Subgroups — C₅×D₃×#470 #14428029

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
4	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5189	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5137	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5052	C₂	1	2	yes	maximal, complemented
8	C₅×#4867	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4816	C₂	1	2	yes	maximal, complemented
11	C₅×D₃×#103	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#470	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
14	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₅×#946	C₂²	1	2	yes	—
19	C₂×C₅×#216	C₂²	1	2	yes	complemented
20	C₅×#924	C₂²	1	2	yes	—
21	C₂×C₅×#208	C₂²	1	1	yes	characteristic
22	C₅×D₃×Q₁₆	—	2	4	no	—
23	C₅×D₃×M₁₆	—	2	4	no	—
24	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
26	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
27	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
29	C₅×#897	C₂²	1	2	yes	—
30	C₅×#896	—	2	2	no	—
31	C₅×D₃×C₄⋊C₄	—	2	2	no	—
32	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
34	C₅×#878	—	2	2	no	—
35	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#103	C₂²	1	2	yes	complemented
37	C₅×#835	C₂²	1	2	yes	complemented
38	C₅×#817	C₂²	1	1	yes	characteristic, complemented
39	C₅×#816	C₂²	1	2	yes	complemented
40	C₅×#810	C₂²	1	2	yes	complemented
41	C₅×#808	C₂²	1	2	yes	complemented
42	D₃×#470	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂²×C₅×Q₁₆	—	3	1	no	—
44	C₂²×C₅×M₁₆	—	3	1	no	—
45	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
46	C₅×#470	—	3	1	no	—
47	C₅×#470	—	3	2	no	—
48	C₅×#470	—	3	1	no	—
49	C₅×#470	—	3	1	no	—
50	C₅×#470	—	3	2	no	—
51	C₅×#470	D₃	1	1	yes	characteristic, direct product factor
52	C₂×C₅×#106	—	3	1	no	—
53	C₂×C₅×#103	—	3	2	no	—
54	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
58	C₅×D₃×Q₈	—	2	4	no	—
59	C₅×D₃×Q₈	—	2	4	no	—
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	—	2	2	no	—
64	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
68	C₂×C₅×Dic₆	—	2	2	no	—
69	C₂×C₅×Dic₆	C₂³	1	2	yes	—
70	C₃×C₅×Q₁₆	—	2	2	no	—
71	C₃×C₅×M₁₆	—	2	2	no	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₅×#217	—	2	2	no	—
78	C₅×#216	—	2	4	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
80	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
81	C₅×C₄⋊Dic₃	—	2	2	no	—
82	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
83	C₅×Dic₃⋊C₄	—	2	2	no	—
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₅×Dic₃⋊C₄	—	2	2	no	—
86	C₅×#208	—	2	2	no	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₅×Dic₁₂	—	2	2	no	—
90	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
91	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
92	C₅×D₃×C₈	—	2	2	no	—
93	C₅×D₃×C₈	D₄	1	4	yes	—
94	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic
96	D₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
97	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
