Finite Group Databasebeta

← #14289843

Subgroups — #14289843

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×#5542C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic
3#11746959C211yesmaximal, characteristic, complemented
4#11746924C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic
6#11745858C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10602725—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#936—21no—
11C5×#926—21no—
12C5×#924—21no—
13C5×#887—21no—
14C5×#879—22no—
15C5×#869C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C3×#3964—21no—
21C3×#3940—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90989—21no—
24#90972—21no—
25#90970—22no—
26#71147—51nomaximal, Hall
27C5×#556—31no—
28#65382—31no—
29#65310—31no—
30#65297D311yescharacteristic
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6D411yescharacteristic
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4D411yescharacteristic
40C3×C5×C22⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C5×#217—22no—
45C5×#217—22no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×C4⋊Dic3D412yes—
49C5×Dic3⋊C4—22no—
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3—22no—
52C4×C5×Dic3—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#5542D511yescharacteristic
57C3×#476—51no—
58#5091—51no—
59#5079—51no—
60D4⋊(C3⋊C8)—51no—
61#4484—51no—
62#4482—51no—
63C5×C4⋊Q8—31no—
64C5×#126—62no—
65C5×#124—61no—
66C5×C22⋊Q8—61no—
67C4×C5×Q8—31no—
68C4×C5×Q8—61no—
69C4×C5×D4C2×D311yescharacteristic
70C5×#117—61no—
71#4015C2×D311yescharacteristic
72#3967—61no—
73#3964—21no—
74#3942—62no—
75#3940—21no—
76#3939—61no—
77C4⋊#168—31no—
78C4⋊#168C2×D311yescharacteristic
79C4×#168—31no—
80#1638—151noSylow
81C23×C3×C5—21no—
82C3×C5×D4—21no—
83C3×C5×D4—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—22no—
93C5×Dic6—21no—
94C5×Dic6—21no—
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×D4C2×D511yescharacteristic
104#936—21no—
105#926—21no—
106#924—21no—
107#887—21no—
108#879—22no—
109#869C2×D511yescharacteristic
110C4×Dic6C2×D511yescharacteristic
111C3×#106—101no—
112C3×C4⋊C8—51no—
113C3×#102—101no—
114#835—102no—
115#810—101no—
116#807—101no—
117C4⋊(C3⋊C8)—51no—
118C4×C3⋊C8—51no—
119C2×C5×Q8—31no—
120C2×C5×Q8—61no—
121C2×C5×D4#6711yescharacteristic
122C22×C4×C5—21no—
123C2×Dic10—21no—
124C5×C4⋊C4—31no—
125C5×C4⋊C4—32no—
126C5×C4⋊C4—62no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4#6711yescharacteristic
130C5×C22⋊C4—21no—
131C5×C22⋊C4—62no—
132C5×C22⋊C4—62no—
133C42×C5—62no—
134C42×C5—61no—
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—151no—
144#476—51no—
145#332—151no—
146Q8⋊C8—151no—
147D4⋊C8—151no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5#12011yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×Dic5—81no—
159C5×Dic3—41no—
160C5×Dic3—42no—
161C5×Dic3—41no—
162C2×C3×Q8—101no—
163C2×C3×D4C22⋊D511yescharacteristic
164C22×C3×C4—21no—
165C2×Dic6—21no—
166C2×Dic6C22⋊D511yescharacteristic
167C2×C3×C8—101no—
168C3×C4⋊C4—101no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4C22⋊D511yescharacteristic
171C3×C22⋊C4—21no—
172C3×C42C22×D511yescharacteristic
173#217—22no—
174#217—22no—
175C4⋊Dic3—21no—
176C4⋊Dic3C22⋊D511yescharacteristic
177C4⋊Dic3C22⋊D512yes—
178Dic3⋊C4—22no—
179Dic3⋊C4—21no—
180C4×Dic3—22no—
181C4×Dic3—21no—
182C2×C3⋊C8—101no—
183C2×C3⋊C8—101no—
184C23×C5—21no—
185C5×Q8—61no—
186C5×Q8—61no—
187C5×Q8—121no—
188C5×Q8—121no—
