Subgroups — C₂×C₃×D₅×#127 #14479959

Order 1920.

6000 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄×D₅	C₂	1	6	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4086	C₂	1	6	yes	maximal, complemented
4	C₃×D₅×#127	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₅×#127	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃×D₅	C₂²	1	4	yes	—
9	C₂²×C₃×C₅×D₄	C₂²	1	6	yes	complemented
10	C₂²×C₃×C₂²⋊D₅	C₂²	1	12	yes	complemented
11	C₂×C₃×D₄×D₅	—	2	48	no	—
12	C₂×C₃×D₄×D₅	C₂²	1	48	yes	complemented
13	C₂²×C₃×D₂₀	C₂²	1	6	yes	complemented
14	C₂²×C₃×C₄×D₅	C₂²	1	3	yes	—
15	C₃×C₅×#127	C₂²	1	8	yes	complemented
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
17	C₃×#4086	C₂²	1	48	yes	complemented
18	C₂×C₃×C₄×Dic₅	C₂²	1	3	yes	complemented
19	C₃×#4020	C₂²	1	8	yes	complemented
20	C₃×C₄²×D₅	C₂²	1	8	yes	complemented
21	C₂²×C₃×#127	—	5	1	no	maximal, Hall
22	C₂²×D₄×D₅	C₂×C₃	1	6	yes	complemented
23	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×#4086	C₂×C₃	1	6	yes	complemented
25	D₅×#127	C₂×C₃	1	16	yes	direct product factor
26	C₂×#4020	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
29	C₂³×C₃×D₅	—	2	48	no	—
30	C₂³×C₃×D₅	C₂³	1	4	yes	—
31	C₂³×C₃×D₅	C₂³	1	16	yes	—
32	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
33	C₂×C₃×C₅×D₄	—	2	24	no	—
34	C₂×C₃×C₅×D₄	C₂³	1	24	yes	complemented
35	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
36	C₂×C₃×C₂²⋊D₅	—	2	48	no	—
37	C₂×C₃×C₂²⋊D₅	C₂³	1	48	yes	complemented
38	C₂²×C₃×Dic₅	C₂³	1	3	yes	—
39	C₃×D₄×D₅	—	2	192	no	—
40	C₂×C₃×D₂₀	—	2	24	no	—
41	C₂×C₃×D₂₀	C₂³	1	24	yes	complemented
42	C₂×C₃×C₄×D₅	D₄	1	24	yes	complemented
43	C₂×C₃×C₄×D₅	C₂³	1	12	yes	—
44	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
45	C₃×C₄×Dic₅	C₂³	1	12	yes	complemented
46	C₂³×C₃×D₄	—	5	6	no	—
47	C₂×C₃×#127	—	5	6	no	—
48	C₂×C₃×#127	—	5	16	no	—
49	C₂×C₃×#127	—	5	1	no	—
50	C₂×C₃×#127	D₅	1	1	yes	characteristic, direct product factor
51	C₂²×C₃×C₄²	—	5	1	no	—
52	C₂⁴×D₅	C₂²×C₃	1	4	yes	—
53	C₂²×C₅×D₄	C₂²×C₃	1	6	yes	complemented
54	C₂²×C₂²⋊D₅	C₂²×C₃	1	12	yes	complemented
55	C₂×D₄×D₅	—	2	48	no	—
56	C₂×D₄×D₅	C₂²×C₃	1	48	yes	complemented
57	C₂²×D₂₀	C₂²×C₃	1	6	yes	complemented
58	C₂²×C₄×D₅	C₂²×C₃	1	3	yes	—
59	C₅×#127	C₂²×C₃	1	8	yes	complemented
60	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
61	#4086	C₂²×C₃	1	48	yes	complemented
62	C₂×C₄×Dic₅	C₂²×C₃	1	3	yes	complemented
63	#4020	C₂²×C₃	1	8	yes	complemented
64	C₄²×D₅	C₂²×C₃	1	8	yes	complemented
65	C₂²×#127	—	5	1	no	Sylow
66	C₂³×C₃×C₅	—	2	24	no	—
67	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
