Finite Group Databasebeta

← C3×C5×#2195 #14275229

Subgroups — C3×C5×#2195 #14275229

Order 1920.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#578C211yesmaximal, characteristic
2C3×C5×#510C211yesmaximal, characteristic, complemented
3C2×C3×C5×Q32C211yesmaximal, characteristic, complemented
4C3×C5×#473C211yesmaximal, characteristic, complemented
5C3×C5×#362C211yesmaximal, characteristic, complemented
6C3×C5×#359C211yesmaximal, characteristic, complemented
7C3×C5×#350C211yesmaximal, characteristic, complemented
8C5×#2195C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×2−1+4—21no—
10C3×C5×#137—22no—
11C3×C5×#137—21no—
12C3×C5×#137—21no—
13C3×C5×#135—21no—
14C3×C5×#135C2211yescharacteristic
15C2×C3×C5×Q16—21no—
16C2×C3×C5×Q16C2211yescharacteristic
17C2×C3×C5×Q16C2211yescharacteristic
18C3×C5×#131C2211yescharacteristic
19C3×C5×Q32—22no—
20C3×C5×Q32—21no—
21C3×C5×SD32—21no—
22C3×C5×M32C2211yescharacteristic
23C2×C3×C5×C16C2211yescharacteristic
24C3×C5×#108C2211yescharacteristic
25C3×C5×#101—21no—
26C3×#2195C511yesmaximal, characteristic, direct product factor, Hall
27C5×#578C2×C311yescharacteristic
28C5×#510C2×C311yescharacteristic, complemented
29C2×C5×Q32C2×C311yescharacteristic, complemented
30C5×#473C2×C311yescharacteristic, complemented
31C5×#362C2×C311yescharacteristic, complemented
32C5×#359C2×C311yescharacteristic, complemented
33C5×#350C2×C311yescharacteristic, complemented
34C3×C5×#41—22no—
35C3×C5×#41—21no—
36C3×C5×#41—42no—
37C3×C5×#41—41no—
38C3×C5×#41D411yescharacteristic
39C2×C3×C5×Q8—22no—
40C2×C3×C5×Q8—21no—
41C2×C3×C5×Q8—21no—
42C2×C3×C5×Q8—41no—
43C3×C5×Q16—22no—
44C3×C5×Q16—21no—
45C3×C5×Q16—21no—
46C3×C5×Q16—21no—
47C3×C5×Q16—41no—
48C3×C5×Q16D411yescharacteristic
49C3×C5×Q16D412yes—
50C3×C5×SD16—22no—
51C3×C5×SD16—21no—
52C3×C5×SD16—41no—
53C3×C5×D8D411yescharacteristic
54C3×C5×M16—21no—
55C3×C5×M16—21no—
56C3×C5×M16D411yescharacteristic
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8C2311yescharacteristic
59C3×C5×C16—21no—
60C3×C5×C16—21no—
61C3×#578C2×C511yescharacteristic
62C3×#510C2×C511yescharacteristic, complemented
63C2×C3×Q32C2×C511yescharacteristic, complemented
64C3×#473C2×C511yescharacteristic, complemented
65C3×#362C2×C511yescharacteristic, complemented
66C3×#359C2×C511yescharacteristic, complemented
67C3×#350C2×C511yescharacteristic, complemented
68C5×2−1+4—21no—
69C5×#137—22no—
70C5×#137—21no—
71C5×#137—21no—
72C5×#135—21no—
73C5×#135C22×C311yescharacteristic
74C2×C5×Q16—21no—
75C2×C5×Q16C22×C311yescharacteristic
76C2×C5×Q16C22×C311yescharacteristic
77C5×#131C22×C311yescharacteristic
78C5×Q32—22no—
79C5×Q32—21no—
80C5×SD32—21no—
81C5×M32C22×C311yescharacteristic
82C2×C5×C16C22×C311yescharacteristic
83C5×#108C22×C311yescharacteristic
84C5×#101—21no—
85#2195C3×C511yescharacteristic, direct product factor, Sylow
86C3×C5×Q8—22no—
87C3×C5×Q8—21no—
88C3×C5×Q8—42no—
89C3×C5×Q8—41no—
90C3×C5×Q8—41no—
91C3×C5×Q8—41no—
92C3×C5×Q8D811yescharacteristic
93C3×C5×D4—21no—
94C3×C5×D4—21no—
95C3×C5×D4—42no—
96C3×C5×D4—41no—
97C3×C5×D4D811yescharacteristic
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—42no—
100C2×C3×C4×C5—42no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C3×C5×C8—21no—
106C3×C5×C8—41no—
107C3×C5×C8C2×D411yescharacteristic
