Finite Group Databasebeta

← C3×C5×#2193 #14275227

Subgroups — C3×C5×#2193 #14275227

Order 1920.

420 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#578C211yesmaximal, characteristic, complemented
2C3×C5×#509C211yesmaximal, characteristic, complemented
3C2×C3×C5×SD32C211yesmaximal, characteristic, complemented
4C3×C5×#472C211yesmaximal, characteristic, complemented
5C3×C5×#362C211yesmaximal, characteristic, complemented
6C3×C5×#359C211yesmaximal, characteristic, complemented
7C3×C5×#350C211yesmaximal, characteristic, complemented
8C5×#2193C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×2−1+4—21no—
10C3×C5×#137—22no—
11C3×C5×#137—21no—
12C3×C5×AGL(1,ℤ/8)—21no—
13C3×C5×#135—21no—
14C3×C5×#135C2211yescharacteristic
15C2×C3×C5×Q16—21no—
16C2×C3×C5×Q16C2211yescharacteristic
17C2×C3×C5×D8C2211yescharacteristic
18C3×C5×#131C2211yescharacteristic
19C3×C5×SD32—22no—
20C3×C5×SD32—21no—
21C3×C5×D16—21no—
22C3×C5×M32C2211yescharacteristic
23C2×C3×C5×C16C2211yescharacteristic
24C3×C5×#108C2211yescharacteristic
25C3×C5×#100—21no—
26C3×#2193C511yesmaximal, characteristic, direct product factor, Hall
27C5×#578C2×C311yescharacteristic, complemented
28C5×#509C2×C311yescharacteristic, complemented
29C2×C5×SD32C2×C311yescharacteristic, complemented
30C5×#472C2×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—41no—
42C2×C3×C5×D4—21no—
43C3×C5×Q16—22no—
44C3×C5×Q16—21no—
45C3×C5×Q16D411yescharacteristic
46C3×C5×Q16D412yes—
47C3×C5×SD16—22no—
48C3×C5×SD16—21no—
49C3×C5×SD16—41no—
50C3×C5×D8—21no—
51C3×C5×D8—21no—
52C3×C5×D8—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, complemented
62C3×#509C2×C511yescharacteristic, complemented
63C2×C3×SD32C2×C511yescharacteristic, complemented
64C3×#472C2×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×AGL(1,ℤ/8)—21no—
72C5×#135—21no—
73C5×#135C22×C311yescharacteristic
74C2×C5×Q16—21no—
75C2×C5×Q16C22×C311yescharacteristic
76C2×C5×D8C22×C311yescharacteristic
77C5×#131C22×C311yescharacteristic
78C5×SD32—22no—
79C5×SD32—21no—
80C5×D16—21no—
81C5×M32C22×C311yescharacteristic
82C2×C5×C16C22×C311yescharacteristic
83C5×#108C22×C311yescharacteristic
84C5×#100—21no—
85#2193C3×C511yescharacteristic, direct product factor, Sylow
86C23×C3×C5—41no—
87C3×C5×Q8—22no—
88C3×C5×Q8—21no—
89C3×C5×Q8—42no—
90C3×C5×Q8—41no—
91C3×C5×Q8D811yescharacteristic
92C3×C5×D4—21no—
93C3×C5×D4—21no—
94C3×C5×D4—42no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C3×C5×D4D811yescharacteristic
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—42no—
101C2×C3×C4×C5—42no—
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×AGL(1,ℤ/8)—21no—
113C3×#135—21no—
114C3×#135C22×C511yescharacteristic
115C2×C3×Q16—21no—
116C2×C3×Q16C22×C511yescharacteristic
117C2×C3×D8C22×C511yescharacteristic
118C3×#131C22×C511yescharacteristic
119C3×SD32—22no—
120C3×SD32—21no—
121C3×D16—21no—
122C3×M32C22×C511yescharacteristic
123C2×C3×C16C22×C511yescharacteristic
124C3×#108C22×C511yescharacteristic
