Finite Group Databasebeta

← #14324367

Subgroups — #14324367

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91829C211yesmaximal, characteristic
2C2×C4×#1220C211yesmaximal, characteristic, complemented
3C2×#91770C211yesmaximal, characteristic, complemented
4C3×C5×#386C211yesmaximal, characteristic, complemented
5#11751321C211yesmaximal, characteristic, complemented
6#11751314C211yesmaximal, characteristic, complemented
7#11751059C211yesmaximal, characteristic, complemented
8#11751058C211yesmaximal, characteristic, complemented
9#11751058C211yesmaximal, characteristic, complemented
10#11751057C211yesmaximal, characteristic, complemented
11#11751057C211yesmaximal, characteristic, complemented
12#11750766C211yesmaximal, characteristic, complemented
13#11750766C211yesmaximal, characteristic, complemented
14#11750751C211yesmaximal, characteristic, complemented
15#11750749C211yesmaximal, characteristic, complemented
16#10606398—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic
23C23×Dic15C2211yescharacteristic
24C22×D60C2211yescharacteristic
25C22×C4×D15C2211yescharacteristic
26C22×C4×D15C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×#6719C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33#91829C418yescomplemented
34C4×#1220—24no—
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic
37C2×#6714C2211yescharacteristic
38C2×#6714C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6714C2211yescharacteristic
41C2×#6712C2211yescharacteristic
42C2×#6712C2211yescharacteristic
43C2×C4×Dic15C2211yescharacteristic
44C2×C4×Dic15C2211yescharacteristic
45C2×C4×Dic15C2211yescharacteristic
46#91770—24no—
47C3×C5×#95C2211yescharacteristic
48C3×C5×#95C2211yescharacteristic
49#91115C2211yescharacteristic
50#91115C2211yescharacteristic
51#91115C2211yescharacteristic
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54#91115C2211yescharacteristic
55#74667—51nomaximal, Hall
56C2×#4086—31no—
57C2×C4×C22⋊D5—31no—
58C2×#4027—31no—
59C5×#386D311yescharacteristic, complemented
60#65509—31no—
61#65502—31no—
62#65247—31no—
63#65246—31no—
64#65246—31no—
65#65245—31no—
66#65245—31no—
67#64954—31no—
68#64954—31no—
69#64939—31no—
70#64937—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×D15C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C2×C3×C5×D4—41no—
76C2×C3×C5×D4—41no—
77C2×C3×C5×D4C2×C414yescomplemented
78C22×C3×C4×C5—22no—
79C22×C3×C4×C5—41no—
80C22×C3×C4×C5—41no—
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—22no—
87C2×#1220—22no—
88C2×#1220—22no—
89C2×#1220—22no—
90C2×#1220—41no—
91C2×#1220—41no—
92C2×#1220—41no—
93C2×#1220—41no—
94C2×#1220C2×C414yescomplemented
95C2×#1220C2×C414yescomplemented
96C2×#1220C2×C414yescomplemented
97C2×#1220C2×C414yescomplemented
98C22×Dic15—22no—
99C22×Dic15—41no—
100C22×Dic15—41no—
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2311yescharacteristic
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C2×D60—41no—
108C2×D60—41no—
109C2×D60C2×C414yescomplemented
110C2×C4×D15—22no—
111C2×C4×D15—22no—
112C2×C4×D15—41no—
113C2×C4×D15—41no—
114C2×C4×D15—41no—
115C2×C4×D15—41no—
116C3×C5×C22⋊C4—22no—
