Finite Group Databasebeta

← C3×#10599145 #14291008

Subgroups — C3×#10599145 #14291008

Order 1920.

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

normal subgroups only

This group has 456 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×#66017C211yesmaximal, characteristic
2C3×#65344C211yesmaximal, characteristic, complemented
3C3×#65004C211yesmaximal, characteristic, complemented
4C3×#65003C211yesmaximal, characteristic, complemented
5C3×C5×#329C211yesmaximal, characteristic, complemented
6C3×#64684C211yesmaximal, characteristic, complemented
7C3×#64684C211yesmaximal, characteristic, complemented
8#10599145C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#124C2211yescharacteristic
10C3×#4093—21no—
11C3×#4083—21no—
12C2×C3×Dic20—21no—
13C2×C3×#677—21no—
14C3×#4031—21no—
15C3×#4031—21no—
16C3×#4028—21no—
17C3×#4028—21no—
18C3×#4021C2211yescharacteristic
19C3×#4021C2211yescharacteristic
20C3×#4015C2211yescharacteristic, complemented
21C3×C5×#97C2211yescharacteristic, complemented
22C3×C5×#97C2211yescharacteristic, complemented
23C3×#3967—21no—
24C3×#3964—21no—
25C3×#3953—21no—
26C3×#3948—21no—
27C3×#3935C2211yescharacteristic, complemented
28C3×#1659—51nomaximal, Hall
29#66017C2×C311yescharacteristic
30#65344C2×C311yescharacteristic, complemented
31#65004C2×C311yescharacteristic, complemented
32#65003C2×C311yescharacteristic, complemented
33C5×#329C2×C311yescharacteristic, complemented
34#64684C2×C311yescharacteristic, complemented
35#64684C2×C311yescharacteristic, complemented
36C23×C3×D5—21no—
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4D411yescharacteristic
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×D20—21no—
42C2×C3×D20D411yescharacteristic
43C2×C3×D20D411yescharacteristic
44C2×C3×Dic10—21no—
45C2×C3×Dic10D411yescharacteristic
46C2×C3×Dic10D411yescharacteristic
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C3×C5×C22⋊C4—21no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5C2311yescharacteristic
52C3×C22⋊Dic5—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C3×C4×Dic5—21no—
62C2×C3×#168—21no—
63C3×Dic20—42no—
64C3×#677—42no—
65C3×H(3,𝔽4)—51no—
66C3×#497—51no—
67C3×#489—51no—
68C3×#489—51no—
69C3×#329—51no—
70C3×#329—51no—
71C3×#329D511yescharacteristic, complemented
72C5×#124C22×C311yescharacteristic
73#4093—21no—
74#4083—21no—
75C2×Dic20—21no—
76C2×#677—21no—
77#4031—21no—
78#4031—21no—
79#4028—21no—
80#4028—21no—
81#4021C22×C311yescharacteristic
82#4021C22×C311yescharacteristic
83#4015C22×C311yescharacteristic, complemented
84C5×#97C22×C311yescharacteristic, complemented
85C5×#97C22×C311yescharacteristic, complemented
86#3967—21no—
87#3964—21no—
88#3953—21no—
89#3948—21no—
90#3935C22×C311yescharacteristic, complemented
91#1659—51noSylow
92C23×C3×C5—21no—
93C22×C3×D5—21no—
94C22×C3×D5—21no—
95C22×C3×D5—81no—
96C22×C3×D5—81no—
97C22×C3×D5—81no—
98C3×C5×Q8—41no—
99C3×C5×D4—41no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C3×C22⋊D5—81no—
105C3×C22⋊D5—81no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—41no—
109C3×D20—41no—
110C3×D20—41no—
111C3×D20—81no—
112C3×Dic10—41no—
113C3×Dic10—41no—
114C3×Dic10—41no—
115C3×Dic10—41no—
116C3×C5×C8—22no—
117C3×C5×C8—41no—
118C3×#168—41no—
119C2×C3×Q16—101no—
120C2×C3×SD16—101no—
121C3×C4⋊Q8—51no—
122C3×#124—51no—
123C3×#124—51no—
124C3×#124—101no—
125C3×#124—101no—
126C3×#124—101no—
127C3×#124C2×D511yescharacteristic
128C3×#120—101no—
129C3×#120—101no—
130C3×#120—101no—
131C3×#103—101no—
132C3×#103—101no—
133C3×#102—101no—
134C3×#102—101no—
135C3×#97—51no—
136C3×#97C2×D511yescharacteristic, complemented
137C3×#97C2×D511yescharacteristic, complemented
138C23×D5—21no—
139C2×C5×Q8C3×D411yescharacteristic
140C2×C5×D4C3×D411yescharacteristic
141C2×C22⋊D5—21no—
142C2×C22⋊D5—21no—
143C2×D20—21no—
144C2×D20C3×D411yescharacteristic
145C2×D20C3×D411yescharacteristic
146C2×Dic10—21no—
147C2×Dic10C3×D411yescharacteristic
148C2×Dic10C3×D411yescharacteristic
149C2×C5×C8—21no—
150C2×C5×C8—21no—
151C5×C22⋊C4—21no—
152C5×C22⋊C4—21no—
153C42×C5C23×C311yescharacteristic
154C22⋊Dic5—21no—
155#685—21no—
156#685—21no—
157#685—21no—
158#685—21no—
159#685—21no—
160#685—21no—
161C4⋊Dic5—21no—
162C4⋊Dic5—21no—
163C4×Dic5—21no—
164C2×#168—21no—
165Dic20—42no—
166#677—42no—
167H(3,𝔽4)—51no—
168#497—51no—
169#489—51no—
170#489—51no—
171#329—51no—
172#329—51no—
173#329C3×D511yescharacteristic, complemented
174C22×C3×C5—41no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5#12011yescharacteristic
178C2×C3×D5—41no—
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C2×C3×D5—41no—
182C2×C3×D5—41no—
183C2×C3×D5—41no—
184C2×C3×D5—84no—
185C3×C4×C5—21no—
186C3×C4×C5—21no—
187C3×C4×C5—21no—
188C3×C4×C5—41no—
189C3×Dic5—41no—
190C3×Dic5—41no—