108C3×C5×C8C2×D411yescharacteristic
109C3×2−1+4—21no—
110C3×#137—22no—
111C3×#137—21no—
112C3×#137—21no—
113C3×#135—21no—
114C3×#135C22×C511yescharacteristic
115C2×C3×Q16—21no—
116C2×C3×Q16C22×C511yescharacteristic
117C2×C3×Q16C22×C511yescharacteristic
118C3×#131C22×C511yescharacteristic
119C3×Q32—22no—
120C3×Q32—21no—
121C3×SD32—21no—
122C3×M32C22×C511yescharacteristic
123C2×C3×C16C22×C511yescharacteristic
124C3×#108C22×C511yescharacteristic
125C3×#101—21no—
126C5×#41—22no—
127C5×#41—21no—
128C5×#41—42no—
129C5×#41—41no—
130C5×#41C3×D411yescharacteristic
131C2×C5×Q8—22no—
132C2×C5×Q8—21no—
133C2×C5×Q8—21no—
134C2×C5×Q8—41no—
135C5×Q16—22no—
136C5×Q16—21no—
137C5×Q16—21no—
138C5×Q16—21no—
139C5×Q16—41no—
140C5×Q16C3×D411yescharacteristic
141C5×Q16C3×D412yes—
142C5×SD16—22no—
143C5×SD16—21no—
144C5×SD16—41no—
145C5×D8C3×D411yescharacteristic
146C5×M16—21no—
147C5×M16—21no—
148C5×M16C3×D411yescharacteristic
149C2×C5×C8—21no—
150C2×C5×C8C23×C311yescharacteristic
151C5×C16—21no—
152C5×C16—21no—
153#578C2×C3×C511yescharacteristic
154#510C2×C3×C511yescharacteristic, complemented
155C2×Q32C2×C3×C511yescharacteristic, complemented
156#473C2×C3×C511yescharacteristic, complemented
157#362C2×C3×C511yescharacteristic, complemented
158#359C2×C3×C511yescharacteristic, complemented
159#350C2×C3×C511yescharacteristic, complemented
160C22×C3×C5—21no—
161C22×C3×C5—41no—
162C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5—41no—
166C3×C4×C5—81no—
167C3×C4×C5#12011yescharacteristic
168C3×C4×C5C2×D811yescharacteristic
169C3×#41—22no—
170C3×#41—21no—
171C3×#41—42no—
172C3×#41—41no—
173C3×#41C5×D411yescharacteristic
174C2×C3×Q8—22no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—41no—
178C3×Q16—22no—
179C3×Q16—21no—
180C3×Q16—21no—
181C3×Q16—21no—
182C3×Q16—41no—
183C3×Q16C5×D411yescharacteristic
184C3×Q16C5×D412yes—
185C3×SD16—22no—
186C3×SD16—21no—
187C3×SD16—41no—
188C3×D8C5×D411yescharacteristic
189C3×M16—21no—
190C3×M16—21no—
191C3×M16C5×D411yescharacteristic
192C2×C3×C8—21no—
193C2×C3×C8C23×C511yescharacteristic
194C3×C16—21no—
195C3×C16—21no—
196C5×Q8—22no—
197C5×Q8—21no—
198C5×Q8—42no—
199C5×Q8—41no—
200C5×Q8—41no—
201C5×Q8—41no—
202C5×Q8C3×D811yescharacteristic
203C5×D4—21no—
204C5×D4—21no—
205C5×D4—42no—
206C5×D4—41no—
207C5×D4C3×D811yescharacteristic
208C2×C4×C5—21no—
209C2×C4×C5—42no—
210C2×C4×C5—42no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5C2×C3×D411yescharacteristic
215C5×C8—21no—
216C5×C8—41no—
217C5×C8C2×C3×D411yescharacteristic
218C5×C8C2×C3×D411yescharacteristic
2192−1+4—21no—
220#137—22no—
221#137—21no—
222#137—21no—
223#135—21no—
224#135C22×C3×C511yescharacteristic
225C2×Q16—21no—
226C2×Q16C22×C3×C511yescharacteristic
227C2×Q16C22×C3×C511yescharacteristic
228#131C22×C3×C511yescharacteristic
229Q32—22no—
230Q32—21no—
231SD32—21no—
232M32C22×C3×C511yescharacteristic
233C2×C16C22×C3×C511yescharacteristic
234#108C22×C3×C511yescharacteristic
235#101—21no—
236C2×C3×C5—21no—
237C2×C3×C5—41no—
238C2×C3×C5—81no—
239C2×C3×C5#44711yescharacteristic
240C3×Q8—22no—
241C3×Q8—21no—
242C3×Q8—42no—
243C3×Q8—41no—
244C3×Q8—41no—
245C3×Q8—41no—
246C3×Q8C5×D811yescharacteristic
247C3×D4—21no—
248C3×D4—21no—
249C3×D4—42no—
250C3×D4—41no—
251C3×D4C5×D811yescharacteristic
