Finite Group Databasebeta

← C3×#10611565 #14435431

Subgroups — C3×#10611565 #14435431

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65914C211yesmaximal, characteristic
2C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
3C3×C5×#441C211yesmaximal, characteristic, complemented
4C3×#65475C211yesmaximal, characteristic, complemented
5C3×#65474C211yesmaximal, characteristic, complemented
6C3×#65319C211yesmaximal, characteristic, complemented
7C3×#65315C211yesmaximal, characteristic, complemented
8C3×#65152C211yesmaximal, characteristic
9C3×#65146C211yesmaximal, characteristic, complemented
10C3×#65098C211yesmaximal, characteristic, complemented
11C3×#65095C211yesmaximal, characteristic
12C3×#65087C211yesmaximal, characteristic, complemented
13C3×#65085C211yesmaximal, characteristic, complemented
14C3×#64999C211yesmaximal, characteristic, complemented
15C3×#64994C211yesmaximal, characteristic, complemented
16#10611565C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×C3×C5×Q16C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20C3×C4×C5×Q8C2211yescharacteristic
21C3×#4093C2211yescharacteristic
22C3×#4092C2211yescharacteristic
23C3×Q8×Dic5C2211yescharacteristic
24C2×C3×#689C2211yescharacteristic
25C2×C3×#688C2211yescharacteristic
26C2×C3×#677C2211yescharacteristic
27C3×#4044—21no—
28C3×#4041C2211yescharacteristic
29C3×#4040—21no—
30C3×D5×C4⋊C4—21no—
31C3×D5×C4⋊C4C2211yescharacteristic
32C3×#4036C2211yescharacteristic
33C3×#4033—21no—
34C3×#4033C2211yescharacteristic
35C3×C4×D20—21no—
36C3×C4×D20C2211yescharacteristic
37C3×#4018—21no—
38C3×C42×D5—21no—
39C3×C42×D5C2211yescharacteristic
40C3×C4×Dic10—21no—
41C3×C4×Dic10C2211yescharacteristic
42C3×C5×#106C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C5×#103C2211yescharacteristic
45C3×C5×#97C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3967C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3952C2211yescharacteristic
50C3×#3952C2211yescharacteristic
51C3×#3950C2211yescharacteristic
52C3×#3948C2211yescharacteristic
53C3×#3946C2211yescharacteristic
54C3×#3946C2211yescharacteristic
55C3×#3942C2211yescharacteristic
56C3×#3941C2211yescharacteristic
57C3×#3940C2211yescharacteristic
58C3×#3939C2211yescharacteristic
59C3×#3935C2211yescharacteristic
60C3×#3117—51nomaximal, Hall
61#65914C2×C311yescharacteristic
62C4×Q8×D5C2×C311yescharacteristic, complemented
63C5×#441C2×C311yescharacteristic, complemented
64#65475C2×C311yescharacteristic, complemented
65#65474C2×C311yescharacteristic, complemented
66#65319C2×C311yescharacteristic, complemented
67#65315C2×C311yescharacteristic, complemented
68#65152C2×C311yescharacteristic
69#65146C2×C311yescharacteristic, complemented
70#65098C2×C311yescharacteristic, complemented
71#65095C2×C311yescharacteristic
72#65087C2×C311yescharacteristic, complemented
