Finite Group Databasebeta

← C3×#10612462 #14458279

Subgroups — C3×#10612462 #14458279

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65945C211yesmaximal, characteristic, complemented
2C3×#65943C211yesmaximal, characteristic, complemented
3C3×C5×#466C211yesmaximal, characteristic, complemented
4C3×#65445C211yesmaximal, characteristic, complemented
5C3×#65439C211yesmaximal, characteristic, complemented
6C2×C3×#3953C211yesmaximal, characteristic, complemented
7C3×C8×C22⋊D5C211yesmaximal, characteristic, complemented
8C3×#65325C211yesmaximal, characteristic, complemented
9C3×#65322C211yesmaximal, characteristic, complemented
10C3×#65179C211yesmaximal, characteristic, complemented
11C3×#65171C211yesmaximal, characteristic, complemented
12C3×#65064C211yesmaximal, characteristic, complemented
13C3×D5×#102C211yesmaximal, characteristic, complemented
14C3×#65049C211yesmaximal, characteristic, complemented
15C3×#65045C211yesmaximal, characteristic, complemented
16#10612462C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#711—21no—
18C2×C3×D4×D5—21no—
19C2×C3×D4×D5C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C2×C3×C5×D8C2211yescharacteristic, complemented
22C22×C3×C5×C8C2211yescharacteristic, complemented
23C3×C5×#121C2211yescharacteristic
24C3×C5×#121C2211yescharacteristic, complemented
25C3×#4086C2211yescharacteristic
26C3×#4084C2211yescharacteristic, complemented
27C3×#4083—21no—
28C3×#4081—21no—
29C3×D4×Dic5C2211yescharacteristic, complemented
30C2×C3×#686C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic, complemented
32C3×C4×C22⋊D5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
34C2×C3×C8×D5C2211yescharacteristic, complemented
35C3×#4041C2211yescharacteristic
36C3×#4039C2211yescharacteristic
37C3×D5×C4⋊C4C2211yescharacteristic, complemented
38C3×#4034C2211yescharacteristic, complemented
39C3×#4030—21no—
40C3×#4029—21no—
41C3×#4028—21no—
42C3×#4024—21no—
43C3×C5×#107C2211yescharacteristic, complemented
44C3×C5×#102C2211yescharacteristic, complemented
45C3×C5×#102C2211yescharacteristic, complemented
46C3×#3964C2211yescharacteristic, complemented
47C3×#3964C2211yescharacteristic, complemented
48C3×C22⋊#168C2211yescharacteristic, complemented
49C3×#3953C2211yescharacteristic
50C3×#3953C2211yescharacteristic
51C3×#3953C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic, complemented
53C3×#3952C2211yescharacteristic, complemented
54C3×#3946C2211yescharacteristic, complemented
55C3×C8×Dic5C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic
57C3×#3941C2211yescharacteristic, complemented
58C3×#3939C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×#3294—51nomaximal, Hall
61#65945C2×C311yescharacteristic, complemented
