Finite Group Databasebeta

← #14330647

Subgroups — #14330647

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91573C211yesmaximal, characteristic
2#11751056C211yesmaximal, characteristic, complemented
3C5×#4957C211yesmaximal, characteristic, complemented
4C3×#65233C211yesmaximal, characteristic, complemented
5#11749519C211yesmaximal, characteristic, complemented
6#11749502C211yesmaximal, characteristic, complemented
7#11749485C211yesmaximal, characteristic, complemented
8#11748909C211yesmaximal, characteristic, complemented
9#11748908C211yesmaximal, characteristic, complemented
10#11748883C211yesmaximal, characteristic, complemented
11#11748883C211yesmaximal, characteristic, complemented
12#11748730C211yesmaximal, characteristic, complemented
13#11748728C211yesmaximal, characteristic, complemented
14#11748727C211yesmaximal, characteristic, complemented
15#11748669C211yesmaximal, characteristic, complemented
16#10608165—31nomaximal, Hall
17C24×D15C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C22×#1203C2211yescharacteristic
20C22×#1203C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic, complemented
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
31C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
32C2×C4×C5×Dic3C2211yescharacteristic, complemented
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic, complemented
36C2×C3×C4×Dic5C2211yescharacteristic, complemented
37#91573C418yescomplemented
38C2×#6668C2211yescharacteristic, complemented
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47C3×#3963C2211yescharacteristic, complemented
48C3×#3963C2211yescharacteristic, complemented
49#90994C2211yescharacteristic, complemented
50#90994C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#75840—51nomaximal, Hall
54C2×#4083—31no—
55C5×#390—31no—
56#65509—31no—
57#65279—31no—
58#65279—31no—
59#65247—31no—
60#65247—31no—
61#65246—31no—
62#65246—31no—
63#65244—31no—
64#65244—31no—
65#65233—31no—
66#65233D311yescharacteristic, complemented
67#65229—31no—
68#65229—31no—
69C24×C3×C5C2311yescharacteristic
70C23×D15—41no—
71C23×D15—41no—
72C23×D15—41no—
73C23×D15—41no—
74C23×D15—41no—
75C23×D15—41no—
76C23×D15C2×C414yescomplemented
77C23×D15C2311yescharacteristic
78C23×D15C2311yescharacteristic
79C23×C5×D3C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C2×C5×#67—41no—
85C2×C5×#67—41no—
86C2×C5×#67C2×C414yes—
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×#1203—41no—
95C2×#1203—41no—
96C2×#1203—41no—
97C2×#1203—41no—
98C2×#1203C2×C414yes—
99C2×#1203C2×C414yes—
100C2×D3×Dic5—41no—
101C2×D3×Dic5—41no—
102C2×D3×Dic5—41no—
103C3×C5×C22⋊C4—41no—
104#6719—41no—
105#6714—41no—
106#6714—41no—
107#6714—41no—
108#6714—41no—
109C5×#217—41no—
110C5×(C2×D3)⋊C4—41no—
111C5×(C2×D3)⋊C4—41no—
112C5×Dic3⋊C4—41no—
113C4×C5×Dic3—41no—
114C3×C22⋊Dic5—41no—
115C3×C22⋊Dic5C2×C414yescomplemented
116C3×#683—41no—
117C3×C4×Dic5—41no—
118#6668—41no—
119#6667—41no—
120#6667—41no—
121#6667—41no—
122#6667—41no—
123#6667C2×C414yescomplemented
124#6667C2×C414yescomplemented
125(C2×D3)⋊Dic5—41no—
126Dic3×Dic5—41no—
127C2×#882—51no—
128C3×#388—51no—
129#4990—51no—
130#4988—51no—
131#4957D511yescharacteristic, complemented
132#4956—51no—
133#4955—51no—
134#4955—51no—
135#4951—51no—
136#4940—51no—
137#4939—51no—
138#4670—51no—
139#4669—51no—
140#4665—51no—
141#4665—51no—
142C24×D5—31no—
143C22×C5×D4—31no—
144C22×C22⋊D5—31no—
145C22×C22⋊D5—31no—
146C23×Dic5—31no—
147C2×C5×C4⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C5×C22⋊C4C2×D311yescharacteristic
