Finite Group Databasebeta

← #14327359

Subgroups — #14327359

Order 1920.

1320 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×#872C211yesmaximal, characteristic, complemented
2C2×#91441C211yesmaximal, characteristic
3C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#11751034C211yesmaximal, characteristic, complemented
5C3×C4×#685C211yesmaximal, characteristic, complemented
6#11748906C211yesmaximal, characteristic
7#11748905C211yesmaximal, characteristic
8#11748878C211yesmaximal, characteristic, complemented
9Dic3×#685C211yesmaximal, characteristic, complemented
10#11748847C211yesmaximal, characteristic, complemented
11#11748782C211yesmaximal, characteristic, complemented
12#11748721C211yesmaximal, characteristic, complemented
13#11748715C211yesmaximal, characteristic, complemented
14#11748652C211yesmaximal, characteristic, complemented
15Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#10614003—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×#1201C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×#6712C2211yescharacteristic
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×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×Dic3⋊Dic5C2211yescharacteristic
35C2×Dic3⋊Dic5C2211yescharacteristic
36C2×#6669C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43#91441C418yescomplemented
44D5×Dic3⋊C4—24no—
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#73461—51nomaximal, Hall
56C2×C5×#117—31no—
57C2×C4×C22⋊D5—31no—
58C2×D5×C4⋊C4—31no—
59#65501—31no—
60#65276—31no—
61#65266—31no—
62C4⋊C4×Dic5—31no—
63#65245—31no—
64#65245—31no—
65#65234—31no—
66#65234—31no—
67C4×#685—31no—
68C4×#685D311yescharacteristic, complemented
69#65222—31no—
70#65222—31no—
71C23×C5×D3C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C2×C4×C5×D3—22no—
84C2×C4×C5×D3—22no—
85C2×C4×C5×D3C2×C414yescomplemented
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×C3×C4×D5—22no—
90C2×C3×C4×D5—22no—
91C2×C3×C4×D5—41no—
92C2×#1201—22no—
93C2×#1201—22no—
94C2×#1201C2×C414yes—
95C2×D5×Dic3—22no—
96C2×D5×Dic3—22no—
97C2×D5×Dic3—22no—
98C2×D5×Dic3—22no—
99C2×D5×Dic3—41no—
100C2×D5×Dic3C2×C414yes—
101C3×C42×C5—22no—
102#6712—22no—
103#6712C2×C414yescomplemented
104C5×(C2×D3)⋊C4—22no—
105C5×(C2×D3)⋊C4—22no—
106C5×Dic3⋊C4—22no—
107C5×Dic3⋊C4D414yescomplemented
108C4×C5×Dic3—22no—
109C3×#685—22no—
110C3×#685C2×C414yes—
111C3×C4×Dic5—41no—
112Dic3⋊Dic5—22no—
113Dic3⋊Dic5—22no—
114#6669—22no—
115(C2×D3)⋊Dic5—41no—
116(C2×D3)⋊Dic5—41no—
117(C2×D3)⋊Dic5C2×C414yescomplemented
118#6665—22no—
119Dic3×Dic5—41no—
120Dic3×Dic5C2×C414yescomplemented
121C22×Dic3⋊C4—51no—
122C2×#67⋊C4—51no—
123C2×#872D511yescharacteristic, complemented
124C3×C4×C22⋊C4—51no—
125#5213—51no—
126#4958—51no—
127#4942—51no—
128Dic3×C22⋊C4—51no—
129#4940—51no—
130#4933—51no—
131C4×Dic3⋊C4—51no—
132#4669—51no—
133#4667—51no—
134#4652—51no—
135#4650—51no—
136C23×C4×C5—31no—
137C22×C22⋊D5—31no—
138C22×C4×D5—31no—
139C22×C4×D5—31no—
140C22×C4×D5C2×D311yescharacteristic
141C5×#117—64no—
142C2×C5×C4⋊C4—31no—
143C2×C5×C4⋊C4—31no—
144C2×C5×C22⋊C4—31no—
145C2×C5×C22⋊C4—31no—
