Finite Group Databasebeta

← C3×#10615177 #14436076

Subgroups — C3×#10615177 #14436076

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#541C211yesmaximal, characteristic, complemented
2C3×#65857C211yesmaximal, characteristic
3C3×#65379C211yesmaximal, characteristic, complemented
4C3×#65372C211yesmaximal, characteristic, complemented
5C3×#65355C211yesmaximal, characteristic, complemented
6C3×#65352C211yesmaximal, characteristic, complemented
7C3×#65336C211yesmaximal, characteristic
8C3×#65336C211yesmaximal, characteristic
9C3×#65333C211yesmaximal, characteristic, complemented
10C3×#65332C211yesmaximal, characteristic, complemented
11C3×#65319C211yesmaximal, characteristic, complemented
12C3×C4×#689C211yesmaximal, characteristic, complemented
13C3×#65315C211yesmaximal, characteristic, complemented
14C3×C4×#688C211yesmaximal, characteristic, complemented
15C3×#65289C211yesmaximal, characteristic, complemented
16#10615177C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#709C2211yescharacteristic
18C3×C5×C4⋊Q8C2211yescharacteristic
19C3×C5×#126—21no—
20C3×C5×#126—21no—
21C3×C5×#125—21no—
22C3×C5×#125—21no—
23C3×C5×#125C2211yescharacteristic
24C3×C5×C22⋊Q8C2211yescharacteristic
25C3×C5×C22⋊Q8C2211yescharacteristic
26C3×C4×C5×Q8C2211yescharacteristic
27C3×C4×C5×Q8C2211yescharacteristic
28C3×C5×#117C2211yescharacteristic
29C2×C3×#689C2211yescharacteristic
30C2×C3×#689C2211yescharacteristic
31C2×C3×#688C2211yescharacteristic
32C2×C3×#688C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C3×#4038—21no—
35C3×D5×C4⋊C4—21no—
36C3×#4027—21no—
37C3×#4027—21no—
38C3×C4×D20C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C3×C4×Dic10C2211yescharacteristic
41C3×C4×Dic10C2211yescharacteristic
42C3×#3967C2211yescharacteristic
43C3×#3967C2211yescharacteristic
44C3×#3967C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×C22⋊#168C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48C3×#3942C2211yescharacteristic
49C3×#3942C2211yescharacteristic
50C3×#3941C2211yescharacteristic
51C3×#3941C2211yescharacteristic
52C3×#3940C2211yescharacteristic
53C3×#3940C2211yescharacteristic
54C3×#3939C2211yescharacteristic
55C3×#3939C2211yescharacteristic
56C3×C4⋊#168C2211yescharacteristic
57C3×C4⋊#168C2211yescharacteristic
58C3×#3935C2211yescharacteristic
59C3×C4×#168C2211yescharacteristic
60C3×#3120—51nomaximal, Hall
61C5×#541C2×C311yescharacteristic, complemented
62#65857C2×C311yescharacteristic
63#65379C2×C311yescharacteristic, complemented
64#65372C2×C311yescharacteristic, complemented
65#65355C2×C311yescharacteristic, complemented
66#65352C2×C311yescharacteristic, complemented
67#65336C2×C311yescharacteristic
68#65336C2×C311yescharacteristic
69#65333C2×C311yescharacteristic, complemented
70#65332C2×C311yescharacteristic, complemented
71#65319C2×C311yescharacteristic, complemented
72C4×#689C2×C311yescharacteristic, complemented
73#65315C2×C311yescharacteristic, complemented
74C4×#688C2×C311yescharacteristic, complemented
75#65289C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×C3×C22⋊D5—21no—
80C22×C3×Dic5—21no—
81C3×#709—22no—
82C3×#709—22no—
83C2×C3×D20C2311yescharacteristic
