Finite Group Databasebeta

← #14330643

Subgroups — #14330643

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×#91577C211yesmaximal, characteristic
2#11751059C211yesmaximal, characteristic, complemented
3C5×#4957C211yesmaximal, characteristic, complemented
4C3×#65246C211yesmaximal, characteristic, complemented
5#11749501C211yesmaximal, characteristic, complemented
6#11749500C211yesmaximal, characteristic, complemented
7#11749483C211yesmaximal, characteristic, complemented
8#11748940C211yesmaximal, characteristic, complemented
9#11748940C211yesmaximal, characteristic, complemented
10#11748728C211yesmaximal, characteristic, complemented
11#11748727C211yesmaximal, characteristic, complemented
12#11748718C211yesmaximal, characteristic, complemented
13#11748714C211yesmaximal, characteristic, complemented
14#11748711C211yesmaximal, characteristic, complemented
15#11748705C211yesmaximal, characteristic, complemented
16#10608165—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C23×Dic15C2211yescharacteristic, complemented
20C22×C5×#67C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic, complemented
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
29C2×C4×C5×Dic3C2211yescharacteristic, complemented
30C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic, complemented
34C2×C3×C4×Dic5C2211yescharacteristic, complemented
35#91577C418yescomplemented
36C2×#6669C2211yescharacteristic, complemented
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49#90994C2211yescharacteristic, complemented
50#90994C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#76434—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#65246D311yescharacteristic, complemented
63#65244—31no—
64#65244—31no—
65#65233—31no—
66#65233—31no—
67#65229—31no—
68#65229—31no—
69C24×C3×C5C2311yescharacteristic
70C23×D15C2311yescharacteristic
71C23×C5×D3C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×D3×D5—41no—
74C22×D3×D5—41no—
75C22×D3×D5—41no—
76C22×D3×D5—41no—
77C22×D3×D5—41no—
78C22×D3×D5—41no—
79C22×D3×D5C2×C414yescomplemented
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—41no—
83C2×#1220—41no—
84C2×#1220C2×C414yes—
85C22×Dic15—41no—
86C22×Dic15—41no—
87C22×Dic15—41no—
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C2×C5×#67—41no—
92C2×C5×#67—41no—
93C2×C5×#67C2×C414yes—
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C2×C3×C22⋊D5—41no—
98C2×C3×C22⋊D5—41no—
99C2×C3×C22⋊D5C2×C414yes—
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C3×C5×C22⋊C4—41no—
104#6714—41no—
105#6714—41no—
106C5×#217—41no—
107C5×(C2×D3)⋊C4—41no—
108C5×(C2×D3)⋊C4—41no—
109C5×Dic3⋊C4—41no—
110C4×C5×Dic3—41no—
111C3×C22⋊Dic5—41no—
112C3×#685—41no—
113C3×#685—41no—
114C3×#683—41no—
115C3×C4×Dic5—41no—
116#6669—41no—
117#6667—41no—
118#6667—41no—
119#6667C2×C414yescomplemented
120(C2×D3)⋊Dic5—41no—
121(C2×D3)⋊Dic5—41no—
122(C2×D3)⋊Dic5C2×C414yescomplemented
123#6665—41no—
124#6665—41no—
125#6665C2×C414yescomplemented
126Dic3×Dic5—41no—
127C2×#937—51no—
128C3×#390—51no—
129#5220—51no—
130#4990—51no—
131#4990—51no—
132#4958—51no—
133#4958—51no—
134#4957—51no—
135#4957D511yescharacteristic, complemented
136#4955—51no—
137#4955—51no—
138#4944—51no—
139#4944—51no—
140#4940—51no—
141#4940—51no—
142C24×D5—31no—
143C22×C5×D4—31no—
144C22×C22⋊D5—31no—
145C22×C22⋊D5C2×D311yescharacteristic
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, complemented
152C2×C42×C5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5—31no—
156C2×C22⋊Dic5C2×D311yescharacteristic, complemented
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×#685C2×D311yescharacteristic
