Finite Group Databasebeta

← #14329061

Subgroups — #14329061

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4027C211yesmaximal, characteristic, complemented
2C2×#91565C211yesmaximal, characteristic
3C2×#91400C211yesmaximal, characteristic, complemented
4#11751045C211yesmaximal, characteristic, complemented
5C5×#4957C211yesmaximal, characteristic, complemented
6#11749492C211yesmaximal, characteristic, complemented
7#11749489C211yesmaximal, characteristic, complemented
8Dic5×#217C211yesmaximal, characteristic, complemented
9#11748916C211yesmaximal, characteristic, complemented
10#11748905C211yesmaximal, characteristic, complemented
11Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#11748801C211yesmaximal, characteristic, complemented
13#11748711C211yesmaximal, characteristic, complemented
14C4×#6665C211yesmaximal, characteristic, complemented
15Dic3×#683C211yesmaximal, characteristic, complemented
16#10608036—31nomaximal, Hall
17C22×C5×#67C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×#1201C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C4×C5×Dic3C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C3×#4027—24no—
37#91565C418yescomplemented
38C2×#6668C2211yescharacteristic
39C2×#6668C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48#91400—24no—
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#82341—51nomaximal, Hall
56C2×#4085—31no—
57C2×#4027D311yescharacteristic, complemented
58C2×#4023—31no—
59C5×#390—31no—
60#65509—31no—
61#65279—31no—
62#65261—31no—
63#65246—31no—
64#65246—31no—
65#65245—31no—
66#65233—31no—
67C22⋊C4×Dic5—31no—
68C22⋊C4×Dic5—31no—
69C4×#685—31no—
70C4×#683—31no—
71C24×C3×C5C2311yescharacteristic
72C23×C5×D3C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C2×C5×#67—41no—
81C2×C5×#67—41no—
82C2×C5×#67C2×C414yescomplemented
83C22×C5×Dic3C2311yescharacteristic
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C2×C3×C22⋊D5—22no—
87C2×C3×C22⋊D5—22no—
88C2×C3×C22⋊D5C2×C414yes—
89C22×C3×Dic5—22no—
90C22×C3×Dic5—22no—
91C22×C3×Dic5—41no—
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—41no—
98C2×#1201—41no—
99C2×#1201—41no—
100C2×#1201C2×C414yescomplemented
101C2×D3×Dic5—22no—
102C2×D3×Dic5—22no—
103C2×D3×Dic5C2×C414yescomplemented
104C3×C5×C22⋊C4—22no—
105#6719—41no—
106#6719C2×C414yescomplemented
107#6712—41no—
108C4×Dic15—22no—
109C5×#217—22no—
110C5×(C2×D3)⋊C4—22no—
111C5×(C2×D3)⋊C4—22no—
112C5×Dic3⋊C4—41no—
113C4×C5×Dic3—41no—
114C3×#685—22no—
115C3×#683D414yescomplemented
116C3×C4×Dic5—22no—
117#6668—22no—
118#6668C2×C414yescomplemented
119(C2×D3)⋊Dic5—22no—
120(C2×D3)⋊Dic5—22no—
121#6665—22no—
122#6665—41no—
123#6665C2×C414yescomplemented
124Dic3×Dic5—22no—
125Dic3×Dic5—22no—
126Dic3×Dic5—41no—
127C2×C3×C4×D4—51no—
128C2×#938—51no—
129C2×#892—51no—
130#5221—51no—
131#5213—51no—
132#5213—51no—
133C4×#217—51no—
134C4×#217—51no—
135Dic3×C4⋊C4—51no—
136#4957—51no—
137#4957D511yescharacteristic, complemented
138#4944—51no—
139#4944—51no—
140C4×(C2×D3)⋊C4—51no—
141#4928—51no—
142C22×C5×D4—31no—
143C22×C22⋊D5—31no—
144C22×C22⋊D5C2×D311yescharacteristic
145C23×Dic5—31no—
146C23×Dic5C2×D311yescharacteristic
147C22×C4×D5C2×D311yescharacteristic
148C2×C5×C4⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C5×C22⋊C4—31no—
152C2×C5×C22⋊C4C2×D311yescharacteristic
153C2×C42×C5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5—31no—
156C2×C22⋊Dic5—31no—
157C2×C22⋊Dic5—31no—
