Subgroups — C₅×#76480 #14321935

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#947	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4977	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4939	C₂	1	1	yes	maximal, characteristic
7	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4670	C₂	1	4	yes	maximal, complemented
9	C₅×#4666	C₂	1	4	yes	maximal, complemented
10	C₄×C₅×#124	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₅×#947	C₄	1	8	yes	complemented
17	C₅×Q₈×Dic₃	—	2	4	no	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
26	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₅×#893	—	2	4	no	—
29	C₃×C₅×#95	C₂²	1	4	yes	—
30	C₅×C₃⋊#95	C₂²	1	4	yes	—
31	#76480	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#124	—	3	1	no	—
33	C₂×C₄×C₅×Q₈	—	3	1	no	—
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₅×#391	D₃	1	1	yes	characteristic, complemented
36	C₅×#390	—	3	1	no	—
37	C₅×#388	—	3	4	no	—
38	C₅×#382	—	3	1	no	—
39	C₄×C₅×C₂²⋊C₄	—	3	4	no	—
40	C₄³×C₅	—	3	1	no	—
41	C₂³×C₅×D₃	C₂³	1	2	yes	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
50	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
51	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
53	C₂×C₅×D₁₂	—	2	2	no	—
54	C₂×C₅×D₁₂	—	2	2	no	—
55	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
56	C₂×C₄×C₅×D₃	—	2	4	no	—
57	C₂×C₄×C₅×D₃	—	2	8	no	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₄²×C₅	—	2	2	no	—
60	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
61	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
62	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	16	yes	complemented
63	C₅×C₄⋊Dic₃	—	2	2	no	—
64	C₅×C₄⋊Dic₃	—	2	4	no	—
65	C₄×C₅×Dic₃	—	2	4	no	—
66	C₄×C₅×Dic₃	—	2	4	no	—
67	C₄×C₅×Dic₃	—	2	4	no	—
68	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
69	C₄×C₅×Dic₃	D₄	1	4	yes	—
70	C₂×#947	C₂×C₅	1	1	yes	characteristic
71	C₂×Q₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#893	C₂×C₅	1	1	yes	characteristic
73	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
74	#4977	C₂×C₅	1	1	yes	characteristic, complemented
75	#4939	C₂×C₅	1	1	yes	characteristic
76	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
77	#4670	C₂×C₅	1	4	yes	complemented
78	#4666	C₂×C₅	1	4	yes	complemented
79	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₅×D₄	—	3	1	no	—
81	C₂³×C₄×C₅	—	3	2	no	—
82	C₅×#124	—	3	8	no	—
83	C₄×C₅×Q₈	—	6	4	no	—
84	C₄×C₅×D₄	—	6	4	no	—
85	C₂×C₅×C₄⋊C₄	—	3	1	no	—
86	C₂×C₅×C₄⋊C₄	—	3	2	no	—
87	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
88	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
89	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
90	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
91	C₂×C₄²×C₅	—	3	1	no	—
92	C₂×C₄²×C₅	—	3	1	no	—
93	C₂×C₄²×C₅	—	3	2	no	—
94	C₂×C₄²×C₅	—	3	2	no	—
95	C₂×C₄²×C₅	—	3	2	no	—
96	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
97	C₅×#95	—	3	4	no	—
98	C₅×#95	C₂×D₃	1	4	yes	—
99	C₄×#124	—	3	1	no	Sylow
100	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
101	C₂²×C₅×D₃	—	2	2	no	—
102	C₂²×C₅×D₃	—	2	4	no	—
103	C₂²×C₅×D₃	—	2	4	no	—
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
106	C₃×C₅×Q₈	—	2	8	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	#41	1	4	yes	—
117	C₂×C₃×C₄×C₅	#41	1	2	yes	—
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	—	2	4	no	—
123	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
124	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
125	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
126	C₂×C₅×Dic₃	#41	1	4	yes	—
127	C₅×D₁₂	—	2	8	no	—
128	C₄×C₅×D₃	—	4	8	no	—
129	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
130	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
