Finite Group Databasebeta

← #14328940

Subgroups — #14328940

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91815C211yesmaximal, characteristic
2C2×C3×#4070C211yesmaximal, characteristic
3C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
4C4×C5×#217C211yesmaximal, characteristic
5#11749486C212yesmaximal
6#11749485C212yesmaximal
7#11748857C211yesmaximal, characteristic, complemented
8Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
9#11748637C212yesmaximal, complemented
10#11748609C211yesmaximal, characteristic, complemented
11#11748601C212yesmaximal, complemented
12#10605199—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×#6719C2212yes—
16#91815—24no—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4×Dic15C2212yes—
20C2×C5×#217C2211yescharacteristic
21C2×C5×#217C2211yescharacteristic
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C3×C22⋊Dic5C2212yes—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C3×#4070C418yescomplemented
27C2×C3×#683C2212yes—
28C2×#6668C2212yes—
29C2×#6668C2212yes—
30C2×Dic3×Dic5C2212yes—
31C2×Dic3×Dic5C2212yes—
32Dic3×Dic10—24no—
33C5×C3⋊#95C2211yescharacteristic
34C5×C3⋊#95C2211yescharacteristic
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82748—51nomaximal, Hall
40C2×#4072—31no—
41C2×#4070D311yescharacteristic
42C2×C4×Dic10—31no—
43C4×C5×C22⋊C4—31no—
44#65234—32no—
45#65233—32no—
46C4×C4⋊Dic5—31no—
47#65218—31no—
48#65217—31no—
49#64941—32no—
50#64938—32no—
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5C2×C414yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15C2312yes—
58C22×Dic15C2312yes—
59C22×C5×Dic3C2311yescharacteristic
60C22×C5×Dic3C2311yescharacteristic
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2311yescharacteristic
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2312yes—
65C2×C3×Dic10—22no—
66C2×C3×Dic10—22no—
67C2×C3×Dic10C2×C414yes—
68#6719—24no—
69C4⋊Dic15—22no—
70C4⋊Dic15D414yes—
71C4×Dic15—24no—
72C5×#217—22no—
73C5×#217—22no—
74C4×C5×Dic3—22no—
75C4×C5×Dic3—22no—
76C3×C22⋊Dic5C2×C418yes—
77C3×C4⋊Dic5C2×C414yes—
78C3×#683C2×C418yes—
79#6668—24no—
80#6668—24no—
81Dic3×Dic5—24no—
82Dic3×Dic5—24no—
83C2×C3×C22⋊Q8—51no—
84C2×Q8×Dic3—51no—
85C2×#926—51no—
86#5229—51no—
87C4×#217D511yescharacteristic
88#4984—51no—
89#4980—52no—
90Dic3×C4⋊C4—51no—
91Dic3×C4⋊C4—52no—
92#4951—52no—
93#4951—52no—
94C23×C4×C5C2×D311yescharacteristic
95C22×Dic10C2×D311yescharacteristic
96C2×C5×C22⋊C4—31no—
97C2×C5×C22⋊C4—31no—
98C2×C42×C5—31no—
99C2×C42×C5—31no—
100C2×C22⋊Dic5—32no—
101C2×C22⋊Dic5C2×D312yes—
102#4072—64no—
103C2×C4⋊Dic5—31no—
104C2×C4⋊Dic5—31no—
105C2×C4⋊Dic5C2×D311yescharacteristic
106#4070Dic318yescomplemented
107C2×#683—32no—
108C2×#683—32no—
109C2×#683C2×D312yes—
110C2×C4×Dic5—32no—
111C2×C4×Dic5—32no—
112C2×C4×Dic5—32no—
113C4×Dic10—64no—
114C5×#95—31no—
115C5×#95—31no—
116#3963—32no—
117#3963—32no—
118#3963—32no—
119#3963—32no—
120#2362—151noSylow
121C23×C3×C5—21no—
122C23×C3×C5—21no—
123C23×C3×C5—21no—
124C23×C3×C5—21no—
125C23×C3×C5—21no—