73#65085C2×C311yescharacteristic, complemented
74#64999C2×C311yescharacteristic, complemented
75#64994C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×Q8C2311yescharacteristic
78C3×Q8×D5—22no—
79C3×Q8×D5—22no—
80C2×C3×D20—21no—
81C2×C3×D20C2311yescharacteristic
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5D411yescharacteristic
86C2×C3×C4×D5D411yescharacteristic
87C2×C3×C4×D5C2311yescharacteristic
88C2×C3×Dic10—21no—
89C2×C3×Dic10C2311yescharacteristic
90C3×C5×Q16—22no—
91C2×C3×C5×C8C2311yescharacteristic
92C2×C3×C5×C8C2311yescharacteristic
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C42×C5—21no—
98C3×C42×C5—21no—
99C3×C42×C5C2311yescharacteristic
100C3×#689—22no—
101C3×#688—22no—
102C3×#685—21no—
103C3×#685—21no—
104C3×#685—21no—
105C3×#685—21no—
106C3×#685—21no—
107C3×C4⋊Dic5—21no—
108C3×C4⋊Dic5—21no—
109C3×C4⋊Dic5C2311yescharacteristic
110C3×C4⋊Dic5C2311yescharacteristic
111C3×#683—21no—
112C3×#683—21no—
113C3×#683—21no—
114C3×#683—21no—
115C3×#683—21no—
116C3×C4×Dic5—21no—
117C3×C4×Dic5—21no—
118C3×C4×Dic5—21no—
119C3×C4×Dic5D411yescharacteristic
120C3×C4×Dic5D411yescharacteristic
121C3×C4×Dic5C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C3×#677—22no—
125C3×#529—51no—
126C2×C3×C4×Q8—51no—
127C3×#484—51no—
128C3×#481—51no—
129C3×#479—51no—
130C3×#479—51no—
131C3×#464—51no—
132C3×#464—51no—
133C3×#451—51no—
134C3×#448—51no—
135C3×#441—51no—
136C3×#441D511yescharacteristic, complemented
137C3×#440—51no—
138C3×#440—51no—
139C3×#432—51no—
140C2×Q8×D5C22×C311yescharacteristic
141C2×C5×Q16C22×C311yescharacteristic
142C4×C5×Q8C22×C311yescharacteristic
143C4×C5×Q8C22×C311yescharacteristic
144#4093C22×C311yescharacteristic
145#4092C22×C311yescharacteristic
146Q8×Dic5C22×C311yescharacteristic
147C2×#689C22×C311yescharacteristic
148C2×#688C22×C311yescharacteristic
149C2×#677C22×C311yescharacteristic
150#4044—21no—
151#4041C22×C311yescharacteristic
152#4040—21no—
153D5×C4⋊C4—21no—
154D5×C4⋊C4C22×C311yescharacteristic
155#4036C22×C311yescharacteristic
156#4033—21no—
157#4033C22×C311yescharacteristic
158C4×D20—21no—
159C4×D20C22×C311yescharacteristic
160#4018—21no—
161C42×D5—21no—
162C42×D5C22×C311yescharacteristic
163C4×Dic10—21no—
164C4×Dic10C22×C311yescharacteristic
165C5×#106C22×C311yescharacteristic
166C5×#103C22×C311yescharacteristic
167C5×#103C22×C311yescharacteristic
168C5×#97C22×C311yescharacteristic
169#3967C22×C311yescharacteristic
170#3967C22×C311yescharacteristic
171#3953C22×C311yescharacteristic
172#3952C22×C311yescharacteristic
173#3952C22×C311yescharacteristic
174#3950C22×C311yescharacteristic
175#3948C22×C311yescharacteristic
176#3946C22×C311yescharacteristic
177#3946C22×C311yescharacteristic
178#3942C22×C311yescharacteristic
179#3941C22×C311yescharacteristic
180#3940C22×C311yescharacteristic
181#3939C22×C311yescharacteristic
182#3935C22×C311yescharacteristic
