Finite Group Databasebeta

← #14419539

Subgroups — #14419539

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11753476C211yesmaximal, characteristic
2#11752364C211yesmaximal, characteristic, complemented
3C3×#65704C211yesmaximal, characteristic, complemented
4#11751911C211yesmaximal, characteristic, complemented
5#11751903C211yesmaximal, characteristic, complemented
6#11751903C211yesmaximal, characteristic, complemented
7#11751874C211yesmaximal, characteristic, complemented
8#11751827C211yesmaximal, characteristic, complemented
9#11751787C211yesmaximal, characteristic, complemented
10#11751781C211yesmaximal, characteristic, complemented
11#11751780C211yesmaximal, characteristic, complemented
12Dic3×#700C211yesmaximal, characteristic, complemented
13#11751769C211yesmaximal, characteristic, complemented
14#11751767C211yesmaximal, characteristic, complemented
15#11751763C211yesmaximal, characteristic, complemented
16#10617333—31nomaximal, Hall
17C2×#6758C2211yescharacteristic
18C2×#6758C2211yescharacteristic
19C2×C3×#700C2211yescharacteristic
20C2×C3×D5⋊C8C2211yescharacteristic
21C2×#6740C2211yescharacteristic
22C2×#6738C2211yescharacteristic
23#91787C411yescharacteristic
24C5×#889C411yescharacteristic
25C3×#4039C2211yescharacteristic
26#91444C2211yescharacteristic
27#91444C2211yescharacteristic
28#91422C411yescharacteristic
29#91413C411yescharacteristic
30#91409C411yescharacteristic
31#91407C411yescharacteristic
32#91402C2211yescharacteristic
33C4×D5×Dic3C2211yescharacteristic
34#91366C411yescharacteristic
35#91358C2211yescharacteristic
36#91353C411yescharacteristic
37#91323C2211yescharacteristic
38#91232C2211yescharacteristic
39#91232C2211yescharacteristic
40C4⋊(C3⋊#170)C2211yescharacteristic
41C4×C3⋊#170C2211yescharacteristic
42C3×#4004C2211yescharacteristic
43C3×#4003C2211yescharacteristic
44C3×#4003C2211yescharacteristic
45C3×#4002C2211yescharacteristic
46#91177C2211yescharacteristic
47#91177C2211yescharacteristic
48#91177C2211yescharacteristic
49Dic3⋊#170C2211yescharacteristic
50#91171C2211yescharacteristic
51#91171C2211yescharacteristic
52#91169C2211yescharacteristic
53#91169C2211yescharacteristic
54#91169C2211yescharacteristic
55#91169C2211yescharacteristic
56#91169C2211yescharacteristic
57Dic3×#170C2211yescharacteristic
58Dic3×#170C2211yescharacteristic
59Dic3×#170C2211yescharacteristic
60#79455—51nomaximal, Hall
61#66025—31no—
62#65707—31no—
63#65707—31no—
64#65706—31no—
65#65706—31no—
66#65705—31no—
67#65705—31no—
68#65704—31no—
69#65704—31no—
70#65704—31no—
71#65704D311yescharacteristic, complemented
72#65701—31no—
73#65701—31no—
74#65684—31no—
75C4×#700—31no—
76C2×C3×D20C2×C411yescharacteristic
77C2×C3×C4×D5C2311yescharacteristic
78C2×C3×C4×D5C2311yescharacteristic
79C2×#1204C2×C411yescharacteristic
80C2×#1202C2×C411yescharacteristic
81C2×#1202C2×C411yescharacteristic
82C2×#1200C2311yescharacteristic
83C2×D5×Dic3C2×C411yescharacteristic
84C2×D5×Dic3C2×C411yescharacteristic
85C2×C3⋊#170C2311yescharacteristic
86C2×C3⋊#170C2311yescharacteristic
87C2×C3⋊#170C2311yescharacteristic
88C2×C3⋊#170C2311yescharacteristic
89#6758—22no—
90#6758—22no—
91C2×C3×#170C2311yescharacteristic
92C2×C3×#170C2311yescharacteristic
93C2×C3×#170C2311yescharacteristic