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4—21no—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4—21no—
96C3×C5×C4⋊C4D411yescharacteristic
97C3×C5×C4⋊C4D411yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4D411yescharacteristic
103C3×C5×C22⋊C4D411yescharacteristic
104C3×C42×C5—21no—
105C3×C42×C5—21no—
106C3×C42×C5C2311yescharacteristic
107C3×C42×C5C2311yescharacteristic
108C3×#689—22no—
109C3×#689—22no—
110C3×#688—22no—
111C3×#688—22no—
112C3×#685—21no—
113C3×#685—21no—
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×#683—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#541D511yescharacteristic, complemented
126C3×#520—51no—
127C3×#484—51no—
128C3×#483—51no—
129C3×#479—51no—
130C3×#478—51no—
131C3×#462—51no—
132C3×#461—51no—
133C3×#452—51no—
134C3×#452—51no—
135C3×#441—51no—
136C3×#440—51no—
137C3×C4×Q16—51no—
138C3×C4×SD16—51no—
139C3×#433—51no—
140C2×#709C22×C311yescharacteristic
141C5×C4⋊Q8C22×C311yescharacteristic
142C5×#126—21no—
143C5×#126—21no—
144C5×#125—21no—
145C5×#125—21no—
146C5×#125C22×C311yescharacteristic
147C5×C22⋊Q8C22×C311yescharacteristic
148C5×C22⋊Q8C22×C311yescharacteristic
149C4×C5×Q8C22×C311yescharacteristic
150C4×C5×Q8C22×C311yescharacteristic
151C5×#117C22×C311yescharacteristic
152C2×#689C22×C311yescharacteristic
153C2×#689C22×C311yescharacteristic
154C2×#688C22×C311yescharacteristic
155C2×#688C22×C311yescharacteristic
156C2×C4⋊Dic5C22×C311yescharacteristic
157#4038—21no—
158D5×C4⋊C4—21no—
159#4027—21no—
160#4027—21no—
161C4×D20C22×C311yescharacteristic
162C4×D20C22×C311yescharacteristic
163C4×Dic10C22×C311yescharacteristic
164C4×Dic10C22×C311yescharacteristic
165#3967C22×C311yescharacteristic
166#3967C22×C311yescharacteristic
167#3967C22×C311yescharacteristic
168#3967C22×C311yescharacteristic
169C22⋊#168C22×C311yescharacteristic
170C22⋊#168C22×C311yescharacteristic
171#3942C22×C311yescharacteristic
172#3942C22×C311yescharacteristic
173#3941C22×C311yescharacteristic
174#3941C22×C311yescharacteristic
175#3940C22×C311yescharacteristic
176#3940C22×C311yescharacteristic
177#3939C22×C311yescharacteristic
178#3939C22×C311yescharacteristic
179C4⋊#168C22×C311yescharacteristic
180C4⋊#168C22×C311yescharacteristic
181#3935C22×C311yescharacteristic
182C4×#168C22×C311yescharacteristic
183#3120—51noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C3×D5—21no—
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202C3×C22⋊D5—24no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—81no—
207C3×D20—21no—
208C3×D20#4112yes—
209C3×C4×D5—24no—
210C3×C4×D5—81no—
211C3×C4×D5—81no—
212C3×Dic10—21no—
213C3×Dic10#4112yes—
214C3×#168—21no—
215C3×#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×C3×#41—51no—
219C2×C3×Q16—51no—
220C2×C3×Q16—51no—
221C2×C3×SD16—51no—
222C2×C3×SD16—51no—
223C3×C4⋊Q8C2×D511yescharacteristic
224C3×#126—21no—
225C3×#126—21no—
226C3×#125—21no—
227C3×#125—21no—
228C3×#125C2×D511yescharacteristic
229C3×C22⋊Q8C2×D511yescharacteristic
230C3×C22⋊Q8C2×D511yescharacteristic
231C3×C4×Q8—51no—
232C3×C4×Q8—51no—
233C3×C4×Q8C2×D511yescharacteristic
234C3×C4×Q8C2×D511yescharacteristic
235C3×C4×D4—51no—
236C3×C4×D4—51no—
237C3×C4×D4—101no—
