Finite Group Databasebeta

← D5×#5834 #14482987

Subgroups — D5×#5834 #14482987

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×C3×D5×#41C211yesmaximal, characteristic, complemented
2C2×D5×#239C211yesmaximal, characteristic, complemented
3#11756593C211yesmaximal, characteristic, complemented
4C5×#5834C211yesmaximal, characteristic, complemented
5#11755254C211yesmaximal, characteristic, complemented
6#11755251C211yesmaximal, characteristic, complemented
7Q8×D5×Dic3C211yesmaximal, characteristic, complemented
8D5×#940C213yesmaximal, complemented
9D5×#938C213yesmaximal, complemented
10#11754938C213yesmaximal, complemented
11#11754799C213yesmaximal, complemented
12D5×#930C213yesmaximal, complemented
13C4×D5×#67C213yesmaximal, complemented
14#11754530C213yesmaximal, complemented
15#11754529C213yesmaximal, complemented
16D5×#550—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C2×#6821C2211yescharacteristic, complemented
19C2×C5×#239C2211yescharacteristic, complemented
20C3×D5×#41—28no—
21C2×C3×#713C2211yescharacteristic, complemented
22C2×C3×Q8×D5C2211yescharacteristic
23C2×C3×#711C2213yescomplemented
24C2×C3×D4×D5C2213yes—
25C2×C3×#709C2213yescomplemented
26C22×C3×C4×D5C2213yes—
27C2×D5×#67C2213yes—
28C2×D5×#67C2216yes—
29D5×#239—28no—
30C2×D5×D12C2213yes—
31C2×C4×D3×D5C2213yes—
32C2×#6769C2213yescomplemented
33C2×#6768C2213yescomplemented
34Q8×Dic15C2211yescharacteristic, complemented
35#91829C2213yescomplemented
36#91827C2213yescomplemented
37#91819C2213yescomplemented
38C4×#1220C2213yescomplemented
39C5×Q8×Dic3C2211yescharacteristic, complemented
40C5×#940C2213yescomplemented
41C5×#938C2213yescomplemented
42C5×#930C2213yescomplemented
43C4×C5×#67C2213yescomplemented
44#91567C2216yescomplemented
45#91567C2216yescomplemented
46#91566C2216yescomplemented
47#91565C2216yescomplemented
48#91552C2213yescomplemented
49Dic5×#67C2213yescomplemented
50D5×#217C2213yes—
51#91533C2216yescomplemented
52D5×(C2×D3)⋊C4C2213yes—
53#91465C2213yescomplemented
54#91463C2213yescomplemented
55#91458C2213yescomplemented
56#91456C2213yescomplemented
57#91450C2213yescomplemented
58#91449C2213yescomplemented
59#91448C2216yescomplemented
60#91444C2213yescomplemented
61C4×#1202C2213yescomplemented
62#91440C2213yescomplemented
63C4×#1201C2213yescomplemented
64D5×C4⋊Dic3C2213yes—
65D5×Dic3⋊C4C2211yescharacteristic
66C4×D5×Dic3C2213yes—
67#91331C2213yescomplemented
68Dic3×Dic10C2213yescomplemented
69C2×#5834—51nomaximal, Hall
70C2×D5×#41—31no—
71C2×D5×#41D311yescharacteristic, complemented
72C5×#550—31no—
73#66168—31no—
74#66168—31no—
75#66052—33no—
76D5×#127—33no—
77D5×#121—33no—
78D5×#121—33no—
79#65933—33no—
80#65933—33no—
81#65911—31no—
