Finite Group Databasebeta

← #14289531

Subgroups — #14289531

Order 1920.

428 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5579C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic, complemented
3#11747103C211yesmaximal, characteristic, complemented
4#11746882C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic
8#10602717—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#946—21no—
11C5×#896—22no—
12C5×D3×C4⋊C4—21no—
13C4×C5×D12—21no—
14C4×C5×D12C2211yescharacteristic
15C5×#870—21no—
16C5×#869C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6661—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C3×#3967—21no—
22C3×#3939—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90986—21no—
25#90966—21no—
26#71156—51nomaximal, Hall
27C5×#554—31no—
28#65381—31no—
29#65310D311yescharacteristic, complemented
30#65297—31no—
31#64766—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C4×C5×D3—22no—
38C2×C5×Dic6D412yes—
39C2×C3×Dic10—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C42×C5—21no—
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C5×(C2×D3)⋊C4—22no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—22no—
52C5×Dic3⋊C4—22no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6661—44no—
57#5579D511yescharacteristic
58C3×#477—51no—
59#5092—51no—
60#5084—51no—
61#4535—51no—
62#4483—51no—
63#4481—51no—
64C5×C4⋊Q8—31no—
65C5×#125—61no—
66C5×C22⋊Q8—62no—
67C5×C22⋊Q8—61no—
68C4×C5×Q8C2×D311yescharacteristic
69C4×C5×D4—31no—
70C4×C5×D4—61no—
71C2×C5×C4⋊C4—61no—
72C2×#689—62no—
73#4015C2×D311yescharacteristic
74#3967—21no—
75#3964—61no—
76#3940—61no—
77#3939—21no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1632—151noSylow
82C22×C5×D3—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C5×Dic3—21no—
91C2×C5×Dic3—22no—
92C5×D12—21no—
93C5×D12Q1612yescomplemented
94C4×C5×D3—41no—
95C4×C5×D3—41no—
96C4×C5×D3—82no—
97C5×Dic6—42no—
98C2×C3×Dic5—41no—
99C3×Dic10—42no—
100C3⋊#168—22no—
101C3⋊#168—41no—
102C3×#168—41no—
103C3×C4⋊Q8—51no—
104C3×C4×Q8C2×D511yescharacteristic
105#946—21no—
106C2×#216—102no—
107#896—22no—
108D3×C4⋊C4—21no—
109C4×D12—21no—
110C4×D12C2×D511yescharacteristic
111#870—21no—
112#869C2×D511yescharacteristic
113C3×#107—101no—
114C3×C4⋊C8—51no—
115C3×#103—101no—
116#809—101no—
117#808—101no—
118C4⋊(C3⋊C8)—51no—
119C4×C3⋊C8—51no—
120C2×C5×Q8—32no—
121C2×C5×Q8#6711yescharacteristic
122C2×C5×D4—31no—
123C22×C4×C5—62no—
124C22×C4×C5—61no—
125C2×Dic10—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—62no—
129C5×C4⋊C4—62no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4#6711yescharacteristic
133C5×C22⋊C4—62no—
134C5×C22⋊C4—61no—
135C42×C5—21no—
136C42×C5C22×D311yescharacteristic
137#689—124no—
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C2×#168—21no—
141C2×#168—61no—
142C2×#168—61no—
143#554—31no—
144#494—151no—
145#477—51no—
146#476—151no—
147#333—151no—
148Q8⋊C8—151no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×C5×D3—22no—
152C2×C5×D3—41no—
153C2×C5×D3—41no—
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5—41no—
157C3×C4×C5C2×Q1611yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×Dic5—81no—
162C5×Dic3—41no—
163C5×Dic3—42no—
164C2×C3×Q8—101no—
165C2×C3×Q8C22⋊D511yescharacteristic
166C2×D12C22⋊D511yescharacteristic
167C2×C4×D3—21no—
168C2×C4×D3—22no—
169C2×Dic6C22⋊D512yes—
170C2×C3×C8—101no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4C22⋊D511yescharacteristic
175C3×C42—21no—
176C3×C42C22×D511yescharacteristic
177#216—204no—
178(C2×D3)⋊C4—22no—
179(C2×D3)⋊C4—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3C22⋊D511yescharacteristic
183Dic3⋊C4—22no—
184Dic3⋊C4—22no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C23×C5—61no—
188C5×Q8—21no—