238C3×C4×D4—101no—
239C3×#117—101no—
240C3×#117C2×D511yescharacteristic
241C2×C3×C4⋊C4—51no—
242C2×C3×C4⋊C4—101no—
243C3×#107—51no—
244C3×#107—51no—
245C3×#106—51no—
246C3×#106—51no—
247C3×C4⋊C8—51no—
248C3×C4⋊C8—51no—
249C3×#103—51no—
250C3×#103—51no—
251C3×#103—51no—
252C3×#103—51no—
253C3×#103—51no—
254C3×#103—51no—
255C3×#102—51no—
256C3×#102—51no—
257C3×C22⋊C8—51no—
258C3×C22⋊C8—51no—
259C3×#97—51no—
260C3×C4×C8—51no—
261C2×C5×Q8C23×C311yescharacteristic
262C2×C5×Q8C23×C311yescharacteristic
263C22×C4×C5C23×C311yescharacteristic
264C2×C22⋊D5—21no—
265C22×Dic5—21no—
266#709—22no—
267#709—22no—
268C2×D20C23×C311yescharacteristic
269C2×C4×D5—21no—
270C2×C4×D5—21no—
271C2×C4×D5—21no—
272C2×Dic10C23×C311yescharacteristic
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—21no—
279C5×C4⋊C4—21no—
280C5×C4⋊C4—21no—
281C5×C4⋊C4C3×D411yescharacteristic
282C5×C4⋊C4C3×D411yescharacteristic
283C5×C4⋊C4C23×C311yescharacteristic
284C5×C4⋊C4C23×C311yescharacteristic
285C5×C22⋊C4—21no—
286C5×C22⋊C4—21no—
287C5×C22⋊C4C3×D411yescharacteristic
288C5×C22⋊C4C3×D411yescharacteristic
289C42×C5—21no—
290C42×C5—21no—
291C42×C5C23×C311yescharacteristic
292C42×C5C23×C311yescharacteristic
293#689—22no—
294#689—22no—
295#688—22no—
296#688—22no—
297#685—21no—
298#685—21no—
299C4⋊Dic5—21no—
300C4⋊Dic5C23×C311yescharacteristic
301C4⋊Dic5C23×C311yescharacteristic
302#683—21no—
303#683—21no—
304C4×Dic5—21no—
305C4×Dic5—21no—
306C2×#168C23×C311yescharacteristic
307C2×#168C23×C311yescharacteristic
308C2×#168C23×C311yescharacteristic
309C2×#168C23×C311yescharacteristic
310#541C3×D511yescharacteristic, complemented
311#520—51no—
312#484—51no—
313#483—51no—
314#479—51no—
315#478—51no—
316#462—51no—
317#461—51no—
318#452—51no—
319#452—51no—
320#441—51no—
321#440—51no—
322C4×Q16—51no—
323C4×SD16—51no—
324#433—51no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C3×D5—22no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—41no—
338C3×C4×C5—41no—
339C3×C4×C5—41no—
340C3×C4×C5—41no—
341C3×C4×C5C2×#4111yescharacteristic
342C3×C4×C5C2×#4111yescharacteristic
343C3×Dic5—22no—
344C3×Dic5—41no—
345C3×Dic5—41no—
346C3×#41—102no—
347C3×#41—102no—
348C2×C3×Q8—51no—
349C2×C3×Q8C22×D511yescharacteristic
350C2×C3×Q8C22×D511yescharacteristic
351C2×C3×D4—51no—
352C2×C3×D4—101no—
353C22×C3×C4—101no—
354C22×C3×C4—101no—
355C22×C3×C4—101no—
356C22×C3×C4—101no—
357C22×C3×C4C22×D511yescharacteristic
358C3×Q16—102no—
359C3×Q16—102no—
360C3×SD16—102no—
361C3×SD16—102no—
362C2×C3×C8—51no—
363C2×C3×C8—51no—
364C2×C3×C8—51no—
365C2×C3×C8—51no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—51no—
375C3×C4⋊C4—51no—
376C3×C4⋊C4—101no—
377C3×C4⋊C4—101no—
378C3×C4⋊C4—101no—
379C3×C4⋊C4C22⋊D511yescharacteristic
380C3×C4⋊C4C22⋊D511yescharacteristic
381C3×C4⋊C4C22×D511yescharacteristic
382C3×C4⋊C4C22×D511yescharacteristic
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—101no—
386C3×C22⋊C4—101no—
387C3×C22⋊C4C22⋊D511yescharacteristic
388C3×C22⋊C4C22⋊D511yescharacteristic
389C3×C42—21no—
390C3×C42—21no—
391C3×C42—101no—
392C3×C42—101no—
393C3×C42C22×D511yescharacteristic
394C3×C42C22×D511yescharacteristic
395C23×C5C2×C3×D411yescharacteristic