82C4×Q8×D5—31no—
83#65887—33no—
84C4×D4×D5—33no—
85C23×C3×D5C2313yes—
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×#67C2313yes—
97C2×C5×#67C2316yes—
98C5×#239—24no—
99C2×C5×D12C2313yes—
100C2×C4×C5×D3C2313yes—
101C2×C3×C22⋊D5C2316yes—
102C22×C3×Dic5C2313yes—
103C3×#713—24no—
104C3×Q8×D5D418yescomplemented
105C3×#711—212no—
106C3×D4×D5—212no—
107C3×#709—212no—
108C2×C3×D20C2313yes—
109C2×C3×C4×D5—212no—
110C2×C3×C4×D5C2311yescharacteristic
111C2×C3×C4×D5C2313yes—
112C2×C3×C4×D5C2313yes—
113C2×C3×C4×D5C2313yes—
114C2×C3×Dic10C2313yes—
115D5×#67—212no—
116D5×#67—412no—
117C2×#1203C2316yes—
118C2×#1202C2313yes—
119C2×#1202C2316yes—
120C2×#1201C2313yes—
121C2×#1201C2316yes—
122C2×#1200C2313yes—
123C2×D3×Dic5C2313yes—
124C2×D5×Dic3C2311yescharacteristic
125C2×D5×Dic3C2313yes—
126C2×D5×Dic3C2311yescharacteristic
127D5×D12—212no—
128C4×D3×D5—212no—
129#6769—212no—
130#6768—212no—
131#6719C2313yes—
132#6714C2313yes—
133C4⋊Dic15C2313yes—
134#6712C2311yescharacteristic
135C4×Dic15C2313yes—
136C5×#217C2313yes—
137C5×(C2×D3)⋊C4C2313yes—
138C5×C4⋊Dic3C2313yes—
139C5×Dic3⋊C4C2311yescharacteristic
140C4×C5×Dic3C2313yes—
141Dic3⋊Dic5C2311yescharacteristic
142#6669C2311yescharacteristic
143#6668C2316yes—
144#6667C2313yes—
145(C2×D3)⋊Dic5C2313yes—
146#6665C2313yes—
147#6665C2313yes—
148Dic3×Dic5C2313yes—
149Dic3×Dic5C2313yes—
150C22×C3×#41—51no—
151C22×#239—51no—
152#5834—51no—
153#5834—51no—
154#5834—51no—
155#5834—53no—
156#5834—53no—
157#5834—53no—
158#5834—53no—
159#5834D511yescharacteristic, direct product factor
160C2×Q8×Dic3—51no—
161C2×#940—53no—
162C2×#938—53no—
163C2×#930—53no—
164C2×C4×#67—53no—
165C2×C5×#41—31no—
166C2×C5×#41C2×D311yescharacteristic, complemented
167D5×#41—28no—
168D5×#41—68no—
169C2×#713—31no—
170C2×#713C2×D311yescharacteristic, complemented
171C2×Q8×D5C2×D311yescharacteristic
172C2×#711—33no—
173C2×#711C2×D313yescomplemented
174C2×D4×D5—33no—
175C2×D4×D5—36no—
176C2×D4×D5—33no—
177C2×D4×D5C2×D313yes—
178C2×#709—33no—
179C2×#709C2×D313yescomplemented
180C22×C4×D5—33no—
181C22×C4×D5C2×D313yes—
182C5×#127—33no—
183C5×#121—33no—
184C5×#121—33no—
185C4×C5×Q8—31no—
186C4×C5×D4—33no—
187Q8×Dic5—31no—
188#4086—33no—
189#4086—36no—
190#4086—36no—
191#4086—33no—
192#4085—36no—
193#4085—36no—
194#4084—33no—
195#4084—33no—
196D4×Dic5—33no—
197#4076—33no—
198#4076—33no—
199C4×C22⋊D5—33no—
200C4×C22⋊D5—33no—
201#4041—33no—
202#4041—33no—
203#4039—33no—
204D5×C4⋊C4—31no—
205D5×C4⋊C4—33no—
206#4033—33no—
207#4030—36no—
208#4030—36no—
209#4027—33no—
210#4027—33no—
211D5×C22⋊C4—33no—
212D5×C22⋊C4—33no—
213#4020—33no—
214C4×D20—33no—
215C42×D5—33no—
216C4×Dic10—33no—
217C2×#550—151noSylow
218C23×C3×C5C2413yes—