158#4085—38no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685C2×D311yescharacteristic
163C2×#683—31no—
164C2×#683—31no—
165C2×#683—31no—
166C2×#683C2×D311yescharacteristic
167C2×C4×Dic5—31no—
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5C2×D311yescharacteristic
172#4027—24no—
173#4023—64no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#2363—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C5×D3—21no—
195C22×C5×D3C22×C412yes—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5C22×C412yes—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5C2×D412yes—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15C22×C412yes—
220C2×Dic15C22×C412yes—
221C5×#67—44no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3C22×C412yes—
230C2×C5×Dic3#4112yes—
231C3×C22⋊D5—28no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—44no—
237C2×C3×Dic5C22×C412yes—
238C2×C3×Dic5C2×D412yes—
239C2×C3×Dic5C2×D412yes—
240C2×C3×Dic5#4112yes—
241C2×C3×Dic5#4112yes—
242C3×C4×D5—44no—
243#1201—44no—
244D3×Dic5—28no—
245C22×C3×D4—51no—
246C23×C3×C4—51no—
247C23×C3×C4—51no—
248C22×#67—51no—
249C22×#67C2×D511yescharacteristic
250C22×C4×D3—51no—
251C3×C4×D4—104no—
252C2×C3×C4⋊C4—51no—
253C2×C3×C22⋊C4—51no—
254C2×C3×C22⋊C4C2×D511yescharacteristic
255C2×C3×C42—51no—
256C2×#217—51no—
257C2×#217—51no—
258C2×#217—51no—
259C2×#217—51no—
260C2×#217—51no—
261C2×#217C2×D511yescharacteristic
262#938—58no—
263C2×(C2×D3)⋊C4—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4C2×D511yescharacteristic
266C2×(C2×D3)⋊C4C2×D511yescharacteristic
267C2×C4⋊Dic3—51no—
268C2×C4⋊Dic3—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4C2×D511yescharacteristic
271C2×C4×Dic3—51no—
272C2×C4×Dic3—51no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3C2×D511yescharacteristic
276#892—104no—
277C3⋊#95—51no—
278C3⋊#95—51no—
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C24×C5—31no—
284C24×C5C22×D311yescharacteristic
285C23×D5C22×D311yescharacteristic
286C2×C5×D4—34no—
287C2×C5×D4—121no—
288C2×C5×D4—121no—
289C22×C4×C5—31no—
290C22×C4×C5—31no—
291C22×C4×C5—31no—
292C22×C4×C5C22×D311yescharacteristic
293C22×C4×C5C22×D311yescharacteristic
294C2×C22⋊D5—22no—
295C2×C22⋊D5—22no—
296C2×C22⋊D5—34no—
297C2×C22⋊D5—121no—
298C2×C22⋊D5—121no—
299C2×C22⋊D5C4×D314yes—
300C22×Dic5—22no—
301C22×Dic5—22no—
302C22×Dic5—31no—
303C22×Dic5—31no—
304C22×Dic5—34no—
305C22×Dic5—31no—
306C22×Dic5—31no—
307C22×Dic5—41no—
308C22×Dic5—62no—
309C22×Dic5—62no—
310C22×Dic5C22×D311yescharacteristic
311C22×Dic5C22×D311yescharacteristic
312C22×Dic5C22×D311yescharacteristic
313C2×C4×D5—22no—
314C2×C4×D5—22no—
315C2×C4×D5—41no—
316C5×C4⋊C4—121no—
317C5×C22⋊C4—22no—
318C5×C22⋊C4—62no—
319C5×C22⋊C4—62no—
320C5×C22⋊C4—62no—
321C42×C5—121no—
322C22⋊Dic5—34no—
323C22⋊Dic5—62no—
324C22⋊Dic5—62no—
325C22⋊Dic5—121no—
326#685—22no—
327#685—34no—
328#685—62no—
329#685—121no—
330#683—34no—
331#683—62no—
332#683—121no—
333#683#6714yescomplemented
334C4×Dic5—22no—
335C4×Dic5—62no—
336C4×Dic5—62no—
337C4×Dic5—62no—
338C4×Dic5—121no—
339C2×#121—151no—
340C2×C4×D4—51no—
341C2×#117—151no—
342#390—31no—
343#390—151no—
344#390—151no—
345#389—151no—
346#388—151no—
347#388—151no—
348#386—151no—
349#386—151no—
350C4×C4⋊C4—151no—
351C4×C22⋊C4—151no—
352C4×C22⋊C4—151no—
353C4×C22⋊C4—151no—
354C22×C3×C5—22no—
355C22×C3×C5—22no—
356C22×C3×C5—22no—
357C22×C3×C5—41no—
358C22×C3×C5—41no—
359C22×C3×C5—41no—
360C22×C3×C5—41no—
361C22×C3×C5C23×C411yescharacteristic