167C2×#685C2×D311yescharacteristic
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#3963—31no—
177#3963—31no—
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×D15C22×C412yes—
194C22×C5×D3—21no—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3C22×C412yes—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5C22×C412yes—
208C2×D3×D5—44no—
209C2×D3×D5—44no—
210C2×D3×D5—44no—
211C2×D3×D5—44no—
212C2×D3×D5—44no—
213C2×D3×D5—44no—
214C2×D3×D5—44no—
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—
221#1220—44no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—44no—
231C2×Dic15C22×C412yes—
232C5×#67—44no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3C22×C412yes—
242C3×C22⋊D5—44no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5C22×C412yes—
252C24×D3—51no—
253C22×C3×D4—51no—
254C22×#67—51no—
255C22×#67C2×D511yescharacteristic
256C23×Dic3—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4—51no—
261C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
262C2×C3×C42—51no—
263C2×#217—51no—
264C2×#217—51no—
265C2×#217—51no—
266C2×#217C2×D511yescharacteristic, complemented
267#937—58no—
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)⋊C4—51no—
276C2×(C2×D3)⋊C4C2×D511yescharacteristic
277C2×(C2×D3)⋊C4C2×D511yescharacteristic
278C2×Dic3⋊C4—51no—
279C2×Dic3⋊C4C2×D511yescharacteristic, complemented
280C2×C4×Dic3—51no—
281C2×C4×Dic3C2×D511yescharacteristic, complemented
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—34no—
292C23×D5—121no—
293C23×D5—121no—
294C23×D5—121no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5—121no—
298C23×D5C22×D311yescharacteristic
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—41no—
309C2×C22⋊D5—41no—
310C2×C22⋊D5—121no—
311C2×C22⋊D5—121no—
312C2×C22⋊D5C4×D314yes—
313C22×Dic5—31no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5—121no—
317C22×Dic5—121no—
318C22×Dic5—121no—
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—34no—
329C22⋊Dic5—41no—
330C22⋊Dic5—121no—
331C22⋊Dic5—121no—
332#685—34no—
333#685—34no—
334#685—41no—
335#685—41no—
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—51no—
349#390—151no—
350#388—151no—
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—41no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C2×C5×D3—22no—
383C2×C5×D3—22no—
384C2×C5×D3—22no—
385C2×C5×D3—41no—
386C2×C5×D3—41no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396D3×D5—416no—
397C3×C4×C5—41no—
398C3×C4×C5—41no—
399Dic15—22no—
400Dic15—41no—
401Dic15—41no—
402C3×Dic5—22no—
403C3×Dic5—41no—
404C3×Dic5—41no—
405C5×Dic3—22no—
406C5×Dic3—41no—
407C5×Dic3—41no—
408C24×C3—51no—
409C24×C3C22×D511yescharacteristic
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
419C2×C3×D4—54no—
420C2×C3×D4—201no—
421C2×C3×D4—201no—
422C22×C3×C4—51no—
423C22×C3×C4—51no—
424C22×C3×C4—51no—
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—41no—
428C2×#67—41no—
429C2×#67—54no—
430C2×#67—201no—
431C2×#67—201no—
432C2×#67C4×D514yes—
433C22×Dic3—51no—
434C22×Dic3—51no—
435C22×Dic3—51no—
436C22×Dic3—201no—
437C22×Dic3—201no—
438C22×Dic3—201no—
439C22×Dic3C22×D511yescharacteristic
440C22×Dic3C22×D511yescharacteristic
441C22×Dic3C22×D511yescharacteristic
442C3×C4⋊C4—201no—
443C3×C22⋊C4—41no—
444C3×C22⋊C4—201no—
445C3×C22⋊C4—201no—
446C3×C22⋊C4—201no—
447C3×C42—201no—
448#217—41no—
449#217—54no—
450#217—201no—
451#217—201no—
452(C2×D3)⋊C4—41no—
453(C2×D3)⋊C4—41no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—54no—
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—
462Dic3⋊C4—41no—
463Dic3⋊C4—201no—