219C22×D15C2413yes—
220C22×C5×D3C2413yes—
221C22×C3×D5—26no—
222C22×C3×D5—26no—
223C22×C3×D5—26no—
224C22×C3×D5C2413yes—
225C22×C3×D5C2411yescharacteristic
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—26no—
242C5×#67—46no—
243C2×C5×Dic3C2413yes—
244C2×C5×Dic3C2411yescharacteristic
245C2×C5×Dic3C2411yescharacteristic
246C5×D12—26no—
247C4×C5×D3—26no—
248C3×C22⋊D5—212no—
249C2×C3×Dic5—26no—
250C2×C3×Dic5C2411yescharacteristic
251C2×C3×Dic5C2413yes—
252C3×D20—26no—
253C3×C4×D5—22no—
254C3×C4×D5—26no—
255C3×C4×D5—26no—
256C3×C4×D5C2×D4112yes—
257C3×Dic10C2×D4112yescomplemented
258#1203—212no—
259#1202—26no—
260#1202—46no—
261#1201—26no—
262#1201—46no—
263#1200—26no—
264D3×Dic5—26no—
265D5×Dic3—22no—
266D5×Dic3—26no—
267D5×Dic3#4114yescomplemented
268C2×C3×#41—51no—
269C2×C3×#41—53no—
270C2×C3×#41—53no—
271C2×C3×#41—108no—
272C2×C3×#41C2×D511yescharacteristic, complemented
273C22×C3×Q8—51no—
274C22×C3×D4—53no—
275C23×C3×C4—53no—
276C22×#67—53no—
277C22×#67—56no—
278C2×#239—51no—
279C2×#239—53no—
280C2×#239—53no—
281C2×#239—108no—
282C2×#239C2×D511yescharacteristic, complemented
283C22×D12—53no—
284C22×C4×D3—53no—
285C2×#217—53no—
286Q8×Dic3—51no—
287Q8×Dic3—53no—
288Q8×Dic3—53no—
289Q8×Dic3C2×D511yescharacteristic, complemented
290#940—53no—
291#940—56no—
292#940—56no—
293#940—53no—
294#940—53no—
295#940C2×D513yescomplemented
296#938—53no—
297#938—56no—
298#938—53no—
299#938—56no—
300#938—53no—
301#938C2×D513yescomplemented
302#930—53no—
303#930—56no—
304#930—53no—
305#930—56no—
306#930—53no—
307#930C2×D513yescomplemented
308C4×#67—53no—
309C4×#67—53no—
310C4×#67—53no—
311C4×#67—53no—
312C4×#67—53no—
313C4×#67—53no—
314C4×#67—53no—
315C4×#67C2×D513yescomplemented
316C2×(C2×D3)⋊C4—53no—
317C2×C4⋊Dic3—53no—
318C2×Dic3⋊C4—51no—
319C2×C4×Dic3—53no—
320C23×D5—33no—
321C23×D5C22×D313yes—
322C5×#41—24no—
323C5×#41—64no—
324C2×C5×Q8C22×D311yescharacteristic
325C2×C5×D4—33no—
326C2×C5×D4—36no—
327C2×C5×D4—33no—
328C2×C5×D4C22×D313yes—
329C22×C4×C5—33no—
330C22×C4×C5C22×D313yes—
331C2×C22⋊D5—33no—
332C2×C22⋊D5—33no—
333C2×C22⋊D5—36no—
334C2×C22⋊D5—36no—
335C2×C22⋊D5—36no—
336C2×C22⋊D5C22×D316yes—
337C22×Dic5—33no—
338C22×Dic5C22×D313yes—
339#713—24no—
340#713—64no—
341Q8×D5#6718yescomplemented
342#711—212no—
343#711—612no—
344D4×D5—212no—
345D4×D5—612no—
346D4×D5—612no—
347D4×D5—1212no—
348#709—212no—
349#709—612no—
350C2×D20—33no—
351C2×D20—33no—
352C2×D20—36no—
353C2×D20C22×D313yes—
354C2×C4×D5—212no—
355C2×C4×D5—31no—
356C2×C4×D5—31no—
357C2×C4×D5—33no—
358C2×C4×D5—33no—
359C2×C4×D5—33no—
360C2×C4×D5—612no—
361C2×C4×D5C22×D311yescharacteristic
362C2×C4×D5C22×D313yes—
363C2×C4×D5C22×D313yes—
364C2×C4×D5C22×D313yes—