183#3117—51noSylow
184C22×C3×D5—21no—
185C22×C3×D5C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8#4112yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5C2×D411yescharacteristic
195C2×C3×C4×C5C2×D411yescharacteristic
196C2×C3×C4×C5C2411yescharacteristic
197C2×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5C2×D411yescharacteristic
201C2×C3×Dic5C2×D411yescharacteristic
202C2×C3×Dic5C2×D411yescharacteristic
203C3×D20—21no—
204C3×D20—21no—
205C3×D20—42no—
206C3×C4×D5—24no—
207C3×C4×D5—22no—
208C3×C4×D5—21no—
209C3×C4×D5—21no—
210C3×C4×D5—41no—
211C3×C4×D5—42no—
212C3×C4×D5—42no—
213C3×Dic10—24no—
214C3×Dic10—21no—
215C3×Dic10#4112yes—
216C3×C5×C8—21no—
217C3×C5×C8—21no—
218C3×#168—21no—
219C3×#168—21no—
220C22×C3×Q8—51no—
221C2×C3×Q16—51no—
222C2×C3×Q16C2×D511yescharacteristic
223C2×C3×SD16—51no—
224C2×C3×SD16—51no—
225C3×#126—101no—
226C3×#125—51no—
227C3×#124—51no—
228C3×#123—101no—
229C3×C22⋊Q8—51no—
230C3×#121—51no—
231C3×C4×Q8—51no—
232C3×C4×Q8—51no—
233C3×C4×Q8—51no—
234C3×C4×Q8—101no—
235C3×C4×Q8—101no—
236C3×C4×Q8C2×D511yescharacteristic
237C3×C4×Q8C2×D511yescharacteristic
238C3×C4×D4—51no—
239C3×C4×D4—101no—
240C3×#117—101no—
241C2×C3×C4⋊C4—51no—
242C2×C3×C4⋊C4—101no—
243C2×C3×C42—51no—
244C2×C3×C42—101no—
245C3×#107—51no—
246C3×#107—51no—
247C3×#106—51no—
248C3×#106C2×D511yescharacteristic
249C3×C4⋊C8—51no—
250C3×C4⋊C8—51no—
251C3×#103—51no—
252C3×#103—51no—
253C3×#103—51no—
254C3×#103—51no—
255C3×#103C2×D511yescharacteristic
256C3×#103C2×D511yescharacteristic
257C3×#102—51no—
258C3×#102—51no—
259C3×C22⋊C8—51no—
260C3×C22⋊C8—51no—
261C3×#97—51no—
262C3×#97C2×D511yescharacteristic
263C2×C5×Q8C23×C311yescharacteristic
264C2×C5×Q8C23×C311yescharacteristic
265Q8×D5—22no—
266Q8×D5—22no—
267C2×D20—21no—
268C2×D20C23×C311yescharacteristic
269C2×C4×D5—21no—
270C2×C4×D5—21no—
271C2×C4×D5—21no—
272C2×C4×D5C3×D411yescharacteristic
273C2×C4×D5C3×D411yescharacteristic
274C2×C4×D5C23×C311yescharacteristic
275C2×Dic10—21no—
276C2×Dic10C23×C311yescharacteristic
277C5×Q16—22no—
278C2×C5×C8C23×C311yescharacteristic
279C2×C5×C8C23×C311yescharacteristic
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4C23×C311yescharacteristic
283C5×C4⋊C4C23×C311yescharacteristic
284C42×C5—21no—
285C42×C5—21no—
286C42×C5C23×C311yescharacteristic
287#689—22no—
288#688—22no—
289#685—21no—
290#685—21no—
291#685—21no—
292#685—21no—
293#685—21no—
294C4⋊Dic5—21no—
295C4⋊Dic5—21no—
296C4⋊Dic5C23×C311yescharacteristic
297C4⋊Dic5C23×C311yescharacteristic
298#683—21no—
299#683—21no—
300#683—21no—
301#683—21no—
302#683—21no—
303C4×Dic5—21no—
304C4×Dic5—21no—
305C4×Dic5—21no—
306C4×Dic5C3×D411yescharacteristic
307C4×Dic5C3×D411yescharacteristic
308C4×Dic5C23×C311yescharacteristic
309C2×#168C23×C311yescharacteristic
310C2×#168C23×C311yescharacteristic
311#677—22no—
312#529—51no—
