Finite Group Databasebeta

← C3×#10613276 #14460103

Subgroups — C3×#10613276 #14460103

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65965C211yesmaximal, characteristic, complemented
2C3×#65866C211yesmaximal, characteristic, complemented
3C3×C5×#485C211yesmaximal, characteristic, complemented
4C3×#65337C211yesmaximal, characteristic, complemented
5C3×#65291C211yesmaximal, characteristic, complemented
6C3×#65177C211yesmaximal, characteristic, complemented
7C3×#65161C211yesmaximal, characteristic, complemented
8C3×#65159C211yesmaximal, characteristic, complemented
9C3×#65153C211yesmaximal, characteristic, complemented
10C3×#65107C211yesmaximal, characteristic, complemented
11C3×#65100C211yesmaximal, characteristic, complemented
12C3×#65093C211yesmaximal, characteristic, complemented
13C3×#65081C211yesmaximal, characteristic, complemented
14C3×#65023C211yesmaximal, characteristic, complemented
15C3×#65014C211yesmaximal, characteristic, complemented
16#10613276C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#709C2211yescharacteristic
19C3×C5×C22⋊Q8C2211yescharacteristic
20C3×C5×#117C2211yescharacteristic
21C3×#4090C2211yescharacteristic
22C2×C3×#688C2211yescharacteristic
23C3×#4076C2211yescharacteristic
24C3×C4×C22⋊D5C2211yescharacteristic
25C22×C3×#168C2211yescharacteristic
26C2×C3×D40C2211yescharacteristic
27C2×C3×#677C2211yescharacteristic
28C2×C3×C8×D5C2211yescharacteristic
29C3×#4043C2211yescharacteristic
30C3×#4041C2211yescharacteristic
31C3×#4040—21no—
32C3×#4039C2211yescharacteristic
33C3×#4039C2211yescharacteristic
34C3×#4038C2211yescharacteristic
35C3×D5×C4⋊C4—21no—
36C3×#4034C2211yescharacteristic
37C3×#4031—21no—
38C3×#4030—21no—
39C3×#4030—21no—
40C3×#4029—21no—
41C3×#4021—21no—
42C3×#4018—21no—
43C3×C5×#107C2211yescharacteristic
44C3×C5×#106C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46C3×C5×#103C2211yescharacteristic
47C3×C5×C22⋊C8C2211yescharacteristic
48C3×#3967C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3952C2211yescharacteristic
51C3×#3948C2211yescharacteristic
52C3×#3946C2211yescharacteristic
53C3×C8×Dic5C2211yescharacteristic
54C3×#3942C2211yescharacteristic
55C3×#3942C2211yescharacteristic
56C3×#3941C2211yescharacteristic
57C3×#3941C2211yescharacteristic
58C3×#3941C2211yescharacteristic
59C3×#3940C2211yescharacteristic
60C3×#3303—51nomaximal, Hall
61#65965C2×C311yescharacteristic, complemented
62#65866C2×C311yescharacteristic, complemented
63C5×#485C2×C311yescharacteristic, complemented
64#65337C2×C311yescharacteristic, complemented
65#65291C2×C311yescharacteristic, complemented
66#65177C2×C311yescharacteristic, complemented
67#65161C2×C311yescharacteristic, complemented
68#65159C2×C311yescharacteristic, complemented
69#65153C2×C311yescharacteristic, complemented
70#65107C2×C311yescharacteristic, complemented
71#65100C2×C311yescharacteristic, complemented
72#65093C2×C311yescharacteristic, complemented