146C2×C42×C5—31no—
147C2×C42×C5C2×D311yescharacteristic
148C2×C22⋊Dic5—31no—
149C2×C22⋊Dic5—31no—
150C2×C22⋊Dic5—31no—
151C4×C22⋊D5—38no—
152C2×#685—31no—
153C2×#685C2×D311yescharacteristic
154C2×#685C2×D311yescharacteristic
155C2×C4⋊Dic5—31no—
156C2×C4⋊Dic5—31no—
157C2×#683—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5C2×D311yescharacteristic
163D5×C4⋊C4—64no—
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#2352—151noSylow
175C23×C3×C5C2411yescharacteristic
176C22×C5×D3—21no—
177C22×C5×D3—21no—
178C22×C5×D3—21no—
179C22×C5×D3—21no—
180C22×C5×D3—21no—
181C22×C5×D3—21no—
182C22×C5×D3C22×C412yes—
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5C22×C412yes—
188C22×C3×D5#4112yes—
189C22×C3×D5#4112yes—
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×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15C22×C412yes—
210C2×Dic15C22×C412yes—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3C22×C412yes—
217C2×C5×Dic3C2×D412yes—
218C2×C5×Dic3C2×D412yes—
219C2×C5×Dic3#4112yes—
220C4×C5×D3—28no—
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×Dic5C22×C412yes—
230C3×C4×D5—44no—
231#1201—28no—
232D5×Dic3—28no—
233D5×Dic3—44no—
234C23×C3×C4—51no—
235C22×#67—51no—
236C23×Dic3—51no—
237C23×Dic3—51no—
238C22×C4×D3C2×D511yescharacteristic
239C2×C3×C22⋊C4—51no—
240C2×C3×C22⋊C4—51no—
241C2×C3×C42—51no—
242C2×C3×C42C2×D511yescharacteristic
243C2×#217—51no—
244C2×(C2×D3)⋊C4—51no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4C2×D511yescharacteristic
248C2×(C2×D3)⋊C4C2×D511yescharacteristic
249C2×Dic3⋊C4—51no—
250C2×Dic3⋊C4—51no—
251C2×Dic3⋊C4—51no—
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4—51no—
254C2×Dic3⋊C4—104no—
255C2×Dic3⋊C4C2×D511yescharacteristic
256C2×Dic3⋊C4C2×D511yescharacteristic
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3C2×D511yescharacteristic
260#67⋊C4—58no—
261#872—24no—
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—
273C23×D5C22×D311yescharacteristic
274C22×C4×C5—31no—
275C22×C4×C5—31no—
276C22×C4×C5—34no—
277C22×C4×C5—31no—
278C22×C4×C5—62no—
279C22×C4×C5—62no—
280C22×C4×C5C22×D311yescharacteristic
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—34no—
284C2×C22⋊D5—62no—
285C2×C22⋊D5—62no—
286C22×Dic5—31no—
287C22×Dic5—31no—
288C22×Dic5—31no—
289C22×Dic5—31no—
290C22×Dic5C22×D311yescharacteristic
291C22×Dic5C22×D311yescharacteristic
292C22×Dic5C22×D311yescharacteristic
293C2×C4×D5—22no—
294C2×C4×D5—22no—
295C2×C4×D5—34no—
296C2×C4×D5—41no—
297C2×C4×D5—62no—
298C2×C4×D5—62no—
299C2×C4×D5—62no—
300C2×C4×D5—62no—
301C2×C4×D5—121no—
302C5×C4⋊C4—34no—
303C5×C4⋊C4—62no—
304C5×C22⋊C4—62no—
305C5×C22⋊C4—62no—
306C42×C5—22no—
307C42×C5—62no—
308C22⋊Dic5—34no—
309C22⋊Dic5—121no—
310C22⋊Dic5—121no—
311#685—22no—
312#685—62no—
313#685C4×D314yes—
314C4⋊Dic5—62no—
315C4⋊Dic5—62no—
316#683—34no—
317#683—62no—
318#683—62no—
319C4×Dic5—34no—
320C4×Dic5—41no—
321C4×Dic5—121no—
322C2×C4×D4—151no—
323C2×#117—31no—
324C22×C4⋊C4—151no—
325#388—151no—
326#388—151no—
327#387—151no—
328#387—151no—
329#386—151no—
330#386—151no—
331#382—151no—
332#380—151no—
333#380—151no—