191C3×Dic5—81no—
192C24×C3—101no—
193C2×C3×Q8—51no—
194C2×C3×Q8—51no—
195C2×C3×Q8—101no—
196C2×C3×Q8D2011yescharacteristic
197C2×C3×D4—51no—
198C2×C3×D4—51no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4D2011yescharacteristic
203C3×Q16—202no—
204C3×SD16—202no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—101no—
208C3×C4⋊C4—101no—
209C3×C4⋊C4—101no—
210C3×C22⋊C4—21no—
211C3×C22⋊C4—21no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C22⋊C4—101no—
215C3×C22⋊C4—101no—
216C3×C22⋊C4—101no—
217C3×C22⋊C4—101no—
218C3×C22⋊C4—101no—
219C3×C42—101no—
220C3×C42C22×D511yescharacteristic
221C23×C5—21no—
222C22×D5—21no—
223C22×D5—21no—
224C22×D5—81no—
225C22×D5—81no—
226C22×D5—81no—
227C5×Q8—41no—
228C5×D4—41no—
229C2×C4×C5—21no—
230C2×C4×C5C2×C3×D411yescharacteristic
231C2×C4×C5C2×C3×D411yescharacteristic
232C2×C4×C5C2×C3×D411yescharacteristic
233C22⋊D5—81no—
234C22⋊D5—81no—
235C2×Dic5—21no—
236C2×Dic5—21no—
237C2×Dic5—41no—
238D20—41no—
239D20—41no—
240D20—81no—
241Dic10—41no—
242Dic10—41no—
243Dic10—41no—
244Dic10—41no—
245C5×C8—22no—
246C5×C8—41no—
247#168—41no—
248C2×Q16—101no—
249C2×SD16—101no—
250C4⋊Q8—51no—
251#124—51no—
252#124—51no—
253#124—101no—
254#124—101no—
255#124—101no—
256#124C2×C3×D511yescharacteristic
257#120—101no—
258#120—101no—
259#120—101no—
260#103—101no—
261#103—101no—
262#102—101no—
263#102—101no—
264#97—51no—
265#97C2×C3×D511yescharacteristic, complemented
266#97C2×C3×D511yescharacteristic, complemented
267C2×C3×C5—81no—
268C2×C3×C5#45311yescharacteristic
269C2×C3×C5#45511yescharacteristic
270C2×C3×C5#45511yescharacteristic
271C3×D5—81no—
272C3×D5—81no—
273C23×C3—21no—
274C23×C3—101no—
275C23×C3—101no—
276C23×C3—401no—
277C23×C3—401no—
278C23×C3—401no—
279C3×Q8—41no—
280C3×Q8—201no—
281C3×Q8—201no—
282C3×Q8—201no—
283C3×Q8—201no—
284C3×D4—41no—
285C3×D4—201no—
286C3×D4—201no—
287C3×D4—401no—
288C3×D4—401no—
289C3×D4—401no—
290C2×C3×C4—21no—
291C2×C3×C4—101no—
292C2×C3×C4—101no—
293C2×C3×C4—201no—
294C2×C3×C4C2×D2011yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C3×C8—22no—
298C3×C8—41no—
299C3×C8—201no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5C3×#12011yescharacteristic
304C2×D5—41no—
305C2×D5—41no—
306C2×D5—41no—
307C2×D5—41no—
308C2×D5—41no—
309C2×D5—41no—
310C2×D5—84no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—41no—
315Dic5—41no—
316Dic5—41no—
317Dic5—81no—
318C24—101no—
319C2×Q8—51no—
320C2×Q8—51no—
321C2×Q8—101no—
322C2×Q8C3×D2011yescharacteristic
323C2×D4—51no—
324C2×D4—51no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4—101no—
328C2×D4C3×D2011yescharacteristic
329Q16—202no—
330SD16—202no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—101no—
334C4⋊C4—101no—
335C4⋊C4—101no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—101no—
339C22⋊C4—101no—
340C22⋊C4—101no—
341C22⋊C4—101no—
342C22⋊C4—101no—
343C22⋊C4—101no—
344C22⋊C4—101no—
345C42—101no—
346C42C22×C3×D511yescharacteristic
347C3×C5#165911yescharacteristic, complemented, Hall
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—201no—
352C22×C3—201no—
353C22×C3—201no—
354C22×C3—201no—
355C22×C3—201no—
356C22×C3—201no—
357C22×C3—404no—
358C22×C3#402811yescharacteristic
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—41no—
363C3×C4—201no—
364C3×C4—201no—
365C3×C4—401no—
366C2×C5—81no—
367C2×C5C3×#45311yescharacteristic
368C2×C5C3×#45511yescharacteristic
369C2×C5C3×#45511yescharacteristic
370D5—81no—
371D5—81no—
372C23—21no—
373C23—101no—
374C23—101no—
375C23—401no—
376C23—401no—
377C23—401no—
378Q8—41no—
379Q8—201no—
380Q8—201no—
381Q8—201no—
382Q8—201no—
383D4—41no—
384D4—201no—
385D4—201no—
386D4—401no—
387D4—401no—
388D4—401no—
389C2×C4—21no—
390C2×C4—101no—
391C2×C4—101no—
392C2×C4—201no—
393C2×C4C2×C3×D2011yescharacteristic
394C2×C4C3×D4×D511yescharacteristic
395C2×C4C3×D4×D511yescharacteristic
396C8—22no—
397C8—41no—
398C8—201no—
399C2×C3—81no—
400C2×C3—401no—
401C2×C3—401no—
402C2×C3#6503511yescharacteristic
403C2×C3#6511111yescharacteristic
404C2×C3#6511411yescharacteristic
405C5C3×#165911yescharacteristic, complemented, Sylow
406C22—41no—
407C22—41no—
408C22—41no—
409C22—201no—
410C22—201no—
411C22—201no—
412C22—201no—
413C22—201no—
414C22—201no—
415C22—404no—
416C22C3×#402811yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—41no—
421C4—201no—
422C4—201no—
423C4—401no—
424C3#1059914511yescharacteristic, direct product factor, Sylow
425C2—81no—
426C2—401no—
427C2—401no—
428C2C3×#6503511yescharacteristic
429C2C3×#6511111yescharacteristic
430C2C3×#6511411yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#329C2
socleC22×C3×C5#120
prime radicalC3×#66017C2
hypercenterC3×#329D5
hypocenterC5C3×#1659
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#329