73#65081C2×C311yescharacteristic, complemented
74#65023C2×C311yescharacteristic, complemented
75#65014C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×C3×C22⋊D5—21no—
79C2×C3×C22⋊D5—21no—
80C2×C3×C22⋊D5D411yescharacteristic
81C3×#713—22no—
82C3×#713—41no—
83C3×#709—22no—
84C3×#709—41no—
85C2×C3×D20—21no—
86C2×C3×D20—21no—
87C2×C3×D20C2311yescharacteristic
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5C2311yescharacteristic
94C2×C3×Dic10—21no—
95C2×C3×Dic10C2311yescharacteristic
96C2×C3×C5×C8C2311yescharacteristic
97C2×C3×C5×C8C2311yescharacteristic
98C3×C5×C4⋊C4—21no—
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C22⋊C4—21no—
103C3×C5×C22⋊C4—21no—
104C3×C42×C5—21no—
105C3×C22⋊Dic5D411yescharacteristic
106C3×#688—41no—
107C3×#685—21no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×#685—21no—
113C3×#685D411yescharacteristic
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C3×#683—21no—
118C3×#683—21no—
119C3×#683D411yescharacteristic
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122C2×C3×#168—41no—
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×D40—22no—
126C3×#677—41no—
127C3×C8×D5—41no—
128C3×#555—51no—
129C3×#547—51no—
130C3×#487—51no—
131C3×#485—51no—
132C3×#485D511yescharacteristic, complemented
133C3×#476—51no—
134C3×#465—51no—
135C3×#465—51no—
136C3×#461—51no—
137C3×#449—51no—
138C3×#449—51no—
139C3×C4×D8—51no—
140C3×C8×D4—51no—
141C3×#416—51no—
142C3×#416—51no—
143C2×#713C22×C311yescharacteristic
144C2×#709C22×C311yescharacteristic
145C5×C22⋊Q8C22×C311yescharacteristic
146C5×#117C22×C311yescharacteristic
147#4090C22×C311yescharacteristic
148C2×#688C22×C311yescharacteristic
149#4076C22×C311yescharacteristic
150C4×C22⋊D5C22×C311yescharacteristic
151C22×#168C22×C311yescharacteristic
152C2×D40C22×C311yescharacteristic
153C2×#677C22×C311yescharacteristic
154C2×C8×D5C22×C311yescharacteristic
155#4043C22×C311yescharacteristic
156#4041C22×C311yescharacteristic
157#4040—21no—
158#4039C22×C311yescharacteristic
159#4039C22×C311yescharacteristic
160#4038C22×C311yescharacteristic
161D5×C4⋊C4—21no—
162#4034C22×C311yescharacteristic
163#4031—21no—
164#4030—21no—
165#4030—21no—
166#4029—21no—
167#4021—21no—
168#4018—21no—
169C5×#107C22×C311yescharacteristic
170C5×#106C22×C311yescharacteristic
171C5×#103C22×C311yescharacteristic
172C5×#103C22×C311yescharacteristic
173C5×C22⋊C8C22×C311yescharacteristic
174#3967C22×C311yescharacteristic
175#3953C22×C311yescharacteristic
176#3952C22×C311yescharacteristic
177#3948C22×C311yescharacteristic
178#3946C22×C311yescharacteristic
179C8×Dic5C22×C311yescharacteristic
180#3942C22×C311yescharacteristic
181#3942C22×C311yescharacteristic
182#3941C22×C311yescharacteristic
183#3941C22×C311yescharacteristic
184#3941C22×C311yescharacteristic
185#3940C22×C311yescharacteristic
186#3303—51noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5C2×D411yescharacteristic
191C3×C5×Q8—21no—