62#65943C2×C311yescharacteristic, complemented
63C5×#466C2×C311yescharacteristic, complemented
64#65445C2×C311yescharacteristic, complemented
65#65439C2×C311yescharacteristic, complemented
66C2×#3953C2×C311yescharacteristic, complemented
67C8×C22⋊D5C2×C311yescharacteristic, complemented
68#65325C2×C311yescharacteristic, complemented
69#65322C2×C311yescharacteristic, complemented
70#65179C2×C311yescharacteristic, complemented
71#65171C2×C311yescharacteristic, complemented
72#65064C2×C311yescharacteristic, complemented
73D5×#102C2×C311yescharacteristic, complemented
74#65049C2×C311yescharacteristic, complemented
75#65045C2×C311yescharacteristic, complemented
76C23×C3×D5—21no—
77C23×C3×D5—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5D411yescharacteristic
88C22×C3×Dic5—21no—
89C22×C3×Dic5—21no—
90C3×#711—44no—
91C3×D4×D5—22no—
92C3×D4×D5—41no—
93C3×D4×D5—44no—
94C2×C3×D20—22no—
95C2×C3×D20—21no—
96C2×C3×D20—21no—
97C2×C3×D20—41no—
98C2×C3×D20C2311yescharacteristic
99C2×C3×D20C2311yescharacteristic
100C2×C3×C4×D5—21no—
101C2×C3×C4×D5—21no—
102C2×C3×C4×D5C2311yescharacteristic
103C2×C3×Dic10—21no—
104C3×C5×D8—41no—
105C2×C3×C5×C8—41no—
106C2×C3×C5×C8C2311yescharacteristic
107C2×C3×C5×C8C2311yescharacteristic
108C3×C5×C4⋊C4C2311yescharacteristic
109C3×C5×C4⋊C4C2311yescharacteristic
110C3×C5×C22⋊C4—21no—
111C3×C5×C22⋊C4—21no—
112C3×C22⋊Dic5—21no—
113C3×C22⋊Dic5—21no—
114C3×C22⋊Dic5D411yescharacteristic
115C3×#686—22no—
116C3×#686—41no—
117C3×#685—21no—
118C3×#685—21no—
119C3×#685D411yescharacteristic
120C3×C4⋊Dic5—21no—
121C3×C4⋊Dic5C2311yescharacteristic
122C3×C4⋊Dic5C2311yescharacteristic
123C3×#683—21no—
124C3×#683—21no—
125C3×#683D411yescharacteristic
126C3×C4×Dic5C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129C3×C8×D5—41no—
130C3×#547—51no—
131C3×D42—51no—
132C3×#486—51no—
133C3×#480—51no—
134C3×#480—51no—
135C3×#474—51no—
136C3×#466—51no—
137C3×#466D511yescharacteristic, complemented
138C3×#459—51no—
139C3×#447—51no—
140C3×#447—51no—
141C3×C4×D8—51no—
142C3×C8×D4—51no—
143C2×C3×#102—51no—
144C2×C3×#102—51no—
145C2×#711—21no—
146C2×D4×D5—21no—
147C2×D4×D5C22×C311yescharacteristic
148C22×D20C22×C311yescharacteristic
149C2×C5×D8C22×C311yescharacteristic, complemented
150C22×C5×C8C22×C311yescharacteristic, complemented
151C5×#121C22×C311yescharacteristic
152C5×#121C22×C311yescharacteristic, complemented
153#4086C22×C311yescharacteristic
154#4084C22×C311yescharacteristic, complemented
155#4083—21no—
156#4081—21no—
157D4×Dic5C22×C311yescharacteristic, complemented
158C2×#686C22×C311yescharacteristic
159C2×#686C22×C311yescharacteristic, complemented
160C4×C22⋊D5C22×C311yescharacteristic
161C2×C4⋊Dic5C22×C311yescharacteristic, complemented
162C2×C8×D5C22×C311yescharacteristic, complemented
