Finite Group Databasebeta

← C3×C5×#1636 #14274670

Subgroups — C3×C5×#1636 #14274670

Order 1920.

376 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#557C211yesmaximal, characteristic
2C3×C5×#487C211yesmaximal, characteristic
3C3×C5×#477C211yesmaximal, characteristic
4C3×C5×#477C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic
6C3×C5×Q8⋊C8C211yesmaximal, characteristic
7C3×C5×Q8⋊C8C211yesmaximal, characteristic
8C5×#1636C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×C4⋊Q8—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×C4⋊Q8C2211yescharacteristic
12C3×C5×#125—22no—
13C3×C5×#125—21no—
14C3×C4×C5×Q8—21no—
15C3×C4×C5×Q8—21no—
16C3×C4×C5×Q8C2211yescharacteristic
17C3×C4×C5×Q8C2211yescharacteristic
18C3×C5×#107—21no—
19C3×C5×#107—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#103—21no—
23C3×C5×#103—21no—
24C3×C5×#103—22no—
25C3×C4×C5×C8C2211yescharacteristic
26C3×#1636C511yesmaximal, characteristic, direct product factor, Hall
27C5×#557C2×C311yescharacteristic
28C5×#487C2×C311yescharacteristic
29C5×#477C2×C311yescharacteristic
30C5×#477C2×C311yescharacteristic
31C5×#332C2×C311yescharacteristic
32C5×Q8⋊C8C2×C311yescharacteristic
33C5×Q8⋊C8C2×C311yescharacteristic
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8—21no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4—22no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C4⋊C4D411yescharacteristic
51C3×C5×C4⋊C4D412yes—
52C3×C42×C5—22no—
53C3×C42×C5—21no—
54C3×C42×C5—21no—
55C3×C42×C5C2311yescharacteristic
56C3×#557C2×C511yescharacteristic
57C3×#487C2×C511yescharacteristic
58C3×#477C2×C511yescharacteristic
59C3×#477C2×C511yescharacteristic
60C3×#332C2×C511yescharacteristic
61C3×Q8⋊C8C2×C511yescharacteristic
62C3×Q8⋊C8C2×C511yescharacteristic
63C5×C4⋊Q8—21no—
64C5×C4⋊Q8C22×C311yescharacteristic
65C5×C4⋊Q8C22×C311yescharacteristic
66C5×#125—22no—
67C5×#125—21no—
68C4×C5×Q8—21no—
69C4×C5×Q8—21no—
70C4×C5×Q8C22×C311yescharacteristic
71C4×C5×Q8C22×C311yescharacteristic
72C5×#107—21no—
73C5×#107—21no—
74C5×C4⋊C8C22×C311yescharacteristic
75C5×C4⋊C8C22×C311yescharacteristic
76C5×#103—21no—
77C5×#103—21no—
78C5×#103—22no—
79C4×C5×C8C22×C311yescharacteristic
80#1636C3×C511yescharacteristic, direct product factor, Sylow
81C3×C5×Q8—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—42no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C3×C5×Q8Q1612yes—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C3×C5×C8—41no—
98C3×C5×C8—41no—
99C3×C5×C8—41no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8C22×C511yescharacteristic
102C3×C4⋊Q8C22×C511yescharacteristic
103C3×#125—22no—
104C3×#125—21no—
105C3×C4×Q8—21no—
106C3×C4×Q8—21no—
107C3×C4×Q8C22×C511yescharacteristic
108C3×C4×Q8C22×C511yescharacteristic
109C3×#107—21no—
110C3×#107—21no—
111C3×C4⋊C8C22×C511yescharacteristic
112C3×C4⋊C8C22×C511yescharacteristic
113C3×#103—21no—
114C3×#103—21no—
115C3×#103—22no—
116C3×C4×C8C22×C511yescharacteristic
117C2×C5×Q8—21no—
118C2×C5×Q8—21no—
119C2×C5×Q8C3×D411yescharacteristic
120C2×C5×Q8C3×D411yescharacteristic
121C2×C5×C8—21no—
122C2×C5×C8—21no—
123C2×C5×C8—21no—
124C5×C4⋊C4—22no—
125C5×C4⋊C4—22no—
126C5×C4⋊C4—22no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4C3×D411yescharacteristic
133C5×C4⋊C4C3×D411yescharacteristic
134C5×C4⋊C4C3×D412yes—
135C42×C5—22no—
136C42×C5—21no—
137C42×C5—21no—
138C42×C5C23×C311yescharacteristic
139#557C2×C3×C511yescharacteristic
140#487C2×C3×C511yescharacteristic
141#477C2×C3×C511yescharacteristic
142#477C2×C3×C511yescharacteristic
143#332C2×C3×C511yescharacteristic
144Q8⋊C8C2×C3×C511yescharacteristic
145Q8⋊C8C2×C3×C511yescharacteristic
146C22×C3×C5#12011yescharacteristic
147C3×C4×C5—22no—
148C3×C4×C5—21no—
149C3×C4×C5—41no—
150C3×C4×C5—42no—
151C3×C4×C5—41no—
152C3×C4×C5—41no—
153C3×C4×C5—81no—
154C3×C4×C5C2×Q1611yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8C5×D411yescharacteristic
