Finite Group Databasebeta

← #14327724

Subgroups — #14327724

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#893C211yesmaximal, characteristic
2C2×#91371C212yesmaximal, complemented
3C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
4C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
5#11748861C211yesmaximal, characteristic, complemented
6C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
7#11748797C211yesmaximal, characteristic
8#11748794C212yesmaximal, complemented
9#11748782C212yesmaximal, complemented
10#11748764C211yesmaximal, characteristic
11#11748747C212yesmaximal, complemented
12#10614068—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×C4×C5×D3C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15C2212yes—
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4C2212yes—
20C2×C4×C5×Dic3C2211yescharacteristic
21C5×#893C418yescomplemented
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×C4×Dic5C2212yes—
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×Dic3⋊Dic5C2212yes—
26C2×Dic3⋊Dic5C2211yescharacteristic
27C2×Dic3⋊Dic5C2212yes—
28C2×Dic3⋊Dic5C2211yescharacteristic
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×(C2×D3)⋊Dic5C2212yes—
31C2×(C2×D3)⋊Dic5C2212yes—
32C2×(C2×D3)⋊Dic5C2212yes—
33#91371—28no—
34#91115C2212yes—
35C3×#3963C2212yes—
36#90994C2211yescharacteristic
37#90994C2211yescharacteristic
38#73639—51nomaximal, Hall
39C2×C4×C5×D4—31no—
40C2×#4072—32no—
41#65510—31no—
42#65510—31no—
43#65501—32no—
44C4⋊C4×Dic5—31no—
45C4⋊C4×Dic5D311yescharacteristic, complemented
46#65240—32no—
47#65240—32no—
48#65224—31no—
49C4×C4⋊Dic5—31no—
50C23×C5×D3C2312yes—
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2311yescharacteristic
56C22×C5×Dic3C2311yescharacteristic
57C22×C5×Dic3C2311yescharacteristic
58C2×C5×D12—22no—
59C2×C5×D12—22no—
60C2×C5×D12C2×C414yes—
61C2×C4×C5×D3—24no—
62C2×C4×C5×D3—24no—
63C2×C4×C5×D3C2×C418yes—
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2312yes—
66C22×C3×Dic5C2311yescharacteristic
67C3×C5×C4⋊C4C2×C414yes—
68C4⋊Dic15—22no—
69C4×Dic15—22no—
70C4×Dic15—24no—
71C5×(C2×D3)⋊C4C2×C418yes—
72C4×C5×Dic3C2×C414yes—
73C3×C4⋊Dic5—22no—
74C3×C4×Dic5—22no—
75C3×C4×Dic5—24no—
76Dic3⋊Dic5—24no—
77Dic3⋊Dic5—22no—
78Dic3⋊Dic5—42no—
79Dic3⋊Dic5D414yescomplemented
80(C2×D3)⋊Dic5—24no—
81(C2×D3)⋊Dic5—24no—
82(C2×D3)⋊Dic5—42no—
83(C2×D3)⋊Dic5—42no—
84C2×#893D511yescharacteristic
85C2×#872—52no—
86C3×C4×C4⋊C4—51no—
87#4988—51no—
88#4975—51no—
89Dic3×C4⋊C4—51no—
90#4940—52no—
91#4939—51no—
92C4×Dic3⋊C4—51no—
93#4669—52no—
94#4667—52no—
95C22×C5×D4—31no—
96C23×C4×C5—32no—
97C4×C5×D4—38no—
98C2×C5×C4⋊C4C2×D311yescharacteristic
99C2×C5×C22⋊C4—32no—
