Finite Group Databasebeta

← #14291201

Subgroups — #14291201

Order 1920.

344 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C5×C3⋊#564C211yesmaximal, characteristic
2C3×#65354C211yesmaximal, characteristic
3#11746969C211yesmaximal, characteristic
4#11746925C211yesmaximal, characteristic
5#11746364C211yesmaximal, characteristic
6#11745850C211yesmaximal, characteristic
7#11745850C211yesmaximal, characteristic
8#10602754—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C5×#890—21no—
11C5×#890—21no—
12C5×#889—21no—
13C5×#889—21no—
14C5×#889—21no—
15C5×#889—21no—
16C5×#870C2211yescharacteristic
17C5×#870C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91087C2211yescharacteristic
20#91087C2211yescharacteristic
21C3×#3940—21no—
22C3×#3939—21no—
23C3×#3935C2211yescharacteristic
24#90989—21no—
25#90986—21no—
26#90970—21no—
27#90970—21no—
28#71393—51nomaximal, Hall
29C5×#564—31no—
30#65358—31no—
31#65354—31no—
32#65354D311yescharacteristic
33#64763—31no—
34#64763—31no—
35#64763—31no—
36C2×C3×Dic10—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4D411yescharacteristic
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×C4⋊Dic3D411yescharacteristic
48C5×C4⋊Dic3D411yescharacteristic
49C5×C4⋊Dic3D411yescharacteristic
50C5×Dic3⋊C4—21no—
51C5×Dic3⋊C4—21no—
52C5×Dic3⋊C4—21no—
53C5×Dic3⋊C4—21no—
54C5×Dic3⋊C4—21no—
55C5×Dic3⋊C4—21no—
56C5×Dic3⋊C4—21no—
57C5×Dic3⋊C4—21no—
58C4×C5×Dic3—21no—
59C4×C5×Dic3—21no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5—21no—
62C2×C3×#168—21no—
63C3⋊#564D511yescharacteristic
64C3×#501—51no—
65#5082—51no—
66#5081—51no—
67#4543—51no—
68#4465—51no—
69#4465—51no—
70C5×#125—31no—
71C5×#125—31no—
72C5×#125—61no—
73C5×#125—61no—
74C5×#125—61no—
75C5×#125—61no—
76C5×#125—61no—
77C5×#125—61no—
78C5×#125C2×D311yescharacteristic
79#4015C2×D311yescharacteristic
80#3942—61no—
81#3942—61no—
82#3940—21no—
83#3940—61no—
84#3939—21no—
85#3939—61no—
86#3935—31no—
87#3935—31no—
88#3935C2×D311yescharacteristic
89#1663—151noSylow
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C5×Dic3—21no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3—21no—
99C2×C3×Dic5—41no—
100C3×Dic10—42no—
101C3⋊#168—22no—
102C3⋊#168—41no—
103C3×#168—22no—
104C3×C4⋊Q8—51no—
105C3×#125C2×D511yescharacteristic
106#890—21no—
107#890—21no—
108#889—21no—
109#889—21no—
110#889—21no—
111#889—21no—
112#870C2×D511yescharacteristic
113#870C2×D511yescharacteristic
114C3×#107—101no—
115C3×#106—101no—
116C3×#97—51no—
117#835—101no—
118#835—101no—
119#808—101no—
120#807—101no—
121#803—51no—
122#803—51no—
123C2×Dic10—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—31no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C5×C4⋊C4—61no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4#6711yescharacteristic
141C5×C4⋊C4#6711yescharacteristic
142C42×C5—61no—
143C42×C5—61no—
144C42×C5C22×D311yescharacteristic
145C4⋊Dic5—21no—
146C4⋊Dic5—21no—
147C2×#168—21no—
148C2×#168—61no—
149C2×#168—61no—
150#564—31no—
151#501—51no—
152#501—151no—
153#491—151no—
154#330—151no—
155#330—151no—
156#330—151no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—41no—
162C3×C4×C5—41no—
163C3×Dic5—81no—
164C5×Dic3—41no—
165C5×Dic3—41no—
166C5×Dic3—41no—
167C5×Dic3—41no—
168C2×C3×Q8—101no—