334C4×C4⋊C4—151no—
335C4×C22⋊C4—51no—
336C4×C22⋊C4—151no—
337C22×C3×C5C23×C411yescharacteristic
338C22×C3×C5C22×D411yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5H(5,𝔽2)11yescharacteristic
343C22×C3×C52−1+411yescharacteristic
344C2×C5×D3—22no—
345C2×C5×D3—22no—
346C2×C5×D3—22no—
347C2×C5×D3—41no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C3×D5—22no—
352C2×C3×D5—22no—
353C2×C3×D5—22no—
354C2×C3×D5—22no—
355C2×C3×D5—22no—
356C2×C3×D5—22no—
357C2×C3×D5#11714yescomplemented
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360C3×C4×C5—41no—
361Dic15—22no—
362Dic15—22no—
363Dic15—41no—
364Dic15—41no—
365C3×Dic5—22no—
366C3×Dic5—41no—
367C3×Dic5—41no—
368C5×Dic3—22no—
369C5×Dic3—41no—
370C5×Dic3C4×D414yes—
371C24×C3—51no—
372C23×D3C22×D511yescharacteristic
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4—51no—
376C22×C3×C4—102no—
377C22×C3×C4—102no—
378C22×C3×C4—201no—
379C22×C3×C4C22×D511yescharacteristic
380C22×C3×C4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C2×#67—54no—
383C2×#67—102no—
384C2×#67—102no—
385C22×Dic3—51no—
386C22×Dic3—51no—
387C22×Dic3—54no—
388C22×Dic3—51no—
389C22×Dic3—51no—
390C22×Dic3—102no—
391C22×Dic3—102no—
392C22×Dic3—102no—
393C22×Dic3—102no—
394C22×Dic3—201no—
395C22×Dic3C22×D511yescharacteristic
396C22×Dic3C22×D511yescharacteristic
397C22×Dic3C22×D511yescharacteristic
398C2×C4×D3—22no—
399C2×C4×D3—22no—
400C2×C4×D3C4×D514yescomplemented
401C3×C22⋊C4—54no—
402C3×C22⋊C4—102no—
403C3×C42—22no—
404C3×C42—201no—
405#217—102no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—54no—
409(C2×D3)⋊C4—201no—
410(C2×D3)⋊C4—201no—
411Dic3⋊C4—22no—
412Dic3⋊C4—54no—
413Dic3⋊C4—102no—
414Dic3⋊C4—102no—
415Dic3⋊C4—102no—
416Dic3⋊C4—102no—
417Dic3⋊C4C22⋊D514yescomplemented
418C4×Dic3—22no—
419C4×Dic3—54no—
420C4×Dic3—201no—
421C23×C5—32no—
422C23×C5—61no—
423C23×C5—61no—
424C23×C5—61no—
425C23×C5—61no—
426C23×C5—61no—
427C23×C5—61no—
428C23×C5C23×D311yescharacteristic
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5—21no—
433C22×D5C2×C4×D312yes—
434C22×D5#23512yes—
435C22×D5#23512yes—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
445C2×C4×C5—32no—
446C2×C4×C5—32no—
447C2×C4×C5—68no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5—61no—
452C2×C4×C5—61no—
453C2×C4×C5C2×C4×D312yes—
454C2×C4×C5D3×D412yes—
455C22⋊D5—68no—
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—32no—
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×Dic5C2×C4×D312yes—
477C4×D5—44no—
478C4×D5—68no—
479C4×D5—124no—
480C22×D4—151no—
481C23×C4—31no—
482C23×C4—51no—
483C23×C4—151no—
484C23×C4—151no—
485C4×D4—158no—
486#117—64no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—151no—
491C2×C4⋊C4—151no—
492C2×C4⋊C4—151no—
493C2×C4⋊C4—151no—
494C2×C4⋊C4—304no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—51no—
499C2×C22⋊C4—151no—
500C2×C22⋊C4—151no—
501C2×C22⋊C4—151no—
502C2×C22⋊C4—151no—
503C2×C42—31no—
504C2×C42—51no—
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—
514#95—151no—
515#95—151no—
516#95—151no—
517#95—151no—
518C2×C3×C5C2×#11711yescharacteristic
519C2×C3×C5C2×C4×D411yescharacteristic