94C2×C3×#170C2311yescharacteristic
95C3×#700—22no—
96C3×D5⋊C8—22no—
97#6740—22no—
98#6738—22no—
99C3×C5×C4⋊C4C2×C411yescharacteristic
100#6714C2×C411yescharacteristic
101#6714C2×C411yescharacteristic
102#6714C2×C411yescharacteristic
103C4⋊Dic15C2×C411yescharacteristic
104#6712C2×C411yescharacteristic
105C4×Dic15C2×C411yescharacteristic
106C5×C4⋊Dic3C2×C411yescharacteristic
107C5×Dic3⋊C4C2×C411yescharacteristic
108C5×Dic3⋊C4C2×C411yescharacteristic
109C5×Dic3⋊C4C2×C411yescharacteristic
110C5×Dic3⋊C4C2×C411yescharacteristic
111C4×C5×Dic3C2×C411yescharacteristic
112C3×#685C2×C411yescharacteristic
113C3×#685C2×C411yescharacteristic
114C3×C4×Dic5C2311yescharacteristic
115Dic3⋊Dic5C2×C411yescharacteristic
116#6668C2×C411yescharacteristic
117#6667C2×C411yescharacteristic
118#6665C2×C411yescharacteristic
119#6665C2×C411yescharacteristic
120#6665C2×C411yescharacteristic
121#6665C2×C411yescharacteristic
122Dic3×Dic5C2311yescharacteristic
123Dic3×Dic5C2311yescharacteristic
124Dic3×Dic5C2311yescharacteristic
125#5538—51no—
126C3×#435—51no—
127#5128—51no—
128Dic3×M16—51no—
129#5111—51no—
130#5101—51no—
131#5012—51no—
132#4840—51no—
133#4831—51no—
134#4728—51no—
135#4728—51no—
136#4720—51no—
137#4719—51no—
138#4708—51no—
139#4701—51no—
140C2×#700—31no—
141C2×#700—31no—
142C2×#700—31no—
143C2×#700C2×D311yescharacteristic
144C2×D5⋊C8—31no—
145C2×D5⋊C8C2×D311yescharacteristic
146C5×#125—31no—
147#4044—31no—
148#4044—31no—
149#4043—31no—
150#4041—31no—
151#4040—31no—
152#4040—31no—
153#4039—31no—
154#4039—31no—
155#4039C2×D311yescharacteristic
156#4038—31no—
157#4038—31no—
158#4033—31no—
159#4021—31no—
160C42×D5—31no—
161#4004—31no—
162#4004—31no—
163#4004—31no—
164#4004C2×D311yescharacteristic
165#4003—31no—
166#4003—31no—
167#4003—31no—
168#4003—31no—
169#4003C2×D311yescharacteristic
170#4003C2×D311yescharacteristic
171#4002—31no—
172#4002—31no—
173#4002—31no—
174#4002—31no—
175#4002—31no—
176#4002C2×D311yescharacteristic
177C4⋊#170—31no—
178C4⋊#170—31no—
179C4×#170—31no—
180C4×#170—31no—
181C4×#170—31no—
182C4×#170—31no—
183#2967—151noSylow
184C22×D15C22×C411yescharacteristic
185C22×C3×D5C22×C411yescharacteristic
186C22×C3×D5C22×C411yescharacteristic
187C2×C3×C4×C5C22×C411yescharacteristic
188C2×C3×C4×C5C22×C411yescharacteristic
189C2×C3×C4×C5C22×C411yescharacteristic
190C2×Dic15C22×C411yescharacteristic
191C2×Dic15C22×C411yescharacteristic
192C2×Dic15C22×C411yescharacteristic
193C2×C5×Dic3C22×C411yescharacteristic
194C2×C5×Dic3C22×C411yescharacteristic
195C2×C5×Dic3C22×C411yescharacteristic
196C2×C5×Dic3C22×C411yescharacteristic
197C2×C3×Dic5C22×C411yescharacteristic
198C2×C3×Dic5C2411yescharacteristic
199C3×D20—41no—
200C3×C4×D5—21no—
201C3×C4×D5—21no—
202C3×C4×D5—21no—
203C3×C4×D5—21no—
204#1204—41no—
205#1202—41no—
206#1202—41no—
207#1200—21no—
208#1200—21no—
209D5×Dic3—41no—
210D5×Dic3—41no—
211C3⋊#170—21no—
212C3⋊#170—21no—
213C3⋊#170—21no—
214C3⋊#170#4112yes—
215C3×#170—21no—
216C3×#170—21no—
217C3×#170—21no—
218C3×#170#4112yes—
219C2×C3×M16—51no—
220C22×C3×C8—51no—
221C3×C4×D4—51no—
222#939—51no—
223#935—51no—
224C4×#67—51no—
225C4×#67—51no—
226#926—51no—
227C2×C4×Dic3—51no—
228C2×#208—51no—
229C2×#208—51no—
230C2×ΓL(1,𝔽25)—51no—
231C2×D3×C8—51no—
232#898—51no—