152C2×C42×C5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5C2×D311yescharacteristic
156C2×C22⋊Dic5C2×D311yescharacteristic
157#4083—38no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#683—31no—
169C2×#683C2×D311yescharacteristic, complemented
170C2×C4×Dic5—31no—
171C2×C4×Dic5C2×D311yescharacteristic, complemented
172#3963—31no—
173#3963—31no—
174#3963—31no—
175#3963—31no—
176#3963C2×D311yescharacteristic, complemented
177#3963C2×D311yescharacteristic, complemented
178#2375—151noSylow
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5C2411yescharacteristic
187C22×D15—21no—
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—44no—
200C22×D15—44no—
201C22×D15—44no—
202C22×D15—44no—
203C22×D15—44no—
204C22×D15—44no—
205C22×D15—44no—
206C22×D15C22×C412yes—
207C22×D15C22×C412yes—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3—21no—
213C22×C5×D3—21no—
214C22×C5×D3C22×C412yes—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C5×#67—44no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3C22×C412yes—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5C22×C412yes—
248C2×C3×Dic5C22×C412yes—
249#1203—44no—
250#1203—44no—
251D3×Dic5—44no—
252C24×D3—51no—
253C22×#67C2×D511yescharacteristic
254C22×D12—51no—
255C22×D12—51no—
256C22×C4×D3—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4C2×D511yescharacteristic
261C2×C3×C42—51no—
262C2×#217—51no—
263C2×#217C2×D511yescharacteristic
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
276C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
277C2×C4⋊Dic3—51no—
278C2×Dic3⋊C4C2×D511yescharacteristic, complemented
279C2×C4×Dic3—51no—
280C2×C4×Dic3C2×D511yescharacteristic, complemented
281#882—58no—
282C3×#95—51no—
283C3×#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C24×C5—31no—
289C24×C5C22×D311yescharacteristic
290C23×D5—31no—
291C23×D5—31no—
292C23×D5—34no—
293C23×D5—121no—
294C23×D5—121no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5—121no—
298C23×D5—121no—
299C2×C5×D4—34no—
300C2×C5×D4—121no—
301C2×C5×D4—121no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C2×C22⋊D5—34no—
308C2×C22⋊D5—34no—
309C2×C22⋊D5—121no—
310C2×C22⋊D5—121no—
311C2×C22⋊D5—121no—
312C2×C22⋊D5—121no—
313C22×Dic5—31no—
314C22×Dic5—31no—
315C22×Dic5—121no—
316C22×Dic5—121no—
317C22×Dic5—121no—
318C22×Dic5C22×D311yescharacteristic
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C5×C4⋊C4—121no—
323C5×C22⋊C4—41no—
324C5×C22⋊C4—121no—
325C5×C22⋊C4—121no—
326C5×C22⋊C4—121no—
327C42×C5—121no—
328C22⋊Dic5—41no—
329C22⋊Dic5—121no—
330C22⋊Dic5—121no—
331C22⋊Dic5C4×D314yescomplemented
332#685—34no—
333#685—34no—
334#685—121no—
335#685—121no—
336#685—121no—
337#685—121no—
338#685—121no—
339#685—121no—
340#685—121no—
341#685—121no—
342#683—41no—
343#683—121no—
344C4×Dic5—41no—
345C4×Dic5—121no—
346C2×#120—151no—
347#390—31no—
348#390—151no—
349#390—151no—
350#388—51no—
351#388—151no—
352#388—151no—
353#388—151no—
354#388—151no—
355#388—151no—
356#386—151no—
357#386—151no—
358#386—151no—
359#379—151no—
360#379—151no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5H(5,𝔽2)11yescharacteristic
370C22×C3×C5H(5,𝔽2)11yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C5H(5,𝔽2)11yescharacteristic
375C2×D15—22no—
376C2×D15—22no—
377C2×D15—22no—
378C2×D15—22no—
379C2×D15—22no—
380C2×D15—22no—
381C2×D15—416no—
382C2×D15—41no—
383C2×D15—41no—
384C2×D15—41no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×C5×D3—22no—
391C2×C5×D3—22no—
392C2×C5×D3—22no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C3×C4×C5—41no—