100C2×C42×C5—31no—
101C2×C22⋊Dic5—32no—
102C2×C22⋊Dic5—32no—
103C2×C22⋊Dic5—32no—
104C2×C22⋊Dic5—32no—
105#4072—68no—
106C2×C4⋊Dic5—31no—
107C2×C4⋊Dic5—31no—
108C2×C4⋊Dic5—32no—
109C2×C4⋊Dic5—31no—
110C2×C4⋊Dic5—32no—
111C2×C4⋊Dic5C2×D311yescharacteristic
112C2×C4×Dic5—32no—
113C2×C4×Dic5—31no—
114C2×C4×Dic5C2×D312yes—
115C2×C4×Dic5C2×D311yescharacteristic
116#3963—32no—
117#3963—31no—
118#3963—31no—
119#3963C2×D312yes—
120#2354—151noSylow
121C23×C3×C5C2411yescharacteristic
122C22×C5×D3—22no—
123C22×C5×D3—22no—
124C22×C5×D3—22no—
125C22×C5×D3—22no—
126C22×C5×D3—22no—
127C22×C5×D3—22no—
128C22×C5×D3C22×C414yes—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C22×C414yes—
132C2×C3×C4×C5C22×C412yes—
133C2×C3×C4×C5#4112yes—
134C2×C3×C4×C5#4112yes—
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15—22no—
138C2×Dic15—21no—
139C2×Dic15—21no—
140C2×Dic15—22no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143C2×Dic15C2×D412yes—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3C22×C412yes—
147C2×C5×Dic3C22×C412yes—
148C2×C5×Dic3C2×D412yes—
149C2×C5×Dic3#4112yes—
150C5×D12—28no—
151C4×C5×D3—216no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C2×D412yes—
161C22×D12C2×D511yescharacteristic
162C22×C4×D3C2×D512yes—
163C2×C3×C4⋊C4—51no—
164C2×C3×C4⋊C4C2×D511yescharacteristic
165C2×C3×C42—51no—
166C2×C3×C42—52no—
167C2×(C2×D3)⋊C4—52no—
168C2×(C2×D3)⋊C4—52no—
169C2×(C2×D3)⋊C4—52no—
170C2×(C2×D3)⋊C4—52no—
171C2×(C2×D3)⋊C4C2×D512yes—
172C2×C4⋊Dic3—51no—
173C2×Dic3⋊C4—51no—
174C2×Dic3⋊C4—51no—
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4—52no—
177C2×C4×Dic3—52no—
178C2×C4×Dic3—51no—
179C2×C4×Dic3C2×D511yescharacteristic
180#893Dic518yescomplemented
181#872—108no—
182C3×#95—52no—
183C3⋊#95—52no—
184C3⋊#95—51no—
185C3⋊#95—51no—
186C24×C5—32no—
187C2×C5×D4—34no—
188C2×C5×D4—62no—
189C2×C5×D4—62no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—38no—
193C22×C4×C5—64no—
194C22×C4×C5—64no—
195C22×C4×C5C22×D312yes—
196C22×C4×C5C22×D311yescharacteristic
197C22×Dic5—31no—
198C22×Dic5—31no—
199C22×Dic5—32no—
200C22×Dic5C22×D311yescharacteristic
201C22×Dic5C22×D312yes—
202C22×Dic5C22×D311yescharacteristic
203C5×C4⋊C4C4×D314yes—
204C5×C22⋊C4—38no—
205C42×C5—34no—
206C22⋊Dic5—64no—
207C22⋊Dic5—64no—
208C22⋊Dic5—122no—
209C22⋊Dic5—122no—
210C4⋊Dic5—22no—
211C4⋊Dic5—34no—
212C4⋊Dic5—62no—
213C4⋊Dic5—64no—
214C4⋊Dic5—62no—
215C4⋊Dic5—122no—
216C4×Dic5—22no—
217C4×Dic5—24no—
218C4×Dic5—64no—
219C4×Dic5—62no—
220C2×C4×D4—31no—
221C2×#117—152no—
222#390—151no—
223#390—151no—
224#388—152no—
225#388—152no—
226#384—151no—
227#380—152no—
228C4×C4⋊C4—51no—
229C4×C4⋊C4—151no—
230C4×C4⋊C4—151no—
231C22×C3×C5C23×C411yescharacteristic
