Subgroups — C₃×C₅×#2095 #14275129

Order 1920.

508 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#107	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal
3	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic
6	C₅×#2095	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#107	—	2	4	no	—
14	C₃×C₅×#103	—	2	4	no	—
15	C₃×C₅×#95	—	2	2	no	—
16	C₃×#2095	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×#107	C₂×C₃	1	2	yes	—
18	C₂×C₅×#103	C₂×C₃	1	2	yes	—
19	C₅×#391	C₂×C₃	1	1	yes	characteristic
20	C₅×#384	C₂×C₃	1	1	yes	characteristic
21	C₅×#336	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×C₅×Q₈	—	2	1	no	—
23	C₂×C₃×C₅×Q₈	—	2	2	no	—
24	C₂×C₃×C₅×Q₈	—	2	2	no	—
25	C₂×C₃×C₅×Q₈	Q₈	1	2	yes	—
26	C₂²×C₃×C₄×C₅	—	2	1	no	—
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	1	no	—
29	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂×C₃×C₅×C₈	—	2	2	no	—
32	C₂×C₃×C₅×C₈	—	2	2	no	—
33	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
34	C₃×C₅×C₄⋊C₄	—	2	2	no	—
35	C₃×C₅×C₄⋊C₄	—	2	2	no	—
36	C₃×C₅×C₄⋊C₄	—	2	2	no	—
37	C₃×C₅×C₄⋊C₄	—	4	4	no	—
38	C₃×C₄²×C₅	—	2	2	no	—
39	C₂×C₃×#107	C₂×C₅	1	2	yes	—
40	C₂×C₃×#103	C₂×C₅	1	2	yes	—
41	C₃×#391	C₂×C₅	1	1	yes	characteristic
42	C₃×#384	C₂×C₅	1	1	yes	characteristic
43	C₃×#336	C₂×C₅	1	1	yes	characteristic
44	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
46	C₂×C₅×C₄⋊C₄	—	2	2	no	—
47	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
48	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
49	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
50	C₅×#107	—	2	4	no	—
51	C₅×#103	—	2	4	no	—
52	C₅×#95	—	2	2	no	—
53	#2095	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
54	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
55	C₃×C₅×Q₈	—	2	4	no	—
56	C₃×C₅×Q₈	—	4	2	no	—
57	C₂×C₃×C₄×C₅	—	2	2	no	—
58	C₂×C₃×C₄×C₅	—	2	2	no	—
59	C₂×C₃×C₄×C₅	—	2	2	no	—
60	C₂×C₃×C₄×C₅	—	4	1	no	—
61	C₂×C₃×C₄×C₅	—	4	1	no	—
62	C₂×C₃×C₄×C₅	—	4	2	no	—
63	C₂×C₃×C₄×C₅	—	4	1	no	—
64	C₂×C₃×C₄×C₅	—	4	4	no	—
65	C₂×C₃×C₄×C₅	—	4	2	no	—
66	C₂×C₃×C₄×C₅	Q₁₆	1	4	yes	—
67	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
68	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	#41	1	2	yes	—
70	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
71	C₃×C₅×C₈	—	2	4	no	—
72	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
73	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
74	C₂×C₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
76	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
77	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
78	C₃×#107	—	2	4	no	—
79	C₃×#103	—	2	4	no	—
80	C₃×#95	—	2	2	no	—
81	C₂×C₅×Q₈	—	2	1	no	—
82	C₂×C₅×Q₈	—	2	2	no	—
83	C₂×C₅×Q₈	—	2	2	no	—
84	C₂×C₅×Q₈	C₃×Q₈	1	2	yes	—
85	C₂²×C₄×C₅	—	2	1	no	—
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	—	2	1	no	—
88	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
89	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
90	C₂×C₅×C₈	—	2	2	no	—
91	C₂×C₅×C₈	—	2	2	no	—
92	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
93	C₅×C₄⋊C₄	—	2	2	no	—
