Finite Group Databasebeta

← C3×#10598996 #14289593

Subgroups — C3×#10598996 #14289593

Order 1920.

436 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65897C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic, complemented
3C3×#65131C211yesmaximal, characteristic, complemented
4C3×#64988C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6C3×#64701C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic, complemented
8#10598996C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C3×#4084—21no—
11C3×#4076—21no—
12C3×#4072—21no—
13C2×C3×Dic20—22no—
14C3×#4038—21no—
15C3×#4031—22no—
16C3×C4×D20C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21C3×#3964—21no—
22C3×#3953—21no—
23C3×#3949—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1634—51nomaximal, Hall
27#65897C2×C311yescharacteristic
28#65297C2×C311yescharacteristic, complemented
29#65131C2×C311yescharacteristic, complemented
30#64988C2×C311yescharacteristic, complemented
31C5×D4⋊C8C2×C311yescharacteristic, complemented
32#64701C2×C311yescharacteristic, complemented
33#64679C2×C311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C3×C22⋊D5—22no—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×Dic10—21no—
40C2×C3×Dic10D412yes—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C3×C22⋊Dic5—22no—
47C3×#685—22no—
48C3×#685—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5D411yescharacteristic
54C3×C4×Dic5—22no—
55C2×C3×#168—21no—
56C3×Dic20—44no—
57C3×#555—51no—
58C3×#494—51no—
59C3×#476—51no—
60C3×#476—51no—
61C3×#333—51no—
62C3×D4⋊C8—51no—
63C3×D4⋊C8D511yescharacteristic, complemented
64C4×C5×D4C22×C311yescharacteristic
65#4084—21no—
66#4076—21no—
67#4072—21no—
68C2×Dic20—22no—
69#4038—21no—
70#4031—22no—
71C4×D20C22×C311yescharacteristic
72#4015C22×C311yescharacteristic
73#4015C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75C4×C5×C8C22×C311yescharacteristic
76#3964—21no—
77#3953—21no—
78#3949—21no—
79#3940—21no—
80C4⋊#168C22×C311yescharacteristic
81#1634—51noSylow
82C23×C3×C5—21no—
83C22×C3×D5—21no—
84C3×C5×D4—21no—
85C3×C5×D4—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C3×C22⋊D5—82no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—22no—
95C2×C3×Dic5—41no—
96C3×D20—21no—
97C3×D20—21no—
98C3×C4×D5—41no—
99C3×C4×D5—41no—
100C3×Dic10—42no—
101C3×Dic10—42no—
102C3×C5×C8—22no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C2×C3×Q16—102no—
106C3×C4⋊Q8—51no—
107C3×C4⋊Q8—51no—
108C3×#124—102no—
109C3×#121—101no—
110C3×#121—101no—
111C3×C4×D4—51no—
112C3×C4×D4C2×D511yescharacteristic
113C3×#117—101no—
114C3×#117—101no—
115C3×#106—101no—
116C3×#106—101no—
117C3×C4⋊C8—51no—
118C3×C4⋊C8C2×D511yescharacteristic
119C3×#102—101no—
120C3×#102—101no—
121C3×C4×C8C2×D511yescharacteristic
122C2×C5×D4C3×D411yescharacteristic
123C22×C4×C5—21no—
124C2×C22⋊D5—22no—
125C2×D20C3×D411yescharacteristic
126C2×C4×D5—21no—
127C2×Dic10—21no—
128C2×Dic10C3×D412yes—
129C2×C5×C8—21no—
130C2×C5×C8—21no—
131C5×C4⋊C4C3×D411yescharacteristic
132C5×C22⋊C4—21no—
133C42×C5C23×C311yescharacteristic
134C22⋊Dic5—22no—
135#685—22no—
136#685—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C4⋊Dic5C3×D411yescharacteristic
142C4×Dic5—22no—
143C2×#168—21no—
144Dic20—44no—
145#555—51no—
146#494—51no—
147#476—51no—
148#476—51no—
149#333—51no—
150D4⋊C8—51no—
151D4⋊C8C3×D511yescharacteristic, complemented
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5#12011yescharacteristic
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C2×C3×D5—41no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C3×Dic5—41no—
166C3×Dic5—42no—
167C3×Dic5—81no—
168C2×C3×Q8—52no—
169C2×C3×Q8—101no—
170C2×C3×D4—51no—
171C2×C3×D4—102no—
172C2×C3×D4D2011yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—101no—
175C3×Q16—204no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4—101no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4D2011yescharacteristic
185C3×C22⋊C4—21no—
186C3×C22⋊C4—102no—
187C3×C22⋊C4—102no—
188C3×C22⋊C4—101no—
189C3×C42—102no—
190C3×C42C22×D511yescharacteristic
191C23×C5—21no—
192C22×D5—21no—
193C5×D4—21no—
194C5×D4—21no—
195C2×C4×C5—21no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5C2×C3×D411yescharacteristic