233#889AGL(1,𝔽5)11yescharacteristic
234#886—51no—
235#885—51no—
236#879—51no—
237#878—51no—
238#872—51no—
239C4×Dic6—51no—
240C3×C4⋊C8—51no—
241C3×C22⋊C8—51no—
242C3×C22⋊C8—51no—
243C3×#97—51no—
244#830—51no—
245#830—51no—
246(C2×D3)⋊C8—51no—
247(C2×D3)⋊C8—51no—
248#815—51no—
249#815—51no—
250#815—51no—
251#815—51no—
252#815—51no—
253Dic3⋊C8—51no—
254Dic3⋊C8—51no—
255Dic3⋊C8—51no—
256Dic3⋊C8—51no—
257C8×Dic3—51no—
258C8×Dic3—51no—
259C8×Dic3—51no—
260C4⋊(C3⋊C8)—51no—
261C4×C3⋊C8—51no—
262C2×D20—31no—
263C2×D20—31no—
264C2×D20C4×D311yescharacteristic
265C2×C4×D5—31no—
266C2×C4×D5—31no—
267C2×C4×D5—31no—
268C2×C4×D5C22×D311yescharacteristic
269C2×C4×D5C22×D311yescharacteristic
270C2×Dic10—31no—
271C2×#170—31no—
272C2×#170—31no—
273C2×#170—31no—
274C2×#170—31no—
275C2×#170C22×D311yescharacteristic
276C2×#170C22×D311yescharacteristic
277C2×#170C22×D311yescharacteristic
278C2×#170C22×D311yescharacteristic
279#700—22no—
280#700—62no—
281#700—62no—
282#700—62no—
283D5⋊C8—22no—
284D5⋊C8—62no—
285C5×C4⋊C4—31no—
286C5×C4⋊C4—31no—
287C5×C4⋊C4—31no—
288C5×C4⋊C4—31no—
289C5×C4⋊C4—31no—
290C5×C4⋊C4C4×D311yescharacteristic
291C42×C5—31no—
292#685—31no—
293#685—31no—
294#685—31no—
295#685—31no—
296#685—31no—
297#685—31no—
298#685—31no—
299#685—31no—
300#685C4×D311yescharacteristic
301#685C4×D311yescharacteristic
302C4⋊Dic5—31no—
303C4⋊Dic5—31no—
304#683—31no—
305#683—31no—
306C4×Dic5—31no—
307C4×Dic5—31no—
308C4×Dic5—31no—
309C4×Dic5—31no—
310C4×Dic5C22×D311yescharacteristic
311#529—151no—
312#446—151no—
313#446—151no—
314#436—151no—
315#436—151no—
316#435—51no—
317#435—151no—
318#435—151no—
319#435—151no—
320#433—151no—
321#433—151no—
322#432—151no—
323#405—151no—
324#405—151no—
325C4×M16—151no—
326C22×C3×C5C23×C411yescharacteristic
327C2×D15—21no—
328C2×D15—21no—
329C2×D15—21no—
330C2×C3×D5—21no—
331C2×C3×D5—21no—
332C2×C3×D5—21no—
333C2×C3×D5—21no—
334C2×C3×D5—21no—
335C2×C3×D5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—21no—
338C3×C4×C5—21no—
339Dic15—21no—
340Dic15—21no—
341Dic15—21no—
342C3×Dic5—21no—
343C3×Dic5C2×#4111yescharacteristic
344C3×Dic5C2×#4111yescharacteristic
345C5×Dic3—21no—
346C5×Dic3—21no—
347C5×Dic3—21no—
348C5×Dic3—21no—
349C2×C3×D4—51no—
350C22×C3×C4—51no—
351C22×C3×C4—51no—
352C2×#67—51no—
353C2×#67—51no—
354C22×Dic3—51no—
355C22×Dic3—51no—
356C2×C4×D3—51no—
357C2×Dic6—51no—
358C3×M16—102no—
359C2×C3×C8—51no—
360C2×C3×C8—51no—
361C2×C3×C8—51no—
362C2×C3×C8—51no—
363C2×C3×C8—102no—
364C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
365C3×C22⋊C4—51no—
366C3×C22⋊C4—51no—
367C3×C42—51no—
368#217—51no—
369#217—51no—
370#217—51no—
371#217—51no—
372(C2×D3)⋊C4—51no—
373(C2×D3)⋊C4—51no—
374(C2×D3)⋊C4—51no—
375(C2×D3)⋊C4—51no—
376C4⋊Dic3—51no—
377C4⋊Dic3—51no—
378C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
379Dic3⋊C4—51no—
380Dic3⋊C4—51no—
381Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
382Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
383Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
384Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
385C4×Dic3—51no—
386C4×Dic3—51no—
387C4×Dic3—51no—
388C4×Dic3—51no—
389C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
390#208—102no—
391#208—102no—
392C2×C3⋊C8—51no—