398C3×C4×C5—41no—
399Dic15—41no—
400Dic15—41no—
401C3×Dic5—22no—
402C3×Dic5—22no—
403C3×Dic5—41no—
404C3×Dic5—41no—
405C5×Dic3—22no—
406C5×Dic3—41no—
407C5×Dic3—41no—
408C24×C3C22×D511yescharacteristic
409C23×D3—51no—
410C23×D3—51no—
411C23×D3—54no—
412C23×D3—201no—
413C23×D3—201no—
414C23×D3—201no—
415C23×D3—201no—
416C23×D3—201no—
417C23×D3—201no—
418C23×D3C22×D511yescharacteristic
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4—51no—
423C22×C3×C4C22×D511yescharacteristic
424C22×C3×C4C22×D511yescharacteristic
425C2×#67—41no—
426C2×#67—41no—
427C2×#67C4×D514yes—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3C22×D511yescharacteristic
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433C2×D12—54no—
434C2×D12—54no—
435C2×D12—201no—
436C2×D12—201no—
437C2×D12—201no—
438C2×D12—201no—
439C2×C4×D3—201no—
440C2×C4×D3—201no—
441C2×C4×D3—201no—
442C3×C4⋊C4—201no—
443C3×C22⋊C4—41no—
444C3×C22⋊C4—54no—
445C3×C22⋊C4—201no—
446C3×C42—201no—
447#217—41no—
448#217—201no—
449(C2×D3)⋊C4—41no—
450(C2×D3)⋊C4—41no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—201no—
454(C2×D3)⋊C4—201no—
455(C2×D3)⋊C4—201no—
456(C2×D3)⋊C4—201no—
457(C2×D3)⋊C4—201no—
458(C2×D3)⋊C4—201no—
459(C2×D3)⋊C4—201no—
460(C2×D3)⋊C4—201no—
461(C2×D3)⋊C4—201no—
462C4⋊Dic3—201no—
463Dic3⋊C4—41no—
464C4×Dic3—41no—
465C4×Dic3—201no—
466C23×C5—21no—
467C23×C5—21no—
468C23×C5—21no—
469C23×C5—21no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5—32no—
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5—61no—
478C23×C5—61no—
479C23×C5C2×C4×D312yes—
480C23×C5C23×D311yescharacteristic
481C22×D5—32no—
482C22×D5—32no—
483C22×D5—61no—
484C22×D5—61no—
485C22×D5—61no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—61no—
494C22×D5—61no—
495C22×D5—124no—
496C22×D5—124no—
497C22×D5—124no—
498C22×D5—124no—
499C22×D5—124no—
500C22×D5—124no—
501C22×D5—124no—
502C5×D4—124no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—32no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—61no—
518C22⋊D5—124no—
519C22⋊D5—124no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—21no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—124no—
537C2×Dic5C2×C4×D312yes—
538C2×Dic5C2×C4×D312yes—
539C25—151no—
540C22×D4—31no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—151no—
544#120—158no—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—51no—
547C2×C4⋊C4—151no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—51no—
553C2×C22⋊C4—151no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4D3×D511yescharacteristic
566C2×C42—31no—
567C2×C42—51no—
568C2×C42—151no—
569#95—51no—
570#95—51no—
571#95—151no—
572#95—151no—
573#95—151no—
574#95—151no—
575C2×C3×C5—42no—
576C2×C3×C5#51811yescharacteristic
577C2×C3×C5#51811yescharacteristic
578C2×C3×C5#51811yescharacteristic
579C2×C3×C5#56011yescharacteristic
580C2×C3×C5#56011yescharacteristic
581C2×C3×C5#56011yescharacteristic
582C2×C3×C5H(3,𝔽4)11yescharacteristic
583D15—42no—
584D15—42no—
585C5×D3—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3C2×C4×D512yes—
593C23×C3C23×D511yescharacteristic
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—52no—
601C22×D3—52no—
602C22×D3—101no—
603C22×D3—101no—
604C22×D3—101no—
605C22×D3—101no—
606C22×D3—101no—
607C22×D3—101no—
608C22×D3—101no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C22×D3—101no—
614C22×D3—204no—
615C22×D3—204no—
616C22×D3—204no—
617C22×D3—204no—
618C22×D3—204no—
619C22×D3—204no—
620C22×D3—204no—
621C22×D3C2×C4×D512yes—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—52no—
