Finite Group Databasebeta

← C3×C5×#1677 #14274711

Subgroups — C3×C5×#1677 #14274711

Order 1920.

352 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#486C211yesmaximal, characteristic, complemented
2C3×C5×#476C211yesmaximal, characteristic, complemented
3C3×C5×#459C211yesmaximal, characteristic
4C3×C5×C8×D4C211yesmaximal, characteristic, complemented
5C3×C5×#334C211yesmaximal, characteristic, complemented
6C3×C5×#333C211yesmaximal, characteristic, complemented
7C3×C5×#331C211yesmaximal, characteristic, complemented
8C5×#1677C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×D8—21no—
10C22×C3×C5×C8—21no—
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×#127C2211yescharacteristic
13C3×C4×C5×D4C2211yescharacteristic
14C3×C5×#106—21no—
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×C4⋊C8C2211yescharacteristic
18C3×C5×#102—21no—
19C3×C5×#102—21no—
20C3×C5×#102—21no—
21C3×C5×#102—21no—
22C3×C5×C22⋊C8—21no—
23C3×C4×C5×C8C2211yescharacteristic
24C3×#1677C511yesmaximal, characteristic, direct product factor, Hall
25C5×#486C2×C311yescharacteristic, complemented
26C5×#476C2×C311yescharacteristic, complemented
27C5×#459C2×C311yescharacteristic
28C5×C8×D4C2×C311yescharacteristic, complemented
29C5×#334C2×C311yescharacteristic, complemented
30C5×#333C2×C311yescharacteristic, complemented
31C5×#331C2×C311yescharacteristic, complemented
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—21no—
38C3×C5×D8—42no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C2×C3×C5×C8—42no—
43C2×C3×C5×C8D411yescharacteristic
44C2×C3×C5×C8D411yescharacteristic
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C22⋊C4—21no—
49C3×C42×C5C2311yescharacteristic
50C3×#486C2×C511yescharacteristic, complemented
51C3×#476C2×C511yescharacteristic, complemented
52C3×#459C2×C511yescharacteristic
53C3×C8×D4C2×C511yescharacteristic, complemented
54C3×#334C2×C511yescharacteristic, complemented
55C3×#333C2×C511yescharacteristic, complemented
56C3×#331C2×C511yescharacteristic, complemented
57C2×C5×D8—21no—
58C22×C5×C8—21no—
59C5×C4⋊Q8C22×C311yescharacteristic
60C5×#127C22×C311yescharacteristic
61C4×C5×D4C22×C311yescharacteristic
62C5×#106—21no—
63C5×C4⋊C8C22×C311yescharacteristic
64C5×C4⋊C8C22×C311yescharacteristic
65C5×C4⋊C8C22×C311yescharacteristic
66C5×#102—21no—
67C5×#102—21no—
68C5×#102—21no—
69C5×#102—21no—
70C5×C22⋊C8—21no—
71C4×C5×C8C22×C311yescharacteristic
72#1677C3×C511yescharacteristic, direct product factor, Sylow
73C23×C3×C5—21no—
74C23×C3×C5—41no—
75C3×C5×Q8—81no—
76C3×C5×D4—21no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—81no—
82C3×C5×D4SD1612yes—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C3×C5×C8—21no—
91C3×C5×C8—21no—
92C3×C5×C8—41no—
93C3×C5×C8—41no—
94C3×C5×C8—41no—
95C2×C3×D8—21no—
96C22×C3×C8—21no—
97C3×C4⋊Q8C22×C511yescharacteristic
98C3×#127C22×C511yescharacteristic
99C3×C4×D4C22×C511yescharacteristic
100C3×#106—21no—
101C3×C4⋊C8C22×C511yescharacteristic
102C3×C4⋊C8C22×C511yescharacteristic
103C3×C4⋊C8C22×C511yescharacteristic
104C3×#102—21no—
105C3×#102—21no—
106C3×#102—21no—
107C3×#102—21no—
108C3×C22⋊C8—21no—
109C3×C4×C8C22×C511yescharacteristic
