Finite Group Databasebeta

← C3×#10599190 #14292100

Subgroups — C3×#10599190 #14292100

Order 1920.

364 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65361C211yesmaximal, characteristic
2C3×#65359C211yesmaximal, characteristic, complemented
3C3×#65130C211yesmaximal, characteristic, complemented
4C3×#65123C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7C3×#64699C211yesmaximal, characteristic, complemented
8#10599190C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#127C2211yescharacteristic
10C2×C3×#686—21no—
11C2×C3×#677—21no—
12C2×C3×C8×D5—21no—
13C3×C4×D20C2211yescharacteristic
14C3×#4015C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×#3964—21no—
18C3×#3964—21no—
19C3×#3964—21no—
20C3×#3952—21no—
21C3×#3948—21no—
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24C3×#1681—51nomaximal, Hall
25#65361C2×C311yescharacteristic
26#65359C2×C311yescharacteristic, complemented
27#65130C2×C311yescharacteristic, complemented
28#65123C2×C311yescharacteristic, complemented
29C5×#331C2×C311yescharacteristic, complemented
30#64706C2×C311yescharacteristic, complemented
31#64699C2×C311yescharacteristic, complemented
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×D20D411yescharacteristic
36C2×C3×C4×D5—21no—
37C2×C3×Dic10—21no—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C3×#686—42no—
42C3×#685—21no—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5D411yescharacteristic
46C2×C3×#168—21no—
47C2×C3×#168D411yescharacteristic
48C2×C3×#168D411yescharacteristic
49C3×#677—42no—
50C3×C8×D5—42no—
51C3×#486—51no—
52C3×#461—51no—
53C3×#459—51no—
54C3×C8×D4—51no—
55C3×#335—51no—
56C3×#332—51no—
57C3×#331D511yescharacteristic, complemented
58C5×#127C22×C311yescharacteristic
59C2×#686—21no—
60C2×#677—21no—
61C2×C8×D5—21no—
62C4×D20C22×C311yescharacteristic
63#4015C22×C311yescharacteristic
64C5×C4⋊C8C22×C311yescharacteristic
65C5×C4⋊C8C22×C311yescharacteristic
66#3964—21no—
67#3964—21no—
68#3964—21no—
69#3952—21no—
70#3948—21no—
71C4⋊#168C22×C311yescharacteristic
72C4×#168C22×C311yescharacteristic
73#1681—51noSylow
74C23×C3×C5—41no—
75C22×C3×D5—21no—
76C3×C5×D4—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—81no—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5#4111yescharacteristic
84C2×C3×Dic5—21no—
85C2×C3×Dic5—41no—
86C3×D20—21no—
87C3×D20D812yes—
88C3×C4×D5—41no—
89C3×C4×D5—41no—
90C3×Dic10—41no—
91C3×Dic10—41no—
92C3×C5×C8—41no—
93C3×C5×C8—41no—
94C3×#168—21no—
95C3×#168—21no—
96C3×#168—41no—
97C2×C3×SD16—101no—
98C2×C3×D8—101no—
99C22×C3×C8—101no—
100C3×C4⋊Q8—51no—
101C3×#127C2×D511yescharacteristic
102C3×C4×D4—51no—
103C3×C4⋊C8—51no—
104C3×C4⋊C8C2×D511yescharacteristic
105C3×C4⋊C8C2×D511yescharacteristic
106C3×#103—101no—
107C3×#102—101no—
108C3×#102—101no—
109C3×#102—101no—
110C3×C22⋊C8—101no—
111C3×C4×C8—51no—