68	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
69	C₂²×C₃×D₅	—	2	24	no	—
70	C₂²×C₃×D₅	—	2	96	no	—
71	C₂²×C₃×D₅	—	4	64	no	—
72	C₂²×C₃×D₅	C₂×D₄	1	12	yes	—
73	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
74	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
75	C₃×C₅×D₄	—	2	48	no	—
76	C₂×C₃×C₄×C₅	C₂×D₄	1	12	yes	complemented
77	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
78	C₃×C₂²⋊D₅	—	2	96	no	—
79	C₂×C₃×Dic₅	C₂×D₄	1	12	yes	complemented
80	C₂×C₃×Dic₅	C₂⁴	1	6	yes	—
81	C₃×D₂₀	—	2	48	no	—
82	C₃×C₄×D₅	C₂×D₄	1	48	yes	complemented
83	C₂⁵×C₃	—	5	4	no	—
84	C₂²×C₃×D₄	—	5	12	no	—
85	C₂²×C₃×D₄	—	5	48	no	—
86	C₂²×C₃×D₄	—	5	6	no	—
87	C₂²×C₃×D₄	—	10	48	no	—
88	C₂²×C₃×D₄	C₂×D₅	1	6	yes	complemented
89	C₂³×C₃×C₄	—	5	3	no	—
90	C₃×#127	—	5	48	no	—
91	C₃×#127	—	5	8	no	—
92	C₃×#127	C₂×D₅	1	8	yes	direct product factor
93	C₂×C₃×C₄²	—	5	3	no	—
94	C₂×C₃×C₄²	—	5	8	no	—
95	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
96	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
97	C₂³×D₅	—	2	48	no	—
98	C₂³×D₅	C₂³×C₃	1	4	yes	—
99	C₂³×D₅	C₂³×C₃	1	16	yes	—
100	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
101	C₂×C₅×D₄	—	2	24	no	—
102	C₂×C₅×D₄	C₂³×C₃	1	24	yes	complemented
103	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
104	C₂×C₂²⋊D₅	—	2	48	no	—
105	C₂×C₂²⋊D₅	C₂³×C₃	1	48	yes	complemented
106	C₂²×Dic₅	C₂³×C₃	1	3	yes	—
107	D₄×D₅	—	2	192	no	—
108	C₂×D₂₀	—	2	24	no	—
109	C₂×D₂₀	C₂³×C₃	1	24	yes	complemented
110	C₂×C₄×D₅	C₃×D₄	1	24	yes	complemented
111	C₂×C₄×D₅	C₂³×C₃	1	12	yes	—
112	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
113	C₄×Dic₅	C₂³×C₃	1	12	yes	complemented
114	C₂³×D₄	—	5	6	no	—
115	C₂×#127	—	5	6	no	—
116	C₂×#127	—	5	16	no	—
117	C₂×#127	—	5	1	no	—
118	C₂×#127	C₃×D₅	1	1	yes	characteristic, direct product factor
119	C₂²×C₄²	—	5	1	no	—
120	C₂²×C₃×C₅	—	2	24	no	—
121	C₂²×C₃×C₅	—	4	16	no	—
122	C₂²×C₃×C₅	C₂²×D₄	1	6	yes	—
123	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
124	C₂×C₃×D₅	—	2	24	no	—
125	C₂×C₃×D₅	—	4	16	no	—
126	C₂×C₃×D₅	—	4	64	no	—
127	C₂×C₃×D₅	#127	1	16	yes	direct product factor
128	C₂×C₃×D₅	C₂²×D₄	1	12	yes	—
129	C₃×C₄×C₅	C₂²×D₄	1	12	yes	complemented
130	C₃×Dic₅	C₂²×D₄	1	12	yes	complemented
131	C₂⁴×C₃	—	5	1	no	—
132	C₂⁴×C₃	—	5	16	no	—
133	C₂⁴×C₃	—	5	4	no	—
134	C₂⁴×C₃	—	10	48	no	—
135	C₂⁴×C₃	C₂²×D₅	1	4	yes	—
136	C₂×C₃×D₄	—	2	24	no	—
137	C₂×C₃×D₄	—	5	48	no	—
138	C₂×C₃×D₄	—	5	24	no	—
139	C₂×C₃×D₄	—	10	192	no	—
140	C₂×C₃×D₄	—	10	48	no	—
141	C₂×C₃×D₄	—	10	24	no	—
142	C₂×C₃×D₄	C₂²×D₅	1	24	yes	complemented