98	#5189	C₂×C₅	1	1	yes	characteristic, complemented
99	#5137	C₂×C₅	1	1	yes	characteristic, complemented
100	#5052	C₂×C₅	1	2	yes	complemented
101	#4867	C₂×C₅	1	1	yes	characteristic, complemented
102	D₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
103	#4816	C₂×C₅	1	2	yes	complemented
104	D₃×#103	C₂×C₅	1	2	yes	complemented
105	C₂²×C₅×Q₈	—	3	2	no	—
106	C₂³×C₄×C₅	—	3	1	no	—
107	C₂×C₅×Q₁₆	—	3	2	no	—
108	C₂×C₅×Q₁₆	—	3	1	no	—
109	C₂×C₅×Q₁₆	—	6	4	no	—
110	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
111	C₂×C₅×M₁₆	—	3	1	no	—
112	C₂×C₅×M₁₆	—	3	1	no	—
113	C₂×C₅×M₁₆	—	3	1	no	—
114	C₂×C₅×M₁₆	—	6	4	no	—
115	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
116	C₂²×C₅×C₈	—	3	1	no	—
117	C₂²×C₅×C₈	—	3	1	no	—
118	C₅×C₂²⋊Q₈	—	3	2	no	—
119	C₅×C₂²⋊Q₈	—	3	2	no	—
120	C₅×C₂²⋊Q₈	—	3	2	no	—
121	C₅×C₂²⋊Q₈	—	6	2	no	—
122	C₅×C₂²⋊Q₈	—	6	2	no	—
123	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
124	C₂×C₅×C₄⋊C₄	—	3	2	no	—
125	C₂×C₅×C₄⋊C₄	—	6	2	no	—
126	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
127	C₅×#106	—	3	1	no	—
128	C₅×#106	—	3	2	no	—
129	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
130	C₅×#103	—	3	2	no	—
131	C₅×#103	—	3	2	no	—
132	C₅×#103	—	3	2	no	—
133	C₅×#103	C₂×D₃	1	2	yes	complemented
134	C₂×#470	—	3	1	no	Sylow
135	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₅×D₃	—	2	2	no	—
137	C₂²×C₅×D₃	—	2	4	no	—
138	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₂×C₅×Dic₃	—	2	2	no	—
149	C₂×C₅×Dic₃	—	2	2	no	—
150	C₂×C₅×Dic₃	—	2	2	no	—
151	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
153	C₄×C₅×D₃	—	2	2	no	—
154	C₄×C₅×D₃	—	2	1	no	—
155	C₄×C₅×D₃	—	2	1	no	—
156	C₄×C₅×D₃	—	2	2	no	—
157	C₄×C₅×D₃	—	4	4	no	—
158	C₄×C₅×D₃	—	4	4	no	—
159	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
160	C₄×C₅×D₃	#41	1	2	yes	—
161	C₅×Dic₆	—	2	2	no	—
162	C₅×Dic₆	—	2	2	no	—
163	C₅×Dic₆	—	4	4	no	—
164	C₃×C₅×C₈	—	2	1	no	—
165	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
166	C₅×C₃⋊C₈	—	2	1	no	—
167	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
168	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
169	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
171	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
172	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
173	#946	C₂²×C₅	1	2	yes	—
174	C₂×#216	C₂²×C₅	1	2	yes	complemented
175	#924	C₂²×C₅	1	2	yes	—
176	C₂×#208	C₂²×C₅	1	1	yes	characteristic
177	D₃×Q₁₆	—	2	4	no	—
178	D₃×M₁₆	—	2	4	no	—
179	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
181	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
182	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
183	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
184	#897	C₂²×C₅	1	2	yes	—
185	#896	—	2	2	no	—
186	D₃×C₄⋊C₄	—	2	2	no	—
187	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
188	D₃×C₂²⋊C₄	—	2	2	no	—
189	#878	—	2	2	no	—
190	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
191	C₃×#103	C₂²×C₅	1	2	yes	complemented