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395C2×C3⋊C8—51no—
396ΓL(1,𝔽25)—102no—
397D3×C8—102no—
398C22×D5—31no—
399C22×D5C2×C4×D311yescharacteristic
400C22×D5C2×C4×D311yescharacteristic
401C2×C4×C5—31no—
402C2×C4×C5—31no—
403C2×C4×C5—31no—
404C2×C4×C5—31no—
405C2×C4×C5C2×C4×D311yescharacteristic
406C2×C4×C5C2×C4×D311yescharacteristic
407C2×C4×C5C2×C4×D311yescharacteristic
408C2×Dic5—31no—
409C2×Dic5—31no—
410C2×Dic5—31no—
411C2×Dic5C2×C4×D311yescharacteristic
412C2×Dic5C23×D311yescharacteristic
413D20—41no—
414D20—121no—
415D20—121no—
416C4×D5—21no—
417C4×D5—21no—
418C4×D5—21no—
419C4×D5—21no—
420C4×D5—61no—
421C4×D5—61no—
422C4×D5—121no—
423C4×D5—121no—
424Dic10—121no—
425#170—21no—
426#170—21no—
427#170—21no—
428#170—32no—
429#170—61no—
430#170—61no—
431#170—61no—
432#170#23712yes—
433C2×M16—51no—
434C2×M16—151no—
435C2×M16—151no—
436C2×M16—151no—
437C22×C8—51no—
438C22×C8—151no—
439#126—151no—
440#126—151no—
441#125—31no—
442#124—151no—
443#123—151no—
444#123—151no—
445C22⋊Q8—151no—
446#121—151no—
447C4×Q8—151no—
448C4×D4—51no—
449C4×D4—151no—
450C4×D4—151no—
451#117—151no—
452#117—151no—
453C2×C42—151no—
454C4⋊C8—51no—
455C4⋊C8—151no—
456C4⋊C8—151no—
457C4⋊C8—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460C22⋊C8—51no—
461C22⋊C8—51no—
462C22⋊C8—151no—
463C22⋊C8—151no—
464C22⋊C8—151no—
465C22⋊C8—151no—
466#97—51no—
467#97—151no—
468#97—151no—
469#97—151no—
470#97—151no—
471#97—151no—
472C4×C8—151no—
473C4×C8—151no—
474C4×C8—151no—
475C4×C8—151no—
476C2×C3×C5C4×#4111yescharacteristic
477C2×C3×C5#56811yescharacteristic
478C2×C3×C5#56811yescharacteristic
479D15—41no—
480C3×D5—41no—
481C3×D5—41no—
482C23×C3—51no—
483C23×C3—51no—
484C22×D3—51no—
485C3×D4—201no—
486C2×C3×C4—51no—
487C2×C3×C4—51no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
493C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
494C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
495#67—201no—
496#67—201no—
497C2×Dic3—51no—
498C2×Dic3—51no—
499C2×Dic3—51no—
500C2×Dic3—201no—
501C2×Dic3—201no—
502C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
503C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
504C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
505C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
506C4×D3—101no—
507C4×D3—101no—
508Dic6—201no—
509C3×C8—52no—
510C3×C8—101no—
511C3×C8—101no—
512C3×C8—101no—
513C3⋊C8—52no—
514C3⋊C8—101no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5C22×C4×D311yescharacteristic
518C2×D5—21no—
519C2×D5—21no—
520C2×D5—21no—
521C2×D5—21no—
522C2×D5—21no—
523C2×D5—21no—
524C2×D5—61no—
525C2×D5—61no—
526C2×D5—61no—
527C4×C5—21no—
528C4×C5—21no—
529C4×C5—21no—
530C4×C5—61no—
531C4×C5—61no—
532C4×C5—61no—
533C4×C5—61no—
534Dic5—21no—
535Dic5—61no—
536Dic5—61no—
537Dic5—61no—
538Dic5C2×#23711yescharacteristic
539Dic5D3×#4111yescharacteristic
540C2×Q8—151no—
541C2×D4—51no—
542C2×D4—151no—
543C2×D4—151no—
544C22×C4—51no—
545C22×C4—51no—
546C22×C4—151no—
547C22×C4—151no—
548C22×C4—151no—
549M16—102no—
550M16—302no—
551M16—302no—
552M16—302no—
553C2×C8—51no—
554C2×C8—51no—
555C2×C8—51no—
556C2×C8—51no—
557C2×C8—102no—
558C2×C8—151no—
559C2×C8—151no—
560C2×C8—151no—
561C2×C8—151no—