126C23×C3×C5—21no—
127C23×C3×C5C22×C412yes—
128C23×C3×C5C2411yescharacteristic
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—28no—
132C2×C3×C4×C5C22×C412yes—
133C2×C3×C4×C5C22×C412yes—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5#4112yes—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15C2×D414yes—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3#4112yes—
153C2×C5×Dic3#4112yes—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5C22×C414yes—
159C2×C3×Dic5C22×C414yes—
160C3×Dic10—28no—
161C22×C3×Q8—51no—
162C23×C3×C4C2×D511yescharacteristic
163C3×C22⋊Q8—58no—
164C2×C3×C4⋊C4—52no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C22⋊C4—52no—
167C2×#217—52no—
168C2×#217C2×D511yescharacteristic
169C2×#217C2×D511yescharacteristic
170Q8×Dic3—104no—
171#926—104no—
172C2×C4⋊Dic3—51no—
173C2×C4⋊Dic3—51no—
174C2×C4⋊Dic3—52no—
175C2×C4⋊Dic3—52no—
176C2×C4×Dic3—52no—
177C2×C4×Dic3—52no—
178C2×C4×Dic3—52no—
179C2×C4×Dic3C2×D511yescharacteristic
180C2×C4×Dic3C2×D511yescharacteristic
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95—52no—
184C3⋊#95—52no—
185C3⋊#95C2×D511yescharacteristic
186C3⋊#95C2×D511yescharacteristic
187C24×C5C22×D311yescharacteristic
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—31no—
193C22×C4×C5—31no—
194C22×C4×C5C2×Dic314yes—
195C22×C4×C5C22×D311yescharacteristic
196C22×C4×C5C22×D311yescharacteristic
197C22×Dic5—32no—
198C22×Dic5—32no—
199C22×Dic5C22×D312yes—
200C22×Dic5C22×D312yes—
201C2×Dic10—22no—
202C2×Dic10—22no—
203C2×Dic10C2×Dic314yes—
204C5×C22⋊C4—62no—
205C5×C22⋊C4—62no—
206C42×C5—62no—
207C42×C5—62no—
208C22⋊Dic5—64no—
209C22⋊Dic5C2×Dic318yes—
210C4⋊Dic5—34no—
211C4⋊Dic5—62no—
212C4⋊Dic5C2×Dic314yes—
213#683—64no—
214#683—64no—
215#683C2×Dic318yes—
216C4×Dic5—64no—
217C4×Dic5—64no—
218C4×Dic5—64no—
219C2×C22⋊Q8—51no—
220C2×C4×Q8—151no—
221C2×#117—151no—
222#391—151no—
223#389—151no—
224#388—152no—
225#388—152no—
226#387—152no—
227C4×C4⋊C4—152no—
228C4×C4⋊C4—151no—
229C4×C22⋊C4—31no—
230C22×C3×C5—22no—
231C22×C3×C5—22no—
232C22×C3×C5—22no—
233C22×C3×C5—41no—
234C22×C3×C5—41no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C52−1+411yescharacteristic
243C22×C3×C52−1+411yescharacteristic
244C3×C4×C5—22no—
245C3×C4×C5C4×D414yes—
246Dic15—24no—
247Dic15—42no—
248C3×Dic5—24no—
249C3×Dic5—24no—
250C5×Dic3—22no—
251C5×Dic3—22no—
252C5×Dic3—41no—
253C5×Dic3—41no—
254C24×C3C22×D511yescharacteristic
255C2×C3×Q8—54no—
256C2×C3×Q8—102no—
257C2×C3×Q8—102no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—52no—
261C22×C3×C4—52no—
262C22×C3×C4C4×D514yes—
263C22×C3×C4C22×D511yescharacteristic
264C22×C3×C4C22×D511yescharacteristic
265C22×Dic3—52no—
266C22×Dic3—52no—
267C22×Dic3C22×D511yescharacteristic
268C22×Dic3C22×D511yescharacteristic
269C22×Dic3C22×D511yescharacteristic
270C22×Dic3C22×D511yescharacteristic
271C3×C4⋊C4—58no—
272C3×C4⋊C4—54no—
273C3×C22⋊C4—58no—
274#217—22no—
275#217—22no—
276#217—104no—
277C4⋊Dic3—54no—
278C4⋊Dic3—104no—
279C4⋊Dic3—102no—
280C4⋊Dic3—104no—
281C4×Dic3—22no—
