Finite Group Databasebeta

← #14323596

Subgroups — #14323596

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#883C211yesmaximal, characteristic
2C2×Dic5×#67C211yesmaximal, characteristic
3C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
4#11751052C211yesmaximal, characteristic, complemented
5C3×#65239C211yesmaximal, characteristic, complemented
6#11749519C211yesmaximal, characteristic
7#11749509C211yesmaximal, characteristic, complemented
8#11749478C211yesmaximal, characteristic, complemented
9#11748897C211yesmaximal, characteristic, complemented
10#11748886C211yesmaximal, characteristic, complemented
11#11748868C211yesmaximal, characteristic, complemented
12#11748777C211yesmaximal, characteristic, complemented
13#11748693C211yesmaximal, characteristic, complemented
14#11748682C211yesmaximal, characteristic, complemented
15#11748673C211yesmaximal, characteristic, complemented
16#10614567—31nomaximal, Hall
17C22×C5×#67C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C5×Dic3⋊C4C2211yescharacteristic
31C5×#883C418yescomplemented
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic
35Dic5×#67—24no—
36C2×Dic3⋊Dic5C2211yescharacteristic
37C2×Dic3⋊Dic5C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×Dic3⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44D3×C4⋊Dic5—24no—
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74593—51nomaximal, Hall
56C2×C5×#123—31no—
57C2×D4×Dic5—31no—
58C22×C4⋊Dic5—31no—
59#65509—31no—
60#65500—31no—
61#65274—31no—
62#65274—31no—
63#65270—31no—
64#65270—31no—
65#65240—31no—
66#65240—31no—
67#65239—31no—
68#65239—31no—
69#65239D311yescharacteristic, complemented
70C22⋊C4×Dic5—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C2×C5×#67—22no—
80C2×C5×#67—22no—
81C2×C5×#67C2×C414yes—
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C2×C4×C5×D3—22no—
86C2×C4×C5×D3—22no—
87C2×C4×C5×D3C2×C414yescomplemented
88C22×C3×Dic5—22no—
89C22×C3×Dic5—41no—
90C22×C3×Dic5—41no—
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×D3×Dic5—22no—
96C2×D3×Dic5—41no—
97C2×D3×Dic5—41no—
98C2×D3×Dic5—41no—
99C2×D3×Dic5—41no—
100C2×D3×Dic5D414yes—
101C3×C5×C22⋊C4C2×C414yescomplemented
102#6719—22no—
103#6719—41no—
104C4⋊Dic15—22no—
105C4×Dic15—41no—
106C5×#217C2×C414yescomplemented
107C5×(C2×D3)⋊C4C2×C414yescomplemented
108C5×C4⋊Dic3C2×C414yescomplemented
109C5×Dic3⋊C4C2×C414yescomplemented
110C3×C22⋊Dic5—41no—
111C3×C4⋊Dic5—22no—
112C3×C4⋊Dic5—41no—
113Dic3⋊Dic5—22no—
114Dic3⋊Dic5—22no—
115Dic3⋊Dic5—22no—
116Dic3⋊Dic5—41no—
117(C2×D3)⋊Dic5—22no—
118(C2×D3)⋊Dic5—22no—
119Dic3×Dic5—22no—
120Dic3×Dic5—41no—
121C2×C4×#67—51no—
122C2×D3×C4⋊C4—51no—
123C2×#883D511yescharacteristic
124C3×#385—51no—
125#5210—51no—
126#4989—51no—
127#4978—51no—
128#4972—51no—
129#4956—51no—
130#4951—51no—
131#4944—51no—
132#4666—51no—
133#4664—51no—
134#4653—51no—
135#4647—51no—
136C22×C5×D4—31no—
137C23×C4×C5—31no—
138C23×Dic5—31no—
139C23×Dic5—31no—
140C23×Dic5C2×D311yescharacteristic
141C5×#123—38no—
142C2×C5×C4⋊C4—31no—
143C2×C5×C4⋊C4—31no—
144C2×C5×C22⋊C4—31no—
145C2×C5×C22⋊C4—31no—
146C2×C5×C22⋊C4C2×D311yescharacteristic
147C2×C22⋊Dic5—31no—
148C2×C22⋊Dic5—31no—
149C2×C22⋊Dic5—31no—
150C2×C22⋊Dic5—31no—
151C2×C22⋊Dic5C2×D311yescharacteristic