134	#947	C₄×C₅	1	8	yes	complemented
135	Q₈×Dic₃	—	2	4	no	—
136	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
137	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
138	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
139	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
140	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
142	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
143	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
144	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
146	#893	—	2	4	no	—
147	C₃×#95	C₂²×C₅	1	4	yes	—
148	C₃⋊#95	C₂²×C₅	1	4	yes	—
149	C₂⁴×C₅	—	3	2	no	—
150	C₂×C₅×Q₈	—	2	2	no	—
151	C₂×C₅×Q₈	—	2	2	no	—
152	C₂×C₅×Q₈	C₄×D₃	1	4	yes	complemented
153	C₂×C₅×D₄	—	3	4	no	—
154	C₂×C₅×D₄	—	6	2	no	—
155	C₂×C₅×D₄	—	6	2	no	—
156	C₂²×C₄×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	3	1	no	—
158	C₂²×C₄×C₅	—	3	2	no	—
159	C₂²×C₄×C₅	—	3	2	no	—
160	C₂²×C₄×C₅	—	6	4	no	—
161	C₂²×C₄×C₅	—	6	8	no	—
162	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
163	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
165	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	6	4	no	—
168	C₅×C₄⋊C₄	—	6	2	no	—
169	C₅×C₂²⋊C₄	—	3	16	no	—
170	C₅×C₂²⋊C₄	—	6	4	no	—
171	C₅×C₂²⋊C₄	—	6	8	no	—
172	C₄²×C₅	—	2	2	no	—
173	C₄²×C₅	—	3	4	no	—
174	C₄²×C₅	—	3	4	no	—
175	C₄²×C₅	—	6	4	no	—
176	C₄²×C₅	—	6	4	no	—
177	C₄²×C₅	—	6	4	no	—
178	C₂×#124	—	3	1	no	—
179	C₂×C₄×Q₈	—	3	1	no	—
180	C₂×C₄×D₄	—	3	1	no	—
181	#391	C₅×D₃	1	1	yes	characteristic, complemented
182	#390	—	3	1	no	—
183	#388	—	3	4	no	—
184	#382	—	3	1	no	—
185	C₄×C₂²⋊C₄	—	3	4	no	—
186	C₄³	—	3	1	no	—
187	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
188	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
190	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
191	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
192	C₂×C₅×D₃	—	2	4	no	—
193	C₂×C₅×D₃	—	2	8	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	4	no	—
196	C₂×C₅×D₃	—	4	2	no	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	2	4	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
201	C₅×Dic₃	—	2	4	no	—
202	C₅×Dic₃	—	2	2	no	—
203	C₅×Dic₃	—	4	2	no	—
204	C₅×Dic₃	#124	1	4	yes	complemented
205	C₂³×D₃	C₂³×C₅	1	2	yes	—
206	C₂×C₃×Q₈	—	2	2	no	—
207	C₂×C₃×Q₈	—	2	2	no	—
208	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
209	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
210	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
212	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
213	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
214	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
215	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
216	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
217	C₂×D₁₂	—	2	2	no	—
218	C₂×D₁₂	—	2	2	no	—
219	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
220	C₂×C₄×D₃	—	2	4	no	—
221	C₂×C₄×D₃	—	2	8	no	—
222	C₃×C₄⋊C₄	—	2	2	no	—
223	C₃×C₄²	—	2	2	no	—
224	(C₂×D₃)⋊C₄	—	2	8	no	—
225	(C₂×D₃)⋊C₄	—	2	4	no	—
226	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
227	C₄⋊Dic₃	—	2	2	no	—
228	C₄⋊Dic₃	—	2	4	no	—
229	C₄×Dic₃	—	2	4	no	—
230	C₄×Dic₃	—	2	4	no	—
231	C₄×Dic₃	—	2	4	no	—
232	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
233	C₄×Dic₃	C₅×D₄	1	4	yes	—
234	C₂³×C₅	—	3	4	no	—
235	C₂³×C₅	—	6	2	no	—
236	C₂³×C₅	—	6	2	no	—
237	C₂³×C₅	—	6	4	no	—
238	C₂³×C₅	—	6	4	no	—
239	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
240	C₅×Q₈	—	2	8	no	—
241	C₅×D₄	—	6	8	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	3	2	no	—
249	C₂×C₄×C₅	—	3	4	no	—
250	C₂×C₄×C₅	—	3	4	no	—
251	C₂×C₄×C₅	—	3	2	no	—
252	C₂×C₄×C₅	—	6	2	no	—
253	C₂×C₄×C₅	—	6	2	no	—
254	C₂×C₄×C₅	—	6	2	no	—