396C22×D5—21no—
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—21no—
400C5×Q8—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
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×C5C2×C3×D411yescharacteristic
410C2×C4×C5C2×C3×D411yescharacteristic
411C2×C4×C5C2×C3×D411yescharacteristic
412C2×C4×C5C24×C311yescharacteristic
413C22⋊D5—24no—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—21no—
417C2×Dic5—81no—
418D20—21no—
419D20C3×#4112yes—
420C4×D5—24no—
421C4×D5—81no—
422C4×D5—81no—
423Dic10—21no—
424Dic10C3×#4112yes—
425#168—21no—
426#168—21no—
427#168—21no—
428#168—21no—
429C2×#41—51no—
430C2×Q16—51no—
431C2×Q16—51no—
432C2×SD16—51no—
433C2×SD16—51no—
434C4⋊Q8C2×C3×D511yescharacteristic
435#126—21no—
436#126—21no—
437#125—21no—
438#125—21no—
439#125C2×C3×D511yescharacteristic
440C22⋊Q8C2×C3×D511yescharacteristic
441C22⋊Q8C2×C3×D511yescharacteristic
442C4×Q8—51no—
443C4×Q8—51no—
444C4×Q8C2×C3×D511yescharacteristic
445C4×Q8C2×C3×D511yescharacteristic
446C4×D4—51no—
447C4×D4—51no—
448C4×D4—101no—
449C4×D4—101no—
450#117—101no—
451#117C2×C3×D511yescharacteristic
452C2×C4⋊C4—51no—
453C2×C4⋊C4—101no—
454#107—51no—
455#107—51no—
456#106—51no—
457#106—51no—
458C4⋊C8—51no—
459C4⋊C8—51no—
460#103—51no—
461#103—51no—
462#103—51no—
463#103—51no—
464#103—51no—
465#103—51no—
466#102—51no—
467#102—51no—
468C22⋊C8—51no—
469C22⋊C8—51no—
470#97—51no—
471C4×C8—51no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C3×D5—42no—
477C23×C3—101no—
478C23×C3C2×C22⋊D511yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—52no—
484C3×Q8—101no—
485C3×D4—52no—
486C3×D4—104no—
487C3×D4—101no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—104no—
495C2×C3×C4—101no—
496C2×C3×C4—101no—
497C2×C3×C4—101no—
498C2×C3×C4—401no—
499C2×C3×C4—401no—
500C2×C3×C4—401no—
501C2×C3×C4C2×C22⋊D511yescharacteristic
502C2×C3×C4C2×C22⋊D511yescharacteristic
503C2×C3×C4C2×C22⋊D511yescharacteristic
504C2×C3×C4C2×C22⋊D511yescharacteristic
505C2×C3×C4C2×C22⋊D511yescharacteristic
506C2×C3×C4C23×D511yescharacteristic
507C3×C8—101no—
508C3×C8—101no—
509C3×C8—101no—
510C3×C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C22×C3×D411yescharacteristic
515C2×D5—22no—
516C2×D5—41no—
517C2×D5—41no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—41no—
524C4×C5—41no—
525C4×C5—41no—
526C4×C5—41no—
527C4×C5C2×C3×#4111yescharacteristic
528C4×C5C2×C3×#4111yescharacteristic
529Dic5—22no—
530Dic5—41no—
531Dic5—41no—
532#41—102no—
533#41—102no—
534C2×Q8—51no—
535C2×Q8C22×C3×D511yescharacteristic
536C2×Q8C22×C3×D511yescharacteristic
537C2×D4—51no—
538C2×D4—101no—
539C22×C4—101no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4C22×C3×D511yescharacteristic
544Q16—102no—
545Q16—102no—
546SD16—102no—
547SD16—102no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8—51no—
551C2×C8—51no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—51no—
561C4⋊C4—51no—
562C4⋊C4—101no—
563C4⋊C4—101no—
564C4⋊C4—101no—
565C4⋊C4C3×C22⋊D511yescharacteristic
566C4⋊C4C3×C22⋊D511yescharacteristic
567C4⋊C4C22×C3×D511yescharacteristic
568C4⋊C4C22×C3×D511yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—101no—
572C22⋊C4—101no—