Complements

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

NH ≅ G/Ntype
2. C3×#65344C2semidirect
3. C3×#65004C2semidirect
4. C3×#65003C2semidirect
5. C3×C5×#329C2semidirect
6. C3×#64684C2semidirect
7. C3×#64684C2semidirect
8. #10599145C3direct (N × H)
20. C3×#4015C22semidirect
21. C3×C5×#97C22semidirect
22. C3×C5×#97C22semidirect
27. C3×#3935C22semidirect
30. #65344C2×C3semidirect
31. #65004C2×C3semidirect
32. #65003C2×C3semidirect
33. C5×#329C2×C3semidirect
34. #64684C2×C3semidirect
35. #64684C2×C3semidirect
71. C3×#329D5semidirect
83. #4015C22×C3semidirect
84. C5×#97C22×C3semidirect
85. C5×#97C22×C3semidirect
90. #3935C22×C3semidirect
136. C3×#97C2×D5semidirect
137. C3×#97C2×D5semidirect
173. #329C3×D5semidirect
265. #97C2×C3×D5semidirect
266. #97C2×C3×D5semidirect
347. C3×C5#1659semidirect
405. C5C3×#1659semidirect
424. C3#10599145direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#660172
C3×#653442
C3×#650042
C3×#650032
C3×C5×#3292
C3×#646842
#105991453
C3×#16595