Subgroups — C₅×#70475 #14297417

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	2	yes	maximal
4	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4550	C₂	1	2	yes	maximal, complemented
6	C₅×#1797	—	3	1	no	maximal, Hall
7	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₅×D₃	C₄	1	1	yes	characteristic
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₄	1	1	yes	characteristic
14	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
16	C₄²×C₅×D₃	—	2	2	no	—
17	C₄²×C₅×D₃	—	2	2	no	—
18	C₃×C₅×C₄⋊C₈	—	2	2	no	—
19	C₅×(C₂×D₃)⋊C₈	—	2	4	no	—
20	C₅×C₄⋊(C₃⋊C₈)	—	2	2	no	—
21	#70475	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₄²×C₅	—	3	1	no	—
23	C₂×C₅×C₄⋊C₈	—	3	1	no	—
24	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
25	C₂×C₅×C₂²⋊C₈	—	3	2	no	—
26	C₅×#336	—	3	2	no	—
27	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×C₅×D₃	—	2	2	no	—
35	C₂×C₄×C₅×D₃	—	2	2	no	—
36	C₂×C₄×C₅×D₃	—	2	2	no	—
37	C₂×C₄×C₅×D₃	—	2	2	no	—
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	1	no	—
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₄×C₅×D₃	—	2	2	no	—
43	C₂×C₄×C₅×D₃	C₈	1	4	yes	complemented
44	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
45	C₂×C₄×C₅×D₃	Q₈	1	2	yes	—
46	C₂×C₃×C₅×C₈	—	2	2	no	—
47	C₂×C₃×C₅×C₈	—	2	2	no	—
48	C₂×C₃×C₅×C₈	—	2	2	no	—
49	C₃×C₄²×C₅	D₄	1	2	yes	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₄×C₅×Dic₃	—	2	2	no	—
52	C₄×C₅×Dic₃	—	2	2	no	—
53	C₄×C₅×Dic₃	—	2	1	no	—
54	C₄×C₅×Dic₃	—	2	1	no	—
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₂×C₅×C₃⋊C₈	—	2	2	no	—
58	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
59	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	2	yes	—
61	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
62	#4550	C₂×C₅	1	2	yes	complemented
63	C₂³×C₄×C₅	—	3	1	no	—
64	C₂³×C₄×C₅	—	3	1	no	—
65	C₂³×C₄×C₅	—	3	1	no	—
66	C₂²×C₅×C₈	—	3	2	no	—
67	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
68	C₂×C₄²×C₅	—	3	1	no	—
69	C₂×C₄²×C₅	—	3	1	no	—
70	C₂×C₄²×C₅	—	3	1	no	—
71	C₂×C₄²×C₅	—	6	2	no	—
72	C₂×C₄²×C₅	—	6	2	no	—
73	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
74	C₅×C₄⋊C₈	—	2	2	no	—
75	C₅×C₄⋊C₈	—	6	2	no	—
76	C₅×C₂²⋊C₈	—	6	4	no	—
77	#1797	—	3	1	no	Sylow
78	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₅×D₃	—	2	1	no	—
80	C₂²×C₅×D₃	—	2	1	no	—
81	C₂²×C₅×D₃	—	2	1	no	—
82	C₂²×C₅×D₃	—	2	1	no	—
83	C₂²×C₅×D₃	C₄⋊C₄	1	2	yes	—
84	C₂²×C₅×D₃	C₂×C₈	1	2	yes	—
85	C₂²×C₅×D₃	M₁₆	1	2	yes	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
91	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₅×Dic₃	—	2	1	no	—
99	C₂×C₅×Dic₃	—	2	1	no	—
100	C₂×C₅×Dic₃	—	2	1	no	—
101	C₂×C₅×Dic₃	—	2	1	no	—
102	C₂×C₅×Dic₃	—	2	1	no	—
103	C₂×C₅×Dic₃	—	2	1	no	—
104	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
105	C₂×C₅×Dic₃	C₂×C₈	1	2	yes	—
106	C₂×C₅×Dic₃	M₁₆	1	2	yes	—
107	C₄×C₅×D₃	—	2	8	no	—
108	C₄×C₅×D₃	—	2	8	no	—
109	C₄×C₅×D₃	—	2	2	no	—
110	C₄×C₅×D₃	—	2	2	no	—
111	C₄×C₅×D₃	—	2	2	no	—
112	C₄×C₅×D₃	—	2	2	no	—
113	C₃×C₅×C₈	—	4	2	no	—
114	C₅×C₃⋊C₈	—	4	2	no	—
115	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
