Finite Group Databasebeta

← #14289796

Subgroups — #14289796

Order 1920.

456 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×D4×Dic10C211yesmaximal, characteristic
2C5×#5008C211yesmaximal, characteristic
3#11746954C211yesmaximal, characteristic, complemented
4#11746923C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic
6#11745855C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10601935—31nomaximal, Hall
9C22×C3×Dic10—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×D4×Dic5—21no—
13C3×#4070—21no—
14C3×#4034—21no—
15C3×#4024—22no—
16C3×#4015C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C4⋊(C3⋊#168)C2211yescharacteristic
19C4×C3⋊#168C2211yescharacteristic
20C5×#832—21no—
21C5×#808—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23#90989—21no—
24#90972—22no—
25#90970—21no—
26#71915—51nomaximal, Hall
27D4×Dic10D311yescharacteristic
28C5×#476—31no—
29#65380—31no—
30#65370—31no—
31D4⋊#168—31no—
32#64706—31no—
33#64704—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×Dic6—21no—
37C22×C3×Dic5—22no—
38C2×C3×Dic10—22no—
39C2×C3×Dic10—21no—
40C2×C3×Dic10—42no—
41C2×C3×Dic10—42no—
42C2×C3×Dic10D411yescharacteristic
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C2×C5×C3⋊C8—21no—
51C3×C22⋊Dic5—22no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5D412yes—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—22no—
56C3×#683—21no—
57C3×C4×Dic5—21no—
58C3×D4×Q8—51no—
59#5093—51no—
60#5021—51no—
61#5008D511yescharacteristic
62#4547—51no—
63#4535—51no—
64D4⋊(C3⋊C8)—51no—
65C22×Dic10—21no—
66C5×C4⋊Q8—31no—
67C4×C5×D4C2×D311yescharacteristic
68D4×Dic5—21no—
69#4070—21no—
70#4034—21no—
71#4024—22no—
72#4015C2×D311yescharacteristic
73C4×Dic10C2×D311yescharacteristic
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#102—61no—
77#3967—62no—
78#3942—61no—
79#3939—61no—
80C4⋊#168—31no—
81C4×#168—31no—
82#1637—151noSylow
83C23×C3×C5—21no—
84C3×C5×D4—21no—
85C3×C5×D4Q1612yes—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C5×Dic3—41no—
93C5×Dic6—42no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—22no—
97C2×C3×Dic5—44no—
98C3×Dic10—21no—
99C3×Dic10—44no—
100C3×Dic10—41no—
101C3×Dic10—41no—
102C3×Dic10SD1612yes—
103C3⋊#168—41no—
104C3⋊#168—41no—
105C5×C3⋊C8—41no—
106C22×C3×Q8—101no—
107C3×C4⋊Q8—51no—
108C3×C4⋊Q8—101no—
109C3×C22⋊Q8—102no—
110C3×C22⋊Q8—101no—
111C3×C4×Q8—51no—
112C3×C4×D4—101no—
113C3×C4×D4C2×D511yescharacteristic
114#869C2×D511yescharacteristic
115#835—101no—
116#832—21no—
117#810—102no—
118#808—21no—
119#807—101no—
120C4⋊(C3⋊C8)—51no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8—51no—
123C2×C5×Q8—61no—
124C2×C5×D4#6711yescharacteristic
125C22×C4×C5—21no—
126C22×Dic5—22no—
127C2×Dic10—22no—
128C2×Dic10—21no—
129C2×Dic10—42no—
130C2×Dic10—42no—
131C2×Dic10#6711yescharacteristic
132C2×C5×C8—61no—
133C5×C4⋊C4—61no—
134C5×C4⋊C4—61no—
135C5×C4⋊C4#6711yescharacteristic
136C5×C22⋊C4—21no—
137C42×C5C22×D311yescharacteristic
138C22⋊Dic5—22no—
139C4⋊Dic5—21no—
140C4⋊Dic5#6711yescharacteristic
141C4⋊Dic5#6712yes—
142#683—22no—
143#683—21no—
144C4×Dic5—21no—
145C2×#168—61no—
146C2×#168—61no—
147D4×Q8—51no—
148#487—151no—
149#477—151no—
150#476—31no—
151#332—151no—
152Q8⋊C8—151no—
153D4⋊C8—151no—
154C22×C3×C5—22no—
155C22×C3×C5—41no—
156C22×C3×C5—41no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5—41no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5C2×Q1611yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×Dic5—22no—
165C3×Dic5—42no—
166C3×Dic5—41no—
167C5×Dic3—81no—
168C2×C3×Q8—51no—
169C2×C3×Q8—102no—
170C2×C3×Q8—101no—
171C2×C3×Q8—202no—
172C2×C3×Q8—202no—
173C2×C3×D4C22⋊D511yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—102no—
176C2×Dic6—21no—
177C3×C4⋊C4—51no—
178C3×C4⋊C4—52no—
179C3×C4⋊C4—102no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C4⋊C4C22⋊D511yescharacteristic
183C3×C22⋊C4—21no—
184C3×C22⋊C4—102no—
185C3×C42—101no—
186C3×C42C22×D511yescharacteristic
