Finite Group Databasebeta

← #14330909

Subgroups — #14330909

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91827C211yesmaximal, characteristic
2C5×#5220C211yesmaximal, characteristic, complemented
3C3×#65509C211yesmaximal, characteristic, complemented
4#11749512C211yesmaximal, characteristic, complemented
5#11749508C211yesmaximal, characteristic, complemented
6#11749498C211yesmaximal, characteristic, complemented
7#11749494C211yesmaximal, characteristic, complemented
8#11749483C211yesmaximal, characteristic, complemented
9#11749483C211yesmaximal, characteristic, complemented
10#11749481C211yesmaximal, characteristic, complemented
11#11749480C211yesmaximal, characteristic, complemented
12#11748863C211yesmaximal, characteristic, complemented
13#11748689C211yesmaximal, characteristic, complemented
14#11748688C211yesmaximal, characteristic, complemented
15#11748606C211yesmaximal, characteristic, complemented
16#10606614—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25#91827C418yescomplemented
26C2×C4⋊Dic15C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C2×C5×#217C2211yescharacteristic
29C2×C5×#217C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6669C2211yescharacteristic
35C2×#6669C2211yescharacteristic
36C2×#6669C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#74883—51nomaximal, Hall
54C2×#4084—31no—
55C5×#386—31no—
56#65509D311yescharacteristic, complemented
57#65502—31no—
58#65499—31no—
59#65247—31no—
60#65246—31no—
61#65246—31no—
62#65235—31no—
63#65234—31no—
64#65233—31no—
65#64956—31no—
66#64953—31no—
67#64943—31no—
68#64942—31no—
69C24×C3×C5C2311yescharacteristic
70C24×C3×C5C2311yescharacteristic
71C23×D15C2311yescharacteristic
72C2×C3×C5×D4—41no—
73C2×C3×C5×D4—41no—
74C2×C3×C5×D4C2×C414yes—
75C22×C3×C4×C5C2311yescharacteristic
76C2×#1220—41no—
77C2×#1220—41no—
78C2×#1220—41no—
79C2×#1220—41no—
80C2×#1220C2×C414yescomplemented
81C2×#1220C2×C414yescomplemented
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C2×C4×D15—41no—
86C2×C4×D15—41no—
87C2×C4×D15C2×C414yescomplemented
88C22×C5×Dic3—41no—
89C22×C5×Dic3—41no—
90C22×C5×Dic3—41no—
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C3×Dic5—41no—
96C22×C3×Dic5—41no—
97C22×C3×Dic5—41no—
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102#6719C2×C414yescomplemented
103#6719C2×C414yescomplemented
104C4⋊Dic15C2×C414yescomplemented
105C5×#217—41no—
106C5×#217—41no—
107C5×#217—41no—
108C3×C22⋊Dic5—41no—
109C3×C22⋊Dic5—41no—
110C3×C22⋊Dic5—41no—
111#6669—41no—
112#6669—41no—
113#6669—41no—
114#6669—41no—
115#6667—41no—
116#6667—41no—
117#6667—41no—
118#6667—41no—
119Dic3×Dic5—41no—
120Dic3×Dic5—41no—
121C2×#938—51no—
122C3×#386—51no—
123#5220D511yescharacteristic, complemented
124#5213—51no—
125#5210—51no—
126#4958—51no—
127#4957—51no—
128#4957—51no—
129#4946—51no—
130#4945—51no—
131#4944—51no—
132#4667—51no—
133#4664—51no—
134#4654—51no—
135#4653—51no—
136C22×C5×D4C2×D311yescharacteristic
137C23×C4×C5—31no—
138C22×C22⋊D5—31no—
139C22×C22⋊D5—31no—
140C23×Dic5C2×D311yescharacteristic
141C22×C4×D5—31no—
142C2×C5×C22⋊C4—31no—
143C2×C5×C22⋊C4—31no—
144C2×C5×C22⋊C4—31no—
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5—31no—
147C2×C22⋊Dic5C2×D311yescharacteristic
148C2×C22⋊Dic5C2×D311yescharacteristic
