Finite Group Databasebeta

← #14289861

Subgroups — #14289861

Order 1920.

388 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5584C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic, complemented
3#11746924C211yesmaximal, characteristic, complemented
4#11746882C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745857C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic
8#10602725—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#946—21no—
11C5×#898—22no—
12C5×#892—21no—
13C5×#875—21no—
14C4×C5×D12C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C4×C5×Dic6—21no—
17C3×#4015C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C3×#3967—21no—
21C3×#3939—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90986—21no—
24#90970—22no—
25#90966—21no—
26#71157—51nomaximal, Hall
27C5×#556—31no—
28#65382—31no—
29#65310D311yescharacteristic, complemented
30#65297—31no—
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6—21no—
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5—21no—
42C3×C42×C5C2311yescharacteristic
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C5×(C2×D3)⋊C4—22no—
46C5×(C2×D3)⋊C4—22no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D412yes—
51C5×Dic3⋊C4—22no—
52C4×C5×Dic3—22no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#5584D511yescharacteristic
57C3×#477—51no—
58#5084—51no—
59#5079—51no—
60#4535—51no—
61#4486—51no—
62#4483—51no—
63C5×C4⋊Q8—31no—
64C5×#126—62no—
65C5×#124—61no—
66C5×C22⋊Q8—61no—
67C4×C5×Q8—61no—
68C4×C5×Q8C2×D311yescharacteristic
69C4×C5×D4—31no—
70C5×#117—61no—
71#4015C2×D311yescharacteristic
72#3967—21no—
73#3964—61no—
74#3942—62no—
75#3940—61no—
76#3939—21no—
77C4⋊#168—31no—
78C4⋊#168C2×D311yescharacteristic
79C4×#168—31no—
80#1638—151noSylow
81C22×C5×D3—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C5×Dic3—21no—
90C2×C5×Dic3—22no—
91C5×D12—21no—
92C5×D12—21no—
93C4×C5×D3—41no—
94C4×C5×D3—41no—
95C5×Dic6—41no—
96C5×Dic6—41no—
97C2×C3×Dic5—41no—
98C3×Dic10—42no—
99C3⋊#168—41no—
100C3⋊#168—41no—
101C3×#168—41no—
102C3×C4⋊Q8—51no—
103C3×C4×Q8C2×D511yescharacteristic
104#946—21no—
105#898—22no—
106#892—21no—
107#875—21no—
108C4×D12C2×D511yescharacteristic
109#869C2×D511yescharacteristic
110C4×Dic6—21no—
111C3×#107—101no—
112C3×C4⋊C8—51no—
113C3×#103—101no—
114#835—102no—
115#809—101no—
116#808—101no—
117C4⋊(C3⋊C8)—51no—
118C4×C3⋊C8—51no—
119C2×C5×Q8—61no—
120C2×C5×Q8#6711yescharacteristic
121C2×C5×D4—31no—
122C22×C4×C5—61no—
123C2×Dic10—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—32no—
127C5×C4⋊C4—62no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4#6711yescharacteristic
130C5×C22⋊C4—62no—
131C5×C22⋊C4—62no—
132C5×C22⋊C4—61no—
133C42×C5—21no—
134C42×C5—62no—
135C42×C5C22×D311yescharacteristic
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C2×#168—21no—
139C2×#168—61no—
140C2×#168—61no—
141#556—31no—
142#487—151no—
143#477—51no—
144#476—151no—
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×C5×D3—41no—
150C2×C5×D3—41no—
151C2×C5×D3—41no—
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5—41no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×Dic5—81no—
160C5×Dic3—42no—
161C5×Dic3—41no—
162C2×C3×Q8—101no—
163C2×C3×Q8C22⋊D511yescharacteristic
164C2×D12C22⋊D511yescharacteristic
165C2×C4×D3—21no—
166C2×Dic6—21no—
167C2×C3×C8—101no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4C22⋊D511yescharacteristic
172C3×C42—21no—
173C3×C42C22×D511yescharacteristic
174(C2×D3)⋊C4—22no—
175(C2×D3)⋊C4—22no—
176(C2×D3)⋊C4—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3C22⋊D511yescharacteristic
179C4⋊Dic3C22⋊D512yes—
180Dic3⋊C4—22no—