161C2×C3×Q8C5×D411yescharacteristic
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4C5×D412yes—
174C3×C4⋊C4C5×D411yescharacteristic
175C3×C4⋊C4C5×D411yescharacteristic
176C3×C42—22no—
177C3×C42—21no—
178C3×C42—21no—
179C3×C42C23×C511yescharacteristic
180C5×Q8—21no—
181C5×Q8—21no—
182C5×Q8—21no—
183C5×Q8—42no—
184C5×Q8—41no—
185C5×Q8—41no—
186C5×Q8C3×Q1612yes—
187C2×C4×C5—21no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—22no—
192C2×C4×C5—41no—
193C2×C4×C5C2×C3×D411yescharacteristic
194C2×C4×C5C2×C3×D411yescharacteristic
195C2×C4×C5C2×C3×D411yescharacteristic
196C5×C8—41no—
197C5×C8—41no—
198C5×C8—41no—
199C4⋊Q8—21no—
200C4⋊Q8C22×C3×C511yescharacteristic
201C4⋊Q8C22×C3×C511yescharacteristic
202#125—22no—
203#125—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8C22×C3×C511yescharacteristic
207C4×Q8C22×C3×C511yescharacteristic
208#107—21no—
209#107—21no—
210C4⋊C8C22×C3×C511yescharacteristic
211C4⋊C8C22×C3×C511yescharacteristic
212#103—21no—
213#103—21no—
214#103—22no—
215C4×C8C22×C3×C511yescharacteristic
216C2×C3×C5#45111yescharacteristic
217C2×C3×C5#45211yescharacteristic
218C2×C3×C5#45411yescharacteristic
219C3×Q8—21no—
220C3×Q8—21no—
221C3×Q8—21no—
222C3×Q8—42no—
223C3×Q8—41no—
224C3×Q8—41no—
225C3×Q8C5×Q1612yes—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—22no—
231C2×C3×C4—41no—
232C2×C3×C4C2×C5×D411yescharacteristic
233C2×C3×C4C2×C5×D411yescharacteristic
234C2×C3×C4C2×C5×D411yescharacteristic
235C3×C8—41no—
236C3×C8—41no—
237C3×C8—41no—
238C22×C5C3×#12011yescharacteristic
239C4×C5—22no—
240C4×C5—21no—
241C4×C5—41no—
242C4×C5—42no—
243C4×C5—41no—
244C4×C5—41no—
245C4×C5—81no—
246C4×C5C2×C3×Q1611yescharacteristic
247C4×C5C3×#13511yescharacteristic
248C4×C5C3×#13711yescharacteristic
249C4×C5C3×#13711yescharacteristic
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8C3×C5×D411yescharacteristic
253C2×Q8C3×C5×D411yescharacteristic
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4C3×C5×D412yes—
266C4⋊C4C3×C5×D411yescharacteristic
267C4⋊C4C3×C5×D411yescharacteristic
268C42—22no—
269C42—21no—
270C42—21no—
271C42C23×C3×C511yescharacteristic
272C3×C5#163611yescharacteristic, direct product factor, Hall
273C22×C3C5×#12011yescharacteristic
274C3×C4—22no—
275C3×C4—21no—
276C3×C4—41no—
277C3×C4—42no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—81no—
281C3×C4C2×C5×Q1611yescharacteristic
282C3×C4C5×#13511yescharacteristic
283C3×C4C5×#13711yescharacteristic
284C3×C4C5×#13711yescharacteristic
285C2×C5C3×#45111yescharacteristic
286C2×C5C3×#45211yescharacteristic
287C2×C5C3×#45411yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—42no—
292Q8—41no—
293Q8—41no—
294Q8C3×C5×Q1612yes—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4C2×C3×C5×D411yescharacteristic
302C2×C4C2×C3×C5×D411yescharacteristic
303C2×C4C2×C3×C5×D411yescharacteristic
304C8—41no—
305C8—41no—
306C8—41no—
307C2×C3C5×#45111yescharacteristic
308C2×C3C5×#45211yescharacteristic
309C2×C3C5×#45411yescharacteristic
310C5C3×#163611yescharacteristic, direct product factor, Sylow
311C22C3×C5×#12011yescharacteristic
312C4—22no—
313C4—21no—
314C4—41no—
315C4—42no—
316C4—41no—
317C4—41no—
318C4—81no—
319C4C2×C3×C5×Q1611yescharacteristic
320C4C3×C5×#13511yescharacteristic
321C4C3×C5×#13711yescharacteristic
322C4C3×C5×#13711yescharacteristic
323C3C5×#163611yescharacteristic, direct product factor, Sylow
324C2C3×C5×#45111yescharacteristic
325C2C3×C5×#45211yescharacteristic
326C2C3×C5×#45411yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
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
8. C5×#1636C3direct (N × H)
26. C3×#1636C5direct (N × H)
80. #1636C3×C5direct (N × H)
272. C3×C5#1636direct (N × H)
310. C5C3×#1636direct (N × H)
323. C3C5×#1636direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5572
C3×C5×#4872
C3×C5×#4772
C3×C5×#3322
C3×C5×Q8⋊C82
C5×#16363
C3×#16365