149C2×C22⋊Dic5C2×D311yescharacteristic
150#4084—38no—
151C2×#685—31no—
152C2×#685—31no—
153C2×#685—31no—
154C2×#685—31no—
155C2×C4⋊Dic5—31no—
156C2×#683—31no—
157C2×#683—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C5×#95—31no—
163C5×#95—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963C2×D311yescharacteristic
171#3963C2×D311yescharacteristic
172#2377—151noSylow
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
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×C5C22×C412yes—
187C23×C3×C5C2411yescharacteristic
188C22×D15—21no—
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15C22×C412yes—
195C3×C5×D4—44no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C22×C412yes—
199#1220—44no—
200#1220—44no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15C22×C412yes—
208C2×Dic15C22×C412yes—
209C2×Dic15C22×C412yes—
210C4×D15—44no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3—21no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—44no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—44no—
237C22×C3×D4C2×D511yescharacteristic
238C23×C3×C4—51no—
239C22×#67—51no—
240C22×#67—51no—
241C23×Dic3C2×D511yescharacteristic
242C22×C4×D3—51no—
243C2×C3×C22⋊C4—51no—
244C2×C3×C22⋊C4—51no—
245C2×C3×C22⋊C4—51no—
246C2×#217—51no—
247C2×#217—51no—
248C2×#217C2×D511yescharacteristic
249C2×#217C2×D511yescharacteristic
250C2×#217C2×D511yescharacteristic
251#938—58no—
252C2×(C2×D3)⋊C4—51no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×C4⋊Dic3—51no—
257C2×Dic3⋊C4—51no—
258C2×Dic3⋊C4—51no—
259C2×Dic3⋊C4—51no—
260C2×Dic3⋊C4—51no—
261C2×C4×Dic3—51no—
262C2×C4×Dic3—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⋊#95C2×D511yescharacteristic
272C3⋊#95C2×D511yescharacteristic
273C24×C5C22×D311yescharacteristic
274C24×C5C22×D311yescharacteristic
275C23×D5—31no—
276C2×C5×D4—41no—
277C2×C5×D4—41no—
278C2×C5×D4C4×D314yes—
279C22×C4×C5—31no—
280C22×C4×C5—31no—
281C22×C4×C5—31no—
282C22×C4×C5—31no—
283C22×C4×C5—121no—
284C22×C4×C5—121no—
285C22×C4×C5—121no—
286C22×C4×C5C22×D311yescharacteristic
287C2×C22⋊D5—34no—
288C2×C22⋊D5—34no—
289C2×C22⋊D5—121no—
290C2×C22⋊D5—121no—
291C2×C22⋊D5—121no—
292C2×C22⋊D5—121no—
293C22×Dic5—31no—
294C22×Dic5—31no—
295C22×Dic5—31no—
296C22×Dic5—41no—
297C22×Dic5—41no—
298C22×Dic5—41no—
299C22×Dic5C22×D311yescharacteristic
300C22×Dic5C22×D311yescharacteristic
301C22×Dic5C22×D311yescharacteristic
302C22×Dic5C22×D311yescharacteristic
303C2×C4×D5—34no—
304C2×C4×D5—121no—
305C2×C4×D5—121no—
306C5×C22⋊C4—121no—
307C5×C22⋊C4—121no—
308C5×C22⋊C4—121no—
309C22⋊Dic5—34no—
310C22⋊Dic5—34no—
311C22⋊Dic5—41no—
312C22⋊Dic5—41no—
313C22⋊Dic5—41no—
314#685—121no—
315#685—121no—
316#685—121no—
317#685—121no—
318C4⋊Dic5—34no—
319#683—121no—
320#683—121no—
321#683—121no—
322#683—121no—
323C4×Dic5—121no—
324C4×Dic5—121no—
325C2×#121—151no—
326#390—151no—
327#390—151no—
328#388—151no—
329#388—151no—
330#387—151no—
331#387—151no—
332#386—31no—
333#386—51no—
334#386—151no—
335#386—151no—
336#385—151no—
337#385—151no—
338#381—151no—
339#380—151no—
340C22×C3×C5—22no—
341C22×C3×C5—22no—
342C22×C3×C5—22no—
343C22×C3×C5—22no—
344C22×C3×C5—22no—
345C22×C3×C5—22no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5—41no—
352C22×C3×C5—41no—
353C22×C3×C5—41no—
354C22×C3×C5C23×C411yescharacteristic