255	C₂×C₄×C₅	—	6	2	no	—
256	C₂×C₄×C₅	—	6	4	no	—
257	C₂×C₄×C₅	—	12	8	no	—
258	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
259	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
260	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
261	C₂×C₄×C₅	#237	1	2	yes	—
262	C₂×C₄×C₅	#239	1	4	yes	—
263	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
264	C₂²×D₄	—	3	1	no	—
265	C₂³×C₄	—	3	2	no	—
266	#124	—	3	8	no	—
267	C₄×Q₈	—	6	4	no	—
268	C₄×D₄	—	6	4	no	—
269	C₂×C₄⋊C₄	—	3	1	no	—
270	C₂×C₄⋊C₄	—	3	2	no	—
271	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	—	3	4	no	—
273	C₂×C₂²⋊C₄	—	3	2	no	—
274	C₂×C₂²⋊C₄	—	3	4	no	—
275	C₂×C₄²	—	3	1	no	—
276	C₂×C₄²	—	3	1	no	—
277	C₂×C₄²	—	3	2	no	—
278	C₂×C₄²	—	3	2	no	—
279	C₂×C₄²	—	3	2	no	—
280	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
281	#95	—	3	4	no	—
282	#95	C₂×C₅×D₃	1	4	yes	—
283	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
284	C₂×C₃×C₅	C₄×#41	1	2	yes	—
285	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
286	C₂×C₃×C₅	#529	1	2	yes	—
287	C₂×C₃×C₅	#532	1	1	yes	characteristic
288	C₅×D₃	—	4	4	no	—
289	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
290	C₂²×D₃	—	2	2	no	—
291	C₂²×D₃	—	2	4	no	—
292	C₂²×D₃	—	2	4	no	—
293	C₂²×D₃	—	2	2	no	—
294	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
295	C₃×Q₈	—	2	8	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	4	no	—
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
303	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
305	C₂×C₃×C₄	C₅×#41	1	2	yes	—
306	C₂×C₃×C₄	C₅×#41	1	4	yes	—
307	C₂×Dic₃	—	2	2	no	—
308	C₂×Dic₃	—	2	2	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	2	2	no	—
311	C₂×Dic₃	—	2	4	no	—
312	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
313	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
314	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
315	C₂×Dic₃	C₅×#41	1	4	yes	—
316	D₁₂	—	2	8	no	—
317	C₄×D₃	—	4	8	no	—
318	C₂²×C₅	—	6	4	no	—
319	C₂²×C₅	—	6	8	no	—
320	C₂²×C₅	—	12	2	no	—
321	C₂²×C₅	—	12	2	no	—
322	C₂²×C₅	—	12	4	no	—
323	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
324	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
325	C₂²×C₅	C₂×#237	1	1	yes	characteristic
326	C₂²×C₅	C₂×#239	1	2	yes	—
327	C₂²×C₅	D₃×#41	1	2	yes	—
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	2	4	no	—
330	C₄×C₅	—	3	4	no	—
331	C₄×C₅	—	4	2	no	—
332	C₄×C₅	—	6	2	no	—
333	C₄×C₅	—	6	4	no	—
334	C₄×C₅	—	12	2	no	—
335	C₄×C₅	#67⋊C₄	1	4	yes	—
336	C₂⁴	—	3	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	C₄×C₅×D₃	1	4	yes	complemented
340	C₂×D₄	—	3	4	no	—
341	C₂×D₄	—	6	2	no	—
342	C₂×D₄	—	6	2	no	—
343	C₂²×C₄	—	3	1	no	—
344	C₂²×C₄	—	3	2	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	3	2	no	—
347	C₂²×C₄	—	6	4	no	—
348	C₂²×C₄	—	6	8	no	—
349	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
350	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
351	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
352	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	6	4	no	—
355	C₄⋊C₄	—	6	2	no	—
356	C₂²⋊C₄	—	3	16	no	—
357	C₂²⋊C₄	—	6	4	no	—
358	C₂²⋊C₄	—	6	8	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	3	4	no	—
361	C₄²	—	3	4	no	—
362	C₄²	—	6	4	no	—
363	C₄²	—	6	4	no	—
364	C₄²	—	6	4	no	—
365	C₃×C₅	C₄×#124	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
367	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
368	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
369	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
370	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
371	C₂×D₃	—	2	4	no	—
372	C₂×D₃	—	2	8	no	—
373	C₂×D₃	—	4	2	no	—
374	C₂×D₃	—	4	4	no	—
375	C₂×D₃	—	4	2	no	—
