Subgroups — C₃×#10600342 #14299100

Order 1920.

496 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3940	C₂	1	2	yes	maximal
3	C₂×C₃×#3939	C₂	1	2	yes	maximal
4	C₃×#65225	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic
6	#10600342	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
10	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
11	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
12	C₃×C₅×#95	—	2	2	no	—
13	C₃×#3963	—	2	2	no	—
14	C₃×#3940	—	2	4	no	—
15	C₃×#3939	—	2	4	no	—
16	C₃×C₄×#168	C₄	1	4	yes	complemented
17	C₃×#1846	—	5	1	no	maximal, Hall
18	C₅×#382	C₂×C₃	1	1	yes	characteristic
19	C₂×#3940	C₂×C₃	1	2	yes	—
20	C₂×#3939	C₂×C₃	1	2	yes	—
21	#65225	C₂×C₃	1	1	yes	characteristic
22	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₃×C₄×C₅	—	2	2	no	—
24	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
25	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
26	C₂²×C₃×Dic₅	—	2	2	no	—
27	C₃×C₅×C₄⋊C₄	—	2	2	no	—
28	C₃×C₅×C₄⋊C₄	—	2	2	no	—
29	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
30	C₃×C₄²×C₅	Q₈	1	2	yes	—
31	C₃×C₄⋊Dic₅	—	2	2	no	—
32	C₃×C₄⋊Dic₅	—	2	2	no	—
33	C₂×C₃×#168	C₂×C₄	1	2	yes	—
34	C₂×C₃×#168	C₂×C₄	1	2	yes	—
35	C₂×C₃×#168	D₄	1	2	yes	—
36	C₂×C₃×#168	D₄	1	2	yes	—
37	C₂×C₃×#168	Q₈	1	2	yes	—
38	C₂×C₃×#168	Q₈	1	2	yes	—
39	C₂×C₃×#107	—	5	2	no	—
40	C₂×C₃×#106	—	5	2	no	—
41	C₂×C₃×C₄×C₈	—	5	1	no	—
42	C₃×#382	—	5	1	no	—
43	C₃×#382	D₅	1	1	yes	characteristic
44	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
45	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
46	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
47	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
48	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
49	C₅×#95	—	2	2	no	—
50	#3963	—	2	2	no	—
51	#3940	—	2	4	no	—
52	#3939	—	2	4	no	—
53	C₄×#168	C₃×C₄	1	4	yes	complemented
54	#1846	—	5	1	no	Sylow
55	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
56	C₂×C₃×C₄×C₅	—	2	4	no	—
57	C₂×C₃×C₄×C₅	—	4	2	no	—
58	C₂×C₃×C₄×C₅	—	4	4	no	—
59	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
60	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
63	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₃×Dic₅	—	4	2	no	—
67	C₂×C₃×Dic₅	—	4	4	no	—
68	C₃×#168	C₄⋊C₄	1	4	yes	—
69	C₃×#168	C₄⋊C₄	1	4	yes	—
70	C₂²×C₃×C₈	—	5	1	no	—
71	C₂²×C₃×C₈	—	5	1	no	—
72	C₂×C₃×C₄⋊C₄	—	5	2	no	—
73	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
74	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
75	C₃×#107	—	10	4	no	—
76	C₃×#106	—	10	4	no	—
77	C₃×C₄×C₈	—	5	4	no	—
78	C₃×#95	—	2	2	no	—
79	C₃×#95	—	10	2	no	—
80	C₂²×C₄×C₅	—	2	2	no	—
81	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
82	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
83	C₂²×Dic₅	—	2	2	no	—
84	C₅×C₄⋊C₄	—	2	2	no	—
85	C₅×C₄⋊C₄	—	2	2	no	—
86	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
87	C₄²×C₅	C₃×Q₈	1	2	yes	—
88	C₄⋊Dic₅	—	2	2	no	—
89	C₄⋊Dic₅	—	2	2	no	—
90	C₂×#168	C₂×C₃×C₄	1	2	yes	—
91	C₂×#168	C₂×C₃×C₄	1	2	yes	—
92	C₂×#168	C₃×D₄	1	2	yes	—
93	C₂×#168	C₃×D₄	1	2	yes	—
94	C₂×#168	C₃×Q₈	1	2	yes	—