355C22×C3×C5H(5,𝔽2)11yescharacteristic
356C22×C3×C5H(5,𝔽2)11yescharacteristic
357C22×C3×C5H(5,𝔽2)11yescharacteristic
358C22×C3×C5H(5,𝔽2)11yescharacteristic
359C22×C3×C5H(5,𝔽2)11yescharacteristic
360C22×C3×C52−1+411yescharacteristic
361C2×D15—22no—
362C2×D15—22no—
363C2×D15—22no—
364C2×D15—41no—
365C2×D15—41no—
366C2×D15—41no—
367C2×D15—41no—
368C3×C4×C5—22no—
369Dic15—22no—
370Dic15—22no—
371Dic15—22no—
372C3×Dic5—41no—
373C3×Dic5—41no—
374C3×Dic5—41no—
375C3×Dic5—41no—
376C5×Dic3—41no—
377C5×Dic3—41no—
378C5×Dic3—41no—
379C5×Dic3—41no—
380C24×C3C22×D511yescharacteristic
381C24×C3C22×D511yescharacteristic
382C23×D3—51no—
383C2×C3×D4—41no—
384C2×C3×D4—41no—
385C2×C3×D4C4×D514yes—
386C22×C3×C4—51no—
387C22×C3×C4—51no—
388C22×C3×C4—51no—
389C22×C3×C4—51no—
390C22×C3×C4—201no—
391C22×C3×C4—201no—
392C22×C3×C4—201no—
393C22×C3×C4C22×D511yescharacteristic
394C2×#67—54no—
395C2×#67—54no—
396C2×#67—201no—
397C2×#67—201no—
398C2×#67—201no—
399C2×#67—201no—
400C22×Dic3—41no—
401C22×Dic3—41no—
402C22×Dic3—41no—
403C22×Dic3—51no—
404C22×Dic3—51no—
405C22×Dic3—51no—
406C22×Dic3C22×D511yescharacteristic
407C22×Dic3C22×D511yescharacteristic
408C22×Dic3C22×D511yescharacteristic
409C22×Dic3C22×D511yescharacteristic
410C2×C4×D3—54no—
411C2×C4×D3—201no—
412C2×C4×D3—201no—
413C3×C22⋊C4—201no—
414C3×C22⋊C4—201no—
415C3×C22⋊C4—201no—
416#217—41no—
417#217—41no—
418#217—41no—
419#217—54no—
420#217—54no—
421(C2×D3)⋊C4—201no—
422(C2×D3)⋊C4—201no—
423(C2×D3)⋊C4—201no—
424(C2×D3)⋊C4—201no—
425C4⋊Dic3—54no—
426Dic3⋊C4—201no—
427Dic3⋊C4—201no—
428Dic3⋊C4—201no—
429Dic3⋊C4—201no—
430C4×Dic3—201no—
431C4×Dic3—201no—
432C23×C5—21no—
433C23×C5—21no—
434C23×C5—21no—
435C23×C5—21no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5—21no—
440C23×C5—21no—
441C23×C5—21no—
442C23×C5—21no—
443C23×C5—21no—
444C23×C5C2×C4×D312yes—
445C23×C5C2×C4×D312yes—
446C23×C5C23×D311yescharacteristic
447C22×D5—32no—
448C22×D5—61no—
449C22×D5—61no—
450C22×D5—61no—
451C22×D5—61no—
452C22×D5—61no—
453C22×D5—61no—
454C5×D4—44no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—61no—
458C2×C4×C5—61no—
459C2×C4×C5—61no—
460C2×C4×C5—61no—
461C2×C4×C5—61no—
462C2×C4×C5—61no—
463C2×C4×C5—61no—
464C2×C4×C5—61no—
465C2×C4×C5—61no—
466C2×C4×C5—61no—
467C2×C4×C5—61no—
468C2×C4×C5—61no—
469C2×C4×C5—124no—
470C2×C4×C5C2×C4×D312yes—
471C22⋊D5—124no—
472C22⋊D5—124no—
473C2×Dic5—21no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—21no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—21no—
481C2×Dic5—21no—
482C2×Dic5—21no—
483C2×Dic5—21no—
484C2×Dic5—21no—
485C2×Dic5—32no—
486C2×Dic5—32no—
487C2×Dic5—32no—
488C2×Dic5—44no—
489C2×Dic5—61no—
490C2×Dic5—61no—
491C2×Dic5—61no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494C2×Dic5—61no—
495C4×D5—124no—
496C22×D4—151no—
497C22×D4—151no—
498C22×D4D3×D511yescharacteristic
499C23×C4—31no—
500C23×C4—51no—
501C23×C4—151no—
502#121—158no—
503C2×C4⋊C4—151no—
504C2×C4⋊C4—151no—
505C2×C4⋊C4—151no—
506C2×C4⋊C4—151no—
507C2×C4⋊C4—151no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—51no—
512C2×C22⋊C4—51no—
513C2×C22⋊C4—51no—
514C2×C22⋊C4—151no—
515C2×C22⋊C4—151no—
516C2×C22⋊C4—151no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C42—151no—
521C2×C42—151no—
522#95—31no—
523#95—31no—
524#95—51no—
525#95—51no—
526#95—151no—
