Finite Group Databasebeta

← C2×#11754188 #14479038

Subgroups — C2×#11754188 #14479038

Order 1920.

2976 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic10C211yesmaximal, characteristic
2C2×#91815C211yesmaximal, characteristic
3C2×C5×#926C211yesmaximal, characteristic
4C2×#91528C214yesmaximal
5#11754188C2116yesmaximal, direct product factor
6C2×#91331C214yesmaximal, complemented
7C2×Dic3×Dic10C214yesmaximal, complemented
8C2×#65850—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C23×C3×Dic5C2212yes—
11C22×C3×Dic10C4116yescomplemented
12C22×C3×Dic10C2212yes—
13C22×C3×Dic10C2212yes—
14C22×C3×Dic10C2218yes—
15C2×#6719C2212yes—
16#91815C2218yes—
17C2×C4⋊Dic15C2212yes—
18C2×C4×Dic15C2212yes—
19C2×C5×#217C2212yes—
20C5×#926C2218yes—
21C2×C5×C4⋊Dic3C2212yes—
22C2×C4×C5×Dic3C2212yes—
23C2×#6668C2218yes—
24#91528C22132yes—
25C2×Dic3×Dic5C2218yes—
26#91331C22132yescomplemented
27Dic3×Dic10C22132yescomplemented
28C2×#5812—51nomaximal, Hall
29C23×Dic10D311yescharacteristic
30C2×C5×#117—31no—
31C2×#4072—31no—
32#65850—316no—
33C2×#4033—34no—
34C2×#4023—34no—
35C2×C4×Dic10—34no—
36C24×C3×C5C2311yescharacteristic
37C22×C3×C4×C5C2×C418yes—
38C22×C3×C4×C5C2311yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×C3×C4×C5C2314yes—
41C22×Dic15C2314yes—
42C22×C5×Dic3C2314yes—
43C22×C3×Dic5C2×C4116yes—
44C22×C3×Dic5C2314yes—
45C22×C3×Dic5C2318yes—
46C2×C3×Dic10C2×C4116yes—
47C2×C3×Dic10C2×C4116yes—
48C2×C3×Dic10C2×C4164yescomplemented
49C2×C3×Dic10C2318yes—
50C2×C3×Dic10C2318yes—
51#6719C2318yes—
52C4⋊Dic15C2318yes—
53C4×Dic15C2318yes—
54C5×#217C2318yes—
55C5×C4⋊Dic3C2318yes—
56C4×C5×Dic3C2318yes—
57#6668C23132yes—
58Dic3×Dic5C23132yes—
59C23×C3×Q8—51no—
60#5812—516no—
61C2×Q8×Dic3—54no—
62C2×Q8×Dic3—54no—
63C2×#926—51no—
64C2×#926—54no—
65C2×#926D511yescharacteristic
66C23×C4×C5C2×D311yescharacteristic
67C23×Dic5C2×D312yes—
68C22×Dic10Dic3116yescomplemented
69C22×Dic10C2×D312yes—
70C22×Dic10C2×D312yes—
71C22×Dic10C2×D318yes—
72C5×#117—38no—
73C2×C5×C4⋊C4—32no—
74C2×C5×C22⋊C4—32no—
75C2×C42×C5—32no—
76C2×C22⋊Dic5—32no—
77#4072—38no—
78C2×C4⋊Dic5—32no—
79C2×#683—38no—
80C2×C4×Dic5—32no—
81C2×C4×Dic5—38no—
82#4033—332no—
83#4023—332no—
84C4×Dic10—332no—
85C2×#519—151noSylow
86C23×C3×C5—24no—
87C23×C3×C5C22×C414yes—
88C23×C3×C5C2412yes—
89C23×C3×C5C2411yescharacteristic
90C2×C3×C4×C5C22×C414yes—
91C2×C3×C4×C5C22×C414yes—
92C2×C3×C4×C5C22×C4116yes—
93C2×C3×C4×C5C2412yes—
94C2×C3×C4×C5C2412yes—
95C2×Dic15—28no—
96C2×Dic15C2418yes—
97C2×C5×Dic3—28no—
98C2×C5×Dic3C2418yes—
99C2×C3×Dic5C22×C4116yes—
100C2×C3×Dic5C22×C4132yes—
101C2×C3×Dic5C2418yes—
102C3×Dic10C22×C4132yes—
103C3×Dic10C22×C4132yes—
104C22×C3×Q8—516no—
105C22×C3×Q8—52no—
106C22×C3×Q8—52no—
107C22×C3×Q8—58no—
108C23×C3×C4—52no—
109C23×C3×C4C2×D511yescharacteristic
110C2×#217—52no—
111C2×#217C2×D512yes—