117C3×C5×C22⋊C4—41no—
118C3×C5×C22⋊C4—41no—
119#6719—22no—
120#6719—41no—
121#6719—41no—
122#6714—22no—
123#6714—22no—
124#6714—41no—
125#6714—41no—
126#6714—41no—
127#6714—41no—
128#6712—22no—
129#6712—22no—
130C4×Dic15—22no—
131C4×Dic15C2×C414yescomplemented
132C4×Dic15D414yescomplemented
133C2×#940—51no—
134C2×C4×#67—51no—
135C2×#67⋊C4—51no—
136C3×#386D511yescharacteristic, complemented
137#5220—51no—
138#5213—51no—
139#4958—51no—
140#4957—51no—
141#4957—51no—
142#4956—51no—
143#4956—51no—
144#4665—51no—
145#4665—51no—
146#4650—51no—
147#4648—51no—
148C22×C5×D4C2×D311yescharacteristic
149C23×C4×C5C2×D311yescharacteristic
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C22×C22⋊D5—31no—
154C23×Dic5—31no—
155C22×D20—31no—
156C22×C4×D5—31no—
157C22×C4×D5—31no—
158C2×C5×C22⋊C4C2×D311yescharacteristic
159C2×C5×C22⋊C4C2×D311yescharacteristic
160C2×C5×C22⋊C4C2×D311yescharacteristic
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5—31no—
164#4086—38no—
165C4×C22⋊D5—64no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#683—31no—
173C2×#683—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177#4027—64no—
178C5×#95C2×D311yescharacteristic
179C5×#95C2×D311yescharacteristic
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#2328—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C2411yescharacteristic
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—21no—
212C22×D15—21no—
213C22×D15—21no—
214C22×D15C22×C412yes—
215C22×D15C22×C412yes—
216C3×C5×D4—44no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—44no—
231C2×C3×C4×C5C22×C412yes—
232C2×C3×C4×C5C2×D412yes—
233#1220—28no—
234#1220—28no—
235#1220—44no—
236#1220—44no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15—21no—
248C2×Dic15—21no—
249C2×Dic15—21no—
250C2×Dic15—44no—
251C2×Dic15C22×C412yes—
252C2×Dic15C22×C412yes—
253C2×Dic15C2×D412yes—
254C2×Dic15C2×D412yes—
255C2×Dic15#4112yes—
256D60—44no—
257C4×D15—44no—
258C4×D15—44no—
259C22×C3×D4C2×D511yescharacteristic
260C23×C3×C4C2×D511yescharacteristic
261C22×#67—51no—
262C22×#67—51no—
263C22×#67—51no—
264C22×#67—51no—
265C23×Dic3—51no—
266C22×D12—51no—
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C2×C3×C22⋊C4C2×D511yescharacteristic
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C22⋊C4C2×D511yescharacteristic
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275#940—58no—
276C4×#67—104no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3—51no—
288#67⋊C4—104no—
289C3×#95C2×D511yescharacteristic
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C24×C5C22×D311yescharacteristic
298C24×C5C22×D311yescharacteristic
299C23×D5—31no—
300C23×D5—31no—
301C2×C5×D4—41no—
302C2×C5×D4—41no—
303C2×C5×D4C4×D314yescomplemented
304C22×C4×C5—22no—
305C22×C4×C5—41no—
306C22×C4×C5—41no—
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C2×C22⋊D5—34no—
313C2×C22⋊D5—34no—
314C2×C22⋊D5—34no—
315C2×C22⋊D5—34no—
316C2×C22⋊D5—62no—
317C2×C22⋊D5—62no—
318C2×C22⋊D5—62no—
319C2×C22⋊D5—62no—
320C2×C22⋊D5—121no—
321C2×C22⋊D5—121no—
322C2×C22⋊D5—121no—
323C2×C22⋊D5—121no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5—31no—
329C22×Dic5—31no—
330C22×Dic5—62no—
