Finite Group Databasebeta

← C3×C5×#1679 #14274713

Subgroups — C3×C5×#1679 #14274713

Order 1920.

332 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#487C211yesmaximal, characteristic, complemented
2C3×C5×#474C211yesmaximal, characteristic
3C3×C5×#461C211yesmaximal, characteristic
4C3×C5×C8×D4C211yesmaximal, characteristic
5C3×C5×#334C211yesmaximal, characteristic, complemented
6C3×C5×#332C211yesmaximal, characteristic, complemented
7C3×C5×#332C211yesmaximal, characteristic, complemented
8C5×#1679C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×SD16—21no—
10C22×C3×C5×C8—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×C4⋊Q8C2211yescharacteristic
13C3×C4×C5×D4C2211yescharacteristic
14C3×C5×#107—21no—
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×C4⋊C8C2211yescharacteristic
18C3×C5×#103—21no—
19C3×C5×#103—21no—
20C3×C5×#103—21no—
21C3×C5×#102—21no—
22C3×C5×C22⋊C8—21no—
23C3×C4×C5×C8C2211yescharacteristic
24C3×#1679C511yesmaximal, characteristic, direct product factor, Hall
25C5×#487C2×C311yescharacteristic, complemented
26C5×#474C2×C311yescharacteristic
27C5×#461C2×C311yescharacteristic
28C5×C8×D4C2×C311yescharacteristic
29C5×#334C2×C311yescharacteristic, complemented
30C5×#332C2×C311yescharacteristic, complemented
31C5×#332C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8—21no—
33C2×C3×C5×Q8—21no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C3×C5×SD16—42no—
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—42no—
41C2×C3×C5×C8D411yescharacteristic
42C2×C3×C5×C8D411yescharacteristic
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C3×C42×C5C2311yescharacteristic
50C3×#487C2×C511yescharacteristic, complemented
51C3×#474C2×C511yescharacteristic
52C3×#461C2×C511yescharacteristic
53C3×C8×D4C2×C511yescharacteristic
54C3×#334C2×C511yescharacteristic, complemented
55C3×#332C2×C511yescharacteristic, complemented
56C3×#332C2×C511yescharacteristic, complemented
57C2×C5×SD16—21no—
58C22×C5×C8—21no—
59C5×C4⋊Q8C22×C311yescharacteristic
60C5×C4⋊Q8C22×C311yescharacteristic
61C4×C5×D4C22×C311yescharacteristic
62C5×#107—21no—
63C5×C4⋊C8C22×C311yescharacteristic
64C5×C4⋊C8C22×C311yescharacteristic
65C5×C4⋊C8C22×C311yescharacteristic
66C5×#103—21no—
67C5×#103—21no—
68C5×#103—21no—
69C5×#102—21no—
70C5×C22⋊C8—21no—
71C4×C5×C8C22×C311yescharacteristic
72#1679C3×C511yescharacteristic, direct product factor, Sylow
73C23×C3×C5—21no—
74C3×C5×Q8—41no—
75C3×C5×Q8—41no—
76C3×C5×Q8—41no—
77C3×C5×Q8—41no—
78C3×C5×D4—21no—
79C3×C5×D4SD1612yes—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5#4111yescharacteristic
88C3×C5×C8—21no—
89C3×C5×C8—21no—
90C3×C5×C8—41no—
91C3×C5×C8—41no—
92C3×C5×C8—41no—
93C2×C3×SD16—21no—
94C22×C3×C8—21no—
95C3×C4⋊Q8C22×C511yescharacteristic
96C3×C4⋊Q8C22×C511yescharacteristic
97C3×C4×D4C22×C511yescharacteristic
98C3×#107—21no—
99C3×C4⋊C8C22×C511yescharacteristic
100C3×C4⋊C8C22×C511yescharacteristic
101C3×C4⋊C8C22×C511yescharacteristic