192	#835	C₂²×C₅	1	2	yes	complemented
193	#817	C₂²×C₅	1	1	yes	characteristic, complemented
194	#816	C₂²×C₅	1	2	yes	complemented
195	#810	C₂²×C₅	1	2	yes	complemented
196	#808	C₂²×C₅	1	2	yes	complemented
197	C₂⁴×C₅	—	3	1	no	—
198	C₂×C₅×Q₈	—	3	2	no	—
199	C₂×C₅×Q₈	—	6	2	no	—
200	C₂×C₅×Q₈	—	6	4	no	—
201	C₂×C₅×Q₈	—	6	4	no	—
202	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
203	C₂²×C₄×C₅	—	3	1	no	—
204	C₂²×C₄×C₅	—	3	1	no	—
205	C₂²×C₄×C₅	—	3	1	no	—
206	C₂²×C₄×C₅	—	3	1	no	—
207	C₂²×C₄×C₅	—	3	1	no	—
208	C₂²×C₄×C₅	—	6	2	no	—
209	C₂²×C₄×C₅	—	6	2	no	—
210	C₂²×C₄×C₅	—	6	2	no	—
211	C₂²×C₄×C₅	—	6	2	no	—
212	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₅×Q₁₆	—	2	2	no	—
214	C₅×Q₁₆	—	6	4	no	—
215	C₅×Q₁₆	—	6	2	no	—
216	C₅×M₁₆	—	2	2	no	—
217	C₅×M₁₆	—	6	2	no	—
218	C₅×M₁₆	—	6	2	no	—
219	C₅×M₁₆	—	6	2	no	—
220	C₂×C₅×C₈	—	3	1	no	—
221	C₂×C₅×C₈	—	3	4	no	—
222	C₂×C₅×C₈	—	3	1	no	—
223	C₂×C₅×C₈	—	6	2	no	—
224	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
225	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
226	C₅×C₄⋊C₄	—	2	2	no	—
227	C₅×C₄⋊C₄	—	3	2	no	—
228	C₅×C₄⋊C₄	—	6	2	no	—
229	C₅×C₄⋊C₄	—	6	2	no	—
230	C₅×C₄⋊C₄	—	6	2	no	—
231	C₅×C₄⋊C₄	—	6	2	no	—
232	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
233	C₅×C₂²⋊C₄	—	2	2	no	—
234	C₅×C₂²⋊C₄	—	6	2	no	—
235	C₅×C₂²⋊C₄	—	6	2	no	—
236	C₅×C₂²⋊C₄	—	6	2	no	—
237	C₂²×Q₁₆	—	3	1	no	—
238	C₂²×M₁₆	—	3	1	no	—
239	C₂×C₂²⋊Q₈	—	3	2	no	—
240	#470	—	3	1	no	—
241	#470	—	3	1	no	—
242	#470	—	3	2	no	—
243	#470	—	3	1	no	—
244	#470	—	3	2	no	—
245	#470	C₅×D₃	1	1	yes	characteristic, direct product factor
246	C₂×#106	—	3	1	no	—
247	C₂×#103	—	3	2	no	—
248	C₂²×C₃×C₅	—	2	1	no	—
249	C₂²×C₃×C₅	—	2	2	no	—
250	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₅×D₃	—	2	1	no	—
252	C₂×C₅×D₃	—	2	2	no	—
253	C₂×C₅×D₃	—	4	4	no	—
254	C₂×C₅×D₃	#121	1	2	yes	—
255	C₂×C₅×D₃	#137	1	4	yes	—
256	C₃×C₄×C₅	—	2	1	no	—
257	C₃×C₄×C₅	—	4	2	no	—
258	C₃×C₄×C₅	—	4	2	no	—
259	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
260	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₅×Dic₃	—	2	1	no	—
262	C₅×Dic₃	—	4	2	no	—
263	C₅×Dic₃	—	4	2	no	—
264	C₅×Dic₃	#121	1	2	yes	—
265	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
266	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
267	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
269	D₃×Q₈	—	2	4	no	—
270	D₃×Q₈	—	2	4	no	—
271	C₂×C₄×D₃	—	2	2	no	—
272	C₂×C₄×D₃	—	2	2	no	—
273	C₂×C₄×D₃	—	2	2	no	—
274	C₂×C₄×D₃	—	2	2	no	—
275	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
276	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
277	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
279	C₂×Dic₆	—	2	2	no	—
280	C₂×Dic₆	C₂³×C₅	1	2	yes	—
281	C₃×Q₁₆	—	2	2	no	—
282	C₃×M₁₆	—	2	2	no	—
283	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
284	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
285	C₃×C₄⋊C₄	—	2	2	no	—
286	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
287	C₃×C₂²⋊C₄	—	2	2	no	—