331C22×Dic5—121no—
332C22×Dic5—121no—
333C2×D20—34no—
334C2×D20—121no—
335C2×D20—121no—
336C2×C4×D5—62no—
337C2×C4×D5—62no—
338C2×C4×D5—121no—
339C2×C4×D5—121no—
340C2×C4×D5—121no—
341C2×C4×D5—121no—
342C5×C22⋊C4—22no—
343C5×C22⋊C4—41no—
344C5×C22⋊C4—41no—
345C22⋊Dic5—62no—
346C22⋊Dic5—121no—
347C22⋊Dic5—121no—
348#685—62no—
349#685—62no—
350#685—121no—
351#685—121no—
352#685—121no—
353#685—121no—
354#683—62no—
355#683—62no—
356C4×Dic5—34no—
357C4×Dic5—34no—
358C4×Dic5—62no—
359C2×#127—151no—
360C2×C4×D4—151no—
361C2×C4×D4—151no—
362#390—151no—
363#390—151no—
364#386—151no—
365#386—151no—
366#386—151no—
367#386—151no—
368#386—151no—
369#386—151no—
370#386—151no—
371#386D1511yescharacteristic, complemented
372#382—151no—
373#376—151no—
374C22×C3×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C23×C411yescharacteristic
389C22×C3×C5C22×D411yescharacteristic
390C22×C3×C5C2×#4111yescharacteristic
391C22×C3×C5H(5,𝔽2)11yescharacteristic
392C22×C3×C5H(5,𝔽2)11yescharacteristic
393C22×C3×C5H(5,𝔽2)11yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C2×D15—22no—
396C2×D15—22no—
397C2×D15—22no—
398C2×D15—22no—
399C2×D15—22no—
400C2×D15—22no—
401C2×D15—41no—
402C2×D15—41no—
403C2×D15—41no—
404C2×D15—41no—
405C2×D15—41no—
406C2×D15—41no—
407C2×D15—41no—
408C2×D15—41no—
409C3×C4×C5—22no—
410C3×C4×C5—22no—
411C3×C4×C5—41no—
412C3×C4×C5—41no—
413C3×C4×C5—41no—
414Dic15—22no—
415Dic15—22no—
416Dic15—41no—
417Dic15—41no—
418Dic15—41no—
419Dic15C4×D414yes—
420C24×C3C22×D511yescharacteristic
421C24×C3C22×D511yescharacteristic
422C23×D3—51no—
423C23×D3—51no—
424C2×C3×D4—41no—
425C2×C3×D4—41no—
426C2×C3×D4C4×D514yescomplemented
427C22×C3×C4—22no—
428C22×C3×C4—41no—
429C22×C3×C4—41no—
430C22×C3×C4C22×D511yescharacteristic
431C22×C3×C4C22×D511yescharacteristic
432C22×C3×C4C22×D511yescharacteristic
433C22×C3×C4C22×D511yescharacteristic
434C22×C3×C4C22×D511yescharacteristic
435C2×#67—54no—
436C2×#67—54no—
437C2×#67—54no—
438C2×#67—54no—
439C2×#67—102no—
440C2×#67—102no—
441C2×#67—102no—
442C2×#67—102no—
443C2×#67—201no—
444C2×#67—201no—
445C2×#67—201no—
446C2×#67—201no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—51no—
453C22×Dic3—102no—
454C22×Dic3—201no—
455C22×Dic3—201no—
456C2×D12—54no—
457C2×D12—201no—
458C2×D12—201no—
459C2×C4×D3—102no—
460C2×C4×D3—102no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3—201no—
464C2×C4×D3—201no—
465C3×C22⋊C4—22no—
466C3×C22⋊C4—41no—
467C3×C22⋊C4—41no—
468#217—102no—
469#217—201no—
470#217—201no—
471(C2×D3)⋊C4—102no—
472(C2×D3)⋊C4—102no—
473(C2×D3)⋊C4—201no—
474(C2×D3)⋊C4—201no—
475(C2×D3)⋊C4—201no—
476(C2×D3)⋊C4—201no—
477Dic3⋊C4—102no—
478Dic3⋊C4—102no—
479C4×Dic3—54no—
480C4×Dic3—54no—
481C4×Dic3—102no—
482C23×C5—21no—
483C23×C5—21no—
484C23×C5—21no—
485C23×C5—21no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—21no—
489C23×C5—21no—
490C23×C5—21no—
491C23×C5—21no—
492C23×C5—21no—
493C23×C5—21no—
494C23×C5C2×C4×D312yes—
495C23×C5C2×C4×D312yes—
496C23×C5C23×D311yescharacteristic
497C22×D5—32no—
498C22×D5—32no—
499C22×D5—61no—
500C22×D5—61no—
501C22×D5—61no—
502C22×D5—61no—
503C22×D5—61no—
504C22×D5—61no—
505C22×D5—61no—