112C2×C5×D4—21no—
113C2×C5×D4—21no—
114C2×C5×D4—21no—
115C2×D20C3×D411yescharacteristic
116C2×C4×D5—21no—
117C2×Dic10—21no—
118C2×C5×C8—21no—
119C2×C5×C8—21no—
120C42×C5C23×C311yescharacteristic
121#686—42no—
122#685—21no—
123C4⋊Dic5—21no—
124C4⋊Dic5—21no—
125C4⋊Dic5C3×D411yescharacteristic
126C2×#168—21no—
127C2×#168C3×D411yescharacteristic
128C2×#168C3×D411yescharacteristic
129#677—42no—
130C8×D5—42no—
131#486—51no—
132#461—51no—
133#459—51no—
134C8×D4—51no—
135#335—51no—
136#332—51no—
137#331C3×D511yescharacteristic, complemented
138C22×C3×C5—81no—
139C22×C3×C5—81no—
140C22×C3×C5—81no—
141C22×C3×C5#12111yescharacteristic
142C2×C3×D5—22no—
143C2×C3×D5—41no—
144C2×C3×D5—41no—
145C3×C4×C5—21no—
146C3×C4×C5C2×D811yescharacteristic
147C3×C4×C5#13511yescharacteristic
148C3×C4×C5#13511yescharacteristic
149C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
150C3×Dic5—41no—
151C3×Dic5—81no—
152C2×C3×Q8—101no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—51no—
157C22×C3×C4—101no—
158C3×SD16—202no—
159C3×D8—202no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—51no—
163C2×C3×C8—51no—
164C2×C3×C8—101no—
165C2×C3×C8—202no—
166C3×C4⋊C4—51no—
167C3×C4⋊C4—101no—
168C3×C4⋊C4—101no—
169C3×C22⋊C4—101no—
170C3×C42C22×D511yescharacteristic
171C23×C5—41no—
172C22×D5—21no—
173C5×D4—41no—
174C5×D4—41no—
175C5×D4—41no—
176C5×D4—41no—
177C5×D4—81no—
178C2×C4×C5C2×C3×D411yescharacteristic
179C2×C4×C5C2×C3×D411yescharacteristic
180C2×C4×C5C3×#4111yescharacteristic
181C2×Dic5—21no—
182C2×Dic5—41no—
183D20—21no—
184D20C3×D812yes—
185C4×D5—41no—
186C4×D5—41no—
187Dic10—41no—
188Dic10—41no—
189C5×C8—41no—
190C5×C8—41no—
191#168—21no—
192#168—21no—
193#168—41no—
194C2×SD16—101no—
195C2×D8—101no—
196C22×C8—101no—
197C4⋊Q8—51no—
198#127C2×C3×D511yescharacteristic
199C4×D4—51no—
200C4⋊C8—51no—
201C4⋊C8C2×C3×D511yescharacteristic
202C4⋊C8C2×C3×D511yescharacteristic
203#103—101no—
204#102—101no—
205#102—101no—
206#102—101no—
207C22⋊C8—101no—
208C4×C8—51no—
209C2×C3×C5—161no—
210C2×C3×C5#46311yescharacteristic
211C2×C3×C5#46611yescharacteristic
212C2×C3×C5#47111yescharacteristic
213C3×D5—42no—
214C23×C3—41no—
215C23×C3—101no—
216C3×Q8—201no—
217C3×Q8—201no—
218C3×D4—41no—
219C3×D4—41no—
220C3×D4—41no—
221C3×D4—41no—
222C3×D4—52no—
223C3×D4—81no—
224C3×D4—101no—
225C2×C3×C4—101no—
226C2×C3×C4—201no—
227C2×C3×C4—201no—
228C2×C3×C4—201no—
229C2×C3×C4#70911yescharacteristic
230C2×C3×C4D4×D511yescharacteristic
231C2×C3×C4D4×D511yescharacteristic
232C3×C8—41no—
233C3×C8—41no—
234C3×C8—101no—
235C3×C8—101no—
236C3×C8—201no—
237C22×C5—81no—
238C22×C5—81no—
239C22×C5—81no—
240C22×C5C3×#12111yescharacteristic
241C2×D5—22no—
242C2×D5—41no—
243C2×D5—41no—
244C4×C5—21no—
245C4×C5C2×C3×D811yescharacteristic
246C4×C5C3×#13511yescharacteristic
247C4×C5C3×#13511yescharacteristic
