Finite Group Databasebeta

← #14327692

Subgroups — #14327692

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#872C211yesmaximal, characteristic, complemented
2C2×#91446C211yesmaximal, characteristic
3C2×#91402C211yesmaximal, characteristic, complemented
4#11751041C211yesmaximal, characteristic, complemented
5C3×C4×#683C211yesmaximal, characteristic, complemented
6#11748909C211yesmaximal, characteristic
7#11748908C211yesmaximal, characteristic
8#11748882C211yesmaximal, characteristic, complemented
9#11748854C211yesmaximal, characteristic, complemented
10#11748782C211yesmaximal, characteristic, complemented
11#11748720C211yesmaximal, characteristic, complemented
12#11748714C211yesmaximal, characteristic, complemented
13#11748641C211yesmaximal, characteristic, complemented
14Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
15Dic3×#683C211yesmaximal, characteristic, complemented
16#10613972—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×#1203C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic
29C2×C4×C5×Dic3C2211yescharacteristic
30C5×#872—24no—
31C2×C3×#683C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47#91446C418yescomplemented
48#91402—24no—
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#73639—51nomaximal, Hall
56C2×C5×#117—31no—
57C2×C4×C22⋊D5—31no—
58C2×#4038—31no—
59#65501—31no—
60#65276—31no—
61#65265—31no—
62C4⋊C4×Dic5—31no—
63#65246—31no—
64#65246—31no—
65#65233—31no—
66#65233—31no—
67#65229—31no—
68#65229—31no—
69C4×#683—31no—
70C4×#683D311yescharacteristic, complemented
71C23×D15C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C2×C4×C5×D3—22no—
83C2×C4×C5×D3—22no—
84C2×C4×C5×D3C2×C414yes—
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×#1203—22no—
90C2×#1203—22no—
91C2×#1203C2×C414yes—
92C2×#1200—22no—
93C2×#1200—22no—
94C2×#1200C2×C414yes—
95C3×C42×C5—22no—
96#6714—22no—
97#6714—41no—
98#6714C2×C414yes—
99#6712—41no—
100C5×(C2×D3)⋊C4—22no—
101C5×(C2×D3)⋊C4—22no—
102C5×Dic3⋊C4—22no—
103C5×Dic3⋊C4D414yescomplemented
104C4×C5×Dic3—22no—
105C3×#683—22no—
106C3×#683C2×C414yes—
107C3×C4×Dic5—22no—
108C3×C4×Dic5—22no—
109Dic3⋊Dic5—22no—
110Dic3⋊Dic5—22no—
111#6669—41no—
112#6668—22no—
113#6667—22no—
114#6667—41no—
115(C2×D3)⋊Dic5—41no—
116(C2×D3)⋊Dic5—41no—
117(C2×D3)⋊Dic5C2×C414yes—
118Dic3×Dic5—22no—
119Dic3×Dic5—22no—
120Dic3×Dic5C2×C414yes—
121C2×#893—51no—
122C2×#872—51no—
123C2×#872D511yescharacteristic, complemented
124C3×C4×C4⋊C4—51no—
125#4988—51no—
126#4975—51no—
127Dic3×C4⋊C4—51no—
128#4940—51no—
129#4940—51no—
130#4939—51no—
131C4×Dic3⋊C4—51no—
132#4669—51no—
133#4669—51no—
134#4667—51no—
135#4667—51no—
136C23×C4×C5—31no—
137C22×C22⋊D5—31no—
138C22×C4×D5—31no—
139C5×#117—64no—
140C2×C5×C4⋊C4—31no—
141C2×C5×C4⋊C4—31no—
142C2×C5×C22⋊C4—31no—
143C2×C5×C22⋊C4—31no—
144C2×C42×C5—31no—
145C2×C42×C5C2×D311yescharacteristic
146C2×C22⋊Dic5—31no—
147C2×C22⋊Dic5—31no—
148C2×C22⋊Dic5—31no—
149C4×C22⋊D5—38no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#685—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×C4⋊Dic5—31no—
156C2×C4⋊Dic5—31no—
157C2×#683—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×#683C2×D311yescharacteristic