192C3×C5×Q8—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2411yescharacteristic
201C3×C22⋊D5—22no—
202C3×C22⋊D5—42no—
203C3×C22⋊D5—81no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5C2×D411yescharacteristic
207C2×C3×Dic5C2×D411yescharacteristic
208C2×C3×Dic5C2×D411yescharacteristic
209C3×D20—21no—
210C3×D20—21no—
211C3×D20—21no—
212C3×D20—42no—
213C3×D20—81no—
214C3×D20#4112yes—
215C3×C4×D5—21no—
216C3×C4×D5—21no—
217C3×C4×D5—42no—
218C3×C4×D5—42no—
219C3×C4×D5—42no—
220C3×C4×D5—42no—
221C3×Dic10—21no—
222C3×Dic10—21no—
223C3×Dic10—81no—
224C3×C5×C8—21no—
225C3×C5×C8—21no—
226C3×#168—21no—
227C3×#168—21no—
228C2×C3×#41—51no—
229C2×C3×#41—51no—
230C2×C3×SD16—51no—
231C2×C3×SD16—51no—
232C2×C3×D8—51no—
233C22×C3×C8—51no—
234C22×C3×C8—51no—
235C3×C4⋊Q8—51no—
236C3×C4⋊Q8—51no—
237C3×#124—101no—
238C3×#124—101no—
239C3×#123—101no—
240C3×#123—101no—
241C3×C22⋊Q8—51no—
242C3×C22⋊Q8C2×D511yescharacteristic
243C3×#121—51no—
244C3×#121—51no—
245C3×#121—101no—
246C3×#121—101no—
247C3×C4×D4—51no—
248C3×C4×D4—51no—
249C3×C4×D4—51no—
250C3×#117—51no—
251C3×#117—101no—
252C3×#117C2×D511yescharacteristic
253C2×C3×C4⋊C4—101no—
254C3×#107C2×D511yescharacteristic
255C3×#106—51no—
256C3×#106C2×D511yescharacteristic
257C3×C4⋊C8—51no—
258C3×#103—51no—
259C3×#103—51no—
260C3×#103—51no—
261C3×#103—51no—
262C3×#103C2×D511yescharacteristic
263C3×#103C2×D511yescharacteristic
264C3×#102—51no—
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×C22⋊C8—51no—
269C3×C22⋊C8C2×D511yescharacteristic
270C3×C4×C8—51no—
271C2×C5×Q8C23×C311yescharacteristic
272C22×C4×C5C23×C311yescharacteristic
273C2×C22⋊D5—21no—
274C2×C22⋊D5—21no—
275C2×C22⋊D5C3×D411yescharacteristic
276#713—22no—
277#713—41no—
278#709—22no—
279#709—41no—
280C2×D20—21no—
281C2×D20—21no—
282C2×D20C23×C311yescharacteristic
283C2×D20C23×C311yescharacteristic
284C2×C4×D5—21no—
285C2×C4×D5—21no—
286C2×C4×D5—21no—
287C2×C4×D5—21no—
288C2×C4×D5C23×C311yescharacteristic
289C2×Dic10—21no—
290C2×Dic10C23×C311yescharacteristic
291C2×C5×C8C23×C311yescharacteristic
292C2×C5×C8C23×C311yescharacteristic
293C5×C4⋊C4—21no—
294C5×C4⋊C4C23×C311yescharacteristic
295C5×C4⋊C4C23×C311yescharacteristic
296C5×C4⋊C4C23×C311yescharacteristic
297C5×C22⋊C4—21no—
298C5×C22⋊C4—21no—
299C42×C5—21no—
300C22⋊Dic5C3×D411yescharacteristic
301#688—41no—
302#685—21no—
303#685—21no—
304#685—21no—
305#685—21no—
306#685—21no—
307#685—21no—
308#685C3×D411yescharacteristic
309C4⋊Dic5—21no—
310C4⋊Dic5C23×C311yescharacteristic
311#683—21no—
312#683—21no—
313#683—21no—
314#683C3×D411yescharacteristic
315C4×Dic5—21no—
316C4×Dic5C23×C311yescharacteristic
317C2×#168—41no—
318C2×#168C23×C311yescharacteristic
319C2×#168C23×C311yescharacteristic
320D40—22no—
321#677—41no—
322C8×D5—41no—
323#555—51no—
324#547—51no—
325#487—51no—
326#485—51no—
327#485C3×D511yescharacteristic, complemented
328#476—51no—
329#465—51no—
330#465—51no—
331#461—51no—
332#449—51no—
333#449—51no—
334C4×D8—51no—
335C8×D4—51no—
