Subgroups — C₃×C₅×#1952 #14274986

Order 1920.

392 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#428	C₂	1	2	yes	maximal
3	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#343	C₂	1	2	yes	maximal
6	C₅×#1952	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
8	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₃×C₅×#108	C₄	1	4	yes	complemented
13	C₃×C₅×#107	—	2	1	no	—
14	C₃×C₅×#107	—	2	1	no	—
15	C₃×C₅×#107	—	2	2	no	—
16	C₃×C₅×#106	—	2	2	no	—
17	C₃×C₅×#97	—	2	1	no	—
18	C₃×C₄×C₅×C₈	—	2	1	no	—
19	C₃×#1952	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic
21	C₅×#428	C₂×C₃	1	2	yes	—
22	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic
23	C₅×#405	C₂×C₃	1	1	yes	characteristic
24	C₅×#343	C₂×C₃	1	2	yes	—
25	C₂²×C₃×C₄×C₅	—	2	2	no	—
26	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
27	C₃×C₅×M₁₆	—	2	2	no	—
28	C₃×C₅×M₁₆	—	2	1	no	—
29	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	—
30	C₃×C₅×M₁₆	Q₈	1	2	yes	—
31	C₂×C₃×C₅×C₈	—	2	1	no	—
32	C₂×C₃×C₅×C₈	—	2	2	no	—
33	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
34	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
35	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
36	C₂×C₃×C₅×C₈	Q₈	1	2	yes	—
37	C₃×C₅×C₄⋊C₄	—	2	2	no	—
38	C₃×C₅×C₄⋊C₄	—	2	2	no	—
39	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
40	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
41	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
42	C₃×C₄²×C₅	—	2	1	no	—
43	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic
44	C₃×#428	C₂×C₅	1	2	yes	—
45	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic
46	C₃×#405	C₂×C₅	1	1	yes	characteristic
47	C₃×#343	C₂×C₅	1	2	yes	—
48	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
49	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
51	C₅×#117	C₂²×C₃	1	1	yes	characteristic
52	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
53	C₅×#108	C₃×C₄	1	4	yes	complemented
54	C₅×#107	—	2	1	no	—
55	C₅×#107	—	2	1	no	—
56	C₅×#107	—	2	2	no	—
57	C₅×#106	—	2	2	no	—
58	C₅×#97	—	2	1	no	—
59	C₄×C₅×C₈	—	2	1	no	—
60	#1952	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
61	C₂³×C₃×C₅	#41	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	—	2	1	no	—
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	—	4	2	no	—
65	C₂×C₃×C₄×C₅	—	8	2	no	—
66	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
68	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
70	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
71	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
72	C₃×C₅×C₈	—	2	4	no	—
73	C₃×C₅×C₈	—	2	2	no	—
74	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
75	C₃×C₅×C₈	C₄⋊C₄	1	2	yes	—
76	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
77	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
78	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
79	C₃×#117	C₂²×C₅	1	1	yes	characteristic
80	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
81	C₃×#108	C₄×C₅	1	4	yes	complemented
82	C₃×#107	—	2	1	no	—
83	C₃×#107	—	2	1	no	—
84	C₃×#107	—	2	2	no	—
85	C₃×#106	—	2	2	no	—
86	C₃×#97	—	2	1	no	—
87	C₃×C₄×C₈	—	2	1	no	—
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
90	C₅×M₁₆	—	2	2	no	—
91	C₅×M₁₆	—	2	1	no	—
92	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	—
93	C₅×M₁₆	C₃×Q₈	1	2	yes	—
94	C₂×C₅×C₈	—	2	1	no	—
95	C₂×C₅×C₈	—	2	2	no	—
96	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
97	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
98	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
99	C₂×C₅×C₈	C₃×Q₈	1	2	yes	—
100	C₅×C₄⋊C₄	—	2	2	no	—