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—101no—
191C2×C3⋊C8—101no—
192C23×C5—21no—
193C5×Q8—122no—
194C5×D4—21no—
195C5×D4#21612yes—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—121no—
200C2×C4×C5C2×#6711yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×Dic5—21no—
204C2×Dic5—21no—
205C2×Dic5—22no—
206C2×Dic5—44no—
207Dic10—21no—
208Dic10—44no—
209Dic10—41no—
210Dic10—41no—
211Dic10#21412yes—
212C5×C8—121no—
213#168—121no—
214#168—121no—
215C22×Q8—101no—
216C4⋊Q8—31no—
217C4⋊Q8—51no—
218C4⋊Q8—101no—
219C22⋊Q8—102no—
220C22⋊Q8—101no—
221C4×Q8—51no—
222C4×D4—101no—
223C4×D4D3×D511yescharacteristic
224#107—301no—
225#106—61no—
226C4⋊C8—31no—
227C4⋊C8—151no—
228#103—302no—
229#103—301no—
230#102—61no—
231C4×C8—151no—
232C2×C3×C5—42no—
233C2×C3×C5#45011yescharacteristic
234C2×C3×C5#45111yescharacteristic
235C2×C3×C5#45411yescharacteristic
236C23×C3—21no—
237C3×Q8—52no—
238C3×Q8—101no—
239C3×Q8—204no—
240C3×Q8—201no—
241C3×Q8—201no—
242C3×D4—21no—
243C3×D4#68912yes—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4—102no—
250C2×C3×C4—204no—
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253C2×C3×C4C2×C22⋊D511yescharacteristic
254C2×Dic3—41no—
255Dic6—42no—
256C3⋊C8—41no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5—22no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5#95311yescharacteristic
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—241no—
266C4×C5#93211yescharacteristic
267C4×C5C2×#21411yescharacteristic
268C4×C5#94211yescharacteristic
269C4×C5C2×#21611yescharacteristic
270Dic5—22no—
271Dic5—42no—
272Dic5—41no—
273C2×Q8—51no—
274C2×Q8—61no—
275C2×Q8—102no—
276C2×Q8—101no—
277C2×Q8—202no—
278C2×Q8—202no—
279C2×D4#120111yescharacteristic
280C22×C4—21no—
281C22×C4—102no—
282C2×C8—61no—
283C2×C8—301no—
284C2×C8—301no—
285C4⋊C4—52no—
286C4⋊C4—51no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—102no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4#120111yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—102no—
295C42—101no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3—22no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3#408311yescharacteristic
302C3×C4—21no—
303C3×C4—41no—
304C3×C4—102no—
305C3×C4—202no—
306C3×C4—201no—
307C3×C4D5×SD1611yescharacteristic
308C3×C4#406011yescharacteristic
309C3×C4C2×#68911yescharacteristic
310C3×C4#409711yescharacteristic
311Dic3—81no—
312C2×C5—42no—
313C2×C5#521811yescharacteristic
314C2×C5#522811yescharacteristic
315C2×C5#524511yescharacteristic
316C23—21no—
317Q8—52no—
318Q8—101no—
319Q8—122no—
320Q8—204no—
321Q8—201no—
322Q8—201no—
323D4—21no—
324D4#666112yes—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—102no—
331C2×C4—121no—
332C2×C4—204no—
333C2×C4C2×#120111yescharacteristic
334C2×C4D5×#6711yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C8—121no—
337C8—601no—
338C8—601no—
339C2×C3—42no—
340C2×C3#6533911yescharacteristic
341C2×C3#6545811yescharacteristic
342C2×C3#6549011yescharacteristic
343C5#7191511yescharacteristic, complemented, Sylow
344C22—22no—
345C22—41no—
346C22—41no—
347C22#9156311yescharacteristic
348C4—21no—
349C4—41no—
350C4—102no—
351C4—201no—
352C4—202no—
353C4—241no—
354C4#9130911yescharacteristic
355C4C2×#666111yescharacteristic
356C4D5×#21411yescharacteristic
357C4#9149111yescharacteristic
358C3#1060193511yescharacteristic, complemented, Sylow
359C2—42no—
360C2#1174855511yescharacteristic
361C2#1174904411yescharacteristic
362C2#1174945611yescharacteristic
subgroupG/H
centerC22#91563
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#1637
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. #11746954C2semidirect
4. #11746923C2semidirect
6. #11745855C2semidirect
7. #11745840C2semidirect
297. C3×C5#1637semidirect
343. C5#71915semidirect
358. C3#10601935semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic102
C5×#50082
#117469542
#117469232
D4⋊(C3⋊#168)2
#117458552
#117458402
#106019353
#719155