629C2×C3×C4—52no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4—101no—
640#67—44no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3C2×C4×D512yes—
656D12—204no—
657D12—204no—
658C4×D3—204no—
659C22×C5—22no—
660C22×C5—22no—
661C22×C5—22no—
662C22×C5—41no—
663C22×C5—41no—
664C22×C5—41no—
665C22×C5—41no—
666C22×C5—62no—
667C22×C5—62no—
668C22×C5—62no—
669C22×C5—121no—
670C22×C5—121no—
671C22×C5—121no—
672C22×C5—121no—
673C22×C5C22×C4×D311yescharacteristic
674C22×C5#100411yescharacteristic
675C22×C5#100411yescharacteristic
676C22×C5#100911yescharacteristic
677C22×C5#100911yescharacteristic
678C22×C5#100911yescharacteristic
679C22×C5#100911yescharacteristic
680C2×D5—62no—
681C2×D5—62no—
682C2×D5—62no—
683C2×D5—62no—
684C2×D5—62no—
685C2×D5—62no—
686C2×D5—1216no—
687C2×D5—121no—
688C2×D5—121no—
689C2×D5—121no—
690C2×D5—121no—
691C2×D5—121no—
692C2×D5—121no—
693C2×D5—121no—
694C2×D5—121no—
695C4×C5—41no—
696C4×C5—41no—
697C4×C5—62no—
698C4×C5—121no—
699C4×C5—121no—
700Dic5—22no—
701Dic5—22no—
702Dic5—41no—
703Dic5—41no—
704Dic5—121no—
705Dic5—121no—
706C24—31no—
707C24—151no—
708C24—151no—
709C24—154no—
710C24—601no—
711C24—601no—
712C24—601no—
713C24—601no—
714C24—601no—
715C24—601no—
716C24C2×D3×D511yescharacteristic
717C2×D4—34no—
718C2×D4—121no—
719C2×D4—121no—
720C2×D4—154no—
721C2×D4—154no—
722C2×D4—601no—
723C2×D4—601no—
724C2×D4—601no—
725C2×D4—601no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—51no—
730C22×C4—51no—
731C22×C4—51no—
732C22×C4—51no—
733C22×C4—151no—
734C22×C4—151no—
735C22×C4—601no—
736C22×C4—601no—
737C22×C4—601no—
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C4⋊C4—121no—
741C4⋊C4—201no—
742C4⋊C4—601no—
743C22⋊C4—41no—
744C22⋊C4—54no—
745C22⋊C4—121no—
746C22⋊C4—121no—
747C22⋊C4—121no—
748C22⋊C4—154no—
749C22⋊C4—154no—
750C22⋊C4—201no—
751C22⋊C4—601no—
752C22⋊C4—601no—
753C22⋊C4—601no—
754C22⋊C4—601no—
755C22⋊C4—601no—
756C22⋊C4—601no—
757C22⋊C4—601no—
758C22⋊C4—601no—
759C22⋊C4—601no—
760C22⋊C4—601no—
761C42—121no—
762C42—201no—
763C42—601no—
764C3×C5#237511yescharacteristic, complemented, Hall
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3C22×C4×D511yescharacteristic
773C22×C3#414411yescharacteristic
774C22×C3#414411yescharacteristic
775C22×C3#414411yescharacteristic
776C22×C3#414411yescharacteristic
777C22×C3#414911yescharacteristic
778C22×C3#414911yescharacteristic
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—102no—
787C2×D3—102no—
788C2×D3—102no—
789C2×D3—102no—
790C2×D3—102no—
791C2×D3—102no—
792C2×D3—2016no—
793C2×D3—201no—
794C2×D3—201no—
795C2×D3—201no—
796C2×D3—201no—
797C2×D3—201no—
798C2×D3—201no—
799C2×D3—201no—
800C2×D3—201no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—102no—
804C3×C4—102no—
805C3×C4—201no—
806C3×C4—201no—
807Dic3—22no—
808Dic3—41no—
809Dic3—41no—
810Dic3—201no—
811Dic3—201no—
812C2×C5—42no—
813C2×C5—122no—
814C2×C5#552111yescharacteristic
815C2×C5#554511yescharacteristic
816C2×C5#554511yescharacteristic
817C2×C5#562011yescharacteristic
818C2×C5#566611yescharacteristic
819C2×C5#568311yescharacteristic
820C2×C5#571111yescharacteristic
821D5—122no—
822D5—122no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—32no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—152no—
837C23—152no—
838C23—301no—
839C23—301no—
840C23—301no—
841C23—301no—
842C23—301no—
843C23—301no—
844C23—301no—
845C23—301no—
846C23—301no—
847C23—301no—
848C23—301no—
849C23—301no—
850C23—604no—
851C23—604no—
852C23—604no—
853C23—604no—
854C23—604no—
855C23—604no—
856C23—604no—
857C23C4×D3×D512yes—