313C2×C4×Q8—51no—
314#484—51no—
315#481—51no—
316#479—51no—
317#479—51no—
318#464—51no—
319#464—51no—
320#451—51no—
321#448—51no—
322#441—51no—
323#441C3×D511yescharacteristic, complemented
324#440—51no—
325#440—51no—
326#432—51no—
327C22×C3×C5C22×D411yescharacteristic
328C2×C3×D5—21no—
329C2×C3×D5—21no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C2×C3×D5—41no—
333C2×C3×D5#13712yes—
334C3×C4×C5—22no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—41no—
338C3×C4×C5—41no—
339C3×C4×C5—41no—
340C3×C4×C5C2×#4111yescharacteristic
341C3×C4×C5C2×#4111yescharacteristic
342C3×Dic5—21no—
343C3×Dic5—22no—
344C3×Dic5—21no—
345C3×Dic5—21no—
346C3×Dic5—41no—
347C3×Dic5—41no—
348C2×C3×Q8—51no—
349C2×C3×Q8—101no—
350C2×C3×Q8—102no—
351C2×C3×Q8—102no—
352C2×C3×Q8C22×D511yescharacteristic
353C2×C3×Q8C22×D511yescharacteristic
354C2×C3×D4—51no—
355C2×C3×D4—101no—
356C22×C3×C4—51no—
357C22×C3×C4—51no—
358C22×C3×C4—51no—
359C22×C3×C4—101no—
360C22×C3×C4—101no—
361C22×C3×C4—101no—
362C3×Q16—22no—
363C3×Q16—102no—
364C3×SD16—102no—
365C3×SD16—102no—
366C2×C3×C8—51no—
367C2×C3×C8—51no—
368C2×C3×C8C22×D511yescharacteristic
369C2×C3×C8C22×D511yescharacteristic
370C3×C4⋊C4—21no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—51no—
373C3×C4⋊C4—51no—
374C3×C4⋊C4—101no—
375C3×C4⋊C4—101no—
376C3×C4⋊C4—101no—
377C3×C4⋊C4—101no—
378C3×C4⋊C4—101no—
379C3×C4⋊C4—101no—
380C3×C4⋊C4—101no—
381C3×C4⋊C4C22×D511yescharacteristic
382C3×C4⋊C4C22×D511yescharacteristic
383C3×C22⋊C4—101no—
384C3×C22⋊C4—101no—
385C3×C22⋊C4—101no—
386C3×C22⋊C4—101no—
387C3×C22⋊C4—101no—
388C3×C42—21no—
389C3×C42—21no—
390C3×C42—51no—
391C3×C42—51no—
392C3×C42—51no—
393C3×C42—101no—
394C3×C42—101no—
395C3×C42—101no—
396C3×C42C22×D511yescharacteristic
397C22×D5—21no—
398C22×D5C2×C3×D411yescharacteristic
399C5×Q8—21no—
400C5×Q8—21no—
401C5×Q8—21no—
402C5×Q8C3×#4112yes—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5C2×C3×D411yescharacteristic
408C2×C4×C5C2×C3×D411yescharacteristic
409C2×C4×C5C24×C311yescharacteristic
410C2×Dic5—21no—
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5C2×C3×D411yescharacteristic
414C2×Dic5C2×C3×D411yescharacteristic
415C2×Dic5C2×C3×D411yescharacteristic
416D20—21no—
417D20—21no—
418D20—42no—
419C4×D5—24no—
420C4×D5—22no—
421C4×D5—21no—
422C4×D5—21no—
423C4×D5—41no—
424C4×D5—42no—
425C4×D5—42no—
426Dic10—24no—
427Dic10—21no—
428Dic10C3×#4112yes—
429C5×C8—21no—
430C5×C8—21no—
431#168—21no—
432#168—21no—
433C22×Q8—51no—
434C2×Q16—51no—
435C2×Q16C2×C3×D511yescharacteristic
436C2×SD16—51no—
437C2×SD16—51no—
438#126—101no—
439#125—51no—
440#124—51no—
441#123—101no—
442C22⋊Q8—51no—
443#121—51no—
444C4×Q8—51no—
445C4×Q8—51no—
446C4×Q8—51no—
447C4×Q8—101no—
448C4×Q8—101no—
449C4×Q8C2×C3×D511yescharacteristic
450C4×Q8C2×C3×D511yescharacteristic
451C4×D4—51no—
452C4×D4—101no—
453#117—101no—
