Finite Group Databasebeta

← C3×#10599933 #14316740

Subgroups — C3×#10599933 #14316740

Order 1920.

492 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 82 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×#65998C211yesmaximal, characteristic, complemented
2C3×#65342C211yesmaximal, characteristic, complemented
3C3×#65036C211yesmaximal, characteristic
4C3×#65031C211yesmaximal, characteristic, complemented
5C3×C5×#352C211yesmaximal, characteristic, complemented
6C3×#64696C211yesmaximal, characteristic, complemented
7C3×#64694C211yesmaximal, characteristic, complemented
8#10599933C311yesmaximal, characteristic, direct product factor, Hall
9C3×#4144C2211yescharacteristic
10C3×C5×#123C2211yescharacteristic
11C3×#4086C2211yescharacteristic
12C3×#4081C2211yescharacteristic
13C3×#4075—21no—
14C3×C4×C22⋊D5—21no—
15C3×#4054—21no—
16C3×#4040—21no—
17C3×#4033—21no—
18C3×#4032—21no—
19C3×#4031—21no—
20C3×#4031—21no—
21C3×#4027—21no—
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3957—21no—
26C3×#3938—21no—
27C3×#3938—21no—
28C3×#2198—51nomaximal, Hall
29#65998C2×C311yescharacteristic, complemented
30#65342C2×C311yescharacteristic, complemented
31#65036C2×C311yescharacteristic
32#65031C2×C311yescharacteristic, complemented
33C5×#352C2×C311yescharacteristic, complemented
34#64696C2×C311yescharacteristic, complemented
35#64694C2×C311yescharacteristic, complemented
36C2×C3×C5×D4C2311yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C2×C3×C22⋊D5—21no—
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C22×C3×Dic5D411yescharacteristic
43C3×#711—41no—
44C3×D4×D5—41no—
45C3×#709—21no—
46C2×C3×D20D411yescharacteristic
47C2×C3×C4×D5—21no—
48C2×C3×Dic10—21no—
49C3×C5×M16—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C5×C22⋊C4D411yescharacteristic
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×C22⋊Dic5D411yescharacteristic
57C3×#685—21no—
58C3×#685—21no—
59C3×#685—21no—
60C3×#685—41no—
61C3×#685—41no—
62C3×C4⋊Dic5—41no—
63C3×#683—21no—
64C3×#683—21no—
65C3×#683—41no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5—21no—
68C3×C4×Dic5D411yescharacteristic
69C3×D40—41no—
70C3×#677—41no—
71C3×#559—51no—
72C3×#458—51no—
73C3×#458—51no—
74C3×#453—51no—
75C3×#353—51no—
76C3×#352—51no—
77C3×#352D511yescharacteristic, complemented
78#4144C22×C311yescharacteristic
79C5×#123C22×C311yescharacteristic
80#4086C22×C311yescharacteristic
81#4081C22×C311yescharacteristic
82#4075—21no—
83C4×C22⋊D5—21no—
84#4054—21no—
85#4040—21no—
86#4033—21no—
87#4032—21no—
88#4031—21no—
89#4031—21no—
90#4027—21no—
91C5×#100C22×C311yescharacteristic
92C5×#99C22×C311yescharacteristic
93#3966C22×C311yescharacteristic
94#3957—21no—
95#3938—21no—
96#3938—21no—
97#2198—51noSylow
98C23×C3×C5C2×D411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C3×D5—21no—
101C22×C3×D5—21no—
102C22×C3×D5—21no—
103C3×C5×D4—41no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C2×D411yescharacteristic
109C3×C22⋊D5—42no—
110C3×C22⋊D5—42no—
111C3×C22⋊D5—41no—
112C3×C22⋊D5—41no—
113C3×C22⋊D5—41no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C2×C3×Dic5—21no—
118C2×C3×Dic5—21no—
119C2×C3×Dic5—41no—
120C2×C3×Dic5—41no—
121C3×D20—21no—
122C3×D20—41no—
123C3×C4×D5—41no—
124C3×C4×D5—81no—
125C3×Dic10—21no—
126C3×Dic10—42no—
127C3×C5×C8—41no—
128C3×H(5,𝔽2)—51no—
129C3×AGL(1,ℤ/8)—101no—
130C3×#127—51no—
131C3×#124—101no—
132C3×#124—101no—
133C3×#123—51no—
134C3×#123—101no—
135C3×#123—101no—
136C3×#123—101no—
137C3×#123C2×D511yescharacteristic
138C3×C4×Q8—101no—
139C3×C4×D4—101no—
140C3×C4×D4—101no—
141C3×#104—101no—
