53no—
303C4×#67—53no—
304#895—53no—
305#895—53no—
306#893—53no—
307D3×C4⋊C4—51no—
308D3×C4⋊C4—53no—
309#887—53no—
310#884—56no—
311#884—56no—
312#67⋊C4—53no—
313#67⋊C4—53no—
314D3×C22⋊C4—53no—
315D3×C22⋊C4—53no—
316#874—53no—
317C4×D12—53no—
318C42×D3—53no—
319C4×Dic6—53no—
320C24×C5—33no—
321C23×D5—33no—
322C5×#41—24no—
323C5×#41—612no—
324C5×#41—612no—
325C5×#41—64no—
326C2×C5×Q8—38no—
327C2×C5×Q8—33no—
328C2×C5×Q8C22×D311yescharacteristic
329C2×C5×D4—36no—
330C2×C5×D4—33no—
331C2×C5×D4—612no—
332C2×C5×D4C22×D313yes—
333C22×C4×C5—33no—
334C22×C4×C5—33no—
335C22×C4×C5—31no—
336C22×C4×C5—33no—
337C22×C4×C5—33no—
338C22×C4×C5—612no—
339C22×C4×C5C22×D313yes—
340C2×C22⋊D5—33no—
341C2×C22⋊D5—33no—
342C2×C22⋊D5—36no—
343C2×C22⋊D5—36no—
344C2×C22⋊D5—33no—
345C2×C22⋊D5—36no—
346C2×C22⋊D5—612no—
347C2×C22⋊D5—1212no—
348C2×C22⋊D5C22×D313yes—
349C2×C22⋊D5C22×D316yes—
350C22×Dic5—31no—
351C22×Dic5—31no—
352C22×Dic5—33no—
353#713—24no—
354#713—612no—
355#713—612no—
356#713—64no—
357C2×D20—36no—
358C2×D20—33no—
359C2×D20—612no—
360C2×D20C22×D313yes—
361C2×C4×D5—33no—
362C2×C4×D5—33no—
363C2×C4×D5—33no—
364C2×C4×D5—612no—
365C2×C4×D5C22×D313yes—
366C22⋊Dic5—33no—
367C22⋊Dic5—33no—
368C22⋊Dic5—33no—
369C22⋊Dic5C22×D313yes—
370#685—33no—
371#685—33no—
372#685—33no—
373#685C22×D313yes—
374C4⋊Dic5—33no—
375C4⋊Dic5—36no—
376C4⋊Dic5C22×D313yes—
377#683—31no—
378#683—31no—
379#683—31no—
380#683C22×D311yescharacteristic
381C4×Dic5—33no—
382C4×Dic5—33no—
383C4×Dic5—33no—
384C4×Dic5C22×D313yes—
385C22×#41—31no—
386C22×#41—151no—
387#550—51no—
388#550—153no—
389#550—151no—
390#550—153no—
391#550—153no—
392#550—153no—
393#550—151no—
394#550—151no—
395C2×#127—153no—
396C2×#121—153no—
397C2×#121—153no—
398C2×C4×Q8—151no—
399C2×C4×D4—153no—
400C22×C3×C5—23no—
401C22×C3×C5—23no—
402C22×C3×C5—23no—
403C22×C3×C5C2511yescharacteristic
404C2×D15—23no—
405C2×D15—23no—
406C2×D15—23no—
407C2×C5×D3—23no—
408C2×C5×D3—23no—
409C2×C5×D3—23no—
410C2×C5×D3—412no—
411C2×C5×D3C22×D412yes—
412C2×C5×D3C2×#4112yes—
413C2×C5×D3H(5,𝔽2)12yes—
414C2×C3×D5—23no—
415C2×C3×D5—23no—
416C2×C3×D5—23no—
417D3×D5—412no—
418C3×C4×C5—21no—
419C3×C4×C5C22×D416yes—
420Dic15—21no—
421Dic15—23no—
422Dic15C2×#4112yescomplemented
423C3×Dic5—21no—
424C3×Dic5—23no—
425C3×Dic5C2×#4112yescomplemented
426C5×Dic3—21no—
427C5×Dic3C22×D416yes—
428C23×D3—53no—
429C23×D3C22×D513yes—
430C3×#41—24no—
431C3×#41—104no—
432C2×C3×Q8C22×D511yescharacteristic
433C2×C3×D4—53no—
434C2×C3×D4—56no—
435C2×C3×D4—53no—
436C2×C3×D4C22×D513yes—
437C22×C3×C4—53no—
438C22×C3×C4C22×D513yes—
439C2×#67—53no—
440C2×#67—53no—
441C2×#67—56no—