454C2×C4⋊C4—51no—
455C2×C4⋊C4—101no—
456C2×C42—51no—
457C2×C42—101no—
458#107—51no—
459#107—51no—
460#106—51no—
461#106C2×C3×D511yescharacteristic
462C4⋊C8—51no—
463C4⋊C8—51no—
464#103—51no—
465#103—51no—
466#103—51no—
467#103—51no—
468#103C2×C3×D511yescharacteristic
469#103C2×C3×D511yescharacteristic
470#102—51no—
471#102—51no—
472C22⋊C8—51no—
473C22⋊C8—51no—
474#97—51no—
475#97C2×C3×D511yescharacteristic
476C2×C3×C5#52511yescharacteristic
477C2×C3×C5C2×#13711yescharacteristic
478C2×C3×C5#57511yescharacteristic
479C3×D5—22no—
480C3×D5—81no—
481C23×C3—51no—
482C23×C3—101no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—52no—
487C3×Q8—104no—
488C3×Q8—101no—
489C3×Q8#70912yes—
490C3×D4—101no—
491C3×D4—101no—
492C3×D4—202no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—51no—
498C2×C3×C4—51no—
499C2×C3×C4—51no—
500C2×C3×C4—102no—
501C2×C3×C4—104no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4—101no—
505C2×C3×C4—101no—
506C2×C3×C4—101no—
507C2×C3×C4—201no—
508C2×C3×C4—202no—
509C2×C3×C4—202no—
510C2×C3×C4D4×D511yescharacteristic
511C2×C3×C4D4×D511yescharacteristic
512C2×C3×C4C23×D511yescharacteristic
513C3×C8—21no—
514C3×C8—21no—
515C3×C8—101no—
516C3×C8—101no—
517C22×C5C22×C3×D411yescharacteristic
518C2×D5—21no—
519C2×D5—21no—
520C2×D5—41no—
521C2×D5—41no—
522C2×D5—41no—
523C2×D5C3×#13712yes—
524C4×C5—21no—
525C4×C5—21no—
526C4×C5—22no—
527C4×C5—41no—
528C4×C5—41no—
529C4×C5—41no—
530C4×C5C2×C3×#4111yescharacteristic
531C4×C5C2×C3×#4111yescharacteristic
532Dic5—21no—
533Dic5—21no—
534Dic5—21no—
535Dic5—22no—
536Dic5—41no—
537Dic5—41no—
538C2×Q8—51no—
539C2×Q8—101no—
540C2×Q8—102no—
541C2×Q8—102no—
542C2×Q8C22×C3×D511yescharacteristic
543C2×Q8C22×C3×D511yescharacteristic
544C2×D4—51no—
545C2×D4—101no—
546C22×C4—51no—
547C22×C4—51no—
548C22×C4—51no—
549C22×C4—101no—
550C22×C4—101no—
551C22×C4—101no—
552Q16—22no—
553Q16—102no—
554SD16—102no—
555SD16—102no—
556C2×C8—51no—
557C2×C8—51no—
558C2×C8C22×C3×D511yescharacteristic
559C2×C8C22×C3×D511yescharacteristic
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—51no—
563C4⋊C4—51no—
564C4⋊C4—101no—
565C4⋊C4—101no—
566C4⋊C4—101no—
567C4⋊C4—101no—
568C4⋊C4—101no—
569C4⋊C4—101no—
570C4⋊C4—101no—
571C4⋊C4C22×C3×D511yescharacteristic
572C4⋊C4C22×C3×D511yescharacteristic
573C22⋊C4—101no—
574C22⋊C4—101no—
575C22⋊C4—101no—
576C22⋊C4—101no—
577C22⋊C4—101no—
578C42—21no—
579C42—21no—
580C42—51no—
581C42—51no—
582C42—51no—
583C42—101no—
584C42—101no—
585C42—101no—
586C42C22×C3×D511yescharacteristic
587C3×C5#311711yescharacteristic, complemented, Hall
588C22×C3—52no—
589C22×C3—101no—
590C22×C3—101no—
591C22×C3—201no—
592C22×C3—201no—
593C22×C3—201no—
594C22×C3C2×D4×D511yescharacteristic
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—22no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—101no—
602C3×C4—101no—