163#4041C22×C311yescharacteristic
164#4039C22×C311yescharacteristic
165D5×C4⋊C4C22×C311yescharacteristic, complemented
166#4034C22×C311yescharacteristic, complemented
167#4030—21no—
168#4029—21no—
169#4028—21no—
170#4024—21no—
171C5×#107C22×C311yescharacteristic, complemented
172C5×#102C22×C311yescharacteristic, complemented
173C5×#102C22×C311yescharacteristic, complemented
174#3964C22×C311yescharacteristic, complemented
175#3964C22×C311yescharacteristic, complemented
176C22⋊#168C22×C311yescharacteristic, complemented
177#3953C22×C311yescharacteristic
178#3953C22×C311yescharacteristic
179#3953C22×C311yescharacteristic, complemented
180#3953C22×C311yescharacteristic, complemented
181#3952C22×C311yescharacteristic, complemented
182#3946C22×C311yescharacteristic, complemented
183C8×Dic5C22×C311yescharacteristic, complemented
184#3941C22×C311yescharacteristic
185#3941C22×C311yescharacteristic, complemented
186#3939C22×C311yescharacteristic, complemented
187#3939C22×C311yescharacteristic, complemented
188#3294—51noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5C2×D411yescharacteristic
192C22×C3×D5—21no—
193C22×C3×D5—21no—
194C22×C3×D5—42no—
195C22×C3×D5—42no—
196C22×C3×D5—42no—
197C22×C3×D5—42no—
198C22×C3×D5—81no—
199C22×C3×D5—81no—
200C22×C3×D5C2×D411yescharacteristic
201C3×C5×D4—21no—
202C3×C5×D4—21no—
203C3×C5×D4—21no—
204C3×C5×D4—21no—
205C3×C5×D4—42no—
206C3×C5×D4—42no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5C2×D411yescharacteristic
212C2×C3×C4×C5C2411yescharacteristic
213C3×C22⋊D5—42no—
214C3×C22⋊D5—42no—
215C3×C22⋊D5—42no—
216C3×C22⋊D5—81no—
217C3×C22⋊D5D814yescomplemented
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—42no—
221C2×C3×Dic5—42no—
222C2×C3×Dic5C2×D411yescharacteristic
223C2×C3×Dic5C2×D411yescharacteristic
224C2×C3×Dic5C2×D411yescharacteristic
225C3×D20—21no—
226C3×D20—21no—
227C3×D20—21no—
228C3×D20—42no—
229C3×D20—42no—
230C3×D20#4112yescomplemented
231C3×C4×D5—21no—
232C3×C4×D5—21no—
233C3×C4×D5—42no—
234C3×C4×D5—42no—
235C3×Dic10—42no—
236C3×C5×C8—21no—
237C3×C5×C8—21no—
238C3×#168—21no—
239C3×#168—21no—
240C2×C3×#41—101no—
241C22×C3×D4—51no—
242C22×C3×D4—51no—
243C22×C3×D4—101no—
244C2×C3×D8—51no—
245C2×C3×D8—51no—
246C2×C3×D8C2×D511yescharacteristic, complemented
247C22×C3×C8—51no—
248C22×C3×C8C2×D511yescharacteristic, complemented
249C3×C4⋊Q8—51no—
250C3×#127—51no—
251C3×#123—101no—
252C3×#123—101no—
253C3×C22⋊Q8—101no—
254C3×#121—51no—
255C3×#121—51no—
256C3×#121—101no—
257C3×#121C2×D511yescharacteristic
258C3×#121C2×D511yescharacteristic, complemented
259C3×#120—101no—
260C3×#120—101no—
261C3×C4×D4—51no—
262C3×C4×D4—51no—
263C3×C4×D4—51no—
264C2×C3×C4⋊C4—51no—
265C2×C3×C4⋊C4—51no—
266C3×#107—51no—
267C3×#107—51no—