362C22×C3×C5C22×D411yescharacteristic
363C22×C3×C5C2×#4111yescharacteristic
364C22×C3×C5C2×#4111yescharacteristic
365C22×C3×C5C2×#4111yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C5H(5,𝔽2)11yescharacteristic
368C2×C5×D3—22no—
369C2×C5×D3—22no—
370C2×C5×D3—22no—
371C2×C5×D3—41no—
372C2×C5×D3—41no—
373C2×C5×D3—41no—
374C2×C5×D3—41no—
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—41no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C3×C4×C5—22no—
383C3×C4×C5—41no—
384Dic15—22no—
385Dic15—22no—
386Dic15—41no—
387Dic15—41no—
388C3×Dic5—22no—
389C3×Dic5—22no—
390C3×Dic5C4×D414yes—
391C5×Dic3—22no—
392C5×Dic3—22no—
393C5×Dic3—41no—
394C24×C3—51no—
395C24×C3C22×D511yescharacteristic
396C23×D3C22×D511yescharacteristic
397C2×C3×D4—54no—
398C2×C3×D4—102no—
399C2×C3×D4—102no—
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4—51no—
403C22×C3×C4—102no—
404C22×C3×C4—102no—
405C22×C3×C4—102no—
406C22×C3×C4—102no—
407C22×C3×C4—201no—
408C22×C3×C4—201no—
409C22×C3×C4C22×D511yescharacteristic
410C22×C3×C4C22×D511yescharacteristic
411C2×#67—41no—
412C2×#67—41no—
413C2×#67—54no—
414C2×#67—201no—
415C2×#67—201no—
416C2×#67C4×D514yescomplemented
417C22×Dic3—51no—
418C22×Dic3—51no—
419C22×Dic3—51no—
420C22×Dic3—51no—
421C22×Dic3C22×D511yescharacteristic
422C22×Dic3C22×D511yescharacteristic
423C22×Dic3C22×D511yescharacteristic
424C2×C4×D3—54no—
425C2×C4×D3—102no—
426C2×C4×D3—102no—
427C3×C4⋊C4—54no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—102no—
430C3×C42—102no—
431#217—22no—
432#217—54no—
433#217—54no—
434#217—102no—
435#217—201no—
436#217—201no—
437(C2×D3)⋊C4—22no—
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—102no—
440(C2×D3)⋊C4—102no—
441C4⋊Dic3—54no—
442C4⋊Dic3—102no—
443Dic3⋊C4—41no—
444Dic3⋊C4—201no—
445C4×Dic3—41no—
446C4×Dic3—102no—
447C4×Dic3—102no—
448C4×Dic3—102no—
449C4×Dic3—201no—
450C23×C5—21no—
451C23×C5—21no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—32no—
457C23×C5—61no—
458C23×C5—61no—
459C23×C5—61no—
460C23×C5—61no—
461C23×C5—61no—
462C23×C5—61no—
463C23×C5C2×C4×D312yes—
464C23×C5C23×D311yescharacteristic
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5C2×C4×D312yes—
472C5×D4—124no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—32no—
479C2×C4×C5—32no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C2×C4×C5C2×#6712yes—
488C22⋊D5—28no—
489C22⋊D5—124no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—32no—
495C2×Dic5—32no—
496C2×Dic5—44no—
497C2×Dic5—61no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C2×Dic5—68no—
502C2×Dic5—61no—
503C2×Dic5—61no—
504C2×Dic5—61no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5—61no—
508C2×Dic5C2×C4×D312yes—
509C2×Dic5#23512yes—
510C2×Dic5#23712yes—
511C2×Dic5C2×#6712yes—
512C2×Dic5C2×#6712yes—
513C4×D5—44no—
514C22×D4—31no—
515C22×D4—51no—
516C22×D4—151no—
517C23×C4—51no—
518C23×C4—51no—
519C23×C4—151no—
520#121—158no—
521C4×D4—104no—
522#117—304no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—51no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—51no—
532C2×C22⋊C4—151no—
533C2×C22⋊C4—151no—
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4D3×D511yescharacteristic
540C2×C42—31no—
541C2×C42—51no—
542C2×C42—151no—
543C2×C42—151no—
544C2×C42—151no—
545C2×C42—151no—
546#95—151no—
547#95—151no—
548#95—151no—
549#95—151no—
550#95—151no—
551#95—151no—
552C2×C3×C5—42no—
553C2×C3×C5C2×C4×D411yescharacteristic
554C2×C3×C5C4×#4111yescharacteristic