101	C₅×C₄⋊C₄	—	2	2	no	—
102	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
103	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
104	C₅×C₂²⋊C₄	—	2	1	no	—
105	C₄²×C₅	—	2	1	no	—
106	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic
107	#428	C₂×C₃×C₅	1	2	yes	—
108	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic
109	#405	C₂×C₃×C₅	1	1	yes	characteristic
110	#343	C₂×C₃×C₅	1	2	yes	—
111	C₂²×C₃×C₅	—	2	1	no	—
112	C₂²×C₃×C₅	—	2	1	no	—
113	C₂²×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
114	C₂²×C₃×C₅	#121	1	1	yes	characteristic
115	C₂²×C₃×C₅	#125	1	1	yes	characteristic
116	C₃×C₄×C₅	—	4	1	no	—
117	C₃×C₄×C₅	—	4	1	no	—
118	C₃×C₄×C₅	—	8	2	no	—
119	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
121	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
122	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
123	C₂²×C₃×C₄	—	2	2	no	—
124	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
125	C₃×M₁₆	—	2	2	no	—
126	C₃×M₁₆	—	2	1	no	—
127	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	—
128	C₃×M₁₆	C₅×Q₈	1	2	yes	—
129	C₂×C₃×C₈	—	2	1	no	—
130	C₂×C₃×C₈	—	2	2	no	—
131	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
132	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
133	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
134	C₂×C₃×C₈	C₅×Q₈	1	2	yes	—
135	C₃×C₄⋊C₄	—	2	2	no	—
136	C₃×C₄⋊C₄	—	2	2	no	—
137	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
138	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
139	C₃×C₂²⋊C₄	—	2	1	no	—
140	C₃×C₄²	—	2	1	no	—
141	C₂³×C₅	C₃×#41	1	1	yes	characteristic
142	C₂×C₄×C₅	—	2	1	no	—
143	C₂×C₄×C₅	—	2	1	no	—
144	C₂×C₄×C₅	—	4	2	no	—
145	C₂×C₄×C₅	—	8	2	no	—
146	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
147	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
148	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
149	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
152	C₅×C₈	—	2	4	no	—
153	C₅×C₈	—	2	2	no	—
154	C₅×C₈	C₃×C₄⋊C₄	1	2	yes	—
155	C₅×C₈	C₃×C₄⋊C₄	1	2	yes	—
156	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
157	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
158	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
159	#117	C₂²×C₃×C₅	1	1	yes	characteristic
160	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
161	#108	C₃×C₄×C₅	1	4	yes	complemented
162	#107	—	2	1	no	—
163	#107	—	2	1	no	—
164	#107	—	2	2	no	—
165	#106	—	2	2	no	—
166	#97	—	2	1	no	—
167	C₄×C₈	—	2	1	no	—
168	C₂×C₃×C₅	—	2	1	no	—
169	C₂×C₃×C₅	—	2	1	no	—
170	C₂×C₃×C₅	#389	1	1	yes	characteristic
171	C₂×C₃×C₅	#472	1	1	yes	characteristic
172	C₂×C₃×C₅	#473	1	1	yes	characteristic
173	C₂³×C₃	C₅×#41	1	1	yes	characteristic
174	C₂×C₃×C₄	—	2	1	no	—
175	C₂×C₃×C₄	—	2	1	no	—
176	C₂×C₃×C₄	—	4	2	no	—
177	C₂×C₃×C₄	—	8	2	no	—
178	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
179	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
180	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
181	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
182	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
183	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
184	C₃×C₈	—	2	4	no	—
185	C₃×C₈	—	2	2	no	—
186	C₃×C₈	C₅×C₄⋊C₄	1	2	yes	—
187	C₃×C₈	C₅×C₄⋊C₄	1	2	yes	—
188	C₂²×C₅	—	2	1	no	—
189	C₂²×C₅	—	2	1	no	—
190	C₂²×C₅	C₃×C₄×Q₈	1	1	yes	characteristic
191	C₂²×C₅	C₃×#121	1	1	yes	characteristic
192	C₂²×C₅	C₃×#125	1	1	yes	characteristic
193	C₄×C₅	—	4	1	no	—
194	C₄×C₅	—	4	1	no	—
195	C₄×C₅	—	8	2	no	—
196	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
197	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