102C3×#103—21no—
103C3×#103—21no—
104C3×#103—21no—
105C3×#102—21no—
106C3×C22⋊C8—21no—
107C3×C4×C8C22×C511yescharacteristic
108C2×C5×Q8—21no—
109C2×C5×Q8—21no—
110C2×C5×D4C3×D411yescharacteristic
111C22×C4×C5—21no—
112C5×SD16—42no—
113C2×C5×C8—21no—
114C2×C5×C8—21no—
115C2×C5×C8—21no—
116C2×C5×C8—42no—
117C2×C5×C8C3×D411yescharacteristic
118C2×C5×C8C3×D411yescharacteristic
119C5×C4⋊C4—21no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—21no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4C3×D411yescharacteristic
124C5×C22⋊C4—21no—
125C42×C5C23×C311yescharacteristic
126#487C2×C3×C511yescharacteristic, complemented
127#474C2×C3×C511yescharacteristic
128#461C2×C3×C511yescharacteristic
129C8×D4C2×C3×C511yescharacteristic
130#334C2×C3×C511yescharacteristic, complemented
131#332C2×C3×C511yescharacteristic, complemented
132#332C2×C3×C511yescharacteristic, complemented
133C22×C3×C5—22no—
134C22×C3×C5—41no—
135C22×C3×C5—41no—
136C22×C3×C5#12111yescharacteristic
137C3×C4×C5—21no—
138C3×C4×C5—41no—
139C3×C4×C5—81no—
140C3×C4×C5—81no—
141C3×C4×C5C2×SD1611yescharacteristic
142C3×C4×C5#13511yescharacteristic
143C3×C4×C5#13511yescharacteristic
144C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
145C2×C3×Q8—21no—
146C2×C3×Q8—21no—
147C2×C3×D4C5×D411yescharacteristic
148C22×C3×C4—21no—
149C3×SD16—42no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—42no—
154C2×C3×C8C5×D411yescharacteristic
155C2×C3×C8C5×D411yescharacteristic
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4C5×D411yescharacteristic
161C3×C22⋊C4—21no—
162C3×C42C23×C511yescharacteristic
163C23×C5—21no—
164C5×Q8—41no—
165C5×Q8—41no—
166C5×Q8—41no—
167C5×Q8—41no—
168C5×D4—21no—
169C5×D4C3×SD1612yes—
170C2×C4×C5—21no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5C2×C3×D411yescharacteristic
176C2×C4×C5C2×C3×D411yescharacteristic
177C2×C4×C5C3×#4111yescharacteristic
178C5×C8—21no—
179C5×C8—21no—
180C5×C8—41no—
181C5×C8—41no—
182C5×C8—41no—
183C2×SD16—21no—
184C22×C8—21no—
185C4⋊Q8C22×C3×C511yescharacteristic
186C4⋊Q8C22×C3×C511yescharacteristic
187C4×D4C22×C3×C511yescharacteristic
188#107—21no—
189C4⋊C8C22×C3×C511yescharacteristic
190C4⋊C8C22×C3×C511yescharacteristic
191C4⋊C8C22×C3×C511yescharacteristic
192#103—21no—
193#103—21no—
194#103—21no—
195#102—21no—
196C22⋊C8—21no—
197C4×C8C22×C3×C511yescharacteristic
198C2×C3×C5—42no—
199C2×C3×C5#46311yescharacteristic
200C2×C3×C5#46511yescharacteristic
201C2×C3×C5#47311yescharacteristic
202C23×C3—21no—
203C3×Q8—41no—
204C3×Q8—41no—
205C3×Q8—41no—
206C3×Q8—41no—
207C3×D4—21no—
208C3×D4C5×SD1612yes—
209C2×C3×C4—21no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4C2×C5×D411yescharacteristic
215C2×C3×C4C2×C5×D411yescharacteristic
216C2×C3×C4C5×#4111yescharacteristic
217C3×C8—21no—
218C3×C8—21no—
219C3×C8—41no—
220C3×C8—41no—
221C3×C8—41no—
222C22×C5—22no—
223C22×C5—41no—
224C22×C5—41no—
225C22×C5C3×#12111yescharacteristic