232C22×C3×C5C22×D411yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C22×C3×C5C2×#4111yescharacteristic
236C22×C3×C5H(5,𝔽2)11yescharacteristic
237C22×C3×C52−1+411yescharacteristic
238C2×C5×D3—24no—
239C2×C5×D3—24no—
240C2×C5×D3—24no—
241C2×C5×D3—42no—
242C2×C5×D3—42no—
243C2×C5×D3—42no—
244C2×C5×D3—42no—
245C3×C4×C5—24no—
246C3×C4×C5#11714yescomplemented
247Dic15—22no—
248Dic15—42no—
249Dic15—41no—
250C3×Dic5—22no—
251C3×Dic5—42no—
252C3×Dic5—41no—
253C5×Dic3—22no—
254C5×Dic3C4×D414yes—
255C23×D3C22×D512yes—
256C22×C3×C4—51no—
257C22×C3×C4—51no—
258C22×C3×C4—52no—
259C22×C3×C4C22×D512yes—
260C22×C3×C4C22×D511yescharacteristic
261C22×Dic3—51no—
262C22×Dic3—51no—
263C22×Dic3—52no—
264C22×Dic3C22×D511yescharacteristic
265C22×Dic3C22×D511yescharacteristic
266C2×D12—22no—
267C2×D12—22no—
268C2×D12C2×Dic514yes—
269C2×C4×D3—24no—
270C2×C4×D3—24no—
271C2×C4×D3C2×Dic518yes—
272C3×C4⋊C4—102no—
273C3×C4⋊C4C2×Dic514yes—
274C3×C42—104no—
275C3×C42—102no—
276(C2×D3)⋊C4—104no—
277(C2×D3)⋊C4—104no—
278(C2×D3)⋊C4—202no—
279(C2×D3)⋊C4—202no—
280(C2×D3)⋊C4C2×Dic518yes—
281C4⋊Dic3—102no—
282Dic3⋊C4—54no—
283Dic3⋊C4—104no—
284Dic3⋊C4—102no—
285Dic3⋊C4—202no—
286C4×Dic3—104no—
287C4×Dic3—102no—
288C4×Dic3C2×Dic514yes—
289C23×C5—34no—
290C23×C5—62no—
291C23×C5—62no—
292C23×C5—62no—
293C23×C5—62no—
294C23×C5—62no—
295C23×C5—62no—
296C23×C5C23×D311yescharacteristic
297C5×D4—68no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5—32no—
301C2×C4×C5—32no—
302C2×C4×C5—32no—
303C2×C4×C5—32no—
304C2×C4×C5—616no—
305C2×C4×C5—61no—
306C2×C4×C5—61no—
307C2×C4×C5C2×C4×D314yes—
308C2×C4×C5C2×C4×D312yes—
309C2×C4×C5#23512yes—
310C2×C4×C5#23512yes—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—22no—
315C2×Dic5—22no—
316C2×Dic5—21no—
317C2×Dic5—22no—
318C2×Dic5—21no—
319C2×Dic5—32no—
320C2×Dic5—61no—
321C2×Dic5—61no—
322C2×Dic5—61no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—61no—
326C2×Dic5—62no—
327C2×Dic5—61no—
328C2×Dic5D3×D412yes—
329C22×D4—31no—
330C23×C4—32no—
331C4×D4—38no—
332#117—308no—
333C2×C4⋊C4—51no—
334C2×C4⋊C4—151no—
335C2×C4⋊C4—152no—
336C2×C4⋊C4—151no—
337C2×C4⋊C4—151no—
338C2×C4⋊C4—152no—
339C2×C4⋊C4D3×D511yescharacteristic
340C2×C22⋊C4—32no—
341C2×C22⋊C4—152no—
342C2×C22⋊C4—152no—
343C2×C22⋊C4—152no—
344C2×C22⋊C4—152no—
345C2×C42—31no—
346C2×C42—52no—
347C2×C42—51no—
348C2×C42—152no—
349C2×C42—151no—
350#95—52no—
351#95—151no—
352#95—151no—
353#95—152no—
354C2×C3×C5C2×#11711yescharacteristic
355C2×C3×C5C2×C4×D411yescharacteristic
356C2×C3×C5#52011yescharacteristic
357C2×C3×C5#54711yescharacteristic
358C2×C3×C5#55011yescharacteristic
359C2×C3×C5#55511yescharacteristic
360C2×C3×C5#55611yescharacteristic