365C2×Dic10C22×D313yes—
366C5×C4⋊C4—31no—
367C5×C4⋊C4—33no—
368C5×C22⋊C4—33no—
369C5×C22⋊C4—33no—
370C42×C5—33no—
371C22⋊Dic5—33no—
372C22⋊Dic5—33no—
373#685—33no—
374#685—33no—
375#685—33no—
376#685—33no—
377C4⋊Dic5—33no—
378C4⋊Dic5—31no—
379#683—31no—
380#683—36no—
381#683—31no—
382C4×Dic5—33no—
383C4×Dic5—33no—
384C4×Dic5—33no—
385C22×#41—51no—
386C22×#41—151no—
387#550—31no—
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×C3×D5—23no—
411C2×C3×D5—23no—
412C2×C3×D5—23no—
413C2×C3×D5—412no—
414C2×C3×D5C22×D412yes—
415C2×C3×D5C2×#4112yes—
416C2×C3×D5H(5,𝔽2)12yes—
417D3×D5—412no—
418C3×C4×C5—21no—
419C3×C4×C5C22×D416yes—
420Dic15—21no—
421Dic15—23no—
422Dic15C2×#4112yescomplemented
423C3×Dic5—21no—
424C3×Dic5C22×D416yes—
425C5×Dic3—21no—
426C5×Dic3—23no—
427C5×Dic3C2×#4112yescomplemented
428C24×C3—53no—
429C23×D3—53no—
430C3×#41—24no—
431C3×#41—1012no—
432C3×#41—1012no—
433C3×#41—104no—
434C2×C3×Q8—58no—
435C2×C3×Q8—53no—
436C2×C3×Q8C22×D511yescharacteristic
437C2×C3×D4—56no—
438C2×C3×D4—53no—
439C2×C3×D4—1012no—
440C2×C3×D4C22×D513yes—
441C22×C3×C4—53no—
442C22×C3×C4—53no—
443C22×C3×C4—51no—
444C22×C3×C4—53no—
445C22×C3×C4—53no—
446C22×C3×C4—1012no—
447C22×C3×C4C22×D513yes—
448C2×#67—53no—
449C2×#67—53no—
450C2×#67—56no—
451C2×#67—56no—
452C2×#67—53no—
453C2×#67—56no—
454C2×#67—1012no—
455C2×#67—2012no—
456C2×#67C22×D513yes—
457C2×#67C22×D516yes—
458C22×Dic3—51no—
459C22×Dic3—53no—
460C22×Dic3—51no—
461#239—24no—
462#239—1012no—
463#239—1012no—
464#239—104no—
465C2×D12—56no—
466C2×D12—53no—
467C2×D12—1012no—
468C2×D12C22×D513yes—
469C2×C4×D3—53no—
470C2×C4×D3—53no—
471C2×C4×D3—53no—
472C2×C4×D3—1012no—
473C2×C4×D3C22×D513yes—
474#217—53no—
475#217—53no—
476#217—53no—
477#217C22×D513yes—
478(C2×D3)⋊C4—53no—
479(C2×D3)⋊C4—53no—
480(C2×D3)⋊C4—53no—
481(C2×D3)⋊C4C22×D513yes—
482C4⋊Dic3—53no—
483C4⋊Dic3—56no—
484C4⋊Dic3C22×D513yes—
485Dic3⋊C4—51no—
486Dic3⋊C4—51no—
487Dic3⋊C4—51no—
488Dic3⋊C4C22×D511yescharacteristic
489C4×Dic3—53no—
490C4×Dic3—53no—
491C4×Dic3—53no—
492C4×Dic3C22×D513yes—
493C23×C5—33no—
494C23×C5C23×D313yes—
495C22×D5—26no—
496C22×D5—26no—
497C22×D5—26no—
498C22×D5—33no—
499C22×D5—66no—
500C22×D5—66no—
501C22×D5—66no—
502C22×D5C23×D313yes—
503C22×D5C23×D311yescharacteristic
504C5×Q8C2×#6714yescomplemented
505C5×D4—26no—
506C5×D4—66no—
507C5×D4—66no—
508C5×D4—126no—
509C2×C4×C5—26no—
510C2×C4×C5—31no—
511C2×C4×C5—33no—
512C2×C4×C5—31no—
513C2×C4×C5—66no—
514C2×C4×C5C23×D311yescharacteristic
515C2×C4×C5C23×D313yes—
516C22⋊D5—212no—
517C22⋊D5—66no—
518C22⋊D5—66no—
519C22⋊D5—612no—
520C22⋊D5—126no—
521C22⋊D5—126no—
522C2×Dic5—26no—
523C2×Dic5—31no—
524C2×Dic5—33no—
525C2×Dic5—31no—
526C2×Dic5—66no—