116	C₂²×C₄×D₃	C₄×C₅	1	1	yes	characteristic
117	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
118	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
119	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
120	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
121	C₂×C₄×Dic₃	C₄×C₅	1	1	yes	characteristic
122	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
123	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
124	C₄²×D₃	—	2	2	no	—
125	C₄²×D₃	—	2	2	no	—
126	C₃×C₄⋊C₈	—	2	2	no	—
127	(C₂×D₃)⋊C₈	—	2	4	no	—
128	C₄⋊(C₃⋊C₈)	—	2	2	no	—
129	C₂⁴×C₅	—	3	1	no	—
130	C₂²×C₄×C₅	—	3	1	no	—
131	C₂²×C₄×C₅	—	3	1	no	—
132	C₂²×C₄×C₅	—	3	1	no	—
133	C₂²×C₄×C₅	—	3	4	no	—
134	C₂²×C₄×C₅	—	3	2	no	—
135	C₂²×C₄×C₅	—	3	2	no	—
136	C₂²×C₄×C₅	—	6	2	no	—
137	C₂²×C₄×C₅	—	6	2	no	—
138	C₂²×C₄×C₅	—	6	2	no	—
139	C₂²×C₄×C₅	—	6	2	no	—
140	C₂²×C₄×C₅	—	6	2	no	—
141	C₂²×C₄×C₅	—	6	1	no	—
142	C₂²×C₄×C₅	—	6	1	no	—
143	C₂²×C₄×C₅	—	6	1	no	—
144	C₂²×C₄×C₅	—	6	1	no	—
145	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	6	2	no	—
152	C₂×C₅×C₈	—	6	2	no	—
153	C₂×C₅×C₈	—	6	2	no	—
154	C₄²×C₅	—	6	2	no	—
155	C₄²×C₅	—	6	2	no	—
156	C₄²×C₅	—	6	1	no	—
157	C₄²×C₅	—	6	1	no	—
158	C₄²×C₅	D₁₂	1	2	yes	—
159	C₄²×C₅	#67	1	2	yes	—
160	C₂²×C₄²	—	3	1	no	—
161	C₂×C₄⋊C₈	—	3	1	no	—
162	C₂×C₄⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
163	C₂×C₂²⋊C₈	—	3	2	no	—
164	#336	—	3	2	no	—
165	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	#117	1	1	yes	characteristic
168	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
169	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
172	C₂×C₅×D₃	—	2	2	no	—
173	C₂×C₅×D₃	—	2	2	no	—
174	C₂×C₅×D₃	—	2	2	no	—
175	C₂×C₅×D₃	—	2	2	no	—
176	C₂×C₅×D₃	—	2	2	no	—
177	C₂×C₅×D₃	—	2	2	no	—
178	C₂×C₅×D₃	C₄⋊C₈	1	4	yes	complemented
179	C₃×C₄×C₅	—	2	2	no	—
180	C₃×C₄×C₅	C₂²⋊C₈	1	4	yes	complemented
181	C₃×C₄×C₅	#121	1	1	yes	characteristic
182	C₃×C₄×C₅	#121	1	1	yes	characteristic
183	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
184	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₅×Dic₃	—	2	2	no	—
186	C₅×Dic₃	—	2	2	no	—
187	C₅×Dic₃	—	2	2	no	—
188	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
193	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
194	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
195	C₂×C₄×D₃	—	2	2	no	—
196	C₂×C₄×D₃	—	2	2	no	—
197	C₂×C₄×D₃	—	2	2	no	—
198	C₂×C₄×D₃	—	2	2	no	—
199	C₂×C₄×D₃	—	2	1	no	—
200	C₂×C₄×D₃	—	2	1	no	—
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×C₄×D₃	—	2	1	no	—
203	C₂×C₄×D₃	—	2	2	no	—
204	C₂×C₄×D₃	C₅×C₈	1	4	yes	complemented
205	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
206	C₂×C₄×D₃	C₅×Q₈	1	2	yes	—
207	C₂×C₃×C₈	—	2	2	no	—
208	C₂×C₃×C₈	—	2	2	no	—
209	C₂×C₃×C₈	—	2	2	no	—
210	C₃×C₄²	C₅×D₄	1	2	yes	—
211	C₃×C₄²	C₅×D₄	1	2	yes	—
212	C₄×Dic₃	—	2	2	no	—
213	C₄×Dic₃	—	2	2	no	—
214	C₄×Dic₃	—	2	1	no	—
215	C₄×Dic₃	—	2	1	no	—
216	C₂×C₃⋊C₈	—	2	2	no	—
217	C₂×C₃⋊C₈	—	2	2	no	—
218	C₂×C₃⋊C₈	—	2	2	no	—
219	C₂³×C₅	—	3	2	no	—
220	C₂³×C₅	—	3	2	no	—
221	C₂³×C₅	—	3	2	no	—
222	C₂³×C₅	—	6	1	no	—