268C3×#107C2×D511yescharacteristic, complemented
269C3×C4⋊C8—51no—
270C3×#102—51no—
271C3×#102—51no—
272C3×#102—51no—
273C3×#102—51no—
274C3×#102—51no—
275C3×#102—51no—
276C3×#102—51no—
277C3×#102—51no—
278C3×#102C2×D511yescharacteristic, complemented
279C3×#102C2×D511yescharacteristic, complemented
280C3×C22⋊C8—51no—
281C3×C22⋊C8—51no—
282C3×C4×C8—51no—
283C23×D5—21no—
284C23×D5—21no—
285C2×C5×D4—21no—
286C2×C5×D4—21no—
287C2×C5×D4C23×C311yescharacteristic
288C2×C5×D4C23×C311yescharacteristic
289C22×C4×C5C23×C311yescharacteristic
290C2×C22⋊D5—21no—
291C2×C22⋊D5—21no—
292C2×C22⋊D5—21no—
293C2×C22⋊D5—21no—
294C2×C22⋊D5C3×D411yescharacteristic
295C22×Dic5—21no—
296C22×Dic5—21no—
297#711—44no—
298D4×D5—22no—
299D4×D5—41no—
300D4×D5—44no—
301C2×D20—22no—
302C2×D20—21no—
303C2×D20—21no—
304C2×D20—41no—
305C2×D20C23×C311yescharacteristic
306C2×D20C23×C311yescharacteristic
307C2×C4×D5—21no—
308C2×C4×D5—21no—
309C2×C4×D5C23×C311yescharacteristic
310C2×Dic10—21no—
311C5×D8—41no—
312C2×C5×C8—41no—
313C2×C5×C8C23×C311yescharacteristic
314C2×C5×C8C23×C311yescharacteristic
315C5×C4⋊C4C23×C311yescharacteristic
316C5×C4⋊C4C23×C311yescharacteristic
317C5×C22⋊C4—21no—
318C5×C22⋊C4—21no—
319C22⋊Dic5—21no—
320C22⋊Dic5—21no—
321C22⋊Dic5C3×D411yescharacteristic
322#686—22no—
323#686—41no—
324#685—21no—
325#685—21no—
326#685C3×D411yescharacteristic
327C4⋊Dic5—21no—
328C4⋊Dic5C23×C311yescharacteristic
329C4⋊Dic5C23×C311yescharacteristic
330#683—21no—
331#683—21no—
332#683C3×D411yescharacteristic
333C4×Dic5C23×C311yescharacteristic
334C2×#168C23×C311yescharacteristic
335C2×#168C23×C311yescharacteristic
336C8×D5—41no—
337#547—51no—
338D42—51no—
339#486—51no—
340#480—51no—
341#480—51no—
342#474—51no—
343#466—51no—
344#466C3×D511yescharacteristic, complemented
345#459—51no—
346#447—51no—
347#447—51no—
348C4×D8—51no—
349C8×D4—51no—
350C2×#102—51no—
351C2×#102—51no—
352C22×C3×C5—21no—
353C22×C3×C5—21no—
354C22×C3×C5—41no—
355C22×C3×C5—41no—
356C22×C3×C5—41no—
357C22×C3×C5—41no—
358C22×C3×C5—41no—
359C22×C3×C5—41no—
360C22×C3×C5C2×D812yes—
361C22×C3×C5C22×D411yescharacteristic
362C2×C3×D5—21no—
363C2×C3×D5—21no—
364C2×C3×D5—22no—
365C2×C3×D5—41no—
366C2×C3×D5—41no—
367C2×C3×D5—41no—
368C2×C3×D5—41no—
369C2×C3×D5—41no—
370C2×C3×D5—84no—
371C2×C3×D5—84no—
372C2×C3×D5C2×D812yes—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5—41no—
376C3×C4×C5C2×#4111yescharacteristic
377C3×C4×C5H(5,𝔽2)11yescharacteristic
378C3×Dic5—21no—
379C3×Dic5—21no—
380C3×Dic5—41no—
381C3×Dic5—41no—
382C3×Dic5C2×D812yes—
383C24×C3—101no—
384C24×C3—101no—
385C3×#41—204no—
386C2×C3×Q8—101no—
387C2×C3×D4—21no—
388C2×C3×D4—21no—
389C2×C3×D4—51no—
390C2×C3×D4—51no—
391C2×C3×D4—51no—
392C2×C3×D4—102no—
393C2×C3×D4—101no—
394C2×C3×D4—101no—