125C3×#100—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—41no—
134C2×C5×D4—21no—
135C5×Q16—22no—
136C5×Q16—21no—
137C5×Q16C3×D411yescharacteristic
138C5×Q16C3×D412yes—
139C5×SD16—22no—
140C5×SD16—21no—
141C5×SD16—41no—
142C5×D8—21no—
143C5×D8—21no—
144C5×D8—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, complemented
154#509C2×C3×C511yescharacteristic, complemented
155C2×SD32C2×C3×C511yescharacteristic, complemented
156#472C2×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×C5—81no—
163C22×C3×C5—161no—
164C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
165C3×C4×C5—21no—
166C3×C4×C5—42no—
167C3×C4×C5—41no—
168C3×C4×C5#12011yescharacteristic
169C3×C4×C5C2×D811yescharacteristic
170C3×#41—22no—
171C3×#41—21no—
172C3×#41—42no—
173C3×#41—41no—
174C3×#41C5×D411yescharacteristic
175C2×C3×Q8—22no—
176C2×C3×Q8—21no—
177C2×C3×Q8—41no—
178C2×C3×D4—21no—
179C3×Q16—22no—
180C3×Q16—21no—
181C3×Q16C5×D411yescharacteristic
182C3×Q16C5×D412yes—
183C3×SD16—22no—
184C3×SD16—21no—
185C3×SD16—41no—
186C3×D8—21no—
187C3×D8—21no—
188C3×D8—41no—
189C3×D8C5×D411yescharacteristic
190C3×M16—21no—
191C3×M16—21no—
192C3×M16C5×D411yescharacteristic
193C2×C3×C8—21no—
194C2×C3×C8C23×C511yescharacteristic
195C3×C16—21no—
196C3×C16—21no—
197C23×C5—41no—
198C5×Q8—22no—
199C5×Q8—21no—
200C5×Q8—42no—
201C5×Q8—41no—
202C5×Q8C3×D811yescharacteristic
203C5×D4—21no—
204C5×D4—21no—
205C5×D4—42no—
206C5×D4—41no—
207C5×D4—41no—
208C5×D4—41no—
209C5×D4C3×D811yescharacteristic
210C2×C4×C5—21no—
211C2×C4×C5—42no—
212C2×C4×C5—42no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5C2×C3×D411yescharacteristic
216C5×C8—21no—
217C5×C8—41no—
218C5×C8C2×C3×D411yescharacteristic
219C5×C8C2×C3×D411yescharacteristic
2202−1+4—21no—
221#137—22no—
222#137—21no—
223AGL(1,ℤ/8)—21no—
224#135—21no—
225#135C22×C3×C511yescharacteristic
226C2×Q16—21no—
227C2×Q16C22×C3×C511yescharacteristic
228C2×D8C22×C3×C511yescharacteristic
229#131C22×C3×C511yescharacteristic
230SD32—22no—
231SD32—21no—
232D16—21no—
233M32C22×C3×C511yescharacteristic
234C2×C16C22×C3×C511yescharacteristic
235#108C22×C3×C511yescharacteristic
236#100—21no—
237C2×C3×C5—21no—
238C2×C3×C5—41no—
239C2×C3×C5—81no—
240C2×C3×C5—161no—
241C2×C3×C5#44711yescharacteristic
242C23×C3—41no—
243C3×Q8—22no—
244C3×Q8—21no—
245C3×Q8—42no—
246C3×Q8—41no—
247C3×Q8C5×D811yescharacteristic
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—42no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4C5×D811yescharacteristic
255C2×C3×C4—21no—
256C2×C3×C4—42no—
257C2×C3×C4—42no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4C2×C5×D411yescharacteristic
261C3×C8—21no—
262C3×C8—41no—
263C3×C8C2×C5×D411yescharacteristic
264C3×C8C2×C5×D411yescharacteristic
265C22×C5—21no—
266C22×C5—41no—
267C22×C5—81no—
268C22×C5—161no—
269C22×C5C3×AGL(1,ℤ/8)11yescharacteristic
270C4×C5—21no—
271C4×C5—42no—
272C4×C5—41no—
273C4×C5C3×#12011yescharacteristic
274C4×C5C2×C3×D811yescharacteristic
275#41—22no—
276#41—21no—