288	#217	—	2	2	no	—
289	#216	—	2	4	no	—
290	(C₂×D₃)⋊C₄	—	2	2	no	—
291	(C₂×D₃)⋊C₄	—	2	2	no	—
292	C₄⋊Dic₃	—	2	2	no	—
293	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
294	Dic₃⋊C₄	—	2	2	no	—
295	Dic₃⋊C₄	—	2	2	no	—
296	Dic₃⋊C₄	—	2	2	no	—
297	#208	—	2	2	no	—
298	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
299	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
300	Dic₁₂	—	2	2	no	—
301	ΓL(1,𝔽₂₅)	—	2	2	no	—
302	ΓL(1,𝔽₂₅)	—	2	2	no	—
303	D₃×C₈	—	2	2	no	—
304	D₃×C₈	C₅×D₄	1	4	yes	—
305	C₂³×C₅	—	3	1	no	—
306	C₂³×C₅	—	3	1	no	—
307	C₂³×C₅	—	6	2	no	—
308	C₂³×C₅	—	6	4	no	—
309	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
310	C₅×Q₈	—	2	2	no	—
311	C₅×Q₈	—	2	2	no	—
312	C₅×Q₈	—	6	2	no	—
313	C₅×Q₈	—	6	2	no	—
314	C₅×Q₈	—	12	4	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	3	1	no	—
320	C₂×C₄×C₅	—	3	2	no	—
321	C₂×C₄×C₅	—	3	2	no	—
322	C₂×C₄×C₅	—	3	1	no	—
323	C₂×C₄×C₅	—	6	2	no	—
324	C₂×C₄×C₅	—	6	2	no	—
325	C₂×C₄×C₅	—	6	2	no	—
326	C₂×C₄×C₅	—	6	1	no	—
327	C₂×C₄×C₅	—	6	1	no	—
328	C₂×C₄×C₅	—	6	2	no	—
329	C₂×C₄×C₅	—	6	2	no	—
330	C₂×C₄×C₅	—	12	4	no	—
331	C₂×C₄×C₅	—	12	4	no	—
332	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
334	C₅×C₈	—	2	1	no	—
335	C₅×C₈	—	3	2	no	—
336	C₅×C₈	—	6	1	no	—
337	C₅×C₈	D₃×D₄	1	2	yes	—
338	C₂²×Q₈	—	3	2	no	—
339	C₂³×C₄	—	3	1	no	—
340	C₂×Q₁₆	—	3	2	no	—
341	C₂×Q₁₆	—	3	1	no	—
342	C₂×Q₁₆	—	6	4	no	—
343	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
344	C₂×M₁₆	—	3	1	no	—
345	C₂×M₁₆	—	3	1	no	—
346	C₂×M₁₆	—	3	1	no	—
347	C₂×M₁₆	—	6	4	no	—
348	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
349	C₂²×C₈	—	3	1	no	—
350	C₂²×C₈	—	3	1	no	—
351	C₂²⋊Q₈	—	3	2	no	—
352	C₂²⋊Q₈	—	3	2	no	—
353	C₂²⋊Q₈	—	3	2	no	—
354	C₂²⋊Q₈	—	6	2	no	—
355	C₂²⋊Q₈	—	6	2	no	—
356	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	—
357	C₂×C₄⋊C₄	—	3	2	no	—
358	C₂×C₄⋊C₄	—	6	2	no	—
359	C₂×C₂²⋊C₄	—	6	2	no	—
360	#106	—	3	1	no	—
361	#106	—	3	2	no	—
362	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
363	#103	—	3	2	no	—
364	#103	—	3	2	no	—
365	#103	—	3	2	no	—
366	#103	C₂×C₅×D₃	1	2	yes	complemented
367	C₂×C₃×C₅	—	4	1	no	—
368	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
369	C₂×C₃×C₅	C₂×#137	1	2	yes	—
370	C₅×D₃	—	4	1	no	—
371	C₅×D₃	#470	1	4	yes	direct product factor
372	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂²×D₃	—	2	2	no	—
374	C₂²×D₃	—	2	4	no	—
375	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
377	C₃×Q₈	—	2	2	no	—
378	C₃×Q₈	—	2	2	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
385	C₂×Dic₃	—	2	2	no	—
386	C₂×Dic₃	—	2	2	no	—
387	C₂×Dic₃	—	2	2	no	—
388	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
390	C₄×D₃	—	2	2	no	—
391	C₄×D₃	—	2	1	no	—
392	C₄×D₃	—	2	1	no	—
393	C₄×D₃	—	2	2	no	—
394	C₄×D₃	—	4	4	no	—
395	C₄×D₃	—	4	4	no	—
396	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
397	C₄×D₃	C₅×#41	1	2	yes	—
398	Dic₆	—	2	2	no	—
399	Dic₆	—	2	2	no	—
400	Dic₆	—	4	4	no	—
401	C₃×C₈	—	2	1	no	—
