Finite Group Databasebeta

← #14312496

Subgroups — #14312496

Order 1920.

356 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#342C211yesmaximal, characteristic
2#11746348C211yesmaximal, characteristic
3#11746348C211yesmaximal, characteristic
4#11746348C211yesmaximal, characteristic
5#11746348C211yesmaximal, characteristic
6#11746347C211yesmaximal, characteristic
7#11746347C211yesmaximal, characteristic
8C5⋊#2104—31nomaximal, Hall
9C2×C3×C5×C22⋊C4C2211yescharacteristic
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×#6719C2211yescharacteristic
16C3⋊#2104—51nomaximal, Hall
17C5×#342D311yescharacteristic
18#64747—31no—
19#64747—31no—
20#64747—31no—
21#64747—31no—
22#64746—31no—
23#64746—31no—
24C24×C3×C5C2311yescharacteristic
25C22×C3×C4×C5—21no—
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5—21no—
28C22×Dic15—21no—
29C22×Dic15—21no—
30C22×Dic15—21no—
31C22×Dic15—21no—
32C3×C5×C22⋊C4—21no—
33C3×C5×C22⋊C4—21no—
34C3×C5×C22⋊C4—21no—
35C3×C5×C22⋊C4—21no—
36C3×C5×C22⋊C4—21no—
37C3×C5×C22⋊C4—21no—
38#6719—21no—
39#6719—21no—
40#6719—21no—
41#6719—21no—
42#6719—21no—
43#6719—21no—
44#6719—21no—
45#6719—21no—
46C3×#342D511yescharacteristic
47#4527—51no—
48#4527—51no—
49#4527—51no—
50#4527—51no—
51#4526—51no—
52#4526—51no—
53C2×C5×C22⋊C4C2×D311yescharacteristic
54C2×C5×C22⋊C4C2×D311yescharacteristic
55C2×C5×C22⋊C4C2×D311yescharacteristic
56C2×C22⋊Dic5—31no—
57C2×C22⋊Dic5—31no—
58C2×C22⋊Dic5—31no—
59C2×C22⋊Dic5—31no—
60#2104—151noSylow
61C23×C3×C5—81no—
62C23×C3×C5#4111yescharacteristic
63C23×C3×C5#4111yescharacteristic
64C23×C3×C5#4111yescharacteristic
65C23×C3×C5#4111yescharacteristic
66C23×C3×C5#4111yescharacteristic
67C23×C3×C5#4111yescharacteristic
68C23×C3×C5#4111yescharacteristic
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5—81no—
73C2×C3×C4×C5—81no—
74C2×C3×C4×C5—81no—
75C2×Dic15—41no—
76C2×Dic15—41no—
77C2×Dic15—41no—
78C2×Dic15—41no—
79C2×Dic15—81no—
80C2×Dic15—81no—
81C2×Dic15—81no—
82C2×Dic15—81no—
83C2×C3×C22⋊C4C2×D511yescharacteristic
84C2×C3×C22⋊C4C2×D511yescharacteristic
85C2×C3×C22⋊C4C2×D511yescharacteristic
86C2×#217—51no—
87C2×#217—51no—
88C2×#217—51no—
89C2×#217—51no—
90C24×C5C22×D311yescharacteristic
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×Dic5—61no—
95C22×Dic5—61no—
96C22×Dic5—61no—
97C22×Dic5—61no—
98C5×C22⋊C4—21no—
99C5×C22⋊C4—21no—
100C5×C22⋊C4—21no—
101C5×C22⋊C4—21no—
102C5×C22⋊C4—21no—
103C5×C22⋊C4—21no—
104C22⋊Dic5—61no—
105C22⋊Dic5—61no—
106C22⋊Dic5—61no—
107C22⋊Dic5—61no—
108C22⋊Dic5—61no—
109C22⋊Dic5—61no—
110C22⋊Dic5—61no—
111C22⋊Dic5—61no—
112#342—151no—
113#342—151no—
114#342—151no—
115#342—151no—
116#342—151no—
117#342—151no—
118#342D1511yescharacteristic
119C22×C3×C5—41no—
120C22×C3×C5—41no—
121C22×C3×C5—41no—
122C22×C3×C5—41no—
123C22×C3×C5—41no—
124C22×C3×C5—41no—
125C22×C3×C5—41no—
126C22×C3×C5#12611yescharacteristic
127C22×C3×C5#12611yescharacteristic
128C22×C3×C5#12611yescharacteristic
129C22×C3×C5#12611yescharacteristic
130C22×C3×C5#12611yescharacteristic
131C22×C3×C5#12611yescharacteristic
132C22×C3×C5#12611yescharacteristic
133C3×C4×C5—81no—
134C3×C4×C5—81no—
135C3×C4×C5—81no—
136Dic15—81no—
137Dic15—81no—
138Dic15—81no—
139Dic15—81no—
140C24×C3C22×D511yescharacteristic
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×Dic3—101no—
145C22×Dic3—101no—
146C22×Dic3—101no—
147C22×Dic3—101no—
148C3×C22⋊C4—21no—
149C3×C22⋊C4—21no—
150C3×C22⋊C4—21no—
151C3×C22⋊C4—21no—
152C3×C22⋊C4—21no—
153C3×C22⋊C4—21no—
154#217—101no—
155#217—101no—
156#217—101no—
157#217—101no—
158#217—101no—
159#217—101no—
160#217—101no—
161#217—101no—
162C23×C5—81no—
163C23×C5#23511yescharacteristic
164C23×C5#23511yescharacteristic
165C23×C5#23511yescharacteristic
166C23×C5#23711yescharacteristic
167C23×C5#23711yescharacteristic
168C23×C5#23711yescharacteristic
169C23×C5#23911yescharacteristic
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—81no—