169C2×C3×C8—101no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4C22⋊D511yescharacteristic
175C3×C4⋊C4C22⋊D511yescharacteristic
176C3×C42C22×D511yescharacteristic
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3C22⋊D511yescharacteristic
180C4⋊Dic3C22⋊D511yescharacteristic
181C4⋊Dic3C22⋊D511yescharacteristic
182C4⋊Dic3C22⋊D511yescharacteristic
183Dic3⋊C4—21no—
184Dic3⋊C4—21no—
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191C4×Dic3—21no—
192C4×Dic3—21no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—61no—
198C2×C4×C5—61no—
199C2×C4×C5—61no—
200C2×C4×C5—61no—
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×Dic5—41no—
205Dic10—42no—
206#168—22no—
207#168—62no—
208#168—121no—
209C4⋊Q8—51no—
210#125—31no—
211#125—31no—
212#125—61no—
213#125—61no—
214#125—61no—
215#125—61no—
216#125—61no—
217#125—61no—
218#125D3×D511yescharacteristic
219#107—101no—
220#107—301no—
221#106—101no—
222#106—301no—
223#103—301no—
224#103—301no—
225#97—51no—
226#97—151no—
227#97—151no—
228C2×C3×C5#45411yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C3×Q8—202no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—201no—
235C2×C3×C4C2×C22⋊D511yescharacteristic
236C2×C3×C4C2×C22⋊D511yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—21no—
242C3×C8—102no—
243C3⋊C8—102no—
244C3⋊C8—201no—
245C22×C5#93711yescharacteristic
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—41no—
250C4×C5—41no—
251C4×C5—121no—
252C4×C5—121no—
253C4×C5—121no—
254C4×C5—121no—
255Dic5—81no—
256C2×Q8—101no—
257C2×C8—101no—
258C2×C8—301no—
259C2×C8—301no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—31no—
263C4⋊C4—31no—
264C4⋊C4—31no—
265C4⋊C4—31no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4—61no—
270C4⋊C4—61no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—101no—
277C4⋊C4—101no—
278C4⋊C4#120111yescharacteristic
279C4⋊C4#120111yescharacteristic
280C42—61no—
281C42—61no—
282C42C2×D3×D511yescharacteristic
283C3×C5#166311yescharacteristic, complemented, Hall
284C22×C3#409911yescharacteristic
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—401no—
291Dic3—41no—
292Dic3—41no—
293Dic3—41no—
294Dic3—41no—
295C2×C5#509511yescharacteristic
296C2×C5#520111yescharacteristic
297C2×C5#520511yescharacteristic
298Q8—202no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—201no—
306C2×C4C2×#120111yescharacteristic
307C2×C4D3×C22⋊D511yescharacteristic
308C2×C4D3×C22⋊D511yescharacteristic
309C8—102no—
310C8—302no—
311C8—601no—
312C2×C3#6553411yescharacteristic
313C2×C3#6553511yescharacteristic
314C2×C3#6553511yescharacteristic
315C5#7139311yescharacteristic, complemented, Sylow
316C22#9156811yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—121no—
323C4—121no—
324C4—121no—
325C4—121no—
326C4—401no—
327C3#1060275411yescharacteristic, complemented, Sylow
328C2#1174939311yescharacteristic
329C2#1174945811yescharacteristic
330C2#1174946511yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socle, prime radicalC22×C3×C5#120
hypercenter#125D3×D5
hypocenterC3×C5#1663
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
283. C3×C5#1663semidirect
315. C5#71393semidirect
327. C3#10602754semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊#5642
C3×#653542
#117469692
#117469252
#117463642
#117458502
#106027543
#713935