Finite Group Databasebeta

← C3×#10599039 #14289497

Subgroups — C3×#10599039 #14289497

Order 1920.

428 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65913C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic, complemented
3C3×#65131C211yesmaximal, characteristic
4C3×#64988C211yesmaximal, characteristic, complemented
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6C3×#64701C211yesmaximal, characteristic, complemented
7C3×#64679C211yesmaximal, characteristic
8#10599039C311yesmaximal, characteristic, direct product factor, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C3×#4092—21no—
11C2×C3×Dic20—22no—
12C3×#4042—22no—
13C3×D5×C4⋊C4—21no—
14C3×C4×D20—21no—
15C3×C4×D20C2211yescharacteristic
16C3×#4016—21no—
17C3×#4015C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21C3×#3967—21no—
22C3×#3953—21no—
23C3×#3949—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26C3×#1632—51nomaximal, Hall
27#65913C2×C311yescharacteristic
28#65310C2×C311yescharacteristic, complemented
29#65131C2×C311yescharacteristic
30#64988C2×C311yescharacteristic, complemented
31C5×Q8⋊C8C2×C311yescharacteristic, complemented
32#64701C2×C311yescharacteristic, complemented
33#64679C2×C311yescharacteristic
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×D20D411yescharacteristic
36C2×C3×C4×D5—21no—
37C2×C3×C4×D5—22no—
38C2×C3×Dic10—21no—
39C2×C3×Dic10D412yes—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C42×C5—21no—
45C3×C42×C5C2311yescharacteristic
46C3×#685—22no—
47C3×#685—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—22no—
54C3×#683—22no—
55C2×C3×#168—21no—
56C3×Dic20—44no—
57C3×#554—51no—
58C3×#494—51no—
59C3×#477—51no—
60C3×#476—51no—
61C3×#333—51no—
62C3×Q8⋊C8D511yescharacteristic, complemented
63C3×D4⋊C8—51no—
64C4×C5×Q8C22×C311yescharacteristic
65#4092—21no—
66C2×Dic20—22no—
67#4042—22no—
68D5×C4⋊C4—21no—
69C4×D20—21no—
70C4×D20C22×C311yescharacteristic
71#4016—21no—
72#4015C22×C311yescharacteristic
73#4015C22×C311yescharacteristic
74C5×C4⋊C8C22×C311yescharacteristic
75C4×C5×C8C22×C311yescharacteristic
76#3967—21no—
77#3953—21no—
78#3949—21no—
79#3939—21no—
80C4⋊#168C22×C311yescharacteristic
81#1632—51noSylow
82C22×C3×D5—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×Dic5—21no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5—41no—
93C3×D20—21no—
94C3×D20Q1612yescomplemented
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97C3×C4×D5—82no—
98C3×Dic10—42no—
99C3×Dic10—42no—
100C3×C5×C8—22no—
101C3×C5×C8—41no—
102C3×#168—41no—
103C2×C3×Q16—102no—
104C3×C4⋊Q8—51no—
105C3×C4⋊Q8—51no—
106C3×#125—101no—
107C3×C22⋊Q8—102no—
108C3×C22⋊Q8—101no—
109C3×C4×Q8C2×D511yescharacteristic
110C3×C4×D4—51no—
111C3×C4×D4—101no—
112C2×C3×C4⋊C4—101no—
113C3×#107—101no—
114C3×#106—101no—
115C3×C4⋊C8—51no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×#103—101no—
118C3×#102—101no—
119C3×C4×C8C2×D511yescharacteristic
120C2×C5×Q8C3×D411yescharacteristic
121C2×D20C3×D411yescharacteristic
122C2×C4×D5—21no—
123C2×C4×D5—22no—
124C2×Dic10—21no—
125C2×Dic10C3×D412yes—
126C2×C5×C8—21no—
127C2×C5×C8—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4C3×D411yescharacteristic
130C42×C5—21no—
131C42×C5C23×C311yescharacteristic
132#685—22no—
133#685—21no—
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5C3×D411yescharacteristic
139#683—22no—
140#683—22no—
141C2×#168—21no—
142Dic20—44no—
143#554—51no—
144#494—51no—
145#477—51no—
146#476—51no—
147#333—51no—
148Q8⋊C8C3×D511yescharacteristic, complemented
149D4⋊C8—51no—
150C22×C3×C5#12011yescharacteristic
151C2×C3×D5—22no—
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5C2×Q1611yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×Dic5—41no—
162C3×Dic5—42no—
163C3×Dic5—81no—
164C2×C3×Q8—52no—
165C2×C3×Q8—101no—
166C2×C3×Q8D2011yescharacteristic
167C2×C3×D4—51no—
168C22×C3×C4—102no—
169C22×C3×C4—101no—
170C3×Q16—204no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—101no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—102no—
177C3×C4⋊C4—102no—
178C3×C4⋊C4—101no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4D2011yescharacteristic
183C3×C22⋊C4—102no—
184C3×C22⋊C4—101no—