402	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
403	C₃⋊C₈	—	2	1	no	—
404	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	—	3	4	no	—
408	C₂²×C₅	—	3	2	no	—
409	C₂²×C₅	—	6	2	no	—
410	C₂²×C₅	—	6	1	no	—
411	C₂²×C₅	—	12	4	no	—
412	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	3	2	no	—
415	C₄×C₅	—	4	2	no	—
416	C₄×C₅	—	4	2	no	—
417	C₄×C₅	—	6	1	no	—
418	C₄×C₅	—	12	2	no	—
419	C₄×C₅	—	12	2	no	—
420	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
421	C₄×C₅	D₃×#41	1	1	yes	characteristic
422	C₂⁴	—	3	1	no	—
423	C₂×Q₈	—	3	2	no	—
424	C₂×Q₈	—	6	2	no	—
425	C₂×Q₈	—	6	4	no	—
426	C₂×Q₈	—	6	4	no	—
427	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
428	C₂²×C₄	—	3	1	no	—
429	C₂²×C₄	—	3	1	no	—
430	C₂²×C₄	—	3	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	6	2	no	—
434	C₂²×C₄	—	6	2	no	—
435	C₂²×C₄	—	6	2	no	—
436	C₂²×C₄	—	6	2	no	—
437	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
438	Q₁₆	—	2	2	no	—
439	Q₁₆	—	6	4	no	—
440	Q₁₆	—	6	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	6	2	no	—
443	M₁₆	—	6	2	no	—
444	M₁₆	—	6	2	no	—
445	C₂×C₈	—	3	1	no	—
446	C₂×C₈	—	3	4	no	—
447	C₂×C₈	—	3	1	no	—
448	C₂×C₈	—	6	2	no	—
449	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
450	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	6	2	no	—
454	C₄⋊C₄	—	6	2	no	—
455	C₄⋊C₄	—	6	2	no	—
456	C₄⋊C₄	—	6	2	no	—
457	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	6	2	no	—
460	C₂²⋊C₄	—	6	2	no	—
461	C₂²⋊C₄	—	6	2	no	—
462	C₃×C₅	C₂×#470	1	1	yes	characteristic, complemented, Hall
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
466	C₂×D₃	—	2	1	no	—
467	C₂×D₃	—	2	2	no	—
468	C₂×D₃	—	4	4	no	—
469	C₂×D₃	C₅×#121	1	2	yes	—
470	C₂×D₃	C₅×#137	1	4	yes	—
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	4	2	no	—
473	C₃×C₄	—	4	2	no	—
474	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
475	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
476	Dic₃	—	2	1	no	—
477	Dic₃	—	4	2	no	—
478	Dic₃	—	4	2	no	—
479	Dic₃	C₅×#121	1	2	yes	—
480	C₂×C₅	—	3	4	no	—
481	C₂×C₅	—	4	1	no	—
482	C₂×C₅	—	12	1	no	—
483	C₂×C₅	D₃×#121	1	1	yes	characteristic
484	C₂×C₅	D₃×#137	1	2	yes	—
485	C₂³	—	3	1	no	—
486	C₂³	—	3	1	no	—
487	C₂³	—	6	2	no	—
488	C₂³	—	6	4	no	—
489	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
490	Q₈	—	2	2	no	—
491	Q₈	—	2	2	no	—
492	Q₈	—	6	2	no	—
493	Q₈	—	6	2	no	—
494	Q₈	—	12	4	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	3	1	no	—
500	C₂×C₄	—	3	2	no	—
501	C₂×C₄	—	3	2	no	—
502	C₂×C₄	—	3	1	no	—
503	C₂×C₄	—	6	2	no	—
504	C₂×C₄	—	6	2	no	—
505	C₂×C₄	—	6	2	no	—
506	C₂×C₄	—	6	1	no	—
507	C₂×C₄	—	6	1	no	—
508	C₂×C₄	—	6	2	no	—
509	C₂×C₄	—	6	2	no	—
510	C₂×C₄	—	12	4	no	—
511	C₂×C₄	—	12	4	no	—
512	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
513	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
514	C₈	—	2	1	no	—
515	C₈	—	3	2	no	—
516	C₈	—	6	1	no	—
517	C₈	C₅×D₃×D₄	1	2	yes	—
518	C₂×C₃	—	4	1	no	—
519	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