282C4×Dic3—22no—
283C4×Dic3—104no—
284C4×Dic3—104no—
285C4×Dic3—104no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5C22×Dic312yes—
293C23×C5C23×D311yescharacteristic
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—28no—
297C2×C4×C5—32no—
298C2×C4×C5—32no—
299C2×C4×C5—61no—
300C2×C4×C5—61no—
301C2×C4×C5—61no—
302C2×C4×C5—61no—
303C2×C4×C5—61no—
304C2×C4×C5—61no—
305C2×C4×C5—61no—
306C2×C4×C5—61no—
307C2×C4×C5—61no—
308C2×C4×C5—61no—
309C2×C4×C5D3×D412yes—
310C2×C4×C5#23712yes—
311C2×C4×C5C22×Dic312yes—
312C2×C4×C5C22×Dic312yes—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—22no—
316C2×Dic5—22no—
317C2×Dic5—34no—
318C2×Dic5—62no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5C22×Dic314yes—
324C2×Dic5C22×Dic314yes—
325Dic10—28no—
326C22×Q8—51no—
327C23×C4D3×D511yescharacteristic
328C22⋊Q8—58no—
329C4×Q8—304no—
330#117—304no—
331C2×C4⋊C4—52no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—151no—
334C2×C4⋊C4—152no—
335C2×C4⋊C4—152no—
336C2×C4⋊C4—151no—
337C2×C22⋊C4—31no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—52no—
340C2×C22⋊C4—152no—
341C2×C42—31no—
342C2×C42—31no—
343C2×C42—152no—
344C2×C42—152no—
345C2×C42—152no—
346#95—31no—
347#95—31no—
348#95—152no—
349#95—152no—
350#95—152no—
351#95—152no—
352C2×C3×C5—42no—
353C2×C3×C5C2×C4×D411yescharacteristic
354C2×C3×C5C4×#4111yescharacteristic
355C2×C3×C5#51911yescharacteristic
356C2×C3×C5#54711yescharacteristic
357C2×C3×C5#54811yescharacteristic
358C2×C3×C5#55211yescharacteristic
359C2×C3×C5#55611yescharacteristic
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3C2×C4×D512yes—
367C23×C3C23×D511yescharacteristic
368C3×Q8—108no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—28no—
372C2×C3×C4—54no—
373C2×C3×C4—54no—
374C2×C3×C4—102no—
375C2×C3×C4—102no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4C2×C4×D512yes—
379C2×C3×C4C2×C4×D512yes—
380C2×C3×C4D4×D512yes—
381C2×C3×C4#71112yes—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—54no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3—102no—
398C2×Dic3#70912yes—
399C2×Dic3#70912yes—
400C22×C5—22no—
401C22×C5—22no—
402C22×C5—22no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5—41no—
407C22×C5C2×D3×D411yescharacteristic
408C22×C5C2×#23711yescharacteristic
409C22×C5#100711yescharacteristic
410C22×C5#100711yescharacteristic
411C22×C5D3×#4111yescharacteristic
412C22×C5D3×#4111yescharacteristic
413C22×C5C23×Dic311yescharacteristic
414C4×C5—22no—
415C4×C5—62no—
416C4×C5—62no—
417C4×C5—121no—
418C4×C5—121no—
419C4×C5D4×Dic314yes—
420Dic5—24no—
421Dic5—24no—
422Dic5—64no—
423Dic5—122no—
424C24C2×D3×D511yescharacteristic
425C2×Q8—54no—
426C2×Q8—102no—
427C2×Q8—102no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—52no—
435C22×C4—52no—
436C22×C4—152no—
437C22×C4—152no—
438C22×C4D5×Dic314yes—
439C22×C4C2×D3×D511yescharacteristic
440C22×C4C2×D3×D511yescharacteristic
441C4⋊C4—58no—
442C4⋊C4—54no—
443C4⋊C4—154no—
444C4⋊C4—304no—
445C4⋊C4—304no—
446C4⋊C4—302no—
447C22⋊C4—58no—
448C22⋊C4—62no—