95	C₂×#168	C₃×Q₈	1	2	yes	—
96	C₂×#107	—	5	2	no	—
97	C₂×#106	—	5	2	no	—
98	C₂×C₄×C₈	—	5	1	no	—
99	#382	—	5	1	no	—
100	#382	C₃×D₅	1	1	yes	characteristic
101	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₃×C₅	#127	1	1	yes	characteristic
103	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
104	C₂²×C₃×C₅	#135	1	4	yes	—
105	C₃×C₄×C₅	—	2	4	no	—
106	C₃×C₄×C₅	—	8	2	no	—
107	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
110	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
111	C₃×Dic₅	—	8	2	no	—
112	C₂²×C₃×C₄	—	2	2	no	—
113	C₂²×C₃×C₄	—	10	2	no	—
114	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
115	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
116	C₂×C₃×C₈	—	5	2	no	—
117	C₂×C₃×C₈	—	5	2	no	—
118	C₂×C₃×C₈	—	5	2	no	—
119	C₂×C₃×C₈	—	5	2	no	—
120	C₂×C₃×C₈	—	5	2	no	—
121	C₂×C₃×C₈	—	5	2	no	—
122	C₃×C₄⋊C₄	—	2	2	no	—
123	C₃×C₄⋊C₄	—	2	2	no	—
124	C₃×C₄⋊C₄	—	10	2	no	—
125	C₃×C₄⋊C₄	—	10	2	no	—
126	C₃×C₄²	Dic₁₀	1	2	yes	—
127	C₃×C₄²	C₄×D₅	1	2	yes	—
128	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
129	C₂×C₄×C₅	—	2	4	no	—
130	C₂×C₄×C₅	—	4	2	no	—
131	C₂×C₄×C₅	—	4	4	no	—
132	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
133	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
134	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
135	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
136	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
138	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
139	C₂×Dic₅	—	4	2	no	—
140	C₂×Dic₅	—	4	4	no	—
141	#168	C₃×C₄⋊C₄	1	4	yes	—
142	#168	C₃×C₄⋊C₄	1	4	yes	—
143	C₂²×C₈	—	5	1	no	—
144	C₂²×C₈	—	5	1	no	—
145	C₂×C₄⋊C₄	—	5	2	no	—
146	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
147	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
148	#107	—	10	4	no	—
149	#106	—	10	4	no	—
150	C₄×C₈	—	5	4	no	—
151	#95	—	2	2	no	—
152	#95	—	10	2	no	—
153	C₂×C₃×C₅	#384	1	1	yes	characteristic
154	C₂×C₃×C₅	#427	1	2	yes	—
155	C₂×C₃×C₅	#495	1	2	yes	—
156	C₂×C₃×C₅	#499	1	2	yes	—
157	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
158	C₂×C₃×C₄	—	2	4	no	—
159	C₂×C₃×C₄	—	4	4	no	—
160	C₂×C₃×C₄	—	4	2	no	—
161	C₂×C₃×C₄	—	20	4	no	—
162	C₂×C₃×C₄	—	20	2	no	—
163	C₂×C₃×C₄	#683	1	4	yes	—
164	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
165	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
166	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
167	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
168	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
169	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
170	C₃×C₈	—	5	4	no	—
171	C₃×C₈	—	5	4	no	—
172	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₅	C₃×#127	1	1	yes	characteristic
174	C₂²×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
175	C₂²×C₅	C₃×#135	1	4	yes	—
176	C₄×C₅	—	2	4	no	—
177	C₄×C₅	—	8	2	no	—
178	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
179	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
180	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
181	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