442C2×#67—56no—
443C2×#67—56no—
444C2×#67C22×D516yes—
445C22×Dic3—53no—
446C22×Dic3C22×D513yes—
447#239—24no—
448#239—104no—
449D3×Q8C22⋊D518yescomplemented
450#237—212no—
451#237—1012no—
452D3×D4—212no—
453D3×D4—1012no—
454D3×D4—1012no—
455D3×D4—2012no—
456#235—212no—
457#235—1012no—
458C2×D12—53no—
459C2×D12—53no—
460C2×D12—56no—
461C2×D12C22×D513yes—
462C2×C4×D3—212no—
463C2×C4×D3—51no—
464C2×C4×D3—53no—
465C2×C4×D3—51no—
466C2×C4×D3—53no—
467C2×C4×D3—53no—
468C2×C4×D3—1012no—
469C2×C4×D3C22×D513yes—
470C2×C4×D3C22×D511yescharacteristic
471C2×C4×D3C22×D513yes—
472C2×C4×D3C22×D513yes—
473C2×Dic6C22×D513yes—
474C3×C4⋊C4—51no—
475C3×C4⋊C4—53no—
476C3×C22⋊C4—53no—
477C3×C22⋊C4—53no—
478C3×C42—53no—
479#217—53no—
480#217—53no—
481(C2×D3)⋊C4—53no—
482(C2×D3)⋊C4—53no—
483(C2×D3)⋊C4—53no—
484(C2×D3)⋊C4—53no—
485C4⋊Dic3—53no—
486C4⋊Dic3—51no—
487Dic3⋊C4—51no—
488Dic3⋊C4—51no—
489Dic3⋊C4—56no—
490C4×Dic3—53no—
491C4×Dic3—53no—
492C4×Dic3—53no—
493C23×C5—31no—
494C23×C5—33no—
495C23×C5—66no—
496C23×C5—66no—
497C23×C5—66no—
498C23×C5C23×D313yes—
499C22×D5—33no—
500C22×D5—66no—
501C22×D5—66no—
502C22×D5—66no—
503C22×D5C23×D313yes—
504C5×Q8—312no—
505C5×Q8D3×D414yescomplemented
506C5×D4—26no—
507C5×D4—612no—
508C5×D4—66no—
509C2×C4×C5—26no—
510C2×C4×C5—33no—
511C2×C4×C5—312no—
512C2×C4×C5—31no—
513C2×C4×C5—66no—
514C2×C4×C5—62no—
515C2×C4×C5—66no—
516C2×C4×C5—66no—
517C2×C4×C5C23×D311yescharacteristic
518C2×C4×C5C23×D313yes—
519C22⋊D5—26no—
520C22⋊D5—46no—
521C22⋊D5—66no—
522C22⋊D5—66no—
523C22⋊D5—66no—
524C22⋊D5—126no—
525C22⋊D5—126no—
526C22⋊D5—126no—
527C2×Dic5—31no—
528C2×Dic5—34no—
529C2×Dic5—33no—
530C2×Dic5—31no—
531C2×Dic5—62no—
532C2×Dic5—66no—
533C2×Dic5C23×D313yes—
534C2×Dic5C23×D311yescharacteristic
535C2×Dic5C23×D311yescharacteristic
536D20—26no—
537D20—612no—
538D20—66no—
539C4×D5—26no—
540C4×D5—66no—
541C4×D5—66no—
542C4×D5—66no—
543C2×#41—31no—
544C2×#41—33no—
545C2×#41—33no—
546C2×#41—51no—
547C2×#41—68no—
548C2×#41—153no—
549C2×#41—153no—
550C2×#41—151no—
551C2×#41—308no—
552C2×#41D3×D511yescharacteristic, complemented
553C22×Q8—31no—
554C22×D4—33no—
555C22×D4—153no—
556C22×D4—153no—
557C22×D4—156no—
558C23×C4—33no—
559C23×C4—153no—
560#127—53no—
561#127—153no—
562#127—156no—
563#127—156no—
564#127—153no—
565#127—153no—
566#121—53no—
567#121—53no—
568#121—156no—
569#121—156no—
570#121—153no—
571#121—153no—
572#121—153no—
573#121—156no—
574#121—153no—
575#121—156no—
576#121—153no—
577#121—153no—
578C4×Q8—51no—
579C4×Q8—153no—
580C4×Q8—153no—
581C4×Q8—151no—
582C4×D4—53no—
583C4×D4—153no—
584C4×D4—153no—
585C4×D4—153no—
586C4×D4—153no—
587C4×D4—153no—