376	C₃×C₄	—	2	4	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	4	2	no	—
379	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
380	Dic₃	—	2	4	no	—
381	Dic₃	—	2	2	no	—
382	Dic₃	—	4	2	no	—
383	Dic₃	C₅×#124	1	4	yes	complemented
384	C₂×C₅	—	12	4	no	—
385	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
386	C₂×C₅	C₄×#239	1	2	yes	—
387	C₂×C₅	#5624	1	2	yes	—
388	C₂×C₅	D₃×#124	1	1	yes	characteristic
389	C₂×C₅	#5725	1	1	yes	characteristic
390	C₂³	—	3	4	no	—
391	C₂³	—	6	2	no	—
392	C₂³	—	6	2	no	—
393	C₂³	—	6	4	no	—
394	C₂³	—	6	4	no	—
395	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
396	Q₈	—	2	8	no	—
397	D₄	—	6	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	3	2	no	—
405	C₂×C₄	—	3	4	no	—
406	C₂×C₄	—	3	4	no	—
407	C₂×C₄	—	3	2	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	—	6	2	no	—
410	C₂×C₄	—	6	2	no	—
411	C₂×C₄	—	6	2	no	—
412	C₂×C₄	—	6	4	no	—
413	C₂×C₄	—	12	8	no	—
414	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
415	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
416	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
417	C₂×C₄	C₅×#237	1	2	yes	—
418	C₂×C₄	C₅×#239	1	4	yes	—
419	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
420	C₂×C₃	C₄×C₅×#41	1	2	yes	—
421	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
422	C₂×C₃	C₅×#529	1	2	yes	—
423	C₂×C₃	C₅×#532	1	1	yes	characteristic
424	D₃	—	4	4	no	—
425	C₅	#76480	1	1	yes	characteristic, direct product factor, Sylow
426	C₂²	—	6	4	no	—
427	C₂²	—	6	8	no	—
428	C₂²	—	12	2	no	—
429	C₂²	—	12	2	no	—
430	C₂²	—	12	4	no	—
431	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
432	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
433	C₂²	C₂×C₅×#237	1	1	yes	characteristic
434	C₂²	C₂×C₅×#239	1	2	yes	—
435	C₂²	C₅×D₃×#41	1	2	yes	—
436	C₄	—	2	4	no	—
437	C₄	—	2	4	no	—
438	C₄	—	3	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	6	2	no	—
441	C₄	—	6	4	no	—
442	C₄	—	12	2	no	—
443	C₄	C₅×#67⋊C₄	1	4	yes	—
444	C₃	C₄×C₅×#124	1	1	yes	characteristic, complemented, Sylow
445	C₂	—	12	4	no	—
446	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
447	C₂	C₄×C₅×#239	1	2	yes	—
448	C₂	C₅×#5624	1	2	yes	—
449	C₂	C₅×D₃×#124	1	1	yes	characteristic
450	C₂	C₅×#5725	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#391	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#391	D₃
hypocenter	C₃	C₄×C₅×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#391

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Q₈×Dic₃	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
5. C₅×#4977	C₂	semidirect
7. C₄²×C₅×Dic₃	C₂	semidirect
8. C₅×#4670	C₂	semidirect
9. C₅×#4666	C₂	semidirect
16. C₅×#947	C₄	semidirect
31. #76480	C₅	direct (N × H)
35. C₅×#391	D₃	semidirect
44. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
62. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
68. C₄×C₅×Dic₃	C₂×C₄	semidirect
71. C₂×Q₈×Dic₃	C₂×C₅	semidirect
73. C₃×#391	C₂×C₅	semidirect
74. #4977	C₂×C₅	semidirect
76. C₄²×Dic₃	C₂×C₅	semidirect
77. #4670	C₂×C₅	semidirect
78. #4666	C₂×C₅	semidirect
134. #947	C₄×C₅	semidirect
152. C₂×C₅×Q₈	C₄×D₃	semidirect
181. #391	C₅×D₃	semidirect
204. C₅×Dic₃	#124	semidirect
208. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
226. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
232. C₄×Dic₃	C₂×C₄×C₅	semidirect
339. C₂×Q₈	C₄×C₅×D₃	semidirect
365. C₃×C₅	C₄×#124	semidirect
383. Dic₃	C₅×#124	semidirect
425. C₅	#76480	direct (N × H)
444. C₃	C₄×C₅×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#947	2
C₂×C₅×Q₈×Dic₃	2
C₂×C₅×#893	2
C₃×C₅×#391	2
C₅×#4977	2
C₅×#4939	2
C₄²×C₅×Dic₃	2
C₅×#4670	2
C₅×#4666	2
C₄×C₅×#124	3
#76480	5

Subgroups — C5×#76480 #14321935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#76480 #14321935