562C2×C8—302no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—151no—
569C4⋊C4—151no—
570C4⋊C4—151no—
571C4⋊C4—151no—
572C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
573C22⋊C4—51no—
574C22⋊C4—51no—
575C22⋊C4—151no—
576C22⋊C4—151no—
577C22⋊C4—151no—
578C22⋊C4—151no—
579C22⋊C4—151no—
580C22⋊C4—151no—
581C22⋊C4—151no—
582C22⋊C4—151no—
583C42—31no—
584C42—51no—
585C42—151no—
586C42—151no—
587C42—151no—
588C42—151no—
589C3×C5#296711yescharacteristic, complemented, Hall
590C22×C3—101no—
591C22×C3—101no—
592C22×C3—101no—
593C22×C3—101no—
594C22×C3—101no—
595C22×C3—101no—
596C22×C3C23×AGL(1,𝔽5)11yescharacteristic
597C2×D3—101no—
598C2×D3—101no—
599C2×D3—101no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—51no—
604C3×C4—51no—
605C3×C4—101no—
606Dic3—21no—
607Dic3—21no—
608Dic3—21no—
609Dic3—21no—
610Dic3—101no—
611Dic3—101no—
612Dic3—101no—
613C2×C5C4×#23711yescharacteristic
614C2×C5#574511yescharacteristic
615C2×C5#575011yescharacteristic
616D5—41no—
617D5—41no—
618D5—121no—
619C23—51no—
620C23—51no—
621C23—151no—
622Q8—601no—
623D4—201no—
624D4—601no—
625D4—601no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—51no—
631C2×C4—51no—
632C2×C4—101no—
633C2×C4—101no—
634C2×C4—101no—
635C2×C4—101no—
636C2×C4—151no—
637C2×C4—151no—
638C2×C4—151no—
639C2×C4—301no—
640C2×C4—301no—
641C2×C4—601no—
642C2×C4—601no—
643C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
644C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
645C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
646C8—52no—
647C8—101no—
648C8—101no—
649C8—101no—
650C8—152no—
651C8—301no—
652C8—301no—
653C8—301no—
654C2×C3—201no—
655C2×C3—201no—
656C2×C3#6626011yescharacteristic
657C2×C3#6626411yescharacteristic
658C2×C3#41×AGL(1,𝔽5)11yescharacteristic
659D3—201no—
660C5#7945511yescharacteristic, complemented, Sylow
661C22—101no—
662C22—101no—
663C22—101no—
664C22—101no—
665C22—101no—
666C22—101no—
667C22—301no—
668C22—301no—
669C22—301no—
670C22C22×D3×AGL(1,𝔽5)11yescharacteristic
671C4—21no—
672C4—21no—
673C4—21no—
674C4—51no—
675C4—51no—
676C4—61no—
677C4—61no—
678C4—61no—
679C4—61no—
680C4—101no—
681C4—301no—
682C4—301no—
683C4—301no—
684C3#1061733311yescharacteristic, complemented, Sylow
685C2—201no—
686C2—201no—
687C2—601no—
688C2#1175682311yescharacteristic
689C2AGL(1,𝔽5)×#23711yescharacteristic
690C2#1175685111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radical#91409C4
cosocleC2×C3×Dic5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2967
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752364C2semidirect
3. C3×#65704C2semidirect
4. #11751911C2semidirect
5. #11751903C2semidirect
6. #11751903C2semidirect
7. #11751874C2semidirect
8. #11751827C2semidirect
9. #11751787C2semidirect
10. #11751781C2semidirect
11. #11751780C2semidirect
12. Dic3×#700C2semidirect
13. #11751769C2semidirect
14. #11751767C2semidirect
15. #11751763C2semidirect
71. #65704D3semidirect
589. C3×C5#2967semidirect
660. C5#79455semidirect
684. C3#10617333semidirect

Maximal subgroups

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

subgroupindex
#117534762
#117523642
C3×#657042
#117519112
#117519032
#117518742
#117518272
#117517872
#117517812
#117517802
Dic3×#7002
#117517692
#117517672
#117517632
#106173333
#794555