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—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—32no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—61no—
494C22×D5—124no—
495C22×D5—124no—
496C22×D5—124no—
497C22×D5—124no—
498C22×D5—124no—
499C22×D5—124no—
500C22×D5—124no—
501C22×D5C2×C4×D312yes—
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—44no—
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—32no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—124no—
538C2×Dic5C2×C4×D312yes—
539C25—151no—
540C22×D4—31no—
541C22×D4—51no—
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—51no—
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, complemented
566C2×C42—31no—
567C2×C42—51no—
568C2×C42—151no—
569#95—151no—
570#95—151no—
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—
584C3×D5—42no—
585C5×D3—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—52no—
593C23×C3—101no—
594C23×C3—101no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3C2×C4×D512yes—
600C23×C3C23×D511yescharacteristic
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—52no—
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—
622C3×D4—204no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
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—
638#67—44no—
639#67—204no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—52no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—204no—
658C2×Dic3C2×C4×D512yes—
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#100411yescharacteristic
677C22×C5#100411yescharacteristic
678C22×C5#100911yescharacteristic
679C22×C5#100911yescharacteristic
680C2×D5—22no—
681C2×D5—22no—
682C2×D5—22no—
683C2×D5—41no—
684C2×D5—41no—
685C2×D5—41no—
686C2×D5—41no—
687C2×D5—62no—
688C2×D5—62no—
689C2×D5—62no—
690C2×D5—1216no—
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—41no—
702Dic5—41no—
703Dic5—62no—
704Dic5—121no—
705Dic5—121no—
706C24—31no—
707C24—51no—
708C24—154no—
709C24—151no—
710C24—601no—
711C24—601no—
712C24—601no—
713C24—601no—
714C24—601no—
715C24—601no—
716C24C2×D3×D511yescharacteristic
717C2×D4—34no—
718C2×D4—54no—
719C2×D4—121no—
720C2×D4—121no—
721C2×D4—154no—
722C2×D4—201no—
723C2×D4—201no—
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—151no—
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—121no—
745C22⋊C4—121no—
746C22⋊C4—121no—
747C22⋊C4—154no—
748C22⋊C4—154no—
749C22⋊C4—154no—
750C22⋊C4—201no—
751C22⋊C4—201no—
752C22⋊C4—201no—
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×C3—102no—
773C22×C3—102no—
774C22×C3—102no—
775C22×C3—201no—
776C22×C3—201no—
777C22×C3—201no—
778C22×C3—201no—
779C22×C3C22×C4×D511yescharacteristic
780C22×C3#414411yescharacteristic
781C22×C3#414411yescharacteristic
782C22×C3#414411yescharacteristic
783C22×C3#414411yescharacteristic
784C22×C3#414911yescharacteristic
785C22×C3#414911yescharacteristic
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—102no—
794C2×D3—102no—
795C2×D3—102no—
796C2×D3—2016no—
797C2×D3—201no—
798C2×D3—201no—
799C2×D3—201no—
800C2×D3—201no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—102no—
804C3×C4—201no—
805C3×C4—201no—
806Dic3—22no—
807Dic3—41no—
808Dic3—41no—
809Dic3—102no—
810Dic3—201no—
811Dic3—201no—
812C2×C5—42no—
813C2×C5—122no—
814C2×C5#548611yescharacteristic
815C2×C5#554511yescharacteristic
816C2×C5#554511yescharacteristic
817C2×C5#562011yescharacteristic
818C2×C5#562011yescharacteristic
819C2×C5#568311yescharacteristic
820C2×C5#572011yescharacteristic
821D5—42no—
822D5—122no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—32no—