527C2×Dic5C23×D311yescharacteristic
528C2×Dic5C23×D313yes—
529D20—26no—
530D20—66no—
531D20—66no—
532D20—126no—
533C4×D5—22no—
534C4×D5—26no—
535C4×D5—26no—
536C4×D5—34no—
537C4×D5—66no—
538C4×D5—62no—
539C4×D5—66no—
540C4×D5—66no—
541C4×D5C2×#67112yes—
542Dic10C2×#67112yescomplemented
543C2×#41—31no—
544C2×#41—51no—
545C2×#41—53no—
546C2×#41—53no—
547C2×#41—108no—
548C2×#41—153no—
549C2×#41—153no—
550C2×#41—151no—
551C2×#41—308no—
552C2×#41D3×D511yescharacteristic, complemented
553C22×Q8—51no—
554C22×D4—53no—
555C22×D4—153no—
556C22×D4—153no—
557C22×D4—156no—
558C23×C4—53no—
559C23×C4—153no—
560#127—33no—
561#127—153no—
562#127—156no—
563#127—156no—
564#127—153no—
565#127—153no—
566#121—33no—
567#121—33no—
568#121—156no—
569#121—156no—
570#121—153no—
571#121—153no—
572#121—153no—
573#121—153no—
574#121—156no—
575#121—156no—
576#121—153no—
577#121—153no—
578C4×Q8—31no—
579C4×Q8—153no—
580C4×Q8—153no—
581C4×Q8—151no—
582C4×D4—33no—
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—
601C3×D5#55014yescomplemented
602C5×D3—43no—
603C23×C3—51no—
604C23×C3—53no—
605C23×C3—106no—
606C23×C3—106no—
607C23×C3—106no—
608C23×C3C23×D513yes—
609C22×D3—53no—
610C22×D3—106no—
611C22×D3—106no—
612C22×D3—106no—
613C22×D3C23×D513yes—
614C3×Q8—512no—
615C3×Q8D4×D514yescomplemented
616C3×D4—26no—
617C3×D4—1012no—
618C3×D4—106no—
619C2×C3×C4—26no—
620C2×C3×C4—53no—
621C2×C3×C4—512no—
622C2×C3×C4—51no—
623C2×C3×C4—106no—
624C2×C3×C4—102no—
625C2×C3×C4—106no—
626C2×C3×C4—106no—
627C2×C3×C4C23×D511yescharacteristic
628C2×C3×C4C23×D513yes—
629#67—26no—
630#67—46no—
631#67—106no—
632#67—106no—
633#67—106no—
634#67—206no—
635#67—206no—
636#67—206no—
637C2×Dic3—51no—
638C2×Dic3—54no—
639C2×Dic3—53no—
640C2×Dic3—51no—
641C2×Dic3—102no—
642C2×Dic3—106no—
643C2×Dic3C23×D513yes—
644C2×Dic3C23×D511yescharacteristic
645C2×Dic3C23×D511yescharacteristic
646D12—26no—
647D12—1012no—
648D12—106no—
649C4×D3—26no—
650C4×D3—106no—
651C4×D3—106no—
652C4×D3—106no—
653C22×C5—23no—
654C22×C5—23no—
655C22×C5—23no—
656C22×C5—63no—
657C22×C5—63no—
658C22×C5—63no—
659C22×C5C24×D311yescharacteristic
660C2×D5—23no—
661C2×D5—23no—
662C2×D5—23no—
663C2×D5—412no—
664C2×D5—63no—
665C2×D5—63no—
666C2×D5—63no—
667C2×D5—1212no—
668C2×D5D3×#4112yes—
669C2×D5#100912yes—
670C2×D5C22×#6712yes—
671C4×C5—21no—
672C4×C5—32no—
673C4×C5—63no—
674C4×C5—61no—
675C4×C5C22×#6716yes—
676Dic5—21no—
677Dic5—32no—
678Dic5—63no—
679Dic5—61no—
680Dic5C22×#6716yes—
681C24—53no—
682C24—153no—
683#41—24no—
684#41—64no—
685#41—1012no—
686#41—1012no—
687#41—104no—
688#41—3012no—
689#41—3012no—
690#41—304no—
691C2×Q8—58no—
692C2×Q8—53no—
693C2×Q8C2×D3×D511yescharacteristic
694C2×D4—33no—