858C23C22×D3×D511yescharacteristic
859D4—124no—
860D4—604no—
861D4—604no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—32no—
869C2×C4—52no—
870C2×C4—52no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—101no—
880C2×C4—101no—
881C2×C4—101no—
882C2×C4—101no—
883C2×C4—101no—
884C2×C4—101no—
885C2×C4—101no—
886C2×C4—101no—
887C2×C4—101no—
888C2×C4—101no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—301no—
894C2×C4—301no—
895C2×C4—604no—
896C2×C3—42no—
897C2×C3#6582011yescharacteristic
898C2×C3#6587911yescharacteristic
899C2×C3#6587911yescharacteristic
900C2×C3#6595411yescharacteristic
901C2×C3#6595411yescharacteristic
902C2×C3#6601711yescharacteristic
903C2×C3#6605411yescharacteristic
904D3—42no—
905D3—202no—
906D3—202no—
907C5#7584011yescharacteristic, complemented, Sylow
908C22—22no—
909C22—22no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—302no—
923C22—302no—
924C22—302no—
925C22—302no—
926C22—302no—
927C22—302no—
928C22—6016no—
929C22—601no—
930C22—601no—
931C22—601no—
932C22—601no—
933C22—601no—
934C22—601no—
935C22—601no—
936C22—601no—
937C22C2×C4×D3×D511yescharacteristic
938C22#9201911yescharacteristic
939C22#9202611yescharacteristic
940C22#9202711yescharacteristic
941C22#9202711yescharacteristic
942C22#9202711yescharacteristic
943C22#9204911yescharacteristic
944C4—41no—
945C4—41no—
946C4—62no—
947C4—102no—
948C4—102no—
949C4—121no—
950C4—121no—
951C4—201no—
952C4—201no—
953C4—601no—
954C4—601no—
955C3#1060816511yescharacteristic, complemented, Sylow
956C2—42no—
957C2—122no—
958C2—602no—
959C2—602no—
960C2#1175306711yescharacteristic
961C2#1175318611yescharacteristic
962C2#1175320411yescharacteristic
963C2#1175330311yescharacteristic
964C2#1175462911yescharacteristic
965C2#1175499511yescharacteristic
966C2#1175500211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91573C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2375
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
2. #11751056C2semidirect
3. C5×#4957C2semidirect
4. C3×#65233C2semidirect
5. #11749519C2semidirect
6. #11749502C2semidirect
7. #11749485C2semidirect
8. #11748909C2semidirect
9. #11748908C2semidirect
10. #11748883C2semidirect
11. #11748883C2semidirect
12. #11748730C2semidirect
13. #11748728C2semidirect
14. #11748727C2semidirect
15. #11748669C2semidirect
21. C22×D3×Dic5C22semidirect
29. C2×C5×(C2×D3)⋊C4C22semidirect
30. C2×C5×(C2×D3)⋊C4C22semidirect
31. C2×C5×Dic3⋊C4C22semidirect
32. C2×C4×C5×Dic3C22semidirect
35. C2×C3×#683C22semidirect
36. C2×C3×C4×Dic5C22semidirect
37. #91573C4semidirect
38. C2×#6668C22semidirect
45. C2×(C2×D3)⋊Dic5C22semidirect
46. C2×Dic3×Dic5C22semidirect
47. C3×#3963C22semidirect
48. C3×#3963C22semidirect
49. #90994C22semidirect
50. #90994C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
66. #65233D3semidirect
76. C23×D15C2×C4semidirect
115. C3×C22⋊Dic5C2×C4semidirect
123. #6667C2×C4semidirect
124. #6667C2×C4semidirect
131. #4957D5semidirect
169. C2×#683C2×D3semidirect
171. C2×C4×Dic5C2×D3semidirect
176. #3963C2×D3semidirect
177. #3963C2×D3semidirect
275. C2×(C2×D3)⋊C4C2×D5semidirect
276. C2×(C2×D3)⋊C4C2×D5semidirect
278. C2×Dic3⋊C4C2×D5semidirect
280. C2×C4×Dic3C2×D5semidirect
331. C22⋊Dic5C4×D3semidirect
764. C3×C5#2375semidirect
907. C5#75840semidirect
955. C3#10608165semidirect

Maximal subgroups

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

subgroupindex
C2×#915732
#117510562
C5×#49572
C3×#652332
#117495192
#117495022
#117494852
#117489092
#117489082
#117488832
#117487302
#117487282
#117487272
#117486692
#106081653
#758405