588C4×D4—153no—
589C4×D4—153no—
590C2×C4⋊C4—151no—
591C2×C4⋊C4—153no—
592C2×C22⋊C4—153no—
593C2×C22⋊C4—153no—
594C2×C42—153no—
595C2×C3×C5—43no—
596C2×C3×C5C23×D411yescharacteristic
597C2×C3×C5C22×#4111yescharacteristic
598C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
599D15—43no—
600C3×D5—43no—
601C5×D3—43no—
602C5×D3#55014yescomplemented
603C23×C3—53no—
604C23×C3C23×D513yes—
605C22×D3—26no—
606C22×D3—26no—
607C22×D3—26no—
608C22×D3—53no—
609C22×D3—106no—
610C22×D3—106no—
611C22×D3—106no—
612C22×D3C23×D513yes—
613C22×D3C23×D511yescharacteristic
614C3×Q8C2×C22⋊D514yescomplemented
615C3×D4—26no—
616C3×D4—106no—
617C3×D4—106no—
618C3×D4—206no—
619C2×C3×C4—26no—
620C2×C3×C4—51no—
621C2×C3×C4—53no—
622C2×C3×C4—51no—
623C2×C3×C4—106no—
624C2×C3×C4C23×D511yescharacteristic
625C2×C3×C4C23×D513yes—
626#67—212no—
627#67—106no—
628#67—106no—
629#67—1012no—
630#67—206no—
631#67—206no—
632C2×Dic3—26no—
633C2×Dic3—51no—
634C2×Dic3—53no—
635C2×Dic3—51no—
636C2×Dic3—106no—
637C2×Dic3C23×D511yescharacteristic
638C2×Dic3C23×D513yes—
639D12—26no—
640D12—106no—
641D12—106no—
642D12—206no—
643C4×D3—22no—
644C4×D3—26no—
645C4×D3—26no—
646C4×D3—54no—
647C4×D3—106no—
648C4×D3—102no—
649C4×D3—106no—
650C4×D3—106no—
651C4×D3C2×C22⋊D5112yes—
652Dic6C2×C22⋊D5112yescomplemented
653C22×C5—23no—
654C22×C5—23no—
655C22×C5—23no—
656C22×C5—32no—
657C22×C5—32no—
658C22×C5—32no—
659C22×C5—63no—
660C22×C5—63no—
661C22×C5—63no—
662C22×C5—1212no—
663C22×C5C24×D311yescharacteristic
664C2×D5—23no—
665C2×D5—23no—
666C2×D5—23no—
667C2×D5—63no—
668C2×D5—63no—
669C2×D5—63no—
670C2×D5—1212no—
671C4×C5—21no—
672C4×C5—36no—
673C4×C5—61no—
674C4×C5C2×D3×D416yes—
675Dic5—21no—
676Dic5—23no—
677Dic5—32no—
678Dic5—61no—
679Dic5—63no—
680Dic5D3×#4112yescomplemented
681C24—33no—
682C24—153no—
683#41—24no—
684#41—612no—
685#41—612no—
686#41—64no—
687#41—104no—
688#41—3012no—
689#41—3012no—
690#41—304no—
691C2×Q8—38no—
692C2×Q8—33no—
693C2×Q8C2×D3×D511yescharacteristic
694C2×D4—36no—
695C2×D4—33no—
696C2×D4—53no—
697C2×D4—56no—
698C2×D4—53no—
699C2×D4—612no—
700C2×D4—156no—
701C2×D4—153no—
702C2×D4—156no—
703C2×D4—153no—
704C2×D4—153no—
705C2×D4—156no—
706C2×D4—156no—
707C2×D4—153no—
708C2×D4—3012no—
709C2×D4—3012no—
710C2×D4—6012no—
711C2×D4C2×D3×D513yes—
712C22×C4—33no—
713C22×C4—33no—
714C22×C4—31no—
715C22×C4—33no—
716C22×C4—33no—
717C22×C4—53no—
718C22×C4—612no—
719C22×C4—153no—
720C22×C4—153no—
721C22×C4—151no—
722C22×C4—153no—
723C22×C4—151no—
724C22×C4—153no—
725C22×C4—3012no—
726C22×C4C2×D3×D513yes—
727C4⋊C4—51no—
728C4⋊C4—53no—
729C4⋊C4—151no—
730C4⋊C4—151no—
731C4⋊C4—156no—