143	C₂²×C₃×C₄	—	5	3	no	—
144	C₂²×C₃×C₄	—	5	24	no	—
145	C₂²×C₃×C₄	—	5	12	no	—
146	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
147	C₃×C₄²	—	5	12	no	—
148	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
149	C₂³×C₅	—	2	24	no	—
150	C₂³×C₅	C₂⁴×C₃	1	8	yes	—
151	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
152	C₂²×D₅	—	2	24	no	—
153	C₂²×D₅	—	2	96	no	—
154	C₂²×D₅	—	4	64	no	—
155	C₂²×D₅	C₂×C₃×D₄	1	12	yes	—
156	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
157	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
158	C₅×D₄	—	2	48	no	—
159	C₂×C₄×C₅	C₂×C₃×D₄	1	12	yes	complemented
160	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
161	C₂²⋊D₅	—	2	96	no	—
162	C₂×Dic₅	C₂×C₃×D₄	1	12	yes	complemented
163	C₂×Dic₅	C₂⁴×C₃	1	6	yes	—
164	D₂₀	—	2	48	no	—
165	C₄×D₅	C₂×C₃×D₄	1	48	yes	complemented
166	C₂⁵	—	5	4	no	—
167	C₂²×D₄	—	5	12	no	—
168	C₂²×D₄	—	5	48	no	—
169	C₂²×D₄	—	5	6	no	—
170	C₂²×D₄	—	10	48	no	—
171	C₂²×D₄	C₂×C₃×D₅	1	6	yes	complemented
172	C₂³×C₄	—	5	3	no	—
173	#127	—	5	48	no	—
174	#127	—	5	8	no	—
175	#127	C₂×C₃×D₅	1	8	yes	direct product factor
176	C₂×C₄²	—	5	3	no	—
177	C₂×C₄²	—	5	8	no	—
178	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
179	C₂×C₃×C₅	—	4	8	no	—
180	C₂×C₃×C₅	C₂×#127	1	4	yes	complemented
181	C₂×C₃×C₅	C₂³×D₄	1	3	yes	—
182	C₃×D₅	—	4	8	no	—
183	C₃×D₅	C₂×#127	1	8	yes	direct product factor
184	C₂³×C₃	—	2	24	no	—
185	C₂³×C₃	—	5	12	no	—
186	C₂³×C₃	—	5	2	no	—
187	C₂³×C₃	—	5	8	no	—
188	C₂³×C₃	—	10	96	no	—
189	C₂³×C₃	—	10	24	no	—
190	C₂³×C₃	—	20	64	no	—
191	C₂³×C₃	C₂³×D₅	1	8	yes	—
192	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
193	C₃×D₄	—	2	48	no	—
194	C₃×D₄	—	10	96	no	—
195	C₃×D₄	—	10	48	no	—
196	C₂×C₃×C₄	—	5	12	no	—
197	C₂×C₃×C₄	—	5	6	no	—
198	C₂×C₃×C₄	—	5	48	no	—
199	C₂×C₃×C₄	D₄×D₅	1	12	yes	complemented
200	C₂×C₃×C₄	C₂³×D₅	1	6	yes	—
201	C₂²×C₅	—	2	24	no	—
202	C₂²×C₅	—	4	16	no	—
203	C₂²×C₅	C₂²×C₃×D₄	1	6	yes	—
204	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
205	C₂×D₅	—	2	24	no	—
206	C₂×D₅	—	4	16	no	—
207	C₂×D₅	—	4	64	no	—
208	C₂×D₅	C₃×#127	1	16	yes	direct product factor
209	C₂×D₅	C₂²×C₃×D₄	1	12	yes	—
210	C₄×C₅	C₂²×C₃×D₄	1	12	yes	complemented
211	Dic₅	C₂²×C₃×D₄	1	12	yes	complemented
212	C₂⁴	—	5	1	no	—
213	C₂⁴	—	5	16	no	—
214	C₂⁴	—	5	4	no	—
215	C₂⁴	—	10	48	no	—
216	C₂⁴	C₂²×C₃×D₅	1	4	yes	—
217	C₂×D₄	—	2	24	no	—
218	C₂×D₄	—	5	48	no	—
219	C₂×D₄	—	5	24	no	—
220	C₂×D₄	—	10	192	no	—
221	C₂×D₄	—	10	48	no	—
222	C₂×D₄	—	10	24	no	—
223	C₂×D₄	C₂²×C₃×D₅	1	24	yes	complemented
224	C₂²×C₄	—	5	3	no	—
