Finite Group Databasebeta

← #14289860

Subgroups — #14289860

Order 1920.

388 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 88 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
1#11756343C211yesmaximal, characteristic
2C5×#5021C211yesmaximal, characteristic, complemented
3#11746929C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic
8#10601950—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11#91787—22no—
12#91781—21no—
13#91764—21no—
14C4×D60C2211yescharacteristic
15#91758C2211yescharacteristic
16C4×Dic30—21no—
17C5×#869C2211yescharacteristic
18C5×#835—21no—
19C5×#807—21no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4×#168C2211yescharacteristic
23#90985—21no—
24#90973—22no—
25#90969—21no—
26#68247—51nomaximal, Hall
27#65918—31no—
28C5×#477—31no—
29#65373—31no—
30#65370—31no—
31Q8⋊#168D311yescharacteristic, complemented
32#64706—31no—
33#64703—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30—21no—
38C2×C5×Dic6—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5—21no—
42C3×C42×C5C2311yescharacteristic
43#6714—22no—
44#6714—22no—
45#6714—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15D412yes—
48C4⋊Dic15D411yescharacteristic
49#6712—22no—
50C4×Dic15—22no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#5584—51no—
57#5021D511yescharacteristic, complemented
58#4842—51no—
59#4681—51no—
60C3×Q8⋊C8—51no—
61#4482—51no—
62#4459—51no—
63C5×C4⋊Q8—31no—
64C4×C5×Q8C2×D311yescharacteristic
65#4092—61no—
66#4044—62no—
67#4038—61no—
68#4021—61no—
69C4×D20—31no—
70#4015—31no—
71C4×Dic10—61no—
72C5×#107—61no—
73C5×C4⋊C8—31no—
74C5×#103—61no—
75#3967—62no—
76#3941—61no—
77#3940—61no—
78C4⋊#168C2×D311yescharacteristic
79C4×#168C2×D311yescharacteristic
80#1638—151noSylow
81C22×D15—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×Dic15—21no—
90C2×Dic15—22no—
91D60—21no—
92D60—21no—
93C4×D15—41no—
94C4×D15—41no—
95Dic30—41no—
96Dic30—41no—
97C2×C5×Dic3—41no—
98C5×Dic6—42no—
99C3×#168—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C3×C4×Q8C2×D511yescharacteristic
103#946—101no—
104#898—102no—
105#892—101no—
106#875—101no—
107C4×D12—51no—
108#869—51no—
109#869C2×D511yescharacteristic
110C4×Dic6—101no—
111C3×C4⋊C8—51no—
112C3×C4×C8—51no—
113#835—21no—
114#821—101no—
115#817—101no—
116#816—102no—
117#807—21no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C2×C5×Q8—61no—
120C2×C5×Q8D1211yescharacteristic
121C2×D20—31no—
122C2×C4×D5—61no—
123C2×Dic10—61no—
124C2×C5×C8—61no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4D1211yescharacteristic
129C42×C5—21no—
130C42×C5C22×D311yescharacteristic
131#685—62no—
132#685—62no—
133#685—61no—
134C4⋊Dic5—31no—
135C4⋊Dic5—32no—
136C4⋊Dic5—61no—
137#683—62no—
138C4×Dic5—62no—
139C2×#168—21no—
140C2×#168—21no—
141#556—151no—
142#487—151no—
143#477—31no—
144#476—151no—
145#332—151no—
146Q8⋊C8—51no—
147D4⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C2×D15—41no—
150C2×D15—41no—
151C2×D15—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
159Dic15—42no—
160Dic15—41no—
161C5×Dic3—81no—
162C2×C3×Q8C22⋊D511yescharacteristic
163C2×D12—51no—
164C2×C4×D3—101no—
165C2×Dic6—21no—
166C2×Dic6—101no—
167C2×C3×C8—101no—
168C2×C3×C8—101no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4C22⋊D511yescharacteristic
171C3×C42—21no—
172C3×C42C22×D511yescharacteristic
173(C2×D3)⋊C4—102no—
174(C2×D3)⋊C4—102no—
175(C2×D3)⋊C4—101no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—52no—
179C4⋊Dic3—51no—
180C4⋊Dic3—101no—
181Dic3⋊C4—102no—
182C4×Dic3—102no—
183C2×C3⋊C8—21no—
184C22×D5—61no—
185C5×Q8—21no—
186C5×Q8—21no—
187C5×Q8—122no—
188C2×C4×C5—21no—
189C2×C4×C5—21no—