732C4⋊C4—151no—
733C4⋊C4—153no—
734C22⋊C4—53no—
735C22⋊C4—53no—
736C22⋊C4—153no—
737C22⋊C4—153no—
738C22⋊C4—153no—
739C22⋊C4—153no—
740C22⋊C4—153no—
741C22⋊C4—153no—
742C42—53no—
743C42—153no—
744C42—153no—
745C42—153no—
746C3×C5C2×#55011yescharacteristic, complemented, Hall
747C22×C3—23no—
748C22×C3—23no—
749C22×C3—23no—
750C22×C3—103no—
751C22×C3—103no—
752C22×C3—103no—
753C22×C3C24×D511yescharacteristic
754C2×D3—23no—
755C2×D3—23no—
756C2×D3—23no—
757C2×D3—412no—
758C2×D3—103no—
759C2×D3—103no—
760C2×D3—103no—
761C2×D3—2012no—
762C2×D3D5×#4112yes—
763C2×D3#414912yes—
764C2×D3C22×C22⋊D512yes—
765C3×C4—21no—
766C3×C4—52no—
767C3×C4—103no—
768C3×C4—101no—
769C3×C4C22×C22⋊D516yes—
770Dic3—21no—
771Dic3—52no—
772Dic3—103no—
773Dic3—101no—
774Dic3C22×C22⋊D516yes—
775C2×C5—34no—
776C2×C5—43no—
777C2×C5—123no—
778C2×C5C22×D3×D411yescharacteristic
779C2×C5C2×D3×#4111yescharacteristic
780C2×C5D3×H(5,𝔽2)11yescharacteristic
781D5—43no—
782D5—123no—
783C23—31no—
784C23—33no—
785C23—53no—
786C23—66no—
787C23—66no—
788C23—66no—
789C23—153no—
790C23—306no—
791C23—306no—
792C23—306no—
793C23C22×D3×D513yes—
794Q8—312no—
795Q8D3×C22⋊D514yescomplemented
796D4—26no—
797D4—612no—
798D4—66no—
799D4—106no—
800D4—106no—
801D4—206no—
802D4—3012no—
803D4—306no—
804D4—306no—
805D4—306no—
806D4—306no—
807D4—606no—
808D4—606no—
809D4—606no—
810C2×C4—26no—
811C2×C4—33no—
812C2×C4—312no—
813C2×C4—31no—
814C2×C4—51no—
815C2×C4—53no—
816C2×C4—51no—
817C2×C4—66no—
818C2×C4—62no—
819C2×C4—66no—
820C2×C4—66no—
821C2×C4—106no—
822C2×C4—154no—
823C2×C4—151no—
824C2×C4—153no—
825C2×C4—151no—
826C2×C4—306no—
827C2×C4—306no—
828C2×C4—302no—
829C2×C4—306no—
830C2×C4—306no—
831C2×C4C22×D3×D511yescharacteristic
832C2×C4C22×D3×D513yes—
833C2×C3—43no—
834C2×C3—203no—
835C2×C3C2×D5×#4111yescharacteristic
836C2×C3C2×#414911yescharacteristic
837C2×C3C23×C22⋊D511yescharacteristic
838D3—43no—
839D3—203no—
840D3#6616814yesdirect product factor
841C5D3×#55011yescharacteristic, complemented, Sylow
842C22—23no—
843C22—23no—
844C22—23no—
845C22—32no—
846C22—32no—
847C22—32no—
848C22—63no—
849C22—63no—
850C22—63no—
851C22—103no—
852C22—103no—
853C22—103no—
854C22—1212no—
855C22—303no—
856C22—303no—
857C22—303no—
858C22—6012no—
859C22C23×D3×D511yescharacteristic
860C4—21no—
861C4—36no—
862C4—52no—
863C4—61no—
864C4—101no—
865C4—103no—
866C4—152no—
867C4—301no—
868C4—303no—
869C4C2×D3×C22⋊D516yes—
870C3C2×#6616811yescharacteristic, complemented, Sylow
871C2—34no—
872C2—43no—
873C2—123no—
874C2—203no—
875C2—603no—
876C2D3×D5×#4111yescharacteristic
877C2D3×#414911yescharacteristic