225	C₂²×C₄	—	5	24	no	—
226	C₂²×C₄	—	5	12	no	—
227	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
228	C₄²	—	5	12	no	—
229	C₄²	C₂²×C₃×D₅	1	4	yes	complemented
230	C₃×C₅	C₂²×#127	1	1	yes	characteristic, complemented, Hall
231	C₂²×C₃	—	2	24	no	—
232	C₂²×C₃	—	4	16	no	—
233	C₂²×C₃	—	5	16	no	—
234	C₂²×C₃	—	5	12	no	—
235	C₂²×C₃	—	10	24	no	—
236	C₂²×C₃	—	20	64	no	—
237	C₂²×C₃	—	20	16	no	—
238	C₂²×C₃	C₂×D₄×D₅	1	6	yes	—
239	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
240	C₃×C₄	—	5	12	no	—
241	C₃×C₄	C₂×D₄×D₅	1	12	yes	complemented
242	C₂×C₅	—	4	8	no	—
243	C₂×C₅	C₂×C₃×#127	1	4	yes	complemented
244	C₂×C₅	C₂³×C₃×D₄	1	3	yes	—
245	D₅	—	4	8	no	—
246	D₅	C₂×C₃×#127	1	8	yes	direct product factor
247	C₂³	—	2	24	no	—
248	C₂³	—	5	12	no	—
249	C₂³	—	5	2	no	—
250	C₂³	—	5	8	no	—
251	C₂³	—	10	96	no	—
252	C₂³	—	10	24	no	—
253	C₂³	—	20	64	no	—
254	C₂³	C₂³×C₃×D₅	1	8	yes	—
255	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
256	D₄	—	2	48	no	—
257	D₄	—	10	96	no	—
258	D₄	—	10	48	no	—
259	C₂×C₄	—	5	12	no	—
260	C₂×C₄	—	5	6	no	—
261	C₂×C₄	—	5	48	no	—
262	C₂×C₄	C₃×D₄×D₅	1	12	yes	complemented
263	C₂×C₄	C₂³×C₃×D₅	1	6	yes	—
264	C₂×C₃	—	4	8	no	—
265	C₂×C₃	—	5	8	no	—
266	C₂×C₃	—	20	8	no	—
267	C₂×C₃	D₅×#127	1	4	yes	direct product factor
268	C₂×C₃	C₂²×D₄×D₅	1	3	yes	—
269	C₅	C₂²×C₃×#127	1	1	yes	characteristic, complemented, Sylow
270	C₂²	—	2	24	no	—
271	C₂²	—	4	16	no	—
272	C₂²	—	5	12	no	—
273	C₂²	—	5	16	no	—
274	C₂²	—	10	24	no	—
275	C₂²	—	20	64	no	—
276	C₂²	—	20	16	no	—
277	C₂²	C₂×C₃×D₄×D₅	1	6	yes	—
278	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
279	C₄	—	5	12	no	—
280	C₄	C₂×C₃×D₄×D₅	1	12	yes	complemented
281	C₃	C₂×D₅×#127	1	1	yes	characteristic, direct product factor, Sylow
282	C₂	—	4	8	no	—
283	C₂	—	5	8	no	—
284	C₂	—	20	8	no	—
285	C₂	C₃×D₅×#127	1	4	yes	direct product factor
286	C₂	C₂²×C₃×D₄×D₅	1	3	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#127	D₅
hypocenter	C₅	C₂²×C₃×#127
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#127

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄×D₅	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₂×C₃×#4086	C₂	semidirect
4. C₃×D₅×#127	C₂	direct (N × H)
5. C₂×C₃×#4020	C₂	semidirect
6. C₂×C₃×C₄²×D₅	C₂	semidirect
7. C₂×D₅×#127	C₃	direct (N × H)
9. C₂²×C₃×C₅×D₄	C₂²	semidirect
10. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
12. C₂×C₃×D₄×D₅	C₂²	semidirect
13. C₂²×C₃×D₂₀	C₂²	semidirect
15. C₃×C₅×#127	C₂²	semidirect
16. C₂×C₃×C₄²×C₅	C₂²	semidirect
17. C₃×#4086	C₂²	semidirect
18. C₂×C₃×C₄×Dic₅	C₂²	semidirect
