Finite Group Databasebeta

← C3×#10602740 #14316818

Subgroups — C3×#10602740 #14316818

Order 1920.

520 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#560C211yesmaximal, characteristic, complemented
2C3×#65366C211yesmaximal, characteristic, complemented
3C3×#65342C211yesmaximal, characteristic, complemented
4C3×#65321C211yesmaximal, characteristic, complemented
5C3×#64765C211yesmaximal, characteristic, complemented
6C3×#64759C211yesmaximal, characteristic, complemented
7C3×#64756C211yesmaximal, characteristic, complemented
8#10602740C311yesmaximal, characteristic, direct product factor, Hall
9C3×#4144C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C3×C5×#126—21no—
12C3×C5×#123—21no—
13C3×C5×#123C2211yescharacteristic
14C3×C5×#121—21no—
15C3×C5×#121—21no—
16C3×C5×#121—21no—
17C3×C5×#120—21no—
18C3×C5×#120C2211yescharacteristic
19C3×#4099—21no—
20C3×#4078—21no—
21C3×#4075—21no—
22C3×#3966C2211yescharacteristic
23C3×#3966C2211yescharacteristic
24C3×#3965C2211yescharacteristic
25C3×#3938—21no—
26C3×#3938—21no—
27C3×#3937—21no—
28C3×#2200—51nomaximal, Hall
29C5×#560C2×C311yescharacteristic, complemented
30#65366C2×C311yescharacteristic, complemented
31#65342C2×C311yescharacteristic, complemented
32#65321C2×C311yescharacteristic, complemented
33#64765C2×C311yescharacteristic, complemented
34#64759C2×C311yescharacteristic, complemented
35#64756C2×C311yescharacteristic, complemented
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4D411yescharacteristic, complemented
43C2×C3×C5×D4C2311yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5D411yescharacteristic, complemented
46C2×C3×C22⋊D5—21no—
47C2×C3×C22⋊D5—21no—
48C2×C3×C22⋊D5—41no—
49C3×#711—41no—
50C3×D4×D5—41no—
51C3×#709—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4D411yescharacteristic
61C3×C5×C22⋊C4D411yescharacteristic, complemented
62C3×C42×C5D411yescharacteristic, complemented
63C3×C22⋊Dic5—21no—
64C3×C22⋊Dic5—21no—
65C3×C22⋊Dic5—41no—
66C3×#687—41no—
67C3×#686—41no—
68C3×#685—41no—
69C3×#683—41no—
70C3×#681—21no—
71C3×#560D511yescharacteristic, complemented
72C3×#458—51no—
73C3×B(4,𝔽2)—51no—
74C3×#453—51no—
75C3×#353—51no—
76C3×#352—51no—
77C3×AΣL(1,𝔽16)—51no—
78#4144C22×C311yescharacteristic
79C5×#127C22×C311yescharacteristic
80C5×#126—21no—
81C5×#123—21no—
82C5×#123C22×C311yescharacteristic
83C5×#121—21no—
84C5×#121—21no—
85C5×#121—21no—
86C5×#120—21no—
87C5×#120C22×C311yescharacteristic
88#4099—21no—
89#4078—21no—
90#4075—21no—
91#3966C22×C311yescharacteristic
92#3966C22×C311yescharacteristic
93#3965C22×C311yescharacteristic
94#3938—21no—
95#3938—21no—
96#3937—21no—
97#2200—51noSylow
98C23×C3×C5—21no—
99C23×C3×C5—21no—
100C23×C3×C5—41no—
101C23×C3×C5—81no—
102C23×C3×C5C2×D411yescharacteristic
103C23×C3×C5C2×D411yescharacteristic
104C22×C3×D5—21no—
105C22×C3×D5—21no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C3×C5×D4—81no—
109C3×C5×D4—81no—
110C3×C5×D4—81no—
111C3×C5×D4—81no—
112C3×C5×D4—81no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—81no—
119C2×C3×C4×C5C2×D411yescharacteristic
120C3×C22⋊D5—41no—
121C3×C22⋊D5—41no—
122C3×C22⋊D5—41no—
123C3×C22⋊D5—82no—
124C2×C3×Dic5—21no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—41no—
127C2×C3×Dic5—41no—
128C3×D20—21no—
129C3×C4×D5—41no—
130C3×Dic10—21no—
131C3×#168—41no—
132C3×H(5,𝔽2)—51no—
133C3×AGL(1,ℤ/8)—101no—
134C3×#127C2×D511yescharacteristic
135C3×#126—21no—
136C3×#123—21no—
137C3×#123—101no—
138C3×#123C2×D511yescharacteristic
139C3×#121—21no—
140C3×#121—21no—
141C3×#121—21no—
142C3×#120—21no—
143C3×#120—101no—
144C3×#120C2×D511yescharacteristic
145C3×#104—101no—
146C3×#100—51no—
147C3×#99—51no—
148C3×#99—51no—
149C3×#99—101no—
150C3×#99—101no—
151C24×C5C3×D411yescharacteristic
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4C3×D411yescharacteristic, complemented
158C2×C5×D4C23×C311yescharacteristic
159C22×C4×C5—21no—
160C22×C4×C5C3×D411yescharacteristic, complemented
161C2×C22⋊D5—21no—
162C2×C22⋊D5—21no—
163C2×C22⋊D5—41no—
164#711—41no—
165D4×D5—41no—
166#709—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—21no—
172C5×C22⋊C4—21no—
173C5×C22⋊C4—21no—
174C5×C22⋊C4—21no—
175C5×C22⋊C4C3×D411yescharacteristic
176C5×C22⋊C4C3×D411yescharacteristic, complemented
177C42×C5C3×D411yescharacteristic, complemented
178C22⋊Dic5—21no—
179C22⋊Dic5—21no—
180C22⋊Dic5—41no—
181#687—41no—
182#686—41no—
183#685—41no—
184#683—41no—
185#681—21no—
186#560C3×D511yescharacteristic, complemented
187#458—51no—
188B(4,𝔽2)—51no—
189#453—51no—
190#353—51no—
191#352—51no—
192AΣL(1,𝔽16)—51no—
193C22×C3×C5—21no—
194C22×C3×C5—21no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5—41no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5—41no—
201C22×C3×C5—42no—
202C22×C3×C5—41no—
203C22×C3×C5—41no—
204C22×C3×C5—81no—
205C22×C3×C5#12011yescharacteristic
206C2×C3×D5—41no—
207C2×C3×D5—81no—
208C2×C3×D5—81no—
209C3×C4×C5—21no—
210C3×C4×C5—41no—
211C3×C4×C5—41no—
212C3×C4×C5—41no—
213C3×C4×C5—41no—
214C3×Dic5—41no—
215C3×Dic5—81no—
216C3×Dic5—81no—
217C24×C3C22⋊D511yescharacteristic
218C3×#41—101no—
219C3×#41—201no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—101no—
226C2×C3×D4—101no—
227C2×C3×D4—201no—