506C22×D5—61no—
507C22×D5—61no—
508C22×D5—61no—
509C22×D5—61no—
510C22×D5—61no—
511C5×D4—44no—
512C2×C4×C5—21no—
513C2×C4×C5—21no—
514C2×C4×C5—21no—
515C2×C4×C5—21no—
516C2×C4×C5—21no—
517C2×C4×C5—21no—
518C2×C4×C5—21no—
519C2×C4×C5—21no—
520C2×C4×C5—21no—
521C2×C4×C5—21no—
522C2×C4×C5—21no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—44no—
526C2×C4×C5C2×C4×D312yes—
527C2×C4×C5D3×D412yes—
528C22⋊D5—68no—
529C22⋊D5—68no—
530C22⋊D5—124no—
531C22⋊D5—124no—
532C2×Dic5—32no—
533C2×Dic5—32no—
534C2×Dic5—32no—
535C2×Dic5—32no—
536C2×Dic5—32no—
537C2×Dic5—61no—
538C2×Dic5—61no—
539C2×Dic5—61no—
540C2×Dic5—61no—
541C2×Dic5—61no—
542C2×Dic5—61no—
543C2×Dic5—61no—
544C2×Dic5—61no—
545C2×Dic5—61no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—61no—
550C2×Dic5—124no—
551D20—124no—
552C4×D5—124no—
553C4×D5—124no—
554C22×D4—151no—
555C22×D4—151no—
556C22×D4—151no—
557C22×D4—151no—
558C22×D4—151no—
559C22×D4C2×D1511yescharacteristic
560C23×C4—151no—
561C23×C4—151no—
562C23×C4—151no—
563C23×C4C2×D1511yescharacteristic
564#127—158no—
565C4×D4—304no—
566C4×D4—304no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C22⋊C4—151no—
572C2×C22⋊C4—151no—
573C2×C22⋊C4—151no—
574C2×C22⋊C4—151no—
575C2×C22⋊C4—151no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4C2×D1511yescharacteristic
579C2×C22⋊C4C2×D1511yescharacteristic
580C2×C22⋊C4C2×D1511yescharacteristic
581C2×C42—151no—
582C2×C42—151no—
583C2×C42—151no—
584#95—151no—
585#95—151no—
586#95—151no—
587#95—151no—
588#95—151no—
589#95—151no—
590#95C2×D1511yescharacteristic
591#95C2×D1511yescharacteristic
592C2×C3×C5—42no—
593C2×C3×C5—42no—
594C2×C3×C5C2×C4×D411yescharacteristic
595C2×C3×C5#51811yescharacteristic
596C2×C3×C5#51811yescharacteristic
597C2×C3×C5#53511yescharacteristic
598C2×C3×C5#53511yescharacteristic
599C2×C3×C5#54011yescharacteristic
600C2×C3×C5#54011yescharacteristic
601D15—42no—
602D15—42no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—21no—
607C23×C3—21no—
608C23×C3—21no—
609C23×C3—21no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3C2×C4×D512yes—
616C23×C3C2×C4×D512yes—
617C23×C3C23×D511yescharacteristic
618C22×D3—52no—
619C22×D3—52no—
620C22×D3—101no—
621C22×D3—101no—
622C22×D3—101no—
623C22×D3—101no—
624C22×D3—101no—
625C22×D3—101no—
626C22×D3—101no—
627C22×D3—101no—
628C22×D3—101no—
629C22×D3—101no—
630C22×D3—101no—
631C22×D3—101no—
632C3×D4—44no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—44no—
647C2×C3×C4C2×C4×D512yes—
648C2×C3×C4D4×D512yes—
649#67—108no—
650#67—108no—
651#67—204no—
652#67—204no—
653C2×Dic3—52no—
654C2×Dic3—52no—
655C2×Dic3—52no—
656C2×Dic3—52no—
657C2×Dic3—52no—
658C2×Dic3—101no—
659C2×Dic3—101no—
660C2×Dic3—101no—
661C2×Dic3—101no—
662C2×Dic3—101no—
663C2×Dic3—101no—
664C2×Dic3—101no—
665C2×Dic3—101no—
666C2×Dic3—101no—
667C2×Dic3—101no—
668C2×Dic3—101no—
669C2×Dic3—101no—
670C2×Dic3—101no—
671C2×Dic3—204no—
672D12—204no—
673C4×D3—204no—
674C4×D3—204no—
675C22×C5—22no—
676C22×C5—22no—
677C22×C5—22no—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—22no—
681C22×C5—41no—
682C22×C5—41no—
683C22×C5—41no—
684C22×C5—41no—
685C22×C5—41no—
686C22×C5—41no—