573C22⋊C4C3×C22⋊D511yescharacteristic
574C22⋊C4C3×C22⋊D511yescharacteristic
575C42—21no—
576C42—21no—
577C42—101no—
578C42—101no—
579C42C22×C3×D511yescharacteristic
580C42C22×C3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—102no—
586C22×C3—201no—
587C22×C3—201no—
588C22×C3C22×C22⋊D511yescharacteristic
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—102no—
599C3×C4—201no—
600C3×C4—201no—
601C3×C4D5×#4111yescharacteristic
602C3×C4D5×#4111yescharacteristic
603C2×C5—41no—
604C2×C5C3×#52511yescharacteristic
605C2×C5C3×#57711yescharacteristic
606C2×C5C3×#57811yescharacteristic
607D5—42no—
608C23—101no—
609C23C2×C3×C22⋊D511yescharacteristic
610Q8—21no—
611Q8—21no—
612Q8—21no—
613Q8—21no—
614Q8—52no—
615Q8—101no—
616D4—52no—
617D4—104no—
618D4—101no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—104no—
626C2×C4—101no—
627C2×C4—101no—
628C2×C4—101no—
629C2×C4—401no—
630C2×C4—401no—
631C2×C4—401no—
632C2×C4C2×C3×C22⋊D511yescharacteristic
633C2×C4C2×C3×C22⋊D511yescharacteristic
634C2×C4C2×C3×C22⋊D511yescharacteristic
635C2×C4C2×C3×C22⋊D511yescharacteristic
636C2×C4C2×C3×C22⋊D511yescharacteristic
637C2×C4C23×C3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—101no—
641C8—101no—
642C2×C3—41no—
643C2×C3—202no—
644C2×C3#6616211yescharacteristic
645C2×C3#6617111yescharacteristic
646C2×C3#6617211yescharacteristic
647C5C3×#312011yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—102no—
652C22—201no—
653C22—201no—
654C22C22×C3×C22⋊D511yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—102no—
665C4—201no—
666C4—201no—
667C4C3×D5×#4111yescharacteristic
668C4C3×D5×#4111yescharacteristic
669C3#1061517711yescharacteristic, direct product factor, Sylow
670C2—41no—
671C2—202no—
672C2C3×#6616211yescharacteristic
673C2C3×#6617111yescharacteristic
674C2C3×#6617211yescharacteristic
subgroupG/H
centerC22×C3C22×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#541C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
hypercenterC3×#541D5
hypocenterC5C3×#3120
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#541

Complements

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

NH ≅ G/Ntype
1. C3×C5×#541C2semidirect
3. C3×#65379C2semidirect
4. C3×#65372C2semidirect
5. C3×#65355C2semidirect
6. C3×#65352C2semidirect
9. C3×#65333C2semidirect
10. C3×#65332C2semidirect
11. C3×#65319C2semidirect
12. C3×C4×#689C2semidirect
13. C3×#65315C2semidirect
14. C3×C4×#688C2semidirect
15. C3×#65289C2semidirect
16. #10615177C3direct (N × H)
61. C5×#541C2×C3semidirect
63. #65379C2×C3semidirect
64. #65372C2×C3semidirect
65. #65355C2×C3semidirect
66. #65352C2×C3semidirect
69. #65333C2×C3semidirect
70. #65332C2×C3semidirect
71. #65319C2×C3semidirect
72. C4×#689C2×C3semidirect
73. #65315C2×C3semidirect
74. C4×#688C2×C3semidirect
75. #65289C2×C3semidirect
125. C3×#541D5semidirect
310. #541C3×D5semidirect
581. C3×C5#3120semidirect
647. C5C3×#3120semidirect
669. C3#10615177direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5412
C3×#658572
C3×#653792
C3×#653722
C3×#653552
C3×#653522
C3×#653362
C3×#653332
C3×#653322
C3×#653192
C3×C4×#6892
C3×#653152
C3×C4×#6882
C3×#652892
#106151773
C3×#31205