228C2×C3×D4—201no—
229C2×C3×D4C22⋊D511yescharacteristic, complemented
230C2×C3×D4C22×D511yescharacteristic
231C22×C3×C4—21no—
232C22×C3×C4C22⋊D511yescharacteristic, complemented
233C3×SD16—201no—
234C3×D8—201no—
235C3×M16—101no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—201no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—101no—
246C3×C22⋊C4—101no—
247C3×C22⋊C4—201no—
248C3×C22⋊C4—201no—
249C3×C22⋊C4C22⋊D511yescharacteristic
250C3×C22⋊C4C22⋊D511yescharacteristic, complemented
251C3×C42C22⋊D511yescharacteristic, complemented
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—41no—
255C23×C5—81no—
256C23×C5C2×C3×D411yescharacteristic
257C23×C5C2×C3×D411yescharacteristic
258C22×D5—21no—
259C22×D5—21no—
260C5×D4—41no—
261C5×D4—41no—
262C5×D4—81no—
263C5×D4—81no—
264C5×D4—81no—
265C5×D4—81no—
266C5×D4—81no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—41no—
272C2×C4×C5—81no—
273C2×C4×C5C2×C3×D411yescharacteristic
274C22⋊D5—41no—
275C22⋊D5—41no—
276C22⋊D5—41no—
277C22⋊D5—82no—
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—41no—
281C2×Dic5—41no—
282D20—21no—
283C4×D5—41no—
284Dic10—21no—
285#168—41no—
286H(5,𝔽2)—51no—
287AGL(1,ℤ/8)—101no—
288#127C2×C3×D511yescharacteristic
289#126—21no—
290#123—21no—
291#123—101no—
292#123C2×C3×D511yescharacteristic
293#121—21no—
294#121—21no—
295#121—21no—
296#120—21no—
297#120—101no—
298#120C2×C3×D511yescharacteristic
299#104—101no—
300#100—51no—
301#99—51no—
302#99—51no—
303#99—101no—
304#99—101no—
305C2×C3×C5—21no—
306C2×C3×C5—41no—
307C2×C3×C5—41no—
308C2×C3×C5—81no—
309C2×C3×C5—81no—
310C2×C3×C5B(4,𝔽2)11yescharacteristic
311C3×D5—81no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—41no—
315C23×C3—81no—
316C23×C3—101no—
317C23×C3—101no—
318C23×C3C2×C22⋊D511yescharacteristic
319C23×C3C2×C22⋊D511yescharacteristic
320C3×Q8—101no—
321C3×D4—41no—
322C3×D4—41no—
323C3×D4—81no—
324C3×D4—81no—
325C3×D4—81no—
326C3×D4—81no—
327C3×D4—81no—
328C3×D4—101no—
329C3×D4—201no—
330C3×D4—201no—
331C3×D4—201no—
332C3×D4—402no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—41no—
338C2×C3×C4—81no—
339C2×C3×C4—101no—
340C2×C3×C4—101no—
341C2×C3×C4—201no—
342C2×C3×C4—201no—
343C2×C3×C4—201no—
344C2×C3×C4C2×C22⋊D511yescharacteristic
345C3×C8—201no—
346C22×C5—21no—
347C22×C5—21no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5—41no—
352C22×C5—41no—
353C22×C5—41no—
354C22×C5—42no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—81no—
358C22×C5C3×#12011yescharacteristic
359C2×D5—41no—
360C2×D5—81no—
361C2×D5—81no—
362C4×C5—21no—
363C4×C5—41no—
364C4×C5—41no—
365C4×C5—41no—
366C4×C5—41no—
367Dic5—41no—
368Dic5—81no—
369Dic5—81no—
370C24C3×C22⋊D511yescharacteristic
371#41—101no—
372#41—201no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—101no—
379C2×D4—101no—
380C2×D4—201no—
381C2×D4—201no—
382C2×D4C3×C22⋊D511yescharacteristic, complemented
383C2×D4C22×C3×D511yescharacteristic
384C22×C4—21no—
385C22×C4C3×C22⋊D511yescharacteristic, complemented
386SD16—201no—
387D8—201no—
388M16—101no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—201no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—101no—
399C22⋊C4—101no—
400C22⋊C4—201no—
401C22⋊C4—201no—
402C22⋊C4C3×C22⋊D511yescharacteristic
403C22⋊C4C3×C22⋊D511yescharacteristic, complemented
404C42C3×C22⋊D511yescharacteristic, complemented
405C3×C5#220011yescharacteristic, complemented, Hall
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—81no—
418C22×C3—201no—
419C22×C3—401no—
420C22×C3—401no—
421C22×C3#409911yescharacteristic
422C3×C4—21no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—41no—
427C3×C4—201no—
428C3×C4—401no—
429C3×C4—401no—
430C2×C5—21no—
431C2×C5—41no—
432C2×C5—41no—
433C2×C5—81no—
434C2×C5—81no—
435C2×C5C3×B(4,𝔽2)11yescharacteristic
436D5—81no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—81no—
441C23—101no—
442C23—101no—
443C23C2×C3×C22⋊D511yescharacteristic
444C23C2×C3×C22⋊D511yescharacteristic
445Q8—101no—
446D4—41no—
447D4—41no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453D4—101no—
454D4—201no—
455D4—201no—
456D4—201no—
457D4—402no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—41no—
463C2×C4—81no—
464C2×C4—101no—
465C2×C4—101no—
466C2×C4—201no—
467C2×C4—201no—
468C2×C4—201no—
469C2×C4C2×C3×C22⋊D511yescharacteristic
470C8—201no—
471C2×C3—21no—
472C2×C3—41no—
473C2×C3—41no—
474C2×C3—81no—
475C2×C3—81no—
476C2×C3—401no—
477C2×C3#6553311yescharacteristic
478C5C3×#220011yescharacteristic, complemented, Sylow
479C22—21no—
480C22—21no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—42no—
488C22—41no—
489C22—41no—
490C22—81no—
491C22—201no—
492C22—401no—
493C22—401no—
494C22C3×#409911yescharacteristic
495C4—21no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—41no—
500C4—201no—
501C4—401no—
502C4—401no—
503C3#1060274011yescharacteristic, direct product factor, Sylow
504C2—21no—
505C2—41no—
506C2—41no—
507C2—81no—
508C2—81no—
509C2—401no—
510C2C3×#6553311yescharacteristic
subgroupG/H
centerC2×C3#65533
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#560C2
socleC2×C3×C5B(4,𝔽2)
hypercenterC3×#560D5
hypocenterC5C3×#2200
LCSG ▷ C2×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#560