110C2×C5×Q8—21no—
111C2×C5×D4—21no—
112C2×C5×D4—21no—
113C2×C5×D4—21no—
114C2×C5×D4C3×D411yescharacteristic
115C22×C4×C5—21no—
116C5×D8—42no—
117C2×C5×C8—21no—
118C2×C5×C8—21no—
119C2×C5×C8—21no—
120C2×C5×C8—42no—
121C2×C5×C8C3×D411yescharacteristic
122C2×C5×C8C3×D411yescharacteristic
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4C3×D411yescharacteristic
126C5×C22⋊C4—21no—
127C42×C5C23×C311yescharacteristic
128#486C2×C3×C511yescharacteristic, complemented
129#476C2×C3×C511yescharacteristic, complemented
130#459C2×C3×C511yescharacteristic
131C8×D4C2×C3×C511yescharacteristic, complemented
132#334C2×C3×C511yescharacteristic, complemented
133#333C2×C3×C511yescharacteristic, complemented
134#331C2×C3×C511yescharacteristic, complemented
135C22×C3×C5—22no—
136C22×C3×C5—41no—
137C22×C3×C5—41no—
138C22×C3×C5—81no—
139C22×C3×C5—81no—
140C22×C3×C5—81no—
141C22×C3×C5#12111yescharacteristic
142C3×C4×C5—21no—
143C3×C4×C5—41no—
144C3×C4×C5—81no—
145C3×C4×C5C2×SD1611yescharacteristic
146C3×C4×C5#13511yescharacteristic
147C3×C4×C5#13511yescharacteristic
148C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
149C2×C3×Q8—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4C5×D411yescharacteristic
154C22×C3×C4—21no—
155C3×D8—42no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—42no—
160C2×C3×C8C5×D411yescharacteristic
161C2×C3×C8C5×D411yescharacteristic
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4C5×D411yescharacteristic
165C3×C22⋊C4—21no—
166C3×C42C23×C511yescharacteristic
167C23×C5—21no—
168C23×C5—41no—
169C5×Q8—81no—
170C5×D4—21no—
171C5×D4—41no—
172C5×D4—41no—
173C5×D4—41no—
174C5×D4—41no—
175C5×D4—81no—
176C5×D4C3×SD1612yes—
177C2×C4×C5—21no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5C2×C3×D411yescharacteristic
182C2×C4×C5C2×C3×D411yescharacteristic
183C2×C4×C5C3×#4111yescharacteristic
184C5×C8—21no—
185C5×C8—21no—
186C5×C8—41no—
187C5×C8—41no—
188C5×C8—41no—
189C2×D8—21no—
190C22×C8—21no—
191C4⋊Q8C22×C3×C511yescharacteristic
192#127C22×C3×C511yescharacteristic
193C4×D4C22×C3×C511yescharacteristic
194#106—21no—
195C4⋊C8C22×C3×C511yescharacteristic
196C4⋊C8C22×C3×C511yescharacteristic
197C4⋊C8C22×C3×C511yescharacteristic
198#102—21no—
199#102—21no—
200#102—21no—
201#102—21no—
202C22⋊C8—21no—
203C4×C8C22×C3×C511yescharacteristic
204C2×C3×C5—42no—
205C2×C3×C5—161no—
206C2×C3×C5#46311yescharacteristic
207C2×C3×C5#46511yescharacteristic
208C2×C3×C5#47211yescharacteristic
209C23×C3—21no—
210C23×C3—41no—
211C3×Q8—81no—
212C3×D4—21no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—41no—
217C3×D4—81no—
218C3×D4C5×SD1612yes—
219C2×C3×C4—21no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4C2×C5×D411yescharacteristic
224C2×C3×C4C2×C5×D411yescharacteristic
225C2×C3×C4C5×#4111yescharacteristic
226C3×C8—21no—
227C3×C8—21no—
228C3×C8—41no—
229C3×C8—41no—
230C3×C8—41no—
231C22×C5—22no—
232C22×C5—41no—
233C22×C5—41no—
234C22×C5—81no—
235C22×C5—81no—
236C22×C5—81no—
237C22×C5C3×#12111yescharacteristic
238C4×C5—21no—
239C4×C5—41no—
240C4×C5—81no—
241C4×C5C2×C3×SD1611yescharacteristic
242C4×C5C3×#13511yescharacteristic
243C4×C5C3×#13511yescharacteristic