336#416—51no—
337#416—51no—
338C22×C3×C5—21no—
339C22×C3×C5—21no—
340C22×C3×C5—21no—
341C22×C3×C5C22×D411yescharacteristic
342C2×C3×D5—21no—
343C2×C3×D5—22no—
344C2×C3×D5—21no—
345C2×C3×D5—21no—
346C2×C3×D5—41no—
347C2×C3×D5—41no—
348C2×C3×D5—41no—
349C2×C3×D5—41no—
350C2×C3×D5—41no—
351C3×C4×C5—21no—
352C3×C4×C5—41no—
353C3×C4×C5—41no—
354C3×C4×C5—41no—
355C3×C4×C5—41no—
356C3×C4×C5C2×#4111yescharacteristic
357C3×C4×C5H(5,𝔽2)11yescharacteristic
358C3×Dic5—21no—
359C3×Dic5—21no—
360C3×Dic5—41no—
361C3×Dic5—41no—
362C3×Dic5#13512yes—
363C3×#41—102no—
364C3×#41—102no—
365C3×#41—201no—
366C3×#41—201no—
367C2×C3×Q8—51no—
368C2×C3×Q8—101no—
369C2×C3×Q8C22×D511yescharacteristic
370C2×C3×D4—51no—
371C2×C3×D4—51no—
372C2×C3×D4—51no—
373C2×C3×D4—101no—
374C2×C3×D4—101no—
375C2×C3×D4—101no—
376C2×C3×D4—101no—
377C22×C3×C4—51no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×C3×C4—101no—
381C22×C3×C4—101no—
382C22×C3×C4C22×D511yescharacteristic
383C3×SD16—201no—
384C3×SD16—201no—
385C3×D8—102no—
386C2×C3×C8—51no—
387C2×C3×C8—51no—
388C2×C3×C8—201no—
389C2×C3×C8—201no—
390C2×C3×C8C22×D511yescharacteristic
391C2×C3×C8C22×D511yescharacteristic
392C3×C4⋊C4—21no—
393C3×C4⋊C4—51no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4—101no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4—101no—
399C3×C4⋊C4C22×D511yescharacteristic
400C3×C4⋊C4C22×D511yescharacteristic
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—51no—
405C3×C22⋊C4—51no—
406C3×C22⋊C4—101no—
407C3×C22⋊C4—101no—
408C3×C22⋊C4—101no—
409C3×C22⋊C4—101no—
410C3×C22⋊C4—101no—
411C3×C22⋊C4—101no—
412C3×C42—21no—
413C3×C42—51no—
414C3×C42—101no—
415C23×C5C2×C3×D411yescharacteristic
416C22×D5—21no—
417C22×D5—21no—
418C22×D5C2×C3×D411yescharacteristic
419C5×Q8—21no—
420C5×Q8—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5C2×C3×D411yescharacteristic
428C2×C4×C5C24×C311yescharacteristic
429C22⋊D5—22no—
430C22⋊D5—42no—
431C22⋊D5—81no—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5C2×C3×D411yescharacteristic
435C2×Dic5C2×C3×D411yescharacteristic
436C2×Dic5C2×C3×D411yescharacteristic
437D20—21no—
438D20—21no—
439D20—21no—
440D20—42no—
441D20—81no—
442D20C3×#4112yes—
443C4×D5—21no—
444C4×D5—21no—
445C4×D5—42no—
446C4×D5—42no—
447C4×D5—42no—
448C4×D5—42no—
449Dic10—21no—
450Dic10—21no—
451Dic10—81no—
452C5×C8—21no—
453C5×C8—21no—
454#168—21no—
455#168—21no—
456C2×#41—51no—
457C2×#41—51no—
458C2×SD16—51no—
459C2×SD16—51no—
460C2×D8—51no—
461C22×C8—51no—
462C22×C8—51no—
463C4⋊Q8—51no—
464C4⋊Q8—51no—
465#124—101no—
466#124—101no—
467#123—101no—
468#123—101no—
469C22⋊Q8—51no—
470C22⋊Q8C2×C3×D511yescharacteristic
471#121—51no—
472#121—51no—
473#121—101no—
474#121—101no—
475C4×D4—51no—
476C4×D4—51no—
477C4×D4—51no—
478#117—51no—
479#117—101no—
480#117C2×C3×D511yescharacteristic
481C2×C4⋊C4—101no—
482#107C2×C3×D511yescharacteristic
483#106—51no—
484#106C2×C3×D511yescharacteristic
485C4⋊C8—51no—
486#103—51no—