520C2×C3×C5#52011yescharacteristic
521C2×C3×C5#54611yescharacteristic
522C2×C3×C5#54811yescharacteristic
523C2×C3×C5#55211yescharacteristic
524C2×C3×C5#55311yescharacteristic
525C3×D5—24no—
526C5×D3—42no—
527C23×C3—52no—
528C23×C3—52no—
529C23×C3—52no—
530C23×C3—101no—
531C23×C3—101no—
532C23×C3—101no—
533C23×C3—101no—
534C23×C3C23×D511yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3C2×C4×D512yes—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—52no—
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×C4C2×C4×D512yes—
560C2×C3×C4C2×C22⋊D512yes—
561#67—108no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—52no—
568C2×Dic3—52no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—108no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3—204no—
581C2×Dic3C2×C4×D512yes—
582C2×Dic3#70912yes—
583C2×Dic3C2×C22⋊D512yes—
584C2×Dic3C2×C22⋊D512yes—
585C4×D3—28no—
586C22×C5—62no—
587C22×C5—62no—
588C22×C5—62no—
589C22×C5—121no—
590C22×C5—121no—
591C22×C5—121no—
592C22×C5—121no—
593C22×C5C22×C4×D311yescharacteristic
594C22×C5C2×#23511yescharacteristic
595C22×C5C2×#23511yescharacteristic
596C22×C5C2×D3×D411yescharacteristic
597C22×C5#100411yescharacteristic
598C22×C5D3×#4111yescharacteristic
599C22×C5#101011yescharacteristic
600C2×D5—22no—
601C2×D5—22no—
602C2×D5—22no—
603C2×D5—22no—
604C2×D5—22no—
605C2×D5—22no—
606C2×D5#87214yescomplemented
607C4×C5—22no—
608C4×C5—22no—
609C4×C5—34no—
610C4×C5—41no—
611C4×C5—62no—
612C4×C5—121no—
613Dic5—22no—
614Dic5—41no—
615Dic5—41no—
616Dic5—62no—
617Dic5—62no—
618Dic5—121no—
619Dic5—121no—
620C24—31no—
621C24—51no—
622C2×D4—154no—
623C2×D4—302no—
624C2×D4—302no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—34no—
628C22×C4—31no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—62no—
633C22×C4—62no—
634C22×C4—102no—
635C22×C4—102no—
636C22×C4—154no—
637C22×C4—151no—
638C22×C4—151no—
639C22×C4—151no—
640C22×C4—151no—
641C22×C4—201no—
642C22×C4—302no—
643C22×C4—302no—
644C22×C4—302no—
645C22×C4—302no—
646C22×C4—601no—
647C22×C4C2×D3×D511yescharacteristic
648C22×C4C2×D3×D511yescharacteristic
649C22×C4C2×D3×D511yescharacteristic
650C4⋊C4—34no—
651C4⋊C4—62no—
652C4⋊C4—154no—
653C4⋊C4—302no—
654C4⋊C4—302no—
655C4⋊C4—302no—
656C4⋊C4—302no—
657C22⋊C4—54no—
658C22⋊C4—62no—
659C22⋊C4—62no—
660C22⋊C4—102no—
661C22⋊C4—154no—
662C22⋊C4—302no—
663C22⋊C4—601no—
664C22⋊C4—601no—
665C42—22no—
666C42—62no—
667C42—154no—
668C42—201no—
669C42—601no—
670C3×C5#235211yescharacteristic, complemented, Hall
671C22×C3—54no—
672C22×C3—102no—
673C22×C3—102no—
674C22×C3—102no—
675C22×C3—102no—
676C22×C3—102no—
677C22×C3—102no—
678C22×C3C22×C4×D511yescharacteristic
679C22×C3C2×#70911yescharacteristic
680C22×C3D5×#4111yescharacteristic
681C22×C3D5×#4111yescharacteristic
682C22×C3#414911yescharacteristic
683C22×C3#415011yescharacteristic
684C22×C3C22×C22⋊D511yescharacteristic
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—41no—
695C3×C4—102no—
696C3×C4—201no—
697C3×C4—201no—
698Dic3—22no—
699Dic3—41no—
700Dic3—102no—
701Dic3—102no—
702Dic3—201no—
703Dic3—201no—
704Dic3C4×C22⋊D514yes—