142C3×#100C2×D511yescharacteristic
143C3×#99—51no—
144C3×#99—101no—
145C3×#99—101no—
146C3×#99C2×D511yescharacteristic
147C2×C5×D4C23×C311yescharacteristic
148C22×C4×C5C3×D411yescharacteristic
149C2×C22⋊D5—21no—
150C2×C22⋊D5—21no—
151C2×C22⋊D5—21no—
152C2×C22⋊D5—21no—
153C22×Dic5C3×D411yescharacteristic
154#711—41no—
155D4×D5—41no—
156#709—21no—
157C2×D20C3×D411yescharacteristic
158C2×C4×D5—21no—
159C2×Dic10—21no—
160C5×M16—21no—
161C5×C4⋊C4—21no—
162C5×C22⋊C4—21no—
163C5×C22⋊C4—21no—
164C5×C22⋊C4C3×D411yescharacteristic
165C22⋊Dic5—21no—
166C22⋊Dic5—21no—
167C22⋊Dic5C3×D411yescharacteristic
168#685—21no—
169#685—21no—
170#685—21no—
171#685—41no—
172#685—41no—
173C4⋊Dic5—41no—
174#683—21no—
175#683—21no—
176#683—41no—
177C4×Dic5—21no—
178C4×Dic5—21no—
179C4×Dic5C3×D411yescharacteristic
180D40—41no—
181#677—41no—
182#559—51no—
183#458—51no—
184#458—51no—
185#453—51no—
186#353—51no—
187#352—51no—
188#352C3×D511yescharacteristic, complemented
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5#12011yescharacteristic
194C2×C3×D5—41no—
195C2×C3×D5—41no—
196C2×C3×D5—41no—
197C2×C3×D5—41no—
198C2×C3×D5—81no—
199C2×C3×D5—81no—
200C3×C4×C5—21no—
201C3×C4×C5—41no—
202C3×C4×C5—41no—
203C3×C4×C5—81no—
204C3×Dic5—22no—
205C3×Dic5—41no—
206C3×Dic5—41no—
207C3×Dic5—41no—
208C3×Dic5—81no—
209C3×#41—101no—
210C3×#41—201no—
211C2×C3×Q8—101no—
212C2×C3×D4—51no—
213C2×C3×D4—101no—
214C2×C3×D4—101no—
215C2×C3×D4—101no—
216C2×C3×D4—101no—
217C2×C3×D4—201no—
218C2×C3×D4C22×D511yescharacteristic
219C22×C3×C4—51no—
220C22×C3×C4—101no—
221C22×C3×C4D2011yescharacteristic
222C3×SD16—201no—
223C3×D8—201no—
224C3×M16—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—101no—
227C3×C4⋊C4—101no—
228C3×C4⋊C4—201no—
229C3×C4⋊C4—201no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C22⋊C4—51no—
233C3×C22⋊C4—101no—
234C3×C22⋊C4—101no—
235C3×C22⋊C4—101no—
236C3×C22⋊C4—101no—
237C3×C22⋊C4—101no—
238C3×C22⋊C4—201no—
239C3×C22⋊C4—201no—
240C3×C22⋊C4D2011yescharacteristic
241C3×C42—51no—
242C3×C42—101no—
243C3×C42—101no—
244C23×C5C2×C3×D411yescharacteristic
245C23×C5C2×C3×D411yescharacteristic
246C22×D5—21no—
247C22×D5—21no—
248C22×D5—21no—
249C5×D4—41no—
250C2×C4×C5—21no—
251C2×C4×C5—21no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5C2×C3×D411yescharacteristic
255C22⋊D5—42no—
256C22⋊D5—42no—
257C22⋊D5—41no—
258C22⋊D5—41no—
259C22⋊D5—41no—
260C2×Dic5—21no—
261C2×Dic5—21no—
262C2×Dic5—21no—
263C2×Dic5—21no—
264C2×Dic5—21no—
265C2×Dic5—41no—
266C2×Dic5—41no—
267D20—21no—
268D20—41no—
269C4×D5—41no—
270C4×D5—81no—
271Dic10—21no—
272Dic10—42no—
273C5×C8—41no—
274H(5,𝔽2)—51no—
275AGL(1,ℤ/8)—101no—
276#127—51no—
277#124—101no—
278#124—101no—
279#123—51no—
280#123—101no—
281#123—101no—
282#123—101no—
283#123C2×C3×D511yescharacteristic
284C4×Q8—101no—
285C4×D4—101no—
286C4×D4—101no—
287#104—101no—
288#100C2×C3×D511yescharacteristic
289#99—51no—
290#99—101no—
291#99—101no—
292#99C2×C3×D511yescharacteristic
293C2×C3×C5—21no—
294C2×C3×C5—41no—
295C2×C3×C5—41no—
296C2×C3×C5B(4,𝔽2)11yescharacteristic
297C3×D5—81no—
298C3×D5—81no—
299C23×C3—101no—
300C23×C3—101no—
301C23×C3—101no—
302C23×C3C2×D2011yescharacteristic
303C23×C3D4×D511yescharacteristic
304C3×Q8—101no—
305C3×Q8—202no—
306C3×D4—41no—
307C3×D4—101no—
308C3×D4—201no—
309C3×D4—202no—
310C3×D4—202no—
311C3×D4—201no—
312C3×D4—201no—
313C3×D4—201no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—101no—
319C2×C3×C4—101no—
320C2×C3×C4—101no—
321C2×C3×C4—101no—
322C2×C3×C4—101no—
323C2×C3×C4—201no—
324C2×C3×C4—201no—
325C2×C3×C4—201no—
326C2×C3×C4—401no—