223	C₂³×C₅	—	6	1	no	—
224	C₂³×C₅	—	6	1	no	—
225	C₂³×C₅	—	6	1	no	—
226	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	3	2	no	—
230	C₂×C₄×C₅	—	3	2	no	—
231	C₂×C₄×C₅	—	3	2	no	—
232	C₂×C₄×C₅	—	6	8	no	—
233	C₂×C₄×C₅	—	6	1	no	—
234	C₂×C₄×C₅	—	6	1	no	—
235	C₂×C₄×C₅	—	6	1	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	6	1	no	—
238	C₂×C₄×C₅	—	6	1	no	—
239	C₂×C₄×C₅	—	6	8	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	D₃×C₈	1	2	yes	—
245	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
246	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
247	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
248	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
249	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	#237	1	1	yes	characteristic
251	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
252	C₂×C₄×C₅	#239	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
254	C₅×C₈	—	4	2	no	—
255	C₅×C₈	—	12	2	no	—
256	C₂³×C₄	—	3	1	no	—
257	C₂³×C₄	—	3	1	no	—
258	C₂³×C₄	—	3	1	no	—
259	C₂²×C₈	—	3	2	no	—
260	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
261	C₂×C₄²	—	3	1	no	—
262	C₂×C₄²	—	3	1	no	—
263	C₂×C₄²	—	3	1	no	—
264	C₂×C₄²	—	6	2	no	—
265	C₂×C₄²	—	6	2	no	—
266	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	6	2	no	—
269	C₂²⋊C₈	—	6	4	no	—
270	C₂×C₃×C₅	#380	1	1	yes	characteristic
271	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
272	C₂×C₃×C₅	#407	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
274	C₂×C₃×C₅	#423	1	1	yes	characteristic
275	C₂×C₃×C₅	#431	1	1	yes	characteristic
276	C₂×C₃×C₅	#432	1	1	yes	characteristic
277	C₅×D₃	—	2	4	no	—
278	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂²×D₃	—	2	1	no	—
280	C₂²×D₃	—	2	1	no	—
281	C₂²×D₃	—	2	1	no	—
282	C₂²×D₃	—	2	1	no	—
283	C₂²×D₃	C₅×C₄⋊C₄	1	2	yes	—
284	C₂²×D₃	C₂×C₅×C₈	1	2	yes	—
285	C₂²×D₃	C₅×M₁₆	1	2	yes	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
289	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
290	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
291	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
292	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
296	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
297	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
298	C₂×Dic₃	—	2	1	no	—
299	C₂×Dic₃	—	2	1	no	—
300	C₂×Dic₃	—	2	1	no	—
301	C₂×Dic₃	—	2	1	no	—
302	C₂×Dic₃	—	2	1	no	—
303	C₂×Dic₃	—	2	1	no	—
304	C₂×Dic₃	C₅×C₄⋊C₄	1	2	yes	—
305	C₂×Dic₃	C₂×C₅×C₈	1	2	yes	—
306	C₂×Dic₃	C₅×M₁₆	1	2	yes	—
307	C₄×D₃	—	2	8	no	—
308	C₄×D₃	—	2	2	no	—
309	C₄×D₃	—	2	2	no	—
310	C₄×D₃	—	2	2	no	—
311	C₄×D₃	—	2	2	no	—
312	C₄×D₃	—	2	8	no	—
313	C₃×C₈	—	4	2	no	—
314	C₃⋊C₈	—	4	2	no	—
315	C₂²×C₅	—	3	4	no	—
316	C₂²×C₅	—	6	2	no	—
317	C₂²×C₅	—	6	2	no	—
318	C₂²×C₅	—	6	2	no	—
319	C₂²×C₅	—	6	2	no	—
320	C₂²×C₅	—	6	2	no	—
321	C₂²×C₅	—	6	2	no	—
322	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
323	C₂²×C₅	#892	1	1	yes	characteristic
324	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
325	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