182	Dic₅	—	8	2	no	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	10	2	no	—
185	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
186	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
187	C₂×C₈	—	5	2	no	—
188	C₂×C₈	—	5	2	no	—
189	C₂×C₈	—	5	2	no	—
190	C₂×C₈	—	5	2	no	—
191	C₂×C₈	—	5	2	no	—
192	C₂×C₈	—	5	2	no	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	10	2	no	—
196	C₄⋊C₄	—	10	2	no	—
197	C₄²	C₃×Dic₁₀	1	2	yes	—
198	C₄²	C₃×C₄×D₅	1	2	yes	—
199	C₃×C₅	#1846	1	1	yes	characteristic, complemented, Hall
200	C₂²×C₃	C₂×#683	1	1	yes	characteristic
201	C₂²×C₃	#4086	1	1	yes	characteristic
202	C₂²×C₃	#4090	1	1	yes	characteristic
203	C₂²×C₃	#4096	1	4	yes	—
204	C₃×C₄	—	2	4	no	—
205	C₃×C₄	—	8	2	no	—
206	C₃×C₄	—	40	2	no	—
207	C₃×C₄	#4034	1	1	yes	characteristic
208	C₃×C₄	#4034	1	1	yes	characteristic
209	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
210	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₅	C₃×#384	1	1	yes	characteristic
212	C₂×C₅	C₃×#427	1	2	yes	—
213	C₂×C₅	C₃×#495	1	2	yes	—
214	C₂×C₅	C₃×#499	1	2	yes	—
215	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	4	no	—
219	C₂×C₄	—	20	2	no	—
220	C₂×C₄	—	20	4	no	—
221	C₂×C₄	C₃×#683	1	4	yes	—
222	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
223	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
224	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
225	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
226	C₂×C₄	C₃×Q₈×D₅	1	1	yes	characteristic
227	C₂×C₄	C₃×Q₈×D₅	1	1	yes	characteristic
228	C₈	—	5	4	no	—
229	C₈	—	5	4	no	—
230	C₂×C₃	#65265	1	1	yes	characteristic
231	C₂×C₃	#65287	1	2	yes	—
232	C₂×C₃	#65348	1	2	yes	—
233	C₂×C₃	#65353	1	2	yes	—
234	C₅	C₃×#1846	1	1	yes	characteristic, complemented, Sylow
235	C₂²	C₂×C₃×#683	1	1	yes	characteristic
236	C₂²	C₃×#4086	1	1	yes	characteristic
237	C₂²	C₃×#4090	1	1	yes	characteristic
238	C₂²	C₃×#4096	1	4	yes	—
239	C₄	—	2	4	no	—
240	C₄	—	8	2	no	—
241	C₄	—	40	2	no	—
242	C₄	C₃×#4034	1	1	yes	characteristic
243	C₄	C₃×#4034	1	1	yes	characteristic
244	C₄	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
245	C₄	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
246	C₃	#10600342	1	1	yes	characteristic, direct product factor, Sylow
247	C₂	C₃×#65265	1	1	yes	characteristic
248	C₂	C₃×#65287	1	2	yes	—
249	C₂	C₃×#65348	1	2	yes	—
250	C₂	C₃×#65353	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#382	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#382	D₅
hypocenter	C₅	C₃×#1846
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#382

Complements

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

N	H ≅ G/N	type
6. #10600342	C₃	direct (N × H)
16. C₃×C₄×#168	C₄	semidirect
53. C₄×#168	C₃×C₄	semidirect
199. C₃×C₅	#1846	semidirect
234. C₅	C₃×#1846	semidirect
246. C₃	#10600342	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#382	2
C₂×C₃×#3940	2
C₂×C₃×#3939	2
C₃×#65225	2
C₂×C₃×C₄×#168	2
#10600342	3
C₃×#1846	5

Subgroups — C3×#10600342 #14299100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600342 #14299100