19. C₃×#4020	C₂²	semidirect
20. C₃×C₄²×D₅	C₂²	semidirect
22. C₂²×D₄×D₅	C₂×C₃	semidirect
23. C₂×C₅×#127	C₂×C₃	semidirect
24. C₂×#4086	C₂×C₃	semidirect
25. D₅×#127	C₂×C₃	direct (N × H)
26. C₂×#4020	C₂×C₃	semidirect
27. C₂×C₄²×D₅	C₂×C₃	semidirect
34. C₂×C₃×C₅×D₄	C₂³	semidirect
37. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
41. C₂×C₃×D₂₀	C₂³	semidirect
42. C₂×C₃×C₄×D₅	D₄	semidirect
44. C₃×C₄²×C₅	C₂³	semidirect
45. C₃×C₄×Dic₅	C₂³	semidirect
50. C₂×C₃×#127	D₅	direct (N × H)
53. C₂²×C₅×D₄	C₂²×C₃	semidirect
54. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
56. C₂×D₄×D₅	C₂²×C₃	semidirect
57. C₂²×D₂₀	C₂²×C₃	semidirect
59. C₅×#127	C₂²×C₃	semidirect
60. C₂×C₄²×C₅	C₂²×C₃	semidirect
61. #4086	C₂²×C₃	semidirect
62. C₂×C₄×Dic₅	C₂²×C₃	semidirect
63. #4020	C₂²×C₃	semidirect
64. C₄²×D₅	C₂²×C₃	semidirect
76. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
79. C₂×C₃×Dic₅	C₂×D₄	semidirect
82. C₃×C₄×D₅	C₂×D₄	semidirect
88. C₂²×C₃×D₄	C₂×D₅	semidirect
92. C₃×#127	C₂×D₅	direct (N × H)
95. C₂×C₃×C₄²	C₂×D₅	semidirect
102. C₂×C₅×D₄	C₂³×C₃	semidirect
105. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
109. C₂×D₂₀	C₂³×C₃	semidirect
110. C₂×C₄×D₅	C₃×D₄	semidirect
112. C₄²×C₅	C₂³×C₃	semidirect
113. C₄×Dic₅	C₂³×C₃	semidirect
118. C₂×#127	C₃×D₅	direct (N × H)
127. C₂×C₃×D₅	#127	direct (N × H)
129. C₃×C₄×C₅	C₂²×D₄	semidirect
130. C₃×Dic₅	C₂²×D₄	semidirect
142. C₂×C₃×D₄	C₂²×D₅	semidirect
148. C₃×C₄²	C₂²×D₅	semidirect
159. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
162. C₂×Dic₅	C₂×C₃×D₄	semidirect
165. C₄×D₅	C₂×C₃×D₄	semidirect
171. C₂²×D₄	C₂×C₃×D₅	semidirect
175. #127	C₂×C₃×D₅	direct (N × H)
178. C₂×C₄²	C₂×C₃×D₅	semidirect
180. C₂×C₃×C₅	C₂×#127	semidirect
183. C₃×D₅	C₂×#127	direct (N × H)
199. C₂×C₃×C₄	D₄×D₅	semidirect
208. C₂×D₅	C₃×#127	direct (N × H)
210. C₄×C₅	C₂²×C₃×D₄	semidirect
211. Dic₅	C₂²×C₃×D₄	semidirect
223. C₂×D₄	C₂²×C₃×D₅	semidirect
229. C₄²	C₂²×C₃×D₅	semidirect
230. C₃×C₅	C₂²×#127	semidirect
241. C₃×C₄	C₂×D₄×D₅	semidirect
243. C₂×C₅	C₂×C₃×#127	semidirect
246. D₅	C₂×C₃×#127	direct (N × H)
262. C₂×C₄	C₃×D₄×D₅	semidirect
267. C₂×C₃	D₅×#127	direct (N × H)
269. C₅	C₂²×C₃×#127	semidirect
280. C₄	C₂×C₃×D₄×D₅	semidirect
281. C₃	C₂×D₅×#127	direct (N × H)
285. C₂	C₃×D₅×#127	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₄×D₅	2
C₂×C₃×C₅×#127	2
C₂×C₃×#4086	2
C₃×D₅×#127	2
C₂×C₃×#4020	2
C₂×C₃×C₄²×D₅	2
C₂×D₅×#127	3
C₂²×C₃×#127	5

Subgroups — C2×C3×D5×#127 #14479959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₅×#127 #14479959