94	C₅×C₄⋊C₄	—	2	2	no	—
95	C₅×C₄⋊C₄	—	2	2	no	—
96	C₅×C₄⋊C₄	—	4	4	no	—
97	C₄²×C₅	—	2	2	no	—
98	C₂×#107	C₂×C₃×C₅	1	2	yes	—
99	C₂×#103	C₂×C₃×C₅	1	2	yes	—
100	#391	C₂×C₃×C₅	1	1	yes	characteristic
101	#384	C₂×C₃×C₅	1	1	yes	characteristic
102	#336	C₂×C₃×C₅	1	1	yes	characteristic
103	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
104	C₂²×C₃×C₅	#123	1	1	yes	characteristic
105	C₂²×C₃×C₅	#127	1	1	yes	characteristic
106	C₂²×C₃×C₅	C₂×Q₁₆	1	2	yes	—
107	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
108	C₃×C₄×C₅	—	2	4	no	—
109	C₃×C₄×C₅	—	4	2	no	—
110	C₃×C₄×C₅	—	8	2	no	—
111	C₃×C₄×C₅	—	8	1	no	—
112	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
113	C₃×C₄×C₅	#123	1	2	yes	—
114	C₂×C₃×Q₈	—	2	1	no	—
115	C₂×C₃×Q₈	—	2	2	no	—
116	C₂×C₃×Q₈	—	2	2	no	—
117	C₂×C₃×Q₈	C₅×Q₈	1	2	yes	—
118	C₂²×C₃×C₄	—	2	1	no	—
119	C₂²×C₃×C₄	—	2	1	no	—
120	C₂²×C₃×C₄	—	2	2	no	—
121	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
122	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
123	C₂×C₃×C₈	—	2	2	no	—
124	C₂×C₃×C₈	—	2	2	no	—
125	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
126	C₃×C₄⋊C₄	—	2	2	no	—
127	C₃×C₄⋊C₄	—	2	2	no	—
128	C₃×C₄⋊C₄	—	2	2	no	—
129	C₃×C₄⋊C₄	—	4	4	no	—
130	C₃×C₄²	—	2	2	no	—
131	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
132	C₅×Q₈	—	2	4	no	—
133	C₅×Q₈	—	4	2	no	—
134	C₂×C₄×C₅	—	2	2	no	—
135	C₂×C₄×C₅	—	2	2	no	—
136	C₂×C₄×C₅	—	2	2	no	—
137	C₂×C₄×C₅	—	4	1	no	—
138	C₂×C₄×C₅	—	4	1	no	—
139	C₂×C₄×C₅	—	4	2	no	—
140	C₂×C₄×C₅	—	4	1	no	—
141	C₂×C₄×C₅	—	4	4	no	—
142	C₂×C₄×C₅	—	4	2	no	—
143	C₂×C₄×C₅	C₃×Q₁₆	1	4	yes	—
144	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
145	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₅	C₃×#41	1	2	yes	—
147	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
148	C₅×C₈	—	2	4	no	—
149	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
150	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
153	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
154	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
155	#107	—	2	4	no	—
156	#103	—	2	4	no	—
157	#95	—	2	2	no	—
158	C₂×C₃×C₅	#399	1	1	yes	characteristic
159	C₂×C₃×C₅	#477	1	2	yes	—
160	C₂×C₃×C₅	#484	1	2	yes	—
161	C₂×C₃×C₅	#494	1	1	yes	characteristic
162	C₂×C₃×C₅	#496	1	1	yes	characteristic
163	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
164	C₃×Q₈	—	2	4	no	—
165	C₃×Q₈	—	4	2	no	—
166	C₂×C₃×C₄	—	2	2	no	—
167	C₂×C₃×C₄	—	2	2	no	—
168	C₂×C₃×C₄	—	2	2	no	—
169	C₂×C₃×C₄	—	4	1	no	—
170	C₂×C₃×C₄	—	4	1	no	—
171	C₂×C₃×C₄	—	4	2	no	—
172	C₂×C₃×C₄	—	4	1	no	—
173	C₂×C₃×C₄	—	4	4	no	—
174	C₂×C₃×C₄	—	4	2	no	—
175	C₂×C₃×C₄	C₅×Q₁₆	1	4	yes	—
176	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
177	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
178	C₂×C₃×C₄	C₅×#41	1	2	yes	—
179	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
180	C₃×C₈	—	2	4	no	—
181	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
182	C₂²×C₅	C₃×#123	1	1	yes	characteristic
183	C₂²×C₅	C₃×#127	1	1	yes	characteristic
184	C₂²×C₅	C₂×C₃×Q₁₆	1	2	yes	—