487#103—51no—
488#103—51no—
489#103—51no—
490#103C2×C3×D511yescharacteristic
491#103C2×C3×D511yescharacteristic
492#102—51no—
493#102—51no—
494#102—51no—
495#102—51no—
496C22⋊C8—51no—
497C22⋊C8C2×C3×D511yescharacteristic
498C4×C8—51no—
499C2×C3×C5—41no—
500C2×C3×C5#54611yescharacteristic
501C2×C3×C5C2×#13511yescharacteristic
502C2×C3×C5#57711yescharacteristic
503C3×D5—41no—
504C3×D5—42no—
505C3×D5—81no—
506C23×C3—51no—
507C23×C3—101no—
508C23×C3—101no—
509C23×C3D4×D511yescharacteristic
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—101no—
513C3×Q8—101no—
514C3×Q8—401no—
515C3×D4—52no—
516C3×D4—102no—
517C3×D4—101no—
518C3×D4—101no—
519C3×D4—101no—
520C3×D4—202no—
521C3×D4—202no—
522C3×D4—401no—
523C3×D4—401no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—51no—
531C2×C3×C4—51no—
532C2×C3×C4—51no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—202no—
538C2×C3×C4—202no—
539C2×C3×C4—202no—
540C2×C3×C4—202no—
541C2×C3×C4D4×D511yescharacteristic
542C2×C3×C4C23×D511yescharacteristic
543C3×C8—21no—
544C3×C8—21no—
545C3×C8—101no—
546C3×C8—101no—
547C22×C5—21no—
548C22×C5—21no—
549C22×C5—21no—
550C22×C5C22×C3×D411yescharacteristic
551C2×D5—21no—
552C2×D5—21no—
553C2×D5—21no—
554C2×D5—22no—
555C2×D5—41no—
556C2×D5—41no—
557C2×D5—41no—
558C2×D5—41no—
559C2×D5—41no—
560C4×C5—21no—
561C4×C5—41no—
562C4×C5—41no—
563C4×C5—41no—
564C4×C5—41no—
565C4×C5C2×C3×#4111yescharacteristic
566C4×C5C3×H(5,𝔽2)11yescharacteristic
567Dic5—21no—
568Dic5—21no—
569Dic5—41no—
570Dic5—41no—
571Dic5C3×#13512yes—
572#41—102no—
573#41—102no—
574#41—201no—
575#41—201no—
576C2×Q8—51no—
577C2×Q8—101no—
578C2×Q8C22×C3×D511yescharacteristic
579C2×D4—51no—
580C2×D4—51no—
581C2×D4—51no—
582C2×D4—101no—
583C2×D4—101no—
584C2×D4—101no—
585C2×D4—101no—
586C22×C4—51no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4C22×C3×D511yescharacteristic
592SD16—201no—
593SD16—201no—
594D8—102no—
595C2×C8—51no—
596C2×C8—51no—
597C2×C8—201no—
598C2×C8—201no—
599C2×C8C22×C3×D511yescharacteristic
600C2×C8C22×C3×D511yescharacteristic
601C4⋊C4—21no—
602C4⋊C4—51no—
603C4⋊C4—51no—
604C4⋊C4—101no—
605C4⋊C4—101no—
606C4⋊C4—101no—
607C4⋊C4—101no—
608C4⋊C4C22×C3×D511yescharacteristic
609C4⋊C4C22×C3×D511yescharacteristic
610C4⋊C4C22×C3×D511yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—51no—
614C22⋊C4—51no—
615C22⋊C4—101no—
616C22⋊C4—101no—
617C22⋊C4—101no—
618C22⋊C4—101no—
619C22⋊C4—101no—
620C22⋊C4—101no—
621C42—21no—
622C42—51no—
623C42—101no—
624C3×C5#330311yescharacteristic, complemented, Hall
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—101no—
629C22×C3—101no—
630C22×C3—101no—
631C22×C3—102no—
632C22×C3—201no—
633C22×C3—201no—
634C22×C3—201no—
635C22×C3—201no—
636C22×C3—201no—
637C22×C3C2×D4×D511yescharacteristic
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—52no—
644C3×C4—101no—
645C3×C4—101no—
646C3×C4—201no—
647C3×C4—201no—
648C3×C4D5×#4111yescharacteristic