161C2×#683C2×D311yescharacteristic
162C2×C4×Dic5—31no—
163C2×C4×Dic5—31no—
164C2×C4×Dic5—31no—
165C2×C4×Dic5C2×D311yescharacteristic
166C2×C4×Dic5C2×D311yescharacteristic
167#4038—64no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963C2×D311yescharacteristic
173#3963C2×D311yescharacteristic
174#2354—151noSylow
175C23×C3×C5C2411yescharacteristic
176C22×D15—21no—
177C22×D15—21no—
178C22×D15—21no—
179C22×D15—21no—
180C22×D15—21no—
181C22×D15—21no—
182C22×D15C22×C412yes—
183C22×C5×D3—21no—
184C22×C5×D3—21no—
185C22×C5×D3—21no—
186C22×C5×D3—21no—
187C22×C5×D3—21no—
188C22×C5×D3—21no—
189C22×C5×D3C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C22×C412yes—
198C2×C3×C4×C5C2×D412yes—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15C22×C412yes—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3C22×C412yes—
214C2×C5×Dic3C2×D412yes—
215C2×C5×Dic3C2×D412yes—
216C2×C5×Dic3#4112yes—
217C4×C5×D3—28no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5C22×C412yes—
227C2×C3×Dic5C22×C412yes—
228C2×C3×Dic5#4112yes—
229C2×C3×Dic5#4112yes—
230#1203—28no—
231#1200—28no—
232C22×D12—51no—
233C22×C4×D3—51no—
234C22×C4×D3C2×D511yescharacteristic
235C2×C3×C4⋊C4—51no—
236C2×C3×C4⋊C4—51no—
237C2×C3×C42—51no—
238C2×C3×C42—51no—
239C2×C3×C42C2×D511yescharacteristic
240C2×(C2×D3)⋊C4—51no—
241C2×(C2×D3)⋊C4—51no—
242C2×(C2×D3)⋊C4—51no—
243C2×(C2×D3)⋊C4—51no—
244C2×(C2×D3)⋊C4—51no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4C2×D511yescharacteristic
249C2×(C2×D3)⋊C4C2×D511yescharacteristic
250C2×C4⋊Dic3—51no—
251C2×Dic3⋊C4—51no—
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4—51no—
254C2×Dic3⋊C4—51no—
255C2×Dic3⋊C4C2×D511yescharacteristic
256C2×Dic3⋊C4C2×D511yescharacteristic
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260C2×C4×Dic3C2×D511yescharacteristic
261#893—58no—
262#872—24no—
263#872—104no—
264C3×#95—51no—
265C3×#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C24×C5—31no—
271C23×D5—31no—
272C22×C4×C5—31no—
273C22×C4×C5—31no—
274C22×C4×C5—34no—
275C22×C4×C5—31no—
276C22×C4×C5—62no—
277C22×C4×C5—62no—
278C22×C4×C5C22×D311yescharacteristic
279C22×C4×C5C22×D311yescharacteristic
280C22×C4×C5C22×D311yescharacteristic
281C2×C22⋊D5—34no—
282C2×C22⋊D5—62no—
283C2×C22⋊D5—62no—
284C22×Dic5—31no—
285C22×Dic5—31no—
286C22×Dic5—31no—
287C22×Dic5C22×D311yescharacteristic
288C22×Dic5C22×D311yescharacteristic
289C22×Dic5C22×D311yescharacteristic
290C22×Dic5C22×D311yescharacteristic
291C2×C4×D5—34no—
292C2×C4×D5—62no—
293C2×C4×D5—62no—
294C5×C4⋊C4—34no—
295C5×C4⋊C4—62no—
296C5×C22⋊C4—62no—
297C5×C22⋊C4—62no—
298C42×C5—22no—
299C42×C5—62no—
300C22⋊Dic5—34no—
301C22⋊Dic5—121no—
302C22⋊Dic5—121no—
303#685—34no—
304#685—62no—
305#685—62no—
306#685—121no—
307#685—121no—
308C4⋊Dic5—62no—
309C4⋊Dic5—62no—
310#683—22no—
311#683—62no—
312#683—121no—
313#683—121no—
314#683C4×D314yes—
315C4×Dic5—22no—
316C4×Dic5—22no—
317C4×Dic5—34no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C2×C4×D4—151no—
321C2×#117—31no—
322C2×#117—151no—
323#390—151no—
324#390—151no—
325#388—151no—
326#388—151no—
327#388—151no—
328#388—151no—
329#384—151no—
330#380—151no—