327C2×C3×C4D4×D511yescharacteristic
328C3×C8—41no—
329C22×C5—21no—
330C22×C5—21no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5C3×#12011yescharacteristic
334C2×D5—41no—
335C2×D5—41no—
336C2×D5—41no—
337C2×D5—41no—
338C2×D5—81no—
339C2×D5—81no—
340C4×C5—21no—
341C4×C5—41no—
342C4×C5—41no—
343C4×C5—81no—
344Dic5—22no—
345Dic5—41no—
346Dic5—41no—
347Dic5—41no—
348Dic5—81no—
349#41—101no—
350#41—201no—
351C2×Q8—101no—
352C2×D4—51no—
353C2×D4—101no—
354C2×D4—101no—
355C2×D4—101no—
356C2×D4—101no—
357C2×D4—201no—
358C2×D4C22×C3×D511yescharacteristic
359C22×C4—51no—
360C22×C4—101no—
361C22×C4C3×D2011yescharacteristic
362SD16—201no—
363D8—201no—
364M16—21no—
365C4⋊C4—21no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C4⋊C4—201no—
369C4⋊C4—201no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—51no—
373C22⋊C4—101no—
374C22⋊C4—101no—
375C22⋊C4—101no—
376C22⋊C4—101no—
377C22⋊C4—101no—
378C22⋊C4—201no—
379C22⋊C4—201no—
380C22⋊C4C3×D2011yescharacteristic
381C42—51no—
382C42—101no—
383C42—101no—
384C3×C5#219811yescharacteristic, complemented, Hall
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—201no—
390C22×C3—201no—
391C22×C3—201no—
392C22×C3—201no—
393C22×C3—401no—
394C22×C3—401no—
395C22×C3#402811yescharacteristic
396C3×C4—21no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—81no—
400C3×C4—102no—
401C3×C4—201no—
402C3×C4—201no—
403C3×C4—201no—
404C3×C4—401no—
405C2×C5—21no—
406C2×C5—41no—
407C2×C5—41no—
408C2×C5C3×B(4,𝔽2)11yescharacteristic
409D5—81no—
410D5—81no—
411C23—101no—
412C23—101no—
413C23—101no—
414C23C2×C3×D2011yescharacteristic
415C23C3×D4×D511yescharacteristic
416Q8—101no—
417Q8—202no—
418D4—41no—
419D4—101no—
420D4—201no—
421D4—202no—
422D4—202no—
423D4—201no—
424D4—201no—
425D4—201no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—101no—
433C2×C4—101no—
434C2×C4—101no—
435C2×C4—201no—
436C2×C4—201no—
437C2×C4—201no—
438C2×C4—401no—
439C2×C4C3×D4×D511yescharacteristic
440C8—41no—
441C2×C3—21no—
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—401no—
445C2×C3—401no—
446C2×C3#6503011yescharacteristic
447C5C3×#219811yescharacteristic, complemented, Sylow
448C22—21no—
449C22—21no—
450C22—41no—
451C22—41no—
452C22—201no—
453C22—201no—
454C22—201no—
455C22—201no—
456C22—401no—
457C22—401no—
458C22C3×#402811yescharacteristic
459C4—21no—
460C4—41no—
461C4—41no—
462C4—81no—
463C4—102no—
464C4—201no—
465C4—201no—
466C4—201no—
467C4—401no—
468C3#1059993311yescharacteristic, direct product factor, Sylow
469C2—21no—
470C2—41no—
471C2—41no—
472C2—401no—
473C2—401no—
474C2C3×#6503011yescharacteristic
subgroupG/H
centerC2×C3#65030
commutator, cosocleC2×C5×D4C23×C3
FrattiniC2×D4C22×C3×D5
FittingC3×C5×#352C2
socleC2×C3×C5B(4,𝔽2)
prime radicalC3×#65036C2
hypercenterC3×#352D5
hypocenterC5C3×#2198
LCSG ▷ C2×C5×D4 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#352

Complements

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

NH ≅ G/Ntype
1. C3×#65998C2semidirect
2. C3×#65342C2semidirect
4. C3×#65031C2semidirect
5. C3×C5×#352C2semidirect
6. C3×#64696C2semidirect
7. C3×#64694C2semidirect
8. #10599933C3direct (N × H)
29. #65998C2×C3semidirect
30. #65342C2×C3semidirect
32. #65031C2×C3semidirect
33. C5×#352C2×C3semidirect
34. #64696C2×C3semidirect
35. #64694C2×C3semidirect
77. C3×#352D5semidirect
188. #352C3×D5semidirect
384. C3×C5#2198semidirect
447. C5C3×#2198semidirect
468. C3#10599933direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659982
C3×#653422
C3×#650362
C3×#650312
C3×C5×#3522
C3×#646962
C3×#646942
#105999333
C3×#21985