189C5×Q8—21no—
190C5×Q8—122no—
191C5×D4—32no—
192C5×D4—61no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—61no—
196C2×C4×C5—62no—
197C2×C4×C5—121no—
198C2×C4×C5—121no—
199C2×C4×C5—242no—
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×Dic5—41no—
204Dic10—42no—
205#168—41no—
206#168—62no—
207#168—121no—
208C2×Q16—302no—
209C4⋊Q8—31no—
210C4⋊Q8—51no—
211#125—61no—
212C22⋊Q8—62no—
213C22⋊Q8—61no—
214C4×Q8D3×D511yescharacteristic
215C4×D4—31no—
216C4×D4—61no—
217C2×C4⋊C4—61no—
218#107—101no—
219#106—301no—
220C4⋊C8—51no—
221C4⋊C8—151no—
222#103—101no—
223#102—301no—
224C4×C8—151no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C5×D3—42no—
229C22×D3—21no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—202no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—201no—
236C2×C3×C4C2×C22⋊D511yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×C3×C4C2×C22⋊D511yescharacteristic
239C2×Dic3—21no—
240C2×Dic3—22no—
241D12—21no—
242D12#68912yescomplemented
243C4×D3—41no—
244C4×D3—41no—
245C4×D3—82no—
246Dic6—42no—
247C3×C8—201no—
248C3⋊C8—102no—
249C3⋊C8—201no—
250C22×C5—62no—
251C22×C5—121no—
252C22×C5—121no—
253C22×C5#93711yescharacteristic
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—122no—
258C4×C5—121no—
259C4×C5D3×Q1611yescharacteristic
260C4×C5#91811yescharacteristic
261C4×C5#94211yescharacteristic
262C4×C5#95011yescharacteristic
263Dic5—81no—
264C2×Q8—32no—
265C2×Q8—101no—
266C2×Q8#120111yescharacteristic
267C2×D4—31no—
268C22×C4—62no—
269C22×C4—61no—
270Q16—604no—
271C2×C8—101no—
272C2×C8—301no—
273C2×C8—301no—
274C4⋊C4—21no—
275C4⋊C4—31no—
276C4⋊C4—62no—
277C4⋊C4—62no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4#120111yescharacteristic
283C22⋊C4—62no—
284C22⋊C4—61no—
285C42—21no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#409911yescharacteristic
289C2×D3—22no—
290C2×D3—41no—
291C2×D3—41no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—401no—
296C3×C4#408811yescharacteristic
297C3×C4C2×#68911yescharacteristic
298C3×C4#409611yescharacteristic
299C3×C4#409711yescharacteristic
300Dic3—41no—
301Dic3—42no—
302C2×C5—122no—
303C2×C5#504711yescharacteristic
304C2×C5#518611yescharacteristic
305C2×C5#519811yescharacteristic
306C23—61no—
307Q8—21no—
308Q8—21no—
309Q8—122no—
310Q8—202no—
311D4—32no—
312D4—61no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—61no—
316C2×C4—62no—
317C2×C4—121no—
318C2×C4—121no—
319C2×C4—201no—
320C2×C4—242no—
321C2×C4C2×#120111yescharacteristic
322C2×C4D3×C22⋊D511yescharacteristic
323C2×C4D3×C22⋊D511yescharacteristic
324C8—201no—
325C8—302no—
326C8—601no—
327C2×C3#6551711yescharacteristic
328C2×C3#6552811yescharacteristic
329C2×C3#6553011yescharacteristic
330D3—42no—
331C5#7115611yescharacteristic, complemented, Sylow
332C22—62no—
333C22—121no—
334C22—121no—
335C22#9156811yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—122no—
340C4—121no—
341C4—401no—
342C4#9129711yescharacteristic
343C4#9130911yescharacteristic
344C4D3×#68911yescharacteristic
345C4#9152011yescharacteristic
346C3#1060271711yescharacteristic, complemented, Sylow
347C2—122no—
348C2#1174853811yescharacteristic
349C2#1174930411yescharacteristic
350C2#1174941911yescharacteristic
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#1632
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. #11747103C2semidirect
5. #11746356C2semidirect
6. #11745862C2semidirect
29. #65310D3semidirect
93. C5×D12Q16semidirect
242. D12#689semidirect
287. C3×C5#1632semidirect
331. C5#71156semidirect
346. C3#10602717semidirect

Maximal subgroups

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

subgroupindex
C5×#55792
C3×#653102
#117471032
#117468822
#117463562
#117458622
#117458362
#106027173
#711565