Finite Group Databasebeta

← #14330645

Subgroups — #14330645

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#11751314C211yesmaximal, characteristic, complemented
3C5×#5213C211yesmaximal, characteristic, complemented
4C3×#65502C211yesmaximal, characteristic, complemented
5#11749489C211yesmaximal, characteristic, complemented
6#11749483C211yesmaximal, characteristic, complemented
7#11749482C211yesmaximal, characteristic, complemented
8#11748940C211yesmaximal, characteristic, complemented
9#11748940C211yesmaximal, characteristic, complemented
10#11748723C211yesmaximal, characteristic, complemented
11#11748721C211yesmaximal, characteristic, complemented
12#11748712C211yesmaximal, characteristic, complemented
13#11748708C211yesmaximal, characteristic, complemented
14#11748671C211yesmaximal, characteristic, complemented
15#11748668C211yesmaximal, characteristic, complemented
16#10606613—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic, complemented
19C22×#1220C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C2×#6719C2211yescharacteristic, complemented
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic, complemented
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31#91577C418yescomplemented
32C2×Dic3⋊Dic5C2211yescharacteristic, complemented
33C2×#6669C2211yescharacteristic, complemented
34C2×#6668C2211yescharacteristic, complemented
35C2×#6667C2211yescharacteristic
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45C2×Dic3×Dic5C2211yescharacteristic, complemented
46C2×Dic3×Dic5C2211yescharacteristic, complemented
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53#74882—51nomaximal, Hall
54C2×#4083—31no—
55C5×#386—31no—
56#65510—31no—
57#65502—31no—
58#65502D311yescharacteristic, complemented
59#65246—31no—
60#65246—31no—
61#65244—31no—
62#65244—31no—
63#65234—31no—
64#65234—31no—
65#64959—31no—
66#64959—31no—
67#64958—31no—
68#64958—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×C5—41no—
81C22×C3×C4×C5—41no—
82C22×C3×C4×C5—41no—
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C2×#1220—41no—
86C2×#1220—41no—
87C2×#1220C2×C414yes—
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
103#6719—41no—
104#6714—41no—
105#6714—41no—
106C5×#217—41no—
107C5×(C2×D3)⋊C4—41no—
108C5×(C2×D3)⋊C4—41no—
109C3×C22⋊Dic5—41no—
110C3×#685—41no—
111C3×#685—41no—
112Dic3⋊Dic5—41no—
113#6669—41no—
114#6668—41no—
115#6667—41no—
116#6667—41no—
117#6667C2×C414yescomplemented
118(C2×D3)⋊Dic5—41no—
119(C2×D3)⋊Dic5—41no—
120(C2×D3)⋊Dic5C2×C414yescomplemented
121#6665—41no—
122#6665—41no—
123#6665C2×C414yescomplemented
124Dic3×Dic5—41no—
125Dic3×Dic5—41no—
126Dic3×Dic5—41no—
127C2×#937—51no—
128C3×#386—51no—
129#5221—51no—
130#5213—51no—
131#5213D511yescharacteristic, complemented
132#4957—51no—
133#4957—51no—
134#4955—51no—
135#4955—51no—
136#4945—51no—
137#4945—51no—
138#4670—51no—
139#4670—51no—
140#4669—51no—
141#4669—51no—
142C24×D5—31no—
143C22×C5×D4—31no—
144C23×C4×C5C2×D311yescharacteristic, complemented
145C22×C22⋊D5—31no—
146C22×C22⋊D5C2×D311yescharacteristic
147C2×C5×C22⋊C4—31no—
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C22⋊Dic5—31no—
151C2×C22⋊Dic5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5C2×D311yescharacteristic, complemented
155#4083—38no—
156C2×#685—31no—
157C2×#685—31no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685C2×D311yescharacteristic
165C2×#685C2×D311yescharacteristic
166C2×C4⋊Dic5—31no—
167C2×#683—31no—
168C2×#683—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5—31no—
172C5×#95—31no—