248C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
249Dic5—41no—
250Dic5—81no—
251C2×Q8—101no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—51no—
256C22×C4—101no—
257SD16—202no—
258D8—202no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—51no—
262C2×C8—51no—
263C2×C8—101no—
264C2×C8—202no—
265C4⋊C4—51no—
266C4⋊C4—101no—
267C4⋊C4—101no—
268C22⋊C4—101no—
269C42C22×C3×D511yescharacteristic
270C3×C5#168111yescharacteristic, complemented, Hall
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3—102no—
275C22×C3—201no—
276C22×C3—201no—
277C22×C3#403011yescharacteristic
278C3×C4—21no—
279C3×C4—201no—
280C3×C4—401no—
281C3×C4D5×D811yescharacteristic
282C3×C4#405711yescharacteristic
283C3×C4#406211yescharacteristic
284C3×C4#406211yescharacteristic
285C2×C5—161no—
286C2×C5C3×#46311yescharacteristic
287C2×C5C3×#46611yescharacteristic
288C2×C5C3×#47111yescharacteristic
289D5—42no—
290C23—41no—
291C23—101no—
292Q8—201no—
293Q8—201no—
294D4—41no—
295D4—41no—
296D4—41no—
297D4—41no—
298D4—52no—
299D4—81no—
300D4—101no—
301C2×C4—101no—
302C2×C4—201no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4C3×#70911yescharacteristic
306C2×C4C3×D4×D511yescharacteristic
307C2×C4C3×D4×D511yescharacteristic
308C8—41no—
309C8—41no—
310C8—101no—
311C8—101no—
312C8—201no—
313C2×C3—161no—
314C2×C3—202no—
315C2×C3#6503711yescharacteristic
316C2×C3#6506411yescharacteristic
317C2×C3#6507611yescharacteristic
318C5C3×#168111yescharacteristic, complemented, Sylow
319C22—81no—
320C22—81no—
321C22—81no—
322C22—102no—
323C22—201no—
324C22—201no—
325C22C3×#403011yescharacteristic
326C4—21no—
327C4—201no—
328C4—401no—
329C4C3×D5×D811yescharacteristic
330C4C3×#405711yescharacteristic
331C4C3×#406211yescharacteristic
332C4C3×#406211yescharacteristic
333C3#1059919011yescharacteristic, direct product factor, Sylow
334C2—161no—
335C2—202no—
336C2C3×#6503711yescharacteristic
337C2C3×#6506411yescharacteristic
338C2C3×#6507611yescharacteristic
subgroupG/H
centerC22×C3#4030
commutator, cosocleC42×C5C23×C3
FrattiniC42C22×C3×D5
FittingC3×C5×#331C2
socleC22×C3×C5#121
prime radicalC3×#65361C2
hypercenterC3×#331D5
hypocenterC5C3×#1681
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
2. C3×#65359C2semidirect
3. C3×#65130C2semidirect
4. C3×#65123C2semidirect
5. C3×C5×#331C2semidirect
6. C3×#64706C2semidirect
7. C3×#64699C2semidirect
8. #10599190C3direct (N × H)
26. #65359C2×C3semidirect
27. #65130C2×C3semidirect
28. #65123C2×C3semidirect
29. C5×#331C2×C3semidirect
30. #64706C2×C3semidirect
31. #64699C2×C3semidirect
57. C3×#331D5semidirect
137. #331C3×D5semidirect
270. C3×C5#1681semidirect
318. C5C3×#1681semidirect
333. C3#10599190direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#653612
C3×#653592
C3×#651302
C3×#651232
C3×C5×#3312
C3×#647062
C3×#646992
#105991903
C3×#16815