331#380—151no—
332C4×C4⋊C4—51no—
333C4×C4⋊C4—151no—
334C4×C4⋊C4—151no—
335C22×C3×C5C23×C411yescharacteristic
336C22×C3×C5C22×D411yescharacteristic
337C22×C3×C5C2×#4111yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5H(5,𝔽2)11yescharacteristic
341C22×C3×C52−1+411yescharacteristic
342C2×D15—22no—
343C2×D15—22no—
344C2×D15—22no—
345C2×D15—41no—
346C2×D15—41no—
347C2×D15—41no—
348C2×D15—41no—
349C2×C5×D3—22no—
350C2×C5×D3—22no—
351C2×C5×D3—22no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C5×D3—41no—
355C2×C5×D3—41no—
356C3×C4×C5—22no—
357C3×C4×C5—22no—
358C3×C4×C5—41no—
359Dic15—22no—
360Dic15—41no—
361Dic15—41no—
362C3×Dic5—22no—
363C3×Dic5—41no—
364C3×Dic5—41no—
365C3×Dic5#11714yescomplemented
366C5×Dic3—22no—
367C5×Dic3—41no—
368C5×Dic3C4×D414yes—
369C23×D3—51no—
370C23×D3C22×D511yescharacteristic
371C22×C3×C4—51no—
372C22×C3×C4—51no—
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4C22×D511yescharacteristic
376C22×C3×C4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C22×Dic3—51no—
379C22×Dic3—51no—
380C22×Dic3—51no—
381C22×Dic3C22×D511yescharacteristic
382C22×Dic3C22×D511yescharacteristic
383C22×Dic3C22×D511yescharacteristic
384C2×D12—54no—
385C2×D12—102no—
386C2×D12—102no—
387C2×C4×D3—22no—
388C2×C4×D3—22no—
389C2×C4×D3—54no—
390C2×C4×D3—102no—
391C2×C4×D3—102no—
392C2×C4×D3C4×D514yes—
393C3×C4⋊C4—54no—
394C3×C4⋊C4—102no—
395C3×C42—22no—
396C3×C42—102no—
397C3×C42—102no—
398(C2×D3)⋊C4—22no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—54no—
401(C2×D3)⋊C4—54no—
402(C2×D3)⋊C4—102no—
403(C2×D3)⋊C4—102no—
404(C2×D3)⋊C4—201no—
405(C2×D3)⋊C4—201no—
406(C2×D3)⋊C4—201no—
407(C2×D3)⋊C4—201no—
408C4⋊Dic3—102no—
409Dic3⋊C4—22no—
410Dic3⋊C4—102no—
411Dic3⋊C4—102no—
412Dic3⋊C4—201no—
413Dic3⋊C4—201no—
414Dic3⋊C4C22⋊D514yescomplemented
415C4×Dic3—22no—
416C4×Dic3—54no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C23×C5—32no—
420C23×C5—61no—
421C23×C5—61no—
422C23×C5—61no—
423C23×C5—61no—
424C23×C5—61no—
425C23×C5—61no—
426C23×C5C23×D311yescharacteristic
427C22×D5—32no—
428C22×D5—61no—
429C22×D5—61no—
430C22×D5—61no—
431C22×D5—61no—
432C22×D5—61no—
433C22×D5—61no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—32no—
442C2×C4×C5—32no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
445C2×C4×C5—68no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5C2×C4×D312yes—
452C2×C4×C5D3×D412yes—
453C22⋊D5—68no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—32no—
463C2×Dic5—61no—
464C2×Dic5—61no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5C2×C4×D312yes—
472C2×Dic5C2×C4×D312yes—
473C2×Dic5#23512yes—
474C2×Dic5#23512yes—
475C4×D5—68no—
476C22×D4—151no—
477C23×C4—31no—
478C23×C4—151no—
479C4×D4—158no—
480#117—64no—
481#117—304no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—151no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—151no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—151no—
494C2×C22⋊C4—151no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4—151no—
499C2×C22⋊C4—151no—
500C2×C22⋊C4—151no—
501C2×C42—31no—
502C2×C42—51no—
503C2×C42—51no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42D3×D511yescharacteristic