112Q8×Dic3—532no—
113Q8×Dic3—532no—
114#926—58no—
115#926—532no—
116#926C2×D518yes—
117C2×C4⋊Dic3—52no—
118C2×C4⋊Dic3—58no—
119C2×C4⋊Dic3C2×D512yes—
120C2×C4×Dic3—52no—
121C2×C4×Dic3—58no—
122C2×C4×Dic3C2×D512yes—
123C24×C5C22×D311yescharacteristic
124C22×C4×C5—34no—
125C22×C4×C5C2×Dic318yes—
126C22×C4×C5C22×D311yescharacteristic
127C22×C4×C5C22×D311yescharacteristic
128C22×C4×C5C22×D314yes—
129C22×Dic5—34no—
130C22×Dic5C2×Dic3116yes—
131C22×Dic5C22×D318yes—
132C22×Dic5C22×D314yes—
133C2×Dic10C2×Dic3116yes—
134C2×Dic10C2×Dic3116yes—
135C2×Dic10C2×Dic3164yescomplemented
136C2×Dic10C22×D318yes—
137C2×Dic10C22×D318yes—
138C5×C4⋊C4—38no—
139C5×C22⋊C4—38no—
140C42×C5—38no—
141C22⋊Dic5—38no—
142C4⋊Dic5—38no—
143#683—332no—
144C4×Dic5—38no—
145C4×Dic5—332no—
146C23×Q8—51no—
147#519—1516no—
148C2×C4×Q8—154no—
149C2×C4×Q8—154no—
150C2×#117—31no—
151C2×#117—154no—
152C2×#117—151no—
153C22×C3×C5—28no—
154C22×C3×C5—24no—
155C22×C3×C5C23×C414yes—
156C22×C3×C5C23×C412yes—
157C22×C3×C52−1+414yes—
158C22×C3×C5C2511yescharacteristic
159C3×C4×C5C23×C414yes—
160C3×C4×C5C23×C414yes—
161Dic15—28no—
162C3×Dic5C23×C4116yes—
163C5×Dic3—28no—
164C24×C3C22×D511yescharacteristic
165C2×C3×Q8—516no—
166C2×C3×Q8—516no—
167C2×C3×Q8—564no—
168C2×C3×Q8—58no—
169C2×C3×Q8—58no—
170C22×C3×C4—516no—
171C22×C3×C4—54no—
172C22×C3×C4—58no—
173C22×C3×C4C4×D518yes—
174C22×C3×C4C22×D511yescharacteristic
175C22×C3×C4C22×D511yescharacteristic
176C22×C3×C4C22×D514yes—
177C22×Dic3—54no—
178C22×Dic3C22×D514yes—
179#217—58no—
180#217C22×D518yes—
181C4⋊Dic3—58no—
182C4⋊Dic3—532no—
183C4⋊Dic3C22×D518yes—
184C4×Dic3—58no—
185C4×Dic3—532no—
186C4×Dic3C22×D518yes—
187C23×C5—24no—
188C23×C5C22×Dic314yes—
189C23×C5C23×D312yes—
190C23×C5C23×D311yescharacteristic
191C2×C4×C5—38no—
192C2×C4×C5—68no—
193C2×C4×C5C22×Dic314yes—
194C2×C4×C5C22×Dic314yes—
195C2×C4×C5C22×Dic3116yes—
196C2×C4×C5C23×D312yes—
197C2×C4×C5C23×D312yes—
198C2×Dic5—38no—
199C2×Dic5—68no—
200C2×Dic5C22×Dic3116yes—
201C2×Dic5C22×Dic3132yes—
202C2×Dic5C23×D318yes—
203Dic10C22×Dic3132yes—
204Dic10C22×Dic3132yes—
205C22×Q8—516no—
206C22×Q8—52no—
207C22×Q8—52no—
208C22×Q8—58no—
209C23×C4—52no—
210C23×C4D3×D511yescharacteristic
211C4×Q8—1532no—
212C4×Q8—1532no—
213#117—38no—
214#117—1532no—
215#117—158no—
216C2×C4⋊C4—32no—
217C2×C4⋊C4—158no—
218C2×C4⋊C4—152no—
219C2×C22⋊C4—32no—
220C2×C22⋊C4—152no—
221C2×C42—32no—
222C2×C42—158no—
223C2×C42—152no—
224C2×C3×C5—24no—
225C2×C3×C5#51914yescomplemented
226C2×C3×C5C24×C411yescharacteristic
227C2×C3×C5C2×2−1+412yes—
228C23×C3—24no—
229C23×C3C2×C4×D514yes—
230C23×C3C23×D512yes—
231C23×C3C23×D511yescharacteristic
232C3×Q8—532no—
233C3×Q8—532no—
234C2×C3×C4—532no—
235C2×C3×C4—516no—
236C2×C3×C4—58no—
237C2×C3×C4C2×C4×D5116yes—
238C2×C3×C4C2×C4×D514yes—
239C2×C3×C4C2×C4×D514yes—
240C2×C3×C4C23×D512yes—