395C2×C3×D4—101no—
396C2×C3×D4—101no—
397C2×C3×D4—102no—
398C2×C3×D4—101no—
399C2×C3×D4—101no—
400C2×C3×D4—201no—
401C2×C3×D4—201no—
402C2×C3×D4—204no—
403C2×C3×D4C22×D511yescharacteristic
404C2×C3×D4C22×D511yescharacteristic
405C22×C3×C4—51no—
406C22×C3×C4—101no—
407C22×C3×C4—101no—
408C22×C3×C4—101no—
409C22×C3×C4—101no—
410C22×C3×C4C22×D511yescharacteristic
411C3×D8—41no—
412C3×D8—102no—
413C3×D8—201no—
414C2×C3×C8—41no—
415C2×C3×C8—51no—
416C2×C3×C8—51no—
417C2×C3×C8—201no—
418C2×C3×C8C22×D511yescharacteristic
419C2×C3×C8C22×D511yescharacteristic
420C3×C4⋊C4—51no—
421C3×C4⋊C4—51no—
422C3×C4⋊C4—51no—
423C3×C4⋊C4—101no—
424C3×C4⋊C4—101no—
425C3×C4⋊C4—101no—
426C3×C4⋊C4C22×D511yescharacteristic
427C3×C4⋊C4C22×D511yescharacteristic
428C3×C22⋊C4—21no—
429C3×C22⋊C4—21no—
430C3×C22⋊C4—51no—
431C3×C22⋊C4—51no—
432C3×C22⋊C4—101no—
433C3×C22⋊C4—101no—
434C3×C22⋊C4—101no—
435C3×C22⋊C4—101no—
436C3×C42—51no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5C2×C3×D411yescharacteristic
440C22×D5—21no—
441C22×D5—21no—
442C22×D5—42no—
443C22×D5—42no—
444C22×D5—42no—
445C22×D5—42no—
446C22×D5—81no—
447C22×D5—81no—
448C22×D5C2×C3×D411yescharacteristic
449C5×D4—21no—
450C5×D4—21no—
451C5×D4—21no—
452C5×D4—21no—
453C5×D4—42no—
454C5×D4—42no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5C2×C3×D411yescharacteristic
460C2×C4×C5C24×C311yescharacteristic
461C22⋊D5—42no—
462C22⋊D5—42no—
463C22⋊D5—42no—
464C22⋊D5—81no—
465C22⋊D5C3×D814yescomplemented
466C2×Dic5—21no—
467C2×Dic5—21no—
468C2×Dic5—42no—
469C2×Dic5—42no—
470C2×Dic5C2×C3×D411yescharacteristic
471C2×Dic5C2×C3×D411yescharacteristic
472C2×Dic5C2×C3×D411yescharacteristic
473D20—21no—
474D20—21no—
475D20—21no—
476D20—42no—
477D20—42no—
478D20C3×#4112yescomplemented
479C4×D5—21no—
480C4×D5—21no—
481C4×D5—42no—
482C4×D5—42no—
483Dic10—42no—
484C5×C8—21no—
485C5×C8—21no—
486#168—21no—
487#168—21no—
488C2×#41—101no—
489C22×D4—51no—
490C22×D4—51no—
491C22×D4—101no—
492C2×D8—51no—
493C2×D8—51no—
494C2×D8C2×C3×D511yescharacteristic, complemented
495C22×C8—51no—
496C22×C8C2×C3×D511yescharacteristic, complemented
497C4⋊Q8—51no—
498#127—51no—
499#123—101no—
500#123—101no—
501C22⋊Q8—101no—
502#121—51no—
503#121—51no—
504#121—101no—
505#121C2×C3×D511yescharacteristic
506#121C2×C3×D511yescharacteristic, complemented
507#120—101no—
508#120—101no—
509C4×D4—51no—
510C4×D4—51no—
511C4×D4—51no—
512C2×C4⋊C4—51no—
513C2×C4⋊C4—51no—
514#107—51no—
515#107—51no—
516#107C2×C3×D511yescharacteristic, complemented
517C4⋊C8—51no—
518#102—51no—
519#102—51no—
520#102—51no—
521#102—51no—
522#102—51no—
523#102—51no—
524#102—51no—
525#102—51no—
526#102C2×C3×D511yescharacteristic, complemented
527#102C2×C3×D511yescharacteristic, complemented
528C22⋊C8—51no—