527#95—151no—
528#95—151no—
529#95—151no—
530#95—151no—
531#95—151no—
532C2×C3×C5—42no—
533C2×C3×C5—42no—
534C2×C3×C5#51811yescharacteristic
535C2×C3×C5#51811yescharacteristic
536C2×C3×C5#52011yescharacteristic
537C2×C3×C5#56011yescharacteristic
538C2×C3×C5#56011yescharacteristic
539C2×C3×C5#56211yescharacteristic
540C2×C3×C5#56211yescharacteristic
541D15—42no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3C2×C4×D512yes—
555C23×C3C2×C4×D512yes—
556C23×C3C23×D511yescharacteristic
557C22×D3—52no—
558C22×D3—101no—
559C22×D3—101no—
560C22×D3—101no—
561C22×D3—101no—
562C22×D3—101no—
563C22×D3—101no—
564C3×D4—44no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—101no—
575C2×C3×C4—101no—
576C2×C3×C4—101no—
577C2×C3×C4—101no—
578C2×C3×C4—101no—
579C2×C3×C4—204no—
580C2×C3×C4C2×C4×D512yes—
581#67—204no—
582#67—204no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—44no—
596C2×Dic3—52no—
597C2×Dic3—52no—
598C2×Dic3—52no—
599C2×Dic3—101no—
600C2×Dic3—101no—
601C2×Dic3—101no—
602C2×Dic3—101no—
603C2×Dic3—101no—
604C2×Dic3—101no—
605C4×D3—204no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—22no—
610C22×C5—22no—
611C22×C5—22no—
612C22×C5—41no—
613C22×C5—41no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—41no—
619C22×C5—41no—
620C22×C5C22×C4×D311yescharacteristic
621C22×C5#100411yescharacteristic
622C22×C5#100411yescharacteristic
623C22×C5#100411yescharacteristic
624C22×C5#100411yescharacteristic
625C22×C5#100911yescharacteristic
626C22×C5#101011yescharacteristic
627C2×D5—62no—
628C2×D5—62no—
629C2×D5—62no—
630C2×D5—121no—
631C2×D5—121no—
632C2×D5—121no—
633C2×D5—121no—
634C4×C5—22no—
635C4×C5—121no—
636C4×C5—121no—
637C4×C5—121no—
638C4×C5—121no—
639Dic5—41no—
640Dic5—41no—
641Dic5—41no—
642Dic5—41no—
643Dic5—62no—
644Dic5—62no—
645Dic5—62no—
646C24—151no—
647C24C2×D3×D511yescharacteristic
648C24C2×D3×D511yescharacteristic
649C2×D4—41no—
650C2×D4—41no—
651C2×D4—154no—
652C2×D4—154no—
653C2×D4—601no—
654C2×D4—601no—
655C2×D4—601no—
656C2×D4—601no—
657C2×D4#120014yes—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—51no—
665C22×C4—51no—
666C22×C4—121no—
667C22×C4—121no—
668C22×C4—121no—
669C22×C4—151no—
670C22×C4—151no—
671C22×C4—151no—
672C22×C4—154no—
673C22×C4—201no—
674C22×C4—201no—
675C22×C4—201no—
676C22×C4—601no—
677C22×C4—601no—
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—154no—
680C4⋊C4—601no—
681C4⋊C4—601no—
682C4⋊C4—601no—
683C4⋊C4—601no—
684C22⋊C4—121no—
685C22⋊C4—121no—
686C22⋊C4—121no—
687C22⋊C4—154no—
688C22⋊C4—154no—
689C22⋊C4—201no—
690C22⋊C4—201no—
691C22⋊C4—201no—
692C22⋊C4—601no—
693C22⋊C4—601no—
694C22⋊C4—601no—
695C22⋊C4—601no—
696C42—601no—
697C42—601no—
698C3×C5#237711yescharacteristic, complemented, Hall
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3C22×C4×D511yescharacteristic
714C22×C3#414411yescharacteristic
715C22×C3#414411yescharacteristic
716C22×C3#414411yescharacteristic
717C22×C3#414411yescharacteristic
718C22×C3#414911yescharacteristic
719C22×C3#415011yescharacteristic
720C2×D3—102no—
721C2×D3—102no—
722C2×D3—102no—
723C2×D3—201no—
724C2×D3—201no—
725C2×D3—201no—
726C2×D3—201no—
727C3×C4—22no—
728C3×C4—201no—
729C3×C4—201no—
730C3×C4—201no—
731C3×C4—201no—
732Dic3—41no—
733Dic3—41no—
734Dic3—41no—
735Dic3—41no—
736Dic3—102no—
737Dic3—102no—