241C2×C3×C4C23×D512yes—
242C2×Dic3—28no—
243C2×Dic3—58no—
244C2×Dic3—108no—
245C2×Dic3C23×D518yes—
246C22×C5—24no—
247C22×C5—28no—
248C22×C5#100714yes—
249C22×C5C23×Dic314yes—
250C22×C5C23×Dic312yes—
251C22×C5C24×D311yescharacteristic
252C4×C5—68no—
253C4×C5C23×Dic314yes—
254C4×C5C23×Dic314yes—
255Dic5—68no—
256Dic5C23×Dic3116yes—
257C24C2×D3×D511yescharacteristic
258C2×Q8—516no—
259C2×Q8—516no—
260C2×Q8—564no—
261C2×Q8—58no—
262C2×Q8—58no—
263C22×C4—34no—
264C22×C4—516no—
265C22×C4—58no—
266C22×C4—54no—
267C22×C4—154no—
268C22×C4D5×Dic318yes—
269C22×C4C2×D3×D514yes—
270C22×C4C2×D3×D511yescharacteristic
271C22×C4C2×D3×D511yescharacteristic
272C4⋊C4—38no—
273C4⋊C4—1532no—
274C4⋊C4—158no—
275C22⋊C4—38no—
276C22⋊C4—158no—
277C42—38no—
278C42—1532no—
279C42—158no—
280C3×C5C2×#51911yescharacteristic, complemented, Hall
281C22×C3—28no—
282C22×C3—24no—
283C22×C3C22×C4×D514yes—
284C22×C3C22×C4×D512yes—
285C22×C3#415014yes—
286C22×C3C24×D511yescharacteristic
287C3×C4—516no—
288C3×C4C22×C4×D514yes—
289C3×C4C22×C4×D514yes—
290Dic3—28no—
291Dic3—108no—
292C2×C5—24no—
293C2×C5#581214yescomplemented
294C2×C5C2×#100712yes—
295C2×C5C24×Dic311yescharacteristic
296C23—24no—
297C23C2×D5×Dic314yes—
298C23C22×D3×D512yes—
299C23C22×D3×D511yescharacteristic
300Q8—532no—
301Q8—532no—
302C2×C4—38no—
303C2×C4—532no—
304C2×C4—516no—
305C2×C4—58no—
306C2×C4—68no—
307C2×C4—158no—
308C2×C4—308no—
309C2×C4C2×D5×Dic3116yes—
310C2×C4C2×D5×Dic314yes—
311C2×C4C2×D5×Dic314yes—
312C2×C4C22×D3×D512yes—
313C2×C4C22×D3×D512yes—
314C2×C3—24no—
315C2×C3#6585014yescomplemented
316C2×C3C23×C4×D511yescharacteristic
317C2×C3C2×#415012yes—
318C5C2×#581211yescharacteristic, complemented, Sylow
319C22—28no—
320C22—24no—
321C22#9200414yes—
322C22C22×D5×Dic314yes—
323C22C22×D5×Dic312yes—
324C22C23×D3×D511yescharacteristic
325C4—516no—
326C4—68no—
327C4—308no—
328C4C22×D5×Dic314yes—
329C4C22×D5×Dic314yes—
330C3C2×#6585011yescharacteristic, complemented, Sylow
331C2—24no—
332C2#1175418814yesdirect product factor
333C2C2×#9200412yes—
334C2C23×D5×Dic311yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC22×C3×C5C25
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#519
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
5. #11754188C2direct (N × H)
6. C2×#91331C2semidirect
7. C2×Dic3×Dic10C2semidirect
11. C22×C3×Dic10C4semidirect
26. #91331C22semidirect
27. Dic3×Dic10C22semidirect
48. C2×C3×Dic10C2×C4semidirect
68. C22×Dic10Dic3semidirect
135. C2×Dic10C2×Dic3semidirect
225. C2×C3×C5#519semidirect
280. C3×C5C2×#519semidirect
293. C2×C5#5812semidirect
315. C2×C3#65850semidirect
318. C5C2×#5812semidirect
330. C3C2×#65850semidirect
332. C2#11754188direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic102
C2×#918152
C2×C5×#9262
C2×#915282
#117541882
C2×#913312
C2×Dic3×Dic102
C2×#658503
C2×#58125