649C3×C4#414911yescharacteristic
650C2×C5—41no—
651C2×C5C3×#54611yescharacteristic
652C2×C5C2×C3×#13511yescharacteristic
653C2×C5C3×#57711yescharacteristic
654D5—41no—
655D5—42no—
656D5—81no—
657C23—51no—
658C23—101no—
659C23—101no—
660C23C3×D4×D511yescharacteristic
661Q8—21no—
662Q8—21no—
663Q8—101no—
664Q8—101no—
665Q8—401no—
666D4—52no—
667D4—102no—
668D4—101no—
669D4—101no—
670D4—101no—
671D4—202no—
672D4—202no—
673D4—401no—
674D4—401no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—51no—
682C2×C4—51no—
683C2×C4—51no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—101no—
688C2×C4—202no—
689C2×C4—202no—
690C2×C4—202no—
691C2×C4—202no—
692C2×C4C3×D4×D511yescharacteristic
693C2×C4C23×C3×D511yescharacteristic
694C8—21no—
695C8—21no—
696C8—101no—
697C8—101no—
698C2×C3—41no—
699C2×C3—201no—
700C2×C3—202no—
701C2×C3—401no—
702C2×C3#6598811yescharacteristic
703C2×C3D5×#13511yescharacteristic
704C2×C3#6611211yescharacteristic
705C5C3×#330311yescharacteristic, complemented, Sylow
706C22—21no—
707C22—21no—
708C22—21no—
709C22—101no—
710C22—101no—
711C22—101no—
712C22—102no—
713C22—201no—
714C22—201no—
715C22—201no—
716C22—201no—
717C22—201no—
718C22C2×C3×D4×D511yescharacteristic
719C4—21no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—52no—
725C4—101no—
726C4—101no—
727C4—201no—
728C4—201no—
729C4C3×D5×#4111yescharacteristic
730C4C3×#414911yescharacteristic
731C3#1061327611yescharacteristic, direct product factor, Sylow
732C2—41no—
733C2—201no—
734C2—202no—
735C2—401no—
736C2C3×#6598811yescharacteristic
737C2C3×D5×#13511yescharacteristic
738C2C3×#6611211yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#485C2
socleC22×C3×C5C22×D4
hypercenterC3×#485D5
hypocenterC5C3×#3303
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
1. C3×#65965C2semidirect
2. C3×#65866C2semidirect
3. C3×C5×#485C2semidirect
4. C3×#65337C2semidirect
5. C3×#65291C2semidirect
6. C3×#65177C2semidirect
7. C3×#65161C2semidirect
8. C3×#65159C2semidirect
9. C3×#65153C2semidirect
10. C3×#65107C2semidirect
11. C3×#65100C2semidirect
12. C3×#65093C2semidirect
13. C3×#65081C2semidirect
14. C3×#65023C2semidirect
15. C3×#65014C2semidirect
16. #10613276C3direct (N × H)
61. #65965C2×C3semidirect
62. #65866C2×C3semidirect
63. C5×#485C2×C3semidirect
64. #65337C2×C3semidirect
65. #65291C2×C3semidirect
66. #65177C2×C3semidirect
67. #65161C2×C3semidirect
68. #65159C2×C3semidirect
69. #65153C2×C3semidirect
70. #65107C2×C3semidirect
71. #65100C2×C3semidirect
72. #65093C2×C3semidirect
73. #65081C2×C3semidirect
74. #65023C2×C3semidirect
75. #65014C2×C3semidirect
132. C3×#485D5semidirect
327. #485C3×D5semidirect
624. C3×C5#3303semidirect
705. C5C3×#3303semidirect
731. C3#10613276direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659652
C3×#658662
C3×C5×#4852
C3×#653372
C3×#652912
C3×#651772
C3×#651612
C3×#651592
C3×#651532
C3×#651072
C3×#651002
C3×#650932
C3×#650812
C3×#650232
C3×#650142
#106132763
C3×#33035