705C2×C5—122no—
706C2×C5C2×#87211yescharacteristic
707C2×C5#549011yescharacteristic
708C2×C5#553111yescharacteristic
709C2×C5#554011yescharacteristic
710C2×C5C4×D3×D411yescharacteristic
711C2×C5#554611yescharacteristic
712C2×C5#555211yescharacteristic
713D5—24no—
714C23—32no—
715C23—52no—
716C23—52no—
717C23—52no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23—101no—
725C23—101no—
726C23—101no—
727C23—101no—
728C23C22×D3×D511yescharacteristic
729D4—308no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—32no—
740C2×C4—32no—
741C2×C4—52no—
742C2×C4—68no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
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—152no—
758C2×C4—204no—
759C2×C4—308no—
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—301no—
770C2×C4—604no—
771C2×C4C4×D3×D512yes—
772C2×C4D3×C22⋊D512yes—
773C2×C3—104no—
774C2×C3D5×#11711yescharacteristic
775C2×C3#6585711yescharacteristic
776C2×C3#6586311yescharacteristic
777C2×C3#6586411yescharacteristic
778C2×C3C2×C4×C22⋊D511yescharacteristic
779C2×C3#6616311yescharacteristic
780C2×C3#6616511yescharacteristic
781D3—42no—
782C5#7346111yescharacteristic, complemented, Sylow
783C22—54no—
784C22—62no—
785C22—62no—
786C22—62no—
787C22—102no—
788C22—102no—
789C22—102no—
790C22—102no—
791C22—102no—
792C22—102no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22#9200111yescharacteristic
798C22C2×C4×D3×D511yescharacteristic
799C22D5×#23511yescharacteristic
800C22D5×#23511yescharacteristic
801C22D3×#70911yescharacteristic
802C22#9201711yescharacteristic
803C22C2×D3×C22⋊D511yescharacteristic
804C4—22no—
805C4—22no—
806C4—34no—
807C4—41no—
808C4—62no—
809C4—102no—
810C4—121no—
811C4—201no—
812C4—201no—
813C4—302no—
814C4—302no—
815C4—601no—
816C4—601no—
817C3#1061400311yescharacteristic, complemented, Sylow
818C2—104no—
819C2—122no—
820C2#1175251811yescharacteristic
821C2#1175256811yescharacteristic
822C2#1175257411yescharacteristic
823C2D5×#87211yescharacteristic
824C2#1175433811yescharacteristic
825C2C4×D3×C22⋊D511yescharacteristic
826C2#1175465011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2352
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×D5×Dic3⋊C4C2semidirect
4. #11751034C2semidirect
5. C3×C4×#685C2semidirect
8. #11748878C2semidirect
9. Dic3×#685C2semidirect
10. #11748847C2semidirect
11. #11748782C2semidirect
12. #11748721C2semidirect
13. #11748715C2semidirect
14. #11748652C2semidirect
15. Dic5×Dic3⋊C4C2semidirect
43. #91441C4semidirect
68. C4×#685D3semidirect
85. C2×C4×C5×D3C2×C4semidirect
103. #6712C2×C4semidirect
107. C5×Dic3⋊C4D4semidirect
117. (C2×D3)⋊Dic5C2×C4semidirect
120. Dic3×Dic5C2×C4semidirect
123. C2×#872D5semidirect
357. C2×C3×D5#117semidirect
400. C2×C4×D3C4×D5semidirect
417. Dic3⋊C4C22⋊D5semidirect
606. C2×D5#872semidirect
670. C3×C5#2352semidirect
782. C5#73461semidirect
817. C3#10614003semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8722
C2×#914412
C2×D5×Dic3⋊C42
#117510342
C3×C4×#6852
#117489062
#117489052
#117488782
Dic3×#6852
#117488472
#117487822
#117487212
#117487152
#117486522
Dic5×Dic3⋊C42
#106140033
#734615