520	C₂×C₃	C₂×C₅×#137	1	2	yes	—
521	D₃	—	4	1	no	—
522	D₃	C₅×#470	1	4	yes	direct product factor
523	C₅	D₃×#470	1	1	yes	characteristic, direct product factor, Sylow
524	C₂²	—	2	2	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	3	4	no	—
527	C₂²	—	3	2	no	—
528	C₂²	—	6	2	no	—
529	C₂²	—	6	1	no	—
530	C₂²	—	12	4	no	—
531	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
532	C₄	—	2	1	no	—
533	C₄	—	3	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	6	1	no	—
537	C₄	—	12	2	no	—
538	C₄	—	12	2	no	—
539	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
540	C₄	C₅×D₃×#41	1	1	yes	characteristic
541	C₃	C₂×C₅×#470	1	1	yes	characteristic, complemented, Sylow
542	C₂	—	3	4	no	—
543	C₂	—	4	1	no	—
544	C₂	—	12	1	no	—
545	C₂	C₅×D₃×#121	1	1	yes	characteristic
546	C₂	C₅×D₃×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#470	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂³×C₅×D₃	D₄
hypercenter	C₅×#470	D₃
hypocenter	C₃	C₂×C₅×#470
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#470

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×Q₁₆	C₂	semidirect
4. C₃×C₅×#470	C₂	semidirect
5. C₅×#5189	C₂	semidirect
6. C₅×#5137	C₂	semidirect
7. C₅×#5052	C₂	semidirect
8. C₅×#4867	C₂	semidirect
9. C₅×D₃×#106	C₂	semidirect
10. C₅×#4816	C₂	semidirect
11. C₅×D₃×#103	C₂	semidirect
15. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
19. C₂×C₅×#216	C₂²	semidirect
24. C₂×C₅×Dic₁₂	C₂²	semidirect
35. C₃×C₅×#106	C₂²	semidirect
36. C₃×C₅×#103	C₂²	semidirect
37. C₅×#835	C₂²	semidirect
38. C₅×#817	C₂²	semidirect
39. C₅×#816	C₂²	semidirect
40. C₅×#810	C₂²	semidirect
41. C₅×#808	C₂²	semidirect
42. D₃×#470	C₅	direct (N × H)
51. C₅×#470	D₃	direct (N × H)
94. C₂×D₃×Q₁₆	C₂×C₅	semidirect
97. C₃×#470	C₂×C₅	semidirect
98. #5189	C₂×C₅	semidirect
99. #5137	C₂×C₅	semidirect
100. #5052	C₂×C₅	semidirect
101. #4867	C₂×C₅	semidirect
102. D₃×#106	C₂×C₅	semidirect
103. #4816	C₂×C₅	semidirect
104. D₃×#103	C₂×C₅	semidirect
110. C₂×C₅×Q₁₆	C₂×D₃	semidirect
129. C₅×#106	C₂×D₃	semidirect
133. C₅×#103	C₂×D₃	semidirect
170. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
174. C₂×#216	C₂²×C₅	semidirect
179. C₂×Dic₁₂	C₂²×C₅	semidirect
190. C₃×#106	C₂²×C₅	semidirect
191. C₃×#103	C₂²×C₅	semidirect
192. #835	C₂²×C₅	semidirect
193. #817	C₂²×C₅	semidirect
194. #816	C₂²×C₅	semidirect
195. #810	C₂²×C₅	semidirect
196. #808	C₂²×C₅	semidirect
245. #470	C₅×D₃	direct (N × H)
343. C₂×Q₁₆	C₂×C₅×D₃	semidirect
362. #106	C₂×C₅×D₃	semidirect
366. #103	C₂×C₅×D₃	semidirect
371. C₅×D₃	#470	direct (N × H)
462. C₃×C₅	C₂×#470	semidirect
522. D₃	C₅×#470	direct (N × H)
523. C₅	D₃×#470	direct (N × H)
541. C₃	C₂×C₅×#470	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×Q₁₆	2
C₂×C₅×D₃×M₁₆	2
C₅×D₃×C₂²⋊Q₈	2
C₃×C₅×#470	2
C₅×#5189	2
C₅×#5137	2
C₅×#5052	2
C₅×#4867	2
C₅×D₃×#106	2
C₅×#4816	2
C₅×D₃×#103	2
C₂×C₅×#470	3
D₃×#470	5

Subgroups — C5×D3×#470 #14428029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#470 #14428029