152D4×Dic5—64no—
153C2×C4⋊Dic5—31no—
154C2×C4⋊Dic5—31no—
155C2×C4⋊Dic5—31no—
156C2×C4⋊Dic5—31no—
157C2×C4⋊Dic5—31no—
158C2×C4⋊Dic5—64no—
159C2×C4⋊Dic5C2×D311yescharacteristic
160C2×C4⋊Dic5C2×D311yescharacteristic
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163C2×C4×Dic5—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963C2×D311yescharacteristic
173#3963C2×D311yescharacteristic
174#2322—151noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5C22×C412yes—
182C23×C3×C5C2411yescharacteristic
183C22×C5×D3—21no—
184C22×C5×D3—21no—
185C22×C5×D3—21no—
186C22×C5×D3—21no—
187C22×C5×D3C22×C412yes—
188C22×C5×D3C2×D412yes—
189C22×C5×D3#4112yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5C22×C412yes—
195C2×C3×C4×C5C22×C412yes—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
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×Dic15C2×D412yes—
208C5×#67—28no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3C22×C412yes—
216C2×C5×Dic3C22×C412yes—
217C2×C5×Dic3C22×C412yes—
218C4×C5×D3—28no—
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×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—44no—
231C2×C3×Dic5C2×D412yes—
232D3×Dic5—44no—
233D3×Dic5—44no—
234C23×C3×C4—51no—
235C22×#67C2×D511yescharacteristic
236C22×C4×D3—51no—
237C22×C4×D3—51no—
238C22×C4×D3C2×D511yescharacteristic
239C2×C3×C4⋊C4—51no—
240C2×C3×C4⋊C4—51no—
241C2×C3×C22⋊C4—51no—
242C2×C3×C22⋊C4C2×D511yescharacteristic
243C2×#217—51no—
244C2×#217—51no—
245C2×#217C2×D511yescharacteristic
246C4×#67—104no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—51no—
249C2×(C2×D3)⋊C4C2×D511yescharacteristic
250C2×C4⋊Dic3—51no—
251C2×C4⋊Dic3C2×D511yescharacteristic
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4—51no—
254C2×Dic3⋊C4—51no—
255C2×Dic3⋊C4—51no—
256C2×Dic3⋊C4C2×D511yescharacteristic
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260D3×C4⋊C4—104no—
261#883Dic518yescomplemented
262C3×#95—51no—
263C3×#95—51no—
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C24×C5—31no—
273C24×C5C22×D311yescharacteristic
274C2×C5×D4—34no—
275C2×C5×D4—62no—
276C2×C5×D4—62no—
277C22×C4×C5—31no—
278C22×C4×C5—31no—
279C22×C4×C5—31no—
280C22×C4×C5—34no—
281C22×C4×C5—62no—
282C22×C4×C5—62no—
283C22×C4×C5C22×D311yescharacteristic
284C22×C4×C5C22×D311yescharacteristic
285C22×Dic5—22no—
286C22×Dic5—31no—
287C22×Dic5—34no—
288C22×Dic5—31no—
289C22×Dic5—31no—
290C22×Dic5—31no—
291C22×Dic5—41no—
292C22×Dic5—41no—
293C22×Dic5—62no—
294C22×Dic5—121no—
295C22×Dic5—121no—
296C22×Dic5—121no—
297C22×Dic5—121no—
298C22×Dic5C22×D311yescharacteristic
299C22×Dic5C22×D311yescharacteristic
300C22×Dic5C22×D311yescharacteristic
301C22×Dic5C22×D311yescharacteristic
302C5×C4⋊C4—34no—
303C5×C4⋊C4—34no—
304C5×C22⋊C4—34no—
305C5×C22⋊C4—34no—
306C5×C22⋊C4C4×D314yescomplemented
307C22⋊Dic5—41no—
308C22⋊Dic5—62no—
309C22⋊Dic5—62no—
310C22⋊Dic5—62no—
311C22⋊Dic5—121no—
312C4⋊Dic5—22no—
313C4⋊Dic5—41no—
314C4⋊Dic5—62no—
315C4⋊Dic5—62no—
316C4⋊Dic5—62no—
317C4⋊Dic5—62no—
318C4⋊Dic5—121no—
319C4×Dic5—62no—
320C4×Dic5—121no—
321C4×Dic5—121no—
322C2×#123—31no—
323C2×C4×D4—151no—
324C22×C4⋊C4—151no—
325#389—151no—
326#389—151no—
327#388—151no—
328#388—151no—
329#387—151no—
330#387—151no—
331#386—151no—