529C22⋊C8—51no—
530C4×C8—51no—
531C2×C3×C5—22no—
532C2×C3×C5—81no—
533C2×C3×C5—81no—
534C2×C3×C5#54611yescharacteristic
535C2×C3×C5C22×D811yescharacteristic
536C2×C3×C5#57711yescharacteristic
537C3×D5—22no—
538C3×D5—42no—
539C3×D5—81no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—51no—
543C23×C3—101no—
544C23×C3—101no—
545C23×C3—202no—
546C23×C3—202no—
547C23×C3—202no—
548C23×C3—202no—
549C23×C3—401no—
550C23×C3—401no—
551C23×C3D4×D511yescharacteristic
552C3×Q8—202no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—42no—
558C3×D4—42no—
559C3×D4—54no—
560C3×D4—52no—
561C3×D4—101no—
562C3×D4—101no—
563C3×D4—101no—
564C3×D4—202no—
565C3×D4—202no—
566C3×D4—202no—
567C3×D4—202no—
568C3×D4—202no—
569C3×D4—401no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—51no—
575C2×C3×C4—51no—
576C2×C3×C4—51no—
577C2×C3×C4—101no—
578C2×C3×C4—101no—
579C2×C3×C4—101no—
580C2×C3×C4—101no—
581C2×C3×C4—202no—
582C2×C3×C4—202no—
583C2×C3×C4—202no—
584C2×C3×C4—202no—
585C2×C3×C4D4×D511yescharacteristic
586C2×C3×C4C23×D511yescharacteristic
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—101no—
590C3×C8—101no—
591C22×C5—21no—
592C22×C5—21no—
593C22×C5—41no—
594C22×C5—41no—
595C22×C5—41no—
596C22×C5—41no—
597C22×C5—41no—
598C22×C5—41no—
599C22×C5C2×C3×D812yes—
600C22×C5C22×C3×D411yescharacteristic
601C2×D5—21no—
602C2×D5—21no—
603C2×D5—22no—
604C2×D5—41no—
605C2×D5—41no—
606C2×D5—41no—
607C2×D5—41no—
608C2×D5—41no—
609C2×D5—84no—
610C2×D5—84no—
611C2×D5C2×C3×D812yes—
612C4×C5—21no—
613C4×C5—41no—
614C4×C5—41no—
615C4×C5C2×C3×#4111yescharacteristic
616C4×C5C3×H(5,𝔽2)11yescharacteristic
617Dic5—21no—
618Dic5—21no—
619Dic5—41no—
620Dic5—41no—
621Dic5C2×C3×D812yes—
622C24—101no—
623C24—101no—
624#41—204no—
625C2×Q8—101no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—51no—
629C2×D4—51no—
630C2×D4—51no—
631C2×D4—102no—
632C2×D4—101no—
633C2×D4—101no—
634C2×D4—101no—
635C2×D4—101no—
636C2×D4—102no—
637C2×D4—101no—
638C2×D4—101no—
639C2×D4—201no—
640C2×D4—201no—
641C2×D4—204no—
642C2×D4C22×C3×D511yescharacteristic
643C2×D4C22×C3×D511yescharacteristic
644C22×C4—51no—
645C22×C4—101no—
646C22×C4—101no—
647C22×C4—101no—
648C22×C4—101no—
649C22×C4C22×C3×D511yescharacteristic
650D8—41no—
651D8—102no—
652D8—201no—
653C2×C8—41no—
654C2×C8—51no—
655C2×C8—51no—
656C2×C8—201no—
657C2×C8C22×C3×D511yescharacteristic
658C2×C8C22×C3×D511yescharacteristic
659C4⋊C4—51no—
660C4⋊C4—51no—
661C4⋊C4—51no—
662C4⋊C4—101no—
663C4⋊C4—101no—
664C4⋊C4—101no—
665C4⋊C4C22×C3×D511yescharacteristic
666C4⋊C4C22×C3×D511yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—51no—
670C22⋊C4—51no—
671C22⋊C4—101no—
672C22⋊C4—101no—
673C22⋊C4—101no—
674C22⋊C4—101no—
675C42—51no—
676C3×C5#329411yescharacteristic, complemented, Hall