199C2×C4×C5C2×C3×D411yescharacteristic
200C2×C4×C5C2×C3×D411yescharacteristic
201C22⋊D5—82no—
202C2×Dic5—21no—
203C2×Dic5—22no—
204C2×Dic5—41no—
205D20—21no—
206D20—21no—
207C4×D5—41no—
208C4×D5—41no—
209Dic10—42no—
210Dic10—42no—
211C5×C8—22no—
212C5×C8—41no—
213#168—41no—
214C2×Q16—102no—
215C4⋊Q8—51no—
216C4⋊Q8—51no—
217#124—102no—
218#121—101no—
219#121—101no—
220C4×D4—51no—
221C4×D4C2×C3×D511yescharacteristic
222#117—101no—
223#117—101no—
224#106—101no—
225#106—101no—
226C4⋊C8—51no—
227C4⋊C8C2×C3×D511yescharacteristic
228#102—101no—
229#102—101no—
230C4×C8C2×C3×D511yescharacteristic
231C2×C3×C5—81no—
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45311yescharacteristic
235C3×D5—81no—
236C23×C3—21no—
237C23×C3—101no—
238C3×Q8—202no—
239C3×Q8—202no—
240C3×D4—21no—
241C3×D4—21no—
242C3×D4—101no—
243C3×D4—101no—
244C3×D4—402no—
245C2×C3×C4—21no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—101no—
249C2×C3×C4—102no—
250C2×C3×C4—201no—
251C2×C3×C4—201no—
252C2×C3×C4—201no—
253C2×C3×C4C2×D2011yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C3×C8—22no—
257C3×C8—41no—
258C3×C8—201no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5C3×#12011yescharacteristic
263C2×D5—41no—
264C2×D5—41no—
265C2×D5—41no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5C3×#13511yescharacteristic
269C4×C5C3×#13511yescharacteristic
270C4×C5C3×#13711yescharacteristic
271C4×C5C3×#13711yescharacteristic
272Dic5—41no—
273Dic5—42no—
274Dic5—81no—
275C2×Q8—52no—
276C2×Q8—101no—
277C2×D4—51no—
278C2×D4—102no—
279C2×D4C3×D2011yescharacteristic
280C22×C4—21no—
281C22×C4—101no—
282Q16—204no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—101no—
286C4⋊C4—51no—
287C4⋊C4—101no—
288C4⋊C4—101no—
289C4⋊C4—101no—
290C4⋊C4—101no—
291C4⋊C4C3×D2011yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—102no—
294C22⋊C4—102no—
295C22⋊C4—101no—
296C42—102no—
297C42C22×C3×D511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—201no—
303C22×C3—201no—
304C22×C3—201no—
305C22×C3#402811yescharacteristic
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—202no—
309C3×C4—201no—
310C3×C4—401no—
311C3×C4#405011yescharacteristic
312C3×C4#405511yescharacteristic
313C3×C4#405811yescharacteristic
314C3×C4#406111yescharacteristic
315C2×C5—81no—
316C2×C5C3×#45211yescharacteristic
317C2×C5C3×#45211yescharacteristic
318C2×C5C3×#45311yescharacteristic
319D5—81no—
320C23—21no—
321C23—101no—
322Q8—202no—
323Q8—202no—
324D4—21no—
325D4—21no—
326D4—101no—
327D4—101no—
328D4—402no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—101no—
333C2×C4—102no—
334C2×C4—201no—
335C2×C4—201no—
336C2×C4—201no—
337C2×C4C2×C3×D2011yescharacteristic
338C2×C4C3×D4×D511yescharacteristic
339C2×C4C3×D4×D511yescharacteristic
340C8—22no—
341C8—41no—
342C8—201no—
343C2×C3—81no—
344C2×C3—401no—
345C2×C3#6502211yescharacteristic
346C2×C3#6507211yescharacteristic
347C2×C3#6511111yescharacteristic
348C5C3×#163411yescharacteristic, complemented, Sylow
349C22—41no—
350C22—41no—
351C22—41no—
352C22—201no—
353C22—201no—
354C22—201no—
355C22C3×#402811yescharacteristic
356C4—21no—
357C4—41no—
358C4—202no—
359C4—201no—
360C4—401no—
361C4C3×#405011yescharacteristic
362C4C3×#405511yescharacteristic
363C4C3×#405811yescharacteristic
364C4C3×#406111yescharacteristic
365C3#1059899611yescharacteristic, direct product factor, Sylow
366C2—81no—
367C2—401no—
368C2C3×#6502211yescharacteristic
369C2C3×#6507211yescharacteristic
370C2C3×#6511111yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC3×#65897C2
hypercenterC3×D4⋊C8D5
hypocenterC5C3×#1634
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65297C2semidirect
3. C3×#65131C2semidirect
4. C3×#64988C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C3×#64701C2semidirect
7. C3×#64679C2semidirect
8. #10598996C3direct (N × H)
28. #65297C2×C3semidirect
29. #65131C2×C3semidirect
30. #64988C2×C3semidirect
31. C5×D4⋊C8C2×C3semidirect
32. #64701C2×C3semidirect
33. #64679C2×C3semidirect
63. C3×D4⋊C8D5semidirect
151. D4⋊C8C3×D5semidirect
298. C3×C5#1634semidirect
348. C5C3×#1634semidirect
365. C3#10598996direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#658972
C3×#652972
C3×#651312
C3×#649882
C3×C5×D4⋊C82
C3×#647012
C3×#646792
#105989963
C3×#16345