226C4×C5—21no—
227C4×C5—41no—
228C4×C5—81no—
229C4×C5—81no—
230C4×C5C2×C3×SD1611yescharacteristic
231C4×C5C3×#13511yescharacteristic
232C4×C5C3×#13511yescharacteristic
233C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
234C2×Q8—21no—
235C2×Q8—21no—
236C2×D4C3×C5×D411yescharacteristic
237C22×C4—21no—
238SD16—42no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—42no—
243C2×C8C3×C5×D411yescharacteristic
244C2×C8C3×C5×D411yescharacteristic
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4C3×C5×D411yescharacteristic
250C22⋊C4—21no—
251C42C23×C3×C511yescharacteristic
252C3×C5#167911yescharacteristic, direct product factor, Hall
253C22×C3—22no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3C5×#12111yescharacteristic
257C3×C4—21no—
258C3×C4—41no—
259C3×C4—81no—
260C3×C4—81no—
261C3×C4C2×C5×SD1611yescharacteristic
262C3×C4C5×#13511yescharacteristic
263C3×C4C5×#13511yescharacteristic
264C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
265C2×C5—42no—
266C2×C5C3×#46311yescharacteristic
267C2×C5C3×#46511yescharacteristic
268C2×C5C3×#47311yescharacteristic
269C23—21no—
270Q8—41no—
271Q8—41no—
272Q8—41no—
273Q8—41no—
274D4—21no—
275D4C3×C5×SD1612yes—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4C2×C3×C5×D411yescharacteristic
282C2×C4C2×C3×C5×D411yescharacteristic
283C2×C4C3×C5×#4111yescharacteristic
284C8—21no—
285C8—21no—
286C8—41no—
287C8—41no—
288C8—41no—
289C2×C3—42no—
290C2×C3C5×#46311yescharacteristic
291C2×C3C5×#46511yescharacteristic
292C2×C3C5×#47311yescharacteristic
293C5C3×#167911yescharacteristic, direct product factor, Sylow
294C22—22no—
295C22—41no—
296C22—41no—
297C22C3×C5×#12111yescharacteristic
298C4—21no—
299C4—41no—
300C4—81no—
301C4—81no—
302C4C2×C3×C5×SD1611yescharacteristic
303C4C3×C5×#13511yescharacteristic
304C4C3×C5×#13511yescharacteristic
305C4C3×C5×AGL(1,ℤ/8)11yescharacteristic
306C3C5×#167911yescharacteristic, direct product factor, Sylow
307C2—42no—
308C2C3×C5×#46311yescharacteristic
309C2C3×C5×#46511yescharacteristic
310C2C3×C5×#47311yescharacteristic
subgroupG/H
center, socleC22×C3×C5#121
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC2×C3×C5×D4D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C5×#487C2semidirect
5. C3×C5×#334C2semidirect
6. C3×C5×#332C2semidirect
7. C3×C5×#332C2semidirect
8. C5×#1679C3direct (N × H)
24. C3×#1679C5direct (N × H)
25. C5×#487C2×C3semidirect
29. C5×#334C2×C3semidirect
30. C5×#332C2×C3semidirect
31. C5×#332C2×C3semidirect
50. C3×#487C2×C5semidirect
54. C3×#334C2×C5semidirect
55. C3×#332C2×C5semidirect
56. C3×#332C2×C5semidirect
72. #1679C3×C5direct (N × H)
126. #487C2×C3×C5semidirect
130. #334C2×C3×C5semidirect
131. #332C2×C3×C5semidirect
132. #332C2×C3×C5semidirect
252. C3×C5#1679direct (N × H)
293. C5C3×#1679direct (N × H)
306. C3C5×#1679direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4872
C3×C5×#4742
C3×C5×#4612
C3×C5×C8×D42
C3×C5×#3342
C3×C5×#3322
C5×#16793
C3×#16795