449C22⋊C4—62no—
450C22⋊C4—304no—
451C42—62no—
452C42—62no—
453C42—304no—
454C42—304no—
455C42—304no—
456C3×C5#236211yescharacteristic, complemented, Hall
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3C22×C4×D511yescharacteristic
465C22×C3C2×#70911yescharacteristic
466C22×C3C2×#70911yescharacteristic
467C22×C3C2×D4×D511yescharacteristic
468C22×C3C2×#71111yescharacteristic
469C22×C3#415011yescharacteristic
470C22×C3#415011yescharacteristic
471C3×C4—22no—
472C3×C4—104no—
473C3×C4—104no—
474C3×C4#402714yes—
475Dic3—22no—
476Dic3—22no—
477Dic3—41no—
478Dic3—41no—
479Dic3—104no—
480Dic3—202no—
481C2×C5—42no—
482C2×C5#563111yescharacteristic
483C2×C5#563311yescharacteristic
484C2×C5#563911yescharacteristic
485C2×C5#564111yescharacteristic
486C2×C5C2×D4×Dic311yescharacteristic
487C2×C5#581211yescharacteristic
488C2×C5Dic3×#4111yescharacteristic
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23C2×D5×Dic312yes—
496C23C22×D3×D511yescharacteristic
497Q8—108no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—28no—
501C2×C4—32no—
502C2×C4—32no—
503C2×C4—54no—
504C2×C4—54no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—102no—
516C2×C4—102no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—154no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4C2×D5×Dic312yes—
526C2×C4C2×D5×Dic312yes—
527C2×C4#678012yes—
528C2×C4#679012yes—
529C2×C3—42no—
530C2×C3C4×#70911yescharacteristic
531C2×C3C2×#402711yescharacteristic
532C2×C3#6585011yescharacteristic
533C2×C3#6587511yescharacteristic
534C2×C3#6587611yescharacteristic
535C2×C3#6588511yescharacteristic
536C2×C3#6588611yescharacteristic
537C5#8274811yescharacteristic, complemented, Sylow
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22#9200411yescharacteristic
546C22#9200411yescharacteristic
547C22D3×#70911yescharacteristic
548C22D3×#70911yescharacteristic
549C22C22×D5×Dic311yescharacteristic
550C22C2×#678011yescharacteristic
551C22C2×#679011yescharacteristic
552C4—22no—
553C4—62no—
554C4—62no—
555C4—104no—
556C4—104no—
557C4—121no—
558C4—121no—
559C4—304no—
560C4—602no—
561C4#9155914yes—
562C3#1060519911yescharacteristic, complemented, Sylow
563C2—42no—
564C2#1175418811yescharacteristic
565C2#1175422311yescharacteristic
566C2#1175423311yescharacteristic
567C2#1175437811yescharacteristic
568C2Dic3×#70911yescharacteristic
569C2#1175443511yescharacteristic
570C2C2×#9155911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#2362
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×Dic10C2semidirect
7. #11748857C2semidirect
8. Dic3×C4⋊Dic5C2semidirect
9. #11748637C2semidirect
10. #11748609C2semidirect
11. #11748601C2semidirect
26. C3×#4070C4semidirect
106. #4070Dic3semidirect
456. C3×C5#2362semidirect
537. C5#82748semidirect
562. C3#10605199semidirect

Maximal subgroups

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

subgroupindex
C2×#918152
C2×C3×#40702
C2×Dic3×Dic102
C4×C5×#2172
#117494862
#117494852
#117488572
Dic3×C4⋊Dic52
#117486372
#117486092
#117486012
#106051993
#827485