332#385—51no—
333#385—151no—
334#385—151no—
335#381—151no—
336C4×C22⋊C4—151no—
337C22×C3×C5—22no—
338C22×C3×C5—22no—
339C22×C3×C5—22no—
340C22×C3×C5—41no—
341C22×C3×C5—41no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5C23×C411yescharacteristic
345C22×C3×C5C22×D411yescharacteristic
346C22×C3×C5C2×#4111yescharacteristic
347C22×C3×C5H(5,𝔽2)11yescharacteristic
348C22×C3×C5H(5,𝔽2)11yescharacteristic
349C22×C3×C52−1+411yescharacteristic
350C22×C3×C52−1+411yescharacteristic
351C2×C5×D3—22no—
352C2×C5×D3—22no—
353C2×C5×D3—22no—
354C2×C5×D3—22no—
355C2×C5×D3—22no—
356C2×C5×D3—22no—
357C2×C5×D3C4×D414yes—
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360Dic15—22no—
361Dic15—41no—
362Dic15—41no—
363Dic15—41no—
364C3×Dic5—22no—
365C3×Dic5—41no—
366C3×Dic5—41no—
367C3×Dic5—41no—
368C5×Dic3—22no—
369C5×Dic3—22no—
370C5×Dic3—22no—
371C24×C3C22×D511yescharacteristic
372C23×D3C22×D511yescharacteristic
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4—51no—
376C22×C3×C4—51no—
377C22×C3×C4—102no—
378C22×C3×C4—201no—
379C22×C3×C4—201no—
380C22×C3×C4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C2×#67—22no—
383C2×#67—22no—
384C2×#67C2×Dic514yes—
385C22×Dic3—51no—
386C22×Dic3—51no—
387C22×Dic3—51no—
388C22×Dic3—51no—
389C22×Dic3C22×D511yescharacteristic
390C22×Dic3C22×D511yescharacteristic
391C22×Dic3C22×D511yescharacteristic
392C2×C4×D3—22no—
393C2×C4×D3—22no—
394C2×C4×D3—54no—
395C2×C4×D3—102no—
396C2×C4×D3—201no—
397C2×C4×D3—201no—
398C2×C4×D3—201no—
399C2×C4×D3—201no—
400C2×C4×D3C2×Dic514yescomplemented
401C3×C4⋊C4—102no—
402C3×C4⋊C4—201no—
403C3×C22⋊C4—201no—
404C3×C22⋊C4C2×Dic514yescomplemented
405#217—102no—
406#217—201no—
407#217C2×Dic514yescomplemented
408(C2×D3)⋊C4—102no—
409(C2×D3)⋊C4—102no—
410(C2×D3)⋊C4C2×Dic514yescomplemented
411C4⋊Dic3—102no—
412C4⋊Dic3C2×Dic514yescomplemented
413Dic3⋊C4—102no—
414Dic3⋊C4—102no—
415Dic3⋊C4—102no—
416Dic3⋊C4—201no—
417Dic3⋊C4C2×Dic514yescomplemented
418C4×Dic3—102no—
419C4×Dic3—201no—
420C4×Dic3—201no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5—21no—
426C23×C5—21no—
427C23×C5—32no—
428C23×C5—32no—
429C23×C5—32no—
430C23×C5—61no—
431C23×C5—61no—
432C23×C5—61no—
433C23×C5—61no—
434C23×C5C2×C4×D312yes—
435C23×C5C23×D311yescharacteristic
436C5×D4—68no—
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—68no—
445C2×C4×C5—61no—
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×C5C2×C4×D312yes—
453C2×Dic5—21no—
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—21no—
463C2×Dic5—21no—
464C2×Dic5—32no—
465C2×Dic5—44no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—61no—
474C2×Dic5—61no—
475C2×Dic5—61no—
476C2×Dic5—61no—
477C2×Dic5—124no—
478C2×Dic5—124no—
479C2×Dic5D3×D412yes—
480C22×D4—31no—
481C23×C4—31no—
482C23×C4—51no—
483C23×C4—151no—
484C23×C4—151no—
485#123—38no—
486C4×D4—304no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—151no—
492C2×C4⋊C4—151no—
493C2×C4⋊C4—151no—
494C2×C4⋊C4—151no—
495C2×C4⋊C4—151no—
496C2×C4⋊C4—304no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—51no—
500C2×C22⋊C4—151no—
501C2×C22⋊C4—151no—
502C2×C22⋊C4—151no—
503C2×C22⋊C4—151no—
504C2×C22⋊C4D3×D511yescharacteristic
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—151no—
508#95—51no—