174C2×C4×C5—81no—
175C2×C4×C5—81no—
176C2×Dic5—121no—
177C2×Dic5—121no—
178C2×Dic5—121no—
179C2×Dic5—121no—
180C2×Dic5—241no—
181C2×Dic5—241no—
182C2×Dic5—241no—
183C2×Dic5—241no—
184C2×C22⋊C4—151no—
185C2×C22⋊C4—151no—
186C2×C22⋊C4—151no—
187C2×C22⋊C4—151no—
188C2×C22⋊C4C2×D1511yescharacteristic
189C2×C22⋊C4C2×D1511yescharacteristic
190C2×C22⋊C4C2×D1511yescharacteristic
191C2×C3×C5—21no—
192C2×C3×C5—21no—
193C2×C3×C5—21no—
194C2×C3×C5—21no—
195C2×C3×C5—21no—
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5#40111yescharacteristic
199C23×C3—81no—
200C23×C3#70911yescharacteristic
201C23×C3#70911yescharacteristic
202C23×C3#70911yescharacteristic
203C23×C3#71111yescharacteristic
204C23×C3#71111yescharacteristic
205C23×C3#71111yescharacteristic
206C23×C3#71311yescharacteristic
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—81no—
211C2×C3×C4—81no—
212C2×C3×C4—81no—
213C2×Dic3—201no—
214C2×Dic3—201no—
215C2×Dic3—201no—
216C2×Dic3—201no—
217C2×Dic3—401no—
218C2×Dic3—401no—
219C2×Dic3—401no—
220C2×Dic3—401no—
221C22×C5—41no—
222C22×C5—41no—
223C22×C5—41no—
224C22×C5—41no—
225C22×C5—41no—
226C22×C5—41no—
227C22×C5—41no—
228C22×C5#87611yescharacteristic
229C22×C5#87911yescharacteristic
230C22×C5#87911yescharacteristic
231C22×C5#87911yescharacteristic
232C22×C5#89811yescharacteristic
233C22×C5#89811yescharacteristic
234C22×C5#89811yescharacteristic
235C4×C5—81no—
236C4×C5—81no—
237C4×C5—81no—
238Dic5—241no—
239Dic5—241no—
240Dic5—241no—
241Dic5—241no—
242C24C22×D1511yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—301no—
247C22×C4—301no—
248C22×C4—301no—
249C22×C4—301no—
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—301no—
257C22⋊C4—301no—
258C22⋊C4—301no—
259C22⋊C4—301no—
260C22⋊C4—301no—
261C22⋊C4—301no—
262C22⋊C4—301no—
263C22⋊C4—301no—
264C3×C5#210411yescharacteristic, complemented, Hall
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3#402211yescharacteristic
273C22×C3#402511yescharacteristic
274C22×C3#402511yescharacteristic
275C22×C3#402511yescharacteristic
276C22×C3#404411yescharacteristic
277C22×C3#404411yescharacteristic
278C22×C3#404411yescharacteristic
279C3×C4—81no—
280C3×C4—81no—
281C3×C4—81no—
282Dic3—401no—
283Dic3—401no—
284Dic3—401no—
285Dic3—401no—
286C2×C5—21no—
287C2×C5—21no—
288C2×C5—21no—
289C2×C5—21no—
290C2×C5—21no—
291C2×C5—21no—
292C2×C5—21no—
293C2×C5C3⋊#40111yescharacteristic
294C23—81no—
295C23#681711yescharacteristic
296C23#681711yescharacteristic
297C23#681711yescharacteristic
298C23#681911yescharacteristic
299C23#681911yescharacteristic
300C23#681911yescharacteristic
301C23#682111yescharacteristic
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—601no—
309C2×C4—601no—
310C2×C4—601no—
311C2×C4—601no—
312C2×C4—1201no—
313C2×C4—1201no—
314C2×C4—1201no—
315C2×C4—1201no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3C5⋊#40111yescharacteristic
324C5C3⋊#210411yescharacteristic, complemented, Sylow
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22#9176511yescharacteristic
333C22#9176811yescharacteristic
334C22#9176811yescharacteristic
335C22#9176811yescharacteristic
336C22#9178711yescharacteristic
337C22#9178711yescharacteristic
338C22#9178711yescharacteristic
339C4—81no—
340C4—81no—
341C4—81no—
342C4—1201no—
343C4—1201no—
344C4—1201no—
345C4—1201no—
346C3C5⋊#210411yescharacteristic, complemented, Sylow
347C2—21no—
348C2—21no—
349C2—21no—
350C2—21no—
351C2—21no—
352C2—21no—
353C2—21no—
354C2#1175076311yescharacteristic
subgroupG/H
centerC2#11750763
commutator, prime radical, cosocleC24×C3×C5C23
FrattiniC24C22×D15
FittingC3×C5×#342C2
socleC2×C3×C5#401
hypercenter#342D15
hypocenterC3×C5#2104
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
264. C3×C5#2104semidirect
324. C5C3⋊#2104semidirect
346. C3C5⋊#2104semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#3422
#117463482
#117463472
C5⋊#21043
C3⋊#21045