878C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC2×C3×C5×#41C22
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#550
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×D3×#41C2semidirect
2. C2×D3×#713C2semidirect
3. #11756593C2semidirect
4. C3×#66168C2semidirect
5. #11755254C2semidirect
6. #11755245C2semidirect
7. D3×Q8×Dic5C2semidirect
8. D3×#4086C2semidirect
9. D3×#4084C2semidirect
10. #11754948C2semidirect
11. #11754807C2semidirect
12. D3×#4076C2semidirect
13. C4×D3×C22⋊D5C2semidirect
14. #11754545C2semidirect
15. #11754535C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C2×#6821C22semidirect
20. C2×C5×#239C22semidirect
22. C2×C5×#237C22semidirect
24. C2×C5×#235C22semidirect
26. C2×C3×#713C22semidirect
32. C2×#6773C22semidirect
33. C2×#6766C22semidirect
34. Q8×Dic15C22semidirect
35. #91829C22semidirect
36. #91827C22semidirect
37. #91819C22semidirect
38. C4×#1220C22semidirect
39. C3×Q8×Dic5C22semidirect
40. C3×#4086C22semidirect
41. C3×#4084C22semidirect
42. C3×#4076C22semidirect
43. C3×C4×C22⋊D5C22semidirect
44. #91569C22semidirect
45. #91567C22semidirect
46. #91567C22semidirect
47. #91557C22semidirect
48. #91556C22semidirect
50. Dic3×C22⋊D5C22semidirect
51. #91549C22semidirect
53. #91466C22semidirect
54. #91463C22semidirect
55. #91460C22semidirect
56. #91456C22semidirect
57. #91454C22semidirect
58. #91451C22semidirect
59. #91449C22semidirect
60. #91446C22semidirect
61. C4×#1203C22semidirect
62. #91441C22semidirect
63. C4×#1201C22semidirect
67. #91344C22semidirect
68. Dic5×Dic6C22semidirect
79. #66168D3direct (N × H)
99. C5×D3×Q8D4semidirect
151. C2×D3×#41D5semidirect
169. C2×C5×#41C2×D3semidirect
179. C2×#713C2×D3semidirect
186. Q8×Dic5C2×D3semidirect
192. #4086C2×D3semidirect
198. #4084C2×D3semidirect
204. #4076C2×D3semidirect
212. C4×C22⋊D5C2×D3semidirect
229. C3×C5×Q8C2×D4semidirect
250. C5×Dic6C2×D4semidirect
266. D3×Dic5#41semidirect
269. C2×C3×#41C2×D5semidirect
273. C2×#239C2×D5semidirect
276. C2×#237C2×D5semidirect
282. C2×#235C2×D5semidirect
422. Dic15C2×#41semidirect
425. C3×Dic5C2×#41semidirect
449. D3×Q8C22⋊D5semidirect
505. C5×Q8D3×D4semidirect
552. C2×#41D3×D5semidirect
602. C5×D3#550semidirect
614. C3×Q8C2×C22⋊D5semidirect
652. Dic6C2×C22⋊D5semidirect
680. Dic5D3×#41semidirect
746. C3×C5C2×#550semidirect
795. Q8D3×C22⋊D5semidirect
840. D3#66168direct (N × H)
841. C5D3×#550semidirect
870. C3C2×#66168semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×#412
C2×D3×#7132
#117565932
C3×#661682
#117552542
#117552452
D3×Q8×Dic52
D3×#40862
D3×#40842
#117549482
#117548072
D3×#40762
C4×D3×C22⋊D52
#117545452
#117545352
C2×#661683
D3×#5505