830C23—52no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—101no—
838C23—101no—
839C23—101no—
840C23—101no—
841C23—101no—
842C23—101no—
843C23—152no—
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—204no—
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—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—101no—
879C2×C4—101no—
880C2×C4—101no—
881C2×C4—101no—
882C2×C4—101no—
883C2×C4—101no—
884C2×C4—101no—
885C2×C4—101no—
886C2×C4—152no—
887C2×C4—301no—
888C2×C4—301no—
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—202no—
898C2×C3#6582011yescharacteristic
899C2×C3#6587911yescharacteristic
900C2×C3#6587911yescharacteristic
901C2×C3#6595411yescharacteristic
902C2×C3#6595411yescharacteristic
903C2×C3#6601711yescharacteristic
904C2×C3#6605411yescharacteristic
905D3—42no—
906D3—202no—
907C5#7643411yescharacteristic, complemented, Sylow
908C22—22no—
909C22—22no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—102no—
919C22—102no—
920C22—102no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—201no—
926C22—201no—
927C22—201no—
928C22—201no—
929C22—302no—
930C22—302no—
931C22—302no—
932C22—6016no—
933C22—601no—
934C22—601no—
935C22—601no—
936C22—601no—
937C22C2×C4×D3×D511yescharacteristic
938C22#9201911yescharacteristic
939C22#9202511yescharacteristic
940C22#9202511yescharacteristic
941C22#9202611yescharacteristic
942C22#9202711yescharacteristic
943C22#9204911yescharacteristic
944C4—41no—
945C4—41no—
946C4—62no—
947C4—102no—
948C4—121no—
949C4—121no—
950C4—201no—
951C4—201no—
952C4—302no—
953C4—601no—
954C4—601no—
955C3#1060816511yescharacteristic, complemented, Sylow
956C2—42no—
957C2—122no—
958C2—202no—
959C2—602no—
960C2#1175320011yescharacteristic
961C2#1175320211yescharacteristic
962C2#1175330111yescharacteristic
963C2#1175330311yescharacteristic
964C2#1175462911yescharacteristic
965C2#1175507911yescharacteristic
966C2#1175508011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91577C2
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. #11751059C2semidirect
3. C5×#4957C2semidirect
4. C3×#65246C2semidirect
5. #11749501C2semidirect
6. #11749500C2semidirect
7. #11749483C2semidirect
8. #11748940C2semidirect
9. #11748940C2semidirect
10. #11748728C2semidirect
11. #11748727C2semidirect
12. #11748718C2semidirect
13. #11748714C2semidirect
14. #11748711C2semidirect
15. #11748705C2semidirect
19. C23×Dic15C22semidirect
22. C2×C3×C5×C22⋊C4C22semidirect
25. C2×C5×#217C22semidirect
28. C2×C5×Dic3⋊C4C22semidirect
29. C2×C4×C5×Dic3C22semidirect
30. C2×C3×C22⋊Dic5C22semidirect
33. C2×C3×#683C22semidirect
34. C2×C3×C4×Dic5C22semidirect
35. #91577C4semidirect
36. C2×#6669C22semidirect
46. C2×Dic3×Dic5C22semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. #90994C22semidirect
50. #90994C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
62. #65246D3semidirect
79. C22×D3×D5C2×C4semidirect
119. #6667C2×C4semidirect
122. (C2×D3)⋊Dic5C2×C4semidirect
125. #6665C2×C4semidirect
135. #4957D5semidirect
151. C2×C5×C22⋊C4C2×D3semidirect
156. C2×C22⋊Dic5C2×D3semidirect
169. C2×#683C2×D3semidirect
171. C2×C4×Dic5C2×D3semidirect
261. C2×C3×C22⋊C4C2×D5semidirect
266. C2×#217C2×D5semidirect
279. C2×Dic3⋊C4C2×D5semidirect
281. C2×C4×Dic3C2×D5semidirect
565. C2×C22⋊C4D3×D5semidirect
764. C3×C5#2375semidirect
907. C5#76434semidirect
955. C3#10608165semidirect

Maximal subgroups

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

subgroupindex
C2×#915772
#117510592
C5×#49572
C3×#652462
#117495012
#117495002
#117494832
#117489402
#117487282
#117487272
#117487182
#117487142
#117487112
#117487052
#106081653
#764345