603C3×C4—101no—
604C3×C4—102no—
605C3×C4—201no—
606C3×C4—201no—
607C3×C4C2×#70911yescharacteristic
608C3×C4D5×#4111yescharacteristic
609C2×C5C3×#52511yescharacteristic
610C2×C5C2×C3×#13711yescharacteristic
611C2×C5C3×#57511yescharacteristic
612D5—22no—
613D5—81no—
614C23—51no—
615C23—101no—
616Q8—21no—
617Q8—21no—
618Q8—21no—
619Q8—52no—
620Q8—104no—
621Q8—101no—
622Q8C3×#70912yes—
623D4—101no—
624D4—101no—
625D4—202no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—51no—
631C2×C4—51no—
632C2×C4—51no—
633C2×C4—102no—
634C2×C4—104no—
635C2×C4—101no—
636C2×C4—101no—
637C2×C4—101no—
638C2×C4—101no—
639C2×C4—101no—
640C2×C4—201no—
641C2×C4—202no—
642C2×C4—202no—
643C2×C4C3×D4×D511yescharacteristic
644C2×C4C3×D4×D511yescharacteristic
645C2×C4C23×C3×D511yescharacteristic
646C8—21no—
647C8—21no—
648C8—101no—
649C8—101no—
650C2×C3—102no—
651C2×C3—401no—
652C2×C3#6588111yescharacteristic
653C2×C3D5×#13711yescharacteristic
654C2×C3#6611111yescharacteristic
655C5C3×#311711yescharacteristic, complemented, Sylow
656C22—52no—
657C22—101no—
658C22—101no—
659C22—201no—
660C22—201no—
661C22—201no—
662C22C2×C3×D4×D511yescharacteristic
663C4—21no—
664C4—21no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—101no—
670C4—101no—
671C4—101no—
672C4—102no—
673C4—201no—
674C4—201no—
675C4C2×C3×#70911yescharacteristic
676C4C3×D5×#4111yescharacteristic
677C3#1061156511yescharacteristic, direct product factor, Sylow
678C2—102no—
679C2—401no—
680C2C3×#6588111yescharacteristic
681C2C3×D5×#13711yescharacteristic
682C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#441C2
socleC22×C3×C5C22×D4
prime radicalC3×#4041C22
hypercenterC3×#441D5
hypocenterC5C3×#3117
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#441

Complements

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

NH ≅ G/Ntype
2. C3×C4×Q8×D5C2semidirect
3. C3×C5×#441C2semidirect
4. C3×#65475C2semidirect
5. C3×#65474C2semidirect
6. C3×#65319C2semidirect
7. C3×#65315C2semidirect
9. C3×#65146C2semidirect
10. C3×#65098C2semidirect
12. C3×#65087C2semidirect
13. C3×#65085C2semidirect
14. C3×#64999C2semidirect
15. C3×#64994C2semidirect
16. #10611565C3direct (N × H)
62. C4×Q8×D5C2×C3semidirect
63. C5×#441C2×C3semidirect
64. #65475C2×C3semidirect
65. #65474C2×C3semidirect
66. #65319C2×C3semidirect
67. #65315C2×C3semidirect
69. #65146C2×C3semidirect
70. #65098C2×C3semidirect
72. #65087C2×C3semidirect
73. #65085C2×C3semidirect
74. #64999C2×C3semidirect
75. #64994C2×C3semidirect
136. C3×#441D5semidirect
323. #441C3×D5semidirect
587. C3×C5#3117semidirect
655. C5C3×#3117semidirect
677. C3#10611565direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659142
C3×C4×Q8×D52
C3×C5×#4412
C3×#654752
C3×#654742
C3×#653192
C3×#653152
C3×#651522
C3×#651462
C3×#650982
C3×#650952
C3×#650872
C3×#650852
C3×#649992
C3×#649942
#106115653
C3×#31175