173C5×#95—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×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—
221C2×C3×C4×C5—44no—
222#1220—44no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
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—
254C23×C3×C4C2×D511yescharacteristic, complemented
255C22×#67—51no—
256C22×#67C2×D511yescharacteristic
257C2×C3×C22⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×#217—51no—
261C2×#217—51no—
262C2×#217—51no—
263C2×#217—51no—
264C2×#217C2×D511yescharacteristic, complemented
265#937—58no—
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)⋊C4C2×D511yescharacteristic
275C2×(C2×D3)⋊C4C2×D511yescharacteristic
276C2×C4⋊Dic3—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C3×#95—51no—
283C3×#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95C2×D511yescharacteristic, complemented
287C3⋊#95C2×D511yescharacteristic, complemented
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×C5—41no—
306C22×C4×C5—41no—
307C22×C4×C5—41no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C2×C22⋊D5—34no—
311C2×C22⋊D5—41no—
312C2×C22⋊D5—41no—
313C2×C22⋊D5—121no—
314C2×C22⋊D5—121no—
315C2×C22⋊D5C4×D314yes—
316C22×Dic5—31no—
317C22×Dic5—31no—
318C22×Dic5—31no—
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C5×C22⋊C4—121no—
323C5×C22⋊C4—121no—
324C5×C22⋊C4—121no—
325C22⋊Dic5—34no—
326C22⋊Dic5—41no—
327C22⋊Dic5—121no—
328C22⋊Dic5—121no—
329C22⋊Dic5—121no—
330#685—34no—
331#685—34no—
332#685—41no—
333#685—41no—
334#685—121no—
335#685—121no—
336#685—121no—
337#685—121no—
338#685—121no—
339#685—121no—
340C4⋊Dic5—121no—
341#683—121no—
342#683—121no—
343C4×Dic5—121no—
344C4×Dic5—121no—
345C4×Dic5—121no—
346C2×#120—151no—
347#390—151no—
348#390—151no—
349#390—151no—
350#388—151no—
351#388—151no—
352#388—151no—
353#388—151no—
354#388—151no—
355#388—151no—
356#386—31no—
357#386—51no—
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—41no—
423C22×C3×C4—41no—
424C22×C3×C4—41no—
425C22×C3×C4—51no—
426C22×C3×C4—51no—
427C22×C3×C4—51no—
428C22×C3×C4C22×D511yescharacteristic
429C22×C3×C4C22×D511yescharacteristic
430C2×#67—41no—
431C2×#67—41no—
432C2×#67—54no—
433C2×#67—201no—
434C2×#67—201no—
435C2×#67C4×D514yes—
436C22×Dic3—51no—
437C22×Dic3—51no—
438C22×Dic3—51no—
439C22×Dic3C22×D511yescharacteristic
440C22×Dic3C22×D511yescharacteristic
441C22×Dic3C22×D511yescharacteristic
442C3×C22⋊C4—201no—
443C3×C22⋊C4—201no—
444C3×C22⋊C4—201no—
445#217—41no—
446#217—54no—
447#217—201no—
448#217—201no—
449#217—201no—
450(C2×D3)⋊C4—41no—
451(C2×D3)⋊C4—41no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
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—
460C4⋊Dic3—201no—
461Dic3⋊C4—201no—
462Dic3⋊C4—201no—
463C4×Dic3—201no—
464C4×Dic3—201no—
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—44no—
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—
518C2×C4×C5—61no—
519C22⋊D5—44no—
520C22⋊D5—124no—
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—32no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5C2×C4×D312yes—
539C25—151no—
540C22×D4—31no—
541C22×D4—51no—
542C22×D4—151no—
543C23×C4D3×D511yescharacteristic, complemented
544#120—158no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4—151no—
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⋊C4—151no—
566C2×C42—151no—
567C2×C42—151no—
568C2×C42—151no—
569#95—31no—
570#95—31no—
571#95—51no—
572#95—51no—
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—44no—
630C2×C3×C4—52no—
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—
639#67—44no—
640#67—204no—