695C2×D4—36no—
696C2×D4—33no—
697C2×D4—56no—
698C2×D4—53no—
699C2×D4—1012no—
700C2×D4—153no—
701C2×D4—156no—
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—53no—
714C22×C4—53no—
715C22×C4—51no—
716C22×C4—53no—
717C22×C4—53no—
718C22×C4—1012no—
719C22×C4—153no—
720C22×C4—151no—
721C22×C4—153no—
722C22×C4—151no—
723C22×C4—153no—
724C22×C4—153no—
725C22×C4—3012no—
726C22×C4C2×D3×D513yes—
727C4⋊C4—31no—
728C4⋊C4—33no—
729C4⋊C4—151no—
730C4⋊C4—151no—
731C4⋊C4—156no—
732C4⋊C4—151no—
733C4⋊C4—153no—
734C22⋊C4—33no—
735C22⋊C4—33no—
736C22⋊C4—153no—
737C22⋊C4—153no—
738C22⋊C4—153no—
739C22⋊C4—153no—
740C22⋊C4—153no—
741C22⋊C4—153no—
742C42—33no—
743C42—153no—
744C42—153no—
745C42—153no—
746C3×C5C2×#55011yescharacteristic, complemented, Hall
747C22×C3—23no—
748C22×C3—23no—
749C22×C3—23no—
750C22×C3—52no—
751C22×C3—52no—
752C22×C3—52no—
753C22×C3—103no—
754C22×C3—103no—
755C22×C3—103no—
756C22×C3—2012no—
757C22×C3C24×D511yescharacteristic
758C2×D3—23no—
759C2×D3—23no—
760C2×D3—23no—
761C2×D3—103no—
762C2×D3—103no—
763C2×D3—103no—
764C2×D3—2012no—
765C3×C4—21no—
766C3×C4—56no—
767C3×C4—101no—
768C3×C4C2×D4×D516yes—
769Dic3—21no—
770Dic3—23no—
771Dic3—52no—
772Dic3—101no—
773Dic3—103no—
774Dic3D5×#4112yescomplemented
775C2×C5—43no—
776C2×C5—123no—
777C2×C5C2×D3×#4111yescharacteristic
778C2×C5C2×#100911yescharacteristic
779C2×C5C23×#6711yescharacteristic
780D5—43no—
781D5—123no—
782D5#583414yesdirect product factor
783C23—33no—
784C23—51no—
785C23—53no—
786C23—106no—
787C23—106no—
788C23—106no—
789C23—153no—
790C23—306no—
791C23—306no—
792C23—306no—
793C23C22×D3×D513yes—
794Q8—512no—
795Q8D5×#6714yescomplemented
796D4—26no—
797D4—66no—
798D4—66no—
799D4—1012no—
800D4—106no—
801D4—126no—
802D4—306no—
803D4—3012no—
804D4—306no—
805D4—306no—
806D4—306no—
807D4—606no—
808D4—606no—
809D4—606no—
810C2×C4—26no—
811C2×C4—31no—
812C2×C4—33no—
813C2×C4—31no—
814C2×C4—53no—
815C2×C4—512no—
816C2×C4—51no—
817C2×C4—66no—
818C2×C4—106no—
819C2×C4—102no—
820C2×C4—106no—
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—54no—
835C2×C3—203no—
836C2×C3C22×D4×D511yescharacteristic
837C2×C3C2×D5×#4111yescharacteristic
838C2×C3D5×H(5,𝔽2)11yescharacteristic
839D3—43no—
840D3—203no—
841C5C2×#583411yescharacteristic, complemented, Sylow
842C22—23no—
843C22—23no—
844C22—23no—
845C22—52no—
846C22—52no—
847C22—52no—
848C22—63no—
849C22—63no—
850C22—63no—
851C22—103no—
852C22—103no—
853C22—103no—
854C22—2012no—
855C22—303no—
856C22—303no—
857C22—303no—
858C22—6012no—
859C22C23×D3×D511yescharacteristic
860C4—21no—
861C4—32no—
862C4—56no—
863C4—61no—
864C4—63no—
865C4—101no—
866C4—152no—
867C4—301no—
868C4—303no—
869C4C2×D5×#6716yes—