687C22×C5—41no—
688C22×C5—41no—
689C22×C5C22×C4×D311yescharacteristic
690C22×C5C2×D3×D411yescharacteristic
691C22×C5#100411yescharacteristic
692C22×C5#100411yescharacteristic
693C22×C5#100411yescharacteristic
694C22×C5D3×#4111yescharacteristic
695C22×C5#100911yescharacteristic
696C2×D5—62no—
697C2×D5—62no—
698C2×D5—62no—
699C2×D5—62no—
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—121no—
703C2×D5—121no—
704C2×D5—121no—
705C2×D5—121no—
706C2×D5—121no—
707C2×D5—121no—
708C2×D5—121no—
709C2×D5—121no—
710C4×C5—22no—
711C4×C5—22no—
712C4×C5—41no—
713C4×C5—41no—
714C4×C5—41no—
715Dic5—34no—
716Dic5—62no—
717Dic5—62no—
718Dic5—121no—
719Dic5—121no—
720Dic5—121no—
721C24—151no—
722C24—151no—
723C24C22×D1511yescharacteristic
724C24C22×D1511yescharacteristic
725C2×D4—41no—
726C2×D4—41no—
727C2×D4—154no—
728C2×D4—154no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—302no—
733C2×D4—302no—
734C2×D4—302no—
735C2×D4—302no—
736C2×D4—601no—
737C2×D4—601no—
738C2×D4—601no—
739C2×D4—601no—
740C2×D4—601no—
741C2×D4—601no—
742C2×D4C4×D1514yescomplemented
743C22×C4—22no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—151no—
747C22×C4—151no—
748C22×C4—151no—
749C22×C4—151no—
750C22×C4—151no—
751C22×C4—151no—
752C22×C4—302no—
753C22×C4—302no—
754C22×C4—302no—
755C22×C4—601no—
756C22×C4—601no—
757C22×C4—601no—
758C22×C4—601no—
759C22×C4—601no—
760C22×C4—601no—
761C22×C4C22×D1511yescharacteristic
762C22×C4C22×D1511yescharacteristic
763C22×C4C22×D1511yescharacteristic
764C22×C4C22×D1511yescharacteristic
765C22×C4C22×D1511yescharacteristic
766C4⋊C4—302no—
767C4⋊C4—302no—
768C22⋊C4—22no—
769C22⋊C4—41no—
770C22⋊C4—41no—
771C22⋊C4—302no—
772C22⋊C4—302no—
773C22⋊C4—302no—
774C22⋊C4—601no—
775C22⋊C4—601no—
776C22⋊C4—601no—
777C22⋊C4—601no—
778C22⋊C4—601no—
779C22⋊C4—601no—
780C42—154no—
781C42—154no—
782C42—302no—
783C3×C5#232811yescharacteristic, complemented, Hall
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3C22×C4×D511yescharacteristic
799C22×C3C2×D4×D511yescharacteristic
800C22×C3#414411yescharacteristic
801C22×C3#414411yescharacteristic
802C22×C3#414411yescharacteristic
803C22×C3D5×#4111yescharacteristic
804C22×C3#414911yescharacteristic
805C2×D3—102no—
806C2×D3—102no—
807C2×D3—102no—
808C2×D3—102no—
809C2×D3—102no—
810C2×D3—102no—
811C2×D3—201no—
812C2×D3—201no—
813C2×D3—201no—
814C2×D3—201no—
815C2×D3—201no—
816C2×D3—201no—
817C2×D3—201no—
818C2×D3—201no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—41no—
824Dic3—54no—
825Dic3—102no—
826Dic3—102no—
827Dic3—201no—
828Dic3—201no—
829Dic3—201no—
830C2×C5—42no—
831C2×C5—42no—
832C2×C5#548611yescharacteristic
833C2×C5C4×D3×D411yescharacteristic
834C2×C5#554511yescharacteristic
835C2×C5#559211yescharacteristic
836C2×C5#560711yescharacteristic
837C2×C5#561511yescharacteristic
838C2×C5#566311yescharacteristic
839D5—122no—
840D5—122no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—152no—
854C23—152no—
855C23—301no—
856C23—301no—
857C23—301no—
858C23—301no—
859C23—301no—
860C23—301no—
861C23—301no—
862C23—301no—
863C23—301no—
864C23—301no—
865C23—301no—
866C23—301no—
867C23C2×C4×D1512yes—
868C23C2×C4×D1512yes—