509#95—51no—
510#95—151no—
511#95—151no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95—151no—
516#95—151no—
517#95—151no—
518C2×C3×C5—42no—
519C2×C3×C5C2×C4×D411yescharacteristic
520C2×C3×C5#52011yescharacteristic
521C2×C3×C5#52011yescharacteristic
522C2×C3×C5#53411yescharacteristic
523C2×C3×C5#53611yescharacteristic
524C2×C3×C5#53911yescharacteristic
525C2×C3×C5#53911yescharacteristic
526C5×D3—24no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3C22×Dic512yes—
534C23×C3C23×D511yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3D4×D512yes—
540C22×D3#71112yes—
541C22×D3C22×Dic512yes—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—52no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
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×C4—101no—
558C2×C3×C4—204no—
559C2×C3×C4C22×Dic512yes—
560C2×C3×C4C22×Dic512yes—
561#67—28no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—52no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3C22×Dic512yes—
581C2×Dic3C22×Dic512yes—
582C2×Dic3C22×Dic512yes—
583C4×D3—28no—
584C4×D3—204no—
585C4×D3—204no—
586C22×C5—22no—
587C22×C5—22no—
588C22×C5—22no—
589C22×C5—34no—
590C22×C5—41no—
591C22×C5—41no—
592C22×C5—41no—
593C22×C5—41no—
594C22×C5—62no—
595C22×C5—62no—
596C22×C5—62no—
597C22×C5—62no—
598C22×C5—62no—
599C22×C5—62no—
600C22×C5C22×C4×D311yescharacteristic
601C22×C5C2×D3×D411yescharacteristic
602C22×C5#100411yescharacteristic
603C22×C5#100411yescharacteristic
604C22×C5#100711yescharacteristic
605C22×C5D3×#4111yescharacteristic
606C22×C5#101011yescharacteristic
607C4×C5—22no—
608C4×C5—22no—
609C4×C5—62no—
610C4×C5—62no—
611C4×C5—62no—
612Dic5—22no—
613Dic5—41no—
614Dic5—41no—
615Dic5—41no—
616Dic5—62no—
617Dic5—121no—
618Dic5—121no—
619Dic5—121no—
620C24—31no—
621C24C2×D3×D511yescharacteristic
622C2×D4—34no—
623C2×D4—62no—
624C2×D4—62no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—34no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—102no—
636C22×C4—154no—
637C22×C4—151no—
638C22×C4—151no—
639C22×C4—151no—
640C22×C4—151no—
641C22×C4—201no—
642C22×C4—201no—
643C22×C4—302no—
644C22×C4—601no—
645C22×C4—601no—
646C22×C4—601no—
647C22×C4—601no—
648C22×C4C2×D3×D511yescharacteristic
649C22×C4C2×D3×D511yescharacteristic
650C4⋊C4—34no—
651C4⋊C4—34no—
652C4⋊C4—102no—
653C4⋊C4—201no—
654C4⋊C4—302no—
655C4⋊C4—302no—
656C4⋊C4—302no—
657C4⋊C4—302no—
658C4⋊C4—601no—
659C22⋊C4—34no—
660C22⋊C4—34no—
661C22⋊C4—201no—
662C22⋊C4—302no—
663C22⋊C4—302no—
664C22⋊C4—302no—
665C22⋊C4—601no—
666C22⋊C4D3×Dic514yescomplemented
667C42—302no—
668C42—601no—
669C42—601no—
670C3×C5#232211yescharacteristic, complemented, Hall
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3C2×D4×D511yescharacteristic
679C22×C3C2×#71111yescharacteristic
680C22×C3#414911yescharacteristic
681C22×C3#414911yescharacteristic
682C22×C3#415011yescharacteristic
683C22×C3#415011yescharacteristic
684C22×C3C23×Dic511yescharacteristic
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3D4×Dic514yes—
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—102no—
695C3×C4—201no—
696C3×C4—201no—
697C3×C4—201no—
698Dic3—22no—
699Dic3—22no—
700Dic3—22no—
701Dic3—102no—
702Dic3—201no—
703Dic3—201no—
704Dic3—201no—
705C2×C5—42no—