190C2×C4×C5—121no—
191C2×C4×C5C2×D1211yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×Dic5—61no—
195C2×Dic5—62no—
196D20—61no—
197D20—61no—
198C4×D5—121no—
199C4×D5—121no—
200Dic10—121no—
201Dic10—121no—
202C5×C8—121no—
203#168—41no—
204#168—41no—
205C4⋊Q8—31no—
206C4⋊Q8—151no—
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—301no—
211C4×Q8D3×D511yescharacteristic
212C4×D4—151no—
213#117—301no—
214#107—61no—
215#106—301no—
216C4⋊C8—31no—
217C4⋊C8—51no—
218#103—61no—
219#103—302no—
220#102—301no—
221C4×C8—51no—
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225D15—81no—
226C22×D3—101no—
227C3×Q8—21no—
228C3×Q8—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4D4×D511yescharacteristic
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4C2×C22⋊D511yescharacteristic
234C2×Dic3—41no—
235C2×Dic3—101no—
236C2×Dic3—102no—
237D12—101no—
238D12—101no—
239C4×D3—201no—
240C4×D3—201no—
241Dic6—42no—
242Dic6—201no—
243Dic6—201no—
244C3×C8—201no—
245C3×C8—201no—
246C3⋊C8—41no—
247C22×C5#88211yescharacteristic
248C2×D5—121no—
249C2×D5—121no—
250C2×D5—121no—
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5—241no—
255C4×C5#90411yescharacteristic
256C4×C5#90911yescharacteristic
257C4×C5#91611yescharacteristic
258C4×C5#91811yescharacteristic
259Dic5—121no—
260Dic5—122no—
261C2×Q8—61no—
262C2×Q8—301no—
263C2×Q8#120311yescharacteristic
264C2×D4—151no—
265C22×C4—301no—
266C2×C8—61no—
267C2×C8—101no—
268C2×C8—101no—
269C4⋊C4—21no—
270C4⋊C4—61no—
271C4⋊C4—61no—
272C4⋊C4—152no—
273C4⋊C4—151no—
274C4⋊C4—302no—
275C4⋊C4—301no—
276C4⋊C4#120311yescharacteristic
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—301no—
280C42—21no—
281C42—302no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#408311yescharacteristic
285C2×D3—201no—
286C2×D3—201no—
287C2×D3—201no—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4#406411yescharacteristic
292C3×C4#406511yescharacteristic
293C3×C4#408811yescharacteristic
294C3×C4#409611yescharacteristic
295Dic3—81no—
296Dic3—201no—
297Dic3—202no—
298C2×C5#473311yescharacteristic
299C2×C5#480811yescharacteristic
300C2×C5#482711yescharacteristic
301D5—241no—
302C23—301no—
303Q8—21no—
304Q8—21no—
305Q8—122no—
306Q8—601no—
307Q8—601no—
308D4—301no—
309D4—301no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—121no—
313C2×C4—301no—
314C2×C4—302no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4C2×#120311yescharacteristic
318C2×C4#679011yescharacteristic
319C2×C4#679011yescharacteristic
320C8—121no—
321C8—201no—
322C8—201no—
323C2×C3#6533611yescharacteristic
324C2×C3#6547611yescharacteristic
325C2×C3#6549011yescharacteristic
326D3—401no—
327C5#6824711yescharacteristic, complemented, Sylow
328C22—601no—
329C22—601no—
330C22—601no—
331C22#9157311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—241no—
336C4—602no—
337C4—601no—
338C4#9130311yescharacteristic
339C4#9132111yescharacteristic
340C4#9151211yescharacteristic
341C4#9152111yescharacteristic
342C3#1060195011yescharacteristic, complemented, Sylow
343C2—1201no—
344C2#1174856611yescharacteristic
345C2#1174930711yescharacteristic
346C2#1174946111yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
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. C5×#5021C2semidirect
3. #11746929C2semidirect
5. C3×Q8⋊#168C2semidirect
6. #11745860C2semidirect
31. Q8⋊#168D3semidirect
57. #5021D5semidirect
283. C3×C5#1638semidirect
327. C5#68247semidirect
342. C3#10601950semidirect

Maximal subgroups

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

subgroupindex
#117563432
C5×#50212
#117469292
#117468852
C3×Q8⋊#1682
#117458602
#117458392
#106019503
#682475