181C4×Dic3—22no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—101no—
184C23×C5—61no—
185C5×Q8—21no—
186C5×Q8—21no—
187C5×Q8—121no—
188C5×Q8—121no—
189C5×D4—61no—
190C5×D4—61no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—61no—
194C2×C4×C5—62no—
195C2×C4×C5—121no—
196C2×C4×C5—121no—
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—41no—
201Dic10—42no—
202#168—41no—
203#168—121no—
204#168—121no—
205C4⋊Q8—31no—
206C4⋊Q8—51no—
207#126—62no—
208#124—61no—
209C22⋊Q8—61no—
210C4×Q8—61no—
211C4×Q8D3×D511yescharacteristic
212C4×D4—31no—
213#117—61no—
214#107—101no—
215#106—301no—
216C4⋊C8—51no—
217C4⋊C8—151no—
218#103—101no—
219#103—302no—
220#102—301no—
221C4×C8—151no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C5×D3—81no—
226C22×D3—21no—
227C3×Q8—21no—
228C3×Q8—21no—
229C3×Q8—202no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—201no—
233C2×C3×C4C2×C22⋊D511yescharacteristic
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C2×C3×C4C2×C22⋊D511yescharacteristic
236C2×Dic3—21no—
237C2×Dic3—22no—
238D12—21no—
239D12—21no—
240C4×D3—41no—
241C4×D3—41no—
242Dic6—41no—
243Dic6—41no—
244C3×C8—201no—
245C3⋊C8—201no—
246C3⋊C8—201no—
247C22×C5—121no—
248C22×C5—121no—
249C22×C5—121no—
250C22×C5#93711yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5—122no—
255C4×C5—121no—
256C4×C5#91811yescharacteristic
257C4×C5#91911yescharacteristic
258C4×C5#94211yescharacteristic
259C4×C5#95011yescharacteristic
260Dic5—81no—
261C2×Q8—61no—
262C2×Q8—101no—
263C2×Q8#120111yescharacteristic
264C2×D4—31no—
265C22×C4—61no—
266C2×C8—101no—
267C2×C8—301no—
268C2×C8—301no—
269C4⋊C4—21no—
270C4⋊C4—32no—
271C4⋊C4—31no—
272C4⋊C4—62no—
273C4⋊C4—61no—
274C4⋊C4—101no—
275C4⋊C4—101no—
276C4⋊C4#120111yescharacteristic
277C22⋊C4—62no—
278C22⋊C4—62no—
279C22⋊C4—61no—
280C42—21no—
281C42—62no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#409911yescharacteristic
285C2×D3—41no—
286C2×D3—41no—
287C2×D3—41no—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4—401no—
292C3×C4#409611yescharacteristic
293C3×C4#409611yescharacteristic
294C3×C4#409711yescharacteristic
295C3×C4#409711yescharacteristic
296Dic3—42no—
297Dic3—41no—
298C2×C5—241no—
299C2×C5#504711yescharacteristic
300C2×C5#518711yescharacteristic
301C2×C5#520111yescharacteristic
302C23—61no—
303Q8—21no—
304Q8—21no—
305Q8—121no—
306Q8—121no—
307Q8—202no—
308D4—61no—
309D4—61no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—61no—
313C2×C4—62no—
314C2×C4—121no—
315C2×C4—121no—
316C2×C4—201no—
317C2×C4C2×#120111yescharacteristic
318C2×C4D3×C22⋊D511yescharacteristic
319C2×C4D3×C22⋊D511yescharacteristic
320C8—201no—
321C8—601no—
322C8—601no—
323C2×C3#6552811yescharacteristic
324C2×C3#6552811yescharacteristic
325C2×C3#6553411yescharacteristic
326D3—81no—
327C5#7115711yescharacteristic, complemented, Sylow
328C22—121no—
329C22—121no—
330C22—121no—
331C22#9156811yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—122no—
336C4—121no—
337C4—401no—
338C4#9129711yescharacteristic
339C4#9130911yescharacteristic
340C4#9151011yescharacteristic
341C4#9151911yescharacteristic
342C3#1060272511yescharacteristic, complemented, Sylow
343C2—241no—
344C2#1174853811yescharacteristic
345C2#1174930511yescharacteristic
346C2#1174945811yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#65310C2semidirect
3. #11746924C2semidirect
5. #11746356C2semidirect
6. #11745857C2semidirect
29. #65310D3semidirect
283. C3×C5#1638semidirect
327. C5#71157semidirect
342. C3#10602725semidirect

Maximal subgroups

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

subgroupindex
C5×#55842
C3×#653102
#117469242
#117468822
#117463562
#117458572
#117458362
#106027253
#711575