185	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
186	C₄×C₅	—	2	4	no	—
187	C₄×C₅	—	4	2	no	—
188	C₄×C₅	—	8	2	no	—
189	C₄×C₅	—	8	1	no	—
190	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
191	C₄×C₅	C₃×#123	1	2	yes	—
192	C₂×Q₈	—	2	1	no	—
193	C₂×Q₈	—	2	2	no	—
194	C₂×Q₈	—	2	2	no	—
195	C₂×Q₈	C₃×C₅×Q₈	1	2	yes	—
196	C₂²×C₄	—	2	1	no	—
197	C₂²×C₄	—	2	1	no	—
198	C₂²×C₄	—	2	2	no	—
199	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
200	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₄⋊C₄	—	2	2	no	—
207	C₄⋊C₄	—	4	4	no	—
208	C₄²	—	2	2	no	—
209	C₃×C₅	#2095	1	1	yes	characteristic, direct product factor, Hall
210	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
211	C₂²×C₃	C₅×#123	1	1	yes	characteristic
212	C₂²×C₃	C₅×#127	1	1	yes	characteristic
213	C₂²×C₃	C₂×C₅×Q₁₆	1	2	yes	—
214	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
215	C₃×C₄	—	2	4	no	—
216	C₃×C₄	—	4	2	no	—
217	C₃×C₄	—	8	2	no	—
218	C₃×C₄	—	8	1	no	—
219	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
220	C₃×C₄	C₅×#123	1	2	yes	—
221	C₂×C₅	C₃×#399	1	1	yes	characteristic
222	C₂×C₅	C₃×#477	1	2	yes	—
223	C₂×C₅	C₃×#484	1	2	yes	—
224	C₂×C₅	C₃×#494	1	1	yes	characteristic
225	C₂×C₅	C₃×#496	1	1	yes	characteristic
226	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
227	Q₈	—	2	4	no	—
228	Q₈	—	4	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	4	1	no	—
233	C₂×C₄	—	4	1	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	1	no	—
236	C₂×C₄	—	4	4	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	C₃×C₅×Q₁₆	1	4	yes	—
239	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
240	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
241	C₂×C₄	C₃×C₅×#41	1	2	yes	—
242	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
243	C₈	—	2	4	no	—
244	C₂×C₃	C₅×#399	1	1	yes	characteristic
245	C₂×C₃	C₅×#477	1	2	yes	—
246	C₂×C₃	C₅×#484	1	2	yes	—
247	C₂×C₃	C₅×#494	1	1	yes	characteristic
248	C₂×C₃	C₅×#496	1	1	yes	characteristic
249	C₅	C₃×#2095	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
251	C₂²	C₃×C₅×#123	1	1	yes	characteristic
252	C₂²	C₃×C₅×#127	1	1	yes	characteristic
253	C₂²	C₂×C₃×C₅×Q₁₆	1	2	yes	—
254	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
255	C₄	—	2	4	no	—
256	C₄	—	4	2	no	—
257	C₄	—	8	2	no	—
258	C₄	—	8	1	no	—
259	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
260	C₄	C₃×C₅×#123	1	2	yes	—
261	C₃	C₅×#2095	1	1	yes	characteristic, direct product factor, Sylow
262	C₂	C₃×C₅×#399	1	1	yes	characteristic
263	C₂	C₃×C₅×#477	1	2	yes	—
264	C₂	C₃×C₅×#484	1	2	yes	—
265	C₂	C₃×C₅×#494	1	1	yes	characteristic
266	C₂	C₃×C₅×#496	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#2095	C₃	direct (N × H)
16. C₃×#2095	C₅	direct (N × H)
53. #2095	C₃×C₅	direct (N × H)
209. C₃×C₅	#2095	direct (N × H)
249. C₅	C₃×#2095	direct (N × H)
261. C₃	C₅×#2095	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#107	2
C₂×C₃×C₅×#103	2
C₃×C₅×#391	2
C₃×C₅×#384	2
C₃×C₅×#336	2
C₅×#2095	3
C₃×#2095	5

Subgroups — C3×C5×#2095 #14275129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2095 #14275129