Complements

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

NH ≅ G/Ntype
1. C3×C5×#560C2semidirect
2. C3×#65366C2semidirect
3. C3×#65342C2semidirect
4. C3×#65321C2semidirect
5. C3×#64765C2semidirect
6. C3×#64759C2semidirect
7. C3×#64756C2semidirect
8. #10602740C3direct (N × H)
29. C5×#560C2×C3semidirect
30. #65366C2×C3semidirect
31. #65342C2×C3semidirect
32. #65321C2×C3semidirect
33. #64765C2×C3semidirect
34. #64759C2×C3semidirect
35. #64756C2×C3semidirect
42. C2×C3×C5×D4D4semidirect
45. C22×C3×C4×C5D4semidirect
61. C3×C5×C22⋊C4D4semidirect
62. C3×C42×C5D4semidirect
71. C3×#560D5semidirect
157. C2×C5×D4C3×D4semidirect
160. C22×C4×C5C3×D4semidirect
176. C5×C22⋊C4C3×D4semidirect
177. C42×C5C3×D4semidirect
186. #560C3×D5semidirect
229. C2×C3×D4C22⋊D5semidirect
232. C22×C3×C4C22⋊D5semidirect
250. C3×C22⋊C4C22⋊D5semidirect
251. C3×C42C22⋊D5semidirect
382. C2×D4C3×C22⋊D5semidirect
385. C22×C4C3×C22⋊D5semidirect
403. C22⋊C4C3×C22⋊D5semidirect
404. C42C3×C22⋊D5semidirect
405. C3×C5#2200semidirect
478. C5C3×#2200semidirect
503. C3#10602740direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5602
C3×#653662
C3×#653422
C3×#653212
C3×#647652
C3×#647592
C3×#647562
#106027403
C3×#22005