555C2×C3×C5#51811yescharacteristic
556C2×C3×C5#54611yescharacteristic
557C2×C3×C5#55011yescharacteristic
558C2×C3×C5#55311yescharacteristic
559C2×C3×C5#55511yescharacteristic
560C3×D5—42no—
561C5×D3—42no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—52no—
569C23×C3—101no—
570C23×C3—101no—
571C23×C3—101no—
572C23×C3—101no—
573C23×C3—101no—
574C23×C3—101no—
575C23×C3C2×C4×D512yes—
576C23×C3C23×D511yescharacteristic
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3C2×C4×D512yes—
584C3×D4—108no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—52no—
591C2×C3×C4—52no—
592C2×C3×C4—52no—
593C2×C3×C4—52no—
594C2×C3×C4—52no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—204no—
600C2×C3×C4—204no—
601C2×C3×C4D4×D512yes—
602#67—44no—
603#67—204no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—52no—
612C2×Dic3—52no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3—101no—
621C2×Dic3—101no—
622C2×Dic3—101no—
623C2×Dic3C2×C4×D512yes—
624C2×Dic3#71112yes—
625C4×D3—108no—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5—41no—
632C22×C5—41no—
633C22×C5—62no—
634C22×C5—62no—
635C22×C5—62no—
636C22×C5—121no—
637C22×C5—121no—
638C22×C5—121no—
639C22×C5—121no—
640C22×C5C22×C4×D311yescharacteristic
641C22×C5C2×#23511yescharacteristic
642C22×C5C2×#23711yescharacteristic
643C22×C5#100411yescharacteristic
644C22×C5D3×#4111yescharacteristic
645C22×C5#100911yescharacteristic
646C22×C5C22×#6711yescharacteristic
647C2×D5—22no—
648C2×D5—22no—
649C2×D5—22no—
650C2×D5—41no—
651C2×D5—41no—
652C2×D5—41no—
653C2×D5—41no—
654C4×C5—22no—
655C4×C5—41no—
656C4×C5—62no—
657C4×C5—62no—
658C4×C5—121no—
659Dic5—22no—
660Dic5—22no—
661Dic5—62no—
662Dic5—62no—
663Dic5—121no—
664Dic5—121no—
665Dic5C4×#6714yes—
666C24—31no—
667C24—51no—
668C24C2×D3×D511yescharacteristic
669C2×D4—34no—
670C2×D4—54no—
671C2×D4—102no—
672C2×D4—102no—
673C2×D4—121no—
674C2×D4—121no—
675C2×D4—154no—
676C2×D4—601no—
677C2×D4—601no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—51no—
682C22×C4—51no—
683C22×C4—51no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—154no—
689C22×C4—151no—
690C22×C4—151no—
691C22×C4—151no—
692C22×C4—151no—
693C22×C4—201no—
694C22×C4—201no—
695C22×C4—302no—
696C22×C4—302no—
697C22×C4C2×D3×D511yescharacteristic
698C22×C4C2×D3×D511yescharacteristic
699C4⋊C4—54no—
700C4⋊C4—121no—
701C4⋊C4—154no—
702C4⋊C4—302no—
703C4⋊C4—601no—
704C22⋊C4—22no—
705C22⋊C4—62no—
706C22⋊C4—62no—
707C22⋊C4—62no—
708C22⋊C4—102no—
709C22⋊C4—154no—
710C22⋊C4—154no—
711C22⋊C4—302no—
712C22⋊C4—302no—
713C22⋊C4—302no—
714C22⋊C4—601no—
715C22⋊C4—601no—
716C42—102no—
717C42—121no—
718C42—302no—
719C42—302no—
720C42—302no—
721C42—601no—
722C3×C5#236311yescharacteristic, complemented, Hall
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—102no—
731C22×C3—102no—
732C22×C3—102no—
733C22×C3—201no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3—201no—
737C22×C3C22×C4×D511yescharacteristic
738C22×C3C2×D4×D511yescharacteristic
739C22×C3C2×#71111yescharacteristic
740C22×C3#414411yescharacteristic
741C22×C3#414411yescharacteristic
742C22×C3D5×#4111yescharacteristic
743C22×C3D5×#4111yescharacteristic
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C3×C4—22no—
752C3×C4—41no—
753C3×C4—54no—
754C3×C4—102no—
755C3×C4—102no—
756Dic3—22no—
757Dic3—22no—
758Dic3—41no—
759Dic3—102no—
760Dic3—102no—
761Dic3—201no—
762Dic3—201no—
763C2×C5—42no—
764C2×C5—122no—
765C2×C5C4×#23711yescharacteristic