198	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
199	C₄×C₅	C₃×C₄⋊Q₈	1	1	yes	characteristic
200	C₂²×C₄	—	2	2	no	—
201	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
202	M₁₆	—	2	2	no	—
203	M₁₆	—	2	1	no	—
204	M₁₆	C₂×C₃×C₄×C₅	1	4	yes	—
205	M₁₆	C₃×C₅×Q₈	1	2	yes	—
206	C₂×C₈	—	2	1	no	—
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
209	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
210	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
211	C₂×C₈	C₃×C₅×Q₈	1	2	yes	—
212	C₄⋊C₄	—	2	2	no	—
213	C₄⋊C₄	—	2	2	no	—
214	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
215	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
216	C₂²⋊C₄	—	2	1	no	—
217	C₄²	—	2	1	no	—
218	C₃×C₅	#1952	1	1	yes	characteristic, direct product factor, Hall
219	C₂²×C₃	—	2	1	no	—
220	C₂²×C₃	—	2	1	no	—
221	C₂²×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
222	C₂²×C₃	C₅×#121	1	1	yes	characteristic
223	C₂²×C₃	C₅×#125	1	1	yes	characteristic
224	C₃×C₄	—	4	1	no	—
225	C₃×C₄	—	4	1	no	—
226	C₃×C₄	—	8	2	no	—
227	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
228	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
229	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
230	C₃×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
231	C₂×C₅	—	2	1	no	—
232	C₂×C₅	—	2	1	no	—
233	C₂×C₅	C₃×#389	1	1	yes	characteristic
234	C₂×C₅	C₃×#472	1	1	yes	characteristic
235	C₂×C₅	C₃×#473	1	1	yes	characteristic
236	C₂³	C₃×C₅×#41	1	1	yes	characteristic
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	8	2	no	—
241	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
242	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
243	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
244	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
245	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
246	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
247	C₈	—	2	4	no	—
248	C₈	—	2	2	no	—
249	C₈	C₃×C₅×C₄⋊C₄	1	2	yes	—
250	C₈	C₃×C₅×C₄⋊C₄	1	2	yes	—
251	C₂×C₃	—	2	1	no	—
252	C₂×C₃	—	2	1	no	—
253	C₂×C₃	C₅×#389	1	1	yes	characteristic
254	C₂×C₃	C₅×#472	1	1	yes	characteristic
255	C₂×C₃	C₅×#473	1	1	yes	characteristic
256	C₅	C₃×#1952	1	1	yes	characteristic, direct product factor, Sylow
257	C₂²	—	2	1	no	—
258	C₂²	—	2	1	no	—
259	C₂²	C₃×C₄×C₅×Q₈	1	1	yes	characteristic
260	C₂²	C₃×C₅×#121	1	1	yes	characteristic
261	C₂²	C₃×C₅×#125	1	1	yes	characteristic
262	C₄	—	4	1	no	—
263	C₄	—	4	1	no	—
264	C₄	—	8	2	no	—
265	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
266	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
267	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
268	C₄	C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
269	C₃	C₅×#1952	1	1	yes	characteristic, direct product factor, Sylow
270	C₂	—	2	1	no	—
271	C₂	—	2	1	no	—
272	C₂	C₃×C₅×#389	1	1	yes	characteristic
273	C₂	C₃×C₅×#472	1	1	yes	characteristic
274	C₂	C₃×C₅×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#121
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂³×C₃×C₅	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₅×#1952	C₃	direct (N × H)
12. C₃×C₅×#108	C₄	semidirect
19. C₃×#1952	C₅	direct (N × H)
53. C₅×#108	C₃×C₄	semidirect
60. #1952	C₃×C₅	direct (N × H)
81. C₃×#108	C₄×C₅	semidirect
161. #108	C₃×C₄×C₅	semidirect
218. C₃×C₅	#1952	direct (N × H)
256. C₅	C₃×#1952	direct (N × H)
269. C₃	C₅×#1952	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×#108	2
C₃×C₅×#428	2
C₂×C₃×C₅×#107	2
C₃×C₅×#405	2
C₃×C₅×#343	2
C₅×#1952	3
C₃×#1952	5

Subgroups — C3×C5×#1952 #14274986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1952 #14274986