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—52no—
686C22×C3—101no—
687C22×C3—101no—
688C22×C3—102no—
689C22×C3—201no—
690C22×C3—201no—
691C22×C3—201no—
692C22×C3—201no—
693C22×C3—201no—
694C22×C3—404no—
695C22×C3—404no—
696C22×C3D5×D812yes—
697C22×C3C2×D4×D511yescharacteristic
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—52no—
702C3×C4—101no—
703C3×C4—101no—
704C3×C4—201no—
705C3×C4—201no—
706C3×C4#414411yescharacteristic
707C3×C4D5×#4111yescharacteristic
708C2×C5—22no—
709C2×C5—81no—
710C2×C5—81no—
711C2×C5C3×#54611yescharacteristic
712C2×C5C22×C3×D811yescharacteristic
713C2×C5C3×#57711yescharacteristic
714D5—22no—
715D5—42no—
716D5—81no—
717C23—21no—
718C23—21no—
719C23—51no—
720C23—101no—
721C23—101no—
722C23—202no—
723C23—202no—
724C23—202no—
725C23—202no—
726C23—401no—
727C23—401no—
728C23C3×D4×D511yescharacteristic
729Q8—202no—
730D4—21no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—42no—
735D4—42no—
736D4—54no—
737D4—52no—
738D4—101no—
739D4—101no—
740D4—101no—
741D4—202no—
742D4—202no—
743D4—202no—
744D4—202no—
745D4—202no—
746D4—401no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—51no—
752C2×C4—51no—
753C2×C4—51no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4C3×D4×D511yescharacteristic
763C2×C4C23×C3×D511yescharacteristic
764C8—21no—
765C8—21no—
766C8—101no—
767C8—101no—
768C2×C3—22no—
769C2×C3—81no—
770C2×C3—81no—
771C2×C3—102no—
772C2×C3—202no—
773C2×C3—401no—
774C2×C3#6594411yescharacteristic
775C2×C3C2×D5×D811yescharacteristic
776C2×C3#6610411yescharacteristic
777C5C3×#329411yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—52no—
787C22—101no—
788C22—101no—
789C22—102no—
790C22—201no—
791C22—201no—
792C22—201no—
793C22—201no—
794C22—201no—
795C22—404no—
796C22—404no—
797C22C3×D5×D812yes—
798C22C2×C3×D4×D511yescharacteristic
799C4—21no—
800C4—41no—
801C4—41no—
802C4—52no—
803C4—101no—
804C4—101no—
805C4—201no—
806C4—201no—
807C4C3×#414411yescharacteristic
808C4C3×D5×#4111yescharacteristic
809C3#1061246211yescharacteristic, direct product factor, Sylow
810C2—22no—
811C2—81no—
812C2—81no—
813C2—102no—
814C2—202no—
815C2—401no—
816C2C3×#6594411yescharacteristic
817C2C2×C3×D5×D811yescharacteristic
818C2C3×#6610411yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#466C2
socleC22×C3×C5C22×D4
hypercenterC3×#466D5
hypocenterC5C3×#3294
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#466

Complements

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

NH ≅ G/Ntype
1. C3×#65945C2semidirect
2. C3×#65943C2semidirect
3. C3×C5×#466C2semidirect
4. C3×#65445C2semidirect
5. C3×#65439C2semidirect
6. C2×C3×#3953C2semidirect
7. C3×C8×C22⋊D5C2semidirect
8. C3×#65325C2semidirect
9. C3×#65322C2semidirect