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—52no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
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—41no—
730C22×C4—41no—
731C22×C4—41no—
732C22×C4—51no—
733C22×C4—51no—
734C22×C4—51no—
735C22×C4—151no—
736C22×C4—151no—
737C22×C4—151no—
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C4⋊C4—601no—
741C4⋊C4—601no—
742C4⋊C4—601no—
743C22⋊C4—121no—
744C22⋊C4—121no—
745C22⋊C4—121no—
746C22⋊C4—154no—
747C22⋊C4—154no—
748C22⋊C4—154no—
749C22⋊C4—201no—
750C22⋊C4—201no—
751C22⋊C4—201no—
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—601no—
762C42—601no—
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#559411yescharacteristic
818C2×C5#562011yescharacteristic
819C2×C5#562011yescharacteristic
820C2×C5#566611yescharacteristic
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—44no—
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—152no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—301no—
894C2×C4—301no—
895C2×C4—301no—
896C2×C3—42no—
897C2×C3—202no—
898C2×C3#6582011yescharacteristic
899C2×C3#6587911yescharacteristic
900C2×C3#6587911yescharacteristic
901C2×C3#6592811yescharacteristic
902C2×C3#6595411yescharacteristic
903C2×C3#6595411yescharacteristic
904C2×C3#6600011yescharacteristic
905D3—42no—
906D3—202no—
907C5#7488211yescharacteristic, 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#9201711yescharacteristic
939C22#9201811yescharacteristic
940C22#9201911yescharacteristic
941C22#9204911yescharacteristic
942C22#9204911yescharacteristic
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#1060661311yescharacteristic, complemented, Sylow
956C2—42no—
957C2—122no—
958C2—202no—
959C2—602no—
960C2#1175462511yescharacteristic
961C2#1175462711yescharacteristic
962C2#1175462911yescharacteristic
963C2#1175468411yescharacteristic
964C2#1175468511yescharacteristic
965C2#1175468611yescharacteristic
966C2#1175544311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91577C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#2375
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751314C2semidirect
3. C5×#5213C2semidirect
4. C3×#65502C2semidirect
5. #11749489C2semidirect
6. #11749483C2semidirect
7. #11749482C2semidirect
8. #11748940C2semidirect
9. #11748940C2semidirect
10. #11748723C2semidirect
11. #11748721C2semidirect
12. #11748712C2semidirect
13. #11748708C2semidirect
14. #11748671C2semidirect
15. #11748668C2semidirect
18. C23×C3×C4×C5C22semidirect
22. C2×#6719C22semidirect
25. C2×C5×#217C22semidirect
28. C2×C3×C22⋊Dic5C22semidirect
31. #91577C4semidirect
32. C2×Dic3⋊Dic5C22semidirect
33. C2×#6669C22semidirect
34. C2×#6668C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. C2×Dic3×Dic5C22semidirect
46. C2×Dic3×Dic5C22semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
58. #65502D3semidirect
79. C22×D3×D5C2×C4semidirect
117. #6667C2×C4semidirect
120. (C2×D3)⋊Dic5C2×C4semidirect
123. #6665C2×C4semidirect
131. #5213D5semidirect
144. C23×C4×C5C2×D3semidirect
154. C2×C22⋊Dic5C2×D3semidirect
176. #3963C2×D3semidirect
177. #3963C2×D3semidirect
254. C23×C3×C4C2×D5semidirect
264. C2×#217C2×D5semidirect
286. C3⋊#95C2×D5semidirect
287. C3⋊#95C2×D5semidirect
543. C23×C4D3×D5semidirect
764. C3×C5#2375semidirect
907. C5#74882semidirect
955. C3#10606613semidirect

Maximal subgroups

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

subgroupindex
C2×#915772
#117513142
C5×#52132
C3×#655022
#117494892
#117494832
#117494822
#117489402
#117487232
#117487212
#117487122
#117487082
#117486712
#117486682
#106066133
#748825