277#41—42no—
278#41—41no—
279#41C3×C5×D411yescharacteristic
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—41no—
283C2×D4—21no—
284Q16—22no—
285Q16—21no—
286Q16C3×C5×D411yescharacteristic
287Q16C3×C5×D412yes—
288SD16—22no—
289SD16—21no—
290SD16—41no—
291D8—21no—
292D8—21no—
293D8—41no—
294D8C3×C5×D411yescharacteristic
295M16—21no—
296M16—21no—
297M16C3×C5×D411yescharacteristic
298C2×C8—21no—
299C2×C8C23×C3×C511yescharacteristic
300C16—21no—
301C16—21no—
302C3×C5#219311yescharacteristic, direct product factor, Hall
303C22×C3—21no—
304C22×C3—41no—
305C22×C3—81no—
306C22×C3—161no—
307C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
308C3×C4—21no—
309C3×C4—42no—
310C3×C4—41no—
311C3×C4C5×#12011yescharacteristic
312C3×C4C2×C5×D811yescharacteristic
313C2×C5—21no—
314C2×C5—41no—
315C2×C5—81no—
316C2×C5—161no—
317C2×C5C3×#44711yescharacteristic
318C23—41no—
319Q8—22no—
320Q8—21no—
321Q8—42no—
322Q8—41no—
323Q8C3×C5×D811yescharacteristic
324D4—21no—
325D4—21no—
326D4—42no—
327D4—41no—
328D4—41no—
329D4—41no—
330D4C3×C5×D811yescharacteristic
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4C2×C3×C5×D411yescharacteristic
337C8—21no—
338C8—41no—
339C8C2×C3×C5×D411yescharacteristic
340C8C2×C3×C5×D411yescharacteristic
341C2×C3—21no—
342C2×C3—41no—
343C2×C3—81no—
344C2×C3—161no—
345C2×C3C5×#44711yescharacteristic
346C5C3×#219311yescharacteristic, direct product factor, Sylow
347C22—21no—
348C22—41no—
349C22—81no—
350C22—161no—
351C22C3×C5×AGL(1,ℤ/8)11yescharacteristic
352C4—21no—
353C4—42no—
354C4—41no—
355C4C3×C5×#12011yescharacteristic
356C4C2×C3×C5×D811yescharacteristic
357C3C5×#219311yescharacteristic, direct product factor, Sylow
358C2—21no—
359C2—41no—
360C2—81no—
361C2—161no—
362C2C3×C5×#44711yescharacteristic
subgroupG/H
center, socleC2×C3×C5#447
commutator, Frattini, cosocleC2×C8C23×C3×C5
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
1. C3×C5×#578C2semidirect
2. C3×C5×#509C2semidirect
3. C2×C3×C5×SD32C2semidirect
4. C3×C5×#472C2semidirect
5. C3×C5×#362C2semidirect
6. C3×C5×#359C2semidirect
7. C3×C5×#350C2semidirect
8. C5×#2193C3direct (N × H)
26. C3×#2193C5direct (N × H)
27. C5×#578C2×C3semidirect
28. C5×#509C2×C3semidirect
29. C2×C5×SD32C2×C3semidirect
30. C5×#472C2×C3semidirect
31. C5×#362C2×C3semidirect
32. C5×#359C2×C3semidirect
33. C5×#350C2×C3semidirect
61. C3×#578C2×C5semidirect
62. C3×#509C2×C5semidirect
63. C2×C3×SD32C2×C5semidirect
64. C3×#472C2×C5semidirect
65. C3×#362C2×C5semidirect
66. C3×#359C2×C5semidirect
67. C3×#350C2×C5semidirect
85. #2193C3×C5direct (N × H)
153. #578C2×C3×C5semidirect
154. #509C2×C3×C5semidirect
155. C2×SD32C2×C3×C5semidirect
156. #472C2×C3×C5semidirect
157. #362C2×C3×C5semidirect
158. #359C2×C3×C5semidirect
159. #350C2×C3×C5semidirect
302. C3×C5#2193direct (N × H)
346. C5C3×#2193direct (N × H)
357. C3C5×#2193direct (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×#5092
C2×C3×C5×SD322
C3×C5×#4722
C3×C5×#3622
C3×C5×#3592
C3×C5×#3502
C5×#21933
C3×#21935