361C5×D3—44no—
362C23×C3C23×D511yescharacteristic
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3C22×Dic514yes—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—52no—
373C2×C3×C4—101no—
374C2×C3×C4—101no—
375C2×C3×C4—101no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—101no—
379C2×C3×C4—102no—
380C2×C3×C4—101no—
381C2×C3×C4#70912yes—
382C2×C3×C4#70912yes—
383C2×C3×C4C22×Dic514yes—
384C2×C3×C4C22×Dic512yes—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—52no—
388C2×Dic3—101no—
389C2×Dic3—101no—
390C2×Dic3—101no—
391C2×Dic3—102no—
392C2×Dic3—102no—
393C2×Dic3—101no—
394C2×Dic3—102no—
395C2×Dic3—101no—
396C2×Dic3D4×D512yes—
397C2×Dic3#71112yes—
398C2×Dic3C22×Dic512yes—
399C2×Dic3C22×Dic512yes—
400D12—28no—
401C4×D3—216no—
402C22×C5—64no—
403C22×C5—64no—
404C22×C5—64no—
405C22×C5—122no—
406C22×C5—122no—
407C22×C5—122no—
408C22×C5—122no—
409C22×C5C22×C4×D311yescharacteristic
410C22×C5C2×#23511yescharacteristic
411C22×C5C2×#23511yescharacteristic
412C22×C5C2×D3×D411yescharacteristic
413C22×C5#100711yescharacteristic
414C22×C5D3×#4111yescharacteristic
415C22×C5#100911yescharacteristic
416C4×C5—24no—
417C4×C5—34no—
418C4×C5—62no—
419C4×C5#87214yescomplemented
420Dic5—22no—
421Dic5—41no—
422Dic5—42no—
423Dic5—62no—
424Dic5—121no—
425Dic5—122no—
426C24—32no—
427C2×D4—34no—
428C2×D4—62no—
429C2×D4—62no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—38no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—52no—
436C22×C4—64no—
437C22×C4—64no—
438C22×C4—151no—
439C22×C4—151no—
440C22×C4—152no—
441C22×C4C2×D3×D512yes—
442C22×C4C2×D3×D511yescharacteristic
443C4⋊C4—102no—
444C4⋊C4—154no—
445C4⋊C4—304no—
446C4⋊C4—302no—
447C4⋊C4—302no—
448C4⋊C4—602no—
449C4⋊C4D3×Dic514yes—
450C22⋊C4—38no—
451C22⋊C4—304no—
452C22⋊C4—304no—
453C22⋊C4—602no—
454C22⋊C4—602no—
455C42—34no—
456C42—104no—
457C42—102no—
458C42—304no—
459C42—302no—
460C3×C5#235411yescharacteristic, complemented, Hall
461C22×C3C2×#70911yescharacteristic
462C22×C3C2×#70911yescharacteristic
463C22×C3C2×D4×D511yescharacteristic
464C22×C3C2×#71111yescharacteristic
465C22×C3#414911yescharacteristic
466C22×C3#415011yescharacteristic
467C22×C3C23×Dic511yescharacteristic
468C2×D3—24no—
469C2×D3—24no—
470C2×D3—24no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C3×C4—24no—
476C3×C4—102no—
477C3×C4—202no—
478C3×C4—201no—
479C3×C4#407214yescomplemented
480Dic3—22no—
481Dic3—102no—
482Dic3—202no—
483Dic3—201no—
484Dic3D4×Dic514yes—
485C2×C5—124no—
486C2×C5C2×#87211yescharacteristic
487C2×C5#550711yescharacteristic
488C2×C5#553211yescharacteristic
489C2×C5C4×D3×D411yescharacteristic
490C2×C5#555311yescharacteristic
491C2×C5#556811yescharacteristic