326	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
327	C₂²×C₅	D₃×M₁₆	1	1	yes	characteristic
328	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
329	C₄×C₅	—	2	2	no	—
330	C₄×C₅	—	6	2	no	—
331	C₄×C₅	—	6	2	no	—
332	C₄×C₅	—	6	2	no	—
333	C₄×C₅	(C₂×D₃)⋊C₈	1	4	yes	complemented
334	C₄×C₅	#895	1	1	yes	characteristic
335	C₄×C₅	#897	1	1	yes	characteristic
336	C₄×C₅	#938	1	1	yes	characteristic
337	C₄×C₅	#946	1	1	yes	characteristic
338	C₂⁴	—	3	1	no	—
339	C₂²×C₄	—	3	1	no	—
340	C₂²×C₄	—	3	1	no	—
341	C₂²×C₄	—	3	1	no	—
342	C₂²×C₄	—	3	4	no	—
343	C₂²×C₄	—	3	2	no	—
344	C₂²×C₄	—	3	2	no	—
345	C₂²×C₄	—	6	2	no	—
346	C₂²×C₄	—	6	2	no	—
347	C₂²×C₄	—	6	2	no	—
348	C₂²×C₄	—	6	2	no	—
349	C₂²×C₄	—	6	2	no	—
350	C₂²×C₄	—	6	1	no	—
351	C₂²×C₄	—	6	1	no	—
352	C₂²×C₄	—	6	1	no	—
353	C₂²×C₄	—	6	1	no	—
354	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
355	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	6	2	no	—
361	C₂×C₈	—	6	2	no	—
362	C₂×C₈	—	6	2	no	—
363	C₄²	—	6	2	no	—
364	C₄²	—	6	2	no	—
365	C₄²	—	6	1	no	—
366	C₄²	—	6	1	no	—
367	C₄²	C₅×D₁₂	1	2	yes	—
368	C₄²	C₅×#67	1	2	yes	—
369	C₃×C₅	#1797	1	1	yes	characteristic, complemented, Hall
370	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
371	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
372	C₂²×C₃	C₅×#117	1	1	yes	characteristic
373	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
374	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
375	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
376	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
377	C₂×D₃	—	2	2	no	—
378	C₂×D₃	—	2	2	no	—
379	C₂×D₃	—	2	2	no	—
380	C₂×D₃	—	2	2	no	—
381	C₂×D₃	—	2	2	no	—
382	C₂×D₃	—	2	2	no	—
383	C₂×D₃	C₅×C₄⋊C₈	1	4	yes	complemented
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	C₅×C₂²⋊C₈	1	4	yes	complemented
386	C₃×C₄	C₅×#121	1	1	yes	characteristic
387	C₃×C₄	C₅×#121	1	1	yes	characteristic
388	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
389	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
390	Dic₃	—	2	2	no	—
391	Dic₃	—	2	2	no	—
392	Dic₃	—	2	2	no	—
393	C₂×C₅	—	6	4	no	—
394	C₂×C₅	D₃×C₄⋊C₈	1	1	yes	characteristic
395	C₂×C₅	#4833	1	1	yes	characteristic
396	C₂×C₅	#4835	1	1	yes	characteristic
397	C₂×C₅	#4837	1	1	yes	characteristic
398	C₂×C₅	#4987	1	1	yes	characteristic
399	C₂×C₅	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
400	C₂×C₅	#5126	1	1	yes	characteristic
401	C₂³	—	3	2	no	—
402	C₂³	—	3	2	no	—
403	C₂³	—	3	2	no	—
404	C₂³	—	6	1	no	—
405	C₂³	—	6	1	no	—
406	C₂³	—	6	1	no	—
407	C₂³	—	6	1	no	—
408	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	3	2	no	—
412	C₂×C₄	—	3	2	no	—
413	C₂×C₄	—	3	2	no	—
414	C₂×C₄	—	6	8	no	—
415	C₂×C₄	—	6	1	no	—
416	C₂×C₄	—	6	1	no	—
417	C₂×C₄	—	6	1	no	—
418	C₂×C₄	—	6	1	no	—
419	C₂×C₄	—	6	1	no	—
420	C₂×C₄	—	6	1	no	—
421	C₂×C₄	—	6	2	no	—
422	C₂×C₄	—	6	2	no	—
423	C₂×C₄	—	6	2	no	—
424	C₂×C₄	—	6	2	no	—
425	C₂×C₄	—	6	8	no	—
426	C₂×C₄	C₅×D₃×C₈	1	2	yes	—
427	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
428	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