508#95—51no—
509#95—51no—
510#95—151no—
511#95—151no—
512#95—151no—
513#95—151no—
514C2×C3×C5C2×#11711yescharacteristic
515C2×C3×C5C2×C4×D411yescharacteristic
516C2×C3×C5#52011yescharacteristic
517C2×C3×C5#54711yescharacteristic
518C2×C3×C5#55011yescharacteristic
519C2×C3×C5#55511yescharacteristic
520C2×C3×C5#55611yescharacteristic
521D15—42no—
522C5×D3—42no—
523C23×C3C23×D511yescharacteristic
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—52no—
531C22×D3—101no—
532C22×D3—101no—
533C22×D3—101no—
534C22×D3—101no—
535C22×D3—101no—
536C22×D3—101no—
537C22×D3C2×C4×D512yes—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—52no—
546C2×C3×C4—52no—
547C2×C3×C4—52no—
548C2×C3×C4—52no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4C2×C4×D512yes—
558C2×C3×C4C2×C22⋊D512yes—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—52no—
565C2×Dic3—101no—
566C2×Dic3—101no—
567C2×Dic3—101no—
568C2×Dic3—101no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3C2×C4×D512yes—
574C2×Dic3#70912yes—
575C2×Dic3C2×C22⋊D512yes—
576C2×Dic3C2×C22⋊D512yes—
577D12—108no—
578C4×D3—28no—
579C4×D3—108no—
580C22×C5—62no—
581C22×C5—62no—
582C22×C5—62no—
583C22×C5—121no—
584C22×C5—121no—
585C22×C5—121no—
586C22×C5—121no—
587C22×C5C22×C4×D311yescharacteristic
588C22×C5C2×#23511yescharacteristic
589C22×C5C2×#23511yescharacteristic
590C22×C5C2×D3×D411yescharacteristic
591C22×C5#100711yescharacteristic
592C22×C5D3×#4111yescharacteristic
593C22×C5#100911yescharacteristic
594C2×D5—62no—
595C2×D5—62no—
596C2×D5—62no—
597C2×D5—121no—
598C2×D5—121no—
599C2×D5—121no—
600C2×D5—121no—
601C4×C5—22no—
602C4×C5—22no—
603C4×C5—34no—
604C4×C5—41no—
605C4×C5—62no—
606C4×C5—121no—
607Dic5—22no—
608Dic5—41no—
609Dic5—41no—
610Dic5—62no—
611Dic5—121no—
612Dic5—121no—
613Dic5#87214yescomplemented
614C24—31no—
615C24—151no—
616C2×D4—154no—
617C2×D4—302no—
618C2×D4—302no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—34no—
622C22×C4—31no—
623C22×C4—51no—
624C22×C4—51no—
625C22×C4—51no—
626C22×C4—51no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—154no—
630C22×C4—151no—
631C22×C4—151no—
632C22×C4—151no—
633C22×C4—302no—
634C22×C4—302no—
635C22×C4C2×D3×D511yescharacteristic
636C22×C4C2×D3×D511yescharacteristic
637C22×C4C2×D3×D511yescharacteristic
638C4⋊C4—34no—
639C4⋊C4—54no—
640C4⋊C4—62no—
641C4⋊C4—102no—
642C4⋊C4—302no—
643C4⋊C4—302no—
644C4⋊C4—302no—
645C4⋊C4—601no—
646C4⋊C4—601no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—154no—
650C22⋊C4—154no—
651C22⋊C4—302no—
652C22⋊C4—302no—
653C22⋊C4—601no—
654C22⋊C4—601no—
655C22⋊C4—601no—
656C22⋊C4—601no—
657C42—22no—
658C42—62no—
659C42—102no—
660C42—102no—
661C42—154no—
662C42—302no—
663C42—302no—
664C3×C5#235411yescharacteristic, complemented, Hall
665C22×C3C22×C4×D511yescharacteristic
666C22×C3C2×#70911yescharacteristic
667C22×C3D5×#4111yescharacteristic
668C22×C3D5×#4111yescharacteristic
669C22×C3#414911yescharacteristic
670C22×C3#415011yescharacteristic
671C22×C3C22×C22⋊D511yescharacteristic
672C2×D3—22no—
673C2×D3—22no—
674C2×D3—22no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—102no—
680C2×D3—102no—
681C2×D3—102no—
682C2×D3—201no—