766C2×C5#554511yescharacteristic
767C2×C5#555811yescharacteristic
768C2×C5#556311yescharacteristic
769C2×C5C2×C4×#6711yescharacteristic
770C2×C5#580611yescharacteristic
771C2×C5#583411yescharacteristic
772D5—42no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—32no—
780C23—52no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—61no—
785C23—61no—
786C23—61no—
787C23—101no—
788C23—101no—
789C23—101no—
790C23—101no—
791C23—101no—
792C23—101no—
793C23C4×D3×D512yes—
794C23C22×D3×D511yescharacteristic
795D4—108no—
796D4—124no—
797D4—604no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—52no—
806C2×C4—52no—
807C2×C4—52no—
808C2×C4—52no—
809C2×C4—52no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—101no—
818C2×C4—101no—
819C2×C4—101no—
820C2×C4—101no—
821C2×C4—152no—
822C2×C4—152no—
823C2×C4—204no—
824C2×C4—204no—
825C2×C4—308no—
826C2×C4—301no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—301no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—301no—
834C2×C4—301no—
835C2×C4—301no—
836C2×C4D5×#6712yes—
837C2×C3—42no—
838C2×C3—202no—
839C2×C3#6582011yescharacteristic
840C2×C3C4×#71111yescharacteristic
841C2×C3C4×D4×D511yescharacteristic
842C2×C3#6593511yescharacteristic
843C2×C3#6594411yescharacteristic
844C2×C3#6600411yescharacteristic
845C2×C3#6605211yescharacteristic
846D3—42no—
847C5#8234111yescharacteristic, complemented, Sylow
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—102no—
859C22—102no—
860C22—102no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—121no—
865C22—201no—
866C22—201no—
867C22—201no—
868C22—201no—
869C22C2×C4×D3×D511yescharacteristic
870C22D5×#23511yescharacteristic
871C22D5×#23711yescharacteristic
872C22D3×#71111yescharacteristic
873C22#9202511yescharacteristic
874C22#9202711yescharacteristic
875C22C2×D5×#6711yescharacteristic
876C4—22no—
877C4—41no—
878C4—54no—
879C4—62no—
880C4—62no—
881C4—102no—
882C4—102no—
883C4—121no—
884C4—302no—
885C4—302no—
886C4—601no—
887C4—601no—
888C3#1060803611yescharacteristic, complemented, Sylow
889C2—42no—
890C2—122no—
891C2—202no—
892C2#1175282011yescharacteristic
893C2#1175309111yescharacteristic
894C2#1175309211yescharacteristic
895C2#1175320211yescharacteristic
896C2C4×D5×#6711yescharacteristic
897C2#1175479111yescharacteristic
898C2#1175479911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91565C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2363
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
1. C2×C3×#4027C2semidirect
3. C2×#91400C2semidirect
4. #11751045C2semidirect
5. C5×#4957C2semidirect
6. #11749492C2semidirect
7. #11749489C2semidirect
8. Dic5×#217C2semidirect
9. #11748916C2semidirect
10. #11748905C2semidirect
11. Dic5×(C2×D3)⋊C4C2semidirect
12. #11748801C2semidirect
13. #11748711C2semidirect
14. C4×#6665C2semidirect
15. Dic3×#683C2semidirect
37. #91565C4semidirect
57. C2×#4027D3semidirect
82. C2×C5×#67C2×C4semidirect
100. C2×#1201C2×C4semidirect
103. C2×D3×Dic5C2×C4semidirect
106. #6719C2×C4semidirect
115. C3×#683D4semidirect
118. #6668C2×C4semidirect
123. #6665C2×C4semidirect
137. #4957D5semidirect
333. #683#67semidirect
416. C2×#67C4×D5semidirect
722. C3×C5#2363semidirect
847. C5#82341semidirect
888. C3#10608036semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40272
C2×#915652
C2×#914002
#117510452
C5×#49572
#117494922
#117494892
Dic5×#2172
#117489162
#117489052
Dic5×(C2×D3)⋊C42
#117488012
#117487112
C4×#66652
Dic3×#6832
#106080363
#823415