189C5×D4—21no—
190C5×D4—21no—
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—61no—
195C2×C4×C5—62no—
196C2×C4×C5—61no—
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—31no—
211C4×Q8—61no—
212C4×D4D3×D511yescharacteristic
213#117—61no—
214#107—301no—
215#106—101no—
216C4⋊C8—51no—
217C4⋊C8—151no—
218#103—302no—
219#103—301no—
220#102—101no—
221C4×C8—151no—
222C2×C3×C5—81no—
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45211yescharacteristic
225C2×C3×C5#45411yescharacteristic
226C23×C3—21no—
227C3×Q8—202no—
228C3×D4—21no—
229C3×D4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—201no—
234C2×C3×C4C2×C22⋊D511yescharacteristic
235C2×C3×C4C2×C22⋊D511yescharacteristic
236C2×C3×C4C2×C22⋊D511yescharacteristic
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—22no—
240Dic6—21no—
241Dic6—21no—
242Dic6—41no—
243Dic6—41no—
244C3×C8—201no—
245C3⋊C8—201no—
246C3⋊C8—201no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5#93711yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—121no—
254C4×C5—121no—
255C4×C5—122no—
256C4×C5#91511yescharacteristic
257C4×C5#91611yescharacteristic
258C4×C5#94211yescharacteristic
259C4×C5#95011yescharacteristic
260Dic5—81no—
261C2×Q8—31no—
262C2×Q8—61no—
263C2×Q8—101no—
264C2×D4#120111yescharacteristic
265C22×C4—21no—
266C2×C8—101no—
267C2×C8—301no—
268C2×C8—301no—
269C4⋊C4—32no—
270C4⋊C4—31no—
271C4⋊C4—62no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—101no—
275C4⋊C4—101no—
276C4⋊C4#120111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—62no—
279C22⋊C4—62no—
280C42—62no—
281C42—61no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3#409911yescharacteristic
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—401no—
291C3×C4#409611yescharacteristic
292C3×C4#409611yescharacteristic
293C3×C4#409711yescharacteristic
294C3×C4#409711yescharacteristic
295Dic3—41no—
296Dic3—42no—
297Dic3—41no—
298C2×C5—81no—
299C2×C5#504711yescharacteristic
300C2×C5#517311yescharacteristic
301C2×C5#520111yescharacteristic
302C23—21no—
303Q8—61no—
304Q8—61no—
305Q8—121no—
306Q8—121no—
307Q8—202no—
308D4—21no—
309D4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—61no—
314C2×C4—62no—
315C2×C4—61no—
316C2×C4—201no—
317C2×C4C2×#120111yescharacteristic
318C2×C4D3×C22⋊D511yescharacteristic
319C2×C4D3×C22⋊D511yescharacteristic
320C8—201no—
321C8—601no—
322C8—601no—
323C2×C3—81no—
324C2×C3#6552811yescharacteristic
325C2×C3#6552811yescharacteristic
326C2×C3#6553411yescharacteristic
327C5#7114711yescharacteristic, complemented, Sylow
328C22—41no—
329C22—41no—
330C22—41no—
331C22#9156811yescharacteristic
332C4—21no—
333C4—41no—
334C4—121no—
335C4—122no—
336C4—121no—
337C4—401no—
338C4#9129711yescharacteristic
339C4#9130911yescharacteristic
340C4#9148611yescharacteristic
341C4#9149511yescharacteristic
342C3#1060272511yescharacteristic, complemented, Sylow
343C2—81no—
344C2#1174853811yescharacteristic
345C2#1174905911yescharacteristic
346C2#1174945811yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#1638
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #11746959C2semidirect
4. #11746924C2semidirect
6. #11745858C2semidirect
7. #11745842C2semidirect
283. C3×C5#1638semidirect
327. C5#71147semidirect
342. C3#10602725semidirect

Maximal subgroups

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

subgroupindex
C5×#55422
C3×#652972
#117469592
#117469242
D4⋊(C3⋊#168)2
#117458582
#117458422
#106027253
#711475