492C2×C5#557411yescharacteristic
493C23—34no—
494C23—62no—
495C23—62no—
496C23—62no—
497C23—62no—
498C23—62no—
499C23—62no—
500C23C22×D3×D511yescharacteristic
501D4—68no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—32no—
505C2×C4—32no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—52no—
509C2×C4—616no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—101no—
513C2×C4—101no—
514C2×C4—101no—
515C2×C4—102no—
516C2×C4—102no—
517C2×C4—101no—
518C2×C4—101no—
519C2×C4—102no—
520C2×C4—152no—
521C2×C4—301no—
522C2×C4—301no—
523C2×C4—301no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—301no—
527C2×C4—301no—
528C2×C4—302no—
529C2×C4#677112yes—
530C2×C4#677112yes—
531C2×C4C2×D3×Dic514yes—
532C2×C4C2×D3×Dic512yes—
533C2×C3#6587611yescharacteristic
534C2×C3#6588511yescharacteristic
535C2×C3#6588711yescharacteristic
536C2×C3#6589711yescharacteristic
537C2×C3C2×#407211yescharacteristic
538C2×C3C2×D4×Dic511yescharacteristic
539C2×C3#6616111yescharacteristic
540D3—44no—
541C5#7363911yescharacteristic, complemented, Sylow
542C22—64no—
543C22—64no—
544C22—64no—
545C22—122no—
546C22—122no—
547C22—122no—
548C22—122no—
549C22C2×#677111yescharacteristic
550C22C2×#677111yescharacteristic
551C22D3×D4×D511yescharacteristic
552C22D3×#71111yescharacteristic
553C22#9203011yescharacteristic
554C22#9203511yescharacteristic
555C22C22×D3×Dic511yescharacteristic
556C4—24no—
557C4—34no—
558C4—62no—
559C4—102no—
560C4—201no—
561C4—202no—
562C4—302no—
563C4—601no—
564C4—602no—
565C4#9137114yescomplemented
566C3#1061406811yescharacteristic, complemented, Sylow
567C2—124no—
568C2#1175335711yescharacteristic
569C2#1175367711yescharacteristic
570C2#1175368711yescharacteristic
571C2#1175376711yescharacteristic
572C2C2×#9137111yescharacteristic
573C2D3×D4×Dic511yescharacteristic
574C2#1175522011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×D12C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2354
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91371C2semidirect
3. C4⋊C4×Dic15C2semidirect
4. C3×C4⋊C4×Dic5C2semidirect
5. #11748861C2semidirect
6. C4×Dic3⋊Dic5C2semidirect
8. #11748794C2semidirect
9. #11748782C2semidirect
11. #11748747C2semidirect
21. C5×#893C4semidirect
45. C4⋊C4×Dic5D3semidirect
79. Dic3⋊Dic5D4semidirect
180. #893Dic5semidirect
246. C3×C4×C5#117semidirect
419. C4×C5#872semidirect
460. C3×C5#2354semidirect
479. C3×C4#4072semidirect
541. C5#73639semidirect
565. C4#91371semidirect
566. C3#10614068semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8932
C2×#913712
C4⋊C4×Dic152
C3×C4⋊C4×Dic52
#117488612
C4×Dic3⋊Dic52
#117487972
#117487942
#117487822
#117487642
#117487472
#106140683
#736395