706C2×C5—64no—
707C2×C5#550411yescharacteristic
708C2×C5C4×D3×D411yescharacteristic
709C2×C5#554611yescharacteristic
710C2×C5#558911yescharacteristic
711C2×C5#562811yescharacteristic
712C2×C5#563811yescharacteristic
713C2×C5#566011yescharacteristic
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—32no—
721C23—32no—
722C23—32no—
723C23—61no—
724C23—61no—
725C23—61no—
726C23—61no—
727C23C2×D3×Dic512yes—
728C23C22×D3×D511yescharacteristic
729D4—68no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—52no—
738C2×C4—68no—
739C2×C4—61no—
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—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—152no—
757C2×C4—204no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—604no—
770C2×C4—604no—
771C2×C4C2×D3×Dic512yes—
772C2×C4C2×D3×Dic512yes—
773C2×C3—42no—
774C2×C3#6598211yescharacteristic
775C2×C3#6598711yescharacteristic
776C2×C3#6599911yescharacteristic
777C2×C3#6599911yescharacteristic
778C2×C3C2×D4×Dic511yescharacteristic
779C2×C3#6616111yescharacteristic
780C2×C3#6616111yescharacteristic
781D3—24no—
782C5#7459311yescharacteristic, complemented, Sylow
783C22—22no—
784C22—22no—
785C22—22no—
786C22—34no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—62no—
792C22—62no—
793C22—62no—
794C22—62no—
795C22—62no—
796C22—62no—
797C22#9200411yescharacteristic
798C22#9201711yescharacteristic
799C22#9202011yescharacteristic
800C22D3×D4×D511yescharacteristic
801C22D3×#71111yescharacteristic
802C22#9202611yescharacteristic
803C22C22×D3×Dic511yescharacteristic
804C4—22no—
805C4—22no—
806C4—62no—
807C4—62no—
808C4—62no—
809C4—102no—
810C4—201no—
811C4—201no—
812C4—201no—
813C4—302no—
814C4—601no—
815C4—601no—
816C4—601no—
817C3#1061456711yescharacteristic, complemented, Sylow
818C2—42no—
819C2—64no—
820C2#1175284411yescharacteristic
821C2#1175298511yescharacteristic
822C2#1175300611yescharacteristic
823C2#1175321211yescharacteristic
824C2#1175449211yescharacteristic
825C2D3×D4×Dic511yescharacteristic
826C2#1175492011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2322
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×D3×C4⋊Dic5C2semidirect
4. #11751052C2semidirect
5. C3×#65239C2semidirect
7. #11749509C2semidirect
8. #11749478C2semidirect
9. #11748897C2semidirect
10. #11748886C2semidirect
11. #11748868C2semidirect
12. #11748777C2semidirect
13. #11748693C2semidirect
14. #11748682C2semidirect
15. #11748673C2semidirect
31. C5×#883C4semidirect
69. #65239D3semidirect
87. C2×C4×C5×D3C2×C4semidirect
101. C3×C5×C22⋊C4C2×C4semidirect
106. C5×#217C2×C4semidirect
107. C5×(C2×D3)⋊C4C2×C4semidirect
108. C5×C4⋊Dic3C2×C4semidirect
109. C5×Dic3⋊C4C2×C4semidirect
261. #883Dic5semidirect
306. C5×C22⋊C4C4×D3semidirect
400. C2×C4×D3C2×Dic5semidirect
404. C3×C22⋊C4C2×Dic5semidirect
407. #217C2×Dic5semidirect
410. (C2×D3)⋊C4C2×Dic5semidirect
412. C4⋊Dic3C2×Dic5semidirect
417. Dic3⋊C4C2×Dic5semidirect
666. C22⋊C4D3×Dic5semidirect
670. C3×C5#2322semidirect
782. C5#74593semidirect
817. C3#10614567semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8832
C2×Dic5×#672
C2×D3×C4⋊Dic52
#117510522
C3×#652392
#117495192
#117495092
#117494782
#117488972
#117488862
#117488682
#117487772
#117486932
#117486822
#117486732
#106145673
#745935