10. C3×#65179C2semidirect
11. C3×#65171C2semidirect
12. C3×#65064C2semidirect
13. C3×D5×#102C2semidirect
14. C3×#65049C2semidirect
15. C3×#65045C2semidirect
16. #10612462C3direct (N × H)
21. C2×C3×C5×D8C22semidirect
22. C22×C3×C5×C8C22semidirect
24. C3×C5×#121C22semidirect
26. C3×#4084C22semidirect
29. C3×D4×Dic5C22semidirect
31. C2×C3×#686C22semidirect
33. C2×C3×C4⋊Dic5C22semidirect
34. C2×C3×C8×D5C22semidirect
37. C3×D5×C4⋊C4C22semidirect
38. C3×#4034C22semidirect
43. C3×C5×#107C22semidirect
44. C3×C5×#102C22semidirect
45. C3×C5×#102C22semidirect
46. C3×#3964C22semidirect
47. C3×#3964C22semidirect
48. C3×C22⋊#168C22semidirect
51. C3×#3953C22semidirect
52. C3×#3953C22semidirect
53. C3×#3952C22semidirect
54. C3×#3946C22semidirect
55. C3×C8×Dic5C22semidirect
57. C3×#3941C22semidirect
58. C3×#3939C22semidirect
59. C3×#3939C22semidirect
61. #65945C2×C3semidirect
62. #65943C2×C3semidirect
63. C5×#466C2×C3semidirect
64. #65445C2×C3semidirect
65. #65439C2×C3semidirect
66. C2×#3953C2×C3semidirect
67. C8×C22⋊D5C2×C3semidirect
68. #65325C2×C3semidirect
69. #65322C2×C3semidirect
70. #65179C2×C3semidirect
71. #65171C2×C3semidirect
72. #65064C2×C3semidirect
73. D5×#102C2×C3semidirect
74. #65049C2×C3semidirect
75. #65045C2×C3semidirect
137. C3×#466D5semidirect
149. C2×C5×D8C22×C3semidirect
150. C22×C5×C8C22×C3semidirect
152. C5×#121C22×C3semidirect
154. #4084C22×C3semidirect
157. D4×Dic5C22×C3semidirect
159. C2×#686C22×C3semidirect
161. C2×C4⋊Dic5C22×C3semidirect
162. C2×C8×D5C22×C3semidirect
165. D5×C4⋊C4C22×C3semidirect
166. #4034C22×C3semidirect
171. C5×#107C22×C3semidirect
172. C5×#102C22×C3semidirect
173. C5×#102C22×C3semidirect
174. #3964C22×C3semidirect
175. #3964C22×C3semidirect
176. C22⋊#168C22×C3semidirect
179. #3953C22×C3semidirect
180. #3953C22×C3semidirect
181. #3952C22×C3semidirect
182. #3946C22×C3semidirect
183. C8×Dic5C22×C3semidirect
185. #3941C22×C3semidirect
186. #3939C22×C3semidirect
187. #3939C22×C3semidirect
217. C3×C22⋊D5D8semidirect
230. C3×D20#41semidirect
246. C2×C3×D8C2×D5semidirect
248. C22×C3×C8C2×D5semidirect
258. C3×#121C2×D5semidirect
268. C3×#107C2×D5semidirect
278. C3×#102C2×D5semidirect
279. C3×#102C2×D5semidirect
344. #466C3×D5semidirect
465. C22⋊D5C3×D8semidirect
478. D20C3×#41semidirect
494. C2×D8C2×C3×D5semidirect
496. C22×C8C2×C3×D5semidirect
506. #121C2×C3×D5semidirect
516. #107C2×C3×D5semidirect
526. #102C2×C3×D5semidirect
527. #102C2×C3×D5semidirect
676. C3×C5#3294semidirect
777. C5C3×#3294semidirect
809. C3#10612462direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659452
C3×#659432
C3×C5×#4662
C3×#654452
C3×#654392
C2×C3×#39532
C3×C8×C22⋊D52
C3×#653252
C3×#653222
C3×#651792
C3×#651712
C3×#650642
C3×D5×#1022
C3×#650492
C3×#650452
#106124623
C3×#32945