683C2×D3—201no—
684C2×D3—201no—
685C2×D3—201no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—41no—
689C3×C4—54no—
690C3×C4—102no—
691C3×C4—201no—
692C3×C4—201no—
693Dic3—22no—
694Dic3—41no—
695Dic3—102no—
696Dic3—201no—
697Dic3—201no—
698Dic3C4×C22⋊D514yes—
699C2×C5—122no—
700C2×C5C2×#87211yescharacteristic
701C2×C5#550711yescharacteristic
702C2×C5#553211yescharacteristic
703C2×C5C4×D3×D411yescharacteristic
704C2×C5#555311yescharacteristic
705C2×C5#556811yescharacteristic
706C2×C5#557411yescharacteristic
707D5—122no—
708C23—32no—
709C23—61no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23—152no—
716C23—301no—
717C23—301no—
718C23—301no—
719C23—301no—
720C23—301no—
721C23—301no—
722C23C22×D3×D511yescharacteristic
723D4—308no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—52no—
736C2×C4—52no—
737C2×C4—52no—
738C2×C4—52no—
739C2×C4—68no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—152no—
754C2×C4—308no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4C4×D3×D512yes—
764C2×C4D3×C22⋊D512yes—
765C2×C3D5×#11711yescharacteristic
766C2×C3#6585711yescharacteristic
767C2×C3#6586611yescharacteristic
768C2×C3#6586711yescharacteristic
769C2×C3C2×C4×C22⋊D511yescharacteristic
770C2×C3#6615811yescharacteristic
771C2×C3#6616811yescharacteristic
772D3—42no—
773D3—202no—
774C5#7363911yescharacteristic, complemented, Sylow
775C22—62no—
776C22—62no—
777C22—62no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—302no—
783C22—302no—
784C22—302no—
785C22—601no—
786C22—601no—
787C22—601no—
788C22—601no—
789C22#9200411yescharacteristic
790C22C2×C4×D3×D511yescharacteristic
791C22D5×#23511yescharacteristic
792C22D5×#23511yescharacteristic
793C22D3×#70911yescharacteristic
794C22#9201911yescharacteristic
795C22C2×D3×C22⋊D511yescharacteristic
796C4—22no—
797C4—22no—
798C4—34no—
799C4—41no—
800C4—54no—
801C4—62no—
802C4—102no—
803C4—121no—
804C4—201no—
805C4—201no—
806C4—302no—
807C4—601no—
808C4—601no—
809C3#1061397211yescharacteristic, complemented, Sylow
810C2—122no—
811C2—602no—
812C2#1175252711yescharacteristic
813C2#1175259211yescharacteristic
814C2#1175268911yescharacteristic
815C2D5×#87211yescharacteristic
816C2#1175434611yescharacteristic
817C2#1175454511yescharacteristic
818C2C4×D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2354
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C5×#872C2semidirect
3. C2×#91402C2semidirect
4. #11751041C2semidirect
5. C3×C4×#683C2semidirect
8. #11748882C2semidirect
9. #11748854C2semidirect
10. #11748782C2semidirect
11. #11748720C2semidirect
12. #11748714C2semidirect
13. #11748641C2semidirect
14. Dic5×Dic3⋊C4C2semidirect
15. Dic3×#683C2semidirect
47. #91446C4semidirect
70. C4×#683D3semidirect
103. C5×Dic3⋊C4D4semidirect
123. C2×#872D5semidirect
365. C3×Dic5#117semidirect
414. Dic3⋊C4C22⋊D5semidirect
613. Dic5#872semidirect
664. C3×C5#2354semidirect
774. C5#73639semidirect
809. C3#10613972semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8722
C2×#914462
C2×#914022
#117510412
C3×C4×#6832
#117489092
#117489082
#117488822
#117488542
#117487822
#117487202
#117487142
#117486412
Dic5×Dic3⋊C42
Dic3×#6832
#106139723
#736395