185C3×C42—21no—
186C3×C42C22×D511yescharacteristic
187C22×D5—21no—
188C5×Q8—21no—
189C5×Q8—21no—
190C2×C4×C5—21no—
191C2×C4×C5—21no—
192C2×C4×C5C2×C3×D411yescharacteristic
193C2×C4×C5C2×C3×D411yescharacteristic
194C2×C4×C5C2×C3×D411yescharacteristic
195C2×Dic5—21no—
196C2×Dic5—22no—
197C2×Dic5—41no—
198D20—21no—
199D20C3×Q1612yescomplemented
200C4×D5—41no—
201C4×D5—41no—
202C4×D5—82no—
203Dic10—42no—
204Dic10—42no—
205C5×C8—22no—
206C5×C8—41no—
207#168—41no—
208C2×Q16—102no—
209C4⋊Q8—51no—
210C4⋊Q8—51no—
211#125—101no—
212C22⋊Q8—102no—
213C22⋊Q8—101no—
214C4×Q8C2×C3×D511yescharacteristic
215C4×D4—51no—
216C4×D4—101no—
217C2×C4⋊C4—101no—
218#107—101no—
219#106—101no—
220C4⋊C8—51no—
221C4⋊C8C2×C3×D511yescharacteristic
222#103—101no—
223#102—101no—
224C4×C8C2×C3×D511yescharacteristic
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C3×D5—42no—
229C23×C3—101no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—202no—
233C3×Q8—202no—
234C3×D4—52no—
235C3×D4—101no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—101no—
239C2×C3×C4—102no—
240C2×C3×C4—201no—
241C2×C3×C4—201no—
242C2×C3×C4—201no—
243C2×C3×C4—402no—
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C3×C8—22no—
248C3×C8—41no—
249C3×C8—201no—
250C22×C5C3×#12011yescharacteristic
251C2×D5—22no—
252C2×D5—41no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5C2×C3×Q1611yescharacteristic
258C4×C5C3×#13511yescharacteristic
259C4×C5C3×#13711yescharacteristic
260C4×C5C3×#13711yescharacteristic
261Dic5—41no—
262Dic5—42no—
263Dic5—81no—
264C2×Q8—52no—
265C2×Q8—101no—
266C2×Q8C3×D2011yescharacteristic
267C2×D4—51no—
268C22×C4—102no—
269C22×C4—101no—
270Q16—204no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—101no—
274C4⋊C4—21no—
275C4⋊C4—51no—
276C4⋊C4—102no—
277C4⋊C4—102no—
278C4⋊C4—101no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4C3×D2011yescharacteristic
283C22⋊C4—102no—
284C22⋊C4—101no—
285C42—21no—
286C42C22×C3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—102no—
289C22×C3—201no—
290C22×C3—201no—
291C22×C3#402811yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—202no—
296C3×C4—201no—
297C3×C4—401no—
298C3×C4#405011yescharacteristic
299C3×C4#405511yescharacteristic
300C3×C4#406111yescharacteristic
301C3×C4D5×Q1611yescharacteristic
302C2×C5C3×#45111yescharacteristic
303C2×C5C3×#45211yescharacteristic
304C2×C5C3×#45311yescharacteristic
305D5—42no—
306C23—101no—
307Q8—21no—
308Q8—21no—
309Q8—202no—
310Q8—202no—
311D4—52no—
312D4—101no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—101no—
316C2×C4—102no—
317C2×C4—201no—
318C2×C4—201no—
319C2×C4—201no—
320C2×C4—402no—
321C2×C4C2×C3×D2011yescharacteristic
322C2×C4C3×D4×D511yescharacteristic
323C2×C4C3×D4×D511yescharacteristic
324C8—22no—
325C8—41no—
326C8—201no—
327C2×C3—202no—
328C2×C3#6502211yescharacteristic
329C2×C3#6509711yescharacteristic
330C2×C3#6511111yescharacteristic
331C5C3×#163211yescharacteristic, complemented, Sylow
332C22—102no—
333C22—201no—
334C22—201no—
335C22C3×#402811yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—202no—
340C4—201no—
341C4—401no—
342C4C3×#405011yescharacteristic
343C4C3×#405511yescharacteristic
344C4C3×#406111yescharacteristic
345C4C3×D5×Q1611yescharacteristic
346C3#1059903911yescharacteristic, direct product factor, Sylow
347C2—202no—
348C2C3×#6502211yescharacteristic
349C2C3×#6509711yescharacteristic
350C2C3×#6511111yescharacteristic
subgroupG/H
centerC22×C3#4028
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC3×Q8⋊C8D5
hypocenterC5C3×#1632
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65310C2semidirect
4. C3×#64988C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. C3×#64701C2semidirect
8. #10599039C3direct (N × H)
28. #65310C2×C3semidirect
30. #64988C2×C3semidirect
31. C5×Q8⋊C8C2×C3semidirect
32. #64701C2×C3semidirect
62. C3×Q8⋊C8D5semidirect
94. C3×D20Q16semidirect
148. Q8⋊C8C3×D5semidirect
199. D20C3×Q16semidirect
287. C3×C5#1632semidirect
331. C5C3×#1632semidirect
346. C3#10599039direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659132
C3×#653102
C3×#651312
C3×#649882
C3×C5×Q8⋊C82
C3×#647012
C3×#646792
#105990393
C3×#16325