738Dic3—102no—
739C2×C5—42no—
740C2×C5—42no—
741C2×C5#548611yescharacteristic
742C2×C5#554511yescharacteristic
743C2×C5#554611yescharacteristic
744C2×C5#559511yescharacteristic
745C2×C5#562011yescharacteristic
746C2×C5#562111yescharacteristic
747C2×C5#566711yescharacteristic
748D5—122no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—152no—
762C23—301no—
763C23—301no—
764C23—301no—
765C23—301no—
766C23—301no—
767C23—301no—
768C23C2×#120012yes—
769C23C2×#120012yes—
770C23C22×D3×D511yescharacteristic
771D4—44no—
772D4—604no—
773D4—604no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—101no—
789C2×C4—101no—
790C2×C4—101no—
791C2×C4—101no—
792C2×C4—101no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—101no—
796C2×C4—101no—
797C2×C4—101no—
798C2×C4—101no—
799C2×C4—101no—
800C2×C4—124no—
801C2×C4—152no—
802C2×C4—152no—
803C2×C4—152no—
804C2×C4—204no—
805C2×C4—301no—
806C2×C4—301no—
807C2×C4—301no—
808C2×C4—301no—
809C2×C4—301no—
810C2×C4—301no—
811C2×C4—604no—
812C2×C4C2×#120012yes—
813C2×C3—42no—
814C2×C3—42no—
815C2×C3#6582011yescharacteristic
816C2×C3#6587911yescharacteristic
817C2×C3#6588011yescharacteristic
818C2×C3#6592911yescharacteristic
819C2×C3#6595411yescharacteristic
820C2×C3#6595511yescharacteristic
821C2×C3#6600111yescharacteristic
822D3—202no—
823C5#7488311yescharacteristic, complemented, Sylow
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—302no—
839C22—302no—
840C22—302no—
841C22—601no—
842C22—601no—
843C22—601no—
844C22—601no—
845C22#9202011yescharacteristic
846C22#9202511yescharacteristic
847C22#9202611yescharacteristic
848C22#9202711yescharacteristic
849C22C22×#120011yescharacteristic
850C22#9204911yescharacteristic
851C22#9204911yescharacteristic
852C4—22no—
853C4—121no—
854C4—121no—
855C4—121no—
856C4—121no—
857C4—201no—
858C4—201no—
859C4—201no—
860C4—201no—
861C4—302no—
862C4—302no—
863C4—302no—
864C3#1060661411yescharacteristic, complemented, Sylow
865C2—42no—
866C2—42no—
867C2—602no—
868C2#1175491611yescharacteristic
869C2#1175492211yescharacteristic
870C2#1175498511yescharacteristic
871C2#1175498911yescharacteristic
872C2#1175499611yescharacteristic
873C2#1175500111yescharacteristic
874C2#1175541311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91827C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2377
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C5×#5220C2semidirect
3. C3×#65509C2semidirect
4. #11749512C2semidirect
5. #11749508C2semidirect
6. #11749498C2semidirect
7. #11749494C2semidirect
8. #11749483C2semidirect
9. #11749483C2semidirect
10. #11749481C2semidirect
11. #11749480C2semidirect
12. #11748863C2semidirect
13. #11748689C2semidirect
14. #11748688C2semidirect
15. #11748606C2semidirect
25. #91827C4semidirect
56. #65509D3semidirect
80. C2×#1220C2×C4semidirect
81. C2×#1220C2×C4semidirect
87. C2×C4×D15C2×C4semidirect
102. #6719C2×C4semidirect
103. #6719C2×C4semidirect
104. C4⋊Dic15C2×C4semidirect
123. #5220D5semidirect
698. C3×C5#2377semidirect
823. C5#74883semidirect
864. C3#10606614semidirect

Maximal subgroups

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

subgroupindex
C2×#918272
C5×#52202
C3×#655092
#117495122
#117495082
#117494982
#117494942
#117494832
#117494812
#117494802
#117488632
#117486892
#117486882
#117486062
#106066143
#748835