870C3D5×#55011yescharacteristic, complemented, Sylow
871C2—43no—
872C2—54no—
873C2—123no—
874C2—203no—
875C2—603no—
876C2D3×D5×#4111yescharacteristic
877C2D5×#100911yescharacteristic
878C2C22×D5×#6711yescharacteristic
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×C3×D5×#41C2semidirect
2. C2×D5×#239C2semidirect
3. #11756593C2semidirect
4. C5×#5834C2semidirect
5. #11755254C2semidirect
6. #11755251C2semidirect
7. Q8×D5×Dic3C2semidirect
8. D5×#940C2semidirect
9. D5×#938C2semidirect
10. #11754938C2semidirect
11. #11754799C2semidirect
12. D5×#930C2semidirect
13. C4×D5×#67C2semidirect
14. #11754530C2semidirect
15. #11754529C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C2×#6821C22semidirect
19. C2×C5×#239C22semidirect
21. C2×C3×#713C22semidirect
23. C2×C3×#711C22semidirect
25. C2×C3×#709C22semidirect
32. C2×#6769C22semidirect
33. C2×#6768C22semidirect
34. Q8×Dic15C22semidirect
35. #91829C22semidirect
36. #91827C22semidirect
37. #91819C22semidirect
38. C4×#1220C22semidirect
39. C5×Q8×Dic3C22semidirect
40. C5×#940C22semidirect
41. C5×#938C22semidirect
42. C5×#930C22semidirect
43. C4×C5×#67C22semidirect
44. #91567C22semidirect
45. #91567C22semidirect
46. #91566C22semidirect
47. #91565C22semidirect
48. #91552C22semidirect
49. Dic5×#67C22semidirect
51. #91533C22semidirect
53. #91465C22semidirect
54. #91463C22semidirect
55. #91458C22semidirect
56. #91456C22semidirect
57. #91450C22semidirect
58. #91449C22semidirect
59. #91448C22semidirect
60. #91444C22semidirect
61. C4×#1202C22semidirect
62. #91440C22semidirect
63. C4×#1201C22semidirect
67. #91331C22semidirect
68. Dic3×Dic10C22semidirect
71. C2×D5×#41D3semidirect
104. C3×Q8×D5D4semidirect
159. #5834D5direct (N × H)
166. C2×C5×#41C2×D3semidirect
170. C2×#713C2×D3semidirect
173. C2×#711C2×D3semidirect
179. C2×#709C2×D3semidirect
229. C3×C5×Q8C2×D4semidirect
257. C3×Dic10C2×D4semidirect
267. D5×Dic3#41semidirect
272. C2×C3×#41C2×D5semidirect
282. C2×#239C2×D5semidirect
289. Q8×Dic3C2×D5semidirect
295. #940C2×D5semidirect
301. #938C2×D5semidirect
307. #930C2×D5semidirect
315. C4×#67C2×D5semidirect
341. Q8×D5#67semidirect
422. Dic15C2×#41semidirect
427. C5×Dic3C2×#41semidirect
504. C5×Q8C2×#67semidirect
542. Dic10C2×#67semidirect
552. C2×#41D3×D5semidirect
601. C3×D5#550semidirect
615. C3×Q8D4×D5semidirect
746. C3×C5C2×#550semidirect
774. Dic3D5×#41semidirect
782. D5#5834direct (N × H)
795. Q8D5×#67semidirect
841. C5C2×#5834semidirect
870. C3D5×#550semidirect

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×D5×#2392
#117565932
C5×#58342
#117552542
#117552512
Q8×D5×Dic32
D5×#9402
D5×#9382
#117549382
#117547992
D5×#9302
C4×D5×#672
#117545302
#117545292
D5×#5503
C2×#58345