252C2×C3×C4—21no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4C2×C5×D411yescharacteristic
259C3×C8—21no—
260C3×C8—41no—
261C3×C8C2×C5×D411yescharacteristic
262C3×C8C2×C5×D411yescharacteristic
263C22×C5—21no—
264C22×C5—41no—
265C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
266C4×C5—21no—
267C4×C5—42no—
268C4×C5—41no—
269C4×C5—81no—
270C4×C5C3×#12011yescharacteristic
271C4×C5C2×C3×D811yescharacteristic
272#41—22no—
273#41—21no—
274#41—42no—
275#41—41no—
276#41C3×C5×D411yescharacteristic
277C2×Q8—22no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—41no—
281Q16—22no—
282Q16—21no—
283Q16—21no—
284Q16—21no—
285Q16—41no—
286Q16C3×C5×D411yescharacteristic
287Q16C3×C5×D412yes—
288SD16—22no—
289SD16—21no—
290SD16—41no—
291D8C3×C5×D411yescharacteristic
292M16—21no—
293M16—21no—
294M16C3×C5×D411yescharacteristic
295C2×C8—21no—
296C2×C8C23×C3×C511yescharacteristic
297C16—21no—
298C16—21no—
299C3×C5#219511yescharacteristic, direct product factor, Hall
300C22×C3—21no—
301C22×C3—41no—
302C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
303C3×C4—21no—
304C3×C4—42no—
305C3×C4—41no—
306C3×C4—81no—
307C3×C4C5×#12011yescharacteristic
308C3×C4C2×C5×D811yescharacteristic
309C2×C5—21no—
310C2×C5—41no—
311C2×C5—81no—
312C2×C5C3×#44711yescharacteristic
313Q8—22no—
314Q8—21no—
315Q8—42no—
316Q8—41no—
317Q8—41no—
318Q8—41no—
319Q8C3×C5×D811yescharacteristic
320D4—21no—
321D4—21no—
322D4—42no—
323D4—41no—
324D4C3×C5×D811yescharacteristic
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4C2×C3×C5×D411yescharacteristic
332C8—21no—
333C8—41no—
334C8C2×C3×C5×D411yescharacteristic
335C8C2×C3×C5×D411yescharacteristic
336C2×C3—21no—
337C2×C3—41no—
338C2×C3—81no—
339C2×C3C5×#44711yescharacteristic
340C5C3×#219511yescharacteristic, direct product factor, Sylow
341C22—21no—
342C22—41no—
343C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
344C4—21no—
345C4—42no—
346C4—41no—
347C4—81no—
348C4C3×C5×#12011yescharacteristic
349C4C2×C3×C5×D811yescharacteristic
350C3C5×#219511yescharacteristic, direct product factor, Sylow
351C2—21no—
352C2—41no—
353C2—81no—
354C2C3×C5×#44711yescharacteristic
subgroupG/H
center, socleC2×C3×C5#447
commutator, Frattini, cosocleC2×C8C23×C3×C5
prime radicalC3×C5×#578C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C5×#510C2semidirect
3. C2×C3×C5×Q32C2semidirect
4. C3×C5×#473C2semidirect
5. C3×C5×#362C2semidirect
6. C3×C5×#359C2semidirect
7. C3×C5×#350C2semidirect
8. C5×#2195C3direct (N × H)
26. C3×#2195C5direct (N × H)
28. C5×#510C2×C3semidirect
29. C2×C5×Q32C2×C3semidirect
30. C5×#473C2×C3semidirect
31. C5×#362C2×C3semidirect
32. C5×#359C2×C3semidirect
33. C5×#350C2×C3semidirect
62. C3×#510C2×C5semidirect
63. C2×C3×Q32C2×C5semidirect
64. C3×#473C2×C5semidirect
65. C3×#362C2×C5semidirect
66. C3×#359C2×C5semidirect
67. C3×#350C2×C5semidirect
85. #2195C3×C5direct (N × H)
154. #510C2×C3×C5semidirect
155. C2×Q32C2×C3×C5semidirect
156. #473C2×C3×C5semidirect
157. #362C2×C3×C5semidirect
158. #359C2×C3×C5semidirect
159. #350C2×C3×C5semidirect
299. C3×C5#2195direct (N × H)
340. C5C3×#2195direct (N × H)
350. C3C5×#2195direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#5782
C3×C5×#5102
C2×C3×C5×Q322
C3×C5×#4732
C3×C5×#3622
C3×C5×#3592
C3×C5×#3502
C5×#21953
C3×#21955