869C23C23×D1511yescharacteristic
870D4—44no—
871D4—308no—
872D4—308no—
873D4—604no—
874D4—604no—
875D4—604no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—44no—
890C2×C4—152no—
891C2×C4—152no—
892C2×C4—152no—
893C2×C4—152no—
894C2×C4—152no—
895C2×C4—301no—
896C2×C4—301no—
897C2×C4—301no—
898C2×C4—301no—
899C2×C4—301no—
900C2×C4—301no—
901C2×C4—301no—
902C2×C4—301no—
903C2×C4—301no—
904C2×C4—301no—
905C2×C4—301no—
906C2×C4—301no—
907C2×C4—301no—
908C2×C4—604no—
909C2×C4—604no—
910C2×C4—604no—
911C2×C4C2×C4×D1512yes—
912C2×C4D4×D1512yes—
913C2×C3—42no—
914C2×C3—42no—
915C2×C3#6582011yescharacteristic
916C2×C3C4×D4×D511yescharacteristic
917C2×C3#6587911yescharacteristic
918C2×C3#6592611yescharacteristic
919C2×C3#6594111yescharacteristic
920C2×C3#6594911yescharacteristic
921C2×C3#6599711yescharacteristic
922D3—202no—
923D3—202no—
924C5#7466711yescharacteristic, complemented, Sylow
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—302no—
940C22—302no—
941C22—302no—
942C22—302no—
943C22—302no—
944C22—302no—
945C22—601no—
946C22—601no—
947C22—601no—
948C22—601no—
949C22—601no—
950C22—601no—
951C22—601no—
952C22—601no—
953C22C22×C4×D1511yescharacteristic
954C22C2×D4×D1511yescharacteristic
955C22#9209511yescharacteristic
956C22#9209511yescharacteristic
957C22#9209511yescharacteristic
958C22#41×D1511yescharacteristic
959C22#9210011yescharacteristic
960C4—22no—
961C4—22no—
962C4—41no—
963C4—41no—
964C4—41no—
965C4—154no—
966C4—302no—
967C4—302no—
968C4—601no—
969C4—601no—
970C4—601no—
971C3#1060639811yescharacteristic, complemented, Sylow
972C2—42no—
973C2—42no—
974C2—602no—
975C2—602no—
976C2#1175624511yescharacteristic
977C2C4×D4×D1511yescharacteristic
978C2#1175630411yescharacteristic
979C2#1175635111yescharacteristic
980C2#1175636611yescharacteristic
981C2#1175637411yescharacteristic
982C2#1175642211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#386C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91829C2
hypercenter#386D15
hypocenterC3×C5#2328
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1220C2semidirect
3. C2×#91770C2semidirect
4. C3×C5×#386C2semidirect
5. #11751321C2semidirect
6. #11751314C2semidirect
7. #11751059C2semidirect
8. #11751058C2semidirect
9. #11751058C2semidirect
10. #11751057C2semidirect
11. #11751057C2semidirect
12. #11750766C2semidirect
13. #11750766C2semidirect
14. #11750751C2semidirect
15. #11750749C2semidirect
33. #91829C4semidirect
59. C5×#386D3semidirect
77. C2×C3×C5×D4C2×C4semidirect
94. C2×#1220C2×C4semidirect
95. C2×#1220C2×C4semidirect
96. C2×#1220C2×C4semidirect
97. C2×#1220C2×C4semidirect
109. C2×D60C2×C4semidirect
131. C4×Dic15C2×C4semidirect
132. C4×Dic15D4semidirect
136. C3×#386D5semidirect
303. C2×C5×D4C4×D3semidirect
371. #386D15semidirect
426. C2×C3×D4C4×D5semidirect
742. C2×D4C4×D15semidirect
783. C3×C5#2328semidirect
924. C5#74667semidirect
971. C3#10606398semidirect

Maximal subgroups

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

subgroupindex
C2×#918292
C2×C4×#12202
C2×#917702
C3×C5×#3862
#117513212
#117513142
#117510592
#117510582
#117510572
#117507662
#117507512
#117507492
#106063983
#746675