429	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
430	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
431	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
432	C₂×C₄	C₅×#237	1	1	yes	characteristic
433	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
434	C₂×C₄	C₅×#239	1	1	yes	characteristic
435	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
436	C₈	—	4	2	no	—
437	C₈	—	12	2	no	—
438	C₂×C₃	C₅×#380	1	1	yes	characteristic
439	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
440	C₂×C₃	C₅×#407	1	1	yes	characteristic
441	C₂×C₃	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
442	C₂×C₃	C₅×#423	1	1	yes	characteristic
443	C₂×C₃	C₅×#431	1	1	yes	characteristic
444	C₂×C₃	C₅×#432	1	1	yes	characteristic
445	D₃	—	2	4	no	—
446	C₅	#70475	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²	—	3	4	no	—
448	C₂²	—	6	2	no	—
449	C₂²	—	6	2	no	—
450	C₂²	—	6	2	no	—
451	C₂²	—	6	2	no	—
452	C₂²	—	6	2	no	—
453	C₂²	—	6	2	no	—
454	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
455	C₂²	C₅×#892	1	1	yes	characteristic
456	C₂²	C₂×C₅×D₃×C₈	1	1	yes	characteristic
457	C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
458	C₂²	C₅×D₃×M₁₆	1	1	yes	characteristic
459	C₂²	C₅×D₃×M₁₆	1	1	yes	characteristic
460	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	6	2	no	—
463	C₄	—	6	2	no	—
464	C₄	—	6	2	no	—
465	C₄	C₅×(C₂×D₃)⋊C₈	1	4	yes	complemented
466	C₄	C₅×#895	1	1	yes	characteristic
467	C₄	C₅×#897	1	1	yes	characteristic
468	C₄	C₅×#938	1	1	yes	characteristic
469	C₄	C₅×#946	1	1	yes	characteristic
470	C₃	C₅×#1797	1	1	yes	characteristic, complemented, Sylow
471	C₂	—	6	4	no	—
472	C₂	C₅×D₃×C₄⋊C₈	1	1	yes	characteristic
473	C₂	C₅×#4833	1	1	yes	characteristic
474	C₂	C₅×#4835	1	1	yes	characteristic
475	C₂	C₅×#4837	1	1	yes	characteristic
476	C₂	C₅×#4987	1	1	yes	characteristic
477	C₂	C₂×C₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic
478	C₂	C₅×#5126	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₅×C₈
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₅×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×C₄⋊C₈	D₃
hypocenter	C₃	C₅×#1797
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
4. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
5. C₅×#4550	C₂	semidirect
21. #70475	C₅	direct (N × H)
24. C₂×C₅×C₄⋊C₈	D₃	semidirect
43. C₂×C₄×C₅×D₃	C₈	semidirect
59. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
61. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
62. #4550	C₂×C₅	semidirect
162. C₂×C₄⋊C₈	C₅×D₃	semidirect
178. C₂×C₅×D₃	C₄⋊C₈	semidirect
180. C₃×C₄×C₅	C₂²⋊C₈	semidirect
204. C₂×C₄×D₃	C₅×C₈	semidirect
333. C₄×C₅	(C₂×D₃)⋊C₈	semidirect
369. C₃×C₅	#1797	semidirect
383. C₂×D₃	C₅×C₄⋊C₈	semidirect
385. C₃×C₄	C₅×C₂²⋊C₈	semidirect
446. C₅	#70475	direct (N × H)
465. C₄	C₅×(C₂×D₃)⋊C₈	semidirect
470. C₃	C₅×#1797	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₅×D₃	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4550	2
C₅×#1797	3
#70475	5

Subgroups — C5×#70475 #14297417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70475 #14297417