244C4×C5C3×AGL(1,ℤ/8)11yescharacteristic
245C2×Q8—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C3×C5×D411yescharacteristic
250C22×C4—21no—
251D8—42no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—42no—
256C2×C8C3×C5×D411yescharacteristic
257C2×C8C3×C5×D411yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4C3×C5×D411yescharacteristic
261C22⋊C4—21no—
262C42C23×C3×C511yescharacteristic
263C3×C5#167711yescharacteristic, direct product factor, Hall
264C22×C3—22no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—81no—
268C22×C3—81no—
269C22×C3—81no—
270C22×C3C5×#12111yescharacteristic
271C3×C4—21no—
272C3×C4—41no—
273C3×C4—81no—
274C3×C4C2×C5×SD1611yescharacteristic
275C3×C4C5×#13511yescharacteristic
276C3×C4C5×#13511yescharacteristic
277C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
278C2×C5—42no—
279C2×C5—161no—
280C2×C5C3×#46311yescharacteristic
281C2×C5C3×#46511yescharacteristic
282C2×C5C3×#47211yescharacteristic
283C23—21no—
284C23—41no—
285Q8—81no—
286D4—21no—
287D4—41no—
288D4—41no—
289D4—41no—
290D4—41no—
291D4—81no—
292D4C3×C5×SD1612yes—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4C2×C3×C5×D411yescharacteristic
298C2×C4C2×C3×C5×D411yescharacteristic
299C2×C4C3×C5×#4111yescharacteristic
300C8—21no—
301C8—21no—
302C8—41no—
303C8—41no—
304C8—41no—
305C2×C3—42no—
306C2×C3—161no—
307C2×C3C5×#46311yescharacteristic
308C2×C3C5×#46511yescharacteristic
309C2×C3C5×#47211yescharacteristic
310C5C3×#167711yescharacteristic, direct product factor, Sylow
311C22—22no—
312C22—41no—
313C22—41no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22C3×C5×#12111yescharacteristic
318C4—21no—
319C4—41no—
320C4—81no—
321C4C2×C3×C5×SD1611yescharacteristic
322C4C3×C5×#13511yescharacteristic
323C4C3×C5×#13511yescharacteristic
324C4C3×C5×AGL(1,ℤ/8)11yescharacteristic
325C3C5×#167711yescharacteristic, direct product factor, Sylow
326C2—42no—
327C2—161no—
328C2C3×C5×#46311yescharacteristic
329C2C3×C5×#46511yescharacteristic
330C2C3×C5×#47211yescharacteristic
subgroupG/H
center, socleC22×C3×C5#121
commutator, Frattini, cosocleC42C23×C3×C5
prime radicalC3×C5×#459C2
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×#486C2semidirect
2. C3×C5×#476C2semidirect
4. C3×C5×C8×D4C2semidirect
5. C3×C5×#334C2semidirect
6. C3×C5×#333C2semidirect
7. C3×C5×#331C2semidirect
8. C5×#1677C3direct (N × H)
24. C3×#1677C5direct (N × H)
25. C5×#486C2×C3semidirect
26. C5×#476C2×C3semidirect
28. C5×C8×D4C2×C3semidirect
29. C5×#334C2×C3semidirect
30. C5×#333C2×C3semidirect
31. C5×#331C2×C3semidirect
50. C3×#486C2×C5semidirect
51. C3×#476C2×C5semidirect
53. C3×C8×D4C2×C5semidirect
54. C3×#334C2×C5semidirect
55. C3×#333C2×C5semidirect
56. C3×#331C2×C5semidirect
72. #1677C3×C5direct (N × H)
128. #486C2×C3×C5semidirect
129. #476C2×C3×C5semidirect
131. C8×D4C2×C3×C5semidirect
132. #334C2×C3×C5semidirect
133. #333C2×C3×C5semidirect
134. #331C2×C3×C5semidirect
263. C3×C5#1677direct (N × H)
310. C5C3×#1677direct (N × H)
325. C3C5×#1677direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4862
C3×C5×#4762
C3×C5×#4592
C3×C5×C8×D42
C3×C5×#3342
C3×C5×#3332
C3×C5×#3312
C5×#16773
C3×#16775